Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.38 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.37 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2502.20i | 1.72786i | 0.503614 | + | 0.863929i | \(0.332003\pi\) | ||||
−0.503614 | + | 0.863929i | \(0.667997\pi\) | |||||||
\(3\) | 102208. | + | 3714.28i | 0.999340 | + | 0.0363163i | ||||
\(4\) | −4.16388e6 | −1.98549 | ||||||||
\(5\) | 1.82569e7 | 0.836067 | 0.418034 | − | 0.908432i | \(-0.362719\pi\) | ||||
0.418034 | + | 0.908432i | \(0.362719\pi\) | |||||||
\(6\) | −9.29389e6 | + | 2.55746e8i | −0.0627493 | + | 1.72672i | ||||
\(7\) | −7.47262e8 | + | 1.20672e7i | −0.999870 | + | 0.0161464i | ||||
\(8\) | − | 5.17136e9i | − | 1.70279i | ||||||
\(9\) | 1.04328e10 | + | 7.59261e8i | 0.997362 | + | 0.0725846i | ||||
\(10\) | 4.56824e10i | 1.44460i | ||||||||
\(11\) | − | 6.04302e10i | − | 0.702475i | −0.936286 | − | 0.351237i | \(-0.885761\pi\) | ||
0.936286 | − | 0.351237i | \(-0.114239\pi\) | |||||||
\(12\) | −4.25583e11 | − | 1.54658e10i | −1.98418 | − | 0.0721056i | ||||
\(13\) | − | 4.37169e11i | − | 0.879517i | −0.898116 | − | 0.439759i | \(-0.855064\pi\) | ||
0.898116 | − | 0.439759i | \(-0.144936\pi\) | |||||||
\(14\) | −3.01945e10 | − | 1.86980e12i | −0.0278987 | − | 1.72763i | ||||
\(15\) | 1.86601e12 | + | 6.78111e10i | 0.835516 | + | 0.0303629i | ||||
\(16\) | 4.20753e12 | 0.956682 | ||||||||
\(17\) | −1.17175e13 | −1.40968 | −0.704842 | − | 0.709364i | \(-0.748982\pi\) | ||||
−0.704842 | + | 0.709364i | \(0.748982\pi\) | |||||||
\(18\) | −1.89983e12 | + | 2.61049e13i | −0.125416 | + | 1.72330i | ||||
\(19\) | 1.52935e13i | 0.572261i | 0.958191 | + | 0.286131i | \(0.0923691\pi\) | ||||
−0.958191 | + | 0.286131i | \(0.907631\pi\) | |||||||
\(20\) | −7.60193e13 | −1.66000 | ||||||||
\(21\) | −7.64213e13 | − | 1.54217e12i | −0.999796 | − | 0.0201758i | ||||
\(22\) | 1.51209e14 | 1.21378 | ||||||||
\(23\) | − | 2.33876e14i | − | 1.17718i | −0.808431 | − | 0.588592i | \(-0.799683\pi\) | ||
0.808431 | − | 0.588592i | \(-0.200317\pi\) | |||||||
\(24\) | 1.92079e13 | − | 5.28557e14i | 0.0618389 | − | 1.70166i | ||||
\(25\) | −1.43524e14 | −0.300992 | ||||||||
\(26\) | 1.09389e15 | 1.51968 | ||||||||
\(27\) | 1.06350e15 | + | 1.16353e14i | 0.994068 | + | 0.108757i | ||||
\(28\) | 3.11151e15 | − | 5.02462e13i | 1.98523 | − | 0.0320585i | ||||
\(29\) | − | 1.65948e15i | − | 0.732477i | −0.930521 | − | 0.366238i | \(-0.880646\pi\) | ||
0.930521 | − | 0.366238i | \(-0.119354\pi\) | |||||||
\(30\) | −1.69677e14 | + | 4.66913e15i | −0.0524627 | + | 1.44365i | ||||
\(31\) | − | 6.51175e15i | − | 1.42692i | −0.700696 | − | 0.713460i | \(-0.747127\pi\) | ||
0.700696 | − | 0.713460i | \(-0.252873\pi\) | |||||||
\(32\) | − | 3.17034e14i | − | 0.0497772i | ||||||
\(33\) | 2.24455e14 | − | 6.17647e15i | 0.0255113 | − | 0.702012i | ||||
\(34\) | − | 2.93196e16i | − | 2.43573i | ||||||
\(35\) | −1.36427e16 | + | 2.20309e14i | −0.835958 | + | 0.0134995i | ||||
\(36\) | −4.34407e16 | − | 3.16147e15i | −1.98025 | − | 0.144116i | ||||
\(37\) | 5.22826e15 | 0.178747 | 0.0893735 | − | 0.995998i | \(-0.471514\pi\) | ||||
0.0893735 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(38\) | −3.82675e16 | −0.988786 | ||||||||
\(39\) | 1.62377e15 | − | 4.46824e16i | 0.0319408 | − | 0.878937i | ||||
\(40\) | − | 9.44129e16i | − | 1.42364i | ||||||
\(41\) | 5.69124e15 | 0.0662180 | 0.0331090 | − | 0.999452i | \(-0.489459\pi\) | ||||
0.0331090 | + | 0.999452i | \(0.489459\pi\) | |||||||
\(42\) | 3.85883e15 | − | 1.91222e17i | 0.0348609 | − | 1.72751i | ||||
\(43\) | −1.25962e17 | −0.888833 | −0.444416 | − | 0.895820i | \(-0.646589\pi\) | ||||
−0.444416 | + | 0.895820i | \(0.646589\pi\) | |||||||
\(44\) | 2.51624e17i | 1.39476i | ||||||||
\(45\) | 1.90470e17 | + | 1.38617e16i | 0.833862 | + | 0.0606856i | ||||
\(46\) | 5.85206e17 | 2.03400 | ||||||||
\(47\) | 2.94625e17 | 0.817037 | 0.408518 | − | 0.912750i | \(-0.366046\pi\) | ||||
0.408518 | + | 0.912750i | \(0.366046\pi\) | |||||||
\(48\) | 4.30045e17 | + | 1.56279e16i | 0.956051 | + | 0.0347431i | ||||
\(49\) | 5.58255e17 | − | 1.80347e16i | 0.999479 | − | 0.0322886i | ||||
\(50\) | − | 3.59126e17i | − | 0.520070i | ||||||
\(51\) | −1.19763e18 | − | 4.35221e16i | −1.40875 | − | 0.0511945i | ||||
\(52\) | 1.82032e18i | 1.74627i | ||||||||
\(53\) | − | 2.27799e18i | − | 1.78918i | −0.446886 | − | 0.894591i | \(-0.647467\pi\) | ||
0.446886 | − | 0.894591i | \(-0.352533\pi\) | |||||||
\(54\) | −2.91139e17 | + | 2.66108e18i | −0.187917 | + | 1.71761i | ||||
\(55\) | − | 1.10327e18i | − | 0.587316i | ||||||
\(56\) | 6.24037e16 | + | 3.86436e18i | 0.0274939 | + | 1.70256i | ||||
\(57\) | −5.68044e16 | + | 1.56313e18i | −0.0207824 | + | 0.571884i | ||||
\(58\) | 4.15236e18 | 1.26561 | ||||||||
\(59\) | −3.70144e18 | −0.942811 | −0.471405 | − | 0.881917i | \(-0.656253\pi\) | ||||
−0.471405 | + | 0.881917i | \(0.656253\pi\) | |||||||
\(60\) | −7.76981e18 | − | 2.82357e17i | −1.65891 | − | 0.0602852i | ||||
\(61\) | 1.05348e19i | 1.89087i | 0.325809 | + | 0.945436i | \(0.394363\pi\) | ||||
−0.325809 | + | 0.945436i | \(0.605637\pi\) | |||||||
\(62\) | 1.62937e19 | 2.46552 | ||||||||
\(63\) | −7.80517e18 | − | 4.41473e17i | −0.998404 | − | 0.0564714i | ||||
\(64\) | 9.61712e18 | 1.04269 | ||||||||
\(65\) | − | 7.98134e18i | − | 0.735336i | ||||||
\(66\) | 1.54548e19 | + | 5.61631e17i | 1.21298 | + | 0.0440798i | ||||
\(67\) | −2.59967e18 | −0.174234 | −0.0871169 | − | 0.996198i | \(-0.527765\pi\) | ||||
−0.0871169 | + | 0.996198i | \(0.527765\pi\) | |||||||
\(68\) | 4.87903e19 | 2.79891 | ||||||||
\(69\) | 8.68682e17 | − | 2.39041e19i | 0.0427509 | − | 1.17641i | ||||
\(70\) | −5.51257e17 | − | 3.41367e19i | −0.0233252 | − | 1.44442i | ||||
\(71\) | 3.94068e19i | 1.43668i | 0.695694 | + | 0.718338i | \(0.255097\pi\) | ||||
−0.695694 | + | 0.718338i | \(0.744903\pi\) | |||||||
\(72\) | 3.92642e18 | − | 5.39516e19i | 0.123596 | − | 1.69830i | ||||
\(73\) | − | 1.65922e19i | − | 0.451871i | −0.974142 | − | 0.225936i | \(-0.927456\pi\) | ||
0.974142 | − | 0.225936i | \(-0.0725439\pi\) | |||||||
\(74\) | 1.30822e19i | 0.308849i | ||||||||
\(75\) | −1.46694e19 | − | 5.33088e17i | −0.300793 | − | 0.0109309i | ||||
\(76\) | − | 6.36803e19i | − | 1.13622i | ||||||
\(77\) | 7.29221e17 | + | 4.51572e19i | 0.0113424 | + | 0.702383i | ||||
\(78\) | 1.11804e20 | + | 4.06300e18i | 1.51868 | + | 0.0551891i | ||||
\(79\) | −5.35555e19 | −0.636384 | −0.318192 | − | 0.948026i | \(-0.603076\pi\) | ||||
−0.318192 | + | 0.948026i | \(0.603076\pi\) | |||||||
\(80\) | 7.68163e19 | 0.799850 | ||||||||
\(81\) | 1.08266e20 | + | 1.58424e19i | 0.989463 | + | 0.144786i | ||||
\(82\) | 1.42406e19i | 0.114415i | ||||||||
\(83\) | 2.97531e19 | 0.210480 | 0.105240 | − | 0.994447i | \(-0.466439\pi\) | ||||
0.105240 | + | 0.994447i | \(0.466439\pi\) | |||||||
\(84\) | 3.18209e20 | + | 6.42142e18i | 1.98509 | + | 0.0400588i | ||||
\(85\) | −2.13925e20 | −1.17859 | ||||||||
\(86\) | − | 3.15182e20i | − | 1.53578i | ||||||
\(87\) | 6.16378e18 | − | 1.69613e20i | 0.0266008 | − | 0.731993i | ||||
\(88\) | −3.12507e20 | −1.19617 | ||||||||
\(89\) | 3.34783e20 | 1.13807 | 0.569034 | − | 0.822314i | \(-0.307317\pi\) | ||||
0.569034 | + | 0.822314i | \(0.307317\pi\) | |||||||
\(90\) | −3.46849e19 | + | 4.76594e20i | −0.104856 | + | 1.44079i | ||||
\(91\) | 5.27540e18 | + | 3.26680e20i | 0.0142010 | + | 0.879403i | ||||
\(92\) | 9.73832e20i | 2.33729i | ||||||||
\(93\) | 2.41865e19 | − | 6.65556e20i | 0.0518205 | − | 1.42598i | ||||
\(94\) | 7.37211e20i | 1.41172i | ||||||||
\(95\) | 2.79212e20i | 0.478449i | ||||||||
\(96\) | 1.17755e18 | − | 3.24035e19i | 0.00180772 | − | 0.0497444i | ||||
\(97\) | 6.17354e20i | 0.850023i | 0.905188 | + | 0.425012i | \(0.139730\pi\) | ||||
−0.905188 | + | 0.425012i | \(0.860270\pi\) | |||||||
\(98\) | 4.51264e19 | + | 1.39687e21i | 0.0557901 | + | 1.72696i | ||||
\(99\) | 4.58823e19 | − | 6.30454e20i | 0.0509889 | − | 0.700622i | ||||
\(100\) | 5.97616e20 | 0.597616 | ||||||||
\(101\) | −1.89205e21 | −1.70435 | −0.852176 | − | 0.523255i | \(-0.824717\pi\) | ||||
−0.852176 | + | 0.523255i | \(0.824717\pi\) | |||||||
\(102\) | 1.08901e20 | − | 2.99671e21i | 0.0884568 | − | 2.43413i | ||||
\(103\) | − | 2.49585e21i | − | 1.82990i | −0.403563 | − | 0.914952i | \(-0.632229\pi\) | ||
0.403563 | − | 0.914952i | \(-0.367771\pi\) | |||||||
\(104\) | −2.26076e21 | −1.49763 | ||||||||
\(105\) | −1.39521e21 | − | 2.81552e19i | −0.835897 | − | 0.0168683i | ||||
\(106\) | 5.69999e21 | 3.09145 | ||||||||
\(107\) | 1.21577e21i | 0.597480i | 0.954335 | + | 0.298740i | \(0.0965663\pi\) | ||||
−0.954335 | + | 0.298740i | \(0.903434\pi\) | |||||||
\(108\) | −4.42826e21 | − | 4.84480e20i | −1.97371 | − | 0.215936i | ||||
\(109\) | −2.44406e21 | −0.988856 | −0.494428 | − | 0.869219i | \(-0.664622\pi\) | ||||
−0.494428 | + | 0.869219i | \(0.664622\pi\) | |||||||
\(110\) | 2.76060e21 | 1.01480 | ||||||||
\(111\) | 5.34372e20 | + | 1.94192e19i | 0.178629 | + | 0.00649143i | ||||
\(112\) | −3.14413e21 | + | 5.07730e19i | −0.956557 | + | 0.0154470i | ||||
\(113\) | 1.46567e21i | 0.406173i | 0.979161 | + | 0.203087i | \(0.0650973\pi\) | ||||
−0.979161 | + | 0.203087i | \(0.934903\pi\) | |||||||
\(114\) | −3.91126e21 | − | 1.42136e20i | −0.988134 | − | 0.0359090i | ||||
\(115\) | − | 4.26985e21i | − | 0.984204i | ||||||
\(116\) | 6.90988e21i | 1.45433i | ||||||||
\(117\) | 3.31926e20 | − | 4.56088e21i | 0.0638395 | − | 0.877198i | ||||
\(118\) | − | 9.26176e21i | − | 1.62904i | ||||||
\(119\) | 8.75605e21 | − | 1.41397e20i | 1.40950 | − | 0.0227613i | ||||
\(120\) | 3.50676e20 | − | 9.64979e21i | 0.0517015 | − | 1.42271i | ||||
\(121\) | 3.74844e21 | 0.506529 | ||||||||
\(122\) | −2.63602e22 | −3.26716 | ||||||||
\(123\) | 5.81692e20 | + | 2.11388e19i | 0.0661743 | + | 0.00240479i | ||||
\(124\) | 2.71141e22i | 2.83314i | ||||||||
\(125\) | −1.13259e22 | −1.08772 | ||||||||
\(126\) | 1.10466e21 | − | 1.95301e22i | 0.0975745 | − | 1.72510i | ||||
\(127\) | −1.56943e22 | −1.27586 | −0.637928 | − | 0.770096i | \(-0.720208\pi\) | ||||
−0.637928 | + | 0.770096i | \(0.720208\pi\) | |||||||
\(128\) | 2.33991e22i | 1.75184i | ||||||||
\(129\) | −1.28744e22 | − | 4.67857e20i | −0.888247 | − | 0.0322791i | ||||
\(130\) | 1.99710e22 | 1.27056 | ||||||||
\(131\) | 1.89203e22 | 1.11066 | 0.555328 | − | 0.831632i | \(-0.312593\pi\) | ||||
0.555328 | + | 0.831632i | \(0.312593\pi\) | |||||||
\(132\) | −9.34601e20 | + | 2.57181e22i | −0.0506524 | + | 1.39384i | ||||
\(133\) | −1.84549e20 | − | 1.14283e22i | −0.00923997 | − | 0.572187i | ||||
\(134\) | − | 6.50490e21i | − | 0.301051i | ||||||
\(135\) | 1.94161e22 | + | 2.12424e21i | 0.831108 | + | 0.0909284i | ||||
\(136\) | 6.05955e22i | 2.40039i | ||||||||
\(137\) | 1.55013e22i | 0.568594i | 0.958736 | + | 0.284297i | \(0.0917602\pi\) | ||||
−0.958736 | + | 0.284297i | \(0.908240\pi\) | |||||||
\(138\) | 5.98130e22 | + | 2.17362e21i | 2.03266 | + | 0.0738675i | ||||
\(139\) | − | 4.26773e22i | − | 1.34444i | −0.740352 | − | 0.672220i | \(-0.765341\pi\) | ||
0.740352 | − | 0.672220i | \(-0.234659\pi\) | |||||||
\(140\) | 5.68063e22 | − | 9.17338e20i | 1.65979 | − | 0.0268031i | ||||
\(141\) | 3.01131e22 | + | 1.09432e21i | 0.816498 | + | 0.0296717i | ||||
\(142\) | −9.86040e22 | −2.48237 | ||||||||
\(143\) | −2.64182e22 | −0.617839 | ||||||||
\(144\) | 4.38962e22 | + | 3.19461e21i | 0.954158 | + | 0.0694404i | ||||
\(145\) | − | 3.02970e22i | − | 0.612400i | ||||||
\(146\) | 4.15171e22 | 0.780769 | ||||||||
\(147\) | 5.71253e22 | + | 2.30219e20i | 0.999992 | + | 0.00403003i | ||||
\(148\) | −2.17698e22 | −0.354901 | ||||||||
\(149\) | − | 5.72238e22i | − | 0.869203i | −0.900623 | − | 0.434601i | \(-0.856889\pi\) | ||
0.900623 | − | 0.434601i | \(-0.143111\pi\) | |||||||
\(150\) | 1.33390e21 | − | 3.67057e22i | 0.0188870 | − | 0.519727i | ||||
\(151\) | 7.59752e22 | 1.00326 | 0.501631 | − | 0.865082i | \(-0.332734\pi\) | ||||
0.501631 | + | 0.865082i | \(0.332734\pi\) | |||||||
\(152\) | 7.90883e22 | 0.974439 | ||||||||
\(153\) | −1.22246e23 | − | 8.89665e21i | −1.40597 | − | 0.102321i | ||||
\(154\) | −1.12993e23 | + | 1.82466e21i | −1.21362 | + | 0.0195981i | ||||
\(155\) | − | 1.18884e23i | − | 1.19300i | ||||||
\(156\) | −6.76117e21 | + | 1.86052e23i | −0.0634182 | + | 1.74512i | ||||
\(157\) | − | 1.67270e23i | − | 1.46714i | −0.679613 | − | 0.733571i | \(-0.737852\pi\) | ||
0.679613 | − | 0.733571i | \(-0.262148\pi\) | |||||||
\(158\) | − | 1.34007e23i | − | 1.09958i | ||||||
\(159\) | 8.46108e21 | − | 2.32829e23i | 0.0649764 | − | 1.78800i | ||||
\(160\) | − | 5.78804e21i | − | 0.0416171i | ||||||
\(161\) | 2.82223e21 | + | 1.74767e23i | 0.0190073 | + | 1.17703i | ||||
\(162\) | −3.96409e22 | + | 2.70904e23i | −0.250170 | + | 1.70965i | ||||
\(163\) | 8.95540e20 | 0.00529804 | 0.00264902 | − | 0.999996i | \(-0.499157\pi\) | ||||
0.00264902 | + | 0.999996i | \(0.499157\pi\) | |||||||
\(164\) | −2.36976e22 | −0.131475 | ||||||||
\(165\) | 4.09784e21 | − | 1.12763e23i | 0.0213291 | − | 0.586929i | ||||
\(166\) | 7.44483e22i | 0.363680i | ||||||||
\(167\) | 1.42420e23 | 0.653204 | 0.326602 | − | 0.945162i | \(-0.394096\pi\) | ||||
0.326602 | + | 0.945162i | \(0.394096\pi\) | |||||||
\(168\) | −7.97514e21 | + | 3.95202e23i | −0.0343551 | + | 1.70244i | ||||
\(169\) | 5.59475e22 | 0.226449 | ||||||||
\(170\) | − | 5.35284e23i | − | 2.03644i | ||||||
\(171\) | −1.16118e22 | + | 1.59554e23i | −0.0415374 | + | 0.570752i | ||||
\(172\) | 5.24489e23 | 1.76477 | ||||||||
\(173\) | −4.51867e22 | −0.143063 | −0.0715314 | − | 0.997438i | \(-0.522789\pi\) | ||||
−0.0715314 | + | 0.997438i | \(0.522789\pi\) | |||||||
\(174\) | 4.24407e23 | + | 1.54230e22i | 1.26478 | + | 0.0459624i | ||||
\(175\) | 1.07250e23 | − | 1.73193e21i | 0.300952 | − | 0.00485993i | ||||
\(176\) | − | 2.54262e23i | − | 0.672045i | ||||||
\(177\) | −3.78318e23 | − | 1.37482e22i | −0.942189 | − | 0.0342394i | ||||
\(178\) | 8.37695e23i | 1.96642i | ||||||||
\(179\) | 3.13845e23i | 0.694637i | 0.937747 | + | 0.347318i | \(0.112908\pi\) | ||||
−0.937747 | + | 0.347318i | \(0.887092\pi\) | |||||||
\(180\) | −7.93091e23 | − | 5.77185e22i | −1.65562 | − | 0.120491i | ||||
\(181\) | − | 2.93796e23i | − | 0.578657i | −0.957230 | − | 0.289329i | \(-0.906568\pi\) | ||
0.957230 | − | 0.289329i | \(-0.0934321\pi\) | |||||||
\(182\) | −8.17420e23 | + | 1.32001e22i | −1.51948 | + | 0.0245374i | ||||
\(183\) | −3.91291e22 | + | 1.07674e24i | −0.0686694 | + | 1.88962i | ||||
\(184\) | −1.20946e24 | −2.00449 | ||||||||
\(185\) | 9.54516e22 | 0.149445 | ||||||||
\(186\) | 1.66536e24 | + | 6.05195e22i | 2.46389 | + | 0.0895383i | ||||
\(187\) | 7.08092e23i | 0.990268i | ||||||||
\(188\) | −1.22678e24 | −1.62222 | ||||||||
\(189\) | −7.96114e23 | − | 7.41128e22i | −0.995695 | − | 0.0926924i | ||||
\(190\) | −6.98645e23 | −0.826691 | ||||||||
\(191\) | − | 1.16683e24i | − | 1.30665i | −0.757079 | − | 0.653323i | \(-0.773374\pi\) | ||
0.757079 | − | 0.653323i | \(-0.226626\pi\) | |||||||
\(192\) | 9.82950e23 | + | 3.57206e22i | 1.04200 | + | 0.0378666i | ||||
\(193\) | −1.14336e24 | −1.14771 | −0.573856 | − | 0.818957i | \(-0.694553\pi\) | ||||
−0.573856 | + | 0.818957i | \(0.694553\pi\) | |||||||
\(194\) | −1.54475e24 | −1.46872 | ||||||||
\(195\) | 2.96449e22 | − | 8.15760e23i | 0.0267047 | − | 0.734851i | ||||
\(196\) | −2.32450e24 | + | 7.50941e22i | −1.98446 | + | 0.0641087i | ||||
\(197\) | − | 1.16336e24i | − | 0.941499i | −0.882267 | − | 0.470750i | \(-0.843984\pi\) | ||
0.882267 | − | 0.470750i | \(-0.156016\pi\) | |||||||
\(198\) | 1.57752e24 | + | 1.14807e23i | 1.21057 | + | 0.0881015i | ||||
\(199\) | − | 2.86453e23i | − | 0.208495i | −0.994551 | − | 0.104248i | \(-0.966757\pi\) | ||
0.994551 | − | 0.104248i | \(-0.0332435\pi\) | |||||||
\(200\) | 7.42215e23i | 0.512524i | ||||||||
\(201\) | −2.65708e23 | − | 9.65589e21i | −0.174119 | − | 0.00632752i | ||||
\(202\) | − | 4.73431e24i | − | 2.94488i | ||||||
\(203\) | 2.00253e22 | + | 1.24007e24i | 0.0118269 | + | 0.732381i | ||||
\(204\) | 4.98678e24 | + | 1.81221e23i | 2.79707 | + | 0.101646i | ||||
\(205\) | 1.03904e23 | 0.0553627 | ||||||||
\(206\) | 6.24513e24 | 3.16181 | ||||||||
\(207\) | 1.77573e23 | − | 2.43998e24i | 0.0854454 | − | 1.17408i | ||||
\(208\) | − | 1.83940e24i | − | 0.841418i | ||||||
\(209\) | 9.24190e23 | 0.401999 | ||||||||
\(210\) | 7.04502e22 | − | 3.49111e24i | 0.0291460 | − | 1.44431i | ||||
\(211\) | 5.84219e23 | 0.229938 | 0.114969 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114969 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(212\) | 9.48525e24i | 3.55240i | ||||||||
\(213\) | −1.46368e23 | + | 4.02771e24i | −0.0521747 | + | 1.43573i | ||||
\(214\) | −3.04211e24 | −1.03236 | ||||||||
\(215\) | −2.29967e24 | −0.743124 | ||||||||
\(216\) | 6.01704e23 | − | 5.49972e24i | 0.185190 | − | 1.69269i | ||||
\(217\) | 7.85784e22 | + | 4.86598e24i | 0.0230396 | + | 1.42673i | ||||
\(218\) | − | 6.11553e24i | − | 1.70860i | ||||||
\(219\) | 6.16282e22 | − | 1.69586e24i | 0.0164103 | − | 0.451573i | ||||
\(220\) | 4.59386e24i | 1.16611i | ||||||||
\(221\) | 5.12254e24i | 1.23984i | ||||||||
\(222\) | −4.85908e22 | + | 1.33711e24i | −0.0112163 | + | 0.308646i | ||||
\(223\) | 4.55822e24i | 1.00368i | 0.864961 | + | 0.501838i | \(0.167343\pi\) | ||||
−0.864961 | + | 0.501838i | \(0.832657\pi\) | |||||||
\(224\) | 3.82570e21 | + | 2.36907e23i | 0.000803724 | + | 0.0497707i | ||||
\(225\) | −1.49735e24 | − | 1.08972e23i | −0.300198 | − | 0.0218474i | ||||
\(226\) | −3.66740e24 | −0.701809 | ||||||||
\(227\) | −5.13660e24 | −0.938434 | −0.469217 | − | 0.883083i | \(-0.655464\pi\) | ||||
−0.469217 | + | 0.883083i | \(0.655464\pi\) | |||||||
\(228\) | 2.36526e23 | − | 6.50866e24i | 0.0412633 | − | 1.13547i | ||||
\(229\) | − | 7.47039e24i | − | 1.24472i | −0.782732 | − | 0.622359i | \(-0.786175\pi\) | ||
0.782732 | − | 0.622359i | \(-0.213825\pi\) | |||||||
\(230\) | 1.06840e25 | 1.70056 | ||||||||
\(231\) | −9.31938e22 | + | 4.61815e24i | −0.0141730 | + | 0.702332i | ||||
\(232\) | −8.58179e24 | −1.24725 | ||||||||
\(233\) | − | 1.62336e23i | − | 0.0225516i | −0.999936 | − | 0.0112758i | \(-0.996411\pi\) | ||
0.999936 | − | 0.0112758i | \(-0.00358928\pi\) | |||||||
\(234\) | 1.14123e25 | + | 8.30546e23i | 1.51567 | + | 0.110305i | ||||
\(235\) | 5.37892e24 | 0.683098 | ||||||||
\(236\) | 1.54123e25 | 1.87194 | ||||||||
\(237\) | −5.47382e24 | − | 1.98920e23i | −0.635964 | − | 0.0231111i | ||||
\(238\) | 3.53805e23 | + | 2.19094e25i | 0.0393283 | + | 2.43542i | ||||
\(239\) | 6.66887e24i | 0.709372i | 0.934985 | + | 0.354686i | \(0.115412\pi\) | ||||
−0.934985 | + | 0.354686i | \(0.884588\pi\) | |||||||
\(240\) | 7.85127e24 | + | 2.85317e23i | 0.799323 | + | 0.0290476i | ||||
\(241\) | 1.61013e25i | 1.56921i | 0.619995 | + | 0.784606i | \(0.287135\pi\) | ||||
−0.619995 | + | 0.784606i | \(0.712865\pi\) | |||||||
\(242\) | 9.37936e24i | 0.875210i | ||||||||
\(243\) | 1.10069e25 | + | 2.02135e24i | 0.983552 | + | 0.180624i | ||||
\(244\) | − | 4.38655e25i | − | 3.75431i | ||||||
\(245\) | 1.01920e25 | − | 3.29257e23i | 0.835631 | − | 0.0269954i | ||||
\(246\) | −5.28937e22 | + | 1.45551e24i | −0.00415514 | + | 0.114340i | ||||
\(247\) | 6.68585e24 | 0.503314 | ||||||||
\(248\) | −3.36746e25 | −2.42974 | ||||||||
\(249\) | 3.04101e24 | + | 1.10511e23i | 0.210342 | + | 0.00764387i | ||||
\(250\) | − | 2.83396e25i | − | 1.87942i | ||||||
\(251\) | −2.18605e25 | −1.39023 | −0.695113 | − | 0.718900i | \(-0.744646\pi\) | ||||
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(252\) | 3.24997e25 | + | 1.83824e24i | 1.98232 | + | 0.112123i | ||||
\(253\) | −1.41332e25 | −0.826942 | ||||||||
\(254\) | − | 3.92702e25i | − | 2.20450i | ||||||
\(255\) | −2.18649e25 | − | 7.94578e23i | −1.17781 | − | 0.0428020i | ||||
\(256\) | −3.83808e25 | −1.98424 | ||||||||
\(257\) | −4.67336e24 | −0.231916 | −0.115958 | − | 0.993254i | \(-0.536994\pi\) | ||||
−0.115958 | + | 0.993254i | \(0.536994\pi\) | |||||||
\(258\) | 1.17067e24 | − | 3.22143e25i | 0.0557737 | − | 1.53476i | ||||
\(259\) | −3.90688e24 | + | 6.30903e22i | −0.178724 | + | 0.00288612i | ||||
\(260\) | 3.32333e25i | 1.46000i | ||||||||
\(261\) | 1.25998e24 | − | 1.73130e25i | 0.0531665 | − | 0.730544i | ||||
\(262\) | 4.73425e25i | 1.91905i | ||||||||
\(263\) | − | 2.03251e25i | − | 0.791586i | −0.918340 | − | 0.395793i | \(-0.870470\pi\) | ||
0.918340 | − | 0.395793i | \(-0.129530\pi\) | |||||||
\(264\) | −3.19408e25 | − | 1.16074e24i | −1.19538 | − | 0.0434403i | ||||
\(265\) | − | 4.15889e25i | − | 1.49588i | ||||||
\(266\) | 2.85958e25 | − | 4.61780e23i | 0.988657 | − | 0.0159653i | ||||
\(267\) | 3.42176e25 | + | 1.24348e24i | 1.13732 | + | 0.0413304i | ||||
\(268\) | 1.08247e25 | 0.345940 | ||||||||
\(269\) | −5.17550e25 | −1.59057 | −0.795286 | − | 0.606235i | \(-0.792679\pi\) | ||||
−0.795286 | + | 0.606235i | \(0.792679\pi\) | |||||||
\(270\) | −5.31529e24 | + | 4.85831e25i | −0.157111 | + | 1.43604i | ||||
\(271\) | 1.89000e25i | 0.537384i | 0.963226 | + | 0.268692i | \(0.0865913\pi\) | ||||
−0.963226 | + | 0.268692i | \(0.913409\pi\) | |||||||
\(272\) | −4.93018e25 | −1.34862 | ||||||||
\(273\) | −6.74191e23 | + | 3.34090e25i | −0.0177450 | + | 0.879338i | ||||
\(274\) | −3.87874e25 | −0.982449 | ||||||||
\(275\) | 8.67318e24i | 0.211439i | ||||||||
\(276\) | −3.61708e24 | + | 9.95338e25i | −0.0848815 | + | 2.33574i | ||||
\(277\) | −3.71578e25 | −0.839485 | −0.419743 | − | 0.907643i | \(-0.637880\pi\) | ||||
−0.419743 | + | 0.907643i | \(0.637880\pi\) | |||||||
\(278\) | 1.06787e26 | 2.32300 | ||||||||
\(279\) | 4.94412e24 | − | 6.79355e25i | 0.103573 | − | 1.42316i | ||||
\(280\) | 1.13930e24 | + | 7.05512e25i | 0.0229867 | + | 1.42346i | ||||
\(281\) | − | 6.37724e25i | − | 1.23941i | −0.784833 | − | 0.619707i | \(-0.787251\pi\) | ||
0.784833 | − | 0.619707i | \(-0.212749\pi\) | |||||||
\(282\) | −2.73821e24 | + | 7.53492e25i | −0.0512685 | + | 1.41079i | ||||
\(283\) | 2.65862e25i | 0.479621i | 0.970820 | + | 0.239810i | \(0.0770853\pi\) | ||||
−0.970820 | + | 0.239810i | \(0.922915\pi\) | |||||||
\(284\) | − | 1.64085e26i | − | 2.85251i | ||||||
\(285\) | −1.03707e24 | + | 2.85378e25i | −0.0173755 | + | 0.478133i | ||||
\(286\) | − | 6.61038e25i | − | 1.06754i | ||||||
\(287\) | −4.25285e24 | + | 6.86771e22i | −0.0662094 | + | 0.00106918i | ||||
\(288\) | 2.40711e23 | − | 3.30754e24i | 0.00361306 | − | 0.0496459i | ||||
\(289\) | 6.82082e25 | 0.987210 | ||||||||
\(290\) | 7.58092e25 | 1.05814 | ||||||||
\(291\) | −2.29302e24 | + | 6.30987e25i | −0.0308697 | + | 0.849463i | ||||
\(292\) | 6.90880e25i | 0.897186i | ||||||||
\(293\) | −8.54153e25 | −1.07010 | −0.535052 | − | 0.844819i | \(-0.679708\pi\) | ||||
−0.535052 | + | 0.844819i | \(0.679708\pi\) | |||||||
\(294\) | −5.76054e23 | + | 1.42939e26i | −0.00696332 | + | 1.72784i | ||||
\(295\) | −6.75767e25 | −0.788253 | ||||||||
\(296\) | − | 2.70372e25i | − | 0.304368i | ||||||
\(297\) | 7.03124e24 | − | 6.42673e25i | 0.0763992 | − | 0.698308i | ||||
\(298\) | 1.43186e26 | 1.50186 | ||||||||
\(299\) | −1.02244e26 | −1.03535 | ||||||||
\(300\) | 6.10814e25 | + | 2.21971e24i | 0.597222 | + | 0.0217032i | ||||
\(301\) | 9.41265e25 | − | 1.52000e24i | 0.888717 | − | 0.0143515i | ||||
\(302\) | 1.90106e26i | 1.73349i | ||||||||
\(303\) | −1.93384e26 | − | 7.02762e24i | −1.70323 | − | 0.0618957i | ||||
\(304\) | 6.43479e25i | 0.547472i | ||||||||
\(305\) | 1.92332e26i | 1.58090i | ||||||||
\(306\) | 2.22612e25 | − | 3.05885e26i | 0.176797 | − | 2.42931i | ||||
\(307\) | − | 1.95485e26i | − | 1.50024i | −0.661302 | − | 0.750120i | \(-0.729996\pi\) | ||
0.661302 | − | 0.750120i | \(-0.270004\pi\) | |||||||
\(308\) | −3.03639e24 | − | 1.88029e26i | −0.0225203 | − | 1.39458i | ||||
\(309\) | 9.27029e24 | − | 2.55097e26i | 0.0664553 | − | 1.82870i | ||||
\(310\) | 2.97472e26 | 2.06134 | ||||||||
\(311\) | 6.31627e25 | 0.423133 | 0.211566 | − | 0.977364i | \(-0.432144\pi\) | ||||
0.211566 | + | 0.977364i | \(0.432144\pi\) | |||||||
\(312\) | −2.31069e26 | − | 8.39710e24i | −1.49664 | − | 0.0543884i | ||||
\(313\) | − | 2.52571e26i | − | 1.58186i | −0.611907 | − | 0.790930i | \(-0.709597\pi\) | ||
0.611907 | − | 0.790930i | \(-0.290403\pi\) | |||||||
\(314\) | 4.18544e26 | 2.53501 | ||||||||
\(315\) | −1.42498e26 | − | 8.05991e24i | −0.834733 | − | 0.0472139i | ||||
\(316\) | 2.22998e26 | 1.26353 | ||||||||
\(317\) | 2.59156e26i | 1.42050i | 0.703952 | + | 0.710248i | \(0.251417\pi\) | ||||
−0.703952 | + | 0.710248i | \(0.748583\pi\) | |||||||
\(318\) | 5.82587e26 | + | 2.11713e25i | 3.08941 | + | 0.112270i | ||||
\(319\) | −1.00283e26 | −0.514546 | ||||||||
\(320\) | 1.75578e26 | 0.871759 | ||||||||
\(321\) | −4.51572e24 | + | 1.24262e26i | −0.0216982 | + | 0.597085i | ||||
\(322\) | −4.37302e26 | + | 7.06178e24i | −2.03374 | + | 0.0328419i | ||||
\(323\) | − | 1.79202e26i | − | 0.806708i | ||||||
\(324\) | −4.50806e26 | − | 6.59657e25i | −1.96457 | − | 0.287472i | ||||
\(325\) | 6.27443e25i | 0.264727i | ||||||||
\(326\) | 2.24082e24i | 0.00915426i | ||||||||
\(327\) | −2.49803e26 | − | 9.07791e24i | −0.988203 | − | 0.0359116i | ||||
\(328\) | − | 2.94315e25i | − | 0.112755i | ||||||
\(329\) | −2.20162e26 | + | 3.55529e24i | −0.816930 | + | 0.0131922i | ||||
\(330\) | 2.82156e26 | + | 1.02536e25i | 1.01413 | + | 0.0368537i | ||||
\(331\) | 1.71522e26 | 0.597209 | 0.298605 | − | 0.954377i | \(-0.403479\pi\) | ||||
0.298605 | + | 0.954377i | \(0.403479\pi\) | |||||||
\(332\) | −1.23888e26 | −0.417907 | ||||||||
\(333\) | 5.45452e25 | + | 3.96961e24i | 0.178276 | + | 0.0129743i | ||||
\(334\) | 3.56365e26i | 1.12864i | ||||||||
\(335\) | −4.74618e25 | −0.145671 | ||||||||
\(336\) | −3.21545e26 | − | 6.48874e24i | −0.956487 | − | 0.0193018i | ||||
\(337\) | 3.61345e25 | 0.104186 | 0.0520928 | − | 0.998642i | \(-0.483411\pi\) | ||||
0.0520928 | + | 0.998642i | \(0.483411\pi\) | |||||||
\(338\) | 1.39992e26i | 0.391272i | ||||||||
\(339\) | −5.44389e24 | + | 1.49803e26i | −0.0147507 | + | 0.405905i | ||||
\(340\) | 8.90758e26 | 2.34008 | ||||||||
\(341\) | −3.93506e26 | −1.00238 | ||||||||
\(342\) | −3.99236e26 | − | 2.90550e25i | −0.986178 | − | 0.0717707i | ||||
\(343\) | −4.16945e26 | + | 2.02132e25i | −0.998827 | + | 0.0484224i | ||||
\(344\) | 6.51394e26i | 1.51349i | ||||||||
\(345\) | 1.58594e25 | − | 4.36414e26i | 0.0357426 | − | 0.983555i | ||||
\(346\) | − | 1.13066e26i | − | 0.247192i | ||||||
\(347\) | 3.43480e26i | 0.728520i | 0.931297 | + | 0.364260i | \(0.118678\pi\) | ||||
−0.931297 | + | 0.364260i | \(0.881322\pi\) | |||||||
\(348\) | −2.56652e25 | + | 7.06248e26i | −0.0528157 | + | 1.45337i | ||||
\(349\) | 7.52353e26i | 1.50229i | 0.660135 | + | 0.751147i | \(0.270499\pi\) | ||||
−0.660135 | + | 0.751147i | \(0.729501\pi\) | |||||||
\(350\) | 4.33364e24 | + | 2.68361e26i | 0.00839727 | + | 0.520003i | ||||
\(351\) | 5.08660e25 | − | 4.64928e26i | 0.0956539 | − | 0.874300i | ||||
\(352\) | −1.91584e25 | −0.0349673 | ||||||||
\(353\) | 5.74039e26 | 1.01697 | 0.508484 | − | 0.861072i | \(-0.330206\pi\) | ||||
0.508484 | + | 0.861072i | \(0.330206\pi\) | |||||||
\(354\) | 3.44007e25 | − | 9.46629e26i | 0.0591607 | − | 1.62797i | ||||
\(355\) | 7.19445e26i | 1.20116i | ||||||||
\(356\) | −1.39399e27 | −2.25962 | ||||||||
\(357\) | 8.95467e26 | + | 1.80704e25i | 1.40940 | + | 0.0284415i | ||||
\(358\) | −7.85303e26 | −1.20023 | ||||||||
\(359\) | − | 2.32932e26i | − | 0.345730i | −0.984946 | − | 0.172865i | \(-0.944698\pi\) | ||
0.984946 | − | 0.172865i | \(-0.0553024\pi\) | |||||||
\(360\) | 7.16840e25 | − | 9.84987e26i | 0.103335 | − | 1.41989i | ||||
\(361\) | 4.80318e26 | 0.672517 | ||||||||
\(362\) | 7.35139e26 | 0.999837 | ||||||||
\(363\) | 3.83122e26 | + | 1.39228e25i | 0.506195 | + | 0.0183952i | ||||
\(364\) | −2.19661e25 | − | 1.36025e27i | −0.0281960 | − | 1.74605i | ||||
\(365\) | − | 3.02922e26i | − | 0.377795i | ||||||
\(366\) | −2.69423e27 | − | 9.79090e25i | −3.26500 | − | 0.118651i | ||||
\(367\) | − | 6.36769e26i | − | 0.749874i | −0.927050 | − | 0.374937i | \(-0.877664\pi\) | ||
0.927050 | − | 0.374937i | \(-0.122336\pi\) | |||||||
\(368\) | − | 9.84042e26i | − | 1.12619i | ||||||
\(369\) | 5.93753e25 | + | 4.32114e24i | 0.0660434 | + | 0.00480641i | ||||
\(370\) | 2.38839e26i | 0.258219i | ||||||||
\(371\) | 2.74889e25 | + | 1.70225e27i | 0.0288889 | + | 1.78895i | ||||
\(372\) | −1.00709e26 | + | 2.77129e27i | −0.102889 | + | 2.83127i | ||||
\(373\) | 1.89302e27 | 1.88024 | 0.940119 | − | 0.340848i | \(-0.110714\pi\) | ||||
0.940119 | + | 0.340848i | \(0.110714\pi\) | |||||||
\(374\) | −1.77179e27 | −1.71104 | ||||||||
\(375\) | −1.15760e27 | − | 4.20674e25i | −1.08700 | − | 0.0395018i | ||||
\(376\) | − | 1.52361e27i | − | 1.39124i | ||||||
\(377\) | −7.25475e26 | −0.644226 | ||||||||
\(378\) | 1.85445e26 | − | 1.99204e27i | 0.160159 | − | 1.72042i | ||||
\(379\) | −1.36236e27 | −1.14441 | −0.572205 | − | 0.820111i | \(-0.693912\pi\) | ||||
−0.572205 | + | 0.820111i | \(0.693912\pi\) | |||||||
\(380\) | − | 1.16260e27i | − | 0.949956i | ||||||
\(381\) | −1.60409e27 | − | 5.82929e25i | −1.27501 | − | 0.0463344i | ||||
\(382\) | 2.91965e27 | 2.25770 | ||||||||
\(383\) | 1.42413e27 | 1.07143 | 0.535713 | − | 0.844400i | \(-0.320043\pi\) | ||||
0.535713 | + | 0.844400i | \(0.320043\pi\) | |||||||
\(384\) | −8.69109e25 | + | 2.39159e27i | −0.0636204 | + | 1.75069i | ||||
\(385\) | 1.33133e25 | + | 8.24429e26i | 0.00948305 | + | 0.587240i | ||||
\(386\) | − | 2.86093e27i | − | 1.98308i | ||||||
\(387\) | −1.31413e27 | − | 9.56379e25i | −0.886488 | − | 0.0645156i | ||||
\(388\) | − | 2.57058e27i | − | 1.68771i | ||||||
\(389\) | 1.78241e27i | 1.13904i | 0.821979 | + | 0.569518i | \(0.192870\pi\) | ||||
−0.821979 | + | 0.569518i | \(0.807130\pi\) | |||||||
\(390\) | 2.04120e27 | + | 7.41777e25i | 1.26972 | + | 0.0461418i | ||||
\(391\) | 2.74045e27i | 1.65946i | ||||||||
\(392\) | −9.32638e25 | − | 2.88694e27i | −0.0549806 | − | 1.70190i | ||||
\(393\) | 1.93381e27 | + | 7.02753e25i | 1.10992 | + | 0.0403349i | ||||
\(394\) | 2.91097e27 | 1.62678 | ||||||||
\(395\) | −9.77755e26 | −0.532060 | ||||||||
\(396\) | −1.91048e26 | + | 2.62513e27i | −0.101238 | + | 1.39108i | ||||
\(397\) | − | 4.68315e26i | − | 0.241678i | −0.992672 | − | 0.120839i | \(-0.961441\pi\) | ||
0.992672 | − | 0.120839i | \(-0.0385585\pi\) | |||||||
\(398\) | 7.16764e26 | 0.360250 | ||||||||
\(399\) | 2.35852e25 | − | 1.16875e27i | 0.0115458 | − | 0.572145i | ||||
\(400\) | −6.03881e26 | −0.287953 | ||||||||
\(401\) | − | 8.07972e26i | − | 0.375302i | −0.982236 | − | 0.187651i | \(-0.939913\pi\) | ||
0.982236 | − | 0.187651i | \(-0.0600873\pi\) | |||||||
\(402\) | 2.41610e25 | − | 6.64855e26i | 0.0109331 | − | 0.300853i | ||||
\(403\) | −2.84674e27 | −1.25500 | ||||||||
\(404\) | 7.87828e27 | 3.38397 | ||||||||
\(405\) | 1.97660e27 | + | 2.89232e26i | 0.827258 | + | 0.121051i | ||||
\(406\) | −3.10290e27 | + | 5.01073e25i | −1.26545 | + | 0.0204351i | ||||
\(407\) | − | 3.15945e26i | − | 0.125565i | ||||||
\(408\) | −2.25069e26 | + | 6.19337e27i | −0.0871733 | + | 2.39881i | ||||
\(409\) | − | 9.79040e26i | − | 0.369578i | −0.982778 | − | 0.184789i | \(-0.940840\pi\) | ||
0.982778 | − | 0.184789i | \(-0.0591601\pi\) | |||||||
\(410\) | 2.59990e26i | 0.0956589i | ||||||||
\(411\) | −5.75762e25 | + | 1.58436e27i | −0.0206492 | + | 0.568219i | ||||
\(412\) | 1.03924e28i | 3.63326i | ||||||||
\(413\) | 2.76594e27 | − | 4.46659e25i | 0.942688 | − | 0.0152230i | ||||
\(414\) | 6.10532e27 | + | 4.44324e26i | 2.02864 | + | 0.147637i | ||||
\(415\) | 5.43198e26 | 0.175976 | ||||||||
\(416\) | −1.38597e26 | −0.0437799 | ||||||||
\(417\) | 1.58515e26 | − | 4.36198e27i | 0.0488250 | − | 1.34355i | ||||
\(418\) | 2.31251e27i | 0.694597i | ||||||||
\(419\) | −7.96227e26 | −0.233233 | −0.116616 | − | 0.993177i | \(-0.537205\pi\) | ||||
−0.116616 | + | 0.993177i | \(0.537205\pi\) | |||||||
\(420\) | 5.80949e27 | + | 1.17235e26i | 1.65967 | + | 0.0334919i | ||||
\(421\) | −4.25993e27 | −1.18697 | −0.593486 | − | 0.804844i | \(-0.702249\pi\) | ||||
−0.593486 | + | 0.804844i | \(0.702249\pi\) | |||||||
\(422\) | 1.46184e27i | 0.397299i | ||||||||
\(423\) | 3.07375e27 | + | 2.23697e26i | 0.814882 | + | 0.0593043i | ||||
\(424\) | −1.17803e28 | −3.04660 | ||||||||
\(425\) | 1.68174e27 | 0.424303 | ||||||||
\(426\) | −1.00782e28 | − | 3.66243e26i | −2.48073 | − | 0.0901505i | ||||
\(427\) | −1.27125e26 | − | 7.87224e27i | −0.0305308 | − | 1.89062i | ||||
\(428\) | − | 5.06233e27i | − | 1.18629i | ||||||
\(429\) | −2.70017e27 | − | 9.81247e25i | −0.617431 | − | 0.0224376i | ||||
\(430\) | − | 5.75424e27i | − | 1.28401i | ||||||
\(431\) | 2.53784e27i | 0.552654i | 0.961064 | + | 0.276327i | \(0.0891173\pi\) | ||||
−0.961064 | + | 0.276327i | \(0.910883\pi\) | |||||||
\(432\) | 4.47469e27 | + | 4.89559e26i | 0.951007 | + | 0.104046i | ||||
\(433\) | − | 1.66290e27i | − | 0.344940i | −0.985015 | − | 0.172470i | \(-0.944825\pi\) | ||
0.985015 | − | 0.172470i | \(-0.0551747\pi\) | |||||||
\(434\) | −1.21757e28 | + | 1.96619e26i | −2.46519 | + | 0.0398092i | ||||
\(435\) | 1.12531e26 | − | 3.09660e27i | 0.0222401 | − | 0.611996i | ||||
\(436\) | 1.01767e28 | 1.96336 | ||||||||
\(437\) | 3.57679e27 | 0.673656 | ||||||||
\(438\) | 4.24340e27 | + | 1.54206e26i | 0.780254 | + | 0.0283546i | ||||
\(439\) | − | 2.77213e27i | − | 0.497664i | −0.968547 | − | 0.248832i | \(-0.919953\pi\) | ||
0.968547 | − | 0.248832i | \(-0.0800466\pi\) | |||||||
\(440\) | −5.70539e27 | −1.00007 | ||||||||
\(441\) | 5.83783e27 | + | 2.35710e26i | 0.999186 | + | 0.0403434i | ||||
\(442\) | −1.28176e28 | −2.14227 | ||||||||
\(443\) | 1.08786e27i | 0.177555i | 0.996051 | + | 0.0887775i | \(0.0282960\pi\) | ||||
−0.996051 | + | 0.0887775i | \(0.971704\pi\) | |||||||
\(444\) | −2.22506e27 | − | 8.08592e25i | −0.354667 | − | 0.0128887i | ||||
\(445\) | 6.11209e27 | 0.951502 | ||||||||
\(446\) | −1.14056e28 | −1.73421 | ||||||||
\(447\) | 2.12545e26 | − | 5.84876e27i | 0.0315662 | − | 0.868629i | ||||
\(448\) | −7.18650e27 | + | 1.16051e26i | −1.04255 | + | 0.0168357i | ||||
\(449\) | 1.24861e28i | 1.76946i | 0.466103 | + | 0.884730i | \(0.345658\pi\) | ||||
−0.466103 | + | 0.884730i | \(0.654342\pi\) | |||||||
\(450\) | 2.72671e26 | − | 3.74668e27i | 0.0377491 | − | 0.518699i | ||||
\(451\) | − | 3.43923e26i | − | 0.0465165i | ||||||
\(452\) | − | 6.10285e27i | − | 0.806453i | ||||||
\(453\) | 7.76530e27 | + | 2.82193e26i | 1.00260 | + | 0.0364347i | ||||
\(454\) | − | 1.28528e28i | − | 1.62148i | ||||||
\(455\) | 9.63122e25 | + | 5.96415e27i | 0.0118730 | + | 0.735240i | ||||
\(456\) | 8.08349e27 | + | 2.93756e26i | 0.973796 | + | 0.0353880i | ||||
\(457\) | 1.54742e27 | 0.182175 | 0.0910874 | − | 0.995843i | \(-0.470966\pi\) | ||||
0.0910874 | + | 0.995843i | \(0.470966\pi\) | |||||||
\(458\) | 1.86924e28 | 2.15069 | ||||||||
\(459\) | −1.24615e28 | − | 1.36337e27i | −1.40132 | − | 0.153313i | ||||
\(460\) | 1.77791e28i | 1.95413i | ||||||||
\(461\) | 1.68747e27 | 0.181291 | 0.0906457 | − | 0.995883i | \(-0.471107\pi\) | ||||
0.0906457 | + | 0.995883i | \(0.471107\pi\) | |||||||
\(462\) | −1.15556e28 | − | 2.33190e26i | −1.21353 | − | 0.0244889i | ||||
\(463\) | 1.68626e28 | 1.73111 | 0.865554 | − | 0.500816i | \(-0.166967\pi\) | ||||
0.865554 | + | 0.500816i | \(0.166967\pi\) | |||||||
\(464\) | − | 6.98232e27i | − | 0.700747i | ||||||
\(465\) | 4.41569e26 | − | 1.21510e28i | 0.0433254 | − | 1.19221i | ||||
\(466\) | 4.06198e26 | 0.0389660 | ||||||||
\(467\) | −7.78290e27 | −0.729985 | −0.364993 | − | 0.931010i | \(-0.618928\pi\) | ||||
−0.364993 | + | 0.931010i | \(0.618928\pi\) | |||||||
\(468\) | −1.38210e27 | + | 1.89909e28i | −0.126753 | + | 1.74167i | ||||
\(469\) | 1.94263e27 | − | 3.13706e25i | 0.174211 | − | 0.00281325i | ||||
\(470\) | 1.34592e28i | 1.18030i | ||||||||
\(471\) | 6.21288e26 | − | 1.70964e28i | 0.0532811 | − | 1.46617i | ||||
\(472\) | 1.91415e28i | 1.60541i | ||||||||
\(473\) | 7.61190e27i | 0.624383i | ||||||||
\(474\) | 4.97738e26 | − | 1.36966e28i | 0.0399327 | − | 1.09886i | ||||
\(475\) | − | 2.19498e27i | − | 0.172246i | ||||||
\(476\) | −3.64591e28 | + | 5.88760e26i | −2.79855 | + | 0.0451924i | ||||
\(477\) | 1.72959e27 | − | 2.37657e28i | 0.129867 | − | 1.78446i | ||||
\(478\) | −1.66869e28 | −1.22569 | ||||||||
\(479\) | 1.15541e28 | 0.830257 | 0.415128 | − | 0.909763i | \(-0.363737\pi\) | ||||
0.415128 | + | 0.909763i | \(0.363737\pi\) | |||||||
\(480\) | 2.14984e25 | − | 5.91587e26i | 0.00151138 | − | 0.0415897i | ||||
\(481\) | − | 2.28563e27i | − | 0.157211i | ||||||
\(482\) | −4.02887e28 | −2.71137 | ||||||||
\(483\) | −3.60678e26 | + | 1.78731e28i | −0.0237506 | + | 1.17694i | ||||
\(484\) | −1.56080e28 | −1.00571 | ||||||||
\(485\) | 1.12709e28i | 0.710677i | ||||||||
\(486\) | −5.05784e27 | + | 2.75414e28i | −0.312093 | + | 1.69944i | ||||
\(487\) | −1.21726e28 | −0.735071 | −0.367536 | − | 0.930009i | \(-0.619798\pi\) | ||||
−0.367536 | + | 0.930009i | \(0.619798\pi\) | |||||||
\(488\) | 5.44792e28 | 3.21975 | ||||||||
\(489\) | 9.15317e25 | + | 3.32629e24i | 0.00529455 | + | 0.000192405i | ||||
\(490\) | 8.23867e26 | + | 2.55024e28i | 0.0466443 | + | 1.44385i | ||||
\(491\) | 2.96382e28i | 1.64246i | 0.570595 | + | 0.821232i | \(0.306713\pi\) | ||||
−0.570595 | + | 0.821232i | \(0.693287\pi\) | |||||||
\(492\) | −2.42209e27 | − | 8.80195e25i | −0.131389 | − | 0.00477469i | ||||
\(493\) | 1.94450e28i | 1.03256i | ||||||||
\(494\) | 1.67294e28i | 0.869654i | ||||||||
\(495\) | 8.37667e26 | − | 1.15101e28i | 0.0426301 | − | 0.585767i | ||||
\(496\) | − | 2.73984e28i | − | 1.36511i | ||||||
\(497\) | −4.75529e26 | − | 2.94472e28i | −0.0231972 | − | 1.43649i | ||||
\(498\) | −2.76522e26 | + | 7.60924e27i | −0.0132075 | + | 0.363440i | ||||
\(499\) | 1.71476e28 | 0.801952 | 0.400976 | − | 0.916089i | \(-0.368671\pi\) | ||||
0.400976 | + | 0.916089i | \(0.368671\pi\) | |||||||
\(500\) | 4.71594e28 | 2.15965 | ||||||||
\(501\) | 1.45566e28 | + | 5.28989e26i | 0.652773 | + | 0.0237219i | ||||
\(502\) | − | 5.46994e28i | − | 2.40211i | ||||||
\(503\) | 3.99652e28 | 1.71877 | 0.859386 | − | 0.511327i | \(-0.170846\pi\) | ||||
0.859386 | + | 0.511327i | \(0.170846\pi\) | |||||||
\(504\) | −2.28302e27 | + | 4.03634e28i | −0.0961587 | + | 1.70007i | ||||
\(505\) | −3.45430e28 | −1.42495 | ||||||||
\(506\) | − | 3.53641e28i | − | 1.42884i | ||||||
\(507\) | 5.71831e27 | + | 2.07805e26i | 0.226300 | + | 0.00822379i | ||||
\(508\) | 6.53489e28 | 2.53320 | ||||||||
\(509\) | 1.77023e28 | 0.672192 | 0.336096 | − | 0.941828i | \(-0.390893\pi\) | ||||
0.336096 | + | 0.941828i | \(0.390893\pi\) | |||||||
\(510\) | 1.98820e27 | − | 5.47106e28i | 0.0739558 | − | 2.03509i | ||||
\(511\) | 2.00221e26 | + | 1.23987e28i | 0.00729610 | + | 0.451812i | ||||
\(512\) | − | 4.69652e28i | − | 1.67665i | ||||||
\(513\) | −1.77945e27 | + | 1.62646e28i | −0.0622376 | + | 0.568867i | ||||
\(514\) | − | 1.16937e28i | − | 0.400718i | ||||||
\(515\) | − | 4.55665e28i | − | 1.52992i | ||||||
\(516\) | 5.36072e28 | + | 1.94810e27i | 1.76360 | + | 0.0640898i | ||||
\(517\) | − | 1.78042e28i | − | 0.573948i | ||||||
\(518\) | −1.57865e26 | − | 9.77581e27i | −0.00498681 | − | 0.308809i | ||||
\(519\) | −4.61846e27 | − | 1.67836e26i | −0.142968 | − | 0.00519551i | ||||
\(520\) | −4.12744e28 | −1.25212 | ||||||||
\(521\) | −5.91540e28 | −1.75869 | −0.879343 | − | 0.476189i | \(-0.842018\pi\) | ||||
−0.879343 | + | 0.476189i | \(0.842018\pi\) | |||||||
\(522\) | 4.33206e28 | + | 3.15273e27i | 1.26228 | + | 0.0918642i | ||||
\(523\) | 1.74278e28i | 0.497709i | 0.968541 | + | 0.248854i | \(0.0800540\pi\) | ||||
−0.968541 | + | 0.248854i | \(0.919946\pi\) | |||||||
\(524\) | −7.87818e28 | −2.20520 | ||||||||
\(525\) | 1.09683e28 | + | 2.21339e26i | 0.300930 | + | 0.00607274i | ||||
\(526\) | 5.08576e28 | 1.36775 | ||||||||
\(527\) | 7.63015e28i | 2.01151i | ||||||||
\(528\) | 9.44400e26 | − | 2.59877e28i | 0.0244062 | − | 0.671602i | ||||
\(529\) | −1.52266e28 | −0.385760 | ||||||||
\(530\) | 1.04064e29 | 2.58466 | ||||||||
\(531\) | −3.86162e28 | − | 2.81036e27i | −0.940324 | − | 0.0684336i | ||||
\(532\) | 7.68441e26 | + | 4.75858e28i | 0.0183459 | + | 1.13607i | ||||
\(533\) | − | 2.48803e27i | − | 0.0582399i | ||||||
\(534\) | −3.11143e27 | + | 8.56195e28i | −0.0714130 | + | 1.96512i | ||||
\(535\) | 2.21962e28i | 0.499533i | ||||||||
\(536\) | 1.34438e28i | 0.296683i | ||||||||
\(537\) | −1.16571e27 | + | 3.20776e28i | −0.0252266 | + | 0.694179i | ||||
\(538\) | − | 1.29502e29i | − | 2.74828i | ||||||
\(539\) | −1.08984e27 | − | 3.37354e28i | −0.0226819 | − | 0.702109i | ||||
\(540\) | −8.08462e28 | − | 8.84508e27i | −1.65016 | − | 0.180537i | ||||
\(541\) | −7.84416e28 | −1.57027 | −0.785137 | − | 0.619322i | \(-0.787407\pi\) | ||||
−0.785137 | + | 0.619322i | \(0.787407\pi\) | |||||||
\(542\) | −4.72917e28 | −0.928522 | ||||||||
\(543\) | 1.09124e27 | − | 3.00285e28i | 0.0210147 | − | 0.578276i | ||||
\(544\) | 3.71485e27i | 0.0701702i | ||||||||
\(545\) | −4.46208e28 | −0.826750 | ||||||||
\(546\) | −8.35962e28 | − | 1.68696e27i | −1.51937 | − | 0.0306608i | ||||
\(547\) | 8.11851e28 | 1.44747 | 0.723734 | − | 0.690079i | \(-0.242424\pi\) | ||||
0.723734 | + | 0.690079i | \(0.242424\pi\) | |||||||
\(548\) | − | 6.45455e28i | − | 1.12894i | ||||||
\(549\) | −7.99864e27 | + | 1.09907e29i | −0.137248 | + | 1.88588i | ||||
\(550\) | −2.17021e28 | −0.365336 | ||||||||
\(551\) | 2.53793e28 | 0.419168 | ||||||||
\(552\) | −1.23617e29 | − | 4.49227e27i | −2.00317 | − | 0.0727957i | ||||
\(553\) | 4.00200e28 | − | 6.46263e26i | 0.636301 | − | 0.0102753i | ||||
\(554\) | − | 9.29765e28i | − | 1.45051i | ||||||
\(555\) | 9.75596e27 | + | 3.54534e26i | 0.149346 | + | 0.00542727i | ||||
\(556\) | 1.77703e29i | 2.66937i | ||||||||
\(557\) | 6.86762e28i | 1.01234i | 0.862433 | + | 0.506170i | \(0.168939\pi\) | ||||
−0.862433 | + | 0.506170i | \(0.831061\pi\) | |||||||
\(558\) | 1.69989e29 | + | 1.23712e28i | 2.45901 | + | 0.178959i | ||||
\(559\) | 5.50666e28i | 0.781744i | ||||||||
\(560\) | −5.74019e28 | + | 9.26956e26i | −0.799746 | + | 0.0129147i | ||||
\(561\) | −2.63005e27 | + | 7.23729e28i | −0.0359628 | + | 0.989615i | ||||
\(562\) | 1.59572e29 | 2.14153 | ||||||||
\(563\) | 2.72494e28 | 0.358938 | 0.179469 | − | 0.983764i | \(-0.442562\pi\) | ||||
0.179469 | + | 0.983764i | \(0.442562\pi\) | |||||||
\(564\) | −1.25387e29 | − | 4.55661e27i | −1.62115 | − | 0.0589130i | ||||
\(565\) | 2.67585e28i | 0.339588i | ||||||||
\(566\) | −6.65240e28 | −0.828716 | ||||||||
\(567\) | −8.10942e28 | − | 1.05319e28i | −0.991672 | − | 0.128791i | ||||
\(568\) | 2.03787e29 | 2.44635 | ||||||||
\(569\) | − | 7.84585e28i | − | 0.924616i | −0.886719 | − | 0.462308i | \(-0.847021\pi\) | ||
0.886719 | − | 0.462308i | \(-0.152979\pi\) | |||||||
\(570\) | −7.14073e28 | − | 2.59496e27i | −0.826146 | − | 0.0300224i | ||||
\(571\) | 2.92469e28 | 0.332201 | 0.166100 | − | 0.986109i | \(-0.446882\pi\) | ||||
0.166100 | + | 0.986109i | \(0.446882\pi\) | |||||||
\(572\) | 1.10002e29 | 1.22671 | ||||||||
\(573\) | 4.33394e27 | − | 1.19260e29i | 0.0474525 | − | 1.30578i | ||||
\(574\) | −1.71844e26 | − | 1.06415e28i | −0.00184740 | − | 0.114400i | ||||
\(575\) | 3.35669e28i | 0.354322i | ||||||||
\(576\) | 1.00333e29 | + | 7.30190e27i | 1.03994 | + | 0.0756833i | ||||
\(577\) | − | 1.12472e29i | − | 1.14472i | −0.820003 | − | 0.572359i | \(-0.806029\pi\) | ||
0.820003 | − | 0.572359i | \(-0.193971\pi\) | |||||||
\(578\) | 1.70671e29i | 1.70576i | ||||||||
\(579\) | −1.16861e29 | − | 4.24677e27i | −1.14695 | − | 0.0416806i | ||||
\(580\) | 1.26153e29i | 1.21591i | ||||||||
\(581\) | −2.22333e28 | + | 3.59035e26i | −0.210453 | + | 0.00339850i | ||||
\(582\) | −1.57886e29 | − | 5.73761e27i | −1.46775 | − | 0.0533384i | ||||
\(583\) | −1.37659e29 | −1.25686 | ||||||||
\(584\) | −8.58044e28 | −0.769440 | ||||||||
\(585\) | 6.05992e27 | − | 8.32674e28i | 0.0533741 | − | 0.733396i | ||||
\(586\) | − | 2.13727e29i | − | 1.84899i | ||||||
\(587\) | −7.19101e28 | −0.611069 | −0.305534 | − | 0.952181i | \(-0.598835\pi\) | ||||
−0.305534 | + | 0.952181i | \(0.598835\pi\) | |||||||
\(588\) | −2.37863e29 | − | 9.58602e26i | −1.98547 | − | 0.00800159i | ||||
\(589\) | 9.95875e28 | 0.816572 | ||||||||
\(590\) | − | 1.69091e29i | − | 1.36199i | ||||||
\(591\) | 4.32106e27 | − | 1.18905e29i | 0.0341917 | − | 0.940878i | ||||
\(592\) | 2.19981e28 | 0.171004 | ||||||||
\(593\) | −1.05302e29 | −0.804198 | −0.402099 | − | 0.915596i | \(-0.631719\pi\) | ||||
−0.402099 | + | 0.915596i | \(0.631719\pi\) | |||||||
\(594\) | 1.60810e29 | + | 1.75936e28i | 1.20658 | + | 0.132007i | ||||
\(595\) | 1.59858e29 | − | 2.58147e27i | 1.17844 | − | 0.0190300i | ||||
\(596\) | 2.38273e29i | 1.72579i | ||||||||
\(597\) | 1.06397e27 | − | 2.92779e28i | 0.00757177 | − | 0.208358i | ||||
\(598\) | − | 2.55834e29i | − | 1.78894i | ||||||
\(599\) | − | 5.84017e28i | − | 0.401277i | −0.979665 | − | 0.200638i | \(-0.935698\pi\) | ||
0.979665 | − | 0.200638i | \(-0.0643016\pi\) | |||||||
\(600\) | −2.75679e27 | + | 7.58606e28i | −0.0186130 | + | 0.512186i | ||||
\(601\) | 1.06053e29i | 0.703625i | 0.936070 | + | 0.351813i | \(0.114435\pi\) | ||||
−0.936070 | + | 0.351813i | \(0.885565\pi\) | |||||||
\(602\) | 3.80336e27 | + | 2.35524e29i | 0.0247973 | + | 1.53558i | ||||
\(603\) | −2.71217e28 | − | 1.97383e27i | −0.173774 | − | 0.0126467i | ||||
\(604\) | −3.16351e29 | −1.99197 | ||||||||
\(605\) | 6.84348e28 | 0.423492 | ||||||||
\(606\) | 1.75845e28 | − | 4.83886e29i | 0.106947 | − | 2.94293i | ||||
\(607\) | − | 1.21676e29i | − | 0.727317i | −0.931532 | − | 0.363659i | \(-0.881527\pi\) | ||
0.931532 | − | 0.363659i | \(-0.118473\pi\) | |||||||
\(608\) | 4.84856e27 | 0.0284856 | ||||||||
\(609\) | −2.55921e27 | + | 1.26820e29i | −0.0147783 | + | 0.732327i | ||||
\(610\) | −4.81254e29 | −2.73156 | ||||||||
\(611\) | − | 1.28801e29i | − | 0.718598i | ||||||
\(612\) | 5.09017e29 | + | 3.70446e28i | 2.79153 | + | 0.203158i | ||||
\(613\) | −8.15440e28 | −0.439599 | −0.219800 | − | 0.975545i | \(-0.570540\pi\) | ||||
−0.219800 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(614\) | 4.89144e29 | 2.59220 | ||||||||
\(615\) | 1.06199e28 | + | 3.85929e26i | 0.0553262 | + | 0.00201057i | ||||
\(616\) | 2.33524e29 | − | 3.77107e27i | 1.19601 | − | 0.0193138i | ||||
\(617\) | 8.97288e28i | 0.451791i | 0.974152 | + | 0.225895i | \(0.0725308\pi\) | ||||
−0.974152 | + | 0.225895i | \(0.927469\pi\) | |||||||
\(618\) | 6.38305e29 | + | 2.31962e28i | 3.15973 | + | 0.114825i | ||||
\(619\) | − | 2.44203e29i | − | 1.18850i | −0.804280 | − | 0.594250i | \(-0.797449\pi\) | ||
0.804280 | − | 0.594250i | \(-0.202551\pi\) | |||||||
\(620\) | 4.95019e29i | 2.36869i | ||||||||
\(621\) | 2.72122e28 | − | 2.48726e29i | 0.128027 | − | 1.17020i | ||||
\(622\) | 1.58046e29i | 0.731113i | ||||||||
\(623\) | −2.50171e29 | + | 4.03988e27i | −1.13792 | + | 0.0183757i | ||||
\(624\) | 6.83206e27 | − | 1.88002e29i | 0.0305572 | − | 0.840863i | ||||
\(625\) | −1.38337e29 | −0.608413 | ||||||||
\(626\) | 6.31984e29 | 2.73323 | ||||||||
\(627\) | 9.44600e28 | + | 3.43270e27i | 0.401734 | + | 0.0145991i | ||||
\(628\) | 6.96492e29i | 2.91300i | ||||||||
\(629\) | −6.12622e28 | −0.251977 | ||||||||
\(630\) | 2.01675e28 | − | 3.56559e29i | 0.0815788 | − | 1.44230i | ||||
\(631\) | 3.66064e29 | 1.45629 | 0.728146 | − | 0.685422i | \(-0.240382\pi\) | ||||
0.728146 | + | 0.685422i | \(0.240382\pi\) | |||||||
\(632\) | 2.76955e29i | 1.08363i | ||||||||
\(633\) | 5.97121e28 | + | 2.16995e27i | 0.229786 | + | 0.00835048i | ||||
\(634\) | −6.48462e29 | −2.45441 | ||||||||
\(635\) | −2.86528e29 | −1.06670 | ||||||||
\(636\) | −3.52309e28 | + | 9.69473e29i | −0.129010 | + | 3.55006i | ||||
\(637\) | −7.88420e27 | − | 2.44052e29i | −0.0283984 | − | 0.879059i | ||||
\(638\) | − | 2.50928e29i | − | 0.889063i | ||||||
\(639\) | −2.99201e28 | + | 4.11122e29i | −0.104281 | + | 1.43289i | ||||
\(640\) | 4.27195e29i | 1.46466i | ||||||||
\(641\) | 1.23048e29i | 0.415015i | 0.978233 | + | 0.207508i | \(0.0665352\pi\) | ||||
−0.978233 | + | 0.207508i | \(0.933465\pi\) | |||||||
\(642\) | −3.10930e29 | − | 1.12993e28i | −1.03168 | − | 0.0374915i | ||||
\(643\) | 2.14552e29i | 0.700352i | 0.936684 | + | 0.350176i | \(0.113878\pi\) | ||||
−0.936684 | + | 0.350176i | \(0.886122\pi\) | |||||||
\(644\) | −1.17514e28 | − | 7.27707e29i | −0.0377388 | − | 2.33698i | ||||
\(645\) | −2.35045e29 | − | 8.54161e27i | −0.742634 | − | 0.0269875i | ||||
\(646\) | 4.48400e29 | 1.39388 | ||||||||
\(647\) | −2.98765e28 | −0.0913766 | −0.0456883 | − | 0.998956i | \(-0.514548\pi\) | ||||
−0.0456883 | + | 0.998956i | \(0.514548\pi\) | |||||||
\(648\) | 8.19267e28 | − | 5.59883e29i | 0.246540 | − | 1.68484i | ||||
\(649\) | 2.23679e29i | 0.662301i | ||||||||
\(650\) | −1.56999e29 | −0.457411 | ||||||||
\(651\) | −1.00422e28 | + | 4.97636e29i | −0.0287893 | + | 1.42663i | ||||
\(652\) | −3.72892e27 | −0.0105192 | ||||||||
\(653\) | − | 3.85689e29i | − | 1.07065i | −0.844645 | − | 0.535326i | \(-0.820189\pi\) | ||
0.844645 | − | 0.535326i | \(-0.179811\pi\) | |||||||
\(654\) | 2.27148e28 | − | 6.25058e29i | 0.0620501 | − | 1.70747i | ||||
\(655\) | 3.45425e29 | 0.928583 | ||||||||
\(656\) | 2.39461e28 | 0.0633496 | ||||||||
\(657\) | 1.25978e28 | − | 1.73103e29i | 0.0327989 | − | 0.450679i | ||||
\(658\) | −8.89605e27 | − | 5.50890e29i | −0.0227943 | − | 1.41154i | ||||
\(659\) | − | 4.97164e29i | − | 1.25373i | −0.779129 | − | 0.626863i | \(-0.784339\pi\) | ||
0.779129 | − | 0.626863i | \(-0.215661\pi\) | |||||||
\(660\) | −1.70629e28 | + | 4.69531e29i | −0.0423488 | + | 1.16534i | ||||
\(661\) | − | 2.77713e29i | − | 0.678392i | −0.940716 | − | 0.339196i | \(-0.889845\pi\) | ||
0.940716 | − | 0.339196i | \(-0.110155\pi\) | |||||||
\(662\) | 4.29184e29i | 1.03189i | ||||||||
\(663\) | −1.90265e28 | + | 5.23566e29i | −0.0450264 | + | 1.23902i | ||||
\(664\) | − | 1.53864e29i | − | 0.358403i | ||||||
\(665\) | −3.36929e27 | − | 2.08644e29i | −0.00772523 | − | 0.478387i | ||||
\(666\) | −9.93278e27 | + | 1.36483e29i | −0.0224177 | + | 0.308035i | ||||
\(667\) | −3.88114e29 | −0.862259 | ||||||||
\(668\) | −5.93020e29 | −1.29693 | ||||||||
\(669\) | −1.69305e28 | + | 4.65888e29i | −0.0364498 | + | 1.00301i | ||||
\(670\) | − | 1.18759e29i | − | 0.251699i | ||||||
\(671\) | 6.36619e29 | 1.32829 | ||||||||
\(672\) | −4.88921e26 | + | 2.42281e28i | −0.00100429 | + | 0.0497671i | ||||
\(673\) | 1.68936e29 | 0.341637 | 0.170818 | − | 0.985303i | \(-0.445359\pi\) | ||||
0.170818 | + | 0.985303i | \(0.445359\pi\) | |||||||
\(674\) | 9.04159e28i | 0.180018i | ||||||||
\(675\) | −1.52637e29 | − | 1.66994e28i | −0.299206 | − | 0.0327350i | ||||
\(676\) | −2.32959e29 | −0.449612 | ||||||||
\(677\) | 6.40443e29 | 1.21702 | 0.608512 | − | 0.793544i | \(-0.291767\pi\) | ||||
0.608512 | + | 0.793544i | \(0.291767\pi\) | |||||||
\(678\) | −3.74839e29 | − | 1.36217e28i | −0.701346 | − | 0.0254871i | ||||
\(679\) | −7.44971e27 | − | 4.61325e29i | −0.0137248 | − | 0.849912i | ||||
\(680\) | 1.10628e30i | 2.00689i | ||||||||
\(681\) | −5.25003e29 | − | 1.90787e28i | −0.937815 | − | 0.0340804i | ||||
\(682\) | − | 9.84633e29i | − | 1.73196i | ||||||
\(683\) | 1.21336e29i | 0.210171i | 0.994463 | + | 0.105086i | \(0.0335116\pi\) | ||||
−0.994463 | + | 0.105086i | \(0.966488\pi\) | |||||||
\(684\) | 4.83499e28 | − | 6.64361e29i | 0.0824721 | − | 1.13322i | ||||
\(685\) | 2.83005e29i | 0.475383i | ||||||||
\(686\) | −5.05775e28 | − | 1.04328e30i | −0.0836670 | − | 1.72583i | ||||
\(687\) | 2.77471e28 | − | 7.63537e29i | 0.0452035 | − | 1.24390i | ||||
\(688\) | −5.29988e29 | −0.850330 | ||||||||
\(689\) | −9.95866e29 | −1.57362 | ||||||||
\(690\) | 1.09200e30 | + | 3.96835e28i | 1.69944 | + | 0.0617582i | ||||
\(691\) | 4.79509e29i | 0.734983i | 0.930027 | + | 0.367491i | \(0.119783\pi\) | ||||
−0.930027 | + | 0.367491i | \(0.880217\pi\) | |||||||
\(692\) | 1.88152e29 | 0.284050 | ||||||||
\(693\) | −2.66783e28 | + | 4.71668e29i | −0.0396697 | + | 0.701354i | ||||
\(694\) | −8.59456e29 | −1.25878 | ||||||||
\(695\) | − | 7.79153e29i | − | 1.12404i | ||||||
\(696\) | −8.77131e29 | − | 3.18752e28i | −1.24643 | − | 0.0452955i | ||||
\(697\) | −6.66872e28 | −0.0933465 | ||||||||
\(698\) | −1.88254e30 | −2.59575 | ||||||||
\(699\) | 6.02962e26 | − | 1.65921e28i | 0.000818991 | − | 0.0225368i | ||||
\(700\) | −4.46575e29 | + | 7.21153e27i | −0.597538 | + | 0.00964935i | ||||
\(701\) | − | 3.19313e29i | − | 0.420898i | −0.977605 | − | 0.210449i | \(-0.932507\pi\) | ||
0.977605 | − | 0.210449i | \(-0.0674926\pi\) | |||||||
\(702\) | 1.16334e30 | + | 1.27277e29i | 1.51067 | + | 0.165276i | ||||
\(703\) | 7.99584e28i | 0.102290i | ||||||||
\(704\) | − | 5.81164e29i | − | 0.732463i | ||||||
\(705\) | 5.49771e29 | + | 1.99788e28i | 0.682647 | + | 0.0248076i | ||||
\(706\) | 1.43636e30i | 1.75717i | ||||||||
\(707\) | 1.41386e30 | − | 2.28317e28i | 1.70413 | − | 0.0275192i | ||||
\(708\) | 1.57527e30 | + | 5.72457e28i | 1.87071 | + | 0.0679819i | ||||
\(709\) | −2.31583e29 | −0.270970 | −0.135485 | − | 0.990779i | \(-0.543259\pi\) | ||||
−0.135485 | + | 0.990779i | \(0.543259\pi\) | |||||||
\(710\) | −1.80020e30 | −2.07543 | ||||||||
\(711\) | −5.58731e29 | − | 4.06626e28i | −0.634706 | − | 0.0461917i | ||||
\(712\) | − | 1.73128e30i | − | 1.93789i | ||||||
\(713\) | −1.52294e30 | −1.67975 | ||||||||
\(714\) | −4.52159e28 | + | 2.24064e30i | −0.0491428 | + | 2.43524i | ||||
\(715\) | −4.82314e29 | −0.516555 | ||||||||
\(716\) | − | 1.30681e30i | − | 1.37919i | ||||||
\(717\) | −2.47700e28 | + | 6.81614e29i | −0.0257618 | + | 0.708904i | ||||
\(718\) | 5.82842e29 | 0.597372 | ||||||||
\(719\) | 9.43702e29 | 0.953194 | 0.476597 | − | 0.879122i | \(-0.341870\pi\) | ||||
0.476597 | + | 0.879122i | \(0.341870\pi\) | |||||||
\(720\) | 8.01406e29 | + | 5.83236e28i | 0.797741 | + | 0.0580569i | ||||
\(721\) | 3.01179e28 | + | 1.86506e30i | 0.0295464 | + | 1.82966i | ||||
\(722\) | 1.20185e30i | 1.16201i | ||||||||
\(723\) | −5.98046e28 | + | 1.64569e30i | −0.0569879 | + | 1.56818i | ||||
\(724\) | 1.22333e30i | 1.14892i | ||||||||
\(725\) | 2.38175e29i | 0.220469i | ||||||||
\(726\) | −3.48376e28 | + | 9.58650e29i | −0.0317844 | + | 0.874632i | ||||
\(727\) | 4.36564e29i | 0.392587i | 0.980545 | + | 0.196294i | \(0.0628906\pi\) | ||||
−0.980545 | + | 0.196294i | \(0.937109\pi\) | |||||||
\(728\) | 1.68938e30 | − | 2.72810e28i | 1.49744 | − | 0.0241814i | ||||
\(729\) | 1.11749e30 | + | 2.47482e29i | 0.976344 | + | 0.216224i | ||||
\(730\) | 7.57973e29 | 0.652775 | ||||||||
\(731\) | 1.47596e30 | 1.25297 | ||||||||
\(732\) | 1.62929e29 | − | 4.48342e30i | 0.136342 | − | 3.75183i | ||||
\(733\) | 7.74686e29i | 0.639049i | 0.947578 | + | 0.319524i | \(0.103523\pi\) | ||||
−0.947578 | + | 0.319524i | \(0.896477\pi\) | |||||||
\(734\) | 1.59333e30 | 1.29568 | ||||||||
\(735\) | 1.04293e30 | + | 4.20307e27i | 0.836060 | + | 0.00336938i | ||||
\(736\) | −7.41467e28 | −0.0585969 | ||||||||
\(737\) | 1.57098e29i | 0.122395i | ||||||||
\(738\) | −1.08124e28 | + | 1.48569e29i | −0.00830479 | + | 0.114114i | ||||
\(739\) | 7.52141e29 | 0.569551 | 0.284775 | − | 0.958594i | \(-0.408081\pi\) | ||||
0.284775 | + | 0.958594i | \(0.408081\pi\) | |||||||
\(740\) | −3.97449e29 | −0.296721 | ||||||||
\(741\) | 6.83350e29 | + | 2.48331e28i | 0.502982 | + | 0.0182785i | ||||
\(742\) | −4.25938e30 | + | 6.87827e28i | −3.09105 | + | 0.0499158i | ||||
\(743\) | 2.56667e29i | 0.183649i | 0.995775 | + | 0.0918243i | \(0.0292698\pi\) | ||||
−0.995775 | + | 0.0918243i | \(0.970730\pi\) | |||||||
\(744\) | −3.44183e30 | − | 1.25077e29i | −2.42814 | − | 0.0882392i | ||||
\(745\) | − | 1.04473e30i | − | 0.726712i | ||||||
\(746\) | 4.73672e30i | 3.24878i | ||||||||
\(747\) | 3.10407e29 | + | 2.25903e28i | 0.209925 | + | 0.0152777i | ||||
\(748\) | − | 2.94841e30i | − | 1.96617i | ||||||
\(749\) | −1.46709e28 | − | 9.08501e29i | −0.00964715 | − | 0.597402i | ||||
\(750\) | 1.05261e29 | − | 2.89654e30i | 0.0682535 | − | 1.87818i | ||||
\(751\) | −3.92938e29 | −0.251249 | −0.125625 | − | 0.992078i | \(-0.540093\pi\) | ||||
−0.125625 | + | 0.992078i | \(0.540093\pi\) | |||||||
\(752\) | 1.23964e30 | 0.781644 | ||||||||
\(753\) | −2.23432e30 | − | 8.11959e28i | −1.38931 | − | 0.0504879i | ||||
\(754\) | − | 1.81529e30i | − | 1.11313i | ||||||
\(755\) | 1.38707e30 | 0.838794 | ||||||||
\(756\) | 3.31492e30 | + | 3.08596e29i | 1.97694 | + | 0.184040i | ||||
\(757\) | 3.06495e30 | 1.80267 | 0.901337 | − | 0.433119i | \(-0.142587\pi\) | ||||
0.901337 | + | 0.433119i | \(0.142587\pi\) | |||||||
\(758\) | − | 3.40891e30i | − | 1.97738i | ||||||
\(759\) | −1.44453e30 | − | 5.24946e28i | −0.826396 | − | 0.0300314i | ||||
\(760\) | 1.44390e30 | 0.814696 | ||||||||
\(761\) | −1.21051e30 | −0.673643 | −0.336822 | − | 0.941568i | \(-0.609352\pi\) | ||||
−0.336822 | + | 0.941568i | \(0.609352\pi\) | |||||||
\(762\) | 1.45861e29 | − | 4.01375e30i | 0.0800591 | − | 2.20304i | ||||
\(763\) | 1.82635e30 | − | 2.94928e28i | 0.988727 | − | 0.0159665i | ||||
\(764\) | 4.85854e30i | 2.59433i | ||||||||
\(765\) | −2.23183e30 | − | 1.62425e29i | −1.17548 | − | 0.0855476i | ||||
\(766\) | 3.56346e30i | 1.85127i | ||||||||
\(767\) | 1.61816e30i | 0.829218i | ||||||||
\(768\) | −3.92284e30 | − | 1.42557e29i | −1.98293 | − | 0.0720603i | ||||
\(769\) | − | 2.92363e30i | − | 1.45779i | −0.684624 | − | 0.728896i | \(-0.740034\pi\) | ||
0.684624 | − | 0.728896i | \(-0.259966\pi\) | |||||||
\(770\) | −2.06289e30 | + | 3.33126e28i | −1.01467 | + | 0.0163854i | ||||
\(771\) | −4.77657e29 | − | 1.73582e28i | −0.231763 | − | 0.00842234i | ||||
\(772\) | 4.76082e30 | 2.27877 | ||||||||
\(773\) | 2.60630e30 | 1.23066 | 0.615331 | − | 0.788269i | \(-0.289022\pi\) | ||||
0.615331 | + | 0.788269i | \(0.289022\pi\) | |||||||
\(774\) | 2.39306e29 | − | 3.28822e30i | 0.111474 | − | 1.53173i | ||||
\(775\) | 9.34592e29i | 0.429491i | ||||||||
\(776\) | 3.19256e30 | 1.44741 | ||||||||
\(777\) | −3.99550e29 | − | 8.06288e27i | −0.178711 | − | 0.00360636i | ||||
\(778\) | −4.45996e30 | −1.96809 | ||||||||
\(779\) | 8.70390e28i | 0.0378940i | ||||||||
\(780\) | −1.23438e29 | + | 3.39672e30i | −0.0530218 | + | 1.45904i | ||||
\(781\) | 2.38136e30 | 1.00923 | ||||||||
\(782\) | −6.85716e30 | −2.86730 | ||||||||
\(783\) | 1.93086e29 | − | 1.76485e30i | 0.0796621 | − | 0.728132i | ||||
\(784\) | 2.34887e30 | − | 7.58814e28i | 0.956183 | − | 0.0308899i | ||||
\(785\) | − | 3.05383e30i | − | 1.22663i | ||||||
\(786\) | −1.75843e29 | + | 4.83880e30i | −0.0696929 | + | 1.91779i | ||||
\(787\) | − | 2.79596e30i | − | 1.09344i | −0.837314 | − | 0.546722i | \(-0.815876\pi\) | ||
0.837314 | − | 0.546722i | \(-0.184124\pi\) | |||||||
\(788\) | 4.84410e30i | 1.86934i | ||||||||
\(789\) | 7.54932e28 | − | 2.07740e30i | 0.0287475 | − | 0.791064i | ||||
\(790\) | − | 2.44654e30i | − | 0.919324i | ||||||
\(791\) | −1.76864e28 | − | 1.09524e30i | −0.00655824 | − | 0.406120i | ||||
\(792\) | −3.26031e30 | − | 2.37274e29i | −1.19301 | − | 0.0868232i | ||||
\(793\) | 4.60548e30 | 1.66305 | ||||||||
\(794\) | 1.17182e30 | 0.417586 | ||||||||
\(795\) | 1.54473e29 | − | 4.25074e30i | 0.0543247 | − | 1.49489i | ||||
\(796\) | 1.19276e30i | 0.413965i | ||||||||
\(797\) | 1.70407e30 | 0.583680 | 0.291840 | − | 0.956467i | \(-0.405732\pi\) | ||||
0.291840 | + | 0.956467i | \(0.405732\pi\) | |||||||
\(798\) | 2.92445e30 | + | 5.90151e28i | 0.988585 | + | 0.0199495i | ||||
\(799\) | −3.45227e30 | −1.15176 | ||||||||
\(800\) | 4.55019e28i | 0.0149825i | ||||||||
\(801\) | 3.49271e30 | + | 2.54188e29i | 1.13507 | + | 0.0826063i | ||||
\(802\) | 2.02171e30 | 0.648468 | ||||||||
\(803\) | −1.00267e30 | −0.317428 | ||||||||
\(804\) | 1.10637e30 | + | 4.02059e28i | 0.345711 | + | 0.0125632i | ||||
\(805\) | 5.15250e28 | + | 3.19070e30i | 0.0158914 | + | 0.984076i | ||||
\(806\) | − | 7.12312e30i | − | 2.16846i | ||||||
\(807\) | −5.28979e30 | − | 1.92232e29i | −1.58952 | − | 0.0577636i | ||||
\(808\) | 9.78450e30i | 2.90215i | ||||||||
\(809\) | 4.11056e30i | 1.20349i | 0.798689 | + | 0.601744i | \(0.205527\pi\) | ||||
−0.798689 | + | 0.601744i | \(0.794473\pi\) | |||||||
\(810\) | −7.23718e29 | + | 4.94585e30i | −0.209159 | + | 1.42938i | ||||
\(811\) | − | 6.74352e29i | − | 0.192384i | −0.995363 | − | 0.0961918i | \(-0.969334\pi\) | ||
0.995363 | − | 0.0961918i | \(-0.0306662\pi\) | |||||||
\(812\) | −8.33827e28 | − | 5.16349e30i | −0.0234821 | − | 1.45414i | ||||
\(813\) | −7.01999e28 | + | 1.93174e30i | −0.0195158 | + | 0.537029i | ||||
\(814\) | 7.90558e29 | 0.216959 | ||||||||
\(815\) | 1.63498e28 | 0.00442952 | ||||||||
\(816\) | −5.03906e30 | − | 1.83121e29i | −1.34773 | − | 0.0489768i | ||||
\(817\) | − | 1.92640e30i | − | 0.508645i | ||||||
\(818\) | 2.44976e30 | 0.638578 | ||||||||
\(819\) | −1.92998e29 | + | 3.41218e30i | −0.0496676 | + | 0.878114i | ||||
\(820\) | −4.32644e29 | −0.109922 | ||||||||
\(821\) | 8.34544e29i | 0.209337i | 0.994507 | + | 0.104668i | \(0.0333781\pi\) | ||||
−0.994507 | + | 0.104668i | \(0.966622\pi\) | |||||||
\(822\) | −3.96440e30 | − | 1.44067e29i | −0.981801 | − | 0.0356789i | ||||
\(823\) | −6.65471e30 | −1.62716 | −0.813582 | − | 0.581451i | \(-0.802485\pi\) | ||||
−0.813582 | + | 0.581451i | \(0.802485\pi\) | |||||||
\(824\) | −1.29070e31 | −3.11593 | ||||||||
\(825\) | −3.22146e28 | + | 8.86472e29i | −0.00767868 | + | 0.211300i | ||||
\(826\) | 1.11763e29 | + | 6.92096e30i | 0.0263032 | + | 1.62883i | ||||
\(827\) | 5.95478e30i | 1.38375i | 0.722017 | + | 0.691875i | \(0.243215\pi\) | ||||
−0.722017 | + | 0.691875i | \(0.756785\pi\) | |||||||
\(828\) | −7.39393e29 | + | 1.01598e31i | −0.169651 | + | 2.33112i | ||||
\(829\) | − | 4.17490e30i | − | 0.945852i | −0.881102 | − | 0.472926i | \(-0.843198\pi\) | ||
0.881102 | − | 0.472926i | \(-0.156802\pi\) | |||||||
\(830\) | 1.35919e30i | 0.304061i | ||||||||
\(831\) | −3.79784e30 | − | 1.38015e29i | −0.838931 | − | 0.0304870i | ||||
\(832\) | − | 4.20431e30i | − | 0.917064i | ||||||
\(833\) | −6.54136e30 | + | 2.11322e29i | −1.40895 | + | 0.0455167i | ||||
\(834\) | 1.09146e31 | + | 3.96638e29i | 2.32147 | + | 0.0843627i | ||||
\(835\) | 2.60015e30 | 0.546123 | ||||||||
\(836\) | −3.84821e30 | −0.798166 | ||||||||
\(837\) | 7.57662e29 | − | 6.92522e30i | 0.155188 | − | 1.41846i | ||||
\(838\) | − | 1.99232e30i | − | 0.402993i | ||||||
\(839\) | −3.22056e30 | −0.643326 | −0.321663 | − | 0.946854i | \(-0.604242\pi\) | ||||
−0.321663 | + | 0.946854i | \(0.604242\pi\) | |||||||
\(840\) | −1.45601e29 | + | 7.21515e30i | −0.0287231 | + | 1.42335i | ||||
\(841\) | 2.37896e30 | 0.463478 | ||||||||
\(842\) | − | 1.06592e31i | − | 2.05092i | ||||||
\(843\) | 2.36869e29 | − | 6.51808e30i | 0.0450109 | − | 1.23860i | ||||
\(844\) | −2.43261e30 | −0.456539 | ||||||||
\(845\) | 1.02143e30 | 0.189327 | ||||||||
\(846\) | −5.59736e29 | + | 7.69115e30i | −0.102469 | + | 1.40800i | ||||
\(847\) | −2.80107e30 | + | 4.52331e28i | −0.506463 | + | 0.00817862i | ||||
\(848\) | − | 9.58470e30i | − | 1.71168i | ||||||
\(849\) | −9.87484e28 | + | 2.71733e30i | −0.0174180 | + | 0.479304i | ||||
\(850\) | 4.20807e30i | 0.733135i | ||||||||
\(851\) | − | 1.22277e30i | − | 0.210418i | ||||||
\(852\) | 6.09458e29 | − | 1.67709e31i | 0.103592 | − | 2.85063i | ||||
\(853\) | − | 5.64652e30i | − | 0.948018i | −0.880520 | − | 0.474009i | \(-0.842806\pi\) | ||
0.880520 | − | 0.474009i | \(-0.157194\pi\) | |||||||
\(854\) | 1.96979e31 | − | 3.18093e29i | 3.26673 | − | 0.0527528i | ||||
\(855\) | −2.11994e29 | + | 2.91295e30i | −0.0347280 | + | 0.477187i | ||||
\(856\) | 6.28721e30 | 1.01738 | ||||||||
\(857\) | −3.54661e30 | −0.566910 | −0.283455 | − | 0.958985i | \(-0.591481\pi\) | ||||
−0.283455 | + | 0.958985i | \(0.591481\pi\) | |||||||
\(858\) | 2.45528e29 | − | 6.75636e30i | 0.0387690 | − | 1.06683i | ||||
\(859\) | 2.64120e30i | 0.411977i | 0.978554 | + | 0.205988i | \(0.0660409\pi\) | ||||
−0.978554 | + | 0.205988i | \(0.933959\pi\) | |||||||
\(860\) | 9.57553e30 | 1.47547 | ||||||||
\(861\) | −4.34932e29 | − | 8.77687e27i | −0.0662046 | − | 0.00133600i | ||||
\(862\) | −6.35020e30 | −0.954908 | ||||||||
\(863\) | − | 3.86700e30i | − | 0.574461i | −0.957861 | − | 0.287231i | \(-0.907265\pi\) | ||
0.957861 | − | 0.287231i | \(-0.0927346\pi\) | |||||||
\(864\) | 3.68878e28 | − | 3.37164e29i | 0.00541364 | − | 0.0494820i | ||||
\(865\) | −8.24968e29 | −0.119610 | ||||||||
\(866\) | 4.16091e30 | 0.596006 | ||||||||
\(867\) | 6.97145e30 | + | 2.53344e29i | 0.986559 | + | 0.0358518i | ||||
\(868\) | −3.27191e29 | − | 2.02613e31i | −0.0457450 | − | 2.83277i | ||||
\(869\) | 3.23637e30i | 0.447044i | ||||||||
\(870\) | 7.74833e30 | + | 2.81576e29i | 1.05744 | + | 0.0384277i | ||||
\(871\) | 1.13649e30i | 0.153242i | ||||||||
\(872\) | 1.26391e31i | 1.68381i | ||||||||
\(873\) | −4.68733e29 | + | 6.44070e30i | −0.0616986 | + | 0.847781i | ||||
\(874\) | 8.94986e30i | 1.16398i | ||||||||
\(875\) | 8.46338e30 | − | 1.36671e29i | 1.08757 | − | 0.0175627i | ||||
\(876\) | −2.56612e29 | + | 7.06137e30i | −0.0325825 | + | 0.896594i | ||||
\(877\) | 3.61378e30 | 0.453384 | 0.226692 | − | 0.973967i | \(-0.427209\pi\) | ||||
0.226692 | + | 0.973967i | \(0.427209\pi\) | |||||||
\(878\) | 6.93643e30 | 0.859892 | ||||||||
\(879\) | −8.73017e30 | − | 3.17256e29i | −1.06940 | − | 0.0388622i | ||||
\(880\) | − | 4.64203e30i | − | 0.561875i | ||||||
\(881\) | −1.06397e31 | −1.27257 | −0.636286 | − | 0.771453i | \(-0.719530\pi\) | ||||
−0.636286 | + | 0.771453i | \(0.719530\pi\) | |||||||
\(882\) | −5.89794e29 | + | 1.46074e31i | −0.0697076 | + | 1.72645i | ||||
\(883\) | 6.65519e30 | 0.777272 | 0.388636 | − | 0.921391i | \(-0.372946\pi\) | ||||
0.388636 | + | 0.921391i | \(0.372946\pi\) | |||||||
\(884\) | − | 2.13296e31i | − | 2.46169i | ||||||
\(885\) | −6.90690e30 | − | 2.50999e29i | −0.787733 | − | 0.0286264i | ||||
\(886\) | −2.72204e30 | −0.306790 | ||||||||
\(887\) | 2.96444e30 | 0.330175 | 0.165087 | − | 0.986279i | \(-0.447209\pi\) | ||||
0.165087 | + | 0.986279i | \(0.447209\pi\) | |||||||
\(888\) | 1.00424e29 | − | 2.76343e30i | 0.0110535 | − | 0.304167i | ||||
\(889\) | 1.17277e31 | − | 1.89385e29i | 1.27569 | − | 0.0206005i | ||||
\(890\) | 1.52937e31i | 1.64406i | ||||||||
\(891\) | 9.57358e29 | − | 6.54254e30i | 0.101709 | − | 0.695073i | ||||
\(892\) | − | 1.89798e31i | − | 1.99279i | ||||||
\(893\) | 4.50585e30i | 0.467559i | ||||||||
\(894\) | 1.46348e31 | + | 5.31832e29i | 1.50087 | + | 0.0545419i | ||||
\(895\) | 5.72982e30i | 0.580763i | ||||||||
\(896\) | −2.82361e29 | − | 1.74853e31i | −0.0282860 | − | 1.75161i | ||||
\(897\) | −1.04502e31 | − | 3.79761e29i | −1.03467 | − | 0.0376002i | ||||
\(898\) | −3.12428e31 | −3.05738 | ||||||||
\(899\) | −1.08061e31 | −1.04519 | ||||||||
\(900\) | 6.23478e30 | + | 4.53746e29i | 0.596039 | + | 0.0433777i | ||||
\(901\) | 2.66923e31i | 2.52218i | ||||||||
\(902\) | 8.60565e29 | 0.0803739 | ||||||||
\(903\) | 9.62616e30 | + | 1.94255e29i | 0.888652 | + | 0.0179329i | ||||
\(904\) | 7.57949e30 | 0.691626 | ||||||||
\(905\) | − | 5.36380e30i | − | 0.483797i | ||||||
\(906\) | −7.06105e29 | + | 1.94304e31i | −0.0629540 | + | 1.73235i | ||||
\(907\) | 1.57592e31 | 1.38886 | 0.694428 | − | 0.719562i | \(-0.255657\pi\) | ||||
0.694428 | + | 0.719562i | \(0.255657\pi\) | |||||||
\(908\) | 2.13881e31 | 1.86325 | ||||||||
\(909\) | −1.97394e31 | − | 1.43656e30i | −1.69986 | − | 0.123710i | ||||
\(910\) | −1.49235e31 | + | 2.40993e29i | −1.27039 | + | 0.0205149i | ||||
\(911\) | 1.02264e31i | 0.860557i | 0.902696 | + | 0.430279i | \(0.141585\pi\) | ||||
−0.902696 | + | 0.430279i | \(0.858415\pi\) | |||||||
\(912\) | −2.39006e29 | + | 6.57690e30i | −0.0198821 | + | 0.547111i | ||||
\(913\) | − | 1.79798e30i | − | 0.147857i | ||||||
\(914\) | 3.87196e30i | 0.314772i | ||||||||
\(915\) | −7.14375e29 | + | 1.96579e31i | −0.0574123 | + | 1.57985i | ||||
\(916\) | 3.11058e31i | 2.47137i | ||||||||
\(917\) | −1.41384e31 | + | 2.28314e29i | −1.11051 | + | 0.0179331i | ||||
\(918\) | 3.41143e30 | − | 3.11813e31i | 0.264904 | − | 2.42129i | ||||
\(919\) | 9.00430e29 | 0.0691253 | 0.0345627 | − | 0.999403i | \(-0.488996\pi\) | ||||
0.0345627 | + | 0.999403i | \(0.488996\pi\) | |||||||
\(920\) | −2.20809e31 | −1.67589 | ||||||||
\(921\) | 7.26086e29 | − | 1.99802e31i | 0.0544831 | − | 1.49925i | ||||
\(922\) | 4.22241e30i | 0.313246i | ||||||||
\(923\) | 1.72275e31 | 1.26358 | ||||||||
\(924\) | 3.88047e29 | − | 1.92294e31i | 0.0281403 | − | 1.39447i | ||||
\(925\) | −7.50380e29 | −0.0538014 | ||||||||
\(926\) | 4.21937e31i | 2.99111i | ||||||||
\(927\) | 1.89500e30 | − | 2.60386e31i | 0.132823 | − | 1.82508i | ||||
\(928\) | −5.26112e29 | −0.0364607 | ||||||||
\(929\) | 4.42530e30 | 0.303234 | 0.151617 | − | 0.988439i | \(-0.451552\pi\) | ||||
0.151617 | + | 0.988439i | \(0.451552\pi\) | |||||||
\(930\) | 3.04042e31 | + | 1.10490e30i | 2.05998 | + | 0.0748601i | ||||
\(931\) | 2.75813e29 | + | 8.53767e30i | 0.0184775 | + | 0.571963i | ||||
\(932\) | 6.75947e29i | 0.0447760i | ||||||||
\(933\) | 6.45576e30 | + | 2.34604e29i | 0.422853 | + | 0.0153666i | ||||
\(934\) | − | 1.94744e31i | − | 1.26131i | ||||||
\(935\) | 1.29275e31i | 0.827931i | ||||||||
\(936\) | −2.35860e31 | − | 1.71651e30i | −1.49368 | − | 0.108705i | ||||
\(937\) | 4.25212e30i | 0.266281i | 0.991097 | + | 0.133141i | \(0.0425062\pi\) | ||||
−0.991097 | + | 0.133141i | \(0.957494\pi\) | |||||||
\(938\) | 7.84957e28 | + | 4.86086e30i | 0.00486089 | + | 0.301012i | ||||
\(939\) | 9.38119e29 | − | 2.58149e31i | 0.0574472 | − | 1.58082i | ||||
\(940\) | −2.23972e31 | −1.35628 | ||||||||
\(941\) | −1.23676e31 | −0.740618 | −0.370309 | − | 0.928909i | \(-0.620748\pi\) | ||||
−0.370309 | + | 0.928909i | \(0.620748\pi\) | |||||||
\(942\) | 4.27787e31 | + | 1.55459e30i | 2.53334 | + | 0.0920622i | ||||
\(943\) | − | 1.33105e30i | − | 0.0779507i | ||||||
\(944\) | −1.55739e31 | −0.901970 | ||||||||
\(945\) | −1.45345e31 | − | 1.35307e30i | −0.832468 | − | 0.0774971i | ||||
\(946\) | −1.90465e31 | −1.07884 | ||||||||
\(947\) | 1.46118e31i | 0.818519i | 0.912418 | + | 0.409260i | \(0.134213\pi\) | ||||
−0.912418 | + | 0.409260i | \(0.865787\pi\) | |||||||
\(948\) | 2.27923e31 | + | 8.28278e29i | 1.26270 | + | 0.0458869i | ||||
\(949\) | −7.25361e30 | −0.397429 | ||||||||
\(950\) | 5.49230e30 | 0.297616 | ||||||||
\(951\) | −9.62579e29 | + | 2.64880e31i | −0.0515871 | + | 1.41956i | ||||
\(952\) | −7.31217e29 | − | 4.52807e31i | −0.0387577 | − | 2.40008i | ||||
\(953\) | 2.04242e31i | 1.07071i | 0.844628 | + | 0.535353i | \(0.179821\pi\) | ||||
−0.844628 | + | 0.535353i | \(0.820179\pi\) | |||||||
\(954\) | 5.94666e31 | + | 4.32778e30i | 3.08330 | + | 0.224392i | ||||
\(955\) | − | 2.13027e31i | − | 1.09244i | ||||||
\(956\) | − | 2.77683e31i | − | 1.40845i | ||||||
\(957\) | −1.02498e31 | − | 3.72479e29i | −0.514207 | − | 0.0186864i | ||||
\(958\) | 2.89107e31i | 1.43457i | ||||||||
\(959\) | −1.87057e29 | − | 1.15835e31i | −0.00918075 | − | 0.568520i | ||||
\(960\) | 1.79456e31 | + | 6.52147e29i | 0.871184 | + | 0.0316590i | ||||
\(961\) | −2.15774e31 | −1.03610 | ||||||||
\(962\) | 5.71912e30 | 0.271638 | ||||||||
\(963\) | −9.23090e29 | + | 1.26839e31i | −0.0433678 | + | 0.595904i | ||||
\(964\) | − | 6.70437e31i | − | 3.11565i | ||||||
\(965\) | −2.08742e31 | −0.959564 | ||||||||
\(966\) | −4.47222e31 | − | 9.02489e29i | −2.03359 | − | 0.0410376i | ||||
\(967\) | 3.06812e31 | 1.38005 | 0.690025 | − | 0.723785i | \(-0.257599\pi\) | ||||
0.690025 | + | 0.723785i | \(0.257599\pi\) | |||||||
\(968\) | − | 1.93846e31i | − | 0.862511i | ||||||
\(969\) | 6.65606e29 | − | 1.83159e31i | 0.0292966 | − | 0.806176i | ||||
\(970\) | −2.82022e31 | −1.22795 | ||||||||
\(971\) | −7.67233e30 | −0.330465 | −0.165232 | − | 0.986255i | \(-0.552837\pi\) | ||||
−0.165232 | + | 0.986255i | \(0.552837\pi\) | |||||||
\(972\) | −4.58312e31 | − | 8.41667e30i | −1.95283 | − | 0.358628i | ||||
\(973\) | 5.14994e29 | + | 3.18911e31i | 0.0217079 | + | 1.34426i | ||||
\(974\) | − | 3.04583e31i | − | 1.27010i | ||||||
\(975\) | −2.33050e29 | + | 6.41299e30i | −0.00961391 | + | 0.264553i | ||||
\(976\) | 4.43254e31i | 1.80896i | ||||||||
\(977\) | − | 7.79765e29i | − | 0.0314826i | −0.999876 | − | 0.0157413i | \(-0.994989\pi\) | ||
0.999876 | − | 0.0157413i | \(-0.00501082\pi\) | |||||||
\(978\) | −8.32305e27 | + | 2.29031e29i | −0.000332449 | + | 0.00914822i | ||||
\(979\) | − | 2.02310e31i | − | 0.799464i | ||||||
\(980\) | −4.24381e31 | + | 1.37098e30i | −1.65914 | + | 0.0535992i | ||||
\(981\) | −2.54983e31 | − | 1.85568e30i | −0.986247 | − | 0.0717757i | ||||
\(982\) | −7.41608e31 | −2.83794 | ||||||||
\(983\) | 3.28437e31 | 1.24348 | 0.621741 | − | 0.783223i | \(-0.286426\pi\) | ||||
0.621741 | + | 0.783223i | \(0.286426\pi\) | |||||||
\(984\) | 1.09317e29 | − | 3.00814e30i | 0.00409485 | − | 0.112681i | ||||
\(985\) | − | 2.12394e31i | − | 0.787157i | ||||||
\(986\) | −4.86554e31 | −1.78412 | ||||||||
\(987\) | −2.25156e31 | − | 4.54362e29i | −0.816871 | − | 0.0164844i | ||||
\(988\) | −2.78391e31 | −0.999325 | ||||||||
\(989\) | 2.94595e31i | 1.04632i | ||||||||
\(990\) | 2.88007e31 | + | 2.09601e30i | 1.01212 | + | 0.0736588i | ||||
\(991\) | 2.67744e31 | 0.930995 | 0.465497 | − | 0.885049i | \(-0.345875\pi\) | ||||
0.465497 | + | 0.885049i | \(0.345875\pi\) | |||||||
\(992\) | −2.06444e30 | −0.0710282 | ||||||||
\(993\) | 1.75310e31 | + | 6.37081e29i | 0.596815 | + | 0.0216884i | ||||
\(994\) | 7.36830e31 | − | 1.18987e30i | 2.48205 | − | 0.0400814i | ||||
\(995\) | − | 5.22974e30i | − | 0.174316i | ||||||
\(996\) | −1.26624e31 | − | 4.60155e29i | −0.417631 | − | 0.0151768i | ||||
\(997\) | − | 5.74615e31i | − | 1.87533i | −0.347542 | − | 0.937664i | \(-0.612984\pi\) | ||
0.347542 | − | 0.937664i | \(-0.387016\pi\) | |||||||
\(998\) | 4.29069e31i | 1.38566i | ||||||||
\(999\) | 5.56023e30 | + | 6.08324e29i | 0.177687 | + | 0.0194400i |
(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 | 21.22.c.b.20.38 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.15 | ✓ | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.16 | yes | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.37 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.15 | ✓ | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.16 | yes | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.37 | yes | 52 | 21.20 | even | 2 | inner | |
21.22.c.b.20.38 | yes | 52 | 1.1 | even | 1 | trivial |