Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.954311 | 0.674800 | 0.337400 | − | 0.941361i | \(-0.390453\pi\) | ||||
0.337400 | + | 0.941361i | \(0.390453\pi\) | |||||||
\(3\) | 0.726487 | 0.419437 | 0.209719 | − | 0.977762i | \(-0.432745\pi\) | ||||
0.209719 | + | 0.977762i | \(0.432745\pi\) | |||||||
\(4\) | −1.08929 | −0.544645 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.693295 | 0.283036 | ||||||||
\(7\) | 1.92977 | 0.729383 | 0.364692 | − | 0.931128i | \(-0.381174\pi\) | ||||
0.364692 | + | 0.931128i | \(0.381174\pi\) | |||||||
\(8\) | −2.94814 | −1.04233 | ||||||||
\(9\) | −2.47222 | −0.824072 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.82880 | −0.852916 | −0.426458 | − | 0.904507i | \(-0.640239\pi\) | ||||
−0.426458 | + | 0.904507i | \(0.640239\pi\) | |||||||
\(12\) | −0.791355 | −0.228445 | ||||||||
\(13\) | 6.44491 | 1.78750 | 0.893748 | − | 0.448570i | \(-0.148066\pi\) | ||||
0.893748 | + | 0.448570i | \(0.148066\pi\) | |||||||
\(14\) | 1.84160 | 0.492188 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.634866 | −0.158717 | ||||||||
\(17\) | 2.15771 | 0.523321 | 0.261660 | − | 0.965160i | \(-0.415730\pi\) | ||||
0.261660 | + | 0.965160i | \(0.415730\pi\) | |||||||
\(18\) | −2.35926 | −0.556084 | ||||||||
\(19\) | 1.30556 | 0.299516 | 0.149758 | − | 0.988723i | \(-0.452151\pi\) | ||||
0.149758 | + | 0.988723i | \(0.452151\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.40195 | 0.305931 | ||||||||
\(22\) | −2.69956 | −0.575547 | ||||||||
\(23\) | −1.78850 | −0.372929 | −0.186464 | − | 0.982462i | \(-0.559703\pi\) | ||||
−0.186464 | + | 0.982462i | \(0.559703\pi\) | |||||||
\(24\) | −2.14179 | −0.437191 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.15045 | 1.20620 | ||||||||
\(27\) | −3.97549 | −0.765084 | ||||||||
\(28\) | −2.10208 | −0.397255 | ||||||||
\(29\) | 3.74238 | 0.694943 | 0.347471 | − | 0.937691i | \(-0.387040\pi\) | ||||
0.347471 | + | 0.937691i | \(0.387040\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.69196 | −1.56112 | −0.780561 | − | 0.625079i | \(-0.785067\pi\) | ||||
−0.780561 | + | 0.625079i | \(0.785067\pi\) | |||||||
\(32\) | 5.29043 | 0.935224 | ||||||||
\(33\) | −2.05509 | −0.357745 | ||||||||
\(34\) | 2.05912 | 0.353137 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.69296 | 0.448827 | ||||||||
\(37\) | 5.53981 | 0.910740 | 0.455370 | − | 0.890302i | \(-0.349507\pi\) | ||||
0.455370 | + | 0.890302i | \(0.349507\pi\) | |||||||
\(38\) | 1.24591 | 0.202113 | ||||||||
\(39\) | 4.68214 | 0.749743 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.83107 | 0.442139 | 0.221069 | − | 0.975258i | \(-0.429045\pi\) | ||||
0.221069 | + | 0.975258i | \(0.429045\pi\) | |||||||
\(42\) | 1.33790 | 0.206442 | ||||||||
\(43\) | −4.52447 | −0.689975 | −0.344987 | − | 0.938607i | \(-0.612117\pi\) | ||||
−0.344987 | + | 0.938607i | \(0.612117\pi\) | |||||||
\(44\) | 3.08139 | 0.464536 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.70679 | −0.251652 | ||||||||
\(47\) | 9.40445 | 1.37178 | 0.685890 | − | 0.727705i | \(-0.259413\pi\) | ||||
0.685890 | + | 0.727705i | \(0.259413\pi\) | |||||||
\(48\) | −0.461222 | −0.0665717 | ||||||||
\(49\) | −3.27600 | −0.468000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.56755 | 0.219500 | ||||||||
\(52\) | −7.02038 | −0.973551 | ||||||||
\(53\) | −4.21628 | −0.579151 | −0.289576 | − | 0.957155i | \(-0.593514\pi\) | ||||
−0.289576 | + | 0.957155i | \(0.593514\pi\) | |||||||
\(54\) | −3.79386 | −0.516279 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −5.68923 | −0.760255 | ||||||||
\(57\) | 0.948471 | 0.125628 | ||||||||
\(58\) | 3.57139 | 0.468947 | ||||||||
\(59\) | −10.2699 | −1.33702 | −0.668512 | − | 0.743702i | \(-0.733068\pi\) | ||||
−0.668512 | + | 0.743702i | \(0.733068\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.2459 | 1.56792 | 0.783962 | − | 0.620808i | \(-0.213195\pi\) | ||||
0.783962 | + | 0.620808i | \(0.213195\pi\) | |||||||
\(62\) | −8.29484 | −1.05345 | ||||||||
\(63\) | −4.77080 | −0.601064 | ||||||||
\(64\) | 6.31845 | 0.789806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.96119 | −0.241406 | ||||||||
\(67\) | 11.8281 | 1.44503 | 0.722514 | − | 0.691356i | \(-0.242986\pi\) | ||||
0.722514 | + | 0.691356i | \(0.242986\pi\) | |||||||
\(68\) | −2.35037 | −0.285024 | ||||||||
\(69\) | −1.29932 | −0.156420 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.42721 | 1.11880 | 0.559402 | − | 0.828897i | \(-0.311031\pi\) | ||||
0.559402 | + | 0.828897i | \(0.311031\pi\) | |||||||
\(72\) | 7.28845 | 0.858952 | ||||||||
\(73\) | −16.8357 | −1.97047 | −0.985237 | − | 0.171198i | \(-0.945236\pi\) | ||||
−0.985237 | + | 0.171198i | \(0.945236\pi\) | |||||||
\(74\) | 5.28670 | 0.614567 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.42213 | −0.163130 | ||||||||
\(77\) | −5.45893 | −0.622102 | ||||||||
\(78\) | 4.46822 | 0.505926 | ||||||||
\(79\) | 16.2958 | 1.83342 | 0.916712 | − | 0.399548i | \(-0.130833\pi\) | ||||
0.916712 | + | 0.399548i | \(0.130833\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.52851 | 0.503167 | ||||||||
\(82\) | 2.70172 | 0.298355 | ||||||||
\(83\) | −5.44188 | −0.597324 | −0.298662 | − | 0.954359i | \(-0.596540\pi\) | ||||
−0.298662 | + | 0.954359i | \(0.596540\pi\) | |||||||
\(84\) | −1.52713 | −0.166624 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.31775 | −0.465595 | ||||||||
\(87\) | 2.71879 | 0.291485 | ||||||||
\(88\) | 8.33971 | 0.889017 | ||||||||
\(89\) | 6.41711 | 0.680212 | 0.340106 | − | 0.940387i | \(-0.389537\pi\) | ||||
0.340106 | + | 0.940387i | \(0.389537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.4372 | 1.30377 | ||||||||
\(92\) | 1.94820 | 0.203114 | ||||||||
\(93\) | −6.31460 | −0.654793 | ||||||||
\(94\) | 8.97477 | 0.925677 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.84343 | 0.392268 | ||||||||
\(97\) | −3.18370 | −0.323256 | −0.161628 | − | 0.986852i | \(-0.551674\pi\) | ||||
−0.161628 | + | 0.986852i | \(0.551674\pi\) | |||||||
\(98\) | −3.12633 | −0.315807 | ||||||||
\(99\) | 6.99341 | 0.702864 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.1222 | 1.10670 | 0.553349 | − | 0.832949i | \(-0.313349\pi\) | ||||
0.553349 | + | 0.832949i | \(0.313349\pi\) | |||||||
\(102\) | 1.49593 | 0.148119 | ||||||||
\(103\) | −1.41993 | −0.139910 | −0.0699551 | − | 0.997550i | \(-0.522286\pi\) | ||||
−0.0699551 | + | 0.997550i | \(0.522286\pi\) | |||||||
\(104\) | −19.0005 | −1.86315 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.02365 | −0.390811 | ||||||||
\(107\) | 7.03950 | 0.680534 | 0.340267 | − | 0.940329i | \(-0.389482\pi\) | ||||
0.340267 | + | 0.940329i | \(0.389482\pi\) | |||||||
\(108\) | 4.33047 | 0.416699 | ||||||||
\(109\) | −8.60893 | −0.824586 | −0.412293 | − | 0.911051i | \(-0.635272\pi\) | ||||
−0.412293 | + | 0.911051i | \(0.635272\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.02460 | 0.381998 | ||||||||
\(112\) | −1.22514 | −0.115765 | ||||||||
\(113\) | 16.1383 | 1.51816 | 0.759081 | − | 0.650996i | \(-0.225649\pi\) | ||||
0.759081 | + | 0.650996i | \(0.225649\pi\) | |||||||
\(114\) | 0.905136 | 0.0847738 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.07654 | −0.378497 | ||||||||
\(117\) | −15.9332 | −1.47303 | ||||||||
\(118\) | −9.80065 | −0.902223 | ||||||||
\(119\) | 4.16387 | 0.381701 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.99788 | −0.272535 | ||||||||
\(122\) | 11.6864 | 1.05804 | ||||||||
\(123\) | 2.05673 | 0.185449 | ||||||||
\(124\) | 9.46807 | 0.850258 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.55283 | −0.405598 | ||||||||
\(127\) | 8.33841 | 0.739914 | 0.369957 | − | 0.929049i | \(-0.379372\pi\) | ||||
0.369957 | + | 0.929049i | \(0.379372\pi\) | |||||||
\(128\) | −4.55109 | −0.402264 | ||||||||
\(129\) | −3.28697 | −0.289401 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.8414 | 1.64618 | 0.823088 | − | 0.567914i | \(-0.192249\pi\) | ||||
0.823088 | + | 0.567914i | \(0.192249\pi\) | |||||||
\(132\) | 2.23859 | 0.194844 | ||||||||
\(133\) | 2.51942 | 0.218462 | ||||||||
\(134\) | 11.2877 | 0.975105 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.36123 | −0.545471 | ||||||||
\(137\) | 19.0380 | 1.62653 | 0.813263 | − | 0.581896i | \(-0.197689\pi\) | ||||
0.813263 | + | 0.581896i | \(0.197689\pi\) | |||||||
\(138\) | −1.23996 | −0.105552 | ||||||||
\(139\) | 19.8989 | 1.68780 | 0.843902 | − | 0.536497i | \(-0.180253\pi\) | ||||
0.843902 | + | 0.536497i | \(0.180253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.83221 | 0.575376 | ||||||||
\(142\) | 8.99649 | 0.754969 | ||||||||
\(143\) | −18.2314 | −1.52458 | ||||||||
\(144\) | 1.56953 | 0.130794 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.0665 | −1.32968 | ||||||||
\(147\) | −2.37997 | −0.196297 | ||||||||
\(148\) | −6.03446 | −0.496030 | ||||||||
\(149\) | −19.4986 | −1.59739 | −0.798695 | − | 0.601736i | \(-0.794476\pi\) | ||||
−0.798695 | + | 0.601736i | \(0.794476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.24829 | −0.589858 | −0.294929 | − | 0.955519i | \(-0.595296\pi\) | ||||
−0.294929 | + | 0.955519i | \(0.595296\pi\) | |||||||
\(152\) | −3.84897 | −0.312193 | ||||||||
\(153\) | −5.33432 | −0.431254 | ||||||||
\(154\) | −5.20951 | −0.419795 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.10021 | −0.408344 | ||||||||
\(157\) | −5.22604 | −0.417083 | −0.208542 | − | 0.978014i | \(-0.566872\pi\) | ||||
−0.208542 | + | 0.978014i | \(0.566872\pi\) | |||||||
\(158\) | 15.5513 | 1.23719 | ||||||||
\(159\) | −3.06308 | −0.242918 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.45139 | −0.272008 | ||||||||
\(162\) | 4.32160 | 0.339537 | ||||||||
\(163\) | 5.26431 | 0.412332 | 0.206166 | − | 0.978517i | \(-0.433901\pi\) | ||||
0.206166 | + | 0.978517i | \(0.433901\pi\) | |||||||
\(164\) | −3.08386 | −0.240809 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.19325 | −0.403074 | ||||||||
\(167\) | 2.09327 | 0.161982 | 0.0809912 | − | 0.996715i | \(-0.474191\pi\) | ||||
0.0809912 | + | 0.996715i | \(0.474191\pi\) | |||||||
\(168\) | −4.13315 | −0.318879 | ||||||||
\(169\) | 28.5368 | 2.19514 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.22762 | −0.246822 | ||||||||
\(172\) | 4.92846 | 0.375791 | ||||||||
\(173\) | 15.6587 | 1.19051 | 0.595254 | − | 0.803538i | \(-0.297051\pi\) | ||||
0.595254 | + | 0.803538i | \(0.297051\pi\) | |||||||
\(174\) | 2.59457 | 0.196694 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.79591 | 0.135372 | ||||||||
\(177\) | −7.46093 | −0.560798 | ||||||||
\(178\) | 6.12392 | 0.459007 | ||||||||
\(179\) | 15.6924 | 1.17291 | 0.586453 | − | 0.809983i | \(-0.300524\pi\) | ||||
0.586453 | + | 0.809983i | \(0.300524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.3735 | −1.88600 | −0.942999 | − | 0.332795i | \(-0.892008\pi\) | ||||
−0.942999 | + | 0.332795i | \(0.892008\pi\) | |||||||
\(182\) | 11.8689 | 0.879783 | ||||||||
\(183\) | 8.89648 | 0.657646 | ||||||||
\(184\) | 5.27276 | 0.388713 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.02609 | −0.441854 | ||||||||
\(187\) | −6.10373 | −0.446349 | ||||||||
\(188\) | −10.2442 | −0.747133 | ||||||||
\(189\) | −7.67177 | −0.558039 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.11508 | 0.225399 | 0.112700 | − | 0.993629i | \(-0.464050\pi\) | ||||
0.112700 | + | 0.993629i | \(0.464050\pi\) | |||||||
\(192\) | 4.59027 | 0.331274 | ||||||||
\(193\) | 1.60613 | 0.115612 | 0.0578058 | − | 0.998328i | \(-0.481590\pi\) | ||||
0.0578058 | + | 0.998328i | \(0.481590\pi\) | |||||||
\(194\) | −3.03824 | −0.218133 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.56852 | 0.254894 | ||||||||
\(197\) | 15.2199 | 1.08437 | 0.542187 | − | 0.840258i | \(-0.317596\pi\) | ||||
0.542187 | + | 0.840258i | \(0.317596\pi\) | |||||||
\(198\) | 6.67389 | 0.474293 | ||||||||
\(199\) | 3.89119 | 0.275839 | 0.137920 | − | 0.990443i | \(-0.455958\pi\) | ||||
0.137920 | + | 0.990443i | \(0.455958\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.59293 | 0.606099 | ||||||||
\(202\) | 10.6140 | 0.746800 | ||||||||
\(203\) | 7.22192 | 0.506879 | ||||||||
\(204\) | −1.70751 | −0.119550 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.35506 | −0.0944114 | ||||||||
\(207\) | 4.42157 | 0.307320 | ||||||||
\(208\) | −4.09165 | −0.283705 | ||||||||
\(209\) | −3.69317 | −0.255462 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3482 | 1.60735 | 0.803677 | − | 0.595066i | \(-0.202874\pi\) | ||||
0.803677 | + | 0.595066i | \(0.202874\pi\) | |||||||
\(212\) | 4.59276 | 0.315432 | ||||||||
\(213\) | 6.84874 | 0.469268 | ||||||||
\(214\) | 6.71788 | 0.459225 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.7203 | 0.797467 | ||||||||
\(217\) | −16.7735 | −1.13866 | ||||||||
\(218\) | −8.21560 | −0.556431 | ||||||||
\(219\) | −12.2309 | −0.826490 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.9062 | 0.935434 | ||||||||
\(222\) | 3.84072 | 0.257772 | ||||||||
\(223\) | 24.7633 | 1.65827 | 0.829135 | − | 0.559048i | \(-0.188833\pi\) | ||||
0.829135 | + | 0.559048i | \(0.188833\pi\) | |||||||
\(224\) | 10.2093 | 0.682137 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 15.4009 | 1.02446 | ||||||||
\(227\) | −4.59488 | −0.304973 | −0.152486 | − | 0.988306i | \(-0.548728\pi\) | ||||
−0.152486 | + | 0.988306i | \(0.548728\pi\) | |||||||
\(228\) | −1.03316 | −0.0684227 | ||||||||
\(229\) | 8.91085 | 0.588846 | 0.294423 | − | 0.955675i | \(-0.404873\pi\) | ||||
0.294423 | + | 0.955675i | \(0.404873\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.96584 | −0.260933 | ||||||||
\(232\) | −11.0331 | −0.724357 | ||||||||
\(233\) | 11.1866 | 0.732858 | 0.366429 | − | 0.930446i | \(-0.380580\pi\) | ||||
0.366429 | + | 0.930446i | \(0.380580\pi\) | |||||||
\(234\) | −15.2052 | −0.993998 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.1869 | 0.728203 | ||||||||
\(237\) | 11.8387 | 0.769007 | ||||||||
\(238\) | 3.97363 | 0.257572 | ||||||||
\(239\) | 9.02136 | 0.583543 | 0.291771 | − | 0.956488i | \(-0.405755\pi\) | ||||
0.291771 | + | 0.956488i | \(0.405755\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −2.86091 | −0.183906 | ||||||||
\(243\) | 15.2164 | 0.976131 | ||||||||
\(244\) | −13.3393 | −0.853963 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.96276 | 0.125141 | ||||||||
\(247\) | 8.41420 | 0.535383 | ||||||||
\(248\) | 25.6252 | 1.62720 | ||||||||
\(249\) | −3.95346 | −0.250540 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.292167 | 0.0184414 | 0.00922072 | − | 0.999957i | \(-0.497065\pi\) | ||||
0.00922072 | + | 0.999957i | \(0.497065\pi\) | |||||||
\(252\) | 5.19679 | 0.327367 | ||||||||
\(253\) | 5.05932 | 0.318077 | ||||||||
\(254\) | 7.95744 | 0.499294 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.9801 | −1.06125 | ||||||||
\(257\) | −1.33623 | −0.0833516 | −0.0416758 | − | 0.999131i | \(-0.513270\pi\) | ||||
−0.0416758 | + | 0.999131i | \(0.513270\pi\) | |||||||
\(258\) | −3.13679 | −0.195288 | ||||||||
\(259\) | 10.6905 | 0.664278 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.25197 | −0.572683 | ||||||||
\(262\) | 17.9805 | 1.11084 | ||||||||
\(263\) | 0.261451 | 0.0161218 | 0.00806089 | − | 0.999968i | \(-0.497434\pi\) | ||||
0.00806089 | + | 0.999968i | \(0.497434\pi\) | |||||||
\(264\) | 6.05869 | 0.372887 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.40431 | 0.147418 | ||||||||
\(267\) | 4.66195 | 0.285306 | ||||||||
\(268\) | −12.8842 | −0.787027 | ||||||||
\(269\) | −31.1244 | −1.89769 | −0.948843 | − | 0.315748i | \(-0.897744\pi\) | ||||
−0.948843 | + | 0.315748i | \(0.897744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.21072 | 0.377274 | 0.188637 | − | 0.982047i | \(-0.439593\pi\) | ||||
0.188637 | + | 0.982047i | \(0.439593\pi\) | |||||||
\(272\) | −1.36986 | −0.0830597 | ||||||||
\(273\) | 9.03544 | 0.546850 | ||||||||
\(274\) | 18.1682 | 1.09758 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.41534 | 0.0851935 | ||||||||
\(277\) | −31.1724 | −1.87297 | −0.936483 | − | 0.350712i | \(-0.885940\pi\) | ||||
−0.936483 | + | 0.350712i | \(0.885940\pi\) | |||||||
\(278\) | 18.9898 | 1.13893 | ||||||||
\(279\) | 21.4884 | 1.28648 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.3646 | −1.81140 | −0.905701 | − | 0.423916i | \(-0.860655\pi\) | ||||
−0.905701 | + | 0.423916i | \(0.860655\pi\) | |||||||
\(282\) | 6.52006 | 0.388264 | ||||||||
\(283\) | −32.8954 | −1.95543 | −0.977715 | − | 0.209937i | \(-0.932674\pi\) | ||||
−0.977715 | + | 0.209937i | \(0.932674\pi\) | |||||||
\(284\) | −10.2690 | −0.609351 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17.3984 | −1.02879 | ||||||||
\(287\) | 5.46330 | 0.322488 | ||||||||
\(288\) | −13.0791 | −0.770692 | ||||||||
\(289\) | −12.3443 | −0.726135 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.31292 | −0.135586 | ||||||||
\(292\) | 18.3390 | 1.07321 | ||||||||
\(293\) | 10.8629 | 0.634616 | 0.317308 | − | 0.948323i | \(-0.397221\pi\) | ||||
0.317308 | + | 0.948323i | \(0.397221\pi\) | |||||||
\(294\) | −2.27123 | −0.132461 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −16.3322 | −0.949288 | ||||||||
\(297\) | 11.2459 | 0.652552 | ||||||||
\(298\) | −18.6078 | −1.07792 | ||||||||
\(299\) | −11.5267 | −0.666608 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.73117 | −0.503256 | ||||||||
\(302\) | −6.91713 | −0.398036 | ||||||||
\(303\) | 8.08012 | 0.464191 | ||||||||
\(304\) | −0.828855 | −0.0475381 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −5.09060 | −0.291010 | ||||||||
\(307\) | 15.4972 | 0.884472 | 0.442236 | − | 0.896899i | \(-0.354185\pi\) | ||||
0.442236 | + | 0.896899i | \(0.354185\pi\) | |||||||
\(308\) | 5.94635 | 0.338825 | ||||||||
\(309\) | −1.03156 | −0.0586836 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.0955 | 0.572465 | 0.286232 | − | 0.958160i | \(-0.407597\pi\) | ||||
0.286232 | + | 0.958160i | \(0.407597\pi\) | |||||||
\(312\) | −13.8036 | −0.781477 | ||||||||
\(313\) | −24.5157 | −1.38571 | −0.692854 | − | 0.721078i | \(-0.743647\pi\) | ||||
−0.692854 | + | 0.721078i | \(0.743647\pi\) | |||||||
\(314\) | −4.98726 | −0.281448 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.7509 | −0.998566 | ||||||||
\(317\) | 21.3367 | 1.19839 | 0.599195 | − | 0.800603i | \(-0.295487\pi\) | ||||
0.599195 | + | 0.800603i | \(0.295487\pi\) | |||||||
\(318\) | −2.92313 | −0.163921 | ||||||||
\(319\) | −10.5865 | −0.592727 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.11411 | 0.285442 | ||||||||
\(322\) | −3.29370 | −0.183551 | ||||||||
\(323\) | 2.81701 | 0.156743 | ||||||||
\(324\) | −4.93286 | −0.274048 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.02379 | 0.278242 | ||||||||
\(327\) | −6.25428 | −0.345862 | ||||||||
\(328\) | −8.34640 | −0.460853 | ||||||||
\(329\) | 18.1484 | 1.00055 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.3486 | 1.00853 | 0.504266 | − | 0.863548i | \(-0.331763\pi\) | ||||
0.504266 | + | 0.863548i | \(0.331763\pi\) | |||||||
\(332\) | 5.92779 | 0.325330 | ||||||||
\(333\) | −13.6956 | −0.750515 | ||||||||
\(334\) | 1.99763 | 0.109306 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.890051 | −0.0485562 | ||||||||
\(337\) | −23.5672 | −1.28379 | −0.641893 | − | 0.766794i | \(-0.721851\pi\) | ||||
−0.641893 | + | 0.766794i | \(0.721851\pi\) | |||||||
\(338\) | 27.2330 | 1.48128 | ||||||||
\(339\) | 11.7243 | 0.636774 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.5878 | 1.33151 | ||||||||
\(342\) | −3.08016 | −0.166556 | ||||||||
\(343\) | −19.8303 | −1.07073 | ||||||||
\(344\) | 13.3388 | 0.719179 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.9433 | 0.803355 | ||||||||
\(347\) | 29.9357 | 1.60703 | 0.803516 | − | 0.595284i | \(-0.202960\pi\) | ||||
0.803516 | + | 0.595284i | \(0.202960\pi\) | |||||||
\(348\) | −2.96155 | −0.158756 | ||||||||
\(349\) | −14.2722 | −0.763973 | −0.381987 | − | 0.924168i | \(-0.624760\pi\) | ||||
−0.381987 | + | 0.924168i | \(0.624760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.6217 | −1.36758 | ||||||||
\(352\) | −14.9656 | −0.797668 | ||||||||
\(353\) | 7.32451 | 0.389844 | 0.194922 | − | 0.980819i | \(-0.437555\pi\) | ||||
0.194922 | + | 0.980819i | \(0.437555\pi\) | |||||||
\(354\) | −7.12005 | −0.378426 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.99009 | −0.370474 | ||||||||
\(357\) | 3.02500 | 0.160100 | ||||||||
\(358\) | 14.9755 | 0.791477 | ||||||||
\(359\) | 1.92275 | 0.101479 | 0.0507394 | − | 0.998712i | \(-0.483842\pi\) | ||||
0.0507394 | + | 0.998712i | \(0.483842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.2955 | −0.910290 | ||||||||
\(362\) | −24.2142 | −1.27267 | ||||||||
\(363\) | −2.17792 | −0.114311 | ||||||||
\(364\) | −13.5477 | −0.710092 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.49001 | 0.443780 | ||||||||
\(367\) | −10.6190 | −0.554305 | −0.277153 | − | 0.960826i | \(-0.589391\pi\) | ||||
−0.277153 | + | 0.960826i | \(0.589391\pi\) | |||||||
\(368\) | 1.13546 | 0.0591899 | ||||||||
\(369\) | −6.99901 | −0.364354 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.13644 | −0.422423 | ||||||||
\(372\) | 6.87843 | 0.356630 | ||||||||
\(373\) | −21.9835 | −1.13826 | −0.569132 | − | 0.822246i | \(-0.692721\pi\) | ||||
−0.569132 | + | 0.822246i | \(0.692721\pi\) | |||||||
\(374\) | −5.82485 | −0.301196 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.7257 | −1.42984 | ||||||||
\(377\) | 24.1193 | 1.24221 | ||||||||
\(378\) | −7.32126 | −0.376565 | ||||||||
\(379\) | 11.7937 | 0.605801 | 0.302901 | − | 0.953022i | \(-0.402045\pi\) | ||||
0.302901 | + | 0.953022i | \(0.402045\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.05775 | 0.310348 | ||||||||
\(382\) | 2.97275 | 0.152099 | ||||||||
\(383\) | −3.77603 | −0.192946 | −0.0964731 | − | 0.995336i | \(-0.530756\pi\) | ||||
−0.0964731 | + | 0.995336i | \(0.530756\pi\) | |||||||
\(384\) | −3.30631 | −0.168724 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.53275 | 0.0780147 | ||||||||
\(387\) | 11.1855 | 0.568589 | ||||||||
\(388\) | 3.46798 | 0.176060 | ||||||||
\(389\) | −5.79768 | −0.293954 | −0.146977 | − | 0.989140i | \(-0.546954\pi\) | ||||
−0.146977 | + | 0.989140i | \(0.546954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.85907 | −0.195161 | ||||||||
\(392\) | 9.65813 | 0.487809 | ||||||||
\(393\) | 13.6880 | 0.690468 | ||||||||
\(394\) | 14.5245 | 0.731735 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.61785 | −0.382812 | ||||||||
\(397\) | −10.3725 | −0.520583 | −0.260291 | − | 0.965530i | \(-0.583819\pi\) | ||||
−0.260291 | + | 0.965530i | \(0.583819\pi\) | |||||||
\(398\) | 3.71341 | 0.186136 | ||||||||
\(399\) | 1.83033 | 0.0916310 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.1753 | 0.707880 | 0.353940 | − | 0.935268i | \(-0.384842\pi\) | ||||
0.353940 | + | 0.935268i | \(0.384842\pi\) | |||||||
\(402\) | 8.20033 | 0.408995 | ||||||||
\(403\) | −56.0189 | −2.79050 | ||||||||
\(404\) | −12.1153 | −0.602758 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.89196 | 0.342042 | ||||||||
\(407\) | −15.6710 | −0.776784 | ||||||||
\(408\) | −4.62135 | −0.228791 | ||||||||
\(409\) | −36.9371 | −1.82642 | −0.913212 | − | 0.407485i | \(-0.866406\pi\) | ||||
−0.913212 | + | 0.407485i | \(0.866406\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.8309 | 0.682226 | ||||||||
\(412\) | 1.54672 | 0.0762014 | ||||||||
\(413\) | −19.8185 | −0.975202 | ||||||||
\(414\) | 4.21955 | 0.207380 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 34.0963 | 1.67171 | ||||||||
\(417\) | 14.4563 | 0.707928 | ||||||||
\(418\) | −3.52443 | −0.172385 | ||||||||
\(419\) | 23.1100 | 1.12899 | 0.564497 | − | 0.825435i | \(-0.309070\pi\) | ||||
0.564497 | + | 0.825435i | \(0.309070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −18.5538 | −0.904255 | −0.452127 | − | 0.891953i | \(-0.649335\pi\) | ||||
−0.452127 | + | 0.891953i | \(0.649335\pi\) | |||||||
\(422\) | 22.2814 | 1.08464 | ||||||||
\(423\) | −23.2498 | −1.13045 | ||||||||
\(424\) | 12.4302 | 0.603664 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.53583 | 0.316662 | ||||||||
\(427\) | 23.6317 | 1.14362 | ||||||||
\(428\) | −7.66806 | −0.370650 | ||||||||
\(429\) | −13.2448 | −0.639467 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.98236 | −0.480833 | −0.240417 | − | 0.970670i | \(-0.577284\pi\) | ||||
−0.240417 | + | 0.970670i | \(0.577284\pi\) | |||||||
\(432\) | 2.52391 | 0.121432 | ||||||||
\(433\) | −15.6993 | −0.754459 | −0.377230 | − | 0.926120i | \(-0.623123\pi\) | ||||
−0.377230 | + | 0.926120i | \(0.623123\pi\) | |||||||
\(434\) | −16.0071 | −0.768365 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.37763 | 0.449107 | ||||||||
\(437\) | −2.33499 | −0.111698 | ||||||||
\(438\) | −11.6721 | −0.557716 | ||||||||
\(439\) | 3.10402 | 0.148147 | 0.0740733 | − | 0.997253i | \(-0.476400\pi\) | ||||
0.0740733 | + | 0.997253i | \(0.476400\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.09899 | 0.385666 | ||||||||
\(442\) | 13.2709 | 0.631231 | ||||||||
\(443\) | −1.81863 | −0.0864058 | −0.0432029 | − | 0.999066i | \(-0.513756\pi\) | ||||
−0.0432029 | + | 0.999066i | \(0.513756\pi\) | |||||||
\(444\) | −4.38396 | −0.208053 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 23.6318 | 1.11900 | ||||||||
\(447\) | −14.1655 | −0.670005 | ||||||||
\(448\) | 12.1931 | 0.576071 | ||||||||
\(449\) | −8.38120 | −0.395533 | −0.197767 | − | 0.980249i | \(-0.563369\pi\) | ||||
−0.197767 | + | 0.980249i | \(0.563369\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.00853 | −0.377107 | ||||||||
\(452\) | −17.5793 | −0.826859 | ||||||||
\(453\) | −5.26579 | −0.247408 | ||||||||
\(454\) | −4.38494 | −0.205796 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.79623 | −0.130945 | ||||||||
\(457\) | 34.0456 | 1.59259 | 0.796294 | − | 0.604910i | \(-0.206791\pi\) | ||||
0.796294 | + | 0.604910i | \(0.206791\pi\) | |||||||
\(458\) | 8.50372 | 0.397353 | ||||||||
\(459\) | −8.57795 | −0.400385 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.0441 | 1.72532 | 0.862659 | − | 0.505786i | \(-0.168797\pi\) | ||||
0.862659 | + | 0.505786i | \(0.168797\pi\) | |||||||
\(462\) | −3.78464 | −0.176078 | ||||||||
\(463\) | −17.9429 | −0.833876 | −0.416938 | − | 0.908935i | \(-0.636897\pi\) | ||||
−0.416938 | + | 0.908935i | \(0.636897\pi\) | |||||||
\(464\) | −2.37591 | −0.110299 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.6755 | 0.494532 | ||||||||
\(467\) | −22.5460 | −1.04330 | −0.521652 | − | 0.853158i | \(-0.674684\pi\) | ||||
−0.521652 | + | 0.853158i | \(0.674684\pi\) | |||||||
\(468\) | 17.3559 | 0.802276 | ||||||||
\(469\) | 22.8254 | 1.05398 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.79665 | −0.174940 | ||||||||
\(472\) | 30.2771 | 1.39361 | ||||||||
\(473\) | 12.7988 | 0.588490 | ||||||||
\(474\) | 11.2978 | 0.518926 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.53566 | −0.207892 | ||||||||
\(477\) | 10.4236 | 0.477262 | ||||||||
\(478\) | 8.60918 | 0.393775 | ||||||||
\(479\) | −6.58124 | −0.300705 | −0.150352 | − | 0.988632i | \(-0.548041\pi\) | ||||
−0.150352 | + | 0.988632i | \(0.548041\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 35.7036 | 1.62794 | ||||||||
\(482\) | 0.954311 | 0.0434677 | ||||||||
\(483\) | −2.50739 | −0.114090 | ||||||||
\(484\) | 3.26556 | 0.148435 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.5212 | 0.658693 | ||||||||
\(487\) | −30.3973 | −1.37743 | −0.688717 | − | 0.725031i | \(-0.741826\pi\) | ||||
−0.688717 | + | 0.725031i | \(0.741826\pi\) | |||||||
\(488\) | −36.1026 | −1.63429 | ||||||||
\(489\) | 3.82445 | 0.172948 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.16398 | −0.278176 | −0.139088 | − | 0.990280i | \(-0.544417\pi\) | ||||
−0.139088 | + | 0.990280i | \(0.544417\pi\) | |||||||
\(492\) | −2.24038 | −0.101004 | ||||||||
\(493\) | 8.07496 | 0.363678 | ||||||||
\(494\) | 8.02977 | 0.361276 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.51823 | 0.247776 | ||||||||
\(497\) | 18.1923 | 0.816036 | ||||||||
\(498\) | −3.77283 | −0.169064 | ||||||||
\(499\) | 10.2121 | 0.457157 | 0.228579 | − | 0.973525i | \(-0.426592\pi\) | ||||
0.228579 | + | 0.973525i | \(0.426592\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.52074 | 0.0679415 | ||||||||
\(502\) | 0.278819 | 0.0124443 | ||||||||
\(503\) | 33.2347 | 1.48186 | 0.740930 | − | 0.671582i | \(-0.234385\pi\) | ||||
0.740930 | + | 0.671582i | \(0.234385\pi\) | |||||||
\(504\) | 14.0650 | 0.626505 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.82816 | 0.214638 | ||||||||
\(507\) | 20.7316 | 0.920724 | ||||||||
\(508\) | −9.08295 | −0.402991 | ||||||||
\(509\) | 32.8944 | 1.45802 | 0.729009 | − | 0.684504i | \(-0.239981\pi\) | ||||
0.729009 | + | 0.684504i | \(0.239981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.4890 | −1.43723 | ||||||||
\(512\) | −7.10207 | −0.313870 | ||||||||
\(513\) | −5.19024 | −0.229155 | ||||||||
\(514\) | −1.27518 | −0.0562457 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.58046 | 0.157621 | ||||||||
\(517\) | −26.6033 | −1.17001 | ||||||||
\(518\) | 10.2021 | 0.448255 | ||||||||
\(519\) | 11.3758 | 0.499344 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.7379 | −0.733302 | −0.366651 | − | 0.930359i | \(-0.619496\pi\) | ||||
−0.366651 | + | 0.930359i | \(0.619496\pi\) | |||||||
\(522\) | −8.82926 | −0.386446 | ||||||||
\(523\) | −1.77831 | −0.0777599 | −0.0388799 | − | 0.999244i | \(-0.512379\pi\) | ||||
−0.0388799 | + | 0.999244i | \(0.512379\pi\) | |||||||
\(524\) | −20.5237 | −0.896582 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.249506 | 0.0108790 | ||||||||
\(527\) | −18.7547 | −0.816968 | ||||||||
\(528\) | 1.30471 | 0.0567800 | ||||||||
\(529\) | −19.8013 | −0.860924 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.3894 | 1.10180 | ||||||||
\(532\) | −2.74438 | −0.118984 | ||||||||
\(533\) | 18.2460 | 0.790321 | ||||||||
\(534\) | 4.44895 | 0.192525 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −34.8708 | −1.50619 | ||||||||
\(537\) | 11.4003 | 0.491961 | ||||||||
\(538\) | −29.7023 | −1.28056 | ||||||||
\(539\) | 9.26716 | 0.399165 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.6472 | 0.715718 | 0.357859 | − | 0.933776i | \(-0.383507\pi\) | ||||
0.357859 | + | 0.933776i | \(0.383507\pi\) | |||||||
\(542\) | 5.92696 | 0.254585 | ||||||||
\(543\) | −18.4335 | −0.791058 | ||||||||
\(544\) | 11.4152 | 0.489423 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.62262 | 0.369014 | ||||||||
\(547\) | −19.0159 | −0.813060 | −0.406530 | − | 0.913637i | \(-0.633261\pi\) | ||||
−0.406530 | + | 0.913637i | \(0.633261\pi\) | |||||||
\(548\) | −20.7379 | −0.885880 | ||||||||
\(549\) | −30.2745 | −1.29208 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.88590 | 0.208146 | ||||||||
\(552\) | 3.83059 | 0.163041 | ||||||||
\(553\) | 31.4472 | 1.33727 | ||||||||
\(554\) | −29.7482 | −1.26388 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.6757 | −0.919254 | ||||||||
\(557\) | −20.6747 | −0.876017 | −0.438008 | − | 0.898971i | \(-0.644316\pi\) | ||||
−0.438008 | + | 0.898971i | \(0.644316\pi\) | |||||||
\(558\) | 20.5066 | 0.868115 | ||||||||
\(559\) | −29.1598 | −1.23333 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.43428 | −0.187215 | ||||||||
\(562\) | −28.9773 | −1.22233 | ||||||||
\(563\) | 33.3776 | 1.40670 | 0.703349 | − | 0.710845i | \(-0.251687\pi\) | ||||
0.703349 | + | 0.710845i | \(0.251687\pi\) | |||||||
\(564\) | −7.44226 | −0.313376 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −31.3925 | −1.31952 | ||||||||
\(567\) | 8.73896 | 0.367002 | ||||||||
\(568\) | −27.7928 | −1.16616 | ||||||||
\(569\) | 28.2188 | 1.18299 | 0.591496 | − | 0.806308i | \(-0.298538\pi\) | ||||
0.591496 | + | 0.806308i | \(0.298538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.6813 | −0.614392 | −0.307196 | − | 0.951646i | \(-0.599391\pi\) | ||||
−0.307196 | + | 0.951646i | \(0.599391\pi\) | |||||||
\(572\) | 19.8592 | 0.830357 | ||||||||
\(573\) | 2.26306 | 0.0945408 | ||||||||
\(574\) | 5.21369 | 0.217615 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −15.6206 | −0.650857 | ||||||||
\(577\) | 5.06714 | 0.210948 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(578\) | −11.7803 | −0.489996 | ||||||||
\(579\) | 1.16683 | 0.0484918 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5016 | −0.435678 | ||||||||
\(582\) | −2.20724 | −0.0914932 | ||||||||
\(583\) | 11.9270 | 0.493967 | ||||||||
\(584\) | 49.6342 | 2.05388 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.3666 | 0.428239 | ||||||||
\(587\) | −37.9278 | −1.56545 | −0.782725 | − | 0.622368i | \(-0.786171\pi\) | ||||
−0.782725 | + | 0.622368i | \(0.786171\pi\) | |||||||
\(588\) | 2.59248 | 0.106912 | ||||||||
\(589\) | −11.3479 | −0.467581 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0571 | 0.454827 | ||||||||
\(592\) | −3.51704 | −0.144549 | ||||||||
\(593\) | −15.7405 | −0.646385 | −0.323193 | − | 0.946333i | \(-0.604756\pi\) | ||||
−0.323193 | + | 0.946333i | \(0.604756\pi\) | |||||||
\(594\) | 10.7321 | 0.440342 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 21.2397 | 0.870011 | ||||||||
\(597\) | 2.82690 | 0.115697 | ||||||||
\(598\) | −11.0001 | −0.449827 | ||||||||
\(599\) | −19.7226 | −0.805842 | −0.402921 | − | 0.915235i | \(-0.632005\pi\) | ||||
−0.402921 | + | 0.915235i | \(0.632005\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4315 | 0.670255 | 0.335127 | − | 0.942173i | \(-0.391221\pi\) | ||||
0.335127 | + | 0.942173i | \(0.391221\pi\) | |||||||
\(602\) | −8.33225 | −0.339597 | ||||||||
\(603\) | −29.2415 | −1.19081 | ||||||||
\(604\) | 7.89550 | 0.321263 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 7.71095 | 0.313236 | ||||||||
\(607\) | −3.48612 | −0.141497 | −0.0707487 | − | 0.997494i | \(-0.522539\pi\) | ||||
−0.0707487 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(608\) | 6.90696 | 0.280114 | ||||||||
\(609\) | 5.24663 | 0.212604 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60.6108 | 2.45205 | ||||||||
\(612\) | 5.81062 | 0.234881 | ||||||||
\(613\) | 26.4960 | 1.07016 | 0.535081 | − | 0.844801i | \(-0.320281\pi\) | ||||
0.535081 | + | 0.844801i | \(0.320281\pi\) | |||||||
\(614\) | 14.7892 | 0.596842 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.0937 | 0.648434 | ||||||||
\(617\) | −38.4572 | −1.54823 | −0.774115 | − | 0.633045i | \(-0.781805\pi\) | ||||
−0.774115 | + | 0.633045i | \(0.781805\pi\) | |||||||
\(618\) | −0.984433 | −0.0395997 | ||||||||
\(619\) | 36.4591 | 1.46542 | 0.732708 | − | 0.680544i | \(-0.238256\pi\) | ||||
0.732708 | + | 0.680544i | \(0.238256\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.11018 | 0.285322 | ||||||||
\(622\) | 9.63427 | 0.386299 | ||||||||
\(623\) | 12.3835 | 0.496135 | ||||||||
\(624\) | −2.97253 | −0.118997 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −23.3956 | −0.935076 | ||||||||
\(627\) | −2.68304 | −0.107150 | ||||||||
\(628\) | 5.69267 | 0.227162 | ||||||||
\(629\) | 11.9533 | 0.476609 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.7324 | 1.18363 | 0.591814 | − | 0.806074i | \(-0.298412\pi\) | ||||
0.591814 | + | 0.806074i | \(0.298412\pi\) | |||||||
\(632\) | −48.0425 | −1.91103 | ||||||||
\(633\) | 16.9621 | 0.674184 | ||||||||
\(634\) | 20.3619 | 0.808674 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.33658 | 0.132304 | ||||||||
\(637\) | −21.1135 | −0.836549 | ||||||||
\(638\) | −10.1028 | −0.399972 | ||||||||
\(639\) | −23.3061 | −0.921975 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.7422 | 0.740274 | 0.370137 | − | 0.928977i | \(-0.379311\pi\) | ||||
0.370137 | + | 0.928977i | \(0.379311\pi\) | |||||||
\(642\) | 4.88045 | 0.192616 | ||||||||
\(643\) | −29.5989 | −1.16727 | −0.583633 | − | 0.812018i | \(-0.698369\pi\) | ||||
−0.583633 | + | 0.812018i | \(0.698369\pi\) | |||||||
\(644\) | 3.75957 | 0.148148 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.68831 | 0.105770 | ||||||||
\(647\) | 37.4655 | 1.47292 | 0.736460 | − | 0.676481i | \(-0.236496\pi\) | ||||
0.736460 | + | 0.676481i | \(0.236496\pi\) | |||||||
\(648\) | −13.3507 | −0.524465 | ||||||||
\(649\) | 29.0514 | 1.14037 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.1857 | −0.477595 | ||||||||
\(652\) | −5.73436 | −0.224575 | ||||||||
\(653\) | −19.4784 | −0.762249 | −0.381124 | − | 0.924524i | \(-0.624463\pi\) | ||||
−0.381124 | + | 0.924524i | \(0.624463\pi\) | |||||||
\(654\) | −5.96853 | −0.233388 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.79735 | −0.0701747 | ||||||||
\(657\) | 41.6216 | 1.62381 | ||||||||
\(658\) | 17.3192 | 0.675173 | ||||||||
\(659\) | 27.6813 | 1.07831 | 0.539155 | − | 0.842206i | \(-0.318744\pi\) | ||||
0.539155 | + | 0.842206i | \(0.318744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.3354 | 1.33549 | 0.667745 | − | 0.744390i | \(-0.267260\pi\) | ||||
0.667745 | + | 0.744390i | \(0.267260\pi\) | |||||||
\(662\) | 17.5103 | 0.680558 | ||||||||
\(663\) | 10.1027 | 0.392356 | ||||||||
\(664\) | 16.0435 | 0.622607 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.0699 | −0.506448 | ||||||||
\(667\) | −6.69326 | −0.259164 | ||||||||
\(668\) | −2.28018 | −0.0882229 | ||||||||
\(669\) | 17.9902 | 0.695541 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −34.6412 | −1.33731 | ||||||||
\(672\) | 7.41692 | 0.286114 | ||||||||
\(673\) | 11.8998 | 0.458702 | 0.229351 | − | 0.973344i | \(-0.426340\pi\) | ||||
0.229351 | + | 0.973344i | \(0.426340\pi\) | |||||||
\(674\) | −22.4904 | −0.866299 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −31.0849 | −1.19557 | ||||||||
\(677\) | −22.0197 | −0.846288 | −0.423144 | − | 0.906063i | \(-0.639073\pi\) | ||||
−0.423144 | + | 0.906063i | \(0.639073\pi\) | |||||||
\(678\) | 11.1886 | 0.429695 | ||||||||
\(679\) | −6.14380 | −0.235777 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.33812 | −0.127917 | ||||||||
\(682\) | 23.4645 | 0.898500 | ||||||||
\(683\) | 47.4084 | 1.81403 | 0.907016 | − | 0.421096i | \(-0.138355\pi\) | ||||
0.907016 | + | 0.421096i | \(0.138355\pi\) | |||||||
\(684\) | 3.51582 | 0.134431 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −18.9243 | −0.722532 | ||||||||
\(687\) | 6.47362 | 0.246984 | ||||||||
\(688\) | 2.87243 | 0.109510 | ||||||||
\(689\) | −27.1736 | −1.03523 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.9505 | −1.25350 | −0.626748 | − | 0.779222i | \(-0.715614\pi\) | ||||
−0.626748 | + | 0.779222i | \(0.715614\pi\) | |||||||
\(692\) | −17.0569 | −0.648404 | ||||||||
\(693\) | 13.4956 | 0.512657 | ||||||||
\(694\) | 28.5679 | 1.08442 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.01539 | −0.303822 | ||||||||
\(697\) | 6.10862 | 0.231380 | ||||||||
\(698\) | −13.6201 | −0.515529 | ||||||||
\(699\) | 8.12691 | 0.307388 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21.4743 | −0.811072 | −0.405536 | − | 0.914079i | \(-0.632915\pi\) | ||||
−0.405536 | + | 0.914079i | \(0.632915\pi\) | |||||||
\(702\) | −24.4511 | −0.922846 | ||||||||
\(703\) | 7.23255 | 0.272781 | ||||||||
\(704\) | −17.8736 | −0.673638 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.98986 | 0.263067 | ||||||||
\(707\) | 21.4632 | 0.807207 | ||||||||
\(708\) | 8.12712 | 0.305436 | ||||||||
\(709\) | 19.2938 | 0.724593 | 0.362296 | − | 0.932063i | \(-0.381993\pi\) | ||||
0.362296 | + | 0.932063i | \(0.381993\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −40.2868 | −1.51087 | ||||||||
\(712\) | −18.9186 | −0.709003 | ||||||||
\(713\) | 15.5456 | 0.582187 | ||||||||
\(714\) | 2.88679 | 0.108035 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −17.0936 | −0.638818 | ||||||||
\(717\) | 6.55390 | 0.244760 | ||||||||
\(718\) | 1.83490 | 0.0684779 | ||||||||
\(719\) | −2.49526 | −0.0930574 | −0.0465287 | − | 0.998917i | \(-0.514816\pi\) | ||||
−0.0465287 | + | 0.998917i | \(0.514816\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.74014 | −0.102048 | ||||||||
\(722\) | −16.5053 | −0.614264 | ||||||||
\(723\) | 0.726487 | 0.0270183 | ||||||||
\(724\) | 27.6391 | 1.02720 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.07842 | −0.0771372 | ||||||||
\(727\) | −24.6994 | −0.916048 | −0.458024 | − | 0.888940i | \(-0.651443\pi\) | ||||
−0.458024 | + | 0.888940i | \(0.651443\pi\) | |||||||
\(728\) | −36.6666 | −1.35895 | ||||||||
\(729\) | −2.53101 | −0.0937412 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.76248 | −0.361078 | ||||||||
\(732\) | −9.69084 | −0.358184 | ||||||||
\(733\) | 8.47061 | 0.312869 | 0.156435 | − | 0.987688i | \(-0.450000\pi\) | ||||
0.156435 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(734\) | −10.1338 | −0.374045 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.46194 | −0.348772 | ||||||||
\(737\) | −33.4592 | −1.23249 | ||||||||
\(738\) | −6.67924 | −0.245866 | ||||||||
\(739\) | 25.6575 | 0.943825 | 0.471913 | − | 0.881645i | \(-0.343564\pi\) | ||||
0.471913 | + | 0.881645i | \(0.343564\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.11281 | 0.224560 | ||||||||
\(742\) | −7.76470 | −0.285051 | ||||||||
\(743\) | −3.16313 | −0.116044 | −0.0580221 | − | 0.998315i | \(-0.518479\pi\) | ||||
−0.0580221 | + | 0.998315i | \(0.518479\pi\) | |||||||
\(744\) | 18.6163 | 0.682508 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.9791 | −0.768100 | ||||||||
\(747\) | 13.4535 | 0.492238 | ||||||||
\(748\) | 6.64873 | 0.243102 | ||||||||
\(749\) | 13.5846 | 0.496370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.3697 | −1.07171 | −0.535857 | − | 0.844309i | \(-0.680012\pi\) | ||||
−0.535857 | + | 0.844309i | \(0.680012\pi\) | |||||||
\(752\) | −5.97057 | −0.217724 | ||||||||
\(753\) | 0.212256 | 0.00773503 | ||||||||
\(754\) | 23.0173 | 0.838241 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.35679 | 0.303933 | ||||||||
\(757\) | 0.0845371 | 0.00307255 | 0.00153628 | − | 0.999999i | \(-0.499511\pi\) | ||||
0.00153628 | + | 0.999999i | \(0.499511\pi\) | |||||||
\(758\) | 11.2549 | 0.408795 | ||||||||
\(759\) | 3.67553 | 0.133413 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.857810 | 0.0310956 | 0.0155478 | − | 0.999879i | \(-0.495051\pi\) | ||||
0.0155478 | + | 0.999879i | \(0.495051\pi\) | |||||||
\(762\) | 5.78098 | 0.209423 | ||||||||
\(763\) | −16.6132 | −0.601439 | ||||||||
\(764\) | −3.39322 | −0.122762 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.60351 | −0.130200 | ||||||||
\(767\) | −66.1884 | −2.38992 | ||||||||
\(768\) | −12.3358 | −0.445129 | ||||||||
\(769\) | 35.8091 | 1.29131 | 0.645655 | − | 0.763629i | \(-0.276584\pi\) | ||||
0.645655 | + | 0.763629i | \(0.276584\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.970752 | −0.0349608 | ||||||||
\(772\) | −1.74954 | −0.0629673 | ||||||||
\(773\) | −22.4083 | −0.805970 | −0.402985 | − | 0.915207i | \(-0.632027\pi\) | ||||
−0.402985 | + | 0.915207i | \(0.632027\pi\) | |||||||
\(774\) | 10.6744 | 0.383684 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.38602 | 0.336938 | ||||||||
\(777\) | 7.76654 | 0.278623 | ||||||||
\(778\) | −5.53279 | −0.198360 | ||||||||
\(779\) | 3.69612 | 0.132427 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.6677 | −0.954245 | ||||||||
\(782\) | −3.68275 | −0.131695 | ||||||||
\(783\) | −14.8778 | −0.531690 | ||||||||
\(784\) | 2.07982 | 0.0742794 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 13.0626 | 0.465928 | ||||||||
\(787\) | 41.4843 | 1.47875 | 0.739377 | − | 0.673291i | \(-0.235120\pi\) | ||||
0.739377 | + | 0.673291i | \(0.235120\pi\) | |||||||
\(788\) | −16.5789 | −0.590599 | ||||||||
\(789\) | 0.189941 | 0.00676208 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 31.1431 | 1.10732 | ||||||||
\(792\) | −20.6176 | −0.732614 | ||||||||
\(793\) | 78.9236 | 2.80266 | ||||||||
\(794\) | −9.89863 | −0.351289 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.23864 | −0.150235 | ||||||||
\(797\) | 14.2759 | 0.505679 | 0.252840 | − | 0.967508i | \(-0.418636\pi\) | ||||
0.252840 | + | 0.967508i | \(0.418636\pi\) | |||||||
\(798\) | 1.74670 | 0.0618326 | ||||||||
\(799\) | 20.2921 | 0.717881 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.8645 | −0.560544 | ||||||||
\(802\) | 13.5276 | 0.477678 | ||||||||
\(803\) | 47.6249 | 1.68065 | ||||||||
\(804\) | −9.36020 | −0.330109 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −53.4595 | −1.88303 | ||||||||
\(807\) | −22.6114 | −0.795961 | ||||||||
\(808\) | −32.7898 | −1.15354 | ||||||||
\(809\) | 28.2967 | 0.994858 | 0.497429 | − | 0.867505i | \(-0.334277\pi\) | ||||
0.497429 | + | 0.867505i | \(0.334277\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.7290 | 0.973696 | 0.486848 | − | 0.873487i | \(-0.338147\pi\) | ||||
0.486848 | + | 0.873487i | \(0.338147\pi\) | |||||||
\(812\) | −7.86677 | −0.276069 | ||||||||
\(813\) | 4.51200 | 0.158243 | ||||||||
\(814\) | −14.9550 | −0.524174 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.995182 | −0.0348384 | ||||||||
\(817\) | −5.90696 | −0.206658 | ||||||||
\(818\) | −35.2495 | −1.23247 | ||||||||
\(819\) | −30.7474 | −1.07440 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.87351 | −0.100286 | −0.0501431 | − | 0.998742i | \(-0.515968\pi\) | ||||
−0.0501431 | + | 0.998742i | \(0.515968\pi\) | |||||||
\(822\) | 13.1989 | 0.460366 | ||||||||
\(823\) | 44.3438 | 1.54573 | 0.772865 | − | 0.634571i | \(-0.218823\pi\) | ||||
0.772865 | + | 0.634571i | \(0.218823\pi\) | |||||||
\(824\) | 4.18617 | 0.145832 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.9130 | −0.658066 | ||||||||
\(827\) | −28.5124 | −0.991474 | −0.495737 | − | 0.868473i | \(-0.665102\pi\) | ||||
−0.495737 | + | 0.868473i | \(0.665102\pi\) | |||||||
\(828\) | −4.81637 | −0.167380 | ||||||||
\(829\) | −20.2274 | −0.702527 | −0.351264 | − | 0.936277i | \(-0.614248\pi\) | ||||
−0.351264 | + | 0.936277i | \(0.614248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.6463 | −0.785592 | ||||||||
\(832\) | 40.7218 | 1.41177 | ||||||||
\(833\) | −7.06866 | −0.244914 | ||||||||
\(834\) | 13.7958 | 0.477710 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.02293 | 0.139136 | ||||||||
\(837\) | 34.5549 | 1.19439 | ||||||||
\(838\) | 22.0541 | 0.761846 | ||||||||
\(839\) | −29.7728 | −1.02787 | −0.513935 | − | 0.857829i | \(-0.671813\pi\) | ||||
−0.513935 | + | 0.857829i | \(0.671813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.9946 | −0.517055 | ||||||||
\(842\) | −17.7061 | −0.610191 | ||||||||
\(843\) | −22.0595 | −0.759770 | ||||||||
\(844\) | −25.4329 | −0.875437 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −22.1876 | −0.762825 | ||||||||
\(847\) | −5.78521 | −0.198782 | ||||||||
\(848\) | 2.67678 | 0.0919209 | ||||||||
\(849\) | −23.8981 | −0.820180 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.90797 | −0.339641 | ||||||||
\(852\) | −7.46027 | −0.255585 | ||||||||
\(853\) | −23.5214 | −0.805356 | −0.402678 | − | 0.915342i | \(-0.631921\pi\) | ||||
−0.402678 | + | 0.915342i | \(0.631921\pi\) | |||||||
\(854\) | 22.5520 | 0.771713 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.7535 | −0.709339 | ||||||||
\(857\) | −0.198145 | −0.00676851 | −0.00338426 | − | 0.999994i | \(-0.501077\pi\) | ||||
−0.00338426 | + | 0.999994i | \(0.501077\pi\) | |||||||
\(858\) | −12.6397 | −0.431512 | ||||||||
\(859\) | 3.33604 | 0.113824 | 0.0569121 | − | 0.998379i | \(-0.481875\pi\) | ||||
0.0569121 | + | 0.998379i | \(0.481875\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.96902 | 0.135264 | ||||||||
\(862\) | −9.52627 | −0.324466 | ||||||||
\(863\) | −38.9081 | −1.32445 | −0.662223 | − | 0.749307i | \(-0.730387\pi\) | ||||
−0.662223 | + | 0.749307i | \(0.730387\pi\) | |||||||
\(864\) | −21.0321 | −0.715525 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.9820 | −0.509109 | ||||||||
\(867\) | −8.96797 | −0.304568 | ||||||||
\(868\) | 18.2712 | 0.620164 | ||||||||
\(869\) | −46.0977 | −1.56376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 76.2308 | 2.58298 | ||||||||
\(872\) | 25.3804 | 0.859488 | ||||||||
\(873\) | 7.87080 | 0.266386 | ||||||||
\(874\) | −2.22831 | −0.0753737 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 13.3230 | 0.450144 | ||||||||
\(877\) | −29.5938 | −0.999311 | −0.499655 | − | 0.866224i | \(-0.666540\pi\) | ||||
−0.499655 | + | 0.866224i | \(0.666540\pi\) | |||||||
\(878\) | 2.96220 | 0.0999693 | ||||||||
\(879\) | 7.89174 | 0.266182 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.5670 | −1.16459 | −0.582296 | − | 0.812977i | \(-0.697846\pi\) | ||||
−0.582296 | + | 0.812977i | \(0.697846\pi\) | |||||||
\(882\) | 7.72895 | 0.260247 | ||||||||
\(883\) | −26.9745 | −0.907765 | −0.453883 | − | 0.891061i | \(-0.649961\pi\) | ||||
−0.453883 | + | 0.891061i | \(0.649961\pi\) | |||||||
\(884\) | −15.1479 | −0.509480 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.73554 | −0.0583066 | ||||||||
\(887\) | −49.5386 | −1.66334 | −0.831672 | − | 0.555267i | \(-0.812616\pi\) | ||||
−0.831672 | + | 0.555267i | \(0.812616\pi\) | |||||||
\(888\) | −11.8651 | −0.398167 | ||||||||
\(889\) | 16.0912 | 0.539681 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.8102 | −0.429159 | ||||||||
\(892\) | −26.9744 | −0.903169 | ||||||||
\(893\) | 12.2781 | 0.410870 | ||||||||
\(894\) | −13.5183 | −0.452120 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.78254 | −0.293404 | ||||||||
\(897\) | −8.37402 | −0.279600 | ||||||||
\(898\) | −7.99827 | −0.266906 | ||||||||
\(899\) | −32.5286 | −1.08489 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.09751 | −0.303082 | ||||||||
\(902\) | −7.64263 | −0.254472 | ||||||||
\(903\) | −6.34308 | −0.211084 | ||||||||
\(904\) | −47.5780 | −1.58242 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.02520 | −0.166951 | ||||||||
\(907\) | −44.9401 | −1.49221 | −0.746106 | − | 0.665827i | \(-0.768079\pi\) | ||||
−0.746106 | + | 0.665827i | \(0.768079\pi\) | |||||||
\(908\) | 5.00516 | 0.166102 | ||||||||
\(909\) | −27.4965 | −0.912000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.879323 | 0.0291333 | 0.0145666 | − | 0.999894i | \(-0.495363\pi\) | ||||
0.0145666 | + | 0.999894i | \(0.495363\pi\) | |||||||
\(912\) | −0.602152 | −0.0199393 | ||||||||
\(913\) | 15.3940 | 0.509467 | ||||||||
\(914\) | 32.4901 | 1.07468 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.70650 | −0.320712 | ||||||||
\(917\) | 36.3594 | 1.20069 | ||||||||
\(918\) | −8.18604 | −0.270179 | ||||||||
\(919\) | −31.1511 | −1.02758 | −0.513789 | − | 0.857916i | \(-0.671759\pi\) | ||||
−0.513789 | + | 0.857916i | \(0.671759\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.2585 | 0.370981 | ||||||||
\(922\) | 35.3516 | 1.16424 | ||||||||
\(923\) | 60.7575 | 1.99986 | ||||||||
\(924\) | 4.31995 | 0.142116 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.1231 | −0.562699 | ||||||||
\(927\) | 3.51039 | 0.115296 | ||||||||
\(928\) | 19.7988 | 0.649927 | ||||||||
\(929\) | −14.7760 | −0.484785 | −0.242393 | − | 0.970178i | \(-0.577932\pi\) | ||||
−0.242393 | + | 0.970178i | \(0.577932\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.27701 | −0.140173 | ||||||||
\(932\) | −12.1854 | −0.399147 | ||||||||
\(933\) | 7.33427 | 0.240113 | ||||||||
\(934\) | −21.5159 | −0.704022 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 46.9734 | 1.53537 | ||||||||
\(937\) | −4.98095 | −0.162720 | −0.0813602 | − | 0.996685i | \(-0.525926\pi\) | ||||
−0.0813602 | + | 0.996685i | \(0.525926\pi\) | |||||||
\(938\) | 21.7825 | 0.711225 | ||||||||
\(939\) | −17.8103 | −0.581218 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6282 | −0.868053 | −0.434026 | − | 0.900900i | \(-0.642908\pi\) | ||||
−0.434026 | + | 0.900900i | \(0.642908\pi\) | |||||||
\(942\) | −3.62318 | −0.118050 | ||||||||
\(943\) | −5.06337 | −0.164886 | ||||||||
\(944\) | 6.52000 | 0.212208 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.2141 | 0.397113 | ||||||||
\(947\) | 34.7075 | 1.12784 | 0.563921 | − | 0.825829i | \(-0.309292\pi\) | ||||
0.563921 | + | 0.825829i | \(0.309292\pi\) | |||||||
\(948\) | −12.8958 | −0.418836 | ||||||||
\(949\) | −108.505 | −3.52221 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 15.5009 | 0.502650 | ||||||||
\(952\) | −12.2757 | −0.397857 | ||||||||
\(953\) | −7.26177 | −0.235232 | −0.117616 | − | 0.993059i | \(-0.537525\pi\) | ||||
−0.117616 | + | 0.993059i | \(0.537525\pi\) | |||||||
\(954\) | 9.94733 | 0.322057 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.82687 | −0.317824 | ||||||||
\(957\) | −7.69092 | −0.248612 | ||||||||
\(958\) | −6.28055 | −0.202916 | ||||||||
\(959\) | 36.7389 | 1.18636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.5502 | 1.43710 | ||||||||
\(962\) | 34.0723 | 1.09854 | ||||||||
\(963\) | −17.4032 | −0.560809 | ||||||||
\(964\) | −1.08929 | −0.0350837 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.39283 | −0.0769881 | ||||||||
\(967\) | −8.56893 | −0.275558 | −0.137779 | − | 0.990463i | \(-0.543996\pi\) | ||||
−0.137779 | + | 0.990463i | \(0.543996\pi\) | |||||||
\(968\) | 8.83819 | 0.284070 | ||||||||
\(969\) | 2.04652 | 0.0657438 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.8300 | 0.411733 | 0.205867 | − | 0.978580i | \(-0.433999\pi\) | ||||
0.205867 | + | 0.978580i | \(0.433999\pi\) | |||||||
\(972\) | −16.5751 | −0.531645 | ||||||||
\(973\) | 38.4003 | 1.23106 | ||||||||
\(974\) | −29.0085 | −0.929492 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.77450 | −0.248856 | ||||||||
\(977\) | 11.6047 | 0.371267 | 0.185633 | − | 0.982619i | \(-0.440566\pi\) | ||||
0.185633 | + | 0.982619i | \(0.440566\pi\) | |||||||
\(978\) | 3.64972 | 0.116705 | ||||||||
\(979\) | −18.1527 | −0.580164 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.2832 | 0.679519 | ||||||||
\(982\) | −5.88235 | −0.187713 | ||||||||
\(983\) | −15.5809 | −0.496953 | −0.248476 | − | 0.968638i | \(-0.579930\pi\) | ||||
−0.248476 | + | 0.968638i | \(0.579930\pi\) | |||||||
\(984\) | −6.06355 | −0.193299 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.70603 | 0.245410 | ||||||||
\(987\) | 13.1846 | 0.419670 | ||||||||
\(988\) | −9.16551 | −0.291594 | ||||||||
\(989\) | 8.09202 | 0.257311 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.9277 | −0.791854 | −0.395927 | − | 0.918282i | \(-0.629577\pi\) | ||||
−0.395927 | + | 0.918282i | \(0.629577\pi\) | |||||||
\(992\) | −45.9842 | −1.46000 | ||||||||
\(993\) | 13.3300 | 0.423016 | ||||||||
\(994\) | 17.3611 | 0.550661 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.30646 | 0.136455 | ||||||||
\(997\) | 11.4849 | 0.363730 | 0.181865 | − | 0.983324i | \(-0.441787\pi\) | ||||
0.181865 | + | 0.983324i | \(0.441787\pi\) | |||||||
\(998\) | 9.74554 | 0.308490 | ||||||||
\(999\) | −22.0235 | −0.696792 |
(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 | 6025.2.a.k.1.15 | 25 | ||
5.4 | even | 2 | 1205.2.a.d.1.11 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.a.d.1.11 | ✓ | 25 | 5.4 | even | 2 | ||
6025.2.a.k.1.15 | 25 | 1.1 | even | 1 | trivial |