Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(289,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.289");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.f (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: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.18 | ||
Character | \(\chi\) | \(=\) | 320.289 |
Dual form | 320.6.f.d.289.19 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 4.76807 | 0.305872 | 0.152936 | − | 0.988236i | \(-0.451127\pi\) | ||||
0.152936 | + | 0.988236i | \(0.451127\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −43.2814 | + | 35.3796i | −0.774242 | + | 0.632890i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 82.4139i | 0.635705i | 0.948140 | + | 0.317852i | \(0.102962\pi\) | ||||
−0.948140 | + | 0.317852i | \(0.897038\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −220.266 | −0.906442 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 109.227i | 0.272175i | 0.990697 | + | 0.136087i | \(0.0434528\pi\) | ||||
−0.990697 | + | 0.136087i | \(0.956547\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −621.825 | −1.02049 | −0.510246 | − | 0.860029i | \(-0.670446\pi\) | ||||
−0.510246 | + | 0.860029i | \(0.670446\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −206.369 | + | 168.693i | −0.236819 | + | 0.193583i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 503.868i | − | 0.422858i | −0.977393 | − | 0.211429i | \(-0.932188\pi\) | ||
0.977393 | − | 0.211429i | \(-0.0678118\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 853.149i | − | 0.542177i | −0.962554 | − | 0.271089i | \(-0.912616\pi\) | ||
0.962554 | − | 0.271089i | \(-0.0873836\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 392.955i | 0.194444i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1424.25i | 0.561394i | 0.959796 | + | 0.280697i | \(0.0905657\pi\) | ||||
−0.959796 | + | 0.280697i | \(0.909434\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 621.562 | − | 3062.56i | 0.198900 | − | 0.980020i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2208.88 | −0.583127 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 275.098i | 0.0607424i | 0.999539 | + | 0.0303712i | \(0.00966894\pi\) | ||||
−0.999539 | + | 0.0303712i | \(0.990331\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6206.91 | 1.16004 | 0.580018 | − | 0.814604i | \(-0.303046\pi\) | ||||
0.580018 | + | 0.814604i | \(0.303046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 520.801i | 0.0832505i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2915.77 | − | 3566.99i | −0.402331 | − | 0.492189i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3668.93 | 0.440590 | 0.220295 | − | 0.975433i | \(-0.429298\pi\) | ||||
0.220295 | + | 0.975433i | \(0.429298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2964.90 | −0.312140 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1266.95 | −0.117706 | −0.0588530 | − | 0.998267i | \(-0.518744\pi\) | ||||
−0.0588530 | + | 0.998267i | \(0.518744\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7494.09 | 0.618084 | 0.309042 | − | 0.951048i | \(-0.399992\pi\) | ||||
0.309042 | + | 0.951048i | \(0.399992\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9533.40 | − | 7792.91i | 0.701805 | − | 0.573679i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 15862.9i | − | 1.04746i | −0.851884 | − | 0.523731i | \(-0.824540\pi\) | ||
0.851884 | − | 0.523731i | \(-0.175460\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10014.9 | 0.595880 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2402.48i | − | 0.129340i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10023.0 | 0.490127 | 0.245064 | − | 0.969507i | \(-0.421191\pi\) | ||||
0.245064 | + | 0.969507i | \(0.421191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3864.41 | − | 4727.49i | −0.172257 | − | 0.210729i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 4067.88i | − | 0.165837i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 27988.4i | − | 1.04676i | −0.852098 | − | 0.523382i | \(-0.824670\pi\) | ||
0.852098 | − | 0.523382i | \(-0.175330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 39901.8i | 1.37299i | 0.727134 | + | 0.686496i | \(0.240852\pi\) | ||||
−0.727134 | + | 0.686496i | \(0.759148\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 18152.9i | − | 0.576230i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 26913.5 | − | 21999.9i | 0.790107 | − | 0.645859i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −66510.4 | −1.81010 | −0.905049 | − | 0.425306i | \(-0.860166\pi\) | ||||
−0.905049 | + | 0.425306i | \(0.860166\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6790.95i | 0.171715i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 32714.8 | 0.770191 | 0.385095 | − | 0.922877i | \(-0.374169\pi\) | ||||
0.385095 | + | 0.922877i | \(0.374169\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 71539.0i | − | 1.57121i | −0.618726 | − | 0.785607i | \(-0.712351\pi\) | ||
0.618726 | − | 0.785607i | \(-0.287649\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2963.65 | − | 14602.5i | 0.0608379 | − | 0.299760i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −9001.81 | −0.173023 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 20741.8 | 0.373920 | 0.186960 | − | 0.982368i | \(-0.440137\pi\) | ||||
0.186960 | + | 0.982368i | \(0.440137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 42992.4 | 0.728080 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −108500. | −1.72876 | −0.864381 | − | 0.502838i | \(-0.832289\pi\) | ||||
−0.864381 | + | 0.502838i | \(0.832289\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17826.7 | + | 21808.1i | 0.267623 | + | 0.327394i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1311.69i | 0.0185794i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 84870.1 | 1.13574 | 0.567871 | − | 0.823117i | \(-0.307767\pi\) | ||||
0.567871 | + | 0.823117i | \(0.307767\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 51247.0i | − | 0.648731i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 29595.0 | 0.354822 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 30184.1 | + | 36925.5i | 0.343139 | + | 0.419776i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 38393.1i | − | 0.414309i | −0.978308 | − | 0.207155i | \(-0.933580\pi\) | ||
0.978308 | − | 0.207155i | \(-0.0664203\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 24058.9i | − | 0.246711i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1331.92i | − | 0.0129919i | −0.999979 | − | 0.00649597i | \(-0.997932\pi\) | ||
0.999979 | − | 0.00649597i | \(-0.00206775\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 114505.i | − | 1.06348i | −0.846907 | − | 0.531741i | \(-0.821538\pi\) | ||
0.846907 | − | 0.531741i | \(-0.178462\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13902.6 | − | 17007.7i | −0.123062 | − | 0.150547i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −78186.5 | −0.660196 | −0.330098 | − | 0.943947i | \(-0.607082\pi\) | ||||
−0.330098 | + | 0.943947i | \(0.607082\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 48709.9i | 0.392691i | 0.980535 | + | 0.196346i | \(0.0629075\pi\) | ||||
−0.980535 | + | 0.196346i | \(0.937093\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17493.7 | 0.134764 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 162096.i | − | 1.19420i | −0.802168 | − | 0.597098i | \(-0.796320\pi\) | ||
0.802168 | − | 0.597098i | \(-0.203680\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −50389.6 | − | 61643.8i | −0.355301 | − | 0.434655i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 136967. | 0.925017 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 41525.8 | 0.268813 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 149121. | 0.925921 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6040.88 | −0.0360029 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 81450.2 | + | 154543.i | 0.466248 | + | 0.884654i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 227166.i | − | 1.24978i | −0.780712 | − | 0.624891i | \(-0.785143\pi\) | ||
0.780712 | − | 0.624891i | \(-0.214857\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 35732.3 | 0.189055 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 194060.i | − | 0.987999i | −0.869462 | − | 0.494000i | \(-0.835534\pi\) | ||
0.869462 | − | 0.494000i | \(-0.164466\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 70311.4 | 0.344664 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 95603.6 | − | 78149.5i | 0.451481 | − | 0.369055i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 153702.i | − | 0.699647i | −0.936816 | − | 0.349823i | \(-0.886242\pi\) | ||
0.936816 | − | 0.349823i | \(-0.113758\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 242909.i | − | 1.06637i | −0.846000 | − | 0.533183i | \(-0.820996\pi\) | ||
0.846000 | − | 0.533183i | \(-0.179004\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 75635.5i | − | 0.320389i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 67919.9i | − | 0.277752i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9732.86 | − | 11906.6i | −0.0384433 | − | 0.0470293i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 47752.0 | 0.182263 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 97400.3i | − | 0.359414i | −0.983720 | − | 0.179707i | \(-0.942485\pi\) | ||
0.983720 | − | 0.179707i | \(-0.0575149\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −161098. | −0.574972 | −0.287486 | − | 0.957785i | \(-0.592819\pi\) | ||||
−0.287486 | + | 0.957785i | \(0.592819\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 110985.i | 0.383297i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −268644. | + | 219598.i | −0.898147 | + | 0.734175i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 168524. | 0.545647 | 0.272824 | − | 0.962064i | \(-0.412042\pi\) | ||||
0.272824 | + | 0.962064i | \(0.412042\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 47790.5 | 0.149916 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −117378. | −0.356881 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 231681. | 0.683000 | 0.341500 | − | 0.939882i | \(-0.389065\pi\) | ||||
0.341500 | + | 0.939882i | \(0.389065\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18425.8 | − | 22541.0i | −0.0526885 | − | 0.0644560i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 674343.i | 1.87107i | 0.353238 | + | 0.935534i | \(0.385081\pi\) | ||||
−0.353238 | + | 0.935534i | \(0.614919\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15372.9 | 0.0414037 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 187919.i | 0.491452i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −637772. | −1.62013 | −0.810065 | − | 0.586340i | \(-0.800568\pi\) | ||||
−0.810065 | + | 0.586340i | \(0.800568\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 252398. | + | 51225.4i | 0.623003 | + | 0.126442i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 133451.i | − | 0.320176i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 341699.i | 0.797096i | 0.917147 | + | 0.398548i | \(0.130486\pi\) | ||||
−0.917147 | + | 0.398548i | \(0.869514\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 123083.i | 0.279256i | 0.990204 | + | 0.139628i | \(0.0445907\pi\) | ||||
−0.990204 | + | 0.139628i | \(0.955409\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 190255.i | 0.419960i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −158796. | + | 129805.i | −0.341123 | + | 0.278845i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 55035.9 | 0.115091 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 182043.i | − | 0.370697i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 354073. | 0.702279 | 0.351139 | − | 0.936323i | \(-0.385794\pi\) | ||||
0.351139 | + | 0.936323i | \(0.385794\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 357838.i | 0.691502i | 0.938326 | + | 0.345751i | \(0.112376\pi\) | ||||
−0.938326 | + | 0.345751i | \(0.887624\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 128325. | − | 104897.i | 0.241672 | − | 0.197550i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −418271. | −0.767878 | −0.383939 | − | 0.923359i | \(-0.625433\pi\) | ||||
−0.383939 | + | 0.923359i | \(0.625433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −969952. | −1.73627 | −0.868136 | − | 0.496326i | \(-0.834682\pi\) | ||||
−0.868136 | + | 0.496326i | \(0.834682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −317126. | −0.553658 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22671.9 | −0.0386142 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 54835.2 | − | 44824.1i | 0.0911328 | − | 0.0744949i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 313714.i | − | 0.508872i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 93186.8 | 0.147567 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 545362.i | 0.843293i | 0.906760 | + | 0.421647i | \(0.138548\pi\) | ||||
−0.906760 | + | 0.421647i | \(0.861452\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 155986. | 0.235580 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −324355. | + | 265138.i | −0.478546 | + | 0.391179i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 511536.i | 0.737440i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 341103.i | − | 0.480590i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 313318.i | 0.431523i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 627315.i | − | 0.844741i | −0.906423 | − | 0.422370i | \(-0.861198\pi\) | ||
0.906423 | − | 0.422370i | \(-0.138802\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −136909. | + | 674577.i | −0.180291 | + | 0.888332i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.00091e6 | 1.28923 | 0.644615 | − | 0.764508i | \(-0.277018\pi\) | ||||
0.644615 | + | 0.764508i | \(0.277018\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 920954.i | − | 1.16051i | −0.814435 | − | 0.580255i | \(-0.802953\pi\) | ||
0.814435 | − | 0.580255i | \(-0.197047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −42921.3 | −0.0529228 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 185771.i | 0.224176i | 0.993698 | + | 0.112088i | \(0.0357538\pi\) | ||||
−0.993698 | + | 0.112088i | \(0.964246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 561224. | + | 686570.i | 0.662929 | + | 0.810989i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 98898.3 | 0.114371 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −665553. | −0.753682 | −0.376841 | − | 0.926278i | \(-0.622990\pi\) | ||||
−0.376841 | + | 0.926278i | \(0.622990\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −761168. | −0.844186 | −0.422093 | − | 0.906553i | \(-0.638704\pi\) | ||||
−0.422093 | + | 0.906553i | \(0.638704\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 741749. | 0.805826 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −433461. | + | 354325.i | −0.461355 | + | 0.377126i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 530509.i | 0.553287i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −517336. | −0.528780 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.24971e6i | 1.25206i | 0.779799 | + | 0.626030i | \(0.215321\pi\) | ||||
−0.779799 | + | 0.626030i | \(0.784679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −155567. | −0.152797 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 84998.9 | + | 103983.i | 0.0818583 | + | 0.100141i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.80658e6i | 1.70617i | 0.521769 | + | 0.853087i | \(0.325272\pi\) | ||||
−0.521769 | + | 0.853087i | \(0.674728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 302371.i | 0.280085i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 60594.5i | − | 0.0550595i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.14041e6i | 1.01665i | 0.861166 | + | 0.508324i | \(0.169735\pi\) | ||||
−0.861166 | + | 0.508324i | \(0.830265\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −433811. | + | 354611.i | −0.379477 | + | 0.310197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 404667. | 0.347392 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.86107e6i | − | 1.56813i | −0.620679 | − | 0.784065i | \(-0.713143\pi\) | ||
0.620679 | − | 0.784065i | \(-0.286857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.08713e6 | 0.899204 | 0.449602 | − | 0.893229i | \(-0.351566\pi\) | ||||
0.449602 | + | 0.893229i | \(0.351566\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 244349.i | − | 0.198429i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 334514. | + | 67891.3i | 0.266736 | + | 0.0541355i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −628877. | −0.492455 | −0.246227 | − | 0.969212i | \(-0.579191\pi\) | ||||
−0.246227 | + | 0.969212i | \(0.579191\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.36717e6 | −1.05150 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −817929. | −0.617945 | −0.308972 | − | 0.951071i | \(-0.599985\pi\) | ||||
−0.308972 | + | 0.951071i | \(0.599985\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 519909. | 0.385888 | 0.192944 | − | 0.981210i | \(-0.438196\pi\) | ||||
0.192944 | + | 0.981210i | \(0.438196\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 143920. | + | 176063.i | 0.104956 | + | 0.128398i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 104414.i | − | 0.0748262i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.16597e6 | 0.821191 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 183061.i | − | 0.126725i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −61931.1 | −0.0421444 | −0.0210722 | − | 0.999778i | \(-0.506708\pi\) | ||||
−0.0210722 | + | 0.999778i | \(0.506708\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 990221. | + | 1.21138e6i | 0.662486 | + | 0.810448i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 241269.i | − | 0.158712i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 885637.i | − | 0.572898i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 617617.i | 0.392919i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 6350.68i | − | 0.00397387i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.41171e6 | − | 1.72701e6i | −0.868953 | − | 1.06303i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.02897e6 | −1.22865 | −0.614327 | − | 0.789051i | \(-0.710573\pi\) | ||||
−0.614327 | + | 0.789051i | \(0.710573\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 545966.i | − | 0.325289i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.44330e6 | −0.846166 | −0.423083 | − | 0.906091i | \(-0.639052\pi\) | ||||
−0.423083 | + | 0.906091i | \(0.639052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 210398.i | 0.121389i | 0.998156 | + | 0.0606947i | \(0.0193316\pi\) | ||||
−0.998156 | + | 0.0606947i | \(0.980668\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 642244. | + | 785685.i | 0.364690 | + | 0.446141i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −719655. | −0.402231 | −0.201116 | − | 0.979567i | \(-0.564457\pi\) | ||||
−0.201116 | + | 0.979567i | \(0.564457\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30048.0 | −0.0165325 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −372799. | −0.201935 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −429875. | −0.229264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −386503. | + | 1.90438e6i | −0.202976 | + | 1.00010i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 232252.i | 0.120113i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.30733e6 | 0.665877 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.34910e6i | − | 0.676822i | −0.940998 | − | 0.338411i | \(-0.890111\pi\) | ||
0.940998 | − | 0.338411i | \(-0.109889\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −808138. | −0.399370 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.87866e6 | − | 2.35311e6i | 1.40145 | − | 1.14559i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.81431e6i | − | 0.870234i | −0.900374 | − | 0.435117i | \(-0.856707\pi\) | ||
0.900374 | − | 0.435117i | \(-0.143293\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 772884.i | − | 0.365271i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 677961.i | 0.315732i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.21050e6i | 1.01451i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −240261. | − | 293922.i | −0.108677 | − | 0.132949i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 826969. | 0.368693 | 0.184347 | − | 0.982861i | \(-0.440983\pi\) | ||||
0.184347 | + | 0.982861i | \(0.440983\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.90016e6i | − | 0.835077i | −0.908659 | − | 0.417538i | \(-0.862893\pi\) | ||
0.908659 | − | 0.417538i | \(-0.137107\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.37354e6 | 0.595076 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.54658e6i | 0.660595i | 0.943877 | + | 0.330298i | \(0.107149\pi\) | ||||
−0.943877 | + | 0.330298i | \(0.892851\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.41594e6 | + | 1.15744e6i | −0.596314 | + | 0.487446i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 197998. | 0.0822223 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.20737e6 | −1.72296 | −0.861479 | − | 0.507792i | \(-0.830462\pi\) | ||||
−0.861479 | + | 0.507792i | \(0.830462\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.74824e6 | 0.706044 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 711017. | 0.283213 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.53102e6 | + | 3.09631e6i | 0.994406 | + | 1.21650i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.08199e6i | − | 1.19445i | −0.802075 | − | 0.597223i | \(-0.796271\pi\) | ||
0.802075 | − | 0.597223i | \(-0.203729\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 279064. | 0.106694 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 826036.i | 0.311576i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.22578e6 | 1.20050 | 0.600252 | − | 0.799811i | \(-0.295067\pi\) | ||||
0.600252 | + | 0.799811i | \(0.295067\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 388361. | + | 736870.i | 0.142612 | + | 0.270591i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 171063.i | − | 0.0619871i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.54075e6i | − | 1.26619i | −0.774076 | − | 0.633093i | \(-0.781785\pi\) | ||
0.774076 | − | 0.633093i | \(-0.218215\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 1.08314e6i | − | 0.382273i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4.84417e6i | − | 1.68742i | −0.536803 | − | 0.843708i | \(-0.680368\pi\) | ||
0.536803 | − | 0.843708i | \(-0.319632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 389611. | − | 318481.i | 0.133961 | − | 0.109504i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.65069e6 | −0.560258 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.70292e6i | − | 0.905648i | −0.891600 | − | 0.452824i | \(-0.850417\pi\) | ||
0.891600 | − | 0.452824i | \(-0.149583\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 717637. | 0.237390 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 925289.i | − | 0.302201i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −897733. | + | 733837.i | −0.289504 | + | 0.236650i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.85969e6 | 0.910631 | 0.455316 | − | 0.890330i | \(-0.349526\pi\) | ||||
0.455316 | + | 0.890330i | \(0.349526\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 335250. | 0.105423 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.78230e6 | 0.864058 | 0.432029 | − | 0.901860i | \(-0.357798\pi\) | ||||
0.432029 | + | 0.901860i | \(0.357798\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.85961e6 | −1.18381 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.86077e6 | + | 1.52106e6i | −0.563710 | + | 0.460795i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 400745.i | 0.119917i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.46827e6 | 1.91196 | 0.955982 | − | 0.293425i | \(-0.0947950\pi\) | ||||
0.955982 | + | 0.293425i | \(0.0947950\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 732863.i | − | 0.214002i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.30664e6 | 0.665432 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.69604e6 | − | 3.83870e6i | 1.33848 | − | 1.09412i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 1.15821e6i | − | 0.326171i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 5.24272e6i | − | 1.45889i | −0.684041 | − | 0.729444i | \(-0.739779\pi\) | ||
0.684041 | − | 0.729444i | \(-0.260221\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.34887e6i | 1.19583i | 0.801558 | + | 0.597917i | \(0.204005\pi\) | ||||
−0.801558 | + | 0.597917i | \(0.795995\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.49405e6i | 0.949464i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.54313e6 | − | 313186.i | −0.414409 | − | 0.0841065i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.28846e6 | −0.872817 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 323847.i | − | 0.0849565i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.96989e6 | 1.54801 | 0.774003 | − | 0.633181i | \(-0.218251\pi\) | ||||
0.774003 | + | 0.633181i | \(0.218251\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.35336e6i | − | 1.62848i | −0.580525 | − | 0.814242i | \(-0.697153\pi\) | ||
0.580525 | − | 0.814242i | \(-0.302847\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −46407.0 | − | 56771.6i | −0.0117587 | − | 0.0143849i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.21510e6 | 0.304375 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.83485e6 | −1.69265 | −0.846326 | − | 0.532666i | \(-0.821190\pi\) | ||||
−0.846326 | + | 0.532666i | \(0.821190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.20595e6 | −0.540131 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.02270e6 | −1.45808 | −0.729041 | − | 0.684470i | \(-0.760034\pi\) | ||||
−0.729041 | + | 0.684470i | \(0.760034\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.67330e6 | + | 3.00267e6i | −0.879339 | + | 0.718800i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 464412.i | − | 0.109935i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.11636e6 | 0.963602 | 0.481801 | − | 0.876281i | \(-0.339983\pi\) | ||||
0.481801 | + | 0.876281i | \(0.339983\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 138384.i | − | 0.0320366i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −768124. | −0.175868 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.81310e6 | + | 2.21804e6i | 0.410576 | + | 0.502275i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 7.61258e6i | − | 1.70507i | −0.522673 | − | 0.852533i | \(-0.675065\pi\) | ||
0.522673 | − | 0.852533i | \(-0.324935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.11299e6i | 0.246580i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.54787e6i | 0.996680i | 0.866982 | + | 0.498340i | \(0.166057\pi\) | ||||
−0.866982 | + | 0.498340i | \(0.833943\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.15983e6i | − | 0.685033i | −0.939512 | − | 0.342516i | \(-0.888721\pi\) | ||
0.939512 | − | 0.342516i | \(-0.111279\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.28091e6 | + | 1.04706e6i | −0.274718 | + | 0.224563i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.77790e6 | 1.22596 | 0.612982 | − | 0.790097i | \(-0.289970\pi\) | ||||
0.612982 | + | 0.790097i | \(0.289970\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.48138e6i | − | 1.15069i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 803533. | 0.166898 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 818555.i | 0.168227i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.61282e6 | − | 530285.i | −0.531344 | − | 0.107839i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.20773e6 | −0.444272 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.83200e6 | −0.962250 | −0.481125 | − | 0.876652i | \(-0.659772\pi\) | ||||
−0.481125 | + | 0.876652i | \(0.659772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.28143e6 | −0.449619 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −559668. | −0.109160 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.35834e6 | + | 1.66171e6i | 0.262212 | + | 0.320775i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.82344e6i | 0.539455i | 0.962937 | + | 0.269728i | \(0.0869337\pi\) | ||||
−0.962937 | + | 0.269728i | \(0.913066\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.10467e6 | 0.208911 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 425391.i | 0.0796314i | 0.999207 | + | 0.0398157i | \(0.0126771\pi\) | ||||
−0.999207 | + | 0.0398157i | \(0.987323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 138613. | 0.0256854 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 851195. | + | 1.04130e6i | 0.156141 | + | 0.191014i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.69615e6i | 0.489614i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.09645e7i | − | 1.97122i | −0.169022 | − | 0.985612i | \(-0.554061\pi\) | ||
0.169022 | − | 0.985612i | \(-0.445939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.21531e6i | 0.572307i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 673131.i | 0.118626i | 0.998239 | + | 0.0593130i | \(0.0188910\pi\) | ||||
−0.998239 | + | 0.0593130i | \(0.981109\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 47122.8 | + | 57647.3i | 0.00822247 | + | 0.0100589i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 73299.1 | 0.0126642 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.03530e7i | − | 1.77122i | −0.464434 | − | 0.885608i | \(-0.653742\pi\) | ||
0.464434 | − | 0.885608i | \(-0.346258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.89580e6 | 0.998828 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.88451e6i | 0.316158i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.05113e6 | + | 4.95592e6i | 0.673067 | + | 0.823392i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.73266e6 | 0.285093 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.04094e6 | −0.495552 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.28373e6 | −0.852799 | −0.426399 | − | 0.904535i | \(-0.640218\pi\) | ||||
−0.426399 | + | 0.904535i | \(0.640218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −208807. | −0.0333803 | −0.0166901 | − | 0.999861i | \(-0.505313\pi\) | ||||
−0.0166901 | + | 0.999861i | \(0.505313\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.20345e6 | + | 244246.i | 0.190559 | + | 0.0386749i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 3.12747e6i | − | 0.490530i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.40784e6 | 0.684836 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.16489e6i | 0.948831i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 787818. | 0.120118 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.38402e6 | − | 2.76621e6i | 0.511151 | − | 0.417831i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.62924e6i | 0.243809i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.09390e6i | 0.162183i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.19366e6i | 1.05671i | 0.849023 | + | 0.528356i | \(0.177191\pi\) | ||||
−0.849023 | + | 0.528356i | \(0.822809\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 586870.i | 0.0854165i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.72334e6 | − | 2.10824e6i | −0.248531 | − | 0.304038i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.32353e6 | −0.189133 | −0.0945664 | − | 0.995519i | \(-0.530146\pi\) | ||||
−0.0945664 | + | 0.995519i | \(0.530146\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 8.78899e6i | − | 1.24454i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 234699. | 0.0329331 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.70941e6i | 0.237702i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −757152. | + | 618921.i | −0.104340 | + | 0.0852909i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 919685. | 0.125603 | 0.0628017 | − | 0.998026i | \(-0.479996\pi\) | ||||
0.0628017 | + | 0.998026i | \(0.479996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.66001e6 | −0.630750 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 262415. | 0.0352032 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.78497e6 | 1.30103 | 0.650517 | − | 0.759492i | \(-0.274552\pi\) | ||||
0.650517 | + | 0.759492i | \(0.274552\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.73489e6 | + | 7.01574e6i | 0.755795 | + | 0.924596i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.54317e6i | 0.462844i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −289576. | −0.0374958 | −0.0187479 | − | 0.999824i | \(-0.505968\pi\) | ||||
−0.0187479 | + | 0.999824i | \(0.505968\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.52990e6i | − | 0.196369i | −0.995168 | − | 0.0981845i | \(-0.968696\pi\) | ||
0.995168 | − | 0.0981845i | \(-0.0313035\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.68825e6 | 0.214807 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.36187e6 | + | 885263.i | 0.550178 | + | 0.111661i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.25795e6i | 0.407385i | 0.979035 | + | 0.203692i | \(0.0652942\pi\) | ||||
−0.979035 | + | 0.203692i | \(0.934706\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.70620e6i | 0.211511i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 8.94192e6i | − | 1.09898i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.09478e6i | 0.133400i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.92811e6 | + | 4.84583e6i | −0.716187 | + | 0.585434i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 902249. | 0.108076 | 0.0540382 | − | 0.998539i | \(-0.482791\pi\) | ||||
0.0540382 | + | 0.998539i | \(0.482791\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 5.29542e6i | − | 0.628944i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.99434e6 | −0.234872 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.13280e7i | 1.32287i | 0.750004 | + | 0.661433i | \(0.230051\pi\) | ||||
−0.750004 | + | 0.661433i | \(0.769949\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.79729e6 | + | 1.46917e6i | −0.208126 | + | 0.170129i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.62480e6 | −0.531077 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.65503e7 | −1.88468 | −0.942342 | − | 0.334651i | \(-0.891382\pi\) | ||||
−0.942342 | + | 0.334651i | \(0.891382\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 204374. | 0.0230802 | 0.0115401 | − | 0.999933i | \(-0.496327\pi\) | ||||
0.0115401 | + | 0.999933i | \(0.496327\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.46499e7 | 1.64075 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.45415e6 | + | 5.27583e6i | −0.716886 | + | 0.586006i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 5.18844e6i | − | 0.571565i | −0.958295 | − | 0.285782i | \(-0.907747\pi\) | ||
0.958295 | − | 0.285782i | \(-0.0922534\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −108101. | −0.0118110 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.86396e6i | 1.06893i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.06424e7 | −1.14390 | −0.571951 | − | 0.820288i | \(-0.693813\pi\) | ||||
−0.571951 | + | 0.820288i | \(0.693813\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 261458. | − | 213724.i | 0.0278750 | − | 0.0227859i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.94619e6i | 0.734571i | 0.930108 | + | 0.367286i | \(0.119713\pi\) | ||||
−0.930108 | + | 0.367286i | \(0.880287\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.38878e6i | 0.250582i | 0.992120 | + | 0.125291i | \(0.0399864\pi\) | ||||
−0.992120 | + | 0.125291i | \(0.960014\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 3.14601e6i | − | 0.327364i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.99448e6i | 0.721997i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.99295e6 | − | 3.80715e6i | −0.920878 | − | 0.389852i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 444321. | 0.0451365 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.84866e6i | − | 0.186307i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.38123e6 | −0.138100 | −0.0690499 | − | 0.997613i | \(-0.521997\pi\) | ||||
−0.0690499 | + | 0.997613i | \(0.521997\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.60032e6i | 0.257940i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.03705e6 | + | 9.83207e6i | 0.790975 | + | 0.967633i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.22754e6 | −0.608090 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.20594e6 | −0.698133 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.39783e7 | −1.34372 | −0.671861 | − | 0.740677i | \(-0.734505\pi\) | ||||
−0.671861 | + | 0.740677i | \(0.734505\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.28822e6 | −0.122875 | −0.0614373 | − | 0.998111i | \(-0.519568\pi\) | ||||
−0.0614373 | + | 0.998111i | \(0.519568\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.54655e6 | + | 1.26420e6i | −0.146374 | + | 0.119651i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.51716e7i | 1.42485i | 0.701746 | + | 0.712427i | \(0.252404\pi\) | ||||
−0.701746 | + | 0.712427i | \(0.747596\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.05709e6 | 0.284902 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.43904e6i | 0.225562i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.46639e7 | −1.34575 | −0.672877 | − | 0.739754i | \(-0.734942\pi\) | ||||
−0.672877 | + | 0.739754i | \(0.734942\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.86576e6 | + | 8.39917e6i | 0.625295 | + | 0.764950i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.57576e7i | 1.42422i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 91638.5i | 0.00821986i | 0.999992 | + | 0.00410993i | \(0.00130824\pi\) | ||||
−0.999992 | + | 0.00410993i | \(0.998692\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.06350e6i | 0.272718i | 0.990659 | + | 0.136359i | \(0.0435400\pi\) | ||||
−0.990659 | + | 0.136359i | \(0.956460\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.49392e6i | 0.131991i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.04318e6 | + | 2.48759e6i | −0.266854 | + | 0.218135i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −391809. | −0.0341004 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 2.99108e6i | − | 0.258382i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.35835e6 | −0.373694 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.55354e7i | − | 1.32216i | −0.750316 | − | 0.661079i | \(-0.770099\pi\) | ||
0.750316 | − | 0.661079i | \(-0.229901\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.37296e6 | + | 6.76484e6i | −0.115984 | + | 0.571476i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.41038e6 | −0.453687 | −0.226843 | − | 0.973931i | \(-0.572841\pi\) | ||||
−0.226843 | + | 0.973931i | \(0.572841\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.16413e6 | 0.263378 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.77241e6 | 0.394339 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.26434e6 | −0.103708 | −0.0518542 | − | 0.998655i | \(-0.516513\pi\) | ||||
−0.0518542 | + | 0.998655i | \(0.516513\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.43793e6 | + | 6.65245e6i | 0.442800 | + | 0.541696i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 4.39117e6i | − | 0.354968i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.23256e6 | −0.500171 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 867712.i | 0.0691323i | 0.999402 | + | 0.0345661i | \(0.0110049\pi\) | ||||
−0.999402 | + | 0.0345661i | \(0.988995\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.98279e6 | 0.156835 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.59402e6 | + | 1.05134e7i | 0.674892 | + | 0.825624i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 638374.i | 0.0497729i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 885770.i | 0.0685690i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 6.82392e6i | − | 0.524492i | −0.965001 | − | 0.262246i | \(-0.915537\pi\) | ||
0.965001 | − | 0.262246i | \(-0.0844632\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.13014e6i | − | 0.238878i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.67596e6 | + | 3.27361e6i | 0.202771 | + | 0.248059i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 109769. | 0.00825904 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.03780e7i | − | 0.775350i | −0.921796 | − | 0.387675i | \(-0.873278\pi\) | ||
0.921796 | − | 0.387675i | \(-0.126722\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.56870e6 | −0.338937 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.84022e6i | 0.651237i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.40298e6 | + | 2.93967e6i | 0.175786 | + | 0.215047i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.17341e6 | −0.230530 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.77556e6 | −0.416650 | −0.208325 | − | 0.978060i | \(-0.566801\pi\) | ||||
−0.208325 | + | 0.978060i | \(0.566801\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.43677e6 | 0.676060 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.62930e6 | −0.258213 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 842504. | + | 170990.i | 0.0595288 | + | 0.0120817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1.08256e7i | − | 0.759653i | −0.925058 | − | 0.379827i | \(-0.875984\pi\) | ||
0.925058 | − | 0.379827i | \(-0.124016\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.91044e6 | −0.481601 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.77603e6i | − | 0.261362i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.58032e7 | 1.77383 | 0.886917 | − | 0.461929i | \(-0.152842\pi\) | ||||
0.886917 | + | 0.461929i | \(0.152842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.06677e6 | + | 1.68945e6i | −0.141115 | + | 0.115352i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.26471e6i | − | 0.492663i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.32347e7i | − | 0.891459i | −0.895168 | − | 0.445730i | \(-0.852944\pi\) | ||
0.895168 | − | 0.445730i | \(-0.147056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.52951e6i | 0.169235i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.33971e7i | − | 0.890304i | −0.895455 | − | 0.445152i | \(-0.853150\pi\) | ||
0.895455 | − | 0.445152i | \(-0.146850\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.44599e6 | + | 4.21562e6i | 0.227469 | + | 0.278273i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.38988e7 | 1.56702 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6.44366e6i | − | 0.419689i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.63485e6 | 0.235173 | 0.117586 | − | 0.993063i | \(-0.462484\pi\) | ||||
0.117586 | + | 0.993063i | \(0.462484\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.95870e6i | 0.382970i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.97253e6 | − | 5.69957e6i | 0.445167 | − | 0.363894i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.53597e7 | 1.60844 | 0.804219 | − | 0.594332i | \(-0.202584\pi\) | ||||
0.804219 | + | 0.594332i | \(0.202584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −741753. | −0.0467364 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.42741e6 | −0.590107 | −0.295053 | − | 0.955481i | \(-0.595337\pi\) | ||||
−0.295053 | + | 0.955481i | \(0.595337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.01438e6 | −0.249636 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.92660e6 | − | 4.80358e6i | −0.242585 | − | 0.296764i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.74039e7i | 1.06821i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.77861e7 | 1.08459 | 0.542293 | − | 0.840189i | \(-0.317556\pi\) | ||||
0.542293 | + | 0.840189i | \(0.317556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.61388e6i | 0.521871i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.23501e7 | −1.34534 | −0.672668 | − | 0.739944i | \(-0.734852\pi\) | ||||
−0.672668 | + | 0.739944i | \(0.734852\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.85798e6 | − | 1.90090e7i | 0.230731 | − | 1.13686i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.44172e6i | 0.0856702i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.08089e6i | 0.0638174i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.57333e6i | 0.209626i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 607659.i | − | 0.0354205i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.29395e6 | + | 5.96231e6i | −0.422463 | + | 0.345335i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.53456e7 | −0.883177 | −0.441589 | − | 0.897218i | \(-0.645585\pi\) | ||||
−0.441589 | + | 0.897218i | \(0.645585\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.43754e6i | 0.310964i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.33589e7 | 0.759156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.48119e7i | − | 1.40113i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.06844e6 | + | 1.69081e6i | −0.116071 | + | 0.0948805i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −986256. | −0.0549976 | −0.0274988 | − | 0.999622i | \(-0.508754\pi\) | ||||
−0.0274988 | + | 0.999622i | \(0.508754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.99282e6 | −0.442928 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.86940e7 | −1.02949 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.81397e6 | 0.427645 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.08030e6 | − | 4.15280e6i | 0.276312 | − | 0.225866i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 8.87371e6i | − | 0.479647i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.05342e6 | 0.0565890 | 0.0282945 | − | 0.999600i | \(-0.490992\pi\) | ||||
0.0282945 | + | 0.999600i | \(0.490992\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.33495e7i | − | 1.24660i | −0.781985 | − | 0.623298i | \(-0.785792\pi\) | ||
0.781985 | − | 0.623298i | \(-0.214208\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.18351e6 | 0.275041 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.00275e7 | + | 8.19678e6i | −0.528807 | + | 0.432264i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.39358e6i | − | 0.335111i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.12879e7i | 0.588038i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.20305e7i | 1.14069i | 0.821405 | + | 0.570345i | \(0.193190\pi\) | ||||
−0.821405 | + | 0.570345i | \(0.806810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1.96355e7i | − | 1.01051i | −0.862969 | − | 0.505257i | \(-0.831398\pi\) | ||
0.862969 | − | 0.505257i | \(-0.168602\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.59499e6 | + | 323710.i | 0.0815872 | + | 0.0165585i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.52997e7 | −0.777891 | −0.388945 | − | 0.921261i | \(-0.627161\pi\) | ||||
−0.388945 | + | 0.921261i | \(0.627161\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.30033e7i | 0.657153i | 0.944477 | + | 0.328577i | \(0.106569\pi\) | ||||
−0.944477 | + | 0.328577i | \(0.893431\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.99853e6 | −0.150628 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5.04622e6i | − | 0.251973i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.38580e7 | − | 2.91865e7i | −1.18418 | − | 1.44866i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.37103e7 | −0.676448 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.78281e7 | 0.874381 | 0.437191 | − | 0.899369i | \(-0.355973\pi\) | ||||
0.437191 | + | 0.899369i | \(0.355973\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.04355e7 | 0.996310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.89994e6 | −0.189012 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −665361. | + | 543888.i | −0.0320565 | + | 0.0262040i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.22896e7i | 0.588612i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.47896e6 | 0.118032 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.22549e6i | 0.247345i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.39396e7 | 0.655963 | 0.327981 | − | 0.944684i | \(-0.393632\pi\) | ||||
0.327981 | + | 0.944684i | \(0.393632\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −6.64852e6 | − | 8.13342e6i | −0.311035 | − | 0.380503i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 4.09468e7i | − | 1.90444i | −0.305412 | − | 0.952220i | \(-0.598794\pi\) | ||
0.305412 | − | 0.952220i | \(-0.401206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.68350e7i | − | 1.24085i | −0.784267 | − | 0.620423i | \(-0.786961\pi\) | ||
0.784267 | − | 0.620423i | \(-0.213039\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 497853.i | − | 0.0228872i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.28078e7i | 1.04245i | 0.853419 | + | 0.521226i | \(0.174525\pi\) | ||||
−0.853419 | + | 0.521226i | \(0.825475\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.76037e7 | − | 2.25641e7i | 1.25437 | − | 1.02536i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.55944e6 | 0.251179 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.26556e6i | 0.101771i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.13578e7 | 1.84719 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.45669e6i | 0.375547i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.27365e7 | + | 6.71263e6i | −0.562379 | + | 0.296396i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.79568e7 | 0.788368 | 0.394184 | − | 0.919031i | \(-0.371027\pi\) | ||||
0.394184 | + | 0.919031i | \(0.371027\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −295292. | −0.0128908 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.16608e7 | 1.37430 | 0.687150 | − | 0.726515i | \(-0.258861\pi\) | ||||
0.687150 | + | 0.726515i | \(0.258861\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.60611e7 | −1.12484 | −0.562420 | − | 0.826852i | \(-0.690129\pi\) | ||||
−0.562420 | + | 0.826852i | \(0.690129\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.72144e6 | + | 5.77594e6i | 0.202636 | + | 0.247893i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.57048e7i | − | 1.09700i | −0.836152 | − | 0.548498i | \(-0.815200\pi\) | ||
0.836152 | − | 0.548498i | \(-0.184800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.87216e7 | 0.794492 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.69592e6i | 0.198165i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.35334e7 | −0.567910 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.20892e7 | − | 1.47892e7i | −0.504474 | − | 0.617145i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.22278e6i | − | 0.175233i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.70751e6i | 0.0704633i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.05028e6i | − | 0.207254i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.94484e6i | 0.120183i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.35464e6 | − | 5.32722e6i | −0.176738 | − | 0.216212i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.57667e7 | −1.44364 | −0.721822 | − | 0.692079i | \(-0.756695\pi\) | ||||
−0.721822 | + | 0.692079i | \(0.756695\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 293376.i | 0.0117764i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.63397e7 | −1.05151 | −0.525757 | − | 0.850635i | \(-0.676218\pi\) | ||||
−0.525757 | + | 0.850635i | \(0.676218\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.18511e7i | − | 0.470525i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.73114e6 | − | 8.23449e6i | −0.265788 | − | 0.325150i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.59932e7 | 0.628076 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.57454e7 | 1.78673 | 0.893364 | − | 0.449333i | \(-0.148338\pi\) | ||||
0.893364 | + | 0.449333i | \(0.148338\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.67428e6 | −0.375811 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.03429e7 | −0.785973 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.28047e6 | − | 1.12363e7i | 0.0876334 | − | 0.431787i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.52214e7i | 0.963985i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.27869e7 | −0.486100 | −0.243050 | − | 0.970014i | \(-0.578148\pi\) | ||||
−0.243050 | + | 0.970014i | \(0.578148\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 8.54425e6i | − | 0.323072i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −6.88175e6 | −0.258818 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.38203e6 | + | 1.94715e6i | −0.0891084 | + | 0.0728401i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.18690e7i | − | 0.813728i | −0.913489 | − | 0.406864i | \(-0.866622\pi\) | ||
0.913489 | − | 0.406864i | \(-0.133378\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.00319e6i | 0.0371296i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.18344e7i | 0.435683i | 0.975984 | + | 0.217842i | \(0.0699016\pi\) | ||||
−0.975984 | + | 0.217842i | \(0.930098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.80445e6i | − | 0.0660794i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.44060e6 | + | 7.87906e6i | 0.234610 | + | 0.287009i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.94759e7 | 0.705704 | 0.352852 | − | 0.935679i | \(-0.385212\pi\) | ||||
0.352852 | + | 0.935679i | \(0.385212\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.44847e7i | 1.60341i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.43136e6 | −0.123031 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.02336e7i | 1.07834i | 0.842195 | + | 0.539172i | \(0.181263\pi\) | ||||
−0.842195 | + | 0.539172i | \(0.818737\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.53248e7 | + | 1.25270e7i | −0.543733 | + | 0.444465i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −143271. | −0.00505684 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.26672e7 | 0.444769 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.89656e6 | 0.345681 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.72218e7 | 0.598429 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.26602e7 | − | 1.54878e7i | −0.437645 | − | 0.535390i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.84618e7i | − | 1.66661i | −0.552814 | − | 0.833304i | \(-0.686446\pi\) | ||
0.552814 | − | 0.833304i | \(-0.313554\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.04967e6 | −0.0701254 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.73687e7i | − | 0.591181i | −0.955315 | − | 0.295590i | \(-0.904484\pi\) | ||
0.955315 | − | 0.295590i | \(-0.0955163\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.00190e7 | 0.677893 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.84287e6 | + | 9.08020e6i | −0.0620846 | + | 0.305903i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.62432e7i | 0.544422i | 0.962238 | + | 0.272211i | \(0.0877549\pi\) | ||||
−0.962238 | + | 0.272211i | \(0.912245\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.27009e6i | 0.309120i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.07291e7i | − | 0.355952i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 2.04107e7i | − | 0.673713i | −0.941556 | − | 0.336856i | \(-0.890636\pi\) | ||
0.941556 | − | 0.336856i | \(-0.109364\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.81034e7 | − | 1.47983e7i | 0.594523 | − | 0.485982i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.23342e6 | 0.203673 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.06735e7i | 0.346989i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.63999e7 | −0.530464 | −0.265232 | − | 0.964185i | \(-0.585449\pi\) | ||||
−0.265232 | + | 0.964185i | \(0.585449\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 6.43261e6i | − | 0.207021i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.19809e7 | − | 3.43166e7i | 1.34429 | − | 1.09887i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.61288e7 | −0.513881 | −0.256941 | − | 0.966427i | \(-0.582715\pi\) | ||||
−0.256941 | + | 0.966427i | \(0.582715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.10423e6 | −0.256920 |
(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 | 320.6.f.d.289.18 | yes | 32 | |
4.3 | odd | 2 | inner | 320.6.f.d.289.15 | yes | 32 | |
5.4 | even | 2 | inner | 320.6.f.d.289.16 | yes | 32 | |
8.3 | odd | 2 | inner | 320.6.f.d.289.20 | yes | 32 | |
8.5 | even | 2 | inner | 320.6.f.d.289.13 | ✓ | 32 | |
20.19 | odd | 2 | inner | 320.6.f.d.289.17 | yes | 32 | |
40.19 | odd | 2 | inner | 320.6.f.d.289.14 | yes | 32 | |
40.29 | even | 2 | inner | 320.6.f.d.289.19 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
320.6.f.d.289.13 | ✓ | 32 | 8.5 | even | 2 | inner | |
320.6.f.d.289.14 | yes | 32 | 40.19 | odd | 2 | inner | |
320.6.f.d.289.15 | yes | 32 | 4.3 | odd | 2 | inner | |
320.6.f.d.289.16 | yes | 32 | 5.4 | even | 2 | inner | |
320.6.f.d.289.17 | yes | 32 | 20.19 | odd | 2 | inner | |
320.6.f.d.289.18 | yes | 32 | 1.1 | even | 1 | trivial | |
320.6.f.d.289.19 | yes | 32 | 40.29 | even | 2 | inner | |
320.6.f.d.289.20 | yes | 32 | 8.3 | odd | 2 | inner |