Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,30,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, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
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: | \(53.2780423830\) |
Analytic rank: | \(1\) |
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: | \( x^{2} - x - 2788867122 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-52809.2\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 16384.0 | 0.707107 | ||||||||
\(3\) | 7.68338e6 | 0.927457 | 0.463729 | − | 0.885977i | \(-0.346511\pi\) | ||||
0.463729 | + | 0.885977i | \(0.346511\pi\) | |||||||
\(4\) | 2.68435e8 | 0.500000 | ||||||||
\(5\) | 6.10352e9 | 0.447214 | ||||||||
\(6\) | 1.25884e11 | 0.655811 | ||||||||
\(7\) | −1.48072e12 | −0.825183 | −0.412592 | − | 0.910916i | \(-0.635376\pi\) | ||||
−0.412592 | + | 0.910916i | \(0.635376\pi\) | |||||||
\(8\) | 4.39805e12 | 0.353553 | ||||||||
\(9\) | −9.59610e12 | −0.139823 | ||||||||
\(10\) | 1.00000e14 | 0.316228 | ||||||||
\(11\) | −1.49204e15 | −1.18464 | −0.592319 | − | 0.805704i | \(-0.701787\pi\) | ||||
−0.592319 | + | 0.805704i | \(0.701787\pi\) | |||||||
\(12\) | 2.06249e15 | 0.463729 | ||||||||
\(13\) | −1.87567e16 | −1.32122 | −0.660612 | − | 0.750727i | \(-0.729703\pi\) | ||||
−0.660612 | + | 0.750727i | \(0.729703\pi\) | |||||||
\(14\) | −2.42601e16 | −0.583493 | ||||||||
\(15\) | 4.68956e16 | 0.414772 | ||||||||
\(16\) | 7.20576e16 | 0.250000 | ||||||||
\(17\) | −5.52201e17 | −0.795405 | −0.397702 | − | 0.917515i | \(-0.630192\pi\) | ||||
−0.397702 | + | 0.917515i | \(0.630192\pi\) | |||||||
\(18\) | −1.57223e17 | −0.0988697 | ||||||||
\(19\) | −3.63993e18 | −1.04512 | −0.522559 | − | 0.852603i | \(-0.675023\pi\) | ||||
−0.522559 | + | 0.852603i | \(0.675023\pi\) | |||||||
\(20\) | 1.63840e18 | 0.223607 | ||||||||
\(21\) | −1.13769e19 | −0.765322 | ||||||||
\(22\) | −2.44455e19 | −0.837665 | ||||||||
\(23\) | 1.19154e19 | 0.214316 | 0.107158 | − | 0.994242i | \(-0.465825\pi\) | ||||
0.107158 | + | 0.994242i | \(0.465825\pi\) | |||||||
\(24\) | 3.37918e19 | 0.327906 | ||||||||
\(25\) | 3.72529e19 | 0.200000 | ||||||||
\(26\) | −3.07309e20 | −0.934247 | ||||||||
\(27\) | −6.01043e20 | −1.05714 | ||||||||
\(28\) | −3.97477e20 | −0.412592 | ||||||||
\(29\) | 1.49220e21 | 0.931226 | 0.465613 | − | 0.884988i | \(-0.345834\pi\) | ||||
0.465613 | + | 0.884988i | \(0.345834\pi\) | |||||||
\(30\) | 7.68338e20 | 0.293288 | ||||||||
\(31\) | 2.12272e20 | 0.0503673 | 0.0251836 | − | 0.999683i | \(-0.491983\pi\) | ||||
0.0251836 | + | 0.999683i | \(0.491983\pi\) | |||||||
\(32\) | 1.18059e21 | 0.176777 | ||||||||
\(33\) | −1.14639e22 | −1.09870 | ||||||||
\(34\) | −9.04727e21 | −0.562436 | ||||||||
\(35\) | −9.03758e21 | −0.369033 | ||||||||
\(36\) | −2.57593e21 | −0.0699115 | ||||||||
\(37\) | 4.36693e22 | 0.796620 | 0.398310 | − | 0.917251i | \(-0.369597\pi\) | ||||
0.398310 | + | 0.917251i | \(0.369597\pi\) | |||||||
\(38\) | −5.96365e22 | −0.739010 | ||||||||
\(39\) | −1.44114e23 | −1.22538 | ||||||||
\(40\) | 2.68435e22 | 0.158114 | ||||||||
\(41\) | 1.24529e23 | 0.512749 | 0.256375 | − | 0.966578i | \(-0.417472\pi\) | ||||
0.256375 | + | 0.966578i | \(0.417472\pi\) | |||||||
\(42\) | −1.86399e23 | −0.541164 | ||||||||
\(43\) | 4.89124e23 | 1.00955 | 0.504774 | − | 0.863252i | \(-0.331576\pi\) | ||||
0.504774 | + | 0.863252i | \(0.331576\pi\) | |||||||
\(44\) | −4.00515e23 | −0.592319 | ||||||||
\(45\) | −5.85700e22 | −0.0625307 | ||||||||
\(46\) | 1.95221e23 | 0.151544 | ||||||||
\(47\) | 3.20595e24 | 1.82195 | 0.910977 | − | 0.412456i | \(-0.135329\pi\) | ||||
0.910977 | + | 0.412456i | \(0.135329\pi\) | |||||||
\(48\) | 5.53646e23 | 0.231864 | ||||||||
\(49\) | −1.02738e24 | −0.319073 | ||||||||
\(50\) | 6.10352e23 | 0.141421 | ||||||||
\(51\) | −4.24277e24 | −0.737704 | ||||||||
\(52\) | −5.03495e24 | −0.660612 | ||||||||
\(53\) | −1.61509e25 | −1.60767 | −0.803834 | − | 0.594854i | \(-0.797210\pi\) | ||||
−0.803834 | + | 0.594854i | \(0.797210\pi\) | |||||||
\(54\) | −9.84750e24 | −0.747509 | ||||||||
\(55\) | −9.10667e24 | −0.529786 | ||||||||
\(56\) | −6.51226e24 | −0.291746 | ||||||||
\(57\) | −2.79669e25 | −0.969302 | ||||||||
\(58\) | 2.44481e25 | 0.658476 | ||||||||
\(59\) | −6.74135e25 | −1.41708 | −0.708538 | − | 0.705673i | \(-0.750645\pi\) | ||||
−0.708538 | + | 0.705673i | \(0.750645\pi\) | |||||||
\(60\) | 1.25884e25 | 0.207386 | ||||||||
\(61\) | −4.59568e25 | −0.595755 | −0.297877 | − | 0.954604i | \(-0.596279\pi\) | ||||
−0.297877 | + | 0.954604i | \(0.596279\pi\) | |||||||
\(62\) | 3.47787e24 | 0.0356151 | ||||||||
\(63\) | 1.42091e25 | 0.115380 | ||||||||
\(64\) | 1.93428e25 | 0.125000 | ||||||||
\(65\) | −1.14482e26 | −0.590870 | ||||||||
\(66\) | −1.87824e26 | −0.776899 | ||||||||
\(67\) | −3.04003e26 | −1.01110 | −0.505548 | − | 0.862798i | \(-0.668710\pi\) | ||||
−0.505548 | + | 0.862798i | \(0.668710\pi\) | |||||||
\(68\) | −1.48230e26 | −0.397702 | ||||||||
\(69\) | 9.15502e25 | 0.198769 | ||||||||
\(70\) | −1.48072e26 | −0.260946 | ||||||||
\(71\) | 8.77630e25 | 0.125912 | 0.0629558 | − | 0.998016i | \(-0.479947\pi\) | ||||
0.0629558 | + | 0.998016i | \(0.479947\pi\) | |||||||
\(72\) | −4.22041e25 | −0.0494349 | ||||||||
\(73\) | −1.54604e27 | −1.48265 | −0.741327 | − | 0.671144i | \(-0.765803\pi\) | ||||
−0.741327 | + | 0.671144i | \(0.765803\pi\) | |||||||
\(74\) | 7.15478e26 | 0.563295 | ||||||||
\(75\) | 2.86228e26 | 0.185491 | ||||||||
\(76\) | −9.77085e26 | −0.522559 | ||||||||
\(77\) | 2.20928e27 | 0.977543 | ||||||||
\(78\) | −2.36117e27 | −0.866474 | ||||||||
\(79\) | 8.64681e25 | 0.0263793 | 0.0131896 | − | 0.999913i | \(-0.495801\pi\) | ||||
0.0131896 | + | 0.999913i | \(0.495801\pi\) | |||||||
\(80\) | 4.39805e26 | 0.111803 | ||||||||
\(81\) | −3.95946e27 | −0.840627 | ||||||||
\(82\) | 2.04028e27 | 0.362568 | ||||||||
\(83\) | 8.92312e27 | 1.33010 | 0.665051 | − | 0.746798i | \(-0.268410\pi\) | ||||
0.665051 | + | 0.746798i | \(0.268410\pi\) | |||||||
\(84\) | −3.05396e27 | −0.382661 | ||||||||
\(85\) | −3.37037e27 | −0.355716 | ||||||||
\(86\) | 8.01381e27 | 0.713858 | ||||||||
\(87\) | 1.14651e28 | 0.863672 | ||||||||
\(88\) | −6.56204e27 | −0.418833 | ||||||||
\(89\) | 4.85579e27 | 0.263090 | 0.131545 | − | 0.991310i | \(-0.458006\pi\) | ||||
0.131545 | + | 0.991310i | \(0.458006\pi\) | |||||||
\(90\) | −9.59610e26 | −0.0442159 | ||||||||
\(91\) | 2.77733e28 | 1.09025 | ||||||||
\(92\) | 3.19851e27 | 0.107158 | ||||||||
\(93\) | 1.63097e27 | 0.0467135 | ||||||||
\(94\) | 5.25263e28 | 1.28832 | ||||||||
\(95\) | −2.22163e28 | −0.467391 | ||||||||
\(96\) | 9.07093e27 | 0.163953 | ||||||||
\(97\) | 6.50601e28 | 1.01187 | 0.505934 | − | 0.862572i | \(-0.331148\pi\) | ||||
0.505934 | + | 0.862572i | \(0.331148\pi\) | |||||||
\(98\) | −1.68327e28 | −0.225619 | ||||||||
\(99\) | 1.43177e28 | 0.165639 | ||||||||
\(100\) | 1.00000e28 | 0.100000 | ||||||||
\(101\) | 2.13267e29 | 1.84614 | 0.923068 | − | 0.384638i | \(-0.125674\pi\) | ||||
0.923068 | + | 0.384638i | \(0.125674\pi\) | |||||||
\(102\) | −6.95136e28 | −0.521635 | ||||||||
\(103\) | −8.52648e28 | −0.555431 | −0.277715 | − | 0.960663i | \(-0.589577\pi\) | ||||
−0.277715 | + | 0.960663i | \(0.589577\pi\) | |||||||
\(104\) | −8.24926e28 | −0.467124 | ||||||||
\(105\) | −6.94391e28 | −0.342262 | ||||||||
\(106\) | −2.64616e29 | −1.13679 | ||||||||
\(107\) | −1.53318e29 | −0.574814 | −0.287407 | − | 0.957809i | \(-0.592793\pi\) | ||||
−0.287407 | + | 0.957809i | \(0.592793\pi\) | |||||||
\(108\) | −1.61341e29 | −0.528569 | ||||||||
\(109\) | −4.55386e28 | −0.130525 | −0.0652627 | − | 0.997868i | \(-0.520789\pi\) | ||||
−0.0652627 | + | 0.997868i | \(0.520789\pi\) | |||||||
\(110\) | −1.49204e29 | −0.374615 | ||||||||
\(111\) | 3.35528e29 | 0.738831 | ||||||||
\(112\) | −1.06697e29 | −0.206296 | ||||||||
\(113\) | −9.49638e29 | −1.61406 | −0.807031 | − | 0.590508i | \(-0.798927\pi\) | ||||
−0.807031 | + | 0.590508i | \(0.798927\pi\) | |||||||
\(114\) | −4.58210e29 | −0.685400 | ||||||||
\(115\) | 7.27256e28 | 0.0958448 | ||||||||
\(116\) | 4.00558e29 | 0.465613 | ||||||||
\(117\) | 1.79991e29 | 0.184738 | ||||||||
\(118\) | −1.10450e30 | −1.00202 | ||||||||
\(119\) | 8.17654e29 | 0.656354 | ||||||||
\(120\) | 2.06249e29 | 0.146644 | ||||||||
\(121\) | 6.39862e29 | 0.403365 | ||||||||
\(122\) | −7.52957e29 | −0.421262 | ||||||||
\(123\) | 9.56804e29 | 0.475553 | ||||||||
\(124\) | 5.69814e28 | 0.0251836 | ||||||||
\(125\) | 2.27374e29 | 0.0894427 | ||||||||
\(126\) | 2.32802e29 | 0.0815856 | ||||||||
\(127\) | −6.99268e28 | −0.0218519 | −0.0109260 | − | 0.999940i | \(-0.503478\pi\) | ||||
−0.0109260 | + | 0.999940i | \(0.503478\pi\) | |||||||
\(128\) | 3.16913e29 | 0.0883883 | ||||||||
\(129\) | 3.75813e30 | 0.936312 | ||||||||
\(130\) | −1.87567e30 | −0.417808 | ||||||||
\(131\) | −1.54928e30 | −0.308814 | −0.154407 | − | 0.988007i | \(-0.549347\pi\) | ||||
−0.154407 | + | 0.988007i | \(0.549347\pi\) | |||||||
\(132\) | −3.07731e30 | −0.549350 | ||||||||
\(133\) | 5.38970e30 | 0.862414 | ||||||||
\(134\) | −4.98078e30 | −0.714953 | ||||||||
\(135\) | −3.66848e30 | −0.472766 | ||||||||
\(136\) | −2.42861e30 | −0.281218 | ||||||||
\(137\) | −5.90514e29 | −0.0614868 | −0.0307434 | − | 0.999527i | \(-0.509787\pi\) | ||||
−0.0307434 | + | 0.999527i | \(0.509787\pi\) | |||||||
\(138\) | 1.49996e30 | 0.140551 | ||||||||
\(139\) | 1.35271e31 | 1.14154 | 0.570769 | − | 0.821111i | \(-0.306645\pi\) | ||||
0.570769 | + | 0.821111i | \(0.306645\pi\) | |||||||
\(140\) | −2.42601e30 | −0.184517 | ||||||||
\(141\) | 2.46325e31 | 1.68979 | ||||||||
\(142\) | 1.43791e30 | 0.0890329 | ||||||||
\(143\) | 2.79856e31 | 1.56517 | ||||||||
\(144\) | −6.91472e29 | −0.0349557 | ||||||||
\(145\) | 9.10764e30 | 0.416457 | ||||||||
\(146\) | −2.53304e31 | −1.04839 | ||||||||
\(147\) | −7.89378e30 | −0.295927 | ||||||||
\(148\) | 1.17224e31 | 0.398310 | ||||||||
\(149\) | 3.78242e31 | 1.16565 | 0.582826 | − | 0.812597i | \(-0.301947\pi\) | ||||
0.582826 | + | 0.812597i | \(0.301947\pi\) | |||||||
\(150\) | 4.68956e30 | 0.131162 | ||||||||
\(151\) | −5.96443e31 | −1.51497 | −0.757483 | − | 0.652854i | \(-0.773571\pi\) | ||||
−0.757483 | + | 0.652854i | \(0.773571\pi\) | |||||||
\(152\) | −1.60086e31 | −0.369505 | ||||||||
\(153\) | 5.29898e30 | 0.111216 | ||||||||
\(154\) | 3.61969e31 | 0.691227 | ||||||||
\(155\) | 1.29561e30 | 0.0225249 | ||||||||
\(156\) | −3.86854e31 | −0.612690 | ||||||||
\(157\) | −6.30671e31 | −0.910454 | −0.455227 | − | 0.890375i | \(-0.650442\pi\) | ||||
−0.455227 | + | 0.890375i | \(0.650442\pi\) | |||||||
\(158\) | 1.41669e30 | 0.0186530 | ||||||||
\(159\) | −1.24093e32 | −1.49104 | ||||||||
\(160\) | 7.20576e30 | 0.0790569 | ||||||||
\(161\) | −1.76433e31 | −0.176850 | ||||||||
\(162\) | −6.48718e31 | −0.594413 | ||||||||
\(163\) | −1.15204e29 | −0.000965486 0 | −0.000482743 | − | 1.00000i | \(-0.500154\pi\) | ||||
−0.000482743 | 1.00000i | \(0.500154\pi\) | ||||||||
\(164\) | 3.34280e31 | 0.256375 | ||||||||
\(165\) | −6.99699e31 | −0.491354 | ||||||||
\(166\) | 1.46196e32 | 0.940523 | ||||||||
\(167\) | −3.21378e32 | −1.89508 | −0.947539 | − | 0.319641i | \(-0.896438\pi\) | ||||
−0.947539 | + | 0.319641i | \(0.896438\pi\) | |||||||
\(168\) | −5.00361e31 | −0.270582 | ||||||||
\(169\) | 1.50274e32 | 0.745635 | ||||||||
\(170\) | −5.52201e31 | −0.251529 | ||||||||
\(171\) | 3.49291e31 | 0.146131 | ||||||||
\(172\) | 1.31298e32 | 0.504774 | ||||||||
\(173\) | 2.25727e32 | 0.797840 | 0.398920 | − | 0.916986i | \(-0.369385\pi\) | ||||
0.398920 | + | 0.916986i | \(0.369385\pi\) | |||||||
\(174\) | 1.87844e32 | 0.610708 | ||||||||
\(175\) | −5.51610e31 | −0.165037 | ||||||||
\(176\) | −1.07513e32 | −0.296159 | ||||||||
\(177\) | −5.17964e32 | −1.31428 | ||||||||
\(178\) | 7.95572e31 | 0.186033 | ||||||||
\(179\) | −1.67639e32 | −0.361415 | −0.180707 | − | 0.983537i | \(-0.557839\pi\) | ||||
−0.180707 | + | 0.983537i | \(0.557839\pi\) | |||||||
\(180\) | −1.57223e31 | −0.0312654 | ||||||||
\(181\) | 5.21905e32 | 0.957751 | 0.478875 | − | 0.877883i | \(-0.341045\pi\) | ||||
0.478875 | + | 0.877883i | \(0.341045\pi\) | |||||||
\(182\) | 4.55038e32 | 0.770925 | ||||||||
\(183\) | −3.53104e32 | −0.552537 | ||||||||
\(184\) | 5.24043e31 | 0.0757720 | ||||||||
\(185\) | 2.66536e32 | 0.356259 | ||||||||
\(186\) | 2.67218e31 | 0.0330314 | ||||||||
\(187\) | 8.23904e32 | 0.942266 | ||||||||
\(188\) | 8.60590e32 | 0.910977 | ||||||||
\(189\) | 8.89975e32 | 0.872332 | ||||||||
\(190\) | −3.63993e32 | −0.330495 | ||||||||
\(191\) | 2.11179e33 | 1.77692 | 0.888460 | − | 0.458955i | \(-0.151776\pi\) | ||||
0.888460 | + | 0.458955i | \(0.151776\pi\) | |||||||
\(192\) | 1.48618e32 | 0.115932 | ||||||||
\(193\) | −1.46578e33 | −1.06045 | −0.530224 | − | 0.847858i | \(-0.677892\pi\) | ||||
−0.530224 | + | 0.847858i | \(0.677892\pi\) | |||||||
\(194\) | 1.06594e33 | 0.715499 | ||||||||
\(195\) | −8.79605e32 | −0.548006 | ||||||||
\(196\) | −2.75786e32 | −0.159536 | ||||||||
\(197\) | −8.00038e32 | −0.429883 | −0.214942 | − | 0.976627i | \(-0.568956\pi\) | ||||
−0.214942 | + | 0.976627i | \(0.568956\pi\) | |||||||
\(198\) | 2.34582e32 | 0.117125 | ||||||||
\(199\) | −3.40186e33 | −1.57887 | −0.789436 | − | 0.613833i | \(-0.789627\pi\) | ||||
−0.789436 | + | 0.613833i | \(0.789627\pi\) | |||||||
\(200\) | 1.63840e32 | 0.0707107 | ||||||||
\(201\) | −2.33577e33 | −0.937749 | ||||||||
\(202\) | 3.49416e33 | 1.30541 | ||||||||
\(203\) | −2.20952e33 | −0.768432 | ||||||||
\(204\) | −1.13891e33 | −0.368852 | ||||||||
\(205\) | 7.60065e32 | 0.229308 | ||||||||
\(206\) | −1.39698e33 | −0.392749 | ||||||||
\(207\) | −1.14341e32 | −0.0299662 | ||||||||
\(208\) | −1.35156e33 | −0.330306 | ||||||||
\(209\) | 5.43090e33 | 1.23809 | ||||||||
\(210\) | −1.13769e33 | −0.242016 | ||||||||
\(211\) | −1.67250e33 | −0.332102 | −0.166051 | − | 0.986117i | \(-0.553102\pi\) | ||||
−0.166051 | + | 0.986117i | \(0.553102\pi\) | |||||||
\(212\) | −4.33547e33 | −0.803834 | ||||||||
\(213\) | 6.74316e32 | 0.116778 | ||||||||
\(214\) | −2.51196e33 | −0.406455 | ||||||||
\(215\) | 2.98538e33 | 0.451483 | ||||||||
\(216\) | −2.64342e33 | −0.373754 | ||||||||
\(217\) | −3.14315e32 | −0.0415622 | ||||||||
\(218\) | −7.46104e32 | −0.0922954 | ||||||||
\(219\) | −1.18788e34 | −1.37510 | ||||||||
\(220\) | −2.44455e33 | −0.264893 | ||||||||
\(221\) | 1.03575e34 | 1.05091 | ||||||||
\(222\) | 5.49729e33 | 0.522432 | ||||||||
\(223\) | 1.89519e34 | 1.68745 | 0.843726 | − | 0.536775i | \(-0.180357\pi\) | ||||
0.843726 | + | 0.536775i | \(0.180357\pi\) | |||||||
\(224\) | −1.74812e33 | −0.145873 | ||||||||
\(225\) | −3.57483e32 | −0.0279646 | ||||||||
\(226\) | −1.55589e34 | −1.14131 | ||||||||
\(227\) | 2.37544e33 | 0.163444 | 0.0817222 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817222 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(228\) | −7.50731e33 | −0.484651 | ||||||||
\(229\) | −3.16033e34 | −1.91478 | −0.957388 | − | 0.288804i | \(-0.906742\pi\) | ||||
−0.957388 | + | 0.288804i | \(0.906742\pi\) | |||||||
\(230\) | 1.19154e33 | 0.0677725 | ||||||||
\(231\) | 1.69747e34 | 0.906629 | ||||||||
\(232\) | 6.56275e33 | 0.329238 | ||||||||
\(233\) | 1.58340e34 | 0.746328 | 0.373164 | − | 0.927765i | \(-0.378273\pi\) | ||||
0.373164 | + | 0.927765i | \(0.378273\pi\) | |||||||
\(234\) | 2.94897e33 | 0.130629 | ||||||||
\(235\) | 1.95676e34 | 0.814803 | ||||||||
\(236\) | −1.80962e34 | −0.708538 | ||||||||
\(237\) | 6.64367e32 | 0.0244657 | ||||||||
\(238\) | 1.33964e34 | 0.464113 | ||||||||
\(239\) | −1.69580e34 | −0.552849 | −0.276424 | − | 0.961036i | \(-0.589150\pi\) | ||||
−0.276424 | + | 0.961036i | \(0.589150\pi\) | |||||||
\(240\) | 3.37918e33 | 0.103693 | ||||||||
\(241\) | −6.52685e33 | −0.188563 | −0.0942815 | − | 0.995546i | \(-0.530055\pi\) | ||||
−0.0942815 | + | 0.995546i | \(0.530055\pi\) | |||||||
\(242\) | 1.04835e34 | 0.285222 | ||||||||
\(243\) | 1.08278e34 | 0.277492 | ||||||||
\(244\) | −1.23364e34 | −0.297877 | ||||||||
\(245\) | −6.27066e33 | −0.142694 | ||||||||
\(246\) | 1.56763e34 | 0.336267 | ||||||||
\(247\) | 6.82728e34 | 1.38084 | ||||||||
\(248\) | 9.33583e32 | 0.0178075 | ||||||||
\(249\) | 6.85597e34 | 1.23361 | ||||||||
\(250\) | 3.72529e33 | 0.0632456 | ||||||||
\(251\) | 8.19176e34 | 1.31253 | 0.656264 | − | 0.754532i | \(-0.272136\pi\) | ||||
0.656264 | + | 0.754532i | \(0.272136\pi\) | |||||||
\(252\) | 3.81423e33 | 0.0576898 | ||||||||
\(253\) | −1.77782e34 | −0.253886 | ||||||||
\(254\) | −1.14568e33 | −0.0154516 | ||||||||
\(255\) | −2.58958e34 | −0.329911 | ||||||||
\(256\) | 5.19230e33 | 0.0625000 | ||||||||
\(257\) | −1.00126e35 | −1.13899 | −0.569493 | − | 0.821996i | \(-0.692861\pi\) | ||||
−0.569493 | + | 0.821996i | \(0.692861\pi\) | |||||||
\(258\) | 6.15731e34 | 0.662073 | ||||||||
\(259\) | −6.46618e34 | −0.657357 | ||||||||
\(260\) | −3.07309e34 | −0.295435 | ||||||||
\(261\) | −1.43193e34 | −0.130207 | ||||||||
\(262\) | −2.53835e34 | −0.218365 | ||||||||
\(263\) | −3.41235e34 | −0.277776 | −0.138888 | − | 0.990308i | \(-0.544353\pi\) | ||||
−0.138888 | + | 0.990308i | \(0.544353\pi\) | |||||||
\(264\) | −5.04187e34 | −0.388449 | ||||||||
\(265\) | −9.85772e34 | −0.718971 | ||||||||
\(266\) | 8.83048e34 | 0.609818 | ||||||||
\(267\) | 3.73088e34 | 0.244005 | ||||||||
\(268\) | −8.16051e34 | −0.505548 | ||||||||
\(269\) | −3.29203e35 | −1.93222 | −0.966109 | − | 0.258133i | \(-0.916893\pi\) | ||||
−0.966109 | + | 0.258133i | \(0.916893\pi\) | |||||||
\(270\) | −6.01043e34 | −0.334296 | ||||||||
\(271\) | −2.96956e35 | −1.56544 | −0.782721 | − | 0.622373i | \(-0.786169\pi\) | ||||
−0.782721 | + | 0.622373i | \(0.786169\pi\) | |||||||
\(272\) | −3.97903e34 | −0.198851 | ||||||||
\(273\) | 2.13393e35 | 1.01116 | ||||||||
\(274\) | −9.67498e33 | −0.0434778 | ||||||||
\(275\) | −5.55827e34 | −0.236927 | ||||||||
\(276\) | 2.45753e34 | 0.0993843 | ||||||||
\(277\) | −1.65686e35 | −0.635813 | −0.317906 | − | 0.948122i | \(-0.602980\pi\) | ||||
−0.317906 | + | 0.948122i | \(0.602980\pi\) | |||||||
\(278\) | 2.21628e35 | 0.807189 | ||||||||
\(279\) | −2.03699e33 | −0.00704250 | ||||||||
\(280\) | −3.97477e34 | −0.130473 | ||||||||
\(281\) | 3.67502e35 | 1.14556 | 0.572781 | − | 0.819708i | \(-0.305865\pi\) | ||||
0.572781 | + | 0.819708i | \(0.305865\pi\) | |||||||
\(282\) | 4.03579e35 | 1.19486 | ||||||||
\(283\) | −2.61559e35 | −0.735641 | −0.367820 | − | 0.929897i | \(-0.619896\pi\) | ||||
−0.367820 | + | 0.929897i | \(0.619896\pi\) | |||||||
\(284\) | 2.35587e34 | 0.0629558 | ||||||||
\(285\) | −1.70697e35 | −0.433485 | ||||||||
\(286\) | 4.58516e35 | 1.10674 | ||||||||
\(287\) | −1.84392e35 | −0.423112 | ||||||||
\(288\) | −1.13291e34 | −0.0247174 | ||||||||
\(289\) | −1.77042e35 | −0.367332 | ||||||||
\(290\) | 1.49220e35 | 0.294479 | ||||||||
\(291\) | 4.99881e35 | 0.938465 | ||||||||
\(292\) | −4.15013e35 | −0.741327 | ||||||||
\(293\) | 8.43142e35 | 1.43324 | 0.716622 | − | 0.697462i | \(-0.245687\pi\) | ||||
0.716622 | + | 0.697462i | \(0.245687\pi\) | |||||||
\(294\) | −1.29332e35 | −0.209252 | ||||||||
\(295\) | −4.11460e35 | −0.633735 | ||||||||
\(296\) | 1.92060e35 | 0.281648 | ||||||||
\(297\) | 8.96779e35 | 1.25232 | ||||||||
\(298\) | 6.19712e35 | 0.824240 | ||||||||
\(299\) | −2.23492e35 | −0.283159 | ||||||||
\(300\) | 7.68338e34 | 0.0927457 | ||||||||
\(301\) | −7.24254e35 | −0.833061 | ||||||||
\(302\) | −9.77212e35 | −1.07124 | ||||||||
\(303\) | 1.63861e36 | 1.71221 | ||||||||
\(304\) | −2.62284e35 | −0.261279 | ||||||||
\(305\) | −2.80498e35 | −0.266430 | ||||||||
\(306\) | 8.68185e34 | 0.0786415 | ||||||||
\(307\) | −1.18090e36 | −1.02025 | −0.510124 | − | 0.860101i | \(-0.670400\pi\) | ||||
−0.510124 | + | 0.860101i | \(0.670400\pi\) | |||||||
\(308\) | 5.93050e35 | 0.488771 | ||||||||
\(309\) | −6.55121e35 | −0.515138 | ||||||||
\(310\) | 2.12272e34 | 0.0159275 | ||||||||
\(311\) | 1.04336e36 | 0.747149 | 0.373574 | − | 0.927600i | \(-0.378132\pi\) | ||||
0.373574 | + | 0.927600i | \(0.378132\pi\) | |||||||
\(312\) | −6.33822e35 | −0.433237 | ||||||||
\(313\) | 2.76507e36 | 1.80432 | 0.902161 | − | 0.431400i | \(-0.141980\pi\) | ||||
0.902161 | + | 0.431400i | \(0.141980\pi\) | |||||||
\(314\) | −1.03329e36 | −0.643788 | ||||||||
\(315\) | 8.67255e34 | 0.0515993 | ||||||||
\(316\) | 2.32111e34 | 0.0131896 | ||||||||
\(317\) | 2.19277e36 | 1.19024 | 0.595119 | − | 0.803638i | \(-0.297105\pi\) | ||||
0.595119 | + | 0.803638i | \(0.297105\pi\) | |||||||
\(318\) | −2.03315e36 | −1.05433 | ||||||||
\(319\) | −2.22641e36 | −1.10316 | ||||||||
\(320\) | 1.18059e35 | 0.0559017 | ||||||||
\(321\) | −1.17800e36 | −0.533116 | ||||||||
\(322\) | −2.89067e35 | −0.125052 | ||||||||
\(323\) | 2.00997e36 | 0.831292 | ||||||||
\(324\) | −1.06286e36 | −0.420313 | ||||||||
\(325\) | −6.98740e35 | −0.264245 | ||||||||
\(326\) | −1.88750e33 | −0.000682702 0 | ||||||||
\(327\) | −3.49890e35 | −0.121057 | ||||||||
\(328\) | 5.47685e35 | 0.181284 | ||||||||
\(329\) | −4.74710e36 | −1.50345 | ||||||||
\(330\) | −1.14639e36 | −0.347440 | ||||||||
\(331\) | 3.32856e35 | 0.0965496 | 0.0482748 | − | 0.998834i | \(-0.484628\pi\) | ||||
0.0482748 | + | 0.998834i | \(0.484628\pi\) | |||||||
\(332\) | 2.39528e36 | 0.665051 | ||||||||
\(333\) | −4.19055e35 | −0.111386 | ||||||||
\(334\) | −5.26545e36 | −1.34002 | ||||||||
\(335\) | −1.85548e36 | −0.452176 | ||||||||
\(336\) | −8.19792e35 | −0.191331 | ||||||||
\(337\) | 4.57852e36 | 1.02351 | 0.511755 | − | 0.859132i | \(-0.328996\pi\) | ||||
0.511755 | + | 0.859132i | \(0.328996\pi\) | |||||||
\(338\) | 2.46209e36 | 0.527244 | ||||||||
\(339\) | −7.29642e36 | −1.49697 | ||||||||
\(340\) | −9.04727e35 | −0.177858 | ||||||||
\(341\) | −3.16718e35 | −0.0596670 | ||||||||
\(342\) | 5.72278e35 | 0.103331 | ||||||||
\(343\) | 6.28903e36 | 1.08848 | ||||||||
\(344\) | 2.15119e36 | 0.356929 | ||||||||
\(345\) | 5.58778e35 | 0.0888920 | ||||||||
\(346\) | 3.69832e36 | 0.564158 | ||||||||
\(347\) | 3.69118e36 | 0.539993 | 0.269997 | − | 0.962861i | \(-0.412977\pi\) | ||||
0.269997 | + | 0.962861i | \(0.412977\pi\) | |||||||
\(348\) | 3.07764e36 | 0.431836 | ||||||||
\(349\) | −2.78937e36 | −0.375438 | −0.187719 | − | 0.982223i | \(-0.560109\pi\) | ||||
−0.187719 | + | 0.982223i | \(0.560109\pi\) | |||||||
\(350\) | −9.03758e35 | −0.116699 | ||||||||
\(351\) | 1.12736e37 | 1.39672 | ||||||||
\(352\) | −1.76149e36 | −0.209416 | ||||||||
\(353\) | −1.23430e37 | −1.40827 | −0.704135 | − | 0.710066i | \(-0.748665\pi\) | ||||
−0.704135 | + | 0.710066i | \(0.748665\pi\) | |||||||
\(354\) | −8.48631e36 | −0.929334 | ||||||||
\(355\) | 5.35663e35 | 0.0563093 | ||||||||
\(356\) | 1.30347e36 | 0.131545 | ||||||||
\(357\) | 6.28234e36 | 0.608741 | ||||||||
\(358\) | −2.74660e36 | −0.255559 | ||||||||
\(359\) | 1.60585e36 | 0.143494 | 0.0717472 | − | 0.997423i | \(-0.477143\pi\) | ||||
0.0717472 | + | 0.997423i | \(0.477143\pi\) | |||||||
\(360\) | −2.57593e35 | −0.0221079 | ||||||||
\(361\) | 1.11924e36 | 0.0922713 | ||||||||
\(362\) | 8.55090e36 | 0.677232 | ||||||||
\(363\) | 4.91630e36 | 0.374104 | ||||||||
\(364\) | 7.45533e36 | 0.545126 | ||||||||
\(365\) | −9.43629e36 | −0.663063 | ||||||||
\(366\) | −5.78525e36 | −0.390703 | ||||||||
\(367\) | −3.15301e36 | −0.204677 | −0.102338 | − | 0.994750i | \(-0.532632\pi\) | ||||
−0.102338 | + | 0.994750i | \(0.532632\pi\) | |||||||
\(368\) | 8.58592e35 | 0.0535789 | ||||||||
\(369\) | −1.19499e36 | −0.0716941 | ||||||||
\(370\) | 4.36693e36 | 0.251913 | ||||||||
\(371\) | 2.39149e37 | 1.32662 | ||||||||
\(372\) | 4.37810e35 | 0.0233568 | ||||||||
\(373\) | 1.47949e37 | 0.759162 | 0.379581 | − | 0.925158i | \(-0.376068\pi\) | ||||
0.379581 | + | 0.925158i | \(0.376068\pi\) | |||||||
\(374\) | 1.34988e37 | 0.666283 | ||||||||
\(375\) | 1.74700e36 | 0.0829543 | ||||||||
\(376\) | 1.40999e37 | 0.644158 | ||||||||
\(377\) | −2.79886e37 | −1.23036 | ||||||||
\(378\) | 1.45813e37 | 0.616832 | ||||||||
\(379\) | −3.91070e37 | −1.59216 | −0.796079 | − | 0.605193i | \(-0.793096\pi\) | ||||
−0.796079 | + | 0.605193i | \(0.793096\pi\) | |||||||
\(380\) | −5.96365e36 | −0.233695 | ||||||||
\(381\) | −5.37274e35 | −0.0202667 | ||||||||
\(382\) | 3.45996e37 | 1.25647 | ||||||||
\(383\) | 1.25775e37 | 0.439757 | 0.219879 | − | 0.975527i | \(-0.429434\pi\) | ||||
0.219879 | + | 0.975527i | \(0.429434\pi\) | |||||||
\(384\) | 2.43496e36 | 0.0819764 | ||||||||
\(385\) | 1.34844e37 | 0.437170 | ||||||||
\(386\) | −2.40154e37 | −0.749850 | ||||||||
\(387\) | −4.69369e36 | −0.141158 | ||||||||
\(388\) | 1.74644e37 | 0.505934 | ||||||||
\(389\) | −5.78321e37 | −1.61398 | −0.806992 | − | 0.590562i | \(-0.798906\pi\) | ||||
−0.806992 | + | 0.590562i | \(0.798906\pi\) | |||||||
\(390\) | −1.44114e37 | −0.387499 | ||||||||
\(391\) | −6.57968e36 | −0.170468 | ||||||||
\(392\) | −4.51849e36 | −0.112809 | ||||||||
\(393\) | −1.19037e37 | −0.286412 | ||||||||
\(394\) | −1.31078e37 | −0.303973 | ||||||||
\(395\) | 5.27759e35 | 0.0117972 | ||||||||
\(396\) | 3.84339e36 | 0.0828197 | ||||||||
\(397\) | −6.66269e37 | −1.38416 | −0.692081 | − | 0.721820i | \(-0.743306\pi\) | ||||
−0.692081 | + | 0.721820i | \(0.743306\pi\) | |||||||
\(398\) | −5.57361e37 | −1.11643 | ||||||||
\(399\) | 4.14111e37 | 0.799852 | ||||||||
\(400\) | 2.68435e36 | 0.0500000 | ||||||||
\(401\) | −8.06663e37 | −1.44910 | −0.724551 | − | 0.689221i | \(-0.757953\pi\) | ||||
−0.724551 | + | 0.689221i | \(0.757953\pi\) | |||||||
\(402\) | −3.82692e37 | −0.663088 | ||||||||
\(403\) | −3.98152e36 | −0.0665465 | ||||||||
\(404\) | 5.72484e37 | 0.923068 | ||||||||
\(405\) | −2.41666e37 | −0.375940 | ||||||||
\(406\) | −3.62008e37 | −0.543363 | ||||||||
\(407\) | −6.51562e37 | −0.943706 | ||||||||
\(408\) | −1.86599e37 | −0.260818 | ||||||||
\(409\) | 1.28165e38 | 1.72895 | 0.864473 | − | 0.502679i | \(-0.167652\pi\) | ||||
0.864473 | + | 0.502679i | \(0.167652\pi\) | |||||||
\(410\) | 1.24529e37 | 0.162145 | ||||||||
\(411\) | −4.53714e36 | −0.0570264 | ||||||||
\(412\) | −2.28881e37 | −0.277715 | ||||||||
\(413\) | 9.98203e37 | 1.16935 | ||||||||
\(414\) | −1.87336e36 | −0.0211893 | ||||||||
\(415\) | 5.44624e37 | 0.594839 | ||||||||
\(416\) | −2.21439e37 | −0.233562 | ||||||||
\(417\) | 1.03934e38 | 1.05873 | ||||||||
\(418\) | 8.89799e37 | 0.875459 | ||||||||
\(419\) | 1.46843e38 | 1.39556 | 0.697780 | − | 0.716312i | \(-0.254171\pi\) | ||||
0.697780 | + | 0.716312i | \(0.254171\pi\) | |||||||
\(420\) | −1.86399e37 | −0.171131 | ||||||||
\(421\) | 2.12573e36 | 0.0188546 | 0.00942732 | − | 0.999956i | \(-0.496999\pi\) | ||||
0.00942732 | + | 0.999956i | \(0.496999\pi\) | |||||||
\(422\) | −2.74023e37 | −0.234832 | ||||||||
\(423\) | −3.07646e37 | −0.254751 | ||||||||
\(424\) | −7.10324e37 | −0.568396 | ||||||||
\(425\) | −2.05711e37 | −0.159081 | ||||||||
\(426\) | 1.10480e37 | 0.0825742 | ||||||||
\(427\) | 6.80490e37 | 0.491607 | ||||||||
\(428\) | −4.11559e37 | −0.287407 | ||||||||
\(429\) | 2.15024e38 | 1.45163 | ||||||||
\(430\) | 4.89124e37 | 0.319247 | ||||||||
\(431\) | 8.37130e37 | 0.528290 | 0.264145 | − | 0.964483i | \(-0.414910\pi\) | ||||
0.264145 | + | 0.964483i | \(0.414910\pi\) | |||||||
\(432\) | −4.33097e37 | −0.264284 | ||||||||
\(433\) | −1.09694e38 | −0.647305 | −0.323652 | − | 0.946176i | \(-0.604911\pi\) | ||||
−0.323652 | + | 0.946176i | \(0.604911\pi\) | |||||||
\(434\) | −5.14974e36 | −0.0293889 | ||||||||
\(435\) | 6.99775e37 | 0.386246 | ||||||||
\(436\) | −1.22242e37 | −0.0652627 | ||||||||
\(437\) | −4.33710e37 | −0.223985 | ||||||||
\(438\) | −1.94623e38 | −0.972341 | ||||||||
\(439\) | 1.66935e38 | 0.806885 | 0.403442 | − | 0.915005i | \(-0.367814\pi\) | ||||
0.403442 | + | 0.915005i | \(0.367814\pi\) | |||||||
\(440\) | −4.00515e37 | −0.187308 | ||||||||
\(441\) | 9.85889e36 | 0.0446137 | ||||||||
\(442\) | 1.69696e38 | 0.743104 | ||||||||
\(443\) | −3.71165e38 | −1.57294 | −0.786472 | − | 0.617626i | \(-0.788094\pi\) | ||||
−0.786472 | + | 0.617626i | \(0.788094\pi\) | |||||||
\(444\) | 9.00675e37 | 0.369416 | ||||||||
\(445\) | 2.96374e37 | 0.117657 | ||||||||
\(446\) | 3.10507e38 | 1.19321 | ||||||||
\(447\) | 2.90618e38 | 1.08109 | ||||||||
\(448\) | −2.86412e37 | −0.103148 | ||||||||
\(449\) | −3.75572e38 | −1.30955 | −0.654774 | − | 0.755825i | \(-0.727236\pi\) | ||||
−0.654774 | + | 0.755825i | \(0.727236\pi\) | |||||||
\(450\) | −5.85700e36 | −0.0197739 | ||||||||
\(451\) | −1.85802e38 | −0.607422 | ||||||||
\(452\) | −2.54916e38 | −0.807031 | ||||||||
\(453\) | −4.58270e38 | −1.40507 | ||||||||
\(454\) | 3.89193e37 | 0.115573 | ||||||||
\(455\) | 1.69515e38 | 0.487576 | ||||||||
\(456\) | −1.23000e38 | −0.342700 | ||||||||
\(457\) | −2.86202e38 | −0.772482 | −0.386241 | − | 0.922398i | \(-0.626227\pi\) | ||||
−0.386241 | + | 0.922398i | \(0.626227\pi\) | |||||||
\(458\) | −5.17789e38 | −1.35395 | ||||||||
\(459\) | 3.31897e38 | 0.840852 | ||||||||
\(460\) | 1.95221e37 | 0.0479224 | ||||||||
\(461\) | −3.46285e38 | −0.823703 | −0.411851 | − | 0.911251i | \(-0.635118\pi\) | ||||
−0.411851 | + | 0.911251i | \(0.635118\pi\) | |||||||
\(462\) | 2.78114e38 | 0.641084 | ||||||||
\(463\) | 5.93445e38 | 1.32573 | 0.662867 | − | 0.748738i | \(-0.269340\pi\) | ||||
0.662867 | + | 0.748738i | \(0.269340\pi\) | |||||||
\(464\) | 1.07524e38 | 0.232806 | ||||||||
\(465\) | 9.95464e36 | 0.0208909 | ||||||||
\(466\) | 2.59424e38 | 0.527734 | ||||||||
\(467\) | 9.62200e37 | 0.189745 | 0.0948725 | − | 0.995489i | \(-0.469756\pi\) | ||||
0.0948725 | + | 0.995489i | \(0.469756\pi\) | |||||||
\(468\) | 4.83159e37 | 0.0923688 | ||||||||
\(469\) | 4.50141e38 | 0.834340 | ||||||||
\(470\) | 3.20595e38 | 0.576153 | ||||||||
\(471\) | −4.84569e38 | −0.844408 | ||||||||
\(472\) | −2.96488e38 | −0.501012 | ||||||||
\(473\) | −7.29791e38 | −1.19595 | ||||||||
\(474\) | 1.08850e37 | 0.0172998 | ||||||||
\(475\) | −1.35598e38 | −0.209024 | ||||||||
\(476\) | 2.19487e38 | 0.328177 | ||||||||
\(477\) | 1.54986e38 | 0.224789 | ||||||||
\(478\) | −2.77841e38 | −0.390923 | ||||||||
\(479\) | −4.88061e38 | −0.666207 | −0.333104 | − | 0.942890i | \(-0.608096\pi\) | ||||
−0.333104 | + | 0.942890i | \(0.608096\pi\) | |||||||
\(480\) | 5.53646e37 | 0.0733219 | ||||||||
\(481\) | −8.19090e38 | −1.05251 | ||||||||
\(482\) | −1.06936e38 | −0.133334 | ||||||||
\(483\) | −1.35560e38 | −0.164020 | ||||||||
\(484\) | 1.71762e38 | 0.201683 | ||||||||
\(485\) | 3.97095e38 | 0.452522 | ||||||||
\(486\) | 1.77403e38 | 0.196216 | ||||||||
\(487\) | 1.54915e38 | 0.166312 | 0.0831558 | − | 0.996537i | \(-0.473500\pi\) | ||||
0.0831558 | + | 0.996537i | \(0.473500\pi\) | |||||||
\(488\) | −2.02120e38 | −0.210631 | ||||||||
\(489\) | −8.85153e35 | −0.000895447 0 | ||||||||
\(490\) | −1.02738e38 | −0.100900 | ||||||||
\(491\) | −8.20640e37 | −0.0782476 | −0.0391238 | − | 0.999234i | \(-0.512457\pi\) | ||||
−0.0391238 | + | 0.999234i | \(0.512457\pi\) | |||||||
\(492\) | 2.56840e38 | 0.237776 | ||||||||
\(493\) | −8.23993e38 | −0.740701 | ||||||||
\(494\) | 1.11858e39 | 0.976398 | ||||||||
\(495\) | 8.73885e37 | 0.0740762 | ||||||||
\(496\) | 1.52958e37 | 0.0125918 | ||||||||
\(497\) | −1.29952e38 | −0.103900 | ||||||||
\(498\) | 1.12328e39 | 0.872295 | ||||||||
\(499\) | 2.36296e39 | 1.78237 | 0.891187 | − | 0.453637i | \(-0.149874\pi\) | ||||
0.891187 | + | 0.453637i | \(0.149874\pi\) | |||||||
\(500\) | 6.10352e37 | 0.0447214 | ||||||||
\(501\) | −2.46927e39 | −1.75760 | ||||||||
\(502\) | 1.34214e39 | 0.928097 | ||||||||
\(503\) | 1.38727e39 | 0.932023 | 0.466011 | − | 0.884779i | \(-0.345691\pi\) | ||||
0.466011 | + | 0.884779i | \(0.345691\pi\) | |||||||
\(504\) | 6.24923e37 | 0.0407928 | ||||||||
\(505\) | 1.30168e39 | 0.825617 | ||||||||
\(506\) | −2.91277e38 | −0.179525 | ||||||||
\(507\) | 1.15461e39 | 0.691545 | ||||||||
\(508\) | −1.87708e37 | −0.0109260 | ||||||||
\(509\) | −2.30259e39 | −1.30259 | −0.651297 | − | 0.758823i | \(-0.725775\pi\) | ||||
−0.651297 | + | 0.758823i | \(0.725775\pi\) | |||||||
\(510\) | −4.24277e38 | −0.233282 | ||||||||
\(511\) | 2.28925e39 | 1.22346 | ||||||||
\(512\) | 8.50706e37 | 0.0441942 | ||||||||
\(513\) | 2.18775e39 | 1.10483 | ||||||||
\(514\) | −1.64047e39 | −0.805385 | ||||||||
\(515\) | −5.20415e38 | −0.248396 | ||||||||
\(516\) | 1.00881e39 | 0.468156 | ||||||||
\(517\) | −4.78339e39 | −2.15836 | ||||||||
\(518\) | −1.05942e39 | −0.464822 | ||||||||
\(519\) | 1.73435e39 | 0.739962 | ||||||||
\(520\) | −5.03495e38 | −0.208904 | ||||||||
\(521\) | 1.16195e39 | 0.468857 | 0.234429 | − | 0.972133i | \(-0.424678\pi\) | ||||
0.234429 | + | 0.972133i | \(0.424678\pi\) | |||||||
\(522\) | −2.34607e38 | −0.0920701 | ||||||||
\(523\) | 4.58242e39 | 1.74912 | 0.874561 | − | 0.484915i | \(-0.161149\pi\) | ||||
0.874561 | + | 0.484915i | \(0.161149\pi\) | |||||||
\(524\) | −4.15883e38 | −0.154407 | ||||||||
\(525\) | −4.23823e38 | −0.153064 | ||||||||
\(526\) | −5.59080e38 | −0.196418 | ||||||||
\(527\) | −1.17217e38 | −0.0400624 | ||||||||
\(528\) | −8.26059e38 | −0.274675 | ||||||||
\(529\) | −2.94908e39 | −0.954069 | ||||||||
\(530\) | −1.61509e39 | −0.508389 | ||||||||
\(531\) | 6.46907e38 | 0.198140 | ||||||||
\(532\) | 1.44679e39 | 0.431207 | ||||||||
\(533\) | −2.33575e39 | −0.677457 | ||||||||
\(534\) | 6.11268e38 | 0.172537 | ||||||||
\(535\) | −9.35777e38 | −0.257065 | ||||||||
\(536\) | −1.33702e39 | −0.357477 | ||||||||
\(537\) | −1.28803e39 | −0.335197 | ||||||||
\(538\) | −5.39367e39 | −1.36628 | ||||||||
\(539\) | 1.53290e39 | 0.377986 | ||||||||
\(540\) | −9.84750e38 | −0.236383 | ||||||||
\(541\) | 3.15300e39 | 0.736824 | 0.368412 | − | 0.929663i | \(-0.379902\pi\) | ||||
0.368412 | + | 0.929663i | \(0.379902\pi\) | |||||||
\(542\) | −4.86532e39 | −1.10693 | ||||||||
\(543\) | 4.01000e39 | 0.888273 | ||||||||
\(544\) | −6.51924e38 | −0.140609 | ||||||||
\(545\) | −2.77945e38 | −0.0583728 | ||||||||
\(546\) | 3.49622e39 | 0.715000 | ||||||||
\(547\) | −1.24403e39 | −0.247750 | −0.123875 | − | 0.992298i | \(-0.539532\pi\) | ||||
−0.123875 | + | 0.992298i | \(0.539532\pi\) | |||||||
\(548\) | −1.58515e38 | −0.0307434 | ||||||||
\(549\) | 4.41006e38 | 0.0833002 | ||||||||
\(550\) | −9.10667e38 | −0.167533 | ||||||||
\(551\) | −5.43148e39 | −0.973241 | ||||||||
\(552\) | 4.02642e38 | 0.0702753 | ||||||||
\(553\) | −1.28035e38 | −0.0217677 | ||||||||
\(554\) | −2.71460e39 | −0.449588 | ||||||||
\(555\) | 2.04790e39 | 0.330415 | ||||||||
\(556\) | 3.63116e39 | 0.570769 | ||||||||
\(557\) | −7.59373e39 | −1.16293 | −0.581467 | − | 0.813570i | \(-0.697521\pi\) | ||||
−0.581467 | + | 0.813570i | \(0.697521\pi\) | |||||||
\(558\) | −3.33740e37 | −0.00497980 | ||||||||
\(559\) | −9.17434e39 | −1.33384 | ||||||||
\(560\) | −6.51226e38 | −0.0922583 | ||||||||
\(561\) | 6.33037e39 | 0.873911 | ||||||||
\(562\) | 6.02116e39 | 0.810035 | ||||||||
\(563\) | −8.33986e38 | −0.109342 | −0.0546710 | − | 0.998504i | \(-0.517411\pi\) | ||||
−0.0546710 | + | 0.998504i | \(0.517411\pi\) | |||||||
\(564\) | 6.61224e39 | 0.844893 | ||||||||
\(565\) | −5.79613e39 | −0.721831 | ||||||||
\(566\) | −4.28538e39 | −0.520177 | ||||||||
\(567\) | 5.86284e39 | 0.693671 | ||||||||
\(568\) | 3.85986e38 | 0.0445164 | ||||||||
\(569\) | −1.07248e40 | −1.20576 | −0.602879 | − | 0.797833i | \(-0.705980\pi\) | ||||
−0.602879 | + | 0.797833i | \(0.705980\pi\) | |||||||
\(570\) | −2.79669e39 | −0.306520 | ||||||||
\(571\) | 1.45529e40 | 1.55498 | 0.777490 | − | 0.628895i | \(-0.216493\pi\) | ||||
0.777490 | + | 0.628895i | \(0.216493\pi\) | |||||||
\(572\) | 7.51233e39 | 0.782586 | ||||||||
\(573\) | 1.62257e40 | 1.64802 | ||||||||
\(574\) | −3.02108e39 | −0.299185 | ||||||||
\(575\) | 4.43882e38 | 0.0428631 | ||||||||
\(576\) | −1.85616e38 | −0.0174779 | ||||||||
\(577\) | 1.89246e40 | 1.73771 | 0.868855 | − | 0.495067i | \(-0.164856\pi\) | ||||
0.868855 | + | 0.495067i | \(0.164856\pi\) | |||||||
\(578\) | −2.90066e39 | −0.259743 | ||||||||
\(579\) | −1.12622e40 | −0.983520 | ||||||||
\(580\) | 2.44481e39 | 0.208228 | ||||||||
\(581\) | −1.32126e40 | −1.09758 | ||||||||
\(582\) | 8.19005e39 | 0.663595 | ||||||||
\(583\) | 2.40977e40 | 1.90450 | ||||||||
\(584\) | −6.79956e39 | −0.524197 | ||||||||
\(585\) | 1.09858e39 | 0.0826171 | ||||||||
\(586\) | 1.38140e40 | 1.01346 | ||||||||
\(587\) | 1.86692e39 | 0.133621 | 0.0668104 | − | 0.997766i | \(-0.478718\pi\) | ||||
0.0668104 | + | 0.997766i | \(0.478718\pi\) | |||||||
\(588\) | −2.11897e39 | −0.147963 | ||||||||
\(589\) | −7.72655e38 | −0.0526398 | ||||||||
\(590\) | −6.74135e39 | −0.448119 | ||||||||
\(591\) | −6.14700e39 | −0.398698 | ||||||||
\(592\) | 3.14670e39 | 0.199155 | ||||||||
\(593\) | 2.24511e40 | 1.38658 | 0.693289 | − | 0.720659i | \(-0.256161\pi\) | ||||
0.693289 | + | 0.720659i | \(0.256161\pi\) | |||||||
\(594\) | 1.46928e40 | 0.885527 | ||||||||
\(595\) | 4.99056e39 | 0.293531 | ||||||||
\(596\) | 1.01534e40 | 0.582826 | ||||||||
\(597\) | −2.61378e40 | −1.46434 | ||||||||
\(598\) | −3.66170e39 | −0.200224 | ||||||||
\(599\) | −1.43934e40 | −0.768198 | −0.384099 | − | 0.923292i | \(-0.625488\pi\) | ||||
−0.384099 | + | 0.923292i | \(0.625488\pi\) | |||||||
\(600\) | 1.25884e39 | 0.0655811 | ||||||||
\(601\) | −3.10527e40 | −1.57914 | −0.789569 | − | 0.613662i | \(-0.789696\pi\) | ||||
−0.789569 | + | 0.613662i | \(0.789696\pi\) | |||||||
\(602\) | −1.18662e40 | −0.589063 | ||||||||
\(603\) | 2.91724e39 | 0.141374 | ||||||||
\(604\) | −1.60106e40 | −0.757483 | ||||||||
\(605\) | 3.90541e39 | 0.180391 | ||||||||
\(606\) | 2.68470e40 | 1.21072 | ||||||||
\(607\) | −3.10127e39 | −0.136554 | −0.0682769 | − | 0.997666i | \(-0.521750\pi\) | ||||
−0.0682769 | + | 0.997666i | \(0.521750\pi\) | |||||||
\(608\) | −4.29727e39 | −0.184752 | ||||||||
\(609\) | −1.69766e40 | −0.712688 | ||||||||
\(610\) | −4.59568e39 | −0.188394 | ||||||||
\(611\) | −6.01329e40 | −2.40721 | ||||||||
\(612\) | 1.42243e39 | 0.0556079 | ||||||||
\(613\) | −3.61509e38 | −0.0138020 | −0.00690101 | − | 0.999976i | \(-0.502197\pi\) | ||||
−0.00690101 | + | 0.999976i | \(0.502197\pi\) | |||||||
\(614\) | −1.93478e40 | −0.721424 | ||||||||
\(615\) | 5.83987e39 | 0.212674 | ||||||||
\(616\) | 9.71653e39 | 0.345614 | ||||||||
\(617\) | −1.26407e40 | −0.439173 | −0.219586 | − | 0.975593i | \(-0.570471\pi\) | ||||
−0.219586 | + | 0.975593i | \(0.570471\pi\) | |||||||
\(618\) | −1.07335e40 | −0.364258 | ||||||||
\(619\) | 8.23888e39 | 0.273120 | 0.136560 | − | 0.990632i | \(-0.456395\pi\) | ||||
0.136560 | + | 0.990632i | \(0.456395\pi\) | |||||||
\(620\) | 3.47787e38 | 0.0112625 | ||||||||
\(621\) | −7.16165e39 | −0.226561 | ||||||||
\(622\) | 1.70944e40 | 0.528314 | ||||||||
\(623\) | −7.19004e39 | −0.217097 | ||||||||
\(624\) | −1.03845e40 | −0.306345 | ||||||||
\(625\) | 1.38778e39 | 0.0400000 | ||||||||
\(626\) | 4.53030e40 | 1.27585 | ||||||||
\(627\) | 4.17277e40 | 1.14827 | ||||||||
\(628\) | −1.69295e40 | −0.455227 | ||||||||
\(629\) | −2.41142e40 | −0.633635 | ||||||||
\(630\) | 1.42091e39 | 0.0364862 | ||||||||
\(631\) | 5.22318e40 | 1.31072 | 0.655359 | − | 0.755317i | \(-0.272517\pi\) | ||||
0.655359 | + | 0.755317i | \(0.272517\pi\) | |||||||
\(632\) | 3.80291e38 | 0.00932648 | ||||||||
\(633\) | −1.28505e40 | −0.308011 | ||||||||
\(634\) | 3.59263e40 | 0.841625 | ||||||||
\(635\) | −4.26799e38 | −0.00977247 | ||||||||
\(636\) | −3.33111e40 | −0.745522 | ||||||||
\(637\) | 1.92703e40 | 0.421567 | ||||||||
\(638\) | −3.64775e40 | −0.780055 | ||||||||
\(639\) | −8.42183e38 | −0.0176053 | ||||||||
\(640\) | 1.93428e39 | 0.0395285 | ||||||||
\(641\) | −4.31938e40 | −0.862940 | −0.431470 | − | 0.902127i | \(-0.642005\pi\) | ||||
−0.431470 | + | 0.902127i | \(0.642005\pi\) | |||||||
\(642\) | −1.93003e40 | −0.376970 | ||||||||
\(643\) | 8.02353e40 | 1.53217 | 0.766084 | − | 0.642740i | \(-0.222202\pi\) | ||||
0.766084 | + | 0.642740i | \(0.222202\pi\) | |||||||
\(644\) | −4.73608e39 | −0.0884248 | ||||||||
\(645\) | 2.29378e40 | 0.418731 | ||||||||
\(646\) | 3.29314e40 | 0.587812 | ||||||||
\(647\) | −8.30129e40 | −1.44888 | −0.724442 | − | 0.689336i | \(-0.757902\pi\) | ||||
−0.724442 | + | 0.689336i | \(0.757902\pi\) | |||||||
\(648\) | −1.74139e40 | −0.297206 | ||||||||
\(649\) | 1.00583e41 | 1.67872 | ||||||||
\(650\) | −1.14482e40 | −0.186849 | ||||||||
\(651\) | −2.41500e39 | −0.0385472 | ||||||||
\(652\) | −3.09247e37 | −0.000482743 0 | ||||||||
\(653\) | −6.89266e40 | −1.05232 | −0.526158 | − | 0.850387i | \(-0.676368\pi\) | ||||
−0.526158 | + | 0.850387i | \(0.676368\pi\) | |||||||
\(654\) | −5.73260e39 | −0.0856001 | ||||||||
\(655\) | −9.45608e39 | −0.138106 | ||||||||
\(656\) | 8.97327e39 | 0.128187 | ||||||||
\(657\) | 1.48360e40 | 0.207309 | ||||||||
\(658\) | −7.77765e40 | −1.06310 | ||||||||
\(659\) | 4.28089e40 | 0.572395 | 0.286198 | − | 0.958171i | \(-0.407609\pi\) | ||||
0.286198 | + | 0.958171i | \(0.407609\pi\) | |||||||
\(660\) | −1.87824e40 | −0.245677 | ||||||||
\(661\) | −3.05389e40 | −0.390780 | −0.195390 | − | 0.980726i | \(-0.562597\pi\) | ||||
−0.195390 | + | 0.980726i | \(0.562597\pi\) | |||||||
\(662\) | 5.45351e39 | 0.0682709 | ||||||||
\(663\) | 7.95802e40 | 0.974673 | ||||||||
\(664\) | 3.92443e40 | 0.470262 | ||||||||
\(665\) | 3.28961e40 | 0.385683 | ||||||||
\(666\) | −6.86580e39 | −0.0787616 | ||||||||
\(667\) | 1.77801e40 | 0.199576 | ||||||||
\(668\) | −8.62692e40 | −0.947539 | ||||||||
\(669\) | 1.45614e41 | 1.56504 | ||||||||
\(670\) | −3.04003e40 | −0.319737 | ||||||||
\(671\) | 6.85692e40 | 0.705753 | ||||||||
\(672\) | −1.34315e40 | −0.135291 | ||||||||
\(673\) | 1.17559e41 | 1.15887 | 0.579437 | − | 0.815017i | \(-0.303273\pi\) | ||||
0.579437 | + | 0.815017i | \(0.303273\pi\) | |||||||
\(674\) | 7.50145e40 | 0.723730 | ||||||||
\(675\) | −2.23906e40 | −0.211427 | ||||||||
\(676\) | 4.03389e40 | 0.372818 | ||||||||
\(677\) | 8.31378e40 | 0.752078 | 0.376039 | − | 0.926604i | \(-0.377286\pi\) | ||||
0.376039 | + | 0.926604i | \(0.377286\pi\) | |||||||
\(678\) | −1.19545e41 | −1.05852 | ||||||||
\(679\) | −9.63355e40 | −0.834977 | ||||||||
\(680\) | −1.48230e40 | −0.125765 | ||||||||
\(681\) | 1.82514e40 | 0.151588 | ||||||||
\(682\) | −5.18911e39 | −0.0421909 | ||||||||
\(683\) | −6.88330e40 | −0.547894 | −0.273947 | − | 0.961745i | \(-0.588329\pi\) | ||||
−0.273947 | + | 0.961745i | \(0.588329\pi\) | |||||||
\(684\) | 9.37621e39 | 0.0730657 | ||||||||
\(685\) | −3.60421e39 | −0.0274977 | ||||||||
\(686\) | 1.03040e41 | 0.769669 | ||||||||
\(687\) | −2.42820e41 | −1.77587 | ||||||||
\(688\) | 3.52451e40 | 0.252387 | ||||||||
\(689\) | 3.02937e41 | 2.12409 | ||||||||
\(690\) | 9.15502e39 | 0.0628561 | ||||||||
\(691\) | −2.86827e41 | −1.92836 | −0.964182 | − | 0.265243i | \(-0.914548\pi\) | ||||
−0.964182 | + | 0.265243i | \(0.914548\pi\) | |||||||
\(692\) | 6.05932e40 | 0.398920 | ||||||||
\(693\) | −2.12005e40 | −0.136683 | ||||||||
\(694\) | 6.04764e40 | 0.381833 | ||||||||
\(695\) | 8.25629e40 | 0.510511 | ||||||||
\(696\) | 5.04241e40 | 0.305354 | ||||||||
\(697\) | −6.87651e40 | −0.407843 | ||||||||
\(698\) | −4.57011e40 | −0.265475 | ||||||||
\(699\) | 1.21659e41 | 0.692188 | ||||||||
\(700\) | −1.48072e40 | −0.0825183 | ||||||||
\(701\) | −3.31493e41 | −1.80952 | −0.904759 | − | 0.425923i | \(-0.859949\pi\) | ||||
−0.904759 | + | 0.425923i | \(0.859949\pi\) | |||||||
\(702\) | 1.84706e41 | 0.987627 | ||||||||
\(703\) | −1.58953e41 | −0.832562 | ||||||||
\(704\) | −2.88602e40 | −0.148080 | ||||||||
\(705\) | 1.50345e41 | 0.755695 | ||||||||
\(706\) | −2.02227e41 | −0.995797 | ||||||||
\(707\) | −3.15788e41 | −1.52340 | ||||||||
\(708\) | −1.39040e41 | −0.657138 | ||||||||
\(709\) | −3.21463e41 | −1.48854 | −0.744271 | − | 0.667878i | \(-0.767203\pi\) | ||||
−0.744271 | + | 0.667878i | \(0.767203\pi\) | |||||||
\(710\) | 8.77630e39 | 0.0398167 | ||||||||
\(711\) | −8.29756e38 | −0.00368843 | ||||||||
\(712\) | 2.13560e40 | 0.0930164 | ||||||||
\(713\) | 2.52930e39 | 0.0107945 | ||||||||
\(714\) | 1.02930e41 | 0.430445 | ||||||||
\(715\) | 1.70811e41 | 0.699966 | ||||||||
\(716\) | −4.50002e40 | −0.180707 | ||||||||
\(717\) | −1.30295e41 | −0.512743 | ||||||||
\(718\) | 2.63102e40 | 0.101466 | ||||||||
\(719\) | −1.53997e41 | −0.582029 | −0.291015 | − | 0.956719i | \(-0.593993\pi\) | ||||
−0.291015 | + | 0.956719i | \(0.593993\pi\) | |||||||
\(720\) | −4.22041e39 | −0.0156327 | ||||||||
\(721\) | 1.26253e41 | 0.458332 | ||||||||
\(722\) | 1.83375e40 | 0.0652457 | ||||||||
\(723\) | −5.01482e40 | −0.174884 | ||||||||
\(724\) | 1.40098e41 | 0.478875 | ||||||||
\(725\) | 5.55886e40 | 0.186245 | ||||||||
\(726\) | 8.05487e40 | 0.264532 | ||||||||
\(727\) | −2.73405e40 | −0.0880153 | −0.0440076 | − | 0.999031i | \(-0.514013\pi\) | ||||
−0.0440076 | + | 0.999031i | \(0.514013\pi\) | |||||||
\(728\) | 1.22148e41 | 0.385462 | ||||||||
\(729\) | 3.54933e41 | 1.09799 | ||||||||
\(730\) | −1.54604e41 | −0.468856 | ||||||||
\(731\) | −2.70095e41 | −0.802999 | ||||||||
\(732\) | −9.47855e40 | −0.276269 | ||||||||
\(733\) | −7.89799e40 | −0.225688 | −0.112844 | − | 0.993613i | \(-0.535996\pi\) | ||||
−0.112844 | + | 0.993613i | \(0.535996\pi\) | |||||||
\(734\) | −5.16590e40 | −0.144728 | ||||||||
\(735\) | −4.81798e40 | −0.132342 | ||||||||
\(736\) | 1.40672e40 | 0.0378860 | ||||||||
\(737\) | 4.53583e41 | 1.19778 | ||||||||
\(738\) | −1.95788e40 | −0.0506954 | ||||||||
\(739\) | −4.82157e41 | −1.22418 | −0.612088 | − | 0.790789i | \(-0.709670\pi\) | ||||
−0.612088 | + | 0.790789i | \(0.709670\pi\) | |||||||
\(740\) | 7.15478e40 | 0.178130 | ||||||||
\(741\) | 5.24566e41 | 1.28067 | ||||||||
\(742\) | 3.91822e41 | 0.938062 | ||||||||
\(743\) | 2.55089e41 | 0.598900 | 0.299450 | − | 0.954112i | \(-0.403197\pi\) | ||||
0.299450 | + | 0.954112i | \(0.403197\pi\) | |||||||
\(744\) | 7.17307e39 | 0.0165157 | ||||||||
\(745\) | 2.30861e41 | 0.521295 | ||||||||
\(746\) | 2.42400e41 | 0.536809 | ||||||||
\(747\) | −8.56272e40 | −0.185979 | ||||||||
\(748\) | 2.21165e41 | 0.471133 | ||||||||
\(749\) | 2.27020e41 | 0.474327 | ||||||||
\(750\) | 2.86228e40 | 0.0586576 | ||||||||
\(751\) | −4.47925e40 | −0.0900380 | −0.0450190 | − | 0.998986i | \(-0.514335\pi\) | ||||
−0.0450190 | + | 0.998986i | \(0.514335\pi\) | |||||||
\(752\) | 2.31013e41 | 0.455489 | ||||||||
\(753\) | 6.29404e41 | 1.21731 | ||||||||
\(754\) | −4.58565e41 | −0.869995 | ||||||||
\(755\) | −3.64040e41 | −0.677514 | ||||||||
\(756\) | 2.38901e41 | 0.436166 | ||||||||
\(757\) | −1.78881e41 | −0.320387 | −0.160194 | − | 0.987086i | \(-0.551212\pi\) | ||||
−0.160194 | + | 0.987086i | \(0.551212\pi\) | |||||||
\(758\) | −6.40729e41 | −1.12583 | ||||||||
\(759\) | −1.36596e41 | −0.235469 | ||||||||
\(760\) | −9.77085e40 | −0.165248 | ||||||||
\(761\) | 4.40276e40 | 0.0730546 | 0.0365273 | − | 0.999333i | \(-0.488370\pi\) | ||||
0.0365273 | + | 0.999333i | \(0.488370\pi\) | |||||||
\(762\) | −8.80269e39 | −0.0143307 | ||||||||
\(763\) | 6.74297e40 | 0.107707 | ||||||||
\(764\) | 5.66880e41 | 0.888460 | ||||||||
\(765\) | 3.23424e40 | 0.0497372 | ||||||||
\(766\) | 2.06070e41 | 0.310955 | ||||||||
\(767\) | 1.26445e42 | 1.87228 | ||||||||
\(768\) | 3.98944e40 | 0.0579661 | ||||||||
\(769\) | −1.76688e41 | −0.251927 | −0.125964 | − | 0.992035i | \(-0.540202\pi\) | ||||
−0.125964 | + | 0.992035i | \(0.540202\pi\) | |||||||
\(770\) | 2.20928e41 | 0.309126 | ||||||||
\(771\) | −7.69309e41 | −1.05636 | ||||||||
\(772\) | −3.93469e41 | −0.530224 | ||||||||
\(773\) | −1.91963e41 | −0.253873 | −0.126936 | − | 0.991911i | \(-0.540514\pi\) | ||||
−0.126936 | + | 0.991911i | \(0.540514\pi\) | |||||||
\(774\) | −7.69014e40 | −0.0998137 | ||||||||
\(775\) | 7.90776e39 | 0.0100735 | ||||||||
\(776\) | 2.86137e41 | 0.357750 | ||||||||
\(777\) | −4.96821e41 | −0.609671 | ||||||||
\(778\) | −9.47521e41 | −1.14126 | ||||||||
\(779\) | −4.53277e41 | −0.535883 | ||||||||
\(780\) | −2.36117e41 | −0.274003 | ||||||||
\(781\) | −1.30946e41 | −0.149159 | ||||||||
\(782\) | −1.07801e41 | −0.120539 | ||||||||
\(783\) | −8.96875e41 | −0.984433 | ||||||||
\(784\) | −7.40309e40 | −0.0797682 | ||||||||
\(785\) | −3.84931e41 | −0.407168 | ||||||||
\(786\) | −1.95031e41 | −0.202524 | ||||||||
\(787\) | 1.48600e42 | 1.51491 | 0.757454 | − | 0.652888i | \(-0.226443\pi\) | ||||
0.757454 | + | 0.652888i | \(0.226443\pi\) | |||||||
\(788\) | −2.14759e41 | −0.214942 | ||||||||
\(789\) | −2.62184e41 | −0.257626 | ||||||||
\(790\) | 8.64681e39 | 0.00834186 | ||||||||
\(791\) | 1.40614e42 | 1.33190 | ||||||||
\(792\) | 6.29700e40 | 0.0585624 | ||||||||
\(793\) | 8.61996e41 | 0.787126 | ||||||||
\(794\) | −1.09161e42 | −0.978751 | ||||||||
\(795\) | −7.57406e41 | −0.666815 | ||||||||
\(796\) | −9.13180e41 | −0.789436 | ||||||||
\(797\) | 6.29245e41 | 0.534163 | 0.267082 | − | 0.963674i | \(-0.413941\pi\) | ||||
0.267082 | + | 0.963674i | \(0.413941\pi\) | |||||||
\(798\) | 6.78479e41 | 0.565581 | ||||||||
\(799\) | −1.77033e42 | −1.44919 | ||||||||
\(800\) | 4.39805e40 | 0.0353553 | ||||||||
\(801\) | −4.65966e40 | −0.0367860 | ||||||||
\(802\) | −1.32164e42 | −1.02467 | ||||||||
\(803\) | 2.30675e42 | 1.75641 | ||||||||
\(804\) | −6.27002e41 | −0.468874 | ||||||||
\(805\) | −1.07686e41 | −0.0790895 | ||||||||
\(806\) | −6.52332e40 | −0.0470555 | ||||||||
\(807\) | −2.52939e42 | −1.79205 | ||||||||
\(808\) | 9.37958e41 | 0.652707 | ||||||||
\(809\) | 8.35891e41 | 0.571342 | 0.285671 | − | 0.958328i | \(-0.407784\pi\) | ||||
0.285671 | + | 0.958328i | \(0.407784\pi\) | |||||||
\(810\) | −3.95946e41 | −0.265829 | ||||||||
\(811\) | 8.80958e41 | 0.580969 | 0.290484 | − | 0.956880i | \(-0.406184\pi\) | ||||
0.290484 | + | 0.956880i | \(0.406184\pi\) | |||||||
\(812\) | −5.93113e41 | −0.384216 | ||||||||
\(813\) | −2.28162e42 | −1.45188 | ||||||||
\(814\) | −1.06752e42 | −0.667301 | ||||||||
\(815\) | −7.03147e38 | −0.000431779 0 | ||||||||
\(816\) | −3.05724e41 | −0.184426 | ||||||||
\(817\) | −1.78038e42 | −1.05510 | ||||||||
\(818\) | 2.09985e42 | 1.22255 | ||||||||
\(819\) | −2.66515e41 | −0.152442 | ||||||||
\(820\) | 2.04028e41 | 0.114654 | ||||||||
\(821\) | 1.16383e42 | 0.642559 | 0.321280 | − | 0.946984i | \(-0.395887\pi\) | ||||
0.321280 | + | 0.946984i | \(0.395887\pi\) | |||||||
\(822\) | −7.43365e40 | −0.0403238 | ||||||||
\(823\) | 3.33222e42 | 1.77597 | 0.887987 | − | 0.459869i | \(-0.152103\pi\) | ||||
0.887987 | + | 0.459869i | \(0.152103\pi\) | |||||||
\(824\) | −3.74998e41 | −0.196374 | ||||||||
\(825\) | −4.27063e41 | −0.219740 | ||||||||
\(826\) | 1.63546e42 | 0.826853 | ||||||||
\(827\) | 2.56265e42 | 1.27309 | 0.636545 | − | 0.771239i | \(-0.280363\pi\) | ||||
0.636545 | + | 0.771239i | \(0.280363\pi\) | |||||||
\(828\) | −3.06932e40 | −0.0149831 | ||||||||
\(829\) | 3.15692e42 | 1.51434 | 0.757169 | − | 0.653219i | \(-0.226582\pi\) | ||||
0.757169 | + | 0.653219i | \(0.226582\pi\) | |||||||
\(830\) | 8.92312e41 | 0.420615 | ||||||||
\(831\) | −1.27303e42 | −0.589689 | ||||||||
\(832\) | −3.62806e41 | −0.165153 | ||||||||
\(833\) | 5.67323e41 | 0.253792 | ||||||||
\(834\) | 1.70285e42 | 0.748634 | ||||||||
\(835\) | −1.96153e42 | −0.847504 | ||||||||
\(836\) | 1.45785e42 | 0.619043 | ||||||||
\(837\) | −1.27585e41 | −0.0532451 | ||||||||
\(838\) | 2.40587e42 | 0.986810 | ||||||||
\(839\) | −2.03367e42 | −0.819846 | −0.409923 | − | 0.912120i | \(-0.634444\pi\) | ||||
−0.409923 | + | 0.912120i | \(0.634444\pi\) | |||||||
\(840\) | −3.05396e41 | −0.121008 | ||||||||
\(841\) | −3.41036e41 | −0.132819 | ||||||||
\(842\) | 3.48280e40 | 0.0133322 | ||||||||
\(843\) | 2.82366e42 | 1.06246 | ||||||||
\(844\) | −4.48959e41 | −0.166051 | ||||||||
\(845\) | 9.17200e41 | 0.333458 | ||||||||
\(846\) | −5.04047e41 | −0.180136 | ||||||||
\(847\) | −9.47455e41 | −0.332850 | ||||||||
\(848\) | −1.16379e42 | −0.401917 | ||||||||
\(849\) | −2.00965e42 | −0.682275 | ||||||||
\(850\) | −3.37037e41 | −0.112487 | ||||||||
\(851\) | 5.20336e41 | 0.170728 | ||||||||
\(852\) | 1.81010e41 | 0.0583888 | ||||||||
\(853\) | −4.30318e42 | −1.36467 | −0.682337 | − | 0.731038i | \(-0.739036\pi\) | ||||
−0.682337 | + | 0.731038i | \(0.739036\pi\) | |||||||
\(854\) | 1.11492e42 | 0.347618 | ||||||||
\(855\) | 2.13190e41 | 0.0653520 | ||||||||
\(856\) | −6.74298e41 | −0.203228 | ||||||||
\(857\) | 1.85145e40 | 0.00548642 | 0.00274321 | − | 0.999996i | \(-0.499127\pi\) | ||||
0.00274321 | + | 0.999996i | \(0.499127\pi\) | |||||||
\(858\) | 3.52295e42 | 1.02646 | ||||||||
\(859\) | −4.76577e42 | −1.36531 | −0.682656 | − | 0.730740i | \(-0.739175\pi\) | ||||
−0.682656 | + | 0.730740i | \(0.739175\pi\) | |||||||
\(860\) | 8.01381e41 | 0.225742 | ||||||||
\(861\) | −1.41676e42 | −0.392418 | ||||||||
\(862\) | 1.37155e42 | 0.373558 | ||||||||
\(863\) | 5.09150e40 | 0.0136361 | 0.00681804 | − | 0.999977i | \(-0.497830\pi\) | ||||
0.00681804 | + | 0.999977i | \(0.497830\pi\) | |||||||
\(864\) | −7.09587e41 | −0.186877 | ||||||||
\(865\) | 1.37773e42 | 0.356805 | ||||||||
\(866\) | −1.79723e42 | −0.457713 | ||||||||
\(867\) | −1.36028e42 | −0.340684 | ||||||||
\(868\) | −8.43733e40 | −0.0207811 | ||||||||
\(869\) | −1.29013e41 | −0.0312499 | ||||||||
\(870\) | 1.14651e42 | 0.273117 | ||||||||
\(871\) | 5.70207e42 | 1.33589 | ||||||||
\(872\) | −2.00281e41 | −0.0461477 | ||||||||
\(873\) | −6.24323e41 | −0.141482 | ||||||||
\(874\) | −7.10591e41 | −0.158381 | ||||||||
\(875\) | −3.36676e41 | −0.0738066 | ||||||||
\(876\) | −3.18870e42 | −0.687549 | ||||||||
\(877\) | 5.73938e42 | 1.21722 | 0.608612 | − | 0.793468i | \(-0.291727\pi\) | ||||
0.608612 | + | 0.793468i | \(0.291727\pi\) | |||||||
\(878\) | 2.73506e42 | 0.570554 | ||||||||
\(879\) | 6.47818e42 | 1.32927 | ||||||||
\(880\) | −6.56204e41 | −0.132446 | ||||||||
\(881\) | −4.61884e42 | −0.917028 | −0.458514 | − | 0.888687i | \(-0.651618\pi\) | ||||
−0.458514 | + | 0.888687i | \(0.651618\pi\) | |||||||
\(882\) | 1.61528e41 | 0.0315467 | ||||||||
\(883\) | −6.74072e42 | −1.29502 | −0.647509 | − | 0.762058i | \(-0.724189\pi\) | ||||
−0.647509 | + | 0.762058i | \(0.724189\pi\) | |||||||
\(884\) | 2.78031e42 | 0.525454 | ||||||||
\(885\) | −3.16140e42 | −0.587762 | ||||||||
\(886\) | −6.08117e42 | −1.11224 | ||||||||
\(887\) | −3.54607e42 | −0.638050 | −0.319025 | − | 0.947746i | \(-0.603355\pi\) | ||||
−0.319025 | + | 0.947746i | \(0.603355\pi\) | |||||||
\(888\) | 1.47567e42 | 0.261216 | ||||||||
\(889\) | 1.03542e41 | 0.0180318 | ||||||||
\(890\) | 4.85579e41 | 0.0831964 | ||||||||
\(891\) | 5.90766e42 | 0.995838 | ||||||||
\(892\) | 5.08735e42 | 0.843726 | ||||||||
\(893\) | −1.16694e43 | −1.90416 | ||||||||
\(894\) | 4.76148e42 | 0.764448 | ||||||||
\(895\) | −1.02319e42 | −0.161630 | ||||||||
\(896\) | −4.69258e41 | −0.0729366 | ||||||||
\(897\) | −1.71718e42 | −0.262618 | ||||||||
\(898\) | −6.15337e42 | −0.925990 | ||||||||
\(899\) | 3.16752e41 | 0.0469033 | ||||||||
\(900\) | −9.59610e40 | −0.0139823 | ||||||||
\(901\) | 8.91854e42 | 1.27875 | ||||||||
\(902\) | −3.04418e42 | −0.429512 | ||||||||
\(903\) | −5.56472e42 | −0.772629 | ||||||||
\(904\) | −4.17655e42 | −0.570657 | ||||||||
\(905\) | 3.18546e42 | 0.428319 | ||||||||
\(906\) | −7.50829e42 | −0.993532 | ||||||||
\(907\) | 8.10190e42 | 1.05507 | 0.527535 | − | 0.849533i | \(-0.323116\pi\) | ||||
0.527535 | + | 0.849533i | \(0.323116\pi\) | |||||||
\(908\) | 6.37654e41 | 0.0817222 | ||||||||
\(909\) | −2.04653e42 | −0.258132 | ||||||||
\(910\) | 2.77733e42 | 0.344768 | ||||||||
\(911\) | 7.96842e42 | 0.973544 | 0.486772 | − | 0.873529i | \(-0.338174\pi\) | ||||
0.486772 | + | 0.873529i | \(0.338174\pi\) | |||||||
\(912\) | −2.01523e42 | −0.242326 | ||||||||
\(913\) | −1.33136e43 | −1.57569 | ||||||||
\(914\) | −4.68914e42 | −0.546227 | ||||||||
\(915\) | −2.15517e42 | −0.247102 | ||||||||
\(916\) | −8.48345e42 | −0.957388 | ||||||||
\(917\) | 2.29405e42 | 0.254828 | ||||||||
\(918\) | 5.43780e42 | 0.594572 | ||||||||
\(919\) | −2.53647e42 | −0.272995 | −0.136497 | − | 0.990640i | \(-0.543585\pi\) | ||||
−0.136497 | + | 0.990640i | \(0.543585\pi\) | |||||||
\(920\) | 3.19851e41 | 0.0338863 | ||||||||
\(921\) | −9.07328e42 | −0.946236 | ||||||||
\(922\) | −5.67354e42 | −0.582446 | ||||||||
\(923\) | −1.64614e42 | −0.166357 | ||||||||
\(924\) | 4.55662e42 | 0.453315 | ||||||||
\(925\) | 1.62681e42 | 0.159324 | ||||||||
\(926\) | 9.72300e42 | 0.937435 | ||||||||
\(927\) | 8.18209e41 | 0.0776619 | ||||||||
\(928\) | 1.76167e42 | 0.164619 | ||||||||
\(929\) | 3.99948e42 | 0.367939 | 0.183970 | − | 0.982932i | \(-0.441105\pi\) | ||||
0.183970 | + | 0.982932i | \(0.441105\pi\) | |||||||
\(930\) | 1.63097e41 | 0.0147721 | ||||||||
\(931\) | 3.73960e42 | 0.333469 | ||||||||
\(932\) | 4.25041e42 | 0.373164 | ||||||||
\(933\) | 8.01650e42 | 0.692949 | ||||||||
\(934\) | 1.57647e42 | 0.134170 | ||||||||
\(935\) | 5.02871e42 | 0.421394 | ||||||||
\(936\) | 7.91608e41 | 0.0653146 | ||||||||
\(937\) | 1.52825e42 | 0.124157 | 0.0620784 | − | 0.998071i | \(-0.480227\pi\) | ||||
0.0620784 | + | 0.998071i | \(0.480227\pi\) | |||||||
\(938\) | 7.37512e42 | 0.589967 | ||||||||
\(939\) | 2.12451e43 | 1.67343 | ||||||||
\(940\) | 5.25263e42 | 0.407401 | ||||||||
\(941\) | 1.35671e42 | 0.103619 | 0.0518093 | − | 0.998657i | \(-0.483501\pi\) | ||||
0.0518093 | + | 0.998657i | \(0.483501\pi\) | |||||||
\(942\) | −7.93917e42 | −0.597086 | ||||||||
\(943\) | 1.48381e42 | 0.109890 | ||||||||
\(944\) | −4.85766e42 | −0.354269 | ||||||||
\(945\) | 5.43198e42 | 0.390119 | ||||||||
\(946\) | −1.19569e43 | −0.845662 | ||||||||
\(947\) | 2.29402e43 | 1.59780 | 0.798901 | − | 0.601463i | \(-0.205415\pi\) | ||||
0.798901 | + | 0.601463i | \(0.205415\pi\) | |||||||
\(948\) | 1.78340e41 | 0.0122328 | ||||||||
\(949\) | 2.89986e43 | 1.95892 | ||||||||
\(950\) | −2.22163e42 | −0.147802 | ||||||||
\(951\) | 1.68479e43 | 1.10389 | ||||||||
\(952\) | 3.59608e42 | 0.232056 | ||||||||
\(953\) | −1.86788e43 | −1.18714 | −0.593570 | − | 0.804782i | \(-0.702282\pi\) | ||||
−0.593570 | + | 0.804782i | \(0.702282\pi\) | |||||||
\(954\) | 2.53928e42 | 0.158950 | ||||||||
\(955\) | 1.28894e43 | 0.794663 | ||||||||
\(956\) | −4.55214e42 | −0.276424 | ||||||||
\(957\) | −1.71064e43 | −1.02314 | ||||||||
\(958\) | −7.99639e42 | −0.471080 | ||||||||
\(959\) | 8.74384e41 | 0.0507379 | ||||||||
\(960\) | 9.07093e41 | 0.0518464 | ||||||||
\(961\) | −1.77168e43 | −0.997463 | ||||||||
\(962\) | −1.34200e43 | −0.744240 | ||||||||
\(963\) | 1.47125e42 | 0.0803722 | ||||||||
\(964\) | −1.75204e42 | −0.0942815 | ||||||||
\(965\) | −8.94644e42 | −0.474247 | ||||||||
\(966\) | −2.22101e42 | −0.115980 | ||||||||
\(967\) | −4.98614e42 | −0.256496 | −0.128248 | − | 0.991742i | \(-0.540935\pi\) | ||||
−0.128248 | + | 0.991742i | \(0.540935\pi\) | |||||||
\(968\) | 2.81414e42 | 0.142611 | ||||||||
\(969\) | 1.54434e43 | 0.770987 | ||||||||
\(970\) | 6.50601e42 | 0.319981 | ||||||||
\(971\) | −1.80120e43 | −0.872735 | −0.436368 | − | 0.899768i | \(-0.643735\pi\) | ||||
−0.436368 | + | 0.899768i | \(0.643735\pi\) | |||||||
\(972\) | 2.90657e42 | 0.138746 | ||||||||
\(973\) | −2.00298e43 | −0.941978 | ||||||||
\(974\) | 2.53812e42 | 0.117600 | ||||||||
\(975\) | −5.36868e42 | −0.245076 | ||||||||
\(976\) | −3.31154e42 | −0.148939 | ||||||||
\(977\) | −2.15005e43 | −0.952747 | −0.476373 | − | 0.879243i | \(-0.658049\pi\) | ||||
−0.476373 | + | 0.879243i | \(0.658049\pi\) | |||||||
\(978\) | −1.45023e40 | −0.000633177 0 | ||||||||
\(979\) | −7.24501e42 | −0.311666 | ||||||||
\(980\) | −1.68327e42 | −0.0713469 | ||||||||
\(981\) | 4.36993e41 | 0.0182505 | ||||||||
\(982\) | −1.34454e42 | −0.0553294 | ||||||||
\(983\) | 2.69873e42 | 0.109429 | 0.0547146 | − | 0.998502i | \(-0.482575\pi\) | ||||
0.0547146 | + | 0.998502i | \(0.482575\pi\) | |||||||
\(984\) | 4.20807e42 | 0.168133 | ||||||||
\(985\) | −4.88305e42 | −0.192250 | ||||||||
\(986\) | −1.35003e43 | −0.523755 | ||||||||
\(987\) | −3.64738e43 | −1.39438 | ||||||||
\(988\) | 1.83268e43 | 0.690418 | ||||||||
\(989\) | 5.82809e42 | 0.216362 | ||||||||
\(990\) | 1.43177e42 | 0.0523798 | ||||||||
\(991\) | −1.68950e43 | −0.609101 | −0.304551 | − | 0.952496i | \(-0.598506\pi\) | ||||
−0.304551 | + | 0.952496i | \(0.598506\pi\) | |||||||
\(992\) | 2.50607e41 | 0.00890376 | ||||||||
\(993\) | 2.55746e42 | 0.0895456 | ||||||||
\(994\) | −2.12914e42 | −0.0734684 | ||||||||
\(995\) | −2.07633e43 | −0.706093 | ||||||||
\(996\) | 1.84039e43 | 0.616806 | ||||||||
\(997\) | 2.21106e41 | 0.00730333 | 0.00365167 | − | 0.999993i | \(-0.498838\pi\) | ||||
0.00365167 | + | 0.999993i | \(0.498838\pi\) | |||||||
\(998\) | 3.87148e43 | 1.26033 | ||||||||
\(999\) | −2.62471e43 | −0.842137 |
(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 | 10.30.a.a.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.30.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |