Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,7,Mod(3,8)]
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([1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (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: | \(1.84043266896\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.3803625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 6x^{2} - 16x + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.4 | ||
Root | \(2.81174 + 2.84502i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.7.d.b.3.3 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.62348 | + | 5.69004i | 0.702934 | + | 0.711255i | ||||
\(3\) | 8.49390 | 0.314589 | 0.157294 | − | 0.987552i | \(-0.449723\pi\) | ||||
0.157294 | + | 0.987552i | \(0.449723\pi\) | |||||||
\(4\) | −0.753049 | + | 63.9956i | −0.0117664 | + | 0.999931i | ||||
\(5\) | − | 59.7107i | − | 0.477686i | −0.971058 | − | 0.238843i | \(-0.923232\pi\) | ||
0.971058 | − | 0.238843i | \(-0.0767681\pi\) | |||||||
\(6\) | 47.7652 | + | 48.3306i | 0.221135 | + | 0.223753i | ||||
\(7\) | − | 483.584i | − | 1.40987i | −0.709274 | − | 0.704933i | \(-0.750977\pi\) | ||
0.709274 | − | 0.704933i | \(-0.249023\pi\) | |||||||
\(8\) | −368.372 | + | 355.593i | −0.719476 | + | 0.694517i | ||||
\(9\) | −656.854 | −0.901034 | ||||||||
\(10\) | 339.756 | − | 335.782i | 0.339756 | − | 0.335782i | ||||
\(11\) | 1412.15 | 1.06097 | 0.530485 | − | 0.847694i | \(-0.322010\pi\) | ||||
0.530485 | + | 0.847694i | \(0.322010\pi\) | |||||||
\(12\) | −6.39633 | + | 543.572i | −0.00370158 | + | 0.314567i | ||||
\(13\) | 3450.70i | 1.57064i | 0.619090 | + | 0.785320i | \(0.287501\pi\) | ||||
−0.619090 | + | 0.785320i | \(0.712499\pi\) | |||||||
\(14\) | 2751.61 | − | 2719.42i | 1.00277 | − | 0.991043i | ||||
\(15\) | − | 507.177i | − | 0.150275i | ||||||
\(16\) | −4094.87 | − | 96.3836i | −0.999723 | − | 0.0235312i | ||||
\(17\) | −3056.78 | −0.622182 | −0.311091 | − | 0.950380i | \(-0.600694\pi\) | ||||
−0.311091 | + | 0.950380i | \(0.600694\pi\) | |||||||
\(18\) | −3693.80 | − | 3737.52i | −0.633368 | − | 0.640864i | ||||
\(19\) | 968.104 | 0.141144 | 0.0705718 | − | 0.997507i | \(-0.477518\pi\) | ||||
0.0705718 | + | 0.997507i | \(0.477518\pi\) | |||||||
\(20\) | 3821.22 | + | 44.9651i | 0.477652 | + | 0.00562064i | ||||
\(21\) | − | 4107.51i | − | 0.443528i | ||||||
\(22\) | 7941.20 | + | 8035.20i | 0.745793 | + | 0.754621i | ||||
\(23\) | − | 3314.31i | − | 0.272401i | −0.990681 | − | 0.136201i | \(-0.956511\pi\) | ||
0.990681 | − | 0.136201i | \(-0.0434892\pi\) | |||||||
\(24\) | −3128.91 | + | 3020.37i | −0.226339 | + | 0.218487i | ||||
\(25\) | 12059.6 | 0.771817 | ||||||||
\(26\) | −19634.6 | + | 19404.9i | −1.11712 | + | 1.10406i | ||||
\(27\) | −11771.3 | −0.598044 | ||||||||
\(28\) | 30947.2 | + | 364.162i | 1.40977 | + | 0.0165890i | ||||
\(29\) | − | 26351.6i | − | 1.08047i | −0.841513 | − | 0.540236i | \(-0.818335\pi\) | ||
0.841513 | − | 0.540236i | \(-0.181665\pi\) | |||||||
\(30\) | 2885.85 | − | 2852.10i | 0.106884 | − | 0.105633i | ||||
\(31\) | 27104.3i | 0.909815i | 0.890539 | + | 0.454907i | \(0.150328\pi\) | ||||
−0.890539 | + | 0.454907i | \(0.849672\pi\) | |||||||
\(32\) | −22479.0 | − | 23842.0i | −0.686003 | − | 0.727599i | ||||
\(33\) | 11994.7 | 0.333770 | ||||||||
\(34\) | −17189.7 | − | 17393.2i | −0.437353 | − | 0.442530i | ||||
\(35\) | −28875.1 | −0.673472 | ||||||||
\(36\) | 494.643 | − | 42035.7i | 0.0106019 | − | 0.900971i | ||||
\(37\) | 36097.0i | 0.712633i | 0.934365 | + | 0.356317i | \(0.115968\pi\) | ||||
−0.934365 | + | 0.356317i | \(0.884032\pi\) | |||||||
\(38\) | 5444.11 | + | 5508.55i | 0.0992147 | + | 0.100389i | ||||
\(39\) | 29309.9i | 0.494106i | ||||||||
\(40\) | 21232.7 | + | 21995.7i | 0.331761 | + | 0.343683i | ||||
\(41\) | −6860.73 | −0.0995449 | −0.0497724 | − | 0.998761i | \(-0.515850\pi\) | ||||
−0.0497724 | + | 0.998761i | \(0.515850\pi\) | |||||||
\(42\) | 23371.9 | − | 23098.5i | 0.315461 | − | 0.311771i | ||||
\(43\) | 92831.6 | 1.16759 | 0.583795 | − | 0.811901i | \(-0.301567\pi\) | ||||
0.583795 | + | 0.811901i | \(0.301567\pi\) | |||||||
\(44\) | −1063.42 | + | 90371.5i | −0.0124838 | + | 1.06090i | ||||
\(45\) | 39221.2i | 0.430411i | ||||||||
\(46\) | 18858.5 | − | 18637.9i | 0.193747 | − | 0.191480i | ||||
\(47\) | − | 159323.i | − | 1.53456i | −0.641309 | − | 0.767282i | \(-0.721608\pi\) | ||
0.641309 | − | 0.767282i | \(-0.278392\pi\) | |||||||
\(48\) | −34781.4 | − | 818.673i | −0.314502 | − | 0.00740264i | ||||
\(49\) | −116204. | −0.987720 | ||||||||
\(50\) | 67817.1 | + | 68619.8i | 0.542536 | + | 0.548958i | ||||
\(51\) | −25964.0 | −0.195732 | ||||||||
\(52\) | −220829. | − | 2598.54i | −1.57053 | − | 0.0184808i | ||||
\(53\) | − | 86612.3i | − | 0.581771i | −0.956758 | − | 0.290885i | \(-0.906050\pi\) | ||
0.956758 | − | 0.290885i | \(-0.0939498\pi\) | |||||||
\(54\) | −66195.6 | − | 66979.2i | −0.420386 | − | 0.425362i | ||||
\(55\) | − | 84320.6i | − | 0.506810i | ||||||
\(56\) | 171959. | + | 178139.i | 0.979175 | + | 1.01436i | ||||
\(57\) | 8222.98 | 0.0444022 | ||||||||
\(58\) | 149942. | − | 148188.i | 0.768491 | − | 0.759501i | ||||
\(59\) | 128806. | 0.627165 | 0.313582 | − | 0.949561i | \(-0.398471\pi\) | ||||
0.313582 | + | 0.949561i | \(0.398471\pi\) | |||||||
\(60\) | 32457.1 | + | 381.929i | 0.150264 | + | 0.00176819i | ||||
\(61\) | 189486.i | 0.834810i | 0.908721 | + | 0.417405i | \(0.137060\pi\) | ||||
−0.908721 | + | 0.417405i | \(0.862940\pi\) | |||||||
\(62\) | −154224. | + | 152420.i | −0.647110 | + | 0.639540i | ||||
\(63\) | 317644.i | 1.27034i | ||||||||
\(64\) | 9251.76 | − | 261981.i | 0.0352927 | − | 0.999377i | ||||
\(65\) | 206043. | 0.750272 | ||||||||
\(66\) | 67451.8 | + | 68250.2i | 0.234618 | + | 0.237395i | ||||
\(67\) | −319835. | −1.06341 | −0.531706 | − | 0.846929i | \(-0.678449\pi\) | ||||
−0.531706 | + | 0.846929i | \(0.678449\pi\) | |||||||
\(68\) | 2301.91 | − | 195620.i | 0.00732084 | − | 0.622139i | ||||
\(69\) | − | 28151.4i | − | 0.0856945i | ||||||
\(70\) | −162379. | − | 164301.i | −0.473407 | − | 0.479010i | ||||
\(71\) | 196890.i | 0.550108i | 0.961429 | + | 0.275054i | \(0.0886957\pi\) | ||||
−0.961429 | + | 0.275054i | \(0.911304\pi\) | |||||||
\(72\) | 241966. | − | 233572.i | 0.648273 | − | 0.625783i | ||||
\(73\) | −63957.9 | −0.164409 | −0.0822046 | − | 0.996615i | \(-0.526196\pi\) | ||||
−0.0822046 | + | 0.996615i | \(0.526196\pi\) | |||||||
\(74\) | −205393. | + | 202991.i | −0.506864 | + | 0.500934i | ||||
\(75\) | 102433. | 0.242805 | ||||||||
\(76\) | −729.030 | + | 61954.3i | −0.00166075 | + | 0.141134i | ||||
\(77\) | − | 682894.i | − | 1.49583i | ||||||
\(78\) | −166774. | + | 164823.i | −0.351435 | + | 0.347324i | ||||
\(79\) | − | 164678.i | − | 0.334006i | −0.985956 | − | 0.167003i | \(-0.946591\pi\) | ||
0.985956 | − | 0.167003i | \(-0.0534090\pi\) | |||||||
\(80\) | −5755.13 | + | 244507.i | −0.0112405 | + | 0.477553i | ||||
\(81\) | 378862. | 0.712896 | ||||||||
\(82\) | −38581.2 | − | 39037.8i | −0.0699735 | − | 0.0708018i | ||||
\(83\) | −802946. | −1.40428 | −0.702138 | − | 0.712041i | \(-0.747771\pi\) | ||||
−0.702138 | + | 0.712041i | \(0.747771\pi\) | |||||||
\(84\) | 262863. | + | 3093.16i | 0.443497 | + | 0.00521873i | ||||
\(85\) | 182522.i | 0.297207i | ||||||||
\(86\) | 522036. | + | 528215.i | 0.820739 | + | 0.830454i | ||||
\(87\) | − | 223828.i | − | 0.339905i | ||||||
\(88\) | −520197. | + | 502151.i | −0.763344 | + | 0.736862i | ||||
\(89\) | −54145.3 | −0.0768052 | −0.0384026 | − | 0.999262i | \(-0.512227\pi\) | ||||
−0.0384026 | + | 0.999262i | \(0.512227\pi\) | |||||||
\(90\) | −223170. | + | 220559.i | −0.306132 | + | 0.302551i | ||||
\(91\) | 1.66870e6 | 2.21439 | ||||||||
\(92\) | 212101. | + | 2495.84i | 0.272383 | + | 0.00320518i | ||||
\(93\) | 230221.i | 0.286218i | ||||||||
\(94\) | 906555. | − | 895950.i | 1.09147 | − | 1.07870i | ||||
\(95\) | − | 57806.1i | − | 0.0674222i | ||||||
\(96\) | −190934. | − | 202511.i | −0.215809 | − | 0.228894i | ||||
\(97\) | −1.10670e6 | −1.21259 | −0.606297 | − | 0.795238i | \(-0.707346\pi\) | ||||
−0.606297 | + | 0.795238i | \(0.707346\pi\) | |||||||
\(98\) | −653472. | − | 661207.i | −0.694302 | − | 0.702520i | ||||
\(99\) | −927577. | −0.955971 | ||||||||
\(100\) | −9081.50 | + | 771763.i | −0.00908150 | + | 0.771763i | ||||
\(101\) | 809583.i | 0.785773i | 0.919587 | + | 0.392887i | \(0.128524\pi\) | ||||
−0.919587 | + | 0.392887i | \(0.871476\pi\) | |||||||
\(102\) | −146008. | − | 147736.i | −0.137586 | − | 0.139215i | ||||
\(103\) | − | 619448.i | − | 0.566883i | −0.958990 | − | 0.283442i | \(-0.908524\pi\) | ||
0.958990 | − | 0.283442i | \(-0.0914762\pi\) | |||||||
\(104\) | −1.22704e6 | − | 1.27114e6i | −1.09084 | − | 1.13004i | ||||
\(105\) | −245262. | −0.211867 | ||||||||
\(106\) | 492827. | − | 487062.i | 0.413787 | − | 0.408947i | ||||
\(107\) | 1.08619e6 | 0.886657 | 0.443328 | − | 0.896359i | \(-0.353798\pi\) | ||||
0.443328 | + | 0.896359i | \(0.353798\pi\) | |||||||
\(108\) | 8864.37 | − | 753311.i | 0.00703682 | − | 0.598003i | ||||
\(109\) | 1.71692e6i | 1.32578i | 0.748717 | + | 0.662890i | \(0.230670\pi\) | ||||
−0.748717 | + | 0.662890i | \(0.769330\pi\) | |||||||
\(110\) | 479787. | − | 474175.i | 0.360471 | − | 0.356255i | ||||
\(111\) | 306604.i | 0.224187i | ||||||||
\(112\) | −46609.6 | + | 1.98021e6i | −0.0331758 | + | 1.40947i | ||||
\(113\) | 645423. | 0.447311 | 0.223655 | − | 0.974668i | \(-0.428201\pi\) | ||||
0.223655 | + | 0.974668i | \(0.428201\pi\) | |||||||
\(114\) | 46241.7 | + | 46789.0i | 0.0312118 | + | 0.0315813i | ||||
\(115\) | −197900. | −0.130122 | ||||||||
\(116\) | 1.68639e6 | + | 19844.1i | 1.08040 | + | 0.0127133i | ||||
\(117\) | − | 2.26660e6i | − | 1.41520i | ||||||
\(118\) | 724340. | + | 732914.i | 0.440856 | + | 0.446074i | ||||
\(119\) | 1.47821e6i | 0.877193i | ||||||||
\(120\) | 180348. | + | 186830.i | 0.104368 | + | 0.108119i | ||||
\(121\) | 222613. | 0.125659 | ||||||||
\(122\) | −1.07818e6 | + | 1.06557e6i | −0.593762 | + | 0.586816i | ||||
\(123\) | −58274.4 | −0.0313157 | ||||||||
\(124\) | −1.73455e6 | − | 20410.9i | −0.909752 | − | 0.0107052i | ||||
\(125\) | − | 1.65307e6i | − | 0.846371i | ||||||
\(126\) | −1.80740e6 | + | 1.78626e6i | −0.903533 | + | 0.892963i | ||||
\(127\) | − | 2.51504e6i | − | 1.22781i | −0.789378 | − | 0.613907i | \(-0.789597\pi\) | ||
0.789378 | − | 0.613907i | \(-0.210403\pi\) | |||||||
\(128\) | 1.54271e6 | − | 1.42060e6i | 0.735620 | − | 0.677394i | ||||
\(129\) | 788502. | 0.367311 | ||||||||
\(130\) | 1.15868e6 | + | 1.17239e6i | 0.527392 | + | 0.533634i | ||||
\(131\) | −3.77470e6 | −1.67907 | −0.839536 | − | 0.543305i | \(-0.817173\pi\) | ||||
−0.839536 | + | 0.543305i | \(0.817173\pi\) | |||||||
\(132\) | −9032.59 | + | 767607.i | −0.00392727 | + | 0.333747i | ||||
\(133\) | − | 468159.i | − | 0.198993i | ||||||
\(134\) | −1.79858e6 | − | 1.81987e6i | −0.747509 | − | 0.756357i | ||||
\(135\) | 702873.i | 0.285677i | ||||||||
\(136\) | 1.12603e6 | − | 1.08697e6i | 0.447645 | − | 0.432116i | ||||
\(137\) | 1.40637e6 | 0.546939 | 0.273470 | − | 0.961881i | \(-0.411829\pi\) | ||||
0.273470 | + | 0.961881i | \(0.411829\pi\) | |||||||
\(138\) | 160183. | − | 158309.i | 0.0609506 | − | 0.0602376i | ||||
\(139\) | 2.31561e6 | 0.862227 | 0.431114 | − | 0.902298i | \(-0.358121\pi\) | ||||
0.431114 | + | 0.902298i | \(0.358121\pi\) | |||||||
\(140\) | 21744.4 | − | 1.84788e6i | 0.00792434 | − | 0.673426i | ||||
\(141\) | − | 1.35327e6i | − | 0.482757i | ||||||
\(142\) | −1.12031e6 | + | 1.10720e6i | −0.391267 | + | 0.386690i | ||||
\(143\) | 4.87291e6i | 1.66640i | ||||||||
\(144\) | 2.68973e6 | + | 63309.9i | 0.900784 | + | 0.0212024i | ||||
\(145\) | −1.57347e6 | −0.516126 | ||||||||
\(146\) | −359666. | − | 363923.i | −0.115569 | − | 0.116937i | ||||
\(147\) | −987028. | −0.310726 | ||||||||
\(148\) | −2.31005e6 | − | 27182.8i | −0.712584 | − | 0.00838512i | ||||
\(149\) | 4.74866e6i | 1.43553i | 0.696285 | + | 0.717765i | \(0.254835\pi\) | ||||
−0.696285 | + | 0.717765i | \(0.745165\pi\) | |||||||
\(150\) | 576031. | + | 582850.i | 0.170676 | + | 0.172696i | ||||
\(151\) | − | 1.11787e6i | − | 0.324684i | −0.986735 | − | 0.162342i | \(-0.948095\pi\) | ||
0.986735 | − | 0.162342i | \(-0.0519047\pi\) | |||||||
\(152\) | −356622. | + | 344251.i | −0.101549 | + | 0.0980266i | ||||
\(153\) | 2.00786e6 | 0.560607 | ||||||||
\(154\) | 3.88569e6 | − | 3.84024e6i | 1.06391 | − | 1.05147i | ||||
\(155\) | 1.61842e6 | 0.434605 | ||||||||
\(156\) | −1.87570e6 | − | 22071.8i | −0.494072 | − | 0.00581384i | ||||
\(157\) | 1.00407e6i | 0.259458i | 0.991550 | + | 0.129729i | \(0.0414107\pi\) | ||||
−0.991550 | + | 0.129729i | \(0.958589\pi\) | |||||||
\(158\) | 937025. | − | 926064.i | 0.237564 | − | 0.234785i | ||||
\(159\) | − | 735676.i | − | 0.183019i | ||||||
\(160\) | −1.42362e6 | + | 1.34223e6i | −0.347563 | + | 0.327694i | ||||
\(161\) | −1.60275e6 | −0.384049 | ||||||||
\(162\) | 2.13052e6 | + | 2.15574e6i | 0.501119 | + | 0.507050i | ||||
\(163\) | 1.47315e6 | 0.340161 | 0.170080 | − | 0.985430i | \(-0.445597\pi\) | ||||
0.170080 | + | 0.985430i | \(0.445597\pi\) | |||||||
\(164\) | 5166.47 | − | 439056.i | 0.00117128 | − | 0.0995380i | ||||
\(165\) | − | 716211.i | − | 0.159437i | ||||||
\(166\) | −4.51535e6 | − | 4.56879e6i | −0.987113 | − | 0.998797i | ||||
\(167\) | − | 5.16350e6i | − | 1.10865i | −0.832300 | − | 0.554326i | \(-0.812976\pi\) | ||
0.832300 | − | 0.554326i | \(-0.187024\pi\) | |||||||
\(168\) | 1.46060e6 | + | 1.51309e6i | 0.308038 | + | 0.319108i | ||||
\(169\) | −7.08049e6 | −1.46691 | ||||||||
\(170\) | −1.03856e6 | + | 1.02641e6i | −0.211390 | + | 0.208917i | ||||
\(171\) | −635902. | −0.127175 | ||||||||
\(172\) | −69906.7 | + | 5.94081e6i | −0.0137383 | + | 1.16751i | ||||
\(173\) | − | 600245.i | − | 0.115928i | −0.998319 | − | 0.0579642i | \(-0.981539\pi\) | ||
0.998319 | − | 0.0579642i | \(-0.0184609\pi\) | |||||||
\(174\) | 1.27359e6 | − | 1.25869e6i | 0.241759 | − | 0.238931i | ||||
\(175\) | − | 5.83184e6i | − | 1.08816i | ||||||
\(176\) | −5.78257e6 | − | 136108.i | −1.06068 | − | 0.0249659i | ||||
\(177\) | 1.09407e6 | 0.197299 | ||||||||
\(178\) | −304485. | − | 308089.i | −0.0539890 | − | 0.0546280i | ||||
\(179\) | 6.34654e6 | 1.10657 | 0.553284 | − | 0.832993i | \(-0.313375\pi\) | ||||
0.553284 | + | 0.832993i | \(0.313375\pi\) | |||||||
\(180\) | −2.50998e6 | − | 29535.5i | −0.430381 | − | 0.00506438i | ||||
\(181\) | − | 1.35031e6i | − | 0.227719i | −0.993497 | − | 0.113859i | \(-0.963679\pi\) | ||
0.993497 | − | 0.113859i | \(-0.0363213\pi\) | |||||||
\(182\) | 9.38389e6 | + | 9.49497e6i | 1.55657 | + | 1.57500i | ||||
\(183\) | 1.60947e6i | 0.262622i | ||||||||
\(184\) | 1.17854e6 | + | 1.22090e6i | 0.189187 | + | 0.195986i | ||||
\(185\) | 2.15538e6 | 0.340415 | ||||||||
\(186\) | −1.30997e6 | + | 1.29464e6i | −0.203574 | + | 0.201192i | ||||
\(187\) | −4.31664e6 | −0.660117 | ||||||||
\(188\) | 1.01960e7 | + | 119978.i | 1.53446 | + | 0.0180563i | ||||
\(189\) | 5.69241e6i | 0.843162i | ||||||||
\(190\) | 328919. | − | 325071.i | 0.0479544 | − | 0.0473934i | ||||
\(191\) | 3.32043e6i | 0.476534i | 0.971200 | + | 0.238267i | \(0.0765794\pi\) | ||||
−0.971200 | + | 0.238267i | \(0.923421\pi\) | |||||||
\(192\) | 78583.5 | − | 2.22524e6i | 0.0111027 | − | 0.314393i | ||||
\(193\) | 5.59202e6 | 0.777852 | 0.388926 | − | 0.921269i | \(-0.372846\pi\) | ||||
0.388926 | + | 0.921269i | \(0.372846\pi\) | |||||||
\(194\) | −6.22351e6 | − | 6.29717e6i | −0.852374 | − | 0.862463i | ||||
\(195\) | 1.75011e6 | 0.236027 | ||||||||
\(196\) | 87507.5 | − | 7.43656e6i | 0.0116219 | − | 0.987652i | ||||
\(197\) | − | 7.19799e6i | − | 0.941483i | −0.882271 | − | 0.470742i | \(-0.843986\pi\) | ||
0.882271 | − | 0.470742i | \(-0.156014\pi\) | |||||||
\(198\) | −5.21621e6 | − | 5.27795e6i | −0.671985 | − | 0.679939i | ||||
\(199\) | 1.15838e7i | 1.46991i | 0.678116 | + | 0.734955i | \(0.262797\pi\) | ||||
−0.678116 | + | 0.734955i | \(0.737203\pi\) | |||||||
\(200\) | −4.44243e6 | + | 4.28832e6i | −0.555304 | + | 0.536040i | ||||
\(201\) | −2.71665e6 | −0.334538 | ||||||||
\(202\) | −4.60656e6 | + | 4.55267e6i | −0.558885 | + | 0.552347i | ||||
\(203\) | −1.27432e7 | −1.52332 | ||||||||
\(204\) | 19552.2 | − | 1.66158e6i | 0.00230306 | − | 0.195718i | ||||
\(205\) | 409659.i | 0.0475511i | ||||||||
\(206\) | 3.52468e6 | − | 3.48345e6i | 0.403198 | − | 0.398482i | ||||
\(207\) | 2.17701e6i | 0.245443i | ||||||||
\(208\) | 332591. | − | 1.41301e7i | 0.0369590 | − | 1.57020i | ||||
\(209\) | 1.36711e6 | 0.149749 | ||||||||
\(210\) | −1.37923e6 | − | 1.39555e6i | −0.148929 | − | 0.150691i | ||||
\(211\) | −639344. | −0.0680592 | −0.0340296 | − | 0.999421i | \(-0.510834\pi\) | ||||
−0.0340296 | + | 0.999421i | \(0.510834\pi\) | |||||||
\(212\) | 5.54280e6 | + | 65223.3i | 0.581730 | + | 0.00684534i | ||||
\(213\) | 1.67236e6i | 0.173058i | ||||||||
\(214\) | 6.10818e6 | + | 6.18048e6i | 0.623262 | + | 0.630639i | ||||
\(215\) | − | 5.54304e6i | − | 0.557741i | ||||||
\(216\) | 4.33622e6 | − | 4.18579e6i | 0.430279 | − | 0.415352i | ||||
\(217\) | 1.31072e7 | 1.28272 | ||||||||
\(218\) | −9.76936e6 | + | 9.65508e6i | −0.942968 | + | 0.931937i | ||||
\(219\) | −543252. | −0.0517213 | ||||||||
\(220\) | 5.39614e6 | + | 63497.6i | 0.506775 | + | 0.00596333i | ||||
\(221\) | − | 1.05480e7i | − | 0.977224i | ||||||
\(222\) | −1.74459e6 | + | 1.72418e6i | −0.159454 | + | 0.157588i | ||||
\(223\) | 9.51144e6i | 0.857693i | 0.903377 | + | 0.428846i | \(0.141080\pi\) | ||||
−0.903377 | + | 0.428846i | \(0.858920\pi\) | |||||||
\(224\) | −1.15296e7 | + | 1.08705e7i | −1.02582 | + | 0.967172i | ||||
\(225\) | −7.92141e6 | −0.695433 | ||||||||
\(226\) | 3.62952e6 | + | 3.67248e6i | 0.314430 | + | 0.318152i | ||||
\(227\) | 1.27875e7 | 1.09322 | 0.546610 | − | 0.837387i | \(-0.315918\pi\) | ||||
0.546610 | + | 0.837387i | \(0.315918\pi\) | |||||||
\(228\) | −6192.31 | + | 526234.i | −0.000522454 | + | 0.0443991i | ||||
\(229\) | 4.61930e6i | 0.384653i | 0.981331 | + | 0.192327i | \(0.0616033\pi\) | ||||
−0.981331 | + | 0.192327i | \(0.938397\pi\) | |||||||
\(230\) | −1.11288e6 | − | 1.12606e6i | −0.0914674 | − | 0.0925500i | ||||
\(231\) | − | 5.80043e6i | − | 0.470570i | ||||||
\(232\) | 9.37045e6 | + | 9.70720e6i | 0.750406 | + | 0.777374i | ||||
\(233\) | −9.41375e6 | −0.744209 | −0.372105 | − | 0.928191i | \(-0.621364\pi\) | ||||
−0.372105 | + | 0.928191i | \(0.621364\pi\) | |||||||
\(234\) | 1.28970e7 | − | 1.27462e7i | 1.00657 | − | 0.994792i | ||||
\(235\) | −9.51329e6 | −0.733039 | ||||||||
\(236\) | −96997.6 | + | 8.24304e6i | −0.00737947 | + | 0.627121i | ||||
\(237\) | − | 1.39876e6i | − | 0.105075i | ||||||
\(238\) | −8.41107e6 | + | 8.31267e6i | −0.623907 | + | 0.616609i | ||||
\(239\) | − | 2.57043e7i | − | 1.88283i | −0.337247 | − | 0.941416i | \(-0.609496\pi\) | ||
0.337247 | − | 0.941416i | \(-0.390504\pi\) | |||||||
\(240\) | −48883.5 | + | 2.07682e6i | −0.00353614 | + | 0.150233i | ||||
\(241\) | 8.16838e6 | 0.583559 | 0.291779 | − | 0.956486i | \(-0.405753\pi\) | ||||
0.291779 | + | 0.956486i | \(0.405753\pi\) | |||||||
\(242\) | 1.25186e6 | + | 1.26668e6i | 0.0883303 | + | 0.0893759i | ||||
\(243\) | 1.17993e7 | 0.822313 | ||||||||
\(244\) | −1.21263e7 | − | 142692.i | −0.834752 | − | 0.00982270i | ||||
\(245\) | 6.93864e6i | 0.471820i | ||||||||
\(246\) | −327705. | − | 331583.i | −0.0220129 | − | 0.0222735i | ||||
\(247\) | 3.34063e6i | 0.221686i | ||||||||
\(248\) | −9.63808e6 | − | 9.98446e6i | −0.631882 | − | 0.654590i | ||||
\(249\) | −6.82015e6 | −0.441769 | ||||||||
\(250\) | 9.40602e6 | − | 9.29599e6i | 0.601985 | − | 0.594943i | ||||
\(251\) | −8.44540e6 | −0.534071 | −0.267035 | − | 0.963687i | \(-0.586044\pi\) | ||||
−0.267035 | + | 0.963687i | \(0.586044\pi\) | |||||||
\(252\) | −2.03278e7 | − | 239201.i | −1.27025 | − | 0.0149473i | ||||
\(253\) | − | 4.68031e6i | − | 0.289010i | ||||||
\(254\) | 1.43106e7 | − | 1.41432e7i | 0.873289 | − | 0.863073i | ||||
\(255\) | 1.55033e6i | 0.0934981i | ||||||||
\(256\) | 1.67586e7 | + | 789356.i | 0.998893 | + | 0.0470493i | ||||
\(257\) | −1.84481e7 | −1.08681 | −0.543403 | − | 0.839472i | \(-0.682864\pi\) | ||||
−0.543403 | + | 0.839472i | \(0.682864\pi\) | |||||||
\(258\) | 4.43412e6 | + | 4.48661e6i | 0.258195 | + | 0.261252i | ||||
\(259\) | 1.74559e7 | 1.00472 | ||||||||
\(260\) | −155161. | + | 1.31859e7i | −0.00882799 | + | 0.750220i | ||||
\(261\) | 1.73092e7i | 0.973542i | ||||||||
\(262\) | −2.12270e7 | − | 2.14782e7i | −1.18028 | − | 1.19425i | ||||
\(263\) | 3.84095e6i | 0.211140i | 0.994412 | + | 0.105570i | \(0.0336668\pi\) | ||||
−0.994412 | + | 0.105570i | \(0.966333\pi\) | |||||||
\(264\) | −4.41850e6 | + | 4.26522e6i | −0.240139 | + | 0.231809i | ||||
\(265\) | −5.17168e6 | −0.277903 | ||||||||
\(266\) | 2.66384e6 | − | 2.63268e6i | 0.141535 | − | 0.139879i | ||||
\(267\) | −459904. | −0.0241621 | ||||||||
\(268\) | 240852. | − | 2.04680e7i | 0.0125125 | − | 1.06334i | ||||
\(269\) | 3.10430e7i | 1.59480i | 0.603451 | + | 0.797400i | \(0.293792\pi\) | ||||
−0.603451 | + | 0.797400i | \(0.706208\pi\) | |||||||
\(270\) | −3.99937e6 | + | 3.95259e6i | −0.203189 | + | 0.200812i | ||||
\(271\) | 2.35560e7i | 1.18357i | 0.806097 | + | 0.591784i | \(0.201576\pi\) | ||||
−0.806097 | + | 0.591784i | \(0.798424\pi\) | |||||||
\(272\) | 1.25171e7 | + | 294624.i | 0.622010 | + | 0.0146407i | ||||
\(273\) | 1.41738e7 | 0.696623 | ||||||||
\(274\) | 7.90871e6 | + | 8.00232e6i | 0.384462 | + | 0.389013i | ||||
\(275\) | 1.70300e7 | 0.818875 | ||||||||
\(276\) | 1.80156e6 | + | 21199.4i | 0.0856885 | + | 0.00100831i | ||||
\(277\) | − | 2.32189e7i | − | 1.09245i | −0.837638 | − | 0.546225i | \(-0.816064\pi\) | ||
0.837638 | − | 0.546225i | \(-0.183936\pi\) | |||||||
\(278\) | 1.30218e7 | + | 1.31759e7i | 0.606089 | + | 0.613263i | ||||
\(279\) | − | 1.78035e7i | − | 0.819774i | ||||||
\(280\) | 1.06368e7 | − | 1.02678e7i | 0.484547 | − | 0.467738i | ||||
\(281\) | 2.99519e7 | 1.34991 | 0.674955 | − | 0.737859i | \(-0.264163\pi\) | ||||
0.674955 | + | 0.737859i | \(0.264163\pi\) | |||||||
\(282\) | 7.70018e6 | − | 7.61011e6i | 0.343363 | − | 0.339347i | ||||
\(283\) | −3.68036e7 | −1.62380 | −0.811898 | − | 0.583800i | \(-0.801565\pi\) | ||||
−0.811898 | + | 0.583800i | \(0.801565\pi\) | |||||||
\(284\) | −1.26001e7 | − | 148268.i | −0.550070 | − | 0.00647279i | ||||
\(285\) | − | 491000.i | − | 0.0212103i | ||||||
\(286\) | −2.77270e7 | + | 2.74027e7i | −1.18524 | + | 1.17137i | ||||
\(287\) | 3.31774e6i | 0.140345i | ||||||||
\(288\) | 1.47654e7 | + | 1.56607e7i | 0.618112 | + | 0.655591i | ||||
\(289\) | −1.47937e7 | −0.612890 | ||||||||
\(290\) | −8.84840e6 | − | 8.95313e6i | −0.362803 | − | 0.367097i | ||||
\(291\) | −9.40021e6 | −0.381469 | ||||||||
\(292\) | 48163.5 | − | 4.09303e6i | 0.00193450 | − | 0.164398i | ||||
\(293\) | − | 3.36919e7i | − | 1.33944i | −0.742615 | − | 0.669718i | \(-0.766415\pi\) | ||
0.742615 | − | 0.669718i | \(-0.233585\pi\) | |||||||
\(294\) | −5.55053e6 | − | 5.61622e6i | −0.218420 | − | 0.221005i | ||||
\(295\) | − | 7.69112e6i | − | 0.299588i | ||||||
\(296\) | −1.28358e7 | − | 1.32971e7i | −0.494936 | − | 0.512723i | ||||
\(297\) | −1.66229e7 | −0.634508 | ||||||||
\(298\) | −2.70201e7 | + | 2.67040e7i | −1.02103 | + | 1.00908i | ||||
\(299\) | 1.14367e7 | 0.427844 | ||||||||
\(300\) | −77137.3 | + | 6.55528e6i | −0.00285694 | + | 0.242788i | ||||
\(301\) | − | 4.48918e7i | − | 1.64614i | ||||||
\(302\) | 6.36072e6 | − | 6.28631e6i | 0.230933 | − | 0.228231i | ||||
\(303\) | 6.87652e6i | 0.247196i | ||||||||
\(304\) | −3.96425e6 | − | 93309.3i | −0.141104 | − | 0.00332127i | ||||
\(305\) | 1.13143e7 | 0.398776 | ||||||||
\(306\) | 1.12911e7 | + | 1.14248e7i | 0.394070 | + | 0.398734i | ||||
\(307\) | −3.69782e7 | −1.27800 | −0.639000 | − | 0.769207i | \(-0.720651\pi\) | ||||
−0.639000 | + | 0.769207i | \(0.720651\pi\) | |||||||
\(308\) | 4.37022e7 | + | 514253.i | 1.49572 | + | 0.0176005i | ||||
\(309\) | − | 5.26153e6i | − | 0.178335i | ||||||
\(310\) | 9.10112e6 | + | 9.20884e6i | 0.305499 | + | 0.309115i | ||||
\(311\) | 3.65356e7i | 1.21461i | 0.794470 | + | 0.607303i | \(0.207749\pi\) | ||||
−0.794470 | + | 0.607303i | \(0.792251\pi\) | |||||||
\(312\) | −1.04224e7 | − | 1.07969e7i | −0.343165 | − | 0.355498i | ||||
\(313\) | 5.50169e7 | 1.79417 | 0.897083 | − | 0.441861i | \(-0.145682\pi\) | ||||
0.897083 | + | 0.441861i | \(0.145682\pi\) | |||||||
\(314\) | −5.71322e6 | + | 5.64638e6i | −0.184541 | + | 0.182382i | ||||
\(315\) | 1.89667e7 | 0.606821 | ||||||||
\(316\) | 1.05387e7 | + | 124011.i | 0.333983 | + | 0.00393005i | ||||
\(317\) | 4.12495e7i | 1.29491i | 0.762102 | + | 0.647457i | \(0.224168\pi\) | ||||
−0.762102 | + | 0.647457i | \(0.775832\pi\) | |||||||
\(318\) | 4.18602e6 | − | 4.13706e6i | 0.130173 | − | 0.128650i | ||||
\(319\) | − | 3.72125e7i | − | 1.14635i | ||||||
\(320\) | −1.56430e7 | − | 552429.i | −0.477388 | − | 0.0168588i | ||||
\(321\) | 9.22601e6 | 0.278932 | ||||||||
\(322\) | −9.01300e6 | − | 9.11968e6i | −0.269961 | − | 0.273157i | ||||
\(323\) | −2.95928e6 | −0.0878170 | ||||||||
\(324\) | −285302. | + | 2.42455e7i | −0.00838821 | + | 0.712846i | ||||
\(325\) | 4.16141e7i | 1.21225i | ||||||||
\(326\) | 8.28422e6 | + | 8.38228e6i | 0.239111 | + | 0.241941i | ||||
\(327\) | 1.45834e7i | 0.417076i | ||||||||
\(328\) | 2.52730e6 | − | 2.43963e6i | 0.0716202 | − | 0.0691356i | ||||
\(329\) | −7.70461e7 | −2.16353 | ||||||||
\(330\) | 4.07527e6 | − | 4.02759e6i | 0.113400 | − | 0.112074i | ||||
\(331\) | 2.72892e7 | 0.752502 | 0.376251 | − | 0.926518i | \(-0.377213\pi\) | ||||
0.376251 | + | 0.926518i | \(0.377213\pi\) | |||||||
\(332\) | 604658. | − | 5.13850e7i | 0.0165233 | − | 1.40418i | ||||
\(333\) | − | 2.37104e7i | − | 0.642107i | ||||||
\(334\) | 2.93805e7 | − | 2.90368e7i | 0.788534 | − | 0.779310i | ||||
\(335\) | 1.90976e7i | 0.507977i | ||||||||
\(336\) | −395897. | + | 1.68197e7i | −0.0104367 | + | 0.443405i | ||||
\(337\) | −1.36843e6 | −0.0357547 | −0.0178774 | − | 0.999840i | \(-0.505691\pi\) | ||||
−0.0178774 | + | 0.999840i | \(0.505691\pi\) | |||||||
\(338\) | −3.98170e7 | − | 4.02882e7i | −1.03114 | − | 1.04335i | ||||
\(339\) | 5.48216e6 | 0.140719 | ||||||||
\(340\) | −1.16806e7 | − | 137448.i | −0.297187 | − | 0.00349706i | ||||
\(341\) | 3.82754e7i | 0.965287i | ||||||||
\(342\) | −3.57598e6 | − | 3.61831e6i | −0.0893958 | − | 0.0904539i | ||||
\(343\) | − | 698651.i | − | 0.0173132i | ||||||
\(344\) | −3.41965e7 | + | 3.30102e7i | −0.840053 | + | 0.810911i | ||||
\(345\) | −1.68094e6 | −0.0409350 | ||||||||
\(346\) | 3.41542e6 | − | 3.37546e6i | 0.0824547 | − | 0.0814901i | ||||
\(347\) | 1.07803e7 | 0.258013 | 0.129006 | − | 0.991644i | \(-0.458821\pi\) | ||||
0.129006 | + | 0.991644i | \(0.458821\pi\) | |||||||
\(348\) | 1.43240e7 | + | 168554.i | 0.339881 | + | 0.00399945i | ||||
\(349\) | − | 1.33186e6i | − | 0.0313316i | −0.999877 | − | 0.0156658i | \(-0.995013\pi\) | ||
0.999877 | − | 0.0156658i | \(-0.00498678\pi\) | |||||||
\(350\) | 3.31834e7 | − | 3.27952e7i | 0.773957 | − | 0.764903i | ||||
\(351\) | − | 4.06192e7i | − | 0.939312i | ||||||
\(352\) | −3.17437e7 | − | 3.36685e7i | −0.727829 | − | 0.771961i | ||||
\(353\) | 798852. | 0.0181611 | 0.00908055 | − | 0.999959i | \(-0.497110\pi\) | ||||
0.00908055 | + | 0.999959i | \(0.497110\pi\) | |||||||
\(354\) | 6.15247e6 | + | 6.22530e6i | 0.138688 | + | 0.140330i | ||||
\(355\) | 1.17564e7 | 0.262779 | ||||||||
\(356\) | 40774.0 | − | 3.46506e6i | 0.000903720 | − | 0.0767998i | ||||
\(357\) | 1.25558e7i | 0.275955i | ||||||||
\(358\) | 3.56896e7 | + | 3.61121e7i | 0.777844 | + | 0.787051i | ||||
\(359\) | − | 5.67611e7i | − | 1.22678i | −0.789779 | − | 0.613392i | \(-0.789805\pi\) | ||
0.789779 | − | 0.613392i | \(-0.210195\pi\) | |||||||
\(360\) | −1.39468e7 | − | 1.44480e7i | −0.298928 | − | 0.309670i | ||||
\(361\) | −4.61087e7 | −0.980078 | ||||||||
\(362\) | 7.68333e6 | − | 7.59345e6i | 0.161966 | − | 0.160071i | ||||
\(363\) | 1.89086e6 | 0.0395311 | ||||||||
\(364\) | −1.25661e6 | + | 1.06789e8i | −0.0260554 | + | 2.21424i | ||||
\(365\) | 3.81897e6i | 0.0785359i | ||||||||
\(366\) | −9.15797e6 | + | 9.05084e6i | −0.186791 | + | 0.184606i | ||||
\(367\) | 1.80379e7i | 0.364911i | 0.983214 | + | 0.182456i | \(0.0584046\pi\) | ||||
−0.983214 | + | 0.182456i | \(0.941595\pi\) | |||||||
\(368\) | −319445. | + | 1.35716e7i | −0.00640992 | + | 0.272326i | ||||
\(369\) | 4.50650e6 | 0.0896933 | ||||||||
\(370\) | 1.21207e7 | + | 1.22642e7i | 0.239289 | + | 0.242121i | ||||
\(371\) | −4.18843e7 | −0.820218 | ||||||||
\(372\) | −1.47331e7 | − | 173368.i | −0.286198 | − | 0.00336775i | ||||
\(373\) | − | 3.58446e7i | − | 0.690712i | −0.938472 | − | 0.345356i | \(-0.887758\pi\) | ||
0.938472 | − | 0.345356i | \(-0.112242\pi\) | |||||||
\(374\) | −2.42745e7 | − | 2.45618e7i | −0.464019 | − | 0.469511i | ||||
\(375\) | − | 1.40410e7i | − | 0.266259i | ||||||
\(376\) | 5.66541e7 | + | 5.86902e7i | 1.06578 | + | 1.10408i | ||||
\(377\) | 9.09315e7 | 1.69703 | ||||||||
\(378\) | −3.23900e7 | + | 3.20111e7i | −0.599703 | + | 0.592687i | ||||
\(379\) | 9.70544e7 | 1.78278 | 0.891390 | − | 0.453238i | \(-0.149731\pi\) | ||||
0.891390 | + | 0.453238i | \(0.149731\pi\) | |||||||
\(380\) | 3.69934e6 | + | 43530.9i | 0.0674176 | + | 0.000793317i | ||||
\(381\) | − | 2.13625e7i | − | 0.386257i | ||||||
\(382\) | −1.88934e7 | + | 1.86723e7i | −0.338937 | + | 0.334972i | ||||
\(383\) | 3.16741e7i | 0.563779i | 0.959447 | + | 0.281889i | \(0.0909611\pi\) | ||||
−0.959447 | + | 0.281889i | \(0.909039\pi\) | |||||||
\(384\) | 1.31036e7 | − | 1.20664e7i | 0.231418 | − | 0.213101i | ||||
\(385\) | −4.07761e7 | −0.714534 | ||||||||
\(386\) | 3.14466e7 | + | 3.18188e7i | 0.546779 | + | 0.553251i | ||||
\(387\) | −6.09768e7 | −1.05204 | ||||||||
\(388\) | 833401. | − | 7.08240e7i | 0.0142679 | − | 1.21251i | ||||
\(389\) | − | 5.50526e7i | − | 0.935252i | −0.883926 | − | 0.467626i | \(-0.845109\pi\) | ||
0.883926 | − | 0.467626i | \(-0.154891\pi\) | |||||||
\(390\) | 9.84171e6 | + | 9.95820e6i | 0.165912 | + | 0.167875i | ||||
\(391\) | 1.01311e7i | 0.169483i | ||||||||
\(392\) | 4.28064e7 | − | 4.13214e7i | 0.710641 | − | 0.685988i | ||||
\(393\) | −3.20620e7 | −0.528217 | ||||||||
\(394\) | 4.09568e7 | − | 4.04777e7i | 0.669634 | − | 0.661801i | ||||
\(395\) | −9.83305e6 | −0.159550 | ||||||||
\(396\) | 698511. | − | 5.93608e7i | 0.0112483 | − | 0.955905i | ||||
\(397\) | 8.33093e7i | 1.33144i | 0.746201 | + | 0.665721i | \(0.231876\pi\) | ||||
−0.746201 | + | 0.665721i | \(0.768124\pi\) | |||||||
\(398\) | −6.59121e7 | + | 6.51410e7i | −1.04548 | + | 1.03325i | ||||
\(399\) | − | 3.97650e6i | − | 0.0626011i | ||||||
\(400\) | −4.93826e7 | − | 1.16235e6i | −0.771603 | − | 0.0181617i | ||||
\(401\) | 4.24726e7 | 0.658682 | 0.329341 | − | 0.944211i | \(-0.393174\pi\) | ||||
0.329341 | + | 0.944211i | \(0.393174\pi\) | |||||||
\(402\) | −1.52770e7 | − | 1.54578e7i | −0.235158 | − | 0.237942i | ||||
\(403\) | −9.35286e7 | −1.42899 | ||||||||
\(404\) | −5.18097e7 | − | 609656.i | −0.785719 | − | 0.00924572i | ||||
\(405\) | − | 2.26221e7i | − | 0.340540i | ||||||
\(406\) | −7.16612e7 | − | 7.25094e7i | −1.07079 | − | 1.08347i | ||||
\(407\) | 5.09745e7i | 0.756083i | ||||||||
\(408\) | 9.56441e6 | − | 9.23260e6i | 0.140824 | − | 0.135939i | ||||
\(409\) | 4.61036e7 | 0.673853 | 0.336926 | − | 0.941531i | \(-0.390613\pi\) | ||||
0.336926 | + | 0.941531i | \(0.390613\pi\) | |||||||
\(410\) | −2.33098e6 | + | 2.30371e6i | −0.0338210 | + | 0.0334253i | ||||
\(411\) | 1.19456e7 | 0.172061 | ||||||||
\(412\) | 3.96420e7 | + | 466475.i | 0.566844 | + | 0.00667017i | ||||
\(413\) | − | 6.22887e7i | − | 0.884218i | ||||||
\(414\) | −1.23873e7 | + | 1.22424e7i | −0.174572 | + | 0.172530i | ||||
\(415\) | 4.79445e7i | 0.670802i | ||||||||
\(416\) | 8.22713e7 | − | 7.75680e7i | 1.14280 | − | 1.07746i | ||||
\(417\) | 1.96686e7 | 0.271247 | ||||||||
\(418\) | 7.68791e6 | + | 7.77891e6i | 0.105264 | + | 0.106510i | ||||
\(419\) | −3.86614e7 | −0.525575 | −0.262788 | − | 0.964854i | \(-0.584642\pi\) | ||||
−0.262788 | + | 0.964854i | \(0.584642\pi\) | |||||||
\(420\) | 184695. | − | 1.56957e7i | 0.00249291 | − | 0.211852i | ||||
\(421\) | 2.58211e7i | 0.346042i | 0.984918 | + | 0.173021i | \(0.0553528\pi\) | ||||
−0.984918 | + | 0.173021i | \(0.944647\pi\) | |||||||
\(422\) | −3.59533e6 | − | 3.63789e6i | −0.0478412 | − | 0.0484074i | ||||
\(423\) | 1.04652e8i | 1.38269i | ||||||||
\(424\) | 3.07987e7 | + | 3.19055e7i | 0.404049 | + | 0.418570i | ||||
\(425\) | −3.68636e7 | −0.480210 | ||||||||
\(426\) | −9.51580e6 | + | 9.40448e6i | −0.123088 | + | 0.121648i | ||||
\(427\) | 9.16323e7 | 1.17697 | ||||||||
\(428\) | −817957. | + | 6.95115e7i | −0.0104328 | + | 0.886595i | ||||
\(429\) | 4.13900e7i | 0.524232i | ||||||||
\(430\) | 3.15401e7 | − | 3.11711e7i | 0.396696 | − | 0.392055i | ||||
\(431\) | − | 3.09589e7i | − | 0.386681i | −0.981132 | − | 0.193341i | \(-0.938068\pi\) | ||
0.981132 | − | 0.193341i | \(-0.0619322\pi\) | |||||||
\(432\) | 4.82019e7 | + | 1.13456e6i | 0.597879 | + | 0.0140727i | ||||
\(433\) | 4.64302e7 | 0.571921 | 0.285961 | − | 0.958241i | \(-0.407687\pi\) | ||||
0.285961 | + | 0.958241i | \(0.407687\pi\) | |||||||
\(434\) | 7.37080e7 | + | 7.45804e7i | 0.901665 | + | 0.912338i | ||||
\(435\) | −1.33649e7 | −0.162368 | ||||||||
\(436\) | −1.09876e8 | − | 1.29293e6i | −1.32569 | − | 0.0155997i | ||||
\(437\) | − | 3.20859e6i | − | 0.0384477i | ||||||
\(438\) | −3.05497e6 | − | 3.09113e6i | −0.0363567 | − | 0.0367870i | ||||
\(439\) | − | 1.33692e8i | − | 1.58020i | −0.612979 | − | 0.790099i | \(-0.710029\pi\) | ||
0.612979 | − | 0.790099i | \(-0.289971\pi\) | |||||||
\(440\) | 2.99838e7 | + | 3.10613e7i | 0.351988 | + | 0.364638i | ||||
\(441\) | 7.63292e7 | 0.889969 | ||||||||
\(442\) | 6.00186e7 | − | 5.93165e7i | 0.695055 | − | 0.686924i | ||||
\(443\) | −5.29536e6 | −0.0609094 | −0.0304547 | − | 0.999536i | \(-0.509696\pi\) | ||||
−0.0304547 | + | 0.999536i | \(0.509696\pi\) | |||||||
\(444\) | −1.96213e7 | − | 230888.i | −0.224171 | − | 0.00263787i | ||||
\(445\) | 3.23305e6i | 0.0366887i | ||||||||
\(446\) | −5.41205e7 | + | 5.34874e7i | −0.610038 | + | 0.602902i | ||||
\(447\) | 4.03347e7i | 0.451602i | ||||||||
\(448\) | −1.26690e8 | − | 4.47400e6i | −1.40899 | − | 0.0497579i | ||||
\(449\) | −1.20011e8 | −1.32582 | −0.662908 | − | 0.748701i | \(-0.730678\pi\) | ||||
−0.662908 | + | 0.748701i | \(0.730678\pi\) | |||||||
\(450\) | −4.45459e7 | − | 4.50731e7i | −0.488844 | − | 0.494630i | ||||
\(451\) | −9.68840e6 | −0.105614 | ||||||||
\(452\) | −486036. | + | 4.13042e7i | −0.00526324 | + | 0.447280i | ||||
\(453\) | − | 9.49508e6i | − | 0.102142i | ||||||
\(454\) | 7.19101e7 | + | 7.27613e7i | 0.768462 | + | 0.777558i | ||||
\(455\) | − | 9.96392e7i | − | 1.05778i | ||||||
\(456\) | −3.02911e6 | + | 2.92403e6i | −0.0319463 | + | 0.0308381i | ||||
\(457\) | −1.84689e8 | −1.93505 | −0.967527 | − | 0.252767i | \(-0.918660\pi\) | ||||
−0.967527 | + | 0.252767i | \(0.918660\pi\) | |||||||
\(458\) | −2.62840e7 | + | 2.59765e7i | −0.273586 | + | 0.270386i | ||||
\(459\) | 3.59823e7 | 0.372092 | ||||||||
\(460\) | 149028. | − | 1.26647e7i | 0.00153107 | − | 0.130113i | ||||
\(461\) | − | 1.46730e8i | − | 1.49767i | −0.662755 | − | 0.748836i | \(-0.730613\pi\) | ||
0.662755 | − | 0.748836i | \(-0.269387\pi\) | |||||||
\(462\) | 3.30047e7 | − | 3.26186e7i | 0.334695 | − | 0.330780i | ||||
\(463\) | − | 1.55124e8i | − | 1.56292i | −0.623956 | − | 0.781459i | \(-0.714476\pi\) | ||
0.623956 | − | 0.781459i | \(-0.285524\pi\) | |||||||
\(464\) | −2.53987e6 | + | 1.07906e8i | −0.0254248 | + | 1.08017i | ||||
\(465\) | 1.37467e7 | 0.136722 | ||||||||
\(466\) | −5.29380e7 | − | 5.35646e7i | −0.523130 | − | 0.529322i | ||||
\(467\) | 1.07539e8 | 1.05589 | 0.527943 | − | 0.849280i | \(-0.322963\pi\) | ||||
0.527943 | + | 0.849280i | \(0.322963\pi\) | |||||||
\(468\) | 1.45052e8 | + | 1.70686e6i | 1.41510 | + | 0.0166518i | ||||
\(469\) | 1.54667e8i | 1.49927i | ||||||||
\(470\) | −5.34978e7 | − | 5.41310e7i | −0.515279 | − | 0.521378i | ||||
\(471\) | 8.52850e6i | 0.0816225i | ||||||||
\(472\) | −4.74487e7 | + | 4.58026e7i | −0.451230 | + | 0.435577i | ||||
\(473\) | 1.31092e8 | 1.23878 | ||||||||
\(474\) | 7.95900e6 | − | 7.86589e6i | 0.0747349 | − | 0.0738606i | ||||
\(475\) | 1.16750e7 | 0.108937 | ||||||||
\(476\) | −9.45988e7 | − | 1.11316e6i | −0.877132 | − | 0.0103214i | ||||
\(477\) | 5.68916e7i | 0.524195i | ||||||||
\(478\) | 1.46258e8 | − | 1.44547e8i | 1.33917 | − | 1.32351i | ||||
\(479\) | 1.48881e7i | 0.135467i | 0.997703 | + | 0.0677333i | \(0.0215767\pi\) | ||||
−0.997703 | + | 0.0677333i | \(0.978423\pi\) | |||||||
\(480\) | −1.20921e7 | + | 1.14008e7i | −0.109340 | + | 0.103089i | ||||
\(481\) | −1.24560e8 | −1.11929 | ||||||||
\(482\) | 4.59347e7 | + | 4.64784e7i | 0.410204 | + | 0.415059i | ||||
\(483\) | −1.36136e7 | −0.120818 | ||||||||
\(484\) | −167639. | + | 1.42463e7i | −0.00147856 | + | 0.125651i | ||||
\(485\) | 6.60819e7i | 0.579239i | ||||||||
\(486\) | 6.63531e7 | + | 6.71384e7i | 0.578032 | + | 0.584874i | ||||
\(487\) | 9.69346e7i | 0.839251i | 0.907697 | + | 0.419625i | \(0.137839\pi\) | ||||
−0.907697 | + | 0.419625i | \(0.862161\pi\) | |||||||
\(488\) | −6.73798e7 | − | 6.98013e7i | −0.579789 | − | 0.600626i | ||||
\(489\) | 1.25128e7 | 0.107011 | ||||||||
\(490\) | −3.94811e7 | + | 3.90193e7i | −0.335584 | + | 0.331658i | ||||
\(491\) | −6.45564e7 | −0.545374 | −0.272687 | − | 0.962103i | \(-0.587912\pi\) | ||||
−0.272687 | + | 0.962103i | \(0.587912\pi\) | |||||||
\(492\) | 43883.5 | − | 3.72930e6i | 0.000368473 | − | 0.0313136i | ||||
\(493\) | 8.05512e7i | 0.672250i | ||||||||
\(494\) | −1.90083e7 | + | 1.87860e7i | −0.157675 | + | 0.155830i | ||||
\(495\) | 5.53863e7i | 0.456653i | ||||||||
\(496\) | 2.61241e6 | − | 1.10988e8i | 0.0214090 | − | 0.909563i | ||||
\(497\) | 9.52126e7 | 0.775578 | ||||||||
\(498\) | −3.83529e7 | − | 3.88069e7i | −0.310535 | − | 0.314211i | ||||
\(499\) | 8.09040e7 | 0.651131 | 0.325565 | − | 0.945520i | \(-0.394445\pi\) | ||||
0.325565 | + | 0.945520i | \(0.394445\pi\) | |||||||
\(500\) | 1.05789e8 | + | 1.24484e6i | 0.846313 | + | 0.00995874i | ||||
\(501\) | − | 4.38583e7i | − | 0.348770i | ||||||
\(502\) | −4.74925e7 | − | 4.80546e7i | −0.375417 | − | 0.379860i | ||||
\(503\) | 1.32342e8i | 1.03990i | 0.854196 | + | 0.519951i | \(0.174050\pi\) | ||||
−0.854196 | + | 0.519951i | \(0.825950\pi\) | |||||||
\(504\) | −1.12952e8 | − | 1.17011e8i | −0.882270 | − | 0.913977i | ||||
\(505\) | 4.83408e7 | 0.375352 | ||||||||
\(506\) | 2.66311e7 | − | 2.63196e7i | 0.205560 | − | 0.203155i | ||||
\(507\) | −6.01410e7 | −0.461473 | ||||||||
\(508\) | 1.60951e8 | + | 1.89395e6i | 1.22773 | + | 0.0144470i | ||||
\(509\) | 1.39233e7i | 0.105582i | 0.998606 | + | 0.0527909i | \(0.0168117\pi\) | ||||
−0.998606 | + | 0.0527909i | \(0.983188\pi\) | |||||||
\(510\) | −8.82142e6 | + | 8.71823e6i | −0.0665010 | + | 0.0657231i | ||||
\(511\) | 3.09290e7i | 0.231795i | ||||||||
\(512\) | 8.97503e7 | + | 9.97962e7i | 0.668692 | + | 0.743540i | ||||
\(513\) | −1.13958e7 | −0.0844101 | ||||||||
\(514\) | −1.03742e8 | − | 1.04970e8i | −0.763953 | − | 0.772995i | ||||
\(515\) | −3.69877e7 | −0.270792 | ||||||||
\(516\) | −593781. | + | 5.04606e7i | −0.00432192 | + | 0.367285i | ||||
\(517\) | − | 2.24989e8i | − | 1.62813i | ||||||
\(518\) | 9.81630e7 | + | 9.93249e7i | 0.706250 | + | 0.714609i | ||||
\(519\) | − | 5.09842e6i | − | 0.0364698i | ||||||
\(520\) | −7.59006e7 | + | 7.32675e7i | −0.539803 | + | 0.521076i | ||||
\(521\) | −9.25151e7 | −0.654183 | −0.327092 | − | 0.944993i | \(-0.606069\pi\) | ||||
−0.327092 | + | 0.944993i | \(0.606069\pi\) | |||||||
\(522\) | −9.84898e7 | + | 9.73377e7i | −0.692436 | + | 0.684336i | ||||
\(523\) | −5.17905e7 | −0.362030 | −0.181015 | − | 0.983480i | \(-0.557938\pi\) | ||||
−0.181015 | + | 0.983480i | \(0.557938\pi\) | |||||||
\(524\) | 2.84254e6 | − | 2.41564e8i | 0.0197566 | − | 1.67895i | ||||
\(525\) | − | 4.95351e7i | − | 0.342322i | ||||||
\(526\) | −2.18551e7 | + | 2.15995e7i | −0.150175 | + | 0.148418i | ||||
\(527\) | − | 8.28518e7i | − | 0.566070i | ||||||
\(528\) | −4.91166e7 | − | 1.15609e6i | −0.333677 | − | 0.00785399i | ||||
\(529\) | 1.37051e8 | 0.925797 | ||||||||
\(530\) | −2.90828e7 | − | 2.94270e7i | −0.195348 | − | 0.197660i | ||||
\(531\) | −8.46070e7 | −0.565097 | ||||||||
\(532\) | 2.99601e7 | + | 352547.i | 0.198980 | + | 0.00234143i | ||||
\(533\) | − | 2.36743e7i | − | 0.156349i | ||||||
\(534\) | −2.58626e6 | − | 2.61687e6i | −0.0169843 | − | 0.0171854i | ||||
\(535\) | − | 6.48573e7i | − | 0.423543i | ||||||
\(536\) | 1.17818e8 | − | 1.13731e8i | 0.765100 | − | 0.738558i | ||||
\(537\) | 5.39069e7 | 0.348114 | ||||||||
\(538\) | −1.76636e8 | + | 1.74569e8i | −1.13431 | + | 1.12104i | ||||
\(539\) | −1.64098e8 | −1.04794 | ||||||||
\(540\) | −4.49807e7 | − | 529298.i | −0.285657 | − | 0.00336139i | ||||
\(541\) | 2.48317e7i | 0.156825i | 0.996921 | + | 0.0784125i | \(0.0249851\pi\) | ||||
−0.996921 | + | 0.0784125i | \(0.975015\pi\) | |||||||
\(542\) | −1.34034e8 | + | 1.32466e8i | −0.841818 | + | 0.831970i | ||||
\(543\) | − | 1.14694e7i | − | 0.0716378i | ||||||
\(544\) | 6.87132e7 | + | 7.28796e7i | 0.426819 | + | 0.452699i | ||||
\(545\) | 1.02519e8 | 0.633306 | ||||||||
\(546\) | 7.97059e7 | + | 8.06493e7i | 0.489680 | + | 0.495476i | ||||
\(547\) | 8.23167e7 | 0.502951 | 0.251476 | − | 0.967864i | \(-0.419084\pi\) | ||||
0.251476 | + | 0.967864i | \(0.419084\pi\) | |||||||
\(548\) | −1.05907e6 | + | 9.00017e7i | −0.00643550 | + | 0.546901i | ||||
\(549\) | − | 1.24465e8i | − | 0.752192i | ||||||
\(550\) | 9.57680e7 | + | 9.69016e7i | 0.575615 | + | 0.582429i | ||||
\(551\) | − | 2.55111e7i | − | 0.152502i | ||||||
\(552\) | 1.00104e7 | + | 1.03702e7i | 0.0595162 | + | 0.0616551i | ||||
\(553\) | −7.96357e7 | −0.470904 | ||||||||
\(554\) | 1.32116e8 | − | 1.30571e8i | 0.777010 | − | 0.767921i | ||||
\(555\) | 1.83076e7 | 0.107091 | ||||||||
\(556\) | −1.74377e6 | + | 1.48189e8i | −0.0101453 | + | 0.862168i | ||||
\(557\) | − | 1.99169e7i | − | 0.115254i | −0.998338 | − | 0.0576271i | \(-0.981647\pi\) | ||
0.998338 | − | 0.0576271i | \(-0.0183534\pi\) | |||||||
\(558\) | 1.01303e8 | − | 1.00118e8i | 0.583068 | − | 0.576247i | ||||
\(559\) | 3.20333e8i | 1.83386i | ||||||||
\(560\) | 1.18240e8 | + | 2.78309e6i | 0.673286 | + | 0.0158476i | ||||
\(561\) | −3.66651e7 | −0.207666 | ||||||||
\(562\) | 1.68434e8 | + | 1.70427e8i | 0.948898 | + | 0.960130i | ||||
\(563\) | 3.05819e8 | 1.71372 | 0.856859 | − | 0.515550i | \(-0.172412\pi\) | ||||
0.856859 | + | 0.515550i | \(0.172412\pi\) | |||||||
\(564\) | 8.66036e7 | + | 1.01908e6i | 0.482724 | + | 0.00568031i | ||||
\(565\) | − | 3.85387e7i | − | 0.213674i | ||||||
\(566\) | −2.06964e8 | − | 2.09414e8i | −1.14142 | − | 1.15493i | ||||
\(567\) | − | 1.83212e8i | − | 1.00509i | ||||||
\(568\) | −7.00125e7 | − | 7.25286e7i | −0.382059 | − | 0.395790i | ||||
\(569\) | −2.25936e6 | −0.0122644 | −0.00613222 | − | 0.999981i | \(-0.501952\pi\) | ||||
−0.00613222 | + | 0.999981i | \(0.501952\pi\) | |||||||
\(570\) | 2.79381e6 | − | 2.76112e6i | 0.0150859 | − | 0.0149094i | ||||
\(571\) | −6.55464e7 | −0.352079 | −0.176040 | − | 0.984383i | \(-0.556329\pi\) | ||||
−0.176040 | + | 0.984383i | \(0.556329\pi\) | |||||||
\(572\) | −3.11844e8 | − | 3.66954e6i | −1.66629 | − | 0.0196076i | ||||
\(573\) | 2.82034e7i | 0.149912i | ||||||||
\(574\) | −1.88781e7 | + | 1.86572e7i | −0.0998209 | + | 0.0986532i | ||||
\(575\) | − | 3.99693e7i | − | 0.210244i | ||||||
\(576\) | −6.07705e6 | + | 1.72083e8i | −0.0317999 | + | 0.900472i | ||||
\(577\) | 5.43876e7 | 0.283121 | 0.141561 | − | 0.989930i | \(-0.454788\pi\) | ||||
0.141561 | + | 0.989930i | \(0.454788\pi\) | |||||||
\(578\) | −8.31918e7 | − | 8.41765e7i | −0.430821 | − | 0.435921i | ||||
\(579\) | 4.74981e7 | 0.244703 | ||||||||
\(580\) | 1.18490e6 | − | 1.00695e8i | 0.00607294 | − | 0.516090i | ||||
\(581\) | 3.88292e8i | 1.97984i | ||||||||
\(582\) | −5.28619e7 | − | 5.34876e7i | −0.268147 | − | 0.271321i | ||||
\(583\) | − | 1.22310e8i | − | 0.617242i | ||||||
\(584\) | 2.35603e7 | − | 2.27430e7i | 0.118288 | − | 0.114185i | ||||
\(585\) | −1.35340e8 | −0.676020 | ||||||||
\(586\) | 1.91708e8 | − | 1.89465e8i | 0.952681 | − | 0.941536i | ||||
\(587\) | −3.85369e8 | −1.90529 | −0.952647 | − | 0.304078i | \(-0.901652\pi\) | ||||
−0.952647 | + | 0.304078i | \(0.901652\pi\) | |||||||
\(588\) | 743280. | − | 6.31654e7i | 0.00365612 | − | 0.310704i | ||||
\(589\) | 2.62398e7i | 0.128414i | ||||||||
\(590\) | 4.37628e7 | − | 4.32509e7i | 0.213083 | − | 0.210590i | ||||
\(591\) | − | 6.11390e7i | − | 0.296180i | ||||||
\(592\) | 3.47916e6 | − | 1.47812e8i | 0.0167691 | − | 0.712436i | ||||
\(593\) | −3.00090e8 | −1.43909 | −0.719545 | − | 0.694446i | \(-0.755650\pi\) | ||||
−0.719545 | + | 0.694446i | \(0.755650\pi\) | |||||||
\(594\) | −9.34783e7 | − | 9.45848e7i | −0.446017 | − | 0.451296i | ||||
\(595\) | 8.82649e7 | 0.419022 | ||||||||
\(596\) | −3.03893e8 | − | 3.57598e6i | −1.43543 | − | 0.0168910i | ||||
\(597\) | 9.83914e7i | 0.462417i | ||||||||
\(598\) | 6.43138e7 | + | 6.50751e7i | 0.300747 | + | 0.304306i | ||||
\(599\) | 3.11371e8i | 1.44876i | 0.689400 | + | 0.724381i | \(0.257874\pi\) | ||||
−0.689400 | + | 0.724381i | \(0.742126\pi\) | |||||||
\(600\) | −3.77336e7 | + | 3.64245e7i | −0.174692 | + | 0.168632i | ||||
\(601\) | 2.10925e8 | 0.971637 | 0.485818 | − | 0.874060i | \(-0.338522\pi\) | ||||
0.485818 | + | 0.874060i | \(0.338522\pi\) | |||||||
\(602\) | 2.55436e8 | − | 2.52448e8i | 1.17083 | − | 1.15713i | ||||
\(603\) | 2.10085e8 | 0.958171 | ||||||||
\(604\) | 7.15387e7 | + | 841811.i | 0.324661 | + | 0.00382036i | ||||
\(605\) | − | 1.32924e7i | − | 0.0600257i | ||||||
\(606\) | −3.91276e7 | + | 3.86699e7i | −0.175819 | + | 0.173762i | ||||
\(607\) | − | 3.28208e8i | − | 1.46752i | −0.679410 | − | 0.733759i | \(-0.737764\pi\) | ||
0.679410 | − | 0.733759i | \(-0.262236\pi\) | |||||||
\(608\) | −2.17620e7 | − | 2.30815e7i | −0.0968249 | − | 0.102696i | ||||
\(609\) | −1.08240e8 | −0.479220 | ||||||||
\(610\) | 6.36259e7 | + | 6.43790e7i | 0.280314 | + | 0.283632i | ||||
\(611\) | 5.49776e8 | 2.41025 | ||||||||
\(612\) | −1.51202e6 | + | 1.28494e8i | −0.00659632 | + | 0.560568i | ||||
\(613\) | 1.43677e8i | 0.623743i | 0.950124 | + | 0.311872i | \(0.100956\pi\) | ||||
−0.950124 | + | 0.311872i | \(0.899044\pi\) | |||||||
\(614\) | −2.07946e8 | − | 2.10407e8i | −0.898350 | − | 0.908983i | ||||
\(615\) | 3.47960e6i | 0.0149591i | ||||||||
\(616\) | 2.42832e8 | + | 2.51559e8i | 1.03888 | + | 1.07621i | ||||
\(617\) | −1.50375e8 | −0.640206 | −0.320103 | − | 0.947383i | \(-0.603717\pi\) | ||||
−0.320103 | + | 0.947383i | \(0.603717\pi\) | |||||||
\(618\) | 2.99383e7 | − | 2.95881e7i | 0.126842 | − | 0.125358i | ||||
\(619\) | −2.07480e8 | −0.874793 | −0.437396 | − | 0.899269i | \(-0.644099\pi\) | ||||
−0.437396 | + | 0.899269i | \(0.644099\pi\) | |||||||
\(620\) | −1.21875e6 | + | 1.03571e8i | −0.00511374 | + | 0.434575i | ||||
\(621\) | 3.90137e7i | 0.162908i | ||||||||
\(622\) | −2.07889e8 | + | 2.05457e8i | −0.863894 | + | 0.853788i | ||||
\(623\) | 2.61838e7i | 0.108285i | ||||||||
\(624\) | 2.82499e6 | − | 1.20020e8i | 0.0116269 | − | 0.493969i | ||||
\(625\) | 8.97259e7 | 0.367517 | ||||||||
\(626\) | 3.09386e8 | + | 3.13048e8i | 1.26118 | + | 1.27611i | ||||
\(627\) | 1.16121e7 | 0.0471094 | ||||||||
\(628\) | −6.42563e7 | − | 756117.i | −0.259440 | − | 0.00305288i | ||||
\(629\) | − | 1.10341e8i | − | 0.443388i | ||||||
\(630\) | 1.06659e8 | + | 1.07921e8i | 0.426556 | + | 0.431604i | ||||
\(631\) | 9.08069e7i | 0.361436i | 0.983535 | + | 0.180718i | \(0.0578421\pi\) | ||||
−0.983535 | + | 0.180718i | \(0.942158\pi\) | |||||||
\(632\) | 5.85583e7 | + | 6.06628e7i | 0.231973 | + | 0.240310i | ||||
\(633\) | −5.43052e6 | −0.0214107 | ||||||||
\(634\) | −2.34711e8 | + | 2.31966e8i | −0.921014 | + | 0.910240i | ||||
\(635\) | −1.50174e8 | −0.586509 | ||||||||
\(636\) | 4.70800e7 | + | 554000.i | 0.183006 | + | 0.00215347i | ||||
\(637\) | − | 4.00986e8i | − | 1.55135i | ||||||
\(638\) | 2.11741e8 | − | 2.09264e8i | 0.815347 | − | 0.805809i | ||||
\(639\) | − | 1.29328e8i | − | 0.495666i | ||||||
\(640\) | −8.48250e7 | − | 9.21161e7i | −0.323582 | − | 0.351395i | ||||
\(641\) | 1.95456e8 | 0.742121 | 0.371061 | − | 0.928609i | \(-0.378994\pi\) | ||||
0.371061 | + | 0.928609i | \(0.378994\pi\) | |||||||
\(642\) | 5.18823e7 | + | 5.24964e7i | 0.196071 | + | 0.198392i | ||||
\(643\) | −3.72026e8 | −1.39939 | −0.699697 | − | 0.714440i | \(-0.746682\pi\) | ||||
−0.699697 | + | 0.714440i | \(0.746682\pi\) | |||||||
\(644\) | 1.20695e6 | − | 1.02569e8i | 0.00451887 | − | 0.384023i | ||||
\(645\) | − | 4.70820e7i | − | 0.175459i | ||||||
\(646\) | −1.66414e7 | − | 1.68384e7i | −0.0617296 | − | 0.0624602i | ||||
\(647\) | − | 2.47447e8i | − | 0.913627i | −0.889563 | − | 0.456813i | \(-0.848991\pi\) | ||
0.889563 | − | 0.456813i | \(-0.151009\pi\) | |||||||
\(648\) | −1.39562e8 | + | 1.34721e8i | −0.512912 | + | 0.495118i | ||||
\(649\) | 1.81894e8 | 0.665404 | ||||||||
\(650\) | −2.36786e8 | + | 2.34016e8i | −0.862215 | + | 0.852129i | ||||
\(651\) | 1.11331e8 | 0.403528 | ||||||||
\(652\) | −1.10935e6 | + | 9.42750e7i | −0.00400246 | + | 0.340137i | ||||
\(653\) | 1.98187e8i | 0.711764i | 0.934531 | + | 0.355882i | \(0.115820\pi\) | ||||
−0.934531 | + | 0.355882i | \(0.884180\pi\) | |||||||
\(654\) | −8.29800e7 | + | 8.20093e7i | −0.296647 | + | 0.293177i | ||||
\(655\) | 2.25390e8i | 0.802068i | ||||||||
\(656\) | 2.80938e7 | + | 661262.i | 0.0995173 | + | 0.00234241i | ||||
\(657\) | 4.20110e7 | 0.148138 | ||||||||
\(658\) | −4.33267e8 | − | 4.38395e8i | −1.52082 | − | 1.53882i | ||||
\(659\) | −5.71625e7 | −0.199735 | −0.0998677 | − | 0.995001i | \(-0.531842\pi\) | ||||
−0.0998677 | + | 0.995001i | \(0.531842\pi\) | |||||||
\(660\) | 4.58343e7 | + | 539342.i | 0.159426 | + | 0.00187600i | ||||
\(661\) | − | 5.04948e8i | − | 1.74841i | −0.485561 | − | 0.874203i | \(-0.661385\pi\) | ||
0.485561 | − | 0.874203i | \(-0.338615\pi\) | |||||||
\(662\) | 1.53460e8 | + | 1.55277e8i | 0.528959 | + | 0.535220i | ||||
\(663\) | − | 8.95938e7i | − | 0.307424i | ||||||
\(664\) | 2.95783e8 | − | 2.85522e8i | 1.01034 | − | 0.975293i | ||||
\(665\) | −2.79541e7 | −0.0950563 | ||||||||
\(666\) | 1.34913e8 | − | 1.33335e8i | 0.456701 | − | 0.451359i | ||||
\(667\) | −8.73374e7 | −0.294322 | ||||||||
\(668\) | 3.30441e8 | + | 3.88837e6i | 1.10858 | + | 0.0130448i | ||||
\(669\) | 8.07893e7i | 0.269821i | ||||||||
\(670\) | −1.08666e8 | + | 1.07395e8i | −0.361301 | + | 0.357074i | ||||
\(671\) | 2.67583e8i | 0.885709i | ||||||||
\(672\) | −9.79311e7 | + | 9.23326e7i | −0.322710 | + | 0.304262i | ||||
\(673\) | −1.59423e8 | −0.523004 | −0.261502 | − | 0.965203i | \(-0.584218\pi\) | ||||
−0.261502 | + | 0.965203i | \(0.584218\pi\) | |||||||
\(674\) | −7.69534e6 | − | 7.78643e6i | −0.0251332 | − | 0.0254307i | ||||
\(675\) | −1.41958e8 | −0.461580 | ||||||||
\(676\) | 5.33196e6 | − | 4.53120e8i | 0.0172602 | − | 1.46681i | ||||
\(677\) | − | 1.89358e8i | − | 0.610265i | −0.952310 | − | 0.305132i | \(-0.901299\pi\) | ||
0.952310 | − | 0.305132i | \(-0.0987007\pi\) | |||||||
\(678\) | 3.08288e7 | + | 3.11937e7i | 0.0989163 | + | 0.100087i | ||||
\(679\) | 5.35183e8i | 1.70959i | ||||||||
\(680\) | −6.49036e7 | − | 6.72362e7i | −0.206416 | − | 0.213834i | ||||
\(681\) | 1.08616e8 | 0.343915 | ||||||||
\(682\) | −2.17788e8 | + | 2.15241e8i | −0.686565 | + | 0.678533i | ||||
\(683\) | 6.31662e7 | 0.198254 | 0.0991272 | − | 0.995075i | \(-0.468395\pi\) | ||||
0.0991272 | + | 0.995075i | \(0.468395\pi\) | |||||||
\(684\) | 478866. | − | 4.06949e7i | 0.00149639 | − | 0.127166i | ||||
\(685\) | − | 8.39755e7i | − | 0.261265i | ||||||
\(686\) | 3.97535e6 | − | 3.92885e6i | 0.0123141 | − | 0.0121701i | ||||
\(687\) | 3.92358e7i | 0.121008i | ||||||||
\(688\) | −3.80133e8 | − | 8.94744e6i | −1.16727 | − | 0.0274747i | ||||
\(689\) | 2.98872e8 | 0.913752 | ||||||||
\(690\) | −9.45272e6 | − | 9.56461e6i | −0.0287746 | − | 0.0291152i | ||||
\(691\) | −1.37266e8 | −0.416033 | −0.208016 | − | 0.978125i | \(-0.566701\pi\) | ||||
−0.208016 | + | 0.978125i | \(0.566701\pi\) | |||||||
\(692\) | 3.84130e7 | + | 452014.i | 0.115920 | + | 0.00136406i | ||||
\(693\) | 4.48561e8i | 1.34779i | ||||||||
\(694\) | 6.06226e7 | + | 6.13401e7i | 0.181366 | + | 0.183513i | ||||
\(695\) | − | 1.38267e8i | − | 0.411873i | ||||||
\(696\) | 7.95917e7 | + | 8.24520e7i | 0.236069 | + | 0.244553i | ||||
\(697\) | 2.09718e7 | 0.0619350 | ||||||||
\(698\) | 7.57834e6 | − | 7.48969e6i | 0.0222847 | − | 0.0220241i | ||||
\(699\) | −7.99595e7 | −0.234120 | ||||||||
\(700\) | 3.73212e8 | + | 4.39166e6i | 1.08808 | + | 0.0128037i | ||||
\(701\) | 6.02955e8i | 1.75037i | 0.483784 | + | 0.875187i | \(0.339262\pi\) | ||||
−0.483784 | + | 0.875187i | \(0.660738\pi\) | |||||||
\(702\) | 2.31125e8 | − | 2.28421e8i | 0.668090 | − | 0.660275i | ||||
\(703\) | 3.49456e7i | 0.100584i | ||||||||
\(704\) | 1.30649e7 | − | 3.69957e8i | 0.0374445 | − | 1.06031i | ||||
\(705\) | −8.08050e7 | −0.230606 | ||||||||
\(706\) | 4.49232e6 | + | 4.54550e6i | 0.0127661 | + | 0.0129172i | ||||
\(707\) | 3.91501e8 | 1.10783 | ||||||||
\(708\) | −823888. | + | 7.00156e7i | −0.00232150 | + | 0.197285i | ||||
\(709\) | 4.41370e7i | 0.123841i | 0.998081 | + | 0.0619205i | \(0.0197225\pi\) | ||||
−0.998081 | + | 0.0619205i | \(0.980277\pi\) | |||||||
\(710\) | 6.61119e7 | + | 6.68945e7i | 0.184716 | + | 0.186902i | ||||
\(711\) | 1.08169e8i | 0.300951i | ||||||||
\(712\) | 1.99456e7 | − | 1.92537e7i | 0.0552595 | − | 0.0533425i | ||||
\(713\) | 8.98319e7 | 0.247835 | ||||||||
\(714\) | −7.14428e7 | + | 7.06070e7i | −0.196274 | + | 0.193978i | ||||
\(715\) | 2.90965e8 | 0.796017 | ||||||||
\(716\) | −4.77926e6 | + | 4.06150e8i | −0.0130203 | + | 1.10649i | ||||
\(717\) | − | 2.18330e8i | − | 0.592318i | ||||||
\(718\) | 3.22973e8 | − | 3.19195e8i | 0.872555 | − | 0.862348i | ||||
\(719\) | − | 3.59817e8i | − | 0.968045i | −0.875056 | − | 0.484022i | \(-0.839175\pi\) | ||
0.875056 | − | 0.484022i | \(-0.160825\pi\) | |||||||
\(720\) | 3.78028e6 | − | 1.60605e8i | 0.0101281 | − | 0.430292i | ||||
\(721\) | −2.99555e8 | −0.799229 | ||||||||
\(722\) | −2.59291e8 | − | 2.62360e8i | −0.688931 | − | 0.697085i | ||||
\(723\) | 6.93814e7 | 0.183581 | ||||||||
\(724\) | 8.64140e7 | + | 1.01685e6i | 0.227703 | + | 0.00267943i | ||||
\(725\) | − | 3.17791e8i | − | 0.833926i | ||||||
\(726\) | 1.06332e7 | + | 1.07590e7i | 0.0277878 | + | 0.0281167i | ||||
\(727\) | − | 1.23355e7i | − | 0.0321035i | −0.999871 | − | 0.0160518i | \(-0.994890\pi\) | ||
0.999871 | − | 0.0160518i | \(-0.00510965\pi\) | |||||||
\(728\) | −6.14702e8 | + | 5.93378e8i | −1.59320 | + | 1.53793i | ||||
\(729\) | −1.75968e8 | −0.454205 | ||||||||
\(730\) | −2.17301e7 | + | 2.14759e7i | −0.0558590 | + | 0.0552056i | ||||
\(731\) | −2.83766e8 | −0.726453 | ||||||||
\(732\) | −1.02999e8 | − | 1.21201e6i | −0.262604 | − | 0.00309011i | ||||
\(733\) | 3.54832e7i | 0.0900972i | 0.998985 | + | 0.0450486i | \(0.0143443\pi\) | ||||
−0.998985 | + | 0.0450486i | \(0.985656\pi\) | |||||||
\(734\) | −1.02636e8 | + | 1.01436e8i | −0.259545 | + | 0.256509i | ||||
\(735\) | 5.89361e7i | 0.148429i | ||||||||
\(736\) | −7.90196e7 | + | 7.45022e7i | −0.198199 | + | 0.186868i | ||||
\(737\) | −4.51656e8 | −1.12825 | ||||||||
\(738\) | 2.53422e7 | + | 2.56421e7i | 0.0630485 | + | 0.0637948i | ||||
\(739\) | −4.32139e8 | −1.07076 | −0.535378 | − | 0.844612i | \(-0.679831\pi\) | ||||
−0.535378 | + | 0.844612i | \(0.679831\pi\) | |||||||
\(740\) | −1.62311e6 | + | 1.37935e8i | −0.00400545 | + | 0.340391i | ||||
\(741\) | 2.83750e7i | 0.0697399i | ||||||||
\(742\) | −2.35535e8 | − | 2.38323e8i | −0.576559 | − | 0.583384i | ||||
\(743\) | − | 7.42345e8i | − | 1.80984i | −0.425586 | − | 0.904918i | \(-0.639932\pi\) | ||
0.425586 | − | 0.904918i | \(-0.360068\pi\) | |||||||
\(744\) | −8.18649e7 | − | 8.48070e7i | −0.198783 | − | 0.205927i | ||||
\(745\) | 2.83546e8 | 0.685732 | ||||||||
\(746\) | 2.03957e8 | − | 2.01571e8i | 0.491272 | − | 0.485525i | ||||
\(747\) | 5.27418e8 | 1.26530 | ||||||||
\(748\) | 3.25064e6 | − | 2.76246e8i | 0.00776720 | − | 0.660071i | ||||
\(749\) | − | 5.25265e8i | − | 1.25007i | ||||||
\(750\) | 7.98938e7 | − | 7.89592e7i | 0.189378 | − | 0.187163i | ||||
\(751\) | − | 6.22745e8i | − | 1.47025i | −0.677933 | − | 0.735124i | \(-0.737124\pi\) | ||
0.677933 | − | 0.735124i | \(-0.262876\pi\) | |||||||
\(752\) | −1.53561e7 | + | 6.52407e8i | −0.0361101 | + | 1.53414i | ||||
\(753\) | −7.17344e7 | −0.168013 | ||||||||
\(754\) | 5.11351e8 | + | 5.17403e8i | 1.19290 | + | 1.20702i | ||||
\(755\) | −6.67488e7 | −0.155097 | ||||||||
\(756\) | −3.64289e8 | − | 4.28667e6i | −0.843103 | − | 0.00992097i | ||||
\(757\) | 8.38267e8i | 1.93239i | 0.257815 | + | 0.966194i | \(0.416998\pi\) | ||||
−0.257815 | + | 0.966194i | \(0.583002\pi\) | |||||||
\(758\) | 5.45783e8 | + | 5.52243e8i | 1.25318 | + | 1.26801i | ||||
\(759\) | − | 3.97541e7i | − | 0.0909193i | ||||||
\(760\) | 2.05554e7 | + | 2.12942e7i | 0.0468259 | + | 0.0485087i | ||||
\(761\) | −6.44538e8 | −1.46250 | −0.731248 | − | 0.682112i | \(-0.761062\pi\) | ||||
−0.731248 | + | 0.682112i | \(0.761062\pi\) | |||||||
\(762\) | 1.21553e8 | − | 1.20131e8i | 0.274727 | − | 0.271513i | ||||
\(763\) | 8.30277e8 | 1.86917 | ||||||||
\(764\) | −2.12493e8 | − | 2.50045e6i | −0.476501 | − | 0.00560709i | ||||
\(765\) | − | 1.19891e8i | − | 0.267794i | ||||||
\(766\) | −1.80227e8 | + | 1.78119e8i | −0.400990 | + | 0.396299i | ||||
\(767\) | 4.44472e8i | 0.985050i | ||||||||
\(768\) | 1.42346e8 | + | 6.70471e6i | 0.314241 | + | 0.0148012i | ||||
\(769\) | 7.83458e8 | 1.72281 | 0.861404 | − | 0.507921i | \(-0.169586\pi\) | ||||
0.861404 | + | 0.507921i | \(0.169586\pi\) | |||||||
\(770\) | −2.29303e8 | − | 2.32017e8i | −0.502271 | − | 0.508216i | ||||
\(771\) | −1.56696e8 | −0.341897 | ||||||||
\(772\) | −4.21107e6 | + | 3.57864e8i | −0.00915251 | + | 0.777798i | ||||
\(773\) | − | 7.79311e7i | − | 0.168722i | −0.996435 | − | 0.0843611i | \(-0.973115\pi\) | ||
0.996435 | − | 0.0843611i | \(-0.0268849\pi\) | |||||||
\(774\) | −3.42901e8 | − | 3.46960e8i | −0.739514 | − | 0.748267i | ||||
\(775\) | 3.26868e8i | 0.702210i | ||||||||
\(776\) | 4.07678e8 | − | 3.93535e8i | 0.872433 | − | 0.842167i | ||||
\(777\) | 1.48269e8 | 0.316073 | ||||||||
\(778\) | 3.13251e8 | − | 3.09587e8i | 0.665203 | − | 0.657421i | ||||
\(779\) | −6.64190e6 | −0.0140501 | ||||||||
\(780\) | −1.31792e6 | + | 1.11999e8i | −0.00277719 | + | 0.236011i | ||||
\(781\) | 2.78038e8i | 0.583649i | ||||||||
\(782\) | −5.76464e7 | + | 5.69720e7i | −0.120546 | + | 0.119136i | ||||
\(783\) | 3.10193e8i | 0.646170i | ||||||||
\(784\) | 4.75841e8 | + | 1.12002e7i | 0.987446 | + | 0.0232422i | ||||
\(785\) | 5.99539e7 | 0.123939 | ||||||||
\(786\) | −1.80300e8 | − | 1.82434e8i | −0.371302 | − | 0.375697i | ||||
\(787\) | −4.76683e8 | −0.977924 | −0.488962 | − | 0.872305i | \(-0.662624\pi\) | ||||
−0.488962 | + | 0.872305i | \(0.662624\pi\) | |||||||
\(788\) | 4.60639e8 | + | 5.42044e6i | 0.941418 | + | 0.0110779i | ||||
\(789\) | 3.26246e7i | 0.0664224i | ||||||||
\(790\) | −5.52959e7 | − | 5.59504e7i | −0.112153 | − | 0.113481i | ||||
\(791\) | − | 3.12116e8i | − | 0.630648i | ||||||
\(792\) | 3.41693e8 | − | 3.29840e8i | 0.687798 | − | 0.663938i | ||||
\(793\) | −6.53858e8 | −1.31118 | ||||||||
\(794\) | −4.74033e8 | + | 4.68488e8i | −0.946994 | + | 0.935916i | ||||
\(795\) | −4.39277e7 | −0.0874253 | ||||||||
\(796\) | −7.41310e8 | − | 8.72315e6i | −1.46981 | − | 0.0172955i | ||||
\(797\) | − | 2.49479e7i | − | 0.0492788i | −0.999696 | − | 0.0246394i | \(-0.992156\pi\) | ||
0.999696 | − | 0.0246394i | \(-0.00784375\pi\) | |||||||
\(798\) | 2.26264e7 | − | 2.23617e7i | 0.0445253 | − | 0.0440045i | ||||
\(799\) | 4.87016e8i | 0.954779i | ||||||||
\(800\) | −2.71088e8 | − | 2.87525e8i | −0.529469 | − | 0.561573i | ||||
\(801\) | 3.55655e7 | 0.0692040 | ||||||||
\(802\) | 2.38844e8 | + | 2.41671e8i | 0.463010 | + | 0.468490i | ||||
\(803\) | −9.03184e7 | −0.174433 | ||||||||
\(804\) | 2.04577e6 | − | 1.73853e8i | 0.00393630 | − | 0.334515i | ||||
\(805\) | 9.57010e7i | 0.183455i | ||||||||
\(806\) | −5.25956e8 | − | 5.32181e8i | −1.00449 | − | 1.01638i | ||||
\(807\) | 2.63676e8i | 0.501707i | ||||||||
\(808\) | −2.87882e8 | − | 2.98228e8i | −0.545733 | − | 0.565345i | ||||
\(809\) | 6.82458e8 | 1.28893 | 0.644467 | − | 0.764632i | \(-0.277079\pi\) | ||||
0.644467 | + | 0.764632i | \(0.277079\pi\) | |||||||
\(810\) | 1.28721e8 | − | 1.27215e8i | 0.242211 | − | 0.239377i | ||||
\(811\) | 3.51060e8 | 0.658140 | 0.329070 | − | 0.944306i | \(-0.393265\pi\) | ||||
0.329070 | + | 0.944306i | \(0.393265\pi\) | |||||||
\(812\) | 9.59628e6 | − | 8.15510e8i | 0.0179240 | − | 1.52321i | ||||
\(813\) | 2.00082e8i | 0.372337i | ||||||||
\(814\) | −2.90047e8 | + | 2.86654e8i | −0.537768 | + | 0.531477i | ||||
\(815\) | − | 8.79628e7i | − | 0.162490i | ||||||
\(816\) | 1.06319e8 | + | 2.50250e6i | 0.195677 | + | 0.00460579i | ||||
\(817\) | 8.98706e7 | 0.164798 | ||||||||
\(818\) | 2.59263e8 | + | 2.62331e8i | 0.473674 | + | 0.479281i | ||||
\(819\) | −1.09609e9 | −1.99524 | ||||||||
\(820\) | −2.62164e7 | − | 308493.i | −0.0475479 | − | 0.000559506i | ||||
\(821\) | − | 6.38664e8i | − | 1.15410i | −0.816709 | − | 0.577049i | \(-0.804204\pi\) | ||
0.816709 | − | 0.577049i | \(-0.195796\pi\) | |||||||
\(822\) | 6.71758e7 | + | 6.79709e7i | 0.120948 | + | 0.122379i | ||||
\(823\) | 1.77607e8i | 0.318611i | 0.987229 | + | 0.159305i | \(0.0509254\pi\) | ||||
−0.987229 | + | 0.159305i | \(0.949075\pi\) | |||||||
\(824\) | 2.20271e8 | + | 2.28187e8i | 0.393710 | + | 0.407859i | ||||
\(825\) | 1.44651e8 | 0.257609 | ||||||||
\(826\) | 3.54425e8 | − | 3.50279e8i | 0.628904 | − | 0.621547i | ||||
\(827\) | 2.12047e7 | 0.0374900 | 0.0187450 | − | 0.999824i | \(-0.494033\pi\) | ||||
0.0187450 | + | 0.999824i | \(0.494033\pi\) | |||||||
\(828\) | −1.39319e8 | − | 1.63940e6i | −0.245426 | − | 0.00288798i | ||||
\(829\) | − | 6.30661e8i | − | 1.10696i | −0.832862 | − | 0.553480i | \(-0.813299\pi\) | ||
0.832862 | − | 0.553480i | \(-0.186701\pi\) | |||||||
\(830\) | −2.72806e8 | + | 2.69615e8i | −0.477111 | + | 0.471530i | ||||
\(831\) | − | 1.97219e8i | − | 0.343673i | ||||||
\(832\) | 9.04016e8 | + | 3.19250e7i | 1.56966 | + | 0.0554321i | ||||
\(833\) | 3.55211e8 | 0.614542 | ||||||||
\(834\) | 1.10606e8 | + | 1.11915e8i | 0.190669 | + | 0.192926i | ||||
\(835\) | −3.08316e8 | −0.529587 | ||||||||
\(836\) | −1.02950e6 | + | 8.74890e7i | −0.00176201 | + | 0.149739i | ||||
\(837\) | − | 3.19053e8i | − | 0.544109i | ||||||
\(838\) | −2.17411e8 | − | 2.19985e8i | −0.369445 | − | 0.373818i | ||||
\(839\) | 9.45472e8i | 1.60089i | 0.599403 | + | 0.800447i | \(0.295405\pi\) | ||||
−0.599403 | + | 0.800447i | \(0.704595\pi\) | |||||||
\(840\) | 9.03478e7 | − | 8.72135e7i | 0.152433 | − | 0.147145i | ||||
\(841\) | −9.95855e7 | −0.167420 | ||||||||
\(842\) | −1.46923e8 | + | 1.45204e8i | −0.246124 | + | 0.243245i | ||||
\(843\) | 2.54408e8 | 0.424667 | ||||||||
\(844\) | 481457. | − | 4.09152e7i | 0.000800811 | − | 0.0680545i | ||||
\(845\) | 4.22781e8i | 0.700721i | ||||||||
\(846\) | −5.95474e8 | + | 5.88508e8i | −0.983448 | + | 0.971944i | ||||
\(847\) | − | 1.07652e8i | − | 0.177163i | ||||||
\(848\) | −8.34800e6 | + | 3.54666e8i | −0.0136897 | + | 0.581609i | ||||
\(849\) | −3.12606e8 | −0.510828 | ||||||||
\(850\) | −2.07302e8 | − | 2.09756e8i | −0.337556 | − | 0.341552i | ||||
\(851\) | 1.19637e8 | 0.194122 | ||||||||
\(852\) | −1.07024e8 | − | 1.25937e6i | −0.173046 | − | 0.00203627i | ||||
\(853\) | − | 3.08597e8i | − | 0.497216i | −0.968604 | − | 0.248608i | \(-0.920027\pi\) | ||
0.968604 | − | 0.248608i | \(-0.0799731\pi\) | |||||||
\(854\) | 5.15292e8 | + | 5.21391e8i | 0.827332 | + | 0.837125i | ||||
\(855\) | 3.79702e7i | 0.0607497i | ||||||||
\(856\) | −4.00123e8 | + | 3.86242e8i | −0.637929 | + | 0.615798i | ||||
\(857\) | 2.45043e8 | 0.389314 | 0.194657 | − | 0.980871i | \(-0.437641\pi\) | ||||
0.194657 | + | 0.980871i | \(0.437641\pi\) | |||||||
\(858\) | −2.35511e8 | + | 2.32756e8i | −0.372862 | + | 0.368501i | ||||
\(859\) | 6.90100e8 | 1.08876 | 0.544380 | − | 0.838839i | \(-0.316765\pi\) | ||||
0.544380 | + | 0.838839i | \(0.316765\pi\) | |||||||
\(860\) | 3.54730e8 | + | 4.17418e6i | 0.557702 | + | 0.00656260i | ||||
\(861\) | 2.81805e7i | 0.0441509i | ||||||||
\(862\) | 1.76157e8 | − | 1.74096e8i | 0.275029 | − | 0.271812i | ||||
\(863\) | − | 6.89145e8i | − | 1.07221i | −0.844153 | − | 0.536103i | \(-0.819896\pi\) | ||
0.844153 | − | 0.536103i | \(-0.180104\pi\) | |||||||
\(864\) | 2.64607e8 | + | 2.80651e8i | 0.410260 | + | 0.435136i | ||||
\(865\) | −3.58410e7 | −0.0553773 | ||||||||
\(866\) | 2.61099e8 | + | 2.64189e8i | 0.402023 | + | 0.406782i | ||||
\(867\) | −1.25656e8 | −0.192808 | ||||||||
\(868\) | −9.87036e6 | + | 8.38802e8i | −0.0150929 | + | 1.28263i | ||||
\(869\) | − | 2.32551e8i | − | 0.354371i | ||||||
\(870\) | −7.51574e7 | − | 7.60470e7i | −0.114134 | − | 0.115485i | ||||
\(871\) | − | 1.10365e9i | − | 1.67024i | ||||||
\(872\) | −6.10526e8 | − | 6.32467e8i | −0.920777 | − | 0.953868i | ||||
\(873\) | 7.26941e8 | 1.09259 | ||||||||
\(874\) | 1.82570e7 | − | 1.80434e7i | 0.0273461 | − | 0.0270262i | ||||
\(875\) | −7.99397e8 | −1.19327 | ||||||||
\(876\) | 409096. | − | 3.47658e7i | 0.000608573 | − | 0.0517177i | ||||
\(877\) | 8.03085e8i | 1.19059i | 0.803507 | + | 0.595296i | \(0.202965\pi\) | ||||
−0.803507 | + | 0.595296i | \(0.797035\pi\) | |||||||
\(878\) | 7.60712e8 | − | 7.51813e8i | 1.12392 | − | 1.11078i | ||||
\(879\) | − | 2.86175e8i | − | 0.421372i | ||||||
\(880\) | −8.12712e6 | + | 3.45282e8i | −0.0119258 | + | 0.506670i | ||||
\(881\) | −4.58820e8 | −0.670988 | −0.335494 | − | 0.942042i | \(-0.608903\pi\) | ||||
−0.335494 | + | 0.942042i | \(0.608903\pi\) | |||||||
\(882\) | 4.29235e8 | + | 4.34316e8i | 0.625590 | + | 0.632995i | ||||
\(883\) | 1.80291e8 | 0.261874 | 0.130937 | − | 0.991391i | \(-0.458201\pi\) | ||||
0.130937 | + | 0.991391i | \(0.458201\pi\) | |||||||
\(884\) | 6.75026e8 | + | 7.94318e6i | 0.977156 | + | 0.0114984i | ||||
\(885\) | − | 6.53277e7i | − | 0.0942469i | ||||||
\(886\) | −2.97783e7 | − | 3.01308e7i | −0.0428153 | − | 0.0433221i | ||||
\(887\) | 6.63542e8i | 0.950818i | 0.879765 | + | 0.475409i | \(0.157700\pi\) | ||||
−0.879765 | + | 0.475409i | \(0.842300\pi\) | |||||||
\(888\) | −1.09026e8 | − | 1.12944e8i | −0.155701 | − | 0.161297i | ||||
\(889\) | −1.21623e9 | −1.73105 | ||||||||
\(890\) | −1.83962e7 | + | 1.81810e7i | −0.0260950 | + | 0.0257898i | ||||
\(891\) | 5.35011e8 | 0.756362 | ||||||||
\(892\) | −6.08690e8 | − | 7.16259e6i | −0.857634 | − | 0.0100920i | ||||
\(893\) | − | 1.54241e8i | − | 0.216594i | ||||||
\(894\) | −2.29506e8 | + | 2.26821e8i | −0.321204 | + | 0.317447i | ||||
\(895\) | − | 3.78956e8i | − | 0.528591i | ||||||
\(896\) | −6.86979e8 | − | 7.46028e8i | −0.955035 | − | 1.03713i | ||||
\(897\) | 9.71419e7 | 0.134595 | ||||||||
\(898\) | −6.74880e8 | − | 6.82869e8i | −0.931961 | − | 0.942992i | ||||
\(899\) | 7.14242e8 | 0.983029 | ||||||||
\(900\) | 5.96521e6 | − | 5.06935e8i | 0.00818274 | − | 0.695385i | ||||
\(901\) | 2.64755e8i | 0.361967i | ||||||||
\(902\) | −5.44825e7 | − | 5.51274e7i | −0.0742399 | − | 0.0751186i | ||||
\(903\) | − | 3.81307e8i | − | 0.517859i | ||||||
\(904\) | −2.37756e8 | + | 2.29508e8i | −0.321830 | + | 0.310665i | ||||
\(905\) | −8.06281e7 | −0.108778 | ||||||||
\(906\) | 5.40273e7 | − | 5.33953e7i | 0.0726489 | − | 0.0717991i | ||||
\(907\) | 2.51825e8 | 0.337503 | 0.168751 | − | 0.985659i | \(-0.446027\pi\) | ||||
0.168751 | + | 0.985659i | \(0.446027\pi\) | |||||||
\(908\) | −9.62961e6 | + | 8.18343e8i | −0.0128633 | + | 1.09314i | ||||
\(909\) | − | 5.31777e8i | − | 0.708008i | ||||||
\(910\) | 5.66951e8 | − | 5.60319e8i | 0.752353 | − | 0.743551i | ||||
\(911\) | 1.33414e9i | 1.76459i | 0.470694 | + | 0.882297i | \(0.344004\pi\) | ||||
−0.470694 | + | 0.882297i | \(0.655996\pi\) | |||||||
\(912\) | −3.36720e7 | − | 792560.i | −0.0443899 | − | 0.00104484i | ||||
\(913\) | −1.13388e9 | −1.48990 | ||||||||
\(914\) | −1.03860e9 | − | 1.05089e9i | −1.36022 | − | 1.37632i | ||||
\(915\) | 9.61028e7 | 0.125451 | ||||||||
\(916\) | −2.95614e8 | − | 3.47856e6i | −0.384627 | − | 0.00452598i | ||||
\(917\) | 1.82539e9i | 2.36726i | ||||||||
\(918\) | 2.02346e8 | + | 2.04741e8i | 0.261557 | + | 0.264652i | ||||
\(919\) | − | 9.68344e8i | − | 1.24762i | −0.781575 | − | 0.623811i | \(-0.785583\pi\) | ||
0.781575 | − | 0.623811i | \(-0.214417\pi\) | |||||||
\(920\) | 7.29007e7 | − | 7.03716e7i | 0.0936199 | − | 0.0903721i | ||||
\(921\) | −3.14089e8 | −0.402044 | ||||||||
\(922\) | 8.34901e8 | − | 8.25134e8i | 1.06523 | − | 1.05277i | ||||
\(923\) | −6.79406e8 | −0.864021 | ||||||||
\(924\) | 3.71202e8 | + | 4.36801e6i | 0.470538 | + | 0.00553692i | ||||
\(925\) | 4.35317e8i | 0.550022i | ||||||||
\(926\) | 8.82662e8 | − | 8.72337e8i | 1.11163 | − | 1.09863i | ||||
\(927\) | 4.06887e8i | 0.510781i | ||||||||
\(928\) | −6.28274e8 | + | 5.92357e8i | −0.786150 | + | 0.741207i | ||||
\(929\) | 9.60464e8 | 1.19794 | 0.598968 | − | 0.800773i | \(-0.295577\pi\) | ||||
0.598968 | + | 0.800773i | \(0.295577\pi\) | |||||||
\(930\) | 7.73040e7 | + | 7.82190e7i | 0.0961066 | + | 0.0972442i | ||||
\(931\) | −1.12498e8 | −0.139410 | ||||||||
\(932\) | 7.08902e6 | − | 6.02438e8i | 0.00875666 | − | 0.744158i | ||||
\(933\) | 3.10330e8i | 0.382102i | ||||||||
\(934\) | 6.04745e8 | + | 6.11903e8i | 0.742219 | + | 0.751004i | ||||
\(935\) | 2.57750e8i | 0.315328i | ||||||||
\(936\) | 8.05987e8 | + | 8.34952e8i | 0.982880 | + | 1.01820i | ||||
\(937\) | 9.88309e8 | 1.20136 | 0.600681 | − | 0.799489i | \(-0.294896\pi\) | ||||
0.600681 | + | 0.799489i | \(0.294896\pi\) | |||||||
\(938\) | −8.80061e8 | + | 8.69766e8i | −1.06636 | + | 1.05389i | ||||
\(939\) | 4.67308e8 | 0.564425 | ||||||||
\(940\) | 7.16398e6 | − | 6.08809e8i | 0.00862523 | − | 0.732989i | ||||
\(941\) | − | 1.34529e8i | − | 0.161454i | −0.996736 | − | 0.0807269i | \(-0.974276\pi\) | ||
0.996736 | − | 0.0807269i | \(-0.0257242\pi\) | |||||||
\(942\) | −4.85275e7 | + | 4.79598e7i | −0.0580544 | + | 0.0573753i | ||||
\(943\) | 2.27386e7i | 0.0271162i | ||||||||
\(944\) | −5.27445e8 | − | 1.24148e7i | −0.626991 | − | 0.0147579i | ||||
\(945\) | 3.39898e8 | 0.402766 | ||||||||
\(946\) | 7.37194e8 | + | 7.45920e8i | 0.870780 | + | 0.881087i | ||||
\(947\) | 4.96808e8 | 0.584976 | 0.292488 | − | 0.956269i | \(-0.405517\pi\) | ||||
0.292488 | + | 0.956269i | \(0.405517\pi\) | |||||||
\(948\) | 8.95144e7 | + | 1.05334e6i | 0.105067 | + | 0.00123635i | ||||
\(949\) | − | 2.20699e8i | − | 0.258227i | ||||||
\(950\) | 6.56539e7 | + | 6.64310e7i | 0.0765755 | + | 0.0774819i | ||||
\(951\) | 3.50369e8i | 0.407366i | ||||||||
\(952\) | −5.25640e8 | − | 5.44531e8i | −0.609225 | − | 0.631120i | ||||
\(953\) | −4.73453e8 | −0.547014 | −0.273507 | − | 0.961870i | \(-0.588184\pi\) | ||||
−0.273507 | + | 0.961870i | \(0.588184\pi\) | |||||||
\(954\) | −3.23715e8 | + | 3.19928e8i | −0.372836 | + | 0.368475i | ||||
\(955\) | 1.98265e8 | 0.227633 | ||||||||
\(956\) | 1.64496e9 | + | 1.93566e7i | 1.88270 | + | 0.0221542i | ||||
\(957\) | − | 3.16080e8i | − | 0.360629i | ||||||
\(958\) | −8.47138e7 | + | 8.37228e7i | −0.0963513 | + | 0.0952242i | ||||
\(959\) | − | 6.80099e8i | − | 0.771110i | ||||||
\(960\) | −1.32871e8 | − | 4.69228e6i | −0.150181 | − | 0.00530359i | ||||
\(961\) | 1.52861e8 | 0.172238 | ||||||||
\(962\) | −7.00459e8 | − | 7.08750e8i | −0.786787 | − | 0.796100i | ||||
\(963\) | −7.13470e8 | −0.798908 | ||||||||
\(964\) | −6.15119e6 | + | 5.22740e8i | −0.00686638 | + | 0.583518i | ||||
\(965\) | − | 3.33903e8i | − | 0.371568i | ||||||
\(966\) | −7.65555e7 | − | 7.74617e7i | −0.0849269 | − | 0.0859321i | ||||
\(967\) | − | 3.26806e8i | − | 0.361418i | −0.983537 | − | 0.180709i | \(-0.942161\pi\) | ||
0.983537 | − | 0.180709i | \(-0.0578393\pi\) | |||||||
\(968\) | −8.20045e7 | + | 7.91597e7i | −0.0904090 | + | 0.0872726i | ||||
\(969\) | −2.51358e7 | −0.0276263 | ||||||||
\(970\) | −3.76009e8 | + | 3.71610e8i | −0.411986 | + | 0.407167i | ||||
\(971\) | −7.38503e8 | −0.806667 | −0.403333 | − | 0.915053i | \(-0.632149\pi\) | ||||
−0.403333 | + | 0.915053i | \(0.632149\pi\) | |||||||
\(972\) | −8.88545e6 | + | 7.55103e8i | −0.00967566 | + | 0.822256i | ||||
\(973\) | − | 1.11979e9i | − | 1.21562i | ||||||
\(974\) | −5.51561e8 | + | 5.45109e8i | −0.596921 | + | 0.589938i | ||||
\(975\) | 3.53466e8i | 0.381359i | ||||||||
\(976\) | 1.82633e7 | − | 7.75919e8i | 0.0196440 | − | 0.834578i | ||||
\(977\) | −8.98069e8 | −0.962999 | −0.481500 | − | 0.876446i | \(-0.659908\pi\) | ||||
−0.481500 | + | 0.876446i | \(0.659908\pi\) | |||||||
\(978\) | 7.03654e7 | + | 7.11982e7i | 0.0752216 | + | 0.0761119i | ||||
\(979\) | −7.64614e7 | −0.0814880 | ||||||||
\(980\) | −4.44042e8 | − | 5.22514e6i | −0.471787 | − | 0.00555161i | ||||
\(981\) | − | 1.12777e9i | − | 1.19457i | ||||||
\(982\) | −3.63031e8 | − | 3.67328e8i | −0.383362 | − | 0.387900i | ||||
\(983\) | 5.63791e8i | 0.593551i | 0.954947 | + | 0.296775i | \(0.0959112\pi\) | ||||
−0.954947 | + | 0.296775i | \(0.904089\pi\) | |||||||
\(984\) | 2.14666e7 | − | 2.07219e7i | 0.0225309 | − | 0.0217493i | ||||
\(985\) | −4.29797e8 | −0.449733 | ||||||||
\(986\) | −4.58339e8 | + | 4.52978e8i | −0.478141 | + | 0.472548i | ||||
\(987\) | −6.54422e8 | −0.680622 | ||||||||
\(988\) | −2.13786e8 | − | 2.51566e6i | −0.221670 | − | 0.00260844i | ||||
\(989\) | − | 3.07672e8i | − | 0.318053i | ||||||
\(990\) | −3.15150e8 | + | 3.11463e8i | −0.324797 | + | 0.320997i | ||||
\(991\) | − | 4.94832e8i | − | 0.508437i | −0.967147 | − | 0.254218i | \(-0.918182\pi\) | ||
0.967147 | − | 0.254218i | \(-0.0818182\pi\) | |||||||
\(992\) | 6.46219e8 | − | 6.09276e8i | 0.661980 | − | 0.624136i | ||||
\(993\) | 2.31792e8 | 0.236729 | ||||||||
\(994\) | 5.35426e8 | + | 5.41764e8i | 0.545180 | + | 0.551633i | ||||
\(995\) | 6.91675e8 | 0.702155 | ||||||||
\(996\) | 5.13591e6 | − | 4.36459e8i | 0.00519803 | − | 0.441739i | ||||
\(997\) | − | 2.35279e8i | − | 0.237409i | −0.992930 | − | 0.118705i | \(-0.962126\pi\) | ||
0.992930 | − | 0.118705i | \(-0.0378742\pi\) | |||||||
\(998\) | 4.54961e8 | + | 4.60347e8i | 0.457702 | + | 0.463120i | ||||
\(999\) | − | 4.24909e8i | − | 0.426186i |
(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 | 8.7.d.b.3.4 | yes | 4 | |
3.2 | odd | 2 | 72.7.b.b.19.1 | 4 | |||
4.3 | odd | 2 | 32.7.d.b.15.1 | 4 | |||
8.3 | odd | 2 | inner | 8.7.d.b.3.3 | ✓ | 4 | |
8.5 | even | 2 | 32.7.d.b.15.2 | 4 | |||
12.11 | even | 2 | 288.7.b.b.271.3 | 4 | |||
16.3 | odd | 4 | 256.7.c.l.255.3 | 8 | |||
16.5 | even | 4 | 256.7.c.l.255.4 | 8 | |||
16.11 | odd | 4 | 256.7.c.l.255.6 | 8 | |||
16.13 | even | 4 | 256.7.c.l.255.5 | 8 | |||
24.5 | odd | 2 | 288.7.b.b.271.2 | 4 | |||
24.11 | even | 2 | 72.7.b.b.19.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.7.d.b.3.3 | ✓ | 4 | 8.3 | odd | 2 | inner | |
8.7.d.b.3.4 | yes | 4 | 1.1 | even | 1 | trivial | |
32.7.d.b.15.1 | 4 | 4.3 | odd | 2 | |||
32.7.d.b.15.2 | 4 | 8.5 | even | 2 | |||
72.7.b.b.19.1 | 4 | 3.2 | odd | 2 | |||
72.7.b.b.19.2 | 4 | 24.11 | even | 2 | |||
256.7.c.l.255.3 | 8 | 16.3 | odd | 4 | |||
256.7.c.l.255.4 | 8 | 16.5 | even | 4 | |||
256.7.c.l.255.5 | 8 | 16.13 | even | 4 | |||
256.7.c.l.255.6 | 8 | 16.11 | odd | 4 | |||
288.7.b.b.271.2 | 4 | 24.5 | odd | 2 | |||
288.7.b.b.271.3 | 4 | 12.11 | even | 2 |