Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2 x^{7} - 13701836 x^{6} + 201589162 x^{5} + 55078074399586 x^{4} + \cdots + 23\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{10}\cdot 5^{14}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-249.679\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −166.679 | −0.115098 | −0.0575488 | − | 0.998343i | \(-0.518328\pi\) | ||||
−0.0575488 | + | 0.998343i | \(0.518328\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | −2.06937e6 | −0.986753 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 9.84223e6 | 0.0664516 | ||||||||
\(7\) | −1.02476e9 | −1.37118 | −0.685588 | − | 0.727990i | \(-0.740455\pi\) | ||||
−0.685588 | + | 0.727990i | \(0.740455\pi\) | |||||||
\(8\) | 6.94472e8 | 0.228670 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.41547e10 | 0.978262 | 0.489131 | − | 0.872210i | \(-0.337314\pi\) | ||||
0.489131 | + | 0.872210i | \(0.337314\pi\) | |||||||
\(12\) | 1.22194e11 | 0.569702 | ||||||||
\(13\) | −6.78961e11 | −1.36596 | −0.682982 | − | 0.730435i | \(-0.739317\pi\) | ||||
−0.682982 | + | 0.730435i | \(0.739317\pi\) | |||||||
\(14\) | 1.70806e11 | 0.157819 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.22403e12 | 0.960433 | ||||||||
\(17\) | 5.16667e12 | 0.621580 | 0.310790 | − | 0.950479i | \(-0.399406\pi\) | ||||
0.310790 | + | 0.950479i | \(0.399406\pi\) | |||||||
\(18\) | −5.81174e11 | −0.0383659 | ||||||||
\(19\) | 5.03610e12 | 0.188444 | 0.0942218 | − | 0.995551i | \(-0.469964\pi\) | ||||
0.0942218 | + | 0.995551i | \(0.469964\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.05111e13 | 0.791649 | ||||||||
\(22\) | −1.40268e13 | −0.112596 | ||||||||
\(23\) | −3.20250e14 | −1.61193 | −0.805966 | − | 0.591961i | \(-0.798354\pi\) | ||||
−0.805966 | + | 0.591961i | \(0.798354\pi\) | |||||||
\(24\) | −4.10079e13 | −0.132023 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.13169e14 | 0.157219 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | 2.12061e15 | 1.35301 | ||||||||
\(29\) | 3.64763e15 | 1.61002 | 0.805010 | − | 0.593261i | \(-0.202160\pi\) | ||||
0.805010 | + | 0.593261i | \(0.202160\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.68906e15 | −1.02751 | −0.513757 | − | 0.857936i | \(-0.671747\pi\) | ||||
−0.513757 | + | 0.857936i | \(0.671747\pi\) | |||||||
\(32\) | −2.16047e15 | −0.339214 | ||||||||
\(33\) | −4.96925e15 | −0.564800 | ||||||||
\(34\) | −8.61176e14 | −0.0715423 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −7.21545e15 | −0.328918 | ||||||||
\(37\) | −5.20866e16 | −1.78077 | −0.890385 | − | 0.455208i | \(-0.849565\pi\) | ||||
−0.890385 | + | 0.455208i | \(0.849565\pi\) | |||||||
\(38\) | −8.39412e14 | −0.0216894 | ||||||||
\(39\) | 4.00920e16 | 0.788640 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.94636e16 | −0.924565 | −0.462283 | − | 0.886733i | \(-0.652969\pi\) | ||||
−0.462283 | + | 0.886733i | \(0.652969\pi\) | |||||||
\(42\) | −1.00859e16 | −0.0911169 | ||||||||
\(43\) | −1.06423e17 | −0.750960 | −0.375480 | − | 0.926830i | \(-0.622522\pi\) | ||||
−0.375480 | + | 0.926830i | \(0.622522\pi\) | |||||||
\(44\) | −1.74147e17 | −0.965303 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.33790e16 | 0.185530 | ||||||||
\(47\) | 1.15217e17 | 0.319512 | 0.159756 | − | 0.987157i | \(-0.448929\pi\) | ||||
0.159756 | + | 0.987157i | \(0.448929\pi\) | |||||||
\(48\) | −2.49425e17 | −0.554506 | ||||||||
\(49\) | 4.91590e17 | 0.880125 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.05087e17 | −0.358869 | ||||||||
\(52\) | 1.40502e18 | 1.34787 | ||||||||
\(53\) | 2.45853e17 | 0.193098 | 0.0965491 | − | 0.995328i | \(-0.469220\pi\) | ||||
0.0965491 | + | 0.995328i | \(0.469220\pi\) | |||||||
\(54\) | 3.43177e16 | 0.0221505 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.11668e17 | −0.313547 | ||||||||
\(57\) | −2.97376e17 | −0.108798 | ||||||||
\(58\) | −6.07983e17 | −0.185309 | ||||||||
\(59\) | −7.28797e18 | −1.85635 | −0.928177 | − | 0.372140i | \(-0.878624\pi\) | ||||
−0.928177 | + | 0.372140i | \(0.878624\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.31633e17 | 0.0236266 | 0.0118133 | − | 0.999930i | \(-0.496240\pi\) | ||||
0.0118133 | + | 0.999930i | \(0.496240\pi\) | |||||||
\(62\) | 7.81568e17 | 0.118264 | ||||||||
\(63\) | −3.57312e18 | −0.457059 | ||||||||
\(64\) | −8.49833e18 | −0.921390 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.28270e17 | 0.0650071 | ||||||||
\(67\) | 1.83759e19 | 1.23158 | 0.615791 | − | 0.787910i | \(-0.288837\pi\) | ||||
0.615791 | + | 0.787910i | \(0.288837\pi\) | |||||||
\(68\) | −1.06918e19 | −0.613346 | ||||||||
\(69\) | 1.89104e19 | 0.930650 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.72795e19 | −1.72369 | −0.861847 | − | 0.507168i | \(-0.830692\pi\) | ||||
−0.861847 | + | 0.507168i | \(0.830692\pi\) | |||||||
\(72\) | 2.42147e18 | 0.0762235 | ||||||||
\(73\) | −3.44105e19 | −0.937133 | −0.468566 | − | 0.883428i | \(-0.655229\pi\) | ||||
−0.468566 | + | 0.883428i | \(0.655229\pi\) | |||||||
\(74\) | 8.68175e18 | 0.204962 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.04215e19 | −0.185947 | ||||||||
\(77\) | −8.62385e19 | −1.34137 | ||||||||
\(78\) | −6.68249e18 | −0.0907706 | ||||||||
\(79\) | −2.81422e19 | −0.334406 | −0.167203 | − | 0.985923i | \(-0.553473\pi\) | ||||
−0.167203 | + | 0.985923i | \(0.553473\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 1.32449e19 | 0.106415 | ||||||||
\(83\) | −2.06872e20 | −1.46346 | −0.731732 | − | 0.681592i | \(-0.761288\pi\) | ||||
−0.731732 | + | 0.681592i | \(0.761288\pi\) | |||||||
\(84\) | −1.25220e20 | −0.781162 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.77385e19 | 0.0864337 | ||||||||
\(87\) | −2.15389e20 | −0.929546 | ||||||||
\(88\) | 5.84431e19 | 0.223700 | ||||||||
\(89\) | −8.54310e19 | −0.290416 | −0.145208 | − | 0.989401i | \(-0.546385\pi\) | ||||
−0.145208 | + | 0.989401i | \(0.546385\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.95773e20 | 1.87298 | ||||||||
\(92\) | 6.62716e20 | 1.59058 | ||||||||
\(93\) | 2.76884e20 | 0.593236 | ||||||||
\(94\) | −1.92042e19 | −0.0367751 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.27574e20 | 0.195845 | ||||||||
\(97\) | −7.33743e20 | −1.01028 | −0.505139 | − | 0.863038i | \(-0.668559\pi\) | ||||
−0.505139 | + | 0.863038i | \(0.668559\pi\) | |||||||
\(98\) | −8.19378e19 | −0.101300 | ||||||||
\(99\) | 2.93429e20 | 0.326087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.64652e20 | 0.418556 | 0.209278 | − | 0.977856i | \(-0.432889\pi\) | ||||
0.209278 | + | 0.977856i | \(0.432889\pi\) | |||||||
\(102\) | 5.08516e19 | 0.0413050 | ||||||||
\(103\) | 1.84494e20 | 0.135267 | 0.0676336 | − | 0.997710i | \(-0.478455\pi\) | ||||
0.0676336 | + | 0.997710i | \(0.478455\pi\) | |||||||
\(104\) | −4.71519e20 | −0.312356 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.09785e19 | −0.0222251 | ||||||||
\(107\) | −4.91756e19 | −0.0241669 | −0.0120834 | − | 0.999927i | \(-0.503846\pi\) | ||||
−0.0120834 | + | 0.999927i | \(0.503846\pi\) | |||||||
\(108\) | 4.26065e20 | 0.189901 | ||||||||
\(109\) | 2.04172e21 | 0.826071 | 0.413035 | − | 0.910715i | \(-0.364469\pi\) | ||||
0.413035 | + | 0.910715i | \(0.364469\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.07566e21 | 1.02813 | ||||||||
\(112\) | −4.32862e21 | −1.31692 | ||||||||
\(113\) | −4.00807e21 | −1.11074 | −0.555369 | − | 0.831604i | \(-0.687423\pi\) | ||||
−0.555369 | + | 0.831604i | \(0.687423\pi\) | |||||||
\(114\) | 4.95664e19 | 0.0125224 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.54829e21 | −1.58869 | ||||||||
\(117\) | −2.36739e21 | −0.455322 | ||||||||
\(118\) | 1.21475e21 | 0.213662 | ||||||||
\(119\) | −5.29460e21 | −0.852296 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.18234e20 | −0.0430031 | ||||||||
\(122\) | −2.19405e19 | −0.00271937 | ||||||||
\(123\) | 4.69224e21 | 0.533798 | ||||||||
\(124\) | 9.70340e21 | 1.01390 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.95565e20 | 0.0526064 | ||||||||
\(127\) | 1.49802e22 | 1.21781 | 0.608903 | − | 0.793244i | \(-0.291610\pi\) | ||||
0.608903 | + | 0.793244i | \(0.291610\pi\) | |||||||
\(128\) | 5.94733e21 | 0.445264 | ||||||||
\(129\) | 6.28417e21 | 0.433567 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.97195e22 | −1.15757 | −0.578784 | − | 0.815481i | \(-0.696473\pi\) | ||||
−0.578784 | + | 0.815481i | \(0.696473\pi\) | |||||||
\(132\) | 1.02832e22 | 0.557318 | ||||||||
\(133\) | −5.16080e21 | −0.258389 | ||||||||
\(134\) | −3.06288e21 | −0.141752 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.58811e21 | 0.142137 | ||||||||
\(137\) | 1.83713e22 | 0.673867 | 0.336934 | − | 0.941528i | \(-0.390610\pi\) | ||||
0.336934 | + | 0.941528i | \(0.390610\pi\) | |||||||
\(138\) | −3.15198e21 | −0.107116 | ||||||||
\(139\) | −2.43375e22 | −0.766690 | −0.383345 | − | 0.923605i | \(-0.625228\pi\) | ||||
−0.383345 | + | 0.923605i | \(0.625228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.80343e21 | −0.184471 | ||||||||
\(142\) | 7.88051e21 | 0.198393 | ||||||||
\(143\) | −5.71378e22 | −1.33627 | ||||||||
\(144\) | 1.47283e22 | 0.320144 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.73551e21 | 0.107862 | ||||||||
\(147\) | −2.90279e22 | −0.508140 | ||||||||
\(148\) | 1.07786e23 | 1.75718 | ||||||||
\(149\) | 3.26853e22 | 0.496474 | 0.248237 | − | 0.968699i | \(-0.420149\pi\) | ||||
0.248237 | + | 0.968699i | \(0.420149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.37656e22 | −0.709981 | −0.354990 | − | 0.934870i | \(-0.615516\pi\) | ||||
−0.354990 | + | 0.934870i | \(0.615516\pi\) | |||||||
\(152\) | 3.49743e21 | 0.0430915 | ||||||||
\(153\) | 1.80151e22 | 0.207193 | ||||||||
\(154\) | 1.43742e22 | 0.154388 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −8.29651e22 | −0.778193 | ||||||||
\(157\) | −7.27689e22 | −0.638262 | −0.319131 | − | 0.947711i | \(-0.603391\pi\) | ||||
−0.319131 | + | 0.947711i | \(0.603391\pi\) | |||||||
\(158\) | 4.69071e21 | 0.0384893 | ||||||||
\(159\) | −1.45174e22 | −0.111485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.28180e23 | 2.21024 | ||||||||
\(162\) | −2.02643e21 | −0.0127886 | ||||||||
\(163\) | −2.15971e23 | −1.27769 | −0.638845 | − | 0.769336i | \(-0.720587\pi\) | ||||
−0.638845 | + | 0.769336i | \(0.720587\pi\) | |||||||
\(164\) | 1.64440e23 | 0.912317 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.44813e22 | 0.168441 | ||||||||
\(167\) | −3.49848e23 | −1.60456 | −0.802282 | − | 0.596945i | \(-0.796381\pi\) | ||||
−0.802282 | + | 0.596945i | \(0.796381\pi\) | |||||||
\(168\) | 4.20233e22 | 0.181027 | ||||||||
\(169\) | 2.13923e23 | 0.865860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.75598e22 | 0.0628145 | ||||||||
\(172\) | 2.20229e23 | 0.741012 | ||||||||
\(173\) | −1.37460e23 | −0.435205 | −0.217602 | − | 0.976037i | \(-0.569824\pi\) | ||||
−0.217602 | + | 0.976037i | \(0.569824\pi\) | |||||||
\(174\) | 3.59008e22 | 0.106988 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.55472e23 | 0.939555 | ||||||||
\(177\) | 4.30347e23 | 1.07177 | ||||||||
\(178\) | 1.42396e22 | 0.0334262 | ||||||||
\(179\) | −6.53841e23 | −1.44716 | −0.723578 | − | 0.690242i | \(-0.757504\pi\) | ||||
−0.723578 | + | 0.690242i | \(0.757504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.73973e22 | −0.0539614 | −0.0269807 | − | 0.999636i | \(-0.508589\pi\) | ||||
−0.0269807 | + | 0.999636i | \(0.508589\pi\) | |||||||
\(182\) | −1.15971e23 | −0.215575 | ||||||||
\(183\) | −7.77280e21 | −0.0136408 | ||||||||
\(184\) | −2.22405e23 | −0.368601 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.61508e22 | −0.0682800 | ||||||||
\(187\) | 4.34800e23 | 0.608068 | ||||||||
\(188\) | −2.38426e23 | −0.315280 | ||||||||
\(189\) | 2.10989e23 | 0.263883 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.68245e23 | 0.860299 | 0.430149 | − | 0.902758i | \(-0.358461\pi\) | ||||
0.430149 | + | 0.902758i | \(0.358461\pi\) | |||||||
\(192\) | 5.01818e23 | 0.531965 | ||||||||
\(193\) | 3.41926e23 | 0.343227 | 0.171613 | − | 0.985164i | \(-0.445102\pi\) | ||||
0.171613 | + | 0.985164i | \(0.445102\pi\) | |||||||
\(194\) | 1.22300e23 | 0.116281 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.01728e24 | −0.868465 | ||||||||
\(197\) | 9.27843e23 | 0.750895 | 0.375447 | − | 0.926844i | \(-0.377489\pi\) | ||||
0.375447 | + | 0.926844i | \(0.377489\pi\) | |||||||
\(198\) | −4.89085e22 | −0.0375319 | ||||||||
\(199\) | 2.42106e24 | 1.76217 | 0.881086 | − | 0.472956i | \(-0.156813\pi\) | ||||
0.881086 | + | 0.472956i | \(0.156813\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.08508e24 | −0.711054 | ||||||||
\(202\) | −7.74478e22 | −0.0481748 | ||||||||
\(203\) | −3.73795e24 | −2.20762 | ||||||||
\(204\) | 6.31337e23 | 0.354115 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.07514e22 | −0.0155689 | ||||||||
\(207\) | −1.11664e24 | −0.537311 | ||||||||
\(208\) | −2.86795e24 | −1.31192 | ||||||||
\(209\) | 4.23811e23 | 0.184347 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.70156e24 | 0.669704 | 0.334852 | − | 0.942271i | \(-0.391314\pi\) | ||||
0.334852 | + | 0.942271i | \(0.391314\pi\) | |||||||
\(212\) | −5.08760e23 | −0.190540 | ||||||||
\(213\) | 2.79181e24 | 0.995175 | ||||||||
\(214\) | 8.19655e21 | 0.00278155 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.42986e23 | −0.0440076 | ||||||||
\(217\) | 4.80517e24 | 1.40890 | ||||||||
\(218\) | −3.40312e23 | −0.0950788 | ||||||||
\(219\) | 2.03191e24 | 0.541054 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.50797e24 | −0.849056 | ||||||||
\(222\) | −5.12649e23 | −0.118335 | ||||||||
\(223\) | 8.45212e24 | 1.86108 | 0.930540 | − | 0.366191i | \(-0.119338\pi\) | ||||
0.930540 | + | 0.366191i | \(0.119338\pi\) | |||||||
\(224\) | 2.21397e24 | 0.465122 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.68061e23 | 0.127843 | ||||||||
\(227\) | 8.35539e24 | 1.52650 | 0.763248 | − | 0.646106i | \(-0.223604\pi\) | ||||
0.763248 | + | 0.646106i | \(0.223604\pi\) | |||||||
\(228\) | 6.15382e23 | 0.107357 | ||||||||
\(229\) | 8.52372e24 | 1.42022 | 0.710112 | − | 0.704089i | \(-0.248644\pi\) | ||||
0.710112 | + | 0.704089i | \(0.248644\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.09230e24 | 0.774440 | ||||||||
\(232\) | 2.53317e24 | 0.368164 | ||||||||
\(233\) | −1.23141e25 | −1.71066 | −0.855331 | − | 0.518081i | \(-0.826646\pi\) | ||||
−0.855331 | + | 0.518081i | \(0.826646\pi\) | |||||||
\(234\) | 3.94594e23 | 0.0524064 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.50815e25 | 1.83176 | ||||||||
\(237\) | 1.66177e24 | 0.193069 | ||||||||
\(238\) | 8.82500e23 | 0.0980972 | ||||||||
\(239\) | 1.32354e25 | 1.40786 | 0.703928 | − | 0.710271i | \(-0.251428\pi\) | ||||
0.703928 | + | 0.710271i | \(0.251428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.15226e24 | 0.794509 | 0.397255 | − | 0.917708i | \(-0.369963\pi\) | ||||
0.397255 | + | 0.917708i | \(0.369963\pi\) | |||||||
\(242\) | 5.30429e22 | 0.00494956 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | −2.72398e23 | −0.0233136 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.82099e23 | −0.0614389 | ||||||||
\(247\) | −3.41931e24 | −0.257407 | ||||||||
\(248\) | −3.25642e24 | −0.234962 | ||||||||
\(249\) | 1.22156e25 | 0.844931 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.18049e25 | −0.750740 | −0.375370 | − | 0.926875i | \(-0.622484\pi\) | ||||
−0.375370 | + | 0.926875i | \(0.622484\pi\) | |||||||
\(252\) | 7.39411e24 | 0.451004 | ||||||||
\(253\) | −2.69506e25 | −1.57689 | ||||||||
\(254\) | −2.49689e24 | −0.140167 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.68310e25 | 0.870142 | ||||||||
\(257\) | −1.84085e24 | −0.0913523 | −0.0456762 | − | 0.998956i | \(-0.514544\pi\) | ||||
−0.0456762 | + | 0.998956i | \(0.514544\pi\) | |||||||
\(258\) | −1.04744e24 | −0.0499025 | ||||||||
\(259\) | 5.33763e25 | 2.44175 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.27185e25 | 0.536673 | ||||||||
\(262\) | 3.28682e24 | 0.133233 | ||||||||
\(263\) | −4.49232e24 | −0.174959 | −0.0874794 | − | 0.996166i | \(-0.527881\pi\) | ||||
−0.0874794 | + | 0.996166i | \(0.527881\pi\) | |||||||
\(264\) | −3.45101e24 | −0.129153 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.60197e23 | 0.0297400 | ||||||||
\(267\) | 5.04462e24 | 0.167672 | ||||||||
\(268\) | −3.80266e25 | −1.21527 | ||||||||
\(269\) | 1.48544e25 | 0.456516 | 0.228258 | − | 0.973601i | \(-0.426697\pi\) | ||||
0.228258 | + | 0.973601i | \(0.426697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.37603e25 | −1.24424 | −0.622119 | − | 0.782923i | \(-0.713728\pi\) | ||||
−0.622119 | + | 0.782923i | \(0.713728\pi\) | |||||||
\(272\) | 2.18242e25 | 0.596986 | ||||||||
\(273\) | −4.10847e25 | −1.08136 | ||||||||
\(274\) | −3.06212e24 | −0.0775605 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.91327e25 | −0.918321 | ||||||||
\(277\) | 3.70091e25 | 0.836125 | 0.418063 | − | 0.908418i | \(-0.362709\pi\) | ||||
0.418063 | + | 0.908418i | \(0.362709\pi\) | |||||||
\(278\) | 4.05655e24 | 0.0882442 | ||||||||
\(279\) | −1.63497e25 | −0.342505 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.63521e25 | 1.87260 | 0.936300 | − | 0.351202i | \(-0.114227\pi\) | ||||
0.936300 | + | 0.351202i | \(0.114227\pi\) | |||||||
\(282\) | 1.13399e24 | 0.0212321 | ||||||||
\(283\) | −6.31416e25 | −1.13909 | −0.569545 | − | 0.821960i | \(-0.692880\pi\) | ||||
−0.569545 | + | 0.821960i | \(0.692880\pi\) | |||||||
\(284\) | 9.78388e25 | 1.70086 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.52367e24 | 0.153802 | ||||||||
\(287\) | 8.14312e25 | 1.26774 | ||||||||
\(288\) | −7.53310e24 | −0.113071 | ||||||||
\(289\) | −4.23975e25 | −0.613638 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.33268e25 | 0.583284 | ||||||||
\(292\) | 7.12081e25 | 0.924718 | ||||||||
\(293\) | −3.04877e25 | −0.381957 | −0.190978 | − | 0.981594i | \(-0.561166\pi\) | ||||
−0.190978 | + | 0.981594i | \(0.561166\pi\) | |||||||
\(294\) | 4.83834e24 | 0.0584857 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.61727e25 | −0.407210 | ||||||||
\(297\) | −1.73267e25 | −0.188267 | ||||||||
\(298\) | −5.44795e24 | −0.0571429 | ||||||||
\(299\) | 2.17437e26 | 2.20184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.09058e26 | 1.02970 | ||||||||
\(302\) | 8.96160e24 | 0.0817171 | ||||||||
\(303\) | −2.74372e25 | −0.241653 | ||||||||
\(304\) | 2.12726e25 | 0.180987 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.00273e24 | −0.0238474 | ||||||||
\(307\) | 6.23769e25 | 0.478709 | 0.239354 | − | 0.970932i | \(-0.423064\pi\) | ||||
0.239354 | + | 0.970932i | \(0.423064\pi\) | |||||||
\(308\) | 1.78459e26 | 1.32360 | ||||||||
\(309\) | −1.08942e25 | −0.0780965 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.51641e25 | −0.570522 | −0.285261 | − | 0.958450i | \(-0.592080\pi\) | ||||
−0.285261 | + | 0.958450i | \(0.592080\pi\) | |||||||
\(312\) | 2.78427e25 | 0.180339 | ||||||||
\(313\) | −4.69068e24 | −0.0293778 | −0.0146889 | − | 0.999892i | \(-0.504676\pi\) | ||||
−0.0146889 | + | 0.999892i | \(0.504676\pi\) | |||||||
\(314\) | 1.21290e25 | 0.0734625 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.82366e25 | 0.329976 | ||||||||
\(317\) | −2.31829e26 | −1.27071 | −0.635353 | − | 0.772222i | \(-0.719145\pi\) | ||||
−0.635353 | + | 0.772222i | \(0.719145\pi\) | |||||||
\(318\) | 2.41974e24 | 0.0128317 | ||||||||
\(319\) | 3.06965e26 | 1.57502 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.90377e24 | 0.0139527 | ||||||||
\(322\) | −5.47007e25 | −0.254394 | ||||||||
\(323\) | 2.60198e25 | 0.117133 | ||||||||
\(324\) | −2.51587e25 | −0.109639 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.59978e25 | 0.147059 | ||||||||
\(327\) | −1.20561e26 | −0.476932 | ||||||||
\(328\) | −5.51852e25 | −0.211421 | ||||||||
\(329\) | −1.18070e26 | −0.438108 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.64099e25 | 0.126773 | 0.0633864 | − | 0.997989i | \(-0.479810\pi\) | ||||
0.0633864 | + | 0.997989i | \(0.479810\pi\) | |||||||
\(332\) | 4.28095e26 | 1.44408 | ||||||||
\(333\) | −1.81615e26 | −0.593590 | ||||||||
\(334\) | 5.83124e25 | 0.184681 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.55601e26 | 0.760326 | ||||||||
\(337\) | −1.45166e26 | −0.418554 | −0.209277 | − | 0.977856i | \(-0.567111\pi\) | ||||
−0.209277 | + | 0.977856i | \(0.567111\pi\) | |||||||
\(338\) | −3.56565e25 | −0.0996584 | ||||||||
\(339\) | 2.36672e26 | 0.641285 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.94607e26 | −1.00518 | ||||||||
\(342\) | −2.92685e24 | −0.00722980 | ||||||||
\(343\) | 6.86138e25 | 0.164370 | ||||||||
\(344\) | −7.39078e25 | −0.171722 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.29118e25 | 0.0500910 | ||||||||
\(347\) | 4.90722e26 | 1.04082 | 0.520411 | − | 0.853916i | \(-0.325779\pi\) | ||||
0.520411 | + | 0.853916i | \(0.325779\pi\) | |||||||
\(348\) | 4.45719e26 | 0.917232 | ||||||||
\(349\) | −3.21582e26 | −0.642133 | −0.321067 | − | 0.947057i | \(-0.604041\pi\) | ||||
−0.321067 | + | 0.947057i | \(0.604041\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.39792e26 | 0.262880 | ||||||||
\(352\) | −1.81814e26 | −0.331840 | ||||||||
\(353\) | 2.77493e26 | 0.491606 | 0.245803 | − | 0.969320i | \(-0.420948\pi\) | ||||
0.245803 | + | 0.969320i | \(0.420948\pi\) | |||||||
\(354\) | −7.17299e25 | −0.123358 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.76788e26 | 0.286569 | ||||||||
\(357\) | 3.12641e26 | 0.492073 | ||||||||
\(358\) | 1.08982e26 | 0.166564 | ||||||||
\(359\) | −9.81194e26 | −1.45634 | −0.728171 | − | 0.685396i | \(-0.759629\pi\) | ||||
−0.728171 | + | 0.685396i | \(0.759629\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.88847e26 | −0.964489 | ||||||||
\(362\) | 4.56656e24 | 0.00621082 | ||||||||
\(363\) | 1.87914e25 | 0.0248279 | ||||||||
\(364\) | −1.43981e27 | −1.84817 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.29556e24 | 0.00157003 | ||||||||
\(367\) | −7.12491e25 | −0.0839046 | −0.0419523 | − | 0.999120i | \(-0.513358\pi\) | ||||
−0.0419523 | + | 0.999120i | \(0.513358\pi\) | |||||||
\(368\) | −1.35275e27 | −1.54815 | ||||||||
\(369\) | −2.77072e26 | −0.308188 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.51940e26 | −0.264772 | ||||||||
\(372\) | −5.72976e26 | −0.585377 | ||||||||
\(373\) | −4.54132e26 | −0.451066 | −0.225533 | − | 0.974236i | \(-0.572412\pi\) | ||||
−0.225533 | + | 0.974236i | \(0.572412\pi\) | |||||||
\(374\) | −7.24720e25 | −0.0699872 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00147e25 | 0.0730630 | ||||||||
\(377\) | −2.47660e27 | −2.19923 | ||||||||
\(378\) | −3.51675e25 | −0.0303723 | ||||||||
\(379\) | 7.47685e26 | 0.628068 | 0.314034 | − | 0.949412i | \(-0.398319\pi\) | ||||
0.314034 | + | 0.949412i | \(0.398319\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.84566e26 | −0.703101 | ||||||||
\(382\) | −1.28050e26 | −0.0990183 | ||||||||
\(383\) | −4.08058e25 | −0.0306998 | −0.0153499 | − | 0.999882i | \(-0.504886\pi\) | ||||
−0.0153499 | + | 0.999882i | \(0.504886\pi\) | |||||||
\(384\) | −3.51184e26 | −0.257073 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.69920e25 | −0.0395046 | ||||||||
\(387\) | −3.71074e26 | −0.250320 | ||||||||
\(388\) | 1.51839e27 | 0.996894 | ||||||||
\(389\) | −3.70541e26 | −0.236791 | −0.118396 | − | 0.992967i | \(-0.537775\pi\) | ||||
−0.118396 | + | 0.992967i | \(0.537775\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.65463e27 | −1.00195 | ||||||||
\(392\) | 3.41396e26 | 0.201258 | ||||||||
\(393\) | 1.16441e27 | 0.668322 | ||||||||
\(394\) | −1.54652e26 | −0.0864262 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.07214e26 | −0.321768 | ||||||||
\(397\) | −4.03203e26 | −0.208077 | −0.104038 | − | 0.994573i | \(-0.533176\pi\) | ||||
−0.104038 | + | 0.994573i | \(0.533176\pi\) | |||||||
\(398\) | −4.03540e26 | −0.202822 | ||||||||
\(399\) | 3.04740e26 | 0.149181 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.04218e27 | 1.41309 | 0.706544 | − | 0.707669i | \(-0.250253\pi\) | ||||
0.706544 | + | 0.707669i | \(0.250253\pi\) | |||||||
\(402\) | 1.80860e26 | 0.0818406 | ||||||||
\(403\) | 3.18369e27 | 1.40355 | ||||||||
\(404\) | −9.61537e26 | −0.413011 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.23037e26 | 0.254092 | ||||||||
\(407\) | −4.38333e27 | −1.74206 | ||||||||
\(408\) | −2.11874e26 | −0.0820628 | ||||||||
\(409\) | −4.71550e27 | −1.78005 | −0.890027 | − | 0.455907i | \(-0.849315\pi\) | ||||
−0.890027 | + | 0.455907i | \(0.849315\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.08481e27 | −0.389058 | ||||||||
\(412\) | −3.81787e26 | −0.133475 | ||||||||
\(413\) | 7.46843e27 | 2.54539 | ||||||||
\(414\) | 1.86121e26 | 0.0618432 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.46688e27 | 0.463354 | ||||||||
\(417\) | 1.43710e27 | 0.442649 | ||||||||
\(418\) | −7.06405e25 | −0.0212179 | ||||||||
\(419\) | −6.10830e27 | −1.78926 | −0.894630 | − | 0.446809i | \(-0.852561\pi\) | ||||
−0.894630 | + | 0.446809i | \(0.852561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.76673e27 | −0.492275 | −0.246138 | − | 0.969235i | \(-0.579162\pi\) | ||||
−0.246138 | + | 0.969235i | \(0.579162\pi\) | |||||||
\(422\) | −2.83615e26 | −0.0770813 | ||||||||
\(423\) | 4.01736e26 | 0.106504 | ||||||||
\(424\) | 1.70738e26 | 0.0441558 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.65336e26 | −0.114542 | ||||||||
\(427\) | −1.34893e26 | −0.0323963 | ||||||||
\(428\) | 1.01763e26 | 0.0238467 | ||||||||
\(429\) | 3.37393e27 | 0.771497 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.90869e26 | −0.150447 | −0.0752236 | − | 0.997167i | \(-0.523967\pi\) | ||||
−0.0752236 | + | 0.997167i | \(0.523967\pi\) | |||||||
\(432\) | −8.69690e26 | −0.184835 | ||||||||
\(433\) | −3.77275e27 | −0.782591 | −0.391296 | − | 0.920265i | \(-0.627973\pi\) | ||||
−0.391296 | + | 0.920265i | \(0.627973\pi\) | |||||||
\(434\) | −8.00921e26 | −0.162161 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.22507e27 | −0.815128 | ||||||||
\(437\) | −1.61281e27 | −0.303758 | ||||||||
\(438\) | −3.38676e26 | −0.0622740 | ||||||||
\(439\) | 6.54147e27 | 1.17435 | 0.587175 | − | 0.809460i | \(-0.300240\pi\) | ||||
0.587175 | + | 0.809460i | \(0.300240\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.71407e27 | 0.293375 | ||||||||
\(442\) | 5.84705e26 | 0.0977243 | ||||||||
\(443\) | −2.70935e27 | −0.442208 | −0.221104 | − | 0.975250i | \(-0.570966\pi\) | ||||
−0.221104 | + | 0.975250i | \(0.570966\pi\) | |||||||
\(444\) | −6.36468e27 | −1.01451 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.40879e27 | −0.214206 | ||||||||
\(447\) | −1.93003e27 | −0.286639 | ||||||||
\(448\) | 8.70876e27 | 1.26339 | ||||||||
\(449\) | −4.24406e27 | −0.601443 | −0.300722 | − | 0.953712i | \(-0.597228\pi\) | ||||
−0.300722 | + | 0.953712i | \(0.597228\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.68723e27 | −0.904467 | ||||||||
\(452\) | 8.29418e27 | 1.09602 | ||||||||
\(453\) | 3.17481e27 | 0.409908 | ||||||||
\(454\) | −1.39267e27 | −0.175696 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.06520e26 | −0.0248789 | ||||||||
\(457\) | −7.12772e27 | −0.839132 | −0.419566 | − | 0.907725i | \(-0.637818\pi\) | ||||
−0.419566 | + | 0.907725i | \(0.637818\pi\) | |||||||
\(458\) | −1.42073e27 | −0.163464 | ||||||||
\(459\) | −1.06377e27 | −0.119623 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.68767e28 | −1.81312 | −0.906560 | − | 0.422076i | \(-0.861302\pi\) | ||||
−0.906560 | + | 0.422076i | \(0.861302\pi\) | |||||||
\(462\) | −8.48779e26 | −0.0891362 | ||||||||
\(463\) | −1.26513e28 | −1.29878 | −0.649391 | − | 0.760455i | \(-0.724976\pi\) | ||||
−0.649391 | + | 0.760455i | \(0.724976\pi\) | |||||||
\(464\) | 1.54077e28 | 1.54632 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.05250e27 | 0.196893 | ||||||||
\(467\) | 4.32488e27 | 0.405645 | 0.202823 | − | 0.979215i | \(-0.434988\pi\) | ||||
0.202823 | + | 0.979215i | \(0.434988\pi\) | |||||||
\(468\) | 4.89901e27 | 0.449290 | ||||||||
\(469\) | −1.88309e28 | −1.68872 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.29693e27 | 0.368501 | ||||||||
\(472\) | −5.06129e27 | −0.424493 | ||||||||
\(473\) | −8.95600e27 | −0.734636 | ||||||||
\(474\) | −2.76982e26 | −0.0222218 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.09565e28 | 0.841005 | ||||||||
\(477\) | 8.57235e26 | 0.0643661 | ||||||||
\(478\) | −2.20606e27 | −0.162041 | ||||||||
\(479\) | −6.12898e27 | −0.440418 | −0.220209 | − | 0.975453i | \(-0.570674\pi\) | ||||
−0.220209 | + | 0.975453i | \(0.570674\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.53648e28 | 2.43247 | ||||||||
\(482\) | −1.35881e27 | −0.0914461 | ||||||||
\(483\) | −1.93787e28 | −1.27609 | ||||||||
\(484\) | 6.58544e26 | 0.0424335 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.19659e26 | 0.00738351 | ||||||||
\(487\) | 1.14277e28 | 0.690086 | 0.345043 | − | 0.938587i | \(-0.387864\pi\) | ||||
0.345043 | + | 0.938587i | \(0.387864\pi\) | |||||||
\(488\) | 9.14155e25 | 0.00540271 | ||||||||
\(489\) | 1.27529e28 | 0.737675 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.32813e27 | −0.0736010 | −0.0368005 | − | 0.999323i | \(-0.511717\pi\) | ||||
−0.0368005 | + | 0.999323i | \(0.511717\pi\) | |||||||
\(492\) | −9.70999e27 | −0.526727 | ||||||||
\(493\) | 1.88461e28 | 1.00076 | ||||||||
\(494\) | 5.69928e26 | 0.0296270 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.98067e28 | −0.986859 | ||||||||
\(497\) | 4.84502e28 | 2.36349 | ||||||||
\(498\) | −2.03608e27 | −0.0972495 | ||||||||
\(499\) | 3.23815e28 | 1.51440 | 0.757200 | − | 0.653183i | \(-0.226567\pi\) | ||||
0.757200 | + | 0.653183i | \(0.226567\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.06582e28 | 0.926396 | ||||||||
\(502\) | 1.96763e27 | 0.0864083 | ||||||||
\(503\) | 2.80905e28 | 1.20808 | 0.604041 | − | 0.796954i | \(-0.293556\pi\) | ||||
0.604041 | + | 0.796954i | \(0.293556\pi\) | |||||||
\(504\) | −2.48143e27 | −0.104516 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.49209e27 | 0.181497 | ||||||||
\(507\) | −1.26320e28 | −0.499904 | ||||||||
\(508\) | −3.09996e28 | −1.20167 | ||||||||
\(509\) | 1.04322e28 | 0.396131 | 0.198065 | − | 0.980189i | \(-0.436534\pi\) | ||||
0.198065 | + | 0.980189i | \(0.436534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.52626e28 | 1.28497 | ||||||||
\(512\) | −1.52778e28 | −0.545415 | ||||||||
\(513\) | −1.03689e27 | −0.0362660 | ||||||||
\(514\) | 3.06830e26 | 0.0105144 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.30043e28 | −0.427823 | ||||||||
\(517\) | 9.69602e27 | 0.312567 | ||||||||
\(518\) | −8.89672e27 | −0.281040 | ||||||||
\(519\) | 8.11690e27 | 0.251266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.95275e28 | 0.580565 | 0.290282 | − | 0.956941i | \(-0.406251\pi\) | ||||
0.290282 | + | 0.956941i | \(0.406251\pi\) | |||||||
\(522\) | −2.11991e27 | −0.0617698 | ||||||||
\(523\) | −5.60979e28 | −1.60206 | −0.801030 | − | 0.598624i | \(-0.795714\pi\) | ||||
−0.801030 | + | 0.598624i | \(0.795714\pi\) | |||||||
\(524\) | 4.08069e28 | 1.14223 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.48777e26 | 0.0201373 | ||||||||
\(527\) | −2.42268e28 | −0.638683 | ||||||||
\(528\) | −2.09903e28 | −0.542453 | ||||||||
\(529\) | 6.30885e28 | 1.59833 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.54116e28 | −0.618784 | ||||||||
\(532\) | 1.06796e28 | 0.254966 | ||||||||
\(533\) | 5.39527e28 | 1.26292 | ||||||||
\(534\) | −8.40832e26 | −0.0192986 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.27616e28 | 0.281626 | ||||||||
\(537\) | 3.86087e28 | 0.835516 | ||||||||
\(538\) | −2.47592e27 | −0.0525439 | ||||||||
\(539\) | 4.13696e28 | 0.860993 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.18651e28 | −1.63881 | −0.819403 | − | 0.573218i | \(-0.805695\pi\) | ||||
−0.819403 | + | 0.573218i | \(0.805695\pi\) | |||||||
\(542\) | 7.29394e27 | 0.143209 | ||||||||
\(543\) | 1.61778e27 | 0.0311546 | ||||||||
\(544\) | −1.11624e28 | −0.210849 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.84796e27 | 0.124462 | ||||||||
\(547\) | −8.60861e27 | −0.153485 | −0.0767425 | − | 0.997051i | \(-0.524452\pi\) | ||||
−0.0767425 | + | 0.997051i | \(0.524452\pi\) | |||||||
\(548\) | −3.80171e28 | −0.664940 | ||||||||
\(549\) | 4.58976e26 | 0.00787555 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.83698e28 | 0.303398 | ||||||||
\(552\) | 1.31328e28 | 0.212812 | ||||||||
\(553\) | 2.88390e28 | 0.458529 | ||||||||
\(554\) | −6.16865e27 | −0.0962360 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.03632e28 | 0.756534 | ||||||||
\(557\) | 1.30988e29 | 1.93086 | 0.965430 | − | 0.260664i | \(-0.0839414\pi\) | ||||
0.965430 | + | 0.260664i | \(0.0839414\pi\) | |||||||
\(558\) | 2.72516e27 | 0.0394215 | ||||||||
\(559\) | 7.22571e28 | 1.02579 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.56745e28 | −0.351068 | ||||||||
\(562\) | −1.60599e28 | −0.215532 | ||||||||
\(563\) | −7.12976e28 | −0.939154 | −0.469577 | − | 0.882891i | \(-0.655594\pi\) | ||||
−0.469577 | + | 0.882891i | \(0.655594\pi\) | |||||||
\(564\) | 1.40788e28 | 0.182027 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.05244e28 | 0.131106 | ||||||||
\(567\) | −1.24587e28 | −0.152353 | ||||||||
\(568\) | −3.28343e28 | −0.394158 | ||||||||
\(569\) | 9.25550e27 | 0.109074 | 0.0545370 | − | 0.998512i | \(-0.482632\pi\) | ||||
0.0545370 | + | 0.998512i | \(0.482632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.74702e28 | −1.10712 | −0.553558 | − | 0.832811i | \(-0.686730\pi\) | ||||
−0.553558 | + | 0.832811i | \(0.686730\pi\) | |||||||
\(572\) | 1.18239e29 | 1.31857 | ||||||||
\(573\) | −4.53641e28 | −0.496694 | ||||||||
\(574\) | −1.35729e28 | −0.145914 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.96318e28 | −0.307130 | ||||||||
\(577\) | 1.53081e29 | 1.55803 | 0.779015 | − | 0.627005i | \(-0.215719\pi\) | ||||
0.779015 | + | 0.627005i | \(0.215719\pi\) | |||||||
\(578\) | 7.06677e27 | 0.0706283 | ||||||||
\(579\) | −2.01904e28 | −0.198162 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.11995e29 | 2.00667 | ||||||||
\(582\) | −7.22167e27 | −0.0671346 | ||||||||
\(583\) | 2.06897e28 | 0.188901 | ||||||||
\(584\) | −2.38971e28 | −0.214295 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.08166e27 | 0.0439623 | ||||||||
\(587\) | −1.14595e29 | −0.973793 | −0.486897 | − | 0.873460i | \(-0.661871\pi\) | ||||
−0.486897 | + | 0.873460i | \(0.661871\pi\) | |||||||
\(588\) | 6.00695e28 | 0.501409 | ||||||||
\(589\) | −2.36146e28 | −0.193629 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.47882e28 | −0.433529 | ||||||||
\(592\) | −2.20015e29 | −1.71031 | ||||||||
\(593\) | −9.22603e28 | −0.704597 | −0.352298 | − | 0.935888i | \(-0.614600\pi\) | ||||
−0.352298 | + | 0.935888i | \(0.614600\pi\) | |||||||
\(594\) | 2.88800e27 | 0.0216690 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.76379e28 | −0.489896 | ||||||||
\(597\) | −1.42961e29 | −1.01739 | ||||||||
\(598\) | −3.62422e28 | −0.253427 | ||||||||
\(599\) | −2.69560e29 | −1.85214 | −0.926070 | − | 0.377351i | \(-0.876835\pi\) | ||||
−0.926070 | + | 0.377351i | \(0.876835\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.71447e29 | 1.13749 | 0.568746 | − | 0.822513i | \(-0.307429\pi\) | ||||
0.568746 | + | 0.822513i | \(0.307429\pi\) | |||||||
\(602\) | −1.81777e28 | −0.118516 | ||||||||
\(603\) | 6.40728e28 | 0.410527 | ||||||||
\(604\) | 1.11261e29 | 0.700575 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.57322e27 | 0.0278137 | ||||||||
\(607\) | −1.08981e29 | −0.651434 | −0.325717 | − | 0.945467i | \(-0.605606\pi\) | ||||
−0.325717 | + | 0.945467i | \(0.605606\pi\) | |||||||
\(608\) | −1.08803e28 | −0.0639227 | ||||||||
\(609\) | 2.20722e29 | 1.27457 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.82276e28 | −0.436443 | ||||||||
\(612\) | −3.72798e28 | −0.204449 | ||||||||
\(613\) | 1.05774e29 | 0.570222 | 0.285111 | − | 0.958494i | \(-0.407969\pi\) | ||||
0.285111 | + | 0.958494i | \(0.407969\pi\) | |||||||
\(614\) | −1.03969e28 | −0.0550982 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5.98902e28 | −0.306732 | ||||||||
\(617\) | 5.81298e28 | 0.292688 | 0.146344 | − | 0.989234i | \(-0.453249\pi\) | ||||
0.146344 | + | 0.989234i | \(0.453249\pi\) | |||||||
\(618\) | 1.81584e27 | 0.00898872 | ||||||||
\(619\) | 8.28280e27 | 0.0403112 | 0.0201556 | − | 0.999797i | \(-0.493584\pi\) | ||||
0.0201556 | + | 0.999797i | \(0.493584\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.59366e28 | 0.310217 | ||||||||
\(622\) | 1.41951e28 | 0.0656657 | ||||||||
\(623\) | 8.75464e28 | 0.398212 | ||||||||
\(624\) | 1.69350e29 | 0.757436 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.81838e26 | 0.00338132 | ||||||||
\(627\) | −2.50256e28 | −0.106433 | ||||||||
\(628\) | 1.50586e29 | 0.629807 | ||||||||
\(629\) | −2.69114e29 | −1.10689 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.70876e28 | 0.187326 | 0.0936630 | − | 0.995604i | \(-0.470142\pi\) | ||||
0.0936630 | + | 0.995604i | \(0.470142\pi\) | |||||||
\(632\) | −1.95440e28 | −0.0764686 | ||||||||
\(633\) | −1.00476e29 | −0.386654 | ||||||||
\(634\) | 3.86410e28 | 0.146255 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.00418e28 | 0.110008 | ||||||||
\(637\) | −3.33770e29 | −1.20222 | ||||||||
\(638\) | −5.11646e28 | −0.181281 | ||||||||
\(639\) | −1.64853e29 | −0.574565 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.35322e29 | 1.13098 | 0.565488 | − | 0.824757i | \(-0.308688\pi\) | ||||
0.565488 | + | 0.824757i | \(0.308688\pi\) | |||||||
\(642\) | −4.83998e26 | −0.00160593 | ||||||||
\(643\) | 2.28214e29 | 0.744951 | 0.372476 | − | 0.928042i | \(-0.378509\pi\) | ||||
0.372476 | + | 0.928042i | \(0.378509\pi\) | |||||||
\(644\) | −6.79126e29 | −2.18096 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.33696e27 | −0.0134817 | ||||||||
\(647\) | 4.05399e29 | 1.23990 | 0.619952 | − | 0.784640i | \(-0.287152\pi\) | ||||
0.619952 | + | 0.784640i | \(0.287152\pi\) | |||||||
\(648\) | 8.44316e27 | 0.0254078 | ||||||||
\(649\) | −6.13317e29 | −1.81600 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.83740e29 | −0.813431 | ||||||||
\(652\) | 4.46924e29 | 1.26076 | ||||||||
\(653\) | −1.27772e28 | −0.0354687 | −0.0177344 | − | 0.999843i | \(-0.505645\pi\) | ||||
−0.0177344 | + | 0.999843i | \(0.505645\pi\) | |||||||
\(654\) | 2.00951e28 | 0.0548937 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.35656e29 | −0.887983 | ||||||||
\(657\) | −1.19982e29 | −0.312378 | ||||||||
\(658\) | 1.96797e28 | 0.0504251 | ||||||||
\(659\) | 6.99206e28 | 0.176323 | 0.0881614 | − | 0.996106i | \(-0.471901\pi\) | ||||
0.0881614 | + | 0.996106i | \(0.471901\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.85023e29 | −1.18481 | −0.592403 | − | 0.805642i | \(-0.701821\pi\) | ||||
−0.592403 | + | 0.805642i | \(0.701821\pi\) | |||||||
\(662\) | −6.06877e27 | −0.0145912 | ||||||||
\(663\) | 2.07142e29 | 0.490203 | ||||||||
\(664\) | −1.43667e29 | −0.334651 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.02714e28 | 0.0683208 | ||||||||
\(667\) | −1.16815e30 | −2.59524 | ||||||||
\(668\) | 7.23966e29 | 1.58331 | ||||||||
\(669\) | −4.99090e29 | −1.07449 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.10775e28 | 0.0231130 | ||||||||
\(672\) | −1.30733e29 | −0.268538 | ||||||||
\(673\) | −1.03296e29 | −0.208893 | −0.104447 | − | 0.994530i | \(-0.533307\pi\) | ||||
−0.104447 | + | 0.994530i | \(0.533307\pi\) | |||||||
\(674\) | 2.41962e28 | 0.0481745 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.42686e29 | −0.854389 | ||||||||
\(677\) | 7.81995e29 | 1.48601 | 0.743007 | − | 0.669284i | \(-0.233399\pi\) | ||||
0.743007 | + | 0.669284i | \(0.233399\pi\) | |||||||
\(678\) | −3.94483e28 | −0.0738103 | ||||||||
\(679\) | 7.51911e29 | 1.38527 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.93378e29 | −0.881322 | ||||||||
\(682\) | 6.57727e28 | 0.115694 | ||||||||
\(683\) | 8.70064e29 | 1.50707 | 0.753535 | − | 0.657407i | \(-0.228347\pi\) | ||||
0.753535 | + | 0.657407i | \(0.228347\pi\) | |||||||
\(684\) | −3.63377e28 | −0.0619824 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.14365e28 | −0.0189186 | ||||||||
\(687\) | −5.03317e29 | −0.819966 | ||||||||
\(688\) | −4.49534e29 | −0.721247 | ||||||||
\(689\) | −1.66924e29 | −0.263765 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.20998e29 | −0.951855 | −0.475928 | − | 0.879484i | \(-0.657888\pi\) | ||||
−0.475928 | + | 0.879484i | \(0.657888\pi\) | |||||||
\(692\) | 2.84457e29 | 0.429439 | ||||||||
\(693\) | −3.00695e29 | −0.447123 | ||||||||
\(694\) | −8.17931e28 | −0.119796 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.49581e29 | −0.212560 | ||||||||
\(697\) | −4.10562e29 | −0.574691 | ||||||||
\(698\) | 5.36011e28 | 0.0739080 | ||||||||
\(699\) | 7.27133e29 | 0.987652 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.69349e29 | 1.14592 | 0.572961 | − | 0.819583i | \(-0.305795\pi\) | ||||
0.572961 | + | 0.819583i | \(0.305795\pi\) | |||||||
\(702\) | −2.33004e28 | −0.0302569 | ||||||||
\(703\) | −2.62313e29 | −0.335575 | ||||||||
\(704\) | −7.15174e29 | −0.901361 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.62522e28 | −0.0565827 | ||||||||
\(707\) | −4.76158e29 | −0.573914 | ||||||||
\(708\) | −8.90548e29 | −1.05757 | ||||||||
\(709\) | −8.90842e29 | −1.04235 | −0.521177 | − | 0.853449i | \(-0.674507\pi\) | ||||
−0.521177 | + | 0.853449i | \(0.674507\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.81258e28 | −0.111469 | ||||||||
\(712\) | −5.93295e28 | −0.0664095 | ||||||||
\(713\) | 1.50167e30 | 1.65628 | ||||||||
\(714\) | −5.21107e28 | −0.0566364 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.35304e30 | 1.42799 | ||||||||
\(717\) | −7.81536e29 | −0.812827 | ||||||||
\(718\) | 1.63544e29 | 0.167621 | ||||||||
\(719\) | −1.39858e29 | −0.141265 | −0.0706323 | − | 0.997502i | \(-0.522502\pi\) | ||||
−0.0706323 | + | 0.997502i | \(0.522502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.89063e29 | −0.185475 | ||||||||
\(722\) | 1.14816e29 | 0.111010 | ||||||||
\(723\) | −4.81383e29 | −0.458710 | ||||||||
\(724\) | 5.66952e28 | 0.0532465 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.13213e27 | −0.00285763 | ||||||||
\(727\) | −6.76901e29 | −0.608714 | −0.304357 | − | 0.952558i | \(-0.598442\pi\) | ||||
−0.304357 | + | 0.952558i | \(0.598442\pi\) | |||||||
\(728\) | 4.83195e29 | 0.428295 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.49853e29 | −0.466782 | ||||||||
\(732\) | 1.60848e28 | 0.0134601 | ||||||||
\(733\) | 6.62441e28 | 0.0546456 | 0.0273228 | − | 0.999627i | \(-0.491302\pi\) | ||||
0.0273228 | + | 0.999627i | \(0.491302\pi\) | |||||||
\(734\) | 1.18757e28 | 0.00965722 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.91891e29 | 0.546790 | ||||||||
\(737\) | 1.54642e30 | 1.20481 | ||||||||
\(738\) | 4.61822e28 | 0.0354717 | ||||||||
\(739\) | 1.30334e29 | 0.0986945 | 0.0493472 | − | 0.998782i | \(-0.484286\pi\) | ||||
0.0493472 | + | 0.998782i | \(0.484286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.01907e29 | 0.148614 | ||||||||
\(742\) | 4.19932e28 | 0.0304746 | ||||||||
\(743\) | −6.32010e28 | −0.0452211 | −0.0226105 | − | 0.999744i | \(-0.507198\pi\) | ||||
−0.0226105 | + | 0.999744i | \(0.507198\pi\) | |||||||
\(744\) | 1.92288e29 | 0.135655 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.56944e28 | 0.0519166 | ||||||||
\(747\) | −7.21319e29 | −0.487821 | ||||||||
\(748\) | −8.99761e29 | −0.600013 | ||||||||
\(749\) | 5.03933e28 | 0.0331370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.68105e30 | 1.71429 | 0.857147 | − | 0.515072i | \(-0.172235\pi\) | ||||
0.857147 | + | 0.515072i | \(0.172235\pi\) | |||||||
\(752\) | 4.86678e29 | 0.306870 | ||||||||
\(753\) | 6.97069e29 | 0.433440 | ||||||||
\(754\) | 4.12797e29 | 0.253126 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.36615e29 | −0.260387 | ||||||||
\(757\) | 1.28440e28 | 0.00755429 | 0.00377714 | − | 0.999993i | \(-0.498798\pi\) | ||||
0.00377714 | + | 0.999993i | \(0.498798\pi\) | |||||||
\(758\) | −1.24623e29 | −0.0722891 | ||||||||
\(759\) | 1.59140e30 | 0.910420 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.48703e29 | 0.527948 | 0.263974 | − | 0.964530i | \(-0.414967\pi\) | ||||
0.263974 | + | 0.964530i | \(0.414967\pi\) | |||||||
\(762\) | 1.47439e29 | 0.0809252 | ||||||||
\(763\) | −2.09227e30 | −1.13269 | ||||||||
\(764\) | −1.58978e30 | −0.848902 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.80148e27 | 0.00353347 | ||||||||
\(767\) | 4.94825e30 | 2.53571 | ||||||||
\(768\) | −9.93853e29 | −0.502377 | ||||||||
\(769\) | 3.31983e30 | 1.65535 | 0.827673 | − | 0.561210i | \(-0.189664\pi\) | ||||
0.827673 | + | 0.561210i | \(0.189664\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.08700e29 | 0.0527423 | ||||||||
\(772\) | −7.07572e29 | −0.338680 | ||||||||
\(773\) | −9.83508e29 | −0.464401 | −0.232200 | − | 0.972668i | \(-0.574593\pi\) | ||||
−0.232200 | + | 0.972668i | \(0.574593\pi\) | |||||||
\(774\) | 6.18503e28 | 0.0288112 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.09564e29 | −0.231021 | ||||||||
\(777\) | −3.15182e30 | −1.40975 | ||||||||
\(778\) | 6.17615e28 | 0.0272541 | ||||||||
\(779\) | −4.00186e29 | −0.174228 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.97879e30 | −1.68623 | ||||||||
\(782\) | 2.75792e29 | 0.115321 | ||||||||
\(783\) | −7.51014e29 | −0.309849 | ||||||||
\(784\) | 2.07649e30 | 0.845301 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.94084e29 | −0.0769223 | ||||||||
\(787\) | −2.08470e30 | −0.815283 | −0.407642 | − | 0.913142i | \(-0.633649\pi\) | ||||
−0.407642 | + | 0.913142i | \(0.633649\pi\) | |||||||
\(788\) | −1.92005e30 | −0.740948 | ||||||||
\(789\) | 2.65267e29 | 0.101013 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.10731e30 | 1.52302 | ||||||||
\(792\) | 2.03778e29 | 0.0745665 | ||||||||
\(793\) | −8.93737e28 | −0.0322732 | ||||||||
\(794\) | 6.72055e28 | 0.0239491 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.01007e30 | −1.73883 | ||||||||
\(797\) | 5.27961e30 | 1.80838 | 0.904189 | − | 0.427132i | \(-0.140476\pi\) | ||||
0.904189 | + | 0.427132i | \(0.140476\pi\) | |||||||
\(798\) | −5.07938e28 | −0.0171704 | ||||||||
\(799\) | 5.95286e29 | 0.198602 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.97880e29 | −0.0968053 | ||||||||
\(802\) | −5.07068e29 | −0.162643 | ||||||||
\(803\) | −2.89581e30 | −0.916762 | ||||||||
\(804\) | 2.24543e30 | 0.701635 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.30654e29 | −0.161545 | ||||||||
\(807\) | −8.77138e29 | −0.263570 | ||||||||
\(808\) | 3.22688e29 | 0.0957114 | ||||||||
\(809\) | 1.28746e30 | 0.376942 | 0.188471 | − | 0.982079i | \(-0.439647\pi\) | ||||
0.188471 | + | 0.982079i | \(0.439647\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.27883e30 | 0.364834 | 0.182417 | − | 0.983221i | \(-0.441608\pi\) | ||||
0.182417 | + | 0.983221i | \(0.441608\pi\) | |||||||
\(812\) | 7.73519e30 | 2.17838 | ||||||||
\(813\) | 2.58400e30 | 0.718361 | ||||||||
\(814\) | 7.30610e29 | 0.200507 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.28870e30 | −0.344670 | ||||||||
\(817\) | −5.35957e29 | −0.141514 | ||||||||
\(818\) | 7.85976e29 | 0.204880 | ||||||||
\(819\) | 2.42601e30 | 0.624326 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.58684e30 | 1.40140 | 0.700702 | − | 0.713454i | \(-0.252870\pi\) | ||||
0.700702 | + | 0.713454i | \(0.252870\pi\) | |||||||
\(822\) | 1.80815e29 | 0.0447796 | ||||||||
\(823\) | −2.60095e30 | −0.635965 | −0.317983 | − | 0.948097i | \(-0.603005\pi\) | ||||
−0.317983 | + | 0.948097i | \(0.603005\pi\) | |||||||
\(824\) | 1.28126e29 | 0.0309316 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.24483e30 | −0.292968 | ||||||||
\(827\) | 2.27379e30 | 0.528374 | 0.264187 | − | 0.964471i | \(-0.414896\pi\) | ||||
0.264187 | + | 0.964471i | \(0.414896\pi\) | |||||||
\(828\) | 2.31075e30 | 0.530193 | ||||||||
\(829\) | 7.80903e30 | 1.76919 | 0.884595 | − | 0.466360i | \(-0.154435\pi\) | ||||
0.884595 | + | 0.466360i | \(0.154435\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.18535e30 | −0.482737 | ||||||||
\(832\) | 5.77003e30 | 1.25859 | ||||||||
\(833\) | 2.53988e30 | 0.547068 | ||||||||
\(834\) | −2.39535e29 | −0.0509478 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8.77022e29 | −0.181905 | ||||||||
\(837\) | 9.65436e29 | 0.197745 | ||||||||
\(838\) | 1.01813e30 | 0.205939 | ||||||||
\(839\) | −9.06205e30 | −1.81020 | −0.905099 | − | 0.425201i | \(-0.860203\pi\) | ||||
−0.905099 | + | 0.425201i | \(0.860203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.17233e30 | 1.59217 | ||||||||
\(842\) | 2.94477e29 | 0.0566597 | ||||||||
\(843\) | −5.68950e30 | −1.08115 | ||||||||
\(844\) | −3.52117e30 | −0.660832 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.69609e28 | −0.0122584 | ||||||||
\(847\) | 3.26114e29 | 0.0589649 | ||||||||
\(848\) | 1.03849e30 | 0.185458 | ||||||||
\(849\) | 3.72845e30 | 0.657654 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.66807e31 | 2.87048 | ||||||||
\(852\) | −5.77728e30 | −0.981992 | ||||||||
\(853\) | 4.21419e29 | 0.0707537 | 0.0353769 | − | 0.999374i | \(-0.488737\pi\) | ||||
0.0353769 | + | 0.999374i | \(0.488737\pi\) | |||||||
\(854\) | 2.24838e28 | 0.00372873 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.41511e28 | −0.00552625 | ||||||||
\(857\) | −1.02690e31 | −1.64146 | −0.820729 | − | 0.571318i | \(-0.806432\pi\) | ||||
−0.820729 | + | 0.571318i | \(0.806432\pi\) | |||||||
\(858\) | −5.62363e29 | −0.0887974 | ||||||||
\(859\) | 1.23241e31 | 1.92232 | 0.961161 | − | 0.275988i | \(-0.0890049\pi\) | ||||
0.961161 | + | 0.275988i | \(0.0890049\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.80843e30 | −0.731931 | ||||||||
\(862\) | 1.15153e29 | 0.0173161 | ||||||||
\(863\) | 8.10217e30 | 1.20362 | 0.601808 | − | 0.798641i | \(-0.294447\pi\) | ||||
0.601808 | + | 0.798641i | \(0.294447\pi\) | |||||||
\(864\) | 4.44822e29 | 0.0652817 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.28838e29 | 0.0900743 | ||||||||
\(867\) | 2.50353e30 | 0.354284 | ||||||||
\(868\) | −9.94367e30 | −1.39024 | ||||||||
\(869\) | −2.36830e30 | −0.327136 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.24765e31 | −1.68230 | ||||||||
\(872\) | 1.41792e30 | 0.188898 | ||||||||
\(873\) | −2.55840e30 | −0.336759 | ||||||||
\(874\) | 2.68822e29 | 0.0349618 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.20477e30 | −0.533886 | ||||||||
\(877\) | −2.22627e30 | −0.279307 | −0.139654 | − | 0.990200i | \(-0.544599\pi\) | ||||
−0.139654 | + | 0.990200i | \(0.544599\pi\) | |||||||
\(878\) | −1.09033e30 | −0.135165 | ||||||||
\(879\) | 1.80027e30 | 0.220523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.32997e29 | 0.0278678 | 0.0139339 | − | 0.999903i | \(-0.495565\pi\) | ||||
0.0139339 | + | 0.999903i | \(0.495565\pi\) | |||||||
\(882\) | −2.85699e29 | −0.0337667 | ||||||||
\(883\) | 1.22673e31 | 1.43272 | 0.716361 | − | 0.697730i | \(-0.245807\pi\) | ||||
0.716361 | + | 0.697730i | \(0.245807\pi\) | |||||||
\(884\) | 7.25928e30 | 0.837809 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.51593e29 | 0.0508971 | ||||||||
\(887\) | 7.18852e30 | 0.800647 | 0.400324 | − | 0.916374i | \(-0.368898\pi\) | ||||
0.400324 | + | 0.916374i | \(0.368898\pi\) | |||||||
\(888\) | 2.13596e30 | 0.235103 | ||||||||
\(889\) | −1.53511e31 | −1.66983 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.02312e30 | 0.108696 | ||||||||
\(892\) | −1.74906e31 | −1.83642 | ||||||||
\(893\) | 5.80242e29 | 0.0602100 | ||||||||
\(894\) | 3.21696e29 | 0.0329915 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.09459e30 | −0.610535 | ||||||||
\(897\) | −1.28395e31 | −1.27124 | ||||||||
\(898\) | 7.07396e29 | 0.0692247 | ||||||||
\(899\) | −1.71039e31 | −1.65432 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.27024e30 | 0.120026 | ||||||||
\(902\) | 1.11462e30 | 0.104102 | ||||||||
\(903\) | −6.43978e30 | −0.594497 | ||||||||
\(904\) | −2.78349e30 | −0.253993 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.29174e29 | −0.0471794 | ||||||||
\(907\) | −4.25095e30 | −0.374636 | −0.187318 | − | 0.982299i | \(-0.559979\pi\) | ||||
−0.187318 | + | 0.982299i | \(0.559979\pi\) | |||||||
\(908\) | −1.72904e31 | −1.50627 | ||||||||
\(909\) | 1.62014e30 | 0.139519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.77961e31 | 1.49755 | 0.748775 | − | 0.662825i | \(-0.230643\pi\) | ||||
0.748775 | + | 0.662825i | \(0.230643\pi\) | |||||||
\(912\) | −1.25613e30 | −0.104493 | ||||||||
\(913\) | −1.74093e31 | −1.43165 | ||||||||
\(914\) | 1.18804e30 | 0.0965820 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.76387e31 | −1.40141 | ||||||||
\(917\) | 2.02077e31 | 1.58723 | ||||||||
\(918\) | 1.77308e29 | 0.0137683 | ||||||||
\(919\) | −1.40986e31 | −1.08234 | −0.541169 | − | 0.840914i | \(-0.682018\pi\) | ||||
−0.541169 | + | 0.840914i | \(0.682018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.68330e30 | −0.276383 | ||||||||
\(922\) | 2.81299e30 | 0.208686 | ||||||||
\(923\) | 3.21009e31 | 2.35451 | ||||||||
\(924\) | −1.05378e31 | −0.764181 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.10872e30 | 0.149487 | ||||||||
\(927\) | 6.43292e29 | 0.0450891 | ||||||||
\(928\) | −7.88059e30 | −0.546141 | ||||||||
\(929\) | −3.66823e29 | −0.0251358 | −0.0125679 | − | 0.999921i | \(-0.504001\pi\) | ||||
−0.0125679 | + | 0.999921i | \(0.504001\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.47569e30 | 0.165854 | ||||||||
\(932\) | 2.54824e31 | 1.68800 | ||||||||
\(933\) | 5.02885e30 | 0.329391 | ||||||||
\(934\) | −7.20867e29 | −0.0466888 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.64409e30 | −0.104119 | ||||||||
\(937\) | −1.83413e31 | −1.14859 | −0.574295 | − | 0.818649i | \(-0.694724\pi\) | ||||
−0.574295 | + | 0.818649i | \(0.694724\pi\) | |||||||
\(938\) | 3.13872e30 | 0.194367 | ||||||||
\(939\) | 2.76980e29 | 0.0169613 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.86445e31 | −1.11650 | −0.558250 | − | 0.829673i | \(-0.688527\pi\) | ||||
−0.558250 | + | 0.829673i | \(0.688527\pi\) | |||||||
\(942\) | −7.16208e29 | −0.0424136 | ||||||||
\(943\) | 2.54482e31 | 1.49034 | ||||||||
\(944\) | −3.07846e31 | −1.78290 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.49278e30 | 0.0845548 | ||||||||
\(947\) | −7.59041e30 | −0.425197 | −0.212599 | − | 0.977140i | \(-0.568193\pi\) | ||||
−0.212599 | + | 0.977140i | \(0.568193\pi\) | |||||||
\(948\) | −3.43881e30 | −0.190511 | ||||||||
\(949\) | 2.33634e31 | 1.28009 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.36892e31 | 0.733642 | ||||||||
\(952\) | −3.67695e30 | −0.194895 | ||||||||
\(953\) | 1.85218e31 | 0.970974 | 0.485487 | − | 0.874244i | \(-0.338642\pi\) | ||||
0.485487 | + | 0.874244i | \(0.338642\pi\) | |||||||
\(954\) | −1.42883e29 | −0.00740838 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.73889e31 | −1.38921 | ||||||||
\(957\) | −1.81260e31 | −0.909339 | ||||||||
\(958\) | 1.02157e30 | 0.0506911 | ||||||||
\(959\) | −1.88262e31 | −0.923991 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.16178e30 | 0.0557865 | ||||||||
\(962\) | −5.89457e30 | −0.279971 | ||||||||
\(963\) | −1.71465e29 | −0.00805562 | ||||||||
\(964\) | −1.68700e31 | −0.783984 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.23002e30 | 0.146874 | ||||||||
\(967\) | −1.68944e31 | −0.759915 | −0.379957 | − | 0.925004i | \(-0.624061\pi\) | ||||
−0.379957 | + | 0.925004i | \(0.624061\pi\) | |||||||
\(968\) | −2.21005e29 | −0.00983354 | ||||||||
\(969\) | −1.53645e30 | −0.0676266 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.19989e31 | −1.80899 | −0.904494 | − | 0.426487i | \(-0.859751\pi\) | ||||
−0.904494 | + | 0.426487i | \(0.859751\pi\) | |||||||
\(972\) | 1.48560e30 | 0.0633002 | ||||||||
\(973\) | 2.49401e31 | 1.05127 | ||||||||
\(974\) | −1.90475e30 | −0.0794272 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.56022e29 | 0.0226918 | ||||||||
\(977\) | −2.58281e31 | −1.04280 | −0.521399 | − | 0.853313i | \(-0.674590\pi\) | ||||
−0.521399 | + | 0.853313i | \(0.674590\pi\) | |||||||
\(978\) | −2.12564e30 | −0.0849045 | ||||||||
\(979\) | −7.18942e30 | −0.284103 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.11903e30 | 0.275357 | ||||||||
\(982\) | 2.21371e29 | 0.00847130 | ||||||||
\(983\) | 2.49436e31 | 0.944382 | 0.472191 | − | 0.881496i | \(-0.343463\pi\) | ||||
0.472191 | + | 0.881496i | \(0.343463\pi\) | |||||||
\(984\) | 3.25863e30 | 0.122064 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.14125e30 | −0.115185 | ||||||||
\(987\) | 6.97189e30 | 0.252942 | ||||||||
\(988\) | 7.07582e30 | 0.253997 | ||||||||
\(989\) | 3.40820e31 | 1.21050 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.31091e31 | 1.15126 | 0.575631 | − | 0.817710i | \(-0.304757\pi\) | ||||
0.575631 | + | 0.817710i | \(0.304757\pi\) | |||||||
\(992\) | 1.01306e31 | 0.348547 | ||||||||
\(993\) | −2.14997e30 | −0.0731923 | ||||||||
\(994\) | −8.07564e30 | −0.272032 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.52786e31 | −0.833738 | ||||||||
\(997\) | −4.06660e31 | −1.32719 | −0.663594 | − | 0.748093i | \(-0.730970\pi\) | ||||
−0.663594 | + | 0.748093i | \(0.730970\pi\) | |||||||
\(998\) | −5.39731e30 | −0.174304 | ||||||||
\(999\) | 1.07242e31 | 0.342709 |
(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 | 75.22.a.l.1.4 | yes | 8 | |
5.2 | odd | 4 | 75.22.b.j.49.8 | 16 | |||
5.3 | odd | 4 | 75.22.b.j.49.9 | 16 | |||
5.4 | even | 2 | 75.22.a.k.1.5 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.22.a.k.1.5 | ✓ | 8 | 5.4 | even | 2 | ||
75.22.a.l.1.4 | yes | 8 | 1.1 | even | 1 | trivial | |
75.22.b.j.49.8 | 16 | 5.2 | odd | 4 | |||
75.22.b.j.49.9 | 16 | 5.3 | odd | 4 |