Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [418,2,Mod(1,418)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(418, 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("418.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 418 = 2 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 418.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: | \(3.33774680449\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{13}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 3 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.30278\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 418.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.302776 | 0.174808 | 0.0874038 | − | 0.996173i | \(-0.472143\pi\) | ||||
0.0874038 | + | 0.996173i | \(0.472143\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.30278 | −1.02983 | −0.514916 | − | 0.857240i | \(-0.672177\pi\) | ||||
−0.514916 | + | 0.857240i | \(0.672177\pi\) | |||||||
\(6\) | −0.302776 | −0.123608 | ||||||||
\(7\) | 1.30278 | 0.492403 | 0.246201 | − | 0.969219i | \(-0.420818\pi\) | ||||
0.246201 | + | 0.969219i | \(0.420818\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.90833 | −0.969442 | ||||||||
\(10\) | 2.30278 | 0.728202 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0.302776 | 0.0874038 | ||||||||
\(13\) | −3.30278 | −0.916025 | −0.458013 | − | 0.888946i | \(-0.651439\pi\) | ||||
−0.458013 | + | 0.888946i | \(0.651439\pi\) | |||||||
\(14\) | −1.30278 | −0.348181 | ||||||||
\(15\) | −0.697224 | −0.180023 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.60555 | −1.11701 | −0.558505 | − | 0.829501i | \(-0.688625\pi\) | ||||
−0.558505 | + | 0.829501i | \(0.688625\pi\) | |||||||
\(18\) | 2.90833 | 0.685499 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | −2.30278 | −0.514916 | ||||||||
\(21\) | 0.394449 | 0.0860758 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −1.39445 | −0.290763 | −0.145381 | − | 0.989376i | \(-0.546441\pi\) | ||||
−0.145381 | + | 0.989376i | \(0.546441\pi\) | |||||||
\(24\) | −0.302776 | −0.0618038 | ||||||||
\(25\) | 0.302776 | 0.0605551 | ||||||||
\(26\) | 3.30278 | 0.647728 | ||||||||
\(27\) | −1.78890 | −0.344273 | ||||||||
\(28\) | 1.30278 | 0.246201 | ||||||||
\(29\) | −8.30278 | −1.54179 | −0.770893 | − | 0.636964i | \(-0.780190\pi\) | ||||
−0.770893 | + | 0.636964i | \(0.780190\pi\) | |||||||
\(30\) | 0.697224 | 0.127295 | ||||||||
\(31\) | −3.30278 | −0.593196 | −0.296598 | − | 0.955002i | \(-0.595852\pi\) | ||||
−0.296598 | + | 0.955002i | \(0.595852\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.302776 | 0.0527065 | ||||||||
\(34\) | 4.60555 | 0.789846 | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | −2.90833 | −0.484721 | ||||||||
\(37\) | 5.21110 | 0.856700 | 0.428350 | − | 0.903613i | \(-0.359095\pi\) | ||||
0.428350 | + | 0.903613i | \(0.359095\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 2.30278 | 0.364101 | ||||||||
\(41\) | 3.90833 | 0.610378 | 0.305189 | − | 0.952292i | \(-0.401280\pi\) | ||||
0.305189 | + | 0.952292i | \(0.401280\pi\) | |||||||
\(42\) | −0.394449 | −0.0608648 | ||||||||
\(43\) | 1.09167 | 0.166479 | 0.0832393 | − | 0.996530i | \(-0.473473\pi\) | ||||
0.0832393 | + | 0.996530i | \(0.473473\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 6.69722 | 0.998363 | ||||||||
\(46\) | 1.39445 | 0.205600 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0.302776 | 0.0437019 | ||||||||
\(49\) | −5.30278 | −0.757539 | ||||||||
\(50\) | −0.302776 | −0.0428189 | ||||||||
\(51\) | −1.39445 | −0.195262 | ||||||||
\(52\) | −3.30278 | −0.458013 | ||||||||
\(53\) | −10.6056 | −1.45678 | −0.728392 | − | 0.685160i | \(-0.759732\pi\) | ||||
−0.728392 | + | 0.685160i | \(0.759732\pi\) | |||||||
\(54\) | 1.78890 | 0.243438 | ||||||||
\(55\) | −2.30278 | −0.310506 | ||||||||
\(56\) | −1.30278 | −0.174091 | ||||||||
\(57\) | 0.302776 | 0.0401036 | ||||||||
\(58\) | 8.30278 | 1.09021 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | −0.697224 | −0.0900113 | ||||||||
\(61\) | 11.2111 | 1.43543 | 0.717717 | − | 0.696335i | \(-0.245187\pi\) | ||||
0.717717 | + | 0.696335i | \(0.245187\pi\) | |||||||
\(62\) | 3.30278 | 0.419453 | ||||||||
\(63\) | −3.78890 | −0.477356 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.60555 | 0.943353 | ||||||||
\(66\) | −0.302776 | −0.0372691 | ||||||||
\(67\) | −6.51388 | −0.795797 | −0.397898 | − | 0.917429i | \(-0.630260\pi\) | ||||
−0.397898 | + | 0.917429i | \(0.630260\pi\) | |||||||
\(68\) | −4.60555 | −0.558505 | ||||||||
\(69\) | −0.422205 | −0.0508275 | ||||||||
\(70\) | 3.00000 | 0.358569 | ||||||||
\(71\) | −9.69722 | −1.15085 | −0.575424 | − | 0.817855i | \(-0.695163\pi\) | ||||
−0.575424 | + | 0.817855i | \(0.695163\pi\) | |||||||
\(72\) | 2.90833 | 0.342750 | ||||||||
\(73\) | −2.60555 | −0.304957 | −0.152478 | − | 0.988307i | \(-0.548725\pi\) | ||||
−0.152478 | + | 0.988307i | \(0.548725\pi\) | |||||||
\(74\) | −5.21110 | −0.605778 | ||||||||
\(75\) | 0.0916731 | 0.0105855 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 1.30278 | 0.148465 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 15.8167 | 1.77951 | 0.889756 | − | 0.456436i | \(-0.150874\pi\) | ||||
0.889756 | + | 0.456436i | \(0.150874\pi\) | |||||||
\(80\) | −2.30278 | −0.257458 | ||||||||
\(81\) | 8.18335 | 0.909261 | ||||||||
\(82\) | −3.90833 | −0.431603 | ||||||||
\(83\) | 14.3028 | 1.56993 | 0.784967 | − | 0.619538i | \(-0.212680\pi\) | ||||
0.784967 | + | 0.619538i | \(0.212680\pi\) | |||||||
\(84\) | 0.394449 | 0.0430379 | ||||||||
\(85\) | 10.6056 | 1.15033 | ||||||||
\(86\) | −1.09167 | −0.117718 | ||||||||
\(87\) | −2.51388 | −0.269516 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 4.60555 | 0.488187 | 0.244094 | − | 0.969752i | \(-0.421510\pi\) | ||||
0.244094 | + | 0.969752i | \(0.421510\pi\) | |||||||
\(90\) | −6.69722 | −0.705949 | ||||||||
\(91\) | −4.30278 | −0.451053 | ||||||||
\(92\) | −1.39445 | −0.145381 | ||||||||
\(93\) | −1.00000 | −0.103695 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | −2.30278 | −0.236260 | ||||||||
\(96\) | −0.302776 | −0.0309019 | ||||||||
\(97\) | 8.00000 | 0.812277 | 0.406138 | − | 0.913812i | \(-0.366875\pi\) | ||||
0.406138 | + | 0.913812i | \(0.366875\pi\) | |||||||
\(98\) | 5.30278 | 0.535661 | ||||||||
\(99\) | −2.90833 | −0.292298 | ||||||||
\(100\) | 0.302776 | 0.0302776 | ||||||||
\(101\) | 7.81665 | 0.777786 | 0.388893 | − | 0.921283i | \(-0.372858\pi\) | ||||
0.388893 | + | 0.921283i | \(0.372858\pi\) | |||||||
\(102\) | 1.39445 | 0.138071 | ||||||||
\(103\) | −1.69722 | −0.167232 | −0.0836162 | − | 0.996498i | \(-0.526647\pi\) | ||||
−0.0836162 | + | 0.996498i | \(0.526647\pi\) | |||||||
\(104\) | 3.30278 | 0.323864 | ||||||||
\(105\) | −0.908327 | −0.0886436 | ||||||||
\(106\) | 10.6056 | 1.03010 | ||||||||
\(107\) | 3.21110 | 0.310429 | 0.155215 | − | 0.987881i | \(-0.450393\pi\) | ||||
0.155215 | + | 0.987881i | \(0.450393\pi\) | |||||||
\(108\) | −1.78890 | −0.172137 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 2.30278 | 0.219561 | ||||||||
\(111\) | 1.57779 | 0.149758 | ||||||||
\(112\) | 1.30278 | 0.123101 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | −0.302776 | −0.0283575 | ||||||||
\(115\) | 3.21110 | 0.299437 | ||||||||
\(116\) | −8.30278 | −0.770893 | ||||||||
\(117\) | 9.60555 | 0.888034 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.00000 | −0.550019 | ||||||||
\(120\) | 0.697224 | 0.0636476 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −11.2111 | −1.01501 | ||||||||
\(123\) | 1.18335 | 0.106699 | ||||||||
\(124\) | −3.30278 | −0.296598 | ||||||||
\(125\) | 10.8167 | 0.967471 | ||||||||
\(126\) | 3.78890 | 0.337542 | ||||||||
\(127\) | −5.39445 | −0.478680 | −0.239340 | − | 0.970936i | \(-0.576931\pi\) | ||||
−0.239340 | + | 0.970936i | \(0.576931\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0.330532 | 0.0291017 | ||||||||
\(130\) | −7.60555 | −0.667051 | ||||||||
\(131\) | 19.1194 | 1.67047 | 0.835236 | − | 0.549891i | \(-0.185331\pi\) | ||||
0.835236 | + | 0.549891i | \(0.185331\pi\) | |||||||
\(132\) | 0.302776 | 0.0263532 | ||||||||
\(133\) | 1.30278 | 0.112965 | ||||||||
\(134\) | 6.51388 | 0.562713 | ||||||||
\(135\) | 4.11943 | 0.354544 | ||||||||
\(136\) | 4.60555 | 0.394923 | ||||||||
\(137\) | −3.48612 | −0.297839 | −0.148920 | − | 0.988849i | \(-0.547580\pi\) | ||||
−0.148920 | + | 0.988849i | \(0.547580\pi\) | |||||||
\(138\) | 0.422205 | 0.0359405 | ||||||||
\(139\) | −6.30278 | −0.534594 | −0.267297 | − | 0.963614i | \(-0.586131\pi\) | ||||
−0.267297 | + | 0.963614i | \(0.586131\pi\) | |||||||
\(140\) | −3.00000 | −0.253546 | ||||||||
\(141\) | −1.81665 | −0.152990 | ||||||||
\(142\) | 9.69722 | 0.813773 | ||||||||
\(143\) | −3.30278 | −0.276192 | ||||||||
\(144\) | −2.90833 | −0.242361 | ||||||||
\(145\) | 19.1194 | 1.58778 | ||||||||
\(146\) | 2.60555 | 0.215637 | ||||||||
\(147\) | −1.60555 | −0.132424 | ||||||||
\(148\) | 5.21110 | 0.428350 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | −0.0916731 | −0.00748508 | ||||||||
\(151\) | −16.4222 | −1.33642 | −0.668210 | − | 0.743973i | \(-0.732939\pi\) | ||||
−0.668210 | + | 0.743973i | \(0.732939\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 13.3944 | 1.08288 | ||||||||
\(154\) | −1.30278 | −0.104981 | ||||||||
\(155\) | 7.60555 | 0.610893 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 1.09167 | 0.0871250 | 0.0435625 | − | 0.999051i | \(-0.486129\pi\) | ||||
0.0435625 | + | 0.999051i | \(0.486129\pi\) | |||||||
\(158\) | −15.8167 | −1.25831 | ||||||||
\(159\) | −3.21110 | −0.254657 | ||||||||
\(160\) | 2.30278 | 0.182050 | ||||||||
\(161\) | −1.81665 | −0.143172 | ||||||||
\(162\) | −8.18335 | −0.642944 | ||||||||
\(163\) | −11.3944 | −0.892482 | −0.446241 | − | 0.894913i | \(-0.647238\pi\) | ||||
−0.446241 | + | 0.894913i | \(0.647238\pi\) | |||||||
\(164\) | 3.90833 | 0.305189 | ||||||||
\(165\) | −0.697224 | −0.0542788 | ||||||||
\(166\) | −14.3028 | −1.11011 | ||||||||
\(167\) | −12.4222 | −0.961259 | −0.480630 | − | 0.876924i | \(-0.659592\pi\) | ||||
−0.480630 | + | 0.876924i | \(0.659592\pi\) | |||||||
\(168\) | −0.394449 | −0.0304324 | ||||||||
\(169\) | −2.09167 | −0.160898 | ||||||||
\(170\) | −10.6056 | −0.813409 | ||||||||
\(171\) | −2.90833 | −0.222405 | ||||||||
\(172\) | 1.09167 | 0.0832393 | ||||||||
\(173\) | −19.3305 | −1.46967 | −0.734837 | − | 0.678244i | \(-0.762741\pi\) | ||||
−0.734837 | + | 0.678244i | \(0.762741\pi\) | |||||||
\(174\) | 2.51388 | 0.190577 | ||||||||
\(175\) | 0.394449 | 0.0298175 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.60555 | −0.345201 | ||||||||
\(179\) | −13.1194 | −0.980592 | −0.490296 | − | 0.871556i | \(-0.663111\pi\) | ||||
−0.490296 | + | 0.871556i | \(0.663111\pi\) | |||||||
\(180\) | 6.69722 | 0.499182 | ||||||||
\(181\) | −15.0278 | −1.11700 | −0.558502 | − | 0.829503i | \(-0.688624\pi\) | ||||
−0.558502 | + | 0.829503i | \(0.688624\pi\) | |||||||
\(182\) | 4.30278 | 0.318943 | ||||||||
\(183\) | 3.39445 | 0.250925 | ||||||||
\(184\) | 1.39445 | 0.102800 | ||||||||
\(185\) | −12.0000 | −0.882258 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | −4.60555 | −0.336791 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | −2.33053 | −0.169521 | ||||||||
\(190\) | 2.30278 | 0.167061 | ||||||||
\(191\) | −6.00000 | −0.434145 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(192\) | 0.302776 | 0.0218509 | ||||||||
\(193\) | −24.7250 | −1.77974 | −0.889872 | − | 0.456211i | \(-0.849206\pi\) | ||||
−0.889872 | + | 0.456211i | \(0.849206\pi\) | |||||||
\(194\) | −8.00000 | −0.574367 | ||||||||
\(195\) | 2.30278 | 0.164905 | ||||||||
\(196\) | −5.30278 | −0.378770 | ||||||||
\(197\) | 21.6333 | 1.54131 | 0.770655 | − | 0.637253i | \(-0.219929\pi\) | ||||
0.770655 | + | 0.637253i | \(0.219929\pi\) | |||||||
\(198\) | 2.90833 | 0.206686 | ||||||||
\(199\) | −2.18335 | −0.154773 | −0.0773867 | − | 0.997001i | \(-0.524658\pi\) | ||||
−0.0773867 | + | 0.997001i | \(0.524658\pi\) | |||||||
\(200\) | −0.302776 | −0.0214095 | ||||||||
\(201\) | −1.97224 | −0.139111 | ||||||||
\(202\) | −7.81665 | −0.549978 | ||||||||
\(203\) | −10.8167 | −0.759180 | ||||||||
\(204\) | −1.39445 | −0.0976309 | ||||||||
\(205\) | −9.00000 | −0.628587 | ||||||||
\(206\) | 1.69722 | 0.118251 | ||||||||
\(207\) | 4.05551 | 0.281878 | ||||||||
\(208\) | −3.30278 | −0.229006 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0.908327 | 0.0626805 | ||||||||
\(211\) | 24.6056 | 1.69392 | 0.846958 | − | 0.531660i | \(-0.178431\pi\) | ||||
0.846958 | + | 0.531660i | \(0.178431\pi\) | |||||||
\(212\) | −10.6056 | −0.728392 | ||||||||
\(213\) | −2.93608 | −0.201177 | ||||||||
\(214\) | −3.21110 | −0.219506 | ||||||||
\(215\) | −2.51388 | −0.171445 | ||||||||
\(216\) | 1.78890 | 0.121719 | ||||||||
\(217\) | −4.30278 | −0.292091 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | −0.788897 | −0.0533087 | ||||||||
\(220\) | −2.30278 | −0.155253 | ||||||||
\(221\) | 15.2111 | 1.02321 | ||||||||
\(222\) | −1.57779 | −0.105895 | ||||||||
\(223\) | −25.2111 | −1.68826 | −0.844130 | − | 0.536138i | \(-0.819883\pi\) | ||||
−0.844130 | + | 0.536138i | \(0.819883\pi\) | |||||||
\(224\) | −1.30278 | −0.0870454 | ||||||||
\(225\) | −0.880571 | −0.0587047 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.81665 | 0.120576 | 0.0602878 | − | 0.998181i | \(-0.480798\pi\) | ||||
0.0602878 | + | 0.998181i | \(0.480798\pi\) | |||||||
\(228\) | 0.302776 | 0.0200518 | ||||||||
\(229\) | 11.9083 | 0.786924 | 0.393462 | − | 0.919341i | \(-0.371277\pi\) | ||||
0.393462 | + | 0.919341i | \(0.371277\pi\) | |||||||
\(230\) | −3.21110 | −0.211734 | ||||||||
\(231\) | 0.394449 | 0.0259528 | ||||||||
\(232\) | 8.30278 | 0.545104 | ||||||||
\(233\) | 9.21110 | 0.603439 | 0.301720 | − | 0.953397i | \(-0.402439\pi\) | ||||
0.301720 | + | 0.953397i | \(0.402439\pi\) | |||||||
\(234\) | −9.60555 | −0.627935 | ||||||||
\(235\) | 13.8167 | 0.901299 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.78890 | 0.311072 | ||||||||
\(238\) | 6.00000 | 0.388922 | ||||||||
\(239\) | −23.9361 | −1.54830 | −0.774148 | − | 0.633004i | \(-0.781822\pi\) | ||||
−0.774148 | + | 0.633004i | \(0.781822\pi\) | |||||||
\(240\) | −0.697224 | −0.0450056 | ||||||||
\(241\) | 13.0917 | 0.843309 | 0.421654 | − | 0.906757i | \(-0.361450\pi\) | ||||
0.421654 | + | 0.906757i | \(0.361450\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 7.84441 | 0.503219 | ||||||||
\(244\) | 11.2111 | 0.717717 | ||||||||
\(245\) | 12.2111 | 0.780139 | ||||||||
\(246\) | −1.18335 | −0.0754474 | ||||||||
\(247\) | −3.30278 | −0.210151 | ||||||||
\(248\) | 3.30278 | 0.209726 | ||||||||
\(249\) | 4.33053 | 0.274436 | ||||||||
\(250\) | −10.8167 | −0.684105 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | −3.78890 | −0.238678 | ||||||||
\(253\) | −1.39445 | −0.0876682 | ||||||||
\(254\) | 5.39445 | 0.338478 | ||||||||
\(255\) | 3.21110 | 0.201087 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −4.60555 | −0.287286 | −0.143643 | − | 0.989630i | \(-0.545882\pi\) | ||||
−0.143643 | + | 0.989630i | \(0.545882\pi\) | |||||||
\(258\) | −0.330532 | −0.0205780 | ||||||||
\(259\) | 6.78890 | 0.421842 | ||||||||
\(260\) | 7.60555 | 0.471676 | ||||||||
\(261\) | 24.1472 | 1.49467 | ||||||||
\(262\) | −19.1194 | −1.18120 | ||||||||
\(263\) | −20.3028 | −1.25192 | −0.625961 | − | 0.779854i | \(-0.715293\pi\) | ||||
−0.625961 | + | 0.779854i | \(0.715293\pi\) | |||||||
\(264\) | −0.302776 | −0.0186346 | ||||||||
\(265\) | 24.4222 | 1.50024 | ||||||||
\(266\) | −1.30278 | −0.0798783 | ||||||||
\(267\) | 1.39445 | 0.0853389 | ||||||||
\(268\) | −6.51388 | −0.397898 | ||||||||
\(269\) | −19.8167 | −1.20824 | −0.604121 | − | 0.796892i | \(-0.706476\pi\) | ||||
−0.604121 | + | 0.796892i | \(0.706476\pi\) | |||||||
\(270\) | −4.11943 | −0.250700 | ||||||||
\(271\) | −6.51388 | −0.395690 | −0.197845 | − | 0.980233i | \(-0.563394\pi\) | ||||
−0.197845 | + | 0.980233i | \(0.563394\pi\) | |||||||
\(272\) | −4.60555 | −0.279253 | ||||||||
\(273\) | −1.30278 | −0.0788476 | ||||||||
\(274\) | 3.48612 | 0.210604 | ||||||||
\(275\) | 0.302776 | 0.0182581 | ||||||||
\(276\) | −0.422205 | −0.0254138 | ||||||||
\(277\) | −10.0000 | −0.600842 | −0.300421 | − | 0.953807i | \(-0.597127\pi\) | ||||
−0.300421 | + | 0.953807i | \(0.597127\pi\) | |||||||
\(278\) | 6.30278 | 0.378015 | ||||||||
\(279\) | 9.60555 | 0.575069 | ||||||||
\(280\) | 3.00000 | 0.179284 | ||||||||
\(281\) | −0.486122 | −0.0289996 | −0.0144998 | − | 0.999895i | \(-0.504616\pi\) | ||||
−0.0144998 | + | 0.999895i | \(0.504616\pi\) | |||||||
\(282\) | 1.81665 | 0.108180 | ||||||||
\(283\) | −18.9361 | −1.12563 | −0.562817 | − | 0.826582i | \(-0.690282\pi\) | ||||
−0.562817 | + | 0.826582i | \(0.690282\pi\) | |||||||
\(284\) | −9.69722 | −0.575424 | ||||||||
\(285\) | −0.697224 | −0.0413000 | ||||||||
\(286\) | 3.30278 | 0.195297 | ||||||||
\(287\) | 5.09167 | 0.300552 | ||||||||
\(288\) | 2.90833 | 0.171375 | ||||||||
\(289\) | 4.21110 | 0.247712 | ||||||||
\(290\) | −19.1194 | −1.12273 | ||||||||
\(291\) | 2.42221 | 0.141992 | ||||||||
\(292\) | −2.60555 | −0.152478 | ||||||||
\(293\) | −25.5416 | −1.49216 | −0.746079 | − | 0.665857i | \(-0.768066\pi\) | ||||
−0.746079 | + | 0.665857i | \(0.768066\pi\) | |||||||
\(294\) | 1.60555 | 0.0936377 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5.21110 | −0.302889 | ||||||||
\(297\) | −1.78890 | −0.103802 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.60555 | 0.266346 | ||||||||
\(300\) | 0.0916731 | 0.00529275 | ||||||||
\(301\) | 1.42221 | 0.0819745 | ||||||||
\(302\) | 16.4222 | 0.944992 | ||||||||
\(303\) | 2.36669 | 0.135963 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −25.8167 | −1.47826 | ||||||||
\(306\) | −13.3944 | −0.765710 | ||||||||
\(307\) | −2.18335 | −0.124610 | −0.0623051 | − | 0.998057i | \(-0.519845\pi\) | ||||
−0.0623051 | + | 0.998057i | \(0.519845\pi\) | |||||||
\(308\) | 1.30278 | 0.0742325 | ||||||||
\(309\) | −0.513878 | −0.0292335 | ||||||||
\(310\) | −7.60555 | −0.431966 | ||||||||
\(311\) | 25.8167 | 1.46393 | 0.731964 | − | 0.681343i | \(-0.238604\pi\) | ||||
0.731964 | + | 0.681343i | \(0.238604\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | 18.1194 | 1.02417 | 0.512085 | − | 0.858935i | \(-0.328873\pi\) | ||||
0.512085 | + | 0.858935i | \(0.328873\pi\) | |||||||
\(314\) | −1.09167 | −0.0616067 | ||||||||
\(315\) | 8.72498 | 0.491597 | ||||||||
\(316\) | 15.8167 | 0.889756 | ||||||||
\(317\) | −13.8167 | −0.776021 | −0.388010 | − | 0.921655i | \(-0.626838\pi\) | ||||
−0.388010 | + | 0.921655i | \(0.626838\pi\) | |||||||
\(318\) | 3.21110 | 0.180070 | ||||||||
\(319\) | −8.30278 | −0.464866 | ||||||||
\(320\) | −2.30278 | −0.128729 | ||||||||
\(321\) | 0.972244 | 0.0542653 | ||||||||
\(322\) | 1.81665 | 0.101238 | ||||||||
\(323\) | −4.60555 | −0.256260 | ||||||||
\(324\) | 8.18335 | 0.454630 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 11.3944 | 0.631080 | ||||||||
\(327\) | 0.605551 | 0.0334871 | ||||||||
\(328\) | −3.90833 | −0.215801 | ||||||||
\(329\) | −7.81665 | −0.430946 | ||||||||
\(330\) | 0.697224 | 0.0383809 | ||||||||
\(331\) | 22.7250 | 1.24908 | 0.624539 | − | 0.780994i | \(-0.285287\pi\) | ||||
0.624539 | + | 0.780994i | \(0.285287\pi\) | |||||||
\(332\) | 14.3028 | 0.784967 | ||||||||
\(333\) | −15.1556 | −0.830521 | ||||||||
\(334\) | 12.4222 | 0.679713 | ||||||||
\(335\) | 15.0000 | 0.819538 | ||||||||
\(336\) | 0.394449 | 0.0215189 | ||||||||
\(337\) | −9.30278 | −0.506754 | −0.253377 | − | 0.967368i | \(-0.581541\pi\) | ||||
−0.253377 | + | 0.967368i | \(0.581541\pi\) | |||||||
\(338\) | 2.09167 | 0.113772 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.6056 | 0.575167 | ||||||||
\(341\) | −3.30278 | −0.178855 | ||||||||
\(342\) | 2.90833 | 0.157264 | ||||||||
\(343\) | −16.0278 | −0.865417 | ||||||||
\(344\) | −1.09167 | −0.0588591 | ||||||||
\(345\) | 0.972244 | 0.0523438 | ||||||||
\(346\) | 19.3305 | 1.03922 | ||||||||
\(347\) | 2.78890 | 0.149716 | 0.0748579 | − | 0.997194i | \(-0.476150\pi\) | ||||
0.0748579 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(348\) | −2.51388 | −0.134758 | ||||||||
\(349\) | 32.4222 | 1.73552 | 0.867760 | − | 0.496983i | \(-0.165559\pi\) | ||||
0.867760 | + | 0.496983i | \(0.165559\pi\) | |||||||
\(350\) | −0.394449 | −0.0210842 | ||||||||
\(351\) | 5.90833 | 0.315363 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −15.2111 | −0.809605 | −0.404803 | − | 0.914404i | \(-0.632660\pi\) | ||||
−0.404803 | + | 0.914404i | \(0.632660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.3305 | 1.18518 | ||||||||
\(356\) | 4.60555 | 0.244094 | ||||||||
\(357\) | −1.81665 | −0.0961475 | ||||||||
\(358\) | 13.1194 | 0.693383 | ||||||||
\(359\) | −9.48612 | −0.500658 | −0.250329 | − | 0.968161i | \(-0.580539\pi\) | ||||
−0.250329 | + | 0.968161i | \(0.580539\pi\) | |||||||
\(360\) | −6.69722 | −0.352975 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 15.0278 | 0.789841 | ||||||||
\(363\) | 0.302776 | 0.0158916 | ||||||||
\(364\) | −4.30278 | −0.225527 | ||||||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | −3.39445 | −0.177431 | ||||||||
\(367\) | −7.21110 | −0.376416 | −0.188208 | − | 0.982129i | \(-0.560268\pi\) | ||||
−0.188208 | + | 0.982129i | \(0.560268\pi\) | |||||||
\(368\) | −1.39445 | −0.0726907 | ||||||||
\(369\) | −11.3667 | −0.591726 | ||||||||
\(370\) | 12.0000 | 0.623850 | ||||||||
\(371\) | −13.8167 | −0.717325 | ||||||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | 7.09167 | 0.367193 | 0.183596 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183596 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(374\) | 4.60555 | 0.238147 | ||||||||
\(375\) | 3.27502 | 0.169121 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 27.4222 | 1.41232 | ||||||||
\(378\) | 2.33053 | 0.119870 | ||||||||
\(379\) | −13.4861 | −0.692736 | −0.346368 | − | 0.938099i | \(-0.612585\pi\) | ||||
−0.346368 | + | 0.938099i | \(0.612585\pi\) | |||||||
\(380\) | −2.30278 | −0.118130 | ||||||||
\(381\) | −1.63331 | −0.0836769 | ||||||||
\(382\) | 6.00000 | 0.306987 | ||||||||
\(383\) | 3.48612 | 0.178133 | 0.0890663 | − | 0.996026i | \(-0.471612\pi\) | ||||
0.0890663 | + | 0.996026i | \(0.471612\pi\) | |||||||
\(384\) | −0.302776 | −0.0154510 | ||||||||
\(385\) | −3.00000 | −0.152894 | ||||||||
\(386\) | 24.7250 | 1.25847 | ||||||||
\(387\) | −3.17494 | −0.161391 | ||||||||
\(388\) | 8.00000 | 0.406138 | ||||||||
\(389\) | 34.5416 | 1.75133 | 0.875665 | − | 0.482919i | \(-0.160423\pi\) | ||||
0.875665 | + | 0.482919i | \(0.160423\pi\) | |||||||
\(390\) | −2.30278 | −0.116606 | ||||||||
\(391\) | 6.42221 | 0.324785 | ||||||||
\(392\) | 5.30278 | 0.267831 | ||||||||
\(393\) | 5.78890 | 0.292011 | ||||||||
\(394\) | −21.6333 | −1.08987 | ||||||||
\(395\) | −36.4222 | −1.83260 | ||||||||
\(396\) | −2.90833 | −0.146149 | ||||||||
\(397\) | −32.7527 | −1.64381 | −0.821906 | − | 0.569623i | \(-0.807089\pi\) | ||||
−0.821906 | + | 0.569623i | \(0.807089\pi\) | |||||||
\(398\) | 2.18335 | 0.109441 | ||||||||
\(399\) | 0.394449 | 0.0197471 | ||||||||
\(400\) | 0.302776 | 0.0151388 | ||||||||
\(401\) | 22.6056 | 1.12887 | 0.564434 | − | 0.825478i | \(-0.309095\pi\) | ||||
0.564434 | + | 0.825478i | \(0.309095\pi\) | |||||||
\(402\) | 1.97224 | 0.0983666 | ||||||||
\(403\) | 10.9083 | 0.543382 | ||||||||
\(404\) | 7.81665 | 0.388893 | ||||||||
\(405\) | −18.8444 | −0.936386 | ||||||||
\(406\) | 10.8167 | 0.536822 | ||||||||
\(407\) | 5.21110 | 0.258305 | ||||||||
\(408\) | 1.39445 | 0.0690355 | ||||||||
\(409\) | 23.1472 | 1.14455 | 0.572277 | − | 0.820060i | \(-0.306060\pi\) | ||||
0.572277 | + | 0.820060i | \(0.306060\pi\) | |||||||
\(410\) | 9.00000 | 0.444478 | ||||||||
\(411\) | −1.05551 | −0.0520646 | ||||||||
\(412\) | −1.69722 | −0.0836162 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.05551 | −0.199318 | ||||||||
\(415\) | −32.9361 | −1.61677 | ||||||||
\(416\) | 3.30278 | 0.161932 | ||||||||
\(417\) | −1.90833 | −0.0934512 | ||||||||
\(418\) | −1.00000 | −0.0489116 | ||||||||
\(419\) | 8.78890 | 0.429366 | 0.214683 | − | 0.976684i | \(-0.431128\pi\) | ||||
0.214683 | + | 0.976684i | \(0.431128\pi\) | |||||||
\(420\) | −0.908327 | −0.0443218 | ||||||||
\(421\) | −30.2389 | −1.47375 | −0.736876 | − | 0.676028i | \(-0.763700\pi\) | ||||
−0.736876 | + | 0.676028i | \(0.763700\pi\) | |||||||
\(422\) | −24.6056 | −1.19778 | ||||||||
\(423\) | 17.4500 | 0.848446 | ||||||||
\(424\) | 10.6056 | 0.515051 | ||||||||
\(425\) | −1.39445 | −0.0676407 | ||||||||
\(426\) | 2.93608 | 0.142254 | ||||||||
\(427\) | 14.6056 | 0.706812 | ||||||||
\(428\) | 3.21110 | 0.155215 | ||||||||
\(429\) | −1.00000 | −0.0482805 | ||||||||
\(430\) | 2.51388 | 0.121230 | ||||||||
\(431\) | 2.78890 | 0.134336 | 0.0671682 | − | 0.997742i | \(-0.478604\pi\) | ||||
0.0671682 | + | 0.997742i | \(0.478604\pi\) | |||||||
\(432\) | −1.78890 | −0.0860684 | ||||||||
\(433\) | −24.2389 | −1.16485 | −0.582423 | − | 0.812886i | \(-0.697895\pi\) | ||||
−0.582423 | + | 0.812886i | \(0.697895\pi\) | |||||||
\(434\) | 4.30278 | 0.206540 | ||||||||
\(435\) | 5.78890 | 0.277556 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | −1.39445 | −0.0667055 | ||||||||
\(438\) | 0.788897 | 0.0376950 | ||||||||
\(439\) | −25.2111 | −1.20326 | −0.601630 | − | 0.798775i | \(-0.705482\pi\) | ||||
−0.601630 | + | 0.798775i | \(0.705482\pi\) | |||||||
\(440\) | 2.30278 | 0.109781 | ||||||||
\(441\) | 15.4222 | 0.734391 | ||||||||
\(442\) | −15.2111 | −0.723518 | ||||||||
\(443\) | 39.6333 | 1.88304 | 0.941518 | − | 0.336964i | \(-0.109400\pi\) | ||||
0.941518 | + | 0.336964i | \(0.109400\pi\) | |||||||
\(444\) | 1.57779 | 0.0748788 | ||||||||
\(445\) | −10.6056 | −0.502751 | ||||||||
\(446\) | 25.2111 | 1.19378 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.30278 | 0.0615504 | ||||||||
\(449\) | −31.8167 | −1.50152 | −0.750760 | − | 0.660575i | \(-0.770313\pi\) | ||||
−0.750760 | + | 0.660575i | \(0.770313\pi\) | |||||||
\(450\) | 0.880571 | 0.0415105 | ||||||||
\(451\) | 3.90833 | 0.184036 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.97224 | −0.233616 | ||||||||
\(454\) | −1.81665 | −0.0852598 | ||||||||
\(455\) | 9.90833 | 0.464510 | ||||||||
\(456\) | −0.302776 | −0.0141788 | ||||||||
\(457\) | 21.8167 | 1.02054 | 0.510270 | − | 0.860014i | \(-0.329545\pi\) | ||||
0.510270 | + | 0.860014i | \(0.329545\pi\) | |||||||
\(458\) | −11.9083 | −0.556440 | ||||||||
\(459\) | 8.23886 | 0.384557 | ||||||||
\(460\) | 3.21110 | 0.149718 | ||||||||
\(461\) | 6.42221 | 0.299112 | 0.149556 | − | 0.988753i | \(-0.452216\pi\) | ||||
0.149556 | + | 0.988753i | \(0.452216\pi\) | |||||||
\(462\) | −0.394449 | −0.0183514 | ||||||||
\(463\) | −1.21110 | −0.0562847 | −0.0281424 | − | 0.999604i | \(-0.508959\pi\) | ||||
−0.0281424 | + | 0.999604i | \(0.508959\pi\) | |||||||
\(464\) | −8.30278 | −0.385447 | ||||||||
\(465\) | 2.30278 | 0.106789 | ||||||||
\(466\) | −9.21110 | −0.426696 | ||||||||
\(467\) | −22.6056 | −1.04606 | −0.523030 | − | 0.852314i | \(-0.675198\pi\) | ||||
−0.523030 | + | 0.852314i | \(0.675198\pi\) | |||||||
\(468\) | 9.60555 | 0.444017 | ||||||||
\(469\) | −8.48612 | −0.391853 | ||||||||
\(470\) | −13.8167 | −0.637315 | ||||||||
\(471\) | 0.330532 | 0.0152301 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.09167 | 0.0501952 | ||||||||
\(474\) | −4.78890 | −0.219961 | ||||||||
\(475\) | 0.302776 | 0.0138923 | ||||||||
\(476\) | −6.00000 | −0.275010 | ||||||||
\(477\) | 30.8444 | 1.41227 | ||||||||
\(478\) | 23.9361 | 1.09481 | ||||||||
\(479\) | 35.7250 | 1.63232 | 0.816158 | − | 0.577829i | \(-0.196100\pi\) | ||||
0.816158 | + | 0.577829i | \(0.196100\pi\) | |||||||
\(480\) | 0.697224 | 0.0318238 | ||||||||
\(481\) | −17.2111 | −0.784759 | ||||||||
\(482\) | −13.0917 | −0.596309 | ||||||||
\(483\) | −0.550039 | −0.0250276 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −18.4222 | −0.836509 | ||||||||
\(486\) | −7.84441 | −0.355830 | ||||||||
\(487\) | −29.3305 | −1.32909 | −0.664547 | − | 0.747247i | \(-0.731375\pi\) | ||||
−0.664547 | + | 0.747247i | \(0.731375\pi\) | |||||||
\(488\) | −11.2111 | −0.507503 | ||||||||
\(489\) | −3.44996 | −0.156013 | ||||||||
\(490\) | −12.2111 | −0.551641 | ||||||||
\(491\) | −14.9361 | −0.674056 | −0.337028 | − | 0.941495i | \(-0.609422\pi\) | ||||
−0.337028 | + | 0.941495i | \(0.609422\pi\) | |||||||
\(492\) | 1.18335 | 0.0533494 | ||||||||
\(493\) | 38.2389 | 1.72219 | ||||||||
\(494\) | 3.30278 | 0.148599 | ||||||||
\(495\) | 6.69722 | 0.301018 | ||||||||
\(496\) | −3.30278 | −0.148299 | ||||||||
\(497\) | −12.6333 | −0.566681 | ||||||||
\(498\) | −4.33053 | −0.194056 | ||||||||
\(499\) | −34.0000 | −1.52205 | −0.761025 | − | 0.648723i | \(-0.775303\pi\) | ||||
−0.761025 | + | 0.648723i | \(0.775303\pi\) | |||||||
\(500\) | 10.8167 | 0.483735 | ||||||||
\(501\) | −3.76114 | −0.168035 | ||||||||
\(502\) | −24.0000 | −1.07117 | ||||||||
\(503\) | 22.1194 | 0.986257 | 0.493128 | − | 0.869957i | \(-0.335853\pi\) | ||||
0.493128 | + | 0.869957i | \(0.335853\pi\) | |||||||
\(504\) | 3.78890 | 0.168771 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | 1.39445 | 0.0619908 | ||||||||
\(507\) | −0.633308 | −0.0281262 | ||||||||
\(508\) | −5.39445 | −0.239340 | ||||||||
\(509\) | −18.4222 | −0.816550 | −0.408275 | − | 0.912859i | \(-0.633870\pi\) | ||||
−0.408275 | + | 0.912859i | \(0.633870\pi\) | |||||||
\(510\) | −3.21110 | −0.142190 | ||||||||
\(511\) | −3.39445 | −0.150162 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.78890 | −0.0789818 | ||||||||
\(514\) | 4.60555 | 0.203142 | ||||||||
\(515\) | 3.90833 | 0.172221 | ||||||||
\(516\) | 0.330532 | 0.0145509 | ||||||||
\(517\) | −6.00000 | −0.263880 | ||||||||
\(518\) | −6.78890 | −0.298287 | ||||||||
\(519\) | −5.85281 | −0.256910 | ||||||||
\(520\) | −7.60555 | −0.333525 | ||||||||
\(521\) | 36.4222 | 1.59569 | 0.797843 | − | 0.602865i | \(-0.205974\pi\) | ||||
0.797843 | + | 0.602865i | \(0.205974\pi\) | |||||||
\(522\) | −24.1472 | −1.05689 | ||||||||
\(523\) | 19.0278 | 0.832026 | 0.416013 | − | 0.909359i | \(-0.363427\pi\) | ||||
0.416013 | + | 0.909359i | \(0.363427\pi\) | |||||||
\(524\) | 19.1194 | 0.835236 | ||||||||
\(525\) | 0.119429 | 0.00521233 | ||||||||
\(526\) | 20.3028 | 0.885243 | ||||||||
\(527\) | 15.2111 | 0.662606 | ||||||||
\(528\) | 0.302776 | 0.0131766 | ||||||||
\(529\) | −21.0555 | −0.915457 | ||||||||
\(530\) | −24.4222 | −1.06083 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.30278 | 0.0564825 | ||||||||
\(533\) | −12.9083 | −0.559122 | ||||||||
\(534\) | −1.39445 | −0.0603437 | ||||||||
\(535\) | −7.39445 | −0.319690 | ||||||||
\(536\) | 6.51388 | 0.281357 | ||||||||
\(537\) | −3.97224 | −0.171415 | ||||||||
\(538\) | 19.8167 | 0.854357 | ||||||||
\(539\) | −5.30278 | −0.228407 | ||||||||
\(540\) | 4.11943 | 0.177272 | ||||||||
\(541\) | 3.81665 | 0.164091 | 0.0820454 | − | 0.996629i | \(-0.473855\pi\) | ||||
0.0820454 | + | 0.996629i | \(0.473855\pi\) | |||||||
\(542\) | 6.51388 | 0.279795 | ||||||||
\(543\) | −4.55004 | −0.195261 | ||||||||
\(544\) | 4.60555 | 0.197461 | ||||||||
\(545\) | −4.60555 | −0.197280 | ||||||||
\(546\) | 1.30278 | 0.0557537 | ||||||||
\(547\) | −4.00000 | −0.171028 | −0.0855138 | − | 0.996337i | \(-0.527253\pi\) | ||||
−0.0855138 | + | 0.996337i | \(0.527253\pi\) | |||||||
\(548\) | −3.48612 | −0.148920 | ||||||||
\(549\) | −32.6056 | −1.39157 | ||||||||
\(550\) | −0.302776 | −0.0129104 | ||||||||
\(551\) | −8.30278 | −0.353710 | ||||||||
\(552\) | 0.422205 | 0.0179702 | ||||||||
\(553\) | 20.6056 | 0.876237 | ||||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | −3.63331 | −0.154225 | ||||||||
\(556\) | −6.30278 | −0.267297 | ||||||||
\(557\) | −27.6333 | −1.17086 | −0.585430 | − | 0.810723i | \(-0.699074\pi\) | ||||
−0.585430 | + | 0.810723i | \(0.699074\pi\) | |||||||
\(558\) | −9.60555 | −0.406635 | ||||||||
\(559\) | −3.60555 | −0.152499 | ||||||||
\(560\) | −3.00000 | −0.126773 | ||||||||
\(561\) | −1.39445 | −0.0588737 | ||||||||
\(562\) | 0.486122 | 0.0205058 | ||||||||
\(563\) | 21.6333 | 0.911735 | 0.455868 | − | 0.890048i | \(-0.349329\pi\) | ||||
0.455868 | + | 0.890048i | \(0.349329\pi\) | |||||||
\(564\) | −1.81665 | −0.0764949 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18.9361 | 0.795943 | ||||||||
\(567\) | 10.6611 | 0.447723 | ||||||||
\(568\) | 9.69722 | 0.406886 | ||||||||
\(569\) | 12.2750 | 0.514596 | 0.257298 | − | 0.966332i | \(-0.417168\pi\) | ||||
0.257298 | + | 0.966332i | \(0.417168\pi\) | |||||||
\(570\) | 0.697224 | 0.0292035 | ||||||||
\(571\) | −6.93608 | −0.290266 | −0.145133 | − | 0.989412i | \(-0.546361\pi\) | ||||
−0.145133 | + | 0.989412i | \(0.546361\pi\) | |||||||
\(572\) | −3.30278 | −0.138096 | ||||||||
\(573\) | −1.81665 | −0.0758918 | ||||||||
\(574\) | −5.09167 | −0.212522 | ||||||||
\(575\) | −0.422205 | −0.0176072 | ||||||||
\(576\) | −2.90833 | −0.121180 | ||||||||
\(577\) | −18.0917 | −0.753166 | −0.376583 | − | 0.926383i | \(-0.622901\pi\) | ||||
−0.376583 | + | 0.926383i | \(0.622901\pi\) | |||||||
\(578\) | −4.21110 | −0.175159 | ||||||||
\(579\) | −7.48612 | −0.311113 | ||||||||
\(580\) | 19.1194 | 0.793891 | ||||||||
\(581\) | 18.6333 | 0.773040 | ||||||||
\(582\) | −2.42221 | −0.100404 | ||||||||
\(583\) | −10.6056 | −0.439237 | ||||||||
\(584\) | 2.60555 | 0.107818 | ||||||||
\(585\) | −22.1194 | −0.914526 | ||||||||
\(586\) | 25.5416 | 1.05512 | ||||||||
\(587\) | 12.0000 | 0.495293 | 0.247647 | − | 0.968850i | \(-0.420343\pi\) | ||||
0.247647 | + | 0.968850i | \(0.420343\pi\) | |||||||
\(588\) | −1.60555 | −0.0662118 | ||||||||
\(589\) | −3.30278 | −0.136088 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.55004 | 0.269433 | ||||||||
\(592\) | 5.21110 | 0.214175 | ||||||||
\(593\) | −42.0000 | −1.72473 | −0.862367 | − | 0.506284i | \(-0.831019\pi\) | ||||
−0.862367 | + | 0.506284i | \(0.831019\pi\) | |||||||
\(594\) | 1.78890 | 0.0733994 | ||||||||
\(595\) | 13.8167 | 0.566428 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.661064 | −0.0270555 | ||||||||
\(598\) | −4.60555 | −0.188335 | ||||||||
\(599\) | −19.8806 | −0.812298 | −0.406149 | − | 0.913807i | \(-0.633129\pi\) | ||||
−0.406149 | + | 0.913807i | \(0.633129\pi\) | |||||||
\(600\) | −0.0916731 | −0.00374254 | ||||||||
\(601\) | 4.09167 | 0.166903 | 0.0834514 | − | 0.996512i | \(-0.473406\pi\) | ||||
0.0834514 | + | 0.996512i | \(0.473406\pi\) | |||||||
\(602\) | −1.42221 | −0.0579648 | ||||||||
\(603\) | 18.9445 | 0.771479 | ||||||||
\(604\) | −16.4222 | −0.668210 | ||||||||
\(605\) | −2.30278 | −0.0936211 | ||||||||
\(606\) | −2.36669 | −0.0961403 | ||||||||
\(607\) | 3.81665 | 0.154913 | 0.0774566 | − | 0.996996i | \(-0.475320\pi\) | ||||
0.0774566 | + | 0.996996i | \(0.475320\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −3.27502 | −0.132710 | ||||||||
\(610\) | 25.8167 | 1.04529 | ||||||||
\(611\) | 19.8167 | 0.801696 | ||||||||
\(612\) | 13.3944 | 0.541438 | ||||||||
\(613\) | 2.00000 | 0.0807792 | 0.0403896 | − | 0.999184i | \(-0.487140\pi\) | ||||
0.0403896 | + | 0.999184i | \(0.487140\pi\) | |||||||
\(614\) | 2.18335 | 0.0881127 | ||||||||
\(615\) | −2.72498 | −0.109882 | ||||||||
\(616\) | −1.30278 | −0.0524903 | ||||||||
\(617\) | 2.09167 | 0.0842076 | 0.0421038 | − | 0.999113i | \(-0.486594\pi\) | ||||
0.0421038 | + | 0.999113i | \(0.486594\pi\) | |||||||
\(618\) | 0.513878 | 0.0206712 | ||||||||
\(619\) | −34.8444 | −1.40052 | −0.700258 | − | 0.713890i | \(-0.746932\pi\) | ||||
−0.700258 | + | 0.713890i | \(0.746932\pi\) | |||||||
\(620\) | 7.60555 | 0.305446 | ||||||||
\(621\) | 2.49453 | 0.100102 | ||||||||
\(622\) | −25.8167 | −1.03515 | ||||||||
\(623\) | 6.00000 | 0.240385 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −26.4222 | −1.05689 | ||||||||
\(626\) | −18.1194 | −0.724198 | ||||||||
\(627\) | 0.302776 | 0.0120917 | ||||||||
\(628\) | 1.09167 | 0.0435625 | ||||||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | −8.72498 | −0.347612 | ||||||||
\(631\) | −45.0278 | −1.79253 | −0.896263 | − | 0.443522i | \(-0.853729\pi\) | ||||
−0.896263 | + | 0.443522i | \(0.853729\pi\) | |||||||
\(632\) | −15.8167 | −0.629153 | ||||||||
\(633\) | 7.44996 | 0.296109 | ||||||||
\(634\) | 13.8167 | 0.548729 | ||||||||
\(635\) | 12.4222 | 0.492960 | ||||||||
\(636\) | −3.21110 | −0.127328 | ||||||||
\(637\) | 17.5139 | 0.693925 | ||||||||
\(638\) | 8.30278 | 0.328710 | ||||||||
\(639\) | 28.2027 | 1.11568 | ||||||||
\(640\) | 2.30278 | 0.0910252 | ||||||||
\(641\) | 20.2389 | 0.799387 | 0.399693 | − | 0.916649i | \(-0.369117\pi\) | ||||
0.399693 | + | 0.916649i | \(0.369117\pi\) | |||||||
\(642\) | −0.972244 | −0.0383714 | ||||||||
\(643\) | 26.4222 | 1.04199 | 0.520995 | − | 0.853560i | \(-0.325561\pi\) | ||||
0.520995 | + | 0.853560i | \(0.325561\pi\) | |||||||
\(644\) | −1.81665 | −0.0715862 | ||||||||
\(645\) | −0.761141 | −0.0299699 | ||||||||
\(646\) | 4.60555 | 0.181203 | ||||||||
\(647\) | 25.8167 | 1.01496 | 0.507479 | − | 0.861664i | \(-0.330578\pi\) | ||||
0.507479 | + | 0.861664i | \(0.330578\pi\) | |||||||
\(648\) | −8.18335 | −0.321472 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | −1.30278 | −0.0510598 | ||||||||
\(652\) | −11.3944 | −0.446241 | ||||||||
\(653\) | 22.3305 | 0.873861 | 0.436931 | − | 0.899495i | \(-0.356066\pi\) | ||||
0.436931 | + | 0.899495i | \(0.356066\pi\) | |||||||
\(654\) | −0.605551 | −0.0236789 | ||||||||
\(655\) | −44.0278 | −1.72031 | ||||||||
\(656\) | 3.90833 | 0.152595 | ||||||||
\(657\) | 7.57779 | 0.295638 | ||||||||
\(658\) | 7.81665 | 0.304725 | ||||||||
\(659\) | 29.0278 | 1.13076 | 0.565380 | − | 0.824830i | \(-0.308729\pi\) | ||||
0.565380 | + | 0.824830i | \(0.308729\pi\) | |||||||
\(660\) | −0.697224 | −0.0271394 | ||||||||
\(661\) | 23.6333 | 0.919229 | 0.459615 | − | 0.888118i | \(-0.347988\pi\) | ||||
0.459615 | + | 0.888118i | \(0.347988\pi\) | |||||||
\(662\) | −22.7250 | −0.883231 | ||||||||
\(663\) | 4.60555 | 0.178865 | ||||||||
\(664\) | −14.3028 | −0.555055 | ||||||||
\(665\) | −3.00000 | −0.116335 | ||||||||
\(666\) | 15.1556 | 0.587267 | ||||||||
\(667\) | 11.5778 | 0.448294 | ||||||||
\(668\) | −12.4222 | −0.480630 | ||||||||
\(669\) | −7.63331 | −0.295121 | ||||||||
\(670\) | −15.0000 | −0.579501 | ||||||||
\(671\) | 11.2111 | 0.432800 | ||||||||
\(672\) | −0.394449 | −0.0152162 | ||||||||
\(673\) | 1.30278 | 0.0502183 | 0.0251092 | − | 0.999685i | \(-0.492007\pi\) | ||||
0.0251092 | + | 0.999685i | \(0.492007\pi\) | |||||||
\(674\) | 9.30278 | 0.358330 | ||||||||
\(675\) | −0.541635 | −0.0208475 | ||||||||
\(676\) | −2.09167 | −0.0804490 | ||||||||
\(677\) | −8.30278 | −0.319102 | −0.159551 | − | 0.987190i | \(-0.551005\pi\) | ||||
−0.159551 | + | 0.987190i | \(0.551005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.4222 | 0.399968 | ||||||||
\(680\) | −10.6056 | −0.406704 | ||||||||
\(681\) | 0.550039 | 0.0210775 | ||||||||
\(682\) | 3.30278 | 0.126470 | ||||||||
\(683\) | −17.5778 | −0.672596 | −0.336298 | − | 0.941756i | \(-0.609175\pi\) | ||||
−0.336298 | + | 0.941756i | \(0.609175\pi\) | |||||||
\(684\) | −2.90833 | −0.111203 | ||||||||
\(685\) | 8.02776 | 0.306725 | ||||||||
\(686\) | 16.0278 | 0.611943 | ||||||||
\(687\) | 3.60555 | 0.137560 | ||||||||
\(688\) | 1.09167 | 0.0416196 | ||||||||
\(689\) | 35.0278 | 1.33445 | ||||||||
\(690\) | −0.972244 | −0.0370127 | ||||||||
\(691\) | 32.4222 | 1.23340 | 0.616699 | − | 0.787199i | \(-0.288469\pi\) | ||||
0.616699 | + | 0.787199i | \(0.288469\pi\) | |||||||
\(692\) | −19.3305 | −0.734837 | ||||||||
\(693\) | −3.78890 | −0.143928 | ||||||||
\(694\) | −2.78890 | −0.105865 | ||||||||
\(695\) | 14.5139 | 0.550543 | ||||||||
\(696\) | 2.51388 | 0.0952883 | ||||||||
\(697\) | −18.0000 | −0.681799 | ||||||||
\(698\) | −32.4222 | −1.22720 | ||||||||
\(699\) | 2.78890 | 0.105486 | ||||||||
\(700\) | 0.394449 | 0.0149088 | ||||||||
\(701\) | −27.6333 | −1.04370 | −0.521848 | − | 0.853039i | \(-0.674757\pi\) | ||||
−0.521848 | + | 0.853039i | \(0.674757\pi\) | |||||||
\(702\) | −5.90833 | −0.222995 | ||||||||
\(703\) | 5.21110 | 0.196540 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 4.18335 | 0.157554 | ||||||||
\(706\) | 15.2111 | 0.572477 | ||||||||
\(707\) | 10.1833 | 0.382984 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.6972 | 0.551966 | 0.275983 | − | 0.961163i | \(-0.410997\pi\) | ||||
0.275983 | + | 0.961163i | \(0.410997\pi\) | |||||||
\(710\) | −22.3305 | −0.838050 | ||||||||
\(711\) | −46.0000 | −1.72513 | ||||||||
\(712\) | −4.60555 | −0.172600 | ||||||||
\(713\) | 4.60555 | 0.172479 | ||||||||
\(714\) | 1.81665 | 0.0679866 | ||||||||
\(715\) | 7.60555 | 0.284431 | ||||||||
\(716\) | −13.1194 | −0.490296 | ||||||||
\(717\) | −7.24726 | −0.270654 | ||||||||
\(718\) | 9.48612 | 0.354019 | ||||||||
\(719\) | −25.8167 | −0.962799 | −0.481399 | − | 0.876501i | \(-0.659871\pi\) | ||||
−0.481399 | + | 0.876501i | \(0.659871\pi\) | |||||||
\(720\) | 6.69722 | 0.249591 | ||||||||
\(721\) | −2.21110 | −0.0823458 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 3.96384 | 0.147417 | ||||||||
\(724\) | −15.0278 | −0.558502 | ||||||||
\(725\) | −2.51388 | −0.0933631 | ||||||||
\(726\) | −0.302776 | −0.0112371 | ||||||||
\(727\) | −0.366692 | −0.0135999 | −0.00679993 | − | 0.999977i | \(-0.502165\pi\) | ||||
−0.00679993 | + | 0.999977i | \(0.502165\pi\) | |||||||
\(728\) | 4.30278 | 0.159471 | ||||||||
\(729\) | −22.1749 | −0.821294 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | −5.02776 | −0.185958 | ||||||||
\(732\) | 3.39445 | 0.125462 | ||||||||
\(733\) | −7.21110 | −0.266348 | −0.133174 | − | 0.991093i | \(-0.542517\pi\) | ||||
−0.133174 | + | 0.991093i | \(0.542517\pi\) | |||||||
\(734\) | 7.21110 | 0.266167 | ||||||||
\(735\) | 3.69722 | 0.136374 | ||||||||
\(736\) | 1.39445 | 0.0514001 | ||||||||
\(737\) | −6.51388 | −0.239942 | ||||||||
\(738\) | 11.3667 | 0.418414 | ||||||||
\(739\) | −40.3583 | −1.48460 | −0.742302 | − | 0.670066i | \(-0.766266\pi\) | ||||
−0.742302 | + | 0.670066i | \(0.766266\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | −1.00000 | −0.0367359 | ||||||||
\(742\) | 13.8167 | 0.507225 | ||||||||
\(743\) | 2.36669 | 0.0868255 | 0.0434128 | − | 0.999057i | \(-0.486177\pi\) | ||||
0.0434128 | + | 0.999057i | \(0.486177\pi\) | |||||||
\(744\) | 1.00000 | 0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −7.09167 | −0.259645 | ||||||||
\(747\) | −41.5971 | −1.52196 | ||||||||
\(748\) | −4.60555 | −0.168396 | ||||||||
\(749\) | 4.18335 | 0.152856 | ||||||||
\(750\) | −3.27502 | −0.119587 | ||||||||
\(751\) | −40.8444 | −1.49043 | −0.745217 | − | 0.666822i | \(-0.767654\pi\) | ||||
−0.745217 | + | 0.666822i | \(0.767654\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | 7.26662 | 0.264810 | ||||||||
\(754\) | −27.4222 | −0.998658 | ||||||||
\(755\) | 37.8167 | 1.37629 | ||||||||
\(756\) | −2.33053 | −0.0847606 | ||||||||
\(757\) | 30.5416 | 1.11005 | 0.555027 | − | 0.831832i | \(-0.312708\pi\) | ||||
0.555027 | + | 0.831832i | \(0.312708\pi\) | |||||||
\(758\) | 13.4861 | 0.489838 | ||||||||
\(759\) | −0.422205 | −0.0153251 | ||||||||
\(760\) | 2.30278 | 0.0835305 | ||||||||
\(761\) | 20.2389 | 0.733658 | 0.366829 | − | 0.930288i | \(-0.380443\pi\) | ||||
0.366829 | + | 0.930288i | \(0.380443\pi\) | |||||||
\(762\) | 1.63331 | 0.0591685 | ||||||||
\(763\) | 2.60555 | 0.0943273 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | −30.8444 | −1.11518 | ||||||||
\(766\) | −3.48612 | −0.125959 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.302776 | 0.0109255 | ||||||||
\(769\) | −37.6333 | −1.35709 | −0.678546 | − | 0.734558i | \(-0.737390\pi\) | ||||
−0.678546 | + | 0.734558i | \(0.737390\pi\) | |||||||
\(770\) | 3.00000 | 0.108112 | ||||||||
\(771\) | −1.39445 | −0.0502198 | ||||||||
\(772\) | −24.7250 | −0.889872 | ||||||||
\(773\) | 48.4222 | 1.74163 | 0.870813 | − | 0.491615i | \(-0.163593\pi\) | ||||
0.870813 | + | 0.491615i | \(0.163593\pi\) | |||||||
\(774\) | 3.17494 | 0.114121 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 2.05551 | 0.0737411 | ||||||||
\(778\) | −34.5416 | −1.23838 | ||||||||
\(779\) | 3.90833 | 0.140030 | ||||||||
\(780\) | 2.30278 | 0.0824526 | ||||||||
\(781\) | −9.69722 | −0.346994 | ||||||||
\(782\) | −6.42221 | −0.229658 | ||||||||
\(783\) | 14.8528 | 0.530796 | ||||||||
\(784\) | −5.30278 | −0.189385 | ||||||||
\(785\) | −2.51388 | −0.0897242 | ||||||||
\(786\) | −5.78890 | −0.206483 | ||||||||
\(787\) | −15.0278 | −0.535682 | −0.267841 | − | 0.963463i | \(-0.586310\pi\) | ||||
−0.267841 | + | 0.963463i | \(0.586310\pi\) | |||||||
\(788\) | 21.6333 | 0.770655 | ||||||||
\(789\) | −6.14719 | −0.218846 | ||||||||
\(790\) | 36.4222 | 1.29584 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2.90833 | 0.103343 | ||||||||
\(793\) | −37.0278 | −1.31489 | ||||||||
\(794\) | 32.7527 | 1.16235 | ||||||||
\(795\) | 7.39445 | 0.262254 | ||||||||
\(796\) | −2.18335 | −0.0773867 | ||||||||
\(797\) | 16.6056 | 0.588199 | 0.294099 | − | 0.955775i | \(-0.404980\pi\) | ||||
0.294099 | + | 0.955775i | \(0.404980\pi\) | |||||||
\(798\) | −0.394449 | −0.0139633 | ||||||||
\(799\) | 27.6333 | 0.977596 | ||||||||
\(800\) | −0.302776 | −0.0107047 | ||||||||
\(801\) | −13.3944 | −0.473270 | ||||||||
\(802\) | −22.6056 | −0.798230 | ||||||||
\(803\) | −2.60555 | −0.0919479 | ||||||||
\(804\) | −1.97224 | −0.0695557 | ||||||||
\(805\) | 4.18335 | 0.147444 | ||||||||
\(806\) | −10.9083 | −0.384229 | ||||||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | −7.81665 | −0.274989 | ||||||||
\(809\) | 33.2111 | 1.16764 | 0.583820 | − | 0.811883i | \(-0.301557\pi\) | ||||
0.583820 | + | 0.811883i | \(0.301557\pi\) | |||||||
\(810\) | 18.8444 | 0.662125 | ||||||||
\(811\) | 29.6333 | 1.04057 | 0.520283 | − | 0.853994i | \(-0.325826\pi\) | ||||
0.520283 | + | 0.853994i | \(0.325826\pi\) | |||||||
\(812\) | −10.8167 | −0.379590 | ||||||||
\(813\) | −1.97224 | −0.0691696 | ||||||||
\(814\) | −5.21110 | −0.182649 | ||||||||
\(815\) | 26.2389 | 0.919107 | ||||||||
\(816\) | −1.39445 | −0.0488155 | ||||||||
\(817\) | 1.09167 | 0.0381928 | ||||||||
\(818\) | −23.1472 | −0.809322 | ||||||||
\(819\) | 12.5139 | 0.437270 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −34.6056 | −1.20774 | −0.603871 | − | 0.797082i | \(-0.706376\pi\) | ||||
−0.603871 | + | 0.797082i | \(0.706376\pi\) | |||||||
\(822\) | 1.05551 | 0.0368152 | ||||||||
\(823\) | 32.0000 | 1.11545 | 0.557725 | − | 0.830026i | \(-0.311674\pi\) | ||||
0.557725 | + | 0.830026i | \(0.311674\pi\) | |||||||
\(824\) | 1.69722 | 0.0591256 | ||||||||
\(825\) | 0.0916731 | 0.00319165 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0555 | 0.766945 | 0.383473 | − | 0.923552i | \(-0.374728\pi\) | ||||
0.383473 | + | 0.923552i | \(0.374728\pi\) | |||||||
\(828\) | 4.05551 | 0.140939 | ||||||||
\(829\) | −27.5778 | −0.957816 | −0.478908 | − | 0.877865i | \(-0.658967\pi\) | ||||
−0.478908 | + | 0.877865i | \(0.658967\pi\) | |||||||
\(830\) | 32.9361 | 1.14323 | ||||||||
\(831\) | −3.02776 | −0.105032 | ||||||||
\(832\) | −3.30278 | −0.114503 | ||||||||
\(833\) | 24.4222 | 0.846179 | ||||||||
\(834\) | 1.90833 | 0.0660800 | ||||||||
\(835\) | 28.6056 | 0.989936 | ||||||||
\(836\) | 1.00000 | 0.0345857 | ||||||||
\(837\) | 5.90833 | 0.204222 | ||||||||
\(838\) | −8.78890 | −0.303607 | ||||||||
\(839\) | 19.8806 | 0.686354 | 0.343177 | − | 0.939271i | \(-0.388497\pi\) | ||||
0.343177 | + | 0.939271i | \(0.388497\pi\) | |||||||
\(840\) | 0.908327 | 0.0313403 | ||||||||
\(841\) | 39.9361 | 1.37711 | ||||||||
\(842\) | 30.2389 | 1.04210 | ||||||||
\(843\) | −0.147186 | −0.00506935 | ||||||||
\(844\) | 24.6056 | 0.846958 | ||||||||
\(845\) | 4.81665 | 0.165698 | ||||||||
\(846\) | −17.4500 | −0.599942 | ||||||||
\(847\) | 1.30278 | 0.0447639 | ||||||||
\(848\) | −10.6056 | −0.364196 | ||||||||
\(849\) | −5.73338 | −0.196769 | ||||||||
\(850\) | 1.39445 | 0.0478292 | ||||||||
\(851\) | −7.26662 | −0.249096 | ||||||||
\(852\) | −2.93608 | −0.100589 | ||||||||
\(853\) | −46.4222 | −1.58947 | −0.794733 | − | 0.606959i | \(-0.792389\pi\) | ||||
−0.794733 | + | 0.606959i | \(0.792389\pi\) | |||||||
\(854\) | −14.6056 | −0.499792 | ||||||||
\(855\) | 6.69722 | 0.229040 | ||||||||
\(856\) | −3.21110 | −0.109753 | ||||||||
\(857\) | −43.5416 | −1.48735 | −0.743677 | − | 0.668539i | \(-0.766920\pi\) | ||||
−0.743677 | + | 0.668539i | \(0.766920\pi\) | |||||||
\(858\) | 1.00000 | 0.0341394 | ||||||||
\(859\) | 8.84441 | 0.301767 | 0.150884 | − | 0.988552i | \(-0.451788\pi\) | ||||
0.150884 | + | 0.988552i | \(0.451788\pi\) | |||||||
\(860\) | −2.51388 | −0.0857225 | ||||||||
\(861\) | 1.54163 | 0.0525388 | ||||||||
\(862\) | −2.78890 | −0.0949902 | ||||||||
\(863\) | −17.7250 | −0.603365 | −0.301683 | − | 0.953408i | \(-0.597548\pi\) | ||||
−0.301683 | + | 0.953408i | \(0.597548\pi\) | |||||||
\(864\) | 1.78890 | 0.0608595 | ||||||||
\(865\) | 44.5139 | 1.51352 | ||||||||
\(866\) | 24.2389 | 0.823670 | ||||||||
\(867\) | 1.27502 | 0.0433019 | ||||||||
\(868\) | −4.30278 | −0.146046 | ||||||||
\(869\) | 15.8167 | 0.536543 | ||||||||
\(870\) | −5.78890 | −0.196262 | ||||||||
\(871\) | 21.5139 | 0.728970 | ||||||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | −23.2666 | −0.787456 | ||||||||
\(874\) | 1.39445 | 0.0471679 | ||||||||
\(875\) | 14.0917 | 0.476385 | ||||||||
\(876\) | −0.788897 | −0.0266544 | ||||||||
\(877\) | 47.5694 | 1.60630 | 0.803152 | − | 0.595774i | \(-0.203155\pi\) | ||||
0.803152 | + | 0.595774i | \(0.203155\pi\) | |||||||
\(878\) | 25.2111 | 0.850833 | ||||||||
\(879\) | −7.73338 | −0.260841 | ||||||||
\(880\) | −2.30278 | −0.0776266 | ||||||||
\(881\) | −33.9083 | −1.14240 | −0.571200 | − | 0.820811i | \(-0.693522\pi\) | ||||
−0.571200 | + | 0.820811i | \(0.693522\pi\) | |||||||
\(882\) | −15.4222 | −0.519293 | ||||||||
\(883\) | −39.0278 | −1.31339 | −0.656694 | − | 0.754157i | \(-0.728046\pi\) | ||||
−0.656694 | + | 0.754157i | \(0.728046\pi\) | |||||||
\(884\) | 15.2111 | 0.511605 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −39.6333 | −1.33151 | ||||||||
\(887\) | 24.8444 | 0.834194 | 0.417097 | − | 0.908862i | \(-0.363048\pi\) | ||||
0.417097 | + | 0.908862i | \(0.363048\pi\) | |||||||
\(888\) | −1.57779 | −0.0529473 | ||||||||
\(889\) | −7.02776 | −0.235703 | ||||||||
\(890\) | 10.6056 | 0.355499 | ||||||||
\(891\) | 8.18335 | 0.274152 | ||||||||
\(892\) | −25.2111 | −0.844130 | ||||||||
\(893\) | −6.00000 | −0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 30.2111 | 1.00985 | ||||||||
\(896\) | −1.30278 | −0.0435227 | ||||||||
\(897\) | 1.39445 | 0.0465593 | ||||||||
\(898\) | 31.8167 | 1.06174 | ||||||||
\(899\) | 27.4222 | 0.914582 | ||||||||
\(900\) | −0.880571 | −0.0293524 | ||||||||
\(901\) | 48.8444 | 1.62724 | ||||||||
\(902\) | −3.90833 | −0.130133 | ||||||||
\(903\) | 0.430609 | 0.0143298 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 34.6056 | 1.15033 | ||||||||
\(906\) | 4.97224 | 0.165192 | ||||||||
\(907\) | −4.84441 | −0.160856 | −0.0804280 | − | 0.996760i | \(-0.525629\pi\) | ||||
−0.0804280 | + | 0.996760i | \(0.525629\pi\) | |||||||
\(908\) | 1.81665 | 0.0602878 | ||||||||
\(909\) | −22.7334 | −0.754019 | ||||||||
\(910\) | −9.90833 | −0.328458 | ||||||||
\(911\) | 27.6333 | 0.915532 | 0.457766 | − | 0.889073i | \(-0.348650\pi\) | ||||
0.457766 | + | 0.889073i | \(0.348650\pi\) | |||||||
\(912\) | 0.302776 | 0.0100259 | ||||||||
\(913\) | 14.3028 | 0.473353 | ||||||||
\(914\) | −21.8167 | −0.721631 | ||||||||
\(915\) | −7.81665 | −0.258411 | ||||||||
\(916\) | 11.9083 | 0.393462 | ||||||||
\(917\) | 24.9083 | 0.822545 | ||||||||
\(918\) | −8.23886 | −0.271923 | ||||||||
\(919\) | 6.11943 | 0.201861 | 0.100931 | − | 0.994893i | \(-0.467818\pi\) | ||||
0.100931 | + | 0.994893i | \(0.467818\pi\) | |||||||
\(920\) | −3.21110 | −0.105867 | ||||||||
\(921\) | −0.661064 | −0.0217828 | ||||||||
\(922\) | −6.42221 | −0.211504 | ||||||||
\(923\) | 32.0278 | 1.05421 | ||||||||
\(924\) | 0.394449 | 0.0129764 | ||||||||
\(925\) | 1.57779 | 0.0518776 | ||||||||
\(926\) | 1.21110 | 0.0397993 | ||||||||
\(927\) | 4.93608 | 0.162122 | ||||||||
\(928\) | 8.30278 | 0.272552 | ||||||||
\(929\) | −8.51388 | −0.279331 | −0.139666 | − | 0.990199i | \(-0.544603\pi\) | ||||
−0.139666 | + | 0.990199i | \(0.544603\pi\) | |||||||
\(930\) | −2.30278 | −0.0755110 | ||||||||
\(931\) | −5.30278 | −0.173791 | ||||||||
\(932\) | 9.21110 | 0.301720 | ||||||||
\(933\) | 7.81665 | 0.255906 | ||||||||
\(934\) | 22.6056 | 0.739676 | ||||||||
\(935\) | 10.6056 | 0.346839 | ||||||||
\(936\) | −9.60555 | −0.313967 | ||||||||
\(937\) | 1.15559 | 0.0377515 | 0.0188757 | − | 0.999822i | \(-0.493991\pi\) | ||||
0.0188757 | + | 0.999822i | \(0.493991\pi\) | |||||||
\(938\) | 8.48612 | 0.277082 | ||||||||
\(939\) | 5.48612 | 0.179033 | ||||||||
\(940\) | 13.8167 | 0.450650 | ||||||||
\(941\) | −57.6333 | −1.87879 | −0.939396 | − | 0.342834i | \(-0.888613\pi\) | ||||
−0.939396 | + | 0.342834i | \(0.888613\pi\) | |||||||
\(942\) | −0.330532 | −0.0107693 | ||||||||
\(943\) | −5.44996 | −0.177475 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.36669 | 0.174579 | ||||||||
\(946\) | −1.09167 | −0.0354934 | ||||||||
\(947\) | 25.8167 | 0.838929 | 0.419464 | − | 0.907772i | \(-0.362218\pi\) | ||||
0.419464 | + | 0.907772i | \(0.362218\pi\) | |||||||
\(948\) | 4.78890 | 0.155536 | ||||||||
\(949\) | 8.60555 | 0.279348 | ||||||||
\(950\) | −0.302776 | −0.00982334 | ||||||||
\(951\) | −4.18335 | −0.135654 | ||||||||
\(952\) | 6.00000 | 0.194461 | ||||||||
\(953\) | −21.6333 | −0.700772 | −0.350386 | − | 0.936605i | \(-0.613950\pi\) | ||||
−0.350386 | + | 0.936605i | \(0.613950\pi\) | |||||||
\(954\) | −30.8444 | −0.998625 | ||||||||
\(955\) | 13.8167 | 0.447096 | ||||||||
\(956\) | −23.9361 | −0.774148 | ||||||||
\(957\) | −2.51388 | −0.0812621 | ||||||||
\(958\) | −35.7250 | −1.15422 | ||||||||
\(959\) | −4.54163 | −0.146657 | ||||||||
\(960\) | −0.697224 | −0.0225028 | ||||||||
\(961\) | −20.0917 | −0.648118 | ||||||||
\(962\) | 17.2111 | 0.554908 | ||||||||
\(963\) | −9.33894 | −0.300943 | ||||||||
\(964\) | 13.0917 | 0.421654 | ||||||||
\(965\) | 56.9361 | 1.83284 | ||||||||
\(966\) | 0.550039 | 0.0176972 | ||||||||
\(967\) | 23.6333 | 0.759996 | 0.379998 | − | 0.924987i | \(-0.375925\pi\) | ||||
0.379998 | + | 0.924987i | \(0.375925\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | −1.39445 | −0.0447961 | ||||||||
\(970\) | 18.4222 | 0.591501 | ||||||||
\(971\) | −23.9361 | −0.768145 | −0.384073 | − | 0.923303i | \(-0.625479\pi\) | ||||
−0.384073 | + | 0.923303i | \(0.625479\pi\) | |||||||
\(972\) | 7.84441 | 0.251610 | ||||||||
\(973\) | −8.21110 | −0.263236 | ||||||||
\(974\) | 29.3305 | 0.939811 | ||||||||
\(975\) | −0.302776 | −0.00969658 | ||||||||
\(976\) | 11.2111 | 0.358859 | ||||||||
\(977\) | 27.6333 | 0.884068 | 0.442034 | − | 0.896998i | \(-0.354257\pi\) | ||||
0.442034 | + | 0.896998i | \(0.354257\pi\) | |||||||
\(978\) | 3.44996 | 0.110318 | ||||||||
\(979\) | 4.60555 | 0.147194 | ||||||||
\(980\) | 12.2111 | 0.390069 | ||||||||
\(981\) | −5.81665 | −0.185711 | ||||||||
\(982\) | 14.9361 | 0.476630 | ||||||||
\(983\) | 23.3028 | 0.743243 | 0.371622 | − | 0.928384i | \(-0.378802\pi\) | ||||
0.371622 | + | 0.928384i | \(0.378802\pi\) | |||||||
\(984\) | −1.18335 | −0.0377237 | ||||||||
\(985\) | −49.8167 | −1.58729 | ||||||||
\(986\) | −38.2389 | −1.21777 | ||||||||
\(987\) | −2.36669 | −0.0753326 | ||||||||
\(988\) | −3.30278 | −0.105075 | ||||||||
\(989\) | −1.52228 | −0.0484058 | ||||||||
\(990\) | −6.69722 | −0.212852 | ||||||||
\(991\) | −25.9083 | −0.823005 | −0.411503 | − | 0.911409i | \(-0.634996\pi\) | ||||
−0.411503 | + | 0.911409i | \(0.634996\pi\) | |||||||
\(992\) | 3.30278 | 0.104863 | ||||||||
\(993\) | 6.88057 | 0.218348 | ||||||||
\(994\) | 12.6333 | 0.400704 | ||||||||
\(995\) | 5.02776 | 0.159391 | ||||||||
\(996\) | 4.33053 | 0.137218 | ||||||||
\(997\) | 0.183346 | 0.00580663 | 0.00290332 | − | 0.999996i | \(-0.499076\pi\) | ||||
0.00290332 | + | 0.999996i | \(0.499076\pi\) | |||||||
\(998\) | 34.0000 | 1.07625 | ||||||||
\(999\) | −9.32213 | −0.294939 |
(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 | 418.2.a.d.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 3762.2.a.bb.1.2 | 2 | |||
4.3 | odd | 2 | 3344.2.a.o.1.1 | 2 | |||
11.10 | odd | 2 | 4598.2.a.bc.1.2 | 2 | |||
19.18 | odd | 2 | 7942.2.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
418.2.a.d.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3344.2.a.o.1.1 | 2 | 4.3 | odd | 2 | |||
3762.2.a.bb.1.2 | 2 | 3.2 | odd | 2 | |||
4598.2.a.bc.1.2 | 2 | 11.10 | odd | 2 | |||
7942.2.a.bb.1.1 | 2 | 19.18 | odd | 2 |