Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,9,Mod(26,75)]
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, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.26");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.c (of order \(2\), degree \(1\), 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: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-14}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.1 | ||
Root | \(-3.74166i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.26 |
Dual form | 75.9.c.c.26.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 22.4499i | − | 1.40312i | −0.712610 | − | 0.701561i | \(-0.752487\pi\) | ||
0.712610 | − | 0.701561i | \(-0.247513\pi\) | |||||||
\(3\) | −45.0000 | + | 67.3498i | −0.555556 | + | 0.831479i | ||||
\(4\) | −248.000 | −0.968750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1512.00 | + | 1010.25i | 1.16667 | + | 0.779512i | ||||
\(7\) | 1750.00 | 0.728863 | 0.364431 | − | 0.931230i | \(-0.381263\pi\) | ||||
0.364431 | + | 0.931230i | \(0.381263\pi\) | |||||||
\(8\) | − | 179.600i | − | 0.0438475i | ||||||
\(9\) | −2511.00 | − | 6061.48i | −0.382716 | − | 0.923866i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6959.48i | 0.475342i | 0.971346 | + | 0.237671i | \(0.0763840\pi\) | ||||
−0.971346 | + | 0.237671i | \(0.923616\pi\) | |||||||
\(12\) | 11160.0 | − | 16702.8i | 0.538194 | − | 0.805496i | ||||
\(13\) | −25730.0 | −0.900879 | −0.450439 | − | 0.892807i | \(-0.648733\pi\) | ||||
−0.450439 | + | 0.892807i | \(0.648733\pi\) | |||||||
\(14\) | − | 39287.4i | − | 1.02268i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −67520.0 | −1.03027 | ||||||||
\(17\) | − | 74893.0i | − | 0.896697i | −0.893859 | − | 0.448348i | \(-0.852012\pi\) | ||
0.893859 | − | 0.448348i | \(-0.147988\pi\) | |||||||
\(18\) | −136080. | + | 56371.8i | −1.29630 | + | 0.536997i | ||||
\(19\) | 18938.0 | 0.145318 | 0.0726590 | − | 0.997357i | \(-0.476852\pi\) | ||||
0.0726590 | + | 0.997357i | \(0.476852\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −78750.0 | + | 117862.i | −0.404924 | + | 0.606035i | ||||
\(22\) | 156240. | 0.666963 | ||||||||
\(23\) | 470461.i | 1.68117i | 0.541678 | + | 0.840586i | \(0.317789\pi\) | ||||
−0.541678 | + | 0.840586i | \(0.682211\pi\) | |||||||
\(24\) | 12096.0 | + | 8081.98i | 0.0364583 | + | 0.0243597i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 577637.i | 1.26404i | ||||||||
\(27\) | 521235. | + | 103651.i | 0.980796 | + | 0.195038i | ||||
\(28\) | −434000. | −0.706086 | ||||||||
\(29\) | 460897.i | 0.651647i | 0.945431 | + | 0.325823i | \(0.105641\pi\) | ||||
−0.945431 | + | 0.325823i | \(0.894359\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −351478. | −0.380585 | −0.190292 | − | 0.981727i | \(-0.560944\pi\) | ||||
−0.190292 | + | 0.981727i | \(0.560944\pi\) | |||||||
\(32\) | 1.46984e6i | 1.40175i | ||||||||
\(33\) | −468720. | − | 313177.i | −0.395237 | − | 0.264079i | ||||
\(34\) | −1.68134e6 | −1.25817 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 622728. | + | 1.50325e6i | 0.370756 | + | 0.894995i | ||||
\(37\) | −1.33517e6 | −0.712409 | −0.356205 | − | 0.934408i | \(-0.615929\pi\) | ||||
−0.356205 | + | 0.934408i | \(0.615929\pi\) | |||||||
\(38\) | − | 425157.i | − | 0.203899i | ||||||
\(39\) | 1.15785e6 | − | 1.73291e6i | 0.500488 | − | 0.749062i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.87547e6i | 0.663704i | 0.943331 | + | 0.331852i | \(0.107673\pi\) | ||||
−0.943331 | + | 0.331852i | \(0.892327\pi\) | |||||||
\(42\) | 2.64600e6 | + | 1.76793e6i | 0.850340 | + | 0.568157i | ||||
\(43\) | 3.52615e6 | 1.03140 | 0.515700 | − | 0.856769i | \(-0.327532\pi\) | ||||
0.515700 | + | 0.856769i | \(0.327532\pi\) | |||||||
\(44\) | − | 1.72595e6i | − | 0.460488i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.05618e7 | 2.35889 | ||||||||
\(47\) | 4.08104e6i | 0.836333i | 0.908370 | + | 0.418167i | \(0.137327\pi\) | ||||
−0.908370 | + | 0.418167i | \(0.862673\pi\) | |||||||
\(48\) | 3.03840e6 | − | 4.54746e6i | 0.572374 | − | 0.856651i | ||||
\(49\) | −2.70230e6 | −0.468759 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.04403e6 | + | 3.37019e6i | 0.745585 | + | 0.498165i | ||||
\(52\) | 6.38104e6 | 0.872726 | ||||||||
\(53\) | 6.60177e6i | 0.836675i | 0.908292 | + | 0.418337i | \(0.137387\pi\) | ||||
−0.908292 | + | 0.418337i | \(0.862613\pi\) | |||||||
\(54\) | 2.32697e6 | − | 1.17017e7i | 0.273663 | − | 1.37618i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 314299.i | − | 0.0319589i | ||||||
\(57\) | −852210. | + | 1.27547e6i | −0.0807323 | + | 0.120829i | ||||
\(58\) | 1.03471e7 | 0.914340 | ||||||||
\(59\) | 1.37149e7i | 1.13184i | 0.824461 | + | 0.565919i | \(0.191479\pi\) | ||||
−0.824461 | + | 0.565919i | \(0.808521\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 753602. | 0.0544280 | 0.0272140 | − | 0.999630i | \(-0.491336\pi\) | ||||
0.0272140 | + | 0.999630i | \(0.491336\pi\) | |||||||
\(62\) | 7.89066e6i | 0.534007i | ||||||||
\(63\) | −4.39425e6 | − | 1.06076e7i | −0.278948 | − | 0.673372i | ||||
\(64\) | 1.57128e7 | 0.936554 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.03080e6 | + | 1.05227e7i | −0.370535 | + | 0.554566i | ||||
\(67\) | −2.26889e6 | −0.112594 | −0.0562969 | − | 0.998414i | \(-0.517929\pi\) | ||||
−0.0562969 | + | 0.998414i | \(0.517929\pi\) | |||||||
\(68\) | 1.85735e7i | 0.868675i | ||||||||
\(69\) | −3.16855e7 | − | 2.11707e7i | −1.39786 | − | 0.933985i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.70220e7i | 0.669849i | 0.942245 | + | 0.334925i | \(0.108711\pi\) | ||||
−0.942245 | + | 0.334925i | \(0.891289\pi\) | |||||||
\(72\) | −1.08864e6 | + | 450974.i | −0.0405093 | + | 0.0167812i | ||||
\(73\) | −2.76728e7 | −0.974454 | −0.487227 | − | 0.873275i | \(-0.661992\pi\) | ||||
−0.487227 | + | 0.873275i | \(0.661992\pi\) | |||||||
\(74\) | 2.99745e7i | 0.999597i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.69662e6 | −0.140777 | ||||||||
\(77\) | 1.21791e7i | 0.346459i | ||||||||
\(78\) | −3.89038e7 | − | 2.59937e7i | −1.05103 | − | 0.702246i | ||||
\(79\) | −2.29810e7 | −0.590011 | −0.295006 | − | 0.955496i | \(-0.595322\pi\) | ||||
−0.295006 | + | 0.955496i | \(0.595322\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.04365e7 | + | 3.04408e7i | −0.707057 | + | 0.707157i | ||||
\(82\) | 4.21042e7 | 0.931257 | ||||||||
\(83\) | 4.63952e7i | 0.977599i | 0.872396 | + | 0.488799i | \(0.162565\pi\) | ||||
−0.872396 | + | 0.488799i | \(0.837435\pi\) | |||||||
\(84\) | 1.95300e7 | − | 2.92298e7i | 0.392270 | − | 0.587096i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 7.91619e7i | − | 1.44718i | ||||||
\(87\) | −3.10414e7 | − | 2.07404e7i | −0.541831 | − | 0.362026i | ||||
\(88\) | 1.24992e6 | 0.0208426 | ||||||||
\(89\) | 7.26152e7i | 1.15736i | 0.815555 | + | 0.578679i | \(0.196432\pi\) | ||||
−0.815555 | + | 0.578679i | \(0.803568\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.50275e7 | −0.656617 | ||||||||
\(92\) | − | 1.16674e8i | − | 1.62864i | ||||||
\(93\) | 1.58165e7 | − | 2.36720e7i | 0.211436 | − | 0.316448i | ||||
\(94\) | 9.16191e7 | 1.17348 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.89937e7 | − | 6.61429e7i | −1.16553 | − | 0.778751i | ||||
\(97\) | −1.47271e8 | −1.66353 | −0.831764 | − | 0.555129i | \(-0.812669\pi\) | ||||
−0.831764 | + | 0.555129i | \(0.812669\pi\) | |||||||
\(98\) | 6.06665e7i | 0.657726i | ||||||||
\(99\) | 4.21848e7 | − | 1.74753e7i | 0.439152 | − | 0.181921i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.03545e8i | − | 0.995045i | −0.867451 | − | 0.497522i | \(-0.834243\pi\) | ||
0.867451 | − | 0.497522i | \(-0.165757\pi\) | |||||||
\(102\) | 7.56605e7 | − | 1.13238e8i | 0.698986 | − | 1.04615i | ||||
\(103\) | 1.66064e8 | 1.47545 | 0.737726 | − | 0.675100i | \(-0.235899\pi\) | ||||
0.737726 | + | 0.675100i | \(0.235899\pi\) | |||||||
\(104\) | 4.62110e6i | 0.0395013i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.48209e8 | 1.17396 | ||||||||
\(107\) | 2.25540e7i | 0.172063i | 0.996292 | + | 0.0860316i | \(0.0274186\pi\) | ||||
−0.996292 | + | 0.0860316i | \(0.972581\pi\) | |||||||
\(108\) | −1.29266e8 | − | 2.57055e7i | −0.950146 | − | 0.188943i | ||||
\(109\) | −1.09975e8 | −0.779091 | −0.389546 | − | 0.921007i | \(-0.627368\pi\) | ||||
−0.389546 | + | 0.921007i | \(0.627368\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00826e7 | − | 8.99235e7i | 0.395783 | − | 0.592354i | ||||
\(112\) | −1.18160e8 | −0.750928 | ||||||||
\(113\) | − | 2.87748e8i | − | 1.76481i | −0.470490 | − | 0.882405i | \(-0.655923\pi\) | ||
0.470490 | − | 0.882405i | \(-0.344077\pi\) | |||||||
\(114\) | 2.86343e7 | + | 1.91321e7i | 0.169538 | + | 0.113277i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.14303e8i | − | 0.631283i | ||||||
\(117\) | 6.46080e7 | + | 1.55962e8i | 0.344781 | + | 0.832291i | ||||
\(118\) | 3.07899e8 | 1.58811 | ||||||||
\(119\) | − | 1.31063e8i | − | 0.653569i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.65924e8 | 0.774050 | ||||||||
\(122\) | − | 1.69183e7i | − | 0.0763692i | ||||||
\(123\) | −1.26312e8 | − | 8.43961e7i | −0.551856 | − | 0.368724i | ||||
\(124\) | 8.71665e7 | 0.368691 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.38140e8 | + | 9.86507e7i | −0.944822 | + | 0.391397i | ||||
\(127\) | −2.75994e8 | −1.06092 | −0.530462 | − | 0.847708i | \(-0.677982\pi\) | ||||
−0.530462 | + | 0.847708i | \(0.677982\pi\) | |||||||
\(128\) | 2.35290e7i | 0.0876523i | ||||||||
\(129\) | −1.58677e8 | + | 2.37486e8i | −0.573000 | + | 0.857588i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.89118e8i | 0.981725i | 0.871237 | + | 0.490862i | \(0.163318\pi\) | ||||
−0.871237 | + | 0.490862i | \(0.836682\pi\) | |||||||
\(132\) | 1.16243e8 | + | 7.76678e7i | 0.382886 | + | 0.255826i | ||||
\(133\) | 3.31415e7 | 0.105917 | ||||||||
\(134\) | 5.09365e7i | 0.157983i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.34508e7 | −0.0393180 | ||||||||
\(137\) | 2.07562e8i | 0.589205i | 0.955620 | + | 0.294602i | \(0.0951872\pi\) | ||||
−0.955620 | + | 0.294602i | \(0.904813\pi\) | |||||||
\(138\) | −4.75282e8 | + | 7.11337e8i | −1.31049 | + | 1.96137i | ||||
\(139\) | −1.42668e8 | −0.382180 | −0.191090 | − | 0.981573i | \(-0.561202\pi\) | ||||
−0.191090 | + | 0.981573i | \(0.561202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.74857e8 | − | 1.83647e8i | −0.695394 | − | 0.464630i | ||||
\(142\) | 3.82143e8 | 0.939880 | ||||||||
\(143\) | − | 1.79067e8i | − | 0.428226i | ||||||
\(144\) | 1.69543e8 | + | 4.09271e8i | 0.394302 | + | 0.951835i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.21252e8i | 1.36728i | ||||||||
\(147\) | 1.21604e8 | − | 1.82000e8i | 0.260422 | − | 0.389763i | ||||
\(148\) | 3.31122e8 | 0.690147 | ||||||||
\(149\) | − | 8.19236e8i | − | 1.66213i | −0.556179 | − | 0.831063i | \(-0.687733\pi\) | ||
0.556179 | − | 0.831063i | \(-0.312267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.23861e8 | 0.815296 | 0.407648 | − | 0.913139i | \(-0.366349\pi\) | ||||
0.407648 | + | 0.913139i | \(0.366349\pi\) | |||||||
\(152\) | − | 3.40126e6i | − | 0.00637184i | ||||||
\(153\) | −4.53963e8 | + | 1.88056e8i | −0.828428 | + | 0.343180i | ||||
\(154\) | 2.73420e8 | 0.486124 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.87147e8 | + | 4.29762e8i | −0.484848 | + | 0.725654i | ||||
\(157\) | 7.59851e8 | 1.25063 | 0.625316 | − | 0.780371i | \(-0.284970\pi\) | ||||
0.625316 | + | 0.780371i | \(0.284970\pi\) | |||||||
\(158\) | 5.15922e8i | 0.827857i | ||||||||
\(159\) | −4.44628e8 | − | 2.97079e8i | −0.695678 | − | 0.464819i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.23307e8i | 1.22534i | ||||||||
\(162\) | 6.83394e8 | + | 6.83297e8i | 0.992227 | + | 0.992087i | ||||
\(163\) | −6.68160e8 | −0.946520 | −0.473260 | − | 0.880923i | \(-0.656923\pi\) | ||||
−0.473260 | + | 0.880923i | \(0.656923\pi\) | |||||||
\(164\) | − | 4.65116e8i | − | 0.642963i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.04157e9 | 1.37169 | ||||||||
\(167\) | − | 1.96306e8i | − | 0.252387i | −0.992006 | − | 0.126194i | \(-0.959724\pi\) | ||
0.992006 | − | 0.126194i | \(-0.0402761\pi\) | |||||||
\(168\) | 2.11680e7 | + | 1.41435e7i | 0.0265731 | + | 0.0177549i | ||||
\(169\) | −1.53698e8 | −0.188417 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.75533e7 | − | 1.14792e8i | −0.0556156 | − | 0.134254i | ||||
\(172\) | −8.74485e8 | −0.999168 | ||||||||
\(173\) | − | 1.02319e9i | − | 1.14228i | −0.820852 | − | 0.571141i | \(-0.806501\pi\) | ||
0.820852 | − | 0.571141i | \(-0.193499\pi\) | |||||||
\(174\) | −4.65620e8 | + | 6.96877e8i | −0.507966 | + | 0.760255i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.69904e8i | − | 0.489732i | ||||||
\(177\) | −9.23696e8 | − | 6.17170e8i | −0.941100 | − | 0.628799i | ||||
\(178\) | 1.63021e9 | 1.62391 | ||||||||
\(179\) | − | 1.28895e9i | − | 1.25552i | −0.778408 | − | 0.627759i | \(-0.783972\pi\) | ||
0.778408 | − | 0.627759i | \(-0.216028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.71707e8 | 0.439499 | 0.219749 | − | 0.975556i | \(-0.429476\pi\) | ||||
0.219749 | + | 0.975556i | \(0.429476\pi\) | |||||||
\(182\) | 1.01086e9i | 0.921314i | ||||||||
\(183\) | −3.39121e7 | + | 5.07550e7i | −0.0302378 | + | 0.0452558i | ||||
\(184\) | 8.44946e7 | 0.0737153 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.31435e8 | − | 3.55080e8i | −0.444016 | − | 0.296670i | ||||
\(187\) | 5.21217e8 | 0.426238 | ||||||||
\(188\) | − | 1.01210e9i | − | 0.810198i | ||||||
\(189\) | 9.12161e8 | + | 1.81390e8i | 0.714866 | + | 0.142156i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.61787e8i | − | 0.121565i | −0.998151 | − | 0.0607827i | \(-0.980640\pi\) | ||
0.998151 | − | 0.0607827i | \(-0.0193597\pi\) | |||||||
\(192\) | −7.07075e8 | + | 1.05825e9i | −0.520308 | + | 0.778725i | ||||
\(193\) | 1.58840e9 | 1.14480 | 0.572401 | − | 0.819974i | \(-0.306012\pi\) | ||||
0.572401 | + | 0.819974i | \(0.306012\pi\) | |||||||
\(194\) | 3.30623e9i | 2.33413i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.70171e8 | 0.454110 | ||||||||
\(197\) | 5.37769e8i | 0.357052i | 0.983935 | + | 0.178526i | \(0.0571328\pi\) | ||||
−0.983935 | + | 0.178526i | \(0.942867\pi\) | |||||||
\(198\) | −3.92319e8 | − | 9.47046e8i | −0.255257 | − | 0.616184i | ||||
\(199\) | 6.47586e8 | 0.412938 | 0.206469 | − | 0.978453i | \(-0.433803\pi\) | ||||
0.206469 | + | 0.978453i | \(0.433803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.02100e8 | − | 1.52809e8i | 0.0625521 | − | 0.0936194i | ||||
\(202\) | −2.32457e9 | −1.39617 | ||||||||
\(203\) | 8.06570e8i | 0.474961i | ||||||||
\(204\) | −1.25092e9 | − | 8.35806e8i | −0.722285 | − | 0.482597i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 3.72812e9i | − | 2.07024i | ||||||
\(207\) | 2.85169e9 | − | 1.18133e9i | 1.55318 | − | 0.643412i | ||||
\(208\) | 1.73729e9 | 0.928152 | ||||||||
\(209\) | 1.31799e8i | 0.0690758i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.81104e7 | 0.0293173 | 0.0146586 | − | 0.999893i | \(-0.495334\pi\) | ||||
0.0146586 | + | 0.999893i | \(0.495334\pi\) | |||||||
\(212\) | − | 1.63724e9i | − | 0.810529i | ||||||
\(213\) | −1.14643e9 | − | 7.65990e8i | −0.556966 | − | 0.372139i | ||||
\(214\) | 5.06336e8 | 0.241426 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.86157e7 | − | 9.36136e7i | 0.00855195 | − | 0.0430055i | ||||
\(217\) | −6.15086e8 | −0.277394 | ||||||||
\(218\) | 2.46893e9i | 1.09316i | ||||||||
\(219\) | 1.24527e9 | − | 1.86376e9i | 0.541363 | − | 0.810238i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.92700e9i | 0.807815i | ||||||||
\(222\) | −2.01878e9 | − | 1.34885e9i | −0.831144 | − | 0.555332i | ||||
\(223\) | −4.40200e9 | −1.78004 | −0.890021 | − | 0.455920i | \(-0.849310\pi\) | ||||
−0.890021 | + | 0.455920i | \(0.849310\pi\) | |||||||
\(224\) | 2.57222e9i | 1.02168i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.45992e9 | −2.47624 | ||||||||
\(227\) | − | 3.53592e9i | − | 1.33168i | −0.746095 | − | 0.665839i | \(-0.768074\pi\) | ||
0.746095 | − | 0.665839i | \(-0.231926\pi\) | |||||||
\(228\) | 2.11348e8 | − | 3.16317e8i | 0.0782094 | − | 0.117053i | ||||
\(229\) | −1.86569e9 | −0.678420 | −0.339210 | − | 0.940711i | \(-0.610160\pi\) | ||||
−0.339210 | + | 0.940711i | \(0.610160\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.20260e8 | − | 5.48059e8i | −0.288074 | − | 0.192477i | ||||
\(232\) | 8.27770e7 | 0.0285731 | ||||||||
\(233\) | 2.72132e9i | 0.923328i | 0.887055 | + | 0.461664i | \(0.152747\pi\) | ||||
−0.887055 | + | 0.461664i | \(0.847253\pi\) | |||||||
\(234\) | 3.50134e9 | − | 1.45045e9i | 1.16781 | − | 0.483769i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 3.40129e9i | − | 1.09647i | ||||||
\(237\) | 1.03414e9 | − | 1.54777e9i | 0.327784 | − | 0.490582i | ||||
\(238\) | −2.94235e9 | −0.917037 | ||||||||
\(239\) | − | 2.27461e9i | − | 0.697132i | −0.937284 | − | 0.348566i | \(-0.886669\pi\) | ||
0.937284 | − | 0.348566i | \(-0.113331\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.74667e9 | −0.517778 | −0.258889 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258889 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(242\) | − | 3.72500e9i | − | 1.08609i | ||||||
\(243\) | −6.80540e8 | − | 3.41973e9i | −0.195177 | − | 0.980768i | ||||
\(244\) | −1.86893e8 | −0.0527272 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.89469e9 | + | 2.83571e9i | −0.517365 | + | 0.774321i | ||||
\(247\) | −4.87275e8 | −0.130914 | ||||||||
\(248\) | 6.31253e7i | 0.0166877i | ||||||||
\(249\) | −3.12471e9 | − | 2.08778e9i | −0.812853 | − | 0.543110i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.37549e9i | 0.346547i | 0.984874 | + | 0.173274i | \(0.0554345\pi\) | ||||
−0.984874 | + | 0.173274i | \(0.944566\pi\) | |||||||
\(252\) | 1.08977e9 | + | 2.63068e9i | 0.270230 | + | 0.652329i | ||||
\(253\) | −3.27417e9 | −0.799132 | ||||||||
\(254\) | 6.19605e9i | 1.48861i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.55069e9 | 1.05954 | ||||||||
\(257\) | 7.93672e9i | 1.81932i | 0.415356 | + | 0.909659i | \(0.363657\pi\) | ||||
−0.415356 | + | 0.909659i | \(0.636343\pi\) | |||||||
\(258\) | 5.33154e9 | + | 3.56228e9i | 1.20330 | + | 0.803988i | ||||
\(259\) | −2.33655e9 | −0.519249 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.79372e9 | − | 1.15731e9i | 0.602034 | − | 0.249396i | ||||
\(262\) | 6.49068e9 | 1.37748 | ||||||||
\(263\) | − | 3.22555e8i | − | 0.0674187i | −0.999432 | − | 0.0337093i | \(-0.989268\pi\) | ||
0.999432 | − | 0.0337093i | \(-0.0107320\pi\) | |||||||
\(264\) | −5.62464e7 | + | 8.41819e7i | −0.0115792 | + | 0.0173302i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 7.44025e8i | − | 0.148614i | ||||||
\(267\) | −4.89062e9 | − | 3.26769e9i | −0.962319 | − | 0.642977i | ||||
\(268\) | 5.62685e8 | 0.109075 | ||||||||
\(269\) | 3.47314e9i | 0.663304i | 0.943402 | + | 0.331652i | \(0.107606\pi\) | ||||
−0.943402 | + | 0.331652i | \(0.892394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.44216e9 | −0.267385 | −0.133693 | − | 0.991023i | \(-0.542683\pi\) | ||||
−0.133693 | + | 0.991023i | \(0.542683\pi\) | |||||||
\(272\) | 5.05678e9i | 0.923843i | ||||||||
\(273\) | 2.02624e9 | − | 3.03259e9i | 0.364787 | − | 0.545964i | ||||
\(274\) | 4.65976e9 | 0.826726 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 7.85800e9 | + | 5.25035e9i | 1.35418 | + | 0.904798i | ||||
\(277\) | −3.38046e9 | −0.574192 | −0.287096 | − | 0.957902i | \(-0.592690\pi\) | ||||
−0.287096 | + | 0.957902i | \(0.592690\pi\) | |||||||
\(278\) | 3.20289e9i | 0.536245i | ||||||||
\(279\) | 8.82561e8 | + | 2.13048e9i | 0.145656 | + | 0.351609i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.02262e9i | 0.645184i | 0.946538 | + | 0.322592i | \(0.104554\pi\) | ||||
−0.946538 | + | 0.322592i | \(0.895446\pi\) | |||||||
\(282\) | −4.12286e9 | + | 6.17053e9i | −0.651932 | + | 0.975722i | ||||
\(283\) | 1.04253e10 | 1.62533 | 0.812666 | − | 0.582730i | \(-0.198016\pi\) | ||||
0.812666 | + | 0.582730i | \(0.198016\pi\) | |||||||
\(284\) | − | 4.22146e9i | − | 0.648917i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.02006e9 | −0.600853 | ||||||||
\(287\) | 3.28207e9i | 0.483749i | ||||||||
\(288\) | 8.90943e9 | − | 3.69078e9i | 1.29503 | − | 0.536473i | ||||
\(289\) | 1.36679e9 | 0.195935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.62720e9 | − | 9.91868e9i | 0.924183 | − | 1.38319i | ||||
\(292\) | 6.86285e9 | 0.944002 | ||||||||
\(293\) | − | 1.03927e10i | − | 1.41012i | −0.709146 | − | 0.705061i | \(-0.750919\pi\) | ||
0.709146 | − | 0.705061i | \(-0.249081\pi\) | |||||||
\(294\) | −4.08588e9 | − | 2.72999e9i | −0.546885 | − | 0.365403i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.39796e8i | 0.0312374i | ||||||||
\(297\) | −7.21360e8 | + | 3.62753e9i | −0.0927099 | + | 0.466213i | ||||
\(298\) | −1.83918e10 | −2.33216 | ||||||||
\(299\) | − | 1.21050e10i | − | 1.51453i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.17076e9 | 0.751749 | ||||||||
\(302\) | − | 9.51565e9i | − | 1.14396i | ||||||
\(303\) | 6.97372e9 | + | 4.65951e9i | 0.827359 | + | 0.552803i | ||||
\(304\) | −1.27869e9 | −0.149717 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.22185e9 | + | 1.01914e10i | 0.481524 | + | 1.16238i | ||||
\(307\) | 2.99309e9 | 0.336951 | 0.168476 | − | 0.985706i | \(-0.446116\pi\) | ||||
0.168476 | + | 0.985706i | \(0.446116\pi\) | |||||||
\(308\) | − | 3.02042e9i | − | 0.335632i | ||||||
\(309\) | −7.47286e9 | + | 1.11843e10i | −0.819696 | + | 1.22681i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.44832e9i | 0.689295i | 0.938732 | + | 0.344647i | \(0.112002\pi\) | ||||
−0.938732 | + | 0.344647i | \(0.887998\pi\) | |||||||
\(312\) | −3.11230e8 | − | 2.07949e8i | −0.0328445 | − | 0.0219452i | ||||
\(313\) | −3.27737e7 | −0.00341467 | −0.00170733 | − | 0.999999i | \(-0.500543\pi\) | ||||
−0.00170733 | + | 0.999999i | \(0.500543\pi\) | |||||||
\(314\) | − | 1.70586e10i | − | 1.75479i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.69928e9 | 0.571573 | ||||||||
\(317\) | 1.17797e10i | 1.16653i | 0.812282 | + | 0.583264i | \(0.198225\pi\) | ||||
−0.812282 | + | 0.583264i | \(0.801775\pi\) | |||||||
\(318\) | −6.66942e9 | + | 9.98187e9i | −0.652198 | + | 0.976120i | ||||
\(319\) | −3.20761e9 | −0.309755 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.51901e9 | − | 1.01493e9i | −0.143067 | − | 0.0955907i | ||||
\(322\) | 1.84832e10 | 1.71931 | ||||||||
\(323\) | − | 1.41832e9i | − | 0.130306i | ||||||
\(324\) | 7.54825e9 | − | 7.54931e9i | 0.684961 | − | 0.685058i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.50002e10i | 1.32808i | ||||||||
\(327\) | 4.94888e9 | − | 7.40680e9i | 0.432829 | − | 0.647798i | ||||
\(328\) | 3.36833e8 | 0.0291018 | ||||||||
\(329\) | 7.14182e9i | 0.609573i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.20100e10 | −1.00053 | −0.500265 | − | 0.865872i | \(-0.666764\pi\) | ||||
−0.500265 | + | 0.865872i | \(0.666764\pi\) | |||||||
\(332\) | − | 1.15060e10i | − | 0.947049i | ||||||
\(333\) | 3.35261e9 | + | 8.09311e9i | 0.272651 | + | 0.658171i | ||||
\(334\) | −4.40705e9 | −0.354130 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 5.31720e9 | − | 7.95806e9i | 0.417182 | − | 0.624381i | ||||
\(337\) | −1.59214e10 | −1.23441 | −0.617207 | − | 0.786801i | \(-0.711736\pi\) | ||||
−0.617207 | + | 0.786801i | \(0.711736\pi\) | |||||||
\(338\) | 3.45051e9i | 0.264372i | ||||||||
\(339\) | 1.93798e10 | + | 1.29486e10i | 1.46740 | + | 0.980451i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.44611e9i | − | 0.180908i | ||||||
\(342\) | −2.57708e9 | + | 1.06757e9i | −0.188375 | + | 0.0780354i | ||||
\(343\) | −1.48174e10 | −1.07052 | ||||||||
\(344\) | − | 6.33295e8i | − | 0.0452243i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.29706e10 | −1.60276 | ||||||||
\(347\) | 4.94792e9i | 0.341275i | 0.985334 | + | 0.170638i | \(0.0545828\pi\) | ||||
−0.985334 | + | 0.170638i | \(0.945417\pi\) | |||||||
\(348\) | 7.69826e9 | + | 5.14361e9i | 0.524899 | + | 0.350713i | ||||
\(349\) | −7.29567e9 | −0.491772 | −0.245886 | − | 0.969299i | \(-0.579079\pi\) | ||||
−0.245886 | + | 0.969299i | \(0.579079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.34114e10 | − | 2.66695e9i | −0.883578 | − | 0.175706i | ||||
\(352\) | −1.02293e10 | −0.666311 | ||||||||
\(353\) | 6.93875e9i | 0.446871i | 0.974719 | + | 0.223436i | \(0.0717272\pi\) | ||||
−0.974719 | + | 0.223436i | \(0.928273\pi\) | |||||||
\(354\) | −1.38554e10 | + | 2.07369e10i | −0.882282 | + | 1.32048i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 1.80086e10i | − | 1.12119i | ||||||
\(357\) | 8.82706e9 | + | 5.89782e9i | 0.543429 | + | 0.363094i | ||||
\(358\) | −2.89368e10 | −1.76164 | ||||||||
\(359\) | 1.60096e10i | 0.963838i | 0.876216 | + | 0.481919i | \(0.160060\pi\) | ||||
−0.876216 | + | 0.481919i | \(0.839940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.66249e10 | −0.978883 | ||||||||
\(362\) | − | 1.05898e10i | − | 0.616670i | ||||||
\(363\) | −7.46660e9 | + | 1.11750e10i | −0.430028 | + | 0.643607i | ||||
\(364\) | 1.11668e10 | 0.636098 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.13945e9 | + | 7.61325e8i | 0.0634994 | + | 0.0424273i | ||||
\(367\) | −1.36364e10 | −0.751686 | −0.375843 | − | 0.926683i | \(-0.622647\pi\) | ||||
−0.375843 | + | 0.926683i | \(0.622647\pi\) | |||||||
\(368\) | − | 3.17655e10i | − | 1.73207i | ||||||
\(369\) | 1.13681e10 | − | 4.70930e9i | 0.613173 | − | 0.254010i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.15531e10i | 0.609821i | ||||||||
\(372\) | −3.92249e9 | + | 5.87065e9i | −0.204829 | + | 0.306559i | ||||
\(373\) | 2.44062e10 | 1.26085 | 0.630427 | − | 0.776248i | \(-0.282880\pi\) | ||||
0.630427 | + | 0.776248i | \(0.282880\pi\) | |||||||
\(374\) | − | 1.17013e10i | − | 0.598063i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.32953e8 | 0.0366712 | ||||||||
\(377\) | − | 1.18589e10i | − | 0.587055i | ||||||
\(378\) | 4.07219e9 | − | 2.04780e10i | 0.199463 | − | 1.00304i | ||||
\(379\) | −1.98392e10 | −0.961542 | −0.480771 | − | 0.876846i | \(-0.659643\pi\) | ||||
−0.480771 | + | 0.876846i | \(0.659643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.24197e10 | − | 1.85881e10i | 0.589403 | − | 0.882137i | ||||
\(382\) | −3.63211e9 | −0.170571 | ||||||||
\(383\) | 1.51133e10i | 0.702366i | 0.936307 | + | 0.351183i | \(0.114220\pi\) | ||||
−0.936307 | + | 0.351183i | \(0.885780\pi\) | |||||||
\(384\) | −1.58467e9 | − | 1.05880e9i | −0.0728811 | − | 0.0486957i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3.56594e10i | − | 1.60630i | ||||||
\(387\) | −8.85416e9 | − | 2.13737e10i | −0.394733 | − | 0.952875i | ||||
\(388\) | 3.65232e10 | 1.61154 | ||||||||
\(389\) | − | 1.79991e10i | − | 0.786056i | −0.919527 | − | 0.393028i | \(-0.871428\pi\) | ||
0.919527 | − | 0.393028i | \(-0.128572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.52342e10 | 1.50750 | ||||||||
\(392\) | 4.85332e8i | 0.0205539i | ||||||||
\(393\) | −1.94720e10 | − | 1.30103e10i | −0.816284 | − | 0.545403i | ||||
\(394\) | 1.20729e10 | 0.500987 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.04618e10 | + | 4.33386e9i | −0.425429 | + | 0.176236i | ||||
\(397\) | 2.35673e10 | 0.948739 | 0.474370 | − | 0.880326i | \(-0.342676\pi\) | ||||
0.474370 | + | 0.880326i | \(0.342676\pi\) | |||||||
\(398\) | − | 1.45383e10i | − | 0.579403i | ||||||
\(399\) | −1.49137e9 | + | 2.23207e9i | −0.0588428 | + | 0.0880678i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.37692e10i | 0.532515i | 0.963902 | + | 0.266257i | \(0.0857871\pi\) | ||||
−0.963902 | + | 0.266257i | \(0.914213\pi\) | |||||||
\(402\) | −3.43056e9 | − | 2.29214e9i | −0.131359 | − | 0.0877682i | ||||
\(403\) | 9.04353e9 | 0.342861 | ||||||||
\(404\) | 2.56791e10i | 0.963950i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.81075e10 | 0.666428 | ||||||||
\(407\) | − | 9.29209e9i | − | 0.338638i | ||||||
\(408\) | 6.05284e8 | − | 9.05906e8i | 0.0218433 | − | 0.0326921i | ||||
\(409\) | 3.58480e10 | 1.28107 | 0.640533 | − | 0.767931i | \(-0.278714\pi\) | ||||
0.640533 | + | 0.767931i | \(0.278714\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.39793e10 | − | 9.34031e9i | −0.489912 | − | 0.327336i | ||||
\(412\) | −4.11838e10 | −1.42934 | ||||||||
\(413\) | 2.40011e10i | 0.824955i | ||||||||
\(414\) | −2.65207e10 | − | 6.40203e10i | −0.902785 | − | 2.17930i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 3.78191e10i | − | 1.26281i | ||||||
\(417\) | 6.42007e9 | − | 9.60868e9i | 0.212322 | − | 0.317775i | ||||
\(418\) | 2.95887e9 | 0.0969217 | ||||||||
\(419\) | 2.23996e10i | 0.726750i | 0.931643 | + | 0.363375i | \(0.118376\pi\) | ||||
−0.931643 | + | 0.363375i | \(0.881624\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49535e10 | −0.476008 | −0.238004 | − | 0.971264i | \(-0.576493\pi\) | ||||
−0.238004 | + | 0.971264i | \(0.576493\pi\) | |||||||
\(422\) | − | 1.30457e9i | − | 0.0411357i | ||||||
\(423\) | 2.47372e10 | − | 1.02475e10i | 0.772660 | − | 0.320078i | ||||
\(424\) | 1.18567e9 | 0.0366861 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.71964e10 | + | 2.57373e10i | −0.522156 | + | 0.781491i | ||||
\(427\) | 1.31880e9 | 0.0396706 | ||||||||
\(428\) | − | 5.59339e9i | − | 0.166686i | ||||||
\(429\) | 1.20602e10 | + | 8.05804e9i | 0.356061 | + | 0.237903i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6.40436e10i | − | 1.85595i | −0.372640 | − | 0.927976i | \(-0.621547\pi\) | ||
0.372640 | − | 0.927976i | \(-0.378453\pi\) | |||||||
\(432\) | −3.51938e10 | − | 6.99854e9i | −1.01049 | − | 0.200943i | ||||
\(433\) | 5.22954e9 | 0.148769 | 0.0743843 | − | 0.997230i | \(-0.476301\pi\) | ||||
0.0743843 | + | 0.997230i | \(0.476301\pi\) | |||||||
\(434\) | 1.38087e10i | 0.389218i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.72738e10 | 0.754745 | ||||||||
\(437\) | 8.90959e9i | 0.244305i | ||||||||
\(438\) | −4.18412e10 | − | 2.79563e10i | −1.13686 | − | 0.759598i | ||||
\(439\) | 4.34801e10 | 1.17066 | 0.585332 | − | 0.810793i | \(-0.300964\pi\) | ||||
0.585332 | + | 0.810793i | \(0.300964\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.78548e9 | + | 1.63800e10i | 0.179402 | + | 0.433070i | ||||
\(442\) | 4.32610e10 | 1.13346 | ||||||||
\(443\) | 3.78737e10i | 0.983383i | 0.870770 | + | 0.491691i | \(0.163621\pi\) | ||||
−0.870770 | + | 0.491691i | \(0.836379\pi\) | |||||||
\(444\) | −1.49005e10 | + | 2.23010e10i | −0.383415 | + | 0.573843i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.88246e10i | 2.49761i | ||||||||
\(447\) | 5.51754e10 | + | 3.68656e10i | 1.38202 | + | 0.923403i | ||||
\(448\) | 2.74973e10 | 0.682620 | ||||||||
\(449\) | 2.95505e10i | 0.727076i | 0.931579 | + | 0.363538i | \(0.118431\pi\) | ||||
−0.931579 | + | 0.363538i | \(0.881569\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.30523e10 | −0.315486 | ||||||||
\(452\) | 7.13614e10i | 1.70966i | ||||||||
\(453\) | −1.90737e10 | + | 2.85469e10i | −0.452942 | + | 0.677902i | ||||
\(454\) | −7.93813e10 | −1.86851 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.29074e8 | + | 1.53057e8i | 0.00529806 | + | 0.00353991i | ||||
\(457\) | 2.02181e10 | 0.463529 | 0.231764 | − | 0.972772i | \(-0.425550\pi\) | ||||
0.231764 | + | 0.972772i | \(0.425550\pi\) | |||||||
\(458\) | 4.18847e10i | 0.951905i | ||||||||
\(459\) | 7.76277e9 | − | 3.90369e10i | 0.174890 | − | 0.879476i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.01826e10i | 1.55391i | 0.629556 | + | 0.776955i | \(0.283237\pi\) | ||||
−0.629556 | + | 0.776955i | \(0.716763\pi\) | |||||||
\(462\) | −1.23039e10 | + | 1.84148e10i | −0.270069 | + | 0.404202i | ||||
\(463\) | −4.16009e9 | −0.0905271 | −0.0452635 | − | 0.998975i | \(-0.514413\pi\) | ||||
−0.0452635 | + | 0.998975i | \(0.514413\pi\) | |||||||
\(464\) | − | 3.11198e10i | − | 0.671374i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.10935e10 | 1.29554 | ||||||||
\(467\) | − | 2.88138e10i | − | 0.605806i | −0.953021 | − | 0.302903i | \(-0.902044\pi\) | ||
0.953021 | − | 0.302903i | \(-0.0979558\pi\) | |||||||
\(468\) | −1.60228e10 | − | 3.86786e10i | −0.334006 | − | 0.806282i | ||||
\(469\) | −3.97056e9 | −0.0820654 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.41933e10 | + | 5.11758e10i | −0.694796 | + | 1.03988i | ||||
\(472\) | 2.46319e9 | 0.0496283 | ||||||||
\(473\) | 2.45402e10i | 0.490268i | ||||||||
\(474\) | −3.47472e10 | − | 2.32165e10i | −0.688346 | − | 0.459921i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.25036e10i | 0.633145i | ||||||||
\(477\) | 4.00165e10 | − | 1.65770e10i | 0.772975 | − | 0.320209i | ||||
\(478\) | −5.10649e10 | −0.978161 | ||||||||
\(479\) | 4.47149e10i | 0.849395i | 0.905335 | + | 0.424698i | \(0.139620\pi\) | ||||
−0.905335 | + | 0.424698i | \(0.860380\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.43539e10 | 0.641795 | ||||||||
\(482\) | 3.92127e10i | 0.726505i | ||||||||
\(483\) | −5.54496e10 | − | 3.70488e10i | −1.01885 | − | 0.680747i | ||||
\(484\) | −4.11493e10 | −0.749861 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.67727e10 | + | 1.52781e10i | −1.37614 | + | 0.273857i | ||||
\(487\) | −5.72836e10 | −1.01839 | −0.509195 | − | 0.860651i | \(-0.670057\pi\) | ||||
−0.509195 | + | 0.860651i | \(0.670057\pi\) | |||||||
\(488\) | − | 1.35347e8i | − | 0.00238654i | ||||||
\(489\) | 3.00672e10 | − | 4.50005e10i | 0.525845 | − | 0.787012i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.25262e10i | − | 1.24787i | −0.781477 | − | 0.623934i | \(-0.785533\pi\) | ||
0.781477 | − | 0.623934i | \(-0.214467\pi\) | |||||||
\(492\) | 3.13255e10 | + | 2.09302e10i | 0.534611 | + | 0.357202i | ||||
\(493\) | 3.45180e10 | 0.584330 | ||||||||
\(494\) | 1.09393e10i | 0.183688i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.37318e10 | 0.392106 | ||||||||
\(497\) | 2.97885e10i | 0.488228i | ||||||||
\(498\) | −4.68706e10 | + | 7.01495e10i | −0.762050 | + | 1.14053i | ||||
\(499\) | −2.64368e10 | −0.426389 | −0.213195 | − | 0.977010i | \(-0.568387\pi\) | ||||
−0.213195 | + | 0.977010i | \(0.568387\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32212e10 | + | 8.83376e9i | 0.209855 | + | 0.140215i | ||||
\(502\) | 3.08797e10 | 0.486248 | ||||||||
\(503\) | − | 7.52828e10i | − | 1.17604i | −0.808845 | − | 0.588022i | \(-0.799907\pi\) | ||
0.808845 | − | 0.588022i | \(-0.200093\pi\) | |||||||
\(504\) | −1.90512e9 | + | 7.89205e8i | −0.0295257 | + | 0.0122312i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 7.35048e10i | 1.12128i | ||||||||
\(507\) | 6.91640e9 | − | 1.03515e10i | 0.104676 | − | 0.156665i | ||||
\(508\) | 6.84465e10 | 1.02777 | ||||||||
\(509\) | − | 6.45184e10i | − | 0.961197i | −0.876941 | − | 0.480599i | \(-0.840419\pi\) | ||
0.876941 | − | 0.480599i | \(-0.159581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.84273e10 | −0.710243 | ||||||||
\(512\) | − | 9.61394e10i | − | 1.39901i | ||||||
\(513\) | 9.87115e9 | + | 1.96295e9i | 0.142527 | + | 0.0283426i | ||||
\(514\) | 1.78179e11 | 2.55272 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.93518e10 | − | 5.88964e10i | 0.555094 | − | 0.830788i | ||||
\(517\) | −2.84019e10 | −0.397544 | ||||||||
\(518\) | 5.24554e10i | 0.728569i | ||||||||
\(519\) | 6.89119e10 | + | 4.60437e10i | 0.949783 | + | 0.634601i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.65146e10i | − | 1.03847i | −0.854632 | − | 0.519235i | \(-0.826217\pi\) | ||
0.854632 | − | 0.519235i | \(-0.173783\pi\) | |||||||
\(522\) | −2.59816e10 | − | 6.27189e10i | −0.349932 | − | 0.844727i | ||||
\(523\) | 8.46771e10 | 1.13177 | 0.565886 | − | 0.824483i | \(-0.308534\pi\) | ||||
0.565886 | + | 0.824483i | \(0.308534\pi\) | |||||||
\(524\) | − | 7.17012e10i | − | 0.951046i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.24133e9 | −0.0945966 | ||||||||
\(527\) | 2.63232e10i | 0.341269i | ||||||||
\(528\) | 3.16480e10 | + | 2.11457e10i | 0.407202 | + | 0.272073i | ||||
\(529\) | −1.43023e11 | −1.82634 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 8.31326e10 | − | 3.44381e10i | 1.04567 | − | 0.433173i | ||||
\(532\) | −8.21909e9 | −0.102607 | ||||||||
\(533\) | − | 4.82558e10i | − | 0.597917i | ||||||
\(534\) | −7.33594e10 | + | 1.09794e11i | −0.902175 | + | 1.35025i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.07492e8i | 0.00493696i | ||||||||
\(537\) | 8.68104e10 | + | 5.80026e10i | 1.04394 | + | 0.697510i | ||||
\(538\) | 7.79717e10 | 0.930696 | ||||||||
\(539\) | − | 1.88066e10i | − | 0.222821i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.43470e11 | 1.67483 | 0.837415 | − | 0.546568i | \(-0.184066\pi\) | ||||
0.837415 | + | 0.546568i | \(0.184066\pi\) | |||||||
\(542\) | 3.23765e10i | 0.375174i | ||||||||
\(543\) | −2.12268e10 | + | 3.17694e10i | −0.244166 | + | 0.365434i | ||||
\(544\) | 1.10081e11 | 1.25695 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −6.80816e10 | − | 4.54889e10i | −0.766053 | − | 0.511841i | ||||
\(547\) | −1.64171e11 | −1.83378 | −0.916892 | − | 0.399134i | \(-0.869311\pi\) | ||||
−0.916892 | + | 0.399134i | \(0.869311\pi\) | |||||||
\(548\) | − | 5.14755e10i | − | 0.570792i | ||||||
\(549\) | −1.89229e9 | − | 4.56795e9i | −0.0208305 | − | 0.0502842i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.72847e9i | 0.0946961i | ||||||||
\(552\) | −3.80226e9 | + | 5.69070e9i | −0.0409529 | + | 0.0612928i | ||||
\(553\) | −4.02167e10 | −0.430037 | ||||||||
\(554\) | 7.58912e10i | 0.805661i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.53817e10 | 0.370237 | ||||||||
\(557\) | − | 1.54420e11i | − | 1.60429i | −0.597130 | − | 0.802145i | \(-0.703692\pi\) | ||
0.597130 | − | 0.802145i | \(-0.296308\pi\) | |||||||
\(558\) | 4.78291e10 | − | 1.98135e10i | 0.493351 | − | 0.204373i | ||||
\(559\) | −9.07278e10 | −0.929166 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.34547e10 | + | 3.51039e10i | −0.236799 | + | 0.354408i | ||||
\(562\) | 9.03075e10 | 0.905271 | ||||||||
\(563\) | − | 1.54622e11i | − | 1.53900i | −0.638646 | − | 0.769500i | \(-0.720505\pi\) | ||
0.638646 | − | 0.769500i | \(-0.279495\pi\) | |||||||
\(564\) | 6.81646e10 | + | 4.55444e10i | 0.673663 | + | 0.450110i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 2.34047e11i | − | 2.28054i | ||||||
\(567\) | −5.32638e10 | + | 5.32714e10i | −0.515348 | + | 0.515420i | ||||
\(568\) | 3.05714e9 | 0.0293712 | ||||||||
\(569\) | − | 1.15380e11i | − | 1.10073i | −0.834925 | − | 0.550364i | \(-0.814489\pi\) | ||
0.834925 | − | 0.550364i | \(-0.185511\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.63410e11 | −1.53722 | −0.768608 | − | 0.639720i | \(-0.779050\pi\) | ||||
−0.768608 | + | 0.639720i | \(0.779050\pi\) | |||||||
\(572\) | 4.44087e10i | 0.414844i | ||||||||
\(573\) | 1.08963e10 | + | 7.28041e9i | 0.101079 | + | 0.0675363i | ||||
\(574\) | 7.36823e10 | 0.678759 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.94548e10 | − | 9.52427e10i | −0.358434 | − | 0.865250i | ||||
\(577\) | −7.42282e10 | −0.669678 | −0.334839 | − | 0.942275i | \(-0.608682\pi\) | ||||
−0.334839 | + | 0.942275i | \(0.608682\pi\) | |||||||
\(578\) | − | 3.06844e10i | − | 0.274920i | ||||||
\(579\) | −7.14779e10 | + | 1.06978e11i | −0.636001 | + | 0.951879i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.11916e10i | 0.712535i | ||||||||
\(582\) | −2.22674e11 | − | 1.48780e11i | −1.94078 | − | 1.29674i | ||||
\(583\) | −4.59449e10 | −0.397707 | ||||||||
\(584\) | 4.97002e9i | 0.0427274i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.33315e11 | −1.97857 | ||||||||
\(587\) | 6.72877e10i | 0.566739i | 0.959011 | + | 0.283369i | \(0.0914523\pi\) | ||||
−0.959011 | + | 0.283369i | \(0.908548\pi\) | |||||||
\(588\) | −3.01577e10 | + | 4.51359e10i | −0.252283 | + | 0.377583i | ||||
\(589\) | −6.65629e9 | −0.0553059 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.62187e10 | − | 2.41996e10i | −0.296881 | − | 0.198362i | ||||
\(592\) | 9.01507e10 | 0.733977 | ||||||||
\(593\) | 2.36444e10i | 0.191210i | 0.995419 | + | 0.0956048i | \(0.0304785\pi\) | ||||
−0.995419 | + | 0.0956048i | \(0.969521\pi\) | |||||||
\(594\) | 8.14378e10 | + | 1.61945e10i | 0.654154 | + | 0.130083i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.03170e11i | 1.61018i | ||||||||
\(597\) | −2.91414e10 | + | 4.36148e10i | −0.229410 | + | 0.343350i | ||||
\(598\) | −2.71756e11 | −2.12507 | ||||||||
\(599\) | 3.03370e10i | 0.235649i | 0.993034 | + | 0.117825i | \(0.0375921\pi\) | ||||
−0.993034 | + | 0.117825i | \(0.962408\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.37911e10 | 0.259003 | 0.129501 | − | 0.991579i | \(-0.458662\pi\) | ||||
0.129501 | + | 0.991579i | \(0.458662\pi\) | |||||||
\(602\) | − | 1.38533e11i | − | 1.05480i | ||||||
\(603\) | 5.69718e9 | + | 1.37528e10i | 0.0430914 | + | 0.104022i | ||||
\(604\) | −1.05117e11 | −0.789818 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.04606e11 | − | 1.56560e11i | 0.775649 | − | 1.16089i | ||||
\(607\) | 3.82366e10 | 0.281660 | 0.140830 | − | 0.990034i | \(-0.455023\pi\) | ||||
0.140830 | + | 0.990034i | \(0.455023\pi\) | |||||||
\(608\) | 2.78359e10i | 0.203700i | ||||||||
\(609\) | −5.43224e10 | − | 3.62957e10i | −0.394920 | − | 0.263867i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.05005e11i | − | 0.753435i | ||||||
\(612\) | 1.12583e11 | − | 4.66380e10i | 0.802539 | − | 0.332456i | ||||
\(613\) | −1.08066e11 | −0.765330 | −0.382665 | − | 0.923887i | \(-0.624994\pi\) | ||||
−0.382665 | + | 0.923887i | \(0.624994\pi\) | |||||||
\(614\) | − | 6.71948e10i | − | 0.472783i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.18736e9 | 0.0151914 | ||||||||
\(617\) | 4.72538e9i | 0.0326059i | 0.999867 | + | 0.0163029i | \(0.00518962\pi\) | ||||
−0.999867 | + | 0.0163029i | \(0.994810\pi\) | |||||||
\(618\) | 2.51088e11 | + | 1.67765e11i | 1.72136 | + | 1.15013i | ||||
\(619\) | 2.29845e10 | 0.156557 | 0.0782786 | − | 0.996932i | \(-0.475058\pi\) | ||||
0.0782786 | + | 0.996932i | \(0.475058\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.87639e10 | + | 2.45221e11i | −0.327893 | + | 1.64889i | ||||
\(622\) | 1.44764e11 | 0.967165 | ||||||||
\(623\) | 1.27077e11i | 0.843555i | ||||||||
\(624\) | −7.81780e10 | + | 1.17006e11i | −0.515640 | + | 0.771739i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.35768e8i | 0.00479119i | ||||||||
\(627\) | −8.87662e9 | − | 5.93094e9i | −0.0574351 | − | 0.0383754i | ||||
\(628\) | −1.88443e11 | −1.21155 | ||||||||
\(629\) | 9.99949e10i | 0.638815i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.01892e11 | −0.642722 | −0.321361 | − | 0.946957i | \(-0.604140\pi\) | ||||
−0.321361 | + | 0.946957i | \(0.604140\pi\) | |||||||
\(632\) | 4.12737e9i | 0.0258705i | ||||||||
\(633\) | −2.61497e9 | + | 3.91372e9i | −0.0162874 | + | 0.0243767i | ||||
\(634\) | 2.64453e11 | 1.63678 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.10268e11 | + | 7.36757e10i | 0.673938 | + | 0.450294i | ||||
\(637\) | 6.95302e10 | 0.422295 | ||||||||
\(638\) | 7.20106e10i | 0.434624i | ||||||||
\(639\) | 1.03179e11 | − | 4.27422e10i | 0.618851 | − | 0.256362i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.17803e11i | 0.697791i | 0.937162 | + | 0.348896i | \(0.113443\pi\) | ||||
−0.937162 | + | 0.348896i | \(0.886557\pi\) | |||||||
\(642\) | −2.27851e10 | + | 3.41016e10i | −0.134125 | + | 0.200740i | ||||
\(643\) | 2.62680e10 | 0.153668 | 0.0768339 | − | 0.997044i | \(-0.475519\pi\) | ||||
0.0768339 | + | 0.997044i | \(0.475519\pi\) | |||||||
\(644\) | − | 2.04180e11i | − | 1.18705i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.18413e10 | −0.182836 | ||||||||
\(647\) | − | 3.10527e11i | − | 1.77208i | −0.463612 | − | 0.886038i | \(-0.653447\pi\) | ||
0.463612 | − | 0.886038i | \(-0.346553\pi\) | |||||||
\(648\) | 5.46715e9 | + | 5.46638e9i | 0.0310071 | + | 0.0310027i | ||||
\(649\) | −9.54486e10 | −0.538010 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.76789e10 | − | 4.14260e10i | 0.154108 | − | 0.230648i | ||||
\(652\) | 1.65704e11 | 0.916942 | ||||||||
\(653\) | − | 3.48345e10i | − | 0.191583i | −0.995401 | − | 0.0957914i | \(-0.969462\pi\) | ||
0.995401 | − | 0.0957914i | \(-0.0305382\pi\) | |||||||
\(654\) | −1.66282e11 | − | 1.11102e11i | −0.908940 | − | 0.607311i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.26632e11i | − | 0.683796i | ||||||
\(657\) | 6.94863e10 | + | 1.67738e11i | 0.372939 | + | 0.900265i | ||||
\(658\) | 1.60333e11 | 0.855304 | ||||||||
\(659\) | 3.77120e10i | 0.199957i | 0.994990 | + | 0.0999787i | \(0.0318775\pi\) | ||||
−0.994990 | + | 0.0999787i | \(0.968123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.39619e11 | −0.731372 | −0.365686 | − | 0.930738i | \(-0.619166\pi\) | ||||
−0.365686 | + | 0.930738i | \(0.619166\pi\) | |||||||
\(662\) | 2.69623e11i | 1.40386i | ||||||||
\(663\) | −1.29783e11 | − | 8.67149e10i | −0.671682 | − | 0.448786i | ||||
\(664\) | 8.33256e9 | 0.0428653 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.81690e11 | − | 7.52659e10i | 0.923494 | − | 0.382562i | ||||
\(667\) | −2.16834e11 | −1.09553 | ||||||||
\(668\) | 4.86838e10i | 0.244500i | ||||||||
\(669\) | 1.98090e11 | − | 2.96474e11i | 0.988912 | − | 1.48007i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.24468e9i | 0.0258719i | ||||||||
\(672\) | −1.73239e11 | − | 1.15750e11i | −0.849510 | − | 0.567603i | ||||
\(673\) | 1.29783e11 | 0.632642 | 0.316321 | − | 0.948652i | \(-0.397552\pi\) | ||||
0.316321 | + | 0.948652i | \(0.397552\pi\) | |||||||
\(674\) | 3.57434e11i | 1.73203i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.81171e10 | 0.182529 | ||||||||
\(677\) | 3.40648e11i | 1.62163i | 0.585306 | + | 0.810813i | \(0.300975\pi\) | ||||
−0.585306 | + | 0.810813i | \(0.699025\pi\) | |||||||
\(678\) | 2.90696e11 | − | 4.35075e11i | 1.37569 | − | 2.05895i | ||||
\(679\) | −2.57724e11 | −1.21248 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.38144e11 | + | 1.59117e11i | 1.10726 | + | 0.739821i | ||||
\(682\) | −5.49149e10 | −0.253836 | ||||||||
\(683\) | − | 1.02876e11i | − | 0.472750i | −0.971662 | − | 0.236375i | \(-0.924041\pi\) | ||
0.971662 | − | 0.236375i | \(-0.0759593\pi\) | |||||||
\(684\) | 1.17932e10 | + | 2.84685e10i | 0.0538776 | + | 0.130059i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.32650e11i | 1.50208i | ||||||||
\(687\) | 8.39562e10 | − | 1.25654e11i | 0.376900 | − | 0.564092i | ||||
\(688\) | −2.38086e11 | −1.06262 | ||||||||
\(689\) | − | 1.69863e11i | − | 0.753742i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.58259e11 | 1.57140 | 0.785698 | − | 0.618611i | \(-0.212304\pi\) | ||||
0.785698 | + | 0.618611i | \(0.212304\pi\) | |||||||
\(692\) | 2.53752e11i | 1.10659i | ||||||||
\(693\) | 7.38234e10 | − | 3.05817e10i | 0.320082 | − | 0.132595i | ||||
\(694\) | 1.11081e11 | 0.478851 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.72496e9 | + | 5.57501e9i | −0.0158740 | + | 0.0237580i | ||||
\(697\) | 1.40459e11 | 0.595141 | ||||||||
\(698\) | 1.63787e11i | 0.690016i | ||||||||
\(699\) | −1.83280e11 | − | 1.22459e11i | −0.767728 | − | 0.512960i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.49323e11i | − | 1.03250i | −0.856438 | − | 0.516250i | \(-0.827327\pi\) | ||
0.856438 | − | 0.516250i | \(-0.172673\pi\) | |||||||
\(702\) | −5.98729e10 | + | 3.01085e11i | −0.246537 | + | 1.23977i | ||||
\(703\) | −2.52854e10 | −0.103526 | ||||||||
\(704\) | 1.09353e11i | 0.445183i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.55775e11 | 0.627015 | ||||||||
\(707\) | − | 1.81203e11i | − | 0.725251i | ||||||
\(708\) | 2.29077e11 | + | 1.53058e11i | 0.911691 | + | 0.609149i | ||||
\(709\) | −3.88874e11 | −1.53895 | −0.769474 | − | 0.638678i | \(-0.779482\pi\) | ||||
−0.769474 | + | 0.638678i | \(0.779482\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.77052e10 | + | 1.39299e11i | 0.225807 | + | 0.545091i | ||||
\(712\) | 1.30417e10 | 0.0507473 | ||||||||
\(713\) | − | 1.65357e11i | − | 0.639829i | ||||||
\(714\) | 1.32406e11 | − | 1.98167e11i | 0.509465 | − | 0.762497i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.19659e11i | 1.21628i | ||||||||
\(717\) | 1.53195e11 | + | 1.02357e11i | 0.579651 | + | 0.387296i | ||||
\(718\) | 3.59416e11 | 1.35238 | ||||||||
\(719\) | 3.35735e10i | 0.125626i | 0.998025 | + | 0.0628132i | \(0.0200072\pi\) | ||||
−0.998025 | + | 0.0628132i | \(0.979993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.90611e11 | 1.07540 | ||||||||
\(722\) | 3.73228e11i | 1.37349i | ||||||||
\(723\) | 7.86002e10 | − | 1.17638e11i | 0.287654 | − | 0.430521i | ||||
\(724\) | −1.16983e11 | −0.425764 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.50878e11 | + | 1.67625e11i | 0.903058 | + | 0.603381i | ||||
\(727\) | −2.53113e11 | −0.906102 | −0.453051 | − | 0.891485i | \(-0.649664\pi\) | ||||
−0.453051 | + | 0.891485i | \(0.649664\pi\) | |||||||
\(728\) | 8.08692e9i | 0.0287911i | ||||||||
\(729\) | 2.60942e11 | + | 1.08053e11i | 0.923920 | + | 0.382586i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.64084e11i | − | 0.924853i | ||||||
\(732\) | 8.41020e9 | − | 1.25872e10i | 0.0292929 | − | 0.0438416i | ||||
\(733\) | −2.07602e11 | −0.719144 | −0.359572 | − | 0.933117i | \(-0.617077\pi\) | ||||
−0.359572 | + | 0.933117i | \(0.617077\pi\) | |||||||
\(734\) | 3.06137e11i | 1.05471i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.91504e11 | −2.35659 | ||||||||
\(737\) | − | 1.57903e10i | − | 0.0535205i | ||||||
\(738\) | −1.05724e11 | − | 2.55214e11i | −0.356407 | − | 0.860357i | ||||
\(739\) | 4.15014e11 | 1.39151 | 0.695753 | − | 0.718281i | \(-0.255071\pi\) | ||||
0.695753 | + | 0.718281i | \(0.255071\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.19274e10 | − | 3.28179e10i | 0.0727300 | − | 0.108852i | ||||
\(742\) | 2.59366e11 | 0.855653 | ||||||||
\(743\) | 3.30690e11i | 1.08509i | 0.840027 | + | 0.542545i | \(0.182539\pi\) | ||||
−0.840027 | + | 0.542545i | \(0.817461\pi\) | |||||||
\(744\) | −4.25148e9 | − | 2.84064e9i | −0.0138755 | − | 0.00927095i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 5.47918e11i | − | 1.76913i | ||||||
\(747\) | 2.81224e11 | − | 1.16498e11i | 0.903170 | − | 0.374143i | ||||
\(748\) | −1.29262e11 | −0.412918 | ||||||||
\(749\) | 3.94695e10i | 0.125411i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.77978e11 | −1.50262 | −0.751308 | − | 0.659952i | \(-0.770577\pi\) | ||||
−0.751308 | + | 0.659952i | \(0.770577\pi\) | |||||||
\(752\) | − | 2.75552e11i | − | 0.861652i | ||||||
\(753\) | −9.26390e10 | − | 6.18970e10i | −0.288147 | − | 0.192526i | ||||
\(754\) | −2.66231e11 | −0.823709 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.26216e11 | − | 4.49847e10i | −0.692526 | − | 0.137714i | ||||
\(757\) | 8.95066e10 | 0.272566 | 0.136283 | − | 0.990670i | \(-0.456484\pi\) | ||||
0.136283 | + | 0.990670i | \(0.456484\pi\) | |||||||
\(758\) | 4.45390e11i | 1.34916i | ||||||||
\(759\) | 1.47337e11 | − | 2.20514e11i | 0.443962 | − | 0.664462i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.71473e11i | 1.70395i | 0.523581 | + | 0.851976i | \(0.324596\pi\) | ||||
−0.523581 | + | 0.851976i | \(0.675404\pi\) | |||||||
\(762\) | −4.17303e11 | − | 2.78822e11i | −1.23775 | − | 0.827004i | ||||
\(763\) | −1.92456e11 | −0.567851 | ||||||||
\(764\) | 4.01231e10i | 0.117766i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.39292e11 | 0.985504 | ||||||||
\(767\) | − | 3.52884e11i | − | 1.01965i | ||||||
\(768\) | −2.04781e11 | + | 3.06488e11i | −0.588634 | + | 0.880986i | ||||
\(769\) | 2.56194e11 | 0.732596 | 0.366298 | − | 0.930498i | \(-0.380625\pi\) | ||||
0.366298 | + | 0.930498i | \(0.380625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.34537e11 | − | 3.57152e11i | −1.51273 | − | 1.01073i | ||||
\(772\) | −3.93923e11 | −1.10903 | ||||||||
\(773\) | 1.00523e11i | 0.281543i | 0.990042 | + | 0.140772i | \(0.0449584\pi\) | ||||
−0.990042 | + | 0.140772i | \(0.955042\pi\) | |||||||
\(774\) | −4.79838e11 | + | 1.98775e11i | −1.33700 | + | 0.553859i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.64498e10i | 0.0729417i | ||||||||
\(777\) | 1.05145e11 | − | 1.57366e11i | 0.288472 | − | 0.431745i | ||||
\(778\) | −4.04080e11 | −1.10293 | ||||||||
\(779\) | 3.55176e10i | 0.0964482i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.18464e11 | −0.318408 | ||||||||
\(782\) | − | 7.91007e11i | − | 2.11521i | ||||||
\(783\) | −4.77727e10 | + | 2.40236e11i | −0.127096 | + | 0.639132i | ||||
\(784\) | 1.82459e11 | 0.482950 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.92081e11 | + | 4.37146e11i | −0.765266 | + | 1.14535i | ||||
\(787\) | 2.15788e11 | 0.562508 | 0.281254 | − | 0.959633i | \(-0.409250\pi\) | ||||
0.281254 | + | 0.959633i | \(0.409250\pi\) | |||||||
\(788\) | − | 1.33367e11i | − | 0.345894i | ||||||
\(789\) | 2.17240e10 | + | 1.45150e10i | 0.0560572 | + | 0.0374548i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 5.03559e11i | − | 1.28631i | ||||||
\(792\) | −3.13855e9 | − | 7.57637e9i | −0.00797679 | − | 0.0192558i | ||||
\(793\) | −1.93902e10 | −0.0490331 | ||||||||
\(794\) | − | 5.29083e11i | − | 1.33120i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.60601e11 | −0.400034 | ||||||||
\(797\) | 6.69766e11i | 1.65993i | 0.557815 | + | 0.829966i | \(0.311640\pi\) | ||||
−0.557815 | + | 0.829966i | \(0.688360\pi\) | |||||||
\(798\) | 5.01099e10 | + | 3.34811e10i | 0.123570 | + | 0.0825636i | ||||
\(799\) | 3.05641e11 | 0.749938 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.40156e11 | − | 1.82337e11i | 1.06924 | − | 0.442940i | ||||
\(802\) | 3.09118e11 | 0.747183 | ||||||||
\(803\) | − | 1.92588e11i | − | 0.463199i | ||||||
\(804\) | −2.53208e10 | + | 3.78967e10i | −0.0605973 | + | 0.0906938i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 2.03027e11i | − | 0.481075i | ||||||
\(807\) | −2.33915e11 | − | 1.56291e11i | −0.551524 | − | 0.368502i | ||||
\(808\) | −1.85966e10 | −0.0436303 | ||||||||
\(809\) | 9.93417e10i | 0.231920i | 0.993254 | + | 0.115960i | \(0.0369944\pi\) | ||||
−0.993254 | + | 0.115960i | \(0.963006\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.71549e11 | −0.627718 | −0.313859 | − | 0.949470i | \(-0.601622\pi\) | ||||
−0.313859 | + | 0.949470i | \(0.601622\pi\) | |||||||
\(812\) | − | 2.00029e11i | − | 0.460119i | ||||||
\(813\) | 6.48974e10 | − | 9.71295e10i | 0.148547 | − | 0.222325i | ||||
\(814\) | −2.08607e11 | −0.475150 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.40573e11 | − | 2.27555e11i | −0.768156 | − | 0.513246i | ||||
\(817\) | 6.67782e10 | 0.149881 | ||||||||
\(818\) | − | 8.04785e11i | − | 1.79749i | ||||||
\(819\) | 1.13064e11 | + | 2.72934e11i | 0.251298 | + | 0.606626i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.63227e11i | 1.23968i | 0.784727 | + | 0.619842i | \(0.212803\pi\) | ||||
−0.784727 | + | 0.619842i | \(0.787197\pi\) | |||||||
\(822\) | −2.09689e11 | + | 3.13834e11i | −0.459292 | + | 0.687406i | ||||
\(823\) | 4.42272e11 | 0.964028 | 0.482014 | − | 0.876164i | \(-0.339905\pi\) | ||||
0.482014 | + | 0.876164i | \(0.339905\pi\) | |||||||
\(824\) | − | 2.98249e10i | − | 0.0646950i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.38823e11 | 1.15751 | ||||||||
\(827\) | − | 4.54543e11i | − | 0.971745i | −0.874030 | − | 0.485873i | \(-0.838502\pi\) | ||
0.874030 | − | 0.485873i | \(-0.161498\pi\) | |||||||
\(828\) | −7.07220e11 | + | 2.92969e11i | −1.50464 | + | 0.623305i | ||||
\(829\) | −1.32535e11 | −0.280615 | −0.140308 | − | 0.990108i | \(-0.544809\pi\) | ||||
−0.140308 | + | 0.990108i | \(0.544809\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.52121e11 | − | 2.27674e11i | 0.318996 | − | 0.477429i | ||||
\(832\) | −4.04290e11 | −0.843722 | ||||||||
\(833\) | 2.02383e11i | 0.420334i | ||||||||
\(834\) | −2.15714e11 | − | 1.44130e11i | −0.445877 | − | 0.297914i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 3.26861e10i | − | 0.0669172i | ||||||
\(837\) | −1.83203e11 | − | 3.64312e10i | −0.373276 | − | 0.0742286i | ||||
\(838\) | 5.02871e11 | 1.01972 | ||||||||
\(839\) | 4.87205e10i | 0.0983250i | 0.998791 | + | 0.0491625i | \(0.0156552\pi\) | ||||
−0.998791 | + | 0.0491625i | \(0.984345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.87820e11 | 0.575357 | ||||||||
\(842\) | 3.35705e11i | 0.667897i | ||||||||
\(843\) | −2.70923e11 | − | 1.81018e11i | −0.536457 | − | 0.358435i | ||||
\(844\) | −1.44114e10 | −0.0284011 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.30056e11 | − | 5.55348e11i | −0.449109 | − | 1.08414i | ||||
\(847\) | 2.90368e11 | 0.564176 | ||||||||
\(848\) | − | 4.45751e11i | − | 0.862004i | ||||||
\(849\) | −4.69138e11 | + | 7.02141e11i | −0.902962 | + | 1.35143i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.28145e11i | − | 1.19768i | ||||||
\(852\) | 2.84314e11 | + | 1.89965e11i | 0.539561 | + | 0.360509i | ||||
\(853\) | 7.24501e11 | 1.36849 | 0.684247 | − | 0.729250i | \(-0.260131\pi\) | ||||
0.684247 | + | 0.729250i | \(0.260131\pi\) | |||||||
\(854\) | − | 2.96071e10i | − | 0.0556626i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.05068e9 | 0.00754455 | ||||||||
\(857\) | 4.16662e11i | 0.772433i | 0.922408 | + | 0.386216i | \(0.126218\pi\) | ||||
−0.922408 | + | 0.386216i | \(0.873782\pi\) | |||||||
\(858\) | 1.80902e11 | − | 2.70750e11i | 0.333807 | − | 0.499597i | ||||
\(859\) | 7.54443e11 | 1.38565 | 0.692826 | − | 0.721105i | \(-0.256366\pi\) | ||||
0.692826 | + | 0.721105i | \(0.256366\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.21047e11 | − | 1.47693e11i | −0.402227 | − | 0.268750i | ||||
\(862\) | −1.43778e12 | −2.60413 | ||||||||
\(863\) | 2.06295e10i | 0.0371916i | 0.999827 | + | 0.0185958i | \(0.00591957\pi\) | ||||
−0.999827 | + | 0.0185958i | \(0.994080\pi\) | |||||||
\(864\) | −1.52351e11 | + | 7.66133e11i | −0.273395 | + | 1.37483i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1.17403e11i | − | 0.208741i | ||||||
\(867\) | −6.15057e10 | + | 9.20533e10i | −0.108853 | + | 0.162916i | ||||
\(868\) | 1.52541e11 | 0.268726 | ||||||||
\(869\) | − | 1.59936e11i | − | 0.280457i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.83785e10 | 0.101433 | ||||||||
\(872\) | 1.97515e10i | 0.0341612i | ||||||||
\(873\) | 3.69798e11 | + | 8.92681e11i | 0.636659 | + | 1.53688i | ||||
\(874\) | 2.00020e11 | 0.342789 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.08828e11 | + | 4.62212e11i | −0.524446 | + | 0.784918i | ||||
\(877\) | −5.98158e11 | −1.01115 | −0.505577 | − | 0.862782i | \(-0.668720\pi\) | ||||
−0.505577 | + | 0.862782i | \(0.668720\pi\) | |||||||
\(878\) | − | 9.76126e11i | − | 1.64259i | ||||||
\(879\) | 6.99945e11 | + | 4.67670e11i | 1.17249 | + | 0.783401i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.62306e11i | 0.269420i | 0.990885 | + | 0.134710i | \(0.0430103\pi\) | ||||
−0.990885 | + | 0.134710i | \(0.956990\pi\) | |||||||
\(882\) | 3.67729e11 | − | 1.52334e11i | 0.607650 | − | 0.251722i | ||||
\(883\) | 6.06459e11 | 0.997605 | 0.498803 | − | 0.866716i | \(-0.333773\pi\) | ||||
0.498803 | + | 0.866716i | \(0.333773\pi\) | |||||||
\(884\) | − | 4.77895e11i | − | 0.782571i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.50262e11 | 1.37981 | ||||||||
\(887\) | − | 4.65904e11i | − | 0.752666i | −0.926484 | − | 0.376333i | \(-0.877185\pi\) | ||
0.926484 | − | 0.376333i | \(-0.122815\pi\) | |||||||
\(888\) | −1.61502e10 | − | 1.07908e10i | −0.0259733 | − | 0.0173541i | ||||
\(889\) | −4.82989e11 | −0.773269 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.11852e11 | − | 2.11822e11i | −0.336141 | − | 0.336094i | ||||
\(892\) | 1.09170e12 | 1.72442 | ||||||||
\(893\) | 7.72867e10i | 0.121534i | ||||||||
\(894\) | 8.27631e11 | − | 1.23868e12i | 1.29565 | − | 1.93915i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.11757e10i | 0.0638865i | ||||||||
\(897\) | 8.15267e11 | + | 5.44723e11i | 1.25930 | + | 0.841407i | ||||
\(898\) | 6.63408e11 | 1.02018 | ||||||||
\(899\) | − | 1.61995e11i | − | 0.248007i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.94426e11 | 0.750243 | ||||||||
\(902\) | 2.93023e11i | 0.442666i | ||||||||
\(903\) | −2.77684e11 | + | 4.15600e11i | −0.417638 | + | 0.625064i | ||||
\(904\) | −5.16794e10 | −0.0773826 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.40877e11 | + | 4.28204e11i | 0.951178 | + | 0.635533i | ||||
\(907\) | −7.47111e11 | −1.10397 | −0.551983 | − | 0.833855i | \(-0.686129\pi\) | ||||
−0.551983 | + | 0.833855i | \(0.686129\pi\) | |||||||
\(908\) | 8.76909e11i | 1.29006i | ||||||||
\(909\) | −6.27635e11 | + | 2.60001e11i | −0.919288 | + | 0.380820i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.01051e11i | 1.30821i | 0.756406 | + | 0.654103i | \(0.226954\pi\) | ||||
−0.756406 | + | 0.654103i | \(0.773046\pi\) | |||||||
\(912\) | 5.75412e10 | − | 8.61198e10i | 0.0831763 | − | 0.124487i | ||||
\(913\) | −3.22887e11 | −0.464694 | ||||||||
\(914\) | − | 4.53896e11i | − | 0.650387i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.62692e11 | 0.657219 | ||||||||
\(917\) | 5.05956e11i | 0.715543i | ||||||||
\(918\) | −8.76375e11 | − | 1.74274e11i | −1.23401 | − | 0.245392i | ||||
\(919\) | −1.14699e12 | −1.60804 | −0.804021 | − | 0.594601i | \(-0.797310\pi\) | ||||
−0.804021 | + | 0.594601i | \(0.797310\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.34689e11 | + | 2.01584e11i | −0.187195 | + | 0.280168i | ||||
\(922\) | 1.57560e12 | 2.18032 | ||||||||
\(923\) | − | 4.37976e11i | − | 0.603453i | ||||||
\(924\) | 2.03424e11 | + | 1.35919e11i | 0.279071 | + | 0.186462i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.33937e10i | 0.127020i | ||||||||
\(927\) | −4.16985e11 | − | 1.00659e12i | −0.564679 | − | 1.36312i | ||||
\(928\) | −6.77447e11 | −0.913447 | ||||||||
\(929\) | − | 4.36054e11i | − | 0.585433i | −0.956199 | − | 0.292716i | \(-0.905441\pi\) | ||
0.956199 | − | 0.292716i | \(-0.0945592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.11762e10 | −0.0681191 | ||||||||
\(932\) | − | 6.74887e11i | − | 0.894474i | ||||||
\(933\) | −4.34293e11 | − | 2.90174e11i | −0.573135 | − | 0.382942i | ||||
\(934\) | −6.46869e11 | −0.850019 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.80107e10 | − | 1.16036e10i | 0.0364939 | − | 0.0151178i | ||||
\(937\) | −1.98881e11 | −0.258009 | −0.129004 | − | 0.991644i | \(-0.541178\pi\) | ||||
−0.129004 | + | 0.991644i | \(0.541178\pi\) | |||||||
\(938\) | 8.91388e10i | 0.115148i | ||||||||
\(939\) | 1.47482e9 | − | 2.20731e9i | 0.00189704 | − | 0.00283923i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.28069e12i | 1.63338i | 0.577079 | + | 0.816689i | \(0.304193\pi\) | ||||
−0.577079 | + | 0.816689i | \(0.695807\pi\) | |||||||
\(942\) | 1.14889e12 | + | 7.67637e11i | 1.45907 | + | 0.974883i | ||||
\(943\) | −8.82335e11 | −1.11580 | ||||||||
\(944\) | − | 9.26030e11i | − | 1.16610i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.50926e11 | 0.687905 | ||||||||
\(947\) | 1.35658e12i | 1.68673i | 0.537337 | + | 0.843367i | \(0.319430\pi\) | ||||
−0.537337 | + | 0.843367i | \(0.680570\pi\) | |||||||
\(948\) | −2.56468e11 | + | 3.83846e11i | −0.317541 | + | 0.475251i | ||||
\(949\) | 7.12020e11 | 0.877865 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.93358e11 | − | 5.30084e11i | −0.969945 | − | 0.648072i | ||||
\(952\) | −2.35388e10 | −0.0286574 | ||||||||
\(953\) | 5.01575e11i | 0.608085i | 0.952658 | + | 0.304042i | \(0.0983365\pi\) | ||||
−0.952658 | + | 0.304042i | \(0.901664\pi\) | |||||||
\(954\) | −3.72153e11 | − | 8.98368e11i | −0.449292 | − | 1.08458i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.64103e11i | 0.675347i | ||||||||
\(957\) | 1.44342e11 | − | 2.16032e11i | 0.172086 | − | 0.257555i | ||||
\(958\) | 1.00385e12 | 1.19180 | ||||||||
\(959\) | 3.63234e11i | 0.429450i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.29354e11 | −0.855155 | ||||||||
\(962\) | − | 7.71244e11i | − | 0.900516i | ||||||
\(963\) | 1.36711e11 | − | 5.66330e10i | 0.158963 | − | 0.0658514i | ||||
\(964\) | 4.33175e11 | 0.501597 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.31744e11 | + | 1.24484e12i | −0.955171 | + | 1.42957i | ||||
\(967\) | −1.10988e11 | −0.126932 | −0.0634661 | − | 0.997984i | \(-0.520215\pi\) | ||||
−0.0634661 | + | 0.997984i | \(0.520215\pi\) | |||||||
\(968\) | − | 2.98000e10i | − | 0.0339402i | ||||||
\(969\) | 9.55239e10 | + | 6.38246e10i | 0.108347 | + | 0.0723924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.95380e11i | − | 0.332280i | −0.986102 | − | 0.166140i | \(-0.946870\pi\) | ||
0.986102 | − | 0.166140i | \(-0.0531304\pi\) | |||||||
\(972\) | 1.68774e11 | + | 8.48092e11i | 0.189078 | + | 0.950119i | ||||
\(973\) | −2.49669e11 | −0.278557 | ||||||||
\(974\) | 1.28601e12i | 1.42892i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.08832e10 | −0.0560758 | ||||||||
\(977\) | 6.09091e11i | 0.668503i | 0.942484 | + | 0.334252i | \(0.108484\pi\) | ||||
−0.942484 | + | 0.334252i | \(0.891516\pi\) | |||||||
\(978\) | −1.01026e12 | − | 6.75007e11i | −1.10427 | − | 0.737824i | ||||
\(979\) | −5.05365e11 | −0.550141 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.76147e11 | + | 6.66612e11i | 0.298171 | + | 0.719776i | ||||
\(982\) | −1.62821e12 | −1.75091 | ||||||||
\(983\) | 1.84012e12i | 1.97076i | 0.170384 | + | 0.985378i | \(0.445499\pi\) | ||||
−0.170384 | + | 0.985378i | \(0.554501\pi\) | |||||||
\(984\) | −1.51575e10 | + | 2.26857e10i | −0.0161677 | + | 0.0241975i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 7.74927e11i | − | 0.819885i | ||||||
\(987\) | −4.81000e11 | − | 3.21382e11i | −0.506847 | − | 0.338651i | ||||
\(988\) | 1.20844e11 | 0.126823 | ||||||||
\(989\) | 1.65892e12i | 1.73396i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.72336e11 | −0.593412 | −0.296706 | − | 0.954969i | \(-0.595888\pi\) | ||||
−0.296706 | + | 0.954969i | \(0.595888\pi\) | |||||||
\(992\) | − | 5.16617e11i | − | 0.533485i | ||||||
\(993\) | 5.40449e11 | − | 8.08870e11i | 0.555850 | − | 0.831920i | ||||
\(994\) | 6.68750e11 | 0.685044 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.74928e11 | + | 5.17770e11i | 0.787451 | + | 0.526138i | ||||
\(997\) | 1.44614e12 | 1.46363 | 0.731813 | − | 0.681505i | \(-0.238674\pi\) | ||||
0.731813 | + | 0.681505i | \(0.238674\pi\) | |||||||
\(998\) | 5.93504e11i | 0.598276i | ||||||||
\(999\) | −6.95937e11 | − | 1.38392e11i | −0.698728 | − | 0.138947i |
(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.c.c.26.1 | 2 | ||
3.2 | odd | 2 | inner | 75.9.c.c.26.2 | 2 | ||
5.2 | odd | 4 | 75.9.d.b.74.4 | 4 | |||
5.3 | odd | 4 | 75.9.d.b.74.1 | 4 | |||
5.4 | even | 2 | 3.9.b.a.2.2 | yes | 2 | ||
15.2 | even | 4 | 75.9.d.b.74.2 | 4 | |||
15.8 | even | 4 | 75.9.d.b.74.3 | 4 | |||
15.14 | odd | 2 | 3.9.b.a.2.1 | ✓ | 2 | ||
20.19 | odd | 2 | 48.9.e.b.17.2 | 2 | |||
40.19 | odd | 2 | 192.9.e.f.65.1 | 2 | |||
40.29 | even | 2 | 192.9.e.e.65.2 | 2 | |||
45.4 | even | 6 | 81.9.d.d.26.1 | 4 | |||
45.14 | odd | 6 | 81.9.d.d.26.2 | 4 | |||
45.29 | odd | 6 | 81.9.d.d.53.1 | 4 | |||
45.34 | even | 6 | 81.9.d.d.53.2 | 4 | |||
60.59 | even | 2 | 48.9.e.b.17.1 | 2 | |||
120.29 | odd | 2 | 192.9.e.e.65.1 | 2 | |||
120.59 | even | 2 | 192.9.e.f.65.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.9.b.a.2.1 | ✓ | 2 | 15.14 | odd | 2 | ||
3.9.b.a.2.2 | yes | 2 | 5.4 | even | 2 | ||
48.9.e.b.17.1 | 2 | 60.59 | even | 2 | |||
48.9.e.b.17.2 | 2 | 20.19 | odd | 2 | |||
75.9.c.c.26.1 | 2 | 1.1 | even | 1 | trivial | ||
75.9.c.c.26.2 | 2 | 3.2 | odd | 2 | inner | ||
75.9.d.b.74.1 | 4 | 5.3 | odd | 4 | |||
75.9.d.b.74.2 | 4 | 15.2 | even | 4 | |||
75.9.d.b.74.3 | 4 | 15.8 | even | 4 | |||
75.9.d.b.74.4 | 4 | 5.2 | odd | 4 | |||
81.9.d.d.26.1 | 4 | 45.4 | even | 6 | |||
81.9.d.d.26.2 | 4 | 45.14 | odd | 6 | |||
81.9.d.d.53.1 | 4 | 45.29 | odd | 6 | |||
81.9.d.d.53.2 | 4 | 45.34 | even | 6 | |||
192.9.e.e.65.1 | 2 | 120.29 | odd | 2 | |||
192.9.e.e.65.2 | 2 | 40.29 | even | 2 | |||
192.9.e.f.65.1 | 2 | 40.19 | odd | 2 | |||
192.9.e.f.65.2 | 2 | 120.59 | even | 2 |