Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(34,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.34");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.13 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.14 |
$q$-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 \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) | \(67\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.886559i | − | 0.156723i | −0.996925 | − | 0.0783615i | \(-0.975031\pi\) | ||
0.996925 | − | 0.0783615i | \(-0.0249688\pi\) | |||||||
\(3\) | − | 9.00000i | − | 0.577350i | ||||||
\(4\) | 31.2140 | 0.975438 | ||||||||
\(5\) | −37.4584 | − | 41.4954i | −0.670076 | − | 0.742293i | ||||
\(6\) | −7.97903 | −0.0904841 | ||||||||
\(7\) | 224.774i | 1.73380i | 0.498478 | + | 0.866902i | \(0.333892\pi\) | ||||
−0.498478 | + | 0.866902i | \(0.666108\pi\) | |||||||
\(8\) | − | 56.0430i | − | 0.309597i | ||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | −36.7881 | + | 33.2091i | −0.116334 | + | 0.105016i | ||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | − | 280.926i | − | 0.563169i | ||||||
\(13\) | − | 1065.64i | − | 1.74884i | −0.485169 | − | 0.874420i | \(-0.661242\pi\) | ||
0.485169 | − | 0.874420i | \(-0.338758\pi\) | |||||||
\(14\) | 199.275 | 0.271727 | ||||||||
\(15\) | −373.459 | + | 337.125i | −0.428563 | + | 0.386868i | ||||
\(16\) | 949.163 | 0.926917 | ||||||||
\(17\) | − | 1347.75i | − | 1.13106i | −0.824727 | − | 0.565531i | \(-0.808671\pi\) | ||
0.824727 | − | 0.565531i | \(-0.191329\pi\) | |||||||
\(18\) | 71.8113i | 0.0522410i | ||||||||
\(19\) | −691.252 | −0.439291 | −0.219646 | − | 0.975580i | \(-0.570490\pi\) | ||||
−0.219646 | + | 0.975580i | \(0.570490\pi\) | |||||||
\(20\) | −1169.23 | − | 1295.24i | −0.653617 | − | 0.724060i | ||||
\(21\) | 2022.96 | 1.00101 | ||||||||
\(22\) | − | 107.274i | − | 0.0472538i | ||||||
\(23\) | − | 3396.13i | − | 1.33864i | −0.742973 | − | 0.669321i | \(-0.766585\pi\) | ||
0.742973 | − | 0.669321i | \(-0.233415\pi\) | |||||||
\(24\) | −504.387 | −0.178746 | ||||||||
\(25\) | −318.739 | + | 3108.70i | −0.101997 | + | 0.994785i | ||||
\(26\) | −944.749 | −0.274084 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | 7016.09i | 1.69122i | ||||||||
\(29\) | −8603.02 | −1.89957 | −0.949786 | − | 0.312900i | \(-0.898699\pi\) | ||||
−0.949786 | + | 0.312900i | \(0.898699\pi\) | |||||||
\(30\) | 298.882 | + | 331.093i | 0.0606312 | + | 0.0671657i | ||||
\(31\) | −320.509 | −0.0599013 | −0.0299507 | − | 0.999551i | \(-0.509535\pi\) | ||||
−0.0299507 | + | 0.999551i | \(0.509535\pi\) | |||||||
\(32\) | − | 2634.86i | − | 0.454866i | ||||||
\(33\) | − | 1089.00i | − | 0.174078i | ||||||
\(34\) | −1194.86 | −0.177263 | ||||||||
\(35\) | 9327.07 | − | 8419.65i | 1.28699 | − | 1.16178i | ||||
\(36\) | −2528.34 | −0.325146 | ||||||||
\(37\) | − | 1906.23i | − | 0.228913i | −0.993428 | − | 0.114457i | \(-0.963487\pi\) | ||
0.993428 | − | 0.114457i | \(-0.0365127\pi\) | |||||||
\(38\) | 612.836i | 0.0688471i | ||||||||
\(39\) | −9590.72 | −1.00969 | ||||||||
\(40\) | −2325.53 | + | 2099.28i | −0.229811 | + | 0.207453i | ||||
\(41\) | 5821.85 | 0.540881 | 0.270440 | − | 0.962737i | \(-0.412831\pi\) | ||||
0.270440 | + | 0.962737i | \(0.412831\pi\) | |||||||
\(42\) | − | 1793.48i | − | 0.156882i | ||||||
\(43\) | − | 1421.42i | − | 0.117234i | −0.998281 | − | 0.0586168i | \(-0.981331\pi\) | ||
0.998281 | − | 0.0586168i | \(-0.0186690\pi\) | |||||||
\(44\) | 3776.90 | 0.294106 | ||||||||
\(45\) | 3034.13 | + | 3361.13i | 0.223359 | + | 0.247431i | ||||
\(46\) | −3010.87 | −0.209796 | ||||||||
\(47\) | − | 6454.51i | − | 0.426205i | −0.977030 | − | 0.213102i | \(-0.931643\pi\) | ||
0.977030 | − | 0.213102i | \(-0.0683568\pi\) | |||||||
\(48\) | − | 8542.47i | − | 0.535156i | ||||||
\(49\) | −33716.2 | −2.00608 | ||||||||
\(50\) | 2756.05 | + | 282.581i | 0.155906 | + | 0.0159852i | ||||
\(51\) | −12129.7 | −0.653019 | ||||||||
\(52\) | − | 33262.8i | − | 1.70589i | ||||||
\(53\) | − | 9109.26i | − | 0.445444i | −0.974882 | − | 0.222722i | \(-0.928506\pi\) | ||
0.974882 | − | 0.222722i | \(-0.0714943\pi\) | |||||||
\(54\) | 646.302 | 0.0301614 | ||||||||
\(55\) | −4532.46 | − | 5020.95i | −0.202035 | − | 0.223810i | ||||
\(56\) | 12597.0 | 0.536780 | ||||||||
\(57\) | 6221.27i | 0.253625i | ||||||||
\(58\) | 7627.08i | 0.297707i | ||||||||
\(59\) | −10213.6 | −0.381989 | −0.190995 | − | 0.981591i | \(-0.561171\pi\) | ||||
−0.190995 | + | 0.981591i | \(0.561171\pi\) | |||||||
\(60\) | −11657.1 | + | 10523.0i | −0.418036 | + | 0.377366i | ||||
\(61\) | −34276.3 | −1.17942 | −0.589712 | − | 0.807614i | \(-0.700759\pi\) | ||||
−0.589712 | + | 0.807614i | \(0.700759\pi\) | |||||||
\(62\) | 284.150i | 0.00938791i | ||||||||
\(63\) | − | 18206.7i | − | 0.577935i | ||||||
\(64\) | 28037.3 | 0.855629 | ||||||||
\(65\) | −44219.0 | + | 39917.0i | −1.29815 | + | 1.17186i | ||||
\(66\) | −965.463 | −0.0272820 | ||||||||
\(67\) | − | 68436.0i | − | 1.86251i | −0.364374 | − | 0.931253i | \(-0.618717\pi\) | ||
0.364374 | − | 0.931253i | \(-0.381283\pi\) | |||||||
\(68\) | − | 42068.6i | − | 1.10328i | ||||||
\(69\) | −30565.2 | −0.772866 | ||||||||
\(70\) | −7464.52 | − | 8269.00i | −0.182078 | − | 0.201701i | ||||
\(71\) | 1883.92 | 0.0443524 | 0.0221762 | − | 0.999754i | \(-0.492941\pi\) | ||||
0.0221762 | + | 0.999754i | \(0.492941\pi\) | |||||||
\(72\) | 4539.48i | 0.103199i | ||||||||
\(73\) | 87733.7i | 1.92690i | 0.267885 | + | 0.963451i | \(0.413675\pi\) | ||||
−0.267885 | + | 0.963451i | \(0.586325\pi\) | |||||||
\(74\) | −1689.99 | −0.0358760 | ||||||||
\(75\) | 27978.3 | + | 2868.66i | 0.574339 | + | 0.0588878i | ||||
\(76\) | −21576.8 | −0.428501 | ||||||||
\(77\) | 27197.6i | 0.522762i | ||||||||
\(78\) | 8502.74i | 0.158242i | ||||||||
\(79\) | 52408.8 | 0.944793 | 0.472397 | − | 0.881386i | \(-0.343389\pi\) | ||||
0.472397 | + | 0.881386i | \(0.343389\pi\) | |||||||
\(80\) | −35554.1 | − | 39385.9i | −0.621105 | − | 0.688044i | ||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | − | 5161.42i | − | 0.0847685i | ||||||
\(83\) | − | 58665.8i | − | 0.934737i | −0.884062 | − | 0.467369i | \(-0.845202\pi\) | ||
0.884062 | − | 0.467369i | \(-0.154798\pi\) | |||||||
\(84\) | 63144.8 | 0.976426 | ||||||||
\(85\) | −55925.4 | + | 50484.5i | −0.839579 | + | 0.757898i | ||||
\(86\) | −1260.17 | −0.0183732 | ||||||||
\(87\) | 77427.1i | 1.09672i | ||||||||
\(88\) | − | 6781.20i | − | 0.0933469i | ||||||
\(89\) | 113843. | 1.52346 | 0.761728 | − | 0.647896i | \(-0.224351\pi\) | ||||
0.761728 | + | 0.647896i | \(0.224351\pi\) | |||||||
\(90\) | 2979.84 | − | 2689.94i | 0.0387781 | − | 0.0350054i | ||||
\(91\) | 239527. | 3.03215 | ||||||||
\(92\) | − | 106007.i | − | 1.30576i | ||||||
\(93\) | 2884.58i | 0.0345840i | ||||||||
\(94\) | −5722.30 | −0.0667961 | ||||||||
\(95\) | 25893.2 | + | 28683.8i | 0.294358 | + | 0.326083i | ||||
\(96\) | −23713.8 | −0.262617 | ||||||||
\(97\) | − | 115329.i | − | 1.24454i | −0.782802 | − | 0.622271i | \(-0.786210\pi\) | ||
0.782802 | − | 0.622271i | \(-0.213790\pi\) | |||||||
\(98\) | 29891.4i | 0.314399i | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | −9949.14 | + | 97035.1i | −0.0994914 | + | 0.970351i | ||||
\(101\) | 39906.6 | 0.389261 | 0.194631 | − | 0.980877i | \(-0.437649\pi\) | ||||
0.194631 | + | 0.980877i | \(0.437649\pi\) | |||||||
\(102\) | 10753.7i | 0.102343i | ||||||||
\(103\) | − | 69320.0i | − | 0.643822i | −0.946770 | − | 0.321911i | \(-0.895675\pi\) | ||
0.946770 | − | 0.321911i | \(-0.104325\pi\) | |||||||
\(104\) | −59721.4 | −0.541435 | ||||||||
\(105\) | −75776.9 | − | 83943.7i | −0.670754 | − | 0.743044i | ||||
\(106\) | −8075.90 | −0.0698114 | ||||||||
\(107\) | 131149.i | 1.10740i | 0.832717 | + | 0.553700i | \(0.186784\pi\) | ||||
−0.832717 | + | 0.553700i | \(0.813216\pi\) | |||||||
\(108\) | 22755.0i | 0.187723i | ||||||||
\(109\) | −146929. | −1.18451 | −0.592257 | − | 0.805749i | \(-0.701763\pi\) | ||||
−0.592257 | + | 0.805749i | \(0.701763\pi\) | |||||||
\(110\) | −4451.37 | + | 4018.30i | −0.0350761 | + | 0.0316636i | ||||
\(111\) | −17156.1 | −0.132163 | ||||||||
\(112\) | 213347.i | 1.60709i | ||||||||
\(113\) | 57346.0i | 0.422481i | 0.977434 | + | 0.211240i | \(0.0677503\pi\) | ||||
−0.977434 | + | 0.211240i | \(0.932250\pi\) | |||||||
\(114\) | 5515.52 | 0.0397489 | ||||||||
\(115\) | −140924. | + | 127214.i | −0.993664 | + | 0.896992i | ||||
\(116\) | −268535. | −1.85291 | ||||||||
\(117\) | 86316.5i | 0.582947i | ||||||||
\(118\) | 9055.00i | 0.0598665i | ||||||||
\(119\) | 302938. | 1.96104 | ||||||||
\(120\) | 18893.5 | + | 20929.7i | 0.119773 | + | 0.132682i | ||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 30388.0i | 0.184843i | ||||||||
\(123\) | − | 52396.7i | − | 0.312278i | ||||||
\(124\) | −10004.4 | −0.0584300 | ||||||||
\(125\) | 140936. | − | 103221.i | 0.806767 | − | 0.590870i | ||||
\(126\) | −16141.3 | −0.0905757 | ||||||||
\(127\) | 172649.i | 0.949852i | 0.880026 | + | 0.474926i | \(0.157525\pi\) | ||||
−0.880026 | + | 0.474926i | \(0.842475\pi\) | |||||||
\(128\) | − | 109172.i | − | 0.588963i | ||||||
\(129\) | −12792.8 | −0.0676848 | ||||||||
\(130\) | 35388.8 | + | 39202.7i | 0.183657 | + | 0.203450i | ||||
\(131\) | 297723. | 1.51577 | 0.757886 | − | 0.652387i | \(-0.226233\pi\) | ||||
0.757886 | + | 0.652387i | \(0.226233\pi\) | |||||||
\(132\) | − | 33992.1i | − | 0.169802i | ||||||
\(133\) | − | 155375.i | − | 0.761645i | ||||||
\(134\) | −60672.6 | −0.291897 | ||||||||
\(135\) | 30250.2 | − | 27307.2i | 0.142854 | − | 0.128956i | ||||
\(136\) | −75531.8 | −0.350173 | ||||||||
\(137\) | − | 45559.8i | − | 0.207387i | −0.994609 | − | 0.103693i | \(-0.966934\pi\) | ||
0.994609 | − | 0.103693i | \(-0.0330661\pi\) | |||||||
\(138\) | 27097.8i | 0.121126i | ||||||||
\(139\) | 124306. | 0.545701 | 0.272850 | − | 0.962056i | \(-0.412034\pi\) | ||||
0.272850 | + | 0.962056i | \(0.412034\pi\) | |||||||
\(140\) | 291135. | − | 262811.i | 1.25538 | − | 1.13324i | ||||
\(141\) | −58090.6 | −0.246070 | ||||||||
\(142\) | − | 1670.21i | − | 0.00695104i | ||||||
\(143\) | − | 128942.i | − | 0.527295i | ||||||
\(144\) | −76882.2 | −0.308972 | ||||||||
\(145\) | 322255. | + | 356986.i | 1.27286 | + | 1.41004i | ||||
\(146\) | 77781.2 | 0.301990 | ||||||||
\(147\) | 303445.i | 1.15821i | ||||||||
\(148\) | − | 59501.1i | − | 0.223291i | ||||||
\(149\) | 107578. | 0.396971 | 0.198485 | − | 0.980104i | \(-0.436398\pi\) | ||||
0.198485 | + | 0.980104i | \(0.436398\pi\) | |||||||
\(150\) | 2543.23 | − | 24804.4i | 0.00922907 | − | 0.0900122i | ||||
\(151\) | 147513. | 0.526487 | 0.263244 | − | 0.964729i | \(-0.415208\pi\) | ||||
0.263244 | + | 0.964729i | \(0.415208\pi\) | |||||||
\(152\) | 38739.8i | 0.136003i | ||||||||
\(153\) | 109168.i | 0.377021i | ||||||||
\(154\) | 24112.3 | 0.0819288 | ||||||||
\(155\) | 12005.8 | + | 13299.7i | 0.0401384 | + | 0.0444643i | ||||
\(156\) | −299365. | −0.984893 | ||||||||
\(157\) | 231901.i | 0.750849i | 0.926853 | + | 0.375425i | \(0.122503\pi\) | ||||
−0.926853 | + | 0.375425i | \(0.877497\pi\) | |||||||
\(158\) | − | 46463.5i | − | 0.148071i | ||||||
\(159\) | −81983.3 | −0.257177 | ||||||||
\(160\) | −109335. | + | 98697.8i | −0.337644 | + | 0.304795i | ||||
\(161\) | 763360. | 2.32094 | ||||||||
\(162\) | − | 5816.72i | − | 0.0174137i | ||||||
\(163\) | 6862.35i | 0.0202304i | 0.999949 | + | 0.0101152i | \(0.00321982\pi\) | ||||
−0.999949 | + | 0.0101152i | \(0.996780\pi\) | |||||||
\(164\) | 181723. | 0.527596 | ||||||||
\(165\) | −45188.5 | + | 40792.2i | −0.129217 | + | 0.116645i | ||||
\(166\) | −52010.7 | −0.146495 | ||||||||
\(167\) | − | 10230.0i | − | 0.0283847i | −0.999899 | − | 0.0141923i | \(-0.995482\pi\) | ||
0.999899 | − | 0.0141923i | \(-0.00451771\pi\) | |||||||
\(168\) | − | 113373.i | − | 0.309910i | ||||||
\(169\) | −764285. | −2.05844 | ||||||||
\(170\) | 44757.5 | + | 49581.2i | 0.118780 | + | 0.131581i | ||||
\(171\) | 55991.4 | 0.146430 | ||||||||
\(172\) | − | 44368.3i | − | 0.114354i | ||||||
\(173\) | − | 421259.i | − | 1.07012i | −0.844813 | − | 0.535062i | \(-0.820288\pi\) | ||
0.844813 | − | 0.535062i | \(-0.179712\pi\) | |||||||
\(174\) | 68643.8 | 0.171881 | ||||||||
\(175\) | −698754. | − | 71644.2i | −1.72476 | − | 0.176842i | ||||
\(176\) | 114849. | 0.279476 | ||||||||
\(177\) | 91922.8i | 0.220541i | ||||||||
\(178\) | − | 100928.i | − | 0.238761i | ||||||
\(179\) | −330517. | −0.771012 | −0.385506 | − | 0.922705i | \(-0.625973\pi\) | ||||
−0.385506 | + | 0.922705i | \(0.625973\pi\) | |||||||
\(180\) | 94707.3 | + | 104914.i | 0.217872 | + | 0.241353i | ||||
\(181\) | 668805. | 1.51741 | 0.758705 | − | 0.651434i | \(-0.225832\pi\) | ||||
0.758705 | + | 0.651434i | \(0.225832\pi\) | |||||||
\(182\) | − | 212355.i | − | 0.475207i | ||||||
\(183\) | 308487.i | 0.680940i | ||||||||
\(184\) | −190329. | −0.414439 | ||||||||
\(185\) | −79099.8 | + | 71404.3i | −0.169921 | + | 0.153389i | ||||
\(186\) | 2557.35 | 0.00542012 | ||||||||
\(187\) | − | 163078.i | − | 0.341028i | ||||||
\(188\) | − | 201471.i | − | 0.415736i | ||||||
\(189\) | −163860. | −0.333671 | ||||||||
\(190\) | 25429.9 | − | 22955.8i | 0.0511047 | − | 0.0461327i | ||||
\(191\) | −961866. | −1.90779 | −0.953896 | − | 0.300137i | \(-0.902967\pi\) | ||||
−0.953896 | + | 0.300137i | \(0.902967\pi\) | |||||||
\(192\) | − | 252335.i | − | 0.493998i | ||||||
\(193\) | 87470.4i | 0.169032i | 0.996422 | + | 0.0845158i | \(0.0269343\pi\) | ||||
−0.996422 | + | 0.0845158i | \(0.973066\pi\) | |||||||
\(194\) | −102246. | −0.195048 | ||||||||
\(195\) | 359253. | + | 397971.i | 0.676571 | + | 0.749488i | ||||
\(196\) | −1.05242e6 | −1.95680 | ||||||||
\(197\) | 799656.i | 1.46804i | 0.679129 | + | 0.734019i | \(0.262358\pi\) | ||||
−0.679129 | + | 0.734019i | \(0.737642\pi\) | |||||||
\(198\) | 8689.17i | 0.0157513i | ||||||||
\(199\) | 635515. | 1.13761 | 0.568804 | − | 0.822473i | \(-0.307406\pi\) | ||||
0.568804 | + | 0.822473i | \(0.307406\pi\) | |||||||
\(200\) | 174221. | + | 17863.1i | 0.307982 | + | 0.0315778i | ||||
\(201\) | −615924. | −1.07532 | ||||||||
\(202\) | − | 35379.6i | − | 0.0610062i | ||||||
\(203\) | − | 1.93373e6i | − | 3.29349i | ||||||
\(204\) | −378618. | −0.636980 | ||||||||
\(205\) | −218077. | − | 241580.i | −0.362431 | − | 0.401492i | ||||
\(206\) | −61456.3 | −0.100902 | ||||||||
\(207\) | 275086.i | 0.446214i | ||||||||
\(208\) | − | 1.01146e6i | − | 1.62103i | ||||||
\(209\) | −83641.5 | −0.132451 | ||||||||
\(210\) | −74421.0 | + | 67180.7i | −0.116452 | + | 0.105123i | ||||
\(211\) | −349594. | −0.540578 | −0.270289 | − | 0.962779i | \(-0.587119\pi\) | ||||
−0.270289 | + | 0.962779i | \(0.587119\pi\) | |||||||
\(212\) | − | 284337.i | − | 0.434503i | ||||||
\(213\) | − | 16955.3i | − | 0.0256069i | ||||||
\(214\) | 116271. | 0.173555 | ||||||||
\(215\) | −58982.5 | + | 53244.2i | −0.0870216 | + | 0.0785554i | ||||
\(216\) | 40855.3 | 0.0595819 | ||||||||
\(217\) | − | 72042.0i | − | 0.103857i | ||||||
\(218\) | 130261.i | 0.185641i | ||||||||
\(219\) | 789604. | 1.11250 | ||||||||
\(220\) | −141476. | − | 156724.i | −0.197073 | − | 0.218312i | ||||
\(221\) | −1.43621e6 | −1.97805 | ||||||||
\(222\) | 15209.9i | 0.0207130i | ||||||||
\(223\) | 309538.i | 0.416824i | 0.978041 | + | 0.208412i | \(0.0668294\pi\) | ||||
−0.978041 | + | 0.208412i | \(0.933171\pi\) | |||||||
\(224\) | 592248. | 0.788648 | ||||||||
\(225\) | 25817.9 | − | 251805.i | 0.0339989 | − | 0.331595i | ||||
\(226\) | 50840.6 | 0.0662124 | ||||||||
\(227\) | − | 509733.i | − | 0.656566i | −0.944579 | − | 0.328283i | \(-0.893530\pi\) | ||
0.944579 | − | 0.328283i | \(-0.106470\pi\) | |||||||
\(228\) | 194191.i | 0.247395i | ||||||||
\(229\) | 1.28351e6 | 1.61737 | 0.808684 | − | 0.588243i | \(-0.200180\pi\) | ||||
0.808684 | + | 0.588243i | \(0.200180\pi\) | |||||||
\(230\) | 112782. | + | 124937.i | 0.140579 | + | 0.155730i | ||||
\(231\) | 244778. | 0.301817 | ||||||||
\(232\) | 482139.i | 0.588101i | ||||||||
\(233\) | − | 312877.i | − | 0.377558i | −0.982020 | − | 0.188779i | \(-0.939547\pi\) | ||
0.982020 | − | 0.188779i | \(-0.0604529\pi\) | |||||||
\(234\) | 76524.7 | 0.0913612 | ||||||||
\(235\) | −267833. | + | 241775.i | −0.316369 | + | 0.285590i | ||||
\(236\) | −318809. | −0.372607 | ||||||||
\(237\) | − | 471679.i | − | 0.545477i | ||||||
\(238\) | − | 268573.i | − | 0.307340i | ||||||
\(239\) | 357254. | 0.404559 | 0.202280 | − | 0.979328i | \(-0.435165\pi\) | ||||
0.202280 | + | 0.979328i | \(0.435165\pi\) | |||||||
\(240\) | −354473. | + | 319987.i | −0.397242 | + | 0.358595i | ||||
\(241\) | −680168. | −0.754351 | −0.377176 | − | 0.926142i | \(-0.623105\pi\) | ||||
−0.377176 | + | 0.926142i | \(0.623105\pi\) | |||||||
\(242\) | − | 12980.1i | − | 0.0142475i | ||||||
\(243\) | − | 59049.0i | − | 0.0641500i | ||||||
\(244\) | −1.06990e6 | −1.15045 | ||||||||
\(245\) | 1.26295e6 | + | 1.39907e6i | 1.34422 | + | 1.48910i | ||||
\(246\) | −46452.8 | −0.0489411 | ||||||||
\(247\) | 736623.i | 0.768250i | ||||||||
\(248\) | 17962.3i | 0.0185452i | ||||||||
\(249\) | −527992. | −0.539671 | ||||||||
\(250\) | −91511.3 | − | 124948.i | −0.0926029 | − | 0.126439i | ||||
\(251\) | 157817. | 0.158114 | 0.0790568 | − | 0.996870i | \(-0.474809\pi\) | ||||
0.0790568 | + | 0.996870i | \(0.474809\pi\) | |||||||
\(252\) | − | 568303.i | − | 0.563740i | ||||||
\(253\) | − | 410932.i | − | 0.403616i | ||||||
\(254\) | 153064. | 0.148864 | ||||||||
\(255\) | 454360. | + | 503328.i | 0.437572 | + | 0.484731i | ||||
\(256\) | 800404. | 0.763325 | ||||||||
\(257\) | 557296.i | 0.526324i | 0.964752 | + | 0.263162i | \(0.0847654\pi\) | ||||
−0.964752 | + | 0.263162i | \(0.915235\pi\) | |||||||
\(258\) | 11341.6i | 0.0106078i | ||||||||
\(259\) | 428470. | 0.396891 | ||||||||
\(260\) | −1.38025e6 | + | 1.24597e6i | −1.26627 | + | 1.14307i | ||||
\(261\) | 696844. | 0.633191 | ||||||||
\(262\) | − | 263949.i | − | 0.237556i | ||||||
\(263\) | 645647.i | 0.575580i | 0.957693 | + | 0.287790i | \(0.0929206\pi\) | ||||
−0.957693 | + | 0.287790i | \(0.907079\pi\) | |||||||
\(264\) | −61030.8 | −0.0538939 | ||||||||
\(265\) | −377993. | + | 341218.i | −0.330650 | + | 0.298482i | ||||
\(266\) | −137749. | −0.119367 | ||||||||
\(267\) | − | 1.02458e6i | − | 0.879568i | ||||||
\(268\) | − | 2.13616e6i | − | 1.81676i | ||||||
\(269\) | 219755. | 0.185165 | 0.0925825 | − | 0.995705i | \(-0.470488\pi\) | ||||
0.0925825 | + | 0.995705i | \(0.470488\pi\) | |||||||
\(270\) | −24209.4 | − | 26818.6i | −0.0202104 | − | 0.0223886i | ||||
\(271\) | 1.54792e6 | 1.28034 | 0.640171 | − | 0.768233i | \(-0.278864\pi\) | ||||
0.640171 | + | 0.768233i | \(0.278864\pi\) | |||||||
\(272\) | − | 1.27923e6i | − | 1.04840i | ||||||
\(273\) | − | 2.15574e6i | − | 1.75061i | ||||||
\(274\) | −40391.5 | −0.0325023 | ||||||||
\(275\) | −38567.5 | + | 376153.i | −0.0307531 | + | 0.299939i | ||||
\(276\) | −954061. | −0.753882 | ||||||||
\(277\) | − | 980724.i | − | 0.767976i | −0.923338 | − | 0.383988i | \(-0.874550\pi\) | ||
0.923338 | − | 0.383988i | \(-0.125450\pi\) | |||||||
\(278\) | − | 110205.i | − | 0.0855239i | ||||||
\(279\) | 25961.2 | 0.0199671 | ||||||||
\(280\) | −471862. | − | 522717.i | −0.359683 | − | 0.398448i | ||||
\(281\) | 2.46283e6 | 1.86067 | 0.930334 | − | 0.366713i | \(-0.119517\pi\) | ||||
0.930334 | + | 0.366713i | \(0.119517\pi\) | |||||||
\(282\) | 51500.7i | 0.0385648i | ||||||||
\(283\) | 838610.i | 0.622435i | 0.950339 | + | 0.311217i | \(0.100737\pi\) | ||||
−0.950339 | + | 0.311217i | \(0.899263\pi\) | |||||||
\(284\) | 58804.8 | 0.0432630 | ||||||||
\(285\) | 258154. | − | 233039.i | 0.188264 | − | 0.169948i | ||||
\(286\) | −114315. | −0.0826393 | ||||||||
\(287\) | 1.30860e6i | 0.937782i | ||||||||
\(288\) | 213424.i | 0.151622i | ||||||||
\(289\) | −396569. | −0.279302 | ||||||||
\(290\) | 316489. | − | 285698.i | 0.220985 | − | 0.199486i | ||||
\(291\) | −1.03796e6 | −0.718536 | ||||||||
\(292\) | 2.73852e6i | 1.87957i | ||||||||
\(293\) | − | 1.32689e6i | − | 0.902955i | −0.892282 | − | 0.451478i | \(-0.850897\pi\) | ||
0.892282 | − | 0.451478i | \(-0.149103\pi\) | |||||||
\(294\) | 269022. | 0.181518 | ||||||||
\(295\) | 382587. | + | 423820.i | 0.255962 | + | 0.283548i | ||||
\(296\) | −106831. | −0.0708708 | ||||||||
\(297\) | 88209.0i | 0.0580259i | ||||||||
\(298\) | − | 95374.4i | − | 0.0622144i | ||||||
\(299\) | −3.61904e6 | −2.34107 | ||||||||
\(300\) | 873316. | + | 89542.2i | 0.560232 | + | 0.0574414i | ||||
\(301\) | 319498. | 0.203260 | ||||||||
\(302\) | − | 130779.i | − | 0.0825126i | ||||||
\(303\) | − | 359159.i | − | 0.224740i | ||||||
\(304\) | −656111. | −0.407187 | ||||||||
\(305\) | 1.28394e6 | + | 1.42231e6i | 0.790303 | + | 0.875477i | ||||
\(306\) | 96783.6 | 0.0590878 | ||||||||
\(307\) | 1.04842e6i | 0.634878i | 0.948279 | + | 0.317439i | \(0.102823\pi\) | ||||
−0.948279 | + | 0.317439i | \(0.897177\pi\) | |||||||
\(308\) | 848946.i | 0.509922i | ||||||||
\(309\) | −623880. | −0.371711 | ||||||||
\(310\) | 11790.9 | − | 10643.8i | 0.00696858 | − | 0.00629062i | ||||
\(311\) | −1.53786e6 | −0.901601 | −0.450801 | − | 0.892625i | \(-0.648861\pi\) | ||||
−0.450801 | + | 0.892625i | \(0.648861\pi\) | |||||||
\(312\) | 537492.i | 0.312598i | ||||||||
\(313\) | 2.58473e6i | 1.49126i | 0.666359 | + | 0.745631i | \(0.267852\pi\) | ||||
−0.666359 | + | 0.745631i | \(0.732148\pi\) | |||||||
\(314\) | 205594. | 0.117675 | ||||||||
\(315\) | −755493. | + | 681992.i | −0.428997 | + | 0.387260i | ||||
\(316\) | 1.63589e6 | 0.921587 | ||||||||
\(317\) | − | 1.29146e6i | − | 0.721827i | −0.932599 | − | 0.360914i | \(-0.882465\pi\) | ||
0.932599 | − | 0.360914i | \(-0.117535\pi\) | |||||||
\(318\) | 72683.1i | 0.0403056i | ||||||||
\(319\) | −1.04096e6 | −0.572742 | ||||||||
\(320\) | −1.05023e6 | − | 1.16342e6i | −0.573336 | − | 0.635127i | ||||
\(321\) | 1.18034e6 | 0.639357 | ||||||||
\(322\) | − | 676764.i | − | 0.363745i | ||||||
\(323\) | 931634.i | 0.496866i | ||||||||
\(324\) | 204795. | 0.108382 | ||||||||
\(325\) | 3.31274e6 | + | 339660.i | 1.73972 | + | 0.178376i | ||||
\(326\) | 6083.88 | 0.00317057 | ||||||||
\(327\) | 1.32236e6i | 0.683880i | ||||||||
\(328\) | − | 326274.i | − | 0.167455i | ||||||
\(329\) | 1.45080e6 | 0.738956 | ||||||||
\(330\) | 36164.7 | + | 40062.3i | 0.0182810 | + | 0.0202512i | ||||
\(331\) | 1.77716e6 | 0.891573 | 0.445787 | − | 0.895139i | \(-0.352924\pi\) | ||||
0.445787 | + | 0.895139i | \(0.352924\pi\) | |||||||
\(332\) | − | 1.83119e6i | − | 0.911778i | ||||||
\(333\) | 154405.i | 0.0763045i | ||||||||
\(334\) | −9069.48 | −0.00444853 | ||||||||
\(335\) | −2.83978e6 | + | 2.56350e6i | −1.38252 | + | 1.24802i | ||||
\(336\) | 1.92012e6 | 0.927856 | ||||||||
\(337\) | 1.99819e6i | 0.958435i | 0.877696 | + | 0.479217i | \(0.159079\pi\) | ||||
−0.877696 | + | 0.479217i | \(0.840921\pi\) | |||||||
\(338\) | 677584.i | 0.322605i | ||||||||
\(339\) | 516114. | 0.243919 | ||||||||
\(340\) | −1.74566e6 | + | 1.57582e6i | −0.818957 | + | 0.739282i | ||||
\(341\) | −38781.6 | −0.0180609 | ||||||||
\(342\) | − | 49639.7i | − | 0.0229490i | ||||||
\(343\) | − | 3.80073e6i | − | 1.74434i | ||||||
\(344\) | −79660.7 | −0.0362951 | ||||||||
\(345\) | 1.14492e6 | + | 1.26831e6i | 0.517879 | + | 0.573692i | ||||
\(346\) | −373471. | −0.167713 | ||||||||
\(347\) | 2.94954e6i | 1.31501i | 0.753449 | + | 0.657507i | \(0.228389\pi\) | ||||
−0.753449 | + | 0.657507i | \(0.771611\pi\) | |||||||
\(348\) | 2.41681e6i | 1.06978i | ||||||||
\(349\) | 1.15473e6 | 0.507476 | 0.253738 | − | 0.967273i | \(-0.418340\pi\) | ||||
0.253738 | + | 0.967273i | \(0.418340\pi\) | |||||||
\(350\) | −63516.8 | + | 619487.i | −0.0277152 | + | 0.270310i | ||||
\(351\) | 776848. | 0.336565 | ||||||||
\(352\) | − | 318819.i | − | 0.137147i | ||||||
\(353\) | 829780.i | 0.354427i | 0.984172 | + | 0.177213i | \(0.0567083\pi\) | ||||
−0.984172 | + | 0.177213i | \(0.943292\pi\) | |||||||
\(354\) | 81495.0 | 0.0345639 | ||||||||
\(355\) | −70568.7 | − | 78174.1i | −0.0297195 | − | 0.0329224i | ||||
\(356\) | 3.55349e6 | 1.48604 | ||||||||
\(357\) | − | 2.72644e6i | − | 1.13221i | ||||||
\(358\) | 293023.i | 0.120835i | ||||||||
\(359\) | −3.60644e6 | −1.47687 | −0.738435 | − | 0.674325i | \(-0.764435\pi\) | ||||
−0.738435 | + | 0.674325i | \(0.764435\pi\) | |||||||
\(360\) | 188368. | − | 170042.i | 0.0766038 | − | 0.0691511i | ||||
\(361\) | −1.99827e6 | −0.807023 | ||||||||
\(362\) | − | 592935.i | − | 0.237813i | ||||||
\(363\) | − | 131769.i | − | 0.0524864i | ||||||
\(364\) | 7.47659e6 | 2.95767 | ||||||||
\(365\) | 3.64055e6 | − | 3.28636e6i | 1.43032 | − | 1.29117i | ||||
\(366\) | 273492. | 0.106719 | ||||||||
\(367\) | − | 403294.i | − | 0.156299i | −0.996942 | − | 0.0781496i | \(-0.975099\pi\) | ||
0.996942 | − | 0.0781496i | \(-0.0249012\pi\) | |||||||
\(368\) | − | 3.22348e6i | − | 1.24081i | ||||||
\(369\) | −471570. | −0.180294 | ||||||||
\(370\) | 63304.2 | + | 70126.7i | 0.0240396 | + | 0.0266305i | ||||
\(371\) | 2.04752e6 | 0.772313 | ||||||||
\(372\) | 90039.4i | 0.0337346i | ||||||||
\(373\) | − | 3.48177e6i | − | 1.29577i | −0.761739 | − | 0.647884i | \(-0.775654\pi\) | ||
0.761739 | − | 0.647884i | \(-0.224346\pi\) | |||||||
\(374\) | −144578. | −0.0534470 | ||||||||
\(375\) | −928987. | − | 1.26843e6i | −0.341139 | − | 0.465787i | ||||
\(376\) | −361730. | −0.131952 | ||||||||
\(377\) | 9.16768e6i | 3.32205i | ||||||||
\(378\) | 145272.i | 0.0522939i | ||||||||
\(379\) | 704863. | 0.252062 | 0.126031 | − | 0.992026i | \(-0.459776\pi\) | ||||
0.126031 | + | 0.992026i | \(0.459776\pi\) | |||||||
\(380\) | 808230. | + | 895336.i | 0.287128 | + | 0.318073i | ||||
\(381\) | 1.55384e6 | 0.548397 | ||||||||
\(382\) | 852751.i | 0.298995i | ||||||||
\(383\) | 2.16463e6i | 0.754028i | 0.926208 | + | 0.377014i | \(0.123049\pi\) | ||||
−0.926208 | + | 0.377014i | \(0.876951\pi\) | |||||||
\(384\) | −982551. | −0.340038 | ||||||||
\(385\) | 1.12858e6 | − | 1.01878e6i | 0.388042 | − | 0.350290i | ||||
\(386\) | 77547.7 | 0.0264911 | ||||||||
\(387\) | 115135.i | 0.0390778i | ||||||||
\(388\) | − | 3.59988e6i | − | 1.21397i | ||||||
\(389\) | −2.50750e6 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(390\) | 352825. | − | 318499.i | 0.117462 | − | 0.106034i | ||||
\(391\) | −4.57713e6 | −1.51409 | ||||||||
\(392\) | 1.88955e6i | 0.621075i | ||||||||
\(393\) | − | 2.67950e6i | − | 0.875131i | ||||||
\(394\) | 708942. | 0.230075 | ||||||||
\(395\) | −1.96315e6 | − | 2.17473e6i | −0.633083 | − | 0.701313i | ||||
\(396\) | −305929. | −0.0980352 | ||||||||
\(397\) | − | 2.75852e6i | − | 0.878417i | −0.898385 | − | 0.439208i | \(-0.855259\pi\) | ||
0.898385 | − | 0.439208i | \(-0.144741\pi\) | |||||||
\(398\) | − | 563422.i | − | 0.178289i | ||||||
\(399\) | −1.39838e6 | −0.439736 | ||||||||
\(400\) | −302536. | + | 2.95067e6i | −0.0945424 | + | 0.922083i | ||||
\(401\) | −6.11243e6 | −1.89825 | −0.949124 | − | 0.314901i | \(-0.898029\pi\) | ||||
−0.949124 | + | 0.314901i | \(0.898029\pi\) | |||||||
\(402\) | 546053.i | 0.168527i | ||||||||
\(403\) | 341546.i | 0.104758i | ||||||||
\(404\) | 1.24565e6 | 0.379700 | ||||||||
\(405\) | −245764. | − | 272251.i | −0.0744529 | − | 0.0824770i | ||||
\(406\) | −1.71437e6 | −0.516165 | ||||||||
\(407\) | − | 230654.i | − | 0.0690200i | ||||||
\(408\) | 679786.i | 0.202172i | ||||||||
\(409\) | −4.96574e6 | −1.46783 | −0.733915 | − | 0.679241i | \(-0.762309\pi\) | ||||
−0.733915 | + | 0.679241i | \(0.762309\pi\) | |||||||
\(410\) | −214175. | + | 193338.i | −0.0629230 | + | 0.0568013i | ||||
\(411\) | −410039. | −0.119735 | ||||||||
\(412\) | − | 2.16376e6i | − | 0.628008i | ||||||
\(413\) | − | 2.29576e6i | − | 0.662294i | ||||||
\(414\) | 243880. | 0.0699320 | ||||||||
\(415\) | −2.43436e6 | + | 2.19753e6i | −0.693849 | + | 0.626345i | ||||
\(416\) | −2.80780e6 | −0.795488 | ||||||||
\(417\) | − | 1.11875e6i | − | 0.315061i | ||||||
\(418\) | 74153.2i | 0.0207582i | ||||||||
\(419\) | 3.30467e6 | 0.919589 | 0.459794 | − | 0.888025i | \(-0.347923\pi\) | ||||
0.459794 | + | 0.888025i | \(0.347923\pi\) | |||||||
\(420\) | −2.36530e6 | − | 2.62022e6i | −0.654279 | − | 0.724793i | ||||
\(421\) | 5.04577e6 | 1.38747 | 0.693733 | − | 0.720232i | \(-0.255965\pi\) | ||||
0.693733 | + | 0.720232i | \(0.255965\pi\) | |||||||
\(422\) | 309936.i | 0.0847209i | ||||||||
\(423\) | 522815.i | 0.142068i | ||||||||
\(424\) | −510510. | −0.137908 | ||||||||
\(425\) | 4.18975e6 | + | 429581.i | 1.12516 | + | 0.115365i | ||||
\(426\) | −15031.9 | −0.00401318 | ||||||||
\(427\) | − | 7.70441e6i | − | 2.04489i | ||||||
\(428\) | 4.09367e6i | 1.08020i | ||||||||
\(429\) | −1.16048e6 | −0.304434 | ||||||||
\(430\) | 47204.1 | + | 52291.5i | 0.0123114 | + | 0.0136383i | ||||
\(431\) | 889002. | 0.230520 | 0.115260 | − | 0.993335i | \(-0.463230\pi\) | ||||
0.115260 | + | 0.993335i | \(0.463230\pi\) | |||||||
\(432\) | 691940.i | 0.178385i | ||||||||
\(433\) | − | 406627.i | − | 0.104226i | −0.998641 | − | 0.0521131i | \(-0.983404\pi\) | ||
0.998641 | − | 0.0521131i | \(-0.0165956\pi\) | |||||||
\(434\) | −63869.5 | −0.0162768 | ||||||||
\(435\) | 3.21287e6 | − | 2.90030e6i | 0.814086 | − | 0.734885i | ||||
\(436\) | −4.58623e6 | −1.15542 | ||||||||
\(437\) | 2.34758e6i | 0.588054i | ||||||||
\(438\) | − | 700031.i | − | 0.174354i | ||||||
\(439\) | 5.04798e6 | 1.25013 | 0.625067 | − | 0.780571i | \(-0.285072\pi\) | ||||
0.625067 | + | 0.780571i | \(0.285072\pi\) | |||||||
\(440\) | −281389. | + | 254013.i | −0.0692907 | + | 0.0625495i | ||||
\(441\) | 2.73101e6 | 0.668693 | ||||||||
\(442\) | 1.27328e6i | 0.310006i | ||||||||
\(443\) | 888258.i | 0.215045i | 0.994203 | + | 0.107523i | \(0.0342918\pi\) | ||||
−0.994203 | + | 0.107523i | \(0.965708\pi\) | |||||||
\(444\) | −535510. | −0.128917 | ||||||||
\(445\) | −4.26436e6 | − | 4.72395e6i | −1.02083 | − | 1.13085i | ||||
\(446\) | 274424. | 0.0653259 | ||||||||
\(447\) | − | 968203.i | − | 0.229191i | ||||||
\(448\) | 6.30203e6i | 1.48349i | ||||||||
\(449\) | −3.82230e6 | −0.894765 | −0.447383 | − | 0.894343i | \(-0.647644\pi\) | ||||
−0.447383 | + | 0.894343i | \(0.647644\pi\) | |||||||
\(450\) | −223240. | − | 22889.1i | −0.0519686 | − | 0.00532841i | ||||
\(451\) | 704444. | 0.163082 | ||||||||
\(452\) | 1.79000e6i | 0.412104i | ||||||||
\(453\) | − | 1.32762e6i | − | 0.303967i | ||||||
\(454\) | −451909. | −0.102899 | ||||||||
\(455\) | −8.97228e6 | − | 9.93926e6i | −2.03177 | − | 2.25074i | ||||
\(456\) | 348658. | 0.0785214 | ||||||||
\(457\) | 2.10600e6i | 0.471703i | 0.971789 | + | 0.235852i | \(0.0757879\pi\) | ||||
−0.971789 | + | 0.235852i | \(0.924212\pi\) | |||||||
\(458\) | − | 1.13790e6i | − | 0.253479i | ||||||
\(459\) | 982509. | 0.217673 | ||||||||
\(460\) | −4.39880e6 | + | 3.97084e6i | −0.969258 | + | 0.874960i | ||||
\(461\) | −2.43217e6 | −0.533017 | −0.266508 | − | 0.963833i | \(-0.585870\pi\) | ||||
−0.266508 | + | 0.963833i | \(0.585870\pi\) | |||||||
\(462\) | − | 217011.i | − | 0.0473016i | ||||||
\(463\) | − | 7.53506e6i | − | 1.63356i | −0.576951 | − | 0.816779i | \(-0.695758\pi\) | ||
0.576951 | − | 0.816779i | \(-0.304242\pi\) | |||||||
\(464\) | −8.16566e6 | −1.76075 | ||||||||
\(465\) | 119697. | − | 108052.i | 0.0256715 | − | 0.0231739i | ||||
\(466\) | −277384. | −0.0591720 | ||||||||
\(467\) | − | 3.17287e6i | − | 0.673225i | −0.941643 | − | 0.336612i | \(-0.890719\pi\) | ||
0.941643 | − | 0.336612i | \(-0.109281\pi\) | |||||||
\(468\) | 2.69428e6i | 0.568628i | ||||||||
\(469\) | 1.53826e7 | 3.22922 | ||||||||
\(470\) | 214348. | + | 237449.i | 0.0447585 | + | 0.0495823i | ||||
\(471\) | 2.08711e6 | 0.433503 | ||||||||
\(472\) | 572403.i | 0.118262i | ||||||||
\(473\) | − | 171992.i | − | 0.0353472i | ||||||
\(474\) | −418172. | −0.0854887 | ||||||||
\(475\) | 220329. | − | 2.14890e6i | 0.0448062 | − | 0.437000i | ||||
\(476\) | 9.45592e6 | 1.91287 | ||||||||
\(477\) | 737850.i | 0.148481i | ||||||||
\(478\) | − | 316727.i | − | 0.0634038i | ||||||
\(479\) | −3.20281e6 | −0.637811 | −0.318905 | − | 0.947787i | \(-0.603315\pi\) | ||||
−0.318905 | + | 0.947787i | \(0.603315\pi\) | |||||||
\(480\) | 888280. | + | 984013.i | 0.175973 | + | 0.194939i | ||||
\(481\) | −2.03135e6 | −0.400333 | ||||||||
\(482\) | 603009.i | 0.118224i | ||||||||
\(483\) | − | 6.87024e6i | − | 1.34000i | ||||||
\(484\) | 457004. | 0.0886762 | ||||||||
\(485\) | −4.78563e6 | + | 4.32004e6i | −0.923814 | + | 0.833937i | ||||
\(486\) | −52350.4 | −0.0100538 | ||||||||
\(487\) | − | 4.45541e6i | − | 0.851266i | −0.904896 | − | 0.425633i | \(-0.860051\pi\) | ||
0.904896 | − | 0.425633i | \(-0.139949\pi\) | |||||||
\(488\) | 1.92095e6i | 0.365145i | ||||||||
\(489\) | 61761.2 | 0.0116800 | ||||||||
\(490\) | 1.24036e6 | − | 1.11968e6i | 0.233376 | − | 0.210671i | ||||
\(491\) | 150957. | 0.0282586 | 0.0141293 | − | 0.999900i | \(-0.495502\pi\) | ||||
0.0141293 | + | 0.999900i | \(0.495502\pi\) | |||||||
\(492\) | − | 1.63551e6i | − | 0.304608i | ||||||
\(493\) | 1.15947e7i | 2.14853i | ||||||||
\(494\) | 653060. | 0.120403 | ||||||||
\(495\) | 367130. | + | 406697.i | 0.0673452 | + | 0.0746032i | ||||
\(496\) | −304216. | −0.0555235 | ||||||||
\(497\) | 423456.i | 0.0768984i | ||||||||
\(498\) | 468096.i | 0.0845789i | ||||||||
\(499\) | 4.56196e6 | 0.820163 | 0.410081 | − | 0.912049i | \(-0.365500\pi\) | ||||
0.410081 | + | 0.912049i | \(0.365500\pi\) | |||||||
\(500\) | 4.39919e6 | − | 3.22193e6i | 0.786951 | − | 0.576357i | ||||
\(501\) | −92069.8 | −0.0163879 | ||||||||
\(502\) | − | 139914.i | − | 0.0247800i | ||||||
\(503\) | 5.18773e6i | 0.914234i | 0.889407 | + | 0.457117i | \(0.151118\pi\) | ||||
−0.889407 | + | 0.457117i | \(0.848882\pi\) | |||||||
\(504\) | −1.02036e6 | −0.178927 | ||||||||
\(505\) | −1.49484e6 | − | 1.65594e6i | −0.260835 | − | 0.288946i | ||||
\(506\) | −364315. | −0.0632559 | ||||||||
\(507\) | 6.87857e6i | 1.18844i | ||||||||
\(508\) | 5.38908e6i | 0.926521i | ||||||||
\(509\) | −6.85927e6 | −1.17350 | −0.586750 | − | 0.809768i | \(-0.699593\pi\) | ||||
−0.586750 | + | 0.809768i | \(0.699593\pi\) | |||||||
\(510\) | 446230. | − | 402817.i | 0.0759685 | − | 0.0685777i | ||||
\(511\) | −1.97202e7 | −3.34087 | ||||||||
\(512\) | − | 4.20312e6i | − | 0.708593i | ||||||
\(513\) | − | 503923.i | − | 0.0845416i | ||||||
\(514\) | 494076. | 0.0824871 | ||||||||
\(515\) | −2.87646e6 | + | 2.59662e6i | −0.477904 | + | 0.431409i | ||||
\(516\) | −399314. | −0.0660223 | ||||||||
\(517\) | − | 780995.i | − | 0.128506i | ||||||
\(518\) | − | 379864.i | − | 0.0622020i | ||||||
\(519\) | −3.79133e6 | −0.617836 | ||||||||
\(520\) | 2.23707e6 | + | 2.47816e6i | 0.362803 | + | 0.401903i | ||||
\(521\) | −3.91860e6 | −0.632466 | −0.316233 | − | 0.948682i | \(-0.602418\pi\) | ||||
−0.316233 | + | 0.948682i | \(0.602418\pi\) | |||||||
\(522\) | − | 617794.i | − | 0.0992356i | ||||||
\(523\) | 3.64804e6i | 0.583183i | 0.956543 | + | 0.291592i | \(0.0941848\pi\) | ||||
−0.956543 | + | 0.291592i | \(0.905815\pi\) | |||||||
\(524\) | 9.29312e6 | 1.47854 | ||||||||
\(525\) | −644798. | + | 6.28879e6i | −0.102100 | + | 0.995792i | ||||
\(526\) | 572405. | 0.0902067 | ||||||||
\(527\) | 431966.i | 0.0677521i | ||||||||
\(528\) | − | 1.03364e6i | − | 0.161356i | ||||||
\(529\) | −5.09735e6 | −0.791964 | ||||||||
\(530\) | 302510. | + | 335113.i | 0.0467789 | + | 0.0518205i | ||||
\(531\) | 827305. | 0.127330 | ||||||||
\(532\) | − | 4.84988e6i | − | 0.742938i | ||||||
\(533\) | − | 6.20397e6i | − | 0.945914i | ||||||
\(534\) | −908355. | −0.137849 | ||||||||
\(535\) | 5.44207e6 | − | 4.91261e6i | 0.822014 | − | 0.742041i | ||||
\(536\) | −3.83536e6 | −0.576625 | ||||||||
\(537\) | 2.97465e6i | 0.445144i | ||||||||
\(538\) | − | 194826.i | − | 0.0290196i | ||||||
\(539\) | −4.07966e6 | −0.604855 | ||||||||
\(540\) | 944229. | − | 852366.i | 0.139345 | − | 0.125789i | ||||
\(541\) | −4.23861e6 | −0.622630 | −0.311315 | − | 0.950307i | \(-0.600769\pi\) | ||||
−0.311315 | + | 0.950307i | \(0.600769\pi\) | |||||||
\(542\) | − | 1.37232e6i | − | 0.200659i | ||||||
\(543\) | − | 6.01924e6i | − | 0.876077i | ||||||
\(544\) | −3.55113e6 | −0.514482 | ||||||||
\(545\) | 5.50371e6 | + | 6.09687e6i | 0.793715 | + | 0.879256i | ||||
\(546\) | −1.91119e6 | −0.274361 | ||||||||
\(547\) | − | 513913.i | − | 0.0734380i | −0.999326 | − | 0.0367190i | \(-0.988309\pi\) | ||
0.999326 | − | 0.0367190i | \(-0.0116907\pi\) | |||||||
\(548\) | − | 1.42211e6i | − | 0.202293i | ||||||
\(549\) | 2.77638e6 | 0.393141 | ||||||||
\(550\) | 333482. | + | 34192.4i | 0.0470073 | + | 0.00481973i | ||||
\(551\) | 5.94685e6 | 0.834465 | ||||||||
\(552\) | 1.71296e6i | 0.239277i | ||||||||
\(553\) | 1.17801e7i | 1.63809i | ||||||||
\(554\) | −869470. | −0.120359 | ||||||||
\(555\) | 642639. | + | 711899.i | 0.0885594 | + | 0.0981038i | ||||
\(556\) | 3.88009e6 | 0.532297 | ||||||||
\(557\) | − | 1.04431e7i | − | 1.42624i | −0.701041 | − | 0.713121i | \(-0.747281\pi\) | ||
0.701041 | − | 0.713121i | \(-0.252719\pi\) | |||||||
\(558\) | − | 23016.2i | − | 0.00312930i | ||||||
\(559\) | −1.51472e6 | −0.205023 | ||||||||
\(560\) | 8.85291e6 | − | 7.99162e6i | 1.19293 | − | 1.07687i | ||||
\(561\) | −1.46770e6 | −0.196893 | ||||||||
\(562\) | − | 2.18345e6i | − | 0.291610i | ||||||
\(563\) | − | 5.42113e6i | − | 0.720806i | −0.932797 | − | 0.360403i | \(-0.882639\pi\) | ||
0.932797 | − | 0.360403i | \(-0.117361\pi\) | |||||||
\(564\) | −1.81324e6 | −0.240026 | ||||||||
\(565\) | 2.37959e6 | − | 2.14809e6i | 0.313604 | − | 0.283094i | ||||
\(566\) | 743477. | 0.0975499 | ||||||||
\(567\) | 1.47474e6i | 0.192645i | ||||||||
\(568\) | − | 105581.i | − | 0.0137313i | ||||||
\(569\) | 4.65152e6 | 0.602301 | 0.301151 | − | 0.953577i | \(-0.402629\pi\) | ||||
0.301151 | + | 0.953577i | \(0.402629\pi\) | |||||||
\(570\) | −206603. | − | 228869.i | −0.0266348 | − | 0.0295053i | ||||
\(571\) | 836920. | 0.107422 | 0.0537111 | − | 0.998557i | \(-0.482895\pi\) | ||||
0.0537111 | + | 0.998557i | \(0.482895\pi\) | |||||||
\(572\) | − | 4.02479e6i | − | 0.514344i | ||||||
\(573\) | 8.65679e6i | 1.10146i | ||||||||
\(574\) | 1.16015e6 | 0.146972 | ||||||||
\(575\) | 1.05576e7 | + | 1.08248e6i | 1.33166 | + | 0.136537i | ||||
\(576\) | −2.27102e6 | −0.285210 | ||||||||
\(577\) | − | 1.22020e7i | − | 1.52578i | −0.646526 | − | 0.762892i | \(-0.723779\pi\) | ||
0.646526 | − | 0.762892i | \(-0.276221\pi\) | |||||||
\(578\) | 351582.i | 0.0437730i | ||||||||
\(579\) | 787233. | 0.0975904 | ||||||||
\(580\) | 1.00589e7 | + | 1.11430e7i | 1.24159 | + | 1.37540i | ||||
\(581\) | 1.31865e7 | 1.62065 | ||||||||
\(582\) | 920214.i | 0.112611i | ||||||||
\(583\) | − | 1.10222e6i | − | 0.134307i | ||||||
\(584\) | 4.91686e6 | 0.596562 | ||||||||
\(585\) | 3.58174e6 | − | 3.23327e6i | 0.432717 | − | 0.390619i | ||||
\(586\) | −1.17637e6 | −0.141514 | ||||||||
\(587\) | − | 4.64629e6i | − | 0.556559i | −0.960500 | − | 0.278279i | \(-0.910236\pi\) | ||
0.960500 | − | 0.278279i | \(-0.0897641\pi\) | |||||||
\(588\) | 9.47175e6i | 1.12976i | ||||||||
\(589\) | 221553. | 0.0263141 | ||||||||
\(590\) | 375741. | − | 339186.i | 0.0444384 | − | 0.0401151i | ||||
\(591\) | 7.19690e6 | 0.847572 | ||||||||
\(592\) | − | 1.80932e6i | − | 0.212184i | ||||||
\(593\) | 3.76104e6i | 0.439209i | 0.975589 | + | 0.219605i | \(0.0704767\pi\) | ||||
−0.975589 | + | 0.219605i | \(0.929523\pi\) | |||||||
\(594\) | 78202.5 | 0.00909399 | ||||||||
\(595\) | −1.13476e7 | − | 1.25705e7i | −1.31405 | − | 1.45567i | ||||
\(596\) | 3.35794e6 | 0.387220 | ||||||||
\(597\) | − | 5.71963e6i | − | 0.656799i | ||||||
\(598\) | 3.20849e6i | 0.366900i | ||||||||
\(599\) | 2.65769e6 | 0.302648 | 0.151324 | − | 0.988484i | \(-0.451646\pi\) | ||||
0.151324 | + | 0.988484i | \(0.451646\pi\) | |||||||
\(600\) | 160768. | − | 1.56799e6i | 0.0182315 | − | 0.177813i | ||||
\(601\) | 5.84003e6 | 0.659521 | 0.329761 | − | 0.944065i | \(-0.393032\pi\) | ||||
0.329761 | + | 0.944065i | \(0.393032\pi\) | |||||||
\(602\) | − | 283254.i | − | 0.0318555i | ||||||
\(603\) | 5.54331e6i | 0.620835i | ||||||||
\(604\) | 4.60447e6 | 0.513555 | ||||||||
\(605\) | −548428. | − | 607534.i | −0.0609160 | − | 0.0674811i | ||||
\(606\) | −318416. | −0.0352220 | ||||||||
\(607\) | − | 7.10119e6i | − | 0.782274i | −0.920332 | − | 0.391137i | \(-0.872082\pi\) | ||
0.920332 | − | 0.391137i | \(-0.127918\pi\) | |||||||
\(608\) | 1.82136e6i | 0.199819i | ||||||||
\(609\) | −1.74036e7 | −1.90150 | ||||||||
\(610\) | 1.26096e6 | − | 1.13828e6i | 0.137207 | − | 0.123859i | ||||
\(611\) | −6.87815e6 | −0.745364 | ||||||||
\(612\) | 3.40756e6i | 0.367760i | ||||||||
\(613\) | 1.10978e7i | 1.19285i | 0.802670 | + | 0.596423i | \(0.203412\pi\) | ||||
−0.802670 | + | 0.596423i | \(0.796588\pi\) | |||||||
\(614\) | 929488. | 0.0995000 | ||||||||
\(615\) | −2.17422e6 | + | 1.96270e6i | −0.231801 | + | 0.209250i | ||||
\(616\) | 1.52423e6 | 0.161845 | ||||||||
\(617\) | 1.34866e7i | 1.42623i | 0.701049 | + | 0.713114i | \(0.252716\pi\) | ||||
−0.701049 | + | 0.713114i | \(0.747284\pi\) | |||||||
\(618\) | 553107.i | 0.0582556i | ||||||||
\(619\) | 1.19228e7 | 1.25069 | 0.625346 | − | 0.780347i | \(-0.284958\pi\) | ||||
0.625346 | + | 0.780347i | \(0.284958\pi\) | |||||||
\(620\) | 374748. | + | 415136.i | 0.0391525 | + | 0.0433722i | ||||
\(621\) | 2.47578e6 | 0.257622 | ||||||||
\(622\) | 1.36340e6i | 0.141302i | ||||||||
\(623\) | 2.55888e7i | 2.64138i | ||||||||
\(624\) | −9.10315e6 | −0.935902 | ||||||||
\(625\) | −9.56244e6 | − | 1.98173e6i | −0.979193 | − | 0.202929i | ||||
\(626\) | 2.29151e6 | 0.233715 | ||||||||
\(627\) | 752774.i | 0.0764708i | ||||||||
\(628\) | 7.23855e6i | 0.732407i | ||||||||
\(629\) | −2.56912e6 | −0.258915 | ||||||||
\(630\) | 604626. | + | 669789.i | 0.0606926 | + | 0.0672337i | ||||
\(631\) | −5.56411e6 | −0.556317 | −0.278159 | − | 0.960535i | \(-0.589724\pi\) | ||||
−0.278159 | + | 0.960535i | \(0.589724\pi\) | |||||||
\(632\) | − | 2.93715e6i | − | 0.292505i | ||||||
\(633\) | 3.14635e6i | 0.312103i | ||||||||
\(634\) | −1.14496e6 | −0.113127 | ||||||||
\(635\) | 7.16416e6 | − | 6.46717e6i | 0.705068 | − | 0.636473i | ||||
\(636\) | −2.55903e6 | −0.250861 | ||||||||
\(637\) | 3.59291e7i | 3.50831i | ||||||||
\(638\) | 922877.i | 0.0897619i | ||||||||
\(639\) | −152598. | −0.0147841 | ||||||||
\(640\) | −4.53015e6 | + | 4.08942e6i | −0.437183 | + | 0.394650i | ||||
\(641\) | 7.43898e6 | 0.715103 | 0.357551 | − | 0.933894i | \(-0.383612\pi\) | ||||
0.357551 | + | 0.933894i | \(0.383612\pi\) | |||||||
\(642\) | − | 1.04644e6i | − | 0.100202i | ||||||
\(643\) | − | 8.56732e6i | − | 0.817180i | −0.912718 | − | 0.408590i | \(-0.866021\pi\) | ||
0.912718 | − | 0.408590i | \(-0.133979\pi\) | |||||||
\(644\) | 2.38275e7 | 2.26394 | ||||||||
\(645\) | 479197. | + | 530842.i | 0.0453540 | + | 0.0502419i | ||||
\(646\) | 825949. | 0.0778703 | ||||||||
\(647\) | − | 1.65852e7i | − | 1.55762i | −0.627263 | − | 0.778808i | \(-0.715825\pi\) | ||
0.627263 | − | 0.778808i | \(-0.284175\pi\) | |||||||
\(648\) | − | 367698.i | − | 0.0343996i | ||||||
\(649\) | −1.23585e6 | −0.115174 | ||||||||
\(650\) | 301129. | − | 2.93694e6i | 0.0279556 | − | 0.272654i | ||||
\(651\) | −648378. | −0.0599620 | ||||||||
\(652\) | 214202.i | 0.0197335i | ||||||||
\(653\) | 7.12943e6i | 0.654292i | 0.944974 | + | 0.327146i | \(0.106087\pi\) | ||||
−0.944974 | + | 0.327146i | \(0.893913\pi\) | |||||||
\(654\) | 1.17235e6 | 0.107180 | ||||||||
\(655\) | −1.11522e7 | − | 1.23541e7i | −1.01568 | − | 1.12515i | ||||
\(656\) | 5.52589e6 | 0.501352 | ||||||||
\(657\) | − | 7.10643e6i | − | 0.642301i | ||||||
\(658\) | − | 1.28622e6i | − | 0.115811i | ||||||
\(659\) | −1.00795e7 | −0.904116 | −0.452058 | − | 0.891988i | \(-0.649310\pi\) | ||||
−0.452058 | + | 0.891988i | \(0.649310\pi\) | |||||||
\(660\) | −1.41051e6 | + | 1.27329e6i | −0.126043 | + | 0.113780i | ||||
\(661\) | 1.12712e7 | 1.00338 | 0.501689 | − | 0.865048i | \(-0.332712\pi\) | ||||
0.501689 | + | 0.865048i | \(0.332712\pi\) | |||||||
\(662\) | − | 1.57556e6i | − | 0.139730i | ||||||
\(663\) | 1.29259e7i | 1.14203i | ||||||||
\(664\) | −3.28780e6 | −0.289392 | ||||||||
\(665\) | −6.44736e6 | + | 5.82010e6i | −0.565364 | + | 0.510360i | ||||
\(666\) | 136889. | 0.0119587 | ||||||||
\(667\) | 2.92170e7i | 2.54285i | ||||||||
\(668\) | − | 319319.i | − | 0.0276875i | ||||||
\(669\) | 2.78585e6 | 0.240653 | ||||||||
\(670\) | 2.27270e6 | + | 2.51763e6i | 0.195593 | + | 0.216673i | ||||
\(671\) | −4.14743e6 | −0.355609 | ||||||||
\(672\) | − | 5.33023e6i | − | 0.455326i | ||||||
\(673\) | 2.71329e6i | 0.230918i | 0.993312 | + | 0.115459i | \(0.0368340\pi\) | ||||
−0.993312 | + | 0.115459i | \(0.963166\pi\) | |||||||
\(674\) | 1.77152e6 | 0.150209 | ||||||||
\(675\) | −2.26624e6 | − | 232361.i | −0.191446 | − | 0.0196293i | ||||
\(676\) | −2.38564e7 | −2.00788 | ||||||||
\(677\) | − | 1.70935e6i | − | 0.143337i | −0.997429 | − | 0.0716686i | \(-0.977168\pi\) | ||
0.997429 | − | 0.0716686i | \(-0.0228324\pi\) | |||||||
\(678\) | − | 457565.i | − | 0.0382278i | ||||||
\(679\) | 2.59229e7 | 2.15779 | ||||||||
\(680\) | 2.82930e6 | + | 3.13422e6i | 0.234642 | + | 0.259931i | ||||
\(681\) | −4.58760e6 | −0.379069 | ||||||||
\(682\) | 34382.2i | 0.00283056i | ||||||||
\(683\) | − | 2.06905e7i | − | 1.69715i | −0.529079 | − | 0.848573i | \(-0.677462\pi\) | ||
0.529079 | − | 0.848573i | \(-0.322538\pi\) | |||||||
\(684\) | 1.74772e6 | 0.142834 | ||||||||
\(685\) | −1.89052e6 | + | 1.70660e6i | −0.153942 | + | 0.138965i | ||||
\(686\) | −3.36957e6 | −0.273379 | ||||||||
\(687\) | − | 1.15516e7i | − | 0.933788i | ||||||
\(688\) | − | 1.34916e6i | − | 0.108666i | ||||||
\(689\) | −9.70715e6 | −0.779011 | ||||||||
\(690\) | 1.12444e6 | − | 1.01504e6i | 0.0899108 | − | 0.0811635i | ||||
\(691\) | 3.42722e6 | 0.273053 | 0.136526 | − | 0.990636i | \(-0.456406\pi\) | ||||
0.136526 | + | 0.990636i | \(0.456406\pi\) | |||||||
\(692\) | − | 1.31492e7i | − | 1.04384i | ||||||
\(693\) | − | 2.20301e6i | − | 0.174254i | ||||||
\(694\) | 2.61494e6 | 0.206093 | ||||||||
\(695\) | −4.65630e6 | − | 5.15812e6i | −0.365661 | − | 0.405070i | ||||
\(696\) | 4.33925e6 | 0.339540 | ||||||||
\(697\) | − | 7.84639e6i | − | 0.611770i | ||||||
\(698\) | − | 1.02373e6i | − | 0.0795331i | ||||||
\(699\) | −2.81589e6 | −0.217983 | ||||||||
\(700\) | −2.18109e7 | − | 2.23630e6i | −1.68240 | − | 0.172499i | ||||
\(701\) | 1.05204e7 | 0.808608 | 0.404304 | − | 0.914625i | \(-0.367514\pi\) | ||||
0.404304 | + | 0.914625i | \(0.367514\pi\) | |||||||
\(702\) | − | 688722.i | − | 0.0527474i | ||||||
\(703\) | 1.31769e6i | 0.100560i | ||||||||
\(704\) | 3.39251e6 | 0.257982 | ||||||||
\(705\) | 2.17598e6 | + | 2.41049e6i | 0.164885 | + | 0.182656i | ||||
\(706\) | 735650. | 0.0555468 | ||||||||
\(707\) | 8.96995e6i | 0.674903i | ||||||||
\(708\) | 2.86928e6i | 0.215124i | ||||||||
\(709\) | 5.27905e6 | 0.394403 | 0.197202 | − | 0.980363i | \(-0.436815\pi\) | ||||
0.197202 | + | 0.980363i | \(0.436815\pi\) | |||||||
\(710\) | −69306.0 | + | 62563.3i | −0.00515971 | + | 0.00465772i | ||||
\(711\) | −4.24512e6 | −0.314931 | ||||||||
\(712\) | − | 6.38008e6i | − | 0.471657i | ||||||
\(713\) | 1.08849e6i | 0.0801864i | ||||||||
\(714\) | −2.41715e6 | −0.177443 | ||||||||
\(715\) | −5.35050e6 | + | 4.82995e6i | −0.391407 | + | 0.353328i | ||||
\(716\) | −1.03168e7 | −0.752074 | ||||||||
\(717\) | − | 3.21529e6i | − | 0.233572i | ||||||
\(718\) | 3.19732e6i | 0.231459i | ||||||||
\(719\) | 5.38506e6 | 0.388480 | 0.194240 | − | 0.980954i | \(-0.437776\pi\) | ||||
0.194240 | + | 0.980954i | \(0.437776\pi\) | |||||||
\(720\) | 2.87988e6 | + | 3.19026e6i | 0.207035 | + | 0.229348i | ||||
\(721\) | 1.55813e7 | 1.11626 | ||||||||
\(722\) | 1.77158e6i | 0.126479i | ||||||||
\(723\) | 6.12151e6i | 0.435525i | ||||||||
\(724\) | 2.08761e7 | 1.48014 | ||||||||
\(725\) | 2.74212e6 | − | 2.67442e7i | 0.193750 | − | 1.88967i | ||||
\(726\) | −116821. | −0.00822583 | ||||||||
\(727\) | − | 1.05731e6i | − | 0.0741934i | −0.999312 | − | 0.0370967i | \(-0.988189\pi\) | ||
0.999312 | − | 0.0370967i | \(-0.0118110\pi\) | |||||||
\(728\) | − | 1.34238e7i | − | 0.938743i | ||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | −2.91356e6 | − | 3.22756e6i | −0.202356 | − | 0.224165i | ||||
\(731\) | −1.91572e6 | −0.132598 | ||||||||
\(732\) | 9.62911e6i | 0.664215i | ||||||||
\(733\) | − | 1.02639e6i | − | 0.0705589i | −0.999377 | − | 0.0352794i | \(-0.988768\pi\) | ||
0.999377 | − | 0.0352794i | \(-0.0112321\pi\) | |||||||
\(734\) | −357544. | −0.0244957 | ||||||||
\(735\) | 1.25916e7 | − | 1.13666e7i | 0.859731 | − | 0.776088i | ||||
\(736\) | −8.94834e6 | −0.608903 | ||||||||
\(737\) | − | 8.28075e6i | − | 0.561566i | ||||||
\(738\) | 418075.i | 0.0282562i | ||||||||
\(739\) | 3.33815e6 | 0.224851 | 0.112426 | − | 0.993660i | \(-0.464138\pi\) | ||||
0.112426 | + | 0.993660i | \(0.464138\pi\) | |||||||
\(740\) | −2.46902e6 | + | 2.22882e6i | −0.165747 | + | 0.149622i | ||||
\(741\) | 6.62960e6 | 0.443550 | ||||||||
\(742\) | − | 1.81525e6i | − | 0.121039i | ||||||
\(743\) | 2.15478e7i | 1.43196i | 0.698120 | + | 0.715981i | \(0.254020\pi\) | ||||
−0.698120 | + | 0.715981i | \(0.745980\pi\) | |||||||
\(744\) | 161661. | 0.0107071 | ||||||||
\(745\) | −4.02970e6 | − | 4.46400e6i | −0.266000 | − | 0.294668i | ||||
\(746\) | −3.08679e6 | −0.203077 | ||||||||
\(747\) | 4.75193e6i | 0.311579i | ||||||||
\(748\) | − | 5.09030e6i | − | 0.332652i | ||||||
\(749\) | −2.94787e7 | −1.92001 | ||||||||
\(750\) | −1.12454e6 | + | 823602.i | −0.0729996 | + | 0.0534643i | ||||
\(751\) | −2.02621e7 | −1.31095 | −0.655474 | − | 0.755218i | \(-0.727531\pi\) | ||||
−0.655474 | + | 0.755218i | \(0.727531\pi\) | |||||||
\(752\) | − | 6.12638e6i | − | 0.395057i | ||||||
\(753\) | − | 1.42035e6i | − | 0.0912869i | ||||||
\(754\) | 8.12769e6 | 0.520641 | ||||||||
\(755\) | −5.52560e6 | − | 6.12111e6i | −0.352786 | − | 0.390807i | ||||
\(756\) | −5.11473e6 | −0.325475 | ||||||||
\(757\) | 1.23455e7i | 0.783012i | 0.920176 | + | 0.391506i | \(0.128046\pi\) | ||||
−0.920176 | + | 0.391506i | \(0.871954\pi\) | |||||||
\(758\) | − | 624903.i | − | 0.0395039i | ||||||
\(759\) | −3.69838e6 | −0.233028 | ||||||||
\(760\) | 1.60753e6 | − | 1.45113e6i | 0.100954 | − | 0.0911324i | ||||
\(761\) | 9.77671e6 | 0.611971 | 0.305986 | − | 0.952036i | \(-0.401014\pi\) | ||||
0.305986 | + | 0.952036i | \(0.401014\pi\) | |||||||
\(762\) | − | 1.37758e6i | − | 0.0859465i | ||||||
\(763\) | − | 3.30257e7i | − | 2.05372i | ||||||
\(764\) | −3.00237e7 | −1.86093 | ||||||||
\(765\) | 4.52996e6 | − | 4.08924e6i | 0.279860 | − | 0.252633i | ||||
\(766\) | 1.91908e6 | 0.118174 | ||||||||
\(767\) | 1.08840e7i | 0.668038i | ||||||||
\(768\) | − | 7.20364e6i | − | 0.440706i | ||||||
\(769\) | 4.31458e6 | 0.263101 | 0.131551 | − | 0.991309i | \(-0.458004\pi\) | ||||
0.131551 | + | 0.991309i | \(0.458004\pi\) | |||||||
\(770\) | −903207. | − | 1.00055e6i | −0.0548985 | − | 0.0608151i | ||||
\(771\) | 5.01567e6 | 0.303873 | ||||||||
\(772\) | 2.73030e6i | 0.164880i | ||||||||
\(773\) | − | 3.28419e7i | − | 1.97688i | −0.151620 | − | 0.988439i | \(-0.548449\pi\) | ||
0.151620 | − | 0.988439i | \(-0.451551\pi\) | |||||||
\(774\) | 102074. | 0.00612440 | ||||||||
\(775\) | 102159. | − | 996368.i | 0.00610973 | − | 0.0595889i | ||||
\(776\) | −6.46338e6 | −0.385306 | ||||||||
\(777\) | − | 3.85623e6i | − | 0.229145i | ||||||
\(778\) | 2.22304e6i | 0.131674i | ||||||||
\(779\) | −4.02437e6 | −0.237604 | ||||||||
\(780\) | 1.12137e7 | + | 1.24223e7i | 0.659953 | + | 0.731079i | ||||
\(781\) | 227955. | 0.0133727 | ||||||||
\(782\) | 4.05790e6i | 0.237292i | ||||||||
\(783\) | − | 6.27160e6i | − | 0.365573i | ||||||
\(784\) | −3.20021e7 | −1.85947 | ||||||||
\(785\) | 9.62281e6 | − | 8.68662e6i | 0.557350 | − | 0.503126i | ||||
\(786\) | −2.37554e6 | −0.137153 | ||||||||
\(787\) | 1.45886e7i | 0.839608i | 0.907615 | + | 0.419804i | \(0.137901\pi\) | ||||
−0.907615 | + | 0.419804i | \(0.862099\pi\) | |||||||
\(788\) | 2.49605e7i | 1.43198i | ||||||||
\(789\) | 5.81083e6 | 0.332312 | ||||||||
\(790\) | −1.92802e6 | + | 1.74045e6i | −0.109912 | + | 0.0992187i | ||||
\(791\) | −1.28899e7 | −0.732499 | ||||||||
\(792\) | 549277.i | 0.0311156i | ||||||||
\(793\) | 3.65261e7i | 2.06262i | ||||||||
\(794\) | −2.44560e6 | −0.137668 | ||||||||
\(795\) | 3.07096e6 | + | 3.40193e6i | 0.172328 | + | 0.190901i | ||||
\(796\) | 1.98370e7 | 1.10967 | ||||||||
\(797\) | 4.63451e6i | 0.258439i | 0.991616 | + | 0.129220i | \(0.0412472\pi\) | ||||
−0.991616 | + | 0.129220i | \(0.958753\pi\) | |||||||
\(798\) | 1.23974e6i | 0.0689168i | ||||||||
\(799\) | −8.69905e6 | −0.482064 | ||||||||
\(800\) | 8.19101e6 | + | 839835.i | 0.452494 | + | 0.0463948i | ||||
\(801\) | −9.22126e6 | −0.507819 | ||||||||
\(802\) | 5.41903e6i | 0.297499i | ||||||||
\(803\) | 1.06158e7i | 0.580983i | ||||||||
\(804\) | −1.92255e7 | −1.04891 | ||||||||
\(805\) | −2.85942e7 | − | 3.16759e7i | −1.55521 | − | 1.72282i | ||||
\(806\) | 302801. | 0.0164180 | ||||||||
\(807\) | − | 1.97780e6i | − | 0.106905i | ||||||
\(808\) | − | 2.23648e6i | − | 0.120514i | ||||||
\(809\) | −1.28933e6 | −0.0692618 | −0.0346309 | − | 0.999400i | \(-0.511026\pi\) | ||||
−0.0346309 | + | 0.999400i | \(0.511026\pi\) | |||||||
\(810\) | −241367. | + | 217885.i | −0.0129260 | + | 0.0116685i | ||||
\(811\) | 6.47343e6 | 0.345607 | 0.172803 | − | 0.984956i | \(-0.444718\pi\) | ||||
0.172803 | + | 0.984956i | \(0.444718\pi\) | |||||||
\(812\) | − | 6.03595e7i | − | 3.21259i | ||||||
\(813\) | − | 1.39313e7i | − | 0.739205i | ||||||
\(814\) | −204488. | −0.0108170 | ||||||||
\(815\) | 284756. | − | 257053.i | 0.0150169 | − | 0.0135559i | ||||
\(816\) | −1.15131e7 | −0.605294 | ||||||||
\(817\) | 982561.i | 0.0514997i | ||||||||
\(818\) | 4.40242e6i | 0.230043i | ||||||||
\(819\) | −1.94017e7 | −1.01072 | ||||||||
\(820\) | −6.80707e6 | − | 7.54069e6i | −0.353529 | − | 0.391630i | ||||
\(821\) | 2.48796e7 | 1.28820 | 0.644102 | − | 0.764939i | \(-0.277231\pi\) | ||||
0.644102 | + | 0.764939i | \(0.277231\pi\) | |||||||
\(822\) | 363524.i | 0.0187652i | ||||||||
\(823\) | − | 2.73317e7i | − | 1.40659i | −0.710898 | − | 0.703295i | \(-0.751711\pi\) | ||
0.710898 | − | 0.703295i | \(-0.248289\pi\) | |||||||
\(824\) | −3.88490e6 | −0.199325 | ||||||||
\(825\) | 3.38538e6 | + | 347107.i | 0.173170 | + | 0.0177553i | ||||
\(826\) | −2.03533e6 | −0.103797 | ||||||||
\(827\) | 3.20369e7i | 1.62887i | 0.580252 | + | 0.814437i | \(0.302954\pi\) | ||||
−0.580252 | + | 0.814437i | \(0.697046\pi\) | |||||||
\(828\) | 8.58655e6i | 0.435254i | ||||||||
\(829\) | 2.54756e7 | 1.28747 | 0.643736 | − | 0.765247i | \(-0.277383\pi\) | ||||
0.643736 | + | 0.765247i | \(0.277383\pi\) | |||||||
\(830\) | 1.94824e6 | + | 2.15821e6i | 0.0981627 | + | 0.108742i | ||||
\(831\) | −8.82652e6 | −0.443391 | ||||||||
\(832\) | − | 2.98775e7i | − | 1.49636i | ||||||
\(833\) | 4.54409e7i | 2.26900i | ||||||||
\(834\) | −991841. | −0.0493772 | ||||||||
\(835\) | −424497. | + | 383199.i | −0.0210697 | + | 0.0190199i | ||||
\(836\) | −2.61079e6 | −0.129198 | ||||||||
\(837\) | − | 233651.i | − | 0.0115280i | ||||||
\(838\) | − | 2.92979e6i | − | 0.144121i | ||||||
\(839\) | 2.56179e7 | 1.25643 | 0.628216 | − | 0.778039i | \(-0.283785\pi\) | ||||
0.628216 | + | 0.778039i | \(0.283785\pi\) | |||||||
\(840\) | −4.70445e6 | + | 4.24676e6i | −0.230044 | + | 0.207663i | ||||
\(841\) | 5.35007e7 | 2.60837 | ||||||||
\(842\) | − | 4.47338e6i | − | 0.217448i | ||||||
\(843\) | − | 2.21655e7i | − | 1.07426i | ||||||
\(844\) | −1.09122e7 | −0.527300 | ||||||||
\(845\) | 2.86289e7 | + | 3.17143e7i | 1.37931 | + | 1.52797i | ||||
\(846\) | 463507. | 0.0222654 | ||||||||
\(847\) | 3.29091e6i | 0.157619i | ||||||||
\(848\) | − | 8.64617e6i | − | 0.412890i | ||||||
\(849\) | 7.54749e6 | 0.359363 | ||||||||
\(850\) | 380849. | − | 3.71446e6i | 0.0180803 | − | 0.176339i | ||||
\(851\) | −6.47381e6 | −0.306433 | ||||||||
\(852\) | − | 529243.i | − | 0.0249779i | ||||||
\(853\) | − | 8.49389e6i | − | 0.399700i | −0.979827 | − | 0.199850i | \(-0.935955\pi\) | ||
0.979827 | − | 0.199850i | \(-0.0640454\pi\) | |||||||
\(854\) | −6.83042e6 | −0.320481 | ||||||||
\(855\) | −2.09735e6 | − | 2.32339e6i | −0.0981195 | − | 0.108694i | ||||
\(856\) | 7.34996e6 | 0.342847 | ||||||||
\(857\) | 2.29100e7i | 1.06555i | 0.846258 | + | 0.532773i | \(0.178850\pi\) | ||||
−0.846258 | + | 0.532773i | \(0.821150\pi\) | |||||||
\(858\) | 1.02883e6i | 0.0477118i | ||||||||
\(859\) | −1.05172e7 | −0.486315 | −0.243158 | − | 0.969987i | \(-0.578183\pi\) | ||||
−0.243158 | + | 0.969987i | \(0.578183\pi\) | |||||||
\(860\) | −1.84108e6 | + | 1.66196e6i | −0.0848841 | + | 0.0766259i | ||||
\(861\) | 1.17774e7 | 0.541429 | ||||||||
\(862\) | − | 788153.i | − | 0.0361279i | ||||||
\(863\) | − | 2.93900e7i | − | 1.34330i | −0.740870 | − | 0.671649i | \(-0.765587\pi\) | ||
0.740870 | − | 0.671649i | \(-0.234413\pi\) | |||||||
\(864\) | 1.92082e6 | 0.0875390 | ||||||||
\(865\) | −1.74803e7 | + | 1.57797e7i | −0.794344 | + | 0.717064i | ||||
\(866\) | −360499. | −0.0163346 | ||||||||
\(867\) | 3.56912e6i | 0.161255i | ||||||||
\(868\) | − | 2.24872e6i | − | 0.101306i | ||||||
\(869\) | 6.34147e6 | 0.284866 | ||||||||
\(870\) | −2.57128e6 | − | 2.84840e6i | −0.115173 | − | 0.127586i | ||||
\(871\) | −7.29278e7 | −3.25722 | ||||||||
\(872\) | 8.23432e6i | 0.366722i | ||||||||
\(873\) | 9.34165e6i | 0.414847i | ||||||||
\(874\) | 2.08127e6 | 0.0921616 | ||||||||
\(875\) | 2.32013e7 | + | 3.16788e7i | 1.02445 | + | 1.39878i | ||||
\(876\) | 2.46467e7 | 1.08517 | ||||||||
\(877\) | − | 3.81404e7i | − | 1.67451i | −0.546816 | − | 0.837253i | \(-0.684160\pi\) | ||
0.546816 | − | 0.837253i | \(-0.315840\pi\) | |||||||
\(878\) | − | 4.47533e6i | − | 0.195925i | ||||||
\(879\) | −1.19420e7 | −0.521321 | ||||||||
\(880\) | −4.30205e6 | − | 4.76570e6i | −0.187270 | − | 0.207453i | ||||
\(881\) | 2.39208e7 | 1.03833 | 0.519165 | − | 0.854674i | \(-0.326243\pi\) | ||||
0.519165 | + | 0.854674i | \(0.326243\pi\) | |||||||
\(882\) | − | 2.42120e6i | − | 0.104800i | ||||||
\(883\) | 1.95650e6i | 0.0844457i | 0.999108 | + | 0.0422229i | \(0.0134440\pi\) | ||||
−0.999108 | + | 0.0422229i | \(0.986556\pi\) | |||||||
\(884\) | −4.48298e7 | −1.92946 | ||||||||
\(885\) | 3.81438e6 | − | 3.44328e6i | 0.163706 | − | 0.147780i | ||||
\(886\) | 787493. | 0.0337025 | ||||||||
\(887\) | − | 2.80192e7i | − | 1.19577i | −0.801583 | − | 0.597884i | \(-0.796008\pi\) | ||
0.801583 | − | 0.597884i | \(-0.203992\pi\) | |||||||
\(888\) | 961478.i | 0.0409173i | ||||||||
\(889\) | −3.88070e7 | −1.64686 | ||||||||
\(890\) | −4.18806e6 | + | 3.78061e6i | −0.177230 | + | 0.159988i | ||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 9.66194e6i | 0.406586i | ||||||||
\(893\) | 4.46169e6i | 0.187228i | ||||||||
\(894\) | −858369. | −0.0359195 | ||||||||
\(895\) | 1.23806e7 | + | 1.37149e7i | 0.516637 | + | 0.572317i | ||||
\(896\) | 2.45391e7 | 1.02115 | ||||||||
\(897\) | 3.25713e7i | 1.35162i | ||||||||
\(898\) | 3.38870e6i | 0.140230i | ||||||||
\(899\) | 2.75735e6 | 0.113787 | ||||||||
\(900\) | 805880. | − | 7.85984e6i | 0.0331638 | − | 0.323450i | ||||
\(901\) | −1.22770e7 | −0.503825 | ||||||||
\(902\) | − | 624532.i | − | 0.0255587i | ||||||
\(903\) | − | 2.87548e6i | − | 0.117352i | ||||||
\(904\) | 3.21384e6 | 0.130799 | ||||||||
\(905\) | −2.50523e7 | − | 2.77523e7i | −1.01678 | − | 1.12636i | ||||
\(906\) | −1.17701e6 | −0.0476387 | ||||||||
\(907\) | − | 5.99454e6i | − | 0.241957i | −0.992655 | − | 0.120978i | \(-0.961397\pi\) | ||
0.992655 | − | 0.120978i | \(-0.0386032\pi\) | |||||||
\(908\) | − | 1.59108e7i | − | 0.640439i | ||||||
\(909\) | −3.23243e6 | −0.129754 | ||||||||
\(910\) | −8.81174e6 | + | 7.95446e6i | −0.352743 | + | 0.318425i | ||||
\(911\) | −3.83047e7 | −1.52917 | −0.764585 | − | 0.644523i | \(-0.777056\pi\) | ||||
−0.764585 | + | 0.644523i | \(0.777056\pi\) | |||||||
\(912\) | 5.90500e6i | 0.235089i | ||||||||
\(913\) | − | 7.09856e6i | − | 0.281834i | ||||||
\(914\) | 1.86710e6 | 0.0739267 | ||||||||
\(915\) | 1.28008e7 | − | 1.15554e7i | 0.505457 | − | 0.456282i | ||||
\(916\) | 4.00634e7 | 1.57764 | ||||||||
\(917\) | 6.69202e7i | 2.62805i | ||||||||
\(918\) | − | 871052.i | − | 0.0341144i | ||||||
\(919\) | 4.41558e7 | 1.72464 | 0.862321 | − | 0.506362i | \(-0.169010\pi\) | ||||
0.862321 | + | 0.506362i | \(0.169010\pi\) | |||||||
\(920\) | 7.12942e6 | + | 7.89779e6i | 0.277706 | + | 0.307635i | ||||
\(921\) | 9.43580e6 | 0.366547 | ||||||||
\(922\) | 2.15626e6i | 0.0835360i | ||||||||
\(923\) | − | 2.00757e6i | − | 0.0775652i | ||||||
\(924\) | 7.64052e6 | 0.294403 | ||||||||
\(925\) | 5.92590e6 | + | 607591.i | 0.227720 | + | 0.0233484i | ||||
\(926\) | −6.68028e6 | −0.256016 | ||||||||
\(927\) | 5.61492e6i | 0.214607i | ||||||||
\(928\) | 2.26678e7i | 0.864050i | ||||||||
\(929\) | −1.00353e7 | −0.381499 | −0.190749 | − | 0.981639i | \(-0.561092\pi\) | ||||
−0.190749 | + | 0.981639i | \(0.561092\pi\) | |||||||
\(930\) | −95794.3 | − | 106118.i | −0.00363189 | − | 0.00402331i | ||||
\(931\) | 2.33064e7 | 0.881253 | ||||||||
\(932\) | − | 9.76613e6i | − | 0.368284i | ||||||
\(933\) | 1.38407e7i | 0.520540i | ||||||||
\(934\) | −2.81294e6 | −0.105510 | ||||||||
\(935\) | −6.76697e6 | + | 6.10862e6i | −0.253143 | + | 0.228515i | ||||
\(936\) | 4.83743e6 | 0.180478 | ||||||||
\(937\) | 3.04913e7i | 1.13456i | 0.823526 | + | 0.567279i | \(0.192004\pi\) | ||||
−0.823526 | + | 0.567279i | \(0.807996\pi\) | |||||||
\(938\) | − | 1.36376e7i | − | 0.506093i | ||||||
\(939\) | 2.32626e7 | 0.860981 | ||||||||
\(940\) | −8.36013e6 | + | 7.54678e6i | −0.308598 | + | 0.278575i | ||||
\(941\) | −4.13865e7 | −1.52365 | −0.761824 | − | 0.647785i | \(-0.775696\pi\) | ||||
−0.761824 | + | 0.647785i | \(0.775696\pi\) | |||||||
\(942\) | − | 1.85034e6i | − | 0.0679399i | ||||||
\(943\) | − | 1.97718e7i | − | 0.724046i | ||||||
\(944\) | −9.69442e6 | −0.354072 | ||||||||
\(945\) | 6.13793e6 | + | 6.79944e6i | 0.223585 | + | 0.247681i | ||||
\(946\) | −152481. | −0.00553973 | ||||||||
\(947\) | − | 9.38834e6i | − | 0.340184i | −0.985428 | − | 0.170092i | \(-0.945594\pi\) | ||
0.985428 | − | 0.170092i | \(-0.0544065\pi\) | |||||||
\(948\) | − | 1.47230e7i | − | 0.532079i | ||||||
\(949\) | 9.34922e7 | 3.36984 | ||||||||
\(950\) | −1.90512e6 | − | 195335.i | −0.0684880 | − | 0.00702217i | ||||
\(951\) | −1.16232e7 | −0.416747 | ||||||||
\(952\) | − | 1.69776e7i | − | 0.607132i | ||||||
\(953\) | − | 3.35369e7i | − | 1.19616i | −0.801435 | − | 0.598081i | \(-0.795930\pi\) | ||
0.801435 | − | 0.598081i | \(-0.204070\pi\) | |||||||
\(954\) | 654148. | 0.0232705 | ||||||||
\(955\) | 3.60299e7 | + | 3.99130e7i | 1.27837 | + | 1.41614i | ||||
\(956\) | 1.11513e7 | 0.394623 | ||||||||
\(957\) | 9.36868e6i | 0.330673i | ||||||||
\(958\) | 2.83948e6i | 0.0999597i | ||||||||
\(959\) | 1.02406e7 | 0.359568 | ||||||||
\(960\) | −1.04708e7 | + | 9.45207e6i | −0.366691 | + | 0.331016i | ||||
\(961\) | −2.85264e7 | −0.996412 | ||||||||
\(962\) | 1.80091e6i | 0.0627414i | ||||||||
\(963\) | − | 1.06230e7i | − | 0.369133i | ||||||
\(964\) | −2.12308e7 | −0.735823 | ||||||||
\(965\) | 3.62962e6 | − | 3.27650e6i | 0.125471 | − | 0.113264i | ||||
\(966\) | −6.09088e6 | −0.210009 | ||||||||
\(967\) | − | 5.35398e7i | − | 1.84124i | −0.390459 | − | 0.920620i | \(-0.627684\pi\) | ||
0.390459 | − | 0.920620i | \(-0.372316\pi\) | |||||||
\(968\) | − | 820525.i | − | 0.0281451i | ||||||
\(969\) | 8.38471e6 | 0.286866 | ||||||||
\(970\) | 3.82997e6 | + | 4.24274e6i | 0.130697 | + | 0.144783i | ||||
\(971\) | −3.17286e7 | −1.07995 | −0.539974 | − | 0.841682i | \(-0.681566\pi\) | ||||
−0.539974 | + | 0.841682i | \(0.681566\pi\) | |||||||
\(972\) | − | 1.84316e6i | − | 0.0625744i | ||||||
\(973\) | 2.79407e7i | 0.946139i | ||||||||
\(974\) | −3.94999e6 | −0.133413 | ||||||||
\(975\) | 3.05694e6 | − | 2.98147e7i | 0.102985 | − | 1.00443i | ||||
\(976\) | −3.25338e7 | −1.09323 | ||||||||
\(977\) | 5.28990e6i | 0.177301i | 0.996063 | + | 0.0886505i | \(0.0282554\pi\) | ||||
−0.996063 | + | 0.0886505i | \(0.971745\pi\) | |||||||
\(978\) | − | 54754.9i | − | 0.00183053i | ||||||
\(979\) | 1.37750e7 | 0.459340 | ||||||||
\(980\) | 3.94218e7 | + | 4.36705e7i | 1.31121 | + | 1.45252i | ||||
\(981\) | 1.19012e7 | 0.394838 | ||||||||
\(982\) | − | 133832.i | − | 0.00442877i | ||||||
\(983\) | 2.55796e7i | 0.844327i | 0.906520 | + | 0.422164i | \(0.138729\pi\) | ||||
−0.906520 | + | 0.422164i | \(0.861271\pi\) | |||||||
\(984\) | −2.93647e6 | −0.0966801 | ||||||||
\(985\) | 3.31820e7 | − | 2.99538e7i | 1.08971 | − | 0.983697i | ||||
\(986\) | 1.02794e7 | 0.336725 | ||||||||
\(987\) | − | 1.30572e7i | − | 0.426637i | ||||||
\(988\) | 2.29930e7i | 0.749380i | ||||||||
\(989\) | −4.82733e6 | −0.156934 | ||||||||
\(990\) | 360561. | − | 325482.i | 0.0116920 | − | 0.0105545i | ||||
\(991\) | 4.14167e7 | 1.33965 | 0.669825 | − | 0.742519i | \(-0.266369\pi\) | ||||
0.669825 | + | 0.742519i | \(0.266369\pi\) | |||||||
\(992\) | 844498.i | 0.0272471i | ||||||||
\(993\) | − | 1.59945e7i | − | 0.514750i | ||||||
\(994\) | 375419. | 0.0120517 | ||||||||
\(995\) | −2.38054e7 | − | 2.63710e7i | −0.762284 | − | 0.844439i | ||||
\(996\) | −1.64808e7 | −0.526415 | ||||||||
\(997\) | 3.02210e7i | 0.962877i | 0.876480 | + | 0.481438i | \(0.159885\pi\) | ||||
−0.876480 | + | 0.481438i | \(0.840115\pi\) | |||||||
\(998\) | − | 4.04445e6i | − | 0.128538i | ||||||
\(999\) | 1.38964e6 | 0.0440544 |
(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 | 165.6.c.b.34.13 | ✓ | 26 | |
5.2 | odd | 4 | 825.6.a.v.1.8 | 13 | |||
5.3 | odd | 4 | 825.6.a.y.1.6 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.14 | yes | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.13 | ✓ | 26 | 1.1 | even | 1 | trivial | |
165.6.c.b.34.14 | yes | 26 | 5.4 | even | 2 | inner | |
825.6.a.v.1.8 | 13 | 5.2 | odd | 4 | |||
825.6.a.y.1.6 | 13 | 5.3 | odd | 4 |