Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,39,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (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: | \(36.5853876134\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.18 | ||
Root | \(0.500000 - 1.42659e8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.17 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 518652. | + | 76670.9i | 0.989249 | + | 0.146238i | ||||
\(3\) | 2.28254e9i | 1.96388i | 0.189187 | + | 0.981941i | \(0.439415\pi\) | ||||
−0.189187 | + | 0.981941i | \(0.560585\pi\) | |||||||
\(4\) | 2.63121e11 | + | 7.95309e10i | 0.957229 | + | 0.289332i | ||||
\(5\) | 1.45926e13 | 0.765074 | 0.382537 | − | 0.923940i | \(-0.375050\pi\) | ||||
0.382537 | + | 0.923940i | \(0.375050\pi\) | |||||||
\(6\) | −1.75005e14 | + | 1.18385e15i | −0.287194 | + | 1.94277i | ||||
\(7\) | 8.90761e15i | 0.781445i | 0.920508 | + | 0.390723i | \(0.127775\pi\) | ||||
−0.920508 | + | 0.390723i | \(0.872225\pi\) | |||||||
\(8\) | 1.30370e17 | + | 6.14226e16i | 0.904627 | + | 0.426205i | ||||
\(9\) | −3.85916e18 | −2.85683 | ||||||||
\(10\) | 7.56849e18 | + | 1.11883e18i | 0.756849 | + | 0.111883i | ||||
\(11\) | 4.38272e19i | 0.716609i | 0.933605 | + | 0.358304i | \(0.116645\pi\) | ||||
−0.933605 | + | 0.358304i | \(0.883355\pi\) | |||||||
\(12\) | −1.81533e20 | + | 6.00586e20i | −0.568214 | + | 1.87988i | ||||
\(13\) | 1.87649e21 | 1.28358 | 0.641791 | − | 0.766880i | \(-0.278192\pi\) | ||||
0.641791 | + | 0.766880i | \(0.278192\pi\) | |||||||
\(14\) | −6.82954e20 | + | 4.61995e21i | −0.114277 | + | 0.773044i | ||||
\(15\) | 3.33083e22i | 1.50252i | ||||||||
\(16\) | 6.29075e22 | + | 4.18525e22i | 0.832574 | + | 0.553914i | ||||
\(17\) | 4.37216e22 | 0.182880 | 0.0914400 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914400 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(18\) | −2.00156e24 | − | 2.95885e23i | −2.82612 | − | 0.417778i | ||||
\(19\) | − | 2.11999e24i | − | 1.07156i | −0.844359 | − | 0.535778i | \(-0.820019\pi\) | ||
0.844359 | − | 0.535778i | \(-0.179981\pi\) | |||||||
\(20\) | 3.83963e24 | + | 1.16057e24i | 0.732351 | + | 0.221360i | ||||
\(21\) | −2.03320e25 | −1.53467 | ||||||||
\(22\) | −3.36027e24 | + | 2.27310e25i | −0.104796 | + | 0.708905i | ||||
\(23\) | 2.46227e25i | 0.329995i | 0.986294 | + | 0.164997i | \(0.0527615\pi\) | ||||
−0.986294 | + | 0.164997i | \(0.947238\pi\) | |||||||
\(24\) | −1.40200e26 | + | 2.97576e26i | −0.837016 | + | 1.77658i | ||||
\(25\) | −1.50853e26 | −0.414661 | ||||||||
\(26\) | 9.73246e26 | + | 1.43872e26i | 1.26978 | + | 0.187708i | ||||
\(27\) | − | 5.72532e27i | − | 3.64660i | ||||||
\(28\) | −7.08431e26 | + | 2.34378e27i | −0.226097 | + | 0.748022i | ||||
\(29\) | 3.71574e27 | 0.608812 | 0.304406 | − | 0.952542i | \(-0.401542\pi\) | ||||
0.304406 | + | 0.952542i | \(0.401542\pi\) | |||||||
\(30\) | −2.55378e27 | + | 1.72754e28i | −0.219725 | + | 1.48636i | ||||
\(31\) | − | 1.46587e28i | − | 0.676429i | −0.941069 | − | 0.338214i | \(-0.890177\pi\) | ||
0.941069 | − | 0.338214i | \(-0.109823\pi\) | |||||||
\(32\) | 2.94182e28 | + | 2.65301e28i | 0.742620 | + | 0.669713i | ||||
\(33\) | −1.00037e29 | −1.40734 | ||||||||
\(34\) | 2.26763e28 | + | 3.35217e27i | 0.180914 | + | 0.0267440i | ||||
\(35\) | 1.29986e29i | 0.597864i | ||||||||
\(36\) | −1.01543e30 | − | 3.06922e29i | −2.73464 | − | 0.826573i | ||||
\(37\) | −3.14590e29 | −0.503399 | −0.251700 | − | 0.967805i | \(-0.580990\pi\) | ||||
−0.251700 | + | 0.967805i | \(0.580990\pi\) | |||||||
\(38\) | 1.62541e29 | − | 1.09953e30i | 0.156702 | − | 1.06004i | ||||
\(39\) | 4.28318e30i | 2.52080i | ||||||||
\(40\) | 1.90245e30 | + | 8.96317e29i | 0.692107 | + | 0.326078i | ||||
\(41\) | −1.59147e30 | −0.362164 | −0.181082 | − | 0.983468i | \(-0.557960\pi\) | ||||
−0.181082 | + | 0.983468i | \(0.557960\pi\) | |||||||
\(42\) | −1.05452e31 | − | 1.55887e30i | −1.51817 | − | 0.224427i | ||||
\(43\) | − | 1.13757e31i | − | 1.04732i | −0.851928 | − | 0.523659i | \(-0.824567\pi\) | ||
0.851928 | − | 0.523659i | \(-0.175433\pi\) | |||||||
\(44\) | −3.48561e30 | + | 1.15318e31i | −0.207338 | + | 0.685959i | ||||
\(45\) | −5.63153e31 | −2.18569 | ||||||||
\(46\) | −1.88784e30 | + | 1.27706e31i | −0.0482578 | + | 0.326447i | ||||
\(47\) | − | 3.60466e31i | − | 0.612358i | −0.951974 | − | 0.306179i | \(-0.900949\pi\) | ||
0.951974 | − | 0.306179i | \(-0.0990505\pi\) | |||||||
\(48\) | −9.55302e31 | + | 1.43589e32i | −1.08782 | + | 1.63508i | ||||
\(49\) | 5.05892e31 | 0.389343 | ||||||||
\(50\) | −7.82401e31 | − | 1.15660e31i | −0.410204 | − | 0.0606393i | ||||
\(51\) | 9.97964e31i | 0.359155i | ||||||||
\(52\) | 4.93745e32 | + | 1.49239e32i | 1.22868 | + | 0.371381i | ||||
\(53\) | 1.01267e32 | 0.175480 | 0.0877402 | − | 0.996143i | \(-0.472035\pi\) | ||||
0.0877402 | + | 0.996143i | \(0.472035\pi\) | |||||||
\(54\) | 4.38965e32 | − | 2.96945e33i | 0.533272 | − | 3.60740i | ||||
\(55\) | 6.39554e32i | 0.548259i | ||||||||
\(56\) | −5.47129e32 | + | 1.16129e33i | −0.333056 | + | 0.706917i | ||||
\(57\) | 4.83896e33 | 2.10441 | ||||||||
\(58\) | 1.92717e33 | + | 2.84889e32i | 0.602266 | + | 0.0890314i | ||||
\(59\) | 1.33527e33i | 0.301565i | 0.988567 | + | 0.150782i | \(0.0481793\pi\) | ||||
−0.988567 | + | 0.150782i | \(0.951821\pi\) | |||||||
\(60\) | −2.64904e33 | + | 8.76412e33i | −0.434726 | + | 1.43825i | ||||
\(61\) | −7.35637e33 | −0.881854 | −0.440927 | − | 0.897543i | \(-0.645350\pi\) | ||||
−0.440927 | + | 0.897543i | \(0.645350\pi\) | |||||||
\(62\) | 1.12389e33 | − | 7.60274e33i | 0.0989196 | − | 0.669157i | ||||
\(63\) | − | 3.43759e34i | − | 2.23246i | ||||||
\(64\) | 1.32237e34 | + | 1.60154e34i | 0.636699 | + | 0.771112i | ||||
\(65\) | 2.73830e34 | 0.982035 | ||||||||
\(66\) | −5.18846e34 | − | 7.66996e33i | −1.39221 | − | 0.205806i | ||||
\(67\) | 3.46090e34i | 0.697859i | 0.937149 | + | 0.348929i | \(0.113455\pi\) | ||||
−0.937149 | + | 0.348929i | \(0.886545\pi\) | |||||||
\(68\) | 1.15041e34 | + | 3.47722e33i | 0.175058 | + | 0.0529130i | ||||
\(69\) | −5.62024e34 | −0.648070 | ||||||||
\(70\) | −9.96610e33 | + | 6.74172e34i | −0.0874304 | + | 0.591436i | ||||
\(71\) | 2.59319e35i | 1.73750i | 0.495249 | + | 0.868751i | \(0.335077\pi\) | ||||
−0.495249 | + | 0.868751i | \(0.664923\pi\) | |||||||
\(72\) | −5.03120e35 | − | 2.37039e35i | −2.58437 | − | 1.21760i | ||||
\(73\) | 3.29372e35 | 1.30182 | 0.650912 | − | 0.759154i | \(-0.274387\pi\) | ||||
0.650912 | + | 0.759154i | \(0.274387\pi\) | |||||||
\(74\) | −1.63163e35 | − | 2.41199e34i | −0.497988 | − | 0.0736162i | ||||
\(75\) | − | 3.44329e35i | − | 0.814346i | ||||||
\(76\) | 1.68604e35 | − | 5.57813e35i | 0.310035 | − | 1.02572i | ||||
\(77\) | −3.90395e35 | −0.559991 | ||||||||
\(78\) | −3.28395e35 | + | 2.22148e36i | −0.368637 | + | 2.49370i | ||||
\(79\) | − | 9.78414e35i | − | 0.862200i | −0.902304 | − | 0.431100i | \(-0.858126\pi\) | ||
0.902304 | − | 0.431100i | \(-0.141874\pi\) | |||||||
\(80\) | 9.17986e35 | + | 6.10739e35i | 0.636981 | + | 0.423785i | ||||
\(81\) | 7.85514e36 | 4.30466 | ||||||||
\(82\) | −8.25420e35 | − | 1.22020e35i | −0.358271 | − | 0.0529622i | ||||
\(83\) | − | 3.96638e36i | − | 1.36745i | −0.729741 | − | 0.683723i | \(-0.760360\pi\) | ||
0.729741 | − | 0.683723i | \(-0.239640\pi\) | |||||||
\(84\) | −5.34978e36 | − | 1.61702e36i | −1.46903 | − | 0.444028i | ||||
\(85\) | 6.38013e35 | 0.139917 | ||||||||
\(86\) | 8.72187e35 | − | 5.90004e36i | 0.153158 | − | 1.03606i | ||||
\(87\) | 8.48133e36i | 1.19563i | ||||||||
\(88\) | −2.69198e36 | + | 5.71377e36i | −0.305422 | + | 0.648264i | ||||
\(89\) | 7.10862e36 | 0.650691 | 0.325346 | − | 0.945595i | \(-0.394519\pi\) | ||||
0.325346 | + | 0.945595i | \(0.394519\pi\) | |||||||
\(90\) | −2.92080e37 | − | 4.31774e36i | −2.16219 | − | 0.319631i | ||||
\(91\) | 1.67151e37i | 1.00305i | ||||||||
\(92\) | −1.95827e36 | + | 6.47875e36i | −0.0954779 | + | 0.315880i | ||||
\(93\) | 3.34590e37 | 1.32843 | ||||||||
\(94\) | 2.76372e36 | − | 1.86956e37i | 0.0895500 | − | 0.605774i | ||||
\(95\) | − | 3.09362e37i | − | 0.819819i | ||||||
\(96\) | −6.05560e37 | + | 6.71484e37i | −1.31524 | + | 1.45842i | ||||
\(97\) | −6.10990e37 | −1.08986 | −0.544930 | − | 0.838481i | \(-0.683444\pi\) | ||||
−0.544930 | + | 0.838481i | \(0.683444\pi\) | |||||||
\(98\) | 2.62382e37 | + | 3.87872e36i | 0.385157 | + | 0.0569368i | ||||
\(99\) | − | 1.69136e38i | − | 2.04723i | ||||||
\(100\) | −3.96926e37 | − | 1.19975e37i | −0.396926 | − | 0.119975i | ||||
\(101\) | 1.26223e38 | 1.04479 | 0.522397 | − | 0.852702i | \(-0.325038\pi\) | ||||
0.522397 | + | 0.852702i | \(0.325038\pi\) | |||||||
\(102\) | −7.65148e36 | + | 5.17596e37i | −0.0525221 | + | 0.355294i | ||||
\(103\) | 3.14830e38i | 1.79543i | 0.440574 | + | 0.897716i | \(0.354775\pi\) | ||||
−0.440574 | + | 0.897716i | \(0.645225\pi\) | |||||||
\(104\) | 2.44639e38 | + | 1.15259e38i | 1.16116 | + | 0.547068i | ||||
\(105\) | −2.96698e38 | −1.17413 | ||||||||
\(106\) | 5.25225e37 | + | 7.76426e36i | 0.173594 | + | 0.0256619i | ||||
\(107\) | 2.88847e38i | 0.798685i | 0.916802 | + | 0.399343i | \(0.130762\pi\) | ||||
−0.916802 | + | 0.399343i | \(0.869238\pi\) | |||||||
\(108\) | 4.55340e38 | − | 1.50645e39i | 1.05508 | − | 3.49063i | ||||
\(109\) | 3.59798e38 | 0.699770 | 0.349885 | − | 0.936793i | \(-0.386221\pi\) | ||||
0.349885 | + | 0.936793i | \(0.386221\pi\) | |||||||
\(110\) | −4.90351e37 | + | 3.31705e38i | −0.0801763 | + | 0.542365i | ||||
\(111\) | − | 7.18067e38i | − | 0.988617i | ||||||
\(112\) | −3.72806e38 | + | 5.60356e38i | −0.432853 | + | 0.650611i | ||||
\(113\) | −1.38882e38 | −0.136194 | −0.0680968 | − | 0.997679i | \(-0.521693\pi\) | ||||
−0.0680968 | + | 0.997679i | \(0.521693\pi\) | |||||||
\(114\) | 2.50974e39 | + | 3.71007e38i | 2.08178 | + | 0.307745i | ||||
\(115\) | 3.59310e38i | 0.252470i | ||||||||
\(116\) | 9.77688e38 | + | 2.95516e38i | 0.582772 | + | 0.176149i | ||||
\(117\) | −7.24168e39 | −3.66698 | ||||||||
\(118\) | −1.02376e38 | + | 6.92539e38i | −0.0441002 | + | 0.298323i | ||||
\(119\) | 3.89455e38i | 0.142911i | ||||||||
\(120\) | −2.04588e39 | + | 4.34242e39i | −0.640379 | + | 1.35922i | ||||
\(121\) | 1.81961e39 | 0.486472 | ||||||||
\(122\) | −3.81539e39 | − | 5.64019e38i | −0.872373 | − | 0.128961i | ||||
\(123\) | − | 3.63261e39i | − | 0.711248i | ||||||
\(124\) | 1.16582e39 | − | 3.85700e39i | 0.195712 | − | 0.647497i | ||||
\(125\) | −7.51011e39 | −1.08232 | ||||||||
\(126\) | 2.63563e39 | − | 1.78291e40i | 0.326470 | − | 2.20846i | ||||
\(127\) | 1.18917e40i | 1.26758i | 0.773507 | + | 0.633788i | \(0.218501\pi\) | ||||
−0.773507 | + | 0.633788i | \(0.781499\pi\) | |||||||
\(128\) | 5.63059e39 | + | 9.32027e39i | 0.517088 | + | 0.855932i | ||||
\(129\) | 2.59656e40 | 2.05681 | ||||||||
\(130\) | 1.42022e40 | + | 2.09948e39i | 0.971478 | + | 0.143611i | ||||
\(131\) | 2.14287e40i | 1.26719i | 0.773666 | + | 0.633593i | \(0.218421\pi\) | ||||
−0.773666 | + | 0.633593i | \(0.781579\pi\) | |||||||
\(132\) | −2.63220e40 | − | 7.95607e39i | −1.34714 | − | 0.407187i | ||||
\(133\) | 1.88840e40 | 0.837362 | ||||||||
\(134\) | −2.65350e39 | + | 1.79500e40i | −0.102053 | + | 0.690356i | ||||
\(135\) | − | 8.35475e40i | − | 2.78992i | ||||||
\(136\) | 5.70000e39 | + | 2.68549e39i | 0.165438 | + | 0.0779443i | ||||
\(137\) | −3.18667e38 | −0.00804723 | −0.00402362 | − | 0.999992i | \(-0.501281\pi\) | ||||
−0.00402362 | + | 0.999992i | \(0.501281\pi\) | |||||||
\(138\) | −2.91495e40 | − | 4.30909e39i | −0.641103 | − | 0.0947725i | ||||
\(139\) | − | 2.48667e40i | − | 0.476800i | −0.971167 | − | 0.238400i | \(-0.923377\pi\) | ||
0.971167 | − | 0.238400i | \(-0.0766229\pi\) | |||||||
\(140\) | −1.03379e40 | + | 3.42019e40i | −0.172981 | + | 0.572292i | ||||
\(141\) | 8.22780e40 | 1.20260 | ||||||||
\(142\) | −1.98822e40 | + | 1.34496e41i | −0.254089 | + | 1.71882i | ||||
\(143\) | 8.22414e40i | 0.919826i | ||||||||
\(144\) | −2.42770e41 | − | 1.61515e41i | −2.37853 | − | 1.58244i | ||||
\(145\) | 5.42224e40 | 0.465786 | ||||||||
\(146\) | 1.70829e41 | + | 2.52532e40i | 1.28783 | + | 0.190376i | ||||
\(147\) | 1.15472e41i | 0.764624i | ||||||||
\(148\) | −8.27754e40 | − | 2.50197e40i | −0.481868 | − | 0.145649i | ||||
\(149\) | −1.44384e41 | −0.739572 | −0.369786 | − | 0.929117i | \(-0.620569\pi\) | ||||
−0.369786 | + | 0.929117i | \(0.620569\pi\) | |||||||
\(150\) | 2.64000e40 | − | 1.78587e41i | 0.119088 | − | 0.805591i | ||||
\(151\) | 4.13386e40i | 0.164359i | 0.996618 | + | 0.0821796i | \(0.0261881\pi\) | ||||
−0.996618 | + | 0.0821796i | \(0.973812\pi\) | |||||||
\(152\) | 1.30215e41 | − | 2.76384e41i | 0.456702 | − | 0.969358i | ||||
\(153\) | −1.68728e41 | −0.522458 | ||||||||
\(154\) | −2.02479e41 | − | 2.99320e40i | −0.553971 | − | 0.0818920i | ||||
\(155\) | − | 2.13908e41i | − | 0.517518i | ||||||
\(156\) | −3.40645e41 | + | 1.12699e42i | −0.729348 | + | 2.41298i | ||||
\(157\) | 6.70769e40 | 0.127198 | 0.0635989 | − | 0.997976i | \(-0.479742\pi\) | ||||
0.0635989 | + | 0.997976i | \(0.479742\pi\) | |||||||
\(158\) | 7.50158e40 | − | 5.07456e41i | 0.126086 | − | 0.852930i | ||||
\(159\) | 2.31147e41i | 0.344623i | ||||||||
\(160\) | 4.29289e41 | + | 3.87143e41i | 0.568160 | + | 0.512380i | ||||
\(161\) | −2.19330e41 | −0.257873 | ||||||||
\(162\) | 4.07408e42 | + | 6.02261e41i | 4.25838 | + | 0.629505i | ||||
\(163\) | − | 1.57199e42i | − | 1.46179i | −0.682490 | − | 0.730895i | \(-0.739103\pi\) | ||
0.682490 | − | 0.730895i | \(-0.260897\pi\) | |||||||
\(164\) | −4.18750e41 | − | 1.26571e41i | −0.346674 | − | 0.104786i | ||||
\(165\) | −1.45981e42 | −1.07672 | ||||||||
\(166\) | 3.04106e41 | − | 2.05717e42i | 0.199973 | − | 1.35275i | ||||
\(167\) | − | 5.86398e41i | − | 0.344017i | −0.985095 | − | 0.172008i | \(-0.944974\pi\) | ||
0.985095 | − | 0.172008i | \(-0.0550256\pi\) | |||||||
\(168\) | −2.65070e42 | − | 1.24885e42i | −1.38830 | − | 0.654082i | ||||
\(169\) | 1.38402e42 | 0.647581 | ||||||||
\(170\) | 3.30906e41 | + | 4.89170e40i | 0.138413 | + | 0.0204612i | ||||
\(171\) | 8.18136e42i | 3.06125i | ||||||||
\(172\) | 9.04722e41 | − | 2.99319e42i | 0.303022 | − | 1.00252i | ||||
\(173\) | −4.64403e42 | −1.39322 | −0.696609 | − | 0.717451i | \(-0.745309\pi\) | ||||
−0.696609 | + | 0.717451i | \(0.745309\pi\) | |||||||
\(174\) | −6.50271e41 | + | 4.39886e42i | −0.174847 | + | 1.18278i | ||||
\(175\) | − | 1.34374e42i | − | 0.324035i | ||||||
\(176\) | −1.83428e42 | + | 2.75706e42i | −0.396939 | + | 0.596630i | ||||
\(177\) | −3.04781e42 | −0.592238 | ||||||||
\(178\) | 3.68689e42 | + | 5.45024e41i | 0.643696 | + | 0.0951558i | ||||
\(179\) | − | 3.70299e42i | − | 0.581226i | −0.956841 | − | 0.290613i | \(-0.906141\pi\) | ||
0.956841 | − | 0.290613i | \(-0.0938592\pi\) | |||||||
\(180\) | −1.48177e43 | − | 4.47881e42i | −2.09220 | − | 0.632389i | ||||
\(181\) | 9.61745e42 | 1.22227 | 0.611135 | − | 0.791527i | \(-0.290713\pi\) | ||||
0.611135 | + | 0.791527i | \(0.290713\pi\) | |||||||
\(182\) | −1.28156e42 | + | 8.66930e42i | −0.146684 | + | 0.992266i | ||||
\(183\) | − | 1.67912e43i | − | 1.73186i | ||||||
\(184\) | −1.51239e42 | + | 3.21007e42i | −0.140645 | + | 0.298522i | ||||
\(185\) | −4.59070e42 | −0.385138 | ||||||||
\(186\) | 1.73536e43 | + | 2.56533e42i | 1.31415 | + | 0.194266i | ||||
\(187\) | 1.91619e42i | 0.131053i | ||||||||
\(188\) | 2.86682e42 | − | 9.48462e42i | 0.177175 | − | 0.586166i | ||||
\(189\) | 5.09989e43 | 2.84962 | ||||||||
\(190\) | 2.37190e42 | − | 1.60451e43i | 0.119889 | − | 0.811006i | ||||
\(191\) | 5.35328e42i | 0.244898i | 0.992475 | + | 0.122449i | \(0.0390748\pi\) | ||||
−0.992475 | + | 0.122449i | \(0.960925\pi\) | |||||||
\(192\) | −3.65558e43 | + | 3.01837e43i | −1.51437 | + | 1.25040i | ||||
\(193\) | 1.22524e43 | 0.459867 | 0.229934 | − | 0.973206i | \(-0.426149\pi\) | ||||
0.229934 | + | 0.973206i | \(0.426149\pi\) | |||||||
\(194\) | −3.16891e43 | − | 4.68451e42i | −1.07814 | − | 0.159379i | ||||
\(195\) | 6.25029e43i | 1.92860i | ||||||||
\(196\) | 1.33111e43 | + | 4.02341e42i | 0.372690 | + | 0.112649i | ||||
\(197\) | 2.06408e42 | 0.0524648 | 0.0262324 | − | 0.999656i | \(-0.491649\pi\) | ||||
0.0262324 | + | 0.999656i | \(0.491649\pi\) | |||||||
\(198\) | 1.29678e43 | − | 8.77226e43i | 0.299383 | − | 2.02522i | ||||
\(199\) | − | 7.29919e43i | − | 1.53132i | −0.643246 | − | 0.765660i | \(-0.722413\pi\) | ||
0.643246 | − | 0.765660i | \(-0.277587\pi\) | |||||||
\(200\) | −1.96668e43 | − | 9.26577e42i | −0.375114 | − | 0.176731i | ||||
\(201\) | −7.89965e43 | −1.37051 | ||||||||
\(202\) | 6.54655e43 | + | 9.67759e42i | 1.03356 | + | 0.152789i | ||||
\(203\) | 3.30983e43i | 0.475753i | ||||||||
\(204\) | −7.93690e42 | + | 2.62585e43i | −0.103915 | + | 0.343793i | ||||
\(205\) | −2.32238e43 | −0.277083 | ||||||||
\(206\) | −2.41383e43 | + | 1.63287e44i | −0.262561 | + | 1.77613i | ||||
\(207\) | − | 9.50229e43i | − | 0.942739i | ||||||
\(208\) | 1.18046e44 | + | 7.85360e43i | 1.06868 | + | 0.710993i | ||||
\(209\) | 9.29130e43 | 0.767886 | ||||||||
\(210\) | −1.53883e44 | − | 2.27481e43i | −1.16151 | − | 0.171703i | ||||
\(211\) | 7.46929e43i | 0.515125i | 0.966262 | + | 0.257563i | \(0.0829194\pi\) | ||||
−0.966262 | + | 0.257563i | \(0.917081\pi\) | |||||||
\(212\) | 2.66456e43 | + | 8.05390e42i | 0.167975 | + | 0.0507720i | ||||
\(213\) | −5.91906e44 | −3.41225 | ||||||||
\(214\) | −2.21461e43 | + | 1.49811e44i | −0.116798 | + | 0.790099i | ||||
\(215\) | − | 1.66002e44i | − | 0.801276i | ||||||
\(216\) | 3.51664e44 | − | 7.46412e44i | 1.55420 | − | 3.29881i | ||||
\(217\) | 1.30574e44 | 0.528592 | ||||||||
\(218\) | 1.86610e44 | + | 2.75860e43i | 0.692247 | + | 0.102333i | ||||
\(219\) | 7.51806e44i | 2.55663i | ||||||||
\(220\) | −5.08643e43 | + | 1.68280e44i | −0.158629 | + | 0.524809i | ||||
\(221\) | 8.20432e43 | 0.234741 | ||||||||
\(222\) | 5.50548e43 | − | 3.72426e44i | 0.144573 | − | 0.977989i | ||||
\(223\) | − | 3.77394e44i | − | 0.909919i | −0.890512 | − | 0.454959i | \(-0.849654\pi\) | ||
0.890512 | − | 0.454959i | \(-0.150346\pi\) | |||||||
\(224\) | −2.36319e44 | + | 2.62046e44i | −0.523344 | + | 0.580317i | ||||
\(225\) | 5.82165e44 | 1.18462 | ||||||||
\(226\) | −7.20315e43 | − | 1.06482e43i | −0.134729 | − | 0.0199167i | ||||
\(227\) | 6.83403e43i | 0.117540i | 0.998272 | + | 0.0587699i | \(0.0187178\pi\) | ||||
−0.998272 | + | 0.0587699i | \(0.981282\pi\) | |||||||
\(228\) | 1.27323e45 | + | 3.84847e44i | 2.01440 | + | 0.608872i | ||||
\(229\) | 3.66784e44 | 0.533994 | 0.266997 | − | 0.963697i | \(-0.413969\pi\) | ||||
0.266997 | + | 0.963697i | \(0.413969\pi\) | |||||||
\(230\) | −2.75486e43 | + | 1.86357e44i | −0.0369208 | + | 0.249756i | ||||
\(231\) | − | 8.91095e44i | − | 1.09976i | ||||||
\(232\) | 4.84422e44 | + | 2.28230e44i | 0.550747 | + | 0.259478i | ||||
\(233\) | −1.01331e45 | −1.06165 | −0.530823 | − | 0.847483i | \(-0.678117\pi\) | ||||
−0.530823 | + | 0.847483i | \(0.678117\pi\) | |||||||
\(234\) | −3.75591e45 | − | 5.55226e44i | −3.62756 | − | 0.536252i | ||||
\(235\) | − | 5.26015e44i | − | 0.468499i | ||||||
\(236\) | −1.06195e44 | + | 3.51337e44i | −0.0872523 | + | 0.288666i | ||||
\(237\) | 2.23327e45 | 1.69326 | ||||||||
\(238\) | −2.98598e43 | + | 2.01991e44i | −0.0208990 | + | 0.141374i | ||||
\(239\) | − | 2.66930e45i | − | 1.72519i | −0.505892 | − | 0.862597i | \(-0.668837\pi\) | ||
0.505892 | − | 0.862597i | \(-0.331163\pi\) | |||||||
\(240\) | −1.39404e45 | + | 2.09534e45i | −0.832264 | + | 1.25096i | ||||
\(241\) | −2.98744e45 | −1.64807 | −0.824035 | − | 0.566538i | \(-0.808282\pi\) | ||||
−0.824035 | + | 0.566538i | \(0.808282\pi\) | |||||||
\(242\) | 9.43746e44 | + | 1.39511e44i | 0.481242 | + | 0.0711407i | ||||
\(243\) | 1.01957e46i | 4.80724i | ||||||||
\(244\) | −1.93562e45 | − | 5.85059e44i | −0.844136 | − | 0.255148i | ||||
\(245\) | 7.38230e44 | 0.297876 | ||||||||
\(246\) | 2.78515e44 | − | 1.88406e45i | 0.104012 | − | 0.703602i | ||||
\(247\) | − | 3.97814e45i | − | 1.37543i | ||||||
\(248\) | 9.00372e44 | − | 1.91106e45i | 0.288297 | − | 0.611916i | ||||
\(249\) | 9.05343e45 | 2.68550 | ||||||||
\(250\) | −3.89513e45 | − | 5.75807e44i | −1.07069 | − | 0.158277i | ||||
\(251\) | − | 4.81645e45i | − | 1.22723i | −0.789605 | − | 0.613616i | \(-0.789715\pi\) | ||
0.789605 | − | 0.613616i | \(-0.210285\pi\) | |||||||
\(252\) | 2.73395e45 | − | 9.04502e45i | 0.645921 | − | 2.13697i | ||||
\(253\) | −1.07914e45 | −0.236477 | ||||||||
\(254\) | −9.11748e44 | + | 6.16766e45i | −0.185368 | + | 1.25395i | ||||
\(255\) | 1.45629e45i | 0.274780i | ||||||||
\(256\) | 2.20572e45 | + | 5.26568e45i | 0.386360 | + | 0.922348i | ||||
\(257\) | −4.53209e45 | −0.737173 | −0.368586 | − | 0.929594i | \(-0.620158\pi\) | ||||
−0.368586 | + | 0.929594i | \(0.620158\pi\) | |||||||
\(258\) | 1.34671e46 | + | 1.99080e45i | 2.03470 | + | 0.300784i | ||||
\(259\) | − | 2.80225e45i | − | 0.393379i | ||||||
\(260\) | 7.20504e45 | + | 2.17779e45i | 0.940032 | + | 0.284134i | ||||
\(261\) | −1.43396e46 | −1.73927 | ||||||||
\(262\) | −1.64295e45 | + | 1.11140e46i | −0.185311 | + | 1.25356i | ||||
\(263\) | − | 7.57752e45i | − | 0.795001i | −0.917602 | − | 0.397500i | \(-0.869878\pi\) | ||
0.917602 | − | 0.397500i | \(-0.130122\pi\) | |||||||
\(264\) | −1.30419e46 | − | 6.14455e45i | −1.27311 | − | 0.599813i | ||||
\(265\) | 1.47776e45 | 0.134255 | ||||||||
\(266\) | 9.79423e45 | + | 1.44785e45i | 0.828360 | + | 0.122454i | ||||
\(267\) | 1.62257e46i | 1.27788i | ||||||||
\(268\) | −2.75248e45 | + | 9.10635e45i | −0.201913 | + | 0.668010i | ||||
\(269\) | 9.75268e45 | 0.666547 | 0.333273 | − | 0.942830i | \(-0.391847\pi\) | ||||
0.333273 | + | 0.942830i | \(0.391847\pi\) | |||||||
\(270\) | 6.40566e45 | − | 4.33320e46i | 0.407992 | − | 2.75993i | ||||
\(271\) | 3.37324e45i | 0.200277i | 0.994974 | + | 0.100138i | \(0.0319285\pi\) | ||||
−0.994974 | + | 0.100138i | \(0.968071\pi\) | |||||||
\(272\) | 2.75042e45 | + | 1.82986e45i | 0.152261 | + | 0.101300i | ||||
\(273\) | −3.81529e46 | −1.96987 | ||||||||
\(274\) | −1.65277e44 | − | 2.44325e43i | −0.00796072 | − | 0.00117681i | ||||
\(275\) | − | 6.61145e45i | − | 0.297150i | ||||||
\(276\) | −1.47880e46 | − | 4.46983e45i | −0.620352 | − | 0.187507i | ||||
\(277\) | −1.89104e46 | −0.740603 | −0.370301 | − | 0.928912i | \(-0.620746\pi\) | ||||
−0.370301 | + | 0.928912i | \(0.620746\pi\) | |||||||
\(278\) | 1.90655e45 | − | 1.28971e46i | 0.0697263 | − | 0.471674i | ||||
\(279\) | 5.65701e46i | 1.93244i | ||||||||
\(280\) | −7.98405e45 | + | 1.69463e46i | −0.254812 | + | 0.540844i | ||||
\(281\) | 2.46698e46 | 0.735775 | 0.367888 | − | 0.929870i | \(-0.380081\pi\) | ||||
0.367888 | + | 0.929870i | \(0.380081\pi\) | |||||||
\(282\) | 4.26736e46 | + | 6.30832e45i | 1.18967 | + | 0.175866i | ||||
\(283\) | − | 4.22253e46i | − | 1.10060i | −0.834966 | − | 0.550302i | \(-0.814513\pi\) | ||
0.834966 | − | 0.550302i | \(-0.185487\pi\) | |||||||
\(284\) | −2.06239e46 | + | 6.82322e46i | −0.502715 | + | 1.66319i | ||||
\(285\) | 7.06132e46 | 1.61003 | ||||||||
\(286\) | −6.30552e45 | + | 4.26546e46i | −0.134514 | + | 0.909937i | ||||
\(287\) | − | 1.41762e46i | − | 0.283012i | ||||||
\(288\) | −1.13530e47 | − | 1.02384e47i | −2.12154 | − | 1.91326i | ||||
\(289\) | −5.52441e46 | −0.966555 | ||||||||
\(290\) | 2.81225e46 | + | 4.15728e45i | 0.460779 | + | 0.0681156i | ||||
\(291\) | − | 1.39461e47i | − | 2.14036i | ||||||
\(292\) | 8.66646e46 | + | 2.61952e46i | 1.24614 | + | 0.376659i | ||||
\(293\) | 4.89119e46 | 0.659067 | 0.329534 | − | 0.944144i | \(-0.393109\pi\) | ||||
0.329534 | + | 0.944144i | \(0.393109\pi\) | |||||||
\(294\) | −8.85335e45 | + | 5.98898e46i | −0.111817 | + | 0.756404i | ||||
\(295\) | 1.94851e46i | 0.230719i | ||||||||
\(296\) | −4.10133e46 | − | 1.93229e46i | −0.455389 | − | 0.214551i | ||||
\(297\) | 2.50924e47 | 2.61319 | ||||||||
\(298\) | −7.48850e46 | − | 1.10701e46i | −0.731621 | − | 0.108153i | ||||
\(299\) | 4.62043e46i | 0.423575i | ||||||||
\(300\) | 2.73848e46 | − | 9.06001e46i | 0.235616 | − | 0.779516i | ||||
\(301\) | 1.01331e47 | 0.818422 | ||||||||
\(302\) | −3.16947e45 | + | 2.14403e46i | −0.0240356 | + | 0.162592i | ||||
\(303\) | 2.88109e47i | 2.05185i | ||||||||
\(304\) | 8.87268e46 | − | 1.33363e47i | 0.593549 | − | 0.892149i | ||||
\(305\) | −1.07349e47 | −0.674684 | ||||||||
\(306\) | −8.75113e46 | − | 1.29366e46i | −0.516841 | − | 0.0764032i | ||||
\(307\) | 3.11195e46i | 0.172744i | 0.996263 | + | 0.0863722i | \(0.0275274\pi\) | ||||
−0.996263 | + | 0.0863722i | \(0.972473\pi\) | |||||||
\(308\) | −1.02721e47 | − | 3.10485e46i | −0.536039 | − | 0.162023i | ||||
\(309\) | −7.18614e47 | −3.52602 | ||||||||
\(310\) | 1.64005e46 | − | 1.10944e47i | 0.0756809 | − | 0.511955i | ||||
\(311\) | − | 1.10257e47i | − | 0.478587i | −0.970947 | − | 0.239293i | \(-0.923084\pi\) | ||
0.970947 | − | 0.239293i | \(-0.0769158\pi\) | |||||||
\(312\) | −2.63084e47 | + | 5.58400e47i | −1.07438 | + | 2.28039i | ||||
\(313\) | 2.97136e47 | 1.14186 | 0.570931 | − | 0.820998i | \(-0.306582\pi\) | ||||
0.570931 | + | 0.820998i | \(0.306582\pi\) | |||||||
\(314\) | 3.47895e46 | + | 5.14284e45i | 0.125830 | + | 0.0186012i | ||||
\(315\) | − | 5.01635e47i | − | 1.70800i | ||||||
\(316\) | 7.78141e46 | − | 2.57441e47i | 0.249462 | − | 0.825322i | ||||
\(317\) | 1.49952e47 | 0.452716 | 0.226358 | − | 0.974044i | \(-0.427318\pi\) | ||||
0.226358 | + | 0.974044i | \(0.427318\pi\) | |||||||
\(318\) | −1.77223e46 | + | 1.19885e47i | −0.0503969 | + | 0.340918i | ||||
\(319\) | 1.62850e47i | 0.436280i | ||||||||
\(320\) | 1.92969e47 | + | 2.33706e47i | 0.487122 | + | 0.589958i | ||||
\(321\) | −6.59305e47 | −1.56852 | ||||||||
\(322\) | −1.13756e47 | − | 1.68162e46i | −0.255100 | − | 0.0377108i | ||||
\(323\) | − | 9.26891e46i | − | 0.195966i | ||||||
\(324\) | 2.06685e48 | + | 6.24727e47i | 4.12054 | + | 1.24547i | ||||
\(325\) | −2.83075e47 | −0.532252 | ||||||||
\(326\) | 1.20526e47 | − | 8.15314e47i | 0.213769 | − | 1.44607i | ||||
\(327\) | 8.21255e47i | 1.37427i | ||||||||
\(328\) | −2.07481e47 | − | 9.77523e46i | −0.327624 | − | 0.154356i | ||||
\(329\) | 3.21089e47 | 0.478524 | ||||||||
\(330\) | −7.57133e47 | − | 1.11925e47i | −1.06514 | − | 0.157457i | ||||
\(331\) | − | 6.23454e47i | − | 0.828080i | −0.910259 | − | 0.414040i | \(-0.864117\pi\) | ||
0.910259 | − | 0.414040i | \(-0.135883\pi\) | |||||||
\(332\) | 3.15450e47 | − | 1.04364e48i | 0.395646 | − | 1.30896i | ||||
\(333\) | 1.21405e48 | 1.43813 | ||||||||
\(334\) | 4.49597e46 | − | 3.04136e47i | 0.0503083 | − | 0.340318i | ||||
\(335\) | 5.05036e47i | 0.533914i | ||||||||
\(336\) | −1.27904e48 | − | 8.50947e47i | −1.27772 | − | 0.850073i | ||||
\(337\) | −1.21282e48 | −1.14506 | −0.572532 | − | 0.819882i | \(-0.694039\pi\) | ||||
−0.572532 | + | 0.819882i | \(0.694039\pi\) | |||||||
\(338\) | 7.17823e47 | + | 1.06114e47i | 0.640619 | + | 0.0947010i | ||||
\(339\) | − | 3.17005e47i | − | 0.267468i | ||||||
\(340\) | 1.67875e47 | + | 5.07417e46i | 0.133932 | + | 0.0404824i | ||||
\(341\) | 6.42447e47 | 0.484735 | ||||||||
\(342\) | −6.27272e47 | + | 4.24328e48i | −0.447672 | + | 3.02834i | ||||
\(343\) | 1.60804e48i | 1.08570i | ||||||||
\(344\) | 6.98726e47 | − | 1.48306e48i | 0.446372 | − | 0.947432i | ||||
\(345\) | −8.20141e47 | −0.495822 | ||||||||
\(346\) | −2.40863e48 | − | 3.56062e47i | −1.37824 | − | 0.203741i | ||||
\(347\) | 1.46129e48i | 0.791546i | 0.918348 | + | 0.395773i | \(0.129523\pi\) | ||||
−0.918348 | + | 0.395773i | \(0.870477\pi\) | |||||||
\(348\) | −6.74528e47 | + | 2.23162e48i | −0.345935 | + | 1.14450i | ||||
\(349\) | 1.40124e48 | 0.680500 | 0.340250 | − | 0.940335i | \(-0.389488\pi\) | ||||
0.340250 | + | 0.940335i | \(0.389488\pi\) | |||||||
\(350\) | 1.03026e47 | − | 6.96933e47i | 0.0473863 | − | 0.320552i | ||||
\(351\) | − | 1.07435e49i | − | 4.68071i | ||||||
\(352\) | −1.16274e48 | + | 1.28932e48i | −0.479922 | + | 0.532168i | ||||
\(353\) | 2.27405e48 | 0.889365 | 0.444682 | − | 0.895688i | \(-0.353317\pi\) | ||||
0.444682 | + | 0.895688i | \(0.353317\pi\) | |||||||
\(354\) | −1.58075e48 | − | 2.33678e47i | −0.585871 | − | 0.0866077i | ||||
\(355\) | 3.78414e48i | 1.32932i | ||||||||
\(356\) | 1.87043e48 | + | 5.65355e47i | 0.622860 | + | 0.188266i | ||||
\(357\) | −8.88948e47 | −0.280660 | ||||||||
\(358\) | 2.83912e47 | − | 1.92056e48i | 0.0849974 | − | 0.574978i | ||||
\(359\) | 2.51644e48i | 0.714482i | 0.934012 | + | 0.357241i | \(0.116283\pi\) | ||||
−0.934012 | + | 0.357241i | \(0.883717\pi\) | |||||||
\(360\) | −7.34185e48 | − | 3.45903e48i | −1.97723 | − | 0.931551i | ||||
\(361\) | −5.80198e47 | −0.148231 | ||||||||
\(362\) | 4.98811e48 | + | 7.37378e47i | 1.20913 | + | 0.178742i | ||||
\(363\) | 4.15335e48i | 0.955373i | ||||||||
\(364\) | −1.32937e48 | + | 4.39809e48i | −0.290214 | + | 0.960147i | ||||
\(365\) | 4.80640e48 | 0.995991 | ||||||||
\(366\) | 1.28740e48 | − | 8.70880e48i | 0.253263 | − | 1.71324i | ||||
\(367\) | 6.41579e48i | 1.19838i | 0.800607 | + | 0.599190i | \(0.204511\pi\) | ||||
−0.800607 | + | 0.599190i | \(0.795489\pi\) | |||||||
\(368\) | −1.03052e48 | + | 1.54895e48i | −0.182788 | + | 0.274745i | ||||
\(369\) | 6.14174e48 | 1.03464 | ||||||||
\(370\) | −2.38098e48 | − | 3.51973e47i | −0.380997 | − | 0.0563218i | ||||
\(371\) | 9.02052e47i | 0.137128i | ||||||||
\(372\) | 8.80378e48 | + | 2.66103e48i | 1.27161 | + | 0.384356i | ||||
\(373\) | −1.20897e49 | −1.65939 | −0.829693 | − | 0.558219i | \(-0.811485\pi\) | ||||
−0.829693 | + | 0.558219i | \(0.811485\pi\) | |||||||
\(374\) | −1.46916e47 | + | 9.93836e47i | −0.0191650 | + | 0.129645i | ||||
\(375\) | − | 1.71422e49i | − | 2.12555i | ||||||
\(376\) | 2.21407e48 | − | 4.69941e48i | 0.260990 | − | 0.553955i | ||||
\(377\) | 6.97256e48 | 0.781459 | ||||||||
\(378\) | 2.64507e49 | + | 3.91013e48i | 2.81898 | + | 0.416723i | ||||
\(379\) | − | 3.23372e48i | − | 0.327761i | −0.986480 | − | 0.163881i | \(-0.947599\pi\) | ||
0.986480 | − | 0.163881i | \(-0.0524012\pi\) | |||||||
\(380\) | 2.46038e48 | − | 8.13996e48i | 0.237200 | − | 0.784755i | ||||
\(381\) | −2.71434e49 | −2.48937 | ||||||||
\(382\) | −4.10440e47 | + | 2.77649e48i | −0.0358135 | + | 0.242266i | ||||
\(383\) | − | 1.94131e49i | − | 1.61182i | −0.592036 | − | 0.805912i | \(-0.701676\pi\) | ||
0.592036 | − | 0.805912i | \(-0.298324\pi\) | |||||||
\(384\) | −2.12739e49 | + | 1.28521e49i | −1.68095 | + | 1.01550i | ||||
\(385\) | −5.69690e48 | −0.428435 | ||||||||
\(386\) | 6.35473e48 | + | 9.39402e47i | 0.454923 | + | 0.0672501i | ||||
\(387\) | 4.39007e49i | 2.99201i | ||||||||
\(388\) | −1.60764e49 | − | 4.85926e48i | −1.04325 | − | 0.315331i | ||||
\(389\) | 3.15655e49 | 1.95061 | 0.975305 | − | 0.220863i | \(-0.0708873\pi\) | ||||
0.975305 | + | 0.220863i | \(0.0708873\pi\) | |||||||
\(390\) | −4.79215e48 | + | 3.24172e49i | −0.282035 | + | 1.90787i | ||||
\(391\) | 1.07654e48i | 0.0603494i | ||||||||
\(392\) | 6.59534e48 | + | 3.10732e48i | 0.352210 | + | 0.165940i | ||||
\(393\) | −4.89119e49 | −2.48860 | ||||||||
\(394\) | 1.07054e48 | + | 1.58255e47i | 0.0519007 | + | 0.00767235i | ||||
\(395\) | − | 1.42776e49i | − | 0.659647i | ||||||
\(396\) | 1.34515e49 | − | 4.45032e49i | 0.592329 | − | 1.95967i | ||||
\(397\) | −3.08835e49 | −1.29630 | −0.648152 | − | 0.761511i | \(-0.724458\pi\) | ||||
−0.648152 | + | 0.761511i | \(0.724458\pi\) | |||||||
\(398\) | 5.59635e48 | − | 3.78573e49i | 0.223937 | − | 1.51486i | ||||
\(399\) | 4.31036e49i | 1.64448i | ||||||||
\(400\) | −9.48979e48 | − | 6.31358e48i | −0.345236 | − | 0.229687i | ||||
\(401\) | 1.42475e49 | 0.494307 | 0.247153 | − | 0.968976i | \(-0.420505\pi\) | ||||
0.247153 | + | 0.968976i | \(0.420505\pi\) | |||||||
\(402\) | −4.09717e49 | − | 6.05673e48i | −1.35578 | − | 0.200421i | ||||
\(403\) | − | 2.75069e49i | − | 0.868252i | ||||||
\(404\) | 3.32118e49 | + | 1.00386e49i | 1.00011 | + | 0.302292i | ||||
\(405\) | 1.14627e50 | 3.29338 | ||||||||
\(406\) | −2.53768e48 | + | 1.71665e49i | −0.0695732 | + | 0.470638i | ||||
\(407\) | − | 1.37876e49i | − | 0.360741i | ||||||
\(408\) | −6.12975e48 | + | 1.30105e49i | −0.153073 | + | 0.324901i | ||||
\(409\) | 3.21318e49 | 0.765936 | 0.382968 | − | 0.923762i | \(-0.374902\pi\) | ||||
0.382968 | + | 0.923762i | \(0.374902\pi\) | |||||||
\(410\) | −1.20450e49 | − | 1.78059e48i | −0.274104 | − | 0.0405200i | ||||
\(411\) | − | 7.27372e47i | − | 0.0158038i | ||||||
\(412\) | −2.50387e49 | + | 8.28384e49i | −0.519476 | + | 1.71864i | ||||
\(413\) | −1.18941e49 | −0.235656 | ||||||||
\(414\) | 7.28548e48 | − | 4.92838e49i | 0.137864 | − | 0.932604i | ||||
\(415\) | − | 5.78799e49i | − | 1.04620i | ||||||
\(416\) | 5.52031e49 | + | 4.97835e49i | 0.953214 | + | 0.859631i | ||||
\(417\) | 5.67593e49 | 0.936379 | ||||||||
\(418\) | 4.81895e49 | + | 7.12372e48i | 0.759631 | + | 0.112294i | ||||
\(419\) | − | 1.02125e50i | − | 1.53839i | −0.639014 | − | 0.769195i | \(-0.720658\pi\) | ||
0.639014 | − | 0.769195i | \(-0.279342\pi\) | |||||||
\(420\) | −7.80674e49 | − | 2.35967e49i | −1.12391 | − | 0.339714i | ||||
\(421\) | −1.69218e49 | −0.232855 | −0.116428 | − | 0.993199i | \(-0.537144\pi\) | ||||
−0.116428 | + | 0.993199i | \(0.537144\pi\) | |||||||
\(422\) | −5.72677e48 | + | 3.87396e49i | −0.0753309 | + | 0.509587i | ||||
\(423\) | 1.39110e50i | 1.74940i | ||||||||
\(424\) | 1.32023e49 | + | 6.22011e48i | 0.158744 | + | 0.0747905i | ||||
\(425\) | −6.59553e48 | −0.0758333 | ||||||||
\(426\) | −3.06993e50 | − | 4.53820e49i | −3.37556 | − | 0.499001i | ||||
\(427\) | − | 6.55277e49i | − | 0.689121i | ||||||
\(428\) | −2.29722e49 | + | 7.60016e49i | −0.231085 | + | 0.764524i | ||||
\(429\) | −1.87720e50 | −1.80643 | ||||||||
\(430\) | 1.27275e49 | − | 8.60971e49i | 0.117177 | − | 0.792662i | ||||
\(431\) | 1.84118e50i | 1.62192i | 0.585105 | + | 0.810958i | \(0.301053\pi\) | ||||
−0.585105 | + | 0.810958i | \(0.698947\pi\) | |||||||
\(432\) | 2.39619e50 | − | 3.60166e50i | 2.01990 | − | 3.03606i | ||||
\(433\) | 6.80095e49 | 0.548655 | 0.274327 | − | 0.961636i | \(-0.411545\pi\) | ||||
0.274327 | + | 0.961636i | \(0.411545\pi\) | |||||||
\(434\) | 6.77223e49 | + | 1.00112e49i | 0.522910 | + | 0.0773003i | ||||
\(435\) | 1.23765e50i | 0.914749i | ||||||||
\(436\) | 9.46704e49 | + | 2.86151e49i | 0.669840 | + | 0.202466i | ||||
\(437\) | 5.21998e49 | 0.353607 | ||||||||
\(438\) | −5.76416e49 | + | 3.89925e50i | −0.373876 | + | 2.52914i | ||||
\(439\) | 7.69130e49i | 0.477720i | 0.971054 | + | 0.238860i | \(0.0767738\pi\) | ||||
−0.971054 | + | 0.238860i | \(0.923226\pi\) | |||||||
\(440\) | −3.92830e49 | + | 8.33789e49i | −0.233671 | + | 0.495970i | ||||
\(441\) | −1.95232e50 | −1.11229 | ||||||||
\(442\) | 4.25519e49 | + | 6.29033e48i | 0.232218 | + | 0.0343281i | ||||
\(443\) | − | 2.32649e50i | − | 1.21627i | −0.793833 | − | 0.608136i | \(-0.791918\pi\) | ||
0.793833 | − | 0.608136i | \(-0.208082\pi\) | |||||||
\(444\) | 5.71085e49 | − | 1.88938e50i | 0.286038 | − | 0.946333i | ||||
\(445\) | 1.03733e50 | 0.497827 | ||||||||
\(446\) | 2.89351e49 | − | 1.95736e50i | 0.133065 | − | 0.900137i | ||||
\(447\) | − | 3.29563e50i | − | 1.45243i | ||||||
\(448\) | −1.42659e50 | + | 1.17792e50i | −0.602582 | + | 0.497546i | ||||
\(449\) | −3.93199e50 | −1.59196 | −0.795981 | − | 0.605322i | \(-0.793044\pi\) | ||||
−0.795981 | + | 0.605322i | \(0.793044\pi\) | |||||||
\(450\) | 3.01941e50 | + | 4.46351e49i | 1.17188 | + | 0.173236i | ||||
\(451\) | − | 6.97497e49i | − | 0.259530i | ||||||
\(452\) | −3.65429e49 | − | 1.10454e49i | −0.130368 | − | 0.0394051i | ||||
\(453\) | −9.43573e49 | −0.322782 | ||||||||
\(454\) | −5.23971e48 | + | 3.54448e49i | −0.0171888 | + | 0.116276i | ||||
\(455\) | 2.43917e50i | 0.767407i | ||||||||
\(456\) | 6.30858e50 | + | 2.97221e50i | 1.90370 | + | 0.896909i | ||||
\(457\) | −1.81880e50 | −0.526475 | −0.263237 | − | 0.964731i | \(-0.584790\pi\) | ||||
−0.263237 | + | 0.964731i | \(0.584790\pi\) | |||||||
\(458\) | 1.90233e50 | + | 2.81216e49i | 0.528253 | + | 0.0780902i | ||||
\(459\) | − | 2.50320e50i | − | 0.666890i | ||||||
\(460\) | −2.85763e49 | + | 9.45420e49i | −0.0730477 | + | 0.241672i | ||||
\(461\) | 7.53980e50 | 1.84945 | 0.924724 | − | 0.380638i | \(-0.124296\pi\) | ||||
0.924724 | + | 0.380638i | \(0.124296\pi\) | |||||||
\(462\) | 6.83210e49 | − | 4.62168e50i | 0.160826 | − | 1.08793i | ||||
\(463\) | 6.29632e50i | 1.42249i | 0.702946 | + | 0.711243i | \(0.251867\pi\) | ||||
−0.702946 | + | 0.711243i | \(0.748133\pi\) | |||||||
\(464\) | 2.33748e50 | + | 1.55513e50i | 0.506881 | + | 0.337229i | ||||
\(465\) | 4.88256e50 | 1.01634 | ||||||||
\(466\) | −5.25555e50 | − | 7.76914e49i | −1.05023 | − | 0.155253i | ||||
\(467\) | 1.81850e48i | 0.00348893i | 0.999998 | + | 0.00174446i | \(0.000555280\pi\) | ||||
−0.999998 | + | 0.00174446i | \(0.999445\pi\) | |||||||
\(468\) | −1.90544e51 | − | 5.75938e50i | −3.51014 | − | 1.06097i | ||||
\(469\) | −3.08283e50 | −0.545339 | ||||||||
\(470\) | 4.03300e49 | − | 2.72818e50i | 0.0685124 | − | 0.463462i | ||||
\(471\) | 1.53106e50i | 0.249801i | ||||||||
\(472\) | −8.20156e49 | + | 1.74080e50i | −0.128528 | + | 0.272804i | ||||
\(473\) | 4.98566e50 | 0.750517 | ||||||||
\(474\) | 1.15829e51 | + | 1.71227e50i | 1.67505 | + | 0.247619i | ||||
\(475\) | 3.19806e50i | 0.444333i | ||||||||
\(476\) | −3.09737e49 | + | 1.02474e50i | −0.0413486 | + | 0.136798i | ||||
\(477\) | −3.90807e50 | −0.501318 | ||||||||
\(478\) | 2.04658e50 | − | 1.38444e51i | 0.252289 | − | 1.70665i | ||||
\(479\) | − | 7.60161e50i | − | 0.900597i | −0.892878 | − | 0.450299i | \(-0.851318\pi\) | ||
0.892878 | − | 0.450299i | \(-0.148682\pi\) | |||||||
\(480\) | −8.83672e50 | + | 9.79872e50i | −1.00625 | + | 1.11580i | ||||
\(481\) | −5.90327e50 | −0.646154 | ||||||||
\(482\) | −1.54944e51 | − | 2.29050e50i | −1.63035 | − | 0.241011i | ||||
\(483\) | − | 5.00629e50i | − | 0.506432i | ||||||
\(484\) | 4.78779e50 | + | 1.44716e50i | 0.465665 | + | 0.140752i | ||||
\(485\) | −8.91595e50 | −0.833824 | ||||||||
\(486\) | −7.81710e50 | + | 5.28799e51i | −0.703002 | + | 4.75556i | ||||
\(487\) | − | 1.04970e51i | − | 0.907848i | −0.891041 | − | 0.453924i | \(-0.850024\pi\) | ||
0.891041 | − | 0.453924i | \(-0.149976\pi\) | |||||||
\(488\) | −9.59053e50 | − | 4.51847e50i | −0.797748 | − | 0.375850i | ||||
\(489\) | 3.58813e51 | 2.87078 | ||||||||
\(490\) | 3.82884e50 | + | 5.66007e49i | 0.294674 | + | 0.0435608i | ||||
\(491\) | 2.37081e51i | 1.75529i | 0.479315 | + | 0.877643i | \(0.340885\pi\) | ||||
−0.479315 | + | 0.877643i | \(0.659115\pi\) | |||||||
\(492\) | 2.88905e50 | − | 9.55815e50i | 0.205787 | − | 0.680827i | ||||
\(493\) | 1.62458e50 | 0.111339 | ||||||||
\(494\) | 3.05007e50 | − | 2.06327e51i | 0.201140 | − | 1.36064i | ||||
\(495\) | − | 2.46814e51i | − | 1.56628i | ||||||
\(496\) | 6.13502e50 | − | 9.22140e50i | 0.374683 | − | 0.563177i | ||||
\(497\) | −2.30991e51 | −1.35776 | ||||||||
\(498\) | 4.69558e51 | + | 6.94135e50i | 2.65663 | + | 0.392723i | ||||
\(499\) | 6.02439e49i | 0.0328098i | 0.999865 | + | 0.0164049i | \(0.00522207\pi\) | ||||
−0.999865 | + | 0.0164049i | \(0.994778\pi\) | |||||||
\(500\) | −1.97607e51 | − | 5.97286e50i | −1.03603 | − | 0.313150i | ||||
\(501\) | 1.33848e51 | 0.675608 | ||||||||
\(502\) | 3.69281e50 | − | 2.49806e51i | 0.179468 | − | 1.21404i | ||||
\(503\) | − | 2.63005e50i | − | 0.123076i | −0.998105 | − | 0.0615378i | \(-0.980400\pi\) | ||
0.998105 | − | 0.0615378i | \(-0.0196005\pi\) | |||||||
\(504\) | 2.11145e51 | − | 4.48160e51i | 0.951484 | − | 2.01954i | ||||
\(505\) | 1.84192e51 | 0.799345 | ||||||||
\(506\) | −5.59699e50 | − | 8.27388e49i | −0.233935 | − | 0.0345819i | ||||
\(507\) | 3.15908e51i | 1.27177i | ||||||||
\(508\) | −9.45759e50 | + | 3.12896e51i | −0.366750 | + | 1.21336i | ||||
\(509\) | 1.66263e51 | 0.621096 | 0.310548 | − | 0.950558i | \(-0.399488\pi\) | ||||
0.310548 | + | 0.950558i | \(0.399488\pi\) | |||||||
\(510\) | −1.11655e50 | + | 7.55308e50i | −0.0401833 | + | 0.271826i | ||||
\(511\) | 2.93392e51i | 1.01730i | ||||||||
\(512\) | 7.40278e50 | + | 2.90017e51i | 0.247324 | + | 0.968933i | ||||
\(513\) | −1.21376e52 | −3.90753 | ||||||||
\(514\) | −2.35058e51 | − | 3.47479e50i | −0.729248 | − | 0.107803i | ||||
\(515\) | 4.59420e51i | 1.37364i | ||||||||
\(516\) | 6.83210e51 | + | 2.06507e51i | 1.96884 | + | 0.595100i | ||||
\(517\) | 1.57982e51 | 0.438821 | ||||||||
\(518\) | 2.14851e50 | − | 1.45339e51i | 0.0575270 | − | 0.389150i | ||||
\(519\) | − | 1.06002e52i | − | 2.73612i | ||||||
\(520\) | 3.56993e51 | + | 1.68193e51i | 0.888375 | + | 0.418548i | ||||
\(521\) | −7.40204e51 | −1.77597 | −0.887983 | − | 0.459876i | \(-0.847894\pi\) | ||||
−0.887983 | + | 0.459876i | \(0.847894\pi\) | |||||||
\(522\) | −7.43726e51 | − | 1.09943e51i | −1.72057 | − | 0.254348i | ||||
\(523\) | − | 8.88656e50i | − | 0.198245i | −0.995075 | − | 0.0991223i | \(-0.968396\pi\) | ||
0.995075 | − | 0.0991223i | \(-0.0316035\pi\) | |||||||
\(524\) | −1.70424e51 | + | 5.63833e51i | −0.366637 | + | 1.21299i | ||||
\(525\) | 3.06715e51 | 0.636367 | ||||||||
\(526\) | 5.80975e50 | − | 3.93009e51i | 0.116259 | − | 0.786454i | ||||
\(527\) | − | 6.40900e50i | − | 0.123705i | ||||||
\(528\) | −6.29311e51 | − | 4.18682e51i | −1.17171 | − | 0.779542i | ||||
\(529\) | 4.96119e51 | 0.891104 | ||||||||
\(530\) | 7.66442e50 | + | 1.13301e50i | 0.132812 | + | 0.0196333i | ||||
\(531\) | − | 5.15301e51i | − | 0.861520i | ||||||
\(532\) | 4.96878e51 | + | 1.50186e51i | 0.801547 | + | 0.242276i | ||||
\(533\) | −2.98639e51 | −0.464868 | ||||||||
\(534\) | −1.24404e51 | + | 8.41550e51i | −0.186875 | + | 1.26414i | ||||
\(535\) | 4.21503e51i | 0.611053i | ||||||||
\(536\) | −2.12577e51 | + | 4.51199e51i | −0.297431 | + | 0.631302i | ||||
\(537\) | 8.45224e51 | 1.14146 | ||||||||
\(538\) | 5.05824e51 | + | 7.47746e50i | 0.659381 | + | 0.0974745i | ||||
\(539\) | 2.21718e51i | 0.279007i | ||||||||
\(540\) | 6.64461e51 | − | 2.19831e52i | 0.807213 | − | 2.67059i | ||||
\(541\) | −3.73036e51 | −0.437524 | −0.218762 | − | 0.975778i | \(-0.570202\pi\) | ||||
−0.218762 | + | 0.975778i | \(0.570202\pi\) | |||||||
\(542\) | −2.58629e50 | + | 1.74953e51i | −0.0292881 | + | 0.198124i | ||||
\(543\) | 2.19523e52i | 2.40039i | ||||||||
\(544\) | 1.28621e51 | + | 1.15994e51i | 0.135810 | + | 0.122477i | ||||
\(545\) | 5.25040e51 | 0.535376 | ||||||||
\(546\) | −1.97881e52 | − | 2.92522e51i | −1.94869 | − | 0.288070i | ||||
\(547\) | − | 5.24333e51i | − | 0.498710i | −0.968412 | − | 0.249355i | \(-0.919781\pi\) | ||
0.968412 | − | 0.249355i | \(-0.0802187\pi\) | |||||||
\(548\) | −8.38480e49 | − | 2.53439e49i | −0.00770304 | − | 0.00232832i | ||||
\(549\) | 2.83894e52 | 2.51931 | ||||||||
\(550\) | 5.06906e50 | − | 3.42904e51i | 0.0434547 | − | 0.293956i | ||||
\(551\) | − | 7.87731e51i | − | 0.652375i | ||||||
\(552\) | −7.32713e51 | − | 3.45210e51i | −0.586262 | − | 0.276211i | ||||
\(553\) | 8.71533e51 | 0.673762 | ||||||||
\(554\) | −9.80791e51 | − | 1.44988e51i | −0.732641 | − | 0.108304i | ||||
\(555\) | − | 1.04785e52i | − | 0.756365i | ||||||
\(556\) | 1.97767e51 | − | 6.54294e51i | 0.137953 | − | 0.456407i | ||||
\(557\) | −1.57359e52 | −1.06082 | −0.530411 | − | 0.847741i | \(-0.677962\pi\) | ||||
−0.530411 | + | 0.847741i | \(0.677962\pi\) | |||||||
\(558\) | −4.33728e51 | + | 2.93402e52i | −0.282597 | + | 1.91167i | ||||
\(559\) | − | 2.13465e52i | − | 1.34432i | ||||||
\(560\) | −5.44022e51 | + | 8.17707e51i | −0.331165 | + | 0.497766i | ||||
\(561\) | −4.37379e51 | −0.257374 | ||||||||
\(562\) | 1.27950e52 | + | 1.89145e51i | 0.727865 | + | 0.107598i | ||||
\(563\) | − | 2.51773e52i | − | 1.38468i | −0.721571 | − | 0.692340i | \(-0.756580\pi\) | ||
0.721571 | − | 0.692340i | \(-0.243420\pi\) | |||||||
\(564\) | 2.16491e52 | + | 6.54364e51i | 1.15116 | + | 0.347950i | ||||
\(565\) | −2.02666e51 | −0.104198 | ||||||||
\(566\) | 3.23745e51 | − | 2.19002e52i | 0.160950 | − | 1.08877i | ||||
\(567\) | 6.99706e52i | 3.36386i | ||||||||
\(568\) | −1.59280e52 | + | 3.38075e52i | −0.740531 | + | 1.57179i | ||||
\(569\) | −8.21227e51 | −0.369258 | −0.184629 | − | 0.982808i | \(-0.559108\pi\) | ||||
−0.184629 | + | 0.982808i | \(0.559108\pi\) | |||||||
\(570\) | 3.66237e52 | + | 5.41398e51i | 1.59272 | + | 0.235447i | ||||
\(571\) | − | 2.98136e52i | − | 1.25409i | −0.778983 | − | 0.627045i | \(-0.784264\pi\) | ||
0.778983 | − | 0.627045i | \(-0.215736\pi\) | |||||||
\(572\) | −6.54073e51 | + | 2.16394e52i | −0.266135 | + | 0.880484i | ||||
\(573\) | −1.22191e52 | −0.480951 | ||||||||
\(574\) | 1.08690e51 | − | 7.35252e51i | 0.0413871 | − | 0.279969i | ||||
\(575\) | − | 3.71441e51i | − | 0.136836i | ||||||
\(576\) | −5.10324e52 | − | 6.18058e52i | −1.81894 | − | 2.20294i | ||||
\(577\) | −3.08063e52 | −1.06243 | −0.531213 | − | 0.847238i | \(-0.678264\pi\) | ||||
−0.531213 | + | 0.847238i | \(0.678264\pi\) | |||||||
\(578\) | −2.86524e52 | − | 4.23561e51i | −0.956164 | − | 0.141347i | ||||
\(579\) | 2.79667e52i | 0.903125i | ||||||||
\(580\) | 1.42670e52 | + | 4.31236e51i | 0.445864 | + | 0.134767i | ||||
\(581\) | 3.53310e52 | 1.06858 | ||||||||
\(582\) | 1.06926e52 | − | 7.23317e52i | 0.313002 | − | 2.11735i | ||||
\(583\) | 4.43826e51i | 0.125751i | ||||||||
\(584\) | 4.29403e52 | + | 2.02309e52i | 1.17766 | + | 0.554843i | ||||
\(585\) | −1.05675e53 | −2.80551 | ||||||||
\(586\) | 2.53682e52 | + | 3.75012e51i | 0.651982 | + | 0.0963807i | ||||
\(587\) | 4.00798e52i | 0.997244i | 0.866819 | + | 0.498622i | \(0.166160\pi\) | ||||
−0.866819 | + | 0.498622i | \(0.833840\pi\) | |||||||
\(588\) | −9.18360e51 | + | 3.03831e52i | −0.221230 | + | 0.731920i | ||||
\(589\) | −3.10762e52 | −0.724831 | ||||||||
\(590\) | −1.49394e51 | + | 1.01060e52i | −0.0337400 | + | 0.228239i | ||||
\(591\) | 4.71135e51i | 0.103035i | ||||||||
\(592\) | −1.97901e52 | − | 1.31664e52i | −0.419117 | − | 0.278840i | ||||
\(593\) | 6.24440e52 | 1.28071 | 0.640356 | − | 0.768078i | \(-0.278787\pi\) | ||||
0.640356 | + | 0.768078i | \(0.278787\pi\) | |||||||
\(594\) | 1.30142e53 | + | 1.92386e52i | 2.58509 | + | 0.382147i | ||||
\(595\) | 5.68317e51i | 0.109337i | ||||||||
\(596\) | −3.79905e52 | − | 1.14830e52i | −0.707939 | − | 0.213982i | ||||
\(597\) | 1.66607e53 | 3.00733 | ||||||||
\(598\) | −3.54253e51 | + | 2.39640e52i | −0.0619428 | + | 0.419021i | ||||
\(599\) | − | 7.16880e52i | − | 1.21433i | −0.794576 | − | 0.607165i | \(-0.792307\pi\) | ||
0.794576 | − | 0.607165i | \(-0.207693\pi\) | |||||||
\(600\) | 2.11495e52 | − | 4.48903e52i | 0.347078 | − | 0.736679i | ||||
\(601\) | −9.82291e52 | −1.56180 | −0.780900 | − | 0.624656i | \(-0.785239\pi\) | ||||
−0.780900 | + | 0.624656i | \(0.785239\pi\) | |||||||
\(602\) | 5.25553e52 | + | 7.76910e51i | 0.809623 | + | 0.119684i | ||||
\(603\) | − | 1.33561e53i | − | 1.99367i | ||||||
\(604\) | −3.28770e51 | + | 1.08771e52i | −0.0475544 | + | 0.157329i | ||||
\(605\) | 2.65530e52 | 0.372187 | ||||||||
\(606\) | −2.20895e52 | + | 1.49428e53i | −0.300059 | + | 2.02979i | ||||
\(607\) | 8.84512e52i | 1.16444i | 0.813030 | + | 0.582222i | \(0.197817\pi\) | ||||
−0.813030 | + | 0.582222i | \(0.802183\pi\) | |||||||
\(608\) | 5.62433e52 | − | 6.23662e52i | 0.717634 | − | 0.795759i | ||||
\(609\) | −7.55484e52 | −0.934323 | ||||||||
\(610\) | −5.56766e52 | − | 8.23052e51i | −0.667430 | − | 0.0986644i | ||||
\(611\) | − | 6.76412e52i | − | 0.786011i | ||||||
\(612\) | −4.43960e52 | − | 1.34191e52i | −0.500111 | − | 0.151164i | ||||
\(613\) | −4.73801e52 | −0.517424 | −0.258712 | − | 0.965954i | \(-0.583298\pi\) | ||||
−0.258712 | + | 0.965954i | \(0.583298\pi\) | |||||||
\(614\) | −2.38596e51 | + | 1.61402e52i | −0.0252618 | + | 0.170887i | ||||
\(615\) | − | 5.30093e52i | − | 0.544158i | ||||||
\(616\) | −5.08960e52 | − | 2.39791e52i | −0.506583 | − | 0.238671i | ||||
\(617\) | 1.61910e53 | 1.56263 | 0.781313 | − | 0.624139i | \(-0.214550\pi\) | ||||
0.781313 | + | 0.624139i | \(0.214550\pi\) | |||||||
\(618\) | −3.72710e53 | − | 5.50967e52i | −3.48811 | − | 0.515638i | ||||
\(619\) | 1.92411e53i | 1.74625i | 0.487494 | + | 0.873126i | \(0.337911\pi\) | ||||
−0.487494 | + | 0.873126i | \(0.662089\pi\) | |||||||
\(620\) | 1.70123e52 | − | 5.62838e52i | 0.149735 | − | 0.495383i | ||||
\(621\) | 1.40973e53 | 1.20336 | ||||||||
\(622\) | 8.45354e51 | − | 5.71852e52i | 0.0699876 | − | 0.473442i | ||||
\(623\) | 6.33208e52i | 0.508480i | ||||||||
\(624\) | −1.79262e53 | + | 2.69444e53i | −1.39631 | + | 2.09876i | ||||
\(625\) | −5.47123e52 | −0.413395 | ||||||||
\(626\) | 1.54110e53 | + | 2.27817e52i | 1.12959 | + | 0.166984i | ||||
\(627\) | 2.12078e53i | 1.50804i | ||||||||
\(628\) | 1.76493e52 | + | 5.33469e51i | 0.121757 | + | 0.0368024i | ||||
\(629\) | −1.37544e52 | −0.0920617 | ||||||||
\(630\) | 3.84608e52 | − | 2.60174e53i | 0.249774 | − | 1.68963i | ||||
\(631\) | 1.89132e52i | 0.119181i | 0.998223 | + | 0.0595905i | \(0.0189795\pi\) | ||||
−0.998223 | + | 0.0595905i | \(0.981021\pi\) | |||||||
\(632\) | 6.00967e52 | − | 1.27556e53i | 0.367473 | − | 0.779969i | ||||
\(633\) | −1.70490e53 | −1.01165 | ||||||||
\(634\) | 7.77728e52 | + | 1.14969e52i | 0.447849 | + | 0.0662043i | ||||
\(635\) | 1.73531e53i | 0.969789i | ||||||||
\(636\) | −1.83834e52 | + | 6.08198e52i | −0.0997103 | + | 0.329883i | ||||
\(637\) | 9.49303e52 | 0.499753 | ||||||||
\(638\) | −1.24859e52 | + | 8.44625e52i | −0.0638007 | + | 0.431590i | ||||
\(639\) | − | 1.00075e54i | − | 4.96375i | ||||||
\(640\) | 8.21652e52 | + | 1.36007e53i | 0.395611 | + | 0.654852i | ||||
\(641\) | 2.93730e52 | 0.137292 | 0.0686461 | − | 0.997641i | \(-0.478132\pi\) | ||||
0.0686461 | + | 0.997641i | \(0.478132\pi\) | |||||||
\(642\) | −3.41950e53 | − | 5.05495e52i | −1.55166 | − | 0.229378i | ||||
\(643\) | − | 2.14021e53i | − | 0.942861i | −0.881903 | − | 0.471430i | \(-0.843738\pi\) | ||
0.881903 | − | 0.471430i | \(-0.156262\pi\) | |||||||
\(644\) | −5.77102e52 | − | 1.74435e52i | −0.246843 | − | 0.0746108i | ||||
\(645\) | 3.78906e53 | 1.57361 | ||||||||
\(646\) | 7.10655e51 | − | 4.80734e52i | 0.0286577 | − | 0.193859i | ||||
\(647\) | 3.12905e53i | 1.22527i | 0.790366 | + | 0.612635i | \(0.209890\pi\) | ||||
−0.790366 | + | 0.612635i | \(0.790110\pi\) | |||||||
\(648\) | 1.02408e54 | + | 4.82483e53i | 3.89411 | + | 1.83467i | ||||
\(649\) | −5.85210e52 | −0.216104 | ||||||||
\(650\) | −1.46817e53 | − | 2.17036e52i | −0.526530 | − | 0.0778354i | ||||
\(651\) | 2.98040e53i | 1.03809i | ||||||||
\(652\) | 1.25022e53 | − | 4.13623e53i | 0.422942 | − | 1.39927i | ||||
\(653\) | 2.09397e53 | 0.688051 | 0.344025 | − | 0.938960i | \(-0.388209\pi\) | ||||
0.344025 | + | 0.938960i | \(0.388209\pi\) | |||||||
\(654\) | −6.29663e52 | + | 4.25945e53i | −0.200970 | + | 1.35949i | ||||
\(655\) | 3.12701e53i | 0.969492i | ||||||||
\(656\) | −1.00116e53 | − | 6.66071e52i | −0.301529 | − | 0.200608i | ||||
\(657\) | −1.27110e54 | −3.71909 | ||||||||
\(658\) | 1.66533e53 | + | 2.46182e52i | 0.473380 | + | 0.0699784i | ||||
\(659\) | − | 1.07866e53i | − | 0.297895i | −0.988845 | − | 0.148947i | \(-0.952411\pi\) | ||
0.988845 | − | 0.148947i | \(-0.0475885\pi\) | |||||||
\(660\) | −3.84107e53 | − | 1.16100e53i | −1.03066 | − | 0.311528i | ||||
\(661\) | −3.83365e53 | −0.999505 | −0.499752 | − | 0.866168i | \(-0.666576\pi\) | ||||
−0.499752 | + | 0.866168i | \(0.666576\pi\) | |||||||
\(662\) | 4.78007e52 | − | 3.23355e53i | 0.121097 | − | 0.819178i | ||||
\(663\) | 1.87267e53i | 0.461004i | ||||||||
\(664\) | 2.43625e53 | − | 5.17099e53i | 0.582812 | − | 1.23703i | ||||
\(665\) | 2.75568e53 | 0.640644 | ||||||||
\(666\) | 6.29671e53 | + | 9.30825e52i | 1.42267 | + | 0.210309i | ||||
\(667\) | 9.14914e52i | 0.200904i | ||||||||
\(668\) | 4.66368e52 | − | 1.54294e53i | 0.0995350 | − | 0.329303i | ||||
\(669\) | 8.61419e53 | 1.78697 | ||||||||
\(670\) | −3.87215e52 | + | 2.61938e53i | −0.0780785 | + | 0.528174i | ||||
\(671\) | − | 3.22409e53i | − | 0.631944i | ||||||
\(672\) | −5.98132e53 | − | 5.39410e53i | −1.13967 | − | 1.02779i | ||||
\(673\) | −7.68413e53 | −1.42334 | −0.711669 | − | 0.702514i | \(-0.752061\pi\) | ||||
−0.711669 | + | 0.702514i | \(0.752061\pi\) | |||||||
\(674\) | −6.29033e53 | − | 9.29883e52i | −1.13275 | − | 0.167452i | ||||
\(675\) | 8.63681e53i | 1.51210i | ||||||||
\(676\) | 3.64164e53 | + | 1.10072e53i | 0.619883 | + | 0.187366i | ||||
\(677\) | −1.93220e53 | −0.319792 | −0.159896 | − | 0.987134i | \(-0.551116\pi\) | ||||
−0.159896 | + | 0.987134i | \(0.551116\pi\) | |||||||
\(678\) | 2.43050e52 | − | 1.64415e53i | 0.0391140 | − | 0.264593i | ||||
\(679\) | − | 5.44246e53i | − | 0.851667i | ||||||
\(680\) | 8.31780e52 | + | 3.91884e52i | 0.126572 | + | 0.0596332i | ||||
\(681\) | −1.55990e53 | −0.230834 | ||||||||
\(682\) | 3.33206e53 | + | 4.92570e52i | 0.479524 | + | 0.0708867i | ||||
\(683\) | − | 6.78686e53i | − | 0.949895i | −0.880014 | − | 0.474947i | \(-0.842467\pi\) | ||
0.880014 | − | 0.474947i | \(-0.157533\pi\) | |||||||
\(684\) | −6.50671e53 | + | 2.15269e54i | −0.885718 | + | 2.93032i | ||||
\(685\) | −4.65019e51 | −0.00615673 | ||||||||
\(686\) | −1.23290e53 | + | 8.34012e53i | −0.158770 | + | 1.07402i | ||||
\(687\) | 8.37200e53i | 1.04870i | ||||||||
\(688\) | 4.76103e53 | − | 7.15619e53i | 0.580123 | − | 0.871970i | ||||
\(689\) | 1.90028e53 | 0.225243 | ||||||||
\(690\) | −4.25367e53 | − | 6.28809e52i | −0.490492 | − | 0.0725080i | ||||
\(691\) | − | 6.69604e53i | − | 0.751165i | −0.926789 | − | 0.375583i | \(-0.877443\pi\) | ||
0.926789 | − | 0.375583i | \(-0.122557\pi\) | |||||||
\(692\) | −1.22194e54 | − | 3.69344e53i | −1.33363 | − | 0.403102i | ||||
\(693\) | 1.50660e54 | 1.59980 | ||||||||
\(694\) | −1.12038e53 | + | 7.57900e53i | −0.115754 | + | 0.783037i | ||||
\(695\) | − | 3.62870e53i | − | 0.364787i | ||||||
\(696\) | −5.20945e53 | + | 1.10572e54i | −0.509585 | + | 1.08160i | ||||
\(697\) | −6.95817e52 | −0.0662326 | ||||||||
\(698\) | 7.26753e53 | + | 1.07434e53i | 0.673184 | + | 0.0995150i | ||||
\(699\) | − | 2.31293e54i | − | 2.08495i | ||||||
\(700\) | 1.06869e53 | − | 3.53566e53i | 0.0937537 | − | 0.310176i | ||||
\(701\) | 1.25735e54 | 1.07353 | 0.536763 | − | 0.843733i | \(-0.319647\pi\) | ||||
0.536763 | + | 0.843733i | \(0.319647\pi\) | |||||||
\(702\) | 8.23715e53 | − | 5.57215e54i | 0.684498 | − | 4.63039i | ||||
\(703\) | 6.66927e53i | 0.539420i | ||||||||
\(704\) | −7.01908e53 | + | 5.79558e53i | −0.552586 | + | 0.456264i | ||||
\(705\) | 1.20065e54 | 0.920077 | ||||||||
\(706\) | 1.17944e54 | + | 1.74353e53i | 0.879804 | + | 0.130059i | ||||
\(707\) | 1.12434e54i | 0.816450i | ||||||||
\(708\) | −8.01943e53 | − | 2.42395e53i | −0.566907 | − | 0.171353i | ||||
\(709\) | −1.55166e54 | −1.06787 | −0.533935 | − | 0.845525i | \(-0.679287\pi\) | ||||
−0.533935 | + | 0.845525i | \(0.679287\pi\) | |||||||
\(710\) | −2.90133e53 | + | 1.96265e54i | −0.194397 | + | 1.31503i | ||||
\(711\) | 3.77585e54i | 2.46316i | ||||||||
\(712\) | 9.26753e53 | + | 4.36629e53i | 0.588633 | + | 0.277328i | ||||
\(713\) | 3.60936e53 | 0.223218 | ||||||||
\(714\) | −4.61054e53 | − | 6.81564e52i | −0.277643 | − | 0.0410431i | ||||
\(715\) | 1.20012e54i | 0.703735i | ||||||||
\(716\) | 2.94502e53 | − | 9.74335e53i | 0.168167 | − | 0.556366i | ||||
\(717\) | 6.09280e54 | 3.38808 | ||||||||
\(718\) | −1.92937e53 | + | 1.30515e54i | −0.104484 | + | 0.706801i | ||||
\(719\) | − | 5.03007e53i | − | 0.265293i | −0.991163 | − | 0.132646i | \(-0.957653\pi\) | ||
0.991163 | − | 0.132646i | \(-0.0423475\pi\) | |||||||
\(720\) | −3.54265e54 | − | 2.35694e54i | −1.81975 | − | 1.21068i | ||||
\(721\) | −2.80439e54 | −1.40303 | ||||||||
\(722\) | −3.00921e53 | − | 4.44843e52i | −0.146637 | − | 0.0216770i | ||||
\(723\) | − | 6.81897e54i | − | 3.23662i | ||||||
\(724\) | 2.53055e54 | + | 7.64885e53i | 1.16999 | + | 0.353642i | ||||
\(725\) | −5.60530e53 | −0.252451 | ||||||||
\(726\) | −3.18441e53 | + | 2.15414e54i | −0.139712 | + | 0.945102i | ||||
\(727\) | 2.18479e54i | 0.933805i | 0.884309 | + | 0.466903i | \(0.154630\pi\) | ||||
−0.884309 | + | 0.466903i | \(0.845370\pi\) | |||||||
\(728\) | −1.02668e54 | + | 2.17915e54i | −0.427504 | + | 0.907385i | ||||
\(729\) | −1.26609e55 | −5.13620 | ||||||||
\(730\) | 2.49285e54 | + | 3.68511e53i | 0.985284 | + | 0.145652i | ||||
\(731\) | − | 4.97365e53i | − | 0.191533i | ||||||
\(732\) | 1.33542e54 | − | 4.41813e54i | 0.501081 | − | 1.65778i | ||||
\(733\) | −1.79061e54 | −0.654675 | −0.327338 | − | 0.944907i | \(-0.606151\pi\) | ||||
−0.327338 | + | 0.944907i | \(0.606151\pi\) | |||||||
\(734\) | −4.91904e53 | + | 3.32756e54i | −0.175249 | + | 1.18550i | ||||
\(735\) | 1.68504e54i | 0.584994i | ||||||||
\(736\) | −6.53242e53 | + | 7.24356e53i | −0.221002 | + | 0.245061i | ||||
\(737\) | −1.51681e54 | −0.500092 | ||||||||
\(738\) | 3.18542e54 | + | 4.70893e53i | 1.02352 | + | 0.151304i | ||||
\(739\) | − | 3.36658e54i | − | 1.05425i | −0.849787 | − | 0.527125i | \(-0.823270\pi\) | ||
0.849787 | − | 0.527125i | \(-0.176730\pi\) | |||||||
\(740\) | −1.20791e54 | − | 3.65103e53i | −0.368665 | − | 0.111433i | ||||
\(741\) | 9.08028e54 | 2.70118 | ||||||||
\(742\) | −6.91611e52 | + | 4.67851e53i | −0.0200534 | + | 0.135654i | ||||
\(743\) | − | 2.39939e54i | − | 0.678131i | −0.940763 | − | 0.339065i | \(-0.889889\pi\) | ||
0.940763 | − | 0.339065i | \(-0.110111\pi\) | |||||||
\(744\) | 4.36207e54 | + | 2.05514e54i | 1.20173 | + | 0.566181i | ||||
\(745\) | −2.10694e54 | −0.565827 | ||||||||
\(746\) | −6.27034e54 | − | 9.26927e53i | −1.64155 | − | 0.242665i | ||||
\(747\) | 1.53069e55i | 3.90657i | ||||||||
\(748\) | −1.52397e53 | + | 5.04190e53i | −0.0379179 | + | 0.125448i | ||||
\(749\) | −2.57293e54 | −0.624129 | ||||||||
\(750\) | 1.31430e54 | − | 8.89081e54i | 0.310836 | − | 2.10270i | ||||
\(751\) | − | 7.21481e54i | − | 1.66367i | −0.555026 | − | 0.831833i | \(-0.687292\pi\) | ||
0.555026 | − | 0.831833i | \(-0.312708\pi\) | |||||||
\(752\) | 1.50864e54 | − | 2.26760e54i | 0.339193 | − | 0.509833i | ||||
\(753\) | 1.09938e55 | 2.41014 | ||||||||
\(754\) | 3.61633e54 | + | 5.34592e53i | 0.773058 | + | 0.114279i | ||||
\(755\) | 6.03239e53i | 0.125747i | ||||||||
\(756\) | 1.34189e55 | + | 4.05599e54i | 2.72774 | + | 0.824485i | ||||
\(757\) | −4.59282e54 | −0.910454 | −0.455227 | − | 0.890375i | \(-0.650442\pi\) | ||||
−0.455227 | + | 0.890375i | \(0.650442\pi\) | |||||||
\(758\) | 2.47932e53 | − | 1.67717e54i | 0.0479312 | − | 0.324238i | ||||
\(759\) | − | 2.46319e54i | − | 0.464413i | ||||||
\(760\) | 1.90018e54 | − | 4.03316e54i | 0.349411 | − | 0.741631i | ||||
\(761\) | −1.06143e54 | −0.190363 | −0.0951816 | − | 0.995460i | \(-0.530343\pi\) | ||||
−0.0951816 | + | 0.995460i | \(0.530343\pi\) | |||||||
\(762\) | −1.40780e55 | − | 2.08111e54i | −2.46261 | − | 0.364040i | ||||
\(763\) | 3.20494e54i | 0.546832i | ||||||||
\(764\) | −4.25751e53 | + | 1.40856e54i | −0.0708569 | + | 0.234424i | ||||
\(765\) | −2.46219e54 | −0.399719 | ||||||||
\(766\) | 1.48842e54 | − | 1.00686e55i | 0.235710 | − | 1.59450i | ||||
\(767\) | 2.50562e54i | 0.387083i | ||||||||
\(768\) | −1.20191e55 | + | 5.03466e54i | −1.81138 | + | 0.758765i | ||||
\(769\) | 5.30962e54 | 0.780662 | 0.390331 | − | 0.920675i | \(-0.372361\pi\) | ||||
0.390331 | + | 0.920675i | \(0.372361\pi\) | |||||||
\(770\) | −2.95470e54 | − | 4.36786e53i | −0.423829 | − | 0.0626534i | ||||
\(771\) | − | 1.03447e55i | − | 1.44772i | ||||||
\(772\) | 3.22387e54 | + | 9.74445e53i | 0.440198 | + | 0.133054i | ||||
\(773\) | 4.72332e54 | 0.629270 | 0.314635 | − | 0.949213i | \(-0.398118\pi\) | ||||
0.314635 | + | 0.949213i | \(0.398118\pi\) | |||||||
\(774\) | −3.36591e54 | + | 2.27692e55i | −0.437546 | + | 2.95985i | ||||
\(775\) | 2.21130e54i | 0.280489i | ||||||||
\(776\) | −7.96550e54 | − | 3.75286e54i | −0.985917 | − | 0.464504i | ||||
\(777\) | 6.39626e54 | 0.772550 | ||||||||
\(778\) | 1.63715e55 | + | 2.42015e54i | 1.92964 | + | 0.285253i | ||||
\(779\) | 3.37390e54i | 0.388079i | ||||||||
\(780\) | −4.97091e54 | + | 1.64458e55i | −0.558006 | + | 1.84611i | ||||
\(781\) | −1.13652e55 | −1.24511 | ||||||||
\(782\) | −8.25395e52 | + | 5.58351e53i | −0.00882538 | + | 0.0597006i | ||||
\(783\) | − | 2.12738e55i | − | 2.22009i | ||||||
\(784\) | 3.18244e54 | + | 2.11729e54i | 0.324157 | + | 0.215662i | ||||
\(785\) | 9.78829e53 | 0.0973158 | ||||||||
\(786\) | −2.53682e55 | − | 3.75012e54i | −2.46185 | − | 0.363929i | ||||
\(787\) | 1.27863e55i | 1.21123i | 0.795758 | + | 0.605615i | \(0.207073\pi\) | ||||
−0.795758 | + | 0.605615i | \(0.792927\pi\) | |||||||
\(788\) | 5.43102e53 | + | 1.64158e53i | 0.0502208 | + | 0.0151797i | ||||
\(789\) | 1.72960e55 | 1.56129 | ||||||||
\(790\) | 1.09468e54 | − | 7.40512e54i | 0.0964654 | − | 0.652555i | ||||
\(791\) | − | 1.23711e54i | − | 0.106428i | ||||||
\(792\) | 1.03888e55 | − | 2.20503e55i | 0.872540 | − | 1.85198i | ||||
\(793\) | −1.38042e55 | −1.13193 | ||||||||
\(794\) | −1.60178e55 | − | 2.36786e54i | −1.28237 | − | 0.189569i | ||||
\(795\) | 3.37305e54i | 0.263662i | ||||||||
\(796\) | 5.80511e54 | − | 1.92057e55i | 0.443060 | − | 1.46582i | ||||
\(797\) | 2.39742e55 | 1.78663 | 0.893317 | − | 0.449428i | \(-0.148372\pi\) | ||||
0.893317 | + | 0.449428i | \(0.148372\pi\) | |||||||
\(798\) | −3.30479e54 | + | 2.23558e55i | −0.240486 | + | 1.62680i | ||||
\(799\) | − | 1.57601e54i | − | 0.111988i | ||||||
\(800\) | −4.43783e54 | − | 4.00214e54i | −0.307936 | − | 0.277704i | ||||
\(801\) | −2.74333e55 | −1.85892 | ||||||||
\(802\) | 7.38950e54 | + | 1.09237e54i | 0.488993 | + | 0.0722864i | ||||
\(803\) | 1.44354e55i | 0.932898i | ||||||||
\(804\) | −2.07856e55 | − | 6.28267e54i | −1.31189 | − | 0.396533i | ||||
\(805\) | −3.20060e54 | −0.197292 | ||||||||
\(806\) | 2.10898e54 | − | 1.42665e55i | 0.126971 | − | 0.858917i | ||||
\(807\) | 2.22609e55i | 1.30902i | ||||||||
\(808\) | 1.64557e55 | + | 7.75291e54i | 0.945149 | + | 0.445296i | ||||
\(809\) | 1.05520e55 | 0.591990 | 0.295995 | − | 0.955190i | \(-0.404349\pi\) | ||||
0.295995 | + | 0.955190i | \(0.404349\pi\) | |||||||
\(810\) | 5.94516e55 | + | 8.78857e54i | 3.25798 | + | 0.481618i | ||||
\(811\) | 2.04697e55i | 1.09576i | 0.836557 | + | 0.547879i | \(0.184565\pi\) | ||||
−0.836557 | + | 0.547879i | \(0.815435\pi\) | |||||||
\(812\) | −2.63234e54 | + | 8.70887e54i | −0.137650 | + | 0.455405i | ||||
\(813\) | −7.69956e54 | −0.393320 | ||||||||
\(814\) | 1.05711e54 | − | 7.15096e54i | 0.0527540 | − | 0.356862i | ||||
\(815\) | − | 2.29395e55i | − | 1.11838i | ||||||
\(816\) | −4.17673e54 | + | 6.27795e54i | −0.198941 | + | 0.299023i | ||||
\(817\) | −2.41164e55 | −1.12226 | ||||||||
\(818\) | 1.66652e55 | + | 2.46357e54i | 0.757701 | + | 0.112009i | ||||
\(819\) | − | 6.45061e55i | − | 2.86554i | ||||||
\(820\) | −6.11066e54 | − | 1.84701e54i | −0.265232 | − | 0.0801688i | ||||
\(821\) | 1.31108e55 | 0.556045 | 0.278023 | − | 0.960575i | \(-0.410321\pi\) | ||||
0.278023 | + | 0.960575i | \(0.410321\pi\) | |||||||
\(822\) | 5.57682e52 | − | 3.77253e53i | 0.00231112 | − | 0.0156339i | ||||
\(823\) | 1.52379e55i | 0.617061i | 0.951214 | + | 0.308531i | \(0.0998372\pi\) | ||||
−0.951214 | + | 0.308531i | \(0.900163\pi\) | |||||||
\(824\) | −1.93377e55 | + | 4.10446e55i | −0.765222 | + | 1.62420i | ||||
\(825\) | 1.50909e55 | 0.583568 | ||||||||
\(826\) | −6.16887e54 | − | 9.11928e53i | −0.233123 | − | 0.0344619i | ||||
\(827\) | 7.79385e54i | 0.287837i | 0.989590 | + | 0.143919i | \(0.0459704\pi\) | ||||
−0.989590 | + | 0.143919i | \(0.954030\pi\) | |||||||
\(828\) | 7.55726e54 | − | 2.50025e55i | 0.272764 | − | 0.902417i | ||||
\(829\) | −7.84920e54 | −0.276879 | −0.138439 | − | 0.990371i | \(-0.544209\pi\) | ||||
−0.138439 | + | 0.990371i | \(0.544209\pi\) | |||||||
\(830\) | 4.43770e54 | − | 3.00195e55i | 0.152994 | − | 1.03495i | ||||
\(831\) | − | 4.31638e55i | − | 1.45446i | ||||||
\(832\) | 2.48142e55 | + | 3.00527e55i | 0.817255 | + | 0.989785i | ||||
\(833\) | 2.21184e54 | 0.0712030 | ||||||||
\(834\) | 2.94383e55 | + | 4.35178e54i | 0.926312 | + | 0.136934i | ||||
\(835\) | − | 8.55709e54i | − | 0.263198i | ||||||
\(836\) | 2.44474e55 | + | 7.38945e54i | 0.735043 | + | 0.222174i | ||||
\(837\) | −8.39255e55 | −2.46667 | ||||||||
\(838\) | 7.83002e54 | − | 5.29674e55i | 0.224971 | − | 1.52185i | ||||
\(839\) | 5.17960e55i | 1.45485i | 0.686186 | + | 0.727426i | \(0.259284\pi\) | ||||
−0.686186 | + | 0.727426i | \(0.740716\pi\) | |||||||
\(840\) | −3.86806e55 | − | 1.82239e55i | −1.06215 | − | 0.500421i | ||||
\(841\) | −2.34431e55 | −0.629349 | ||||||||
\(842\) | −8.77651e54 | − | 1.29741e54i | −0.230352 | − | 0.0340523i | ||||
\(843\) | 5.63099e55i | 1.44498i | ||||||||
\(844\) | −5.94040e54 | + | 1.96533e55i | −0.149042 | + | 0.493093i | ||||
\(845\) | 2.01965e55 | 0.495448 | ||||||||
\(846\) | −1.06656e55 | + | 7.21494e55i | −0.255829 | + | 1.73060i | ||||
\(847\) | 1.62084e55i | 0.380151i | ||||||||
\(848\) | 6.37049e54 | + | 4.23830e54i | 0.146100 | + | 0.0972009i | ||||
\(849\) | 9.63812e55 | 2.16146 | ||||||||
\(850\) | −3.42078e54 | − | 5.05685e53i | −0.0750180 | − | 0.0110897i | ||||
\(851\) | − | 7.74607e54i | − | 0.166119i | ||||||
\(852\) | −1.55743e56 | − | 4.70749e55i | −3.26630 | − | 0.987272i | ||||
\(853\) | −7.94807e55 | −1.63016 | −0.815080 | − | 0.579349i | \(-0.803307\pi\) | ||||
−0.815080 | + | 0.579349i | \(0.803307\pi\) | |||||||
\(854\) | 5.02406e54 | − | 3.39860e55i | 0.100776 | − | 0.681712i | ||||
\(855\) | 1.19388e56i | 2.34209i | ||||||||
\(856\) | −1.77417e55 | + | 3.76571e55i | −0.340403 | + | 0.722512i | ||||
\(857\) | 8.22446e55 | 1.54338 | 0.771688 | − | 0.636002i | \(-0.219413\pi\) | ||||
0.771688 | + | 0.636002i | \(0.219413\pi\) | |||||||
\(858\) | −9.73611e55 | − | 1.43926e55i | −1.78701 | − | 0.264169i | ||||
\(859\) | − | 7.27918e55i | − | 1.30681i | −0.757008 | − | 0.653405i | \(-0.773340\pi\) | ||
0.757008 | − | 0.653405i | \(-0.226660\pi\) | |||||||
\(860\) | 1.32023e55 | − | 4.36786e55i | 0.231835 | − | 0.767004i | ||||
\(861\) | 3.23579e55 | 0.555802 | ||||||||
\(862\) | −1.41165e55 | + | 9.54931e55i | −0.237186 | + | 1.60448i | ||||
\(863\) | − | 1.16155e56i | − | 1.90911i | −0.298032 | − | 0.954556i | \(-0.596330\pi\) | ||
0.298032 | − | 0.954556i | \(-0.403670\pi\) | |||||||
\(864\) | 1.51893e56 | − | 1.68429e56i | 2.44217 | − | 2.70804i | ||||
\(865\) | −6.77686e55 | −1.06592 | ||||||||
\(866\) | 3.52732e55 | + | 5.21434e54i | 0.542757 | + | 0.0802342i | ||||
\(867\) | − | 1.26097e56i | − | 1.89820i | ||||||
\(868\) | 3.43567e55 | + | 1.03846e55i | 0.505984 | + | 0.152939i | ||||
\(869\) | 4.28811e55 | 0.617860 | ||||||||
\(870\) | −9.48917e54 | + | 6.41909e55i | −0.133771 | + | 0.904915i | ||||
\(871\) | 6.49435e55i | 0.895758i | ||||||||
\(872\) | 4.69070e55 | + | 2.20997e55i | 0.633031 | + | 0.298245i | ||||
\(873\) | 2.35791e56 | 3.11355 | ||||||||
\(874\) | 2.70735e55 | + | 4.00220e54i | 0.349806 | + | 0.0517109i | ||||
\(875\) | − | 6.68972e55i | − | 0.845775i | ||||||
\(876\) | −5.97918e55 | + | 1.97816e56i | −0.739714 | + | 2.44728i | ||||
\(877\) | 1.78105e55 | 0.215618 | 0.107809 | − | 0.994172i | \(-0.465617\pi\) | ||||
0.107809 | + | 0.994172i | \(0.465617\pi\) | |||||||
\(878\) | −5.89698e54 | + | 3.98910e55i | −0.0698609 | + | 0.472585i | ||||
\(879\) | 1.11644e56i | 1.29433i | ||||||||
\(880\) | −2.67669e55 | + | 4.02327e55i | −0.303688 | + | 0.456466i | ||||
\(881\) | −3.22754e55 | −0.358368 | −0.179184 | − | 0.983816i | \(-0.557346\pi\) | ||||
−0.179184 | + | 0.983816i | \(0.557346\pi\) | |||||||
\(882\) | −1.01257e56 | − | 1.49686e55i | −1.10033 | − | 0.162659i | ||||
\(883\) | − | 9.47388e55i | − | 1.00757i | −0.863830 | − | 0.503784i | \(-0.831941\pi\) | ||
0.863830 | − | 0.503784i | \(-0.168059\pi\) | |||||||
\(884\) | 2.15873e55 | + | 6.52498e54i | 0.224701 | + | 0.0679181i | ||||
\(885\) | −4.44756e55 | −0.453106 | ||||||||
\(886\) | 1.78374e55 | − | 1.20664e56i | 0.177865 | − | 1.20320i | ||||
\(887\) | − | 8.28656e55i | − | 0.808771i | −0.914589 | − | 0.404386i | \(-0.867485\pi\) | ||
0.914589 | − | 0.404386i | \(-0.132515\pi\) | |||||||
\(888\) | 4.41055e55 | − | 9.36147e55i | 0.421353 | − | 0.894330i | ||||
\(889\) | −1.05927e56 | −0.990541 | ||||||||
\(890\) | 5.38015e55 | + | 7.95333e54i | 0.492475 | + | 0.0728013i | ||||
\(891\) | 3.44269e56i | 3.08476i | ||||||||
\(892\) | 3.00145e55 | − | 9.93003e55i | 0.263268 | − | 0.871001i | ||||
\(893\) | −7.64183e55 | −0.656175 | ||||||||
\(894\) | 2.52679e55 | − | 1.70928e56i | 0.212401 | − | 1.43682i | ||||
\(895\) | − | 5.40364e55i | − | 0.444681i | ||||||
\(896\) | −8.30214e55 | + | 5.01552e55i | −0.668864 | + | 0.404076i | ||||
\(897\) | −1.05463e56 | −0.831851 | ||||||||
\(898\) | −2.03934e56 | − | 3.01469e55i | −1.57485 | − | 0.232805i | ||||
\(899\) | − | 5.44677e55i | − | 0.411818i | ||||||
\(900\) | 1.53180e56 | + | 4.63001e55i | 1.13395 | + | 0.342748i | ||||
\(901\) | 4.42757e54 | 0.0320918 | ||||||||
\(902\) | 5.34777e54 | − | 3.61758e55i | 0.0379532 | − | 0.256740i | ||||
\(903\) | 2.31292e56i | 1.60728i | ||||||||
\(904\) | −1.81061e55 | − | 8.53050e54i | −0.123204 | − | 0.0580463i | ||||
\(905\) | 1.40344e56 | 0.935127 | ||||||||
\(906\) | −4.89385e55 | − | 7.23445e54i | −0.319312 | − | 0.0472030i | ||||
\(907\) | − | 3.74844e55i | − | 0.239504i | −0.992804 | − | 0.119752i | \(-0.961790\pi\) | ||
0.992804 | − | 0.119752i | \(-0.0382099\pi\) | |||||||
\(908\) | −5.43516e54 | + | 1.79818e55i | −0.0340080 | + | 0.112513i | ||||
\(909\) | −4.87113e56 | −2.98480 | ||||||||
\(910\) | −1.87013e55 | + | 1.26508e56i | −0.112224 | + | 0.759157i | ||||
\(911\) | − | 6.42369e55i | − | 0.377516i | −0.982024 | − | 0.188758i | \(-0.939554\pi\) | ||
0.982024 | − | 0.188758i | \(-0.0604462\pi\) | |||||||
\(912\) | 3.04407e56 | + | 2.02523e56i | 1.75208 | + | 1.16566i | ||||
\(913\) | 1.73835e56 | 0.979925 | ||||||||
\(914\) | −9.43324e55 | − | 1.39449e55i | −0.520815 | − | 0.0769906i | ||||
\(915\) | − | 2.45028e56i | − | 1.32500i | ||||||
\(916\) | 9.65086e55 | + | 2.91707e55i | 0.511154 | + | 0.154501i | ||||
\(917\) | −1.90878e56 | −0.990237 | ||||||||
\(918\) | 1.91922e55 | − | 1.29829e56i | 0.0975247 | − | 0.659721i | ||||
\(919\) | 2.37138e56i | 1.18034i | 0.807280 | + | 0.590169i | \(0.200939\pi\) | ||||
−0.807280 | + | 0.590169i | \(0.799061\pi\) | |||||||
\(920\) | −2.20697e55 | + | 4.68434e55i | −0.107604 | + | 0.228391i | ||||
\(921\) | −7.10317e55 | −0.339250 | ||||||||
\(922\) | 3.91053e56 | + | 5.78083e55i | 1.82957 | + | 0.270460i | ||||
\(923\) | 4.86610e56i | 2.23022i | ||||||||
\(924\) | 7.08696e55 | − | 2.34466e56i | 0.318194 | − | 1.05272i | ||||
\(925\) | 4.74569e55 | 0.208740 | ||||||||
\(926\) | −4.82744e55 | + | 3.26560e56i | −0.208022 | + | 1.40719i | ||||
\(927\) | − | 1.21498e57i | − | 5.12925i | ||||||
\(928\) | 1.09310e56 | + | 9.85787e55i | 0.452116 | + | 0.407729i | ||||
\(929\) | 2.13714e56 | 0.866032 | 0.433016 | − | 0.901386i | \(-0.357449\pi\) | ||||
0.433016 | + | 0.901386i | \(0.357449\pi\) | |||||||
\(930\) | 2.53235e56 | + | 3.74350e55i | 1.00542 | + | 0.148628i | ||||
\(931\) | − | 1.07248e56i | − | 0.417203i | ||||||
\(932\) | −2.66623e56 | − | 8.05895e55i | −1.01624 | − | 0.307168i | ||||
\(933\) | 2.51668e56 | 0.939888 | ||||||||
\(934\) | −1.39426e53 | + | 9.43166e53i | −0.000510214 | + | 0.00345142i | ||||
\(935\) | 2.79623e55i | 0.100266i | ||||||||
\(936\) | −9.44102e56 | − | 4.44803e56i | −3.31725 | − | 1.56288i | ||||
\(937\) | 1.68115e56 | 0.578834 | 0.289417 | − | 0.957203i | \(-0.406539\pi\) | ||||
0.289417 | + | 0.957203i | \(0.406539\pi\) | |||||||
\(938\) | −1.59892e56 | − | 2.36364e55i | −0.539476 | − | 0.0797492i | ||||
\(939\) | 6.78227e56i | 2.24248i | ||||||||
\(940\) | 4.18344e55 | − | 1.38406e56i | 0.135552 | − | 0.448461i | ||||
\(941\) | −5.50586e56 | −1.74832 | −0.874162 | − | 0.485634i | \(-0.838589\pi\) | ||||
−0.874162 | + | 0.485634i | \(0.838589\pi\) | |||||||
\(942\) | −1.17388e55 | + | 7.94087e55i | −0.0365305 | + | 0.247116i | ||||
\(943\) | − | 3.91863e55i | − | 0.119512i | ||||||
\(944\) | −5.58844e55 | + | 8.39985e55i | −0.167041 | + | 0.251075i | ||||
\(945\) | 7.44209e56 | 2.18017 | ||||||||
\(946\) | 2.58582e56 | + | 3.82255e55i | 0.742449 | + | 0.109754i | ||||
\(947\) | 3.71320e56i | 1.04496i | 0.852652 | + | 0.522480i | \(0.174993\pi\) | ||||
−0.852652 | + | 0.522480i | \(0.825007\pi\) | |||||||
\(948\) | 5.87621e56 | + | 1.77614e56i | 1.62084 | + | 0.489913i | ||||
\(949\) | 6.18064e56 | 1.67100 | ||||||||
\(950\) | −2.45198e55 | + | 1.65868e56i | −0.0649783 | + | 0.439556i | ||||
\(951\) | 3.42272e56i | 0.889081i | ||||||||
\(952\) | −2.39213e55 | + | 5.07734e55i | −0.0609092 | + | 0.129281i | ||||
\(953\) | −2.83958e56 | −0.708743 | −0.354371 | − | 0.935105i | \(-0.615305\pi\) | ||||
−0.354371 | + | 0.935105i | \(0.615305\pi\) | |||||||
\(954\) | −2.02693e56 | − | 2.99635e55i | −0.495928 | − | 0.0733118i | ||||
\(955\) | 7.81184e55i | 0.187365i | ||||||||
\(956\) | 2.12292e56 | − | 7.02350e56i | 0.499153 | − | 1.65140i | ||||
\(957\) | −3.71713e56 | −0.856802 | ||||||||
\(958\) | 5.82822e55 | − | 3.94259e56i | 0.131702 | − | 0.890915i | ||||
\(959\) | − | 2.83856e54i | − | 0.00628847i | ||||||
\(960\) | −5.33445e56 | + | 4.40460e56i | −1.15861 | + | 0.956650i | ||||
\(961\) | 2.54741e56 | 0.542444 | ||||||||
\(962\) | −3.06174e56 | − | 4.52609e55i | −0.639208 | − | 0.0944923i | ||||
\(963\) | − | 1.11470e57i | − | 2.28171i | ||||||
\(964\) | −7.86059e56 | − | 2.37594e56i | −1.57758 | − | 0.476839i | ||||
\(965\) | 1.78795e56 | 0.351833 | ||||||||
\(966\) | 3.83837e55 | − | 2.59652e56i | 0.0740596 | − | 0.500987i | ||||
\(967\) | − | 2.40616e56i | − | 0.455221i | −0.973752 | − | 0.227610i | \(-0.926909\pi\) | ||
0.973752 | − | 0.227610i | \(-0.0730913\pi\) | |||||||
\(968\) | 2.37224e56 | + | 1.11765e56i | 0.440075 | + | 0.207336i | ||||
\(969\) | 2.11567e56 | 0.384854 | ||||||||
\(970\) | −4.62427e56 | − | 6.83594e55i | −0.824860 | − | 0.121937i | ||||
\(971\) | 7.55418e55i | 0.132136i | 0.997815 | + | 0.0660681i | \(0.0210455\pi\) | ||||
−0.997815 | + | 0.0660681i | \(0.978955\pi\) | |||||||
\(972\) | −8.10870e56 | + | 2.68269e57i | −1.39089 | + | 4.60163i | ||||
\(973\) | 2.21503e56 | 0.372593 | ||||||||
\(974\) | 8.04810e55 | − | 5.44426e56i | 0.132762 | − | 0.898088i | ||||
\(975\) | − | 6.46130e56i | − | 1.04528i | ||||||
\(976\) | −4.62771e56 | − | 3.07883e56i | −0.734209 | − | 0.488471i | ||||
\(977\) | −1.07830e57 | −1.67781 | −0.838905 | − | 0.544278i | \(-0.816804\pi\) | ||||
−0.838905 | + | 0.544278i | \(0.816804\pi\) | |||||||
\(978\) | 1.86099e57 | + | 2.75105e56i | 2.83992 | + | 0.419818i | ||||
\(979\) | 3.11550e56i | 0.466291i | ||||||||
\(980\) | 1.94244e56 | + | 5.87121e55i | 0.285136 | + | 0.0861851i | ||||
\(981\) | −1.38852e57 | −1.99913 | ||||||||
\(982\) | −1.81772e56 | + | 1.22962e57i | −0.256690 | + | 1.73642i | ||||
\(983\) | 4.14254e56i | 0.573786i | 0.957963 | + | 0.286893i | \(0.0926224\pi\) | ||||
−0.957963 | + | 0.286893i | \(0.907378\pi\) | |||||||
\(984\) | 2.23124e56 | − | 4.73584e56i | 0.303137 | − | 0.643414i | ||||
\(985\) | 3.01203e55 | 0.0401394 | ||||||||
\(986\) | 8.42590e55 | + | 1.24558e55i | 0.110142 | + | 0.0162821i | ||||
\(987\) | 7.32901e56i | 0.939765i | ||||||||
\(988\) | 3.16385e56 | − | 1.04673e57i | 0.397955 | − | 1.31660i | ||||
\(989\) | 2.80101e56 | 0.345609 | ||||||||
\(990\) | 1.89234e56 | − | 1.28010e57i | 0.229050 | − | 1.54945i | ||||
\(991\) | 4.03281e56i | 0.478860i | 0.970914 | + | 0.239430i | \(0.0769606\pi\) | ||||
−0.970914 | + | 0.239430i | \(0.923039\pi\) | |||||||
\(992\) | 3.88895e56 | − | 4.31232e56i | 0.453013 | − | 0.502330i | ||||
\(993\) | 1.42306e57 | 1.62625 | ||||||||
\(994\) | −1.19804e57 | − | 1.77103e56i | −1.34317 | − | 0.198557i | ||||
\(995\) | − | 1.06514e57i | − | 1.17157i | ||||||
\(996\) | 2.38215e57 | + | 7.20028e56i | 2.57064 | + | 0.777002i | ||||
\(997\) | 5.30858e56 | 0.562044 | 0.281022 | − | 0.959701i | \(-0.409327\pi\) | ||||
0.281022 | + | 0.959701i | \(0.409327\pi\) | |||||||
\(998\) | −4.61896e54 | + | 3.12456e55i | −0.00479804 | + | 0.0324570i | ||||
\(999\) | 1.80113e57i | 1.83570i |
(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 | 4.39.b.a.3.18 | yes | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.17 | ✓ | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.17 | ✓ | 18 | 4.3 | odd | 2 | inner | |
4.39.b.a.3.18 | yes | 18 | 1.1 | even | 1 | trivial |