Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,3,Mod(22,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.22");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.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: | \(13.1607967686\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.19 | ||
Character | \(\chi\) | \(=\) | 483.22 |
Dual form | 483.3.f.a.22.20 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.876983 | −0.438491 | −0.219246 | − | 0.975670i | \(-0.570360\pi\) | ||||
−0.219246 | + | 0.975670i | \(0.570360\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −3.23090 | −0.807725 | ||||||||
\(5\) | 8.50705i | 1.70141i | 0.525644 | + | 0.850705i | \(0.323824\pi\) | ||||
−0.525644 | + | 0.850705i | \(0.676176\pi\) | |||||||
\(6\) | −1.51898 | −0.253163 | ||||||||
\(7\) | 2.64575i | 0.377964i | ||||||||
\(8\) | 6.34138 | 0.792672 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 7.46053i | − | 0.746053i | ||||||
\(11\) | − | 12.5240i | − | 1.13855i | −0.822148 | − | 0.569275i | \(-0.807224\pi\) | ||
0.822148 | − | 0.569275i | \(-0.192776\pi\) | |||||||
\(12\) | −5.59608 | −0.466340 | ||||||||
\(13\) | 23.0788 | 1.77529 | 0.887647 | − | 0.460525i | \(-0.152339\pi\) | ||||
0.887647 | + | 0.460525i | \(0.152339\pi\) | |||||||
\(14\) | − | 2.32028i | − | 0.165734i | ||||||
\(15\) | 14.7346i | 0.982309i | ||||||||
\(16\) | 7.36233 | 0.460145 | ||||||||
\(17\) | 13.0806i | 0.769445i | 0.923032 | + | 0.384723i | \(0.125703\pi\) | ||||
−0.923032 | + | 0.384723i | \(0.874297\pi\) | |||||||
\(18\) | −2.63095 | −0.146164 | ||||||||
\(19\) | 23.2463i | 1.22349i | 0.791056 | + | 0.611744i | \(0.209532\pi\) | ||||
−0.791056 | + | 0.611744i | \(0.790468\pi\) | |||||||
\(20\) | − | 27.4854i | − | 1.37427i | ||||||
\(21\) | 4.58258i | 0.218218i | ||||||||
\(22\) | 10.9834i | 0.499244i | ||||||||
\(23\) | −19.0867 | + | 12.8334i | −0.829858 | + | 0.557974i | ||||
\(24\) | 10.9836 | 0.457649 | ||||||||
\(25\) | −47.3698 | −1.89479 | ||||||||
\(26\) | −20.2397 | −0.778451 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | − | 8.54816i | − | 0.305291i | ||||||
\(29\) | −13.6391 | −0.470315 | −0.235158 | − | 0.971957i | \(-0.575561\pi\) | ||||
−0.235158 | + | 0.971957i | \(0.575561\pi\) | |||||||
\(30\) | − | 12.9220i | − | 0.430734i | ||||||
\(31\) | −23.6204 | −0.761947 | −0.380973 | − | 0.924586i | \(-0.624411\pi\) | ||||
−0.380973 | + | 0.924586i | \(0.624411\pi\) | |||||||
\(32\) | −31.8221 | −0.994442 | ||||||||
\(33\) | − | 21.6923i | − | 0.657342i | ||||||
\(34\) | − | 11.4714i | − | 0.337395i | ||||||
\(35\) | −22.5075 | −0.643072 | ||||||||
\(36\) | −9.69270 | −0.269242 | ||||||||
\(37\) | 38.3359i | 1.03610i | 0.855349 | + | 0.518052i | \(0.173343\pi\) | ||||
−0.855349 | + | 0.518052i | \(0.826657\pi\) | |||||||
\(38\) | − | 20.3866i | − | 0.536489i | ||||||
\(39\) | 39.9737 | 1.02497 | ||||||||
\(40\) | 53.9464i | 1.34866i | ||||||||
\(41\) | −27.0412 | −0.659542 | −0.329771 | − | 0.944061i | \(-0.606972\pi\) | ||||
−0.329771 | + | 0.944061i | \(0.606972\pi\) | |||||||
\(42\) | − | 4.01884i | − | 0.0956867i | ||||||
\(43\) | − | 5.04663i | − | 0.117363i | −0.998277 | − | 0.0586817i | \(-0.981310\pi\) | ||
0.998277 | − | 0.0586817i | \(-0.0186897\pi\) | |||||||
\(44\) | 40.4639i | 0.919635i | ||||||||
\(45\) | 25.5211i | 0.567136i | ||||||||
\(46\) | 16.7387 | − | 11.2547i | 0.363886 | − | 0.244667i | ||||
\(47\) | −21.8114 | −0.464071 | −0.232036 | − | 0.972707i | \(-0.574539\pi\) | ||||
−0.232036 | + | 0.972707i | \(0.574539\pi\) | |||||||
\(48\) | 12.7519 | 0.265665 | ||||||||
\(49\) | −7.00000 | −0.142857 | ||||||||
\(50\) | 41.5425 | 0.830851 | ||||||||
\(51\) | 22.6562i | 0.444239i | ||||||||
\(52\) | −74.5654 | −1.43395 | ||||||||
\(53\) | 55.7900i | 1.05264i | 0.850286 | + | 0.526321i | \(0.176429\pi\) | ||||
−0.850286 | + | 0.526321i | \(0.823571\pi\) | |||||||
\(54\) | −4.55694 | −0.0843877 | ||||||||
\(55\) | 106.543 | 1.93714 | ||||||||
\(56\) | 16.7777i | 0.299602i | ||||||||
\(57\) | 40.2637i | 0.706381i | ||||||||
\(58\) | 11.9613 | 0.206229 | ||||||||
\(59\) | 50.7804 | 0.860685 | 0.430342 | − | 0.902666i | \(-0.358393\pi\) | ||||
0.430342 | + | 0.902666i | \(0.358393\pi\) | |||||||
\(60\) | − | 47.6061i | − | 0.793436i | ||||||
\(61\) | − | 68.5432i | − | 1.12366i | −0.827253 | − | 0.561830i | \(-0.810098\pi\) | ||
0.827253 | − | 0.561830i | \(-0.189902\pi\) | |||||||
\(62\) | 20.7146 | 0.334107 | ||||||||
\(63\) | 7.93725i | 0.125988i | ||||||||
\(64\) | −1.54183 | −0.0240911 | ||||||||
\(65\) | 196.333i | 3.02050i | ||||||||
\(66\) | 19.0238i | 0.288239i | ||||||||
\(67\) | − | 34.3720i | − | 0.513015i | −0.966542 | − | 0.256508i | \(-0.917428\pi\) | ||
0.966542 | − | 0.256508i | \(-0.0825719\pi\) | |||||||
\(68\) | − | 42.2620i | − | 0.621500i | ||||||
\(69\) | −33.0592 | + | 22.2281i | −0.479119 | + | 0.322146i | ||||
\(70\) | 19.7387 | 0.281982 | ||||||||
\(71\) | −103.295 | −1.45486 | −0.727431 | − | 0.686181i | \(-0.759286\pi\) | ||||
−0.727431 | + | 0.686181i | \(0.759286\pi\) | |||||||
\(72\) | 19.0241 | 0.264224 | ||||||||
\(73\) | 128.233 | 1.75662 | 0.878308 | − | 0.478096i | \(-0.158673\pi\) | ||||
0.878308 | + | 0.478096i | \(0.158673\pi\) | |||||||
\(74\) | − | 33.6199i | − | 0.454323i | ||||||
\(75\) | −82.0470 | −1.09396 | ||||||||
\(76\) | − | 75.1064i | − | 0.988242i | ||||||
\(77\) | 33.1355 | 0.430331 | ||||||||
\(78\) | −35.0562 | −0.449439 | ||||||||
\(79\) | − | 130.267i | − | 1.64894i | −0.565903 | − | 0.824472i | \(-0.691472\pi\) | ||
0.565903 | − | 0.824472i | \(-0.308528\pi\) | |||||||
\(80\) | 62.6316i | 0.782896i | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 23.7147 | 0.289204 | ||||||||
\(83\) | 39.2795i | 0.473247i | 0.971601 | + | 0.236624i | \(0.0760409\pi\) | ||||
−0.971601 | + | 0.236624i | \(0.923959\pi\) | |||||||
\(84\) | − | 14.8058i | − | 0.176260i | ||||||
\(85\) | −111.277 | −1.30914 | ||||||||
\(86\) | 4.42581i | 0.0514629i | ||||||||
\(87\) | −23.6237 | −0.271537 | ||||||||
\(88\) | − | 79.4196i | − | 0.902496i | ||||||
\(89\) | 5.35404i | 0.0601578i | 0.999548 | + | 0.0300789i | \(0.00957586\pi\) | ||||
−0.999548 | + | 0.0300789i | \(0.990424\pi\) | |||||||
\(90\) | − | 22.3816i | − | 0.248684i | ||||||
\(91\) | 61.0608i | 0.670998i | ||||||||
\(92\) | 61.6674 | − | 41.4635i | 0.670298 | − | 0.450690i | ||||
\(93\) | −40.9117 | −0.439910 | ||||||||
\(94\) | 19.1282 | 0.203491 | ||||||||
\(95\) | −197.757 | −2.08165 | ||||||||
\(96\) | −55.1176 | −0.574141 | ||||||||
\(97\) | 142.335i | 1.46737i | 0.679487 | + | 0.733687i | \(0.262202\pi\) | ||||
−0.679487 | + | 0.733687i | \(0.737798\pi\) | |||||||
\(98\) | 6.13888 | 0.0626416 | ||||||||
\(99\) | − | 37.5721i | − | 0.379516i | ||||||
\(100\) | 153.047 | 1.53047 | ||||||||
\(101\) | 83.7772 | 0.829477 | 0.414738 | − | 0.909941i | \(-0.363873\pi\) | ||||
0.414738 | + | 0.909941i | \(0.363873\pi\) | |||||||
\(102\) | − | 19.8691i | − | 0.194795i | ||||||
\(103\) | 45.4480i | 0.441243i | 0.975360 | + | 0.220621i | \(0.0708085\pi\) | ||||
−0.975360 | + | 0.220621i | \(0.929192\pi\) | |||||||
\(104\) | 146.351 | 1.40723 | ||||||||
\(105\) | −38.9842 | −0.371278 | ||||||||
\(106\) | − | 48.9269i | − | 0.461574i | ||||||
\(107\) | 93.2200i | 0.871215i | 0.900137 | + | 0.435607i | \(0.143466\pi\) | ||||
−0.900137 | + | 0.435607i | \(0.856534\pi\) | |||||||
\(108\) | −16.7883 | −0.155447 | ||||||||
\(109\) | − | 121.762i | − | 1.11708i | −0.829476 | − | 0.558542i | \(-0.811361\pi\) | ||
0.829476 | − | 0.558542i | \(-0.188639\pi\) | |||||||
\(110\) | −93.4360 | −0.849418 | ||||||||
\(111\) | 66.3997i | 0.598195i | ||||||||
\(112\) | 19.4789i | 0.173919i | ||||||||
\(113\) | 139.100i | 1.23098i | 0.788146 | + | 0.615488i | \(0.211041\pi\) | ||||
−0.788146 | + | 0.615488i | \(0.788959\pi\) | |||||||
\(114\) | − | 35.3106i | − | 0.309742i | ||||||
\(115\) | −109.174 | − | 162.372i | −0.949342 | − | 1.41193i | ||||
\(116\) | 44.0667 | 0.379886 | ||||||||
\(117\) | 69.2365 | 0.591765 | ||||||||
\(118\) | −44.5336 | −0.377403 | ||||||||
\(119\) | −34.6079 | −0.290823 | ||||||||
\(120\) | 93.4379i | 0.778649i | ||||||||
\(121\) | −35.8516 | −0.296294 | ||||||||
\(122\) | 60.1113i | 0.492715i | ||||||||
\(123\) | −46.8368 | −0.380787 | ||||||||
\(124\) | 76.3150 | 0.615444 | ||||||||
\(125\) | − | 190.301i | − | 1.52241i | ||||||
\(126\) | − | 6.96084i | − | 0.0552447i | ||||||
\(127\) | −202.970 | −1.59819 | −0.799096 | − | 0.601204i | \(-0.794688\pi\) | ||||
−0.799096 | + | 0.601204i | \(0.794688\pi\) | |||||||
\(128\) | 128.641 | 1.00501 | ||||||||
\(129\) | − | 8.74102i | − | 0.0677598i | ||||||
\(130\) | − | 172.180i | − | 1.32446i | ||||||
\(131\) | −28.7014 | −0.219095 | −0.109547 | − | 0.993982i | \(-0.534940\pi\) | ||||
−0.109547 | + | 0.993982i | \(0.534940\pi\) | |||||||
\(132\) | 70.0856i | 0.530951i | ||||||||
\(133\) | −61.5039 | −0.462435 | ||||||||
\(134\) | 30.1437i | 0.224953i | ||||||||
\(135\) | 44.2039i | 0.327436i | ||||||||
\(136\) | 82.9488i | 0.609918i | ||||||||
\(137\) | 156.835i | 1.14478i | 0.819982 | + | 0.572389i | \(0.193983\pi\) | ||||
−0.819982 | + | 0.572389i | \(0.806017\pi\) | |||||||
\(138\) | 28.9924 | − | 19.4937i | 0.210090 | − | 0.141258i | ||||
\(139\) | 159.986 | 1.15098 | 0.575488 | − | 0.817810i | \(-0.304812\pi\) | ||||
0.575488 | + | 0.817810i | \(0.304812\pi\) | |||||||
\(140\) | 72.7196 | 0.519426 | ||||||||
\(141\) | −37.7784 | −0.267932 | ||||||||
\(142\) | 90.5881 | 0.637944 | ||||||||
\(143\) | − | 289.040i | − | 2.02126i | ||||||
\(144\) | 22.0870 | 0.153382 | ||||||||
\(145\) | − | 116.029i | − | 0.800199i | ||||||
\(146\) | −112.458 | −0.770261 | ||||||||
\(147\) | −12.1244 | −0.0824786 | ||||||||
\(148\) | − | 123.859i | − | 0.836888i | ||||||
\(149\) | − | 248.689i | − | 1.66905i | −0.550970 | − | 0.834525i | \(-0.685742\pi\) | ||
0.550970 | − | 0.834525i | \(-0.314258\pi\) | |||||||
\(150\) | 71.9538 | 0.479692 | ||||||||
\(151\) | 127.529 | 0.844560 | 0.422280 | − | 0.906465i | \(-0.361230\pi\) | ||||
0.422280 | + | 0.906465i | \(0.361230\pi\) | |||||||
\(152\) | 147.413i | 0.969825i | ||||||||
\(153\) | 39.2417i | 0.256482i | ||||||||
\(154\) | −29.0593 | −0.188696 | ||||||||
\(155\) | − | 200.939i | − | 1.29638i | ||||||
\(156\) | −129.151 | −0.827891 | ||||||||
\(157\) | − | 30.5819i | − | 0.194789i | −0.995246 | − | 0.0973946i | \(-0.968949\pi\) | ||
0.995246 | − | 0.0973946i | \(-0.0310509\pi\) | |||||||
\(158\) | 114.242i | 0.723048i | ||||||||
\(159\) | 96.6311i | 0.607743i | ||||||||
\(160\) | − | 270.712i | − | 1.69195i | ||||||
\(161\) | −33.9540 | − | 50.4988i | −0.210894 | − | 0.313657i | ||||
\(162\) | −7.89285 | −0.0487213 | ||||||||
\(163\) | 272.859 | 1.67398 | 0.836990 | − | 0.547218i | \(-0.184313\pi\) | ||||
0.836990 | + | 0.547218i | \(0.184313\pi\) | |||||||
\(164\) | 87.3676 | 0.532729 | ||||||||
\(165\) | 184.537 | 1.11841 | ||||||||
\(166\) | − | 34.4475i | − | 0.207515i | ||||||
\(167\) | −87.5074 | −0.523996 | −0.261998 | − | 0.965068i | \(-0.584381\pi\) | ||||
−0.261998 | + | 0.965068i | \(0.584381\pi\) | |||||||
\(168\) | 29.0598i | 0.172975i | ||||||||
\(169\) | 363.632 | 2.15167 | ||||||||
\(170\) | 97.5880 | 0.574047 | ||||||||
\(171\) | 69.7388i | 0.407829i | ||||||||
\(172\) | 16.3052i | 0.0947974i | ||||||||
\(173\) | 255.005 | 1.47402 | 0.737008 | − | 0.675884i | \(-0.236238\pi\) | ||||
0.737008 | + | 0.675884i | \(0.236238\pi\) | |||||||
\(174\) | 20.7176 | 0.119067 | ||||||||
\(175\) | − | 125.329i | − | 0.716165i | ||||||
\(176\) | − | 92.2061i | − | 0.523898i | ||||||
\(177\) | 87.9543 | 0.496917 | ||||||||
\(178\) | − | 4.69541i | − | 0.0263787i | ||||||
\(179\) | −341.018 | −1.90513 | −0.952564 | − | 0.304337i | \(-0.901565\pi\) | ||||
−0.952564 | + | 0.304337i | \(0.901565\pi\) | |||||||
\(180\) | − | 82.4563i | − | 0.458090i | ||||||
\(181\) | 292.617i | 1.61667i | 0.588725 | + | 0.808334i | \(0.299630\pi\) | ||||
−0.588725 | + | 0.808334i | \(0.700370\pi\) | |||||||
\(182\) | − | 53.5493i | − | 0.294227i | ||||||
\(183\) | − | 118.720i | − | 0.648745i | ||||||
\(184\) | −121.036 | + | 81.3814i | −0.657806 | + | 0.442290i | ||||
\(185\) | −326.125 | −1.76284 | ||||||||
\(186\) | 35.8788 | 0.192897 | ||||||||
\(187\) | 163.822 | 0.876051 | ||||||||
\(188\) | 70.4703 | 0.374842 | ||||||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 173.430 | 0.912787 | ||||||||
\(191\) | 115.651i | 0.605504i | 0.953069 | + | 0.302752i | \(0.0979054\pi\) | ||||
−0.953069 | + | 0.302752i | \(0.902095\pi\) | |||||||
\(192\) | −2.67053 | −0.0139090 | ||||||||
\(193\) | −134.250 | −0.695598 | −0.347799 | − | 0.937569i | \(-0.613071\pi\) | ||||
−0.347799 | + | 0.937569i | \(0.613071\pi\) | |||||||
\(194\) | − | 124.826i | − | 0.643431i | ||||||
\(195\) | 340.058i | 1.74389i | ||||||||
\(196\) | 22.6163 | 0.115389 | ||||||||
\(197\) | 186.004 | 0.944182 | 0.472091 | − | 0.881550i | \(-0.343499\pi\) | ||||
0.472091 | + | 0.881550i | \(0.343499\pi\) | |||||||
\(198\) | 32.9501i | 0.166415i | ||||||||
\(199\) | 51.5488i | 0.259039i | 0.991577 | + | 0.129520i | \(0.0413435\pi\) | ||||
−0.991577 | + | 0.129520i | \(0.958656\pi\) | |||||||
\(200\) | −300.390 | −1.50195 | ||||||||
\(201\) | − | 59.5341i | − | 0.296190i | ||||||
\(202\) | −73.4711 | −0.363719 | ||||||||
\(203\) | − | 36.0858i | − | 0.177763i | ||||||
\(204\) | − | 73.2000i | − | 0.358823i | ||||||
\(205\) | − | 230.041i | − | 1.12215i | ||||||
\(206\) | − | 39.8571i | − | 0.193481i | ||||||
\(207\) | −57.2602 | + | 38.5002i | −0.276619 | + | 0.185991i | ||||
\(208\) | 169.914 | 0.816893 | ||||||||
\(209\) | 291.137 | 1.39300 | ||||||||
\(210\) | 34.1885 | 0.162802 | ||||||||
\(211\) | 348.367 | 1.65103 | 0.825513 | − | 0.564382i | \(-0.190886\pi\) | ||||
0.825513 | + | 0.564382i | \(0.190886\pi\) | |||||||
\(212\) | − | 180.252i | − | 0.850245i | ||||||
\(213\) | −178.912 | −0.839964 | ||||||||
\(214\) | − | 81.7523i | − | 0.382020i | ||||||
\(215\) | 42.9319 | 0.199683 | ||||||||
\(216\) | 32.9508 | 0.152550 | ||||||||
\(217\) | − | 62.4936i | − | 0.287989i | ||||||
\(218\) | 106.783i | 0.489832i | ||||||||
\(219\) | 222.106 | 1.01418 | ||||||||
\(220\) | −344.229 | −1.56468 | ||||||||
\(221\) | 301.884i | 1.36599i | ||||||||
\(222\) | − | 58.2314i | − | 0.262303i | ||||||
\(223\) | −238.570 | −1.06982 | −0.534911 | − | 0.844909i | \(-0.679655\pi\) | ||||
−0.534911 | + | 0.844909i | \(0.679655\pi\) | |||||||
\(224\) | − | 84.1935i | − | 0.375864i | ||||||
\(225\) | −142.109 | −0.631598 | ||||||||
\(226\) | − | 121.989i | − | 0.539773i | ||||||
\(227\) | − | 119.769i | − | 0.527615i | −0.964575 | − | 0.263807i | \(-0.915022\pi\) | ||
0.964575 | − | 0.263807i | \(-0.0849783\pi\) | |||||||
\(228\) | − | 130.088i | − | 0.570562i | ||||||
\(229\) | − | 224.050i | − | 0.978382i | −0.872177 | − | 0.489191i | \(-0.837292\pi\) | ||
0.872177 | − | 0.489191i | \(-0.162708\pi\) | |||||||
\(230\) | 95.7440 | + | 142.397i | 0.416278 | + | 0.619119i | ||||
\(231\) | 57.3924 | 0.248452 | ||||||||
\(232\) | −86.4910 | −0.372806 | ||||||||
\(233\) | 352.648 | 1.51351 | 0.756756 | − | 0.653697i | \(-0.226783\pi\) | ||||
0.756756 | + | 0.653697i | \(0.226783\pi\) | |||||||
\(234\) | −60.7192 | −0.259484 | ||||||||
\(235\) | − | 185.550i | − | 0.789575i | ||||||
\(236\) | −164.066 | −0.695197 | ||||||||
\(237\) | − | 225.628i | − | 0.952018i | ||||||
\(238\) | 30.3506 | 0.127523 | ||||||||
\(239\) | −365.595 | −1.52969 | −0.764844 | − | 0.644216i | \(-0.777184\pi\) | ||||
−0.764844 | + | 0.644216i | \(0.777184\pi\) | |||||||
\(240\) | 108.481i | 0.452005i | ||||||||
\(241\) | − | 91.4962i | − | 0.379652i | −0.981818 | − | 0.189826i | \(-0.939208\pi\) | ||
0.981818 | − | 0.189826i | \(-0.0607924\pi\) | |||||||
\(242\) | 31.4412 | 0.129922 | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 221.456i | 0.907608i | ||||||||
\(245\) | − | 59.5493i | − | 0.243058i | ||||||
\(246\) | 41.0751 | 0.166972 | ||||||||
\(247\) | 536.496i | 2.17205i | ||||||||
\(248\) | −149.786 | −0.603974 | ||||||||
\(249\) | 68.0342i | 0.273230i | ||||||||
\(250\) | 166.891i | 0.667563i | ||||||||
\(251\) | − | 219.581i | − | 0.874826i | −0.899261 | − | 0.437413i | \(-0.855895\pi\) | ||
0.899261 | − | 0.437413i | \(-0.144105\pi\) | |||||||
\(252\) | − | 25.6445i | − | 0.101764i | ||||||
\(253\) | 160.726 | + | 239.043i | 0.635281 | + | 0.944834i | ||||
\(254\) | 178.001 | 0.700793 | ||||||||
\(255\) | −192.737 | −0.755833 | ||||||||
\(256\) | −106.648 | −0.416595 | ||||||||
\(257\) | −358.124 | −1.39348 | −0.696740 | − | 0.717324i | \(-0.745367\pi\) | ||||
−0.696740 | + | 0.717324i | \(0.745367\pi\) | |||||||
\(258\) | 7.66572i | 0.0297121i | ||||||||
\(259\) | −101.427 | −0.391611 | ||||||||
\(260\) | − | 634.331i | − | 2.43973i | ||||||
\(261\) | −40.9174 | −0.156772 | ||||||||
\(262\) | 25.1706 | 0.0960711 | ||||||||
\(263\) | − | 12.2132i | − | 0.0464378i | −0.999730 | − | 0.0232189i | \(-0.992609\pi\) | ||
0.999730 | − | 0.0232189i | \(-0.00739148\pi\) | |||||||
\(264\) | − | 137.559i | − | 0.521056i | ||||||
\(265\) | −474.608 | −1.79097 | ||||||||
\(266\) | 53.9378 | 0.202774 | ||||||||
\(267\) | 9.27348i | 0.0347321i | ||||||||
\(268\) | 111.053i | 0.414376i | ||||||||
\(269\) | 76.6918 | 0.285100 | 0.142550 | − | 0.989788i | \(-0.454470\pi\) | ||||
0.142550 | + | 0.989788i | \(0.454470\pi\) | |||||||
\(270\) | − | 38.7661i | − | 0.143578i | ||||||
\(271\) | 182.371 | 0.672955 | 0.336477 | − | 0.941692i | \(-0.390764\pi\) | ||||
0.336477 | + | 0.941692i | \(0.390764\pi\) | |||||||
\(272\) | 96.3034i | 0.354057i | ||||||||
\(273\) | 105.760i | 0.387401i | ||||||||
\(274\) | − | 137.541i | − | 0.501975i | ||||||
\(275\) | 593.262i | 2.15731i | ||||||||
\(276\) | 106.811 | − | 71.8168i | 0.386996 | − | 0.260206i | ||||
\(277\) | −267.169 | −0.964510 | −0.482255 | − | 0.876031i | \(-0.660182\pi\) | ||||
−0.482255 | + | 0.876031i | \(0.660182\pi\) | |||||||
\(278\) | −140.305 | −0.504693 | ||||||||
\(279\) | −70.8611 | −0.253982 | ||||||||
\(280\) | −142.729 | −0.509745 | ||||||||
\(281\) | − | 307.421i | − | 1.09402i | −0.837125 | − | 0.547012i | \(-0.815765\pi\) | ||
0.837125 | − | 0.547012i | \(-0.184235\pi\) | |||||||
\(282\) | 33.1310 | 0.117486 | ||||||||
\(283\) | − | 135.101i | − | 0.477389i | −0.971095 | − | 0.238694i | \(-0.923281\pi\) | ||
0.971095 | − | 0.238694i | \(-0.0767194\pi\) | |||||||
\(284\) | 333.736 | 1.17513 | ||||||||
\(285\) | −342.525 | −1.20184 | ||||||||
\(286\) | 253.483i | 0.886305i | ||||||||
\(287\) | − | 71.5444i | − | 0.249284i | ||||||
\(288\) | −95.4664 | −0.331481 | ||||||||
\(289\) | 117.899 | 0.407954 | ||||||||
\(290\) | 101.755i | 0.350880i | ||||||||
\(291\) | 246.532i | 0.847189i | ||||||||
\(292\) | −414.308 | −1.41886 | ||||||||
\(293\) | 430.595i | 1.46961i | 0.678280 | + | 0.734803i | \(0.262726\pi\) | ||||
−0.678280 | + | 0.734803i | \(0.737274\pi\) | |||||||
\(294\) | 10.6329 | 0.0361662 | ||||||||
\(295\) | 431.991i | 1.46438i | ||||||||
\(296\) | 243.102i | 0.821291i | ||||||||
\(297\) | − | 65.0768i | − | 0.219114i | ||||||
\(298\) | 218.096i | 0.731864i | ||||||||
\(299\) | −440.499 | + | 296.180i | −1.47324 | + | 0.990568i | ||||
\(300\) | 265.086 | 0.883619 | ||||||||
\(301\) | 13.3521 | 0.0443592 | ||||||||
\(302\) | −111.840 | −0.370333 | ||||||||
\(303\) | 145.106 | 0.478899 | ||||||||
\(304\) | 171.147i | 0.562982i | ||||||||
\(305\) | 583.101 | 1.91181 | ||||||||
\(306\) | − | 34.4143i | − | 0.112465i | ||||||
\(307\) | 197.821 | 0.644368 | 0.322184 | − | 0.946677i | \(-0.395583\pi\) | ||||
0.322184 | + | 0.946677i | \(0.395583\pi\) | |||||||
\(308\) | −107.057 | −0.347589 | ||||||||
\(309\) | 78.7182i | 0.254752i | ||||||||
\(310\) | 176.220i | 0.568453i | ||||||||
\(311\) | 113.735 | 0.365707 | 0.182853 | − | 0.983140i | \(-0.441467\pi\) | ||||
0.182853 | + | 0.983140i | \(0.441467\pi\) | |||||||
\(312\) | 253.488 | 0.812462 | ||||||||
\(313\) | 360.036i | 1.15027i | 0.818057 | + | 0.575137i | \(0.195051\pi\) | ||||
−0.818057 | + | 0.575137i | \(0.804949\pi\) | |||||||
\(314\) | 26.8198i | 0.0854134i | ||||||||
\(315\) | −67.5226 | −0.214357 | ||||||||
\(316\) | 420.878i | 1.33189i | ||||||||
\(317\) | 379.702 | 1.19780 | 0.598899 | − | 0.800824i | \(-0.295605\pi\) | ||||
0.598899 | + | 0.800824i | \(0.295605\pi\) | |||||||
\(318\) | − | 84.7438i | − | 0.266490i | ||||||
\(319\) | 170.817i | 0.535477i | ||||||||
\(320\) | − | 13.1164i | − | 0.0409888i | ||||||
\(321\) | 161.462i | 0.502996i | ||||||||
\(322\) | 29.7771 | + | 44.2866i | 0.0924754 | + | 0.137536i | ||||
\(323\) | −304.074 | −0.941407 | ||||||||
\(324\) | −29.0781 | −0.0897473 | ||||||||
\(325\) | −1093.24 | −3.36381 | ||||||||
\(326\) | −239.292 | −0.734026 | ||||||||
\(327\) | − | 210.898i | − | 0.644949i | ||||||
\(328\) | −171.479 | −0.522801 | ||||||||
\(329\) | − | 57.7074i | − | 0.175402i | ||||||
\(330\) | −161.836 | −0.490412 | ||||||||
\(331\) | 406.011 | 1.22662 | 0.613309 | − | 0.789843i | \(-0.289838\pi\) | ||||
0.613309 | + | 0.789843i | \(0.289838\pi\) | |||||||
\(332\) | − | 126.908i | − | 0.382254i | ||||||
\(333\) | 115.008i | 0.345368i | ||||||||
\(334\) | 76.7425 | 0.229768 | ||||||||
\(335\) | 292.405 | 0.872849 | ||||||||
\(336\) | 33.7384i | 0.100412i | ||||||||
\(337\) | 471.913i | 1.40034i | 0.713978 | + | 0.700168i | \(0.246892\pi\) | ||||
−0.713978 | + | 0.700168i | \(0.753108\pi\) | |||||||
\(338\) | −318.899 | −0.943488 | ||||||||
\(339\) | 240.929i | 0.710705i | ||||||||
\(340\) | 359.525 | 1.05743 | ||||||||
\(341\) | 295.822i | 0.867514i | ||||||||
\(342\) | − | 61.1597i | − | 0.178830i | ||||||
\(343\) | − | 18.5203i | − | 0.0539949i | ||||||
\(344\) | − | 32.0026i | − | 0.0930307i | ||||||
\(345\) | −189.096 | − | 281.236i | −0.548103 | − | 0.815177i | ||||
\(346\) | −223.635 | −0.646343 | ||||||||
\(347\) | 372.428 | 1.07328 | 0.536639 | − | 0.843812i | \(-0.319694\pi\) | ||||
0.536639 | + | 0.843812i | \(0.319694\pi\) | |||||||
\(348\) | 76.3258 | 0.219327 | ||||||||
\(349\) | 33.8607 | 0.0970222 | 0.0485111 | − | 0.998823i | \(-0.484552\pi\) | ||||
0.0485111 | + | 0.998823i | \(0.484552\pi\) | |||||||
\(350\) | 109.911i | 0.314032i | ||||||||
\(351\) | 119.921 | 0.341655 | ||||||||
\(352\) | 398.542i | 1.13222i | ||||||||
\(353\) | 128.147 | 0.363023 | 0.181512 | − | 0.983389i | \(-0.441901\pi\) | ||||
0.181512 | + | 0.983389i | \(0.441901\pi\) | |||||||
\(354\) | −77.1344 | −0.217894 | ||||||||
\(355\) | − | 878.736i | − | 2.47531i | ||||||
\(356\) | − | 17.2984i | − | 0.0485910i | ||||||
\(357\) | −59.9427 | −0.167907 | ||||||||
\(358\) | 299.067 | 0.835383 | ||||||||
\(359\) | − | 495.508i | − | 1.38025i | −0.723692 | − | 0.690123i | \(-0.757556\pi\) | ||
0.723692 | − | 0.690123i | \(-0.242444\pi\) | |||||||
\(360\) | 161.839i | 0.449553i | ||||||||
\(361\) | −179.389 | −0.496923 | ||||||||
\(362\) | − | 256.620i | − | 0.708895i | ||||||
\(363\) | −62.0967 | −0.171065 | ||||||||
\(364\) | − | 197.281i | − | 0.541982i | ||||||
\(365\) | 1090.88i | 2.98872i | ||||||||
\(366\) | 104.116i | 0.284469i | ||||||||
\(367\) | − | 551.754i | − | 1.50342i | −0.659495 | − | 0.751709i | \(-0.729230\pi\) | ||
0.659495 | − | 0.751709i | \(-0.270770\pi\) | |||||||
\(368\) | −140.523 | + | 94.4837i | −0.381855 | + | 0.256749i | ||||
\(369\) | −81.1237 | −0.219847 | ||||||||
\(370\) | 286.006 | 0.772989 | ||||||||
\(371\) | −147.606 | −0.397861 | ||||||||
\(372\) | 132.182 | 0.355327 | ||||||||
\(373\) | − | 351.979i | − | 0.943643i | −0.881694 | − | 0.471821i | \(-0.843597\pi\) | ||
0.881694 | − | 0.471821i | \(-0.156403\pi\) | |||||||
\(374\) | −143.669 | −0.384141 | ||||||||
\(375\) | − | 329.611i | − | 0.878963i | ||||||
\(376\) | −138.314 | −0.367856 | ||||||||
\(377\) | −314.775 | −0.834948 | ||||||||
\(378\) | − | 12.0565i | − | 0.0318956i | ||||||
\(379\) | − | 42.9132i | − | 0.113227i | −0.998396 | − | 0.0566137i | \(-0.981970\pi\) | ||
0.998396 | − | 0.0566137i | \(-0.0180303\pi\) | |||||||
\(380\) | 638.934 | 1.68140 | ||||||||
\(381\) | −351.555 | −0.922716 | ||||||||
\(382\) | − | 101.424i | − | 0.265508i | ||||||
\(383\) | 57.1916i | 0.149325i | 0.997209 | + | 0.0746626i | \(0.0237880\pi\) | ||||
−0.997209 | + | 0.0746626i | \(0.976212\pi\) | |||||||
\(384\) | 222.812 | 0.580240 | ||||||||
\(385\) | 281.885i | 0.732169i | ||||||||
\(386\) | 117.735 | 0.305014 | ||||||||
\(387\) | − | 15.1399i | − | 0.0391211i | ||||||
\(388\) | − | 459.871i | − | 1.18524i | ||||||
\(389\) | − | 360.807i | − | 0.927524i | −0.885960 | − | 0.463762i | \(-0.846499\pi\) | ||
0.885960 | − | 0.463762i | \(-0.153501\pi\) | |||||||
\(390\) | − | 298.225i | − | 0.764680i | ||||||
\(391\) | −167.868 | − | 249.665i | −0.429330 | − | 0.638530i | ||||
\(392\) | −44.3896 | −0.113239 | ||||||||
\(393\) | −49.7123 | −0.126494 | ||||||||
\(394\) | −163.122 | −0.414016 | ||||||||
\(395\) | 1108.18 | 2.80553 | ||||||||
\(396\) | 121.392i | 0.306545i | ||||||||
\(397\) | 130.989 | 0.329948 | 0.164974 | − | 0.986298i | \(-0.447246\pi\) | ||||
0.164974 | + | 0.986298i | \(0.447246\pi\) | |||||||
\(398\) | − | 45.2074i | − | 0.113587i | ||||||
\(399\) | −106.528 | −0.266987 | ||||||||
\(400\) | −348.752 | −0.871880 | ||||||||
\(401\) | 439.104i | 1.09502i | 0.836799 | + | 0.547511i | \(0.184425\pi\) | ||||
−0.836799 | + | 0.547511i | \(0.815575\pi\) | |||||||
\(402\) | 52.2104i | 0.129877i | ||||||||
\(403\) | −545.130 | −1.35268 | ||||||||
\(404\) | −270.676 | −0.669989 | ||||||||
\(405\) | 76.5634i | 0.189045i | ||||||||
\(406\) | 31.6466i | 0.0779473i | ||||||||
\(407\) | 480.120 | 1.17966 | ||||||||
\(408\) | 143.672i | 0.352136i | ||||||||
\(409\) | 349.213 | 0.853822 | 0.426911 | − | 0.904294i | \(-0.359602\pi\) | ||||
0.426911 | + | 0.904294i | \(0.359602\pi\) | |||||||
\(410\) | 201.742i | 0.492054i | ||||||||
\(411\) | 271.645i | 0.660938i | ||||||||
\(412\) | − | 146.838i | − | 0.356403i | ||||||
\(413\) | 134.352i | 0.325308i | ||||||||
\(414\) | 50.2162 | − | 33.7640i | 0.121295 | − | 0.0815556i | ||||
\(415\) | −334.153 | −0.805188 | ||||||||
\(416\) | −734.417 | −1.76543 | ||||||||
\(417\) | 277.103 | 0.664516 | ||||||||
\(418\) | −255.322 | −0.610819 | ||||||||
\(419\) | 286.780i | 0.684438i | 0.939620 | + | 0.342219i | \(0.111178\pi\) | ||||
−0.939620 | + | 0.342219i | \(0.888822\pi\) | |||||||
\(420\) | 125.954 | 0.299891 | ||||||||
\(421\) | − | 242.493i | − | 0.575993i | −0.957631 | − | 0.287997i | \(-0.907011\pi\) | ||
0.957631 | − | 0.287997i | \(-0.0929892\pi\) | |||||||
\(422\) | −305.512 | −0.723961 | ||||||||
\(423\) | −65.4341 | −0.154690 | ||||||||
\(424\) | 353.785i | 0.834400i | ||||||||
\(425\) | − | 619.624i | − | 1.45794i | ||||||
\(426\) | 156.903 | 0.368317 | ||||||||
\(427\) | 181.348 | 0.424703 | ||||||||
\(428\) | − | 301.185i | − | 0.703702i | ||||||
\(429\) | − | 500.632i | − | 1.16697i | ||||||
\(430\) | −37.6505 | −0.0875594 | ||||||||
\(431\) | − | 332.399i | − | 0.771227i | −0.922660 | − | 0.385614i | \(-0.873990\pi\) | ||
0.922660 | − | 0.385614i | \(-0.126010\pi\) | |||||||
\(432\) | 38.2558 | 0.0885550 | ||||||||
\(433\) | − | 478.058i | − | 1.10406i | −0.833824 | − | 0.552030i | \(-0.813854\pi\) | ||
0.833824 | − | 0.552030i | \(-0.186146\pi\) | |||||||
\(434\) | 54.8058i | 0.126281i | ||||||||
\(435\) | − | 200.968i | − | 0.461995i | ||||||
\(436\) | 393.401i | 0.902297i | ||||||||
\(437\) | −298.329 | − | 443.696i | −0.682675 | − | 1.01532i | ||||
\(438\) | −194.783 | −0.444710 | ||||||||
\(439\) | −63.2723 | −0.144128 | −0.0720641 | − | 0.997400i | \(-0.522959\pi\) | ||||
−0.0720641 | + | 0.997400i | \(0.522959\pi\) | |||||||
\(440\) | 675.627 | 1.53551 | ||||||||
\(441\) | −21.0000 | −0.0476190 | ||||||||
\(442\) | − | 264.747i | − | 0.598975i | ||||||
\(443\) | 228.582 | 0.515987 | 0.257993 | − | 0.966147i | \(-0.416939\pi\) | ||||
0.257993 | + | 0.966147i | \(0.416939\pi\) | |||||||
\(444\) | − | 214.531i | − | 0.483177i | ||||||
\(445\) | −45.5471 | −0.102353 | ||||||||
\(446\) | 209.222 | 0.469108 | ||||||||
\(447\) | − | 430.741i | − | 0.963627i | ||||||
\(448\) | − | 4.07930i | − | 0.00910558i | ||||||
\(449\) | −100.730 | −0.224343 | −0.112171 | − | 0.993689i | \(-0.535781\pi\) | ||||
−0.112171 | + | 0.993689i | \(0.535781\pi\) | |||||||
\(450\) | 124.628 | 0.276950 | ||||||||
\(451\) | 338.666i | 0.750921i | ||||||||
\(452\) | − | 449.419i | − | 0.994291i | ||||||
\(453\) | 220.886 | 0.487607 | ||||||||
\(454\) | 105.035i | 0.231354i | ||||||||
\(455\) | −519.447 | −1.14164 | ||||||||
\(456\) | 255.327i | 0.559929i | ||||||||
\(457\) | 15.9353i | 0.0348695i | 0.999848 | + | 0.0174347i | \(0.00554993\pi\) | ||||
−0.999848 | + | 0.0174347i | \(0.994450\pi\) | |||||||
\(458\) | 196.488i | 0.429012i | ||||||||
\(459\) | 67.9686i | 0.148080i | ||||||||
\(460\) | 352.732 | + | 524.607i | 0.766808 | + | 1.14045i | ||||
\(461\) | 166.928 | 0.362100 | 0.181050 | − | 0.983474i | \(-0.442050\pi\) | ||||
0.181050 | + | 0.983474i | \(0.442050\pi\) | |||||||
\(462\) | −50.3321 | −0.108944 | ||||||||
\(463\) | 540.984 | 1.16843 | 0.584216 | − | 0.811598i | \(-0.301402\pi\) | ||||
0.584216 | + | 0.811598i | \(0.301402\pi\) | |||||||
\(464\) | −100.416 | −0.216413 | ||||||||
\(465\) | − | 348.037i | − | 0.748467i | ||||||
\(466\) | −309.267 | −0.663662 | ||||||||
\(467\) | − | 177.590i | − | 0.380279i | −0.981757 | − | 0.190139i | \(-0.939106\pi\) | ||
0.981757 | − | 0.190139i | \(-0.0608940\pi\) | |||||||
\(468\) | −223.696 | −0.477983 | ||||||||
\(469\) | 90.9399 | 0.193902 | ||||||||
\(470\) | 162.724i | 0.346222i | ||||||||
\(471\) | − | 52.9694i | − | 0.112462i | ||||||
\(472\) | 322.018 | 0.682241 | ||||||||
\(473\) | −63.2042 | −0.133624 | ||||||||
\(474\) | 197.872i | 0.417452i | ||||||||
\(475\) | − | 1101.17i | − | 2.31826i | ||||||
\(476\) | 111.815 | 0.234905 | ||||||||
\(477\) | 167.370i | 0.350881i | ||||||||
\(478\) | 320.621 | 0.670755 | ||||||||
\(479\) | 67.8651i | 0.141681i | 0.997488 | + | 0.0708404i | \(0.0225681\pi\) | ||||
−0.997488 | + | 0.0708404i | \(0.977432\pi\) | |||||||
\(480\) | − | 468.888i | − | 0.976849i | ||||||
\(481\) | 884.746i | 1.83939i | ||||||||
\(482\) | 80.2406i | 0.166474i | ||||||||
\(483\) | −58.8100 | − | 87.4664i | −0.121760 | − | 0.181090i | ||||
\(484\) | 115.833 | 0.239324 | ||||||||
\(485\) | −1210.85 | −2.49660 | ||||||||
\(486\) | −13.6708 | −0.0281292 | ||||||||
\(487\) | −406.664 | −0.835039 | −0.417520 | − | 0.908668i | \(-0.637100\pi\) | ||||
−0.417520 | + | 0.908668i | \(0.637100\pi\) | |||||||
\(488\) | − | 434.659i | − | 0.890694i | ||||||
\(489\) | 472.605 | 0.966473 | ||||||||
\(490\) | 52.2237i | 0.106579i | ||||||||
\(491\) | −23.5446 | −0.0479524 | −0.0239762 | − | 0.999713i | \(-0.507633\pi\) | ||||
−0.0239762 | + | 0.999713i | \(0.507633\pi\) | |||||||
\(492\) | 151.325 | 0.307571 | ||||||||
\(493\) | − | 178.408i | − | 0.361882i | ||||||
\(494\) | − | 470.498i | − | 0.952425i | ||||||
\(495\) | 319.628 | 0.645713 | ||||||||
\(496\) | −173.901 | −0.350606 | ||||||||
\(497\) | − | 273.293i | − | 0.549886i | ||||||
\(498\) | − | 59.6648i | − | 0.119809i | ||||||
\(499\) | 485.859 | 0.973665 | 0.486832 | − | 0.873495i | \(-0.338152\pi\) | ||||
0.486832 | + | 0.873495i | \(0.338152\pi\) | |||||||
\(500\) | 614.844i | 1.22969i | ||||||||
\(501\) | −151.567 | −0.302529 | ||||||||
\(502\) | 192.569i | 0.383604i | ||||||||
\(503\) | − | 19.6069i | − | 0.0389799i | −0.999810 | − | 0.0194900i | \(-0.993796\pi\) | ||
0.999810 | − | 0.0194900i | \(-0.00620424\pi\) | |||||||
\(504\) | 50.3331i | 0.0998673i | ||||||||
\(505\) | 712.696i | 1.41128i | ||||||||
\(506\) | −140.954 | − | 209.637i | −0.278565 | − | 0.414302i | ||||
\(507\) | 629.829 | 1.24227 | ||||||||
\(508\) | 655.777 | 1.29090 | ||||||||
\(509\) | −271.092 | −0.532597 | −0.266299 | − | 0.963891i | \(-0.585801\pi\) | ||||
−0.266299 | + | 0.963891i | \(0.585801\pi\) | |||||||
\(510\) | 169.027 | 0.331426 | ||||||||
\(511\) | 339.272i | 0.663938i | ||||||||
\(512\) | −421.034 | −0.822332 | ||||||||
\(513\) | 120.791i | 0.235460i | ||||||||
\(514\) | 314.069 | 0.611029 | ||||||||
\(515\) | −386.628 | −0.750734 | ||||||||
\(516\) | 28.2414i | 0.0547313i | ||||||||
\(517\) | 273.166i | 0.528368i | ||||||||
\(518\) | 88.9499 | 0.171718 | ||||||||
\(519\) | 441.681 | 0.851023 | ||||||||
\(520\) | 1245.02i | 2.39427i | ||||||||
\(521\) | 262.852i | 0.504514i | 0.967660 | + | 0.252257i | \(0.0811729\pi\) | ||||
−0.967660 | + | 0.252257i | \(0.918827\pi\) | |||||||
\(522\) | 35.8839 | 0.0687431 | ||||||||
\(523\) | 699.055i | 1.33662i | 0.743881 | + | 0.668312i | \(0.232983\pi\) | ||||
−0.743881 | + | 0.668312i | \(0.767017\pi\) | |||||||
\(524\) | 92.7314 | 0.176968 | ||||||||
\(525\) | − | 217.076i | − | 0.413478i | ||||||
\(526\) | 10.7107i | 0.0203626i | ||||||||
\(527\) | − | 308.968i | − | 0.586276i | ||||||
\(528\) | − | 159.706i | − | 0.302473i | ||||||
\(529\) | 199.608 | − | 489.896i | 0.377330 | − | 0.926079i | ||||
\(530\) | 416.223 | 0.785327 | ||||||||
\(531\) | 152.341 | 0.286895 | ||||||||
\(532\) | 198.713 | 0.373520 | ||||||||
\(533\) | −624.080 | −1.17088 | ||||||||
\(534\) | − | 8.13268i | − | 0.0152297i | ||||||
\(535\) | −793.027 | −1.48229 | ||||||||
\(536\) | − | 217.966i | − | 0.406653i | ||||||
\(537\) | −590.661 | −1.09993 | ||||||||
\(538\) | −67.2574 | −0.125014 | ||||||||
\(539\) | 87.6683i | 0.162650i | ||||||||
\(540\) | − | 142.818i | − | 0.264479i | ||||||
\(541\) | −128.516 | −0.237553 | −0.118777 | − | 0.992921i | \(-0.537897\pi\) | ||||
−0.118777 | + | 0.992921i | \(0.537897\pi\) | |||||||
\(542\) | −159.936 | −0.295085 | ||||||||
\(543\) | 506.827i | 0.933383i | ||||||||
\(544\) | − | 416.252i | − | 0.765168i | ||||||
\(545\) | 1035.84 | 1.90062 | ||||||||
\(546\) | − | 92.7501i | − | 0.169872i | ||||||
\(547\) | 827.377 | 1.51257 | 0.756286 | − | 0.654241i | \(-0.227012\pi\) | ||||
0.756286 | + | 0.654241i | \(0.227012\pi\) | |||||||
\(548\) | − | 506.717i | − | 0.924666i | ||||||
\(549\) | − | 205.630i | − | 0.374553i | ||||||
\(550\) | − | 520.280i | − | 0.945964i | ||||||
\(551\) | − | 317.059i | − | 0.575425i | ||||||
\(552\) | −209.641 | + | 140.957i | −0.379784 | + | 0.255356i | ||||
\(553\) | 344.653 | 0.623242 | ||||||||
\(554\) | 234.303 | 0.422929 | ||||||||
\(555\) | −564.865 | −1.01777 | ||||||||
\(556\) | −516.898 | −0.929672 | ||||||||
\(557\) | 9.93497i | 0.0178366i | 0.999960 | + | 0.00891828i | \(0.00283882\pi\) | ||||
−0.999960 | + | 0.00891828i | \(0.997161\pi\) | |||||||
\(558\) | 62.1439 | 0.111369 | ||||||||
\(559\) | − | 116.470i | − | 0.208355i | ||||||
\(560\) | −165.708 | −0.295907 | ||||||||
\(561\) | 283.747 | 0.505788 | ||||||||
\(562\) | 269.603i | 0.479720i | ||||||||
\(563\) | 30.4387i | 0.0540651i | 0.999635 | + | 0.0270326i | \(0.00860578\pi\) | ||||
−0.999635 | + | 0.0270326i | \(0.991394\pi\) | |||||||
\(564\) | 122.058 | 0.216415 | ||||||||
\(565\) | −1183.33 | −2.09439 | ||||||||
\(566\) | 118.481i | 0.209331i | ||||||||
\(567\) | 23.8118i | 0.0419961i | ||||||||
\(568\) | −655.033 | −1.15323 | ||||||||
\(569\) | 575.238i | 1.01096i | 0.862837 | + | 0.505481i | \(0.168685\pi\) | ||||
−0.862837 | + | 0.505481i | \(0.831315\pi\) | |||||||
\(570\) | 300.389 | 0.526998 | ||||||||
\(571\) | 501.266i | 0.877875i | 0.898518 | + | 0.438937i | \(0.144645\pi\) | ||||
−0.898518 | + | 0.438937i | \(0.855355\pi\) | |||||||
\(572\) | 933.860i | 1.63262i | ||||||||
\(573\) | 200.314i | 0.349588i | ||||||||
\(574\) | 62.7432i | 0.109309i | ||||||||
\(575\) | 904.136 | − | 607.916i | 1.57241 | − | 1.05725i | ||||
\(576\) | −4.62549 | −0.00803036 | ||||||||
\(577\) | 152.556 | 0.264396 | 0.132198 | − | 0.991223i | \(-0.457797\pi\) | ||||
0.132198 | + | 0.991223i | \(0.457797\pi\) | |||||||
\(578\) | −103.395 | −0.178884 | ||||||||
\(579\) | −232.529 | −0.401604 | ||||||||
\(580\) | 374.878i | 0.646341i | ||||||||
\(581\) | −103.924 | −0.178871 | ||||||||
\(582\) | − | 216.204i | − | 0.371485i | ||||||
\(583\) | 698.716 | 1.19848 | ||||||||
\(584\) | 813.173 | 1.39242 | ||||||||
\(585\) | 588.998i | 1.00683i | ||||||||
\(586\) | − | 377.624i | − | 0.644410i | ||||||
\(587\) | −636.140 | −1.08371 | −0.541857 | − | 0.840471i | \(-0.682278\pi\) | ||||
−0.541857 | + | 0.840471i | \(0.682278\pi\) | |||||||
\(588\) | 39.1726 | 0.0666201 | ||||||||
\(589\) | − | 549.085i | − | 0.932233i | ||||||
\(590\) | − | 378.849i | − | 0.642117i | ||||||
\(591\) | 322.168 | 0.545124 | ||||||||
\(592\) | 282.241i | 0.476759i | ||||||||
\(593\) | 396.439 | 0.668531 | 0.334266 | − | 0.942479i | \(-0.391512\pi\) | ||||
0.334266 | + | 0.942479i | \(0.391512\pi\) | |||||||
\(594\) | 57.0713i | 0.0960796i | ||||||||
\(595\) | − | 294.411i | − | 0.494809i | ||||||
\(596\) | 803.488i | 1.34813i | ||||||||
\(597\) | 89.2852i | 0.149556i | ||||||||
\(598\) | 386.310 | − | 259.745i | 0.646004 | − | 0.434355i | ||||
\(599\) | 654.905 | 1.09333 | 0.546665 | − | 0.837351i | \(-0.315897\pi\) | ||||
0.546665 | + | 0.837351i | \(0.315897\pi\) | |||||||
\(600\) | −520.291 | −0.867151 | ||||||||
\(601\) | 232.243 | 0.386428 | 0.193214 | − | 0.981157i | \(-0.438109\pi\) | ||||
0.193214 | + | 0.981157i | \(0.438109\pi\) | |||||||
\(602\) | −11.7096 | −0.0194511 | ||||||||
\(603\) | − | 103.116i | − | 0.171005i | ||||||
\(604\) | −412.032 | −0.682173 | ||||||||
\(605\) | − | 304.991i | − | 0.504117i | ||||||
\(606\) | −127.256 | −0.209993 | ||||||||
\(607\) | 590.271 | 0.972439 | 0.486220 | − | 0.873837i | \(-0.338375\pi\) | ||||
0.486220 | + | 0.873837i | \(0.338375\pi\) | |||||||
\(608\) | − | 739.746i | − | 1.21669i | ||||||
\(609\) | − | 62.5024i | − | 0.102631i | ||||||
\(610\) | −511.369 | −0.838310 | ||||||||
\(611\) | −503.380 | −0.823863 | ||||||||
\(612\) | − | 126.786i | − | 0.207167i | ||||||
\(613\) | − | 677.917i | − | 1.10590i | −0.833214 | − | 0.552950i | \(-0.813502\pi\) | ||
0.833214 | − | 0.552950i | \(-0.186498\pi\) | |||||||
\(614\) | −173.486 | −0.282550 | ||||||||
\(615\) | − | 398.443i | − | 0.647875i | ||||||
\(616\) | 210.125 | 0.341111 | ||||||||
\(617\) | 700.862i | 1.13592i | 0.823057 | + | 0.567959i | \(0.192267\pi\) | ||||
−0.823057 | + | 0.567959i | \(0.807733\pi\) | |||||||
\(618\) | − | 69.0345i | − | 0.111706i | ||||||
\(619\) | − | 821.711i | − | 1.32748i | −0.747963 | − | 0.663741i | \(-0.768968\pi\) | ||
0.747963 | − | 0.663741i | \(-0.231032\pi\) | |||||||
\(620\) | 649.215i | 1.04712i | ||||||||
\(621\) | −99.1776 | + | 66.6843i | −0.159706 | + | 0.107382i | ||||
\(622\) | −99.7435 | −0.160359 | ||||||||
\(623\) | −14.1655 | −0.0227375 | ||||||||
\(624\) | 294.299 | 0.471633 | ||||||||
\(625\) | 434.655 | 0.695448 | ||||||||
\(626\) | − | 315.745i | − | 0.504385i | ||||||
\(627\) | 504.264 | 0.804250 | ||||||||
\(628\) | 98.8071i | 0.157336i | ||||||||
\(629\) | −501.455 | −0.797225 | ||||||||
\(630\) | 59.2162 | 0.0939939 | ||||||||
\(631\) | 473.991i | 0.751174i | 0.926787 | + | 0.375587i | \(0.122559\pi\) | ||||
−0.926787 | + | 0.375587i | \(0.877441\pi\) | |||||||
\(632\) | − | 826.069i | − | 1.30707i | ||||||
\(633\) | 603.389 | 0.953221 | ||||||||
\(634\) | −332.992 | −0.525224 | ||||||||
\(635\) | − | 1726.68i | − | 2.71918i | ||||||
\(636\) | − | 312.206i | − | 0.490889i | ||||||
\(637\) | −161.552 | −0.253613 | ||||||||
\(638\) | − | 149.804i | − | 0.234802i | ||||||
\(639\) | −309.885 | −0.484954 | ||||||||
\(640\) | 1094.35i | 1.70993i | ||||||||
\(641\) | − | 865.776i | − | 1.35066i | −0.737514 | − | 0.675332i | \(-0.764000\pi\) | ||
0.737514 | − | 0.675332i | \(-0.236000\pi\) | |||||||
\(642\) | − | 141.599i | − | 0.220559i | ||||||
\(643\) | − | 875.488i | − | 1.36157i | −0.732484 | − | 0.680784i | \(-0.761639\pi\) | ||
0.732484 | − | 0.680784i | \(-0.238361\pi\) | |||||||
\(644\) | 109.702 | + | 163.157i | 0.170345 | + | 0.253349i | ||||
\(645\) | 74.3602 | 0.115287 | ||||||||
\(646\) | 266.668 | 0.412799 | ||||||||
\(647\) | 421.449 | 0.651389 | 0.325694 | − | 0.945475i | \(-0.394402\pi\) | ||||
0.325694 | + | 0.945475i | \(0.394402\pi\) | |||||||
\(648\) | 57.0724 | 0.0880747 | ||||||||
\(649\) | − | 635.976i | − | 0.979932i | ||||||
\(650\) | 958.752 | 1.47500 | ||||||||
\(651\) | − | 108.242i | − | 0.166270i | ||||||
\(652\) | −881.580 | −1.35212 | ||||||||
\(653\) | 292.745 | 0.448307 | 0.224154 | − | 0.974554i | \(-0.428038\pi\) | ||||
0.224154 | + | 0.974554i | \(0.428038\pi\) | |||||||
\(654\) | 184.954i | 0.282805i | ||||||||
\(655\) | − | 244.164i | − | 0.372770i | ||||||
\(656\) | −199.086 | −0.303485 | ||||||||
\(657\) | 384.699 | 0.585538 | ||||||||
\(658\) | 50.6084i | 0.0769125i | ||||||||
\(659\) | 148.383i | 0.225164i | 0.993642 | + | 0.112582i | \(0.0359121\pi\) | ||||
−0.993642 | + | 0.112582i | \(0.964088\pi\) | |||||||
\(660\) | −596.221 | −0.903366 | ||||||||
\(661\) | 929.771i | 1.40661i | 0.710887 | + | 0.703306i | \(0.248294\pi\) | ||||
−0.710887 | + | 0.703306i | \(0.751706\pi\) | |||||||
\(662\) | −356.064 | −0.537861 | ||||||||
\(663\) | 522.878i | 0.788655i | ||||||||
\(664\) | 249.086i | 0.375130i | ||||||||
\(665\) | − | 523.216i | − | 0.786791i | ||||||
\(666\) | − | 100.860i | − | 0.151441i | ||||||
\(667\) | 260.327 | − | 175.037i | 0.390295 | − | 0.262424i | ||||
\(668\) | 282.728 | 0.423245 | ||||||||
\(669\) | −413.216 | −0.617662 | ||||||||
\(670\) | −256.434 | −0.382737 | ||||||||
\(671\) | −858.438 | −1.27934 | ||||||||
\(672\) | − | 145.827i | − | 0.217005i | ||||||
\(673\) | 38.3818 | 0.0570308 | 0.0285154 | − | 0.999593i | \(-0.490922\pi\) | ||||
0.0285154 | + | 0.999593i | \(0.490922\pi\) | |||||||
\(674\) | − | 413.860i | − | 0.614036i | ||||||
\(675\) | −246.141 | −0.364653 | ||||||||
\(676\) | −1174.86 | −1.73796 | ||||||||
\(677\) | − | 849.717i | − | 1.25512i | −0.778568 | − | 0.627561i | \(-0.784053\pi\) | ||
0.778568 | − | 0.627561i | \(-0.215947\pi\) | |||||||
\(678\) | − | 211.291i | − | 0.311638i | ||||||
\(679\) | −376.584 | −0.554615 | ||||||||
\(680\) | −705.649 | −1.03772 | ||||||||
\(681\) | − | 207.445i | − | 0.304618i | ||||||
\(682\) | − | 259.431i | − | 0.380397i | ||||||
\(683\) | 626.374 | 0.917092 | 0.458546 | − | 0.888671i | \(-0.348370\pi\) | ||||
0.458546 | + | 0.888671i | \(0.348370\pi\) | |||||||
\(684\) | − | 225.319i | − | 0.329414i | ||||||
\(685\) | −1334.20 | −1.94774 | ||||||||
\(686\) | 16.2420i | 0.0236763i | ||||||||
\(687\) | − | 388.065i | − | 0.564869i | ||||||
\(688\) | − | 37.1549i | − | 0.0540042i | ||||||
\(689\) | 1287.57i | 1.86875i | ||||||||
\(690\) | 165.834 | + | 246.639i | 0.240338 | + | 0.357448i | ||||
\(691\) | −839.803 | −1.21535 | −0.607673 | − | 0.794188i | \(-0.707897\pi\) | ||||
−0.607673 | + | 0.794188i | \(0.707897\pi\) | |||||||
\(692\) | −823.895 | −1.19060 | ||||||||
\(693\) | 99.4065 | 0.143444 | ||||||||
\(694\) | −326.613 | −0.470624 | ||||||||
\(695\) | 1361.01i | 1.95828i | ||||||||
\(696\) | −149.807 | −0.215240 | ||||||||
\(697\) | − | 353.715i | − | 0.507482i | ||||||
\(698\) | −29.6953 | −0.0425434 | ||||||||
\(699\) | 610.805 | 0.873827 | ||||||||
\(700\) | 404.925i | 0.578464i | ||||||||
\(701\) | 60.0039i | 0.0855976i | 0.999084 | + | 0.0427988i | \(0.0136274\pi\) | ||||
−0.999084 | + | 0.0427988i | \(0.986373\pi\) | |||||||
\(702\) | −105.169 | −0.149813 | ||||||||
\(703\) | −891.166 | −1.26766 | ||||||||
\(704\) | 19.3099i | 0.0274289i | ||||||||
\(705\) | − | 321.382i | − | 0.455861i | ||||||
\(706\) | −112.383 | −0.159183 | ||||||||
\(707\) | 221.654i | 0.313513i | ||||||||
\(708\) | −284.171 | −0.401372 | ||||||||
\(709\) | − | 513.355i | − | 0.724056i | −0.932167 | − | 0.362028i | \(-0.882085\pi\) | ||
0.932167 | − | 0.362028i | \(-0.117915\pi\) | |||||||
\(710\) | 770.637i | 1.08540i | ||||||||
\(711\) | − | 390.800i | − | 0.549648i | ||||||
\(712\) | 33.9520i | 0.0476854i | ||||||||
\(713\) | 450.836 | − | 303.130i | 0.632308 | − | 0.425147i | ||||
\(714\) | 52.5687 | 0.0736256 | ||||||||
\(715\) | 2458.88 | 3.43899 | ||||||||
\(716\) | 1101.80 | 1.53882 | ||||||||
\(717\) | −633.230 | −0.883166 | ||||||||
\(718\) | 434.552i | 0.605226i | ||||||||
\(719\) | 715.154 | 0.994651 | 0.497326 | − | 0.867564i | \(-0.334315\pi\) | ||||
0.497326 | + | 0.867564i | \(0.334315\pi\) | |||||||
\(720\) | 187.895i | 0.260965i | ||||||||
\(721\) | −120.244 | −0.166774 | ||||||||
\(722\) | 157.321 | 0.217896 | ||||||||
\(723\) | − | 158.476i | − | 0.219192i | ||||||
\(724\) | − | 945.416i | − | 1.30582i | ||||||
\(725\) | 646.084 | 0.891150 | ||||||||
\(726\) | 54.4578 | 0.0750107 | ||||||||
\(727\) | 740.130i | 1.01806i | 0.860749 | + | 0.509030i | \(0.169996\pi\) | ||||
−0.860749 | + | 0.509030i | \(0.830004\pi\) | |||||||
\(728\) | 387.210i | 0.531881i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | − | 956.686i | − | 1.31053i | ||||||
\(731\) | 66.0128 | 0.0903047 | ||||||||
\(732\) | 383.574i | 0.524008i | ||||||||
\(733\) | 762.622i | 1.04041i | 0.854041 | + | 0.520206i | \(0.174145\pi\) | ||||
−0.854041 | + | 0.520206i | \(0.825855\pi\) | |||||||
\(734\) | 483.879i | 0.659236i | ||||||||
\(735\) | − | 103.142i | − | 0.140330i | ||||||
\(736\) | 607.381 | − | 408.386i | 0.825246 | − | 0.554873i | ||||
\(737\) | −430.477 | −0.584093 | ||||||||
\(738\) | 71.1441 | 0.0964012 | ||||||||
\(739\) | 389.726 | 0.527369 | 0.263685 | − | 0.964609i | \(-0.415062\pi\) | ||||
0.263685 | + | 0.964609i | \(0.415062\pi\) | |||||||
\(740\) | 1053.68 | 1.42389 | ||||||||
\(741\) | 929.239i | 1.25403i | ||||||||
\(742\) | 129.448 | 0.174459 | ||||||||
\(743\) | − | 1256.31i | − | 1.69086i | −0.534084 | − | 0.845432i | \(-0.679343\pi\) | ||
0.534084 | − | 0.845432i | \(-0.320657\pi\) | |||||||
\(744\) | −259.436 | −0.348705 | ||||||||
\(745\) | 2115.60 | 2.83974 | ||||||||
\(746\) | 308.679i | 0.413779i | ||||||||
\(747\) | 117.839i | 0.157749i | ||||||||
\(748\) | −529.291 | −0.707608 | ||||||||
\(749\) | −246.637 | −0.329288 | ||||||||
\(750\) | 289.063i | 0.385418i | ||||||||
\(751\) | 1129.63i | 1.50417i | 0.659066 | + | 0.752085i | \(0.270952\pi\) | ||||
−0.659066 | + | 0.752085i | \(0.729048\pi\) | |||||||
\(752\) | −160.582 | −0.213540 | ||||||||
\(753\) | − | 380.326i | − | 0.505081i | ||||||
\(754\) | 276.053 | 0.366118 | ||||||||
\(755\) | 1084.89i | 1.43694i | ||||||||
\(756\) | − | 44.4175i | − | 0.0587534i | ||||||
\(757\) | − | 288.263i | − | 0.380796i | −0.981707 | − | 0.190398i | \(-0.939022\pi\) | ||
0.981707 | − | 0.190398i | \(-0.0609779\pi\) | |||||||
\(758\) | 37.6341i | 0.0496492i | ||||||||
\(759\) | 278.386 | + | 414.035i | 0.366780 | + | 0.545500i | ||||
\(760\) | −1254.05 | −1.65007 | ||||||||
\(761\) | −550.487 | −0.723374 | −0.361687 | − | 0.932300i | \(-0.617799\pi\) | ||||
−0.361687 | + | 0.932300i | \(0.617799\pi\) | |||||||
\(762\) | 308.308 | 0.404603 | ||||||||
\(763\) | 322.152 | 0.422218 | ||||||||
\(764\) | − | 373.658i | − | 0.489081i | ||||||
\(765\) | −333.831 | −0.436380 | ||||||||
\(766\) | − | 50.1560i | − | 0.0654778i | ||||||
\(767\) | 1171.95 | 1.52797 | ||||||||
\(768\) | −184.720 | −0.240521 | ||||||||
\(769\) | − | 544.260i | − | 0.707750i | −0.935293 | − | 0.353875i | \(-0.884864\pi\) | ||
0.935293 | − | 0.353875i | \(-0.115136\pi\) | |||||||
\(770\) | − | 247.208i | − | 0.321050i | ||||||
\(771\) | −620.289 | −0.804526 | ||||||||
\(772\) | 433.750 | 0.561852 | ||||||||
\(773\) | 291.565i | 0.377187i | 0.982055 | + | 0.188593i | \(0.0603928\pi\) | ||||
−0.982055 | + | 0.188593i | \(0.939607\pi\) | |||||||
\(774\) | 13.2774i | 0.0171543i | ||||||||
\(775\) | 1118.89 | 1.44373 | ||||||||
\(776\) | 902.602i | 1.16315i | ||||||||
\(777\) | −175.677 | −0.226096 | ||||||||
\(778\) | 316.421i | 0.406711i | ||||||||
\(779\) | − | 628.608i | − | 0.806942i | ||||||
\(780\) | − | 1098.69i | − | 1.40858i | ||||||
\(781\) | 1293.67i | 1.65643i | ||||||||
\(782\) | 147.218 | + | 218.952i | 0.188258 | + | 0.279990i | ||||
\(783\) | −70.8711 | −0.0905122 | ||||||||
\(784\) | −51.5363 | −0.0657350 | ||||||||
\(785\) | 260.162 | 0.331416 | ||||||||
\(786\) | 43.5968 | 0.0554667 | ||||||||
\(787\) | 1263.89i | 1.60595i | 0.596009 | + | 0.802977i | \(0.296752\pi\) | ||||
−0.596009 | + | 0.802977i | \(0.703248\pi\) | |||||||
\(788\) | −600.960 | −0.762640 | ||||||||
\(789\) | − | 21.1538i | − | 0.0268109i | ||||||
\(790\) | −971.858 | −1.23020 | ||||||||
\(791\) | −368.025 | −0.465265 | ||||||||
\(792\) | − | 238.259i | − | 0.300832i | ||||||
\(793\) | − | 1581.90i | − | 1.99483i | ||||||
\(794\) | −114.876 | −0.144679 | ||||||||
\(795\) | −822.045 | −1.03402 | ||||||||
\(796\) | − | 166.549i | − | 0.209233i | ||||||
\(797\) | 1323.97i | 1.66120i | 0.556872 | + | 0.830598i | \(0.312001\pi\) | ||||
−0.556872 | + | 0.830598i | \(0.687999\pi\) | |||||||
\(798\) | 93.4231 | 0.117071 | ||||||||
\(799\) | − | 285.305i | − | 0.357077i | ||||||
\(800\) | 1507.41 | 1.88426 | ||||||||
\(801\) | 16.0621i | 0.0200526i | ||||||||
\(802\) | − | 385.086i | − | 0.480158i | ||||||
\(803\) | − | 1605.99i | − | 1.99999i | ||||||
\(804\) | 192.349i | 0.239240i | ||||||||
\(805\) | 429.595 | − | 288.848i | 0.533659 | − | 0.358818i | ||||
\(806\) | 478.070 | 0.593138 | ||||||||
\(807\) | 132.834 | 0.164602 | ||||||||
\(808\) | 531.263 | 0.657503 | ||||||||
\(809\) | −1225.98 | −1.51543 | −0.757713 | − | 0.652588i | \(-0.773683\pi\) | ||||
−0.757713 | + | 0.652588i | \(0.773683\pi\) | |||||||
\(810\) | − | 67.1448i | − | 0.0828948i | ||||||
\(811\) | −496.612 | −0.612345 | −0.306172 | − | 0.951976i | \(-0.599048\pi\) | ||||
−0.306172 | + | 0.951976i | \(0.599048\pi\) | |||||||
\(812\) | 116.590i | 0.143583i | ||||||||
\(813\) | 315.875 | 0.388531 | ||||||||
\(814\) | −421.057 | −0.517269 | ||||||||
\(815\) | 2321.22i | 2.84813i | ||||||||
\(816\) | 166.802i | 0.204415i | ||||||||
\(817\) | 117.315 | 0.143593 | ||||||||
\(818\) | −306.254 | −0.374394 | ||||||||
\(819\) | 183.182i | 0.223666i | ||||||||
\(820\) | 743.240i | 0.906390i | ||||||||
\(821\) | 987.326 | 1.20259 | 0.601295 | − | 0.799027i | \(-0.294652\pi\) | ||||
0.601295 | + | 0.799027i | \(0.294652\pi\) | |||||||
\(822\) | − | 238.228i | − | 0.289816i | ||||||
\(823\) | 710.196 | 0.862936 | 0.431468 | − | 0.902128i | \(-0.357996\pi\) | ||||
0.431468 | + | 0.902128i | \(0.357996\pi\) | |||||||
\(824\) | 288.203i | 0.349761i | ||||||||
\(825\) | 1027.56i | 1.24553i | ||||||||
\(826\) | − | 117.825i | − | 0.142645i | ||||||
\(827\) | − | 1078.33i | − | 1.30391i | −0.758258 | − | 0.651954i | \(-0.773949\pi\) | ||
0.758258 | − | 0.651954i | \(-0.226051\pi\) | |||||||
\(828\) | 185.002 | − | 124.390i | 0.223433 | − | 0.150230i | ||||
\(829\) | −946.344 | −1.14155 | −0.570774 | − | 0.821107i | \(-0.693357\pi\) | ||||
−0.570774 | + | 0.821107i | \(0.693357\pi\) | |||||||
\(830\) | 293.046 | 0.353068 | ||||||||
\(831\) | −462.751 | −0.556860 | ||||||||
\(832\) | −35.5836 | −0.0427688 | ||||||||
\(833\) | − | 91.5640i | − | 0.109921i | ||||||
\(834\) | −243.015 | −0.291385 | ||||||||
\(835\) | − | 744.429i | − | 0.891532i | ||||||
\(836\) | −940.636 | −1.12516 | ||||||||
\(837\) | −122.735 | −0.146637 | ||||||||
\(838\) | − | 251.501i | − | 0.300120i | ||||||
\(839\) | 274.185i | 0.326800i | 0.986560 | + | 0.163400i | \(0.0522461\pi\) | ||||
−0.986560 | + | 0.163400i | \(0.947754\pi\) | |||||||
\(840\) | −247.213 | −0.294302 | ||||||||
\(841\) | −654.974 | −0.778803 | ||||||||
\(842\) | 212.662i | 0.252568i | ||||||||
\(843\) | − | 532.469i | − | 0.631635i | ||||||
\(844\) | −1125.54 | −1.33358 | ||||||||
\(845\) | 3093.43i | 3.66087i | ||||||||
\(846\) | 57.3846 | 0.0678304 | ||||||||
\(847\) | − | 94.8543i | − | 0.111989i | ||||||
\(848\) | 410.744i | 0.484368i | ||||||||
\(849\) | − | 234.002i | − | 0.275621i | ||||||
\(850\) | 543.400i | 0.639294i | ||||||||
\(851\) | −491.980 | − | 731.707i | −0.578119 | − | 0.859820i | ||||
\(852\) | 578.048 | 0.678460 | ||||||||
\(853\) | −1427.43 | −1.67343 | −0.836713 | − | 0.547642i | \(-0.815525\pi\) | ||||
−0.836713 | + | 0.547642i | \(0.815525\pi\) | |||||||
\(854\) | −159.039 | −0.186229 | ||||||||
\(855\) | −593.271 | −0.693885 | ||||||||
\(856\) | 591.143i | 0.690588i | ||||||||
\(857\) | −220.849 | −0.257700 | −0.128850 | − | 0.991664i | \(-0.541129\pi\) | ||||
−0.128850 | + | 0.991664i | \(0.541129\pi\) | |||||||
\(858\) | 439.046i | 0.511708i | ||||||||
\(859\) | 369.199 | 0.429800 | 0.214900 | − | 0.976636i | \(-0.431057\pi\) | ||||
0.214900 | + | 0.976636i | \(0.431057\pi\) | |||||||
\(860\) | −138.709 | −0.161289 | ||||||||
\(861\) | − | 123.919i | − | 0.143924i | ||||||
\(862\) | 291.508i | 0.338177i | ||||||||
\(863\) | −1632.21 | −1.89132 | −0.945661 | − | 0.325155i | \(-0.894583\pi\) | ||||
−0.945661 | + | 0.325155i | \(0.894583\pi\) | |||||||
\(864\) | −165.353 | −0.191380 | ||||||||
\(865\) | 2169.34i | 2.50790i | ||||||||
\(866\) | 419.248i | 0.484121i | ||||||||
\(867\) | 204.207 | 0.235533 | ||||||||
\(868\) | 201.911i | 0.232616i | ||||||||
\(869\) | −1631.46 | −1.87740 | ||||||||
\(870\) | 176.245i | 0.202581i | ||||||||
\(871\) | − | 793.266i | − | 0.910753i | ||||||
\(872\) | − | 772.140i | − | 0.885481i | ||||||
\(873\) | 427.006i | 0.489125i | ||||||||
\(874\) | 261.629 | + | 389.113i | 0.299347 | + | 0.445210i | ||||
\(875\) | 503.490 | 0.575417 | ||||||||
\(876\) | −717.602 | −0.819181 | ||||||||
\(877\) | 206.417 | 0.235367 | 0.117683 | − | 0.993051i | \(-0.462453\pi\) | ||||
0.117683 | + | 0.993051i | \(0.462453\pi\) | |||||||
\(878\) | 55.4887 | 0.0631990 | ||||||||
\(879\) | 745.812i | 0.848478i | ||||||||
\(880\) | 784.401 | 0.891365 | ||||||||
\(881\) | 55.8054i | 0.0633432i | 0.999498 | + | 0.0316716i | \(0.0100831\pi\) | ||||
−0.999498 | + | 0.0316716i | \(0.989917\pi\) | |||||||
\(882\) | 18.4166 | 0.0208805 | ||||||||
\(883\) | 630.662 | 0.714226 | 0.357113 | − | 0.934061i | \(-0.383761\pi\) | ||||
0.357113 | + | 0.934061i | \(0.383761\pi\) | |||||||
\(884\) | − | 975.357i | − | 1.10335i | ||||||
\(885\) | 748.231i | 0.845459i | ||||||||
\(886\) | −200.463 | −0.226256 | ||||||||
\(887\) | 1456.52 | 1.64207 | 0.821035 | − | 0.570877i | \(-0.193397\pi\) | ||||
0.821035 | + | 0.570877i | \(0.193397\pi\) | |||||||
\(888\) | 421.065i | 0.474173i | ||||||||
\(889\) | − | 537.009i | − | 0.604059i | ||||||
\(890\) | 39.9440 | 0.0448809 | ||||||||
\(891\) | − | 112.716i | − | 0.126505i | ||||||
\(892\) | 770.797 | 0.864122 | ||||||||
\(893\) | − | 507.033i | − | 0.567786i | ||||||
\(894\) | 377.753i | 0.422542i | ||||||||
\(895\) | − | 2901.06i | − | 3.24140i | ||||||
\(896\) | 340.351i | 0.379856i | ||||||||
\(897\) | −762.967 | + | 512.998i | −0.850577 | + | 0.571905i | ||||
\(898\) | 88.3384 | 0.0983724 | ||||||||
\(899\) | 322.161 | 0.358355 | ||||||||
\(900\) | 459.142 | 0.510157 | ||||||||
\(901\) | −729.765 | −0.809950 | ||||||||
\(902\) | − | 297.004i | − | 0.329273i | ||||||
\(903\) | 23.1266 | 0.0256108 | ||||||||
\(904\) | 882.088i | 0.975761i | ||||||||
\(905\) | −2489.30 | −2.75061 | ||||||||
\(906\) | −193.713 | −0.213812 | ||||||||
\(907\) | − | 457.001i | − | 0.503860i | −0.967746 | − | 0.251930i | \(-0.918935\pi\) | ||
0.967746 | − | 0.251930i | \(-0.0810652\pi\) | |||||||
\(908\) | 386.960i | 0.426168i | ||||||||
\(909\) | 251.331 | 0.276492 | ||||||||
\(910\) | 455.546 | 0.500600 | ||||||||
\(911\) | − | 262.220i | − | 0.287837i | −0.989590 | − | 0.143919i | \(-0.954030\pi\) | ||
0.989590 | − | 0.143919i | \(-0.0459703\pi\) | |||||||
\(912\) | 296.435i | 0.325038i | ||||||||
\(913\) | 491.938 | 0.538815 | ||||||||
\(914\) | − | 13.9750i | − | 0.0152900i | ||||||
\(915\) | 1009.96 | 1.10378 | ||||||||
\(916\) | 723.882i | 0.790264i | ||||||||
\(917\) | − | 75.9368i | − | 0.0828100i | ||||||
\(918\) | − | 59.6073i | − | 0.0649317i | ||||||
\(919\) | − | 847.074i | − | 0.921735i | −0.887469 | − | 0.460867i | \(-0.847538\pi\) | ||
0.887469 | − | 0.460867i | \(-0.152462\pi\) | |||||||
\(920\) | −692.316 | − | 1029.66i | −0.752517 | − | 1.11920i | ||||
\(921\) | 342.636 | 0.372026 | ||||||||
\(922\) | −146.393 | −0.158778 | ||||||||
\(923\) | −2383.93 | −2.58281 | ||||||||
\(924\) | −185.429 | −0.200681 | ||||||||
\(925\) | − | 1815.96i | − | 1.96320i | ||||||
\(926\) | −474.433 | −0.512347 | ||||||||
\(927\) | 136.344i | 0.147081i | ||||||||
\(928\) | 434.027 | 0.467701 | ||||||||
\(929\) | −909.557 | −0.979071 | −0.489535 | − | 0.871983i | \(-0.662834\pi\) | ||||
−0.489535 | + | 0.871983i | \(0.662834\pi\) | |||||||
\(930\) | 305.223i | 0.328197i | ||||||||
\(931\) | − | 162.724i | − | 0.174784i | ||||||
\(932\) | −1139.37 | −1.22250 | ||||||||
\(933\) | 196.994 | 0.211141 | ||||||||
\(934\) | 155.744i | 0.166749i | ||||||||
\(935\) | 1393.64i | 1.49052i | ||||||||
\(936\) | 439.054 | 0.469075 | ||||||||
\(937\) | − | 646.176i | − | 0.689622i | −0.938672 | − | 0.344811i | \(-0.887943\pi\) | ||
0.938672 | − | 0.344811i | \(-0.112057\pi\) | |||||||
\(938\) | −79.7527 | −0.0850242 | ||||||||
\(939\) | 623.600i | 0.664111i | ||||||||
\(940\) | 599.494i | 0.637760i | ||||||||
\(941\) | − | 891.060i | − | 0.946929i | −0.880813 | − | 0.473464i | \(-0.843003\pi\) | ||
0.880813 | − | 0.473464i | \(-0.156997\pi\) | |||||||
\(942\) | 46.4533i | 0.0493135i | ||||||||
\(943\) | 516.129 | − | 347.031i | 0.547327 | − | 0.368008i | ||||
\(944\) | 373.862 | 0.396040 | ||||||||
\(945\) | −116.953 | −0.123759 | ||||||||
\(946\) | 55.4290 | 0.0585930 | ||||||||
\(947\) | −210.772 | −0.222568 | −0.111284 | − | 0.993789i | \(-0.535496\pi\) | ||||
−0.111284 | + | 0.993789i | \(0.535496\pi\) | |||||||
\(948\) | 728.983i | 0.768969i | ||||||||
\(949\) | 2959.46 | 3.11851 | ||||||||
\(950\) | 965.709i | 1.01654i | ||||||||
\(951\) | 657.663 | 0.691549 | ||||||||
\(952\) | −219.462 | −0.230527 | ||||||||
\(953\) | 922.418i | 0.967910i | 0.875093 | + | 0.483955i | \(0.160800\pi\) | ||||
−0.875093 | + | 0.483955i | \(0.839200\pi\) | |||||||
\(954\) | − | 146.781i | − | 0.153858i | ||||||
\(955\) | −983.851 | −1.03021 | ||||||||
\(956\) | 1181.20 | 1.23557 | ||||||||
\(957\) | 295.864i | 0.309158i | ||||||||
\(958\) | − | 59.5166i | − | 0.0621259i | ||||||
\(959\) | −414.945 | −0.432685 | ||||||||
\(960\) | − | 22.7183i | − | 0.0236649i | ||||||
\(961\) | −403.079 | −0.419437 | ||||||||
\(962\) | − | 775.907i | − | 0.806556i | ||||||
\(963\) | 279.660i | 0.290405i | ||||||||
\(964\) | 295.615i | 0.306655i | ||||||||
\(965\) | − | 1142.07i | − | 1.18350i | ||||||
\(966\) | 51.5754 | + | 76.7066i | 0.0533907 | + | 0.0794064i | ||||
\(967\) | 170.846 | 0.176676 | 0.0883381 | − | 0.996091i | \(-0.471844\pi\) | ||||
0.0883381 | + | 0.996091i | \(0.471844\pi\) | |||||||
\(968\) | −227.348 | −0.234864 | ||||||||
\(969\) | −526.672 | −0.543521 | ||||||||
\(970\) | 1061.90 | 1.09474 | ||||||||
\(971\) | − | 1022.83i | − | 1.05338i | −0.850059 | − | 0.526688i | \(-0.823434\pi\) | ||
0.850059 | − | 0.526688i | \(-0.176566\pi\) | |||||||
\(972\) | −50.3648 | −0.0518156 | ||||||||
\(973\) | 423.282i | 0.435028i | ||||||||
\(974\) | 356.637 | 0.366157 | ||||||||
\(975\) | −1893.55 | −1.94210 | ||||||||
\(976\) | − | 504.638i | − | 0.517047i | ||||||
\(977\) | − | 1778.11i | − | 1.81997i | −0.414645 | − | 0.909983i | \(-0.636094\pi\) | ||
0.414645 | − | 0.909983i | \(-0.363906\pi\) | |||||||
\(978\) | −414.467 | −0.423790 | ||||||||
\(979\) | 67.0543 | 0.0684926 | ||||||||
\(980\) | 192.398i | 0.196324i | ||||||||
\(981\) | − | 365.286i | − | 0.372361i | ||||||
\(982\) | 20.6482 | 0.0210267 | ||||||||
\(983\) | − | 1436.39i | − | 1.46123i | −0.682787 | − | 0.730617i | \(-0.739232\pi\) | ||
0.682787 | − | 0.730617i | \(-0.260768\pi\) | |||||||
\(984\) | −297.010 | −0.301839 | ||||||||
\(985\) | 1582.34i | 1.60644i | ||||||||
\(986\) | 156.461i | 0.158682i | ||||||||
\(987\) | − | 99.9522i | − | 0.101269i | ||||||
\(988\) | − | 1733.37i | − | 1.75442i | ||||||
\(989\) | 64.7654 | + | 96.3237i | 0.0654858 | + | 0.0973950i | ||||
\(990\) | −280.308 | −0.283139 | ||||||||
\(991\) | −576.904 | −0.582143 | −0.291072 | − | 0.956701i | \(-0.594012\pi\) | ||||
−0.291072 | + | 0.956701i | \(0.594012\pi\) | |||||||
\(992\) | 751.650 | 0.757712 | ||||||||
\(993\) | 703.231 | 0.708188 | ||||||||
\(994\) | 239.673i | 0.241120i | ||||||||
\(995\) | −438.528 | −0.440732 | ||||||||
\(996\) | − | 219.812i | − | 0.220694i | ||||||
\(997\) | 590.258 | 0.592035 | 0.296017 | − | 0.955183i | \(-0.404341\pi\) | ||||
0.296017 | + | 0.955183i | \(0.404341\pi\) | |||||||
\(998\) | −426.090 | −0.426944 | ||||||||
\(999\) | 199.199i | 0.199398i |
(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 | 483.3.f.a.22.19 | ✓ | 48 | |
23.22 | odd | 2 | inner | 483.3.f.a.22.20 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.3.f.a.22.19 | ✓ | 48 | 1.1 | even | 1 | trivial | |
483.3.f.a.22.20 | yes | 48 | 23.22 | odd | 2 | inner |