Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,26,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(39.5996779952\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 6900880 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2627.45\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | −1.63785e6 | −1.77934 | −0.889668 | − | 0.456608i | \(-0.849064\pi\) | ||||
−0.889668 | + | 0.456608i | \(0.849064\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 2.44141e8 | 0.447214 | ||||||||
\(6\) | 6.70863e9 | 1.25818 | ||||||||
\(7\) | −2.07876e10 | −0.567647 | −0.283824 | − | 0.958877i | \(-0.591603\pi\) | ||||
−0.283824 | + | 0.958877i | \(0.591603\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 1.83526e12 | 2.16604 | ||||||||
\(10\) | −1.00000e12 | −0.316228 | ||||||||
\(11\) | 4.14605e12 | 0.398314 | 0.199157 | − | 0.979968i | \(-0.436180\pi\) | ||||
0.199157 | + | 0.979968i | \(0.436180\pi\) | |||||||
\(12\) | −2.74785e13 | −0.889668 | ||||||||
\(13\) | −1.30955e14 | −1.55894 | −0.779469 | − | 0.626441i | \(-0.784511\pi\) | ||||
−0.779469 | + | 0.626441i | \(0.784511\pi\) | |||||||
\(14\) | 8.51459e13 | 0.401387 | ||||||||
\(15\) | −3.99865e14 | −0.795743 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −4.62477e15 | −1.92521 | −0.962606 | − | 0.270904i | \(-0.912677\pi\) | ||||
−0.962606 | + | 0.270904i | \(0.912677\pi\) | |||||||
\(18\) | −7.51722e15 | −1.53162 | ||||||||
\(19\) | −5.62727e15 | −0.583280 | −0.291640 | − | 0.956528i | \(-0.594201\pi\) | ||||
−0.291640 | + | 0.956528i | \(0.594201\pi\) | |||||||
\(20\) | 4.09600e15 | 0.223607 | ||||||||
\(21\) | 3.40469e16 | 1.01004 | ||||||||
\(22\) | −1.69822e16 | −0.281651 | ||||||||
\(23\) | −2.45654e16 | −0.233737 | −0.116868 | − | 0.993147i | \(-0.537286\pi\) | ||||
−0.116868 | + | 0.993147i | \(0.537286\pi\) | |||||||
\(24\) | 1.12552e17 | 0.629090 | ||||||||
\(25\) | 5.96046e16 | 0.200000 | ||||||||
\(26\) | 5.36390e17 | 1.10234 | ||||||||
\(27\) | −1.61815e18 | −2.07477 | ||||||||
\(28\) | −3.48758e17 | −0.283824 | ||||||||
\(29\) | −1.86225e18 | −0.977382 | −0.488691 | − | 0.872457i | \(-0.662525\pi\) | ||||
−0.488691 | + | 0.872457i | \(0.662525\pi\) | |||||||
\(30\) | 1.63785e18 | 0.562676 | ||||||||
\(31\) | 7.10276e17 | 0.161959 | 0.0809796 | − | 0.996716i | \(-0.474195\pi\) | ||||
0.0809796 | + | 0.996716i | \(0.474195\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | −6.79060e18 | −0.708735 | ||||||||
\(34\) | 1.89431e19 | 1.36133 | ||||||||
\(35\) | −5.07509e18 | −0.253860 | ||||||||
\(36\) | 3.07905e19 | 1.08302 | ||||||||
\(37\) | 5.29105e19 | 1.32136 | 0.660679 | − | 0.750669i | \(-0.270269\pi\) | ||||
0.660679 | + | 0.750669i | \(0.270269\pi\) | |||||||
\(38\) | 2.30493e19 | 0.412442 | ||||||||
\(39\) | 2.14484e20 | 2.77387 | ||||||||
\(40\) | −1.67772e19 | −0.158114 | ||||||||
\(41\) | −2.57715e20 | −1.78378 | −0.891892 | − | 0.452249i | \(-0.850622\pi\) | ||||
−0.891892 | + | 0.452249i | \(0.850622\pi\) | |||||||
\(42\) | −1.39456e20 | −0.714203 | ||||||||
\(43\) | −1.94678e19 | −0.0742954 | −0.0371477 | − | 0.999310i | \(-0.511827\pi\) | ||||
−0.0371477 | + | 0.999310i | \(0.511827\pi\) | |||||||
\(44\) | 6.95591e19 | 0.199157 | ||||||||
\(45\) | 4.48061e20 | 0.968681 | ||||||||
\(46\) | 1.00620e20 | 0.165277 | ||||||||
\(47\) | 1.05479e21 | 1.32417 | 0.662085 | − | 0.749428i | \(-0.269672\pi\) | ||||
0.662085 | + | 0.749428i | \(0.269672\pi\) | |||||||
\(48\) | −4.61013e20 | −0.444834 | ||||||||
\(49\) | −9.08945e20 | −0.677777 | ||||||||
\(50\) | −2.44141e20 | −0.141421 | ||||||||
\(51\) | 7.57467e21 | 3.42560 | ||||||||
\(52\) | −2.19705e21 | −0.779469 | ||||||||
\(53\) | 1.71922e21 | 0.480709 | 0.240354 | − | 0.970685i | \(-0.422736\pi\) | ||||
0.240354 | + | 0.970685i | \(0.422736\pi\) | |||||||
\(54\) | 6.62792e21 | 1.46709 | ||||||||
\(55\) | 1.01222e21 | 0.178132 | ||||||||
\(56\) | 1.42851e21 | 0.200694 | ||||||||
\(57\) | 9.21661e21 | 1.03785 | ||||||||
\(58\) | 7.62780e21 | 0.691113 | ||||||||
\(59\) | −2.29629e22 | −1.68026 | −0.840130 | − | 0.542386i | \(-0.817521\pi\) | ||||
−0.840130 | + | 0.542386i | \(0.817521\pi\) | |||||||
\(60\) | −6.70863e21 | −0.397872 | ||||||||
\(61\) | −9.00207e20 | −0.0434230 | −0.0217115 | − | 0.999764i | \(-0.506912\pi\) | ||||
−0.0217115 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(62\) | −2.90929e21 | −0.114523 | ||||||||
\(63\) | −3.81506e22 | −1.22955 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | −3.19713e22 | −0.697178 | ||||||||
\(66\) | 2.78143e22 | 0.501151 | ||||||||
\(67\) | −1.50272e22 | −0.224358 | −0.112179 | − | 0.993688i | \(-0.535783\pi\) | ||||
−0.112179 | + | 0.993688i | \(0.535783\pi\) | |||||||
\(68\) | −7.75908e22 | −0.962606 | ||||||||
\(69\) | 4.02345e22 | 0.415896 | ||||||||
\(70\) | 2.07876e22 | 0.179506 | ||||||||
\(71\) | 2.23447e23 | 1.61602 | 0.808008 | − | 0.589172i | \(-0.200546\pi\) | ||||
0.808008 | + | 0.589172i | \(0.200546\pi\) | |||||||
\(72\) | −1.26118e23 | −0.765810 | ||||||||
\(73\) | −3.25252e23 | −1.66220 | −0.831101 | − | 0.556122i | \(-0.812289\pi\) | ||||
−0.831101 | + | 0.556122i | \(0.812289\pi\) | |||||||
\(74\) | −2.16721e23 | −0.934341 | ||||||||
\(75\) | −9.76234e22 | −0.355867 | ||||||||
\(76\) | −9.44099e22 | −0.291640 | ||||||||
\(77\) | −8.61863e22 | −0.226102 | ||||||||
\(78\) | −8.78525e23 | −1.96142 | ||||||||
\(79\) | 6.06979e23 | 1.15567 | 0.577837 | − | 0.816152i | \(-0.303897\pi\) | ||||
0.577837 | + | 0.816152i | \(0.303897\pi\) | |||||||
\(80\) | 6.87195e22 | 0.111803 | ||||||||
\(81\) | 1.09528e24 | 1.52568 | ||||||||
\(82\) | 1.05560e24 | 1.26133 | ||||||||
\(83\) | −7.26128e23 | −0.745653 | −0.372827 | − | 0.927901i | \(-0.621611\pi\) | ||||
−0.372827 | + | 0.927901i | \(0.621611\pi\) | |||||||
\(84\) | 5.71212e23 | 0.505018 | ||||||||
\(85\) | −1.12909e24 | −0.860981 | ||||||||
\(86\) | 7.97403e22 | 0.0525348 | ||||||||
\(87\) | 3.05009e24 | 1.73909 | ||||||||
\(88\) | −2.84914e23 | −0.140825 | ||||||||
\(89\) | 1.91182e24 | 0.820488 | 0.410244 | − | 0.911976i | \(-0.365444\pi\) | ||||
0.410244 | + | 0.911976i | \(0.365444\pi\) | |||||||
\(90\) | −1.83526e24 | −0.684961 | ||||||||
\(91\) | 2.72223e24 | 0.884926 | ||||||||
\(92\) | −4.12140e23 | −0.116868 | ||||||||
\(93\) | −1.16332e24 | −0.288180 | ||||||||
\(94\) | −4.32043e24 | −0.936330 | ||||||||
\(95\) | −1.37384e24 | −0.260851 | ||||||||
\(96\) | 1.88831e24 | 0.314545 | ||||||||
\(97\) | −1.71656e24 | −0.251195 | −0.125598 | − | 0.992081i | \(-0.540085\pi\) | ||||
−0.125598 | + | 0.992081i | \(0.540085\pi\) | |||||||
\(98\) | 3.72304e24 | 0.479260 | ||||||||
\(99\) | 7.60907e24 | 0.862763 | ||||||||
\(100\) | 1.00000e24 | 0.100000 | ||||||||
\(101\) | 1.34215e25 | 1.18518 | 0.592590 | − | 0.805504i | \(-0.298105\pi\) | ||||
0.592590 | + | 0.805504i | \(0.298105\pi\) | |||||||
\(102\) | −3.10259e25 | −2.42227 | ||||||||
\(103\) | 2.08010e25 | 1.43754 | 0.718769 | − | 0.695249i | \(-0.244706\pi\) | ||||
0.718769 | + | 0.695249i | \(0.244706\pi\) | |||||||
\(104\) | 8.99913e24 | 0.551168 | ||||||||
\(105\) | 8.31223e24 | 0.451701 | ||||||||
\(106\) | −7.04191e24 | −0.339912 | ||||||||
\(107\) | 2.98949e25 | 1.28322 | 0.641609 | − | 0.767032i | \(-0.278267\pi\) | ||||
0.641609 | + | 0.767032i | \(0.278267\pi\) | |||||||
\(108\) | −2.71480e25 | −1.03739 | ||||||||
\(109\) | 5.99753e24 | 0.204240 | 0.102120 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102120 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(110\) | −4.14605e24 | −0.125958 | ||||||||
\(111\) | −8.66594e25 | −2.35114 | ||||||||
\(112\) | −5.85118e24 | −0.141912 | ||||||||
\(113\) | −3.21651e25 | −0.698080 | −0.349040 | − | 0.937108i | \(-0.613492\pi\) | ||||
−0.349040 | + | 0.937108i | \(0.613492\pi\) | |||||||
\(114\) | −3.77512e25 | −0.733872 | ||||||||
\(115\) | −5.99742e24 | −0.104530 | ||||||||
\(116\) | −3.12435e25 | −0.488691 | ||||||||
\(117\) | −2.40335e26 | −3.37672 | ||||||||
\(118\) | 9.40560e25 | 1.18812 | ||||||||
\(119\) | 9.61378e25 | 1.09284 | ||||||||
\(120\) | 2.74785e25 | 0.281338 | ||||||||
\(121\) | −9.11573e25 | −0.841346 | ||||||||
\(122\) | 3.68725e24 | 0.0307047 | ||||||||
\(123\) | 4.22099e26 | 3.17395 | ||||||||
\(124\) | 1.19165e25 | 0.0809796 | ||||||||
\(125\) | 1.45519e25 | 0.0894427 | ||||||||
\(126\) | 1.56265e26 | 0.869420 | ||||||||
\(127\) | −1.12460e26 | −0.566829 | −0.283414 | − | 0.958998i | \(-0.591467\pi\) | ||||
−0.283414 | + | 0.958998i | \(0.591467\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | 3.18854e25 | 0.132197 | ||||||||
\(130\) | 1.30955e26 | 0.492979 | ||||||||
\(131\) | 2.26749e26 | 0.775630 | 0.387815 | − | 0.921737i | \(-0.373230\pi\) | ||||
0.387815 | + | 0.921737i | \(0.373230\pi\) | |||||||
\(132\) | −1.13927e26 | −0.354367 | ||||||||
\(133\) | 1.16977e26 | 0.331098 | ||||||||
\(134\) | 6.15513e25 | 0.158645 | ||||||||
\(135\) | −3.95055e26 | −0.927867 | ||||||||
\(136\) | 3.17812e26 | 0.680665 | ||||||||
\(137\) | 6.81423e26 | 1.33171 | 0.665855 | − | 0.746081i | \(-0.268067\pi\) | ||||
0.665855 | + | 0.746081i | \(0.268067\pi\) | |||||||
\(138\) | −1.64800e26 | −0.294083 | ||||||||
\(139\) | 5.03091e26 | 0.820279 | 0.410140 | − | 0.912023i | \(-0.365480\pi\) | ||||
0.410140 | + | 0.912023i | \(0.365480\pi\) | |||||||
\(140\) | −8.51459e25 | −0.126930 | ||||||||
\(141\) | −1.72759e27 | −2.35614 | ||||||||
\(142\) | −9.15240e26 | −1.14270 | ||||||||
\(143\) | −5.42944e26 | −0.620947 | ||||||||
\(144\) | 5.16579e26 | 0.541509 | ||||||||
\(145\) | −4.54652e26 | −0.437098 | ||||||||
\(146\) | 1.33223e27 | 1.17535 | ||||||||
\(147\) | 1.48871e27 | 1.20599 | ||||||||
\(148\) | 8.87691e26 | 0.660679 | ||||||||
\(149\) | 7.27393e26 | 0.497669 | 0.248835 | − | 0.968546i | \(-0.419952\pi\) | ||||
0.248835 | + | 0.968546i | \(0.419952\pi\) | |||||||
\(150\) | 3.99865e26 | 0.251636 | ||||||||
\(151\) | 9.92827e25 | 0.0574992 | 0.0287496 | − | 0.999587i | \(-0.490847\pi\) | ||||
0.0287496 | + | 0.999587i | \(0.490847\pi\) | |||||||
\(152\) | 3.86703e26 | 0.206221 | ||||||||
\(153\) | −8.48765e27 | −4.17008 | ||||||||
\(154\) | 3.53019e26 | 0.159878 | ||||||||
\(155\) | 1.73407e26 | 0.0724304 | ||||||||
\(156\) | 3.59844e27 | 1.38694 | ||||||||
\(157\) | −2.27168e26 | −0.0808355 | −0.0404177 | − | 0.999183i | \(-0.512869\pi\) | ||||
−0.0404177 | + | 0.999183i | \(0.512869\pi\) | |||||||
\(158\) | −2.48619e27 | −0.817184 | ||||||||
\(159\) | −2.81581e27 | −0.855342 | ||||||||
\(160\) | −2.81475e26 | −0.0790569 | ||||||||
\(161\) | 5.10656e26 | 0.132680 | ||||||||
\(162\) | −4.48628e27 | −1.07882 | ||||||||
\(163\) | 5.17654e27 | 1.15264 | 0.576322 | − | 0.817223i | \(-0.304488\pi\) | ||||
0.576322 | + | 0.817223i | \(0.304488\pi\) | |||||||
\(164\) | −4.32375e27 | −0.891892 | ||||||||
\(165\) | −1.65786e27 | −0.316956 | ||||||||
\(166\) | 2.97422e27 | 0.527256 | ||||||||
\(167\) | 1.02965e27 | 0.169330 | 0.0846652 | − | 0.996409i | \(-0.473018\pi\) | ||||
0.0846652 | + | 0.996409i | \(0.473018\pi\) | |||||||
\(168\) | −2.33969e27 | −0.357101 | ||||||||
\(169\) | 1.00927e28 | 1.43029 | ||||||||
\(170\) | 4.62477e27 | 0.608806 | ||||||||
\(171\) | −1.03275e28 | −1.26341 | ||||||||
\(172\) | −3.26616e26 | −0.0371477 | ||||||||
\(173\) | 1.24548e28 | 1.31753 | 0.658766 | − | 0.752348i | \(-0.271079\pi\) | ||||
0.658766 | + | 0.752348i | \(0.271079\pi\) | |||||||
\(174\) | −1.24932e28 | −1.22972 | ||||||||
\(175\) | −1.23904e27 | −0.113529 | ||||||||
\(176\) | 1.16701e27 | 0.0995785 | ||||||||
\(177\) | 3.76097e28 | 2.98975 | ||||||||
\(178\) | −7.83082e27 | −0.580173 | ||||||||
\(179\) | 4.58615e27 | 0.316800 | 0.158400 | − | 0.987375i | \(-0.449366\pi\) | ||||
0.158400 | + | 0.987375i | \(0.449366\pi\) | |||||||
\(180\) | 7.51722e27 | 0.484341 | ||||||||
\(181\) | −1.24754e28 | −0.750019 | −0.375010 | − | 0.927021i | \(-0.622361\pi\) | ||||
−0.375010 | + | 0.927021i | \(0.622361\pi\) | |||||||
\(182\) | −1.11502e28 | −0.625737 | ||||||||
\(183\) | 1.47440e27 | 0.0772641 | ||||||||
\(184\) | 1.68812e27 | 0.0826384 | ||||||||
\(185\) | 1.29176e28 | 0.590929 | ||||||||
\(186\) | 4.76498e27 | 0.203774 | ||||||||
\(187\) | −1.91745e28 | −0.766839 | ||||||||
\(188\) | 1.76965e28 | 0.662085 | ||||||||
\(189\) | 3.36373e28 | 1.17774 | ||||||||
\(190\) | 5.62727e27 | 0.184449 | ||||||||
\(191\) | −5.82809e28 | −1.78900 | −0.894498 | − | 0.447072i | \(-0.852467\pi\) | ||||
−0.894498 | + | 0.447072i | \(0.852467\pi\) | |||||||
\(192\) | −7.73452e27 | −0.222417 | ||||||||
\(193\) | −2.07224e28 | −0.558437 | −0.279218 | − | 0.960228i | \(-0.590075\pi\) | ||||
−0.279218 | + | 0.960228i | \(0.590075\pi\) | |||||||
\(194\) | 7.03102e27 | 0.177622 | ||||||||
\(195\) | 5.23642e28 | 1.24051 | ||||||||
\(196\) | −1.52496e28 | −0.338888 | ||||||||
\(197\) | 2.21753e28 | 0.462425 | 0.231213 | − | 0.972903i | \(-0.425731\pi\) | ||||
0.231213 | + | 0.972903i | \(0.425731\pi\) | |||||||
\(198\) | −3.11668e28 | −0.610066 | ||||||||
\(199\) | −2.56881e28 | −0.472138 | −0.236069 | − | 0.971736i | \(-0.575859\pi\) | ||||
−0.236069 | + | 0.971736i | \(0.575859\pi\) | |||||||
\(200\) | −4.09600e27 | −0.0707107 | ||||||||
\(201\) | 2.46122e28 | 0.399209 | ||||||||
\(202\) | −5.49745e28 | −0.838049 | ||||||||
\(203\) | 3.87118e28 | 0.554808 | ||||||||
\(204\) | 1.27082e29 | 1.71280 | ||||||||
\(205\) | −6.29188e28 | −0.797732 | ||||||||
\(206\) | −8.52010e28 | −1.01649 | ||||||||
\(207\) | −4.50839e28 | −0.506282 | ||||||||
\(208\) | −3.68604e28 | −0.389734 | ||||||||
\(209\) | −2.33309e28 | −0.232329 | ||||||||
\(210\) | −3.40469e28 | −0.319401 | ||||||||
\(211\) | −1.69750e29 | −1.50065 | −0.750323 | − | 0.661072i | \(-0.770102\pi\) | ||||
−0.750323 | + | 0.661072i | \(0.770102\pi\) | |||||||
\(212\) | 2.88437e28 | 0.240354 | ||||||||
\(213\) | −3.65973e29 | −2.87543 | ||||||||
\(214\) | −1.22450e29 | −0.907372 | ||||||||
\(215\) | −4.75289e27 | −0.0332259 | ||||||||
\(216\) | 1.11198e29 | 0.733543 | ||||||||
\(217\) | −1.47649e28 | −0.0919357 | ||||||||
\(218\) | −2.45659e28 | −0.144420 | ||||||||
\(219\) | 5.32713e29 | 2.95762 | ||||||||
\(220\) | 1.69822e28 | 0.0890658 | ||||||||
\(221\) | 6.05635e29 | 3.00129 | ||||||||
\(222\) | 3.54957e29 | 1.66251 | ||||||||
\(223\) | −1.64686e29 | −0.729197 | −0.364598 | − | 0.931165i | \(-0.618794\pi\) | ||||
−0.364598 | + | 0.931165i | \(0.618794\pi\) | |||||||
\(224\) | 2.39665e28 | 0.100347 | ||||||||
\(225\) | 1.09390e29 | 0.433207 | ||||||||
\(226\) | 1.31748e29 | 0.493617 | ||||||||
\(227\) | −5.10933e29 | −1.81151 | −0.905754 | − | 0.423803i | \(-0.860695\pi\) | ||||
−0.905754 | + | 0.423803i | \(0.860695\pi\) | |||||||
\(228\) | 1.54629e29 | 0.518926 | ||||||||
\(229\) | 1.25023e29 | 0.397235 | 0.198617 | − | 0.980077i | \(-0.436355\pi\) | ||||
0.198617 | + | 0.980077i | \(0.436355\pi\) | |||||||
\(230\) | 2.45654e28 | 0.0739140 | ||||||||
\(231\) | 1.41160e29 | 0.402311 | ||||||||
\(232\) | 1.27973e29 | 0.345557 | ||||||||
\(233\) | −5.70548e29 | −1.45997 | −0.729984 | − | 0.683464i | \(-0.760472\pi\) | ||||
−0.729984 | + | 0.683464i | \(0.760472\pi\) | |||||||
\(234\) | 9.84414e29 | 2.38770 | ||||||||
\(235\) | 2.57518e29 | 0.592187 | ||||||||
\(236\) | −3.85253e29 | −0.840130 | ||||||||
\(237\) | −9.94140e29 | −2.05633 | ||||||||
\(238\) | −3.93780e29 | −0.772756 | ||||||||
\(239\) | 6.05498e29 | 1.12756 | 0.563780 | − | 0.825925i | \(-0.309347\pi\) | ||||
0.563780 | + | 0.825925i | \(0.309347\pi\) | |||||||
\(240\) | −1.12552e29 | −0.198936 | ||||||||
\(241\) | −5.11295e29 | −0.857943 | −0.428972 | − | 0.903318i | \(-0.641124\pi\) | ||||
−0.428972 | + | 0.903318i | \(0.641124\pi\) | |||||||
\(242\) | 3.73380e29 | 0.594921 | ||||||||
\(243\) | −4.22872e29 | −0.639927 | ||||||||
\(244\) | −1.51030e28 | −0.0217115 | ||||||||
\(245\) | −2.21910e29 | −0.303111 | ||||||||
\(246\) | −1.72892e30 | −2.24432 | ||||||||
\(247\) | 7.36916e29 | 0.909298 | ||||||||
\(248\) | −4.88098e28 | −0.0572613 | ||||||||
\(249\) | 1.18929e30 | 1.32677 | ||||||||
\(250\) | −5.96046e28 | −0.0632456 | ||||||||
\(251\) | 2.51767e29 | 0.254142 | 0.127071 | − | 0.991894i | \(-0.459442\pi\) | ||||
0.127071 | + | 0.991894i | \(0.459442\pi\) | |||||||
\(252\) | −6.40061e29 | −0.614773 | ||||||||
\(253\) | −1.01850e29 | −0.0931006 | ||||||||
\(254\) | 4.60636e29 | 0.400808 | ||||||||
\(255\) | 1.84929e30 | 1.53198 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 4.32516e29 | 0.324967 | 0.162483 | − | 0.986711i | \(-0.448050\pi\) | ||||
0.162483 | + | 0.986711i | \(0.448050\pi\) | |||||||
\(258\) | −1.30603e29 | −0.0934771 | ||||||||
\(259\) | −1.09988e30 | −0.750065 | ||||||||
\(260\) | −5.36390e29 | −0.348589 | ||||||||
\(261\) | −3.41772e30 | −2.11705 | ||||||||
\(262\) | −9.28765e29 | −0.548454 | ||||||||
\(263\) | 3.00951e30 | 1.69453 | 0.847265 | − | 0.531171i | \(-0.178248\pi\) | ||||
0.847265 | + | 0.531171i | \(0.178248\pi\) | |||||||
\(264\) | 4.66646e29 | 0.250576 | ||||||||
\(265\) | 4.19730e29 | 0.214979 | ||||||||
\(266\) | −4.79139e29 | −0.234121 | ||||||||
\(267\) | −3.13127e30 | −1.45992 | ||||||||
\(268\) | −2.52114e29 | −0.112179 | ||||||||
\(269\) | 5.09495e29 | 0.216390 | 0.108195 | − | 0.994130i | \(-0.465493\pi\) | ||||
0.108195 | + | 0.994130i | \(0.465493\pi\) | |||||||
\(270\) | 1.61815e30 | 0.656101 | ||||||||
\(271\) | 1.05937e30 | 0.410140 | 0.205070 | − | 0.978747i | \(-0.434258\pi\) | ||||
0.205070 | + | 0.978747i | \(0.434258\pi\) | |||||||
\(272\) | −1.30176e30 | −0.481303 | ||||||||
\(273\) | −4.45860e30 | −1.57458 | ||||||||
\(274\) | −2.79111e30 | −0.941661 | ||||||||
\(275\) | 2.47124e29 | 0.0796628 | ||||||||
\(276\) | 6.75022e29 | 0.207948 | ||||||||
\(277\) | 5.67674e30 | 1.67148 | 0.835741 | − | 0.549124i | \(-0.185039\pi\) | ||||
0.835741 | + | 0.549124i | \(0.185039\pi\) | |||||||
\(278\) | −2.06066e30 | −0.580025 | ||||||||
\(279\) | 1.30354e30 | 0.350810 | ||||||||
\(280\) | 3.48758e29 | 0.0897529 | ||||||||
\(281\) | −1.50424e30 | −0.370245 | −0.185122 | − | 0.982715i | \(-0.559268\pi\) | ||||
−0.185122 | + | 0.982715i | \(0.559268\pi\) | |||||||
\(282\) | 7.07621e30 | 1.66605 | ||||||||
\(283\) | −4.46973e30 | −1.00682 | −0.503409 | − | 0.864048i | \(-0.667921\pi\) | ||||
−0.503409 | + | 0.864048i | \(0.667921\pi\) | |||||||
\(284\) | 3.74882e30 | 0.808008 | ||||||||
\(285\) | 2.25015e30 | 0.464142 | ||||||||
\(286\) | 2.22390e30 | 0.439076 | ||||||||
\(287\) | 5.35728e30 | 1.01256 | ||||||||
\(288\) | −2.11591e30 | −0.382905 | ||||||||
\(289\) | 1.56179e31 | 2.70644 | ||||||||
\(290\) | 1.86225e30 | 0.309075 | ||||||||
\(291\) | 2.81146e30 | 0.446961 | ||||||||
\(292\) | −5.45682e30 | −0.831101 | ||||||||
\(293\) | 4.32602e30 | 0.631311 | 0.315655 | − | 0.948874i | \(-0.397776\pi\) | ||||
0.315655 | + | 0.948874i | \(0.397776\pi\) | |||||||
\(294\) | −6.09777e30 | −0.852766 | ||||||||
\(295\) | −5.60617e30 | −0.751435 | ||||||||
\(296\) | −3.63598e30 | −0.467170 | ||||||||
\(297\) | −6.70891e30 | −0.826411 | ||||||||
\(298\) | −2.97940e30 | −0.351905 | ||||||||
\(299\) | 3.21696e30 | 0.364381 | ||||||||
\(300\) | −1.63785e30 | −0.177934 | ||||||||
\(301\) | 4.04689e29 | 0.0421736 | ||||||||
\(302\) | −4.06662e29 | −0.0406581 | ||||||||
\(303\) | −2.19824e31 | −2.10883 | ||||||||
\(304\) | −1.58393e30 | −0.145820 | ||||||||
\(305\) | −2.19777e29 | −0.0194193 | ||||||||
\(306\) | 3.47654e31 | 2.94869 | ||||||||
\(307\) | 1.40982e31 | 1.14798 | 0.573991 | − | 0.818862i | \(-0.305395\pi\) | ||||
0.573991 | + | 0.818862i | \(0.305395\pi\) | |||||||
\(308\) | −1.44597e30 | −0.113051 | ||||||||
\(309\) | −3.40689e31 | −2.55786 | ||||||||
\(310\) | −7.10276e29 | −0.0512160 | ||||||||
\(311\) | −4.30946e30 | −0.298482 | −0.149241 | − | 0.988801i | \(-0.547683\pi\) | ||||
−0.149241 | + | 0.988801i | \(0.547683\pi\) | |||||||
\(312\) | −1.47392e31 | −0.980712 | ||||||||
\(313\) | −2.24958e30 | −0.143813 | −0.0719065 | − | 0.997411i | \(-0.522908\pi\) | ||||
−0.0719065 | + | 0.997411i | \(0.522908\pi\) | |||||||
\(314\) | 9.30481e29 | 0.0571593 | ||||||||
\(315\) | −9.31411e30 | −0.549869 | ||||||||
\(316\) | 1.01834e31 | 0.577837 | ||||||||
\(317\) | 7.47129e30 | 0.407525 | 0.203763 | − | 0.979020i | \(-0.434683\pi\) | ||||
0.203763 | + | 0.979020i | \(0.434683\pi\) | |||||||
\(318\) | 1.15336e31 | 0.604818 | ||||||||
\(319\) | −7.72100e30 | −0.389305 | ||||||||
\(320\) | 1.15292e30 | 0.0559017 | ||||||||
\(321\) | −4.89634e31 | −2.28328 | ||||||||
\(322\) | −2.09165e30 | −0.0938189 | ||||||||
\(323\) | 2.60248e31 | 1.12294 | ||||||||
\(324\) | 1.83758e31 | 0.762840 | ||||||||
\(325\) | −7.80550e30 | −0.311787 | ||||||||
\(326\) | −2.12031e31 | −0.815042 | ||||||||
\(327\) | −9.82304e30 | −0.363412 | ||||||||
\(328\) | 1.77101e31 | 0.630663 | ||||||||
\(329\) | −2.19266e31 | −0.751662 | ||||||||
\(330\) | 6.79060e30 | 0.224122 | ||||||||
\(331\) | −1.01412e31 | −0.322286 | −0.161143 | − | 0.986931i | \(-0.551518\pi\) | ||||
−0.161143 | + | 0.986931i | \(0.551518\pi\) | |||||||
\(332\) | −1.21824e31 | −0.372827 | ||||||||
\(333\) | 9.71045e31 | 2.86211 | ||||||||
\(334\) | −4.21746e30 | −0.119735 | ||||||||
\(335\) | −3.66874e30 | −0.100336 | ||||||||
\(336\) | 9.58335e30 | 0.252509 | ||||||||
\(337\) | −4.27054e31 | −1.08420 | −0.542099 | − | 0.840315i | \(-0.682370\pi\) | ||||
−0.542099 | + | 0.840315i | \(0.682370\pi\) | |||||||
\(338\) | −4.13396e31 | −1.01136 | ||||||||
\(339\) | 5.26816e31 | 1.24212 | ||||||||
\(340\) | −1.89431e31 | −0.430491 | ||||||||
\(341\) | 2.94484e30 | 0.0645107 | ||||||||
\(342\) | 4.23014e31 | 0.893364 | ||||||||
\(343\) | 4.67723e31 | 0.952385 | ||||||||
\(344\) | 1.33782e30 | 0.0262674 | ||||||||
\(345\) | 9.82287e30 | 0.185994 | ||||||||
\(346\) | −5.10149e31 | −0.931636 | ||||||||
\(347\) | 1.42992e30 | 0.0251880 | 0.0125940 | − | 0.999921i | \(-0.495991\pi\) | ||||
0.0125940 | + | 0.999921i | \(0.495991\pi\) | |||||||
\(348\) | 5.11720e31 | 0.869545 | ||||||||
\(349\) | 3.55571e30 | 0.0582920 | 0.0291460 | − | 0.999575i | \(-0.490721\pi\) | ||||
0.0291460 | + | 0.999575i | \(0.490721\pi\) | |||||||
\(350\) | 5.07509e30 | 0.0802774 | ||||||||
\(351\) | 2.11903e32 | 3.23444 | ||||||||
\(352\) | −4.78007e30 | −0.0704127 | ||||||||
\(353\) | 6.63973e31 | 0.943988 | 0.471994 | − | 0.881602i | \(-0.343534\pi\) | ||||
0.471994 | + | 0.881602i | \(0.343534\pi\) | |||||||
\(354\) | −1.54049e32 | −2.11407 | ||||||||
\(355\) | 5.45525e31 | 0.722704 | ||||||||
\(356\) | 3.20750e31 | 0.410244 | ||||||||
\(357\) | −1.57459e32 | −1.94453 | ||||||||
\(358\) | −1.87849e31 | −0.224012 | ||||||||
\(359\) | −1.86335e31 | −0.214593 | −0.107296 | − | 0.994227i | \(-0.534219\pi\) | ||||
−0.107296 | + | 0.994227i | \(0.534219\pi\) | |||||||
\(360\) | −3.07905e31 | −0.342481 | ||||||||
\(361\) | −6.14104e31 | −0.659784 | ||||||||
\(362\) | 5.10992e31 | 0.530344 | ||||||||
\(363\) | 1.49302e32 | 1.49704 | ||||||||
\(364\) | 4.56714e31 | 0.442463 | ||||||||
\(365\) | −7.94071e31 | −0.743359 | ||||||||
\(366\) | −6.03915e30 | −0.0546339 | ||||||||
\(367\) | 8.66272e31 | 0.757406 | 0.378703 | − | 0.925518i | \(-0.376370\pi\) | ||||
0.378703 | + | 0.925518i | \(0.376370\pi\) | |||||||
\(368\) | −6.91456e30 | −0.0584341 | ||||||||
\(369\) | −4.72975e32 | −3.86374 | ||||||||
\(370\) | −5.29105e31 | −0.417850 | ||||||||
\(371\) | −3.57383e31 | −0.272873 | ||||||||
\(372\) | −1.95173e31 | −0.144090 | ||||||||
\(373\) | −2.52885e32 | −1.80536 | −0.902678 | − | 0.430316i | \(-0.858402\pi\) | ||||
−0.902678 | + | 0.430316i | \(0.858402\pi\) | |||||||
\(374\) | 7.85388e31 | 0.542237 | ||||||||
\(375\) | −2.38338e31 | −0.159149 | ||||||||
\(376\) | −7.24848e31 | −0.468165 | ||||||||
\(377\) | 2.43871e32 | 1.52368 | ||||||||
\(378\) | −1.37779e32 | −0.832787 | ||||||||
\(379\) | −7.89983e31 | −0.461985 | −0.230992 | − | 0.972956i | \(-0.574197\pi\) | ||||
−0.230992 | + | 0.972956i | \(0.574197\pi\) | |||||||
\(380\) | −2.30493e31 | −0.130425 | ||||||||
\(381\) | 1.84192e32 | 1.00858 | ||||||||
\(382\) | 2.38719e32 | 1.26501 | ||||||||
\(383\) | 2.10109e32 | 1.07761 | 0.538803 | − | 0.842432i | \(-0.318877\pi\) | ||||
0.538803 | + | 0.842432i | \(0.318877\pi\) | |||||||
\(384\) | 3.16806e31 | 0.157273 | ||||||||
\(385\) | −2.10416e31 | −0.101116 | ||||||||
\(386\) | 8.48790e31 | 0.394874 | ||||||||
\(387\) | −3.57285e31 | −0.160927 | ||||||||
\(388\) | −2.87991e31 | −0.125598 | ||||||||
\(389\) | 1.39534e32 | 0.589264 | 0.294632 | − | 0.955611i | \(-0.404803\pi\) | ||||
0.294632 | + | 0.955611i | \(0.404803\pi\) | |||||||
\(390\) | −2.14484e32 | −0.877176 | ||||||||
\(391\) | 1.13610e32 | 0.449993 | ||||||||
\(392\) | 6.24622e31 | 0.239630 | ||||||||
\(393\) | −3.71381e32 | −1.38011 | ||||||||
\(394\) | −9.08300e31 | −0.326984 | ||||||||
\(395\) | 1.48188e32 | 0.516833 | ||||||||
\(396\) | 1.27659e32 | 0.431382 | ||||||||
\(397\) | −1.58963e32 | −0.520494 | −0.260247 | − | 0.965542i | \(-0.583804\pi\) | ||||
−0.260247 | + | 0.965542i | \(0.583804\pi\) | |||||||
\(398\) | 1.05219e32 | 0.333852 | ||||||||
\(399\) | −1.91591e32 | −0.589134 | ||||||||
\(400\) | 1.67772e31 | 0.0500000 | ||||||||
\(401\) | 4.43370e32 | 1.28074 | 0.640371 | − | 0.768066i | \(-0.278781\pi\) | ||||
0.640371 | + | 0.768066i | \(0.278781\pi\) | |||||||
\(402\) | −1.00812e32 | −0.282283 | ||||||||
\(403\) | −9.30138e31 | −0.252484 | ||||||||
\(404\) | 2.25176e32 | 0.592590 | ||||||||
\(405\) | 2.67403e32 | 0.682305 | ||||||||
\(406\) | −1.58563e32 | −0.392308 | ||||||||
\(407\) | 2.19369e32 | 0.526315 | ||||||||
\(408\) | −5.20528e32 | −1.21113 | ||||||||
\(409\) | −1.41371e32 | −0.319021 | −0.159510 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159510 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(410\) | 2.57715e32 | 0.564082 | ||||||||
\(411\) | −1.11607e33 | −2.36956 | ||||||||
\(412\) | 3.48983e32 | 0.718769 | ||||||||
\(413\) | 4.77343e32 | 0.953795 | ||||||||
\(414\) | 1.84664e32 | 0.357996 | ||||||||
\(415\) | −1.77277e32 | −0.333466 | ||||||||
\(416\) | 1.50980e32 | 0.275584 | ||||||||
\(417\) | −8.23987e32 | −1.45955 | ||||||||
\(418\) | 9.55634e31 | 0.164281 | ||||||||
\(419\) | 5.65693e32 | 0.943856 | 0.471928 | − | 0.881637i | \(-0.343558\pi\) | ||||
0.471928 | + | 0.881637i | \(0.343558\pi\) | |||||||
\(420\) | 1.39456e32 | 0.225851 | ||||||||
\(421\) | −9.28896e32 | −1.46030 | −0.730148 | − | 0.683289i | \(-0.760549\pi\) | ||||
−0.730148 | + | 0.683289i | \(0.760549\pi\) | |||||||
\(422\) | 6.95294e32 | 1.06112 | ||||||||
\(423\) | 1.93582e33 | 2.86820 | ||||||||
\(424\) | −1.18144e32 | −0.169956 | ||||||||
\(425\) | −2.75658e32 | −0.385043 | ||||||||
\(426\) | 1.49902e33 | 2.03324 | ||||||||
\(427\) | 1.87131e31 | 0.0246489 | ||||||||
\(428\) | 5.01554e32 | 0.641609 | ||||||||
\(429\) | 8.89260e32 | 1.10487 | ||||||||
\(430\) | 1.94678e31 | 0.0234943 | ||||||||
\(431\) | −1.00278e33 | −1.17555 | −0.587773 | − | 0.809026i | \(-0.699995\pi\) | ||||
−0.587773 | + | 0.809026i | \(0.699995\pi\) | |||||||
\(432\) | −4.55467e32 | −0.518693 | ||||||||
\(433\) | −5.32205e31 | −0.0588817 | −0.0294408 | − | 0.999567i | \(-0.509373\pi\) | ||||
−0.0294408 | + | 0.999567i | \(0.509373\pi\) | |||||||
\(434\) | 6.04771e31 | 0.0650084 | ||||||||
\(435\) | 7.44651e32 | 0.777745 | ||||||||
\(436\) | 1.00622e32 | 0.102120 | ||||||||
\(437\) | 1.38236e32 | 0.136334 | ||||||||
\(438\) | −2.18199e33 | −2.09135 | ||||||||
\(439\) | −4.95347e32 | −0.461427 | −0.230714 | − | 0.973022i | \(-0.574106\pi\) | ||||
−0.230714 | + | 0.973022i | \(0.574106\pi\) | |||||||
\(440\) | −6.95591e31 | −0.0629790 | ||||||||
\(441\) | −1.66815e33 | −1.46809 | ||||||||
\(442\) | −2.48068e33 | −2.12223 | ||||||||
\(443\) | −6.00200e32 | −0.499171 | −0.249585 | − | 0.968353i | \(-0.580294\pi\) | ||||
−0.249585 | + | 0.968353i | \(0.580294\pi\) | |||||||
\(444\) | −1.45390e33 | −1.17557 | ||||||||
\(445\) | 4.66753e32 | 0.366933 | ||||||||
\(446\) | 6.74552e32 | 0.515620 | ||||||||
\(447\) | −1.19136e33 | −0.885521 | ||||||||
\(448\) | −9.81666e31 | −0.0709559 | ||||||||
\(449\) | 2.44542e31 | 0.0171899 | 0.00859497 | − | 0.999963i | \(-0.497264\pi\) | ||||
0.00859497 | + | 0.999963i | \(0.497264\pi\) | |||||||
\(450\) | −4.48061e32 | −0.306324 | ||||||||
\(451\) | −1.06850e33 | −0.710506 | ||||||||
\(452\) | −5.39642e32 | −0.349040 | ||||||||
\(453\) | −1.62610e32 | −0.102310 | ||||||||
\(454\) | 2.09278e33 | 1.28093 | ||||||||
\(455\) | 6.64606e32 | 0.395751 | ||||||||
\(456\) | −6.33361e32 | −0.366936 | ||||||||
\(457\) | −1.65246e33 | −0.931492 | −0.465746 | − | 0.884918i | \(-0.654214\pi\) | ||||
−0.465746 | + | 0.884918i | \(0.654214\pi\) | |||||||
\(458\) | −5.12095e32 | −0.280887 | ||||||||
\(459\) | 7.48355e33 | 3.99438 | ||||||||
\(460\) | −1.00620e32 | −0.0522651 | ||||||||
\(461\) | 1.16768e33 | 0.590284 | 0.295142 | − | 0.955453i | \(-0.404633\pi\) | ||||
0.295142 | + | 0.955453i | \(0.404633\pi\) | |||||||
\(462\) | −5.78192e32 | −0.284477 | ||||||||
\(463\) | −2.39229e33 | −1.14565 | −0.572823 | − | 0.819679i | \(-0.694152\pi\) | ||||
−0.572823 | + | 0.819679i | \(0.694152\pi\) | |||||||
\(464\) | −5.24178e32 | −0.244345 | ||||||||
\(465\) | −2.84015e32 | −0.128878 | ||||||||
\(466\) | 2.33697e33 | 1.03235 | ||||||||
\(467\) | 4.47360e33 | 1.92396 | 0.961981 | − | 0.273116i | \(-0.0880544\pi\) | ||||
0.961981 | + | 0.273116i | \(0.0880544\pi\) | |||||||
\(468\) | −4.03216e33 | −1.68836 | ||||||||
\(469\) | 3.12379e32 | 0.127356 | ||||||||
\(470\) | −1.05479e33 | −0.418740 | ||||||||
\(471\) | 3.72067e32 | 0.143834 | ||||||||
\(472\) | 1.57800e33 | 0.594061 | ||||||||
\(473\) | −8.07146e31 | −0.0295929 | ||||||||
\(474\) | 4.07200e33 | 1.45405 | ||||||||
\(475\) | −3.35411e32 | −0.116656 | ||||||||
\(476\) | 1.61292e33 | 0.546421 | ||||||||
\(477\) | 3.15521e33 | 1.04123 | ||||||||
\(478\) | −2.48012e33 | −0.797305 | ||||||||
\(479\) | 2.33765e33 | 0.732127 | 0.366064 | − | 0.930590i | \(-0.380705\pi\) | ||||
0.366064 | + | 0.930590i | \(0.380705\pi\) | |||||||
\(480\) | 4.61013e32 | 0.140669 | ||||||||
\(481\) | −6.92887e33 | −2.05991 | ||||||||
\(482\) | 2.09426e33 | 0.606657 | ||||||||
\(483\) | −8.36377e32 | −0.236082 | ||||||||
\(484\) | −1.52937e33 | −0.420673 | ||||||||
\(485\) | −4.19082e32 | −0.112338 | ||||||||
\(486\) | 1.73208e33 | 0.452496 | ||||||||
\(487\) | −1.27777e33 | −0.325343 | −0.162672 | − | 0.986680i | \(-0.552011\pi\) | ||||
−0.162672 | + | 0.986680i | \(0.552011\pi\) | |||||||
\(488\) | 6.18618e31 | 0.0153523 | ||||||||
\(489\) | −8.47839e33 | −2.05094 | ||||||||
\(490\) | 9.08945e32 | 0.214332 | ||||||||
\(491\) | 5.48118e33 | 1.25996 | 0.629978 | − | 0.776613i | \(-0.283064\pi\) | ||||
0.629978 | + | 0.776613i | \(0.283064\pi\) | |||||||
\(492\) | 7.08164e33 | 1.58698 | ||||||||
\(493\) | 8.61250e33 | 1.88167 | ||||||||
\(494\) | −3.01841e33 | −0.642970 | ||||||||
\(495\) | 1.85768e33 | 0.385840 | ||||||||
\(496\) | 1.99925e32 | 0.0404898 | ||||||||
\(497\) | −4.64493e33 | −0.917327 | ||||||||
\(498\) | −4.87132e33 | −0.938167 | ||||||||
\(499\) | 3.23941e33 | 0.608429 | 0.304214 | − | 0.952604i | \(-0.401606\pi\) | ||||
0.304214 | + | 0.952604i | \(0.401606\pi\) | |||||||
\(500\) | 2.44141e32 | 0.0447214 | ||||||||
\(501\) | −1.68642e33 | −0.301296 | ||||||||
\(502\) | −1.03124e33 | −0.179706 | ||||||||
\(503\) | −4.70148e33 | −0.799162 | −0.399581 | − | 0.916698i | \(-0.630844\pi\) | ||||
−0.399581 | + | 0.916698i | \(0.630844\pi\) | |||||||
\(504\) | 2.62169e33 | 0.434710 | ||||||||
\(505\) | 3.27674e33 | 0.530029 | ||||||||
\(506\) | 4.17176e32 | 0.0658321 | ||||||||
\(507\) | −1.65303e34 | −2.54496 | ||||||||
\(508\) | −1.88677e33 | −0.283414 | ||||||||
\(509\) | −7.74677e32 | −0.113540 | −0.0567699 | − | 0.998387i | \(-0.518080\pi\) | ||||
−0.0567699 | + | 0.998387i | \(0.518080\pi\) | |||||||
\(510\) | −7.57467e33 | −1.08327 | ||||||||
\(511\) | 6.76120e33 | 0.943544 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | 9.10574e33 | 1.21017 | ||||||||
\(514\) | −1.77159e33 | −0.229786 | ||||||||
\(515\) | 5.07837e33 | 0.642887 | ||||||||
\(516\) | 5.34948e32 | 0.0660983 | ||||||||
\(517\) | 4.37322e33 | 0.527436 | ||||||||
\(518\) | 4.50512e33 | 0.530376 | ||||||||
\(519\) | −2.03991e34 | −2.34433 | ||||||||
\(520\) | 2.19705e33 | 0.246490 | ||||||||
\(521\) | −7.09925e33 | −0.777573 | −0.388786 | − | 0.921328i | \(-0.627106\pi\) | ||||
−0.388786 | + | 0.921328i | \(0.627106\pi\) | |||||||
\(522\) | 1.39990e34 | 1.49698 | ||||||||
\(523\) | −8.65615e33 | −0.903761 | −0.451880 | − | 0.892079i | \(-0.649247\pi\) | ||||
−0.451880 | + | 0.892079i | \(0.649247\pi\) | |||||||
\(524\) | 3.80422e33 | 0.387815 | ||||||||
\(525\) | 2.02935e33 | 0.202007 | ||||||||
\(526\) | −1.23270e34 | −1.19821 | ||||||||
\(527\) | −3.28486e33 | −0.311806 | ||||||||
\(528\) | −1.91138e33 | −0.177184 | ||||||||
\(529\) | −1.04423e34 | −0.945367 | ||||||||
\(530\) | −1.71922e33 | −0.152013 | ||||||||
\(531\) | −4.21428e34 | −3.63950 | ||||||||
\(532\) | 1.96255e33 | 0.165549 | ||||||||
\(533\) | 3.37490e34 | 2.78081 | ||||||||
\(534\) | 1.28257e34 | 1.03232 | ||||||||
\(535\) | 7.29857e33 | 0.573873 | ||||||||
\(536\) | 1.03266e33 | 0.0793226 | ||||||||
\(537\) | −7.51142e33 | −0.563694 | ||||||||
\(538\) | −2.08689e33 | −0.153011 | ||||||||
\(539\) | −3.76853e33 | −0.269968 | ||||||||
\(540\) | −6.62792e33 | −0.463933 | ||||||||
\(541\) | 2.82575e34 | 1.93272 | 0.966358 | − | 0.257202i | \(-0.0828007\pi\) | ||||
0.966358 | + | 0.257202i | \(0.0828007\pi\) | |||||||
\(542\) | −4.33918e33 | −0.290013 | ||||||||
\(543\) | 2.04328e34 | 1.33454 | ||||||||
\(544\) | 5.33200e33 | 0.340333 | ||||||||
\(545\) | 1.46424e33 | 0.0913389 | ||||||||
\(546\) | 1.82624e34 | 1.11340 | ||||||||
\(547\) | 1.70002e34 | 1.01300 | 0.506502 | − | 0.862239i | \(-0.330938\pi\) | ||||
0.506502 | + | 0.862239i | \(0.330938\pi\) | |||||||
\(548\) | 1.14324e34 | 0.665855 | ||||||||
\(549\) | −1.65211e33 | −0.0940558 | ||||||||
\(550\) | −1.01222e33 | −0.0563301 | ||||||||
\(551\) | 1.04794e34 | 0.570088 | ||||||||
\(552\) | −2.76489e33 | −0.147041 | ||||||||
\(553\) | −1.26176e34 | −0.656015 | ||||||||
\(554\) | −2.32519e34 | −1.18192 | ||||||||
\(555\) | −2.11571e34 | −1.05146 | ||||||||
\(556\) | 8.44047e33 | 0.410140 | ||||||||
\(557\) | 1.04504e34 | 0.496529 | 0.248264 | − | 0.968692i | \(-0.420140\pi\) | ||||
0.248264 | + | 0.968692i | \(0.420140\pi\) | |||||||
\(558\) | −5.33930e33 | −0.248060 | ||||||||
\(559\) | 2.54940e33 | 0.115822 | ||||||||
\(560\) | −1.42851e33 | −0.0634649 | ||||||||
\(561\) | 3.14050e34 | 1.36447 | ||||||||
\(562\) | 6.16138e33 | 0.261803 | ||||||||
\(563\) | −1.28118e34 | −0.532421 | −0.266211 | − | 0.963915i | \(-0.585772\pi\) | ||||
−0.266211 | + | 0.963915i | \(0.585772\pi\) | |||||||
\(564\) | −2.89842e34 | −1.17807 | ||||||||
\(565\) | −7.85282e33 | −0.312191 | ||||||||
\(566\) | 1.83080e34 | 0.711927 | ||||||||
\(567\) | −2.27683e34 | −0.866048 | ||||||||
\(568\) | −1.53552e34 | −0.571348 | ||||||||
\(569\) | −6.19441e33 | −0.225474 | −0.112737 | − | 0.993625i | \(-0.535962\pi\) | ||||
−0.112737 | + | 0.993625i | \(0.535962\pi\) | |||||||
\(570\) | −9.21661e33 | −0.328198 | ||||||||
\(571\) | 5.43372e32 | 0.0189298 | 0.00946490 | − | 0.999955i | \(-0.496987\pi\) | ||||
0.00946490 | + | 0.999955i | \(0.496987\pi\) | |||||||
\(572\) | −9.10908e33 | −0.310473 | ||||||||
\(573\) | 9.54553e34 | 3.18322 | ||||||||
\(574\) | −2.19434e34 | −0.715988 | ||||||||
\(575\) | −1.46421e33 | −0.0467473 | ||||||||
\(576\) | 8.66677e33 | 0.270755 | ||||||||
\(577\) | 1.51288e34 | 0.462495 | 0.231248 | − | 0.972895i | \(-0.425719\pi\) | ||||
0.231248 | + | 0.972895i | \(0.425719\pi\) | |||||||
\(578\) | −6.39708e34 | −1.91374 | ||||||||
\(579\) | 3.39402e34 | 0.993646 | ||||||||
\(580\) | −7.62780e33 | −0.218549 | ||||||||
\(581\) | 1.50944e34 | 0.423268 | ||||||||
\(582\) | −1.15157e34 | −0.316049 | ||||||||
\(583\) | 7.12795e33 | 0.191473 | ||||||||
\(584\) | 2.23511e34 | 0.587677 | ||||||||
\(585\) | −5.86756e34 | −1.51011 | ||||||||
\(586\) | −1.77194e34 | −0.446404 | ||||||||
\(587\) | −3.71765e33 | −0.0916837 | −0.0458418 | − | 0.998949i | \(-0.514597\pi\) | ||||
−0.0458418 | + | 0.998949i | \(0.514597\pi\) | |||||||
\(588\) | 2.49765e34 | 0.602996 | ||||||||
\(589\) | −3.99691e33 | −0.0944677 | ||||||||
\(590\) | 2.29629e34 | 0.531345 | ||||||||
\(591\) | −3.63198e34 | −0.822810 | ||||||||
\(592\) | 1.48930e34 | 0.330339 | ||||||||
\(593\) | −4.27000e34 | −0.927351 | −0.463676 | − | 0.886005i | \(-0.653470\pi\) | ||||
−0.463676 | + | 0.886005i | \(0.653470\pi\) | |||||||
\(594\) | 2.74797e34 | 0.584361 | ||||||||
\(595\) | 2.34711e34 | 0.488734 | ||||||||
\(596\) | 1.22036e34 | 0.248835 | ||||||||
\(597\) | 4.20733e34 | 0.840093 | ||||||||
\(598\) | −1.31767e34 | −0.257656 | ||||||||
\(599\) | −3.95633e34 | −0.757631 | −0.378816 | − | 0.925472i | \(-0.623669\pi\) | ||||
−0.378816 | + | 0.925472i | \(0.623669\pi\) | |||||||
\(600\) | 6.70863e33 | 0.125818 | ||||||||
\(601\) | −5.03622e33 | −0.0925069 | −0.0462535 | − | 0.998930i | \(-0.514728\pi\) | ||||
−0.0462535 | + | 0.998930i | \(0.514728\pi\) | |||||||
\(602\) | −1.65761e33 | −0.0298212 | ||||||||
\(603\) | −2.75787e34 | −0.485969 | ||||||||
\(604\) | 1.66569e33 | 0.0287496 | ||||||||
\(605\) | −2.22552e34 | −0.376261 | ||||||||
\(606\) | 9.00400e34 | 1.49117 | ||||||||
\(607\) | −1.09922e35 | −1.78331 | −0.891655 | − | 0.452716i | \(-0.850455\pi\) | ||||
−0.891655 | + | 0.452716i | \(0.850455\pi\) | |||||||
\(608\) | 6.48780e33 | 0.103110 | ||||||||
\(609\) | −6.34040e34 | −0.987190 | ||||||||
\(610\) | 9.00207e32 | 0.0137315 | ||||||||
\(611\) | −1.38130e35 | −2.06430 | ||||||||
\(612\) | −1.42399e35 | −2.08504 | ||||||||
\(613\) | −7.49713e34 | −1.07557 | −0.537786 | − | 0.843082i | \(-0.680739\pi\) | ||||
−0.537786 | + | 0.843082i | \(0.680739\pi\) | |||||||
\(614\) | −5.77463e34 | −0.811745 | ||||||||
\(615\) | 1.03051e35 | 1.41943 | ||||||||
\(616\) | 5.92268e33 | 0.0799391 | ||||||||
\(617\) | 9.19873e34 | 1.21664 | 0.608321 | − | 0.793691i | \(-0.291843\pi\) | ||||
0.608321 | + | 0.793691i | \(0.291843\pi\) | |||||||
\(618\) | 1.39546e35 | 1.80868 | ||||||||
\(619\) | 1.17365e35 | 1.49075 | 0.745375 | − | 0.666646i | \(-0.232271\pi\) | ||||
0.745375 | + | 0.666646i | \(0.232271\pi\) | |||||||
\(620\) | 2.90929e33 | 0.0362152 | ||||||||
\(621\) | 3.97505e34 | 0.484950 | ||||||||
\(622\) | 1.76515e34 | 0.211058 | ||||||||
\(623\) | −3.97422e34 | −0.465748 | ||||||||
\(624\) | 6.03718e34 | 0.693468 | ||||||||
\(625\) | 3.55271e33 | 0.0400000 | ||||||||
\(626\) | 9.21430e33 | 0.101691 | ||||||||
\(627\) | 3.82125e34 | 0.413391 | ||||||||
\(628\) | −3.81125e33 | −0.0404177 | ||||||||
\(629\) | −2.44699e35 | −2.54389 | ||||||||
\(630\) | 3.81506e34 | 0.388816 | ||||||||
\(631\) | −5.93583e34 | −0.593082 | −0.296541 | − | 0.955020i | \(-0.595833\pi\) | ||||
−0.296541 | + | 0.955020i | \(0.595833\pi\) | |||||||
\(632\) | −4.17113e34 | −0.408592 | ||||||||
\(633\) | 2.78024e35 | 2.67015 | ||||||||
\(634\) | −3.06024e34 | −0.288164 | ||||||||
\(635\) | −2.74561e34 | −0.253493 | ||||||||
\(636\) | −4.72415e34 | −0.427671 | ||||||||
\(637\) | 1.19030e35 | 1.05661 | ||||||||
\(638\) | 3.16252e34 | 0.275280 | ||||||||
\(639\) | 4.10083e35 | 3.50035 | ||||||||
\(640\) | −4.72237e33 | −0.0395285 | ||||||||
\(641\) | −6.98225e34 | −0.573152 | −0.286576 | − | 0.958058i | \(-0.592517\pi\) | ||||
−0.286576 | + | 0.958058i | \(0.592517\pi\) | |||||||
\(642\) | 2.00554e35 | 1.61452 | ||||||||
\(643\) | 4.37990e34 | 0.345802 | 0.172901 | − | 0.984939i | \(-0.444686\pi\) | ||||
0.172901 | + | 0.984939i | \(0.444686\pi\) | |||||||
\(644\) | 8.56739e33 | 0.0663400 | ||||||||
\(645\) | 7.78452e33 | 0.0591201 | ||||||||
\(646\) | −1.06598e35 | −0.794038 | ||||||||
\(647\) | 2.19963e35 | 1.60711 | 0.803555 | − | 0.595231i | \(-0.202939\pi\) | ||||
0.803555 | + | 0.595231i | \(0.202939\pi\) | |||||||
\(648\) | −7.52673e34 | −0.539410 | ||||||||
\(649\) | −9.52052e34 | −0.669271 | ||||||||
\(650\) | 3.19713e34 | 0.220467 | ||||||||
\(651\) | 2.41827e34 | 0.163585 | ||||||||
\(652\) | 8.68480e34 | 0.576322 | ||||||||
\(653\) | −5.77474e34 | −0.375939 | −0.187970 | − | 0.982175i | \(-0.560191\pi\) | ||||
−0.187970 | + | 0.982175i | \(0.560191\pi\) | |||||||
\(654\) | 4.02352e34 | 0.256971 | ||||||||
\(655\) | 5.53587e34 | 0.346872 | ||||||||
\(656\) | −7.25404e34 | −0.445946 | ||||||||
\(657\) | −5.96921e35 | −3.60039 | ||||||||
\(658\) | 8.98113e34 | 0.531505 | ||||||||
\(659\) | −2.55494e34 | −0.148359 | −0.0741793 | − | 0.997245i | \(-0.523634\pi\) | ||||
−0.0741793 | + | 0.997245i | \(0.523634\pi\) | |||||||
\(660\) | −2.78143e34 | −0.158478 | ||||||||
\(661\) | 1.14583e35 | 0.640623 | 0.320312 | − | 0.947312i | \(-0.396212\pi\) | ||||
0.320312 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(662\) | 4.15385e34 | 0.227890 | ||||||||
\(663\) | −9.91938e35 | −5.34030 | ||||||||
\(664\) | 4.98991e34 | 0.263628 | ||||||||
\(665\) | 2.85589e34 | 0.148071 | ||||||||
\(666\) | −3.97740e35 | −2.02382 | ||||||||
\(667\) | 4.57471e34 | 0.228450 | ||||||||
\(668\) | 1.72747e34 | 0.0846652 | ||||||||
\(669\) | 2.69730e35 | 1.29749 | ||||||||
\(670\) | 1.50272e34 | 0.0709483 | ||||||||
\(671\) | −3.73230e33 | −0.0172960 | ||||||||
\(672\) | −3.92534e34 | −0.178551 | ||||||||
\(673\) | 1.32743e34 | 0.0592683 | 0.0296342 | − | 0.999561i | \(-0.490566\pi\) | ||||
0.0296342 | + | 0.999561i | \(0.490566\pi\) | |||||||
\(674\) | 1.74921e35 | 0.766644 | ||||||||
\(675\) | −9.64490e34 | −0.414955 | ||||||||
\(676\) | 1.69327e35 | 0.715143 | ||||||||
\(677\) | −1.09080e35 | −0.452257 | −0.226128 | − | 0.974098i | \(-0.572607\pi\) | ||||
−0.226128 | + | 0.974098i | \(0.572607\pi\) | |||||||
\(678\) | −2.15784e35 | −0.878310 | ||||||||
\(679\) | 3.56831e34 | 0.142590 | ||||||||
\(680\) | 7.75908e34 | 0.304403 | ||||||||
\(681\) | 8.36830e35 | 3.22328 | ||||||||
\(682\) | −1.20621e34 | −0.0456159 | ||||||||
\(683\) | −2.56303e35 | −0.951690 | −0.475845 | − | 0.879529i | \(-0.657858\pi\) | ||||
−0.475845 | + | 0.879529i | \(0.657858\pi\) | |||||||
\(684\) | −1.73267e35 | −0.631704 | ||||||||
\(685\) | 1.66363e35 | 0.595559 | ||||||||
\(686\) | −1.91580e35 | −0.673438 | ||||||||
\(687\) | −2.04769e35 | −0.706814 | ||||||||
\(688\) | −5.47971e33 | −0.0185739 | ||||||||
\(689\) | −2.25139e35 | −0.749395 | ||||||||
\(690\) | −4.02345e34 | −0.131518 | ||||||||
\(691\) | 1.27544e35 | 0.409436 | 0.204718 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204718 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(692\) | 2.08957e35 | 0.658766 | ||||||||
\(693\) | −1.58174e35 | −0.489745 | ||||||||
\(694\) | −5.85696e33 | −0.0178106 | ||||||||
\(695\) | 1.22825e35 | 0.366840 | ||||||||
\(696\) | −2.09601e35 | −0.614861 | ||||||||
\(697\) | 1.19187e36 | 3.43416 | ||||||||
\(698\) | −1.45642e34 | −0.0412187 | ||||||||
\(699\) | 9.34471e35 | 2.59777 | ||||||||
\(700\) | −2.07876e34 | −0.0567647 | ||||||||
\(701\) | −3.29520e35 | −0.883907 | −0.441953 | − | 0.897038i | \(-0.645714\pi\) | ||||
−0.441953 | + | 0.897038i | \(0.645714\pi\) | |||||||
\(702\) | −8.67957e35 | −2.28709 | ||||||||
\(703\) | −2.97742e35 | −0.770722 | ||||||||
\(704\) | 1.95792e34 | 0.0497893 | ||||||||
\(705\) | −4.21775e35 | −1.05370 | ||||||||
\(706\) | −2.71963e35 | −0.667500 | ||||||||
\(707\) | −2.79001e35 | −0.672764 | ||||||||
\(708\) | 6.30987e35 | 1.49487 | ||||||||
\(709\) | −3.54372e35 | −0.824863 | −0.412432 | − | 0.910989i | \(-0.635320\pi\) | ||||
−0.412432 | + | 0.910989i | \(0.635320\pi\) | |||||||
\(710\) | −2.23447e35 | −0.511029 | ||||||||
\(711\) | 1.11396e36 | 2.50323 | ||||||||
\(712\) | −1.31379e35 | −0.290086 | ||||||||
\(713\) | −1.74482e34 | −0.0378558 | ||||||||
\(714\) | 6.44953e35 | 1.37499 | ||||||||
\(715\) | −1.32555e35 | −0.277696 | ||||||||
\(716\) | 7.69429e34 | 0.158400 | ||||||||
\(717\) | −9.91715e35 | −2.00631 | ||||||||
\(718\) | 7.63230e34 | 0.151740 | ||||||||
\(719\) | 8.25549e34 | 0.161299 | 0.0806495 | − | 0.996743i | \(-0.474301\pi\) | ||||
0.0806495 | + | 0.996743i | \(0.474301\pi\) | |||||||
\(720\) | 1.26118e35 | 0.242170 | ||||||||
\(721\) | −4.32403e35 | −0.816014 | ||||||||
\(722\) | 2.51537e35 | 0.466538 | ||||||||
\(723\) | 8.37424e35 | 1.52657 | ||||||||
\(724\) | −2.09302e35 | −0.375010 | ||||||||
\(725\) | −1.10999e35 | −0.195476 | ||||||||
\(726\) | −6.11541e35 | −1.05857 | ||||||||
\(727\) | 8.59682e35 | 1.46271 | 0.731354 | − | 0.681998i | \(-0.238889\pi\) | ||||
0.731354 | + | 0.681998i | \(0.238889\pi\) | |||||||
\(728\) | −1.87070e35 | −0.312869 | ||||||||
\(729\) | −2.35421e35 | −0.387036 | ||||||||
\(730\) | 3.25252e35 | 0.525634 | ||||||||
\(731\) | 9.00343e34 | 0.143035 | ||||||||
\(732\) | 2.47364e34 | 0.0386320 | ||||||||
\(733\) | 1.11362e36 | 1.70977 | 0.854883 | − | 0.518821i | \(-0.173629\pi\) | ||||
0.854883 | + | 0.518821i | \(0.173629\pi\) | |||||||
\(734\) | −3.54825e35 | −0.535567 | ||||||||
\(735\) | 3.63456e35 | 0.539336 | ||||||||
\(736\) | 2.83220e34 | 0.0413192 | ||||||||
\(737\) | −6.23034e34 | −0.0893651 | ||||||||
\(738\) | 1.93730e36 | 2.73208 | ||||||||
\(739\) | 8.39662e34 | 0.116426 | 0.0582129 | − | 0.998304i | \(-0.481460\pi\) | ||||
0.0582129 | + | 0.998304i | \(0.481460\pi\) | |||||||
\(740\) | 2.16721e35 | 0.295465 | ||||||||
\(741\) | −1.20696e36 | −1.61795 | ||||||||
\(742\) | 1.46384e35 | 0.192950 | ||||||||
\(743\) | −8.61824e35 | −1.11701 | −0.558506 | − | 0.829500i | \(-0.688625\pi\) | ||||
−0.558506 | + | 0.829500i | \(0.688625\pi\) | |||||||
\(744\) | 7.99430e34 | 0.101887 | ||||||||
\(745\) | 1.77586e35 | 0.222564 | ||||||||
\(746\) | 1.03582e36 | 1.27658 | ||||||||
\(747\) | −1.33263e36 | −1.61511 | ||||||||
\(748\) | −3.21695e35 | −0.383420 | ||||||||
\(749\) | −6.21444e35 | −0.728415 | ||||||||
\(750\) | 9.76234e34 | 0.112535 | ||||||||
\(751\) | −8.00202e35 | −0.907195 | −0.453597 | − | 0.891207i | \(-0.649860\pi\) | ||||
−0.453597 | + | 0.891207i | \(0.649860\pi\) | |||||||
\(752\) | 2.96898e35 | 0.331043 | ||||||||
\(753\) | −4.12356e35 | −0.452204 | ||||||||
\(754\) | −9.98894e35 | −1.07740 | ||||||||
\(755\) | 2.42389e34 | 0.0257144 | ||||||||
\(756\) | 5.64341e35 | 0.588869 | ||||||||
\(757\) | −7.91448e35 | −0.812314 | −0.406157 | − | 0.913803i | \(-0.633131\pi\) | ||||
−0.406157 | + | 0.913803i | \(0.633131\pi\) | |||||||
\(758\) | 3.23577e35 | 0.326673 | ||||||||
\(759\) | 1.66814e35 | 0.165657 | ||||||||
\(760\) | 9.44099e34 | 0.0922247 | ||||||||
\(761\) | 2.09934e34 | 0.0201732 | 0.0100866 | − | 0.999949i | \(-0.496789\pi\) | ||||
0.0100866 | + | 0.999949i | \(0.496789\pi\) | |||||||
\(762\) | −7.54452e35 | −0.713173 | ||||||||
\(763\) | −1.24674e35 | −0.115936 | ||||||||
\(764\) | −9.77792e35 | −0.894498 | ||||||||
\(765\) | −2.07218e36 | −1.86492 | ||||||||
\(766\) | −8.60607e35 | −0.761983 | ||||||||
\(767\) | 3.00709e36 | 2.61942 | ||||||||
\(768\) | −1.29764e35 | −0.111209 | ||||||||
\(769\) | −7.23123e35 | −0.609723 | −0.304862 | − | 0.952397i | \(-0.598610\pi\) | ||||
−0.304862 | + | 0.952397i | \(0.598610\pi\) | |||||||
\(770\) | 8.61863e34 | 0.0714997 | ||||||||
\(771\) | −7.08396e35 | −0.578225 | ||||||||
\(772\) | −3.47664e35 | −0.279218 | ||||||||
\(773\) | −1.19333e36 | −0.943014 | −0.471507 | − | 0.881862i | \(-0.656290\pi\) | ||||
−0.471507 | + | 0.881862i | \(0.656290\pi\) | |||||||
\(774\) | 1.46344e35 | 0.113792 | ||||||||
\(775\) | 4.23357e34 | 0.0323919 | ||||||||
\(776\) | 1.17961e35 | 0.0888110 | ||||||||
\(777\) | 1.80144e36 | 1.33462 | ||||||||
\(778\) | −5.71531e35 | −0.416672 | ||||||||
\(779\) | 1.45023e36 | 1.04045 | ||||||||
\(780\) | 8.78525e35 | 0.620257 | ||||||||
\(781\) | 9.26423e35 | 0.643682 | ||||||||
\(782\) | −4.65345e35 | −0.318193 | ||||||||
\(783\) | 3.01340e36 | 2.02784 | ||||||||
\(784\) | −2.55845e35 | −0.169444 | ||||||||
\(785\) | −5.54610e34 | −0.0361507 | ||||||||
\(786\) | 1.52118e36 | 0.975883 | ||||||||
\(787\) | 4.78974e35 | 0.302432 | 0.151216 | − | 0.988501i | \(-0.451681\pi\) | ||||
0.151216 | + | 0.988501i | \(0.451681\pi\) | |||||||
\(788\) | 3.72040e35 | 0.231213 | ||||||||
\(789\) | −4.92912e36 | −3.01514 | ||||||||
\(790\) | −6.06979e35 | −0.365456 | ||||||||
\(791\) | 6.68636e35 | 0.396263 | ||||||||
\(792\) | −5.22891e35 | −0.305033 | ||||||||
\(793\) | 1.17886e35 | 0.0676937 | ||||||||
\(794\) | 6.51114e35 | 0.368045 | ||||||||
\(795\) | −6.87455e35 | −0.382521 | ||||||||
\(796\) | −4.30975e35 | −0.236069 | ||||||||
\(797\) | 2.29881e36 | 1.23958 | 0.619788 | − | 0.784769i | \(-0.287218\pi\) | ||||
0.619788 | + | 0.784769i | \(0.287218\pi\) | |||||||
\(798\) | 7.84757e35 | 0.416581 | ||||||||
\(799\) | −4.87818e36 | −2.54931 | ||||||||
\(800\) | −6.87195e34 | −0.0353553 | ||||||||
\(801\) | 3.50869e36 | 1.77721 | ||||||||
\(802\) | −1.81604e36 | −0.905621 | ||||||||
\(803\) | −1.34851e36 | −0.662078 | ||||||||
\(804\) | 4.12925e35 | 0.199604 | ||||||||
\(805\) | 1.24672e35 | 0.0593363 | ||||||||
\(806\) | 3.80985e35 | 0.178533 | ||||||||
\(807\) | −8.34476e35 | −0.385030 | ||||||||
\(808\) | −9.22320e35 | −0.419025 | ||||||||
\(809\) | 1.08839e36 | 0.486885 | 0.243442 | − | 0.969915i | \(-0.421723\pi\) | ||||
0.243442 | + | 0.969915i | \(0.421723\pi\) | |||||||
\(810\) | −1.09528e36 | −0.482463 | ||||||||
\(811\) | 4.47699e36 | 1.94189 | 0.970946 | − | 0.239299i | \(-0.0769178\pi\) | ||||
0.970946 | + | 0.239299i | \(0.0769178\pi\) | |||||||
\(812\) | 6.49476e35 | 0.277404 | ||||||||
\(813\) | −1.73509e36 | −0.729776 | ||||||||
\(814\) | −8.98537e35 | −0.372161 | ||||||||
\(815\) | 1.26380e36 | 0.515478 | ||||||||
\(816\) | 2.13208e36 | 0.856400 | ||||||||
\(817\) | 1.09551e35 | 0.0433351 | ||||||||
\(818\) | 5.79056e35 | 0.225582 | ||||||||
\(819\) | 4.99599e36 | 1.91678 | ||||||||
\(820\) | −1.05560e36 | −0.398866 | ||||||||
\(821\) | 3.35501e36 | 1.24855 | 0.624274 | − | 0.781206i | \(-0.285395\pi\) | ||||
0.624274 | + | 0.781206i | \(0.285395\pi\) | |||||||
\(822\) | 4.57141e36 | 1.67553 | ||||||||
\(823\) | −1.04609e36 | −0.377636 | −0.188818 | − | 0.982012i | \(-0.560466\pi\) | ||||
−0.188818 | + | 0.982012i | \(0.560466\pi\) | |||||||
\(824\) | −1.42944e36 | −0.508246 | ||||||||
\(825\) | −4.04751e35 | −0.141747 | ||||||||
\(826\) | −1.95520e36 | −0.674435 | ||||||||
\(827\) | −1.70274e36 | −0.578535 | −0.289267 | − | 0.957248i | \(-0.593412\pi\) | ||||
−0.289267 | + | 0.957248i | \(0.593412\pi\) | |||||||
\(828\) | −7.56383e35 | −0.253141 | ||||||||
\(829\) | 3.63214e36 | 1.19738 | 0.598688 | − | 0.800983i | \(-0.295689\pi\) | ||||
0.598688 | + | 0.800983i | \(0.295689\pi\) | |||||||
\(830\) | 7.26128e35 | 0.235796 | ||||||||
\(831\) | −9.29763e36 | −2.97413 | ||||||||
\(832\) | −6.18415e35 | −0.194867 | ||||||||
\(833\) | 4.20366e36 | 1.30486 | ||||||||
\(834\) | 3.37505e36 | 1.03206 | ||||||||
\(835\) | 2.51380e35 | 0.0757269 | ||||||||
\(836\) | −3.91428e35 | −0.116164 | ||||||||
\(837\) | −1.14933e36 | −0.336029 | ||||||||
\(838\) | −2.31708e36 | −0.667407 | ||||||||
\(839\) | −4.10710e36 | −1.16550 | −0.582748 | − | 0.812653i | \(-0.698023\pi\) | ||||
−0.582748 | + | 0.812653i | \(0.698023\pi\) | |||||||
\(840\) | −5.71212e35 | −0.159701 | ||||||||
\(841\) | −1.62368e35 | −0.0447251 | ||||||||
\(842\) | 3.80476e36 | 1.03258 | ||||||||
\(843\) | 2.46372e36 | 0.658790 | ||||||||
\(844\) | −2.84793e36 | −0.750323 | ||||||||
\(845\) | 2.46403e36 | 0.639643 | ||||||||
\(846\) | −7.92911e36 | −2.02813 | ||||||||
\(847\) | 1.89494e36 | 0.477588 | ||||||||
\(848\) | 4.83916e35 | 0.120177 | ||||||||
\(849\) | 7.32074e36 | 1.79147 | ||||||||
\(850\) | 1.12909e36 | 0.272266 | ||||||||
\(851\) | −1.29977e36 | −0.308850 | ||||||||
\(852\) | −6.14000e36 | −1.43772 | ||||||||
\(853\) | 2.01380e36 | 0.464680 | 0.232340 | − | 0.972635i | \(-0.425362\pi\) | ||||
0.232340 | + | 0.972635i | \(0.425362\pi\) | |||||||
\(854\) | −7.66490e34 | −0.0174294 | ||||||||
\(855\) | −2.52136e36 | −0.565013 | ||||||||
\(856\) | −2.05437e36 | −0.453686 | ||||||||
\(857\) | −3.20819e36 | −0.698232 | −0.349116 | − | 0.937080i | \(-0.613518\pi\) | ||||
−0.349116 | + | 0.937080i | \(0.613518\pi\) | |||||||
\(858\) | −3.64241e36 | −0.781263 | ||||||||
\(859\) | −1.62270e36 | −0.343024 | −0.171512 | − | 0.985182i | \(-0.554865\pi\) | ||||
−0.171512 | + | 0.985182i | \(0.554865\pi\) | |||||||
\(860\) | −7.97403e34 | −0.0166130 | ||||||||
\(861\) | −8.77441e36 | −1.80168 | ||||||||
\(862\) | 4.10739e36 | 0.831237 | ||||||||
\(863\) | 2.34665e36 | 0.468074 | 0.234037 | − | 0.972228i | \(-0.424806\pi\) | ||||
0.234037 | + | 0.972228i | \(0.424806\pi\) | |||||||
\(864\) | 1.86559e36 | 0.366771 | ||||||||
\(865\) | 3.04073e36 | 0.589218 | ||||||||
\(866\) | 2.17991e35 | 0.0416356 | ||||||||
\(867\) | −2.55797e37 | −4.81567 | ||||||||
\(868\) | −2.47714e35 | −0.0459679 | ||||||||
\(869\) | 2.51656e36 | 0.460321 | ||||||||
\(870\) | −3.05009e36 | −0.549949 | ||||||||
\(871\) | 1.96788e36 | 0.349761 | ||||||||
\(872\) | −4.12147e35 | −0.0722098 | ||||||||
\(873\) | −3.15033e36 | −0.544099 | ||||||||
\(874\) | −5.66216e35 | −0.0964027 | ||||||||
\(875\) | −3.02499e35 | −0.0507719 | ||||||||
\(876\) | 8.93744e36 | 1.47881 | ||||||||
\(877\) | −1.82745e36 | −0.298092 | −0.149046 | − | 0.988830i | \(-0.547620\pi\) | ||||
−0.149046 | + | 0.988830i | \(0.547620\pi\) | |||||||
\(878\) | 2.02894e36 | 0.326278 | ||||||||
\(879\) | −7.08537e36 | −1.12331 | ||||||||
\(880\) | 2.84914e35 | 0.0445329 | ||||||||
\(881\) | 1.92548e36 | 0.296715 | 0.148358 | − | 0.988934i | \(-0.452601\pi\) | ||||
0.148358 | + | 0.988934i | \(0.452601\pi\) | |||||||
\(882\) | 6.83274e36 | 1.03810 | ||||||||
\(883\) | 5.88853e36 | 0.882060 | 0.441030 | − | 0.897492i | \(-0.354613\pi\) | ||||
0.441030 | + | 0.897492i | \(0.354613\pi\) | |||||||
\(884\) | 1.01609e37 | 1.50064 | ||||||||
\(885\) | 9.18206e36 | 1.33706 | ||||||||
\(886\) | 2.45842e36 | 0.352967 | ||||||||
\(887\) | 1.17351e37 | 1.66128 | 0.830640 | − | 0.556809i | \(-0.187975\pi\) | ||||
0.830640 | + | 0.556809i | \(0.187975\pi\) | |||||||
\(888\) | 5.95519e36 | 0.831253 | ||||||||
\(889\) | 2.33777e36 | 0.321759 | ||||||||
\(890\) | −1.91182e36 | −0.259461 | ||||||||
\(891\) | 4.54110e36 | 0.607700 | ||||||||
\(892\) | −2.76296e36 | −0.364598 | ||||||||
\(893\) | −5.93560e36 | −0.772363 | ||||||||
\(894\) | 4.87981e36 | 0.626158 | ||||||||
\(895\) | 1.11967e36 | 0.141677 | ||||||||
\(896\) | 4.02090e35 | 0.0501734 | ||||||||
\(897\) | −5.26889e36 | −0.648356 | ||||||||
\(898\) | −1.00164e35 | −0.0121551 | ||||||||
\(899\) | −1.32271e36 | −0.158296 | ||||||||
\(900\) | 1.83526e36 | 0.216604 | ||||||||
\(901\) | −7.95098e36 | −0.925467 | ||||||||
\(902\) | 4.37658e36 | 0.502404 | ||||||||
\(903\) | −6.62820e35 | −0.0750410 | ||||||||
\(904\) | 2.21037e36 | 0.246808 | ||||||||
\(905\) | −3.04575e36 | −0.335419 | ||||||||
\(906\) | 6.66051e35 | 0.0723444 | ||||||||
\(907\) | 9.60913e36 | 1.02942 | 0.514711 | − | 0.857364i | \(-0.327899\pi\) | ||||
0.514711 | + | 0.857364i | \(0.327899\pi\) | |||||||
\(908\) | −8.57203e36 | −0.905754 | ||||||||
\(909\) | 2.46320e37 | 2.56715 | ||||||||
\(910\) | −2.72223e36 | −0.279838 | ||||||||
\(911\) | 3.31132e36 | 0.335754 | 0.167877 | − | 0.985808i | \(-0.446309\pi\) | ||||
0.167877 | + | 0.985808i | \(0.446309\pi\) | |||||||
\(912\) | 2.59424e36 | 0.259463 | ||||||||
\(913\) | −3.01056e36 | −0.297004 | ||||||||
\(914\) | 6.76849e36 | 0.658665 | ||||||||
\(915\) | 3.59962e35 | 0.0345535 | ||||||||
\(916\) | 2.09754e36 | 0.198617 | ||||||||
\(917\) | −4.71357e36 | −0.440284 | ||||||||
\(918\) | −3.06526e37 | −2.82445 | ||||||||
\(919\) | −6.37787e36 | −0.579738 | −0.289869 | − | 0.957066i | \(-0.593612\pi\) | ||||
−0.289869 | + | 0.957066i | \(0.593612\pi\) | |||||||
\(920\) | 4.12140e35 | 0.0369570 | ||||||||
\(921\) | −2.30908e37 | −2.04264 | ||||||||
\(922\) | −4.78281e36 | −0.417394 | ||||||||
\(923\) | −2.92614e37 | −2.51927 | ||||||||
\(924\) | 2.36827e36 | 0.201156 | ||||||||
\(925\) | 3.15371e36 | 0.264272 | ||||||||
\(926\) | 9.79880e36 | 0.810094 | ||||||||
\(927\) | 3.81753e37 | 3.11376 | ||||||||
\(928\) | 2.14703e36 | 0.172778 | ||||||||
\(929\) | −1.01760e37 | −0.807940 | −0.403970 | − | 0.914772i | \(-0.632370\pi\) | ||||
−0.403970 | + | 0.914772i | \(0.632370\pi\) | |||||||
\(930\) | 1.16332e36 | 0.0911305 | ||||||||
\(931\) | 5.11488e36 | 0.395334 | ||||||||
\(932\) | −9.57221e36 | −0.729984 | ||||||||
\(933\) | 7.05824e36 | 0.531099 | ||||||||
\(934\) | −1.83239e37 | −1.36045 | ||||||||
\(935\) | −4.68128e36 | −0.342941 | ||||||||
\(936\) | 1.65157e37 | 1.19385 | ||||||||
\(937\) | 5.01714e36 | 0.357859 | 0.178929 | − | 0.983862i | \(-0.442737\pi\) | ||||
0.178929 | + | 0.983862i | \(0.442737\pi\) | |||||||
\(938\) | −1.27950e36 | −0.0900546 | ||||||||
\(939\) | 3.68448e36 | 0.255892 | ||||||||
\(940\) | 4.32043e36 | 0.296094 | ||||||||
\(941\) | 1.04889e37 | 0.709348 | 0.354674 | − | 0.934990i | \(-0.384592\pi\) | ||||
0.354674 | + | 0.934990i | \(0.384592\pi\) | |||||||
\(942\) | −1.52399e36 | −0.101706 | ||||||||
\(943\) | 6.33089e36 | 0.416936 | ||||||||
\(944\) | −6.46348e36 | −0.420065 | ||||||||
\(945\) | 8.21224e36 | 0.526701 | ||||||||
\(946\) | 3.30607e35 | 0.0209254 | ||||||||
\(947\) | −3.09440e37 | −1.93286 | −0.966432 | − | 0.256923i | \(-0.917291\pi\) | ||||
−0.966432 | + | 0.256923i | \(0.917291\pi\) | |||||||
\(948\) | −1.66789e37 | −1.02817 | ||||||||
\(949\) | 4.25932e37 | 2.59127 | ||||||||
\(950\) | 1.37384e36 | 0.0824883 | ||||||||
\(951\) | −1.22368e37 | −0.725125 | ||||||||
\(952\) | −6.60654e36 | −0.386378 | ||||||||
\(953\) | −2.63074e34 | −0.00151851 | −0.000759254 | − | 1.00000i | \(-0.500242\pi\) | ||||
−0.000759254 | 1.00000i | \(0.500242\pi\) | ||||||||
\(954\) | −1.29237e37 | −0.736263 | ||||||||
\(955\) | −1.42287e37 | −0.800063 | ||||||||
\(956\) | 1.01586e37 | 0.563780 | ||||||||
\(957\) | 1.26458e37 | 0.692704 | ||||||||
\(958\) | −9.57503e36 | −0.517692 | ||||||||
\(959\) | −1.41651e37 | −0.755941 | ||||||||
\(960\) | −1.88831e36 | −0.0994679 | ||||||||
\(961\) | −1.87283e37 | −0.973769 | ||||||||
\(962\) | 2.83807e37 | 1.45658 | ||||||||
\(963\) | 5.48650e37 | 2.77950 | ||||||||
\(964\) | −8.57811e36 | −0.428972 | ||||||||
\(965\) | −5.05918e36 | −0.249740 | ||||||||
\(966\) | 3.42580e36 | 0.166935 | ||||||||
\(967\) | −1.63641e37 | −0.787158 | −0.393579 | − | 0.919291i | \(-0.628763\pi\) | ||||
−0.393579 | + | 0.919291i | \(0.628763\pi\) | |||||||
\(968\) | 6.26429e36 | 0.297461 | ||||||||
\(969\) | −4.26247e37 | −1.99809 | ||||||||
\(970\) | 1.71656e36 | 0.0794350 | ||||||||
\(971\) | −3.01907e37 | −1.37922 | −0.689610 | − | 0.724181i | \(-0.742218\pi\) | ||||
−0.689610 | + | 0.724181i | \(0.742218\pi\) | |||||||
\(972\) | −7.09461e36 | −0.319963 | ||||||||
\(973\) | −1.04581e37 | −0.465629 | ||||||||
\(974\) | 5.23376e36 | 0.230053 | ||||||||
\(975\) | 1.27842e37 | 0.554775 | ||||||||
\(976\) | −2.53386e35 | −0.0108557 | ||||||||
\(977\) | −3.79611e36 | −0.160567 | −0.0802837 | − | 0.996772i | \(-0.525583\pi\) | ||||
−0.0802837 | + | 0.996772i | \(0.525583\pi\) | |||||||
\(978\) | 3.47275e37 | 1.45023 | ||||||||
\(979\) | 7.92650e36 | 0.326812 | ||||||||
\(980\) | −3.72304e36 | −0.151555 | ||||||||
\(981\) | 1.10070e37 | 0.442392 | ||||||||
\(982\) | −2.24509e37 | −0.890923 | ||||||||
\(983\) | −6.46957e36 | −0.253487 | −0.126744 | − | 0.991936i | \(-0.540453\pi\) | ||||
−0.126744 | + | 0.991936i | \(0.540453\pi\) | |||||||
\(984\) | −2.90064e37 | −1.12216 | ||||||||
\(985\) | 5.41389e36 | 0.206803 | ||||||||
\(986\) | −3.52768e37 | −1.33054 | ||||||||
\(987\) | 3.59124e37 | 1.33746 | ||||||||
\(988\) | 1.23634e37 | 0.454649 | ||||||||
\(989\) | 4.78236e35 | 0.0173656 | ||||||||
\(990\) | −7.60907e36 | −0.272830 | ||||||||
\(991\) | −3.19318e37 | −1.13058 | −0.565291 | − | 0.824891i | \(-0.691236\pi\) | ||||
−0.565291 | + | 0.824891i | \(0.691236\pi\) | |||||||
\(992\) | −8.18892e35 | −0.0286306 | ||||||||
\(993\) | 1.66098e37 | 0.573455 | ||||||||
\(994\) | 1.90256e37 | 0.648648 | ||||||||
\(995\) | −6.27152e36 | −0.211147 | ||||||||
\(996\) | 1.99529e37 | 0.663384 | ||||||||
\(997\) | 3.10721e37 | 1.02019 | 0.510095 | − | 0.860118i | \(-0.329610\pi\) | ||||
0.510095 | + | 0.860118i | \(0.329610\pi\) | |||||||
\(998\) | −1.32686e37 | −0.430224 | ||||||||
\(999\) | −8.56169e37 | −2.74152 |
(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 | 10.26.a.b.1.1 | ✓ | 2 | |
5.2 | odd | 4 | 50.26.b.f.49.2 | 4 | |||
5.3 | odd | 4 | 50.26.b.f.49.3 | 4 | |||
5.4 | even | 2 | 50.26.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.26.a.f.1.2 | 2 | 5.4 | even | 2 | |||
50.26.b.f.49.2 | 4 | 5.2 | odd | 4 | |||
50.26.b.f.49.3 | 4 | 5.3 | odd | 4 |