Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(189.798744245\) |
Analytic rank: | \(0\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.28 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 152.658 | 1.68664 | 0.843322 | − | 0.537409i | \(-0.180597\pi\) | ||||
0.843322 | + | 0.537409i | \(0.180597\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 15112.3 | 1.84477 | ||||||||
\(5\) | −3728.44 | −0.106714 | −0.0533571 | − | 0.998575i | \(-0.516992\pi\) | ||||
−0.0533571 | + | 0.998575i | \(0.516992\pi\) | |||||||
\(6\) | 111287. | 0.973784 | ||||||||
\(7\) | 589623. | 1.89425 | 0.947125 | − | 0.320864i | \(-0.103973\pi\) | ||||
0.947125 | + | 0.320864i | \(0.103973\pi\) | |||||||
\(8\) | 1.05644e6 | 1.42482 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −569175. | −0.179989 | ||||||||
\(11\) | 5.43191e6 | 0.924486 | 0.462243 | − | 0.886753i | \(-0.347045\pi\) | ||||
0.462243 | + | 0.886753i | \(0.347045\pi\) | |||||||
\(12\) | 1.10169e7 | 1.06508 | ||||||||
\(13\) | 2.28754e7 | 1.31443 | 0.657215 | − | 0.753703i | \(-0.271734\pi\) | ||||
0.657215 | + | 0.753703i | \(0.271734\pi\) | |||||||
\(14\) | 9.00105e7 | 3.19493 | ||||||||
\(15\) | −2.71803e6 | −0.0616115 | ||||||||
\(16\) | 3.74734e7 | 0.558397 | ||||||||
\(17\) | −1.09897e7 | −0.110425 | −0.0552125 | − | 0.998475i | \(-0.517584\pi\) | ||||
−0.0552125 | + | 0.998475i | \(0.517584\pi\) | |||||||
\(18\) | 8.11285e7 | 0.562215 | ||||||||
\(19\) | 2.75303e8 | 1.34249 | 0.671247 | − | 0.741233i | \(-0.265759\pi\) | ||||
0.671247 | + | 0.741233i | \(0.265759\pi\) | |||||||
\(20\) | −5.63454e7 | −0.196863 | ||||||||
\(21\) | 4.29835e8 | 1.09365 | ||||||||
\(22\) | 8.29222e8 | 1.55928 | ||||||||
\(23\) | −7.85204e7 | −0.110599 | −0.0552995 | − | 0.998470i | \(-0.517611\pi\) | ||||
−0.0552995 | + | 0.998470i | \(0.517611\pi\) | |||||||
\(24\) | 7.70145e8 | 0.822620 | ||||||||
\(25\) | −1.20680e9 | −0.988612 | ||||||||
\(26\) | 3.49211e9 | 2.21697 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | 8.91058e9 | 3.49445 | ||||||||
\(29\) | −3.24056e8 | −0.101166 | −0.0505828 | − | 0.998720i | \(-0.516108\pi\) | ||||
−0.0505828 | + | 0.998720i | \(0.516108\pi\) | |||||||
\(30\) | −4.14929e8 | −0.103917 | ||||||||
\(31\) | −7.36239e9 | −1.48994 | −0.744968 | − | 0.667100i | \(-0.767535\pi\) | ||||
−0.744968 | + | 0.667100i | \(0.767535\pi\) | |||||||
\(32\) | −2.93376e9 | −0.483003 | ||||||||
\(33\) | 3.95986e9 | 0.533752 | ||||||||
\(34\) | −1.67766e9 | −0.186248 | ||||||||
\(35\) | −2.19838e9 | −0.202144 | ||||||||
\(36\) | 8.03131e9 | 0.614922 | ||||||||
\(37\) | −1.97544e10 | −1.26576 | −0.632881 | − | 0.774249i | \(-0.718128\pi\) | ||||
−0.632881 | + | 0.774249i | \(0.718128\pi\) | |||||||
\(38\) | 4.20271e10 | 2.26431 | ||||||||
\(39\) | 1.66762e10 | 0.758886 | ||||||||
\(40\) | −3.93888e9 | −0.152049 | ||||||||
\(41\) | 3.27680e10 | 1.07734 | 0.538672 | − | 0.842515i | \(-0.318926\pi\) | ||||
0.538672 | + | 0.842515i | \(0.318926\pi\) | |||||||
\(42\) | 6.56176e10 | 1.84459 | ||||||||
\(43\) | 1.31535e10 | 0.317318 | 0.158659 | − | 0.987333i | \(-0.449283\pi\) | ||||
0.158659 | + | 0.987333i | \(0.449283\pi\) | |||||||
\(44\) | 8.20888e10 | 1.70546 | ||||||||
\(45\) | −1.98145e9 | −0.0355714 | ||||||||
\(46\) | −1.19867e10 | −0.186541 | ||||||||
\(47\) | −1.06879e11 | −1.44629 | −0.723146 | − | 0.690695i | \(-0.757305\pi\) | ||||
−0.723146 | + | 0.690695i | \(0.757305\pi\) | |||||||
\(48\) | 2.73181e10 | 0.322391 | ||||||||
\(49\) | 2.50767e11 | 2.58818 | ||||||||
\(50\) | −1.84227e11 | −1.66744 | ||||||||
\(51\) | −8.01149e9 | −0.0637540 | ||||||||
\(52\) | 3.45701e11 | 2.42482 | ||||||||
\(53\) | −1.42998e11 | −0.886210 | −0.443105 | − | 0.896470i | \(-0.646123\pi\) | ||||
−0.443105 | + | 0.896470i | \(0.646123\pi\) | |||||||
\(54\) | 5.91427e10 | 0.324595 | ||||||||
\(55\) | −2.02526e10 | −0.0986558 | ||||||||
\(56\) | 6.22902e11 | 2.69897 | ||||||||
\(57\) | 2.00696e11 | 0.775090 | ||||||||
\(58\) | −4.94695e10 | −0.170630 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −4.10758e10 | −0.113659 | ||||||||
\(61\) | −2.06447e11 | −0.513056 | −0.256528 | − | 0.966537i | \(-0.582579\pi\) | ||||
−0.256528 | + | 0.966537i | \(0.582579\pi\) | |||||||
\(62\) | −1.12392e12 | −2.51299 | ||||||||
\(63\) | 3.13350e11 | 0.631417 | ||||||||
\(64\) | −7.54843e11 | −1.37305 | ||||||||
\(65\) | −8.52897e10 | −0.140268 | ||||||||
\(66\) | 6.04503e11 | 0.900250 | ||||||||
\(67\) | 3.95170e11 | 0.533701 | 0.266850 | − | 0.963738i | \(-0.414017\pi\) | ||||
0.266850 | + | 0.963738i | \(0.414017\pi\) | |||||||
\(68\) | −1.66080e11 | −0.203709 | ||||||||
\(69\) | −5.72413e10 | −0.0638544 | ||||||||
\(70\) | −3.35599e11 | −0.340944 | ||||||||
\(71\) | 9.27090e11 | 0.858900 | 0.429450 | − | 0.903091i | \(-0.358707\pi\) | ||||
0.429450 | + | 0.903091i | \(0.358707\pi\) | |||||||
\(72\) | 5.61436e11 | 0.474940 | ||||||||
\(73\) | −1.26876e12 | −0.981254 | −0.490627 | − | 0.871370i | \(-0.663232\pi\) | ||||
−0.490627 | + | 0.871370i | \(0.663232\pi\) | |||||||
\(74\) | −3.01566e12 | −2.13489 | ||||||||
\(75\) | −8.79759e11 | −0.570775 | ||||||||
\(76\) | 4.16047e12 | 2.47659 | ||||||||
\(77\) | 3.20278e12 | 1.75121 | ||||||||
\(78\) | 2.54575e12 | 1.27997 | ||||||||
\(79\) | 1.43511e12 | 0.664214 | 0.332107 | − | 0.943242i | \(-0.392240\pi\) | ||||
0.332107 | + | 0.943242i | \(0.392240\pi\) | |||||||
\(80\) | −1.39717e11 | −0.0595890 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 5.00228e12 | 1.81710 | ||||||||
\(83\) | 2.65875e12 | 0.892626 | 0.446313 | − | 0.894877i | \(-0.352737\pi\) | ||||
0.446313 | + | 0.894877i | \(0.352737\pi\) | |||||||
\(84\) | 6.49581e12 | 2.01752 | ||||||||
\(85\) | 4.09745e10 | 0.0117839 | ||||||||
\(86\) | 2.00797e12 | 0.535203 | ||||||||
\(87\) | −2.36237e11 | −0.0584079 | ||||||||
\(88\) | 5.73849e12 | 1.31723 | ||||||||
\(89\) | −4.12973e12 | −0.880819 | −0.440409 | − | 0.897797i | \(-0.645167\pi\) | ||||
−0.440409 | + | 0.897797i | \(0.645167\pi\) | |||||||
\(90\) | −3.02483e11 | −0.0599963 | ||||||||
\(91\) | 1.34879e13 | 2.48986 | ||||||||
\(92\) | −1.18663e12 | −0.204029 | ||||||||
\(93\) | −5.36718e12 | −0.860215 | ||||||||
\(94\) | −1.63159e13 | −2.43938 | ||||||||
\(95\) | −1.02645e12 | −0.143263 | ||||||||
\(96\) | −2.13871e12 | −0.278862 | ||||||||
\(97\) | −8.48986e12 | −1.03487 | −0.517433 | − | 0.855724i | \(-0.673112\pi\) | ||||
−0.517433 | + | 0.855724i | \(0.673112\pi\) | |||||||
\(98\) | 3.82814e13 | 4.36535 | ||||||||
\(99\) | 2.88674e12 | 0.308162 | ||||||||
\(100\) | −1.82376e13 | −1.82376 | ||||||||
\(101\) | 5.35984e12 | 0.502415 | 0.251207 | − | 0.967933i | \(-0.419172\pi\) | ||||
0.251207 | + | 0.967933i | \(0.419172\pi\) | |||||||
\(102\) | −1.22301e12 | −0.107530 | ||||||||
\(103\) | 5.96798e11 | 0.0492477 | 0.0246238 | − | 0.999697i | \(-0.492161\pi\) | ||||
0.0246238 | + | 0.999697i | \(0.492161\pi\) | |||||||
\(104\) | 2.41665e13 | 1.87283 | ||||||||
\(105\) | −1.60262e12 | −0.116708 | ||||||||
\(106\) | −2.18297e13 | −1.49472 | ||||||||
\(107\) | −4.76546e12 | −0.306980 | −0.153490 | − | 0.988150i | \(-0.549051\pi\) | ||||
−0.153490 | + | 0.988150i | \(0.549051\pi\) | |||||||
\(108\) | 5.85483e12 | 0.355026 | ||||||||
\(109\) | 1.72499e13 | 0.985177 | 0.492589 | − | 0.870262i | \(-0.336051\pi\) | ||||
0.492589 | + | 0.870262i | \(0.336051\pi\) | |||||||
\(110\) | −3.09171e12 | −0.166397 | ||||||||
\(111\) | −1.44009e13 | −0.730788 | ||||||||
\(112\) | 2.20952e13 | 1.05774 | ||||||||
\(113\) | −8.56566e12 | −0.387036 | −0.193518 | − | 0.981097i | \(-0.561990\pi\) | ||||
−0.193518 | + | 0.981097i | \(0.561990\pi\) | |||||||
\(114\) | 3.06378e13 | 1.30730 | ||||||||
\(115\) | 2.92759e11 | 0.0118025 | ||||||||
\(116\) | −4.89723e12 | −0.186627 | ||||||||
\(117\) | 1.21569e13 | 0.438143 | ||||||||
\(118\) | −6.43918e12 | −0.219582 | ||||||||
\(119\) | −6.47978e12 | −0.209173 | ||||||||
\(120\) | −2.87144e12 | −0.0877853 | ||||||||
\(121\) | −5.01704e12 | −0.145326 | ||||||||
\(122\) | −3.15157e13 | −0.865342 | ||||||||
\(123\) | 2.38879e13 | 0.622005 | ||||||||
\(124\) | −1.11263e14 | −2.74858 | ||||||||
\(125\) | 9.05081e12 | 0.212213 | ||||||||
\(126\) | 4.78352e13 | 1.06498 | ||||||||
\(127\) | 8.94189e12 | 0.189106 | 0.0945530 | − | 0.995520i | \(-0.469858\pi\) | ||||
0.0945530 | + | 0.995520i | \(0.469858\pi\) | |||||||
\(128\) | −9.11991e13 | −1.83285 | ||||||||
\(129\) | 9.58887e12 | 0.183204 | ||||||||
\(130\) | −1.30201e13 | −0.236583 | ||||||||
\(131\) | 1.09136e14 | 1.88670 | 0.943350 | − | 0.331798i | \(-0.107655\pi\) | ||||
0.943350 | + | 0.331798i | \(0.107655\pi\) | |||||||
\(132\) | 5.98428e13 | 0.984648 | ||||||||
\(133\) | 1.62325e14 | 2.54302 | ||||||||
\(134\) | 6.03257e13 | 0.900163 | ||||||||
\(135\) | −1.44448e12 | −0.0205372 | ||||||||
\(136\) | −1.16100e13 | −0.157336 | ||||||||
\(137\) | 6.92853e13 | 0.895277 | 0.447639 | − | 0.894215i | \(-0.352265\pi\) | ||||
0.447639 | + | 0.894215i | \(0.352265\pi\) | |||||||
\(138\) | −8.73832e12 | −0.107700 | ||||||||
\(139\) | −8.52271e13 | −1.00226 | −0.501131 | − | 0.865371i | \(-0.667083\pi\) | ||||
−0.501131 | + | 0.865371i | \(0.667083\pi\) | |||||||
\(140\) | −3.32226e13 | −0.372908 | ||||||||
\(141\) | −7.79147e13 | −0.835017 | ||||||||
\(142\) | 1.41527e14 | 1.44866 | ||||||||
\(143\) | 1.24257e14 | 1.21517 | ||||||||
\(144\) | 1.99149e13 | 0.186132 | ||||||||
\(145\) | 1.20822e12 | 0.0107958 | ||||||||
\(146\) | −1.93686e14 | −1.65503 | ||||||||
\(147\) | 1.82809e14 | 1.49429 | ||||||||
\(148\) | −2.98535e14 | −2.33504 | ||||||||
\(149\) | 1.19681e14 | 0.896010 | 0.448005 | − | 0.894031i | \(-0.352135\pi\) | ||||
0.448005 | + | 0.894031i | \(0.352135\pi\) | |||||||
\(150\) | −1.34302e14 | −0.962695 | ||||||||
\(151\) | −1.12308e14 | −0.771010 | −0.385505 | − | 0.922706i | \(-0.625973\pi\) | ||||
−0.385505 | + | 0.922706i | \(0.625973\pi\) | |||||||
\(152\) | 2.90841e14 | 1.91281 | ||||||||
\(153\) | −5.84038e12 | −0.0368084 | ||||||||
\(154\) | 4.88929e14 | 2.95366 | ||||||||
\(155\) | 2.74502e13 | 0.158997 | ||||||||
\(156\) | 2.52016e14 | 1.39997 | ||||||||
\(157\) | −4.74552e12 | −0.0252893 | −0.0126446 | − | 0.999920i | \(-0.504025\pi\) | ||||
−0.0126446 | + | 0.999920i | \(0.504025\pi\) | |||||||
\(158\) | 2.19080e14 | 1.12029 | ||||||||
\(159\) | −1.04245e14 | −0.511653 | ||||||||
\(160\) | 1.09384e13 | 0.0515433 | ||||||||
\(161\) | −4.62974e13 | −0.209502 | ||||||||
\(162\) | 4.31150e13 | 0.187405 | ||||||||
\(163\) | −3.13861e14 | −1.31074 | −0.655372 | − | 0.755307i | \(-0.727488\pi\) | ||||
−0.655372 | + | 0.755307i | \(0.727488\pi\) | |||||||
\(164\) | 4.95201e14 | 1.98745 | ||||||||
\(165\) | −1.47641e13 | −0.0569590 | ||||||||
\(166\) | 4.05878e14 | 1.50554 | ||||||||
\(167\) | 2.18550e14 | 0.779639 | 0.389820 | − | 0.920891i | \(-0.372537\pi\) | ||||
0.389820 | + | 0.920891i | \(0.372537\pi\) | |||||||
\(168\) | 4.54095e14 | 1.55825 | ||||||||
\(169\) | 2.20410e14 | 0.727725 | ||||||||
\(170\) | 6.25506e12 | 0.0198753 | ||||||||
\(171\) | 1.46307e14 | 0.447498 | ||||||||
\(172\) | 1.98779e14 | 0.585378 | ||||||||
\(173\) | −6.49174e13 | −0.184103 | −0.0920516 | − | 0.995754i | \(-0.529342\pi\) | ||||
−0.0920516 | + | 0.995754i | \(0.529342\pi\) | |||||||
\(174\) | −3.60633e13 | −0.0985134 | ||||||||
\(175\) | −7.11559e14 | −1.87268 | ||||||||
\(176\) | 2.03552e14 | 0.516230 | ||||||||
\(177\) | −3.07496e13 | −0.0751646 | ||||||||
\(178\) | −6.30434e14 | −1.48563 | ||||||||
\(179\) | 2.14196e14 | 0.486706 | 0.243353 | − | 0.969938i | \(-0.421753\pi\) | ||||
0.243353 | + | 0.969938i | \(0.421753\pi\) | |||||||
\(180\) | −2.99443e13 | −0.0656210 | ||||||||
\(181\) | −5.05300e14 | −1.06816 | −0.534082 | − | 0.845432i | \(-0.679343\pi\) | ||||
−0.534082 | + | 0.845432i | \(0.679343\pi\) | |||||||
\(182\) | 2.05903e15 | 4.19950 | ||||||||
\(183\) | −1.50500e14 | −0.296213 | ||||||||
\(184\) | −8.29521e13 | −0.157584 | ||||||||
\(185\) | 7.36531e13 | 0.135075 | ||||||||
\(186\) | −8.19340e14 | −1.45088 | ||||||||
\(187\) | −5.96951e13 | −0.102086 | ||||||||
\(188\) | −1.61519e15 | −2.66807 | ||||||||
\(189\) | 2.28432e14 | 0.364549 | ||||||||
\(190\) | −1.56696e14 | −0.241634 | ||||||||
\(191\) | 3.23683e13 | 0.0482394 | 0.0241197 | − | 0.999709i | \(-0.492322\pi\) | ||||
0.0241197 | + | 0.999709i | \(0.492322\pi\) | |||||||
\(192\) | −5.50280e14 | −0.792731 | ||||||||
\(193\) | −8.88242e14 | −1.23711 | −0.618555 | − | 0.785741i | \(-0.712282\pi\) | ||||
−0.618555 | + | 0.785741i | \(0.712282\pi\) | |||||||
\(194\) | −1.29604e15 | −1.74545 | ||||||||
\(195\) | −6.21762e13 | −0.0809840 | ||||||||
\(196\) | 3.78967e15 | 4.77460 | ||||||||
\(197\) | 7.18560e14 | 0.875855 | 0.437928 | − | 0.899010i | \(-0.355713\pi\) | ||||
0.437928 | + | 0.899010i | \(0.355713\pi\) | |||||||
\(198\) | 4.40683e14 | 0.519759 | ||||||||
\(199\) | −6.24778e14 | −0.713149 | −0.356575 | − | 0.934267i | \(-0.616055\pi\) | ||||
−0.356575 | + | 0.934267i | \(0.616055\pi\) | |||||||
\(200\) | −1.27491e15 | −1.40859 | ||||||||
\(201\) | 2.88079e14 | 0.308132 | ||||||||
\(202\) | 8.18219e14 | 0.847395 | ||||||||
\(203\) | −1.91071e14 | −0.191633 | ||||||||
\(204\) | −1.21072e14 | −0.117611 | ||||||||
\(205\) | −1.22174e14 | −0.114968 | ||||||||
\(206\) | 9.11058e13 | 0.0830633 | ||||||||
\(207\) | −4.17289e13 | −0.0368663 | ||||||||
\(208\) | 8.57220e14 | 0.733974 | ||||||||
\(209\) | 1.49542e15 | 1.24112 | ||||||||
\(210\) | −2.44652e14 | −0.196844 | ||||||||
\(211\) | 2.02198e15 | 1.57740 | 0.788698 | − | 0.614781i | \(-0.210755\pi\) | ||||
0.788698 | + | 0.614781i | \(0.210755\pi\) | |||||||
\(212\) | −2.16103e15 | −1.63485 | ||||||||
\(213\) | 6.75849e14 | 0.495886 | ||||||||
\(214\) | −7.27484e14 | −0.517766 | ||||||||
\(215\) | −4.90419e13 | −0.0338624 | ||||||||
\(216\) | 4.09287e14 | 0.274207 | ||||||||
\(217\) | −4.34103e15 | −2.82231 | ||||||||
\(218\) | 2.63333e15 | 1.66164 | ||||||||
\(219\) | −9.24927e14 | −0.566527 | ||||||||
\(220\) | −3.06064e14 | −0.181997 | ||||||||
\(221\) | −2.51394e14 | −0.145146 | ||||||||
\(222\) | −2.19841e15 | −1.23258 | ||||||||
\(223\) | −2.84503e15 | −1.54919 | −0.774597 | − | 0.632455i | \(-0.782047\pi\) | ||||
−0.774597 | + | 0.632455i | \(0.782047\pi\) | |||||||
\(224\) | −1.72981e15 | −0.914929 | ||||||||
\(225\) | −6.41344e14 | −0.329537 | ||||||||
\(226\) | −1.30761e15 | −0.652791 | ||||||||
\(227\) | 1.84605e14 | 0.0895522 | 0.0447761 | − | 0.998997i | \(-0.485743\pi\) | ||||
0.0447761 | + | 0.998997i | \(0.485743\pi\) | |||||||
\(228\) | 3.03298e15 | 1.42986 | ||||||||
\(229\) | −1.29996e15 | −0.595660 | −0.297830 | − | 0.954619i | \(-0.596263\pi\) | ||||
−0.297830 | + | 0.954619i | \(0.596263\pi\) | |||||||
\(230\) | 4.46918e13 | 0.0199066 | ||||||||
\(231\) | 2.33483e15 | 1.01106 | ||||||||
\(232\) | −3.42345e14 | −0.144143 | ||||||||
\(233\) | −4.49509e15 | −1.84045 | −0.920227 | − | 0.391385i | \(-0.871996\pi\) | ||||
−0.920227 | + | 0.391385i | \(0.871996\pi\) | |||||||
\(234\) | 1.85585e15 | 0.738991 | ||||||||
\(235\) | 3.98492e14 | 0.154340 | ||||||||
\(236\) | −6.37446e14 | −0.240168 | ||||||||
\(237\) | 1.04619e15 | 0.383484 | ||||||||
\(238\) | −9.89188e14 | −0.352800 | ||||||||
\(239\) | 3.10807e15 | 1.07871 | 0.539355 | − | 0.842078i | \(-0.318668\pi\) | ||||
0.539355 | + | 0.842078i | \(0.318668\pi\) | |||||||
\(240\) | −1.01854e14 | −0.0344037 | ||||||||
\(241\) | 1.98521e15 | 0.652673 | 0.326337 | − | 0.945254i | \(-0.394186\pi\) | ||||
0.326337 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(242\) | −7.65890e14 | −0.245113 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −3.11989e15 | −0.946468 | ||||||||
\(245\) | −9.34969e14 | −0.276196 | ||||||||
\(246\) | 3.64666e15 | 1.04910 | ||||||||
\(247\) | 6.29767e15 | 1.76461 | ||||||||
\(248\) | −7.77792e15 | −2.12289 | ||||||||
\(249\) | 1.93823e15 | 0.515358 | ||||||||
\(250\) | 1.38167e15 | 0.357928 | ||||||||
\(251\) | −7.19917e15 | −1.81720 | −0.908601 | − | 0.417666i | \(-0.862848\pi\) | ||||
−0.908601 | + | 0.417666i | \(0.862848\pi\) | |||||||
\(252\) | 4.73545e15 | 1.16482 | ||||||||
\(253\) | −4.26516e14 | −0.102247 | ||||||||
\(254\) | 1.36505e15 | 0.318954 | ||||||||
\(255\) | 2.98704e13 | 0.00680346 | ||||||||
\(256\) | −7.73856e15 | −1.71831 | ||||||||
\(257\) | 6.27503e15 | 1.35847 | 0.679236 | − | 0.733920i | \(-0.262311\pi\) | ||||
0.679236 | + | 0.733920i | \(0.262311\pi\) | |||||||
\(258\) | 1.46381e15 | 0.308999 | ||||||||
\(259\) | −1.16476e16 | −2.39767 | ||||||||
\(260\) | −1.28893e15 | −0.258762 | ||||||||
\(261\) | −1.72216e14 | −0.0337218 | ||||||||
\(262\) | 1.66604e16 | 3.18219 | ||||||||
\(263\) | 3.04483e15 | 0.567350 | 0.283675 | − | 0.958920i | \(-0.408446\pi\) | ||||
0.283675 | + | 0.958920i | \(0.408446\pi\) | |||||||
\(264\) | 4.18336e15 | 0.760501 | ||||||||
\(265\) | 5.33159e14 | 0.0945712 | ||||||||
\(266\) | 2.47802e16 | 4.28917 | ||||||||
\(267\) | −3.01057e15 | −0.508541 | ||||||||
\(268\) | 5.97194e15 | 0.984553 | ||||||||
\(269\) | −4.95500e15 | −0.797359 | −0.398680 | − | 0.917090i | \(-0.630531\pi\) | ||||
−0.398680 | + | 0.917090i | \(0.630531\pi\) | |||||||
\(270\) | −2.20510e14 | −0.0346389 | ||||||||
\(271\) | −4.41996e15 | −0.677825 | −0.338913 | − | 0.940818i | \(-0.610059\pi\) | ||||
−0.338913 | + | 0.940818i | \(0.610059\pi\) | |||||||
\(272\) | −4.11821e14 | −0.0616611 | ||||||||
\(273\) | 9.83267e15 | 1.43752 | ||||||||
\(274\) | 1.05769e16 | 1.51001 | ||||||||
\(275\) | −6.55524e15 | −0.913958 | ||||||||
\(276\) | −8.65050e14 | −0.117796 | ||||||||
\(277\) | 2.65957e15 | 0.353747 | 0.176874 | − | 0.984234i | \(-0.443402\pi\) | ||||
0.176874 | + | 0.984234i | \(0.443402\pi\) | |||||||
\(278\) | −1.30106e16 | −1.69046 | ||||||||
\(279\) | −3.91267e15 | −0.496645 | ||||||||
\(280\) | −2.32245e15 | −0.288018 | ||||||||
\(281\) | 1.37797e16 | 1.66974 | 0.834872 | − | 0.550445i | \(-0.185542\pi\) | ||||
0.834872 | + | 0.550445i | \(0.185542\pi\) | |||||||
\(282\) | −1.18943e16 | −1.40838 | ||||||||
\(283\) | 9.87686e15 | 1.14290 | 0.571448 | − | 0.820638i | \(-0.306382\pi\) | ||||
0.571448 | + | 0.820638i | \(0.306382\pi\) | |||||||
\(284\) | 1.40105e16 | 1.58447 | ||||||||
\(285\) | −7.48283e14 | −0.0827131 | ||||||||
\(286\) | 1.89688e16 | 2.04956 | ||||||||
\(287\) | 1.93208e16 | 2.04076 | ||||||||
\(288\) | −1.55912e15 | −0.161001 | ||||||||
\(289\) | −9.78380e15 | −0.987806 | ||||||||
\(290\) | 1.84444e14 | 0.0182087 | ||||||||
\(291\) | −6.18911e15 | −0.597481 | ||||||||
\(292\) | −1.91739e16 | −1.81018 | ||||||||
\(293\) | −8.99561e15 | −0.830598 | −0.415299 | − | 0.909685i | \(-0.636323\pi\) | ||||
−0.415299 | + | 0.909685i | \(0.636323\pi\) | |||||||
\(294\) | 2.79072e16 | 2.52033 | ||||||||
\(295\) | 1.57268e14 | 0.0138930 | ||||||||
\(296\) | −2.08693e16 | −1.80348 | ||||||||
\(297\) | 2.10443e15 | 0.177917 | ||||||||
\(298\) | 1.82701e16 | 1.51125 | ||||||||
\(299\) | −1.79619e15 | −0.145375 | ||||||||
\(300\) | −1.32952e16 | −1.05295 | ||||||||
\(301\) | 7.75559e15 | 0.601080 | ||||||||
\(302\) | −1.71446e16 | −1.30042 | ||||||||
\(303\) | 3.90732e15 | 0.290069 | ||||||||
\(304\) | 1.03165e16 | 0.749646 | ||||||||
\(305\) | 7.69726e14 | 0.0547504 | ||||||||
\(306\) | −8.91578e14 | −0.0620826 | ||||||||
\(307\) | −1.50563e16 | −1.02641 | −0.513204 | − | 0.858267i | \(-0.671542\pi\) | ||||
−0.513204 | + | 0.858267i | \(0.671542\pi\) | |||||||
\(308\) | 4.84015e16 | 3.23057 | ||||||||
\(309\) | 4.35066e14 | 0.0284332 | ||||||||
\(310\) | 4.19049e15 | 0.268172 | ||||||||
\(311\) | −1.08453e16 | −0.679672 | −0.339836 | − | 0.940485i | \(-0.610372\pi\) | ||||
−0.339836 | + | 0.940485i | \(0.610372\pi\) | |||||||
\(312\) | 1.76174e16 | 1.08128 | ||||||||
\(313\) | 1.05865e16 | 0.636375 | 0.318187 | − | 0.948028i | \(-0.396926\pi\) | ||||
0.318187 | + | 0.948028i | \(0.396926\pi\) | |||||||
\(314\) | −7.24439e14 | −0.0426540 | ||||||||
\(315\) | −1.16831e15 | −0.0673812 | ||||||||
\(316\) | 2.16878e16 | 1.22532 | ||||||||
\(317\) | 3.53509e16 | 1.95666 | 0.978330 | − | 0.207052i | \(-0.0663869\pi\) | ||||
0.978330 | + | 0.207052i | \(0.0663869\pi\) | |||||||
\(318\) | −1.59139e16 | −0.862977 | ||||||||
\(319\) | −1.76024e15 | −0.0935261 | ||||||||
\(320\) | 2.81439e15 | 0.146524 | ||||||||
\(321\) | −3.47402e15 | −0.177235 | ||||||||
\(322\) | −7.06765e15 | −0.353356 | ||||||||
\(323\) | −3.02550e15 | −0.148245 | ||||||||
\(324\) | 4.26817e15 | 0.204974 | ||||||||
\(325\) | −2.76061e16 | −1.29946 | ||||||||
\(326\) | −4.79132e16 | −2.21076 | ||||||||
\(327\) | 1.25752e16 | 0.568792 | ||||||||
\(328\) | 3.46174e16 | 1.53502 | ||||||||
\(329\) | −6.30183e16 | −2.73964 | ||||||||
\(330\) | −2.25386e15 | −0.0960695 | ||||||||
\(331\) | 1.03400e16 | 0.432152 | 0.216076 | − | 0.976377i | \(-0.430674\pi\) | ||||
0.216076 | + | 0.976377i | \(0.430674\pi\) | |||||||
\(332\) | 4.01799e16 | 1.64669 | ||||||||
\(333\) | −1.04983e16 | −0.421921 | ||||||||
\(334\) | 3.33633e16 | 1.31497 | ||||||||
\(335\) | −1.47337e15 | −0.0569535 | ||||||||
\(336\) | 1.61074e16 | 0.610689 | ||||||||
\(337\) | −5.59310e15 | −0.207998 | −0.103999 | − | 0.994577i | \(-0.533164\pi\) | ||||
−0.103999 | + | 0.994577i | \(0.533164\pi\) | |||||||
\(338\) | 3.36472e16 | 1.22741 | ||||||||
\(339\) | −6.24437e15 | −0.223455 | ||||||||
\(340\) | 6.19219e14 | 0.0217386 | ||||||||
\(341\) | −3.99918e16 | −1.37742 | ||||||||
\(342\) | 2.23349e16 | 0.754770 | ||||||||
\(343\) | 9.07299e16 | 3.00842 | ||||||||
\(344\) | 1.38958e16 | 0.452121 | ||||||||
\(345\) | 2.13421e14 | 0.00681417 | ||||||||
\(346\) | −9.91013e15 | −0.310516 | ||||||||
\(347\) | 4.98969e16 | 1.53438 | 0.767189 | − | 0.641422i | \(-0.221655\pi\) | ||||
0.767189 | + | 0.641422i | \(0.221655\pi\) | |||||||
\(348\) | −3.57008e15 | −0.107749 | ||||||||
\(349\) | 5.12688e16 | 1.51876 | 0.759378 | − | 0.650650i | \(-0.225503\pi\) | ||||
0.759378 | + | 0.650650i | \(0.225503\pi\) | |||||||
\(350\) | −1.08625e17 | −3.15854 | ||||||||
\(351\) | 8.86241e15 | 0.252962 | ||||||||
\(352\) | −1.59359e16 | −0.446529 | ||||||||
\(353\) | −4.97761e16 | −1.36926 | −0.684629 | − | 0.728892i | \(-0.740036\pi\) | ||||
−0.684629 | + | 0.728892i | \(0.740036\pi\) | |||||||
\(354\) | −4.69416e15 | −0.126776 | ||||||||
\(355\) | −3.45660e15 | −0.0916569 | ||||||||
\(356\) | −6.24098e16 | −1.62491 | ||||||||
\(357\) | −4.72376e15 | −0.120766 | ||||||||
\(358\) | 3.26986e16 | 0.820899 | ||||||||
\(359\) | −4.26935e13 | −0.00105256 | −0.000526281 | − | 1.00000i | \(-0.500168\pi\) | ||||
−0.000526281 | 1.00000i | \(0.500168\pi\) | ||||||||
\(360\) | −2.09328e15 | −0.0506829 | ||||||||
\(361\) | 3.37388e16 | 0.802293 | ||||||||
\(362\) | −7.71378e16 | −1.80161 | ||||||||
\(363\) | −3.65742e15 | −0.0839039 | ||||||||
\(364\) | 2.03833e17 | 4.59321 | ||||||||
\(365\) | 4.73050e15 | 0.104714 | ||||||||
\(366\) | −2.29749e16 | −0.499606 | ||||||||
\(367\) | 5.34119e16 | 1.14106 | 0.570530 | − | 0.821277i | \(-0.306738\pi\) | ||||
0.570530 | + | 0.821277i | \(0.306738\pi\) | |||||||
\(368\) | −2.94243e15 | −0.0617582 | ||||||||
\(369\) | 1.74143e16 | 0.359115 | ||||||||
\(370\) | 1.12437e16 | 0.227823 | ||||||||
\(371\) | −8.43149e16 | −1.67870 | ||||||||
\(372\) | −8.11106e16 | −1.58690 | ||||||||
\(373\) | 8.78818e16 | 1.68963 | 0.844815 | − | 0.535059i | \(-0.179710\pi\) | ||||
0.844815 | + | 0.535059i | \(0.179710\pi\) | |||||||
\(374\) | −9.11290e15 | −0.172183 | ||||||||
\(375\) | 6.59804e15 | 0.122521 | ||||||||
\(376\) | −1.12911e17 | −2.06071 | ||||||||
\(377\) | −7.41291e15 | −0.132975 | ||||||||
\(378\) | 3.48719e16 | 0.614864 | ||||||||
\(379\) | −8.28194e16 | −1.43541 | −0.717707 | − | 0.696345i | \(-0.754808\pi\) | ||||
−0.717707 | + | 0.696345i | \(0.754808\pi\) | |||||||
\(380\) | −1.55121e16 | −0.264287 | ||||||||
\(381\) | 6.51864e15 | 0.109180 | ||||||||
\(382\) | 4.94126e15 | 0.0813628 | ||||||||
\(383\) | 1.06814e17 | 1.72916 | 0.864582 | − | 0.502491i | \(-0.167583\pi\) | ||||
0.864582 | + | 0.502491i | \(0.167583\pi\) | |||||||
\(384\) | −6.64841e16 | −1.05819 | ||||||||
\(385\) | −1.19414e16 | −0.186879 | ||||||||
\(386\) | −1.35597e17 | −2.08657 | ||||||||
\(387\) | 6.99029e15 | 0.105773 | ||||||||
\(388\) | −1.28302e17 | −1.90909 | ||||||||
\(389\) | 1.75112e16 | 0.256239 | 0.128119 | − | 0.991759i | \(-0.459106\pi\) | ||||
0.128119 | + | 0.991759i | \(0.459106\pi\) | |||||||
\(390\) | −9.49166e15 | −0.136591 | ||||||||
\(391\) | 8.62915e14 | 0.0122129 | ||||||||
\(392\) | 2.64920e17 | 3.68770 | ||||||||
\(393\) | 7.95599e16 | 1.08929 | ||||||||
\(394\) | 1.09694e17 | 1.47726 | ||||||||
\(395\) | −5.35071e15 | −0.0708811 | ||||||||
\(396\) | 4.36254e16 | 0.568487 | ||||||||
\(397\) | −2.57669e16 | −0.330311 | −0.165156 | − | 0.986268i | \(-0.552813\pi\) | ||||
−0.165156 | + | 0.986268i | \(0.552813\pi\) | |||||||
\(398\) | −9.53770e16 | −1.20283 | ||||||||
\(399\) | 1.18335e17 | 1.46821 | ||||||||
\(400\) | −4.52230e16 | −0.552038 | ||||||||
\(401\) | −2.00205e16 | −0.240456 | −0.120228 | − | 0.992746i | \(-0.538363\pi\) | ||||
−0.120228 | + | 0.992746i | \(0.538363\pi\) | |||||||
\(402\) | 4.39774e16 | 0.519709 | ||||||||
\(403\) | −1.68418e17 | −1.95842 | ||||||||
\(404\) | 8.09996e16 | 0.926838 | ||||||||
\(405\) | −1.05302e15 | −0.0118571 | ||||||||
\(406\) | −2.91684e16 | −0.323216 | ||||||||
\(407\) | −1.07304e17 | −1.17018 | ||||||||
\(408\) | −8.46366e15 | −0.0908379 | ||||||||
\(409\) | 4.44128e16 | 0.469144 | 0.234572 | − | 0.972099i | \(-0.424631\pi\) | ||||
0.234572 | + | 0.972099i | \(0.424631\pi\) | |||||||
\(410\) | −1.86507e16 | −0.193910 | ||||||||
\(411\) | 5.05090e16 | 0.516889 | ||||||||
\(412\) | 9.01901e15 | 0.0908505 | ||||||||
\(413\) | −2.48706e16 | −0.246610 | ||||||||
\(414\) | −6.37024e15 | −0.0621804 | ||||||||
\(415\) | −9.91299e15 | −0.0952560 | ||||||||
\(416\) | −6.71110e16 | −0.634873 | ||||||||
\(417\) | −6.21306e16 | −0.578657 | ||||||||
\(418\) | 2.28287e17 | 2.09332 | ||||||||
\(419\) | −1.91747e17 | −1.73116 | −0.865581 | − | 0.500770i | \(-0.833050\pi\) | ||||
−0.865581 | + | 0.500770i | \(0.833050\pi\) | |||||||
\(420\) | −2.42193e16 | −0.215298 | ||||||||
\(421\) | 8.96505e16 | 0.784728 | 0.392364 | − | 0.919810i | \(-0.371657\pi\) | ||||
0.392364 | + | 0.919810i | \(0.371657\pi\) | |||||||
\(422\) | 3.08670e17 | 2.66051 | ||||||||
\(423\) | −5.67998e16 | −0.482097 | ||||||||
\(424\) | −1.51069e17 | −1.26269 | ||||||||
\(425\) | 1.32624e16 | 0.109168 | ||||||||
\(426\) | 1.03173e17 | 0.836383 | ||||||||
\(427\) | −1.21726e17 | −0.971856 | ||||||||
\(428\) | −7.20172e16 | −0.566307 | ||||||||
\(429\) | 9.05836e16 | 0.701580 | ||||||||
\(430\) | −7.48662e15 | −0.0571138 | ||||||||
\(431\) | −4.39883e16 | −0.330548 | −0.165274 | − | 0.986248i | \(-0.552851\pi\) | ||||
−0.165274 | + | 0.986248i | \(0.552851\pi\) | |||||||
\(432\) | 1.45180e16 | 0.107464 | ||||||||
\(433\) | −1.69538e17 | −1.23622 | −0.618111 | − | 0.786091i | \(-0.712102\pi\) | ||||
−0.618111 | + | 0.786091i | \(0.712102\pi\) | |||||||
\(434\) | −6.62692e17 | −4.76023 | ||||||||
\(435\) | 8.80794e14 | 0.00623296 | ||||||||
\(436\) | 2.60686e17 | 1.81742 | ||||||||
\(437\) | −2.16169e16 | −0.148479 | ||||||||
\(438\) | −1.41197e17 | −0.955529 | ||||||||
\(439\) | −7.60767e16 | −0.507262 | −0.253631 | − | 0.967301i | \(-0.581625\pi\) | ||||
−0.253631 | + | 0.967301i | \(0.581625\pi\) | |||||||
\(440\) | −2.13956e16 | −0.140567 | ||||||||
\(441\) | 1.33268e17 | 0.862728 | ||||||||
\(442\) | −3.83772e16 | −0.244810 | ||||||||
\(443\) | −1.35028e17 | −0.848791 | −0.424395 | − | 0.905477i | \(-0.639513\pi\) | ||||
−0.424395 | + | 0.905477i | \(0.639513\pi\) | |||||||
\(444\) | −2.17632e17 | −1.34813 | ||||||||
\(445\) | 1.53975e16 | 0.0939959 | ||||||||
\(446\) | −4.34316e17 | −2.61294 | ||||||||
\(447\) | 8.72471e16 | 0.517312 | ||||||||
\(448\) | −4.45073e17 | −2.60090 | ||||||||
\(449\) | −2.93046e17 | −1.68785 | −0.843925 | − | 0.536460i | \(-0.819761\pi\) | ||||
−0.843925 | + | 0.536460i | \(0.819761\pi\) | |||||||
\(450\) | −9.79060e16 | −0.555812 | ||||||||
\(451\) | 1.77993e17 | 0.995990 | ||||||||
\(452\) | −1.29447e17 | −0.713990 | ||||||||
\(453\) | −8.18724e16 | −0.445143 | ||||||||
\(454\) | 2.81814e16 | 0.151043 | ||||||||
\(455\) | −5.02888e16 | −0.265703 | ||||||||
\(456\) | 2.12023e17 | 1.10436 | ||||||||
\(457\) | −1.25854e17 | −0.646268 | −0.323134 | − | 0.946353i | \(-0.604736\pi\) | ||||
−0.323134 | + | 0.946353i | \(0.604736\pi\) | |||||||
\(458\) | −1.98448e17 | −1.00467 | ||||||||
\(459\) | −4.25763e15 | −0.0212513 | ||||||||
\(460\) | 4.42427e15 | 0.0217728 | ||||||||
\(461\) | 3.67569e16 | 0.178354 | 0.0891769 | − | 0.996016i | \(-0.471576\pi\) | ||||
0.0891769 | + | 0.996016i | \(0.471576\pi\) | |||||||
\(462\) | 3.56429e17 | 1.70530 | ||||||||
\(463\) | −1.80159e17 | −0.849923 | −0.424962 | − | 0.905211i | \(-0.639712\pi\) | ||||
−0.424962 | + | 0.905211i | \(0.639712\pi\) | |||||||
\(464\) | −1.21435e16 | −0.0564906 | ||||||||
\(465\) | 2.00112e16 | 0.0917972 | ||||||||
\(466\) | −6.86210e17 | −3.10419 | ||||||||
\(467\) | −3.35310e15 | −0.0149585 | −0.00747923 | − | 0.999972i | \(-0.502381\pi\) | ||||
−0.00747923 | + | 0.999972i | \(0.502381\pi\) | |||||||
\(468\) | 1.83720e17 | 0.808272 | ||||||||
\(469\) | 2.33001e17 | 1.01096 | ||||||||
\(470\) | 6.08328e16 | 0.260317 | ||||||||
\(471\) | −3.45948e15 | −0.0146008 | ||||||||
\(472\) | −4.45612e16 | −0.185496 | ||||||||
\(473\) | 7.14484e16 | 0.293356 | ||||||||
\(474\) | 1.59709e17 | 0.646801 | ||||||||
\(475\) | −3.32236e17 | −1.32721 | ||||||||
\(476\) | −9.79246e16 | −0.385875 | ||||||||
\(477\) | −7.59949e16 | −0.295403 | ||||||||
\(478\) | 4.74471e17 | 1.81940 | ||||||||
\(479\) | −3.44522e17 | −1.30328 | −0.651638 | − | 0.758530i | \(-0.725918\pi\) | ||||
−0.651638 | + | 0.758530i | \(0.725918\pi\) | |||||||
\(480\) | 7.97406e15 | 0.0297585 | ||||||||
\(481\) | −4.51890e17 | −1.66376 | ||||||||
\(482\) | 3.03057e17 | 1.10083 | ||||||||
\(483\) | −3.37508e16 | −0.120956 | ||||||||
\(484\) | −7.58192e16 | −0.268092 | ||||||||
\(485\) | 3.16540e16 | 0.110435 | ||||||||
\(486\) | 3.14308e16 | 0.108198 | ||||||||
\(487\) | −5.87042e17 | −1.99403 | −0.997014 | − | 0.0772206i | \(-0.975395\pi\) | ||||
−0.997014 | + | 0.0772206i | \(0.975395\pi\) | |||||||
\(488\) | −2.18099e17 | −0.731012 | ||||||||
\(489\) | −2.28804e17 | −0.756758 | ||||||||
\(490\) | −1.42730e17 | −0.465845 | ||||||||
\(491\) | −4.10341e17 | −1.32165 | −0.660823 | − | 0.750542i | \(-0.729793\pi\) | ||||
−0.660823 | + | 0.750542i | \(0.729793\pi\) | |||||||
\(492\) | 3.61001e17 | 1.14745 | ||||||||
\(493\) | 3.56127e15 | 0.0111712 | ||||||||
\(494\) | 9.61387e17 | 2.97628 | ||||||||
\(495\) | −1.07630e16 | −0.0328853 | ||||||||
\(496\) | −2.75894e17 | −0.831976 | ||||||||
\(497\) | 5.46634e17 | 1.62697 | ||||||||
\(498\) | 2.95885e17 | 0.869225 | ||||||||
\(499\) | −2.56903e17 | −0.744930 | −0.372465 | − | 0.928046i | \(-0.621487\pi\) | ||||
−0.372465 | + | 0.928046i | \(0.621487\pi\) | |||||||
\(500\) | 1.36779e17 | 0.391484 | ||||||||
\(501\) | 1.59323e17 | 0.450125 | ||||||||
\(502\) | −1.09901e18 | −3.06497 | ||||||||
\(503\) | 3.08442e17 | 0.849143 | 0.424572 | − | 0.905394i | \(-0.360425\pi\) | ||||
0.424572 | + | 0.905394i | \(0.360425\pi\) | |||||||
\(504\) | 3.31036e17 | 0.899655 | ||||||||
\(505\) | −1.99838e16 | −0.0536148 | ||||||||
\(506\) | −6.51108e16 | −0.172455 | ||||||||
\(507\) | 1.60679e17 | 0.420152 | ||||||||
\(508\) | 1.35133e17 | 0.348856 | ||||||||
\(509\) | 4.12094e17 | 1.05034 | 0.525171 | − | 0.850997i | \(-0.324001\pi\) | ||||
0.525171 | + | 0.850997i | \(0.324001\pi\) | |||||||
\(510\) | 4.55994e15 | 0.0114750 | ||||||||
\(511\) | −7.48091e17 | −1.85874 | ||||||||
\(512\) | −4.34246e17 | −1.06532 | ||||||||
\(513\) | 1.06658e17 | 0.258363 | ||||||||
\(514\) | 9.57931e17 | 2.29126 | ||||||||
\(515\) | −2.22513e15 | −0.00525543 | ||||||||
\(516\) | 1.44910e17 | 0.337968 | ||||||||
\(517\) | −5.80557e17 | −1.33708 | ||||||||
\(518\) | −1.77810e18 | −4.04402 | ||||||||
\(519\) | −4.73248e16 | −0.106292 | ||||||||
\(520\) | −9.01035e16 | −0.199857 | ||||||||
\(521\) | −3.15331e17 | −0.690751 | −0.345376 | − | 0.938465i | \(-0.612248\pi\) | ||||
−0.345376 | + | 0.938465i | \(0.612248\pi\) | |||||||
\(522\) | −2.62901e16 | −0.0568767 | ||||||||
\(523\) | −7.00011e17 | −1.49570 | −0.747849 | − | 0.663869i | \(-0.768913\pi\) | ||||
−0.747849 | + | 0.663869i | \(0.768913\pi\) | |||||||
\(524\) | 1.64929e18 | 3.48052 | ||||||||
\(525\) | −5.18726e17 | −1.08119 | ||||||||
\(526\) | 4.64817e17 | 0.956917 | ||||||||
\(527\) | 8.09104e16 | 0.164526 | ||||||||
\(528\) | 1.48390e17 | 0.298046 | ||||||||
\(529\) | −4.97871e17 | −0.987768 | ||||||||
\(530\) | 8.13908e16 | 0.159508 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | 2.45311e18 | 4.69128 | ||||||||
\(533\) | 7.49582e17 | 1.41609 | ||||||||
\(534\) | −4.59587e17 | −0.857727 | ||||||||
\(535\) | 1.77678e16 | 0.0327592 | ||||||||
\(536\) | 4.17474e17 | 0.760428 | ||||||||
\(537\) | 1.56149e17 | 0.281000 | ||||||||
\(538\) | −7.56418e17 | −1.34486 | ||||||||
\(539\) | 1.36214e18 | 2.39274 | ||||||||
\(540\) | −2.18294e16 | −0.0378863 | ||||||||
\(541\) | 1.10711e18 | 1.89849 | 0.949243 | − | 0.314543i | \(-0.101851\pi\) | ||||
0.949243 | + | 0.314543i | \(0.101851\pi\) | |||||||
\(542\) | −6.74740e17 | −1.14325 | ||||||||
\(543\) | −3.68363e17 | −0.616705 | ||||||||
\(544\) | 3.22411e16 | 0.0533356 | ||||||||
\(545\) | −6.43153e16 | −0.105132 | ||||||||
\(546\) | 1.50103e18 | 2.42459 | ||||||||
\(547\) | 1.04012e18 | 1.66022 | 0.830112 | − | 0.557597i | \(-0.188277\pi\) | ||||
0.830112 | + | 0.557597i | \(0.188277\pi\) | |||||||
\(548\) | 1.04706e18 | 1.65158 | ||||||||
\(549\) | −1.09714e17 | −0.171019 | ||||||||
\(550\) | −1.00071e18 | −1.54152 | ||||||||
\(551\) | −8.92135e16 | −0.135814 | ||||||||
\(552\) | −6.04721e16 | −0.0909810 | ||||||||
\(553\) | 8.46172e17 | 1.25819 | ||||||||
\(554\) | 4.06003e17 | 0.596645 | ||||||||
\(555\) | 5.36931e16 | 0.0779855 | ||||||||
\(556\) | −1.28798e18 | −1.84894 | ||||||||
\(557\) | −6.27117e17 | −0.889794 | −0.444897 | − | 0.895582i | \(-0.646760\pi\) | ||||
−0.444897 | + | 0.895582i | \(0.646760\pi\) | |||||||
\(558\) | −5.97299e17 | −0.837664 | ||||||||
\(559\) | 3.00891e17 | 0.417092 | ||||||||
\(560\) | −8.23807e16 | −0.112876 | ||||||||
\(561\) | −4.35177e16 | −0.0589396 | ||||||||
\(562\) | 2.10358e18 | 2.81626 | ||||||||
\(563\) | 2.96789e17 | 0.392775 | 0.196388 | − | 0.980526i | \(-0.437079\pi\) | ||||
0.196388 | + | 0.980526i | \(0.437079\pi\) | |||||||
\(564\) | −1.17747e18 | −1.54041 | ||||||||
\(565\) | 3.19366e16 | 0.0413022 | ||||||||
\(566\) | 1.50778e18 | 1.92766 | ||||||||
\(567\) | 1.66527e17 | 0.210472 | ||||||||
\(568\) | 9.79415e17 | 1.22378 | ||||||||
\(569\) | 6.18879e17 | 0.764497 | 0.382248 | − | 0.924060i | \(-0.375150\pi\) | ||||
0.382248 | + | 0.924060i | \(0.375150\pi\) | |||||||
\(570\) | −1.14231e17 | −0.139508 | ||||||||
\(571\) | 2.66375e17 | 0.321632 | 0.160816 | − | 0.986984i | \(-0.448588\pi\) | ||||
0.160816 | + | 0.986984i | \(0.448588\pi\) | |||||||
\(572\) | 1.87782e18 | 2.24171 | ||||||||
\(573\) | 2.35965e16 | 0.0278511 | ||||||||
\(574\) | 2.94946e18 | 3.44204 | ||||||||
\(575\) | 9.47585e16 | 0.109340 | ||||||||
\(576\) | −4.01154e17 | −0.457684 | ||||||||
\(577\) | −1.03017e18 | −1.16216 | −0.581081 | − | 0.813846i | \(-0.697370\pi\) | ||||
−0.581081 | + | 0.813846i | \(0.697370\pi\) | |||||||
\(578\) | −1.49357e18 | −1.66608 | ||||||||
\(579\) | −6.47528e17 | −0.714246 | ||||||||
\(580\) | 1.82591e16 | 0.0199157 | ||||||||
\(581\) | 1.56766e18 | 1.69086 | ||||||||
\(582\) | −9.44814e17 | −1.00774 | ||||||||
\(583\) | −7.76752e17 | −0.819288 | ||||||||
\(584\) | −1.34037e18 | −1.39811 | ||||||||
\(585\) | −4.53264e16 | −0.0467561 | ||||||||
\(586\) | −1.37325e18 | −1.40092 | ||||||||
\(587\) | 4.28882e17 | 0.432703 | 0.216352 | − | 0.976315i | \(-0.430584\pi\) | ||||
0.216352 | + | 0.976315i | \(0.430584\pi\) | |||||||
\(588\) | 2.76267e18 | 2.75662 | ||||||||
\(589\) | −2.02689e18 | −2.00023 | ||||||||
\(590\) | 2.40081e16 | 0.0234326 | ||||||||
\(591\) | 5.23830e17 | 0.505675 | ||||||||
\(592\) | −7.40264e17 | −0.706798 | ||||||||
\(593\) | 1.50466e18 | 1.42097 | 0.710484 | − | 0.703713i | \(-0.248476\pi\) | ||||
0.710484 | + | 0.703713i | \(0.248476\pi\) | |||||||
\(594\) | 3.21258e17 | 0.300083 | ||||||||
\(595\) | 2.41595e16 | 0.0223217 | ||||||||
\(596\) | 1.80865e18 | 1.65293 | ||||||||
\(597\) | −4.55463e17 | −0.411737 | ||||||||
\(598\) | −2.74201e17 | −0.245195 | ||||||||
\(599\) | −1.65999e18 | −1.46835 | −0.734177 | − | 0.678958i | \(-0.762432\pi\) | ||||
−0.734177 | + | 0.678958i | \(0.762432\pi\) | |||||||
\(600\) | −9.29412e17 | −0.813252 | ||||||||
\(601\) | 1.36382e18 | 1.18052 | 0.590261 | − | 0.807213i | \(-0.299025\pi\) | ||||
0.590261 | + | 0.807213i | \(0.299025\pi\) | |||||||
\(602\) | 1.18395e18 | 1.01381 | ||||||||
\(603\) | 2.10010e17 | 0.177900 | ||||||||
\(604\) | −1.69723e18 | −1.42233 | ||||||||
\(605\) | 1.87058e16 | 0.0155083 | ||||||||
\(606\) | 5.96482e17 | 0.489244 | ||||||||
\(607\) | −9.40198e17 | −0.762944 | −0.381472 | − | 0.924380i | \(-0.624583\pi\) | ||||
−0.381472 | + | 0.924380i | \(0.624583\pi\) | |||||||
\(608\) | −8.07673e17 | −0.648429 | ||||||||
\(609\) | −1.39291e17 | −0.110639 | ||||||||
\(610\) | 1.17504e17 | 0.0923443 | ||||||||
\(611\) | −2.44490e18 | −1.90105 | ||||||||
\(612\) | −8.82617e16 | −0.0679028 | ||||||||
\(613\) | −1.67828e18 | −1.27753 | −0.638765 | − | 0.769402i | \(-0.720555\pi\) | ||||
−0.638765 | + | 0.769402i | \(0.720555\pi\) | |||||||
\(614\) | −2.29846e18 | −1.73118 | ||||||||
\(615\) | −8.90645e16 | −0.0663768 | ||||||||
\(616\) | 3.38355e18 | 2.49516 | ||||||||
\(617\) | −2.35454e18 | −1.71812 | −0.859059 | − | 0.511876i | \(-0.828951\pi\) | ||||
−0.859059 | + | 0.511876i | \(0.828951\pi\) | |||||||
\(618\) | 6.64161e16 | 0.0479566 | ||||||||
\(619\) | 1.89405e18 | 1.35332 | 0.676662 | − | 0.736294i | \(-0.263426\pi\) | ||||
0.676662 | + | 0.736294i | \(0.263426\pi\) | |||||||
\(620\) | 4.14837e17 | 0.293313 | ||||||||
\(621\) | −3.04204e16 | −0.0212848 | ||||||||
\(622\) | −1.65562e18 | −1.14636 | ||||||||
\(623\) | −2.43499e18 | −1.66849 | ||||||||
\(624\) | 6.24913e17 | 0.423760 | ||||||||
\(625\) | 1.43940e18 | 0.965966 | ||||||||
\(626\) | 1.61610e18 | 1.07334 | ||||||||
\(627\) | 1.09016e18 | 0.716560 | ||||||||
\(628\) | −7.17159e16 | −0.0466528 | ||||||||
\(629\) | 2.17095e17 | 0.139772 | ||||||||
\(630\) | −1.78351e17 | −0.113648 | ||||||||
\(631\) | −2.34490e18 | −1.47888 | −0.739440 | − | 0.673223i | \(-0.764910\pi\) | ||||
−0.739440 | + | 0.673223i | \(0.764910\pi\) | |||||||
\(632\) | 1.51610e18 | 0.946386 | ||||||||
\(633\) | 1.47402e18 | 0.910710 | ||||||||
\(634\) | 5.39658e18 | 3.30019 | ||||||||
\(635\) | −3.33393e16 | −0.0201803 | ||||||||
\(636\) | −1.57539e18 | −0.943881 | ||||||||
\(637\) | 5.73639e18 | 3.40199 | ||||||||
\(638\) | −2.68714e17 | −0.157745 | ||||||||
\(639\) | 4.92694e17 | 0.286300 | ||||||||
\(640\) | 3.40031e17 | 0.195591 | ||||||||
\(641\) | −2.94203e17 | −0.167521 | −0.0837606 | − | 0.996486i | \(-0.526693\pi\) | ||||
−0.0837606 | + | 0.996486i | \(0.526693\pi\) | |||||||
\(642\) | −5.30336e17 | −0.298933 | ||||||||
\(643\) | 1.10539e18 | 0.616801 | 0.308400 | − | 0.951257i | \(-0.400206\pi\) | ||||
0.308400 | + | 0.951257i | \(0.400206\pi\) | |||||||
\(644\) | −6.99662e17 | −0.386483 | ||||||||
\(645\) | −3.57516e16 | −0.0195505 | ||||||||
\(646\) | −4.61865e17 | −0.250037 | ||||||||
\(647\) | −2.06742e18 | −1.10803 | −0.554013 | − | 0.832508i | \(-0.686904\pi\) | ||||
−0.554013 | + | 0.832508i | \(0.686904\pi\) | |||||||
\(648\) | 2.98370e17 | 0.158313 | ||||||||
\(649\) | −2.29121e17 | −0.120358 | ||||||||
\(650\) | −4.21428e18 | −2.19173 | ||||||||
\(651\) | −3.16461e18 | −1.62946 | ||||||||
\(652\) | −4.74317e18 | −2.41802 | ||||||||
\(653\) | 1.93951e18 | 0.978940 | 0.489470 | − | 0.872020i | \(-0.337190\pi\) | ||||
0.489470 | + | 0.872020i | \(0.337190\pi\) | |||||||
\(654\) | 1.91970e18 | 0.959350 | ||||||||
\(655\) | −4.06906e17 | −0.201338 | ||||||||
\(656\) | 1.22793e18 | 0.601586 | ||||||||
\(657\) | −6.74272e17 | −0.327085 | ||||||||
\(658\) | −9.62022e18 | −4.62080 | ||||||||
\(659\) | 1.27523e18 | 0.606505 | 0.303253 | − | 0.952910i | \(-0.401927\pi\) | ||||
0.303253 | + | 0.952910i | \(0.401927\pi\) | |||||||
\(660\) | −2.23120e17 | −0.105076 | ||||||||
\(661\) | −2.10805e18 | −0.983042 | −0.491521 | − | 0.870866i | \(-0.663559\pi\) | ||||
−0.491521 | + | 0.870866i | \(0.663559\pi\) | |||||||
\(662\) | 1.57847e18 | 0.728887 | ||||||||
\(663\) | −1.83266e17 | −0.0838001 | ||||||||
\(664\) | 2.80881e18 | 1.27183 | ||||||||
\(665\) | −6.05220e17 | −0.271377 | ||||||||
\(666\) | −1.60264e18 | −0.711630 | ||||||||
\(667\) | 2.54450e16 | 0.0111888 | ||||||||
\(668\) | 3.30280e18 | 1.43825 | ||||||||
\(669\) | −2.07403e18 | −0.894428 | ||||||||
\(670\) | −2.24921e17 | −0.0960602 | ||||||||
\(671\) | −1.12140e18 | −0.474313 | ||||||||
\(672\) | −1.26103e18 | −0.528234 | ||||||||
\(673\) | 2.24879e18 | 0.932933 | 0.466467 | − | 0.884539i | \(-0.345527\pi\) | ||||
0.466467 | + | 0.884539i | \(0.345527\pi\) | |||||||
\(674\) | −8.53829e17 | −0.350818 | ||||||||
\(675\) | −4.67540e17 | −0.190258 | ||||||||
\(676\) | 3.33091e18 | 1.34248 | ||||||||
\(677\) | 3.03040e18 | 1.20969 | 0.604844 | − | 0.796344i | \(-0.293236\pi\) | ||||
0.604844 | + | 0.796344i | \(0.293236\pi\) | |||||||
\(678\) | −9.53250e17 | −0.376889 | ||||||||
\(679\) | −5.00582e18 | −1.96030 | ||||||||
\(680\) | 4.32871e16 | 0.0167900 | ||||||||
\(681\) | 1.34577e17 | 0.0517030 | ||||||||
\(682\) | −6.10506e18 | −2.32322 | ||||||||
\(683\) | −1.63290e18 | −0.615494 | −0.307747 | − | 0.951468i | \(-0.599575\pi\) | ||||
−0.307747 | + | 0.951468i | \(0.599575\pi\) | |||||||
\(684\) | 2.21104e18 | 0.825530 | ||||||||
\(685\) | −2.58326e17 | −0.0955389 | ||||||||
\(686\) | 1.38506e19 | 5.07413 | ||||||||
\(687\) | −9.47669e17 | −0.343904 | ||||||||
\(688\) | 4.92905e17 | 0.177190 | ||||||||
\(689\) | −3.27114e18 | −1.16486 | ||||||||
\(690\) | 3.25803e16 | 0.0114931 | ||||||||
\(691\) | −9.29015e16 | −0.0324650 | −0.0162325 | − | 0.999868i | \(-0.505167\pi\) | ||||
−0.0162325 | + | 0.999868i | \(0.505167\pi\) | |||||||
\(692\) | −9.81053e17 | −0.339627 | ||||||||
\(693\) | 1.70209e18 | 0.583736 | ||||||||
\(694\) | 7.61714e18 | 2.58795 | ||||||||
\(695\) | 3.17764e17 | 0.106956 | ||||||||
\(696\) | −2.49570e17 | −0.0832208 | ||||||||
\(697\) | −3.60110e17 | −0.118966 | ||||||||
\(698\) | 7.82657e18 | 2.56160 | ||||||||
\(699\) | −3.27692e18 | −1.06259 | ||||||||
\(700\) | −1.07533e19 | −3.45466 | ||||||||
\(701\) | 1.37308e17 | 0.0437046 | 0.0218523 | − | 0.999761i | \(-0.493044\pi\) | ||||
0.0218523 | + | 0.999761i | \(0.493044\pi\) | |||||||
\(702\) | 1.35291e18 | 0.426657 | ||||||||
\(703\) | −5.43844e18 | −1.69928 | ||||||||
\(704\) | −4.10024e18 | −1.26937 | ||||||||
\(705\) | 2.90501e17 | 0.0891082 | ||||||||
\(706\) | −7.59869e18 | −2.30945 | ||||||||
\(707\) | 3.16028e18 | 0.951700 | ||||||||
\(708\) | −4.64698e17 | −0.138661 | ||||||||
\(709\) | −1.89261e18 | −0.559577 | −0.279788 | − | 0.960062i | \(-0.590264\pi\) | ||||
−0.279788 | + | 0.960062i | \(0.590264\pi\) | |||||||
\(710\) | −5.27676e17 | −0.154592 | ||||||||
\(711\) | 7.62675e17 | 0.221405 | ||||||||
\(712\) | −4.36281e18 | −1.25501 | ||||||||
\(713\) | 5.78097e17 | 0.164785 | ||||||||
\(714\) | −7.21118e17 | −0.203689 | ||||||||
\(715\) | −4.63286e17 | −0.129676 | ||||||||
\(716\) | 3.23700e18 | 0.897858 | ||||||||
\(717\) | 2.26579e18 | 0.622794 | ||||||||
\(718\) | −6.51748e15 | −0.00177530 | ||||||||
\(719\) | 4.89899e18 | 1.32242 | 0.661209 | − | 0.750202i | \(-0.270044\pi\) | ||||
0.661209 | + | 0.750202i | \(0.270044\pi\) | |||||||
\(720\) | −7.42516e16 | −0.0198630 | ||||||||
\(721\) | 3.51886e17 | 0.0932874 | ||||||||
\(722\) | 5.15048e18 | 1.35318 | ||||||||
\(723\) | 1.44722e18 | 0.376821 | ||||||||
\(724\) | −7.63625e18 | −1.97051 | ||||||||
\(725\) | 3.91071e17 | 0.100013 | ||||||||
\(726\) | −5.58333e17 | −0.141516 | ||||||||
\(727\) | 2.01727e18 | 0.506746 | 0.253373 | − | 0.967369i | \(-0.418460\pi\) | ||||
0.253373 | + | 0.967369i | \(0.418460\pi\) | |||||||
\(728\) | 1.42491e19 | 3.54760 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 7.22147e17 | 0.176615 | ||||||||
\(731\) | −1.44553e17 | −0.0350399 | ||||||||
\(732\) | −2.27440e18 | −0.546444 | ||||||||
\(733\) | 7.91301e18 | 1.88437 | 0.942184 | − | 0.335095i | \(-0.108768\pi\) | ||||
0.942184 | + | 0.335095i | \(0.108768\pi\) | |||||||
\(734\) | 8.15373e18 | 1.92456 | ||||||||
\(735\) | −6.81593e17 | −0.159462 | ||||||||
\(736\) | 2.30360e17 | 0.0534197 | ||||||||
\(737\) | 2.14653e18 | 0.493399 | ||||||||
\(738\) | 2.65842e18 | 0.605699 | ||||||||
\(739\) | −3.52219e18 | −0.795470 | −0.397735 | − | 0.917500i | \(-0.630204\pi\) | ||||
−0.397735 | + | 0.917500i | \(0.630204\pi\) | |||||||
\(740\) | 1.11307e18 | 0.249182 | ||||||||
\(741\) | 4.59100e18 | 1.01880 | ||||||||
\(742\) | −1.28713e19 | −2.83137 | ||||||||
\(743\) | 6.44962e18 | 1.40639 | 0.703196 | − | 0.710996i | \(-0.251755\pi\) | ||||
0.703196 | + | 0.710996i | \(0.251755\pi\) | |||||||
\(744\) | −5.67010e18 | −1.22565 | ||||||||
\(745\) | −4.46222e17 | −0.0956170 | ||||||||
\(746\) | 1.34158e19 | 2.84980 | ||||||||
\(747\) | 1.41297e18 | 0.297542 | ||||||||
\(748\) | −9.02132e17 | −0.188326 | ||||||||
\(749\) | −2.80983e18 | −0.581498 | ||||||||
\(750\) | 1.00724e18 | 0.206650 | ||||||||
\(751\) | −1.56414e18 | −0.318139 | −0.159070 | − | 0.987267i | \(-0.550849\pi\) | ||||
−0.159070 | + | 0.987267i | \(0.550849\pi\) | |||||||
\(752\) | −4.00512e18 | −0.807606 | ||||||||
\(753\) | −5.24819e18 | −1.04916 | ||||||||
\(754\) | −1.13164e18 | −0.224281 | ||||||||
\(755\) | 4.18733e17 | 0.0822778 | ||||||||
\(756\) | 3.45214e18 | 0.672507 | ||||||||
\(757\) | −9.31417e18 | −1.79896 | −0.899478 | − | 0.436965i | \(-0.856053\pi\) | ||||
−0.899478 | + | 0.436965i | \(0.856053\pi\) | |||||||
\(758\) | −1.26430e19 | −2.42103 | ||||||||
\(759\) | −3.10930e17 | −0.0590325 | ||||||||
\(760\) | −1.08438e18 | −0.204125 | ||||||||
\(761\) | −3.18294e18 | −0.594057 | −0.297029 | − | 0.954869i | \(-0.595996\pi\) | ||||
−0.297029 | + | 0.954869i | \(0.595996\pi\) | |||||||
\(762\) | 9.95120e17 | 0.184148 | ||||||||
\(763\) | 1.01709e19 | 1.86617 | ||||||||
\(764\) | 4.89160e17 | 0.0889905 | ||||||||
\(765\) | 2.17755e16 | 0.00392798 | ||||||||
\(766\) | 1.63060e19 | 2.91648 | ||||||||
\(767\) | −9.64897e17 | −0.171124 | ||||||||
\(768\) | −5.64141e18 | −0.992064 | ||||||||
\(769\) | 9.15451e18 | 1.59630 | 0.798149 | − | 0.602460i | \(-0.205813\pi\) | ||||
0.798149 | + | 0.602460i | \(0.205813\pi\) | |||||||
\(770\) | −1.82294e18 | −0.315198 | ||||||||
\(771\) | 4.57450e18 | 0.784314 | ||||||||
\(772\) | −1.34234e19 | −2.28218 | ||||||||
\(773\) | 2.02144e18 | 0.340796 | 0.170398 | − | 0.985375i | \(-0.445495\pi\) | ||||
0.170398 | + | 0.985375i | \(0.445495\pi\) | |||||||
\(774\) | 1.06712e18 | 0.178401 | ||||||||
\(775\) | 8.88494e18 | 1.47297 | ||||||||
\(776\) | −8.96903e18 | −1.47450 | ||||||||
\(777\) | −8.49113e18 | −1.38430 | ||||||||
\(778\) | 2.67322e18 | 0.432183 | ||||||||
\(779\) | 9.02113e18 | 1.44633 | ||||||||
\(780\) | −9.39627e17 | −0.149397 | ||||||||
\(781\) | 5.03587e18 | 0.794041 | ||||||||
\(782\) | 1.31731e17 | 0.0205988 | ||||||||
\(783\) | −1.25546e17 | −0.0194693 | ||||||||
\(784\) | 9.39708e18 | 1.44524 | ||||||||
\(785\) | 1.76934e16 | 0.00269872 | ||||||||
\(786\) | 1.21454e19 | 1.83724 | ||||||||
\(787\) | −9.55199e17 | −0.143304 | −0.0716520 | − | 0.997430i | \(-0.522827\pi\) | ||||
−0.0716520 | + | 0.997430i | \(0.522827\pi\) | |||||||
\(788\) | 1.08591e19 | 1.61575 | ||||||||
\(789\) | 2.21968e18 | 0.327560 | ||||||||
\(790\) | −8.16827e17 | −0.119551 | ||||||||
\(791\) | −5.05051e18 | −0.733142 | ||||||||
\(792\) | 3.04967e18 | 0.439075 | ||||||||
\(793\) | −4.72256e18 | −0.674376 | ||||||||
\(794\) | −3.93351e18 | −0.557118 | ||||||||
\(795\) | 3.88673e17 | 0.0546007 | ||||||||
\(796\) | −9.44184e18 | −1.31559 | ||||||||
\(797\) | 2.63426e18 | 0.364065 | 0.182032 | − | 0.983293i | \(-0.441732\pi\) | ||||
0.182032 | + | 0.983293i | \(0.441732\pi\) | |||||||
\(798\) | 1.80647e19 | 2.47635 | ||||||||
\(799\) | 1.17457e18 | 0.159707 | ||||||||
\(800\) | 3.54047e18 | 0.477503 | ||||||||
\(801\) | −2.19471e18 | −0.293606 | ||||||||
\(802\) | −3.05628e18 | −0.405564 | ||||||||
\(803\) | −6.89180e18 | −0.907155 | ||||||||
\(804\) | 4.35354e18 | 0.568432 | ||||||||
\(805\) | 1.72617e17 | 0.0223569 | ||||||||
\(806\) | −2.57102e19 | −3.30315 | ||||||||
\(807\) | −3.61220e18 | −0.460355 | ||||||||
\(808\) | 5.66235e18 | 0.715851 | ||||||||
\(809\) | −1.15455e19 | −1.44793 | −0.723964 | − | 0.689838i | \(-0.757682\pi\) | ||||
−0.723964 | + | 0.689838i | \(0.757682\pi\) | |||||||
\(810\) | −1.60752e17 | −0.0199988 | ||||||||
\(811\) | 6.67328e18 | 0.823577 | 0.411788 | − | 0.911280i | \(-0.364904\pi\) | ||||
0.411788 | + | 0.911280i | \(0.364904\pi\) | |||||||
\(812\) | −2.88752e18 | −0.353518 | ||||||||
\(813\) | −3.22215e18 | −0.391342 | ||||||||
\(814\) | −1.63808e19 | −1.97368 | ||||||||
\(815\) | 1.17021e18 | 0.139875 | ||||||||
\(816\) | −3.00218e17 | −0.0356000 | ||||||||
\(817\) | 3.62119e18 | 0.425998 | ||||||||
\(818\) | 6.77995e18 | 0.791279 | ||||||||
\(819\) | 7.16801e18 | 0.829953 | ||||||||
\(820\) | −1.84633e18 | −0.212089 | ||||||||
\(821\) | 8.25197e18 | 0.940432 | 0.470216 | − | 0.882551i | \(-0.344176\pi\) | ||||
0.470216 | + | 0.882551i | \(0.344176\pi\) | |||||||
\(822\) | 7.71058e18 | 0.871807 | ||||||||
\(823\) | 3.25044e18 | 0.364622 | 0.182311 | − | 0.983241i | \(-0.441642\pi\) | ||||
0.182311 | + | 0.983241i | \(0.441642\pi\) | |||||||
\(824\) | 6.30482e17 | 0.0701691 | ||||||||
\(825\) | −4.77877e18 | −0.527674 | ||||||||
\(826\) | −3.79669e18 | −0.415944 | ||||||||
\(827\) | 3.22113e18 | 0.350125 | 0.175062 | − | 0.984557i | \(-0.443987\pi\) | ||||
0.175062 | + | 0.984557i | \(0.443987\pi\) | |||||||
\(828\) | −6.30621e17 | −0.0680098 | ||||||||
\(829\) | 2.07018e18 | 0.221515 | 0.110758 | − | 0.993847i | \(-0.464672\pi\) | ||||
0.110758 | + | 0.993847i | \(0.464672\pi\) | |||||||
\(830\) | −1.51329e18 | −0.160663 | ||||||||
\(831\) | 1.93883e18 | 0.204236 | ||||||||
\(832\) | −1.72673e19 | −1.80478 | ||||||||
\(833\) | −2.75585e18 | −0.285801 | ||||||||
\(834\) | −9.48470e18 | −0.975988 | ||||||||
\(835\) | −8.14851e17 | −0.0831986 | ||||||||
\(836\) | 2.25993e19 | 2.28957 | ||||||||
\(837\) | −2.85234e18 | −0.286738 | ||||||||
\(838\) | −2.92716e19 | −2.91985 | ||||||||
\(839\) | 3.34739e18 | 0.331324 | 0.165662 | − | 0.986183i | \(-0.447024\pi\) | ||||
0.165662 | + | 0.986183i | \(0.447024\pi\) | |||||||
\(840\) | −1.69307e18 | −0.166287 | ||||||||
\(841\) | −1.01556e19 | −0.989766 | ||||||||
\(842\) | 1.36858e19 | 1.32356 | ||||||||
\(843\) | 1.00454e19 | 0.964027 | ||||||||
\(844\) | 3.05568e19 | 2.90993 | ||||||||
\(845\) | −8.21785e17 | −0.0776586 | ||||||||
\(846\) | −8.67092e18 | −0.813126 | ||||||||
\(847\) | −2.95817e18 | −0.275284 | ||||||||
\(848\) | −5.35862e18 | −0.494857 | ||||||||
\(849\) | 7.20023e18 | 0.659852 | ||||||||
\(850\) | 2.02460e18 | 0.184127 | ||||||||
\(851\) | 1.55112e18 | 0.139992 | ||||||||
\(852\) | 1.02136e19 | 0.914794 | ||||||||
\(853\) | 2.19915e19 | 1.95473 | 0.977363 | − | 0.211571i | \(-0.0678580\pi\) | ||||
0.977363 | + | 0.211571i | \(0.0678580\pi\) | |||||||
\(854\) | −1.85824e19 | −1.63917 | ||||||||
\(855\) | −5.45498e17 | −0.0477544 | ||||||||
\(856\) | −5.03443e18 | −0.437392 | ||||||||
\(857\) | −1.22000e19 | −1.05192 | −0.525962 | − | 0.850508i | \(-0.676294\pi\) | ||||
−0.525962 | + | 0.850508i | \(0.676294\pi\) | |||||||
\(858\) | 1.38283e19 | 1.18331 | ||||||||
\(859\) | −5.56749e18 | −0.472829 | −0.236414 | − | 0.971652i | \(-0.575972\pi\) | ||||
−0.236414 | + | 0.971652i | \(0.575972\pi\) | |||||||
\(860\) | −7.41137e17 | −0.0624682 | ||||||||
\(861\) | 1.40848e19 | 1.17823 | ||||||||
\(862\) | −6.71515e18 | −0.557517 | ||||||||
\(863\) | 2.53657e17 | 0.0209015 | 0.0104507 | − | 0.999945i | \(-0.496673\pi\) | ||||
0.0104507 | + | 0.999945i | \(0.496673\pi\) | |||||||
\(864\) | −1.13660e18 | −0.0929540 | ||||||||
\(865\) | 2.42041e17 | 0.0196464 | ||||||||
\(866\) | −2.58813e19 | −2.08506 | ||||||||
\(867\) | −7.13239e18 | −0.570310 | ||||||||
\(868\) | −6.56031e19 | −5.20651 | ||||||||
\(869\) | 7.79537e18 | 0.614057 | ||||||||
\(870\) | 1.34460e17 | 0.0105128 | ||||||||
\(871\) | 9.03968e18 | 0.701512 | ||||||||
\(872\) | 1.82235e19 | 1.40370 | ||||||||
\(873\) | −4.51186e18 | −0.344956 | ||||||||
\(874\) | −3.29998e18 | −0.250431 | ||||||||
\(875\) | 5.33657e18 | 0.401985 | ||||||||
\(876\) | −1.39778e19 | −1.04511 | ||||||||
\(877\) | −7.95224e18 | −0.590191 | −0.295095 | − | 0.955468i | \(-0.595351\pi\) | ||||
−0.295095 | + | 0.955468i | \(0.595351\pi\) | |||||||
\(878\) | −1.16137e19 | −0.855570 | ||||||||
\(879\) | −6.55780e18 | −0.479546 | ||||||||
\(880\) | −7.58933e17 | −0.0550891 | ||||||||
\(881\) | 2.23727e19 | 1.61203 | 0.806017 | − | 0.591892i | \(-0.201619\pi\) | ||||
0.806017 | + | 0.591892i | \(0.201619\pi\) | |||||||
\(882\) | 2.03443e19 | 1.45512 | ||||||||
\(883\) | −7.26839e18 | −0.516052 | −0.258026 | − | 0.966138i | \(-0.583072\pi\) | ||||
−0.258026 | + | 0.966138i | \(0.583072\pi\) | |||||||
\(884\) | −3.79915e18 | −0.267761 | ||||||||
\(885\) | 1.14648e17 | 0.00802113 | ||||||||
\(886\) | −2.06131e19 | −1.43161 | ||||||||
\(887\) | −1.76105e19 | −1.21414 | −0.607068 | − | 0.794650i | \(-0.707654\pi\) | ||||
−0.607068 | + | 0.794650i | \(0.707654\pi\) | |||||||
\(888\) | −1.52137e19 | −1.04124 | ||||||||
\(889\) | 5.27235e18 | 0.358214 | ||||||||
\(890\) | 2.35054e18 | 0.158538 | ||||||||
\(891\) | 1.53413e18 | 0.102721 | ||||||||
\(892\) | −4.29951e19 | −2.85790 | ||||||||
\(893\) | −2.94241e19 | −1.94164 | ||||||||
\(894\) | 1.33189e19 | 0.872520 | ||||||||
\(895\) | −7.98617e17 | −0.0519384 | ||||||||
\(896\) | −5.37731e19 | −3.47187 | ||||||||
\(897\) | −1.30942e18 | −0.0839321 | ||||||||
\(898\) | −4.47356e19 | −2.84680 | ||||||||
\(899\) | 2.38582e18 | 0.150730 | ||||||||
\(900\) | −9.69220e18 | −0.607920 | ||||||||
\(901\) | 1.57150e18 | 0.0978598 | ||||||||
\(902\) | 2.71720e19 | 1.67988 | ||||||||
\(903\) | 5.65382e18 | 0.347034 | ||||||||
\(904\) | −9.04911e18 | −0.551456 | ||||||||
\(905\) | 1.88398e18 | 0.113988 | ||||||||
\(906\) | −1.24984e19 | −0.750797 | ||||||||
\(907\) | 4.16084e18 | 0.248161 | 0.124081 | − | 0.992272i | \(-0.460402\pi\) | ||||
0.124081 | + | 0.992272i | \(0.460402\pi\) | |||||||
\(908\) | 2.78982e18 | 0.165203 | ||||||||
\(909\) | 2.84844e18 | 0.167472 | ||||||||
\(910\) | −7.67696e18 | −0.448147 | ||||||||
\(911\) | −1.26272e19 | −0.731877 | −0.365938 | − | 0.930639i | \(-0.619252\pi\) | ||||
−0.365938 | + | 0.930639i | \(0.619252\pi\) | |||||||
\(912\) | 7.52076e18 | 0.432808 | ||||||||
\(913\) | 1.44421e19 | 0.825221 | ||||||||
\(914\) | −1.92126e19 | −1.09002 | ||||||||
\(915\) | 5.61130e17 | 0.0316101 | ||||||||
\(916\) | −1.96454e19 | −1.09885 | ||||||||
\(917\) | 6.43489e19 | 3.57388 | ||||||||
\(918\) | −6.49960e17 | −0.0358434 | ||||||||
\(919\) | 2.11333e19 | 1.15722 | 0.578611 | − | 0.815604i | \(-0.303595\pi\) | ||||
0.578611 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(920\) | 3.09282e17 | 0.0168164 | ||||||||
\(921\) | −1.09761e19 | −0.592597 | ||||||||
\(922\) | 5.61121e18 | 0.300819 | ||||||||
\(923\) | 2.12076e19 | 1.12896 | ||||||||
\(924\) | 3.52847e19 | 1.86517 | ||||||||
\(925\) | 2.38396e19 | 1.25135 | ||||||||
\(926\) | −2.75026e19 | −1.43352 | ||||||||
\(927\) | 3.17163e17 | 0.0164159 | ||||||||
\(928\) | 9.50701e17 | 0.0488632 | ||||||||
\(929\) | 8.38667e18 | 0.428043 | 0.214022 | − | 0.976829i | \(-0.431344\pi\) | ||||
0.214022 | + | 0.976829i | \(0.431344\pi\) | |||||||
\(930\) | 3.05486e18 | 0.154829 | ||||||||
\(931\) | 6.90368e19 | 3.47463 | ||||||||
\(932\) | −6.79313e19 | −3.39521 | ||||||||
\(933\) | −7.90623e18 | −0.392409 | ||||||||
\(934\) | −5.11876e17 | −0.0252296 | ||||||||
\(935\) | 2.22570e17 | 0.0108941 | ||||||||
\(936\) | 1.28431e19 | 0.624275 | ||||||||
\(937\) | 2.76916e19 | 1.33672 | 0.668359 | − | 0.743839i | \(-0.266997\pi\) | ||||
0.668359 | + | 0.743839i | \(0.266997\pi\) | |||||||
\(938\) | 3.55694e19 | 1.70513 | ||||||||
\(939\) | 7.71754e18 | 0.367411 | ||||||||
\(940\) | 6.02214e18 | 0.284721 | ||||||||
\(941\) | 3.92882e19 | 1.84472 | 0.922358 | − | 0.386337i | \(-0.126260\pi\) | ||||
0.922358 | + | 0.386337i | \(0.126260\pi\) | |||||||
\(942\) | −5.28116e17 | −0.0246263 | ||||||||
\(943\) | −2.57295e18 | −0.119153 | ||||||||
\(944\) | −1.58065e18 | −0.0726971 | ||||||||
\(945\) | −8.51696e17 | −0.0389025 | ||||||||
\(946\) | 1.09071e19 | 0.494787 | ||||||||
\(947\) | 3.81184e19 | 1.71735 | 0.858677 | − | 0.512517i | \(-0.171287\pi\) | ||||
0.858677 | + | 0.512517i | \(0.171287\pi\) | |||||||
\(948\) | 1.58104e19 | 0.707439 | ||||||||
\(949\) | −2.90235e19 | −1.28979 | ||||||||
\(950\) | −5.07184e19 | −2.23852 | ||||||||
\(951\) | 2.57708e19 | 1.12968 | ||||||||
\(952\) | −6.84550e18 | −0.298034 | ||||||||
\(953\) | 3.75528e19 | 1.62382 | 0.811912 | − | 0.583780i | \(-0.198427\pi\) | ||||
0.811912 | + | 0.583780i | \(0.198427\pi\) | |||||||
\(954\) | −1.16012e19 | −0.498240 | ||||||||
\(955\) | −1.20683e17 | −0.00514784 | ||||||||
\(956\) | 4.69702e19 | 1.98997 | ||||||||
\(957\) | −1.28322e18 | −0.0539973 | ||||||||
\(958\) | −5.25939e19 | −2.19816 | ||||||||
\(959\) | 4.08523e19 | 1.69588 | ||||||||
\(960\) | 2.05169e18 | 0.0845957 | ||||||||
\(961\) | 2.97872e19 | 1.21991 | ||||||||
\(962\) | −6.89844e19 | −2.80616 | ||||||||
\(963\) | −2.53256e18 | −0.102327 | ||||||||
\(964\) | 3.00011e19 | 1.20403 | ||||||||
\(965\) | 3.31176e18 | 0.132017 | ||||||||
\(966\) | −5.15232e18 | −0.204010 | ||||||||
\(967\) | 6.34636e17 | 0.0249605 | 0.0124802 | − | 0.999922i | \(-0.496027\pi\) | ||||
0.0124802 | + | 0.999922i | \(0.496027\pi\) | |||||||
\(968\) | −5.30021e18 | −0.207063 | ||||||||
\(969\) | −2.20559e18 | −0.0855894 | ||||||||
\(970\) | 4.83222e18 | 0.186265 | ||||||||
\(971\) | 4.95806e18 | 0.189839 | 0.0949197 | − | 0.995485i | \(-0.469741\pi\) | ||||
0.0949197 | + | 0.995485i | \(0.469741\pi\) | |||||||
\(972\) | 3.11149e18 | 0.118342 | ||||||||
\(973\) | −5.02519e19 | −1.89854 | ||||||||
\(974\) | −8.96165e19 | −3.36321 | ||||||||
\(975\) | −2.01248e19 | −0.750244 | ||||||||
\(976\) | −7.73627e18 | −0.286489 | ||||||||
\(977\) | 4.91389e19 | 1.80764 | 0.903818 | − | 0.427917i | \(-0.140752\pi\) | ||||
0.903818 | + | 0.427917i | \(0.140752\pi\) | |||||||
\(978\) | −3.49287e19 | −1.27638 | ||||||||
\(979\) | −2.24323e19 | −0.814305 | ||||||||
\(980\) | −1.41296e19 | −0.509518 | ||||||||
\(981\) | 9.16730e18 | 0.328392 | ||||||||
\(982\) | −6.26417e19 | −2.22915 | ||||||||
\(983\) | −5.14976e19 | −1.82049 | −0.910246 | − | 0.414068i | \(-0.864108\pi\) | ||||
−0.910246 | + | 0.414068i | \(0.864108\pi\) | |||||||
\(984\) | 2.52361e19 | 0.886246 | ||||||||
\(985\) | −2.67911e18 | −0.0934662 | ||||||||
\(986\) | 5.43655e17 | 0.0188419 | ||||||||
\(987\) | −4.59403e19 | −1.58173 | ||||||||
\(988\) | 9.51725e19 | 3.25530 | ||||||||
\(989\) | −1.03281e18 | −0.0350951 | ||||||||
\(990\) | −1.64306e18 | −0.0554657 | ||||||||
\(991\) | −6.03400e18 | −0.202361 | −0.101180 | − | 0.994868i | \(-0.532262\pi\) | ||||
−0.101180 | + | 0.994868i | \(0.532262\pi\) | |||||||
\(992\) | 2.15995e19 | 0.719643 | ||||||||
\(993\) | 7.53783e18 | 0.249503 | ||||||||
\(994\) | 8.34478e19 | 2.74412 | ||||||||
\(995\) | 2.32945e18 | 0.0761032 | ||||||||
\(996\) | 2.92911e19 | 0.950715 | ||||||||
\(997\) | 1.33645e19 | 0.430958 | 0.215479 | − | 0.976508i | \(-0.430869\pi\) | ||||
0.215479 | + | 0.976508i | \(0.430869\pi\) | |||||||
\(998\) | −3.92182e19 | −1.25643 | ||||||||
\(999\) | −7.65325e18 | −0.243596 |
(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 | 177.14.a.c.1.28 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.c.1.28 | ✓ | 31 | 1.1 | even | 1 | trivial |