Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,10,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(4.12028668931\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 59x^{6} - 313x^{5} - 315x^{4} - 92091x^{3} + 1261649x^{2} - 16074123x + 251007534 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{28}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.6 | ||
Root | \(-2.43481 - 11.2224i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.10.b.a.5.5 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.86961 | + | 22.4447i | 0.126820 | + | 0.991926i | ||||
\(3\) | − | 247.414i | − | 1.76351i | −0.471704 | − | 0.881757i | \(-0.656361\pi\) | ||
0.471704 | − | 0.881757i | \(-0.343639\pi\) | |||||||
\(4\) | −495.531 | + | 128.815i | −0.967833 | + | 0.251592i | ||||
\(5\) | − | 1417.55i | − | 1.01432i | −0.861853 | − | 0.507159i | \(-0.830696\pi\) | ||
0.861853 | − | 0.507159i | \(-0.169304\pi\) | |||||||
\(6\) | 5553.14 | − | 709.983i | 1.74928 | − | 0.223649i | ||||
\(7\) | 5087.57 | 0.800883 | 0.400441 | − | 0.916322i | \(-0.368857\pi\) | ||||
0.400441 | + | 0.916322i | \(0.368857\pi\) | |||||||
\(8\) | −4313.20 | − | 10752.4i | −0.372302 | − | 0.928112i | ||||
\(9\) | −41530.8 | −2.10998 | ||||||||
\(10\) | 31816.6 | − | 4067.83i | 1.00613 | − | 0.128636i | ||||
\(11\) | 14811.2i | 0.305016i | 0.988302 | + | 0.152508i | \(0.0487349\pi\) | ||||
−0.988302 | + | 0.152508i | \(0.951265\pi\) | |||||||
\(12\) | 31870.7 | + | 122601.i | 0.443687 | + | 1.70679i | ||||
\(13\) | − | 64089.8i | − | 0.622363i | −0.950351 | − | 0.311181i | \(-0.899275\pi\) | ||
0.950351 | − | 0.311181i | \(-0.100725\pi\) | |||||||
\(14\) | 14599.3 | + | 114189.i | 0.101568 | + | 0.794416i | ||||
\(15\) | −350723. | −1.78876 | ||||||||
\(16\) | 228957. | − | 127664.i | 0.873403 | − | 0.486999i | ||||
\(17\) | 251342. | 0.729868 | 0.364934 | − | 0.931033i | \(-0.381092\pi\) | ||||
0.364934 | + | 0.931033i | \(0.381092\pi\) | |||||||
\(18\) | −119177. | − | 932147.i | −0.267588 | − | 2.09295i | ||||
\(19\) | 511568.i | 0.900558i | 0.892888 | + | 0.450279i | \(0.148676\pi\) | ||||
−0.892888 | + | 0.450279i | \(0.851324\pi\) | |||||||
\(20\) | 182602. | + | 702441.i | 0.255195 | + | 0.981691i | ||||
\(21\) | − | 1.25874e6i | − | 1.41237i | ||||||
\(22\) | −332432. | + | 42502.3i | −0.302553 | + | 0.0386821i | ||||
\(23\) | 1.96905e6 | 1.46718 | 0.733588 | − | 0.679594i | \(-0.237844\pi\) | ||||
0.733588 | + | 0.679594i | \(0.237844\pi\) | |||||||
\(24\) | −2.66030e6 | + | 1.06715e6i | −1.63674 | + | 0.656559i | ||||
\(25\) | −56329.6 | −0.0288408 | ||||||||
\(26\) | 1.43848e6 | − | 183913.i | 0.617337 | − | 0.0789281i | ||||
\(27\) | 5.40545e6i | 1.95747i | ||||||||
\(28\) | −2.52105e6 | + | 655356.i | −0.775121 | + | 0.201496i | ||||
\(29\) | − | 2.16116e6i | − | 0.567409i | −0.958912 | − | 0.283705i | \(-0.908436\pi\) | ||
0.958912 | − | 0.283705i | \(-0.0915636\pi\) | |||||||
\(30\) | −1.00644e6 | − | 7.87187e6i | −0.226851 | − | 1.77432i | ||||
\(31\) | −3.03997e6 | −0.591210 | −0.295605 | − | 0.955310i | \(-0.595521\pi\) | ||||
−0.295605 | + | 0.955310i | \(0.595521\pi\) | |||||||
\(32\) | 3.52240e6 | + | 4.77253e6i | 0.593832 | + | 0.804589i | ||||
\(33\) | 3.66449e6 | 0.537899 | ||||||||
\(34\) | 721253. | + | 5.64129e6i | 0.0925620 | + | 0.723975i | ||||
\(35\) | − | 7.21189e6i | − | 0.812350i | ||||||
\(36\) | 2.05798e7 | − | 5.34980e6i | 2.04211 | − | 0.530855i | ||||
\(37\) | − | 8.74315e6i | − | 0.766938i | −0.923554 | − | 0.383469i | \(-0.874729\pi\) | ||
0.923554 | − | 0.383469i | \(-0.125271\pi\) | |||||||
\(38\) | −1.14820e7 | + | 1.46800e6i | −0.893287 | + | 0.114209i | ||||
\(39\) | −1.58567e7 | −1.09755 | ||||||||
\(40\) | −1.52421e7 | + | 6.11419e6i | −0.941400 | + | 0.377632i | ||||
\(41\) | −1.48418e7 | −0.820274 | −0.410137 | − | 0.912024i | \(-0.634519\pi\) | ||||
−0.410137 | + | 0.912024i | \(0.634519\pi\) | |||||||
\(42\) | 2.82520e7 | − | 3.61208e6i | 1.40096 | − | 0.179117i | ||||
\(43\) | − | 153307.i | − | 0.00683840i | −0.999994 | − | 0.00341920i | \(-0.998912\pi\) | ||
0.999994 | − | 0.00341920i | \(-0.00108837\pi\) | |||||||
\(44\) | −1.90790e6 | − | 7.33938e6i | −0.0767396 | − | 0.295204i | ||||
\(45\) | 5.88721e7i | 2.14019i | ||||||||
\(46\) | 5.65042e6 | + | 4.41949e7i | 0.186068 | + | 1.45533i | ||||
\(47\) | 5.17595e7 | 1.54721 | 0.773605 | − | 0.633668i | \(-0.218451\pi\) | ||||
0.773605 | + | 0.633668i | \(0.218451\pi\) | |||||||
\(48\) | −3.15858e7 | − | 5.66473e7i | −0.858829 | − | 1.54026i | ||||
\(49\) | −1.44703e7 | −0.358587 | ||||||||
\(50\) | −161644. | − | 1.26430e6i | −0.00365759 | − | 0.0286079i | ||||
\(51\) | − | 6.21855e7i | − | 1.28713i | ||||||
\(52\) | 8.25574e6 | + | 3.17584e7i | 0.156582 | + | 0.602343i | ||||
\(53\) | − | 4.26277e7i | − | 0.742080i | −0.928617 | − | 0.371040i | \(-0.879001\pi\) | ||
0.928617 | − | 0.371040i | \(-0.120999\pi\) | |||||||
\(54\) | −1.21324e8 | + | 1.55116e7i | −1.94166 | + | 0.248247i | ||||
\(55\) | 2.09956e7 | 0.309383 | ||||||||
\(56\) | −2.19437e7 | − | 5.47035e7i | −0.298170 | − | 0.743309i | ||||
\(57\) | 1.26569e8 | 1.58815 | ||||||||
\(58\) | 4.85067e7 | − | 6.20170e6i | 0.562828 | − | 0.0719589i | ||||
\(59\) | − | 1.15231e7i | − | 0.123804i | −0.998082 | − | 0.0619021i | \(-0.980283\pi\) | ||
0.998082 | − | 0.0619021i | \(-0.0197167\pi\) | |||||||
\(60\) | 1.73794e8 | − | 4.51784e7i | 1.73123 | − | 0.450039i | ||||
\(61\) | 1.95800e8i | 1.81062i | 0.424748 | + | 0.905312i | \(0.360363\pi\) | ||||
−0.424748 | + | 0.905312i | \(0.639637\pi\) | |||||||
\(62\) | −8.72353e6 | − | 6.82312e7i | −0.0749773 | − | 0.586436i | ||||
\(63\) | −2.11291e8 | −1.68985 | ||||||||
\(64\) | −9.70103e7 | + | 9.27545e7i | −0.722783 | + | 0.691075i | ||||
\(65\) | −9.08506e7 | −0.631274 | ||||||||
\(66\) | 1.05157e7 | + | 8.22485e7i | 0.0682165 | + | 0.533556i | ||||
\(67\) | 1.69718e8i | 1.02894i | 0.857508 | + | 0.514470i | \(0.172011\pi\) | ||||
−0.857508 | + | 0.514470i | \(0.827989\pi\) | |||||||
\(68\) | −1.24547e8 | + | 3.23766e7i | −0.706390 | + | 0.183629i | ||||
\(69\) | − | 4.87172e8i | − | 2.58739i | ||||||
\(70\) | 1.61869e8 | − | 2.06953e7i | 0.805790 | − | 0.103022i | ||||
\(71\) | 2.23552e8 | 1.04404 | 0.522018 | − | 0.852934i | \(-0.325179\pi\) | ||||
0.522018 | + | 0.852934i | \(0.325179\pi\) | |||||||
\(72\) | 1.79131e8 | + | 4.46555e8i | 0.785550 | + | 1.95830i | ||||
\(73\) | −4.10130e8 | −1.69032 | −0.845159 | − | 0.534514i | \(-0.820495\pi\) | ||||
−0.845159 | + | 0.534514i | \(0.820495\pi\) | |||||||
\(74\) | 1.96238e8 | − | 2.50895e7i | 0.760746 | − | 0.0972632i | ||||
\(75\) | 1.39367e7i | 0.0508611i | ||||||||
\(76\) | −6.58977e7 | − | 2.53497e8i | −0.226574 | − | 0.871590i | ||||
\(77\) | 7.53528e7i | 0.244282i | ||||||||
\(78\) | −4.55026e7 | − | 3.55899e8i | −0.139191 | − | 1.08868i | ||||
\(79\) | 2.51240e7 | 0.0725716 | 0.0362858 | − | 0.999341i | \(-0.488447\pi\) | ||||
0.0362858 | + | 0.999341i | \(0.488447\pi\) | |||||||
\(80\) | −1.80970e8 | − | 3.24559e8i | −0.493972 | − | 0.885908i | ||||
\(81\) | 5.19935e8 | 1.34204 | ||||||||
\(82\) | −4.25902e7 | − | 3.33120e8i | −0.104027 | − | 0.813651i | ||||
\(83\) | 4.73174e8i | 1.09438i | 0.837008 | + | 0.547191i | \(0.184303\pi\) | ||||
−0.837008 | + | 0.547191i | \(0.815697\pi\) | |||||||
\(84\) | 1.62144e8 | + | 6.23742e8i | 0.355341 | + | 1.36694i | ||||
\(85\) | − | 3.56290e8i | − | 0.740318i | ||||||
\(86\) | 3.44094e6 | − | 439932.i | 0.00678318 | − | 0.000867247i | ||||
\(87\) | −5.34702e8 | −1.00063 | ||||||||
\(88\) | 1.59255e8 | − | 6.38836e7i | 0.283089 | − | 0.113558i | ||||
\(89\) | 8.45560e8 | 1.42853 | 0.714265 | − | 0.699875i | \(-0.246761\pi\) | ||||
0.714265 | + | 0.699875i | \(0.246761\pi\) | |||||||
\(90\) | −1.32137e9 | + | 1.68940e8i | −2.12291 | + | 0.271420i | ||||
\(91\) | − | 3.26061e8i | − | 0.498439i | ||||||
\(92\) | −9.75726e8 | + | 2.53644e8i | −1.41998 | + | 0.369130i | ||||
\(93\) | 7.52131e8i | 1.04261i | ||||||||
\(94\) | 1.48530e8 | + | 1.16173e9i | 0.196217 | + | 1.53472i | ||||
\(95\) | 7.25174e8 | 0.913452 | ||||||||
\(96\) | 1.18079e9 | − | 8.71491e8i | 1.41890 | − | 1.04723i | ||||
\(97\) | −7.97179e8 | −0.914288 | −0.457144 | − | 0.889393i | \(-0.651128\pi\) | ||||
−0.457144 | + | 0.889393i | \(0.651128\pi\) | |||||||
\(98\) | −4.15241e7 | − | 3.24781e8i | −0.0454760 | − | 0.355692i | ||||
\(99\) | − | 6.15119e8i | − | 0.643578i | ||||||
\(100\) | 2.79130e7 | − | 7.25611e6i | 0.0279130 | − | 0.00725611i | ||||
\(101\) | 8.00801e8i | 0.765735i | 0.923803 | + | 0.382868i | \(0.125063\pi\) | ||||
−0.923803 | + | 0.382868i | \(0.874937\pi\) | |||||||
\(102\) | 1.39574e9 | − | 1.78448e8i | 1.27674 | − | 0.163234i | ||||
\(103\) | 8.20324e8 | 0.718155 | 0.359077 | − | 0.933308i | \(-0.383091\pi\) | ||||
0.359077 | + | 0.933308i | \(0.383091\pi\) | |||||||
\(104\) | −6.89118e8 | + | 2.76432e8i | −0.577622 | + | 0.231707i | ||||
\(105\) | −1.78432e9 | −1.43259 | ||||||||
\(106\) | 9.56767e8 | − | 1.22325e8i | 0.736088 | − | 0.0941107i | ||||
\(107\) | − | 5.88826e8i | − | 0.434270i | −0.976142 | − | 0.217135i | \(-0.930329\pi\) | ||
0.976142 | − | 0.217135i | \(-0.0696712\pi\) | |||||||
\(108\) | −6.96305e8 | − | 2.67857e9i | −0.492484 | − | 1.89450i | ||||
\(109\) | − | 8.89549e8i | − | 0.603602i | −0.953371 | − | 0.301801i | \(-0.902412\pi\) | ||
0.953371 | − | 0.301801i | \(-0.0975878\pi\) | |||||||
\(110\) | 6.02492e7 | + | 4.71240e8i | 0.0392360 | + | 0.306885i | ||||
\(111\) | −2.16318e9 | −1.35251 | ||||||||
\(112\) | 1.16484e9 | − | 6.49498e8i | 0.699493 | − | 0.390029i | ||||
\(113\) | 3.64198e8 | 0.210128 | 0.105064 | − | 0.994465i | \(-0.466495\pi\) | ||||
0.105064 | + | 0.994465i | \(0.466495\pi\) | |||||||
\(114\) | 3.63204e8 | + | 2.84081e9i | 0.201409 | + | 1.57532i | ||||
\(115\) | − | 2.79124e9i | − | 1.48818i | ||||||
\(116\) | 2.78391e8 | + | 1.07092e9i | 0.142756 | + | 0.549158i | ||||
\(117\) | 2.66170e9i | 1.31317i | ||||||||
\(118\) | 2.58633e8 | − | 3.30669e7i | 0.122805 | − | 0.0157009i | ||||
\(119\) | 1.27872e9 | 0.584539 | ||||||||
\(120\) | 1.51274e9 | + | 3.77111e9i | 0.665960 | + | 1.66017i | ||||
\(121\) | 2.13858e9 | 0.906965 | ||||||||
\(122\) | −4.39467e9 | + | 5.61870e8i | −1.79600 | + | 0.229624i | ||||
\(123\) | 3.67207e9i | 1.44656i | ||||||||
\(124\) | 1.50640e9 | − | 3.91594e8i | 0.572192 | − | 0.148744i | ||||
\(125\) | − | 2.68881e9i | − | 0.985064i | ||||||
\(126\) | −6.06322e8 | − | 4.74236e9i | −0.214307 | − | 1.67620i | ||||
\(127\) | −3.86422e9 | −1.31809 | −0.659046 | − | 0.752103i | \(-0.729040\pi\) | ||||
−0.659046 | + | 0.752103i | \(0.729040\pi\) | |||||||
\(128\) | −2.36023e9 | − | 1.91120e9i | −0.777159 | − | 0.629305i | ||||
\(129\) | −3.79304e7 | −0.0120596 | ||||||||
\(130\) | −2.60706e8 | − | 2.03912e9i | −0.0800582 | − | 0.626176i | ||||
\(131\) | 3.05723e9i | 0.907000i | 0.891256 | + | 0.453500i | \(0.149825\pi\) | ||||
−0.891256 | + | 0.453500i | \(0.850175\pi\) | |||||||
\(132\) | −1.81587e9 | + | 4.72043e8i | −0.520597 | + | 0.135331i | ||||
\(133\) | 2.60263e9i | 0.721242i | ||||||||
\(134\) | −3.80926e9 | + | 4.87024e8i | −1.02063 | + | 0.130490i | ||||
\(135\) | 7.66251e9 | 1.98550 | ||||||||
\(136\) | −1.08409e9 | − | 2.70252e9i | −0.271731 | − | 0.677399i | ||||
\(137\) | 3.15497e9 | 0.765160 | 0.382580 | − | 0.923922i | \(-0.375036\pi\) | ||||
0.382580 | + | 0.923922i | \(0.375036\pi\) | |||||||
\(138\) | 1.09344e10 | − | 1.39799e9i | 2.56649 | − | 0.328133i | ||||
\(139\) | − | 1.46170e9i | − | 0.332117i | −0.986116 | − | 0.166058i | \(-0.946896\pi\) | ||
0.986116 | − | 0.166058i | \(-0.0531040\pi\) | |||||||
\(140\) | 9.29002e8 | + | 3.57371e9i | 0.204381 | + | 0.786219i | ||||
\(141\) | − | 1.28060e10i | − | 2.72853i | ||||||
\(142\) | 6.41507e8 | + | 5.01756e9i | 0.132405 | + | 1.03561i | ||||
\(143\) | 9.49244e8 | 0.189830 | ||||||||
\(144\) | −9.50877e9 | + | 5.30198e9i | −1.84286 | + | 1.02756i | ||||
\(145\) | −3.06356e9 | −0.575534 | ||||||||
\(146\) | −1.17691e9 | − | 9.20525e9i | −0.214367 | − | 1.67667i | ||||
\(147\) | 3.58015e9i | 0.632373i | ||||||||
\(148\) | 1.12625e9 | + | 4.33250e9i | 0.192956 | + | 0.742268i | ||||
\(149\) | 2.14316e9i | 0.356218i | 0.984011 | + | 0.178109i | \(0.0569980\pi\) | ||||
−0.984011 | + | 0.178109i | \(0.943002\pi\) | |||||||
\(150\) | −3.12806e8 | + | 3.99931e7i | −0.0504504 | + | 0.00645021i | ||||
\(151\) | −4.26252e9 | −0.667222 | −0.333611 | − | 0.942711i | \(-0.608267\pi\) | ||||
−0.333611 | + | 0.942711i | \(0.608267\pi\) | |||||||
\(152\) | 5.50058e9 | − | 2.20650e9i | 0.835819 | − | 0.335279i | ||||
\(153\) | −1.04384e10 | −1.54001 | ||||||||
\(154\) | −1.69127e9 | + | 2.16233e8i | −0.242309 | + | 0.0309798i | ||||
\(155\) | 4.30931e9i | 0.599674i | ||||||||
\(156\) | 7.85749e9 | − | 2.04259e9i | 1.06224 | − | 0.276134i | ||||
\(157\) | 1.08699e10i | 1.42783i | 0.700232 | + | 0.713915i | \(0.253080\pi\) | ||||
−0.700232 | + | 0.713915i | \(0.746920\pi\) | |||||||
\(158\) | 7.20961e7 | + | 5.63901e8i | 0.00920354 | + | 0.0719856i | ||||
\(159\) | −1.05467e10 | −1.30867 | ||||||||
\(160\) | 6.76532e9 | − | 4.99318e9i | 0.816109 | − | 0.602334i | ||||
\(161\) | 1.00177e10 | 1.17504 | ||||||||
\(162\) | 1.49201e9 | + | 1.16698e10i | 0.170198 | + | 1.33121i | ||||
\(163\) | − | 4.36394e9i | − | 0.484211i | −0.970250 | − | 0.242105i | \(-0.922162\pi\) | ||
0.970250 | − | 0.242105i | \(-0.0778380\pi\) | |||||||
\(164\) | 7.35456e9 | − | 1.91185e9i | 0.793888 | − | 0.206375i | ||||
\(165\) | − | 5.19461e9i | − | 0.545601i | ||||||
\(166\) | −1.06203e10 | + | 1.35783e9i | −1.08555 | + | 0.138790i | ||||
\(167\) | −7.71676e8 | −0.0767734 | −0.0383867 | − | 0.999263i | \(-0.512222\pi\) | ||||
−0.0383867 | + | 0.999263i | \(0.512222\pi\) | |||||||
\(168\) | −1.35344e10 | + | 5.42918e9i | −1.31084 | + | 0.525827i | ||||
\(169\) | 6.49700e9 | 0.612665 | ||||||||
\(170\) | 7.99683e9 | − | 1.02241e9i | 0.734341 | − | 0.0938872i | ||||
\(171\) | − | 2.12458e10i | − | 1.90016i | ||||||
\(172\) | 1.97483e7 | + | 7.59684e7i | 0.00172049 | + | 0.00661843i | ||||
\(173\) | 1.47368e9i | 0.125082i | 0.998042 | + | 0.0625411i | \(0.0199204\pi\) | ||||
−0.998042 | + | 0.0625411i | \(0.980080\pi\) | |||||||
\(174\) | −1.53439e9 | − | 1.20012e10i | −0.126901 | − | 0.992555i | ||||
\(175\) | −2.86581e8 | −0.0230981 | ||||||||
\(176\) | 1.89085e9 | + | 3.39112e9i | 0.148542 | + | 0.266401i | ||||
\(177\) | −2.85098e9 | −0.218331 | ||||||||
\(178\) | 2.42643e9 | + | 1.89784e10i | 0.181166 | + | 1.41700i | ||||
\(179\) | − | 1.18045e9i | − | 0.0859429i | −0.999076 | − | 0.0429714i | \(-0.986318\pi\) | ||
0.999076 | − | 0.0429714i | \(-0.0136825\pi\) | |||||||
\(180\) | −7.58362e9 | − | 2.91729e10i | −0.538456 | − | 2.07135i | ||||
\(181\) | 1.33366e10i | 0.923616i | 0.886980 | + | 0.461808i | \(0.152799\pi\) | ||||
−0.886980 | + | 0.461808i | \(0.847201\pi\) | |||||||
\(182\) | 7.31834e9 | − | 9.35668e8i | 0.494415 | − | 0.0632122i | ||||
\(183\) | 4.84437e10 | 3.19306 | ||||||||
\(184\) | −8.49293e9 | − | 2.11720e10i | −0.546232 | − | 1.36170i | ||||
\(185\) | −1.23939e10 | −0.777919 | ||||||||
\(186\) | −1.68814e10 | + | 2.15833e9i | −1.03419 | + | 0.132224i | ||||
\(187\) | 3.72266e9i | 0.222621i | ||||||||
\(188\) | −2.56484e10 | + | 6.66741e9i | −1.49744 | + | 0.389266i | ||||
\(189\) | 2.75006e10i | 1.56770i | ||||||||
\(190\) | 2.08097e9 | + | 1.62763e10i | 0.115844 | + | 0.906077i | ||||
\(191\) | −2.67293e10 | −1.45324 | −0.726619 | − | 0.687040i | \(-0.758910\pi\) | ||||
−0.726619 | + | 0.687040i | \(0.758910\pi\) | |||||||
\(192\) | 2.29488e10 | + | 2.40017e10i | 1.21872 | + | 1.27464i | ||||
\(193\) | −1.13253e10 | −0.587548 | −0.293774 | − | 0.955875i | \(-0.594911\pi\) | ||||
−0.293774 | + | 0.955875i | \(0.594911\pi\) | |||||||
\(194\) | −2.28759e9 | − | 1.78924e10i | −0.115950 | − | 0.906905i | ||||
\(195\) | 2.24777e10i | 1.11326i | ||||||||
\(196\) | 7.17047e9 | − | 1.86399e9i | 0.347052 | − | 0.0902177i | ||||
\(197\) | − | 3.97475e10i | − | 1.88024i | −0.340850 | − | 0.940118i | \(-0.610715\pi\) | ||
0.340850 | − | 0.940118i | \(-0.389285\pi\) | |||||||
\(198\) | 1.38062e10 | − | 1.76515e9i | 0.638381 | − | 0.0816186i | ||||
\(199\) | 2.07651e10 | 0.938630 | 0.469315 | − | 0.883031i | \(-0.344501\pi\) | ||||
0.469315 | + | 0.883031i | \(0.344501\pi\) | |||||||
\(200\) | 2.42961e8 | + | 6.05678e8i | 0.0107375 | + | 0.0267674i | ||||
\(201\) | 4.19905e10 | 1.81455 | ||||||||
\(202\) | −1.79738e10 | + | 2.29799e9i | −0.759552 | + | 0.0971107i | ||||
\(203\) | − | 1.09951e10i | − | 0.454428i | ||||||
\(204\) | 8.01044e9 | + | 3.08148e10i | 0.323833 | + | 1.24573i | ||||
\(205\) | 2.10390e10i | 0.832018i | ||||||||
\(206\) | 2.35401e9 | + | 1.84120e10i | 0.0910765 | + | 0.712356i | ||||
\(207\) | −8.17763e10 | −3.09572 | ||||||||
\(208\) | −8.18194e9 | − | 1.46738e10i | −0.303090 | − | 0.543573i | ||||
\(209\) | −7.57691e9 | −0.274684 | ||||||||
\(210\) | −5.12032e9 | − | 4.00487e10i | −0.181681 | − | 1.42102i | ||||
\(211\) | − | 5.11435e10i | − | 1.77631i | −0.459541 | − | 0.888157i | \(-0.651986\pi\) | ||
0.459541 | − | 0.888157i | \(-0.348014\pi\) | |||||||
\(212\) | 5.49110e9 | + | 2.11233e10i | 0.186702 | + | 0.718210i | ||||
\(213\) | − | 5.53099e10i | − | 1.84117i | ||||||
\(214\) | 1.32160e10 | − | 1.68970e9i | 0.430763 | − | 0.0550742i | ||||
\(215\) | −2.17321e8 | −0.00693631 | ||||||||
\(216\) | 5.81216e10 | − | 2.33148e10i | 1.81675 | − | 0.728769i | ||||
\(217\) | −1.54660e10 | −0.473490 | ||||||||
\(218\) | 1.99657e10 | − | 2.55266e9i | 0.598728 | − | 0.0765489i | ||||
\(219\) | 1.01472e11i | 2.98090i | ||||||||
\(220\) | −1.04040e10 | + | 2.70455e9i | −0.299431 | + | 0.0778383i | ||||
\(221\) | − | 1.61084e10i | − | 0.454243i | ||||||
\(222\) | −6.20749e9 | − | 4.85520e10i | −0.171525 | − | 1.34159i | ||||
\(223\) | 4.79011e10 | 1.29710 | 0.648550 | − | 0.761172i | \(-0.275376\pi\) | ||||
0.648550 | + | 0.761172i | \(0.275376\pi\) | |||||||
\(224\) | 1.79204e10 | + | 2.42806e10i | 0.475590 | + | 0.644382i | ||||
\(225\) | 2.33941e9 | 0.0608535 | ||||||||
\(226\) | 1.04511e9 | + | 8.17432e9i | 0.0266485 | + | 0.208432i | ||||
\(227\) | 4.51527e10i | 1.12867i | 0.825545 | + | 0.564336i | \(0.190868\pi\) | ||||
−0.825545 | + | 0.564336i | \(0.809132\pi\) | |||||||
\(228\) | −6.27189e10 | + | 1.63040e10i | −1.53706 | + | 0.399566i | ||||
\(229\) | 1.30792e10i | 0.314282i | 0.987576 | + | 0.157141i | \(0.0502278\pi\) | ||||
−0.987576 | + | 0.157141i | \(0.949772\pi\) | |||||||
\(230\) | 6.26485e10 | − | 8.00977e9i | 1.47617 | − | 0.188732i | ||||
\(231\) | 1.86433e10 | 0.430794 | ||||||||
\(232\) | −2.32377e10 | + | 9.32154e9i | −0.526619 | + | 0.211247i | ||||
\(233\) | −7.90446e10 | −1.75700 | −0.878498 | − | 0.477746i | \(-0.841454\pi\) | ||||
−0.878498 | + | 0.477746i | \(0.841454\pi\) | |||||||
\(234\) | −5.97410e10 | + | 7.63804e9i | −1.30257 | + | 0.166537i | ||||
\(235\) | − | 7.33717e10i | − | 1.56936i | ||||||
\(236\) | 1.48435e9 | + | 5.71005e9i | 0.0311482 | + | 0.119822i | ||||
\(237\) | − | 6.21603e9i | − | 0.127981i | ||||||
\(238\) | 3.66942e9 | + | 2.87004e10i | 0.0741313 | + | 0.579819i | ||||
\(239\) | 1.26518e10 | 0.250819 | 0.125410 | − | 0.992105i | \(-0.459975\pi\) | ||||
0.125410 | + | 0.992105i | \(0.459975\pi\) | |||||||
\(240\) | −8.03005e10 | + | 4.47746e10i | −1.56231 | + | 0.871126i | ||||
\(241\) | 5.85645e10 | 1.11830 | 0.559149 | − | 0.829067i | \(-0.311128\pi\) | ||||
0.559149 | + | 0.829067i | \(0.311128\pi\) | |||||||
\(242\) | 6.13689e9 | + | 4.79998e10i | 0.115021 | + | 0.899642i | ||||
\(243\) | − | 2.22438e10i | − | 0.409243i | ||||||
\(244\) | −2.52220e10 | − | 9.70248e10i | −0.455539 | − | 1.75238i | ||||
\(245\) | 2.05124e10i | 0.363721i | ||||||||
\(246\) | −8.24186e10 | + | 1.05374e10i | −1.43488 | + | 0.183454i | ||||
\(247\) | 3.27862e10 | 0.560474 | ||||||||
\(248\) | 1.31120e10 | + | 3.26869e10i | 0.220108 | + | 0.548709i | ||||
\(249\) | 1.17070e11 | 1.92996 | ||||||||
\(250\) | 6.03495e10 | − | 7.71583e9i | 0.977111 | − | 0.124926i | ||||
\(251\) | 6.88194e10i | 1.09441i | 0.837000 | + | 0.547204i | \(0.184308\pi\) | ||||
−0.837000 | + | 0.547204i | \(0.815692\pi\) | |||||||
\(252\) | 1.04701e11 | − | 2.72175e10i | 1.63549 | − | 0.425153i | ||||
\(253\) | 2.91640e10i | 0.447512i | ||||||||
\(254\) | −1.10888e10 | − | 8.67314e10i | −0.167161 | − | 1.30745i | ||||
\(255\) | −8.81512e10 | −1.30556 | ||||||||
\(256\) | 3.61234e10 | − | 5.84591e10i | 0.525664 | − | 0.850692i | ||||
\(257\) | −1.19348e10 | −0.170654 | −0.0853271 | − | 0.996353i | \(-0.527194\pi\) | ||||
−0.0853271 | + | 0.996353i | \(0.527194\pi\) | |||||||
\(258\) | −1.08845e8 | − | 8.51336e8i | −0.00152940 | − | 0.0119622i | ||||
\(259\) | − | 4.44814e10i | − | 0.614227i | ||||||
\(260\) | 4.50192e10 | − | 1.17029e10i | 0.610968 | − | 0.158824i | ||||
\(261\) | 8.97548e10i | 1.19722i | ||||||||
\(262\) | −6.86187e10 | + | 8.77307e9i | −0.899677 | + | 0.115026i | ||||
\(263\) | 3.19598e10 | 0.411911 | 0.205956 | − | 0.978561i | \(-0.433970\pi\) | ||||
0.205956 | + | 0.978561i | \(0.433970\pi\) | |||||||
\(264\) | −1.58057e10 | − | 3.94021e10i | −0.200261 | − | 0.499231i | ||||
\(265\) | −6.04270e10 | −0.752705 | ||||||||
\(266\) | −5.84154e10 | + | 7.46855e9i | −0.715418 | + | 0.0914680i | ||||
\(267\) | − | 2.09204e11i | − | 2.51923i | ||||||
\(268\) | −2.18622e10 | − | 8.41003e10i | −0.258874 | − | 0.995843i | ||||
\(269\) | − | 7.08498e10i | − | 0.824999i | −0.910958 | − | 0.412500i | \(-0.864656\pi\) | ||
0.910958 | − | 0.412500i | \(-0.135344\pi\) | |||||||
\(270\) | 2.19884e10 | + | 1.71983e11i | 0.251801 | + | 1.96947i | ||||
\(271\) | −8.70264e10 | −0.980143 | −0.490071 | − | 0.871682i | \(-0.663029\pi\) | ||||
−0.490071 | + | 0.871682i | \(0.663029\pi\) | |||||||
\(272\) | 5.75465e10 | − | 3.20872e10i | 0.637469 | − | 0.355445i | ||||
\(273\) | −8.06721e10 | −0.879005 | ||||||||
\(274\) | 9.05354e9 | + | 7.08124e10i | 0.0970378 | + | 0.758982i | ||||
\(275\) | − | 8.34307e8i | − | 0.00879688i | ||||||
\(276\) | 6.27552e10 | + | 2.41409e11i | 0.650967 | + | 2.50416i | ||||
\(277\) | 1.55080e11i | 1.58270i | 0.611365 | + | 0.791349i | \(0.290621\pi\) | ||||
−0.611365 | + | 0.791349i | \(0.709379\pi\) | |||||||
\(278\) | 3.28074e10 | − | 4.19450e9i | 0.329435 | − | 0.0421191i | ||||
\(279\) | 1.26252e11 | 1.24744 | ||||||||
\(280\) | −7.75451e10 | + | 3.11064e10i | −0.753951 | + | 0.302439i | ||||
\(281\) | −2.79959e10 | −0.267865 | −0.133933 | − | 0.990990i | \(-0.542761\pi\) | ||||
−0.133933 | + | 0.990990i | \(0.542761\pi\) | |||||||
\(282\) | 2.87428e11 | − | 3.67483e10i | 2.70650 | − | 0.346032i | ||||
\(283\) | 9.14271e10i | 0.847298i | 0.905826 | + | 0.423649i | \(0.139251\pi\) | ||||
−0.905826 | + | 0.423649i | \(0.860749\pi\) | |||||||
\(284\) | −1.10777e11 | + | 2.87969e10i | −1.01045 | + | 0.262672i | ||||
\(285\) | − | 1.79418e11i | − | 1.61089i | ||||||
\(286\) | 2.72396e9 | + | 2.13055e10i | 0.0240743 | + | 0.188298i | ||||
\(287\) | −7.55086e10 | −0.656943 | ||||||||
\(288\) | −1.46288e11 | − | 1.98207e11i | −1.25297 | − | 1.69767i | ||||
\(289\) | −5.54153e10 | −0.467293 | ||||||||
\(290\) | −8.79123e9 | − | 6.87608e10i | −0.0729892 | − | 0.570887i | ||||
\(291\) | 1.97233e11i | 1.61236i | ||||||||
\(292\) | 2.03232e11 | − | 5.28310e10i | 1.63595 | − | 0.425271i | ||||
\(293\) | 9.37104e10i | 0.742819i | 0.928469 | + | 0.371410i | \(0.121125\pi\) | ||||
−0.928469 | + | 0.371410i | \(0.878875\pi\) | |||||||
\(294\) | −8.03555e10 | + | 1.02736e10i | −0.627267 | + | 0.0801977i | ||||
\(295\) | −1.63346e10 | −0.125577 | ||||||||
\(296\) | −9.40098e10 | + | 3.77110e10i | −0.711804 | + | 0.285532i | ||||
\(297\) | −8.00610e10 | −0.597059 | ||||||||
\(298\) | −4.81026e10 | + | 6.15004e9i | −0.353342 | + | 0.0451757i | ||||
\(299\) | − | 1.26196e11i | − | 0.913116i | ||||||
\(300\) | −1.79527e9 | − | 6.90608e9i | −0.0127963 | − | 0.0492251i | ||||
\(301\) | − | 7.79960e8i | − | 0.00547676i | ||||||
\(302\) | −1.22318e10 | − | 9.56711e10i | −0.0846172 | − | 0.661835i | ||||
\(303\) | 1.98130e11 | 1.35038 | ||||||||
\(304\) | 6.53087e10 | + | 1.17127e11i | 0.438571 | + | 0.786550i | ||||
\(305\) | 2.77557e11 | 1.83655 | ||||||||
\(306\) | −2.99542e10 | − | 2.34287e11i | −0.195304 | − | 1.52757i | ||||
\(307\) | − | 1.03026e11i | − | 0.661951i | −0.943639 | − | 0.330976i | \(-0.892622\pi\) | ||
0.943639 | − | 0.330976i | \(-0.107378\pi\) | |||||||
\(308\) | −9.70659e9 | − | 3.73396e10i | −0.0614594 | − | 0.236424i | ||||
\(309\) | − | 2.02960e11i | − | 1.26648i | ||||||
\(310\) | −9.67213e10 | + | 1.23661e10i | −0.594833 | + | 0.0760508i | ||||
\(311\) | −1.43254e11 | −0.868333 | −0.434167 | − | 0.900833i | \(-0.642957\pi\) | ||||
−0.434167 | + | 0.900833i | \(0.642957\pi\) | |||||||
\(312\) | 6.83932e10 | + | 1.70498e11i | 0.408618 | + | 1.01864i | ||||
\(313\) | 2.53850e11 | 1.49495 | 0.747477 | − | 0.664287i | \(-0.231265\pi\) | ||||
0.747477 | + | 0.664287i | \(0.231265\pi\) | |||||||
\(314\) | −2.43972e11 | + | 3.11924e10i | −1.41630 | + | 0.181078i | ||||
\(315\) | 2.99516e11i | 1.71404i | ||||||||
\(316\) | −1.24497e10 | + | 3.23635e9i | −0.0702372 | + | 0.0182585i | ||||
\(317\) | − | 2.17416e11i | − | 1.20927i | −0.796502 | − | 0.604636i | \(-0.793318\pi\) | ||
0.796502 | − | 0.604636i | \(-0.206682\pi\) | |||||||
\(318\) | −3.02650e10 | − | 2.36718e11i | −0.165966 | − | 1.29810i | ||||
\(319\) | 3.20093e10 | 0.173069 | ||||||||
\(320\) | 1.31484e11 | + | 1.37517e11i | 0.700970 | + | 0.733132i | ||||
\(321\) | −1.45684e11 | −0.765841 | ||||||||
\(322\) | 2.87469e10 | + | 2.24844e11i | 0.149018 | + | 1.16555i | ||||
\(323\) | 1.28578e11i | 0.657289i | ||||||||
\(324\) | −2.57644e11 | + | 6.69756e10i | −1.29887 | + | 0.337648i | ||||
\(325\) | 3.61015e9i | 0.0179494i | ||||||||
\(326\) | 9.79474e10 | − | 1.25228e10i | 0.480301 | − | 0.0614077i | ||||
\(327\) | −2.20087e11 | −1.06446 | ||||||||
\(328\) | 6.40157e10 | + | 1.59585e11i | 0.305389 | + | 0.761306i | ||||
\(329\) | 2.63330e11 | 1.23913 | ||||||||
\(330\) | 1.16592e11 | − | 1.49065e10i | 0.541196 | − | 0.0691932i | ||||
\(331\) | 2.98163e10i | 0.136530i | 0.997667 | + | 0.0682650i | \(0.0217463\pi\) | ||||
−0.997667 | + | 0.0682650i | \(0.978254\pi\) | |||||||
\(332\) | −6.09520e10 | − | 2.34472e11i | −0.275338 | − | 1.05918i | ||||
\(333\) | 3.63110e11i | 1.61823i | ||||||||
\(334\) | −2.21441e9 | − | 1.73201e10i | −0.00973642 | − | 0.0761535i | ||||
\(335\) | 2.40584e11 | 1.04367 | ||||||||
\(336\) | −1.60695e11 | − | 2.88197e11i | −0.687822 | − | 1.23357i | ||||
\(337\) | −3.56448e11 | −1.50543 | −0.752716 | − | 0.658346i | \(-0.771257\pi\) | ||||
−0.752716 | + | 0.658346i | \(0.771257\pi\) | |||||||
\(338\) | 1.86439e10 | + | 1.45823e11i | 0.0776982 | + | 0.607718i | ||||
\(339\) | − | 9.01078e10i | − | 0.370564i | ||||||
\(340\) | 4.58956e10 | + | 1.76553e11i | 0.186258 | + | 0.716505i | ||||
\(341\) | − | 4.50255e10i | − | 0.180328i | ||||||
\(342\) | 4.76856e11 | − | 6.09672e10i | 1.88482 | − | 0.240979i | ||||
\(343\) | −2.78920e11 | −1.08807 | ||||||||
\(344\) | −1.64842e9 | + | 6.61245e8i | −0.00634680 | + | 0.00254595i | ||||
\(345\) | −6.90592e11 | −2.62443 | ||||||||
\(346\) | −3.30763e10 | + | 4.22889e9i | −0.124072 | + | 0.0158629i | ||||
\(347\) | 3.73598e10i | 0.138332i | 0.997605 | + | 0.0691659i | \(0.0220338\pi\) | ||||
−0.997605 | + | 0.0691659i | \(0.977966\pi\) | |||||||
\(348\) | 2.64961e11 | − | 6.88778e10i | 0.968448 | − | 0.251752i | ||||
\(349\) | − | 1.15752e11i | − | 0.417653i | −0.977953 | − | 0.208827i | \(-0.933036\pi\) | ||
0.977953 | − | 0.208827i | \(-0.0669644\pi\) | |||||||
\(350\) | −8.22375e8 | − | 6.43222e9i | −0.00292930 | − | 0.0229116i | ||||
\(351\) | 3.46434e11 | 1.21826 | ||||||||
\(352\) | −7.06868e10 | + | 5.21708e10i | −0.245412 | + | 0.181128i | ||||
\(353\) | 1.94182e11 | 0.665614 | 0.332807 | − | 0.942995i | \(-0.392004\pi\) | ||||
0.332807 | + | 0.942995i | \(0.392004\pi\) | |||||||
\(354\) | −8.18121e9 | − | 6.39895e10i | −0.0276887 | − | 0.216568i | ||||
\(355\) | − | 3.16897e11i | − | 1.05899i | ||||||
\(356\) | −4.19001e11 | + | 1.08921e11i | −1.38258 | + | 0.359407i | ||||
\(357\) | − | 3.16373e11i | − | 1.03084i | ||||||
\(358\) | 2.64949e10 | − | 3.38744e9i | 0.0852490 | − | 0.0108993i | ||||
\(359\) | 2.22958e11 | 0.708432 | 0.354216 | − | 0.935164i | \(-0.384748\pi\) | ||||
0.354216 | + | 0.935164i | \(0.384748\pi\) | |||||||
\(360\) | 6.33016e11 | − | 2.53927e11i | 1.98634 | − | 0.796797i | ||||
\(361\) | 6.09863e10 | 0.188995 | ||||||||
\(362\) | −2.99336e11 | + | 3.82708e10i | −0.916158 | + | 0.117133i | ||||
\(363\) | − | 5.29114e11i | − | 1.59945i | ||||||
\(364\) | 4.20016e10 | + | 1.61573e11i | 0.125404 | + | 0.482406i | ||||
\(365\) | 5.81381e11i | 1.71452i | ||||||||
\(366\) | 1.39015e11 | + | 1.08730e12i | 0.404944 | + | 3.16728i | ||||
\(367\) | −2.95151e11 | −0.849272 | −0.424636 | − | 0.905364i | \(-0.639598\pi\) | ||||
−0.424636 | + | 0.905364i | \(0.639598\pi\) | |||||||
\(368\) | 4.50829e11 | − | 2.51377e11i | 1.28144 | − | 0.714513i | ||||
\(369\) | 6.16391e11 | 1.73076 | ||||||||
\(370\) | −3.55656e10 | − | 2.78177e11i | −0.0986558 | − | 0.771638i | ||||
\(371\) | − | 2.16871e11i | − | 0.594319i | ||||||
\(372\) | −9.68860e10 | − | 3.72704e11i | −0.262312 | − | 1.00907i | ||||
\(373\) | − | 1.80321e10i | − | 0.0482343i | −0.999709 | − | 0.0241172i | \(-0.992323\pi\) | ||
0.999709 | − | 0.0241172i | \(-0.00767748\pi\) | |||||||
\(374\) | −8.35541e10 | + | 1.06826e10i | −0.220824 | + | 0.0282328i | ||||
\(375\) | −6.65249e11 | −1.73717 | ||||||||
\(376\) | −2.23249e11 | − | 5.56538e11i | −0.576029 | − | 1.43598i | ||||
\(377\) | −1.38508e11 | −0.353134 | ||||||||
\(378\) | −6.17243e11 | + | 7.89160e10i | −1.55505 | + | 0.198816i | ||||
\(379\) | 6.09778e11i | 1.51808i | 0.651042 | + | 0.759042i | \(0.274332\pi\) | ||||
−0.651042 | + | 0.759042i | \(0.725668\pi\) | |||||||
\(380\) | −3.59346e11 | + | 9.34135e10i | −0.884070 | + | 0.229818i | ||||
\(381\) | 9.56064e11i | 2.32447i | ||||||||
\(382\) | −7.67026e10 | − | 5.99931e11i | −0.184300 | − | 1.44150i | ||||
\(383\) | 1.33302e11 | 0.316549 | 0.158274 | − | 0.987395i | \(-0.449407\pi\) | ||||
0.158274 | + | 0.987395i | \(0.449407\pi\) | |||||||
\(384\) | −4.72858e11 | + | 5.83955e11i | −1.10979 | + | 1.37053i | ||||
\(385\) | 1.06816e11 | 0.247779 | ||||||||
\(386\) | −3.24993e10 | − | 2.54194e11i | −0.0745129 | − | 0.582804i | ||||
\(387\) | 6.36697e9i | 0.0144289i | ||||||||
\(388\) | 3.95026e11 | − | 1.02689e11i | 0.884878 | − | 0.230028i | ||||
\(389\) | 2.05551e10i | 0.0455142i | 0.999741 | + | 0.0227571i | \(0.00724444\pi\) | ||||
−0.999741 | + | 0.0227571i | \(0.992756\pi\) | |||||||
\(390\) | −5.04506e11 | + | 6.45023e10i | −1.10427 | + | 0.141184i | ||||
\(391\) | 4.94905e11 | 1.07084 | ||||||||
\(392\) | 6.24132e10 | + | 1.55590e11i | 0.133503 | + | 0.332809i | ||||
\(393\) | 7.56402e11 | 1.59951 | ||||||||
\(394\) | 8.92122e11 | − | 1.14060e11i | 1.86505 | − | 0.238452i | ||||
\(395\) | − | 3.56146e10i | − | 0.0736107i | ||||||
\(396\) | 7.92367e10 | + | 3.04810e11i | 0.161919 | + | 0.622876i | ||||
\(397\) | − | 5.93486e11i | − | 1.19909i | −0.800339 | − | 0.599547i | \(-0.795347\pi\) | ||
0.800339 | − | 0.599547i | \(-0.204653\pi\) | |||||||
\(398\) | 5.95877e10 | + | 4.66066e11i | 0.119037 | + | 0.931051i | ||||
\(399\) | 6.43929e11 | 1.27192 | ||||||||
\(400\) | −1.28971e10 | + | 7.19125e9i | −0.0251896 | + | 0.0140454i | ||||
\(401\) | −1.00640e12 | −1.94367 | −0.971836 | − | 0.235660i | \(-0.924275\pi\) | ||||
−0.971836 | + | 0.235660i | \(0.924275\pi\) | |||||||
\(402\) | 1.20497e11 | + | 9.42466e11i | 0.230122 | + | 1.79990i | ||||
\(403\) | 1.94831e11i | 0.367947i | ||||||||
\(404\) | −1.03155e11 | − | 3.96822e11i | −0.192653 | − | 0.741104i | ||||
\(405\) | − | 7.37035e11i | − | 1.36126i | ||||||
\(406\) | 2.46781e11 | − | 3.15516e10i | 0.450759 | − | 0.0576307i | ||||
\(407\) | 1.29496e11 | 0.233928 | ||||||||
\(408\) | −6.68643e11 | + | 2.68219e11i | −1.19460 | + | 0.479202i | ||||
\(409\) | −3.40532e11 | −0.601732 | −0.300866 | − | 0.953666i | \(-0.597276\pi\) | ||||
−0.300866 | + | 0.953666i | \(0.597276\pi\) | |||||||
\(410\) | −4.72215e11 | + | 6.03738e10i | −0.825301 | + | 0.105517i | ||||
\(411\) | − | 7.80584e11i | − | 1.34937i | ||||||
\(412\) | −4.06496e11 | + | 1.05670e11i | −0.695054 | + | 0.180682i | ||||
\(413\) | − | 5.86246e10i | − | 0.0991527i | ||||||
\(414\) | −2.34666e11 | − | 1.83545e12i | −0.392599 | − | 3.07072i | ||||
\(415\) | 6.70749e11 | 1.11005 | ||||||||
\(416\) | 3.05871e11 | − | 2.25750e11i | 0.500746 | − | 0.369579i | ||||
\(417\) | −3.61644e11 | −0.585692 | ||||||||
\(418\) | −2.17428e10 | − | 1.70062e11i | −0.0348355 | − | 0.272466i | ||||
\(419\) | 8.47876e11i | 1.34391i | 0.740593 | + | 0.671953i | \(0.234544\pi\) | ||||
−0.740593 | + | 0.671953i | \(0.765456\pi\) | |||||||
\(420\) | 8.84187e11 | − | 2.29848e11i | 1.38651 | − | 0.360429i | ||||
\(421\) | − | 5.27094e11i | − | 0.817747i | −0.912591 | − | 0.408873i | \(-0.865922\pi\) | ||
0.912591 | − | 0.408873i | \(-0.134078\pi\) | |||||||
\(422\) | 1.14790e12 | − | 1.46762e11i | 1.76197 | − | 0.225272i | ||||
\(423\) | −2.14961e12 | −3.26459 | ||||||||
\(424\) | −4.58350e11 | + | 1.83862e11i | −0.688733 | + | 0.276278i | ||||
\(425\) | −1.41580e10 | −0.0210499 | ||||||||
\(426\) | 1.24142e12 | − | 1.58718e11i | 1.82631 | − | 0.233498i | ||||
\(427\) | 9.96145e11i | 1.45010i | ||||||||
\(428\) | 7.58497e10 | + | 2.91781e11i | 0.109259 | + | 0.420301i | ||||
\(429\) | − | 2.34856e11i | − | 0.334768i | ||||||
\(430\) | −6.23627e8 | − | 4.87771e9i | −0.000879664 | − | 0.00688030i | ||||
\(431\) | 1.12919e11 | 0.157622 | 0.0788112 | − | 0.996890i | \(-0.474888\pi\) | ||||
0.0788112 | + | 0.996890i | \(0.474888\pi\) | |||||||
\(432\) | 6.90081e11 | + | 1.23762e12i | 0.953286 | + | 1.70966i | ||||
\(433\) | 9.18037e11 | 1.25506 | 0.627530 | − | 0.778592i | \(-0.284066\pi\) | ||||
0.627530 | + | 0.778592i | \(0.284066\pi\) | |||||||
\(434\) | −4.43815e10 | − | 3.47131e11i | −0.0600480 | − | 0.469666i | ||||
\(435\) | 7.57969e11i | 1.01496i | ||||||||
\(436\) | 1.14588e11 | + | 4.40799e11i | 0.151862 | + | 0.584186i | ||||
\(437\) | 1.00730e12i | 1.32128i | ||||||||
\(438\) | −2.27751e12 | + | 2.91185e11i | −2.95683 | + | 0.378038i | ||||
\(439\) | −9.32700e11 | −1.19854 | −0.599269 | − | 0.800548i | \(-0.704542\pi\) | ||||
−0.599269 | + | 0.800548i | \(0.704542\pi\) | |||||||
\(440\) | −9.05583e10 | − | 2.25753e11i | −0.115184 | − | 0.287142i | ||||
\(441\) | 6.00962e11 | 0.756612 | ||||||||
\(442\) | 3.61549e11 | − | 4.62249e10i | 0.450575 | − | 0.0576071i | ||||
\(443\) | − | 1.58499e12i | − | 1.95528i | −0.210283 | − | 0.977641i | \(-0.567439\pi\) | ||
0.210283 | − | 0.977641i | \(-0.432561\pi\) | |||||||
\(444\) | 1.07192e12 | − | 2.78651e11i | 1.30900 | − | 0.340280i | ||||
\(445\) | − | 1.19863e12i | − | 1.44898i | ||||||
\(446\) | 1.37457e11 | + | 1.07513e12i | 0.164498 | + | 1.28663i | ||||
\(447\) | 5.30248e11 | 0.628196 | ||||||||
\(448\) | −4.93546e11 | + | 4.71895e11i | −0.578864 | + | 0.553470i | ||||
\(449\) | −5.33305e11 | −0.619251 | −0.309626 | − | 0.950859i | \(-0.600204\pi\) | ||||
−0.309626 | + | 0.950859i | \(0.600204\pi\) | |||||||
\(450\) | 6.71321e9 | + | 5.25075e10i | 0.00771745 | + | 0.0603621i | ||||
\(451\) | − | 2.19824e11i | − | 0.250196i | ||||||
\(452\) | −1.80471e11 | + | 4.69143e10i | −0.203369 | + | 0.0528667i | ||||
\(453\) | 1.05461e12i | 1.17666i | ||||||||
\(454\) | −1.01344e12 | + | 1.29571e11i | −1.11956 | + | 0.143138i | ||||
\(455\) | −4.62208e11 | −0.505576 | ||||||||
\(456\) | −5.45918e11 | − | 1.36092e12i | −0.591270 | − | 1.47398i | ||||
\(457\) | −6.95059e11 | −0.745416 | −0.372708 | − | 0.927949i | \(-0.621571\pi\) | ||||
−0.372708 | + | 0.927949i | \(0.621571\pi\) | |||||||
\(458\) | −2.93558e11 | + | 3.75321e10i | −0.311745 | + | 0.0398573i | ||||
\(459\) | 1.35862e12i | 1.42869i | ||||||||
\(460\) | 3.59554e11 | + | 1.38314e12i | 0.374415 | + | 1.44031i | ||||
\(461\) | − | 1.51250e12i | − | 1.55970i | −0.625966 | − | 0.779851i | \(-0.715295\pi\) | ||
0.625966 | − | 0.779851i | \(-0.284705\pi\) | |||||||
\(462\) | 5.34992e10 | + | 4.18445e11i | 0.0546334 | + | 0.427316i | ||||
\(463\) | 1.10015e12 | 1.11260 | 0.556300 | − | 0.830981i | \(-0.312220\pi\) | ||||
0.556300 | + | 0.830981i | \(0.312220\pi\) | |||||||
\(464\) | −2.75902e11 | − | 4.94814e11i | −0.276328 | − | 0.495577i | ||||
\(465\) | 1.06619e12 | 1.05753 | ||||||||
\(466\) | −2.26827e11 | − | 1.77413e12i | −0.222823 | − | 1.74281i | ||||
\(467\) | − | 7.29651e11i | − | 0.709887i | −0.934888 | − | 0.354944i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354944i | \(-0.115500\pi\) | |||||||
\(468\) | −3.42867e11 | − | 1.31895e12i | −0.330385 | − | 1.27093i | ||||
\(469\) | 8.63450e11i | 0.824061i | ||||||||
\(470\) | 1.64681e12 | − | 2.10548e11i | 1.55669 | − | 0.199027i | ||||
\(471\) | 2.68936e12 | 2.51800 | ||||||||
\(472\) | −1.23901e11 | + | 4.97015e10i | −0.114904 | + | 0.0460925i | ||||
\(473\) | 2.27066e9 | 0.00208582 | ||||||||
\(474\) | 1.39517e11 | − | 1.78376e10i | 0.126948 | − | 0.0162306i | ||||
\(475\) | − | 2.88164e10i | − | 0.0259728i | ||||||
\(476\) | −6.33644e11 | + | 1.64718e11i | −0.565736 | + | 0.147065i | ||||
\(477\) | 1.77036e12i | 1.56578i | ||||||||
\(478\) | 3.63057e10 | + | 2.83965e11i | 0.0318089 | + | 0.248794i | ||||
\(479\) | −9.75429e11 | −0.846614 | −0.423307 | − | 0.905986i | \(-0.639131\pi\) | ||||
−0.423307 | + | 0.905986i | \(0.639131\pi\) | |||||||
\(480\) | −1.23538e12 | − | 1.67384e12i | −1.06222 | − | 1.43922i | ||||
\(481\) | −5.60346e11 | −0.477314 | ||||||||
\(482\) | 1.68057e11 | + | 1.31446e12i | 0.141823 | + | 1.10927i | ||||
\(483\) | − | 2.47852e12i | − | 2.07219i | ||||||
\(484\) | −1.05973e12 | + | 2.75481e11i | −0.877791 | + | 0.228186i | ||||
\(485\) | 1.13004e12i | 0.927378i | ||||||||
\(486\) | 4.99256e11 | − | 6.38311e10i | 0.405938 | − | 0.0519002i | ||||
\(487\) | 7.09068e11 | 0.571225 | 0.285613 | − | 0.958345i | \(-0.407803\pi\) | ||||
0.285613 | + | 0.958345i | \(0.407803\pi\) | |||||||
\(488\) | 2.10532e12 | − | 8.44525e11i | 1.68046 | − | 0.674098i | ||||
\(489\) | −1.07970e12 | −0.853913 | ||||||||
\(490\) | −4.60394e11 | + | 5.88626e10i | −0.360784 | + | 0.0461272i | ||||
\(491\) | 8.30763e10i | 0.0645075i | 0.999480 | + | 0.0322538i | \(0.0102685\pi\) | ||||
−0.999480 | + | 0.0322538i | \(0.989732\pi\) | |||||||
\(492\) | −4.73019e11 | − | 1.81962e12i | −0.363945 | − | 1.40003i | ||||
\(493\) | − | 5.43190e11i | − | 0.414134i | ||||||
\(494\) | 9.40838e10 | + | 7.35878e11i | 0.0710794 | + | 0.555948i | ||||
\(495\) | −8.71964e11 | −0.652792 | ||||||||
\(496\) | −6.96023e11 | + | 3.88094e11i | −0.516364 | + | 0.287918i | ||||
\(497\) | 1.13734e12 | 0.836151 | ||||||||
\(498\) | 3.35945e11 | + | 2.62760e12i | 0.244758 | + | 1.91438i | ||||
\(499\) | 1.54674e12i | 1.11677i | 0.829581 | + | 0.558386i | \(0.188579\pi\) | ||||
−0.829581 | + | 0.558386i | \(0.811421\pi\) | |||||||
\(500\) | 3.46359e11 | + | 1.33239e12i | 0.247835 | + | 0.953378i | ||||
\(501\) | 1.90924e11i | 0.135391i | ||||||||
\(502\) | −1.54463e12 | + | 1.97485e11i | −1.08557 | + | 0.138793i | ||||
\(503\) | −9.81095e11 | −0.683369 | −0.341684 | − | 0.939815i | \(-0.610997\pi\) | ||||
−0.341684 | + | 0.939815i | \(0.610997\pi\) | |||||||
\(504\) | 9.11339e11 | + | 2.27188e12i | 0.629133 | + | 1.56837i | ||||
\(505\) | 1.13518e12 | 0.776699 | ||||||||
\(506\) | −6.54577e11 | + | 8.36893e10i | −0.443898 | + | 0.0567535i | ||||
\(507\) | − | 1.60745e12i | − | 1.08044i | ||||||
\(508\) | 1.91484e12 | − | 4.97771e11i | 1.27569 | − | 0.331622i | ||||
\(509\) | − | 1.02396e12i | − | 0.676167i | −0.941116 | − | 0.338083i | \(-0.890221\pi\) | ||
0.941116 | − | 0.338083i | \(-0.109779\pi\) | |||||||
\(510\) | −2.52960e11 | − | 1.97853e12i | −0.165571 | − | 1.29502i | ||||
\(511\) | −2.08656e12 | −1.35375 | ||||||||
\(512\) | 1.41576e12 | + | 6.43024e11i | 0.910488 | + | 0.413535i | ||||
\(513\) | −2.76525e12 | −1.76282 | ||||||||
\(514\) | −3.42483e10 | − | 2.67874e11i | −0.0216424 | − | 0.169276i | ||||
\(515\) | − | 1.16285e12i | − | 0.728437i | ||||||
\(516\) | 1.87957e10 | − | 4.88601e9i | 0.0116717 | − | 0.00303411i | ||||
\(517\) | 7.66618e11i | 0.471923i | ||||||||
\(518\) | 9.98372e11 | − | 1.27644e11i | 0.609268 | − | 0.0778964i | ||||
\(519\) | 3.64609e11 | 0.220584 | ||||||||
\(520\) | 3.91857e11 | + | 9.76861e11i | 0.235024 | + | 0.585892i | ||||
\(521\) | 1.53658e11 | 0.0913664 | 0.0456832 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456832 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(522\) | −2.01452e12 | + | 2.57561e11i | −1.18756 | + | 0.151832i | ||||
\(523\) | 2.08535e12i | 1.21877i | 0.792875 | + | 0.609385i | \(0.208583\pi\) | ||||
−0.792875 | + | 0.609385i | \(0.791417\pi\) | |||||||
\(524\) | −3.93818e11 | − | 1.51495e12i | −0.228194 | − | 0.877825i | ||||
\(525\) | 7.09041e10i | 0.0407338i | ||||||||
\(526\) | 9.17123e10 | + | 7.17329e11i | 0.0522386 | + | 0.408585i | ||||
\(527\) | −7.64071e11 | −0.431505 | ||||||||
\(528\) | 8.39012e11 | − | 4.67823e11i | 0.469803 | − | 0.261956i | ||||
\(529\) | 2.07602e12 | 1.15261 | ||||||||
\(530\) | −1.73402e11 | − | 1.35627e12i | −0.0954582 | − | 0.746628i | ||||
\(531\) | 4.78564e11i | 0.261225i | ||||||||
\(532\) | −3.35259e11 | − | 1.28968e12i | −0.181459 | − | 0.698042i | ||||
\(533\) | 9.51207e11i | 0.510508i | ||||||||
\(534\) | 4.69552e12 | − | 6.00333e11i | 2.49889 | − | 0.319490i | ||||
\(535\) | −8.34691e11 | −0.440488 | ||||||||
\(536\) | 1.82487e12 | − | 7.32027e11i | 0.954972 | − | 0.383076i | ||||
\(537\) | −2.92061e11 | −0.151562 | ||||||||
\(538\) | 1.59020e12 | − | 2.03312e11i | 0.818338 | − | 0.104627i | ||||
\(539\) | − | 2.14322e11i | − | 0.109375i | ||||||
\(540\) | −3.79701e12 | + | 9.87048e11i | −1.92163 | + | 0.499536i | ||||
\(541\) | − | 4.46995e11i | − | 0.224344i | −0.993689 | − | 0.112172i | \(-0.964219\pi\) | ||
0.993689 | − | 0.112172i | \(-0.0357808\pi\) | |||||||
\(542\) | −2.49732e11 | − | 1.95328e12i | −0.124302 | − | 0.972229i | ||||
\(543\) | 3.29966e12 | 1.62881 | ||||||||
\(544\) | 8.85325e11 | + | 1.19954e12i | 0.433419 | + | 0.587244i | ||||
\(545\) | −1.26098e12 | −0.612244 | ||||||||
\(546\) | −2.31498e11 | − | 1.81066e12i | −0.111476 | − | 0.871908i | ||||
\(547\) | 3.46729e11i | 0.165595i | 0.996566 | + | 0.0827974i | \(0.0263854\pi\) | ||||
−0.996566 | + | 0.0827974i | \(0.973615\pi\) | |||||||
\(548\) | −1.56338e12 | + | 4.06408e11i | −0.740548 | + | 0.192508i | ||||
\(549\) | − | 8.13172e12i | − | 3.82038i | ||||||
\(550\) | 1.87258e10 | − | 2.39414e9i | 0.00872585 | − | 0.00111562i | ||||
\(551\) | 1.10558e12 | 0.510985 | ||||||||
\(552\) | −5.23826e12 | + | 2.10127e12i | −2.40138 | + | 0.963288i | ||||
\(553\) | 1.27820e11 | 0.0581213 | ||||||||
\(554\) | −3.48073e12 | + | 4.45020e11i | −1.56992 | + | 0.200718i | ||||
\(555\) | 3.06642e12i | 1.37187i | ||||||||
\(556\) | 1.88289e11 | + | 7.24315e11i | 0.0835580 | + | 0.321434i | ||||
\(557\) | 5.59793e11i | 0.246422i | 0.992380 | + | 0.123211i | \(0.0393192\pi\) | ||||
−0.992380 | + | 0.123211i | \(0.960681\pi\) | |||||||
\(558\) | 3.62295e11 | + | 2.83370e12i | 0.158201 | + | 1.23737i | ||||
\(559\) | −9.82542e9 | −0.00425596 | ||||||||
\(560\) | −9.20698e11 | − | 1.65121e12i | −0.395613 | − | 0.709508i | ||||
\(561\) | 9.21039e11 | 0.392595 | ||||||||
\(562\) | −8.03374e10 | − | 6.28360e11i | −0.0339707 | − | 0.265702i | ||||
\(563\) | 2.30313e12i | 0.966119i | 0.875587 | + | 0.483060i | \(0.160475\pi\) | ||||
−0.875587 | + | 0.483060i | \(0.839525\pi\) | |||||||
\(564\) | 1.64961e12 | + | 6.34578e12i | 0.686477 | + | 2.64076i | ||||
\(565\) | − | 5.16270e11i | − | 0.213137i | ||||||
\(566\) | −2.05206e12 | + | 2.62360e11i | −0.840457 | + | 0.107454i | ||||
\(567\) | 2.64520e12 | 1.07482 | ||||||||
\(568\) | −9.64225e11 | − | 2.40372e12i | −0.388697 | − | 0.968983i | ||||
\(569\) | −8.14910e11 | −0.325915 | −0.162958 | − | 0.986633i | \(-0.552103\pi\) | ||||
−0.162958 | + | 0.986633i | \(0.552103\pi\) | |||||||
\(570\) | 4.02699e12 | − | 5.14861e11i | 1.59788 | − | 0.204293i | ||||
\(571\) | − | 3.63502e12i | − | 1.43102i | −0.698605 | − | 0.715508i | \(-0.746195\pi\) | ||
0.698605 | − | 0.715508i | \(-0.253805\pi\) | |||||||
\(572\) | −4.70379e11 | + | 1.22277e11i | −0.183724 | + | 0.0477599i | ||||
\(573\) | 6.61320e12i | 2.56281i | ||||||||
\(574\) | −2.16680e11 | − | 1.69477e12i | −0.0833136 | − | 0.651639i | ||||
\(575\) | −1.10916e11 | −0.0423145 | ||||||||
\(576\) | 4.02891e12 | − | 3.85217e12i | 1.52506 | − | 1.45816i | ||||
\(577\) | 2.45038e11 | 0.0920326 | 0.0460163 | − | 0.998941i | \(-0.485347\pi\) | ||||
0.0460163 | + | 0.998941i | \(0.485347\pi\) | |||||||
\(578\) | −1.59020e11 | − | 1.24378e12i | −0.0592621 | − | 0.463520i | ||||
\(579\) | 2.80205e12i | 1.03615i | ||||||||
\(580\) | 1.51809e12 | − | 3.94634e11i | 0.557021 | − | 0.144800i | ||||
\(581\) | 2.40730e12i | 0.876472i | ||||||||
\(582\) | −4.42685e12 | + | 5.65983e11i | −1.59934 | + | 0.204480i | ||||
\(583\) | 6.31366e11 | 0.226346 | ||||||||
\(584\) | 1.76897e12 | + | 4.40988e12i | 0.629309 | + | 1.56880i | ||||
\(585\) | 3.77310e12 | 1.33198 | ||||||||
\(586\) | −2.10330e12 | + | 2.68912e11i | −0.736822 | + | 0.0942045i | ||||
\(587\) | 2.81390e12i | 0.978223i | 0.872221 | + | 0.489112i | \(0.162679\pi\) | ||||
−0.872221 | + | 0.489112i | \(0.837321\pi\) | |||||||
\(588\) | −4.61178e11 | − | 1.77407e12i | −0.159100 | − | 0.612032i | ||||
\(589\) | − | 1.55515e12i | − | 0.532419i | ||||||
\(590\) | −4.68740e10 | − | 3.66626e11i | −0.0159257 | − | 0.124563i | ||||
\(591\) | −9.83410e12 | −3.31582 | ||||||||
\(592\) | −1.11618e12 | − | 2.00181e12i | −0.373498 | − | 0.669846i | ||||
\(593\) | 7.42491e11 | 0.246573 | 0.123286 | − | 0.992371i | \(-0.460657\pi\) | ||||
0.123286 | + | 0.992371i | \(0.460657\pi\) | |||||||
\(594\) | −2.29744e11 | − | 1.79695e12i | −0.0757191 | − | 0.592238i | ||||
\(595\) | − | 1.81265e12i | − | 0.592908i | ||||||
\(596\) | −2.76072e11 | − | 1.06200e12i | −0.0896218 | − | 0.344760i | ||||
\(597\) | − | 5.13757e12i | − | 1.65529i | ||||||
\(598\) | 2.83244e12 | − | 3.62134e11i | 0.905743 | − | 0.115801i | ||||
\(599\) | 8.31869e11 | 0.264018 | 0.132009 | − | 0.991248i | \(-0.457857\pi\) | ||||
0.132009 | + | 0.991248i | \(0.457857\pi\) | |||||||
\(600\) | 1.49853e11 | − | 6.01120e10i | 0.0472048 | − | 0.0189357i | ||||
\(601\) | −1.71774e12 | −0.537060 | −0.268530 | − | 0.963271i | \(-0.586538\pi\) | ||||
−0.268530 | + | 0.963271i | \(0.586538\pi\) | |||||||
\(602\) | 1.75060e10 | − | 2.23818e9i | 0.00543253 | − | 0.000694563i | ||||
\(603\) | − | 7.04851e12i | − | 2.17105i | ||||||
\(604\) | 2.11221e12 | − | 5.49078e11i | 0.645760 | − | 0.167868i | ||||
\(605\) | − | 3.03155e12i | − | 0.919951i | ||||||
\(606\) | 5.68555e11 | + | 4.44696e12i | 0.171256 | + | 1.33948i | ||||
\(607\) | −2.97709e12 | −0.890107 | −0.445053 | − | 0.895504i | \(-0.646815\pi\) | ||||
−0.445053 | + | 0.895504i | \(0.646815\pi\) | |||||||
\(608\) | −2.44147e12 | + | 1.80194e12i | −0.724580 | + | 0.534780i | ||||
\(609\) | −2.72033e12 | −0.801391 | ||||||||
\(610\) | 7.96480e11 | + | 6.22968e12i | 0.232911 | + | 1.82172i | ||||
\(611\) | − | 3.31725e12i | − | 0.962926i | ||||||
\(612\) | 5.17255e12 | − | 1.34463e12i | 1.49047 | − | 0.387454i | ||||
\(613\) | 3.26103e12i | 0.932788i | 0.884577 | + | 0.466394i | \(0.154447\pi\) | ||||
−0.884577 | + | 0.466394i | \(0.845553\pi\) | |||||||
\(614\) | 2.31240e12 | − | 2.95646e11i | 0.656607 | − | 0.0839488i | ||||
\(615\) | 5.20535e12 | 1.46728 | ||||||||
\(616\) | 8.10223e11 | − | 3.25012e11i | 0.226721 | − | 0.0909465i | ||||
\(617\) | 4.07434e12 | 1.13181 | 0.565906 | − | 0.824470i | \(-0.308527\pi\) | ||||
0.565906 | + | 0.824470i | \(0.308527\pi\) | |||||||
\(618\) | 4.55538e12 | − | 5.82416e11i | 1.25625 | − | 0.160615i | ||||
\(619\) | − | 3.60019e12i | − | 0.985638i | −0.870132 | − | 0.492819i | \(-0.835966\pi\) | ||
0.870132 | − | 0.492819i | \(-0.164034\pi\) | |||||||
\(620\) | −5.55106e11 | − | 2.13540e12i | −0.150873 | − | 0.580385i | ||||
\(621\) | 1.06436e13i | 2.87195i | ||||||||
\(622\) | −4.11085e11 | − | 3.21531e12i | −0.110122 | − | 0.861322i | ||||
\(623\) | 4.30184e12 | 1.14409 | ||||||||
\(624\) | −3.63051e12 | + | 2.02433e12i | −0.958599 | + | 0.534503i | ||||
\(625\) | −3.92154e12 | −1.02801 | ||||||||
\(626\) | 7.28452e11 | + | 5.69760e12i | 0.189590 | + | 1.48288i | ||||
\(627\) | 1.87464e12i | 0.484410i | ||||||||
\(628\) | −1.40021e12 | − | 5.38636e12i | −0.359231 | − | 1.38190i | ||||
\(629\) | − | 2.19752e12i | − | 0.559763i | ||||||
\(630\) | −6.72254e12 | + | 8.59493e11i | −1.70020 | + | 0.217375i | ||||
\(631\) | 4.14069e12 | 1.03978 | 0.519890 | − | 0.854233i | \(-0.325973\pi\) | ||||
0.519890 | + | 0.854233i | \(0.325973\pi\) | |||||||
\(632\) | −1.08365e11 | − | 2.70143e11i | −0.0270185 | − | 0.0673546i | ||||
\(633\) | −1.26536e13 | −3.13255 | ||||||||
\(634\) | 4.87984e12 | − | 6.23899e11i | 1.19951 | − | 0.153360i | ||||
\(635\) | 5.47774e12i | 1.33696i | ||||||||
\(636\) | 5.22622e12 | − | 1.35858e12i | 1.26657 | − | 0.329251i | ||||
\(637\) | 9.27396e11i | 0.223171i | ||||||||
\(638\) | 9.18544e10 | + | 7.18441e11i | 0.0219486 | + | 0.171671i | ||||
\(639\) | −9.28429e12 | −2.20290 | ||||||||
\(640\) | −2.70922e12 | + | 3.34575e12i | −0.638315 | + | 0.788286i | ||||
\(641\) | 1.23747e12 | 0.289516 | 0.144758 | − | 0.989467i | \(-0.453760\pi\) | ||||
0.144758 | + | 0.989467i | \(0.453760\pi\) | |||||||
\(642\) | −4.18056e11 | − | 3.26983e12i | −0.0971241 | − | 0.759657i | ||||
\(643\) | − | 2.36693e12i | − | 0.546054i | −0.962006 | − | 0.273027i | \(-0.911975\pi\) | ||
0.962006 | − | 0.273027i | \(-0.0880248\pi\) | |||||||
\(644\) | −4.96407e12 | + | 1.29043e12i | −1.13724 | + | 0.295630i | ||||
\(645\) | 5.37683e10i | 0.0122323i | ||||||||
\(646\) | −2.88590e12 | + | 3.68970e11i | −0.651982 | + | 0.0833574i | ||||
\(647\) | 5.75807e12 | 1.29184 | 0.645918 | − | 0.763406i | \(-0.276475\pi\) | ||||
0.645918 | + | 0.763406i | \(0.276475\pi\) | |||||||
\(648\) | −2.24259e12 | − | 5.59055e12i | −0.499645 | − | 1.24557i | ||||
\(649\) | 1.70671e11 | 0.0377622 | ||||||||
\(650\) | −8.10288e10 | + | 1.03597e10i | −0.0178045 | + | 0.00227635i | ||||
\(651\) | 3.82652e12i | 0.835006i | ||||||||
\(652\) | 5.62142e11 | + | 2.16247e12i | 0.121824 | + | 0.468635i | ||||
\(653\) | − | 1.19202e12i | − | 0.256552i | −0.991739 | − | 0.128276i | \(-0.959056\pi\) | ||
0.991739 | − | 0.128276i | \(-0.0409443\pi\) | |||||||
\(654\) | −6.31565e11 | − | 4.93979e12i | −0.134995 | − | 1.05587i | ||||
\(655\) | 4.33379e12 | 0.919987 | ||||||||
\(656\) | −3.39814e12 | + | 1.89476e12i | −0.716429 | + | 0.399472i | ||||
\(657\) | 1.70330e13 | 3.56654 | ||||||||
\(658\) | 7.55654e11 | + | 5.91036e12i | 0.157147 | + | 1.22913i | ||||
\(659\) | − | 6.40718e11i | − | 0.132337i | −0.997808 | − | 0.0661687i | \(-0.978922\pi\) | ||
0.997808 | − | 0.0661687i | \(-0.0210776\pi\) | |||||||
\(660\) | 6.69145e11 | + | 2.57409e12i | 0.137269 | + | 0.528051i | ||||
\(661\) | 6.37585e12i | 1.29907i | 0.760333 | + | 0.649533i | \(0.225036\pi\) | ||||
−0.760333 | + | 0.649533i | \(0.774964\pi\) | |||||||
\(662\) | −6.69219e11 | + | 8.55613e10i | −0.135428 | + | 0.0173148i | ||||
\(663\) | −3.98545e12 | −0.801063 | ||||||||
\(664\) | 5.08775e12 | − | 2.04089e12i | 1.01571 | − | 0.407440i | ||||
\(665\) | 3.68937e12 | 0.731568 | ||||||||
\(666\) | −8.14990e12 | + | 1.04198e12i | −1.60516 | + | 0.205224i | ||||
\(667\) | − | 4.25545e12i | − | 0.832490i | ||||||
\(668\) | 3.82389e11 | − | 9.94037e10i | 0.0743039 | − | 0.0193156i | ||||
\(669\) | − | 1.18514e13i | − | 2.28745i | ||||||
\(670\) | 6.90382e11 | + | 5.39983e12i | 0.132359 | + | 1.03525i | ||||
\(671\) | −2.90002e12 | −0.552268 | ||||||||
\(672\) | 6.00736e12 | − | 4.43377e12i | 1.13638 | − | 0.838709i | ||||
\(673\) | −5.29863e12 | −0.995624 | −0.497812 | − | 0.867285i | \(-0.665863\pi\) | ||||
−0.497812 | + | 0.867285i | \(0.665863\pi\) | |||||||
\(674\) | −1.02287e12 | − | 8.00036e12i | −0.190919 | − | 1.49328i | ||||
\(675\) | − | 3.04487e11i | − | 0.0564549i | ||||||
\(676\) | −3.21946e12 | + | 8.36913e11i | −0.592957 | + | 0.154142i | ||||
\(677\) | 2.91606e12i | 0.533516i | 0.963764 | + | 0.266758i | \(0.0859525\pi\) | ||||
−0.963764 | + | 0.266758i | \(0.914048\pi\) | |||||||
\(678\) | 2.02244e12 | − | 2.58574e11i | 0.367572 | − | 0.0469950i | ||||
\(679\) | −4.05570e12 | −0.732237 | ||||||||
\(680\) | −3.83097e12 | + | 1.53675e12i | −0.687098 | + | 0.275622i | ||||
\(681\) | 1.11714e13 | 1.99043 | ||||||||
\(682\) | 1.01058e12 | − | 1.29206e11i | 0.178872 | − | 0.0228692i | ||||
\(683\) | − | 1.41684e12i | − | 0.249131i | −0.992211 | − | 0.124565i | \(-0.960246\pi\) | ||
0.992211 | − | 0.124565i | \(-0.0397536\pi\) | |||||||
\(684\) | 2.73678e12 | + | 1.05279e13i | 0.478066 | + | 1.83904i | ||||
\(685\) | − | 4.47233e12i | − | 0.776116i | ||||||
\(686\) | −8.00393e11 | − | 6.26028e12i | −0.137989 | − | 1.07928i | ||||
\(687\) | 3.23597e12 | 0.554241 | ||||||||
\(688\) | −1.95718e10 | − | 3.51008e10i | −0.00333029 | − | 0.00597268i | ||||
\(689\) | −2.73200e12 | −0.461843 | ||||||||
\(690\) | −1.98173e12 | − | 1.55001e13i | −0.332831 | − | 2.60324i | ||||
\(691\) | 1.87083e12i | 0.312164i | 0.987744 | + | 0.156082i | \(0.0498865\pi\) | ||||
−0.987744 | + | 0.156082i | \(0.950114\pi\) | |||||||
\(692\) | −1.89832e11 | − | 7.30253e11i | −0.0314697 | − | 0.121059i | ||||
\(693\) | − | 3.12946e12i | − | 0.515430i | ||||||
\(694\) | −8.38530e11 | + | 1.07208e11i | −0.137215 | + | 0.0175433i | ||||
\(695\) | −2.07203e12 | −0.336872 | ||||||||
\(696\) | 2.30628e12 | + | 5.74933e12i | 0.372538 | + | 0.928701i | ||||
\(697\) | −3.73036e12 | −0.598692 | ||||||||
\(698\) | 2.59803e12 | − | 3.32165e11i | 0.414281 | − | 0.0529668i | ||||
\(699\) | 1.95568e13i | 3.09849i | ||||||||
\(700\) | 1.42009e11 | − | 3.69160e10i | 0.0223551 | − | 0.00581130i | ||||
\(701\) | − | 8.31406e12i | − | 1.30042i | −0.759757 | − | 0.650208i | \(-0.774682\pi\) | ||
0.759757 | − | 0.650208i | \(-0.225318\pi\) | |||||||
\(702\) | 9.94131e11 | + | 7.77561e12i | 0.154499 | + | 1.20842i | ||||
\(703\) | 4.47271e12 | 0.690672 | ||||||||
\(704\) | −1.37380e12 | − | 1.43684e12i | −0.210789 | − | 0.220460i | ||||
\(705\) | −1.81532e13 | −2.76759 | ||||||||
\(706\) | 5.57227e11 | + | 4.35836e12i | 0.0844133 | + | 0.660240i | ||||
\(707\) | 4.07413e12i | 0.613264i | ||||||||
\(708\) | 1.41275e12 | − | 3.67250e11i | 0.211308 | − | 0.0549303i | ||||
\(709\) | 1.00136e13i | 1.48827i | 0.668030 | + | 0.744134i | \(0.267138\pi\) | ||||
−0.668030 | + | 0.744134i | \(0.732862\pi\) | |||||||
\(710\) | 7.11265e12 | − | 9.09370e11i | 1.05043 | − | 0.134301i | ||||
\(711\) | −1.04342e12 | −0.153125 | ||||||||
\(712\) | −3.64707e12 | − | 9.09180e12i | −0.531844 | − | 1.32584i | ||||
\(713\) | −5.98586e12 | −0.867409 | ||||||||
\(714\) | 7.10090e12 | − | 9.07867e11i | 1.02252 | − | 0.130732i | ||||
\(715\) | − | 1.34560e12i | − | 0.192548i | ||||||
\(716\) | 1.52060e11 | + | 5.84951e11i | 0.0216226 | + | 0.0831784i | ||||
\(717\) | − | 3.13023e12i | − | 0.442323i | ||||||
\(718\) | 6.39803e11 | + | 5.00423e12i | 0.0898435 | + | 0.702712i | ||||
\(719\) | −3.50640e12 | −0.489307 | −0.244654 | − | 0.969611i | \(-0.578674\pi\) | ||||
−0.244654 | + | 0.969611i | \(0.578674\pi\) | |||||||
\(720\) | 7.51583e12 | + | 1.34792e13i | 1.04227 | + | 1.86925i | ||||
\(721\) | 4.17346e12 | 0.575158 | ||||||||
\(722\) | 1.75007e11 | + | 1.36882e12i | 0.0239683 | + | 0.187469i | ||||
\(723\) | − | 1.44897e13i | − | 1.97213i | ||||||
\(724\) | −1.71796e12 | − | 6.60869e12i | −0.232375 | − | 0.893906i | ||||
\(725\) | 1.21737e11i | 0.0163645i | ||||||||
\(726\) | 1.18758e13 | − | 1.51835e12i | 1.58653 | − | 0.202842i | ||||
\(727\) | −2.99547e11 | −0.0397703 | −0.0198852 | − | 0.999802i | \(-0.506330\pi\) | ||||
−0.0198852 | + | 0.999802i | \(0.506330\pi\) | |||||||
\(728\) | −3.50594e12 | + | 1.40637e12i | −0.462608 | + | 0.185570i | ||||
\(729\) | 4.73045e12 | 0.620338 | ||||||||
\(730\) | −1.30489e13 | + | 1.66834e12i | −1.70068 | + | 0.217436i | ||||
\(731\) | − | 3.85325e10i | − | 0.00499113i | ||||||
\(732\) | −2.40053e13 | + | 6.24028e12i | −3.09035 | + | 0.803349i | ||||
\(733\) | 6.88627e10i | 0.00881082i | 0.999990 | + | 0.00440541i | \(0.00140229\pi\) | ||||
−0.999990 | + | 0.00440541i | \(0.998598\pi\) | |||||||
\(734\) | −8.46968e11 | − | 6.62457e12i | −0.107705 | − | 0.842414i | ||||
\(735\) | 5.07505e12 | 0.641427 | ||||||||
\(736\) | 6.93579e12 | + | 9.39738e12i | 0.871256 | + | 1.18047i | ||||
\(737\) | −2.51372e12 | −0.313843 | ||||||||
\(738\) | 1.76880e12 | + | 1.38347e13i | 0.219496 | + | 1.71679i | ||||
\(739\) | 9.78319e12i | 1.20665i | 0.797496 | + | 0.603324i | \(0.206157\pi\) | ||||
−0.797496 | + | 0.603324i | \(0.793843\pi\) | |||||||
\(740\) | 6.14154e12 | − | 1.59652e12i | 0.752896 | − | 0.195718i | ||||
\(741\) | − | 8.11178e12i | − | 0.988404i | ||||||
\(742\) | 4.86762e12 | − | 6.22337e11i | 0.589520 | − | 0.0753716i | ||||
\(743\) | −1.30634e12 | −0.157256 | −0.0786279 | − | 0.996904i | \(-0.525054\pi\) | ||||
−0.0786279 | + | 0.996904i | \(0.525054\pi\) | |||||||
\(744\) | 8.08721e12 | − | 3.24410e12i | 0.967655 | − | 0.388164i | ||||
\(745\) | 3.03804e12 | 0.361319 | ||||||||
\(746\) | 4.04725e11 | − | 5.17451e10i | 0.0478449 | − | 0.00611709i | ||||
\(747\) | − | 1.96513e13i | − | 2.30913i | ||||||
\(748\) | −4.79536e11 | − | 1.84469e12i | −0.0560098 | − | 0.215460i | ||||
\(749\) | − | 2.99569e12i | − | 0.347799i | ||||||
\(750\) | −1.90901e12 | − | 1.49313e13i | −0.220309 | − | 1.72315i | ||||
\(751\) | −1.05656e13 | −1.21204 | −0.606019 | − | 0.795451i | \(-0.707234\pi\) | ||||
−0.606019 | + | 0.795451i | \(0.707234\pi\) | |||||||
\(752\) | 1.18507e13 | − | 6.60781e12i | 1.35134 | − | 0.753490i | ||||
\(753\) | 1.70269e13 | 1.93000 | ||||||||
\(754\) | −3.97465e11 | − | 3.10878e12i | −0.0447846 | − | 0.350283i | ||||
\(755\) | 6.04235e12i | 0.676775i | ||||||||
\(756\) | −3.54250e12 | − | 1.36274e13i | −0.394422 | − | 1.51728i | ||||
\(757\) | 1.53287e13i | 1.69658i | 0.529535 | + | 0.848288i | \(0.322366\pi\) | ||||
−0.529535 | + | 0.848288i | \(0.677634\pi\) | |||||||
\(758\) | −1.36863e13 | + | 1.74983e12i | −1.50583 | + | 0.192524i | ||||
\(759\) | 7.21558e12 | 0.789193 | ||||||||
\(760\) | −3.12782e12 | − | 7.79736e12i | −0.340080 | − | 0.847786i | ||||
\(761\) | −3.80613e12 | −0.411389 | −0.205695 | − | 0.978616i | \(-0.565945\pi\) | ||||
−0.205695 | + | 0.978616i | \(0.565945\pi\) | |||||||
\(762\) | −2.14586e13 | + | 2.74353e12i | −2.30571 | + | 0.294790i | ||||
\(763\) | − | 4.52564e12i | − | 0.483414i | ||||||
\(764\) | 1.32452e13 | − | 3.44314e12i | 1.40649 | − | 0.365624i | ||||
\(765\) | 1.47970e13i | 1.56206i | ||||||||
\(766\) | 3.82524e11 | + | 2.99192e12i | 0.0401448 | + | 0.313993i | ||||
\(767\) | −7.38513e11 | −0.0770511 | ||||||||
\(768\) | −1.44636e13 | − | 8.93743e12i | −1.50021 | − | 0.927016i | ||||
\(769\) | 3.96740e12 | 0.409107 | 0.204554 | − | 0.978855i | \(-0.434426\pi\) | ||||
0.204554 | + | 0.978855i | \(0.434426\pi\) | |||||||
\(770\) | 3.06522e11 | + | 2.39747e12i | 0.0314234 | + | 0.245779i | ||||
\(771\) | 2.95285e12i | 0.300951i | ||||||||
\(772\) | 5.61205e12 | − | 1.45888e12i | 0.568648 | − | 0.147823i | ||||
\(773\) | 7.06875e12i | 0.712090i | 0.934469 | + | 0.356045i | \(0.115875\pi\) | ||||
−0.934469 | + | 0.356045i | \(0.884125\pi\) | |||||||
\(774\) | −1.42905e11 | + | 1.82707e10i | −0.0143124 | + | 0.00182988i | ||||
\(775\) | 1.71240e11 | 0.0170509 | ||||||||
\(776\) | 3.43839e12 | + | 8.57158e12i | 0.340391 | + | 0.848561i | ||||
\(777\) | −1.10053e13 | −1.08320 | ||||||||
\(778\) | −4.61354e11 | + | 5.89853e10i | −0.0451467 | + | 0.00577212i | ||||
\(779\) | − | 7.59258e12i | − | 0.738704i | ||||||
\(780\) | −2.89547e12 | − | 1.11384e13i | −0.280088 | − | 1.07745i | ||||
\(781\) | 3.31106e12i | 0.318448i | ||||||||
\(782\) | 1.42019e12 | + | 1.11080e13i | 0.135805 | + | 1.06220i | ||||
\(783\) | 1.16821e13 | 1.11069 | ||||||||
\(784\) | −3.31307e12 | + | 1.84733e12i | −0.313191 | + | 0.174631i | ||||
\(785\) | 1.54086e13 | 1.44827 | ||||||||
\(786\) | 2.17058e12 | + | 1.69772e13i | 0.202850 | + | 1.58659i | ||||
\(787\) | − | 8.40522e12i | − | 0.781021i | −0.920598 | − | 0.390511i | \(-0.872298\pi\) | ||
0.920598 | − | 0.390511i | \(-0.127702\pi\) | |||||||
\(788\) | 5.12009e12 | + | 1.96961e13i | 0.473053 | + | 1.81975i | ||||
\(789\) | − | 7.90732e12i | − | 0.726411i | ||||||
\(790\) | 7.99359e11 | − | 1.02200e11i | 0.0730163 | − | 0.00933532i | ||||
\(791\) | 1.85288e12 | 0.168288 | ||||||||
\(792\) | −6.61400e12 | + | 2.65313e12i | −0.597312 | + | 0.239605i | ||||
\(793\) | 1.25488e13 | 1.12686 | ||||||||
\(794\) | 1.33206e13 | − | 1.70308e12i | 1.18941 | − | 0.152069i | ||||
\(795\) | 1.49505e13i | 1.32741i | ||||||||
\(796\) | −1.02897e13 | + | 2.67486e12i | −0.908438 | + | 0.236152i | ||||
\(797\) | 2.76521e11i | 0.0242754i | 0.999926 | + | 0.0121377i | \(0.00386364\pi\) | ||||
−0.999926 | + | 0.0121377i | \(0.996136\pi\) | |||||||
\(798\) | 1.84783e12 | + | 1.44528e13i | 0.161305 | + | 1.26165i | ||||
\(799\) | 1.30093e13 | 1.12926 | ||||||||
\(800\) | −1.98415e11 | − | 2.68835e11i | −0.0171266 | − | 0.0232050i | ||||
\(801\) | −3.51168e13 | −3.01417 | ||||||||
\(802\) | −2.88799e12 | − | 2.25885e13i | −0.246497 | − | 1.92798i | ||||
\(803\) | − | 6.07450e12i | − | 0.515574i | ||||||
\(804\) | −2.08076e13 | + | 5.40902e12i | −1.75618 | + | 0.456527i | ||||
\(805\) | − | 1.42006e13i | − | 1.19186i | ||||||
\(806\) | −4.37292e12 | + | 5.59089e11i | −0.364976 | + | 0.0466631i | ||||
\(807\) | −1.75292e13 | −1.45490 | ||||||||
\(808\) | 8.61053e12 | − | 3.45402e12i | 0.710688 | − | 0.285084i | ||||
\(809\) | −1.10211e13 | −0.904601 | −0.452300 | − | 0.891866i | \(-0.649396\pi\) | ||||
−0.452300 | + | 0.891866i | \(0.649396\pi\) | |||||||
\(810\) | 1.65425e13 | − | 2.11501e12i | 1.35027 | − | 0.172635i | ||||
\(811\) | − | 2.02649e13i | − | 1.64494i | −0.568808 | − | 0.822470i | \(-0.692595\pi\) | ||
0.568808 | − | 0.822470i | \(-0.307405\pi\) | |||||||
\(812\) | 1.41633e12 | + | 5.44839e12i | 0.114331 | + | 0.439811i | ||||
\(813\) | 2.15316e13i | 1.72850i | ||||||||
\(814\) | 3.71604e11 | + | 2.90651e12i | 0.0296668 | + | 0.232039i | ||||
\(815\) | −6.18611e12 | −0.491144 | ||||||||
\(816\) | −7.93884e12 | − | 1.42378e13i | −0.626832 | − | 1.12418i | ||||
\(817\) | 7.84270e10 | 0.00615838 | ||||||||
\(818\) | −9.77195e11 | − | 7.64314e12i | −0.0763117 | − | 0.596873i | ||||
\(819\) | 1.35416e13i | 1.05170i | ||||||||
\(820\) | −2.71015e12 | − | 1.04255e13i | −0.209329 | − | 0.805255i | ||||
\(821\) | − | 4.75674e12i | − | 0.365397i | −0.983169 | − | 0.182699i | \(-0.941517\pi\) | ||
0.983169 | − | 0.182699i | \(-0.0584833\pi\) | |||||||
\(822\) | 1.75200e13 | − | 2.23997e12i | 1.33848 | − | 0.171127i | ||||
\(823\) | −1.58721e13 | −1.20596 | −0.602981 | − | 0.797755i | \(-0.706021\pi\) | ||||
−0.602981 | + | 0.797755i | \(0.706021\pi\) | |||||||
\(824\) | −3.53823e12 | − | 8.82045e12i | −0.267370 | − | 0.666528i | ||||
\(825\) | −2.06419e11 | −0.0155134 | ||||||||
\(826\) | 1.31581e12 | − | 1.68230e11i | 0.0983521 | − | 0.0125746i | ||||
\(827\) | 1.83601e13i | 1.36490i | 0.730932 | + | 0.682451i | \(0.239086\pi\) | ||||
−0.730932 | + | 0.682451i | \(0.760914\pi\) | |||||||
\(828\) | 4.05227e13 | − | 1.05340e13i | 2.99614 | − | 0.778858i | ||||
\(829\) | − | 6.16980e12i | − | 0.453707i | −0.973929 | − | 0.226854i | \(-0.927156\pi\) | ||
0.973929 | − | 0.226854i | \(-0.0728439\pi\) | |||||||
\(830\) | 1.92479e12 | + | 1.50548e13i | 0.140777 | + | 1.10109i | ||||
\(831\) | 3.83691e13 | 2.79111 | ||||||||
\(832\) | 5.94461e12 | + | 6.21736e12i | 0.430099 | + | 0.449833i | ||||
\(833\) | −3.63698e12 | −0.261721 | ||||||||
\(834\) | −1.03778e12 | − | 8.11701e12i | −0.0742776 | − | 0.580963i | ||||
\(835\) | 1.09389e12i | 0.0778727i | ||||||||
\(836\) | 3.75459e12 | − | 9.76022e11i | 0.265849 | − | 0.0691085i | ||||
\(837\) | − | 1.64324e13i | − | 1.15727i | ||||||
\(838\) | −1.90303e13 | + | 2.43307e12i | −1.33306 | + | 0.170434i | ||||
\(839\) | −2.48397e13 | −1.73068 | −0.865342 | − | 0.501183i | \(-0.832899\pi\) | ||||
−0.865342 | + | 0.501183i | \(0.832899\pi\) | |||||||
\(840\) | 7.69615e12 | + | 1.91858e13i | 0.533356 | + | 1.32960i | ||||
\(841\) | 9.83652e12 | 0.678047 | ||||||||
\(842\) | 1.18305e13 | − | 1.51256e12i | 0.811144 | − | 0.103707i | ||||
\(843\) | 6.92659e12i | 0.472384i | ||||||||
\(844\) | 6.58807e12 | + | 2.53432e13i | 0.446907 | + | 1.71918i | ||||
\(845\) | − | 9.20984e12i | − | 0.621437i | ||||||
\(846\) | −6.16855e12 | − | 4.82474e13i | −0.414015 | − | 3.23823i | ||||
\(847\) | 1.08802e13 | 0.726373 | ||||||||
\(848\) | −5.44202e12 | − | 9.75993e12i | −0.361392 | − | 0.648135i | ||||
\(849\) | 2.26204e13 | 1.49422 | ||||||||
\(850\) | −4.06279e10 | − | 3.17772e11i | −0.00266956 | − | 0.0208800i | ||||
\(851\) | − | 1.72157e13i | − | 1.12523i | ||||||
\(852\) | 7.12476e12 | + | 2.74078e13i | 0.463225 | + | 1.78195i | ||||
\(853\) | − | 2.52887e13i | − | 1.63552i | −0.575560 | − | 0.817760i | \(-0.695216\pi\) | ||
0.575560 | − | 0.817760i | \(-0.304784\pi\) | |||||||
\(854\) | −2.23582e13 | + | 2.85855e12i | −1.43839 | + | 0.183901i | ||||
\(855\) | −3.01170e13 | −1.92737 | ||||||||
\(856\) | −6.33129e12 | + | 2.53972e12i | −0.403051 | + | 0.161679i | ||||
\(857\) | −1.49919e13 | −0.949387 | −0.474693 | − | 0.880151i | \(-0.657441\pi\) | ||||
−0.474693 | + | 0.880151i | \(0.657441\pi\) | |||||||
\(858\) | 5.27128e12 | − | 6.73947e11i | 0.332065 | − | 0.0424554i | ||||
\(859\) | 1.48492e13i | 0.930540i | 0.885169 | + | 0.465270i | \(0.154043\pi\) | ||||
−0.885169 | + | 0.465270i | \(0.845957\pi\) | |||||||
\(860\) | 1.07689e11 | − | 2.79943e10i | 0.00671319 | − | 0.00174512i | ||||
\(861\) | 1.86819e13i | 1.15853i | ||||||||
\(862\) | 3.24033e11 | + | 2.53443e12i | 0.0199897 | + | 0.156350i | ||||
\(863\) | −2.31037e13 | −1.41786 | −0.708928 | − | 0.705281i | \(-0.750821\pi\) | ||||
−0.708928 | + | 0.705281i | \(0.750821\pi\) | |||||||
\(864\) | −2.57977e13 | + | 1.90401e13i | −1.57496 | + | 1.16241i | ||||
\(865\) | 2.08902e12 | 0.126873 | ||||||||
\(866\) | 2.63441e12 | + | 2.06051e13i | 0.159167 | + | 1.24493i | ||||
\(867\) | 1.37105e13i | 0.824077i | ||||||||
\(868\) | 7.66390e12 | − | 1.99226e12i | 0.458259 | − | 0.119126i | ||||
\(869\) | 3.72116e11i | 0.0221355i | ||||||||
\(870\) | −1.70124e13 | + | 2.17508e12i | −1.00677 | + | 0.128718i | ||||
\(871\) | 1.08772e13 | 0.640374 | ||||||||
\(872\) | −9.56478e12 | + | 3.83681e12i | −0.560210 | + | 0.224722i | ||||
\(873\) | 3.31074e13 | 1.92913 | ||||||||
\(874\) | −2.26087e13 | + | 2.89057e12i | −1.31061 | + | 0.167565i | ||||
\(875\) | − | 1.36795e13i | − | 0.788921i | ||||||
\(876\) | −1.30711e13 | − | 5.02825e13i | −0.749972 | − | 2.88502i | ||||
\(877\) | − | 1.71535e11i | − | 0.00979164i | −0.999988 | − | 0.00489582i | \(-0.998442\pi\) | ||
0.999988 | − | 0.00489582i | \(-0.00155839\pi\) | |||||||
\(878\) | −2.67649e12 | − | 2.09342e13i | −0.151999 | − | 1.18886i | ||||
\(879\) | 2.31853e13 | 1.30997 | ||||||||
\(880\) | 4.80709e12 | − | 2.68038e12i | 0.270216 | − | 0.150669i | ||||
\(881\) | 1.01574e13 | 0.568058 | 0.284029 | − | 0.958816i | \(-0.408329\pi\) | ||||
0.284029 | + | 0.958816i | \(0.408329\pi\) | |||||||
\(882\) | 1.72453e12 | + | 1.34884e13i | 0.0959537 | + | 0.750503i | ||||
\(883\) | 1.93867e13i | 1.07320i | 0.843837 | + | 0.536600i | \(0.180292\pi\) | ||||
−0.843837 | + | 0.536600i | \(0.819708\pi\) | |||||||
\(884\) | 2.07501e12 | + | 7.98222e12i | 0.114284 | + | 0.439631i | ||||
\(885\) | 4.04141e12i | 0.221457i | ||||||||
\(886\) | 3.55746e13 | − | 4.54830e12i | 1.93949 | − | 0.247969i | ||||
\(887\) | 2.56537e13 | 1.39153 | 0.695766 | − | 0.718268i | \(-0.255065\pi\) | ||||
0.695766 | + | 0.718268i | \(0.255065\pi\) | |||||||
\(888\) | 9.33023e12 | + | 2.32594e13i | 0.503540 | + | 1.25528i | ||||
\(889\) | −1.96595e13 | −1.05564 | ||||||||
\(890\) | 2.69028e13 | − | 3.43959e12i | 1.43728 | − | 0.183760i | ||||
\(891\) | 7.70084e12i | 0.409344i | ||||||||
\(892\) | −2.37364e13 | + | 6.17039e12i | −1.25538 | + | 0.326340i | ||||
\(893\) | 2.64785e13i | 1.39335i | ||||||||
\(894\) | 1.52161e12 | + | 1.19013e13i | 0.0796679 | + | 0.623124i | ||||
\(895\) | −1.67335e12 | −0.0871734 | ||||||||
\(896\) | −1.20078e13 | − | 9.72335e12i | −0.622413 | − | 0.503999i | ||||
\(897\) | −3.12227e13 | −1.61029 | ||||||||
\(898\) | −1.53038e12 | − | 1.19699e13i | −0.0785335 | − | 0.614251i | ||||
\(899\) | 6.56987e12i | 0.335458i | ||||||||
\(900\) | −1.15925e12 | + | 3.01352e11i | −0.0588960 | + | 0.0153103i | ||||
\(901\) | − | 1.07141e13i | − | 0.541621i | ||||||
\(902\) | 4.93389e12 | − | 6.30810e11i | 0.248176 | − | 0.0317299i | ||||
\(903\) | −1.92973e11 | −0.00965834 | ||||||||
\(904\) | −1.57086e12 | − | 3.91600e12i | −0.0782312 | − | 0.195023i | ||||
\(905\) | 1.89053e13 | 0.936840 | ||||||||
\(906\) | −2.36704e13 | + | 3.02632e12i | −1.16715 | + | 0.149224i | ||||
\(907\) | 3.07269e13i | 1.50760i | 0.657105 | + | 0.753799i | \(0.271781\pi\) | ||||
−0.657105 | + | 0.753799i | \(0.728219\pi\) | |||||||
\(908\) | −5.81636e12 | − | 2.23746e13i | −0.283965 | − | 1.09237i | ||||
\(909\) | − | 3.32579e13i | − | 1.61569i | ||||||
\(910\) | −1.32636e12 | − | 1.03741e13i | −0.0641172 | − | 0.501494i | ||||
\(911\) | 2.80997e13 | 1.35166 | 0.675832 | − | 0.737056i | \(-0.263785\pi\) | ||||
0.675832 | + | 0.737056i | \(0.263785\pi\) | |||||||
\(912\) | 2.89789e13 | − | 1.61583e13i | 1.38709 | − | 0.773426i | ||||
\(913\) | −7.00825e12 | −0.333804 | ||||||||
\(914\) | −1.99455e12 | − | 1.56004e13i | −0.0945337 | − | 0.739397i | ||||
\(915\) | − | 6.86714e13i | − | 3.23878i | ||||||
\(916\) | −1.68479e12 | − | 6.48112e12i | −0.0790710 | − | 0.304173i | ||||
\(917\) | 1.55539e13i | 0.726401i | ||||||||
\(918\) | −3.04937e13 | + | 3.89870e12i | −1.41716 | + | 0.181187i | ||||
\(919\) | 1.57307e13 | 0.727494 | 0.363747 | − | 0.931498i | \(-0.381497\pi\) | ||||
0.363747 | + | 0.931498i | \(0.381497\pi\) | |||||||
\(920\) | −3.00125e13 | + | 1.20392e13i | −1.38120 | + | 0.554053i | ||||
\(921\) | −2.54902e13 | −1.16736 | ||||||||
\(922\) | 3.39476e13 | − | 4.34029e12i | 1.54711 | − | 0.197802i | ||||
\(923\) | − | 1.43274e13i | − | 0.649770i | ||||||
\(924\) | −9.23835e12 | + | 2.40155e12i | −0.416937 | + | 0.108385i | ||||
\(925\) | 4.92498e11i | 0.0221191i | ||||||||
\(926\) | 3.15702e12 | + | 2.46927e13i | 0.141100 | + | 1.10362i | ||||
\(927\) | −3.40687e13 | −1.51529 | ||||||||
\(928\) | 1.03142e13 | − | 7.61247e12i | 0.456532 | − | 0.336946i | ||||
\(929\) | −6.66185e12 | −0.293443 | −0.146722 | − | 0.989178i | \(-0.546872\pi\) | ||||
−0.146722 | + | 0.989178i | \(0.546872\pi\) | |||||||
\(930\) | 3.05954e12 | + | 2.39302e13i | 0.134117 | + | 1.04900i | ||||
\(931\) | − | 7.40252e12i | − | 0.322928i | ||||||
\(932\) | 3.91690e13 | − | 1.01822e13i | 1.70048 | − | 0.442047i | ||||
\(933\) | 3.54432e13i | 1.53132i | ||||||||
\(934\) | 1.63768e13 | − | 2.09382e12i | 0.704155 | − | 0.0900280i | ||||
\(935\) | 5.27707e12 | 0.225809 | ||||||||
\(936\) | 2.86196e13 | − | 1.14804e13i | 1.21877 | − | 0.488897i | ||||
\(937\) | 2.89231e12 | 0.122579 | 0.0612897 | − | 0.998120i | \(-0.480479\pi\) | ||||
0.0612897 | + | 0.998120i | \(0.480479\pi\) | |||||||
\(938\) | −1.93799e13 | + | 2.47777e12i | −0.817407 | + | 0.104507i | ||||
\(939\) | − | 6.28061e13i | − | 2.63637i | ||||||
\(940\) | 9.45140e12 | + | 3.63579e13i | 0.394840 | + | 1.51888i | ||||
\(941\) | − | 7.76858e12i | − | 0.322990i | −0.986874 | − | 0.161495i | \(-0.948369\pi\) | ||
0.986874 | − | 0.161495i | \(-0.0516315\pi\) | |||||||
\(942\) | 7.71743e12 | + | 6.03620e13i | 0.319333 | + | 2.49767i | ||||
\(943\) | −2.92243e13 | −1.20349 | ||||||||
\(944\) | −1.47108e12 | − | 2.63830e12i | −0.0602925 | − | 0.108131i | ||||
\(945\) | 3.89835e13 | 1.59015 | ||||||||
\(946\) | 6.51591e9 | + | 5.09643e10i | 0.000264524 | + | 0.00206898i | ||||
\(947\) | 9.80623e12i | 0.396212i | 0.980181 | + | 0.198106i | \(0.0634790\pi\) | ||||
−0.980181 | + | 0.198106i | \(0.936521\pi\) | |||||||
\(948\) | 8.00720e11 | + | 3.08023e12i | 0.0321991 | + | 0.123864i | ||||
\(949\) | 2.62851e13i | 1.05199i | ||||||||
\(950\) | 6.46776e11 | − | 8.26919e10i | 0.0257631 | − | 0.00329387i | ||||
\(951\) | −5.37917e13 | −2.13257 | ||||||||
\(952\) | −5.51537e12 | − | 1.37493e13i | −0.217625 | − | 0.542517i | ||||
\(953\) | 2.10091e12 | 0.0825067 | 0.0412534 | − | 0.999149i | \(-0.486865\pi\) | ||||
0.0412534 | + | 0.999149i | \(0.486865\pi\) | |||||||
\(954\) | −3.97353e13 | + | 5.08026e12i | −1.55313 | + | 0.198572i | ||||
\(955\) | 3.78901e13i | 1.47405i | ||||||||
\(956\) | −6.26934e12 | + | 1.62974e12i | −0.242751 | + | 0.0631042i | ||||
\(957\) | − | 7.91956e12i | − | 0.305209i | ||||||
\(958\) | −2.79910e12 | − | 2.18932e13i | −0.107368 | − | 0.839779i | ||||
\(959\) | 1.60511e13 | 0.612804 | ||||||||
\(960\) | 3.40237e13 | − | 3.25311e13i | 1.29289 | − | 1.23617i | ||||
\(961\) | −1.71982e13 | −0.650471 | ||||||||
\(962\) | −1.60798e12 | − | 1.25768e13i | −0.0605330 | − | 0.473460i | ||||
\(963\) | 2.44544e13i | 0.916302i | ||||||||
\(964\) | −2.90205e13 | + | 7.54400e12i | −1.08233 | + | 0.281355i | ||||
\(965\) | 1.60543e13i | 0.595960i | ||||||||
\(966\) | 5.56297e13 | − | 7.11239e12i | 2.05546 | − | 0.262796i | ||||
\(967\) | −3.69001e13 | −1.35709 | −0.678544 | − | 0.734560i | \(-0.737389\pi\) | ||||
−0.678544 | + | 0.734560i | \(0.737389\pi\) | |||||||
\(968\) | −9.22412e12 | − | 2.29948e13i | −0.337665 | − | 0.841765i | ||||
\(969\) | 3.18121e13 | 1.15914 | ||||||||
\(970\) | −2.53635e13 | + | 3.24278e12i | −0.919890 | + | 0.117610i | ||||
\(971\) | 1.52779e13i | 0.551542i | 0.961223 | + | 0.275771i | \(0.0889331\pi\) | ||||
−0.961223 | + | 0.275771i | \(0.911067\pi\) | |||||||
\(972\) | 2.86534e12 | + | 1.10225e13i | 0.102962 | + | 0.396079i | ||||
\(973\) | − | 7.43648e12i | − | 0.265986i | ||||||
\(974\) | 2.03475e12 | + | 1.59148e13i | 0.0724429 | + | 0.566613i | ||||
\(975\) | 8.93202e11 | 0.0316540 | ||||||||
\(976\) | 2.49966e13 | + | 4.48298e13i | 0.881771 | + | 1.58140i | ||||
\(977\) | −1.67353e13 | −0.587637 | −0.293818 | − | 0.955861i | \(-0.594926\pi\) | ||||
−0.293818 | + | 0.955861i | \(0.594926\pi\) | |||||||
\(978\) | −3.09832e12 | − | 2.42336e13i | −0.108293 | − | 0.847018i | ||||
\(979\) | 1.25237e13i | 0.435724i | ||||||||
\(980\) | −2.64231e12 | − | 1.01645e13i | −0.0915095 | − | 0.352021i | ||||
\(981\) | 3.69437e13i | 1.27359i | ||||||||
\(982\) | −1.86462e12 | + | 2.38397e11i | −0.0639867 | + | 0.00818085i | ||||
\(983\) | 4.18461e13 | 1.42943 | 0.714717 | − | 0.699414i | \(-0.246556\pi\) | ||||
0.714717 | + | 0.699414i | \(0.246556\pi\) | |||||||
\(984\) | 3.94835e13 | − | 1.58384e13i | 1.34257 | − | 0.538558i | ||||
\(985\) | −5.63442e13 | −1.90716 | ||||||||
\(986\) | 1.21918e13 | − | 1.55875e12i | 0.410790 | − | 0.0525205i | ||||
\(987\) | − | 6.51515e13i | − | 2.18523i | ||||||
\(988\) | −1.62466e13 | + | 4.22337e12i | −0.542445 | + | 0.141011i | ||||
\(989\) | − | 3.01870e11i | − | 0.0100331i | ||||||
\(990\) | −2.50220e12 | − | 1.95710e13i | −0.0827872 | − | 0.647521i | ||||
\(991\) | 4.79950e13 | 1.58075 | 0.790377 | − | 0.612620i | \(-0.209885\pi\) | ||||
0.790377 | + | 0.612620i | \(0.209885\pi\) | |||||||
\(992\) | −1.07080e13 | − | 1.45084e13i | −0.351079 | − | 0.475681i | ||||
\(993\) | 7.37698e12 | 0.240773 | ||||||||
\(994\) | 3.26371e12 | + | 2.55272e13i | 0.106041 | + | 0.829400i | ||||
\(995\) | − | 2.94356e13i | − | 0.952069i | ||||||
\(996\) | −5.80117e13 | + | 1.50804e13i | −1.86788 | + | 0.485563i | ||||
\(997\) | − | 3.46659e13i | − | 1.11115i | −0.831465 | − | 0.555576i | \(-0.812498\pi\) | ||
0.831465 | − | 0.555576i | \(-0.187502\pi\) | |||||||
\(998\) | −3.47161e13 | + | 4.43854e12i | −1.10776 | + | 0.141629i | ||||
\(999\) | 4.72607e13 | 1.50126 |
(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 | 8.10.b.a.5.6 | yes | 8 | |
3.2 | odd | 2 | 72.10.d.b.37.3 | 8 | |||
4.3 | odd | 2 | 32.10.b.a.17.8 | 8 | |||
8.3 | odd | 2 | 32.10.b.a.17.1 | 8 | |||
8.5 | even | 2 | inner | 8.10.b.a.5.5 | ✓ | 8 | |
12.11 | even | 2 | 288.10.d.b.145.7 | 8 | |||
16.3 | odd | 4 | 256.10.a.s.1.1 | 8 | |||
16.5 | even | 4 | 256.10.a.p.1.1 | 8 | |||
16.11 | odd | 4 | 256.10.a.s.1.8 | 8 | |||
16.13 | even | 4 | 256.10.a.p.1.8 | 8 | |||
24.5 | odd | 2 | 72.10.d.b.37.4 | 8 | |||
24.11 | even | 2 | 288.10.d.b.145.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.10.b.a.5.5 | ✓ | 8 | 8.5 | even | 2 | inner | |
8.10.b.a.5.6 | yes | 8 | 1.1 | even | 1 | trivial | |
32.10.b.a.17.1 | 8 | 8.3 | odd | 2 | |||
32.10.b.a.17.8 | 8 | 4.3 | odd | 2 | |||
72.10.d.b.37.3 | 8 | 3.2 | odd | 2 | |||
72.10.d.b.37.4 | 8 | 24.5 | odd | 2 | |||
256.10.a.p.1.1 | 8 | 16.5 | even | 4 | |||
256.10.a.p.1.8 | 8 | 16.13 | even | 4 | |||
256.10.a.s.1.1 | 8 | 16.3 | odd | 4 | |||
256.10.a.s.1.8 | 8 | 16.11 | odd | 4 | |||
288.10.d.b.145.2 | 8 | 24.11 | even | 2 | |||
288.10.d.b.145.7 | 8 | 12.11 | even | 2 |