Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(74,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.74");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.d (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(30.5533957546\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 3278 x^{18} + 4245491 x^{16} + 2854629536 x^{14} + 1117319469691 x^{12} + 266849787342054 x^{10} + \cdots + 89\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{22}\cdot 5^{26} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 74.8 | ||
Root | \(14.7835i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.74 |
Dual form | 75.9.d.d.74.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.2639 | −1.01649 | −0.508246 | − | 0.861212i | \(-0.669706\pi\) | ||||
−0.508246 | + | 0.861212i | \(0.669706\pi\) | |||||||
\(3\) | 22.8278 | + | 77.7167i | 0.281825 | + | 0.959466i | ||||
\(4\) | 8.51375 | 0.0332569 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −371.269 | − | 1263.98i | −0.286473 | − | 0.975290i | ||||
\(7\) | 569.895i | 0.237357i | 0.992933 | + | 0.118679i | \(0.0378658\pi\) | ||||
−0.992933 | + | 0.118679i | \(0.962134\pi\) | |||||||
\(8\) | 4025.09 | 0.982687 | ||||||||
\(9\) | −5518.78 | + | 3548.20i | −0.841150 | + | 0.540802i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6582.70i | 0.449607i | 0.974404 | + | 0.224804i | \(0.0721741\pi\) | ||||
−0.974404 | + | 0.224804i | \(0.927826\pi\) | |||||||
\(12\) | 194.350 | + | 661.661i | 0.00937260 | + | 0.0319088i | ||||
\(13\) | − | 28214.2i | − | 0.987858i | −0.869502 | − | 0.493929i | \(-0.835560\pi\) | ||
0.869502 | − | 0.493929i | \(-0.164440\pi\) | |||||||
\(14\) | − | 9268.70i | − | 0.241272i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −67643.0 | −1.03215 | ||||||||
\(17\) | −151139. | −1.80960 | −0.904798 | − | 0.425840i | \(-0.859979\pi\) | ||||
−0.904798 | + | 0.425840i | \(0.859979\pi\) | |||||||
\(18\) | 89756.8 | − | 57707.6i | 0.855022 | − | 0.549721i | ||||
\(19\) | −41572.9 | −0.319004 | −0.159502 | − | 0.987198i | \(-0.550989\pi\) | ||||
−0.159502 | + | 0.987198i | \(0.550989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −44290.4 | + | 13009.4i | −0.227736 | + | 0.0668931i | ||||
\(22\) | − | 107060.i | − | 0.457022i | ||||||
\(23\) | 173241. | 0.619071 | 0.309536 | − | 0.950888i | \(-0.399826\pi\) | ||||
0.309536 | + | 0.950888i | \(0.399826\pi\) | |||||||
\(24\) | 91883.9 | + | 312817.i | 0.276945 | + | 0.942855i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 458873.i | 1.00415i | ||||||||
\(27\) | −401737. | − | 347904.i | −0.755938 | − | 0.654643i | ||||
\(28\) | 4851.94i | 0.00789375i | ||||||||
\(29\) | 783419.i | 1.10765i | 0.832634 | + | 0.553824i | \(0.186832\pi\) | ||||
−0.832634 | + | 0.553824i | \(0.813168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −215271. | −0.233098 | −0.116549 | − | 0.993185i | \(-0.537183\pi\) | ||||
−0.116549 | + | 0.993185i | \(0.537183\pi\) | |||||||
\(32\) | 69716.1 | 0.0664864 | ||||||||
\(33\) | −511586. | + | 150269.i | −0.431383 | + | 0.126710i | ||||
\(34\) | 2.45811e6 | 1.83944 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −46985.6 | + | 30208.5i | −0.0279740 | + | 0.0179854i | ||||
\(37\) | − | 2.71385e6i | − | 1.44804i | −0.689781 | − | 0.724018i | \(-0.742293\pi\) | ||
0.689781 | − | 0.724018i | \(-0.257707\pi\) | |||||||
\(38\) | 676137. | 0.324265 | ||||||||
\(39\) | 2.19272e6 | − | 644068.i | 0.947816 | − | 0.278403i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 676092.i | − | 0.239260i | −0.992819 | − | 0.119630i | \(-0.961829\pi\) | ||
0.992819 | − | 0.119630i | \(-0.0381709\pi\) | |||||||
\(42\) | 720333. | − | 211584.i | 0.231492 | − | 0.0679963i | ||||
\(43\) | − | 4.21531e6i | − | 1.23298i | −0.787364 | − | 0.616489i | \(-0.788555\pi\) | ||
0.787364 | − | 0.616489i | \(-0.211445\pi\) | |||||||
\(44\) | 56043.5i | 0.0149525i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.81758e6 | −0.629281 | ||||||||
\(47\) | 8.87092e6 | 1.81793 | 0.908965 | − | 0.416872i | \(-0.136874\pi\) | ||||
0.908965 | + | 0.416872i | \(0.136874\pi\) | |||||||
\(48\) | −1.54414e6 | − | 5.25700e6i | −0.290886 | − | 0.990314i | ||||
\(49\) | 5.44002e6 | 0.943662 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.45018e6 | − | 1.17461e7i | −0.509989 | − | 1.73625i | ||||
\(52\) | − | 240209.i | − | 0.0328531i | ||||||
\(53\) | 6.53406e6 | 0.828094 | 0.414047 | − | 0.910255i | \(-0.364115\pi\) | ||||
0.414047 | + | 0.910255i | \(0.364115\pi\) | |||||||
\(54\) | 6.53379e6 | + | 5.65827e6i | 0.768405 | + | 0.665440i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.29387e6i | 0.233248i | ||||||||
\(57\) | −949019. | − | 3.23091e6i | −0.0899032 | − | 0.306074i | ||||
\(58\) | − | 1.27414e7i | − | 1.12592i | ||||||
\(59\) | − | 1.54958e7i | − | 1.27881i | −0.768871 | − | 0.639403i | \(-0.779181\pi\) | ||
0.768871 | − | 0.639403i | \(-0.220819\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.68344e6 | −0.627152 | −0.313576 | − | 0.949563i | \(-0.601527\pi\) | ||||
−0.313576 | + | 0.949563i | \(0.601527\pi\) | |||||||
\(62\) | 3.50114e6 | 0.236942 | ||||||||
\(63\) | −2.02210e6 | − | 3.14512e6i | −0.128363 | − | 0.199653i | ||||
\(64\) | 1.61828e7 | 0.964568 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.32037e6 | − | 2.44395e6i | 0.438497 | − | 0.128800i | ||||
\(67\) | − | 2.87523e7i | − | 1.42684i | −0.700739 | − | 0.713418i | \(-0.747146\pi\) | ||
0.700739 | − | 0.713418i | \(-0.252854\pi\) | |||||||
\(68\) | −1.28676e6 | −0.0601815 | ||||||||
\(69\) | 3.95472e6 | + | 1.34638e7i | 0.174470 | + | 0.593978i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.73955e7i | 1.47159i | 0.677207 | + | 0.735793i | \(0.263190\pi\) | ||||
−0.677207 | + | 0.735793i | \(0.736810\pi\) | |||||||
\(72\) | −2.22136e7 | + | 1.42818e7i | −0.826587 | + | 0.531439i | ||||
\(73\) | 3.75089e7i | 1.32082i | 0.750907 | + | 0.660408i | \(0.229617\pi\) | ||||
−0.750907 | + | 0.660408i | \(0.770383\pi\) | |||||||
\(74\) | 4.41378e7i | 1.47192i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −353942. | −0.0106091 | ||||||||
\(77\) | −3.75145e6 | −0.106718 | ||||||||
\(78\) | −3.56621e7 | + | 1.04751e7i | −0.963448 | + | 0.282994i | ||||
\(79\) | −4.22725e7 | −1.08530 | −0.542649 | − | 0.839959i | \(-0.682579\pi\) | ||||
−0.542649 | + | 0.839959i | \(0.682579\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.78672e7 | − | 3.91635e7i | 0.415066 | − | 0.909791i | ||||
\(82\) | 1.09959e7i | 0.243206i | ||||||||
\(83\) | 7.28474e7 | 1.53498 | 0.767488 | − | 0.641064i | \(-0.221507\pi\) | ||||
0.767488 | + | 0.641064i | \(0.221507\pi\) | |||||||
\(84\) | −377077. | + | 110759.i | −0.00757379 | + | 0.00222465i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.85572e7i | 1.25331i | ||||||||
\(87\) | −6.08847e7 | + | 1.78837e7i | −1.06275 | + | 0.312163i | ||||
\(88\) | 2.64959e7i | 0.441823i | ||||||||
\(89\) | − | 5.99236e7i | − | 0.955077i | −0.878611 | − | 0.477538i | \(-0.841529\pi\) | ||
0.878611 | − | 0.477538i | \(-0.158471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.60791e7 | 0.234475 | ||||||||
\(92\) | 1.47494e6 | 0.0205884 | ||||||||
\(93\) | −4.91416e6 | − | 1.67302e7i | −0.0656928 | − | 0.223650i | ||||
\(94\) | −1.44276e8 | −1.84791 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.59146e6 | + | 5.41811e6i | 0.0187375 | + | 0.0637915i | ||||
\(97\) | 1.15177e7i | 0.130100i | 0.997882 | + | 0.0650500i | \(0.0207207\pi\) | ||||
−0.997882 | + | 0.0650500i | \(0.979279\pi\) | |||||||
\(98\) | −8.84758e7 | −0.959225 | ||||||||
\(99\) | −2.33568e7 | − | 3.63285e7i | −0.243149 | − | 0.378187i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 9.81566e7i | − | 0.943266i | −0.881795 | − | 0.471633i | \(-0.843665\pi\) | ||
0.881795 | − | 0.471633i | \(-0.156335\pi\) | |||||||
\(102\) | 5.61133e7 | + | 1.91036e8i | 0.518400 | + | 1.76488i | ||||
\(103\) | 1.66920e7i | 0.148306i | 0.997247 | + | 0.0741529i | \(0.0236253\pi\) | ||||
−0.997247 | + | 0.0741529i | \(0.976375\pi\) | |||||||
\(104\) | − | 1.13565e8i | − | 0.970755i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.06269e8 | −0.841751 | ||||||||
\(107\) | 4.28172e7 | 0.326651 | 0.163325 | − | 0.986572i | \(-0.447778\pi\) | ||||
0.163325 | + | 0.986572i | \(0.447778\pi\) | |||||||
\(108\) | −3.42029e6 | − | 2.96197e6i | −0.0251401 | − | 0.0217714i | ||||
\(109\) | −1.49703e8 | −1.06053 | −0.530266 | − | 0.847831i | \(-0.677908\pi\) | ||||
−0.530266 | + | 0.847831i | \(0.677908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.10912e8 | − | 6.19513e7i | 1.38934 | − | 0.408092i | ||||
\(112\) | − | 3.85494e7i | − | 0.244988i | ||||||
\(113\) | 1.27819e7 | 0.0783937 | 0.0391969 | − | 0.999232i | \(-0.487520\pi\) | ||||
0.0391969 | + | 0.999232i | \(0.487520\pi\) | |||||||
\(114\) | 1.54347e7 | + | 5.25472e7i | 0.0913860 | + | 0.311122i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.66983e6i | 0.0368369i | ||||||||
\(117\) | 1.00110e8 | + | 1.55708e8i | 0.534236 | + | 0.830937i | ||||
\(118\) | 2.52021e8i | 1.29990i | ||||||||
\(119\) | − | 8.61335e7i | − | 0.429521i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.71027e8 | 0.797853 | ||||||||
\(122\) | 1.41226e8 | 0.637495 | ||||||||
\(123\) | 5.25437e7 | − | 1.54337e7i | 0.229562 | − | 0.0674295i | ||||
\(124\) | −1.83276e6 | −0.00775211 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 3.28872e7 | + | 5.11519e7i | 0.130480 | + | 0.202946i | ||||
\(127\) | − | 2.68115e8i | − | 1.03064i | −0.856998 | − | 0.515320i | \(-0.827673\pi\) | ||
0.856998 | − | 0.515320i | \(-0.172327\pi\) | |||||||
\(128\) | −2.81042e8 | −1.04696 | ||||||||
\(129\) | 3.27600e8 | − | 9.62261e7i | 1.18300 | − | 0.347484i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.50651e6i | 0.0186978i | 0.999956 | + | 0.00934892i | \(0.00297590\pi\) | ||||
−0.999956 | + | 0.00934892i | \(0.997024\pi\) | |||||||
\(132\) | −4.35552e6 | + | 1.27935e6i | −0.0143464 | + | 0.00421399i | ||||
\(133\) | − | 2.36922e7i | − | 0.0757179i | ||||||
\(134\) | 4.67624e8i | 1.45037i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.08349e8 | −1.77827 | ||||||||
\(137\) | −5.57045e8 | −1.58128 | −0.790639 | − | 0.612283i | \(-0.790251\pi\) | ||||
−0.790639 | + | 0.612283i | \(0.790251\pi\) | |||||||
\(138\) | −6.43191e7 | − | 2.18973e8i | −0.177347 | − | 0.603774i | ||||
\(139\) | 3.34413e7 | 0.0895827 | 0.0447914 | − | 0.998996i | \(-0.485738\pi\) | ||||
0.0447914 | + | 0.998996i | \(0.485738\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.02504e8 | + | 6.89419e8i | 0.512338 | + | 1.74424i | ||||
\(142\) | − | 6.08195e8i | − | 1.49586i | ||||||
\(143\) | 1.85726e8 | 0.444148 | ||||||||
\(144\) | 3.73307e8 | − | 2.40011e8i | 0.868193 | − | 0.558190i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 6.10040e8i | − | 1.34260i | ||||||
\(147\) | 1.24184e8 | + | 4.22781e8i | 0.265947 | + | 0.905411i | ||||
\(148\) | − | 2.31051e7i | − | 0.0481571i | ||||||
\(149\) | 4.46572e8i | 0.906037i | 0.891501 | + | 0.453019i | \(0.149653\pi\) | ||||
−0.891501 | + | 0.453019i | \(0.850347\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.41495e8 | −0.464515 | −0.232257 | − | 0.972654i | \(-0.574611\pi\) | ||||
−0.232257 | + | 0.972654i | \(0.574611\pi\) | |||||||
\(152\) | −1.67335e8 | −0.313481 | ||||||||
\(153\) | 8.34105e8 | − | 5.36273e8i | 1.52214 | − | 0.978634i | ||||
\(154\) | 6.10130e7 | 0.108478 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.86683e7 | − | 5.48344e6i | 0.0315214 | − | 0.00925880i | ||||
\(157\) | − | 1.12488e9i | − | 1.85143i | −0.378226 | − | 0.925713i | \(-0.623466\pi\) | ||
0.378226 | − | 0.925713i | \(-0.376534\pi\) | |||||||
\(158\) | 6.87514e8 | 1.10320 | ||||||||
\(159\) | 1.49158e8 | + | 5.07806e8i | 0.233377 | + | 0.794528i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.87294e7i | 0.146941i | ||||||||
\(162\) | −2.90590e8 | + | 6.36951e8i | −0.421911 | + | 0.924796i | ||||
\(163\) | − | 1.05083e9i | − | 1.48861i | −0.667838 | − | 0.744307i | \(-0.732780\pi\) | ||
0.667838 | − | 0.744307i | \(-0.267220\pi\) | |||||||
\(164\) | − | 5.75609e6i | − | 0.00795705i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.18478e9 | −1.56029 | ||||||||
\(167\) | 1.52565e8 | 0.196150 | 0.0980751 | − | 0.995179i | \(-0.468731\pi\) | ||||
0.0980751 | + | 0.995179i | \(0.468731\pi\) | |||||||
\(168\) | −1.78272e8 | + | 5.23641e7i | −0.223793 | + | 0.0657350i | ||||
\(169\) | 1.96888e7 | 0.0241364 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.29432e8 | − | 1.47509e8i | 0.268330 | − | 0.172518i | ||||
\(172\) | − | 3.58881e7i | − | 0.0410050i | ||||||
\(173\) | −1.48867e9 | −1.66193 | −0.830967 | − | 0.556321i | \(-0.812212\pi\) | ||||
−0.830967 | + | 0.556321i | \(0.812212\pi\) | |||||||
\(174\) | 9.90222e8 | − | 2.90859e8i | 1.08028 | − | 0.317311i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.45274e8i | − | 0.464063i | ||||||
\(177\) | 1.20428e9 | − | 3.53734e8i | 1.22697 | − | 0.360399i | ||||
\(178\) | 9.74591e8i | 0.970828i | ||||||||
\(179\) | − | 6.73543e8i | − | 0.656074i | −0.944665 | − | 0.328037i | \(-0.893613\pi\) | ||
0.944665 | − | 0.328037i | \(-0.106387\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.31938e8 | 0.868306 | 0.434153 | − | 0.900839i | \(-0.357048\pi\) | ||||
0.434153 | + | 0.900839i | \(0.357048\pi\) | |||||||
\(182\) | −2.61509e8 | −0.238342 | ||||||||
\(183\) | −1.98224e8 | − | 6.74849e8i | −0.176747 | − | 0.601731i | ||||
\(184\) | 6.97312e8 | 0.608353 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.99233e7 | + | 2.72097e8i | 0.0667762 | + | 0.227338i | ||||
\(187\) | − | 9.94905e8i | − | 0.813608i | ||||||
\(188\) | 7.55248e7 | 0.0604586 | ||||||||
\(189\) | 1.98269e8 | − | 2.28947e8i | 0.155384 | − | 0.179427i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.44104e7i | − | 0.0483974i | −0.999707 | − | 0.0241987i | \(-0.992297\pi\) | ||
0.999707 | − | 0.0241987i | \(-0.00770344\pi\) | |||||||
\(192\) | 3.69417e8 | + | 1.25767e9i | 0.271839 | + | 0.925470i | ||||
\(193\) | 9.15124e8i | 0.659554i | 0.944059 | + | 0.329777i | \(0.106974\pi\) | ||||
−0.944059 | + | 0.329777i | \(0.893026\pi\) | |||||||
\(194\) | − | 1.87322e8i | − | 0.132246i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.63150e7 | 0.0313832 | ||||||||
\(197\) | 1.99042e9 | 1.32154 | 0.660769 | − | 0.750589i | \(-0.270230\pi\) | ||||
0.660769 | + | 0.750589i | \(0.270230\pi\) | |||||||
\(198\) | 3.79872e8 | + | 5.90842e8i | 0.247159 | + | 0.384424i | ||||
\(199\) | −2.33793e9 | −1.49080 | −0.745400 | − | 0.666618i | \(-0.767741\pi\) | ||||
−0.745400 | + | 0.666618i | \(0.767741\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.23454e9 | − | 6.56352e8i | 1.36900 | − | 0.402117i | ||||
\(202\) | 1.59641e9i | 0.958823i | ||||||||
\(203\) | −4.46466e8 | −0.262908 | ||||||||
\(204\) | −2.93740e7 | − | 1.00003e8i | −0.0169606 | − | 0.0577421i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 2.71476e8i | − | 0.150752i | ||||||
\(207\) | −9.56082e8 | + | 6.14696e8i | −0.520732 | + | 0.334795i | ||||
\(208\) | 1.90850e9i | 1.01962i | ||||||||
\(209\) | − | 2.73662e8i | − | 0.143427i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.72705e7 | −0.0188034 | −0.00940168 | − | 0.999956i | \(-0.502993\pi\) | ||||
−0.00940168 | + | 0.999956i | \(0.502993\pi\) | |||||||
\(212\) | 5.56294e7 | 0.0275398 | ||||||||
\(213\) | −2.90625e9 | + | 8.53656e8i | −1.41194 | + | 0.414729i | ||||
\(214\) | −6.96374e8 | −0.332038 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.61702e9 | − | 1.40034e9i | −0.742851 | − | 0.643309i | ||||
\(217\) | − | 1.22682e8i | − | 0.0553275i | ||||||
\(218\) | 2.43475e9 | 1.07802 | ||||||||
\(219\) | −2.91507e9 | + | 8.56245e8i | −1.26728 | + | 0.372239i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.26428e9i | 1.78762i | ||||||||
\(222\) | −3.43024e9 | + | 1.00757e9i | −1.41225 | + | 0.414823i | ||||
\(223\) | − | 2.51046e9i | − | 1.01516i | −0.861606 | − | 0.507578i | \(-0.830541\pi\) | ||
0.861606 | − | 0.507578i | \(-0.169459\pi\) | |||||||
\(224\) | 3.97308e7i | 0.0157810i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.07883e8 | −0.0796866 | ||||||||
\(227\) | −1.11767e9 | −0.420930 | −0.210465 | − | 0.977601i | \(-0.567498\pi\) | ||||
−0.210465 | + | 0.977601i | \(0.567498\pi\) | |||||||
\(228\) | −8.07971e6 | − | 2.75072e7i | −0.00298990 | − | 0.0101790i | ||||
\(229\) | −3.29155e9 | −1.19690 | −0.598450 | − | 0.801160i | \(-0.704217\pi\) | ||||
−0.598450 | + | 0.801160i | \(0.704217\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.56372e7 | − | 2.91550e8i | −0.0300756 | − | 0.102392i | ||||
\(232\) | 3.15333e9i | 1.08847i | ||||||||
\(233\) | 1.74654e9 | 0.592591 | 0.296296 | − | 0.955096i | \(-0.404249\pi\) | ||||
0.296296 | + | 0.955096i | \(0.404249\pi\) | |||||||
\(234\) | −1.62817e9 | − | 2.53242e9i | −0.543047 | − | 0.844641i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1.31927e8i | − | 0.0425291i | ||||||
\(237\) | −9.64988e8 | − | 3.28528e9i | −0.305864 | − | 1.04131i | ||||
\(238\) | 1.40086e9i | 0.436605i | ||||||||
\(239\) | − | 3.20404e9i | − | 0.981988i | −0.871163 | − | 0.490994i | \(-0.836634\pi\) | ||
0.871163 | − | 0.490994i | \(-0.163366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.32540e9 | 0.689334 | 0.344667 | − | 0.938725i | \(-0.387992\pi\) | ||||
0.344667 | + | 0.938725i | \(0.387992\pi\) | |||||||
\(242\) | −2.78156e9 | −0.811012 | ||||||||
\(243\) | 3.45153e9 | + | 4.94565e8i | 0.989890 | + | 0.141840i | ||||
\(244\) | −7.39287e7 | −0.0208571 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −8.54564e8 | + | 2.51012e8i | −0.233348 | + | 0.0685415i | ||||
\(247\) | 1.17295e9i | 0.315131i | ||||||||
\(248\) | −8.66484e8 | −0.229062 | ||||||||
\(249\) | 1.66294e9 | + | 5.66146e9i | 0.432594 | + | 1.47276i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.38503e9i | 0.852840i | 0.904525 | + | 0.426420i | \(0.140225\pi\) | ||||
−0.904525 | + | 0.426420i | \(0.859775\pi\) | |||||||
\(252\) | −1.72157e7 | − | 2.67768e7i | −0.00426896 | − | 0.00663983i | ||||
\(253\) | 1.14040e9i | 0.278339i | ||||||||
\(254\) | 4.36059e9i | 1.04764i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.28043e8 | 0.0996614 | ||||||||
\(257\) | −9.71066e8 | −0.222595 | −0.111298 | − | 0.993787i | \(-0.535501\pi\) | ||||
−0.111298 | + | 0.993787i | \(0.535501\pi\) | |||||||
\(258\) | −5.32804e9 | + | 1.56501e9i | −1.20251 | + | 0.353214i | ||||
\(259\) | 1.54661e9 | 0.343702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.77973e9 | − | 4.32352e9i | −0.599019 | − | 0.931698i | ||||
\(262\) | − | 8.95573e7i | − | 0.0190062i | ||||||
\(263\) | −2.06605e8 | −0.0431835 | −0.0215918 | − | 0.999767i | \(-0.506873\pi\) | ||||
−0.0215918 | + | 0.999767i | \(0.506873\pi\) | |||||||
\(264\) | −2.05918e9 | + | 6.04844e8i | −0.423914 | + | 0.124517i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.85327e8i | 0.0769667i | ||||||||
\(267\) | 4.65707e9 | − | 1.36792e9i | 0.916363 | − | 0.269164i | ||||
\(268\) | − | 2.44790e8i | − | 0.0474520i | ||||||
\(269\) | − | 3.12793e9i | − | 0.597376i | −0.954351 | − | 0.298688i | \(-0.903451\pi\) | ||
0.954351 | − | 0.298688i | \(-0.0965489\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.61051e9 | 0.854814 | 0.427407 | − | 0.904059i | \(-0.359427\pi\) | ||||
0.427407 | + | 0.904059i | \(0.359427\pi\) | |||||||
\(272\) | 1.02235e10 | 1.86778 | ||||||||
\(273\) | 3.67051e8 | + | 1.24962e9i | 0.0660809 | + | 0.224971i | ||||
\(274\) | 9.05972e9 | 1.60736 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.36695e7 | + | 1.14627e8i | 0.00580231 | + | 0.0197538i | ||||
\(277\) | 1.77445e9i | 0.301401i | 0.988579 | + | 0.150700i | \(0.0481529\pi\) | ||||
−0.988579 | + | 0.150700i | \(0.951847\pi\) | |||||||
\(278\) | −5.43886e8 | −0.0910602 | ||||||||
\(279\) | 1.18803e9 | − | 7.63825e8i | 0.196070 | − | 0.126060i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.80582e7i | 0.0125197i | 0.999980 | + | 0.00625984i | \(0.00199258\pi\) | ||||
−0.999980 | + | 0.00625984i | \(0.998007\pi\) | |||||||
\(282\) | −3.29349e9 | − | 1.12126e10i | −0.520787 | − | 1.77301i | ||||
\(283\) | − | 8.12145e9i | − | 1.26616i | −0.774088 | − | 0.633079i | \(-0.781791\pi\) | ||
0.774088 | − | 0.633079i | \(-0.218209\pi\) | |||||||
\(284\) | 3.18376e8i | 0.0489403i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.02062e9 | −0.451473 | ||||||||
\(287\) | 3.85301e8 | 0.0567902 | ||||||||
\(288\) | −3.84748e8 | + | 2.47367e8i | −0.0559250 | + | 0.0359560i | ||||
\(289\) | 1.58673e10 | 2.27464 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.95115e8 | + | 2.62923e8i | −0.124826 | + | 0.0366654i | ||||
\(292\) | 3.19341e8i | 0.0439262i | ||||||||
\(293\) | −2.52625e9 | −0.342773 | −0.171386 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171386 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(294\) | −2.01971e9 | − | 6.87605e9i | −0.270333 | − | 0.920344i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 1.09235e10i | − | 1.42297i | ||||||
\(297\) | 2.29015e9 | − | 2.64451e9i | 0.294332 | − | 0.339875i | ||||
\(298\) | − | 7.26299e9i | − | 0.920980i | ||||||
\(299\) | − | 4.88787e9i | − | 0.611554i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.40228e9 | 0.292656 | ||||||||
\(302\) | 3.92764e9 | 0.472176 | ||||||||
\(303\) | 7.62841e9 | − | 2.24070e9i | 0.905032 | − | 0.265836i | ||||
\(304\) | 2.81212e9 | 0.329260 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.35658e10 | + | 8.72188e9i | −1.54725 | + | 0.994774i | ||||
\(307\) | 1.03150e10i | 1.16123i | 0.814180 | + | 0.580613i | \(0.197187\pi\) | ||||
−0.814180 | + | 0.580613i | \(0.802813\pi\) | |||||||
\(308\) | −3.19389e7 | −0.00354909 | ||||||||
\(309\) | −1.29724e9 | + | 3.81040e8i | −0.142294 | + | 0.0417962i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.72354e10i | − | 1.84239i | −0.389106 | − | 0.921193i | \(-0.627216\pi\) | ||
0.389106 | − | 0.921193i | \(-0.372784\pi\) | |||||||
\(312\) | 8.82587e9 | − | 2.59243e9i | 0.931407 | − | 0.273583i | ||||
\(313\) | − | 5.42800e9i | − | 0.565539i | −0.959188 | − | 0.282770i | \(-0.908747\pi\) | ||
0.959188 | − | 0.282770i | \(-0.0912532\pi\) | |||||||
\(314\) | 1.82949e10i | 1.88196i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.59897e8 | −0.0360936 | ||||||||
\(317\) | −1.16981e10 | −1.15845 | −0.579226 | − | 0.815167i | \(-0.696645\pi\) | ||||
−0.579226 | + | 0.815167i | \(0.696645\pi\) | |||||||
\(318\) | −2.42589e9 | − | 8.25889e9i | −0.237226 | − | 0.807632i | ||||
\(319\) | −5.15701e9 | −0.498007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.77423e8 | + | 3.32761e9i | 0.0920582 | + | 0.313410i | ||||
\(322\) | − | 1.60572e9i | − | 0.149364i | ||||||
\(323\) | 6.28331e9 | 0.577269 | ||||||||
\(324\) | 1.52117e8 | − | 3.33429e8i | 0.0138038 | − | 0.0302568i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.70906e10i | 1.51316i | ||||||||
\(327\) | −3.41738e9 | − | 1.16344e10i | −0.298884 | − | 1.01754i | ||||
\(328\) | − | 2.72133e9i | − | 0.235118i | ||||||
\(329\) | 5.05549e9i | 0.431499i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.03632e9 | −0.502875 | −0.251438 | − | 0.967873i | \(-0.580903\pi\) | ||||
−0.251438 | + | 0.967873i | \(0.580903\pi\) | |||||||
\(332\) | 6.20205e8 | 0.0510485 | ||||||||
\(333\) | 9.62930e9 | + | 1.49772e10i | 0.783101 | + | 1.21801i | ||||
\(334\) | −2.48130e9 | −0.199385 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.99593e9 | − | 8.79998e8i | 0.235058 | − | 0.0690438i | ||||
\(337\) | 1.35475e9i | 0.105037i | 0.998620 | + | 0.0525183i | \(0.0167248\pi\) | ||||
−0.998620 | + | 0.0525183i | \(0.983275\pi\) | |||||||
\(338\) | −3.20216e8 | −0.0245345 | ||||||||
\(339\) | 2.91782e8 | + | 9.93367e8i | 0.0220933 | + | 0.0752161i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.41706e9i | − | 0.104803i | ||||||
\(342\) | −3.73146e9 | + | 2.39907e9i | −0.272756 | + | 0.175363i | ||||
\(343\) | 6.38557e9i | 0.461342i | ||||||||
\(344\) | − | 1.69670e10i | − | 1.21163i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.42115e10 | 1.68934 | ||||||||
\(347\) | −2.47345e10 | −1.70602 | −0.853012 | − | 0.521891i | \(-0.825227\pi\) | ||||
−0.853012 | + | 0.521891i | \(0.825227\pi\) | |||||||
\(348\) | −5.18358e8 | + | 1.52258e8i | −0.0353437 | + | 0.0103815i | ||||
\(349\) | 9.08306e9 | 0.612253 | 0.306126 | − | 0.951991i | \(-0.400967\pi\) | ||||
0.306126 | + | 0.951991i | \(0.400967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.81584e9 | + | 1.13347e10i | −0.646694 | + | 0.746760i | ||||
\(352\) | 4.58920e8i | 0.0298928i | ||||||||
\(353\) | −1.66294e10 | −1.07097 | −0.535485 | − | 0.844545i | \(-0.679871\pi\) | ||||
−0.535485 | + | 0.844545i | \(0.679871\pi\) | |||||||
\(354\) | −1.95863e10 | + | 5.75309e9i | −1.24721 | + | 0.366343i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 5.10175e8i | − | 0.0317628i | ||||||
\(357\) | 6.69401e9 | − | 1.96624e9i | 0.412111 | − | 0.121050i | ||||
\(358\) | 1.09544e10i | 0.666894i | ||||||||
\(359\) | 6.51832e9i | 0.392426i | 0.980561 | + | 0.196213i | \(0.0628644\pi\) | ||||
−0.980561 | + | 0.196213i | \(0.937136\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.52553e10 | −0.898236 | ||||||||
\(362\) | −1.51569e10 | −0.882626 | ||||||||
\(363\) | 3.90417e9 | + | 1.32917e10i | 0.224855 | + | 0.765513i | ||||
\(364\) | 1.36894e8 | 0.00779791 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.22389e9 | + | 1.09757e10i | 0.179662 | + | 0.611655i | ||||
\(367\) | 1.72068e10i | 0.948498i | 0.880391 | + | 0.474249i | \(0.157280\pi\) | ||||
−0.880391 | + | 0.474249i | \(0.842720\pi\) | |||||||
\(368\) | −1.17186e10 | −0.638975 | ||||||||
\(369\) | 2.39891e9 | + | 3.73121e9i | 0.129393 | + | 0.201254i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.72373e9i | 0.196554i | ||||||||
\(372\) | −4.18380e7 | − | 1.42436e8i | −0.00218474 | − | 0.00743789i | ||||
\(373\) | 1.47580e10i | 0.762418i | 0.924489 | + | 0.381209i | \(0.124492\pi\) | ||||
−0.924489 | + | 0.381209i | \(0.875508\pi\) | |||||||
\(374\) | 1.61810e10i | 0.827026i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.57062e10 | 1.78646 | ||||||||
\(377\) | 2.21035e10 | 1.09420 | ||||||||
\(378\) | −3.22462e9 | + | 3.72357e9i | −0.157947 | + | 0.182387i | ||||
\(379\) | −3.28781e10 | −1.59349 | −0.796746 | − | 0.604315i | \(-0.793447\pi\) | ||||
−0.796746 | + | 0.604315i | \(0.793447\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.08370e10 | − | 6.12048e9i | 0.988863 | − | 0.290460i | ||||
\(382\) | 1.04756e9i | 0.0491956i | ||||||||
\(383\) | −1.11696e10 | −0.519089 | −0.259544 | − | 0.965731i | \(-0.583572\pi\) | ||||
−0.259544 | + | 0.965731i | \(0.583572\pi\) | |||||||
\(384\) | −6.41557e9 | − | 2.18417e10i | −0.295060 | − | 1.00452i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.48835e10i | − | 0.670432i | ||||||
\(387\) | 1.49568e10 | + | 2.32634e10i | 0.666797 | + | 1.03712i | ||||
\(388\) | 9.80585e7i | 0.00432672i | ||||||||
\(389\) | − | 3.14195e10i | − | 1.37215i | −0.727533 | − | 0.686073i | \(-0.759333\pi\) | ||
0.727533 | − | 0.686073i | \(-0.240667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.61836e10 | −1.12027 | ||||||||
\(392\) | 2.18966e10 | 0.927324 | ||||||||
\(393\) | −4.27948e8 | + | 1.25702e8i | −0.0179399 | + | 0.00526951i | ||||
\(394\) | −3.23719e10 | −1.34333 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.98854e8 | − | 3.09292e8i | −0.00808636 | − | 0.0125773i | ||||
\(397\) | 8.73430e9i | 0.351614i | 0.984425 | + | 0.175807i | \(0.0562534\pi\) | ||||
−0.984425 | + | 0.175807i | \(0.943747\pi\) | |||||||
\(398\) | 3.80238e10 | 1.51539 | ||||||||
\(399\) | 1.84128e9 | − | 5.40841e8i | 0.0726488 | − | 0.0213392i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.27867e9i | − | 0.0494516i | −0.999694 | − | 0.0247258i | \(-0.992129\pi\) | ||
0.999694 | − | 0.0247258i | \(-0.00787127\pi\) | |||||||
\(402\) | −3.63422e10 | + | 1.06748e10i | −1.39158 | + | 0.408749i | ||||
\(403\) | 6.07370e9i | 0.230268i | ||||||||
\(404\) | − | 8.35682e8i | − | 0.0313701i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.26127e9 | 0.267244 | ||||||||
\(407\) | 1.78645e10 | 0.651047 | ||||||||
\(408\) | −1.38873e10 | − | 4.72789e10i | −0.501160 | − | 1.70619i | ||||
\(409\) | −1.02810e10 | −0.367401 | −0.183701 | − | 0.982982i | \(-0.558808\pi\) | ||||
−0.183701 | + | 0.982982i | \(0.558808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.27161e10 | − | 4.32917e10i | −0.445643 | − | 1.51718i | ||||
\(412\) | 1.42111e8i | 0.00493219i | ||||||||
\(413\) | 8.83095e9 | 0.303534 | ||||||||
\(414\) | 1.55496e10 | − | 9.99734e9i | 0.529320 | − | 0.340317i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 1.96698e9i | − | 0.0656792i | ||||||
\(417\) | 7.63392e8 | + | 2.59895e9i | 0.0252466 | + | 0.0859516i | ||||
\(418\) | 4.45081e9i | 0.145792i | ||||||||
\(419\) | − | 3.60565e10i | − | 1.16984i | −0.811090 | − | 0.584922i | \(-0.801125\pi\) | ||
0.811090 | − | 0.584922i | \(-0.198875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.63986e10 | −1.15866 | −0.579331 | − | 0.815092i | \(-0.696686\pi\) | ||||
−0.579331 | + | 0.815092i | \(0.696686\pi\) | |||||||
\(422\) | 6.06163e8 | 0.0191135 | ||||||||
\(423\) | −4.89567e10 | + | 3.14758e10i | −1.52915 | + | 0.983141i | ||||
\(424\) | 2.63002e10 | 0.813757 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.72670e10 | − | 1.38838e10i | 1.43522 | − | 0.421569i | ||||
\(427\) | − | 4.94865e9i | − | 0.148859i | ||||||
\(428\) | 3.64535e8 | 0.0108634 | ||||||||
\(429\) | 4.23971e9 | + | 1.44340e10i | 0.125172 | + | 0.426145i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.03555e10i | 0.879686i | 0.898075 | + | 0.439843i | \(0.144966\pi\) | ||||
−0.898075 | + | 0.439843i | \(0.855034\pi\) | |||||||
\(432\) | 2.71747e10 | + | 2.35333e10i | 0.780242 | + | 0.675690i | ||||
\(433\) | − | 3.45811e10i | − | 0.983757i | −0.870664 | − | 0.491878i | \(-0.836310\pi\) | ||
0.870664 | − | 0.491878i | \(-0.163690\pi\) | |||||||
\(434\) | 1.99528e9i | 0.0562400i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.27453e9 | −0.0352700 | ||||||||
\(437\) | −7.20216e9 | −0.197486 | ||||||||
\(438\) | 4.74103e10 | − | 1.39259e10i | 1.28818 | − | 0.378378i | ||||
\(439\) | 1.76997e9 | 0.0476549 | 0.0238275 | − | 0.999716i | \(-0.492415\pi\) | ||||
0.0238275 | + | 0.999716i | \(0.492415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00223e10 | + | 1.93023e10i | −0.793761 | + | 0.510334i | ||||
\(442\) | − | 6.93537e10i | − | 1.81711i | ||||||
\(443\) | −3.19676e10 | −0.830033 | −0.415017 | − | 0.909814i | \(-0.636224\pi\) | ||||
−0.415017 | + | 0.909814i | \(0.636224\pi\) | |||||||
\(444\) | 1.79565e9 | − | 5.27438e8i | 0.0462051 | − | 0.0135719i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.08297e10i | 1.03190i | ||||||||
\(447\) | −3.47061e10 | + | 1.01942e10i | −0.869312 | + | 0.255344i | ||||
\(448\) | 9.22247e9i | 0.228947i | ||||||||
\(449\) | 8.00746e10i | 1.97020i | 0.171994 | + | 0.985098i | \(0.444979\pi\) | ||||
−0.171994 | + | 0.985098i | \(0.555021\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.45051e9 | 0.107573 | ||||||||
\(452\) | 1.08822e8 | 0.00260713 | ||||||||
\(453\) | −5.51279e9 | − | 1.87682e10i | −0.130912 | − | 0.445686i | ||||
\(454\) | 1.81777e10 | 0.427873 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.81988e9 | − | 1.30047e10i | −0.0883468 | − | 0.300775i | ||||
\(457\) | − | 5.45219e10i | − | 1.24999i | −0.780629 | − | 0.624994i | \(-0.785101\pi\) | ||
0.780629 | − | 0.624994i | \(-0.214899\pi\) | |||||||
\(458\) | 5.35333e10 | 1.21664 | ||||||||
\(459\) | 6.07182e10 | + | 5.25820e10i | 1.36794 | + | 1.18464i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.66539e8i | − | 0.00811552i | −0.999992 | − | 0.00405776i | \(-0.998708\pi\) | ||
0.999992 | − | 0.00405776i | \(-0.00129163\pi\) | |||||||
\(462\) | 1.39279e9 | + | 4.74174e9i | 0.0305716 | + | 0.104081i | ||||
\(463\) | 3.22822e10i | 0.702488i | 0.936284 | + | 0.351244i | \(0.114241\pi\) | ||||
−0.936284 | + | 0.351244i | \(0.885759\pi\) | |||||||
\(464\) | − | 5.29928e10i | − | 1.14326i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.84055e10 | −0.602365 | ||||||||
\(467\) | 2.11777e10 | 0.445258 | 0.222629 | − | 0.974903i | \(-0.428536\pi\) | ||||
0.222629 | + | 0.974903i | \(0.428536\pi\) | |||||||
\(468\) | 8.52310e8 | + | 1.32566e9i | 0.0177670 | + | 0.0276343i | ||||
\(469\) | 1.63858e10 | 0.338670 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.74218e10 | − | 2.56785e10i | 1.77638 | − | 0.521778i | ||||
\(472\) | − | 6.23718e10i | − | 1.25667i | ||||||
\(473\) | 2.77481e10 | 0.554356 | ||||||||
\(474\) | 1.56944e10 | + | 5.34314e10i | 0.310908 | + | 1.05848i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 7.33319e8i | − | 0.0142845i | ||||||
\(477\) | −3.60601e10 | + | 2.31842e10i | −0.696551 | + | 0.447835i | ||||
\(478\) | 5.21101e10i | 0.998184i | ||||||||
\(479\) | 4.69016e10i | 0.890934i | 0.895298 | + | 0.445467i | \(0.146962\pi\) | ||||
−0.895298 | + | 0.445467i | \(0.853038\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.65692e10 | −1.43045 | ||||||||
\(482\) | −3.78201e10 | −0.700703 | ||||||||
\(483\) | −7.67293e9 | + | 2.25377e9i | −0.140985 | + | 0.0414116i | ||||
\(484\) | 1.45608e9 | 0.0265341 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5.61353e10 | − | 8.04354e9i | −1.00622 | − | 0.144179i | ||||
\(487\) | − | 1.34767e10i | − | 0.239590i | −0.992799 | − | 0.119795i | \(-0.961776\pi\) | ||
0.992799 | − | 0.119795i | \(-0.0382237\pi\) | |||||||
\(488\) | −3.49516e10 | −0.616294 | ||||||||
\(489\) | 8.16671e10 | − | 2.39881e10i | 1.42827 | − | 0.419528i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.27160e10i | 1.42319i | 0.702589 | + | 0.711596i | \(0.252027\pi\) | ||||
−0.702589 | + | 0.711596i | \(0.747973\pi\) | |||||||
\(492\) | 4.47344e8 | − | 1.31399e8i | 0.00763451 | − | 0.00224249i | ||||
\(493\) | − | 1.18405e11i | − | 2.00440i | ||||||
\(494\) | − | 1.90767e10i | − | 0.320328i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.45616e10 | 0.240592 | ||||||||
\(497\) | −2.13115e10 | −0.349291 | ||||||||
\(498\) | −2.70459e10 | − | 9.20773e10i | −0.439728 | − | 1.49705i | ||||
\(499\) | −1.96950e10 | −0.317653 | −0.158827 | − | 0.987307i | \(-0.550771\pi\) | ||||
−0.158827 | + | 0.987307i | \(0.550771\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.48272e9 | + | 1.18569e10i | 0.0552800 | + | 0.188199i | ||||
\(502\) | − | 5.50537e10i | − | 0.866906i | ||||||
\(503\) | 5.14640e10 | 0.803955 | 0.401978 | − | 0.915649i | \(-0.368323\pi\) | ||||
0.401978 | + | 0.915649i | \(0.368323\pi\) | |||||||
\(504\) | −8.13914e9 | − | 1.26594e10i | −0.126141 | − | 0.196196i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.85473e10i | − | 0.282929i | ||||||
\(507\) | 4.49452e8 | + | 1.53015e9i | 0.00680223 | + | 0.0231580i | ||||
\(508\) | − | 2.28267e9i | − | 0.0342758i | ||||||
\(509\) | − | 7.84617e8i | − | 0.0116893i | −0.999983 | − | 0.00584463i | \(-0.998140\pi\) | ||
0.999983 | − | 0.00584463i | \(-0.00186041\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.13761e10 | −0.313505 | ||||||||
\(512\) | 6.49851e10 | 0.945657 | ||||||||
\(513\) | 1.67014e10 | + | 1.44634e10i | 0.241147 | + | 0.208834i | ||||
\(514\) | 1.57933e10 | 0.226267 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.78910e9 | − | 8.19246e8i | 0.0393429 | − | 0.0115562i | ||||
\(517\) | 5.83946e10i | 0.817355i | ||||||||
\(518\) | −2.51539e10 | −0.349370 | ||||||||
\(519\) | −3.39830e10 | − | 1.15695e11i | −0.468374 | − | 1.59457i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.39001e11i | − | 1.88654i | −0.332024 | − | 0.943271i | \(-0.607731\pi\) | ||
0.332024 | − | 0.943271i | \(-0.392269\pi\) | |||||||
\(522\) | 4.52092e10 | + | 7.03172e10i | 0.608898 | + | 0.947064i | ||||
\(523\) | 9.91022e9i | 0.132457i | 0.997804 | + | 0.0662287i | \(0.0210967\pi\) | ||||
−0.997804 | + | 0.0662287i | \(0.978903\pi\) | |||||||
\(524\) | 4.68811e7i | 0.000621831i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.36020e9 | 0.0438957 | ||||||||
\(527\) | 3.25359e10 | 0.421814 | ||||||||
\(528\) | 3.46052e10 | − | 1.01646e10i | 0.445252 | − | 0.130784i | ||||
\(529\) | −4.82984e10 | −0.616751 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.49821e10 | + | 8.55178e10i | 0.691582 | + | 1.07567i | ||||
\(532\) | − | 2.01710e8i | − | 0.00251814i | ||||||
\(533\) | −1.90754e10 | −0.236355 | ||||||||
\(534\) | −7.57420e10 | + | 2.22478e10i | −0.931477 | + | 0.273603i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 1.15731e11i | − | 1.40213i | ||||||
\(537\) | 5.23455e10 | − | 1.53755e10i | 0.629481 | − | 0.184898i | ||||
\(538\) | 5.08722e10i | 0.607228i | ||||||||
\(539\) | 3.58100e10i | 0.424277i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.74155e10 | −0.320042 | −0.160021 | − | 0.987114i | \(-0.551156\pi\) | ||||
−0.160021 | + | 0.987114i | \(0.551156\pi\) | |||||||
\(542\) | −7.49848e10 | −0.868912 | ||||||||
\(543\) | 2.12741e10 | + | 7.24272e10i | 0.244710 | + | 0.833110i | ||||
\(544\) | −1.05368e10 | −0.120314 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −5.96967e9 | − | 2.03236e10i | −0.0671707 | − | 0.228681i | ||||
\(547\) | 8.62303e10i | 0.963187i | 0.876395 | + | 0.481594i | \(0.159942\pi\) | ||||
−0.876395 | + | 0.481594i | \(0.840058\pi\) | |||||||
\(548\) | −4.74255e9 | −0.0525883 | ||||||||
\(549\) | 4.79220e10 | − | 3.08106e10i | 0.527528 | − | 0.339165i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.25690e10i | − | 0.353344i | ||||||
\(552\) | 1.59181e10 | + | 5.41928e10i | 0.171449 | + | 0.583694i | ||||
\(553\) | − | 2.40909e10i | − | 0.257603i | ||||||
\(554\) | − | 2.88594e10i | − | 0.306372i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.84711e8 | 0.00297924 | ||||||||
\(557\) | 6.87189e10 | 0.713929 | 0.356965 | − | 0.934118i | \(-0.383812\pi\) | ||||
0.356965 | + | 0.934118i | \(0.383812\pi\) | |||||||
\(558\) | −1.93220e10 | + | 1.24228e10i | −0.199304 | + | 0.128139i | ||||
\(559\) | −1.18932e11 | −1.21801 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.73208e10 | − | 2.27115e10i | 0.780629 | − | 0.229295i | ||||
\(562\) | − | 1.26953e9i | − | 0.0127262i | ||||||
\(563\) | −9.04024e10 | −0.899801 | −0.449901 | − | 0.893079i | \(-0.648541\pi\) | ||||
−0.449901 | + | 0.893079i | \(0.648541\pi\) | |||||||
\(564\) | 1.72407e9 | + | 5.86954e9i | 0.0170387 | + | 0.0580080i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.32086e11i | 1.28704i | ||||||||
\(567\) | 2.23191e10 | + | 1.01824e10i | 0.215946 | + | 0.0985188i | ||||
\(568\) | 1.50520e11i | 1.44611i | ||||||||
\(569\) | − | 1.77922e11i | − | 1.69739i | −0.528886 | − | 0.848693i | \(-0.677390\pi\) | ||
0.528886 | − | 0.848693i | \(-0.322610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.96988e11 | 1.85309 | 0.926543 | − | 0.376189i | \(-0.122766\pi\) | ||||
0.926543 | + | 0.376189i | \(0.122766\pi\) | |||||||
\(572\) | 1.58122e9 | 0.0147710 | ||||||||
\(573\) | 5.00576e9 | − | 1.47035e9i | 0.0464357 | − | 0.0136396i | ||||
\(574\) | −6.26650e9 | −0.0577268 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −8.93092e10 | + | 5.74197e10i | −0.811346 | + | 0.521641i | ||||
\(577\) | − | 2.39252e10i | − | 0.215850i | −0.994159 | − | 0.107925i | \(-0.965579\pi\) | ||
0.994159 | − | 0.107925i | \(-0.0344206\pi\) | |||||||
\(578\) | −2.58064e11 | −2.31215 | ||||||||
\(579\) | −7.11204e10 | + | 2.08903e10i | −0.632820 | + | 0.185879i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.15153e10i | 0.364337i | ||||||||
\(582\) | 1.45580e10 | − | 4.27614e9i | 0.126885 | − | 0.0372701i | ||||
\(583\) | 4.30118e10i | 0.372317i | ||||||||
\(584\) | 1.50976e11i | 1.29795i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.10866e10 | 0.348426 | ||||||||
\(587\) | −2.02670e11 | −1.70701 | −0.853505 | − | 0.521085i | \(-0.825528\pi\) | ||||
−0.853505 | + | 0.521085i | \(0.825528\pi\) | |||||||
\(588\) | 1.05727e9 | + | 3.59945e9i | 0.00884456 | + | 0.0301111i | ||||
\(589\) | 8.94945e9 | 0.0743593 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.54369e10 | + | 1.54689e11i | 0.372442 | + | 1.26797i | ||||
\(592\) | 1.83573e11i | 1.49459i | ||||||||
\(593\) | 1.89947e11 | 1.53608 | 0.768039 | − | 0.640403i | \(-0.221233\pi\) | ||||
0.768039 | + | 0.640403i | \(0.221233\pi\) | |||||||
\(594\) | −3.72467e10 | + | 4.30100e10i | −0.299187 | + | 0.345481i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.80200e9i | 0.0301320i | ||||||||
\(597\) | −5.33698e10 | − | 1.81696e11i | −0.420144 | − | 1.43037i | ||||
\(598\) | 7.94958e10i | 0.621640i | ||||||||
\(599\) | 3.15053e10i | 0.244724i | 0.992486 | + | 0.122362i | \(0.0390469\pi\) | ||||
−0.992486 | + | 0.122362i | \(0.960953\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.47794e10 | 0.189930 | 0.0949649 | − | 0.995481i | \(-0.469726\pi\) | ||||
0.0949649 | + | 0.995481i | \(0.469726\pi\) | |||||||
\(602\) | −3.90704e10 | −0.297483 | ||||||||
\(603\) | 1.02019e11 | + | 1.58678e11i | 0.771636 | + | 1.20018i | ||||
\(604\) | −2.05603e9 | −0.0154483 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.24068e11 | + | 3.64425e10i | −0.919958 | + | 0.270220i | ||||
\(607\) | − | 6.54251e10i | − | 0.481936i | −0.970533 | − | 0.240968i | \(-0.922535\pi\) | ||
0.970533 | − | 0.240968i | \(-0.0774649\pi\) | |||||||
\(608\) | −2.89830e9 | −0.0212094 | ||||||||
\(609\) | −1.01918e10 | − | 3.46979e10i | −0.0740940 | − | 0.252252i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.50286e11i | − | 1.79586i | ||||||
\(612\) | 7.10137e9 | − | 4.56570e9i | 0.0506216 | − | 0.0325463i | ||||
\(613\) | − | 1.70377e11i | − | 1.20661i | −0.797509 | − | 0.603307i | \(-0.793849\pi\) | ||
0.797509 | − | 0.603307i | \(-0.206151\pi\) | |||||||
\(614\) | − | 1.67762e11i | − | 1.18038i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50999e10 | −0.104870 | ||||||||
\(617\) | −8.96664e10 | −0.618713 | −0.309356 | − | 0.950946i | \(-0.600114\pi\) | ||||
−0.309356 | + | 0.950946i | \(0.600114\pi\) | |||||||
\(618\) | 2.10982e10 | − | 6.19720e9i | 0.144641 | − | 0.0424856i | ||||
\(619\) | −1.34052e11 | −0.913085 | −0.456542 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456542 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.95974e10 | − | 6.02714e10i | −0.467979 | − | 0.405271i | ||||
\(622\) | 2.80315e11i | 1.87277i | ||||||||
\(623\) | 3.41502e10 | 0.226694 | ||||||||
\(624\) | −1.48322e11 | + | 4.35667e10i | −0.978289 | + | 0.287354i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.82804e10i | 0.574867i | ||||||||
\(627\) | 2.12681e10 | − | 6.24711e9i | 0.137613 | − | 0.0404212i | ||||
\(628\) | − | 9.57693e9i | − | 0.0615726i | ||||||
\(629\) | 4.10170e11i | 2.62036i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.60073e9 | −0.0227130 | −0.0113565 | − | 0.999936i | \(-0.503615\pi\) | ||||
−0.0113565 | + | 0.999936i | \(0.503615\pi\) | |||||||
\(632\) | −1.70150e11 | −1.06651 | ||||||||
\(633\) | −8.50804e8 | − | 2.89654e9i | −0.00529925 | − | 0.0180412i | ||||
\(634\) | 1.90256e11 | 1.17756 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.26990e9 | + | 4.32333e9i | 0.00776140 | + | 0.0264235i | ||||
\(637\) | − | 1.53486e11i | − | 0.932204i | ||||||
\(638\) | 8.38730e10 | 0.506220 | ||||||||
\(639\) | −1.32687e11 | − | 2.06377e11i | −0.795837 | − | 1.23782i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.77443e11i | 1.05106i | 0.850775 | + | 0.525530i | \(0.176133\pi\) | ||||
−0.850775 | + | 0.525530i | \(0.823867\pi\) | |||||||
\(642\) | −1.58967e10 | − | 5.41199e10i | −0.0935764 | − | 0.318579i | ||||
\(643\) | − | 1.47027e11i | − | 0.860110i | −0.902803 | − | 0.430055i | \(-0.858494\pi\) | ||
0.902803 | − | 0.430055i | \(-0.141506\pi\) | |||||||
\(644\) | 8.40558e8i | 0.00488680i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.02191e11 | −0.586789 | ||||||||
\(647\) | 2.73529e11 | 1.56094 | 0.780471 | − | 0.625192i | \(-0.214979\pi\) | ||||
0.780471 | + | 0.625192i | \(0.214979\pi\) | |||||||
\(648\) | 7.19171e10 | − | 1.57637e11i | 0.407880 | − | 0.894040i | ||||
\(649\) | 1.02004e11 | 0.574961 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.53443e9 | − | 2.80055e9i | 0.0530849 | − | 0.0155927i | ||||
\(652\) | − | 8.94651e9i | − | 0.0495066i | ||||||
\(653\) | 1.23992e11 | 0.681933 | 0.340967 | − | 0.940075i | \(-0.389246\pi\) | ||||
0.340967 | + | 0.940075i | \(0.389246\pi\) | |||||||
\(654\) | 5.55799e10 | + | 1.89221e11i | 0.303813 | + | 1.03433i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.57329e10i | 0.246953i | ||||||||
\(657\) | −1.33089e11 | − | 2.07003e11i | −0.714301 | − | 1.11100i | ||||
\(658\) | − | 8.22219e10i | − | 0.438615i | ||||||
\(659\) | − | 2.37796e11i | − | 1.26085i | −0.776251 | − | 0.630424i | \(-0.782881\pi\) | ||
0.776251 | − | 0.630424i | \(-0.217119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.33114e10 | 0.436414 | 0.218207 | − | 0.975903i | \(-0.429979\pi\) | ||||
0.218207 | + | 0.975903i | \(0.429979\pi\) | |||||||
\(662\) | 9.81740e10 | 0.511169 | ||||||||
\(663\) | −3.31406e11 | + | 9.73441e10i | −1.71517 | + | 0.503797i | ||||
\(664\) | 2.93217e11 | 1.50840 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.56610e11 | − | 2.43587e11i | −0.796016 | − | 1.23810i | ||||
\(667\) | 1.35721e11i | 0.685713i | ||||||||
\(668\) | 1.29890e9 | 0.00652334 | ||||||||
\(669\) | 1.95104e11 | − | 5.73082e10i | 0.974008 | − | 0.286096i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 5.71605e10i | − | 0.281972i | ||||||
\(672\) | −3.08775e9 | + | 9.06967e8i | −0.0151414 | + | 0.00444748i | ||||
\(673\) | − | 3.96318e11i | − | 1.93189i | −0.258742 | − | 0.965947i | \(-0.583308\pi\) | ||
0.258742 | − | 0.965947i | \(-0.416692\pi\) | |||||||
\(674\) | − | 2.20335e10i | − | 0.106769i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.67626e8 | 0.000802700 | ||||||||
\(677\) | 3.22020e11 | 1.53295 | 0.766474 | − | 0.642275i | \(-0.222009\pi\) | ||||
0.766474 | + | 0.642275i | \(0.222009\pi\) | |||||||
\(678\) | −4.74551e9 | − | 1.61560e10i | −0.0224577 | − | 0.0764566i | ||||
\(679\) | −6.56385e9 | −0.0308802 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.55140e10 | − | 8.68617e10i | −0.118629 | − | 0.403868i | ||||
\(682\) | 2.30470e10i | 0.106531i | ||||||||
\(683\) | 3.92810e10 | 0.180510 | 0.0902548 | − | 0.995919i | \(-0.471232\pi\) | ||||
0.0902548 | + | 0.995919i | \(0.471232\pi\) | |||||||
\(684\) | 1.95333e9 | − | 1.25586e9i | 0.00892382 | − | 0.00573741i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 1.03854e11i | − | 0.468951i | ||||||
\(687\) | −7.51387e10 | − | 2.55808e11i | −0.337316 | − | 1.14839i | ||||
\(688\) | 2.85136e11i | 1.27262i | ||||||||
\(689\) | − | 1.84353e11i | − | 0.818039i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.54272e10 | 0.155391 | 0.0776954 | − | 0.996977i | \(-0.475244\pi\) | ||||
0.0776954 | + | 0.996977i | \(0.475244\pi\) | |||||||
\(692\) | −1.26742e10 | −0.0552707 | ||||||||
\(693\) | 2.07034e10 | − | 1.33109e10i | 0.0897654 | − | 0.0577131i | ||||
\(694\) | 4.02279e11 | 1.73416 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.45066e11 | + | 7.19835e10i | −1.04435 | + | 0.306758i | ||||
\(697\) | 1.02184e11i | 0.432965i | ||||||||
\(698\) | −1.47726e11 | −0.622350 | ||||||||
\(699\) | 3.98697e10 | + | 1.35736e11i | 0.167007 | + | 0.568571i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 3.64764e9i | − | 0.0151057i | −0.999971 | − | 0.00755284i | \(-0.997596\pi\) | ||
0.999971 | − | 0.00755284i | \(-0.00240417\pi\) | |||||||
\(702\) | 1.59644e11 | − | 1.84346e11i | 0.657360 | − | 0.759075i | ||||
\(703\) | 1.12823e11i | 0.461929i | ||||||||
\(704\) | 1.06526e11i | 0.433677i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.70458e11 | 1.08863 | ||||||||
\(707\) | 5.59389e10 | 0.223891 | ||||||||
\(708\) | 1.02529e10 | − | 3.01161e9i | 0.0408052 | − | 0.0119857i | ||||
\(709\) | 2.79311e11 | 1.10536 | 0.552678 | − | 0.833395i | \(-0.313606\pi\) | ||||
0.552678 | + | 0.833395i | \(0.313606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.33293e11 | − | 1.49991e11i | 0.912899 | − | 0.586932i | ||||
\(712\) | − | 2.41198e11i | − | 0.938541i | ||||||
\(713\) | −3.72939e10 | −0.144304 | ||||||||
\(714\) | −1.08871e11 | + | 3.19787e10i | −0.418907 | + | 0.123046i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 5.73438e9i | − | 0.0218190i | ||||||
\(717\) | 2.49008e11 | − | 7.31412e10i | 0.942184 | − | 0.276749i | ||||
\(718\) | − | 1.06013e11i | − | 0.398898i | ||||||
\(719\) | 1.75259e11i | 0.655789i | 0.944714 | + | 0.327895i | \(0.106339\pi\) | ||||
−0.944714 | + | 0.327895i | \(0.893661\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.51265e9 | −0.0352015 | ||||||||
\(722\) | 2.48110e11 | 0.913050 | ||||||||
\(723\) | 5.30838e10 | + | 1.80723e11i | 0.194271 | + | 0.661393i | ||||
\(724\) | 7.93429e9 | 0.0288771 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −6.34969e10 | − | 2.16174e11i | −0.228563 | − | 0.778138i | ||||
\(727\) | 3.76305e11i | 1.34711i | 0.739137 | + | 0.673555i | \(0.235233\pi\) | ||||
−0.739137 | + | 0.673555i | \(0.764767\pi\) | |||||||
\(728\) | 6.47199e10 | 0.230416 | ||||||||
\(729\) | 4.03549e10 | + | 2.79532e11i | 0.142885 | + | 0.989739i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.37098e11i | 2.23119i | ||||||||
\(732\) | −1.68763e9 | − | 5.74550e9i | −0.00587804 | − | 0.0200117i | ||||
\(733\) | − | 2.94004e11i | − | 1.01845i | −0.860635 | − | 0.509223i | \(-0.829933\pi\) | ||
0.860635 | − | 0.509223i | \(-0.170067\pi\) | |||||||
\(734\) | − | 2.79850e11i | − | 0.964141i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.20777e10 | 0.0411598 | ||||||||
\(737\) | 1.89268e11 | 0.641515 | ||||||||
\(738\) | −3.90156e10 | − | 6.06839e10i | −0.131527 | − | 0.204573i | ||||
\(739\) | −2.57966e11 | −0.864939 | −0.432470 | − | 0.901649i | \(-0.642358\pi\) | ||||
−0.432470 | + | 0.901649i | \(0.642358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.11577e10 | + | 2.67758e10i | −0.302357 | + | 0.0888117i | ||||
\(742\) | − | 6.05622e10i | − | 0.199796i | ||||||
\(743\) | −8.70436e10 | −0.285615 | −0.142808 | − | 0.989750i | \(-0.545613\pi\) | ||||
−0.142808 | + | 0.989750i | \(0.545613\pi\) | |||||||
\(744\) | −1.97799e10 | − | 6.73403e10i | −0.0645555 | − | 0.219778i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 2.40023e11i | − | 0.774992i | ||||||
\(747\) | −4.02029e11 | + | 2.58477e11i | −1.29114 | + | 0.830118i | ||||
\(748\) | − | 8.47038e9i | − | 0.0270580i | ||||||
\(749\) | 2.44013e10i | 0.0775328i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.07477e11 | −0.966613 | −0.483306 | − | 0.875451i | \(-0.660564\pi\) | ||||
−0.483306 | + | 0.875451i | \(0.660564\pi\) | |||||||
\(752\) | −6.00056e11 | −1.87638 | ||||||||
\(753\) | −2.63074e11 | + | 7.72728e10i | −0.818271 | + | 0.240351i | ||||
\(754\) | −3.59489e11 | −1.11225 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.68801e9 | − | 1.94920e9i | 0.00516759 | − | 0.00596719i | ||||
\(757\) | − | 3.68112e11i | − | 1.12098i | −0.828163 | − | 0.560488i | \(-0.810614\pi\) | ||
0.828163 | − | 0.560488i | \(-0.189386\pi\) | |||||||
\(758\) | 5.34725e11 | 1.61977 | ||||||||
\(759\) | −8.86279e10 | + | 2.60327e10i | −0.267057 | + | 0.0784428i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.79849e11i | 0.536252i | 0.963384 | + | 0.268126i | \(0.0864043\pi\) | ||||
−0.963384 | + | 0.268126i | \(0.913596\pi\) | |||||||
\(762\) | −3.38891e11 | + | 9.95427e10i | −1.00517 | + | 0.295250i | ||||
\(763\) | − | 8.53148e10i | − | 0.251725i | ||||||
\(764\) | − | 5.48374e8i | − | 0.00160955i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.81661e11 | 0.527650 | ||||||||
\(767\) | −4.37201e11 | −1.26328 | ||||||||
\(768\) | 9.77127e9 | + | 3.32661e10i | 0.0280871 | + | 0.0956218i | ||||
\(769\) | 4.66289e11 | 1.33337 | 0.666684 | − | 0.745341i | \(-0.267713\pi\) | ||||
0.666684 | + | 0.745341i | \(0.267713\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.21673e10 | − | 7.54681e10i | −0.0627329 | − | 0.213573i | ||||
\(772\) | 7.79114e9i | 0.0219347i | ||||||||
\(773\) | 3.85685e10 | 0.108023 | 0.0540114 | − | 0.998540i | \(-0.482799\pi\) | ||||
0.0540114 | + | 0.998540i | \(0.482799\pi\) | |||||||
\(774\) | −2.43255e11 | − | 3.78352e11i | −0.677794 | − | 1.05422i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.63596e10i | 0.127848i | ||||||||
\(777\) | 3.53057e10 | + | 1.20197e11i | 0.0968636 | + | 0.329770i | ||||
\(778\) | 5.11002e11i | 1.39478i | ||||||||
\(779\) | 2.81072e10i | 0.0763250i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.46163e11 | −0.661636 | ||||||||
\(782\) | 4.25847e11 | 1.13875 | ||||||||
\(783\) | 2.72555e11 | − | 3.14728e11i | 0.725114 | − | 0.837314i | ||||
\(784\) | −3.67980e11 | −0.974001 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.96010e9 | − | 2.04439e9i | 0.0182358 | − | 0.00535642i | ||||
\(787\) | 5.13745e11i | 1.33921i | 0.742717 | + | 0.669605i | \(0.233537\pi\) | ||||
−0.742717 | + | 0.669605i | \(0.766463\pi\) | |||||||
\(788\) | 1.69459e10 | 0.0439502 | ||||||||
\(789\) | −4.71634e9 | − | 1.60567e10i | −0.0121702 | − | 0.0414331i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.28433e9i | 0.0186073i | ||||||||
\(792\) | −9.40130e10 | − | 1.46225e11i | −0.238939 | − | 0.371640i | ||||
\(793\) | 2.44996e11i | 0.619537i | ||||||||
\(794\) | − | 1.42054e11i | − | 0.357413i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.99046e10 | −0.0495793 | ||||||||
\(797\) | −5.20760e11 | −1.29064 | −0.645318 | − | 0.763914i | \(-0.723275\pi\) | ||||
−0.645318 | + | 0.763914i | \(0.723275\pi\) | |||||||
\(798\) | −2.99464e10 | + | 8.79617e9i | −0.0738469 | + | 0.0216911i | ||||
\(799\) | −1.34074e12 | −3.28972 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.12621e11 | + | 3.30706e11i | 0.516508 | + | 0.803362i | ||||
\(802\) | 2.07961e10i | 0.0502672i | ||||||||
\(803\) | −2.46910e11 | −0.593849 | ||||||||
\(804\) | 1.90243e10 | − | 5.58802e9i | 0.0455286 | − | 0.0133732i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 9.87820e10i | − | 0.234066i | ||||||
\(807\) | 2.43092e11 | − | 7.14037e10i | 0.573162 | − | 0.168355i | ||||
\(808\) | − | 3.95089e11i | − | 0.926935i | ||||||
\(809\) | 7.88009e11i | 1.83966i | 0.392320 | + | 0.919829i | \(0.371673\pi\) | ||||
−0.392320 | + | 0.919829i | \(0.628327\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.15883e11 | 1.19253 | 0.596263 | − | 0.802789i | \(-0.296651\pi\) | ||||
0.596263 | + | 0.802789i | \(0.296651\pi\) | |||||||
\(812\) | −3.80110e9 | −0.00874350 | ||||||||
\(813\) | 1.05248e11 | + | 3.58314e11i | 0.240908 | + | 0.820165i | ||||
\(814\) | −2.90546e11 | −0.661785 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.33381e11 | + | 7.94539e11i | 0.526386 | + | 1.79207i | ||||
\(817\) | 1.75243e11i | 0.393325i | ||||||||
\(818\) | 1.67208e11 | 0.373461 | ||||||||
\(819\) | −8.87372e10 | + | 5.70520e10i | −0.197229 | + | 0.126805i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 5.32514e11i | − | 1.17208i | −0.810281 | − | 0.586041i | \(-0.800686\pi\) | ||
0.810281 | − | 0.586041i | \(-0.199314\pi\) | |||||||
\(822\) | 2.06813e11 | + | 7.04092e11i | 0.452993 | + | 1.54220i | ||||
\(823\) | 6.35863e11i | 1.38600i | 0.720936 | + | 0.693002i | \(0.243712\pi\) | ||||
−0.720936 | + | 0.693002i | \(0.756288\pi\) | |||||||
\(824\) | 6.71865e10i | 0.145738i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.43626e11 | −0.308540 | ||||||||
\(827\) | −1.67343e10 | −0.0357756 | −0.0178878 | − | 0.999840i | \(-0.505694\pi\) | ||||
−0.0178878 | + | 0.999840i | \(0.505694\pi\) | |||||||
\(828\) | −8.13985e9 | + | 5.23337e9i | −0.0173179 | + | 0.0111342i | ||||
\(829\) | 5.88172e11 | 1.24534 | 0.622668 | − | 0.782486i | \(-0.286049\pi\) | ||||
0.622668 | + | 0.782486i | \(0.286049\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.37904e11 | + | 4.05068e10i | −0.289184 | + | 0.0849422i | ||||
\(832\) | − | 4.56584e11i | − | 0.952856i | ||||||
\(833\) | −8.22201e11 | −1.70765 | ||||||||
\(834\) | −1.24157e10 | − | 4.22690e10i | −0.0256630 | − | 0.0873691i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 2.32989e9i | − | 0.00476992i | ||||||
\(837\) | 8.64822e10 | + | 7.48937e10i | 0.176208 | + | 0.152596i | ||||
\(838\) | 5.86419e11i | 1.18914i | ||||||||
\(839\) | − | 9.03790e11i | − | 1.82398i | −0.410215 | − | 0.911989i | \(-0.634546\pi\) | ||
0.410215 | − | 0.911989i | \(-0.365454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.13498e11 | −0.226885 | ||||||||
\(842\) | 5.91983e11 | 1.17777 | ||||||||
\(843\) | −6.06643e9 | + | 1.78190e9i | −0.0120122 | + | 0.00352836i | ||||
\(844\) | −3.17312e8 | −0.000625341 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 7.96225e11 | − | 5.11919e11i | 1.55437 | − | 0.999355i | ||||
\(847\) | 9.74673e10i | 0.189376i | ||||||||
\(848\) | −4.41984e11 | −0.854718 | ||||||||
\(849\) | 6.31172e11 | − | 1.85395e11i | 1.21483 | − | 0.356834i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.70152e11i | − | 0.896437i | ||||||
\(852\) | −2.47431e10 | + | 7.26782e9i | −0.0469566 | + | 0.0137926i | ||||
\(853\) | 2.17472e11i | 0.410779i | 0.978680 | + | 0.205389i | \(0.0658461\pi\) | ||||
−0.978680 | + | 0.205389i | \(0.934154\pi\) | |||||||
\(854\) | 8.04842e10i | 0.151314i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.72343e11 | 0.320995 | ||||||||
\(857\) | −5.72821e10 | −0.106193 | −0.0530964 | − | 0.998589i | \(-0.516909\pi\) | ||||
−0.0530964 | + | 0.998589i | \(0.516909\pi\) | |||||||
\(858\) | −6.89541e10 | − | 2.34753e11i | −0.127236 | − | 0.433173i | ||||
\(859\) | −2.59635e11 | −0.476860 | −0.238430 | − | 0.971160i | \(-0.576633\pi\) | ||||
−0.238430 | + | 0.971160i | \(0.576633\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.79558e9 | + | 2.99444e10i | 0.0160049 | + | 0.0544882i | ||||
\(862\) | − | 4.93697e11i | − | 0.894194i | ||||||
\(863\) | 9.75428e10 | 0.175854 | 0.0879270 | − | 0.996127i | \(-0.471976\pi\) | ||||
0.0879270 | + | 0.996127i | \(0.471976\pi\) | |||||||
\(864\) | −2.80075e10 | − | 2.42545e10i | −0.0502596 | − | 0.0435249i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.62424e11i | 0.999982i | ||||||||
\(867\) | 3.62216e11 | + | 1.23316e12i | 0.641050 | + | 2.18244i | ||||
\(868\) | − | 1.04448e9i | − | 0.00184002i | ||||||
\(869\) | − | 2.78267e11i | − | 0.487958i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.11224e11 | −1.40951 | ||||||||
\(872\) | −6.02566e11 | −1.04217 | ||||||||
\(873\) | −4.08670e10 | − | 6.35634e10i | −0.0703584 | − | 0.109434i | ||||
\(874\) | 1.17135e11 | 0.200743 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.48182e10 | + | 7.28986e9i | −0.0421457 | + | 0.0123795i | ||||
\(877\) | − | 9.16421e11i | − | 1.54916i | −0.632476 | − | 0.774580i | \(-0.717961\pi\) | ||
0.632476 | − | 0.774580i | \(-0.282039\pi\) | |||||||
\(878\) | −2.87866e10 | −0.0484409 | ||||||||
\(879\) | −5.76688e10 | − | 1.96332e11i | −0.0966018 | − | 0.328879i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 5.22036e11i | − | 0.866557i | −0.901260 | − | 0.433279i | \(-0.857357\pi\) | ||
0.901260 | − | 0.433279i | \(-0.142643\pi\) | |||||||
\(882\) | 4.88279e11 | − | 3.13930e11i | 0.806852 | − | 0.518751i | ||||
\(883\) | − | 2.66487e11i | − | 0.438363i | −0.975684 | − | 0.219181i | \(-0.929661\pi\) | ||
0.975684 | − | 0.219181i | \(-0.0703386\pi\) | |||||||
\(884\) | 3.63050e10i | 0.0594508i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.19917e11 | 0.843722 | ||||||||
\(887\) | 4.32506e11 | 0.698710 | 0.349355 | − | 0.936990i | \(-0.386401\pi\) | ||||
0.349355 | + | 0.936990i | \(0.386401\pi\) | |||||||
\(888\) | 8.48938e11 | − | 2.49359e11i | 1.36529 | − | 0.401027i | ||||
\(889\) | 1.52797e11 | 0.244630 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.57802e11 | + | 1.17615e11i | 0.409049 | + | 0.186617i | ||||
\(892\) | − | 2.13734e10i | − | 0.0337609i | ||||||
\(893\) | −3.68790e11 | −0.579927 | ||||||||
\(894\) | 5.64456e11 | − | 1.65798e11i | 0.883649 | − | 0.259555i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.60164e11i | − | 0.248504i | ||||||
\(897\) | 3.79870e11 | − | 1.11579e11i | 0.586766 | − | 0.172351i | ||||
\(898\) | − | 1.30232e12i | − | 2.00269i | ||||||
\(899\) | − | 1.68647e11i | − | 0.258191i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.87554e11 | −1.49852 | ||||||||
\(902\) | −7.23826e10 | −0.109347 | ||||||||
\(903\) | 5.48388e10 | + | 1.86697e11i | 0.0824777 | + | 0.280794i | ||||
\(904\) | 5.14482e10 | 0.0770365 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.96593e10 | + | 3.05243e11i | 0.133071 | + | 0.453037i | ||||
\(907\) | 1.46416e10i | 0.0216352i | 0.999941 | + | 0.0108176i | \(0.00344341\pi\) | ||||
−0.999941 | + | 0.0108176i | \(0.996557\pi\) | |||||||
\(908\) | −9.51557e9 | −0.0139988 | ||||||||
\(909\) | 3.48280e11 | + | 5.41705e11i | 0.510120 | + | 0.793428i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.82789e11i | − | 0.700944i | −0.936573 | − | 0.350472i | \(-0.886021\pi\) | ||
0.936573 | − | 0.350472i | \(-0.113979\pi\) | |||||||
\(912\) | 6.41945e10 | + | 2.18549e11i | 0.0927937 | + | 0.315914i | ||||
\(913\) | 4.79532e11i | 0.690136i | ||||||||
\(914\) | 8.86737e11i | 1.27060i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.80234e10 | −0.0398051 | ||||||||
\(917\) | −3.13813e9 | −0.00443807 | ||||||||
\(918\) | −9.87513e11 | − | 8.55187e11i | −1.39050 | − | 1.20418i | ||||
\(919\) | −2.79672e11 | −0.392090 | −0.196045 | − | 0.980595i | \(-0.562810\pi\) | ||||
−0.196045 | + | 0.980595i | \(0.562810\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.01650e11 | + | 2.35469e11i | −1.11416 | + | 0.327262i | ||||
\(922\) | 5.96134e9i | 0.00824936i | ||||||||
\(923\) | 1.05508e12 | 1.45372 | ||||||||
\(924\) | −7.29094e8 | − | 2.48219e9i | −0.00100022 | − | 0.00340523i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 5.25034e11i | − | 0.714074i | ||||||
\(927\) | −5.92264e10 | − | 9.21193e10i | −0.0802041 | − | 0.124747i | ||||
\(928\) | 5.46169e10i | 0.0736436i | ||||||||
\(929\) | 9.95357e10i | 0.133634i | 0.997765 | + | 0.0668169i | \(0.0212843\pi\) | ||||
−0.997765 | + | 0.0668169i | \(0.978716\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.26158e11 | −0.301032 | ||||||||
\(932\) | 1.48696e10 | 0.0197077 | ||||||||
\(933\) | 1.33948e12 | − | 3.93447e11i | 1.76771 | − | 0.519230i | ||||
\(934\) | −3.44432e11 | −0.452601 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.02951e11 | + | 6.26739e11i | 0.524987 | + | 0.816551i | ||||
\(937\) | − | 8.34167e11i | − | 1.08217i | −0.840968 | − | 0.541084i | \(-0.818014\pi\) | ||
0.840968 | − | 0.541084i | \(-0.181986\pi\) | |||||||
\(938\) | −2.66497e11 | −0.344255 | ||||||||
\(939\) | 4.21847e11 | − | 1.23909e11i | 0.542616 | − | 0.159383i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.45126e11i | 0.312630i | 0.987707 | + | 0.156315i | \(0.0499615\pi\) | ||||
−0.987707 | + | 0.156315i | \(0.950039\pi\) | |||||||
\(942\) | −1.42182e12 | + | 4.17632e11i | −1.80568 | + | 0.530383i | ||||
\(943\) | − | 1.17127e11i | − | 0.148119i | ||||||
\(944\) | 1.04818e12i | 1.31992i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.51292e11 | −0.563498 | ||||||||
\(947\) | −1.34423e12 | −1.67137 | −0.835685 | − | 0.549209i | \(-0.814929\pi\) | ||||
−0.835685 | + | 0.549209i | \(0.814929\pi\) | |||||||
\(948\) | −8.21567e9 | − | 2.79701e10i | −0.0101721 | − | 0.0346306i | ||||
\(949\) | 1.05828e12 | 1.30478 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.67042e11 | − | 9.09137e11i | −0.326480 | − | 1.11149i | ||||
\(952\) | − | 3.46695e11i | − | 0.422085i | ||||||
\(953\) | 1.02998e12 | 1.24870 | 0.624351 | − | 0.781144i | \(-0.285363\pi\) | ||||
0.624351 | + | 0.781144i | \(0.285363\pi\) | |||||||
\(954\) | 5.86477e11 | − | 3.77065e11i | 0.708039 | − | 0.455221i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.72784e10i | − | 0.0326578i | ||||||
\(957\) | −1.17723e11 | − | 4.00786e11i | −0.140351 | − | 0.477820i | ||||
\(958\) | − | 7.62802e11i | − | 0.905628i | ||||||
\(959\) | − | 3.17457e11i | − | 0.375328i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.06549e11 | −0.945665 | ||||||||
\(962\) | 1.24531e12 | 1.45405 | ||||||||
\(963\) | −2.36299e11 | + | 1.51924e11i | −0.274762 | + | 0.176653i | ||||
\(964\) | 1.97979e10 | 0.0229251 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.24792e11 | − | 3.66551e10i | 0.143310 | − | 0.0420946i | ||||
\(967\) | − | 8.83788e11i | − | 1.01075i | −0.862901 | − | 0.505373i | \(-0.831355\pi\) | ||
0.862901 | − | 0.505373i | \(-0.168645\pi\) | |||||||
\(968\) | 6.88398e11 | 0.784040 | ||||||||
\(969\) | 1.43434e11 | + | 4.88318e11i | 0.162689 | + | 0.553870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.36295e12i | 1.53321i | 0.642117 | + | 0.766607i | \(0.278057\pi\) | ||||
−0.642117 | + | 0.766607i | \(0.721943\pi\) | |||||||
\(972\) | 2.93855e10 | + | 4.21060e9i | 0.0329206 | + | 0.00471714i | ||||
\(973\) | 1.90580e10i | 0.0212631i | ||||||||
\(974\) | 2.19184e11i | 0.243541i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.87374e11 | 0.647315 | ||||||||
\(977\) | 8.27099e10 | 0.0907777 | 0.0453888 | − | 0.998969i | \(-0.485547\pi\) | ||||
0.0453888 | + | 0.998969i | \(0.485547\pi\) | |||||||
\(978\) | −1.32822e12 | + | 3.90140e11i | −1.45183 | + | 0.426447i | ||||
\(979\) | 3.94459e11 | 0.429409 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.26177e11 | − | 5.31176e11i | 0.892066 | − | 0.573538i | ||||
\(982\) | − | 1.34528e12i | − | 1.44666i | ||||||
\(983\) | −1.05894e12 | −1.13412 | −0.567058 | − | 0.823678i | \(-0.691918\pi\) | ||||
−0.567058 | + | 0.823678i | \(0.691918\pi\) | |||||||
\(984\) | 2.11493e11 | − | 6.21220e10i | 0.225588 | − | 0.0662621i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.92573e12i | 2.03745i | ||||||||
\(987\) | −3.92896e11 | + | 1.15406e11i | −0.414008 | + | 0.121607i | ||||
\(988\) | 9.98619e9i | 0.0104803i | ||||||||
\(989\) | − | 7.30266e11i | − | 0.763301i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.36731e11 | 0.141766 | 0.0708828 | − | 0.997485i | \(-0.477418\pi\) | ||||
0.0708828 | + | 0.997485i | \(0.477418\pi\) | |||||||
\(992\) | −1.50078e10 | −0.0154979 | ||||||||
\(993\) | −1.37796e11 | − | 4.69123e11i | −0.141723 | − | 0.482492i | ||||
\(994\) | 3.46607e11 | 0.355052 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.41579e10 | + | 4.82003e10i | 0.0143867 | + | 0.0489793i | ||||
\(997\) | 1.12309e12i | 1.13667i | 0.822798 | + | 0.568334i | \(0.192412\pi\) | ||||
−0.822798 | + | 0.568334i | \(0.807588\pi\) | |||||||
\(998\) | 3.20317e11 | 0.322892 | ||||||||
\(999\) | −9.44160e11 | + | 1.09025e12i | −0.947947 | + | 1.09463i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 75.9.d.d.74.8 | 20 | ||
3.2 | odd | 2 | inner | 75.9.d.d.74.14 | 20 | ||
5.2 | odd | 4 | 75.9.c.f.26.4 | yes | 10 | ||
5.3 | odd | 4 | 75.9.c.e.26.7 | yes | 10 | ||
5.4 | even | 2 | inner | 75.9.d.d.74.13 | 20 | ||
15.2 | even | 4 | 75.9.c.f.26.7 | yes | 10 | ||
15.8 | even | 4 | 75.9.c.e.26.4 | ✓ | 10 | ||
15.14 | odd | 2 | inner | 75.9.d.d.74.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.9.c.e.26.4 | ✓ | 10 | 15.8 | even | 4 | ||
75.9.c.e.26.7 | yes | 10 | 5.3 | odd | 4 | ||
75.9.c.f.26.4 | yes | 10 | 5.2 | odd | 4 | ||
75.9.c.f.26.7 | yes | 10 | 15.2 | even | 4 | ||
75.9.d.d.74.7 | 20 | 15.14 | odd | 2 | inner | ||
75.9.d.d.74.8 | 20 | 1.1 | even | 1 | trivial | ||
75.9.d.d.74.13 | 20 | 5.4 | even | 2 | inner | ||
75.9.d.d.74.14 | 20 | 3.2 | odd | 2 | inner |