Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,94,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 94, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 94);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 94 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(54.7725430605\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} + \cdots - 13\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{88}\cdot 3^{34}\cdot 5^{10}\cdot 7^{6}\cdot 13^{2}\cdot 19\cdot 23\cdot 31^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.98834e10\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.20495e12 | −0.0523024 | −0.0261512 | − | 0.999658i | \(-0.508325\pi\) | ||||
−0.0261512 | + | 0.999658i | \(0.508325\pi\) | |||||||
\(3\) | −1.59625e22 | −1.03983 | −0.519916 | − | 0.854218i | \(-0.674037\pi\) | ||||
−0.519916 | + | 0.854218i | \(0.674037\pi\) | |||||||
\(4\) | −9.87643e27 | −0.997264 | ||||||||
\(5\) | −3.34454e32 | −1.05252 | −0.526262 | − | 0.850323i | \(-0.676407\pi\) | ||||
−0.526262 | + | 0.850323i | \(0.676407\pi\) | |||||||
\(6\) | 8.30840e34 | 0.0543857 | ||||||||
\(7\) | −2.46426e38 | −0.124345 | −0.0621725 | − | 0.998065i | \(-0.519803\pi\) | ||||
−0.0621725 | + | 0.998065i | \(0.519803\pi\) | |||||||
\(8\) | 1.02954e41 | 0.104462 | ||||||||
\(9\) | 1.91468e43 | 0.0812492 | ||||||||
\(10\) | 1.74082e45 | 0.0550495 | ||||||||
\(11\) | 2.07952e48 | 0.781993 | 0.390997 | − | 0.920392i | \(-0.372130\pi\) | ||||
0.390997 | + | 0.920392i | \(0.372130\pi\) | |||||||
\(12\) | 1.57653e50 | 1.03699 | ||||||||
\(13\) | 2.80456e51 | 0.446168 | 0.223084 | − | 0.974799i | \(-0.428388\pi\) | ||||
0.223084 | + | 0.974799i | \(0.428388\pi\) | |||||||
\(14\) | 1.28264e51 | 0.00650354 | ||||||||
\(15\) | 5.33873e54 | 1.09445 | ||||||||
\(16\) | 9.72755e55 | 0.991801 | ||||||||
\(17\) | −1.34822e57 | −0.820135 | −0.410068 | − | 0.912055i | \(-0.634495\pi\) | ||||
−0.410068 | + | 0.912055i | \(0.634495\pi\) | |||||||
\(18\) | −9.96580e55 | −0.00424953 | ||||||||
\(19\) | 5.04213e59 | 1.74009 | 0.870046 | − | 0.492971i | \(-0.164089\pi\) | ||||
0.870046 | + | 0.492971i | \(0.164089\pi\) | |||||||
\(20\) | 3.30321e60 | 1.04964 | ||||||||
\(21\) | 3.93358e60 | 0.129298 | ||||||||
\(22\) | −1.08238e61 | −0.0409001 | ||||||||
\(23\) | −1.78821e63 | −0.855212 | −0.427606 | − | 0.903965i | \(-0.640643\pi\) | ||||
−0.427606 | + | 0.903965i | \(0.640643\pi\) | |||||||
\(24\) | −1.64340e63 | −0.108623 | ||||||||
\(25\) | 1.08855e64 | 0.107805 | ||||||||
\(26\) | −1.45976e64 | −0.0233356 | ||||||||
\(27\) | 3.45602e66 | 0.955346 | ||||||||
\(28\) | 2.43381e66 | 0.124005 | ||||||||
\(29\) | −1.40036e68 | −1.39551 | −0.697753 | − | 0.716338i | \(-0.745817\pi\) | ||||
−0.697753 | + | 0.716338i | \(0.745817\pi\) | |||||||
\(30\) | −2.77878e67 | −0.0572422 | ||||||||
\(31\) | 3.47640e69 | 1.55888 | 0.779438 | − | 0.626479i | \(-0.215505\pi\) | ||||
0.779438 | + | 0.626479i | \(0.215505\pi\) | |||||||
\(32\) | −1.52592e69 | −0.156335 | ||||||||
\(33\) | −3.31943e70 | −0.813141 | ||||||||
\(34\) | 7.01740e69 | 0.0428950 | ||||||||
\(35\) | 8.24184e70 | 0.130876 | ||||||||
\(36\) | −1.89102e71 | −0.0810270 | ||||||||
\(37\) | 3.66085e72 | 0.438734 | 0.219367 | − | 0.975642i | \(-0.429601\pi\) | ||||
0.219367 | + | 0.975642i | \(0.429601\pi\) | |||||||
\(38\) | −2.62440e72 | −0.0910109 | ||||||||
\(39\) | −4.47677e73 | −0.463939 | ||||||||
\(40\) | −3.44333e73 | −0.109948 | ||||||||
\(41\) | 5.70517e74 | 0.577856 | 0.288928 | − | 0.957351i | \(-0.406701\pi\) | ||||
0.288928 | + | 0.957351i | \(0.406701\pi\) | |||||||
\(42\) | −2.04741e73 | −0.00676259 | ||||||||
\(43\) | 1.54775e75 | 0.171166 | 0.0855828 | − | 0.996331i | \(-0.472725\pi\) | ||||
0.0855828 | + | 0.996331i | \(0.472725\pi\) | |||||||
\(44\) | −2.05382e76 | −0.779854 | ||||||||
\(45\) | −6.40373e75 | −0.0855167 | ||||||||
\(46\) | 9.30752e75 | 0.0447296 | ||||||||
\(47\) | 7.65372e77 | 1.35308 | 0.676538 | − | 0.736408i | \(-0.263480\pi\) | ||||
0.676538 | + | 0.736408i | \(0.263480\pi\) | |||||||
\(48\) | −1.55276e78 | −1.03131 | ||||||||
\(49\) | −3.86679e78 | −0.984538 | ||||||||
\(50\) | −5.66586e76 | −0.00563846 | ||||||||
\(51\) | 2.15210e79 | 0.852802 | ||||||||
\(52\) | −2.76990e79 | −0.444947 | ||||||||
\(53\) | −2.23629e80 | −1.48149 | −0.740747 | − | 0.671784i | \(-0.765528\pi\) | ||||
−0.740747 | + | 0.671784i | \(0.765528\pi\) | |||||||
\(54\) | −1.79884e79 | −0.0499669 | ||||||||
\(55\) | −6.95504e80 | −0.823066 | ||||||||
\(56\) | −2.53705e79 | −0.0129893 | ||||||||
\(57\) | −8.04851e81 | −1.80940 | ||||||||
\(58\) | 7.28878e80 | 0.0729883 | ||||||||
\(59\) | −3.20335e82 | −1.44872 | −0.724361 | − | 0.689421i | \(-0.757865\pi\) | ||||
−0.724361 | + | 0.689421i | \(0.757865\pi\) | |||||||
\(60\) | −5.27276e82 | −1.09145 | ||||||||
\(61\) | −1.20647e83 | −1.15792 | −0.578962 | − | 0.815354i | \(-0.696542\pi\) | ||||
−0.578962 | + | 0.815354i | \(0.696542\pi\) | |||||||
\(62\) | −1.80945e82 | −0.0815329 | ||||||||
\(63\) | −4.71827e81 | −0.0101029 | ||||||||
\(64\) | −9.55428e83 | −0.983624 | ||||||||
\(65\) | −9.37996e83 | −0.469602 | ||||||||
\(66\) | 1.72775e83 | 0.0425292 | ||||||||
\(67\) | 6.65601e84 | 0.814208 | 0.407104 | − | 0.913382i | \(-0.366539\pi\) | ||||
0.407104 | + | 0.913382i | \(0.366539\pi\) | |||||||
\(68\) | 1.33156e85 | 0.817892 | ||||||||
\(69\) | 2.85443e85 | 0.889276 | ||||||||
\(70\) | −4.28983e83 | −0.00684513 | ||||||||
\(71\) | 8.45355e85 | 0.697471 | 0.348735 | − | 0.937221i | \(-0.386611\pi\) | ||||
0.348735 | + | 0.937221i | \(0.386611\pi\) | |||||||
\(72\) | 1.97123e84 | 0.00848743 | ||||||||
\(73\) | 7.12259e86 | 1.61482 | 0.807412 | − | 0.589988i | \(-0.200868\pi\) | ||||
0.807412 | + | 0.589988i | \(0.200868\pi\) | |||||||
\(74\) | −1.90545e85 | −0.0229469 | ||||||||
\(75\) | −1.73760e86 | −0.112099 | ||||||||
\(76\) | −4.97983e87 | −1.73533 | ||||||||
\(77\) | −5.12448e86 | −0.0972370 | ||||||||
\(78\) | 2.33014e86 | 0.0242651 | ||||||||
\(79\) | −1.51164e87 | −0.0870537 | −0.0435269 | − | 0.999052i | \(-0.513859\pi\) | ||||
−0.0435269 | + | 0.999052i | \(0.513859\pi\) | |||||||
\(80\) | −3.25342e88 | −1.04389 | ||||||||
\(81\) | −5.96787e88 | −1.07465 | ||||||||
\(82\) | −2.96951e87 | −0.0302232 | ||||||||
\(83\) | 1.58486e89 | 0.918037 | 0.459019 | − | 0.888427i | \(-0.348201\pi\) | ||||
0.459019 | + | 0.888427i | \(0.348201\pi\) | |||||||
\(84\) | −3.88498e88 | −0.128944 | ||||||||
\(85\) | 4.50917e89 | 0.863211 | ||||||||
\(86\) | −8.05593e87 | −0.00895237 | ||||||||
\(87\) | 2.23532e90 | 1.45109 | ||||||||
\(88\) | 2.14094e89 | 0.0816883 | ||||||||
\(89\) | −1.03503e90 | −0.233516 | −0.116758 | − | 0.993160i | \(-0.537250\pi\) | ||||
−0.116758 | + | 0.993160i | \(0.537250\pi\) | |||||||
\(90\) | 3.33311e88 | 0.00447273 | ||||||||
\(91\) | −6.91117e89 | −0.0554787 | ||||||||
\(92\) | 1.76611e91 | 0.852872 | ||||||||
\(93\) | −5.54922e91 | −1.62097 | ||||||||
\(94\) | −3.98372e90 | −0.0707691 | ||||||||
\(95\) | −1.68636e92 | −1.83149 | ||||||||
\(96\) | 2.43575e91 | 0.162562 | ||||||||
\(97\) | 1.83199e92 | 0.755159 | 0.377579 | − | 0.925977i | \(-0.376757\pi\) | ||||
0.377579 | + | 0.925977i | \(0.376757\pi\) | |||||||
\(98\) | 2.01264e91 | 0.0514937 | ||||||||
\(99\) | 3.98161e91 | 0.0635363 | ||||||||
\(100\) | −1.07510e92 | −0.107510 | ||||||||
\(101\) | 1.09411e93 | 0.688839 | 0.344420 | − | 0.938816i | \(-0.388076\pi\) | ||||
0.344420 | + | 0.938816i | \(0.388076\pi\) | |||||||
\(102\) | −1.12015e92 | −0.0446036 | ||||||||
\(103\) | 6.53274e93 | 1.65259 | 0.826294 | − | 0.563239i | \(-0.190445\pi\) | ||||
0.826294 | + | 0.563239i | \(0.190445\pi\) | |||||||
\(104\) | 2.88739e92 | 0.0466074 | ||||||||
\(105\) | −1.31560e93 | −0.136089 | ||||||||
\(106\) | 1.16398e93 | 0.0774857 | ||||||||
\(107\) | −2.96413e94 | −1.27512 | −0.637561 | − | 0.770400i | \(-0.720057\pi\) | ||||
−0.637561 | + | 0.770400i | \(0.720057\pi\) | |||||||
\(108\) | −3.41331e94 | −0.952732 | ||||||||
\(109\) | 2.56283e94 | 0.466002 | 0.233001 | − | 0.972477i | \(-0.425146\pi\) | ||||
0.233001 | + | 0.972477i | \(0.425146\pi\) | |||||||
\(110\) | 3.62006e93 | 0.0430483 | ||||||||
\(111\) | −5.84364e94 | −0.456210 | ||||||||
\(112\) | −2.39713e94 | −0.123326 | ||||||||
\(113\) | −2.20850e95 | −0.751536 | −0.375768 | − | 0.926714i | \(-0.622621\pi\) | ||||
−0.375768 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(114\) | 4.18921e94 | 0.0946360 | ||||||||
\(115\) | 5.98074e95 | 0.900130 | ||||||||
\(116\) | 1.38305e96 | 1.39169 | ||||||||
\(117\) | 5.36982e94 | 0.0362508 | ||||||||
\(118\) | 1.66732e95 | 0.0757716 | ||||||||
\(119\) | 3.32237e95 | 0.101980 | ||||||||
\(120\) | 5.49642e95 | 0.114328 | ||||||||
\(121\) | −2.74724e96 | −0.388487 | ||||||||
\(122\) | 6.27963e95 | 0.0605622 | ||||||||
\(123\) | −9.10689e96 | −0.600873 | ||||||||
\(124\) | −3.43345e97 | −1.55461 | ||||||||
\(125\) | 3.01305e97 | 0.939056 | ||||||||
\(126\) | 2.45584e94 | 0.000528408 0 | ||||||||
\(127\) | −5.47224e97 | −0.815253 | −0.407627 | − | 0.913149i | \(-0.633643\pi\) | ||||
−0.407627 | + | 0.913149i | \(0.633643\pi\) | |||||||
\(128\) | 2.00849e97 | 0.207781 | ||||||||
\(129\) | −2.47059e97 | −0.177983 | ||||||||
\(130\) | 4.88222e96 | 0.0245613 | ||||||||
\(131\) | 5.22366e98 | 1.84018 | 0.920089 | − | 0.391710i | \(-0.128116\pi\) | ||||
0.920089 | + | 0.391710i | \(0.128116\pi\) | |||||||
\(132\) | 3.27842e98 | 0.810917 | ||||||||
\(133\) | −1.24252e98 | −0.216372 | ||||||||
\(134\) | −3.46442e97 | −0.0425850 | ||||||||
\(135\) | −1.15588e99 | −1.00552 | ||||||||
\(136\) | −1.38804e98 | −0.0856727 | ||||||||
\(137\) | 1.27800e99 | 0.561079 | 0.280539 | − | 0.959843i | \(-0.409487\pi\) | ||||
0.280539 | + | 0.959843i | \(0.409487\pi\) | |||||||
\(138\) | −1.48571e98 | −0.0465112 | ||||||||
\(139\) | −3.03718e99 | −0.679646 | −0.339823 | − | 0.940489i | \(-0.610367\pi\) | ||||
−0.339823 | + | 0.940489i | \(0.610367\pi\) | |||||||
\(140\) | −8.13999e98 | −0.130518 | ||||||||
\(141\) | −1.22173e100 | −1.40697 | ||||||||
\(142\) | −4.40003e98 | −0.0364794 | ||||||||
\(143\) | 5.83212e99 | 0.348900 | ||||||||
\(144\) | 1.86251e99 | 0.0805831 | ||||||||
\(145\) | 4.68356e100 | 1.46880 | ||||||||
\(146\) | −3.70727e99 | −0.0844591 | ||||||||
\(147\) | 6.17236e100 | 1.02375 | ||||||||
\(148\) | −3.61561e100 | −0.437534 | ||||||||
\(149\) | −3.01665e99 | −0.0266909 | −0.0133455 | − | 0.999911i | \(-0.504248\pi\) | ||||
−0.0133455 | + | 0.999911i | \(0.504248\pi\) | |||||||
\(150\) | 9.04413e98 | 0.00586305 | ||||||||
\(151\) | −6.70032e100 | −0.318910 | −0.159455 | − | 0.987205i | \(-0.550974\pi\) | ||||
−0.159455 | + | 0.987205i | \(0.550974\pi\) | |||||||
\(152\) | 5.19106e100 | 0.181773 | ||||||||
\(153\) | −2.58141e100 | −0.0666353 | ||||||||
\(154\) | 2.66727e99 | 0.00508572 | ||||||||
\(155\) | −1.16270e102 | −1.64075 | ||||||||
\(156\) | 4.42145e101 | 0.462670 | ||||||||
\(157\) | −1.54216e102 | −1.19894 | −0.599468 | − | 0.800399i | \(-0.704621\pi\) | ||||
−0.599468 | + | 0.800399i | \(0.704621\pi\) | |||||||
\(158\) | 7.86798e99 | 0.00455312 | ||||||||
\(159\) | 3.56968e102 | 1.54050 | ||||||||
\(160\) | 5.10350e101 | 0.164546 | ||||||||
\(161\) | 4.40662e101 | 0.106341 | ||||||||
\(162\) | 3.10625e101 | 0.0562066 | ||||||||
\(163\) | 7.03093e102 | 0.955628 | 0.477814 | − | 0.878461i | \(-0.341429\pi\) | ||||
0.477814 | + | 0.878461i | \(0.341429\pi\) | |||||||
\(164\) | −5.63467e102 | −0.576275 | ||||||||
\(165\) | 1.11020e103 | 0.855850 | ||||||||
\(166\) | −8.24912e101 | −0.0480155 | ||||||||
\(167\) | −1.74320e103 | −0.767417 | −0.383709 | − | 0.923454i | \(-0.625353\pi\) | ||||
−0.383709 | + | 0.923454i | \(0.625353\pi\) | |||||||
\(168\) | 4.04977e101 | 0.0135067 | ||||||||
\(169\) | −3.16467e103 | −0.800934 | ||||||||
\(170\) | −2.34700e102 | −0.0451480 | ||||||||
\(171\) | 9.65407e102 | 0.141381 | ||||||||
\(172\) | −1.52862e103 | −0.170697 | ||||||||
\(173\) | −1.25289e104 | −1.06849 | −0.534243 | − | 0.845331i | \(-0.679403\pi\) | ||||
−0.534243 | + | 0.845331i | \(0.679403\pi\) | |||||||
\(174\) | −1.16347e103 | −0.0758956 | ||||||||
\(175\) | −2.68248e102 | −0.0134050 | ||||||||
\(176\) | 2.02286e104 | 0.775581 | ||||||||
\(177\) | 5.11334e104 | 1.50643 | ||||||||
\(178\) | 5.38726e102 | 0.0122134 | ||||||||
\(179\) | 4.81939e104 | 0.842027 | 0.421013 | − | 0.907054i | \(-0.361675\pi\) | ||||
0.421013 | + | 0.907054i | \(0.361675\pi\) | |||||||
\(180\) | 6.32460e103 | 0.0852828 | ||||||||
\(181\) | −1.90449e105 | −1.98484 | −0.992420 | − | 0.122890i | \(-0.960784\pi\) | ||||
−0.992420 | + | 0.122890i | \(0.960784\pi\) | |||||||
\(182\) | 3.59722e102 | 0.00290167 | ||||||||
\(183\) | 1.92583e105 | 1.20405 | ||||||||
\(184\) | −1.84102e104 | −0.0893368 | ||||||||
\(185\) | −1.22439e105 | −0.461778 | ||||||||
\(186\) | 2.88834e104 | 0.0847805 | ||||||||
\(187\) | −2.80364e105 | −0.641340 | ||||||||
\(188\) | −7.55914e105 | −1.34937 | ||||||||
\(189\) | −8.51653e104 | −0.118793 | ||||||||
\(190\) | 8.77743e104 | 0.0957911 | ||||||||
\(191\) | 6.29379e105 | 0.538097 | 0.269048 | − | 0.963127i | \(-0.413291\pi\) | ||||
0.269048 | + | 0.963127i | \(0.413291\pi\) | |||||||
\(192\) | 1.52510e106 | 1.02280 | ||||||||
\(193\) | 5.60111e105 | 0.295025 | 0.147513 | − | 0.989060i | \(-0.452873\pi\) | ||||
0.147513 | + | 0.989060i | \(0.452873\pi\) | |||||||
\(194\) | −9.53543e104 | −0.0394966 | ||||||||
\(195\) | 1.49728e106 | 0.488307 | ||||||||
\(196\) | 3.81901e106 | 0.981845 | ||||||||
\(197\) | −6.48534e106 | −1.31599 | −0.657996 | − | 0.753021i | \(-0.728596\pi\) | ||||
−0.657996 | + | 0.753021i | \(0.728596\pi\) | |||||||
\(198\) | −2.07241e104 | −0.00332310 | ||||||||
\(199\) | 3.45706e106 | 0.438570 | 0.219285 | − | 0.975661i | \(-0.429628\pi\) | ||||
0.219285 | + | 0.975661i | \(0.429628\pi\) | |||||||
\(200\) | 1.12070e105 | 0.0112615 | ||||||||
\(201\) | −1.06247e107 | −0.846639 | ||||||||
\(202\) | −5.69480e105 | −0.0360279 | ||||||||
\(203\) | 3.45085e106 | 0.173524 | ||||||||
\(204\) | −2.12550e107 | −0.850469 | ||||||||
\(205\) | −1.90812e107 | −0.608207 | ||||||||
\(206\) | −3.40026e106 | −0.0864343 | ||||||||
\(207\) | −3.42384e106 | −0.0694853 | ||||||||
\(208\) | 2.72815e107 | 0.442510 | ||||||||
\(209\) | 1.04852e108 | 1.36074 | ||||||||
\(210\) | 6.84765e105 | 0.00711778 | ||||||||
\(211\) | −3.50564e107 | −0.292169 | −0.146084 | − | 0.989272i | \(-0.546667\pi\) | ||||
−0.146084 | + | 0.989272i | \(0.546667\pi\) | |||||||
\(212\) | 2.20866e108 | 1.47744 | ||||||||
\(213\) | −1.34940e108 | −0.725252 | ||||||||
\(214\) | 1.54281e107 | 0.0666919 | ||||||||
\(215\) | −5.17650e107 | −0.180156 | ||||||||
\(216\) | 3.55809e107 | 0.0997970 | ||||||||
\(217\) | −8.56678e107 | −0.193838 | ||||||||
\(218\) | −1.33394e107 | −0.0243730 | ||||||||
\(219\) | −1.13694e109 | −1.67914 | ||||||||
\(220\) | 6.86910e108 | 0.820814 | ||||||||
\(221\) | −3.78115e108 | −0.365918 | ||||||||
\(222\) | 3.04158e107 | 0.0238609 | ||||||||
\(223\) | −3.78721e108 | −0.241070 | −0.120535 | − | 0.992709i | \(-0.538461\pi\) | ||||
−0.120535 | + | 0.992709i | \(0.538461\pi\) | |||||||
\(224\) | 3.76026e107 | 0.0194395 | ||||||||
\(225\) | 2.08423e107 | 0.00875908 | ||||||||
\(226\) | 1.14951e108 | 0.0393071 | ||||||||
\(227\) | −2.11337e109 | −0.588538 | −0.294269 | − | 0.955723i | \(-0.595076\pi\) | ||||
−0.294269 | + | 0.955723i | \(0.595076\pi\) | |||||||
\(228\) | 7.94906e109 | 1.80445 | ||||||||
\(229\) | 6.82619e109 | 1.26424 | 0.632118 | − | 0.774872i | \(-0.282186\pi\) | ||||
0.632118 | + | 0.774872i | \(0.282186\pi\) | |||||||
\(230\) | −3.11294e108 | −0.0470789 | ||||||||
\(231\) | 8.17996e108 | 0.101110 | ||||||||
\(232\) | −1.44172e109 | −0.145777 | ||||||||
\(233\) | −1.83357e110 | −1.51791 | −0.758956 | − | 0.651142i | \(-0.774290\pi\) | ||||
−0.758956 | + | 0.651142i | \(0.774290\pi\) | |||||||
\(234\) | −2.79496e107 | −0.00189600 | ||||||||
\(235\) | −2.55982e110 | −1.42414 | ||||||||
\(236\) | 3.16376e110 | 1.44476 | ||||||||
\(237\) | 2.41295e109 | 0.0905212 | ||||||||
\(238\) | −1.72927e108 | −0.00533378 | ||||||||
\(239\) | −4.39834e110 | −1.11631 | −0.558157 | − | 0.829735i | \(-0.688491\pi\) | ||||
−0.558157 | + | 0.829735i | \(0.688491\pi\) | |||||||
\(240\) | 5.19328e110 | 1.08547 | ||||||||
\(241\) | −1.05972e111 | −1.82557 | −0.912785 | − | 0.408440i | \(-0.866073\pi\) | ||||
−0.912785 | + | 0.408440i | \(0.866073\pi\) | |||||||
\(242\) | 1.42992e109 | 0.0203188 | ||||||||
\(243\) | 1.38195e110 | 0.162107 | ||||||||
\(244\) | 1.19156e111 | 1.15476 | ||||||||
\(245\) | 1.29326e111 | 1.03625 | ||||||||
\(246\) | 4.74009e109 | 0.0314271 | ||||||||
\(247\) | 1.41409e111 | 0.776372 | ||||||||
\(248\) | 3.57908e110 | 0.162843 | ||||||||
\(249\) | −2.52984e111 | −0.954604 | ||||||||
\(250\) | −1.56828e110 | −0.0491149 | ||||||||
\(251\) | −4.74458e110 | −0.123416 | −0.0617078 | − | 0.998094i | \(-0.519655\pi\) | ||||
−0.0617078 | + | 0.998094i | \(0.519655\pi\) | |||||||
\(252\) | 4.65997e109 | 0.0100753 | ||||||||
\(253\) | −3.71861e111 | −0.668770 | ||||||||
\(254\) | 2.84827e110 | 0.0426397 | ||||||||
\(255\) | −7.19778e111 | −0.897594 | ||||||||
\(256\) | 9.35756e111 | 0.972757 | ||||||||
\(257\) | −1.10497e112 | −0.958210 | −0.479105 | − | 0.877758i | \(-0.659039\pi\) | ||||
−0.479105 | + | 0.877758i | \(0.659039\pi\) | |||||||
\(258\) | 1.28593e110 | 0.00930895 | ||||||||
\(259\) | −9.02130e110 | −0.0545544 | ||||||||
\(260\) | 9.26405e111 | 0.468317 | ||||||||
\(261\) | −2.68123e111 | −0.113384 | ||||||||
\(262\) | −2.71889e111 | −0.0962457 | ||||||||
\(263\) | 2.33330e112 | 0.691877 | 0.345938 | − | 0.938257i | \(-0.387561\pi\) | ||||
0.345938 | + | 0.938257i | \(0.387561\pi\) | |||||||
\(264\) | −3.41748e111 | −0.0849421 | ||||||||
\(265\) | 7.47937e112 | 1.55931 | ||||||||
\(266\) | 6.46722e110 | 0.0113168 | ||||||||
\(267\) | 1.65216e112 | 0.242817 | ||||||||
\(268\) | −6.57376e112 | −0.811981 | ||||||||
\(269\) | −4.45387e111 | −0.0462654 | −0.0231327 | − | 0.999732i | \(-0.507364\pi\) | ||||
−0.0231327 | + | 0.999732i | \(0.507364\pi\) | |||||||
\(270\) | 6.01629e111 | 0.0525913 | ||||||||
\(271\) | −1.06412e113 | −0.783282 | −0.391641 | − | 0.920118i | \(-0.628093\pi\) | ||||
−0.391641 | + | 0.920118i | \(0.628093\pi\) | |||||||
\(272\) | −1.31149e113 | −0.813411 | ||||||||
\(273\) | 1.10320e112 | 0.0576885 | ||||||||
\(274\) | −6.65191e111 | −0.0293457 | ||||||||
\(275\) | 2.26367e112 | 0.0843028 | ||||||||
\(276\) | −2.81916e113 | −0.886843 | ||||||||
\(277\) | 3.13894e113 | 0.834590 | 0.417295 | − | 0.908771i | \(-0.362978\pi\) | ||||
0.417295 | + | 0.908771i | \(0.362978\pi\) | |||||||
\(278\) | 1.58084e112 | 0.0355471 | ||||||||
\(279\) | 6.65620e112 | 0.126657 | ||||||||
\(280\) | 8.48527e111 | 0.0136715 | ||||||||
\(281\) | 7.34181e113 | 1.00221 | 0.501105 | − | 0.865386i | \(-0.332927\pi\) | ||||
0.501105 | + | 0.865386i | \(0.332927\pi\) | |||||||
\(282\) | 6.35901e112 | 0.0735879 | ||||||||
\(283\) | −4.42262e113 | −0.434120 | −0.217060 | − | 0.976158i | \(-0.569647\pi\) | ||||
−0.217060 | + | 0.976158i | \(0.569647\pi\) | |||||||
\(284\) | −8.34909e113 | −0.695563 | ||||||||
\(285\) | 2.69186e114 | 1.90444 | ||||||||
\(286\) | −3.03559e112 | −0.0182483 | ||||||||
\(287\) | −1.40591e113 | −0.0718535 | ||||||||
\(288\) | −2.92164e112 | −0.0127021 | ||||||||
\(289\) | −8.84708e113 | −0.327379 | ||||||||
\(290\) | −2.43777e113 | −0.0768219 | ||||||||
\(291\) | −2.92432e114 | −0.785238 | ||||||||
\(292\) | −7.03458e114 | −1.61041 | ||||||||
\(293\) | −2.57943e114 | −0.503709 | −0.251854 | − | 0.967765i | \(-0.581040\pi\) | ||||
−0.251854 | + | 0.967765i | \(0.581040\pi\) | |||||||
\(294\) | −3.21268e113 | −0.0535448 | ||||||||
\(295\) | 1.07137e115 | 1.52481 | ||||||||
\(296\) | 3.76898e113 | 0.0458309 | ||||||||
\(297\) | 7.18685e114 | 0.747074 | ||||||||
\(298\) | 1.57015e112 | 0.00139600 | ||||||||
\(299\) | −5.01513e114 | −0.381568 | ||||||||
\(300\) | 1.71613e114 | 0.111792 | ||||||||
\(301\) | −3.81405e113 | −0.0212836 | ||||||||
\(302\) | 3.48748e113 | 0.0166797 | ||||||||
\(303\) | −1.74648e115 | −0.716277 | ||||||||
\(304\) | 4.90476e115 | 1.72582 | ||||||||
\(305\) | 4.03510e115 | 1.21874 | ||||||||
\(306\) | 1.34361e113 | 0.00348519 | ||||||||
\(307\) | −4.52736e115 | −1.00905 | −0.504523 | − | 0.863399i | \(-0.668331\pi\) | ||||
−0.504523 | + | 0.863399i | \(0.668331\pi\) | |||||||
\(308\) | 5.06116e114 | 0.0969710 | ||||||||
\(309\) | −1.04279e116 | −1.71841 | ||||||||
\(310\) | 6.05178e114 | 0.0858153 | ||||||||
\(311\) | −6.25405e115 | −0.763490 | −0.381745 | − | 0.924268i | \(-0.624677\pi\) | ||||
−0.381745 | + | 0.924268i | \(0.624677\pi\) | |||||||
\(312\) | −4.60900e114 | −0.0484639 | ||||||||
\(313\) | 1.19220e115 | 0.108028 | 0.0540142 | − | 0.998540i | \(-0.482798\pi\) | ||||
0.0540142 | + | 0.998540i | \(0.482798\pi\) | |||||||
\(314\) | 8.02687e114 | 0.0627072 | ||||||||
\(315\) | 1.57805e114 | 0.0106336 | ||||||||
\(316\) | 1.49296e115 | 0.0868156 | ||||||||
\(317\) | 2.10233e116 | 1.05547 | 0.527733 | − | 0.849410i | \(-0.323042\pi\) | ||||
0.527733 | + | 0.849410i | \(0.323042\pi\) | |||||||
\(318\) | −1.85800e115 | −0.0805721 | ||||||||
\(319\) | −2.91207e116 | −1.09128 | ||||||||
\(320\) | 3.19547e116 | 1.03529 | ||||||||
\(321\) | 4.73150e116 | 1.32591 | ||||||||
\(322\) | −2.29362e114 | −0.00556190 | ||||||||
\(323\) | −6.79790e116 | −1.42711 | ||||||||
\(324\) | 5.89413e116 | 1.07171 | ||||||||
\(325\) | 3.05291e115 | 0.0480991 | ||||||||
\(326\) | −3.65956e115 | −0.0499816 | ||||||||
\(327\) | −4.09092e116 | −0.484563 | ||||||||
\(328\) | 5.87368e115 | 0.0603638 | ||||||||
\(329\) | −1.88608e116 | −0.168248 | ||||||||
\(330\) | −5.77853e115 | −0.0447630 | ||||||||
\(331\) | −7.97816e116 | −0.536909 | −0.268455 | − | 0.963292i | \(-0.586513\pi\) | ||||
−0.268455 | + | 0.963292i | \(0.586513\pi\) | |||||||
\(332\) | −1.56528e117 | −0.915526 | ||||||||
\(333\) | 7.00935e115 | 0.0356468 | ||||||||
\(334\) | 9.07326e115 | 0.0401377 | ||||||||
\(335\) | −2.22613e117 | −0.856973 | ||||||||
\(336\) | 3.82642e116 | 0.128238 | ||||||||
\(337\) | 5.50832e117 | 1.60779 | 0.803894 | − | 0.594773i | \(-0.202758\pi\) | ||||
0.803894 | + | 0.594773i | \(0.202758\pi\) | |||||||
\(338\) | 1.64719e116 | 0.0418908 | ||||||||
\(339\) | 3.52532e117 | 0.781471 | ||||||||
\(340\) | −4.45345e117 | −0.860850 | ||||||||
\(341\) | 7.22925e117 | 1.21903 | ||||||||
\(342\) | −5.02489e115 | −0.00739457 | ||||||||
\(343\) | 1.92072e117 | 0.246767 | ||||||||
\(344\) | 1.59346e116 | 0.0178802 | ||||||||
\(345\) | −9.54676e117 | −0.935983 | ||||||||
\(346\) | 6.52122e116 | 0.0558843 | ||||||||
\(347\) | 1.41492e118 | 1.06025 | 0.530127 | − | 0.847918i | \(-0.322144\pi\) | ||||
0.530127 | + | 0.847918i | \(0.322144\pi\) | |||||||
\(348\) | −2.20770e118 | −1.44712 | ||||||||
\(349\) | −6.54379e117 | −0.375359 | −0.187680 | − | 0.982230i | \(-0.560097\pi\) | ||||
−0.187680 | + | 0.982230i | \(0.560097\pi\) | |||||||
\(350\) | 1.39622e115 | 0.000701114 0 | ||||||||
\(351\) | 9.69259e117 | 0.426244 | ||||||||
\(352\) | −3.17317e117 | −0.122253 | ||||||||
\(353\) | −1.68481e118 | −0.568888 | −0.284444 | − | 0.958693i | \(-0.591809\pi\) | ||||
−0.284444 | + | 0.958693i | \(0.591809\pi\) | |||||||
\(354\) | −2.66147e117 | −0.0787897 | ||||||||
\(355\) | −2.82733e118 | −0.734104 | ||||||||
\(356\) | 1.02224e118 | 0.232877 | ||||||||
\(357\) | −5.30333e117 | −0.106042 | ||||||||
\(358\) | −2.50846e117 | −0.0440400 | ||||||||
\(359\) | 5.68638e118 | 0.876888 | 0.438444 | − | 0.898758i | \(-0.355530\pi\) | ||||
0.438444 | + | 0.898758i | \(0.355530\pi\) | |||||||
\(360\) | −6.59287e116 | −0.00893322 | ||||||||
\(361\) | 1.70269e119 | 2.02792 | ||||||||
\(362\) | 9.91278e117 | 0.103812 | ||||||||
\(363\) | 4.38528e118 | 0.403961 | ||||||||
\(364\) | 6.82576e117 | 0.0553270 | ||||||||
\(365\) | −2.38218e119 | −1.69964 | ||||||||
\(366\) | −1.00239e118 | −0.0629745 | ||||||||
\(367\) | 1.30818e118 | 0.0723928 | 0.0361964 | − | 0.999345i | \(-0.488476\pi\) | ||||
0.0361964 | + | 0.999345i | \(0.488476\pi\) | |||||||
\(368\) | −1.73949e119 | −0.848200 | ||||||||
\(369\) | 1.09236e118 | 0.0469503 | ||||||||
\(370\) | 6.37287e117 | 0.0241521 | ||||||||
\(371\) | 5.51081e118 | 0.184216 | ||||||||
\(372\) | 5.48064e119 | 1.61653 | ||||||||
\(373\) | −6.77024e119 | −1.76256 | −0.881279 | − | 0.472597i | \(-0.843317\pi\) | ||||
−0.881279 | + | 0.472597i | \(0.843317\pi\) | |||||||
\(374\) | 1.45928e118 | 0.0335436 | ||||||||
\(375\) | −4.80959e119 | −0.976460 | ||||||||
\(376\) | 7.87977e118 | 0.141345 | ||||||||
\(377\) | −3.92738e119 | −0.622630 | ||||||||
\(378\) | 4.43281e117 | 0.00621313 | ||||||||
\(379\) | 6.89871e118 | 0.0855154 | 0.0427577 | − | 0.999085i | \(-0.486386\pi\) | ||||
0.0427577 | + | 0.999085i | \(0.486386\pi\) | |||||||
\(380\) | 1.66553e120 | 1.82648 | ||||||||
\(381\) | 8.73508e119 | 0.847726 | ||||||||
\(382\) | −3.27588e118 | −0.0281438 | ||||||||
\(383\) | 4.25482e119 | 0.323697 | 0.161848 | − | 0.986816i | \(-0.448254\pi\) | ||||
0.161848 | + | 0.986816i | \(0.448254\pi\) | |||||||
\(384\) | −3.20605e119 | −0.216057 | ||||||||
\(385\) | 1.71391e119 | 0.102344 | ||||||||
\(386\) | −2.91535e118 | −0.0154305 | ||||||||
\(387\) | 2.96344e118 | 0.0139071 | ||||||||
\(388\) | −1.80936e120 | −0.753093 | ||||||||
\(389\) | −1.18067e120 | −0.435985 | −0.217992 | − | 0.975950i | \(-0.569951\pi\) | ||||
−0.217992 | + | 0.975950i | \(0.569951\pi\) | |||||||
\(390\) | −7.79325e118 | −0.0255396 | ||||||||
\(391\) | 2.41089e120 | 0.701389 | ||||||||
\(392\) | −3.98100e119 | −0.102847 | ||||||||
\(393\) | −8.33828e120 | −1.91347 | ||||||||
\(394\) | 3.37559e119 | 0.0688295 | ||||||||
\(395\) | 5.05573e119 | 0.0916261 | ||||||||
\(396\) | −3.93241e119 | −0.0633625 | ||||||||
\(397\) | 4.35484e120 | 0.624041 | 0.312021 | − | 0.950075i | \(-0.398994\pi\) | ||||
0.312021 | + | 0.950075i | \(0.398994\pi\) | |||||||
\(398\) | −1.79938e119 | −0.0229383 | ||||||||
\(399\) | 1.98337e120 | 0.224990 | ||||||||
\(400\) | 1.05890e120 | 0.106921 | ||||||||
\(401\) | 1.70110e119 | 0.0152938 | 0.00764691 | − | 0.999971i | \(-0.497566\pi\) | ||||
0.00764691 | + | 0.999971i | \(0.497566\pi\) | |||||||
\(402\) | 5.53008e119 | 0.0442812 | ||||||||
\(403\) | 9.74977e120 | 0.695520 | ||||||||
\(404\) | −1.08059e121 | −0.686955 | ||||||||
\(405\) | 1.99598e121 | 1.13109 | ||||||||
\(406\) | −1.79615e119 | −0.00907574 | ||||||||
\(407\) | 7.61281e120 | 0.343087 | ||||||||
\(408\) | 2.21566e120 | 0.0890851 | ||||||||
\(409\) | 7.63285e120 | 0.273875 | 0.136938 | − | 0.990580i | \(-0.456274\pi\) | ||||
0.136938 | + | 0.990580i | \(0.456274\pi\) | |||||||
\(410\) | 9.93166e119 | 0.0318107 | ||||||||
\(411\) | −2.04001e121 | −0.583427 | ||||||||
\(412\) | −6.45202e121 | −1.64807 | ||||||||
\(413\) | 7.89389e120 | 0.180141 | ||||||||
\(414\) | 1.78209e119 | 0.00363425 | ||||||||
\(415\) | −5.30064e121 | −0.966255 | ||||||||
\(416\) | −4.27952e120 | −0.0697517 | ||||||||
\(417\) | 4.84811e121 | 0.706717 | ||||||||
\(418\) | −5.45750e120 | −0.0711699 | ||||||||
\(419\) | −3.78980e121 | −0.442246 | −0.221123 | − | 0.975246i | \(-0.570972\pi\) | ||||
−0.221123 | + | 0.975246i | \(0.570972\pi\) | |||||||
\(420\) | 1.29935e121 | 0.135717 | ||||||||
\(421\) | 1.35355e122 | 1.26578 | 0.632889 | − | 0.774242i | \(-0.281869\pi\) | ||||
0.632889 | + | 0.774242i | \(0.281869\pi\) | |||||||
\(422\) | 1.82467e120 | 0.0152811 | ||||||||
\(423\) | 1.46544e121 | 0.109936 | ||||||||
\(424\) | −2.30234e121 | −0.154759 | ||||||||
\(425\) | −1.46761e121 | −0.0884147 | ||||||||
\(426\) | 7.02355e120 | 0.0379324 | ||||||||
\(427\) | 2.97307e121 | 0.143982 | ||||||||
\(428\) | 2.92750e122 | 1.27163 | ||||||||
\(429\) | −9.30954e121 | −0.362797 | ||||||||
\(430\) | 2.69434e120 | 0.00942257 | ||||||||
\(431\) | −3.82844e122 | −1.20179 | −0.600895 | − | 0.799328i | \(-0.705189\pi\) | ||||
−0.600895 | + | 0.799328i | \(0.705189\pi\) | |||||||
\(432\) | 3.36186e122 | 0.947513 | ||||||||
\(433\) | 3.72282e122 | 0.942290 | 0.471145 | − | 0.882056i | \(-0.343841\pi\) | ||||
0.471145 | + | 0.882056i | \(0.343841\pi\) | |||||||
\(434\) | 4.45896e120 | 0.0101382 | ||||||||
\(435\) | −7.47613e122 | −1.52731 | ||||||||
\(436\) | −2.53116e122 | −0.464727 | ||||||||
\(437\) | −9.01638e122 | −1.48815 | ||||||||
\(438\) | 5.91774e121 | 0.0878232 | ||||||||
\(439\) | −5.30815e121 | −0.0708505 | −0.0354253 | − | 0.999372i | \(-0.511279\pi\) | ||||
−0.0354253 | + | 0.999372i | \(0.511279\pi\) | |||||||
\(440\) | −7.16046e121 | −0.0859788 | ||||||||
\(441\) | −7.40366e121 | −0.0799930 | ||||||||
\(442\) | 1.96807e121 | 0.0191384 | ||||||||
\(443\) | 2.18090e123 | 1.90924 | 0.954622 | − | 0.297819i | \(-0.0962593\pi\) | ||||
0.954622 | + | 0.297819i | \(0.0962593\pi\) | |||||||
\(444\) | 5.77143e122 | 0.454962 | ||||||||
\(445\) | 3.46169e122 | 0.245781 | ||||||||
\(446\) | 1.97122e121 | 0.0126085 | ||||||||
\(447\) | 4.81534e121 | 0.0277541 | ||||||||
\(448\) | 2.35443e122 | 0.122309 | ||||||||
\(449\) | −2.75797e123 | −1.29162 | −0.645811 | − | 0.763498i | \(-0.723480\pi\) | ||||
−0.645811 | + | 0.763498i | \(0.723480\pi\) | |||||||
\(450\) | −1.08483e120 | −0.000458121 0 | ||||||||
\(451\) | 1.18640e123 | 0.451879 | ||||||||
\(452\) | 2.18121e123 | 0.749480 | ||||||||
\(453\) | 1.06954e123 | 0.331612 | ||||||||
\(454\) | 1.10000e122 | 0.0307819 | ||||||||
\(455\) | 2.31147e122 | 0.0583927 | ||||||||
\(456\) | −8.28623e122 | −0.189013 | ||||||||
\(457\) | −3.11961e123 | −0.642684 | −0.321342 | − | 0.946963i | \(-0.604134\pi\) | ||||
−0.321342 | + | 0.946963i | \(0.604134\pi\) | |||||||
\(458\) | −3.55299e122 | −0.0661226 | ||||||||
\(459\) | −4.65946e123 | −0.783513 | ||||||||
\(460\) | −5.90683e123 | −0.897668 | ||||||||
\(461\) | −4.69038e123 | −0.644340 | −0.322170 | − | 0.946682i | \(-0.604412\pi\) | ||||
−0.322170 | + | 0.946682i | \(0.604412\pi\) | |||||||
\(462\) | −4.25763e121 | −0.00528830 | ||||||||
\(463\) | 1.16779e124 | 1.31174 | 0.655871 | − | 0.754873i | \(-0.272302\pi\) | ||||
0.655871 | + | 0.754873i | \(0.272302\pi\) | |||||||
\(464\) | −1.36221e124 | −1.38406 | ||||||||
\(465\) | 1.85596e124 | 1.70611 | ||||||||
\(466\) | 9.54362e122 | 0.0793904 | ||||||||
\(467\) | 1.86132e123 | 0.140148 | 0.0700741 | − | 0.997542i | \(-0.477676\pi\) | ||||
0.0700741 | + | 0.997542i | \(0.477676\pi\) | |||||||
\(468\) | −5.30347e122 | −0.0361516 | ||||||||
\(469\) | −1.64022e123 | −0.101243 | ||||||||
\(470\) | 1.33237e123 | 0.0744861 | ||||||||
\(471\) | 2.46168e124 | 1.24669 | ||||||||
\(472\) | −3.29796e123 | −0.151336 | ||||||||
\(473\) | 3.21857e123 | 0.133850 | ||||||||
\(474\) | −1.25593e122 | −0.00473447 | ||||||||
\(475\) | 5.48863e123 | 0.187591 | ||||||||
\(476\) | −3.28131e123 | −0.101701 | ||||||||
\(477\) | −4.28178e123 | −0.120370 | ||||||||
\(478\) | 2.28931e123 | 0.0583859 | ||||||||
\(479\) | −6.91509e124 | −1.60028 | −0.800141 | − | 0.599812i | \(-0.795242\pi\) | ||||
−0.800141 | + | 0.599812i | \(0.795242\pi\) | |||||||
\(480\) | −8.14646e123 | −0.171101 | ||||||||
\(481\) | 1.02671e124 | 0.195749 | ||||||||
\(482\) | 5.51578e123 | 0.0954817 | ||||||||
\(483\) | −7.03407e123 | −0.110577 | ||||||||
\(484\) | 2.71329e124 | 0.387424 | ||||||||
\(485\) | −6.12718e124 | −0.794822 | ||||||||
\(486\) | −7.19298e122 | −0.00847856 | ||||||||
\(487\) | 3.42647e124 | 0.367071 | 0.183536 | − | 0.983013i | \(-0.441246\pi\) | ||||
0.183536 | + | 0.983013i | \(0.441246\pi\) | |||||||
\(488\) | −1.24211e124 | −0.120959 | ||||||||
\(489\) | −1.12231e125 | −0.993692 | ||||||||
\(490\) | −6.73137e123 | −0.0541983 | ||||||||
\(491\) | 9.44249e124 | 0.691508 | 0.345754 | − | 0.938325i | \(-0.387623\pi\) | ||||
0.345754 | + | 0.938325i | \(0.387623\pi\) | |||||||
\(492\) | 8.99435e124 | 0.599229 | ||||||||
\(493\) | 1.88799e125 | 1.14450 | ||||||||
\(494\) | −7.36029e123 | −0.0406061 | ||||||||
\(495\) | −1.33167e124 | −0.0668735 | ||||||||
\(496\) | 3.38169e125 | 1.54609 | ||||||||
\(497\) | −2.08318e124 | −0.0867270 | ||||||||
\(498\) | 1.31677e124 | 0.0499281 | ||||||||
\(499\) | −3.71278e125 | −1.28240 | −0.641200 | − | 0.767374i | \(-0.721563\pi\) | ||||
−0.641200 | + | 0.767374i | \(0.721563\pi\) | |||||||
\(500\) | −2.97582e125 | −0.936487 | ||||||||
\(501\) | 2.78259e125 | 0.797984 | ||||||||
\(502\) | 2.46953e123 | 0.00645493 | ||||||||
\(503\) | −5.04296e125 | −1.20164 | −0.600820 | − | 0.799385i | \(-0.705159\pi\) | ||||
−0.600820 | + | 0.799385i | \(0.705159\pi\) | |||||||
\(504\) | −4.85763e122 | −0.00105537 | ||||||||
\(505\) | −3.65931e125 | −0.725019 | ||||||||
\(506\) | 1.93552e124 | 0.0349782 | ||||||||
\(507\) | 5.05161e125 | 0.832837 | ||||||||
\(508\) | 5.40462e125 | 0.813023 | ||||||||
\(509\) | −1.02099e126 | −1.40167 | −0.700836 | − | 0.713323i | \(-0.747189\pi\) | ||||
−0.700836 | + | 0.713323i | \(0.747189\pi\) | |||||||
\(510\) | 3.74640e124 | 0.0469463 | ||||||||
\(511\) | −1.75519e125 | −0.200795 | ||||||||
\(512\) | −2.47617e125 | −0.258659 | ||||||||
\(513\) | 1.74257e126 | 1.66239 | ||||||||
\(514\) | 5.75132e124 | 0.0501167 | ||||||||
\(515\) | −2.18491e126 | −1.73939 | ||||||||
\(516\) | 2.44006e125 | 0.177496 | ||||||||
\(517\) | 1.59160e126 | 1.05810 | ||||||||
\(518\) | 4.69554e123 | 0.00285333 | ||||||||
\(519\) | 1.99992e126 | 1.11104 | ||||||||
\(520\) | −9.65700e124 | −0.0490554 | ||||||||
\(521\) | 1.22845e126 | 0.570696 | 0.285348 | − | 0.958424i | \(-0.407891\pi\) | ||||
0.285348 | + | 0.958424i | \(0.407891\pi\) | |||||||
\(522\) | 1.39557e124 | 0.00593025 | ||||||||
\(523\) | 3.73258e126 | 1.45105 | 0.725523 | − | 0.688198i | \(-0.241598\pi\) | ||||
0.725523 | + | 0.688198i | \(0.241598\pi\) | |||||||
\(524\) | −5.15911e126 | −1.83514 | ||||||||
\(525\) | 4.28191e124 | 0.0139390 | ||||||||
\(526\) | −1.21447e125 | −0.0361868 | ||||||||
\(527\) | −4.68695e126 | −1.27849 | ||||||||
\(528\) | −3.22900e126 | −0.806474 | ||||||||
\(529\) | −1.17440e126 | −0.268613 | ||||||||
\(530\) | −3.89297e125 | −0.0815555 | ||||||||
\(531\) | −6.13338e125 | −0.117708 | ||||||||
\(532\) | 1.22716e126 | 0.215780 | ||||||||
\(533\) | 1.60005e126 | 0.257821 | ||||||||
\(534\) | −8.59942e124 | −0.0126999 | ||||||||
\(535\) | 9.91367e126 | 1.34210 | ||||||||
\(536\) | 6.85260e125 | 0.0850535 | ||||||||
\(537\) | −7.69295e126 | −0.875566 | ||||||||
\(538\) | 2.31822e124 | 0.00241979 | ||||||||
\(539\) | −8.04106e126 | −0.769902 | ||||||||
\(540\) | 1.14160e127 | 1.00277 | ||||||||
\(541\) | −7.69343e126 | −0.620079 | −0.310040 | − | 0.950724i | \(-0.600342\pi\) | ||||
−0.310040 | + | 0.950724i | \(0.600342\pi\) | |||||||
\(542\) | 5.53868e125 | 0.0409675 | ||||||||
\(543\) | 3.04005e127 | 2.06390 | ||||||||
\(544\) | 2.05727e126 | 0.128216 | ||||||||
\(545\) | −8.57149e126 | −0.490478 | ||||||||
\(546\) | −5.74207e124 | −0.00301725 | ||||||||
\(547\) | 2.71689e127 | 1.31118 | 0.655589 | − | 0.755118i | \(-0.272420\pi\) | ||||
0.655589 | + | 0.755118i | \(0.272420\pi\) | |||||||
\(548\) | −1.26221e127 | −0.559544 | ||||||||
\(549\) | −2.31001e126 | −0.0940805 | ||||||||
\(550\) | −1.17823e125 | −0.00440924 | ||||||||
\(551\) | −7.06079e127 | −2.42831 | ||||||||
\(552\) | 2.93874e126 | 0.0928952 | ||||||||
\(553\) | 3.72507e125 | 0.0108247 | ||||||||
\(554\) | −1.63380e126 | −0.0436511 | ||||||||
\(555\) | 1.95443e127 | 0.480171 | ||||||||
\(556\) | 2.99965e127 | 0.677787 | ||||||||
\(557\) | −8.81073e127 | −1.83124 | −0.915620 | − | 0.402045i | \(-0.868299\pi\) | ||||
−0.915620 | + | 0.402045i | \(0.868299\pi\) | |||||||
\(558\) | −3.46452e125 | −0.00662449 | ||||||||
\(559\) | 4.34074e126 | 0.0763686 | ||||||||
\(560\) | 8.01729e126 | 0.129803 | ||||||||
\(561\) | 4.47532e127 | 0.666885 | ||||||||
\(562\) | −3.82137e126 | −0.0524180 | ||||||||
\(563\) | −6.45622e127 | −0.815338 | −0.407669 | − | 0.913130i | \(-0.633658\pi\) | ||||
−0.407669 | + | 0.913130i | \(0.633658\pi\) | |||||||
\(564\) | 1.20663e128 | 1.40312 | ||||||||
\(565\) | 7.38643e127 | 0.791009 | ||||||||
\(566\) | 2.30195e126 | 0.0227055 | ||||||||
\(567\) | 1.47064e127 | 0.133627 | ||||||||
\(568\) | 8.70323e126 | 0.0728589 | ||||||||
\(569\) | 5.12368e127 | 0.395241 | 0.197621 | − | 0.980279i | \(-0.436679\pi\) | ||||
0.197621 | + | 0.980279i | \(0.436679\pi\) | |||||||
\(570\) | −1.40110e127 | −0.0996066 | ||||||||
\(571\) | −3.30044e127 | −0.216268 | −0.108134 | − | 0.994136i | \(-0.534488\pi\) | ||||
−0.108134 | + | 0.994136i | \(0.534488\pi\) | |||||||
\(572\) | −5.76006e127 | −0.347946 | ||||||||
\(573\) | −1.00465e128 | −0.559530 | ||||||||
\(574\) | 7.31766e125 | 0.00375811 | ||||||||
\(575\) | −1.94656e127 | −0.0921961 | ||||||||
\(576\) | −1.82934e127 | −0.0799187 | ||||||||
\(577\) | 2.92806e128 | 1.18006 | 0.590031 | − | 0.807381i | \(-0.299116\pi\) | ||||
0.590031 | + | 0.807381i | \(0.299116\pi\) | |||||||
\(578\) | 4.60486e126 | 0.0171227 | ||||||||
\(579\) | −8.94077e127 | −0.306776 | ||||||||
\(580\) | −4.62568e128 | −1.46479 | ||||||||
\(581\) | −3.90552e127 | −0.114153 | ||||||||
\(582\) | 1.52209e127 | 0.0410698 | ||||||||
\(583\) | −4.65041e128 | −1.15852 | ||||||||
\(584\) | 7.33296e127 | 0.168687 | ||||||||
\(585\) | −1.79596e127 | −0.0381548 | ||||||||
\(586\) | 1.34258e127 | 0.0263452 | ||||||||
\(587\) | 2.06516e128 | 0.374353 | 0.187176 | − | 0.982326i | \(-0.440066\pi\) | ||||
0.187176 | + | 0.982326i | \(0.440066\pi\) | |||||||
\(588\) | −6.09609e128 | −1.02095 | ||||||||
\(589\) | 1.75285e129 | 2.71259 | ||||||||
\(590\) | −5.57644e127 | −0.0797514 | ||||||||
\(591\) | 1.03522e129 | 1.36841 | ||||||||
\(592\) | 3.56111e128 | 0.435137 | ||||||||
\(593\) | −8.47498e128 | −0.957404 | −0.478702 | − | 0.877977i | \(-0.658893\pi\) | ||||
−0.478702 | + | 0.877977i | \(0.658893\pi\) | |||||||
\(594\) | −3.74072e127 | −0.0390737 | ||||||||
\(595\) | −1.11118e128 | −0.107336 | ||||||||
\(596\) | 2.97938e127 | 0.0266179 | ||||||||
\(597\) | −5.51834e128 | −0.456039 | ||||||||
\(598\) | 2.61035e127 | 0.0199569 | ||||||||
\(599\) | 3.98262e128 | 0.281723 | 0.140861 | − | 0.990029i | \(-0.455013\pi\) | ||||
0.140861 | + | 0.990029i | \(0.455013\pi\) | |||||||
\(600\) | −1.78892e127 | −0.0117101 | ||||||||
\(601\) | −2.03200e129 | −1.23101 | −0.615505 | − | 0.788133i | \(-0.711048\pi\) | ||||
−0.615505 | + | 0.788133i | \(0.711048\pi\) | |||||||
\(602\) | 1.98519e126 | 0.00111318 | ||||||||
\(603\) | 1.27441e128 | 0.0661538 | ||||||||
\(604\) | 6.61753e128 | 0.318037 | ||||||||
\(605\) | 9.18825e128 | 0.408891 | ||||||||
\(606\) | 9.09032e127 | 0.0374630 | ||||||||
\(607\) | −3.34725e129 | −1.27766 | −0.638828 | − | 0.769349i | \(-0.720581\pi\) | ||||
−0.638828 | + | 0.769349i | \(0.720581\pi\) | |||||||
\(608\) | −7.69388e128 | −0.272038 | ||||||||
\(609\) | −5.50842e128 | −0.180436 | ||||||||
\(610\) | −2.10025e128 | −0.0637431 | ||||||||
\(611\) | 2.14653e129 | 0.603698 | ||||||||
\(612\) | 2.54951e128 | 0.0664531 | ||||||||
\(613\) | −3.69786e129 | −0.893383 | −0.446692 | − | 0.894688i | \(-0.647398\pi\) | ||||
−0.446692 | + | 0.894688i | \(0.647398\pi\) | |||||||
\(614\) | 2.35647e128 | 0.0527755 | ||||||||
\(615\) | 3.04584e129 | 0.632432 | ||||||||
\(616\) | −5.27584e127 | −0.0101575 | ||||||||
\(617\) | 9.34186e129 | 1.66791 | 0.833956 | − | 0.551830i | \(-0.186070\pi\) | ||||
0.833956 | + | 0.551830i | \(0.186070\pi\) | |||||||
\(618\) | 5.42767e128 | 0.0898771 | ||||||||
\(619\) | 1.99467e128 | 0.0306377 | 0.0153188 | − | 0.999883i | \(-0.495124\pi\) | ||||
0.0153188 | + | 0.999883i | \(0.495124\pi\) | |||||||
\(620\) | 1.14833e130 | 1.63626 | ||||||||
\(621\) | −6.18007e129 | −0.817023 | ||||||||
\(622\) | 3.25520e128 | 0.0399324 | ||||||||
\(623\) | 2.55058e128 | 0.0290365 | ||||||||
\(624\) | −4.35481e129 | −0.460135 | ||||||||
\(625\) | −1.11765e130 | −1.09618 | ||||||||
\(626\) | −6.20535e127 | −0.00565014 | ||||||||
\(627\) | −1.67370e130 | −1.41494 | ||||||||
\(628\) | 1.52311e130 | 1.19566 | ||||||||
\(629\) | −4.93562e129 | −0.359822 | ||||||||
\(630\) | −8.21365e126 | −0.000556161 0 | ||||||||
\(631\) | −3.91510e129 | −0.246251 | −0.123125 | − | 0.992391i | \(-0.539292\pi\) | ||||
−0.123125 | + | 0.992391i | \(0.539292\pi\) | |||||||
\(632\) | −1.55628e128 | −0.00909378 | ||||||||
\(633\) | 5.59589e129 | 0.303806 | ||||||||
\(634\) | −1.09425e129 | −0.0552034 | ||||||||
\(635\) | 1.83022e130 | 0.858073 | ||||||||
\(636\) | −3.52557e130 | −1.53629 | ||||||||
\(637\) | −1.08446e130 | −0.439269 | ||||||||
\(638\) | 1.51572e129 | 0.0570764 | ||||||||
\(639\) | 1.61858e129 | 0.0566690 | ||||||||
\(640\) | −6.71748e129 | −0.218694 | ||||||||
\(641\) | 3.64405e130 | 1.10328 | 0.551640 | − | 0.834083i | \(-0.314002\pi\) | ||||
0.551640 | + | 0.834083i | \(0.314002\pi\) | |||||||
\(642\) | −2.46272e129 | −0.0693483 | ||||||||
\(643\) | 4.68261e130 | 1.22653 | 0.613264 | − | 0.789878i | \(-0.289856\pi\) | ||||
0.613264 | + | 0.789878i | \(0.289856\pi\) | |||||||
\(644\) | −4.35216e129 | −0.106050 | ||||||||
\(645\) | 8.26300e129 | 0.187332 | ||||||||
\(646\) | 3.53827e129 | 0.0746412 | ||||||||
\(647\) | 6.34581e130 | 1.24577 | 0.622885 | − | 0.782313i | \(-0.285960\pi\) | ||||
0.622885 | + | 0.782313i | \(0.285960\pi\) | |||||||
\(648\) | −6.14414e129 | −0.112260 | ||||||||
\(649\) | −6.66142e130 | −1.13289 | ||||||||
\(650\) | −1.58902e128 | −0.00251570 | ||||||||
\(651\) | 1.36747e130 | 0.201559 | ||||||||
\(652\) | −6.94404e130 | −0.953014 | ||||||||
\(653\) | 9.09354e130 | 1.16217 | 0.581085 | − | 0.813843i | \(-0.302628\pi\) | ||||
0.581085 | + | 0.813843i | \(0.302628\pi\) | |||||||
\(654\) | 2.12930e129 | 0.0253438 | ||||||||
\(655\) | −1.74708e131 | −1.93683 | ||||||||
\(656\) | 5.54974e130 | 0.573118 | ||||||||
\(657\) | 1.36375e130 | 0.131203 | ||||||||
\(658\) | 9.81693e128 | 0.00879978 | ||||||||
\(659\) | −1.50199e131 | −1.25457 | −0.627284 | − | 0.778791i | \(-0.715833\pi\) | ||||
−0.627284 | + | 0.778791i | \(0.715833\pi\) | |||||||
\(660\) | −1.09648e131 | −0.853509 | ||||||||
\(661\) | 5.08430e130 | 0.368861 | 0.184431 | − | 0.982846i | \(-0.440956\pi\) | ||||
0.184431 | + | 0.982846i | \(0.440956\pi\) | |||||||
\(662\) | 4.15259e129 | 0.0280816 | ||||||||
\(663\) | 6.03567e130 | 0.380493 | ||||||||
\(664\) | 1.63167e130 | 0.0958997 | ||||||||
\(665\) | 4.15565e130 | 0.227736 | ||||||||
\(666\) | −3.64833e128 | −0.00186441 | ||||||||
\(667\) | 2.50413e131 | 1.19345 | ||||||||
\(668\) | 1.72166e131 | 0.765318 | ||||||||
\(669\) | 6.04533e130 | 0.250672 | ||||||||
\(670\) | 1.15869e130 | 0.0448217 | ||||||||
\(671\) | −2.50888e131 | −0.905489 | ||||||||
\(672\) | −6.00232e129 | −0.0202138 | ||||||||
\(673\) | −1.25378e131 | −0.394022 | −0.197011 | − | 0.980401i | \(-0.563123\pi\) | ||||
−0.197011 | + | 0.980401i | \(0.563123\pi\) | |||||||
\(674\) | −2.86705e130 | −0.0840911 | ||||||||
\(675\) | 3.76205e130 | 0.102991 | ||||||||
\(676\) | 3.12557e131 | 0.798743 | ||||||||
\(677\) | 1.65408e131 | 0.394623 | 0.197312 | − | 0.980341i | \(-0.436779\pi\) | ||||
0.197312 | + | 0.980341i | \(0.436779\pi\) | |||||||
\(678\) | −1.83491e130 | −0.0408728 | ||||||||
\(679\) | −4.51452e130 | −0.0939002 | ||||||||
\(680\) | 4.64236e130 | 0.0901725 | ||||||||
\(681\) | 3.37348e131 | 0.611980 | ||||||||
\(682\) | −3.76278e130 | −0.0637582 | ||||||||
\(683\) | −1.09448e132 | −1.73239 | −0.866194 | − | 0.499708i | \(-0.833441\pi\) | ||||
−0.866194 | + | 0.499708i | \(0.833441\pi\) | |||||||
\(684\) | −9.53477e130 | −0.140994 | ||||||||
\(685\) | −4.27432e131 | −0.590548 | ||||||||
\(686\) | −9.99725e129 | −0.0129065 | ||||||||
\(687\) | −1.08963e132 | −1.31459 | ||||||||
\(688\) | 1.50558e131 | 0.169762 | ||||||||
\(689\) | −6.27180e131 | −0.660995 | ||||||||
\(690\) | 4.96904e130 | 0.0489542 | ||||||||
\(691\) | 1.49686e132 | 1.37864 | 0.689320 | − | 0.724457i | \(-0.257909\pi\) | ||||
0.689320 | + | 0.724457i | \(0.257909\pi\) | |||||||
\(692\) | 1.23741e132 | 1.06556 | ||||||||
\(693\) | −9.81174e129 | −0.00790043 | ||||||||
\(694\) | −7.36456e130 | −0.0554538 | ||||||||
\(695\) | 1.01580e132 | 0.715343 | ||||||||
\(696\) | 2.30134e131 | 0.151583 | ||||||||
\(697\) | −7.69182e131 | −0.473920 | ||||||||
\(698\) | 3.40601e130 | 0.0196322 | ||||||||
\(699\) | 2.92684e132 | 1.57837 | ||||||||
\(700\) | 2.64933e130 | 0.0133683 | ||||||||
\(701\) | −4.03873e132 | −1.90703 | −0.953514 | − | 0.301349i | \(-0.902563\pi\) | ||||
−0.953514 | + | 0.301349i | \(0.902563\pi\) | |||||||
\(702\) | −5.04494e130 | −0.0222936 | ||||||||
\(703\) | 1.84585e132 | 0.763438 | ||||||||
\(704\) | −1.98683e132 | −0.769187 | ||||||||
\(705\) | 4.08611e132 | 1.48087 | ||||||||
\(706\) | 8.76933e130 | 0.0297542 | ||||||||
\(707\) | −2.69618e131 | −0.0856538 | ||||||||
\(708\) | −5.05016e132 | −1.50231 | ||||||||
\(709\) | 2.29100e132 | 0.638228 | 0.319114 | − | 0.947716i | \(-0.396615\pi\) | ||||
0.319114 | + | 0.947716i | \(0.396615\pi\) | |||||||
\(710\) | 1.47161e131 | 0.0383954 | ||||||||
\(711\) | −2.89430e130 | −0.00707305 | ||||||||
\(712\) | −1.06560e131 | −0.0243935 | ||||||||
\(713\) | −6.21653e132 | −1.33317 | ||||||||
\(714\) | 2.76036e130 | 0.00554623 | ||||||||
\(715\) | −1.95058e132 | −0.367225 | ||||||||
\(716\) | −4.75983e132 | −0.839723 | ||||||||
\(717\) | 7.02085e132 | 1.16078 | ||||||||
\(718\) | −2.95973e131 | −0.0458633 | ||||||||
\(719\) | −4.76634e132 | −0.692296 | −0.346148 | − | 0.938180i | \(-0.612510\pi\) | ||||
−0.346148 | + | 0.938180i | \(0.612510\pi\) | |||||||
\(720\) | −6.22926e131 | −0.0848155 | ||||||||
\(721\) | −1.60984e132 | −0.205491 | ||||||||
\(722\) | −8.86240e131 | −0.106065 | ||||||||
\(723\) | 1.69158e133 | 1.89829 | ||||||||
\(724\) | 1.88096e133 | 1.97941 | ||||||||
\(725\) | −1.52436e132 | −0.150443 | ||||||||
\(726\) | −2.28251e131 | −0.0211281 | ||||||||
\(727\) | −1.12628e133 | −0.977903 | −0.488952 | − | 0.872311i | \(-0.662621\pi\) | ||||
−0.488952 | + | 0.872311i | \(0.662621\pi\) | |||||||
\(728\) | −7.11529e130 | −0.00579540 | ||||||||
\(729\) | 1.18577e133 | 0.906084 | ||||||||
\(730\) | 1.23991e132 | 0.0888952 | ||||||||
\(731\) | −2.08670e132 | −0.140379 | ||||||||
\(732\) | −1.90204e133 | −1.20075 | ||||||||
\(733\) | 3.96038e132 | 0.234640 | 0.117320 | − | 0.993094i | \(-0.462570\pi\) | ||||
0.117320 | + | 0.993094i | \(0.462570\pi\) | |||||||
\(734\) | −6.80901e130 | −0.00378632 | ||||||||
\(735\) | −2.06437e133 | −1.07752 | ||||||||
\(736\) | 2.72866e132 | 0.133700 | ||||||||
\(737\) | 1.38413e133 | 0.636705 | ||||||||
\(738\) | −5.68566e130 | −0.00245561 | ||||||||
\(739\) | −1.41364e132 | −0.0573288 | −0.0286644 | − | 0.999589i | \(-0.509125\pi\) | ||||
−0.0286644 | + | 0.999589i | \(0.509125\pi\) | |||||||
\(740\) | 1.20926e133 | 0.460515 | ||||||||
\(741\) | −2.25725e133 | −0.807296 | ||||||||
\(742\) | −2.86835e131 | −0.00963496 | ||||||||
\(743\) | −4.02843e133 | −1.27103 | −0.635515 | − | 0.772089i | \(-0.719212\pi\) | ||||
−0.635515 | + | 0.772089i | \(0.719212\pi\) | |||||||
\(744\) | −5.71311e132 | −0.169329 | ||||||||
\(745\) | 1.00893e132 | 0.0280928 | ||||||||
\(746\) | 3.52387e132 | 0.0921859 | ||||||||
\(747\) | 3.03450e132 | 0.0745898 | ||||||||
\(748\) | 2.76900e133 | 0.639586 | ||||||||
\(749\) | 7.30440e132 | 0.158555 | ||||||||
\(750\) | 2.50337e132 | 0.0510712 | ||||||||
\(751\) | −2.45927e133 | −0.471573 | −0.235787 | − | 0.971805i | \(-0.575767\pi\) | ||||
−0.235787 | + | 0.971805i | \(0.575767\pi\) | |||||||
\(752\) | 7.44519e133 | 1.34198 | ||||||||
\(753\) | 7.57355e132 | 0.128331 | ||||||||
\(754\) | 2.04418e132 | 0.0325650 | ||||||||
\(755\) | 2.24095e133 | 0.335660 | ||||||||
\(756\) | 8.41129e132 | 0.118468 | ||||||||
\(757\) | −1.74934e133 | −0.231694 | −0.115847 | − | 0.993267i | \(-0.536958\pi\) | ||||
−0.115847 | + | 0.993267i | \(0.536958\pi\) | |||||||
\(758\) | −3.59074e131 | −0.00447266 | ||||||||
\(759\) | 5.93584e133 | 0.695408 | ||||||||
\(760\) | −1.73617e133 | −0.191320 | ||||||||
\(761\) | 2.60917e133 | 0.270468 | 0.135234 | − | 0.990814i | \(-0.456821\pi\) | ||||
0.135234 | + | 0.990814i | \(0.456821\pi\) | |||||||
\(762\) | −4.54656e132 | −0.0443381 | ||||||||
\(763\) | −6.31549e132 | −0.0579450 | ||||||||
\(764\) | −6.21602e133 | −0.536625 | ||||||||
\(765\) | 8.63362e132 | 0.0701352 | ||||||||
\(766\) | −2.21461e132 | −0.0169301 | ||||||||
\(767\) | −8.98396e133 | −0.646373 | ||||||||
\(768\) | −1.49370e134 | −1.01150 | ||||||||
\(769\) | −2.71565e134 | −1.73101 | −0.865503 | − | 0.500905i | \(-0.833001\pi\) | ||||
−0.865503 | + | 0.500905i | \(0.833001\pi\) | |||||||
\(770\) | −8.92079e131 | −0.00535284 | ||||||||
\(771\) | 1.76381e134 | 0.996377 | ||||||||
\(772\) | −5.53189e133 | −0.294218 | ||||||||
\(773\) | 2.21657e134 | 1.11003 | 0.555015 | − | 0.831841i | \(-0.312713\pi\) | ||||
0.555015 | + | 0.831841i | \(0.312713\pi\) | |||||||
\(774\) | −1.54245e131 | −0.000727373 0 | ||||||||
\(775\) | 3.78425e133 | 0.168055 | ||||||||
\(776\) | 1.88610e133 | 0.0788851 | ||||||||
\(777\) | 1.44003e133 | 0.0567274 | ||||||||
\(778\) | 6.14531e132 | 0.0228030 | ||||||||
\(779\) | 2.87662e134 | 1.00552 | ||||||||
\(780\) | −1.47877e134 | −0.486971 | ||||||||
\(781\) | 1.75793e134 | 0.545417 | ||||||||
\(782\) | −1.25486e133 | −0.0366843 | ||||||||
\(783\) | −4.83966e134 | −1.33319 | ||||||||
\(784\) | −3.76144e134 | −0.976466 | ||||||||
\(785\) | 5.15783e134 | 1.26191 | ||||||||
\(786\) | 4.34003e133 | 0.100079 | ||||||||
\(787\) | 7.01625e134 | 1.52503 | 0.762517 | − | 0.646968i | \(-0.223963\pi\) | ||||
0.762517 | + | 0.646968i | \(0.223963\pi\) | |||||||
\(788\) | 6.40520e134 | 1.31239 | ||||||||
\(789\) | −3.72454e134 | −0.719435 | ||||||||
\(790\) | −2.63148e132 | −0.00479226 | ||||||||
\(791\) | 5.44233e133 | 0.0934498 | ||||||||
\(792\) | 4.09921e132 | 0.00663711 | ||||||||
\(793\) | −3.38362e134 | −0.516629 | ||||||||
\(794\) | −2.26667e133 | −0.0326389 | ||||||||
\(795\) | −1.19390e135 | −1.62142 | ||||||||
\(796\) | −3.41434e134 | −0.437370 | ||||||||
\(797\) | −2.56830e134 | −0.310337 | −0.155168 | − | 0.987888i | \(-0.549592\pi\) | ||||
−0.155168 | + | 0.987888i | \(0.549592\pi\) | |||||||
\(798\) | −1.03233e133 | −0.0117675 | ||||||||
\(799\) | −1.03189e135 | −1.10970 | ||||||||
\(800\) | −1.66104e133 | −0.0168537 | ||||||||
\(801\) | −1.98175e133 | −0.0189730 | ||||||||
\(802\) | −8.85412e131 | −0.000799903 0 | ||||||||
\(803\) | 1.48116e135 | 1.26278 | ||||||||
\(804\) | 1.04934e135 | 0.844323 | ||||||||
\(805\) | −1.47381e134 | −0.111927 | ||||||||
\(806\) | −5.07470e133 | −0.0363774 | ||||||||
\(807\) | 7.10950e133 | 0.0481082 | ||||||||
\(808\) | 1.12643e134 | 0.0719573 | ||||||||
\(809\) | 2.92460e134 | 0.176384 | 0.0881921 | − | 0.996103i | \(-0.471891\pi\) | ||||
0.0881921 | + | 0.996103i | \(0.471891\pi\) | |||||||
\(810\) | −1.03890e134 | −0.0591588 | ||||||||
\(811\) | 3.24175e134 | 0.174305 | 0.0871526 | − | 0.996195i | \(-0.472223\pi\) | ||||
0.0871526 | + | 0.996195i | \(0.472223\pi\) | |||||||
\(812\) | −3.40821e134 | −0.173050 | ||||||||
\(813\) | 1.69860e135 | 0.814481 | ||||||||
\(814\) | −3.96242e133 | −0.0179443 | ||||||||
\(815\) | −2.35152e135 | −1.00582 | ||||||||
\(816\) | 2.09346e135 | 0.845810 | ||||||||
\(817\) | 7.80394e134 | 0.297844 | ||||||||
\(818\) | −3.97286e133 | −0.0143243 | ||||||||
\(819\) | −1.32327e133 | −0.00450760 | ||||||||
\(820\) | 1.88454e135 | 0.606543 | ||||||||
\(821\) | −2.21028e135 | −0.672187 | −0.336094 | − | 0.941829i | \(-0.609106\pi\) | ||||
−0.336094 | + | 0.941829i | \(0.609106\pi\) | |||||||
\(822\) | 1.06181e134 | 0.0305146 | ||||||||
\(823\) | −9.21561e134 | −0.250283 | −0.125142 | − | 0.992139i | \(-0.539939\pi\) | ||||
−0.125142 | + | 0.992139i | \(0.539939\pi\) | |||||||
\(824\) | 6.72569e134 | 0.172632 | ||||||||
\(825\) | −3.61338e134 | −0.0876607 | ||||||||
\(826\) | −4.10873e133 | −0.00942183 | ||||||||
\(827\) | −7.22312e135 | −1.56574 | −0.782868 | − | 0.622188i | \(-0.786244\pi\) | ||||
−0.782868 | + | 0.622188i | \(0.786244\pi\) | |||||||
\(828\) | 3.38153e134 | 0.0692952 | ||||||||
\(829\) | −1.60908e135 | −0.311740 | −0.155870 | − | 0.987778i | \(-0.549818\pi\) | ||||
−0.155870 | + | 0.987778i | \(0.549818\pi\) | |||||||
\(830\) | 2.75896e134 | 0.0505375 | ||||||||
\(831\) | −5.01053e135 | −0.867833 | ||||||||
\(832\) | −2.67955e135 | −0.438861 | ||||||||
\(833\) | 5.21327e135 | 0.807454 | ||||||||
\(834\) | −2.52341e134 | −0.0369630 | ||||||||
\(835\) | 5.83021e135 | 0.807724 | ||||||||
\(836\) | −1.03556e136 | −1.35702 | ||||||||
\(837\) | 1.20145e136 | 1.48927 | ||||||||
\(838\) | 1.97257e134 | 0.0231305 | ||||||||
\(839\) | 1.01984e136 | 1.13136 | 0.565682 | − | 0.824624i | \(-0.308613\pi\) | ||||
0.565682 | + | 0.824624i | \(0.308613\pi\) | |||||||
\(840\) | −1.35446e134 | −0.0142161 | ||||||||
\(841\) | 9.54037e135 | 0.947440 | ||||||||
\(842\) | −7.04517e134 | −0.0662032 | ||||||||
\(843\) | −1.17194e136 | −1.04213 | ||||||||
\(844\) | 3.46232e135 | 0.291369 | ||||||||
\(845\) | 1.05844e136 | 0.843002 | ||||||||
\(846\) | −7.62754e133 | −0.00574993 | ||||||||
\(847\) | 6.76991e134 | 0.0483064 | ||||||||
\(848\) | −2.17536e136 | −1.46935 | ||||||||
\(849\) | 7.05961e135 | 0.451412 | ||||||||
\(850\) | 7.63881e133 | 0.00462430 | ||||||||
\(851\) | −6.54636e135 | −0.375211 | ||||||||
\(852\) | 1.33272e136 | 0.723268 | ||||||||
\(853\) | −1.53845e135 | −0.0790596 | −0.0395298 | − | 0.999218i | \(-0.512586\pi\) | ||||
−0.0395298 | + | 0.999218i | \(0.512586\pi\) | |||||||
\(854\) | −1.54747e134 | −0.00753061 | ||||||||
\(855\) | −3.22885e135 | −0.148807 | ||||||||
\(856\) | −3.05168e135 | −0.133201 | ||||||||
\(857\) | −4.43080e136 | −1.83178 | −0.915891 | − | 0.401428i | \(-0.868514\pi\) | ||||
−0.915891 | + | 0.401428i | \(0.868514\pi\) | |||||||
\(858\) | 4.84556e134 | 0.0189752 | ||||||||
\(859\) | 6.46834e135 | 0.239945 | 0.119972 | − | 0.992777i | \(-0.461719\pi\) | ||||
0.119972 | + | 0.992777i | \(0.461719\pi\) | |||||||
\(860\) | 5.11254e135 | 0.179663 | ||||||||
\(861\) | 2.24418e135 | 0.0747155 | ||||||||
\(862\) | 1.99268e135 | 0.0628565 | ||||||||
\(863\) | −3.32946e136 | −0.995111 | −0.497555 | − | 0.867432i | \(-0.665769\pi\) | ||||
−0.497555 | + | 0.867432i | \(0.665769\pi\) | |||||||
\(864\) | −5.27359e135 | −0.149354 | ||||||||
\(865\) | 4.19034e136 | 1.12461 | ||||||||
\(866\) | −1.93771e135 | −0.0492840 | ||||||||
\(867\) | 1.41222e136 | 0.340418 | ||||||||
\(868\) | 8.46092e135 | 0.193308 | ||||||||
\(869\) | −3.14347e135 | −0.0680754 | ||||||||
\(870\) | 3.89129e135 | 0.0798818 | ||||||||
\(871\) | 1.86671e136 | 0.363273 | ||||||||
\(872\) | 2.63852e135 | 0.0486793 | ||||||||
\(873\) | 3.50768e135 | 0.0613561 | ||||||||
\(874\) | 4.69298e135 | 0.0778336 | ||||||||
\(875\) | −7.42496e135 | −0.116767 | ||||||||
\(876\) | 1.12290e137 | 1.67455 | ||||||||
\(877\) | 1.12855e136 | 0.159602 | 0.0798012 | − | 0.996811i | \(-0.474571\pi\) | ||||
0.0798012 | + | 0.996811i | \(0.474571\pi\) | |||||||
\(878\) | 2.76286e134 | 0.00370565 | ||||||||
\(879\) | 4.11742e136 | 0.523772 | ||||||||
\(880\) | −6.76555e136 | −0.816317 | ||||||||
\(881\) | −1.99955e136 | −0.228851 | −0.114426 | − | 0.993432i | \(-0.536503\pi\) | ||||
−0.114426 | + | 0.993432i | \(0.536503\pi\) | |||||||
\(882\) | 3.85356e134 | 0.00418382 | ||||||||
\(883\) | −1.56519e137 | −1.61211 | −0.806056 | − | 0.591840i | \(-0.798402\pi\) | ||||
−0.806056 | + | 0.591840i | \(0.798402\pi\) | |||||||
\(884\) | 3.73443e136 | 0.364917 | ||||||||
\(885\) | −1.71018e137 | −1.58555 | ||||||||
\(886\) | −1.13514e136 | −0.0998580 | ||||||||
\(887\) | 4.03132e136 | 0.336511 | 0.168256 | − | 0.985743i | \(-0.446187\pi\) | ||||
0.168256 | + | 0.985743i | \(0.446187\pi\) | |||||||
\(888\) | −6.01623e135 | −0.0476564 | ||||||||
\(889\) | 1.34851e136 | 0.101373 | ||||||||
\(890\) | −1.80179e135 | −0.0128549 | ||||||||
\(891\) | −1.24103e137 | −0.840367 | ||||||||
\(892\) | 3.74041e136 | 0.240410 | ||||||||
\(893\) | 3.85911e137 | 2.35447 | ||||||||
\(894\) | −2.50636e134 | −0.00145160 | ||||||||
\(895\) | −1.61186e137 | −0.886253 | ||||||||
\(896\) | −4.94945e135 | −0.0258365 | ||||||||
\(897\) | 8.00540e136 | 0.396766 | ||||||||
\(898\) | 1.43551e136 | 0.0675549 | ||||||||
\(899\) | −4.86821e137 | −2.17542 | ||||||||
\(900\) | −2.05847e135 | −0.00873512 | ||||||||
\(901\) | 3.01501e137 | 1.21503 | ||||||||
\(902\) | −6.17515e135 | −0.0236344 | ||||||||
\(903\) | 6.08819e135 | 0.0221313 | ||||||||
\(904\) | −2.27373e136 | −0.0785067 | ||||||||
\(905\) | 6.36966e137 | 2.08909 | ||||||||
\(906\) | −5.56690e135 | −0.0173441 | ||||||||
\(907\) | 1.62643e137 | 0.481391 | 0.240695 | − | 0.970601i | \(-0.422625\pi\) | ||||
0.240695 | + | 0.970601i | \(0.422625\pi\) | |||||||
\(908\) | 2.08726e137 | 0.586928 | ||||||||
\(909\) | 2.09487e136 | 0.0559677 | ||||||||
\(910\) | −1.20311e135 | −0.00305407 | ||||||||
\(911\) | 4.81504e136 | 0.116144 | 0.0580718 | − | 0.998312i | \(-0.481505\pi\) | ||||
0.0580718 | + | 0.998312i | \(0.481505\pi\) | |||||||
\(912\) | −7.82924e137 | −1.79457 | ||||||||
\(913\) | 3.29575e137 | 0.717899 | ||||||||
\(914\) | 1.62374e136 | 0.0336139 | ||||||||
\(915\) | −6.44104e137 | −1.26729 | ||||||||
\(916\) | −6.74184e137 | −1.26078 | ||||||||
\(917\) | −1.28725e137 | −0.228817 | ||||||||
\(918\) | 2.42523e136 | 0.0409796 | ||||||||
\(919\) | −5.40959e137 | −0.868947 | −0.434473 | − | 0.900685i | \(-0.643065\pi\) | ||||
−0.434473 | + | 0.900685i | \(0.643065\pi\) | |||||||
\(920\) | 6.15738e136 | 0.0940291 | ||||||||
\(921\) | 7.22680e137 | 1.04924 | ||||||||
\(922\) | 2.44132e136 | 0.0337005 | ||||||||
\(923\) | 2.37084e137 | 0.311189 | ||||||||
\(924\) | −8.07888e136 | −0.100833 | ||||||||
\(925\) | 3.98503e136 | 0.0472978 | ||||||||
\(926\) | −6.07828e136 | −0.0686072 | ||||||||
\(927\) | 1.25081e137 | 0.134272 | ||||||||
\(928\) | 2.13683e137 | 0.218167 | ||||||||
\(929\) | 4.56779e137 | 0.443583 | 0.221792 | − | 0.975094i | \(-0.428809\pi\) | ||||
0.221792 | + | 0.975094i | \(0.428809\pi\) | |||||||
\(930\) | −9.66017e136 | −0.0892334 | ||||||||
\(931\) | −1.94969e138 | −1.71319 | ||||||||
\(932\) | 1.81091e138 | 1.51376 | ||||||||
\(933\) | 9.98304e137 | 0.793901 | ||||||||
\(934\) | −9.68810e135 | −0.00733008 | ||||||||
\(935\) | 9.37691e137 | 0.675025 | ||||||||
\(936\) | 5.52842e135 | 0.00378682 | ||||||||
\(937\) | −1.76214e138 | −1.14855 | −0.574276 | − | 0.818662i | \(-0.694716\pi\) | ||||
−0.574276 | + | 0.818662i | \(0.694716\pi\) | |||||||
\(938\) | 8.53723e135 | 0.00529523 | ||||||||
\(939\) | −1.90305e137 | −0.112331 | ||||||||
\(940\) | 2.52819e138 | 1.42025 | ||||||||
\(941\) | 1.71831e138 | 0.918722 | 0.459361 | − | 0.888250i | \(-0.348078\pi\) | ||||
0.459361 | + | 0.888250i | \(0.348078\pi\) | |||||||
\(942\) | −1.28129e137 | −0.0652049 | ||||||||
\(943\) | −1.02020e138 | −0.494189 | ||||||||
\(944\) | −3.11607e138 | −1.43684 | ||||||||
\(945\) | 2.84839e137 | 0.125032 | ||||||||
\(946\) | −1.67525e136 | −0.00700069 | ||||||||
\(947\) | −9.56790e137 | −0.380665 | −0.190332 | − | 0.981720i | \(-0.560957\pi\) | ||||
−0.190332 | + | 0.981720i | \(0.560957\pi\) | |||||||
\(948\) | −2.38313e137 | −0.0902736 | ||||||||
\(949\) | 1.99757e138 | 0.720482 | ||||||||
\(950\) | −2.85680e136 | −0.00981143 | ||||||||
\(951\) | −3.35584e138 | −1.09751 | ||||||||
\(952\) | 3.42049e136 | 0.0106530 | ||||||||
\(953\) | −6.46995e138 | −1.91903 | −0.959513 | − | 0.281664i | \(-0.909114\pi\) | ||||
−0.959513 | + | 0.281664i | \(0.909114\pi\) | |||||||
\(954\) | 2.22864e136 | 0.00629565 | ||||||||
\(955\) | −2.10499e138 | −0.566360 | ||||||||
\(956\) | 4.34399e138 | 1.11326 | ||||||||
\(957\) | 4.64839e138 | 1.13474 | ||||||||
\(958\) | 3.59927e137 | 0.0836985 | ||||||||
\(959\) | −3.14932e137 | −0.0697673 | ||||||||
\(960\) | −5.10077e138 | −1.07652 | ||||||||
\(961\) | 7.11217e138 | 1.43009 | ||||||||
\(962\) | −5.34395e136 | −0.0102381 | ||||||||
\(963\) | −5.67536e137 | −0.103603 | ||||||||
\(964\) | 1.04662e139 | 1.82058 | ||||||||
\(965\) | −1.87331e138 | −0.310521 | ||||||||
\(966\) | 3.66119e136 | 0.00578344 | ||||||||
\(967\) | −6.69840e138 | −1.00842 | −0.504209 | − | 0.863582i | \(-0.668216\pi\) | ||||
−0.504209 | + | 0.863582i | \(0.668216\pi\) | |||||||
\(968\) | −2.82838e137 | −0.0405820 | ||||||||
\(969\) | 1.08512e139 | 1.48395 | ||||||||
\(970\) | 3.18916e137 | 0.0415711 | ||||||||
\(971\) | −4.20821e138 | −0.522882 | −0.261441 | − | 0.965219i | \(-0.584198\pi\) | ||||
−0.261441 | + | 0.965219i | \(0.584198\pi\) | |||||||
\(972\) | −1.36487e138 | −0.161663 | ||||||||
\(973\) | 7.48442e137 | 0.0845106 | ||||||||
\(974\) | −1.78346e137 | −0.0191987 | ||||||||
\(975\) | −4.87321e137 | −0.0500150 | ||||||||
\(976\) | −1.17360e139 | −1.14843 | ||||||||
\(977\) | 1.33674e139 | 1.24724 | 0.623619 | − | 0.781729i | \(-0.285662\pi\) | ||||
0.623619 | + | 0.781729i | \(0.285662\pi\) | |||||||
\(978\) | 5.84158e137 | 0.0519725 | ||||||||
\(979\) | −2.15236e138 | −0.182608 | ||||||||
\(980\) | −1.27728e139 | −1.03341 | ||||||||
\(981\) | 4.90699e137 | 0.0378623 | ||||||||
\(982\) | −4.91477e137 | −0.0361675 | ||||||||
\(983\) | −2.28662e139 | −1.60493 | −0.802463 | − | 0.596702i | \(-0.796477\pi\) | ||||
−0.802463 | + | 0.596702i | \(0.796477\pi\) | |||||||
\(984\) | −9.37587e137 | −0.0627682 | ||||||||
\(985\) | 2.16905e139 | 1.38511 | ||||||||
\(986\) | −9.82687e137 | −0.0598603 | ||||||||
\(987\) | 3.01065e138 | 0.174950 | ||||||||
\(988\) | −1.39662e139 | −0.774249 | ||||||||
\(989\) | −2.76769e138 | −0.146383 | ||||||||
\(990\) | 6.93126e136 | 0.00349764 | ||||||||
\(991\) | −1.20136e138 | −0.0578426 | −0.0289213 | − | 0.999582i | \(-0.509207\pi\) | ||||
−0.0289213 | + | 0.999582i | \(0.509207\pi\) | |||||||
\(992\) | −5.30470e138 | −0.243707 | ||||||||
\(993\) | 1.27351e139 | 0.558295 | ||||||||
\(994\) | 1.08428e137 | 0.00453603 | ||||||||
\(995\) | −1.15623e139 | −0.461605 | ||||||||
\(996\) | 2.49858e139 | 0.951993 | ||||||||
\(997\) | 2.75431e139 | 1.00159 | 0.500793 | − | 0.865567i | \(-0.333042\pi\) | ||||
0.500793 | + | 0.865567i | \(0.333042\pi\) | |||||||
\(998\) | 1.93248e138 | 0.0670725 | ||||||||
\(999\) | 1.26520e139 | 0.419143 |
(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 | 1.94.a.a.1.4 | ✓ | 7 | |
3.2 | odd | 2 | 9.94.a.b.1.4 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.94.a.a.1.4 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.94.a.b.1.4 | 7 | 3.2 | odd | 2 |