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: | \(40\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.810170 | −0.572877 | −0.286439 | − | 0.958099i | \(-0.592471\pi\) | ||||
−0.286439 | + | 0.958099i | \(0.592471\pi\) | |||||||
\(3\) | 2.88822 | 1.66751 | 0.833756 | − | 0.552133i | \(-0.186186\pi\) | ||||
0.833756 | + | 0.552133i | \(0.186186\pi\) | |||||||
\(4\) | −1.34362 | −0.671812 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.33995 | −0.955279 | ||||||||
\(7\) | 3.73380 | 1.41124 | 0.705621 | − | 0.708589i | \(-0.250668\pi\) | ||||
0.705621 | + | 0.708589i | \(0.250668\pi\) | |||||||
\(8\) | 2.70891 | 0.957743 | ||||||||
\(9\) | 5.34179 | 1.78060 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.363723 | 0.109667 | 0.0548333 | − | 0.998496i | \(-0.482537\pi\) | ||||
0.0548333 | + | 0.998496i | \(0.482537\pi\) | |||||||
\(12\) | −3.88067 | −1.12025 | ||||||||
\(13\) | 1.90909 | 0.529486 | 0.264743 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264743 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(14\) | −3.02501 | −0.808468 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.492573 | 0.123143 | ||||||||
\(17\) | 1.56783 | 0.380254 | 0.190127 | − | 0.981760i | \(-0.439110\pi\) | ||||
0.190127 | + | 0.981760i | \(0.439110\pi\) | |||||||
\(18\) | −4.32776 | −1.02006 | ||||||||
\(19\) | −4.74495 | −1.08857 | −0.544283 | − | 0.838902i | \(-0.683198\pi\) | ||||
−0.544283 | + | 0.838902i | \(0.683198\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.7840 | 2.35326 | ||||||||
\(22\) | −0.294678 | −0.0628255 | ||||||||
\(23\) | −0.210707 | −0.0439354 | −0.0219677 | − | 0.999759i | \(-0.506993\pi\) | ||||
−0.0219677 | + | 0.999759i | \(0.506993\pi\) | |||||||
\(24\) | 7.82390 | 1.59705 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.54669 | −0.303330 | ||||||||
\(27\) | 6.76358 | 1.30165 | ||||||||
\(28\) | −5.01682 | −0.948089 | ||||||||
\(29\) | 3.72590 | 0.691883 | 0.345941 | − | 0.938256i | \(-0.387560\pi\) | ||||
0.345941 | + | 0.938256i | \(0.387560\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.95609 | 0.530929 | 0.265464 | − | 0.964121i | \(-0.414475\pi\) | ||||
0.265464 | + | 0.964121i | \(0.414475\pi\) | |||||||
\(32\) | −5.81688 | −1.02829 | ||||||||
\(33\) | 1.05051 | 0.182870 | ||||||||
\(34\) | −1.27021 | −0.217839 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.17735 | −1.19623 | ||||||||
\(37\) | −2.19189 | −0.360345 | −0.180173 | − | 0.983635i | \(-0.557666\pi\) | ||||
−0.180173 | + | 0.983635i | \(0.557666\pi\) | |||||||
\(38\) | 3.84422 | 0.623614 | ||||||||
\(39\) | 5.51386 | 0.882924 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.8082 | 1.84412 | 0.922062 | − | 0.387042i | \(-0.126503\pi\) | ||||
0.922062 | + | 0.387042i | \(0.126503\pi\) | |||||||
\(42\) | −8.73688 | −1.34813 | ||||||||
\(43\) | 5.79164 | 0.883217 | 0.441609 | − | 0.897208i | \(-0.354408\pi\) | ||||
0.441609 | + | 0.897208i | \(0.354408\pi\) | |||||||
\(44\) | −0.488707 | −0.0736754 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.170708 | 0.0251696 | ||||||||
\(47\) | −3.70475 | −0.540394 | −0.270197 | − | 0.962805i | \(-0.587089\pi\) | ||||
−0.270197 | + | 0.962805i | \(0.587089\pi\) | |||||||
\(48\) | 1.42266 | 0.205343 | ||||||||
\(49\) | 6.94123 | 0.991604 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.52822 | 0.634077 | ||||||||
\(52\) | −2.56510 | −0.355715 | ||||||||
\(53\) | −2.34533 | −0.322156 | −0.161078 | − | 0.986942i | \(-0.551497\pi\) | ||||
−0.161078 | + | 0.986942i | \(0.551497\pi\) | |||||||
\(54\) | −5.47966 | −0.745687 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.1145 | 1.35161 | ||||||||
\(57\) | −13.7044 | −1.81520 | ||||||||
\(58\) | −3.01862 | −0.396364 | ||||||||
\(59\) | −5.13708 | −0.668791 | −0.334395 | − | 0.942433i | \(-0.608532\pi\) | ||||
−0.334395 | + | 0.942433i | \(0.608532\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.62512 | 0.464149 | 0.232074 | − | 0.972698i | \(-0.425449\pi\) | ||||
0.232074 | + | 0.972698i | \(0.425449\pi\) | |||||||
\(62\) | −2.39493 | −0.304157 | ||||||||
\(63\) | 19.9451 | 2.51285 | ||||||||
\(64\) | 3.72752 | 0.465940 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.851093 | −0.104762 | ||||||||
\(67\) | −1.38724 | −0.169478 | −0.0847392 | − | 0.996403i | \(-0.527006\pi\) | ||||
−0.0847392 | + | 0.996403i | \(0.527006\pi\) | |||||||
\(68\) | −2.10657 | −0.255459 | ||||||||
\(69\) | −0.608567 | −0.0732628 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.880976 | −0.104553 | −0.0522763 | − | 0.998633i | \(-0.516648\pi\) | ||||
−0.0522763 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(72\) | 14.4704 | 1.70535 | ||||||||
\(73\) | 6.39905 | 0.748953 | 0.374476 | − | 0.927236i | \(-0.377823\pi\) | ||||
0.374476 | + | 0.927236i | \(0.377823\pi\) | |||||||
\(74\) | 1.77581 | 0.206433 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.37543 | 0.731312 | ||||||||
\(77\) | 1.35807 | 0.154766 | ||||||||
\(78\) | −4.46716 | −0.505807 | ||||||||
\(79\) | −0.286499 | −0.0322337 | −0.0161168 | − | 0.999870i | \(-0.505130\pi\) | ||||
−0.0161168 | + | 0.999870i | \(0.505130\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50933 | 0.389925 | ||||||||
\(82\) | −9.56662 | −1.05646 | ||||||||
\(83\) | 6.19569 | 0.680065 | 0.340032 | − | 0.940414i | \(-0.389562\pi\) | ||||
0.340032 | + | 0.940414i | \(0.389562\pi\) | |||||||
\(84\) | −14.4896 | −1.58095 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.69222 | −0.505975 | ||||||||
\(87\) | 10.7612 | 1.15372 | ||||||||
\(88\) | 0.985291 | 0.105032 | ||||||||
\(89\) | −2.54350 | −0.269610 | −0.134805 | − | 0.990872i | \(-0.543041\pi\) | ||||
−0.134805 | + | 0.990872i | \(0.543041\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.12814 | 0.747233 | ||||||||
\(92\) | 0.283111 | 0.0295163 | ||||||||
\(93\) | 8.53781 | 0.885330 | ||||||||
\(94\) | 3.00148 | 0.309579 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −16.8004 | −1.71468 | ||||||||
\(97\) | −8.23089 | −0.835720 | −0.417860 | − | 0.908511i | \(-0.637220\pi\) | ||||
−0.417860 | + | 0.908511i | \(0.637220\pi\) | |||||||
\(98\) | −5.62358 | −0.568067 | ||||||||
\(99\) | 1.94293 | 0.195272 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.3898 | 1.53135 | 0.765673 | − | 0.643230i | \(-0.222406\pi\) | ||||
0.765673 | + | 0.643230i | \(0.222406\pi\) | |||||||
\(102\) | −3.66863 | −0.363248 | ||||||||
\(103\) | −9.05525 | −0.892240 | −0.446120 | − | 0.894973i | \(-0.647195\pi\) | ||||
−0.446120 | + | 0.894973i | \(0.647195\pi\) | |||||||
\(104\) | 5.17154 | 0.507111 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.90012 | 0.184556 | ||||||||
\(107\) | −15.2953 | −1.47865 | −0.739327 | − | 0.673347i | \(-0.764856\pi\) | ||||
−0.739327 | + | 0.673347i | \(0.764856\pi\) | |||||||
\(108\) | −9.08771 | −0.874466 | ||||||||
\(109\) | 6.31702 | 0.605061 | 0.302530 | − | 0.953140i | \(-0.402169\pi\) | ||||
0.302530 | + | 0.953140i | \(0.402169\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.33066 | −0.600880 | ||||||||
\(112\) | 1.83917 | 0.173785 | ||||||||
\(113\) | −5.72064 | −0.538153 | −0.269076 | − | 0.963119i | \(-0.586718\pi\) | ||||
−0.269076 | + | 0.963119i | \(0.586718\pi\) | |||||||
\(114\) | 11.1029 | 1.03988 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.00621 | −0.464815 | ||||||||
\(117\) | 10.1979 | 0.942800 | ||||||||
\(118\) | 4.16191 | 0.383135 | ||||||||
\(119\) | 5.85394 | 0.536630 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8677 | −0.987973 | ||||||||
\(122\) | −2.93696 | −0.265900 | ||||||||
\(123\) | 34.1045 | 3.07510 | ||||||||
\(124\) | −3.97187 | −0.356684 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −16.1590 | −1.43955 | ||||||||
\(127\) | 13.6961 | 1.21534 | 0.607668 | − | 0.794191i | \(-0.292105\pi\) | ||||
0.607668 | + | 0.794191i | \(0.292105\pi\) | |||||||
\(128\) | 8.61383 | 0.761362 | ||||||||
\(129\) | 16.7275 | 1.47277 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.8734 | 1.38686 | 0.693431 | − | 0.720523i | \(-0.256098\pi\) | ||||
0.693431 | + | 0.720523i | \(0.256098\pi\) | |||||||
\(132\) | −1.41149 | −0.122855 | ||||||||
\(133\) | −17.7167 | −1.53623 | ||||||||
\(134\) | 1.12390 | 0.0970903 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.24709 | 0.364185 | ||||||||
\(137\) | 1.09189 | 0.0932863 | 0.0466432 | − | 0.998912i | \(-0.485148\pi\) | ||||
0.0466432 | + | 0.998912i | \(0.485148\pi\) | |||||||
\(138\) | 0.493043 | 0.0419706 | ||||||||
\(139\) | 10.9871 | 0.931910 | 0.465955 | − | 0.884808i | \(-0.345711\pi\) | ||||
0.465955 | + | 0.884808i | \(0.345711\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.7001 | −0.901113 | ||||||||
\(142\) | 0.713740 | 0.0598958 | ||||||||
\(143\) | 0.694379 | 0.0580669 | ||||||||
\(144\) | 2.63122 | 0.219268 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.18432 | −0.429058 | ||||||||
\(147\) | 20.0478 | 1.65351 | ||||||||
\(148\) | 2.94508 | 0.242084 | ||||||||
\(149\) | 9.67482 | 0.792592 | 0.396296 | − | 0.918123i | \(-0.370295\pi\) | ||||
0.396296 | + | 0.918123i | \(0.370295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2525 | −0.834339 | −0.417170 | − | 0.908829i | \(-0.636978\pi\) | ||||
−0.417170 | + | 0.908829i | \(0.636978\pi\) | |||||||
\(152\) | −12.8536 | −1.04257 | ||||||||
\(153\) | 8.37499 | 0.677078 | ||||||||
\(154\) | −1.10027 | −0.0886620 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.40855 | −0.593159 | ||||||||
\(157\) | −1.76906 | −0.141186 | −0.0705930 | − | 0.997505i | \(-0.522489\pi\) | ||||
−0.0705930 | + | 0.997505i | \(0.522489\pi\) | |||||||
\(158\) | 0.232113 | 0.0184659 | ||||||||
\(159\) | −6.77382 | −0.537199 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.786736 | −0.0620035 | ||||||||
\(162\) | −2.84315 | −0.223379 | ||||||||
\(163\) | 9.69938 | 0.759714 | 0.379857 | − | 0.925045i | \(-0.375973\pi\) | ||||
0.379857 | + | 0.925045i | \(0.375973\pi\) | |||||||
\(164\) | −15.8657 | −1.23890 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.01956 | −0.389594 | ||||||||
\(167\) | −11.6371 | −0.900505 | −0.450252 | − | 0.892901i | \(-0.648666\pi\) | ||||
−0.450252 | + | 0.892901i | \(0.648666\pi\) | |||||||
\(168\) | 29.2128 | 2.25382 | ||||||||
\(169\) | −9.35538 | −0.719645 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −25.3465 | −1.93830 | ||||||||
\(172\) | −7.78179 | −0.593356 | ||||||||
\(173\) | 3.10327 | 0.235937 | 0.117969 | − | 0.993017i | \(-0.462362\pi\) | ||||
0.117969 | + | 0.993017i | \(0.462362\pi\) | |||||||
\(174\) | −8.71841 | −0.660941 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.179160 | 0.0135047 | ||||||||
\(177\) | −14.8370 | −1.11522 | ||||||||
\(178\) | 2.06067 | 0.154454 | ||||||||
\(179\) | −4.47412 | −0.334411 | −0.167206 | − | 0.985922i | \(-0.553474\pi\) | ||||
−0.167206 | + | 0.985922i | \(0.553474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.1406 | −1.86868 | −0.934342 | − | 0.356378i | \(-0.884012\pi\) | ||||
−0.934342 | + | 0.356378i | \(0.884012\pi\) | |||||||
\(182\) | −5.77501 | −0.428072 | ||||||||
\(183\) | 10.4701 | 0.773973 | ||||||||
\(184\) | −0.570785 | −0.0420788 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −6.91708 | −0.507185 | ||||||||
\(187\) | 0.570254 | 0.0417011 | ||||||||
\(188\) | 4.97779 | 0.363043 | ||||||||
\(189\) | 25.2538 | 1.83695 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.6068 | −1.49105 | −0.745527 | − | 0.666475i | \(-0.767802\pi\) | ||||
−0.745527 | + | 0.666475i | \(0.767802\pi\) | |||||||
\(192\) | 10.7659 | 0.776960 | ||||||||
\(193\) | 0.420838 | 0.0302926 | 0.0151463 | − | 0.999885i | \(-0.495179\pi\) | ||||
0.0151463 | + | 0.999885i | \(0.495179\pi\) | |||||||
\(194\) | 6.66842 | 0.478765 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.32640 | −0.666172 | ||||||||
\(197\) | −17.1310 | −1.22053 | −0.610266 | − | 0.792197i | \(-0.708937\pi\) | ||||
−0.610266 | + | 0.792197i | \(0.708937\pi\) | |||||||
\(198\) | −1.57411 | −0.111867 | ||||||||
\(199\) | 4.57679 | 0.324440 | 0.162220 | − | 0.986755i | \(-0.448135\pi\) | ||||
0.162220 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00665 | −0.282607 | ||||||||
\(202\) | −12.4684 | −0.877273 | ||||||||
\(203\) | 13.9118 | 0.976414 | ||||||||
\(204\) | −6.08422 | −0.425981 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.33630 | 0.511144 | ||||||||
\(207\) | −1.12555 | −0.0782312 | ||||||||
\(208\) | 0.940365 | 0.0652026 | ||||||||
\(209\) | −1.72585 | −0.119379 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9965 | −0.757029 | −0.378515 | − | 0.925595i | \(-0.623565\pi\) | ||||
−0.378515 | + | 0.925595i | \(0.623565\pi\) | |||||||
\(212\) | 3.15124 | 0.216428 | ||||||||
\(213\) | −2.54445 | −0.174343 | ||||||||
\(214\) | 12.3918 | 0.847087 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 18.3219 | 1.24665 | ||||||||
\(217\) | 11.0374 | 0.749269 | ||||||||
\(218\) | −5.11786 | −0.346625 | ||||||||
\(219\) | 18.4818 | 1.24889 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.99312 | 0.201339 | ||||||||
\(222\) | 5.12891 | 0.344230 | ||||||||
\(223\) | 15.9121 | 1.06555 | 0.532775 | − | 0.846257i | \(-0.321149\pi\) | ||||
0.532775 | + | 0.846257i | \(0.321149\pi\) | |||||||
\(224\) | −21.7190 | −1.45116 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.63470 | 0.308295 | ||||||||
\(227\) | 3.82315 | 0.253751 | 0.126876 | − | 0.991919i | \(-0.459505\pi\) | ||||
0.126876 | + | 0.991919i | \(0.459505\pi\) | |||||||
\(228\) | 18.4136 | 1.21947 | ||||||||
\(229\) | −2.04619 | −0.135216 | −0.0676080 | − | 0.997712i | \(-0.521537\pi\) | ||||
−0.0676080 | + | 0.997712i | \(0.521537\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.92239 | 0.258074 | ||||||||
\(232\) | 10.0931 | 0.662645 | ||||||||
\(233\) | 7.43671 | 0.487195 | 0.243597 | − | 0.969876i | \(-0.421672\pi\) | ||||
0.243597 | + | 0.969876i | \(0.421672\pi\) | |||||||
\(234\) | −8.26207 | −0.540108 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.90230 | 0.449302 | ||||||||
\(237\) | −0.827472 | −0.0537501 | ||||||||
\(238\) | −4.74269 | −0.307423 | ||||||||
\(239\) | −24.2338 | −1.56755 | −0.783777 | − | 0.621042i | \(-0.786709\pi\) | ||||
−0.783777 | + | 0.621042i | \(0.786709\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | ||||||||
\(242\) | 8.80469 | 0.565987 | ||||||||
\(243\) | −10.1551 | −0.651448 | ||||||||
\(244\) | −4.87079 | −0.311821 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −27.6305 | −1.76165 | ||||||||
\(247\) | −9.05853 | −0.576380 | ||||||||
\(248\) | 8.00775 | 0.508493 | ||||||||
\(249\) | 17.8945 | 1.13402 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.7129 | 1.87546 | 0.937730 | − | 0.347366i | \(-0.112924\pi\) | ||||
0.937730 | + | 0.347366i | \(0.112924\pi\) | |||||||
\(252\) | −26.7988 | −1.68816 | ||||||||
\(253\) | −0.0766390 | −0.00481825 | ||||||||
\(254\) | −11.0962 | −0.696238 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.4337 | −0.902107 | ||||||||
\(257\) | −9.33011 | −0.581996 | −0.290998 | − | 0.956724i | \(-0.593987\pi\) | ||||
−0.290998 | + | 0.956724i | \(0.593987\pi\) | |||||||
\(258\) | −13.5521 | −0.843719 | ||||||||
\(259\) | −8.18408 | −0.508534 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.9030 | 1.23196 | ||||||||
\(262\) | −12.8601 | −0.794502 | ||||||||
\(263\) | 10.0899 | 0.622173 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(264\) | 2.84573 | 0.175143 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.3535 | 0.880071 | ||||||||
\(267\) | −7.34617 | −0.449578 | ||||||||
\(268\) | 1.86393 | 0.113858 | ||||||||
\(269\) | −8.13602 | −0.496062 | −0.248031 | − | 0.968752i | \(-0.579784\pi\) | ||||
−0.248031 | + | 0.968752i | \(0.579784\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.40501 | −0.389077 | −0.194538 | − | 0.980895i | \(-0.562321\pi\) | ||||
−0.194538 | + | 0.980895i | \(0.562321\pi\) | |||||||
\(272\) | 0.772268 | 0.0468256 | ||||||||
\(273\) | 20.5876 | 1.24602 | ||||||||
\(274\) | −0.884616 | −0.0534416 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.817685 | 0.0492188 | ||||||||
\(277\) | 19.3496 | 1.16261 | 0.581304 | − | 0.813687i | \(-0.302543\pi\) | ||||
0.581304 | + | 0.813687i | \(0.302543\pi\) | |||||||
\(278\) | −8.90139 | −0.533870 | ||||||||
\(279\) | 15.7908 | 0.945369 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.41886 | −0.323262 | −0.161631 | − | 0.986851i | \(-0.551675\pi\) | ||||
−0.161631 | + | 0.986851i | \(0.551675\pi\) | |||||||
\(282\) | 8.66892 | 0.516227 | ||||||||
\(283\) | 18.4017 | 1.09387 | 0.546935 | − | 0.837175i | \(-0.315794\pi\) | ||||
0.546935 | + | 0.837175i | \(0.315794\pi\) | |||||||
\(284\) | 1.18370 | 0.0702397 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.562566 | −0.0332652 | ||||||||
\(287\) | 44.0892 | 2.60251 | ||||||||
\(288\) | −31.0725 | −1.83097 | ||||||||
\(289\) | −14.5419 | −0.855407 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.7726 | −1.39357 | ||||||||
\(292\) | −8.59792 | −0.503155 | ||||||||
\(293\) | 11.9473 | 0.697971 | 0.348985 | − | 0.937128i | \(-0.386526\pi\) | ||||
0.348985 | + | 0.937128i | \(0.386526\pi\) | |||||||
\(294\) | −16.2421 | −0.947259 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.93763 | −0.345118 | ||||||||
\(297\) | 2.46007 | 0.142748 | ||||||||
\(298\) | −7.83825 | −0.454058 | ||||||||
\(299\) | −0.402258 | −0.0232632 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.6248 | 1.24643 | ||||||||
\(302\) | 8.30630 | 0.477974 | ||||||||
\(303\) | 44.4491 | 2.55354 | ||||||||
\(304\) | −2.33723 | −0.134049 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.78517 | −0.387882 | ||||||||
\(307\) | 28.9265 | 1.65092 | 0.825462 | − | 0.564458i | \(-0.190915\pi\) | ||||
0.825462 | + | 0.564458i | \(0.190915\pi\) | |||||||
\(308\) | −1.82473 | −0.103974 | ||||||||
\(309\) | −26.1535 | −1.48782 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.9958 | 0.623512 | 0.311756 | − | 0.950162i | \(-0.399083\pi\) | ||||
0.311756 | + | 0.950162i | \(0.399083\pi\) | |||||||
\(312\) | 14.9365 | 0.845614 | ||||||||
\(313\) | −29.3670 | −1.65992 | −0.829960 | − | 0.557822i | \(-0.811637\pi\) | ||||
−0.829960 | + | 0.557822i | \(0.811637\pi\) | |||||||
\(314\) | 1.43324 | 0.0808823 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.384947 | 0.0216550 | ||||||||
\(317\) | 9.21630 | 0.517639 | 0.258820 | − | 0.965926i | \(-0.416667\pi\) | ||||
0.258820 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(318\) | 5.48795 | 0.307749 | ||||||||
\(319\) | 1.35520 | 0.0758764 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −44.1762 | −2.46567 | ||||||||
\(322\) | 0.637391 | 0.0355204 | ||||||||
\(323\) | −7.43925 | −0.413931 | ||||||||
\(324\) | −4.71521 | −0.261956 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.85815 | −0.435223 | ||||||||
\(327\) | 18.2449 | 1.00895 | ||||||||
\(328\) | 31.9872 | 1.76620 | ||||||||
\(329\) | −13.8328 | −0.762626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.4522 | 1.72877 | 0.864386 | − | 0.502829i | \(-0.167708\pi\) | ||||
0.864386 | + | 0.502829i | \(0.167708\pi\) | |||||||
\(332\) | −8.32467 | −0.456876 | ||||||||
\(333\) | −11.7086 | −0.641629 | ||||||||
\(334\) | 9.42802 | 0.515878 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.31191 | 0.289788 | ||||||||
\(337\) | −8.48911 | −0.462431 | −0.231216 | − | 0.972903i | \(-0.574270\pi\) | ||||
−0.231216 | + | 0.972903i | \(0.574270\pi\) | |||||||
\(338\) | 7.57945 | 0.412268 | ||||||||
\(339\) | −16.5224 | −0.897376 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.07520 | 0.0582252 | ||||||||
\(342\) | 20.5350 | 1.11041 | ||||||||
\(343\) | −0.219435 | −0.0118484 | ||||||||
\(344\) | 15.6890 | 0.845895 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.51418 | −0.135163 | ||||||||
\(347\) | 9.35352 | 0.502123 | 0.251062 | − | 0.967971i | \(-0.419220\pi\) | ||||
0.251062 | + | 0.967971i | \(0.419220\pi\) | |||||||
\(348\) | −14.4590 | −0.775084 | ||||||||
\(349\) | 6.74485 | 0.361044 | 0.180522 | − | 0.983571i | \(-0.442221\pi\) | ||||
0.180522 | + | 0.983571i | \(0.442221\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.9123 | 0.689206 | ||||||||
\(352\) | −2.11573 | −0.112769 | ||||||||
\(353\) | 27.5391 | 1.46576 | 0.732878 | − | 0.680360i | \(-0.238177\pi\) | ||||
0.732878 | + | 0.680360i | \(0.238177\pi\) | |||||||
\(354\) | 12.0205 | 0.638882 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.41750 | 0.181127 | ||||||||
\(357\) | 16.9074 | 0.894837 | ||||||||
\(358\) | 3.62480 | 0.191577 | ||||||||
\(359\) | 6.29764 | 0.332377 | 0.166188 | − | 0.986094i | \(-0.446854\pi\) | ||||
0.166188 | + | 0.986094i | \(0.446854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51454 | 0.184976 | ||||||||
\(362\) | 20.3681 | 1.07053 | ||||||||
\(363\) | −31.3883 | −1.64746 | ||||||||
\(364\) | −9.57755 | −0.502000 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −8.48258 | −0.443391 | ||||||||
\(367\) | 9.13283 | 0.476730 | 0.238365 | − | 0.971176i | \(-0.423389\pi\) | ||||
0.238365 | + | 0.971176i | \(0.423389\pi\) | |||||||
\(368\) | −0.103788 | −0.00541035 | ||||||||
\(369\) | 63.0767 | 3.28364 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.75698 | −0.454640 | ||||||||
\(372\) | −11.4716 | −0.594775 | ||||||||
\(373\) | −25.1732 | −1.30342 | −0.651709 | − | 0.758469i | \(-0.725948\pi\) | ||||
−0.651709 | + | 0.758469i | \(0.725948\pi\) | |||||||
\(374\) | −0.462003 | −0.0238896 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.0358 | −0.517558 | ||||||||
\(377\) | 7.11307 | 0.366342 | ||||||||
\(378\) | −20.4599 | −1.05234 | ||||||||
\(379\) | −33.6035 | −1.72610 | −0.863048 | − | 0.505122i | \(-0.831447\pi\) | ||||
−0.863048 | + | 0.505122i | \(0.831447\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 39.5574 | 2.02659 | ||||||||
\(382\) | 16.6950 | 0.854190 | ||||||||
\(383\) | 18.3265 | 0.936443 | 0.468221 | − | 0.883611i | \(-0.344895\pi\) | ||||
0.468221 | + | 0.883611i | \(0.344895\pi\) | |||||||
\(384\) | 24.8786 | 1.26958 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.340950 | −0.0173539 | ||||||||
\(387\) | 30.9377 | 1.57265 | ||||||||
\(388\) | 11.0592 | 0.561447 | ||||||||
\(389\) | 30.4975 | 1.54629 | 0.773143 | − | 0.634232i | \(-0.218684\pi\) | ||||
0.773143 | + | 0.634232i | \(0.218684\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.330352 | −0.0167066 | ||||||||
\(392\) | 18.8031 | 0.949702 | ||||||||
\(393\) | 45.8457 | 2.31261 | ||||||||
\(394\) | 13.8790 | 0.699214 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −2.61057 | −0.131186 | ||||||||
\(397\) | 6.27221 | 0.314793 | 0.157397 | − | 0.987535i | \(-0.449690\pi\) | ||||
0.157397 | + | 0.987535i | \(0.449690\pi\) | |||||||
\(398\) | −3.70798 | −0.185864 | ||||||||
\(399\) | −51.1696 | −2.56168 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1113 | 0.554870 | 0.277435 | − | 0.960744i | \(-0.410516\pi\) | ||||
0.277435 | + | 0.960744i | \(0.410516\pi\) | |||||||
\(402\) | 3.24607 | 0.161899 | ||||||||
\(403\) | 5.64343 | 0.281119 | ||||||||
\(404\) | −20.6781 | −1.02878 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.2709 | −0.559365 | ||||||||
\(407\) | −0.797242 | −0.0395178 | ||||||||
\(408\) | 12.2665 | 0.607283 | ||||||||
\(409\) | 5.94001 | 0.293714 | 0.146857 | − | 0.989158i | \(-0.453084\pi\) | ||||
0.146857 | + | 0.989158i | \(0.453084\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.15361 | 0.155556 | ||||||||
\(412\) | 12.1668 | 0.599418 | ||||||||
\(413\) | −19.1808 | −0.943826 | ||||||||
\(414\) | 0.911888 | 0.0448169 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11.1049 | −0.544464 | ||||||||
\(417\) | 31.7330 | 1.55397 | ||||||||
\(418\) | 1.39823 | 0.0683897 | ||||||||
\(419\) | 17.6829 | 0.863865 | 0.431933 | − | 0.901906i | \(-0.357832\pi\) | ||||
0.431933 | + | 0.901906i | \(0.357832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.0390 | −1.70770 | −0.853849 | − | 0.520521i | \(-0.825738\pi\) | ||||
−0.853849 | + | 0.520521i | \(0.825738\pi\) | |||||||
\(422\) | 8.90903 | 0.433685 | ||||||||
\(423\) | −19.7900 | −0.962222 | ||||||||
\(424\) | −6.35328 | −0.308542 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.06144 | 0.0998769 | ||||||||
\(427\) | 13.5354 | 0.655026 | ||||||||
\(428\) | 20.5511 | 0.993377 | ||||||||
\(429\) | 2.00552 | 0.0968273 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.76649 | 0.181426 | 0.0907128 | − | 0.995877i | \(-0.471085\pi\) | ||||
0.0907128 | + | 0.995877i | \(0.471085\pi\) | |||||||
\(432\) | 3.33156 | 0.160290 | ||||||||
\(433\) | −18.9073 | −0.908629 | −0.454315 | − | 0.890841i | \(-0.650116\pi\) | ||||
−0.454315 | + | 0.890841i | \(0.650116\pi\) | |||||||
\(434\) | −8.94219 | −0.429239 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.48770 | −0.406487 | ||||||||
\(437\) | 0.999793 | 0.0478266 | ||||||||
\(438\) | −14.9734 | −0.715459 | ||||||||
\(439\) | 21.9399 | 1.04714 | 0.523568 | − | 0.851984i | \(-0.324601\pi\) | ||||
0.523568 | + | 0.851984i | \(0.324601\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 37.0786 | 1.76565 | ||||||||
\(442\) | −2.42494 | −0.115342 | ||||||||
\(443\) | −1.03097 | −0.0489829 | −0.0244915 | − | 0.999700i | \(-0.507797\pi\) | ||||
−0.0244915 | + | 0.999700i | \(0.507797\pi\) | |||||||
\(444\) | 8.50603 | 0.403678 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.8915 | −0.610430 | ||||||||
\(447\) | 27.9430 | 1.32166 | ||||||||
\(448\) | 13.9178 | 0.657554 | ||||||||
\(449\) | −15.7218 | −0.741960 | −0.370980 | − | 0.928641i | \(-0.620978\pi\) | ||||
−0.370980 | + | 0.928641i | \(0.620978\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.29490 | 0.202239 | ||||||||
\(452\) | 7.68639 | 0.361537 | ||||||||
\(453\) | −29.6115 | −1.39127 | ||||||||
\(454\) | −3.09740 | −0.145368 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −37.1240 | −1.73849 | ||||||||
\(457\) | 9.35883 | 0.437787 | 0.218894 | − | 0.975749i | \(-0.429755\pi\) | ||||
0.218894 | + | 0.975749i | \(0.429755\pi\) | |||||||
\(458\) | 1.65776 | 0.0774621 | ||||||||
\(459\) | 10.6041 | 0.494958 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.5562 | 1.37657 | 0.688286 | − | 0.725440i | \(-0.258364\pi\) | ||||
0.688286 | + | 0.725440i | \(0.258364\pi\) | |||||||
\(462\) | −3.17781 | −0.147845 | ||||||||
\(463\) | −10.4336 | −0.484890 | −0.242445 | − | 0.970165i | \(-0.577949\pi\) | ||||
−0.242445 | + | 0.970165i | \(0.577949\pi\) | |||||||
\(464\) | 1.83528 | 0.0852006 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.02500 | −0.279103 | ||||||||
\(467\) | 0.425612 | 0.0196950 | 0.00984748 | − | 0.999952i | \(-0.496865\pi\) | ||||
0.00984748 | + | 0.999952i | \(0.496865\pi\) | |||||||
\(468\) | −13.7022 | −0.633384 | ||||||||
\(469\) | −5.17967 | −0.239175 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.10942 | −0.235429 | ||||||||
\(472\) | −13.9159 | −0.640529 | ||||||||
\(473\) | 2.10655 | 0.0968595 | ||||||||
\(474\) | 0.670393 | 0.0307922 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.86549 | −0.360514 | ||||||||
\(477\) | −12.5283 | −0.573629 | ||||||||
\(478\) | 19.6335 | 0.898016 | ||||||||
\(479\) | 33.5508 | 1.53298 | 0.766488 | − | 0.642258i | \(-0.222002\pi\) | ||||
0.766488 | + | 0.642258i | \(0.222002\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.18452 | −0.190798 | ||||||||
\(482\) | 0.810170 | 0.0369023 | ||||||||
\(483\) | −2.27226 | −0.103392 | ||||||||
\(484\) | 14.6021 | 0.663732 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.22733 | 0.373199 | ||||||||
\(487\) | −9.18309 | −0.416126 | −0.208063 | − | 0.978115i | \(-0.566716\pi\) | ||||
−0.208063 | + | 0.978115i | \(0.566716\pi\) | |||||||
\(488\) | 9.82010 | 0.444535 | ||||||||
\(489\) | 28.0139 | 1.26683 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.2635 | 0.869349 | 0.434675 | − | 0.900588i | \(-0.356863\pi\) | ||||
0.434675 | + | 0.900588i | \(0.356863\pi\) | |||||||
\(492\) | −45.8236 | −2.06589 | ||||||||
\(493\) | 5.84156 | 0.263091 | ||||||||
\(494\) | 7.33895 | 0.330195 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.45609 | 0.0653802 | ||||||||
\(497\) | −3.28938 | −0.147549 | ||||||||
\(498\) | −14.4976 | −0.649652 | ||||||||
\(499\) | −12.8283 | −0.574273 | −0.287137 | − | 0.957890i | \(-0.592703\pi\) | ||||
−0.287137 | + | 0.957890i | \(0.592703\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −33.6104 | −1.50160 | ||||||||
\(502\) | −24.0725 | −1.07441 | ||||||||
\(503\) | 0.634256 | 0.0282801 | 0.0141400 | − | 0.999900i | \(-0.495499\pi\) | ||||
0.0141400 | + | 0.999900i | \(0.495499\pi\) | |||||||
\(504\) | 54.0295 | 2.40666 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.0620906 | 0.00276026 | ||||||||
\(507\) | −27.0204 | −1.20002 | ||||||||
\(508\) | −18.4025 | −0.816478 | ||||||||
\(509\) | −24.5805 | −1.08951 | −0.544756 | − | 0.838595i | \(-0.683378\pi\) | ||||
−0.544756 | + | 0.838595i | \(0.683378\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.8928 | 1.05695 | ||||||||
\(512\) | −5.53390 | −0.244566 | ||||||||
\(513\) | −32.0929 | −1.41693 | ||||||||
\(514\) | 7.55898 | 0.333412 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −22.4755 | −0.989428 | ||||||||
\(517\) | −1.34750 | −0.0592631 | ||||||||
\(518\) | 6.63050 | 0.291327 | ||||||||
\(519\) | 8.96290 | 0.393428 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.1620 | 0.489017 | 0.244509 | − | 0.969647i | \(-0.421373\pi\) | ||||
0.244509 | + | 0.969647i | \(0.421373\pi\) | |||||||
\(522\) | −16.1248 | −0.705763 | ||||||||
\(523\) | −24.1026 | −1.05393 | −0.526967 | − | 0.849886i | \(-0.676671\pi\) | ||||
−0.526967 | + | 0.849886i | \(0.676671\pi\) | |||||||
\(524\) | −21.3278 | −0.931711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.17458 | −0.356429 | ||||||||
\(527\) | 4.63463 | 0.201887 | ||||||||
\(528\) | 0.517453 | 0.0225192 | ||||||||
\(529\) | −22.9556 | −0.998070 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.4412 | −1.19085 | ||||||||
\(532\) | 23.8045 | 1.03206 | ||||||||
\(533\) | 22.5428 | 0.976438 | ||||||||
\(534\) | 5.95165 | 0.257553 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.75790 | −0.162317 | ||||||||
\(537\) | −12.9222 | −0.557635 | ||||||||
\(538\) | 6.59157 | 0.284183 | ||||||||
\(539\) | 2.52469 | 0.108746 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.4447 | −1.26593 | −0.632963 | − | 0.774182i | \(-0.718162\pi\) | ||||
−0.632963 | + | 0.774182i | \(0.718162\pi\) | |||||||
\(542\) | 5.18915 | 0.222893 | ||||||||
\(543\) | −72.6114 | −3.11605 | ||||||||
\(544\) | −9.11985 | −0.391010 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −16.6795 | −0.713816 | ||||||||
\(547\) | 3.78570 | 0.161865 | 0.0809324 | − | 0.996720i | \(-0.474210\pi\) | ||||
0.0809324 | + | 0.996720i | \(0.474210\pi\) | |||||||
\(548\) | −1.46709 | −0.0626709 | ||||||||
\(549\) | 19.3646 | 0.826461 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.6792 | −0.753160 | ||||||||
\(552\) | −1.64855 | −0.0701669 | ||||||||
\(553\) | −1.06973 | −0.0454895 | ||||||||
\(554\) | −15.6765 | −0.666031 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.7625 | −0.626068 | ||||||||
\(557\) | −33.1324 | −1.40387 | −0.701933 | − | 0.712243i | \(-0.747679\pi\) | ||||
−0.701933 | + | 0.712243i | \(0.747679\pi\) | |||||||
\(558\) | −12.7932 | −0.541580 | ||||||||
\(559\) | 11.0568 | 0.467651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.64702 | 0.0695371 | ||||||||
\(562\) | 4.39020 | 0.185190 | ||||||||
\(563\) | −35.1874 | −1.48297 | −0.741486 | − | 0.670968i | \(-0.765879\pi\) | ||||
−0.741486 | + | 0.670968i | \(0.765879\pi\) | |||||||
\(564\) | 14.3769 | 0.605378 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.9086 | −0.626653 | ||||||||
\(567\) | 13.1031 | 0.550279 | ||||||||
\(568\) | −2.38648 | −0.100134 | ||||||||
\(569\) | 4.18986 | 0.175648 | 0.0878239 | − | 0.996136i | \(-0.472009\pi\) | ||||
0.0878239 | + | 0.996136i | \(0.472009\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23.7814 | 0.995221 | 0.497610 | − | 0.867401i | \(-0.334211\pi\) | ||||
0.497610 | + | 0.867401i | \(0.334211\pi\) | |||||||
\(572\) | −0.932985 | −0.0390101 | ||||||||
\(573\) | −59.5168 | −2.48635 | ||||||||
\(574\) | −35.7198 | −1.49092 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 19.9116 | 0.829650 | ||||||||
\(577\) | 30.9793 | 1.28968 | 0.644842 | − | 0.764316i | \(-0.276923\pi\) | ||||
0.644842 | + | 0.764316i | \(0.276923\pi\) | |||||||
\(578\) | 11.7814 | 0.490043 | ||||||||
\(579\) | 1.21547 | 0.0505132 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 23.1334 | 0.959736 | ||||||||
\(582\) | 19.2598 | 0.798346 | ||||||||
\(583\) | −0.853051 | −0.0353298 | ||||||||
\(584\) | 17.3344 | 0.717304 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.67938 | −0.399851 | ||||||||
\(587\) | −11.5211 | −0.475527 | −0.237763 | − | 0.971323i | \(-0.576414\pi\) | ||||
−0.237763 | + | 0.971323i | \(0.576414\pi\) | |||||||
\(588\) | −26.9367 | −1.11085 | ||||||||
\(589\) | −14.0265 | −0.577951 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −49.4779 | −2.03525 | ||||||||
\(592\) | −1.07967 | −0.0443740 | ||||||||
\(593\) | −16.2886 | −0.668894 | −0.334447 | − | 0.942415i | \(-0.608550\pi\) | ||||
−0.334447 | + | 0.942415i | \(0.608550\pi\) | |||||||
\(594\) | −1.99308 | −0.0817770 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.9993 | −0.532473 | ||||||||
\(597\) | 13.2188 | 0.541008 | ||||||||
\(598\) | 0.325898 | 0.0133269 | ||||||||
\(599\) | 18.8786 | 0.771358 | 0.385679 | − | 0.922633i | \(-0.373967\pi\) | ||||
0.385679 | + | 0.922633i | \(0.373967\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.39444 | 0.301626 | 0.150813 | − | 0.988562i | \(-0.451811\pi\) | ||||
0.150813 | + | 0.988562i | \(0.451811\pi\) | |||||||
\(602\) | −17.5198 | −0.714053 | ||||||||
\(603\) | −7.41034 | −0.301773 | ||||||||
\(604\) | 13.7756 | 0.560519 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −36.0114 | −1.46286 | ||||||||
\(607\) | 14.8548 | 0.602939 | 0.301469 | − | 0.953476i | \(-0.402523\pi\) | ||||
0.301469 | + | 0.953476i | \(0.402523\pi\) | |||||||
\(608\) | 27.6008 | 1.11936 | ||||||||
\(609\) | 40.1801 | 1.62818 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.07270 | −0.286131 | ||||||||
\(612\) | −11.2528 | −0.454869 | ||||||||
\(613\) | −12.4420 | −0.502529 | −0.251264 | − | 0.967919i | \(-0.580846\pi\) | ||||
−0.251264 | + | 0.967919i | \(0.580846\pi\) | |||||||
\(614\) | −23.4354 | −0.945776 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.67888 | 0.148226 | ||||||||
\(617\) | 21.2628 | 0.856008 | 0.428004 | − | 0.903777i | \(-0.359217\pi\) | ||||
0.428004 | + | 0.903777i | \(0.359217\pi\) | |||||||
\(618\) | 21.1888 | 0.852339 | ||||||||
\(619\) | −29.0488 | −1.16757 | −0.583785 | − | 0.811909i | \(-0.698429\pi\) | ||||
−0.583785 | + | 0.811909i | \(0.698429\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.42513 | −0.0571886 | ||||||||
\(622\) | −8.90844 | −0.357196 | ||||||||
\(623\) | −9.49690 | −0.380485 | ||||||||
\(624\) | 2.71598 | 0.108726 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.7923 | 0.950930 | ||||||||
\(627\) | −4.98462 | −0.199067 | ||||||||
\(628\) | 2.37695 | 0.0948505 | ||||||||
\(629\) | −3.43651 | −0.137022 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.0424 | −1.71349 | −0.856746 | − | 0.515738i | \(-0.827518\pi\) | ||||
−0.856746 | + | 0.515738i | \(0.827518\pi\) | |||||||
\(632\) | −0.776100 | −0.0308716 | ||||||||
\(633\) | −31.7602 | −1.26236 | ||||||||
\(634\) | −7.46678 | −0.296544 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 9.10146 | 0.360897 | ||||||||
\(637\) | 13.2514 | 0.525040 | ||||||||
\(638\) | −1.09794 | −0.0434679 | ||||||||
\(639\) | −4.70598 | −0.186166 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.23954 | 0.0489589 | 0.0244795 | − | 0.999700i | \(-0.492207\pi\) | ||||
0.0244795 | + | 0.999700i | \(0.492207\pi\) | |||||||
\(642\) | 35.7902 | 1.41253 | ||||||||
\(643\) | 0.818429 | 0.0322757 | 0.0161378 | − | 0.999870i | \(-0.494863\pi\) | ||||
0.0161378 | + | 0.999870i | \(0.494863\pi\) | |||||||
\(644\) | 1.05708 | 0.0416547 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.02706 | 0.237132 | ||||||||
\(647\) | −47.0773 | −1.85080 | −0.925400 | − | 0.378991i | \(-0.876271\pi\) | ||||
−0.925400 | + | 0.378991i | \(0.876271\pi\) | |||||||
\(648\) | 9.50643 | 0.373448 | ||||||||
\(649\) | −1.86847 | −0.0733440 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 31.8784 | 1.24941 | ||||||||
\(652\) | −13.0323 | −0.510385 | ||||||||
\(653\) | −9.23889 | −0.361546 | −0.180773 | − | 0.983525i | \(-0.557860\pi\) | ||||
−0.180773 | + | 0.983525i | \(0.557860\pi\) | |||||||
\(654\) | −14.7815 | −0.578002 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.81638 | 0.227091 | ||||||||
\(657\) | 34.1824 | 1.33358 | ||||||||
\(658\) | 11.2069 | 0.436891 | ||||||||
\(659\) | −22.1226 | −0.861775 | −0.430888 | − | 0.902406i | \(-0.641799\pi\) | ||||
−0.430888 | + | 0.902406i | \(0.641799\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0734 | 0.469601 | 0.234801 | − | 0.972044i | \(-0.424556\pi\) | ||||
0.234801 | + | 0.972044i | \(0.424556\pi\) | |||||||
\(662\) | −25.4817 | −0.990373 | ||||||||
\(663\) | 8.64477 | 0.335735 | ||||||||
\(664\) | 16.7835 | 0.651327 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.48598 | 0.367574 | ||||||||
\(667\) | −0.785073 | −0.0303982 | ||||||||
\(668\) | 15.6359 | 0.604970 | ||||||||
\(669\) | 45.9575 | 1.77682 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.31854 | 0.0509016 | ||||||||
\(672\) | −62.7292 | −2.41983 | ||||||||
\(673\) | −46.8488 | −1.80589 | −0.902944 | − | 0.429759i | \(-0.858598\pi\) | ||||
−0.902944 | + | 0.429759i | \(0.858598\pi\) | |||||||
\(674\) | 6.87762 | 0.264916 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.5701 | 0.483466 | ||||||||
\(677\) | −49.5645 | −1.90492 | −0.952459 | − | 0.304666i | \(-0.901455\pi\) | ||||
−0.952459 | + | 0.304666i | \(0.901455\pi\) | |||||||
\(678\) | 13.3860 | 0.514086 | ||||||||
\(679\) | −30.7325 | −1.17940 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.0421 | 0.423134 | ||||||||
\(682\) | −0.871092 | −0.0333559 | ||||||||
\(683\) | −21.2955 | −0.814851 | −0.407426 | − | 0.913238i | \(-0.633573\pi\) | ||||
−0.407426 | + | 0.913238i | \(0.633573\pi\) | |||||||
\(684\) | 34.0562 | 1.30217 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.177780 | 0.00678767 | ||||||||
\(687\) | −5.90984 | −0.225474 | ||||||||
\(688\) | 2.85281 | 0.108762 | ||||||||
\(689\) | −4.47744 | −0.170577 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.2164 | 1.87228 | 0.936140 | − | 0.351629i | \(-0.114372\pi\) | ||||
0.936140 | + | 0.351629i | \(0.114372\pi\) | |||||||
\(692\) | −4.16962 | −0.158505 | ||||||||
\(693\) | 7.25451 | 0.275576 | ||||||||
\(694\) | −7.57795 | −0.287655 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 29.1511 | 1.10497 | ||||||||
\(697\) | 18.5131 | 0.701235 | ||||||||
\(698\) | −5.46448 | −0.206834 | ||||||||
\(699\) | 21.4788 | 0.812403 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0057 | 1.58653 | 0.793267 | − | 0.608874i | \(-0.208379\pi\) | ||||
0.793267 | + | 0.608874i | \(0.208379\pi\) | |||||||
\(702\) | −10.4611 | −0.394831 | ||||||||
\(703\) | 10.4004 | 0.392259 | ||||||||
\(704\) | 1.35578 | 0.0510980 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.3113 | −0.839698 | ||||||||
\(707\) | 57.4625 | 2.16110 | ||||||||
\(708\) | 19.9353 | 0.749216 | ||||||||
\(709\) | −3.83105 | −0.143878 | −0.0719391 | − | 0.997409i | \(-0.522919\pi\) | ||||
−0.0719391 | + | 0.997409i | \(0.522919\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.53042 | −0.0573952 | ||||||||
\(712\) | −6.89009 | −0.258217 | ||||||||
\(713\) | −0.622867 | −0.0233266 | ||||||||
\(714\) | −13.6979 | −0.512631 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.01153 | 0.224662 | ||||||||
\(717\) | −69.9924 | −2.61391 | ||||||||
\(718\) | −5.10216 | −0.190411 | ||||||||
\(719\) | 16.0121 | 0.597151 | 0.298575 | − | 0.954386i | \(-0.403489\pi\) | ||||
0.298575 | + | 0.954386i | \(0.403489\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −33.8105 | −1.25917 | ||||||||
\(722\) | −2.84738 | −0.105968 | ||||||||
\(723\) | −2.88822 | −0.107414 | ||||||||
\(724\) | 33.7795 | 1.25540 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 25.4298 | 0.943790 | ||||||||
\(727\) | 38.8351 | 1.44031 | 0.720157 | − | 0.693811i | \(-0.244070\pi\) | ||||
0.720157 | + | 0.693811i | \(0.244070\pi\) | |||||||
\(728\) | 19.3095 | 0.715657 | ||||||||
\(729\) | −39.8580 | −1.47622 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.08028 | 0.335846 | ||||||||
\(732\) | −14.0679 | −0.519964 | ||||||||
\(733\) | 5.45600 | 0.201522 | 0.100761 | − | 0.994911i | \(-0.467872\pi\) | ||||
0.100761 | + | 0.994911i | \(0.467872\pi\) | |||||||
\(734\) | −7.39915 | −0.273108 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.22566 | 0.0451783 | ||||||||
\(737\) | −0.504571 | −0.0185861 | ||||||||
\(738\) | −51.1028 | −1.88112 | ||||||||
\(739\) | −37.1163 | −1.36535 | −0.682673 | − | 0.730724i | \(-0.739183\pi\) | ||||
−0.682673 | + | 0.730724i | \(0.739183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −26.1630 | −0.961121 | ||||||||
\(742\) | 7.09465 | 0.260453 | ||||||||
\(743\) | 19.5501 | 0.717223 | 0.358611 | − | 0.933487i | \(-0.383250\pi\) | ||||
0.358611 | + | 0.933487i | \(0.383250\pi\) | |||||||
\(744\) | 23.1281 | 0.847918 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.3946 | 0.746698 | ||||||||
\(747\) | 33.0960 | 1.21092 | ||||||||
\(748\) | −0.766207 | −0.0280153 | ||||||||
\(749\) | −57.1096 | −2.08674 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.61687 | 0.131981 | 0.0659907 | − | 0.997820i | \(-0.478979\pi\) | ||||
0.0659907 | + | 0.997820i | \(0.478979\pi\) | |||||||
\(752\) | −1.82486 | −0.0665458 | ||||||||
\(753\) | 85.8171 | 3.12735 | ||||||||
\(754\) | −5.76280 | −0.209869 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −33.9317 | −1.23408 | ||||||||
\(757\) | −44.2825 | −1.60947 | −0.804737 | − | 0.593631i | \(-0.797694\pi\) | ||||
−0.804737 | + | 0.593631i | \(0.797694\pi\) | |||||||
\(758\) | 27.2246 | 0.988840 | ||||||||
\(759\) | −0.221350 | −0.00803449 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.3597 | 0.665539 | 0.332770 | − | 0.943008i | \(-0.392017\pi\) | ||||
0.332770 | + | 0.943008i | \(0.392017\pi\) | |||||||
\(762\) | −32.0483 | −1.16099 | ||||||||
\(763\) | 23.5865 | 0.853887 | ||||||||
\(764\) | 27.6878 | 1.00171 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.8476 | −0.536466 | ||||||||
\(767\) | −9.80714 | −0.354115 | ||||||||
\(768\) | −41.6877 | −1.50427 | ||||||||
\(769\) | 25.7436 | 0.928339 | 0.464170 | − | 0.885746i | \(-0.346353\pi\) | ||||
0.464170 | + | 0.885746i | \(0.346353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.9474 | −0.970486 | ||||||||
\(772\) | −0.565447 | −0.0203509 | ||||||||
\(773\) | 6.64313 | 0.238937 | 0.119468 | − | 0.992838i | \(-0.461881\pi\) | ||||
0.119468 | + | 0.992838i | \(0.461881\pi\) | |||||||
\(774\) | −25.0648 | −0.900936 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −22.2967 | −0.800405 | ||||||||
\(777\) | −23.6374 | −0.847987 | ||||||||
\(778\) | −24.7082 | −0.885831 | ||||||||
\(779\) | −56.0291 | −2.00745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.320431 | −0.0114659 | ||||||||
\(782\) | 0.267641 | 0.00957083 | ||||||||
\(783\) | 25.2004 | 0.900591 | ||||||||
\(784\) | 3.41906 | 0.122109 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −37.1428 | −1.32484 | ||||||||
\(787\) | 34.7919 | 1.24020 | 0.620098 | − | 0.784524i | \(-0.287093\pi\) | ||||
0.620098 | + | 0.784524i | \(0.287093\pi\) | |||||||
\(788\) | 23.0176 | 0.819968 | ||||||||
\(789\) | 29.1419 | 1.03748 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.3597 | −0.759464 | ||||||||
\(792\) | 5.26322 | 0.187020 | ||||||||
\(793\) | 6.92067 | 0.245760 | ||||||||
\(794\) | −5.08156 | −0.180338 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.14949 | −0.217963 | ||||||||
\(797\) | −6.42823 | −0.227700 | −0.113850 | − | 0.993498i | \(-0.536318\pi\) | ||||
−0.113850 | + | 0.993498i | \(0.536318\pi\) | |||||||
\(798\) | 41.4561 | 1.46753 | ||||||||
\(799\) | −5.80840 | −0.205487 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.5868 | −0.480067 | ||||||||
\(802\) | −9.00202 | −0.317872 | ||||||||
\(803\) | 2.32748 | 0.0821351 | ||||||||
\(804\) | 5.38343 | 0.189859 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.57214 | −0.161047 | ||||||||
\(807\) | −23.4986 | −0.827189 | ||||||||
\(808\) | 41.6896 | 1.46663 | ||||||||
\(809\) | −0.268221 | −0.00943014 | −0.00471507 | − | 0.999989i | \(-0.501501\pi\) | ||||
−0.00471507 | + | 0.999989i | \(0.501501\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.7359 | −1.88692 | −0.943461 | − | 0.331482i | \(-0.892451\pi\) | ||||
−0.943461 | + | 0.331482i | \(0.892451\pi\) | |||||||
\(812\) | −18.6922 | −0.655966 | ||||||||
\(813\) | −18.4991 | −0.648790 | ||||||||
\(814\) | 0.645902 | 0.0226389 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.23048 | 0.0780823 | ||||||||
\(817\) | −27.4810 | −0.961440 | ||||||||
\(818\) | −4.81242 | −0.168262 | ||||||||
\(819\) | 38.0770 | 1.33052 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.8673 | −0.623572 | −0.311786 | − | 0.950152i | \(-0.600927\pi\) | ||||
−0.311786 | + | 0.950152i | \(0.600927\pi\) | |||||||
\(822\) | −2.55496 | −0.0891145 | ||||||||
\(823\) | 22.3833 | 0.780233 | 0.390117 | − | 0.920765i | \(-0.372435\pi\) | ||||
0.390117 | + | 0.920765i | \(0.372435\pi\) | |||||||
\(824\) | −24.5298 | −0.854537 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.5397 | 0.540696 | ||||||||
\(827\) | 31.0041 | 1.07812 | 0.539059 | − | 0.842268i | \(-0.318780\pi\) | ||||
0.539059 | + | 0.842268i | \(0.318780\pi\) | |||||||
\(828\) | 1.51232 | 0.0525567 | ||||||||
\(829\) | −28.6243 | −0.994162 | −0.497081 | − | 0.867704i | \(-0.665595\pi\) | ||||
−0.497081 | + | 0.867704i | \(0.665595\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.8859 | 1.93866 | ||||||||
\(832\) | 7.11616 | 0.246708 | ||||||||
\(833\) | 10.8826 | 0.377061 | ||||||||
\(834\) | −25.7091 | −0.890234 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.31889 | 0.0802005 | ||||||||
\(837\) | 19.9937 | 0.691084 | ||||||||
\(838\) | −14.3261 | −0.494888 | ||||||||
\(839\) | −42.5973 | −1.47062 | −0.735311 | − | 0.677730i | \(-0.762964\pi\) | ||||
−0.735311 | + | 0.677730i | \(0.762964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1177 | −0.521298 | ||||||||
\(842\) | 28.3876 | 0.978300 | ||||||||
\(843\) | −15.6508 | −0.539044 | ||||||||
\(844\) | 14.7751 | 0.508581 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 16.0333 | 0.551235 | ||||||||
\(847\) | −40.5778 | −1.39427 | ||||||||
\(848\) | −1.15525 | −0.0396713 | ||||||||
\(849\) | 53.1482 | 1.82404 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.461847 | 0.0158319 | ||||||||
\(852\) | 3.41878 | 0.117125 | ||||||||
\(853\) | 48.2378 | 1.65163 | 0.825815 | − | 0.563942i | \(-0.190716\pi\) | ||||
0.825815 | + | 0.563942i | \(0.190716\pi\) | |||||||
\(854\) | −10.9660 | −0.375249 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −41.4336 | −1.41617 | ||||||||
\(857\) | −5.24655 | −0.179219 | −0.0896094 | − | 0.995977i | \(-0.528562\pi\) | ||||
−0.0896094 | + | 0.995977i | \(0.528562\pi\) | |||||||
\(858\) | −1.62481 | −0.0554701 | ||||||||
\(859\) | 14.5107 | 0.495098 | 0.247549 | − | 0.968875i | \(-0.420375\pi\) | ||||
0.247549 | + | 0.968875i | \(0.420375\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 127.339 | 4.33971 | ||||||||
\(862\) | −3.05150 | −0.103935 | ||||||||
\(863\) | −4.24273 | −0.144424 | −0.0722122 | − | 0.997389i | \(-0.523006\pi\) | ||||
−0.0722122 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(864\) | −39.3429 | −1.33847 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 15.3182 | 0.520533 | ||||||||
\(867\) | −42.0002 | −1.42640 | ||||||||
\(868\) | −14.8301 | −0.503368 | ||||||||
\(869\) | −0.104206 | −0.00353496 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.64836 | −0.0897364 | ||||||||
\(872\) | 17.1122 | 0.579492 | ||||||||
\(873\) | −43.9677 | −1.48808 | ||||||||
\(874\) | −0.810003 | −0.0273988 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.8326 | −0.839017 | ||||||||
\(877\) | 43.9611 | 1.48446 | 0.742231 | − | 0.670144i | \(-0.233768\pi\) | ||||
0.742231 | + | 0.670144i | \(0.233768\pi\) | |||||||
\(878\) | −17.7751 | −0.599880 | ||||||||
\(879\) | 34.5065 | 1.16387 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.7746 | 0.363005 | 0.181503 | − | 0.983390i | \(-0.441904\pi\) | ||||
0.181503 | + | 0.983390i | \(0.441904\pi\) | |||||||
\(882\) | −30.0400 | −1.01150 | ||||||||
\(883\) | −0.839677 | −0.0282574 | −0.0141287 | − | 0.999900i | \(-0.504497\pi\) | ||||
−0.0141287 | + | 0.999900i | \(0.504497\pi\) | |||||||
\(884\) | −4.02162 | −0.135262 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.835262 | 0.0280612 | ||||||||
\(887\) | 23.0506 | 0.773965 | 0.386982 | − | 0.922087i | \(-0.373517\pi\) | ||||
0.386982 | + | 0.922087i | \(0.373517\pi\) | |||||||
\(888\) | −17.1492 | −0.575488 | ||||||||
\(889\) | 51.1386 | 1.71513 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.27642 | 0.0427618 | ||||||||
\(892\) | −21.3798 | −0.715850 | ||||||||
\(893\) | 17.5789 | 0.588254 | ||||||||
\(894\) | −22.6386 | −0.757147 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 32.1623 | 1.07447 | ||||||||
\(897\) | −1.16181 | −0.0387916 | ||||||||
\(898\) | 12.7374 | 0.425052 | ||||||||
\(899\) | 11.0141 | 0.367340 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.67707 | −0.122501 | ||||||||
\(902\) | −3.47960 | −0.115858 | ||||||||
\(903\) | 62.4571 | 2.07844 | ||||||||
\(904\) | −15.4967 | −0.515412 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 23.9904 | 0.797027 | ||||||||
\(907\) | 1.71072 | 0.0568036 | 0.0284018 | − | 0.999597i | \(-0.490958\pi\) | ||||
0.0284018 | + | 0.999597i | \(0.490958\pi\) | |||||||
\(908\) | −5.13688 | −0.170473 | ||||||||
\(909\) | 82.2092 | 2.72671 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.0421 | −0.895944 | −0.447972 | − | 0.894048i | \(-0.647854\pi\) | ||||
−0.447972 | + | 0.894048i | \(0.647854\pi\) | |||||||
\(912\) | −6.75043 | −0.223529 | ||||||||
\(913\) | 2.25351 | 0.0745804 | ||||||||
\(914\) | −7.58224 | −0.250798 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.74931 | 0.0908397 | ||||||||
\(917\) | 59.2679 | 1.95720 | ||||||||
\(918\) | −8.59115 | −0.283550 | ||||||||
\(919\) | −31.9673 | −1.05450 | −0.527251 | − | 0.849709i | \(-0.676777\pi\) | ||||
−0.527251 | + | 0.849709i | \(0.676777\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 83.5460 | 2.75293 | ||||||||
\(922\) | −23.9456 | −0.788606 | ||||||||
\(923\) | −1.68186 | −0.0553591 | ||||||||
\(924\) | −5.27022 | −0.173377 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 8.45299 | 0.277782 | ||||||||
\(927\) | −48.3712 | −1.58872 | ||||||||
\(928\) | −21.6731 | −0.711455 | ||||||||
\(929\) | −13.0426 | −0.427913 | −0.213956 | − | 0.976843i | \(-0.568635\pi\) | ||||
−0.213956 | + | 0.976843i | \(0.568635\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −32.9358 | −1.07943 | ||||||||
\(932\) | −9.99214 | −0.327303 | ||||||||
\(933\) | 31.7581 | 1.03971 | ||||||||
\(934\) | −0.344818 | −0.0112828 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 27.6253 | 0.902960 | ||||||||
\(937\) | 3.71766 | 0.121451 | 0.0607254 | − | 0.998155i | \(-0.480659\pi\) | ||||
0.0607254 | + | 0.998155i | \(0.480659\pi\) | |||||||
\(938\) | 4.19642 | 0.137018 | ||||||||
\(939\) | −84.8182 | −2.76794 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.90979 | −0.127455 | −0.0637277 | − | 0.997967i | \(-0.520299\pi\) | ||||
−0.0637277 | + | 0.997967i | \(0.520299\pi\) | |||||||
\(942\) | 4.13950 | 0.134872 | ||||||||
\(943\) | −2.48806 | −0.0810224 | ||||||||
\(944\) | −2.53039 | −0.0823570 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.70667 | −0.0554886 | ||||||||
\(947\) | −7.99856 | −0.259918 | −0.129959 | − | 0.991519i | \(-0.541485\pi\) | ||||
−0.129959 | + | 0.991519i | \(0.541485\pi\) | |||||||
\(948\) | 1.11181 | 0.0361099 | ||||||||
\(949\) | 12.2164 | 0.396560 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.6187 | 0.863169 | ||||||||
\(952\) | 15.8578 | 0.513953 | ||||||||
\(953\) | 6.18501 | 0.200352 | 0.100176 | − | 0.994970i | \(-0.468059\pi\) | ||||
0.100176 | + | 0.994970i | \(0.468059\pi\) | |||||||
\(954\) | 10.1500 | 0.328619 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 32.5611 | 1.05310 | ||||||||
\(957\) | 3.91410 | 0.126525 | ||||||||
\(958\) | −27.1819 | −0.878207 | ||||||||
\(959\) | 4.07689 | 0.131650 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2616 | −0.718115 | ||||||||
\(962\) | 3.39017 | 0.109304 | ||||||||
\(963\) | −81.7043 | −2.63288 | ||||||||
\(964\) | 1.34362 | 0.0432752 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.84092 | 0.0592307 | ||||||||
\(967\) | 3.11816 | 0.100273 | 0.0501366 | − | 0.998742i | \(-0.484034\pi\) | ||||
0.0501366 | + | 0.998742i | \(0.484034\pi\) | |||||||
\(968\) | −29.4396 | −0.946224 | ||||||||
\(969\) | −21.4862 | −0.690235 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −56.5229 | −1.81391 | −0.906953 | − | 0.421231i | \(-0.861598\pi\) | ||||
−0.906953 | + | 0.421231i | \(0.861598\pi\) | |||||||
\(972\) | 13.6446 | 0.437650 | ||||||||
\(973\) | 41.0234 | 1.31515 | ||||||||
\(974\) | 7.43987 | 0.238389 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.78563 | 0.0571567 | ||||||||
\(977\) | 4.97426 | 0.159141 | 0.0795703 | − | 0.996829i | \(-0.474645\pi\) | ||||
0.0795703 | + | 0.996829i | \(0.474645\pi\) | |||||||
\(978\) | −22.6960 | −0.725739 | ||||||||
\(979\) | −0.925129 | −0.0295673 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.7442 | 1.07737 | ||||||||
\(982\) | −15.6067 | −0.498030 | ||||||||
\(983\) | −22.5018 | −0.717696 | −0.358848 | − | 0.933396i | \(-0.616830\pi\) | ||||
−0.358848 | + | 0.933396i | \(0.616830\pi\) | |||||||
\(984\) | 92.3859 | 2.94515 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.73266 | −0.150719 | ||||||||
\(987\) | −39.9521 | −1.27169 | ||||||||
\(988\) | 12.1713 | 0.387219 | ||||||||
\(989\) | −1.22034 | −0.0388045 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.13964 | 0.131500 | 0.0657500 | − | 0.997836i | \(-0.479056\pi\) | ||||
0.0657500 | + | 0.997836i | \(0.479056\pi\) | |||||||
\(992\) | −17.1952 | −0.545948 | ||||||||
\(993\) | 90.8408 | 2.88275 | ||||||||
\(994\) | 2.66496 | 0.0845274 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −24.0434 | −0.761846 | ||||||||
\(997\) | 2.34256 | 0.0741896 | 0.0370948 | − | 0.999312i | \(-0.488190\pi\) | ||||
0.0370948 | + | 0.999312i | \(0.488190\pi\) | |||||||
\(998\) | 10.3931 | 0.328988 | ||||||||
\(999\) | −14.8251 | −0.469044 |
(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.o.1.13 | yes | 40 | |
5.4 | even | 2 | 6025.2.a.l.1.28 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6025.2.a.l.1.28 | ✓ | 40 | 5.4 | even | 2 | ||
6025.2.a.o.1.13 | yes | 40 | 1.1 | even | 1 | trivial |