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: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.33 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.30874 | 0.925421 | 0.462711 | − | 0.886509i | \(-0.346877\pi\) | ||||
0.462711 | + | 0.886509i | \(0.346877\pi\) | |||||||
\(3\) | 1.88426 | 1.08788 | 0.543939 | − | 0.839125i | \(-0.316932\pi\) | ||||
0.543939 | + | 0.839125i | \(0.316932\pi\) | |||||||
\(4\) | −0.287190 | −0.143595 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.46601 | 1.00675 | ||||||||
\(7\) | −1.28779 | −0.486739 | −0.243370 | − | 0.969934i | \(-0.578253\pi\) | ||||
−0.243370 | + | 0.969934i | \(0.578253\pi\) | |||||||
\(8\) | −2.99335 | −1.05831 | ||||||||
\(9\) | 0.550432 | 0.183477 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.698979 | 0.210750 | 0.105375 | − | 0.994433i | \(-0.466396\pi\) | ||||
0.105375 | + | 0.994433i | \(0.466396\pi\) | |||||||
\(12\) | −0.541141 | −0.156214 | ||||||||
\(13\) | 5.53802 | 1.53597 | 0.767985 | − | 0.640468i | \(-0.221259\pi\) | ||||
0.767985 | + | 0.640468i | \(0.221259\pi\) | |||||||
\(14\) | −1.68539 | −0.450439 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.34314 | −0.835785 | ||||||||
\(17\) | −3.43199 | −0.832380 | −0.416190 | − | 0.909278i | \(-0.636635\pi\) | ||||
−0.416190 | + | 0.909278i | \(0.636635\pi\) | |||||||
\(18\) | 0.720375 | 0.169794 | ||||||||
\(19\) | −3.98407 | −0.914009 | −0.457004 | − | 0.889464i | \(-0.651078\pi\) | ||||
−0.457004 | + | 0.889464i | \(0.651078\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.42653 | −0.529513 | ||||||||
\(22\) | 0.914784 | 0.195033 | ||||||||
\(23\) | −6.27054 | −1.30750 | −0.653749 | − | 0.756712i | \(-0.726805\pi\) | ||||
−0.653749 | + | 0.756712i | \(0.726805\pi\) | |||||||
\(24\) | −5.64024 | −1.15131 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.24785 | 1.42142 | ||||||||
\(27\) | −4.61562 | −0.888276 | ||||||||
\(28\) | 0.369841 | 0.0698935 | ||||||||
\(29\) | 6.15912 | 1.14372 | 0.571859 | − | 0.820352i | \(-0.306222\pi\) | ||||
0.571859 | + | 0.820352i | \(0.306222\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.212499 | −0.0381660 | −0.0190830 | − | 0.999818i | \(-0.506075\pi\) | ||||
−0.0190830 | + | 0.999818i | \(0.506075\pi\) | |||||||
\(32\) | 1.61138 | 0.284854 | ||||||||
\(33\) | 1.31706 | 0.229270 | ||||||||
\(34\) | −4.49160 | −0.770302 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.158079 | −0.0263465 | ||||||||
\(37\) | 5.91052 | 0.971683 | 0.485841 | − | 0.874047i | \(-0.338513\pi\) | ||||
0.485841 | + | 0.874047i | \(0.338513\pi\) | |||||||
\(38\) | −5.21413 | −0.845843 | ||||||||
\(39\) | 10.4351 | 1.67095 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.65382 | −1.50767 | −0.753837 | − | 0.657062i | \(-0.771799\pi\) | ||||
−0.753837 | + | 0.657062i | \(0.771799\pi\) | |||||||
\(42\) | −3.17571 | −0.490023 | ||||||||
\(43\) | 7.78957 | 1.18790 | 0.593949 | − | 0.804502i | \(-0.297568\pi\) | ||||
0.593949 | + | 0.804502i | \(0.297568\pi\) | |||||||
\(44\) | −0.200740 | −0.0302627 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.20652 | −1.20999 | ||||||||
\(47\) | −3.86035 | −0.563090 | −0.281545 | − | 0.959548i | \(-0.590847\pi\) | ||||
−0.281545 | + | 0.959548i | \(0.590847\pi\) | |||||||
\(48\) | −6.29934 | −0.909232 | ||||||||
\(49\) | −5.34159 | −0.763085 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.46676 | −0.905527 | ||||||||
\(52\) | −1.59047 | −0.220558 | ||||||||
\(53\) | −10.2480 | −1.40767 | −0.703837 | − | 0.710361i | \(-0.748532\pi\) | ||||
−0.703837 | + | 0.710361i | \(0.748532\pi\) | |||||||
\(54\) | −6.04066 | −0.822030 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.85481 | 0.515120 | ||||||||
\(57\) | −7.50702 | −0.994329 | ||||||||
\(58\) | 8.06070 | 1.05842 | ||||||||
\(59\) | −9.54071 | −1.24209 | −0.621047 | − | 0.783773i | \(-0.713293\pi\) | ||||
−0.621047 | + | 0.783773i | \(0.713293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82214 | 1.12956 | 0.564779 | − | 0.825242i | \(-0.308961\pi\) | ||||
0.564779 | + | 0.825242i | \(0.308961\pi\) | |||||||
\(62\) | −0.278107 | −0.0353196 | ||||||||
\(63\) | −0.708842 | −0.0893057 | ||||||||
\(64\) | 8.79516 | 1.09940 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.72369 | 0.212172 | ||||||||
\(67\) | −7.38392 | −0.902089 | −0.451045 | − | 0.892501i | \(-0.648948\pi\) | ||||
−0.451045 | + | 0.892501i | \(0.648948\pi\) | |||||||
\(68\) | 0.985635 | 0.119526 | ||||||||
\(69\) | −11.8153 | −1.42240 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00088 | −0.712174 | −0.356087 | − | 0.934453i | \(-0.615889\pi\) | ||||
−0.356087 | + | 0.934453i | \(0.615889\pi\) | |||||||
\(72\) | −1.64763 | −0.194176 | ||||||||
\(73\) | 2.96121 | 0.346584 | 0.173292 | − | 0.984870i | \(-0.444560\pi\) | ||||
0.173292 | + | 0.984870i | \(0.444560\pi\) | |||||||
\(74\) | 7.73535 | 0.899216 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.14419 | 0.131247 | ||||||||
\(77\) | −0.900139 | −0.102580 | ||||||||
\(78\) | 13.6568 | 1.54633 | ||||||||
\(79\) | −6.80832 | −0.765996 | −0.382998 | − | 0.923749i | \(-0.625108\pi\) | ||||
−0.382998 | + | 0.923749i | \(0.625108\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3483 | −1.14981 | ||||||||
\(82\) | −12.6344 | −1.39523 | ||||||||
\(83\) | −16.1202 | −1.76942 | −0.884709 | − | 0.466144i | \(-0.845643\pi\) | ||||
−0.884709 | + | 0.466144i | \(0.845643\pi\) | |||||||
\(84\) | 0.696877 | 0.0760355 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.1946 | 1.09931 | ||||||||
\(87\) | 11.6054 | 1.24423 | ||||||||
\(88\) | −2.09228 | −0.223038 | ||||||||
\(89\) | 1.74849 | 0.185340 | 0.0926698 | − | 0.995697i | \(-0.470460\pi\) | ||||
0.0926698 | + | 0.995697i | \(0.470460\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.13182 | −0.747617 | ||||||||
\(92\) | 1.80084 | 0.187750 | ||||||||
\(93\) | −0.400404 | −0.0415199 | ||||||||
\(94\) | −5.05221 | −0.521096 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.03625 | 0.309886 | ||||||||
\(97\) | −0.714461 | −0.0725425 | −0.0362713 | − | 0.999342i | \(-0.511548\pi\) | ||||
−0.0362713 | + | 0.999342i | \(0.511548\pi\) | |||||||
\(98\) | −6.99077 | −0.706175 | ||||||||
\(99\) | 0.384741 | 0.0386679 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.31355 | −0.230207 | −0.115104 | − | 0.993353i | \(-0.536720\pi\) | ||||
−0.115104 | + | 0.993353i | \(0.536720\pi\) | |||||||
\(102\) | −8.46333 | −0.837994 | ||||||||
\(103\) | 2.90751 | 0.286485 | 0.143243 | − | 0.989688i | \(-0.454247\pi\) | ||||
0.143243 | + | 0.989688i | \(0.454247\pi\) | |||||||
\(104\) | −16.5772 | −1.62553 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.4120 | −1.30269 | ||||||||
\(107\) | −14.8579 | −1.43637 | −0.718186 | − | 0.695851i | \(-0.755027\pi\) | ||||
−0.718186 | + | 0.695851i | \(0.755027\pi\) | |||||||
\(108\) | 1.32556 | 0.127552 | ||||||||
\(109\) | −11.2125 | −1.07396 | −0.536980 | − | 0.843595i | \(-0.680435\pi\) | ||||
−0.536980 | + | 0.843595i | \(0.680435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.1369 | 1.05707 | ||||||||
\(112\) | 4.30527 | 0.406810 | ||||||||
\(113\) | −15.7753 | −1.48402 | −0.742009 | − | 0.670390i | \(-0.766127\pi\) | ||||
−0.742009 | + | 0.670390i | \(0.766127\pi\) | |||||||
\(114\) | −9.82477 | −0.920174 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.76884 | −0.164233 | ||||||||
\(117\) | 3.04831 | 0.281816 | ||||||||
\(118\) | −12.4863 | −1.14946 | ||||||||
\(119\) | 4.41969 | 0.405152 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.5114 | −0.955584 | ||||||||
\(122\) | 11.5459 | 1.04532 | ||||||||
\(123\) | −18.1903 | −1.64016 | ||||||||
\(124\) | 0.0610277 | 0.00548045 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.927693 | −0.0826454 | ||||||||
\(127\) | 12.8024 | 1.13603 | 0.568016 | − | 0.823018i | \(-0.307711\pi\) | ||||
0.568016 | + | 0.823018i | \(0.307711\pi\) | |||||||
\(128\) | 8.28786 | 0.732550 | ||||||||
\(129\) | 14.6776 | 1.29229 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.22476 | −0.107008 | −0.0535039 | − | 0.998568i | \(-0.517039\pi\) | ||||
−0.0535039 | + | 0.998568i | \(0.517039\pi\) | |||||||
\(132\) | −0.378246 | −0.0329221 | ||||||||
\(133\) | 5.13065 | 0.444884 | ||||||||
\(134\) | −9.66366 | −0.834813 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.2731 | 0.880914 | ||||||||
\(137\) | 2.83614 | 0.242308 | 0.121154 | − | 0.992634i | \(-0.461341\pi\) | ||||
0.121154 | + | 0.992634i | \(0.461341\pi\) | |||||||
\(138\) | −15.4632 | −1.31632 | ||||||||
\(139\) | 2.03279 | 0.172419 | 0.0862095 | − | 0.996277i | \(-0.472525\pi\) | ||||
0.0862095 | + | 0.996277i | \(0.472525\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.27390 | −0.612573 | ||||||||
\(142\) | −7.85362 | −0.659061 | ||||||||
\(143\) | 3.87096 | 0.323706 | ||||||||
\(144\) | −1.84017 | −0.153348 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.87547 | 0.320736 | ||||||||
\(147\) | −10.0649 | −0.830143 | ||||||||
\(148\) | −1.69744 | −0.139529 | ||||||||
\(149\) | 21.0260 | 1.72252 | 0.861259 | − | 0.508166i | \(-0.169676\pi\) | ||||
0.861259 | + | 0.508166i | \(0.169676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.32656 | 0.433469 | 0.216735 | − | 0.976231i | \(-0.430459\pi\) | ||||
0.216735 | + | 0.976231i | \(0.430459\pi\) | |||||||
\(152\) | 11.9257 | 0.967302 | ||||||||
\(153\) | −1.88908 | −0.152723 | ||||||||
\(154\) | −1.17805 | −0.0949300 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.99685 | −0.239940 | ||||||||
\(157\) | 16.8020 | 1.34094 | 0.670471 | − | 0.741936i | \(-0.266092\pi\) | ||||
0.670471 | + | 0.741936i | \(0.266092\pi\) | |||||||
\(158\) | −8.91035 | −0.708869 | ||||||||
\(159\) | −19.3099 | −1.53138 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.07514 | 0.636410 | ||||||||
\(162\) | −13.5433 | −1.06406 | ||||||||
\(163\) | 6.28719 | 0.492450 | 0.246225 | − | 0.969213i | \(-0.420810\pi\) | ||||
0.246225 | + | 0.969213i | \(0.420810\pi\) | |||||||
\(164\) | 2.77249 | 0.216495 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −21.0972 | −1.63746 | ||||||||
\(167\) | −15.4202 | −1.19325 | −0.596626 | − | 0.802519i | \(-0.703492\pi\) | ||||
−0.596626 | + | 0.802519i | \(0.703492\pi\) | |||||||
\(168\) | 7.26345 | 0.560387 | ||||||||
\(169\) | 17.6697 | 1.35921 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.19296 | −0.167700 | ||||||||
\(172\) | −2.23709 | −0.170577 | ||||||||
\(173\) | −3.72835 | −0.283461 | −0.141731 | − | 0.989905i | \(-0.545267\pi\) | ||||
−0.141731 | + | 0.989905i | \(0.545267\pi\) | |||||||
\(174\) | 15.1885 | 1.15143 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.33678 | −0.176142 | ||||||||
\(177\) | −17.9772 | −1.35125 | ||||||||
\(178\) | 2.28833 | 0.171517 | ||||||||
\(179\) | 10.9282 | 0.816811 | 0.408405 | − | 0.912801i | \(-0.366085\pi\) | ||||
0.408405 | + | 0.912801i | \(0.366085\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.6140 | 0.937590 | 0.468795 | − | 0.883307i | \(-0.344688\pi\) | ||||
0.468795 | + | 0.883307i | \(0.344688\pi\) | |||||||
\(182\) | −9.33372 | −0.691861 | ||||||||
\(183\) | 16.6232 | 1.22882 | ||||||||
\(184\) | 18.7699 | 1.38373 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.524026 | −0.0384234 | ||||||||
\(187\) | −2.39889 | −0.175424 | ||||||||
\(188\) | 1.10866 | 0.0808571 | ||||||||
\(189\) | 5.94396 | 0.432359 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.4657 | 1.04670 | 0.523349 | − | 0.852118i | \(-0.324682\pi\) | ||||
0.523349 | + | 0.852118i | \(0.324682\pi\) | |||||||
\(192\) | 16.5724 | 1.19601 | ||||||||
\(193\) | −8.80554 | −0.633837 | −0.316918 | − | 0.948453i | \(-0.602648\pi\) | ||||
−0.316918 | + | 0.948453i | \(0.602648\pi\) | |||||||
\(194\) | −0.935046 | −0.0671324 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.53405 | 0.109575 | ||||||||
\(197\) | 20.3391 | 1.44910 | 0.724552 | − | 0.689220i | \(-0.242047\pi\) | ||||
0.724552 | + | 0.689220i | \(0.242047\pi\) | |||||||
\(198\) | 0.503527 | 0.0357841 | ||||||||
\(199\) | 18.6435 | 1.32160 | 0.660800 | − | 0.750562i | \(-0.270217\pi\) | ||||
0.660800 | + | 0.750562i | \(0.270217\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.9132 | −0.981363 | ||||||||
\(202\) | −3.02785 | −0.213039 | ||||||||
\(203\) | −7.93166 | −0.556693 | ||||||||
\(204\) | 1.85719 | 0.130029 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.80518 | 0.265120 | ||||||||
\(207\) | −3.45151 | −0.239896 | ||||||||
\(208\) | −18.5144 | −1.28374 | ||||||||
\(209\) | −2.78478 | −0.192627 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.60455 | −0.661205 | −0.330602 | − | 0.943770i | \(-0.607252\pi\) | ||||
−0.330602 | + | 0.943770i | \(0.607252\pi\) | |||||||
\(212\) | 2.94314 | 0.202135 | ||||||||
\(213\) | −11.3072 | −0.774758 | ||||||||
\(214\) | −19.4452 | −1.32925 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.8161 | 0.940070 | ||||||||
\(217\) | 0.273655 | 0.0185769 | ||||||||
\(218\) | −14.6743 | −0.993866 | ||||||||
\(219\) | 5.57970 | 0.377041 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.0064 | −1.27851 | ||||||||
\(222\) | 14.5754 | 0.978237 | ||||||||
\(223\) | −21.8910 | −1.46593 | −0.732967 | − | 0.680265i | \(-0.761865\pi\) | ||||
−0.732967 | + | 0.680265i | \(0.761865\pi\) | |||||||
\(224\) | −2.07512 | −0.138650 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.6459 | −1.37334 | ||||||||
\(227\) | −25.5764 | −1.69757 | −0.848783 | − | 0.528742i | \(-0.822664\pi\) | ||||
−0.848783 | + | 0.528742i | \(0.822664\pi\) | |||||||
\(228\) | 2.15595 | 0.142781 | ||||||||
\(229\) | 17.6417 | 1.16580 | 0.582899 | − | 0.812544i | \(-0.301918\pi\) | ||||
0.582899 | + | 0.812544i | \(0.301918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.69609 | −0.111595 | ||||||||
\(232\) | −18.4364 | −1.21041 | ||||||||
\(233\) | −9.74499 | −0.638416 | −0.319208 | − | 0.947685i | \(-0.603417\pi\) | ||||
−0.319208 | + | 0.947685i | \(0.603417\pi\) | |||||||
\(234\) | 3.98945 | 0.260799 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.74000 | 0.178359 | ||||||||
\(237\) | −12.8286 | −0.833310 | ||||||||
\(238\) | 5.78424 | 0.374936 | ||||||||
\(239\) | −29.1323 | −1.88441 | −0.942205 | − | 0.335037i | \(-0.891251\pi\) | ||||
−0.942205 | + | 0.335037i | \(0.891251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | −13.7568 | −0.884318 | ||||||||
\(243\) | −5.65206 | −0.362580 | ||||||||
\(244\) | −2.53363 | −0.162199 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −23.8064 | −1.51784 | ||||||||
\(247\) | −22.0639 | −1.40389 | ||||||||
\(248\) | 0.636084 | 0.0403913 | ||||||||
\(249\) | −30.3746 | −1.92491 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.9810 | 1.13495 | 0.567474 | − | 0.823391i | \(-0.307921\pi\) | ||||
0.567474 | + | 0.823391i | \(0.307921\pi\) | |||||||
\(252\) | 0.203573 | 0.0128239 | ||||||||
\(253\) | −4.38297 | −0.275555 | ||||||||
\(254\) | 16.7551 | 1.05131 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.74365 | −0.421478 | ||||||||
\(257\) | 20.0744 | 1.25221 | 0.626105 | − | 0.779739i | \(-0.284648\pi\) | ||||
0.626105 | + | 0.779739i | \(0.284648\pi\) | |||||||
\(258\) | 19.2092 | 1.19591 | ||||||||
\(259\) | −7.61151 | −0.472956 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.39018 | 0.209847 | ||||||||
\(262\) | −1.60290 | −0.0990273 | ||||||||
\(263\) | 15.6319 | 0.963906 | 0.481953 | − | 0.876197i | \(-0.339928\pi\) | ||||
0.481953 | + | 0.876197i | \(0.339928\pi\) | |||||||
\(264\) | −3.94241 | −0.242638 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 6.71471 | 0.411705 | ||||||||
\(267\) | 3.29461 | 0.201627 | ||||||||
\(268\) | 2.12059 | 0.129536 | ||||||||
\(269\) | 22.2853 | 1.35876 | 0.679379 | − | 0.733787i | \(-0.262249\pi\) | ||||
0.679379 | + | 0.733787i | \(0.262249\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.6867 | −1.19588 | −0.597939 | − | 0.801541i | \(-0.704014\pi\) | ||||
−0.597939 | + | 0.801541i | \(0.704014\pi\) | |||||||
\(272\) | 11.4736 | 0.695691 | ||||||||
\(273\) | −13.4382 | −0.813316 | ||||||||
\(274\) | 3.71178 | 0.224237 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.39325 | 0.204249 | ||||||||
\(277\) | 19.8218 | 1.19097 | 0.595487 | − | 0.803365i | \(-0.296959\pi\) | ||||
0.595487 | + | 0.803365i | \(0.296959\pi\) | |||||||
\(278\) | 2.66040 | 0.159560 | ||||||||
\(279\) | −0.116966 | −0.00700260 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −25.1818 | −1.50222 | −0.751111 | − | 0.660176i | \(-0.770482\pi\) | ||||
−0.751111 | + | 0.660176i | \(0.770482\pi\) | |||||||
\(282\) | −9.51967 | −0.566888 | ||||||||
\(283\) | −1.69555 | −0.100790 | −0.0503950 | − | 0.998729i | \(-0.516048\pi\) | ||||
−0.0503950 | + | 0.998729i | \(0.516048\pi\) | |||||||
\(284\) | 1.72340 | 0.102265 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.06609 | 0.299564 | ||||||||
\(287\) | 12.4321 | 0.733844 | ||||||||
\(288\) | 0.886955 | 0.0522643 | ||||||||
\(289\) | −5.22144 | −0.307144 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.34623 | −0.0789174 | ||||||||
\(292\) | −0.850433 | −0.0497678 | ||||||||
\(293\) | −21.2874 | −1.24362 | −0.621811 | − | 0.783167i | \(-0.713603\pi\) | ||||
−0.621811 | + | 0.783167i | \(0.713603\pi\) | |||||||
\(294\) | −13.1724 | −0.768232 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −17.6922 | −1.02834 | ||||||||
\(297\) | −3.22622 | −0.187204 | ||||||||
\(298\) | 27.5177 | 1.59405 | ||||||||
\(299\) | −34.7264 | −2.00828 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.0313 | −0.578197 | ||||||||
\(302\) | 6.97110 | 0.401142 | ||||||||
\(303\) | −4.35933 | −0.250437 | ||||||||
\(304\) | 13.3193 | 0.763915 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.47232 | −0.141333 | ||||||||
\(307\) | 17.5022 | 0.998901 | 0.499450 | − | 0.866342i | \(-0.333535\pi\) | ||||
0.499450 | + | 0.866342i | \(0.333535\pi\) | |||||||
\(308\) | 0.258511 | 0.0147300 | ||||||||
\(309\) | 5.47850 | 0.311661 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.1108 | −1.53732 | −0.768658 | − | 0.639661i | \(-0.779075\pi\) | ||||
−0.768658 | + | 0.639661i | \(0.779075\pi\) | |||||||
\(312\) | −31.2358 | −1.76838 | ||||||||
\(313\) | 5.43613 | 0.307268 | 0.153634 | − | 0.988128i | \(-0.450902\pi\) | ||||
0.153634 | + | 0.988128i | \(0.450902\pi\) | |||||||
\(314\) | 21.9894 | 1.24094 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.95528 | 0.109993 | ||||||||
\(317\) | −1.24021 | −0.0696573 | −0.0348287 | − | 0.999393i | \(-0.511089\pi\) | ||||
−0.0348287 | + | 0.999393i | \(0.511089\pi\) | |||||||
\(318\) | −25.2718 | −1.41717 | ||||||||
\(319\) | 4.30509 | 0.241039 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.9962 | −1.56260 | ||||||||
\(322\) | 10.5683 | 0.588948 | ||||||||
\(323\) | 13.6733 | 0.760802 | ||||||||
\(324\) | 2.97194 | 0.165108 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.22831 | 0.455724 | ||||||||
\(327\) | −21.1272 | −1.16834 | ||||||||
\(328\) | 28.8972 | 1.59558 | ||||||||
\(329\) | 4.97133 | 0.274078 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6324 | −0.749307 | −0.374654 | − | 0.927165i | \(-0.622238\pi\) | ||||
−0.374654 | + | 0.927165i | \(0.622238\pi\) | |||||||
\(332\) | 4.62956 | 0.254080 | ||||||||
\(333\) | 3.25334 | 0.178282 | ||||||||
\(334\) | −20.1811 | −1.10426 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 8.11224 | 0.442559 | ||||||||
\(337\) | 9.45300 | 0.514938 | 0.257469 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257469 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(338\) | 23.1251 | 1.25784 | ||||||||
\(339\) | −29.7248 | −1.61443 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.148532 | −0.00804348 | ||||||||
\(342\) | −2.87002 | −0.155193 | ||||||||
\(343\) | 15.8934 | 0.858163 | ||||||||
\(344\) | −23.3169 | −1.25716 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.87945 | −0.262321 | ||||||||
\(347\) | 25.8641 | 1.38846 | 0.694230 | − | 0.719754i | \(-0.255745\pi\) | ||||
0.694230 | + | 0.719754i | \(0.255745\pi\) | |||||||
\(348\) | −3.33295 | −0.178665 | ||||||||
\(349\) | 10.7675 | 0.576372 | 0.288186 | − | 0.957575i | \(-0.406948\pi\) | ||||
0.288186 | + | 0.957575i | \(0.406948\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.5614 | −1.36437 | ||||||||
\(352\) | 1.12632 | 0.0600330 | ||||||||
\(353\) | 29.7801 | 1.58504 | 0.792518 | − | 0.609848i | \(-0.208770\pi\) | ||||
0.792518 | + | 0.609848i | \(0.208770\pi\) | |||||||
\(354\) | −23.5275 | −1.25047 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −0.502150 | −0.0266139 | ||||||||
\(357\) | 8.32784 | 0.440756 | ||||||||
\(358\) | 14.3022 | 0.755894 | ||||||||
\(359\) | 9.88958 | 0.521952 | 0.260976 | − | 0.965345i | \(-0.415956\pi\) | ||||
0.260976 | + | 0.965345i | \(0.415956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.12718 | −0.164588 | ||||||||
\(362\) | 16.5085 | 0.867666 | ||||||||
\(363\) | −19.8063 | −1.03956 | ||||||||
\(364\) | 2.04819 | 0.107354 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 21.7555 | 1.13718 | ||||||||
\(367\) | −24.3156 | −1.26926 | −0.634631 | − | 0.772815i | \(-0.718848\pi\) | ||||
−0.634631 | + | 0.772815i | \(0.718848\pi\) | |||||||
\(368\) | 20.9633 | 1.09279 | ||||||||
\(369\) | −5.31378 | −0.276624 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.1973 | 0.685171 | ||||||||
\(372\) | 0.114992 | 0.00596206 | ||||||||
\(373\) | 6.98503 | 0.361671 | 0.180836 | − | 0.983513i | \(-0.442120\pi\) | ||||
0.180836 | + | 0.983513i | \(0.442120\pi\) | |||||||
\(374\) | −3.13953 | −0.162341 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.5554 | 0.595923 | ||||||||
\(377\) | 34.1093 | 1.75672 | ||||||||
\(378\) | 7.77911 | 0.400114 | ||||||||
\(379\) | 24.8142 | 1.27462 | 0.637309 | − | 0.770608i | \(-0.280047\pi\) | ||||
0.637309 | + | 0.770608i | \(0.280047\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.1231 | 1.23586 | ||||||||
\(382\) | 18.9318 | 0.968637 | ||||||||
\(383\) | 7.88965 | 0.403142 | 0.201571 | − | 0.979474i | \(-0.435395\pi\) | ||||
0.201571 | + | 0.979474i | \(0.435395\pi\) | |||||||
\(384\) | 15.6165 | 0.796924 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.5242 | −0.586566 | ||||||||
\(387\) | 4.28763 | 0.217953 | ||||||||
\(388\) | 0.205186 | 0.0104168 | ||||||||
\(389\) | −18.8488 | −0.955670 | −0.477835 | − | 0.878450i | \(-0.658578\pi\) | ||||
−0.477835 | + | 0.878450i | \(0.658578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 21.5204 | 1.08833 | ||||||||
\(392\) | 15.9892 | 0.807578 | ||||||||
\(393\) | −2.30776 | −0.116411 | ||||||||
\(394\) | 26.6187 | 1.34103 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.110494 | −0.00555252 | ||||||||
\(397\) | −0.758306 | −0.0380583 | −0.0190292 | − | 0.999819i | \(-0.506058\pi\) | ||||
−0.0190292 | + | 0.999819i | \(0.506058\pi\) | |||||||
\(398\) | 24.3995 | 1.22304 | ||||||||
\(399\) | 9.66748 | 0.483979 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.8303 | −1.73934 | −0.869672 | − | 0.493629i | \(-0.835670\pi\) | ||||
−0.869672 | + | 0.493629i | \(0.835670\pi\) | |||||||
\(402\) | −18.2088 | −0.908174 | ||||||||
\(403\) | −1.17682 | −0.0586218 | ||||||||
\(404\) | 0.664431 | 0.0330567 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −10.3805 | −0.515176 | ||||||||
\(407\) | 4.13132 | 0.204782 | ||||||||
\(408\) | 19.3572 | 0.958326 | ||||||||
\(409\) | 17.3471 | 0.857760 | 0.428880 | − | 0.903361i | \(-0.358908\pi\) | ||||
0.428880 | + | 0.903361i | \(0.358908\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.34402 | 0.263601 | ||||||||
\(412\) | −0.835008 | −0.0411379 | ||||||||
\(413\) | 12.2864 | 0.604576 | ||||||||
\(414\) | −4.51714 | −0.222005 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 8.92384 | 0.437527 | ||||||||
\(417\) | 3.83031 | 0.187571 | ||||||||
\(418\) | −3.64456 | −0.178261 | ||||||||
\(419\) | −22.5895 | −1.10357 | −0.551786 | − | 0.833986i | \(-0.686053\pi\) | ||||
−0.551786 | + | 0.833986i | \(0.686053\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.8005 | −1.35491 | −0.677457 | − | 0.735563i | \(-0.736918\pi\) | ||||
−0.677457 | + | 0.735563i | \(0.736918\pi\) | |||||||
\(422\) | −12.5699 | −0.611893 | ||||||||
\(423\) | −2.12486 | −0.103314 | ||||||||
\(424\) | 30.6759 | 1.48975 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.7982 | −0.716977 | ||||||||
\(427\) | −11.3611 | −0.549801 | ||||||||
\(428\) | 4.26706 | 0.206256 | ||||||||
\(429\) | 7.29389 | 0.352152 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.6040 | −0.847957 | −0.423978 | − | 0.905672i | \(-0.639367\pi\) | ||||
−0.423978 | + | 0.905672i | \(0.639367\pi\) | |||||||
\(432\) | 15.4307 | 0.742408 | ||||||||
\(433\) | 7.38130 | 0.354723 | 0.177361 | − | 0.984146i | \(-0.443244\pi\) | ||||
0.177361 | + | 0.984146i | \(0.443244\pi\) | |||||||
\(434\) | 0.358144 | 0.0171915 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.22012 | 0.154216 | ||||||||
\(437\) | 24.9823 | 1.19506 | ||||||||
\(438\) | 7.30239 | 0.348922 | ||||||||
\(439\) | 2.17048 | 0.103591 | 0.0517956 | − | 0.998658i | \(-0.483506\pi\) | ||||
0.0517956 | + | 0.998658i | \(0.483506\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.94019 | −0.140009 | ||||||||
\(442\) | −24.8745 | −1.18316 | ||||||||
\(443\) | −12.7026 | −0.603518 | −0.301759 | − | 0.953384i | \(-0.597574\pi\) | ||||
−0.301759 | + | 0.953384i | \(0.597574\pi\) | |||||||
\(444\) | −3.19842 | −0.151790 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −28.6498 | −1.35661 | ||||||||
\(447\) | 39.6185 | 1.87389 | ||||||||
\(448\) | −11.3263 | −0.535119 | ||||||||
\(449\) | −4.30823 | −0.203318 | −0.101659 | − | 0.994819i | \(-0.532415\pi\) | ||||
−0.101659 | + | 0.994819i | \(0.532415\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.74781 | −0.317742 | ||||||||
\(452\) | 4.53052 | 0.213098 | ||||||||
\(453\) | 10.0366 | 0.471561 | ||||||||
\(454\) | −33.4730 | −1.57096 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.4711 | 1.05231 | ||||||||
\(457\) | 3.68356 | 0.172310 | 0.0861548 | − | 0.996282i | \(-0.472542\pi\) | ||||
0.0861548 | + | 0.996282i | \(0.472542\pi\) | |||||||
\(458\) | 23.0885 | 1.07886 | ||||||||
\(459\) | 15.8408 | 0.739384 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.3221 | 1.73826 | 0.869131 | − | 0.494582i | \(-0.164679\pi\) | ||||
0.869131 | + | 0.494582i | \(0.164679\pi\) | |||||||
\(462\) | −2.21975 | −0.103272 | ||||||||
\(463\) | 12.4345 | 0.577880 | 0.288940 | − | 0.957347i | \(-0.406697\pi\) | ||||
0.288940 | + | 0.957347i | \(0.406697\pi\) | |||||||
\(464\) | −20.5908 | −0.955903 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.7537 | −0.590804 | ||||||||
\(467\) | −3.71254 | −0.171796 | −0.0858980 | − | 0.996304i | \(-0.527376\pi\) | ||||
−0.0858980 | + | 0.996304i | \(0.527376\pi\) | |||||||
\(468\) | −0.875444 | −0.0404674 | ||||||||
\(469\) | 9.50895 | 0.439082 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.6592 | 1.45878 | ||||||||
\(472\) | 28.5586 | 1.31452 | ||||||||
\(473\) | 5.44475 | 0.250350 | ||||||||
\(474\) | −16.7894 | −0.771163 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.26929 | −0.0581779 | ||||||||
\(477\) | −5.64085 | −0.258277 | ||||||||
\(478\) | −38.1267 | −1.74387 | ||||||||
\(479\) | −32.8371 | −1.50036 | −0.750182 | − | 0.661231i | \(-0.770034\pi\) | ||||
−0.750182 | + | 0.661231i | \(0.770034\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.7326 | 1.49248 | ||||||||
\(482\) | 1.30874 | 0.0596116 | ||||||||
\(483\) | 15.2157 | 0.692337 | ||||||||
\(484\) | 3.01878 | 0.137217 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.39710 | −0.335539 | ||||||||
\(487\) | 27.1109 | 1.22851 | 0.614256 | − | 0.789107i | \(-0.289456\pi\) | ||||
0.614256 | + | 0.789107i | \(0.289456\pi\) | |||||||
\(488\) | −26.4077 | −1.19542 | ||||||||
\(489\) | 11.8467 | 0.535726 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.70831 | −0.302742 | −0.151371 | − | 0.988477i | \(-0.548369\pi\) | ||||
−0.151371 | + | 0.988477i | \(0.548369\pi\) | |||||||
\(492\) | 5.22408 | 0.235520 | ||||||||
\(493\) | −21.1380 | −0.952009 | ||||||||
\(494\) | −28.8759 | −1.29919 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.710415 | 0.0318986 | ||||||||
\(497\) | 7.72789 | 0.346643 | ||||||||
\(498\) | −39.7525 | −1.78135 | ||||||||
\(499\) | −33.9775 | −1.52104 | −0.760520 | − | 0.649314i | \(-0.775056\pi\) | ||||
−0.760520 | + | 0.649314i | \(0.775056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.0557 | −1.29811 | ||||||||
\(502\) | 23.5325 | 1.05031 | ||||||||
\(503\) | 6.74907 | 0.300926 | 0.150463 | − | 0.988616i | \(-0.451924\pi\) | ||||
0.150463 | + | 0.988616i | \(0.451924\pi\) | |||||||
\(504\) | 2.12181 | 0.0945129 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.73618 | −0.255005 | ||||||||
\(507\) | 33.2942 | 1.47865 | ||||||||
\(508\) | −3.67674 | −0.163129 | ||||||||
\(509\) | −5.20927 | −0.230897 | −0.115448 | − | 0.993313i | \(-0.536831\pi\) | ||||
−0.115448 | + | 0.993313i | \(0.536831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.81343 | −0.168696 | ||||||||
\(512\) | −25.4014 | −1.12259 | ||||||||
\(513\) | 18.3890 | 0.811892 | ||||||||
\(514\) | 26.2723 | 1.15882 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.21526 | −0.185566 | ||||||||
\(517\) | −2.69830 | −0.118671 | ||||||||
\(518\) | −9.96152 | −0.437684 | ||||||||
\(519\) | −7.02518 | −0.308371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.39792 | 0.192676 | 0.0963382 | − | 0.995349i | \(-0.469287\pi\) | ||||
0.0963382 | + | 0.995349i | \(0.469287\pi\) | |||||||
\(522\) | 4.43687 | 0.194197 | ||||||||
\(523\) | 28.7186 | 1.25578 | 0.627889 | − | 0.778303i | \(-0.283919\pi\) | ||||
0.627889 | + | 0.778303i | \(0.283919\pi\) | |||||||
\(524\) | 0.351739 | 0.0153658 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20.4582 | 0.892019 | ||||||||
\(527\) | 0.729295 | 0.0317686 | ||||||||
\(528\) | −4.40311 | −0.191621 | ||||||||
\(529\) | 16.3196 | 0.709549 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.25152 | −0.227896 | ||||||||
\(532\) | −1.47347 | −0.0638832 | ||||||||
\(533\) | −53.4631 | −2.31574 | ||||||||
\(534\) | 4.31180 | 0.186590 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22.1026 | 0.954688 | ||||||||
\(537\) | 20.5915 | 0.888590 | ||||||||
\(538\) | 29.1657 | 1.25742 | ||||||||
\(539\) | −3.73366 | −0.160820 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.5157 | −0.495099 | −0.247549 | − | 0.968875i | \(-0.579625\pi\) | ||||
−0.247549 | + | 0.968875i | \(0.579625\pi\) | |||||||
\(542\) | −25.7648 | −1.10669 | ||||||||
\(543\) | 23.7680 | 1.01998 | ||||||||
\(544\) | −5.53023 | −0.237107 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −17.5871 | −0.752660 | ||||||||
\(547\) | −1.46564 | −0.0626662 | −0.0313331 | − | 0.999509i | \(-0.509975\pi\) | ||||
−0.0313331 | + | 0.999509i | \(0.509975\pi\) | |||||||
\(548\) | −0.814512 | −0.0347942 | ||||||||
\(549\) | 4.85599 | 0.207249 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.5384 | −1.04537 | ||||||||
\(552\) | 35.3673 | 1.50533 | ||||||||
\(553\) | 8.76770 | 0.372840 | ||||||||
\(554\) | 25.9416 | 1.10215 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.583798 | −0.0247586 | ||||||||
\(557\) | −9.02751 | −0.382508 | −0.191254 | − | 0.981541i | \(-0.561255\pi\) | ||||
−0.191254 | + | 0.981541i | \(0.561255\pi\) | |||||||
\(558\) | −0.153079 | −0.00648035 | ||||||||
\(559\) | 43.1388 | 1.82458 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.52013 | −0.190840 | ||||||||
\(562\) | −32.9566 | −1.39019 | ||||||||
\(563\) | 1.03855 | 0.0437698 | 0.0218849 | − | 0.999760i | \(-0.493033\pi\) | ||||
0.0218849 | + | 0.999760i | \(0.493033\pi\) | |||||||
\(564\) | 2.08900 | 0.0879626 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.21904 | −0.0932732 | ||||||||
\(567\) | 13.3265 | 0.559660 | ||||||||
\(568\) | 17.9627 | 0.753699 | ||||||||
\(569\) | −16.4700 | −0.690458 | −0.345229 | − | 0.938519i | \(-0.612199\pi\) | ||||
−0.345229 | + | 0.938519i | \(0.612199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.2521 | 1.43341 | 0.716703 | − | 0.697378i | \(-0.245650\pi\) | ||||
0.716703 | + | 0.697378i | \(0.245650\pi\) | |||||||
\(572\) | −1.11170 | −0.0464826 | ||||||||
\(573\) | 27.2570 | 1.13868 | ||||||||
\(574\) | 16.2704 | 0.679115 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.84114 | 0.201714 | ||||||||
\(577\) | 3.72767 | 0.155185 | 0.0775924 | − | 0.996985i | \(-0.475277\pi\) | ||||
0.0775924 | + | 0.996985i | \(0.475277\pi\) | |||||||
\(578\) | −6.83353 | −0.284237 | ||||||||
\(579\) | −16.5919 | −0.689537 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.7594 | 0.861245 | ||||||||
\(582\) | −1.76187 | −0.0730318 | ||||||||
\(583\) | −7.16315 | −0.296667 | ||||||||
\(584\) | −8.86394 | −0.366792 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.8597 | −1.15088 | ||||||||
\(587\) | 29.8715 | 1.23293 | 0.616464 | − | 0.787383i | \(-0.288565\pi\) | ||||
0.616464 | + | 0.787383i | \(0.288565\pi\) | |||||||
\(588\) | 2.89056 | 0.119205 | ||||||||
\(589\) | 0.846612 | 0.0348840 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 38.3242 | 1.57645 | ||||||||
\(592\) | −19.7597 | −0.812118 | ||||||||
\(593\) | 37.2358 | 1.52909 | 0.764546 | − | 0.644569i | \(-0.222963\pi\) | ||||
0.764546 | + | 0.644569i | \(0.222963\pi\) | |||||||
\(594\) | −4.22229 | −0.173243 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.03847 | −0.247345 | ||||||||
\(597\) | 35.1291 | 1.43774 | ||||||||
\(598\) | −45.4479 | −1.85850 | ||||||||
\(599\) | −14.2870 | −0.583753 | −0.291877 | − | 0.956456i | \(-0.594280\pi\) | ||||
−0.291877 | + | 0.956456i | \(0.594280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.96440 | −0.243293 | −0.121647 | − | 0.992573i | \(-0.538817\pi\) | ||||
−0.121647 | + | 0.992573i | \(0.538817\pi\) | |||||||
\(602\) | −13.1285 | −0.535076 | ||||||||
\(603\) | −4.06435 | −0.165513 | ||||||||
\(604\) | −1.52974 | −0.0622441 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.70525 | −0.231760 | ||||||||
\(607\) | −2.52516 | −0.102493 | −0.0512466 | − | 0.998686i | \(-0.516319\pi\) | ||||
−0.0512466 | + | 0.998686i | \(0.516319\pi\) | |||||||
\(608\) | −6.41984 | −0.260359 | ||||||||
\(609\) | −14.9453 | −0.605614 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −21.3787 | −0.864890 | ||||||||
\(612\) | 0.542525 | 0.0219303 | ||||||||
\(613\) | −9.04094 | −0.365160 | −0.182580 | − | 0.983191i | \(-0.558445\pi\) | ||||
−0.182580 | + | 0.983191i | \(0.558445\pi\) | |||||||
\(614\) | 22.9058 | 0.924404 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.69443 | 0.108562 | ||||||||
\(617\) | 38.5569 | 1.55224 | 0.776120 | − | 0.630585i | \(-0.217185\pi\) | ||||
0.776120 | + | 0.630585i | \(0.217185\pi\) | |||||||
\(618\) | 7.16995 | 0.288418 | ||||||||
\(619\) | −18.0419 | −0.725166 | −0.362583 | − | 0.931951i | \(-0.618105\pi\) | ||||
−0.362583 | + | 0.931951i | \(0.618105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.9424 | 1.16142 | ||||||||
\(622\) | −35.4811 | −1.42266 | ||||||||
\(623\) | −2.25169 | −0.0902121 | ||||||||
\(624\) | −34.8859 | −1.39655 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.11449 | 0.284352 | ||||||||
\(627\) | −5.24725 | −0.209555 | ||||||||
\(628\) | −4.82536 | −0.192553 | ||||||||
\(629\) | −20.2848 | −0.808809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.00131 | −0.159290 | −0.0796448 | − | 0.996823i | \(-0.525379\pi\) | ||||
−0.0796448 | + | 0.996823i | \(0.525379\pi\) | |||||||
\(632\) | 20.3797 | 0.810659 | ||||||||
\(633\) | −18.0975 | −0.719310 | ||||||||
\(634\) | −1.62312 | −0.0644624 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.54563 | 0.219899 | ||||||||
\(637\) | −29.5818 | −1.17208 | ||||||||
\(638\) | 5.63426 | 0.223062 | ||||||||
\(639\) | −3.30308 | −0.130668 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.4959 | 1.91547 | 0.957736 | − | 0.287650i | \(-0.0928741\pi\) | ||||
0.957736 | + | 0.287650i | \(0.0928741\pi\) | |||||||
\(642\) | −36.6399 | −1.44606 | ||||||||
\(643\) | 24.8486 | 0.979935 | 0.489967 | − | 0.871741i | \(-0.337009\pi\) | ||||
0.489967 | + | 0.871741i | \(0.337009\pi\) | |||||||
\(644\) | −2.31910 | −0.0913855 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.8948 | 0.704063 | ||||||||
\(647\) | 43.2159 | 1.69899 | 0.849496 | − | 0.527595i | \(-0.176906\pi\) | ||||
0.849496 | + | 0.527595i | \(0.176906\pi\) | |||||||
\(648\) | 30.9761 | 1.21686 | ||||||||
\(649\) | −6.66875 | −0.261771 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.515636 | 0.0202094 | ||||||||
\(652\) | −1.80562 | −0.0707135 | ||||||||
\(653\) | 1.40884 | 0.0551323 | 0.0275662 | − | 0.999620i | \(-0.491224\pi\) | ||||
0.0275662 | + | 0.999620i | \(0.491224\pi\) | |||||||
\(654\) | −27.6501 | −1.08120 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 32.2741 | 1.26009 | ||||||||
\(657\) | 1.62995 | 0.0635904 | ||||||||
\(658\) | 6.50619 | 0.253638 | ||||||||
\(659\) | −4.34247 | −0.169158 | −0.0845792 | − | 0.996417i | \(-0.526955\pi\) | ||||
−0.0845792 | + | 0.996417i | \(0.526955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.3595 | 1.02527 | 0.512633 | − | 0.858608i | \(-0.328670\pi\) | ||||
0.512633 | + | 0.858608i | \(0.328670\pi\) | |||||||
\(662\) | −17.8414 | −0.693425 | ||||||||
\(663\) | −35.8130 | −1.39086 | ||||||||
\(664\) | 48.2532 | 1.87259 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.25779 | 0.164986 | ||||||||
\(667\) | −38.6210 | −1.49541 | ||||||||
\(668\) | 4.42854 | 0.171345 | ||||||||
\(669\) | −41.2484 | −1.59476 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.16648 | 0.238054 | ||||||||
\(672\) | −3.91006 | −0.150834 | ||||||||
\(673\) | 1.88857 | 0.0727989 | 0.0363995 | − | 0.999337i | \(-0.488411\pi\) | ||||
0.0363995 | + | 0.999337i | \(0.488411\pi\) | |||||||
\(674\) | 12.3716 | 0.476534 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.07456 | −0.195175 | ||||||||
\(677\) | −40.6860 | −1.56369 | −0.781845 | − | 0.623473i | \(-0.785721\pi\) | ||||
−0.781845 | + | 0.623473i | \(0.785721\pi\) | |||||||
\(678\) | −38.9021 | −1.49403 | ||||||||
\(679\) | 0.920077 | 0.0353093 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −48.1926 | −1.84674 | ||||||||
\(682\) | −0.194391 | −0.00744361 | ||||||||
\(683\) | 13.1902 | 0.504710 | 0.252355 | − | 0.967635i | \(-0.418795\pi\) | ||||
0.252355 | + | 0.967635i | \(0.418795\pi\) | |||||||
\(684\) | 0.629798 | 0.0240809 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.8004 | 0.794162 | ||||||||
\(687\) | 33.2416 | 1.26825 | ||||||||
\(688\) | −26.0416 | −0.992828 | ||||||||
\(689\) | −56.7538 | −2.16215 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4420 | −0.815692 | −0.407846 | − | 0.913051i | \(-0.633720\pi\) | ||||
−0.407846 | + | 0.913051i | \(0.633720\pi\) | |||||||
\(692\) | 1.07075 | 0.0407037 | ||||||||
\(693\) | −0.495466 | −0.0188212 | ||||||||
\(694\) | 33.8495 | 1.28491 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −34.7389 | −1.31677 | ||||||||
\(697\) | 33.1318 | 1.25496 | ||||||||
\(698\) | 14.0919 | 0.533387 | ||||||||
\(699\) | −18.3621 | −0.694518 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.8950 | 0.600348 | 0.300174 | − | 0.953885i | \(-0.402955\pi\) | ||||
0.300174 | + | 0.953885i | \(0.402955\pi\) | |||||||
\(702\) | −33.4533 | −1.26261 | ||||||||
\(703\) | −23.5479 | −0.888126 | ||||||||
\(704\) | 6.14763 | 0.231698 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 38.9746 | 1.46683 | ||||||||
\(707\) | 2.97937 | 0.112051 | ||||||||
\(708\) | 5.16287 | 0.194033 | ||||||||
\(709\) | −38.8392 | −1.45864 | −0.729318 | − | 0.684175i | \(-0.760162\pi\) | ||||
−0.729318 | + | 0.684175i | \(0.760162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.74752 | −0.140543 | ||||||||
\(712\) | −5.23384 | −0.196146 | ||||||||
\(713\) | 1.33248 | 0.0499019 | ||||||||
\(714\) | 10.8990 | 0.407885 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.13847 | −0.117290 | ||||||||
\(717\) | −54.8927 | −2.05001 | ||||||||
\(718\) | 12.9429 | 0.483025 | ||||||||
\(719\) | −1.15150 | −0.0429436 | −0.0214718 | − | 0.999769i | \(-0.506835\pi\) | ||||
−0.0214718 | + | 0.999769i | \(0.506835\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.74426 | −0.139444 | ||||||||
\(722\) | −4.09267 | −0.152314 | ||||||||
\(723\) | 1.88426 | 0.0700764 | ||||||||
\(724\) | −3.62262 | −0.134634 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −25.9213 | −0.962030 | ||||||||
\(727\) | 2.07741 | 0.0770469 | 0.0385234 | − | 0.999258i | \(-0.487735\pi\) | ||||
0.0385234 | + | 0.999258i | \(0.487735\pi\) | |||||||
\(728\) | 21.3480 | 0.791209 | ||||||||
\(729\) | 20.3950 | 0.755371 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.7337 | −0.988783 | ||||||||
\(732\) | −4.77402 | −0.176453 | ||||||||
\(733\) | 0.247310 | 0.00913459 | 0.00456729 | − | 0.999990i | \(-0.498546\pi\) | ||||
0.00456729 | + | 0.999990i | \(0.498546\pi\) | |||||||
\(734\) | −31.8228 | −1.17460 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.1042 | −0.372446 | ||||||||
\(737\) | −5.16120 | −0.190115 | ||||||||
\(738\) | −6.95437 | −0.255994 | ||||||||
\(739\) | −41.8038 | −1.53778 | −0.768889 | − | 0.639382i | \(-0.779190\pi\) | ||||
−0.768889 | + | 0.639382i | \(0.779190\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.5740 | −1.52726 | ||||||||
\(742\) | 17.2719 | 0.634072 | ||||||||
\(743\) | 16.1617 | 0.592916 | 0.296458 | − | 0.955046i | \(-0.404195\pi\) | ||||
0.296458 | + | 0.955046i | \(0.404195\pi\) | |||||||
\(744\) | 1.19855 | 0.0439408 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.14162 | 0.334698 | ||||||||
\(747\) | −8.87306 | −0.324648 | ||||||||
\(748\) | 0.688938 | 0.0251901 | ||||||||
\(749\) | 19.1339 | 0.699139 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.92639 | −0.325729 | −0.162864 | − | 0.986648i | \(-0.552073\pi\) | ||||
−0.162864 | + | 0.986648i | \(0.552073\pi\) | |||||||
\(752\) | 12.9057 | 0.470622 | ||||||||
\(753\) | 33.8808 | 1.23468 | ||||||||
\(754\) | 44.6403 | 1.62570 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.70705 | −0.0620847 | ||||||||
\(757\) | 2.30487 | 0.0837720 | 0.0418860 | − | 0.999122i | \(-0.486663\pi\) | ||||
0.0418860 | + | 0.999122i | \(0.486663\pi\) | |||||||
\(758\) | 32.4754 | 1.17956 | ||||||||
\(759\) | −8.25865 | −0.299770 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.45934 | −0.197901 | −0.0989505 | − | 0.995092i | \(-0.531549\pi\) | ||||
−0.0989505 | + | 0.995092i | \(0.531549\pi\) | |||||||
\(762\) | 31.5709 | 1.14369 | ||||||||
\(763\) | 14.4393 | 0.522739 | ||||||||
\(764\) | −4.15440 | −0.150301 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.3255 | 0.373076 | ||||||||
\(767\) | −52.8366 | −1.90782 | ||||||||
\(768\) | −12.7068 | −0.458516 | ||||||||
\(769\) | 20.6287 | 0.743890 | 0.371945 | − | 0.928255i | \(-0.378691\pi\) | ||||
0.371945 | + | 0.928255i | \(0.378691\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.8254 | 1.36225 | ||||||||
\(772\) | 2.52887 | 0.0910159 | ||||||||
\(773\) | −36.9986 | −1.33075 | −0.665374 | − | 0.746510i | \(-0.731728\pi\) | ||||
−0.665374 | + | 0.746510i | \(0.731728\pi\) | |||||||
\(774\) | 5.61141 | 0.201698 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.13863 | 0.0767723 | ||||||||
\(777\) | −14.3421 | −0.514519 | ||||||||
\(778\) | −24.6682 | −0.884398 | ||||||||
\(779\) | 38.4615 | 1.37803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.19449 | −0.150091 | ||||||||
\(782\) | 28.1647 | 1.00717 | ||||||||
\(783\) | −28.4281 | −1.01594 | ||||||||
\(784\) | 17.8577 | 0.637775 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.02027 | −0.107730 | ||||||||
\(787\) | −9.55601 | −0.340635 | −0.170317 | − | 0.985389i | \(-0.554479\pi\) | ||||
−0.170317 | + | 0.985389i | \(0.554479\pi\) | |||||||
\(788\) | −5.84121 | −0.208084 | ||||||||
\(789\) | 29.4546 | 1.04861 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.3153 | 0.722330 | ||||||||
\(792\) | −1.15166 | −0.0409225 | ||||||||
\(793\) | 48.8572 | 1.73497 | ||||||||
\(794\) | −0.992428 | −0.0352200 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.35423 | −0.189776 | ||||||||
\(797\) | −31.5410 | −1.11724 | −0.558620 | − | 0.829424i | \(-0.688669\pi\) | ||||
−0.558620 | + | 0.829424i | \(0.688669\pi\) | |||||||
\(798\) | 12.6523 | 0.447885 | ||||||||
\(799\) | 13.2487 | 0.468705 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.962426 | 0.0340056 | ||||||||
\(802\) | −45.5840 | −1.60963 | ||||||||
\(803\) | 2.06983 | 0.0730426 | ||||||||
\(804\) | 3.99574 | 0.140919 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.54016 | −0.0542499 | ||||||||
\(807\) | 41.9913 | 1.47816 | ||||||||
\(808\) | 6.92527 | 0.243630 | ||||||||
\(809\) | 26.1016 | 0.917685 | 0.458842 | − | 0.888518i | \(-0.348264\pi\) | ||||
0.458842 | + | 0.888518i | \(0.348264\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.3946 | −1.20776 | −0.603880 | − | 0.797076i | \(-0.706379\pi\) | ||||
−0.603880 | + | 0.797076i | \(0.706379\pi\) | |||||||
\(812\) | 2.27790 | 0.0799385 | ||||||||
\(813\) | −37.0948 | −1.30097 | ||||||||
\(814\) | 5.40684 | 0.189510 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 21.6193 | 0.756826 | ||||||||
\(817\) | −31.0342 | −1.08575 | ||||||||
\(818\) | 22.7029 | 0.793790 | ||||||||
\(819\) | −3.92558 | −0.137171 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.9922 | 1.84944 | 0.924720 | − | 0.380647i | \(-0.124299\pi\) | ||||
0.924720 | + | 0.380647i | \(0.124299\pi\) | |||||||
\(822\) | 6.99395 | 0.243942 | ||||||||
\(823\) | 20.4286 | 0.712095 | 0.356047 | − | 0.934468i | \(-0.384124\pi\) | ||||
0.356047 | + | 0.934468i | \(0.384124\pi\) | |||||||
\(824\) | −8.70318 | −0.303189 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.0798 | 0.559488 | ||||||||
\(827\) | −40.8210 | −1.41949 | −0.709743 | − | 0.704461i | \(-0.751189\pi\) | ||||
−0.709743 | + | 0.704461i | \(0.751189\pi\) | |||||||
\(828\) | 0.991240 | 0.0344480 | ||||||||
\(829\) | 7.89986 | 0.274374 | 0.137187 | − | 0.990545i | \(-0.456194\pi\) | ||||
0.137187 | + | 0.990545i | \(0.456194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 37.3494 | 1.29563 | ||||||||
\(832\) | 48.7078 | 1.68864 | ||||||||
\(833\) | 18.3323 | 0.635176 | ||||||||
\(834\) | 5.01289 | 0.173582 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.799762 | 0.0276604 | ||||||||
\(837\) | 0.980816 | 0.0339019 | ||||||||
\(838\) | −29.5639 | −1.02127 | ||||||||
\(839\) | 45.1697 | 1.55943 | 0.779716 | − | 0.626133i | \(-0.215363\pi\) | ||||
0.779716 | + | 0.626133i | \(0.215363\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.93470 | 0.308093 | ||||||||
\(842\) | −36.3837 | −1.25387 | ||||||||
\(843\) | −47.4491 | −1.63423 | ||||||||
\(844\) | 2.75834 | 0.0949458 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.78090 | −0.0956093 | ||||||||
\(847\) | 13.5365 | 0.465121 | ||||||||
\(848\) | 34.2606 | 1.17651 | ||||||||
\(849\) | −3.19486 | −0.109647 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.0621 | −1.27047 | ||||||||
\(852\) | 3.24732 | 0.111252 | ||||||||
\(853\) | −33.8378 | −1.15859 | −0.579293 | − | 0.815120i | \(-0.696671\pi\) | ||||
−0.579293 | + | 0.815120i | \(0.696671\pi\) | |||||||
\(854\) | −14.8687 | −0.508797 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.4750 | 1.52012 | ||||||||
\(857\) | −22.0350 | −0.752701 | −0.376351 | − | 0.926477i | \(-0.622821\pi\) | ||||
−0.376351 | + | 0.926477i | \(0.622821\pi\) | |||||||
\(858\) | 9.54583 | 0.325889 | ||||||||
\(859\) | −43.0953 | −1.47039 | −0.735197 | − | 0.677853i | \(-0.762910\pi\) | ||||
−0.735197 | + | 0.677853i | \(0.762910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.4253 | 0.798333 | ||||||||
\(862\) | −23.0392 | −0.784717 | ||||||||
\(863\) | 41.5592 | 1.41469 | 0.707347 | − | 0.706867i | \(-0.249892\pi\) | ||||
0.707347 | + | 0.706867i | \(0.249892\pi\) | |||||||
\(864\) | −7.43751 | −0.253029 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.66022 | 0.328268 | ||||||||
\(867\) | −9.83855 | −0.334135 | ||||||||
\(868\) | −0.0785910 | −0.00266755 | ||||||||
\(869\) | −4.75887 | −0.161434 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.8923 | −1.38558 | ||||||||
\(872\) | 33.5628 | 1.13658 | ||||||||
\(873\) | −0.393263 | −0.0133099 | ||||||||
\(874\) | 32.6954 | 1.10594 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.60244 | −0.0541413 | ||||||||
\(877\) | −41.5051 | −1.40153 | −0.700763 | − | 0.713394i | \(-0.747157\pi\) | ||||
−0.700763 | + | 0.713394i | \(0.747157\pi\) | |||||||
\(878\) | 2.84060 | 0.0958655 | ||||||||
\(879\) | −40.1110 | −1.35291 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.22392 | 0.175998 | 0.0879991 | − | 0.996121i | \(-0.471953\pi\) | ||||
0.0879991 | + | 0.996121i | \(0.471953\pi\) | |||||||
\(882\) | −3.84795 | −0.129567 | ||||||||
\(883\) | 31.9624 | 1.07562 | 0.537810 | − | 0.843066i | \(-0.319252\pi\) | ||||
0.537810 | + | 0.843066i | \(0.319252\pi\) | |||||||
\(884\) | 5.45847 | 0.183588 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.6244 | −0.558509 | ||||||||
\(887\) | −26.7513 | −0.898222 | −0.449111 | − | 0.893476i | \(-0.648259\pi\) | ||||
−0.449111 | + | 0.893476i | \(0.648259\pi\) | |||||||
\(888\) | −33.3367 | −1.11871 | ||||||||
\(889\) | −16.4869 | −0.552952 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7.23326 | −0.242323 | ||||||||
\(892\) | 6.28690 | 0.210501 | ||||||||
\(893\) | 15.3799 | 0.514669 | ||||||||
\(894\) | 51.8504 | 1.73414 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −10.6730 | −0.356561 | ||||||||
\(897\) | −65.4335 | −2.18476 | ||||||||
\(898\) | −5.63837 | −0.188155 | ||||||||
\(899\) | −1.30881 | −0.0436512 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 35.1711 | 1.17172 | ||||||||
\(902\) | −8.83116 | −0.294045 | ||||||||
\(903\) | −18.9017 | −0.629008 | ||||||||
\(904\) | 47.2210 | 1.57055 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 13.1354 | 0.436393 | ||||||||
\(907\) | 23.1619 | 0.769078 | 0.384539 | − | 0.923109i | \(-0.374360\pi\) | ||||
0.384539 | + | 0.923109i | \(0.374360\pi\) | |||||||
\(908\) | 7.34530 | 0.243762 | ||||||||
\(909\) | −1.27346 | −0.0422378 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.1366 | 1.62797 | 0.813984 | − | 0.580888i | \(-0.197294\pi\) | ||||
0.813984 | + | 0.580888i | \(0.197294\pi\) | |||||||
\(912\) | 25.0970 | 0.831046 | ||||||||
\(913\) | −11.2676 | −0.372905 | ||||||||
\(914\) | 4.82083 | 0.159459 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.06654 | −0.167403 | ||||||||
\(917\) | 1.57724 | 0.0520849 | ||||||||
\(918\) | 20.7315 | 0.684241 | ||||||||
\(919\) | −52.6144 | −1.73559 | −0.867794 | − | 0.496923i | \(-0.834463\pi\) | ||||
−0.867794 | + | 0.496923i | \(0.834463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.9786 | 1.08668 | ||||||||
\(922\) | 48.8450 | 1.60862 | ||||||||
\(923\) | −33.2330 | −1.09388 | ||||||||
\(924\) | 0.487102 | 0.0160245 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 16.2736 | 0.534782 | ||||||||
\(927\) | 1.60039 | 0.0525636 | ||||||||
\(928\) | 9.92466 | 0.325793 | ||||||||
\(929\) | 11.0619 | 0.362930 | 0.181465 | − | 0.983397i | \(-0.441916\pi\) | ||||
0.181465 | + | 0.983397i | \(0.441916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.2813 | 0.697466 | ||||||||
\(932\) | 2.79867 | 0.0916735 | ||||||||
\(933\) | −51.0839 | −1.67241 | ||||||||
\(934\) | −4.85877 | −0.158984 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.12463 | −0.298248 | ||||||||
\(937\) | −47.7232 | −1.55905 | −0.779525 | − | 0.626371i | \(-0.784539\pi\) | ||||
−0.779525 | + | 0.626371i | \(0.784539\pi\) | |||||||
\(938\) | 12.4448 | 0.406336 | ||||||||
\(939\) | 10.2431 | 0.334270 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.26848 | −0.236946 | −0.118473 | − | 0.992957i | \(-0.537800\pi\) | ||||
−0.118473 | + | 0.992957i | \(0.537800\pi\) | |||||||
\(942\) | 41.4338 | 1.34999 | ||||||||
\(943\) | 60.5346 | 1.97128 | ||||||||
\(944\) | 31.8959 | 1.03812 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.12577 | 0.231679 | ||||||||
\(947\) | 42.4508 | 1.37947 | 0.689734 | − | 0.724063i | \(-0.257728\pi\) | ||||
0.689734 | + | 0.724063i | \(0.257728\pi\) | |||||||
\(948\) | 3.68426 | 0.119659 | ||||||||
\(949\) | 16.3993 | 0.532343 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.33688 | −0.0757787 | ||||||||
\(952\) | −13.2297 | −0.428776 | ||||||||
\(953\) | 31.8336 | 1.03119 | 0.515596 | − | 0.856832i | \(-0.327571\pi\) | ||||
0.515596 | + | 0.856832i | \(0.327571\pi\) | |||||||
\(954\) | −7.38242 | −0.239015 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 8.36651 | 0.270592 | ||||||||
\(957\) | 8.11190 | 0.262221 | ||||||||
\(958\) | −42.9753 | −1.38847 | ||||||||
\(959\) | −3.65236 | −0.117941 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9548 | −0.998543 | ||||||||
\(962\) | 42.8385 | 1.38117 | ||||||||
\(963\) | −8.17830 | −0.263542 | ||||||||
\(964\) | −0.287190 | −0.00924978 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 19.9134 | 0.640703 | ||||||||
\(967\) | −1.98161 | −0.0637242 | −0.0318621 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318621 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(968\) | 31.4643 | 1.01130 | ||||||||
\(969\) | 25.7640 | 0.827660 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.3073 | −0.780057 | −0.390029 | − | 0.920803i | \(-0.627535\pi\) | ||||
−0.390029 | + | 0.920803i | \(0.627535\pi\) | |||||||
\(972\) | 1.62322 | 0.0520647 | ||||||||
\(973\) | −2.61781 | −0.0839232 | ||||||||
\(974\) | 35.4812 | 1.13689 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −29.4936 | −0.944068 | ||||||||
\(977\) | 22.5696 | 0.722064 | 0.361032 | − | 0.932553i | \(-0.382424\pi\) | ||||
0.361032 | + | 0.932553i | \(0.382424\pi\) | |||||||
\(978\) | 15.5043 | 0.495772 | ||||||||
\(979\) | 1.22216 | 0.0390603 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.17171 | −0.197048 | ||||||||
\(982\) | −8.77946 | −0.280164 | ||||||||
\(983\) | 27.4009 | 0.873953 | 0.436976 | − | 0.899473i | \(-0.356049\pi\) | ||||
0.436976 | + | 0.899473i | \(0.356049\pi\) | |||||||
\(984\) | 54.4499 | 1.73580 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −27.6643 | −0.881009 | ||||||||
\(987\) | 9.36727 | 0.298164 | ||||||||
\(988\) | 6.33653 | 0.201592 | ||||||||
\(989\) | −48.8448 | −1.55317 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.0711 | −1.24114 | −0.620568 | − | 0.784153i | \(-0.713098\pi\) | ||||
−0.620568 | + | 0.784153i | \(0.713098\pi\) | |||||||
\(992\) | −0.342416 | −0.0108717 | ||||||||
\(993\) | −25.6871 | −0.815154 | ||||||||
\(994\) | 10.1138 | 0.320791 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.72329 | 0.276408 | ||||||||
\(997\) | −55.0824 | −1.74448 | −0.872239 | − | 0.489080i | \(-0.837333\pi\) | ||||
−0.872239 | + | 0.489080i | \(0.837333\pi\) | |||||||
\(998\) | −44.4678 | −1.40760 | ||||||||
\(999\) | −27.2807 | −0.863123 |
(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.p.1.33 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.33 | yes | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.14 | ✓ | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.14 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.14 | ✓ | 46 | 5.3 | odd | 4 | ||
1205.2.b.c.724.33 | yes | 46 | 5.2 | odd | 4 | ||
6025.2.a.p.1.14 | 46 | 5.4 | even | 2 | inner | ||
6025.2.a.p.1.33 | 46 | 1.1 | even | 1 | trivial |