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 | 34.14 | ||
Character | \(\chi\) | \(=\) | 165.34 |
Dual form | 165.6.c.b.34.13 |
$q$-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 | \(0.0249688\pi\) | ||||
−0.996925 | + | 0.0783615i | \(0.975031\pi\) | |||||||
\(3\) | 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 | \(-0.666108\pi\) | ||
0.498478 | − | 0.866902i | \(-0.333892\pi\) | |||||||
\(8\) | 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 | \(0.338758\pi\) | ||||
−0.485169 | + | 0.874420i | \(0.661242\pi\) | |||||||
\(14\) | 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 | \(0.191329\pi\) | ||||
−0.824727 | + | 0.565531i | \(0.808671\pi\) | |||||||
\(18\) | − | 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 | \(0.233415\pi\) | ||||
−0.742973 | + | 0.669321i | \(0.766585\pi\) | |||||||
\(24\) | −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 | \(0.0365127\pi\) | ||||
−0.993428 | + | 0.114457i | \(0.963487\pi\) | |||||||
\(38\) | − | 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 | \(0.0186690\pi\) | ||||
−0.998281 | + | 0.0586168i | \(0.981331\pi\) | |||||||
\(44\) | 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 | \(0.0683568\pi\) | ||||
−0.977030 | + | 0.213102i | \(0.931643\pi\) | |||||||
\(48\) | 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 | \(0.0714943\pi\) | ||||
−0.974882 | + | 0.222722i | \(0.928506\pi\) | |||||||
\(54\) | 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 | \(0.381283\pi\) | ||||
−0.364374 | + | 0.931253i | \(0.618717\pi\) | |||||||
\(68\) | 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 | \(-0.586325\pi\) | ||
0.267885 | − | 0.963451i | \(-0.413675\pi\) | |||||||
\(74\) | −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 | \(0.154798\pi\) | ||||
−0.884062 | + | 0.467369i | \(0.845202\pi\) | |||||||
\(84\) | 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 | \(0.213790\pi\) | ||||
−0.782802 | + | 0.622271i | \(0.786210\pi\) | |||||||
\(98\) | − | 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 | \(0.104325\pi\) | ||||
−0.946770 | + | 0.321911i | \(0.895675\pi\) | |||||||
\(104\) | −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 | \(-0.813216\pi\) | ||
0.832717 | − | 0.553700i | \(-0.186784\pi\) | |||||||
\(108\) | − | 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 | \(-0.932250\pi\) | ||
0.977434 | − | 0.211240i | \(-0.0677503\pi\) | |||||||
\(114\) | 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 | \(-0.842475\pi\) | ||
0.880026 | − | 0.474926i | \(-0.157525\pi\) | |||||||
\(128\) | 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 | \(0.0330661\pi\) | ||||
−0.994609 | + | 0.103693i | \(0.966934\pi\) | |||||||
\(138\) | − | 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 | \(-0.877497\pi\) | ||
0.926853 | − | 0.375425i | \(-0.122503\pi\) | |||||||
\(158\) | 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 | \(-0.996780\pi\) | ||
0.999949 | − | 0.0101152i | \(-0.00321982\pi\) | |||||||
\(164\) | 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 | \(0.00451771\pi\) | ||||
−0.999899 | + | 0.0141923i | \(0.995482\pi\) | |||||||
\(168\) | 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 | \(0.179712\pi\) | ||||
−0.844813 | + | 0.535062i | \(0.820288\pi\) | |||||||
\(174\) | 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 | \(-0.973066\pi\) | ||
0.996422 | − | 0.0845158i | \(-0.0269343\pi\) | |||||||
\(194\) | −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 | \(-0.737642\pi\) | ||
0.679129 | − | 0.734019i | \(-0.262358\pi\) | |||||||
\(198\) | − | 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 | \(-0.933171\pi\) | ||
0.978041 | − | 0.208412i | \(-0.0668294\pi\) | |||||||
\(224\) | 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 | \(0.106470\pi\) | ||||
−0.944579 | + | 0.328283i | \(0.893530\pi\) | |||||||
\(228\) | − | 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 | \(0.0604529\pi\) | ||||
−0.982020 | + | 0.188779i | \(0.939547\pi\) | |||||||
\(234\) | 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 | \(-0.915235\pi\) | ||
0.964752 | − | 0.263162i | \(-0.0847654\pi\) | |||||||
\(258\) | − | 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 | \(-0.907079\pi\) | ||
0.957693 | − | 0.287790i | \(-0.0929206\pi\) | |||||||
\(264\) | −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 | \(0.125450\pi\) | ||||
−0.923338 | + | 0.383988i | \(0.874550\pi\) | |||||||
\(278\) | 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 | \(-0.899263\pi\) | ||
0.950339 | − | 0.311217i | \(-0.100737\pi\) | |||||||
\(284\) | 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 | \(0.149103\pi\) | ||||
−0.892282 | + | 0.451478i | \(0.850897\pi\) | |||||||
\(294\) | 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 | \(-0.897177\pi\) | ||
0.948279 | − | 0.317439i | \(-0.102823\pi\) | |||||||
\(308\) | − | 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 | \(-0.732148\pi\) | ||
0.666359 | − | 0.745631i | \(-0.267852\pi\) | |||||||
\(314\) | 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 | \(0.117535\pi\) | ||||
−0.932599 | + | 0.360914i | \(0.882465\pi\) | |||||||
\(318\) | − | 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 | \(-0.840921\pi\) | ||
0.877696 | − | 0.479217i | \(-0.159079\pi\) | |||||||
\(338\) | − | 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 | \(-0.771611\pi\) | ||
0.753449 | − | 0.657507i | \(-0.228389\pi\) | |||||||
\(348\) | − | 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 | \(-0.943292\pi\) | ||
0.984172 | − | 0.177213i | \(-0.0567083\pi\) | |||||||
\(354\) | 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 | \(0.0249012\pi\) | ||||
−0.996942 | + | 0.0781496i | \(0.975099\pi\) | |||||||
\(368\) | 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 | \(0.224346\pi\) | ||||
−0.761739 | + | 0.647884i | \(0.775654\pi\) | |||||||
\(374\) | −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 | \(-0.876951\pi\) | ||
0.926208 | − | 0.377014i | \(-0.123049\pi\) | |||||||
\(384\) | −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 | \(0.144741\pi\) | ||||
−0.898385 | + | 0.439208i | \(0.855259\pi\) | |||||||
\(398\) | 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 | \(0.0165956\pi\) | ||||
−0.998641 | + | 0.0521131i | \(0.983404\pi\) | |||||||
\(434\) | −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 | \(-0.965708\pi\) | ||
0.994203 | − | 0.107523i | \(-0.0342918\pi\) | |||||||
\(444\) | −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 | \(-0.924212\pi\) | ||
0.971789 | − | 0.235852i | \(-0.0757879\pi\) | |||||||
\(458\) | 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 | \(0.304242\pi\) | ||||
−0.576951 | + | 0.816779i | \(0.695758\pi\) | |||||||
\(464\) | −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 | \(0.109281\pi\) | ||||
−0.941643 | + | 0.336612i | \(0.890719\pi\) | |||||||
\(468\) | − | 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 | \(0.139949\pi\) | ||||
−0.904896 | + | 0.425633i | \(0.860051\pi\) | |||||||
\(488\) | − | 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 | \(-0.848882\pi\) | ||
0.889407 | − | 0.457117i | \(-0.151118\pi\) | |||||||
\(504\) | −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 | \(-0.905815\pi\) | ||
0.956543 | − | 0.291592i | \(-0.0941848\pi\) | |||||||
\(524\) | 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 | \(0.0116907\pi\) | ||||
−0.999326 | + | 0.0367190i | \(0.988309\pi\) | |||||||
\(548\) | 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 | \(0.252719\pi\) | ||||
−0.701041 | + | 0.713121i | \(0.747281\pi\) | |||||||
\(558\) | 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 | \(0.117361\pi\) | ||||
−0.932797 | + | 0.360403i | \(0.882639\pi\) | |||||||
\(564\) | −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 | \(0.276221\pi\) | ||||
−0.646526 | + | 0.762892i | \(0.723779\pi\) | |||||||
\(578\) | − | 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 | \(0.0897641\pi\) | ||||
−0.960500 | + | 0.278279i | \(0.910236\pi\) | |||||||
\(588\) | − | 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 | \(-0.929523\pi\) | ||
0.975589 | − | 0.219605i | \(-0.0704767\pi\) | |||||||
\(594\) | 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 | \(0.127918\pi\) | ||||
−0.920332 | + | 0.391137i | \(0.872082\pi\) | |||||||
\(608\) | − | 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 | \(-0.796588\pi\) | ||
0.802670 | − | 0.596423i | \(-0.203412\pi\) | |||||||
\(614\) | 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 | \(-0.747284\pi\) | ||
0.701049 | − | 0.713114i | \(-0.252716\pi\) | |||||||
\(618\) | − | 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 | \(0.133979\pi\) | ||||
−0.912718 | + | 0.408590i | \(0.866021\pi\) | |||||||
\(644\) | 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 | \(0.284175\pi\) | ||||
−0.627263 | + | 0.778808i | \(0.715825\pi\) | |||||||
\(648\) | 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 | \(-0.893913\pi\) | ||
0.944974 | − | 0.327146i | \(-0.106087\pi\) | |||||||
\(654\) | 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 | \(-0.963166\pi\) | ||
0.993312 | − | 0.115459i | \(-0.0368340\pi\) | |||||||
\(674\) | 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 | \(0.0228324\pi\) | ||||
−0.997429 | + | 0.0716686i | \(0.977168\pi\) | |||||||
\(678\) | 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 | \(0.322538\pi\) | ||||
−0.529079 | + | 0.848573i | \(0.677462\pi\) | |||||||
\(684\) | 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 | \(0.0118110\pi\) | ||||
−0.999312 | + | 0.0370967i | \(0.988189\pi\) | |||||||
\(728\) | 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 | \(0.0112321\pi\) | ||||
−0.999377 | + | 0.0352794i | \(0.988768\pi\) | |||||||
\(734\) | −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 | \(-0.745980\pi\) | ||
0.698120 | − | 0.715981i | \(-0.254020\pi\) | |||||||
\(744\) | 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 | \(-0.871954\pi\) | ||
0.920176 | − | 0.391506i | \(-0.128046\pi\) | |||||||
\(758\) | 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 | \(0.451551\pi\) | ||||
−0.151620 | + | 0.988439i | \(0.548449\pi\) | |||||||
\(774\) | 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 | \(-0.862099\pi\) | ||
0.907615 | − | 0.419804i | \(-0.137901\pi\) | |||||||
\(788\) | − | 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 | \(-0.958753\pi\) | ||
0.991616 | − | 0.129220i | \(-0.0412472\pi\) | |||||||
\(798\) | − | 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 | \(0.248289\pi\) | ||||
−0.710898 | + | 0.703295i | \(0.751711\pi\) | |||||||
\(824\) | −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 | \(-0.697046\pi\) | ||
0.580252 | − | 0.814437i | \(-0.302954\pi\) | |||||||
\(828\) | − | 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 | \(0.0640454\pi\) | ||||
−0.979827 | + | 0.199850i | \(0.935955\pi\) | |||||||
\(854\) | −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 | \(-0.821150\pi\) | ||
0.846258 | − | 0.532773i | \(-0.178850\pi\) | |||||||
\(858\) | − | 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 | \(0.234413\pi\) | ||||
−0.740870 | + | 0.671649i | \(0.765587\pi\) | |||||||
\(864\) | 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 | \(0.315840\pi\) | ||||
−0.546816 | + | 0.837253i | \(0.684160\pi\) | |||||||
\(878\) | 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 | \(-0.986556\pi\) | ||
0.999108 | − | 0.0422229i | \(-0.0134440\pi\) | |||||||
\(884\) | −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 | \(0.203992\pi\) | ||||
−0.801583 | + | 0.597884i | \(0.796008\pi\) | |||||||
\(888\) | − | 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 | \(0.0386032\pi\) | ||||
−0.992655 | + | 0.120978i | \(0.961397\pi\) | |||||||
\(908\) | 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 | \(-0.807996\pi\) | ||
0.823526 | − | 0.567279i | \(-0.192004\pi\) | |||||||
\(938\) | 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 | \(0.0544065\pi\) | ||||
−0.985428 | + | 0.170092i | \(0.945594\pi\) | |||||||
\(948\) | 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 | \(0.204070\pi\) | ||||
−0.801435 | + | 0.598081i | \(0.795930\pi\) | |||||||
\(954\) | 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 | \(0.372316\pi\) | ||||
−0.390459 | + | 0.920620i | \(0.627684\pi\) | |||||||
\(968\) | 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 | \(-0.971745\pi\) | ||
0.996063 | − | 0.0886505i | \(-0.0282554\pi\) | |||||||
\(978\) | 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 | \(-0.861271\pi\) | ||
0.906520 | − | 0.422164i | \(-0.138729\pi\) | |||||||
\(984\) | −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 | \(-0.840115\pi\) | ||
0.876480 | − | 0.481438i | \(-0.159885\pi\) | |||||||
\(998\) | 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.34.14 | yes | 26 | |
5.2 | odd | 4 | 825.6.a.y.1.6 | 13 | |||
5.3 | odd | 4 | 825.6.a.v.1.8 | 13 | |||
5.4 | even | 2 | inner | 165.6.c.b.34.13 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.13 | ✓ | 26 | 5.4 | even | 2 | inner | |
165.6.c.b.34.14 | yes | 26 | 1.1 | even | 1 | trivial | |
825.6.a.v.1.8 | 13 | 5.3 | odd | 4 | |||
825.6.a.y.1.6 | 13 | 5.2 | odd | 4 |