Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,3,Mod(91,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("230.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.26704608029\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.9 | ||
Root | \(6.02373i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.91 |
Dual form | 230.3.d.a.91.10 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −3.79379 | −1.26460 | −0.632299 | − | 0.774724i | \(-0.717889\pi\) | ||||
−0.632299 | + | 0.774724i | \(0.717889\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | −5.36524 | −0.894206 | ||||||||
\(7\) | 7.10180i | 1.01454i | 0.861787 | + | 0.507271i | \(0.169346\pi\) | ||||
−0.861787 | + | 0.507271i | \(0.830654\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 5.39287 | 0.599208 | ||||||||
\(10\) | − | 3.16228i | − | 0.316228i | ||||||
\(11\) | 11.2644i | 1.02403i | 0.858975 | + | 0.512017i | \(0.171101\pi\) | ||||
−0.858975 | + | 0.512017i | \(0.828899\pi\) | |||||||
\(12\) | −7.58759 | −0.632299 | ||||||||
\(13\) | 20.0597 | 1.54306 | 0.771528 | − | 0.636195i | \(-0.219493\pi\) | ||||
0.771528 | + | 0.636195i | \(0.219493\pi\) | |||||||
\(14\) | 10.0435i | 0.717390i | ||||||||
\(15\) | 8.48318i | 0.565545i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 1.63128i | 0.0959575i | 0.998848 | + | 0.0479788i | \(0.0152780\pi\) | ||||
−0.998848 | + | 0.0479788i | \(0.984722\pi\) | |||||||
\(18\) | 7.62667 | 0.423704 | ||||||||
\(19\) | 29.4164i | 1.54823i | 0.633044 | + | 0.774116i | \(0.281805\pi\) | ||||
−0.633044 | + | 0.774116i | \(0.718195\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | − | 26.9428i | − | 1.28299i | ||||||
\(22\) | 15.9302i | 0.724101i | ||||||||
\(23\) | 20.0280 | + | 11.3084i | 0.870783 | + | 0.491668i | ||||
\(24\) | −10.7305 | −0.447103 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | 28.3688 | 1.09111 | ||||||||
\(27\) | 13.6847 | 0.506841 | ||||||||
\(28\) | 14.2036i | 0.507271i | ||||||||
\(29\) | −50.3233 | −1.73529 | −0.867644 | − | 0.497187i | \(-0.834366\pi\) | ||||
−0.867644 | + | 0.497187i | \(0.834366\pi\) | |||||||
\(30\) | 11.9970i | 0.399901i | ||||||||
\(31\) | 11.1316 | 0.359084 | 0.179542 | − | 0.983750i | \(-0.442538\pi\) | ||||
0.179542 | + | 0.983750i | \(0.442538\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 42.7347i | − | 1.29499i | ||||||
\(34\) | 2.30698i | 0.0678522i | ||||||||
\(35\) | 15.8801 | 0.453717 | ||||||||
\(36\) | 10.7857 | 0.299604 | ||||||||
\(37\) | 40.5429i | 1.09575i | 0.836559 | + | 0.547877i | \(0.184564\pi\) | ||||
−0.836559 | + | 0.547877i | \(0.815436\pi\) | |||||||
\(38\) | 41.6011i | 1.09477i | ||||||||
\(39\) | −76.1025 | −1.95135 | ||||||||
\(40\) | − | 6.32456i | − | 0.158114i | ||||||
\(41\) | −7.24039 | −0.176595 | −0.0882975 | − | 0.996094i | \(-0.528143\pi\) | ||||
−0.0882975 | + | 0.996094i | \(0.528143\pi\) | |||||||
\(42\) | − | 38.1028i | − | 0.907210i | ||||||
\(43\) | − | 71.7020i | − | 1.66749i | −0.552150 | − | 0.833745i | \(-0.686192\pi\) | ||
0.552150 | − | 0.833745i | \(-0.313808\pi\) | |||||||
\(44\) | 22.5287i | 0.512017i | ||||||||
\(45\) | − | 12.0588i | − | 0.267974i | ||||||
\(46\) | 28.3239 | + | 15.9924i | 0.615736 | + | 0.347662i | ||||
\(47\) | −6.40666 | −0.136312 | −0.0681560 | − | 0.997675i | \(-0.521712\pi\) | ||||
−0.0681560 | + | 0.997675i | \(0.521712\pi\) | |||||||
\(48\) | −15.1752 | −0.316150 | ||||||||
\(49\) | −1.43550 | −0.0292959 | ||||||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | − | 6.18873i | − | 0.121348i | ||||||
\(52\) | 40.1195 | 0.771528 | ||||||||
\(53\) | − | 20.4148i | − | 0.385184i | −0.981279 | − | 0.192592i | \(-0.938311\pi\) | ||
0.981279 | − | 0.192592i | \(-0.0616894\pi\) | |||||||
\(54\) | 19.3531 | 0.358390 | ||||||||
\(55\) | 25.1879 | 0.457962 | ||||||||
\(56\) | 20.0869i | 0.358695i | ||||||||
\(57\) | − | 111.600i | − | 1.95789i | ||||||
\(58\) | −71.1679 | −1.22703 | ||||||||
\(59\) | −65.8889 | −1.11676 | −0.558381 | − | 0.829585i | \(-0.688577\pi\) | ||||
−0.558381 | + | 0.829585i | \(0.688577\pi\) | |||||||
\(60\) | 16.9664i | 0.282773i | ||||||||
\(61\) | − | 37.7281i | − | 0.618493i | −0.950982 | − | 0.309247i | \(-0.899923\pi\) | ||
0.950982 | − | 0.309247i | \(-0.100077\pi\) | |||||||
\(62\) | 15.7425 | 0.253911 | ||||||||
\(63\) | 38.2991i | 0.607922i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 44.8549i | − | 0.690076i | ||||||
\(66\) | − | 60.4360i | − | 0.915697i | ||||||
\(67\) | − | 124.242i | − | 1.85437i | −0.374609 | − | 0.927183i | \(-0.622223\pi\) | ||
0.374609 | − | 0.927183i | \(-0.377777\pi\) | |||||||
\(68\) | 3.26256i | 0.0479788i | ||||||||
\(69\) | −75.9821 | − | 42.9016i | −1.10119 | − | 0.621763i | ||||
\(70\) | 22.4578 | 0.320826 | ||||||||
\(71\) | 43.5656 | 0.613600 | 0.306800 | − | 0.951774i | \(-0.400742\pi\) | ||||
0.306800 | + | 0.951774i | \(0.400742\pi\) | |||||||
\(72\) | 15.2533 | 0.211852 | ||||||||
\(73\) | 48.1194 | 0.659169 | 0.329585 | − | 0.944126i | \(-0.393091\pi\) | ||||
0.329585 | + | 0.944126i | \(0.393091\pi\) | |||||||
\(74\) | 57.3363i | 0.774815i | ||||||||
\(75\) | 18.9690 | 0.252920 | ||||||||
\(76\) | 58.8328i | 0.774116i | ||||||||
\(77\) | −79.9972 | −1.03893 | ||||||||
\(78\) | −107.625 | −1.37981 | ||||||||
\(79\) | 101.026i | 1.27882i | 0.768868 | + | 0.639408i | \(0.220821\pi\) | ||||
−0.768868 | + | 0.639408i | \(0.779179\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | −100.453 | −1.24016 | ||||||||
\(82\) | −10.2395 | −0.124871 | ||||||||
\(83\) | 102.409i | 1.23384i | 0.787025 | + | 0.616921i | \(0.211620\pi\) | ||||
−0.787025 | + | 0.616921i | \(0.788380\pi\) | |||||||
\(84\) | − | 53.8855i | − | 0.641494i | ||||||
\(85\) | 3.64765 | 0.0429135 | ||||||||
\(86\) | − | 101.402i | − | 1.17909i | ||||||
\(87\) | 190.916 | 2.19444 | ||||||||
\(88\) | 31.8604i | 0.362050i | ||||||||
\(89\) | − | 9.63875i | − | 0.108301i | −0.998533 | − | 0.0541503i | \(-0.982755\pi\) | ||
0.998533 | − | 0.0541503i | \(-0.0172450\pi\) | |||||||
\(90\) | − | 17.0538i | − | 0.189486i | ||||||
\(91\) | 142.460i | 1.56550i | ||||||||
\(92\) | 40.0560 | + | 22.6167i | 0.435391 | + | 0.245834i | ||||
\(93\) | −42.2310 | −0.454097 | ||||||||
\(94\) | −9.06039 | −0.0963871 | ||||||||
\(95\) | 65.7771 | 0.692390 | ||||||||
\(96\) | −21.4609 | −0.223551 | ||||||||
\(97\) | 143.631i | 1.48074i | 0.672202 | + | 0.740368i | \(0.265349\pi\) | ||||
−0.672202 | + | 0.740368i | \(0.734651\pi\) | |||||||
\(98\) | −2.03010 | −0.0207154 | ||||||||
\(99\) | 60.7473i | 0.613609i | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | 103.099 | 1.02078 | 0.510391 | − | 0.859943i | \(-0.329501\pi\) | ||||
0.510391 | + | 0.859943i | \(0.329501\pi\) | |||||||
\(102\) | − | 8.75219i | − | 0.0858058i | ||||||
\(103\) | 98.8637i | 0.959841i | 0.877312 | + | 0.479921i | \(0.159335\pi\) | ||||
−0.877312 | + | 0.479921i | \(0.840665\pi\) | |||||||
\(104\) | 56.7375 | 0.545553 | ||||||||
\(105\) | −60.2458 | −0.573770 | ||||||||
\(106\) | − | 28.8708i | − | 0.272366i | ||||||
\(107\) | 22.5494i | 0.210742i | 0.994433 | + | 0.105371i | \(0.0336029\pi\) | ||||
−0.994433 | + | 0.105371i | \(0.966397\pi\) | |||||||
\(108\) | 27.3694 | 0.253420 | ||||||||
\(109\) | − | 30.2389i | − | 0.277421i | −0.990333 | − | 0.138711i | \(-0.955704\pi\) | ||
0.990333 | − | 0.138711i | \(-0.0442958\pi\) | |||||||
\(110\) | 35.6211 | 0.323828 | ||||||||
\(111\) | − | 153.811i | − | 1.38569i | ||||||
\(112\) | 28.4072i | 0.253636i | ||||||||
\(113\) | − | 213.437i | − | 1.88882i | −0.328771 | − | 0.944410i | \(-0.606635\pi\) | ||
0.328771 | − | 0.944410i | \(-0.393365\pi\) | |||||||
\(114\) | − | 157.826i | − | 1.38444i | ||||||
\(115\) | 25.2863 | − | 44.7840i | 0.219881 | − | 0.389426i | ||||
\(116\) | −100.647 | −0.867644 | ||||||||
\(117\) | 108.180 | 0.924612 | ||||||||
\(118\) | −93.1810 | −0.789670 | ||||||||
\(119\) | −11.5850 | −0.0973530 | ||||||||
\(120\) | 23.9941i | 0.199951i | ||||||||
\(121\) | −5.88598 | −0.0486445 | ||||||||
\(122\) | − | 53.3556i | − | 0.437341i | ||||||
\(123\) | 27.4686 | 0.223322 | ||||||||
\(124\) | 22.2632 | 0.179542 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 54.1631i | 0.429866i | ||||||||
\(127\) | −29.9509 | −0.235834 | −0.117917 | − | 0.993023i | \(-0.537622\pi\) | ||||
−0.117917 | + | 0.993023i | \(0.537622\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | 272.023i | 2.10870i | ||||||||
\(130\) | − | 63.4345i | − | 0.487957i | ||||||
\(131\) | −116.486 | −0.889208 | −0.444604 | − | 0.895727i | \(-0.646656\pi\) | ||||
−0.444604 | + | 0.895727i | \(0.646656\pi\) | |||||||
\(132\) | − | 85.4694i | − | 0.647495i | ||||||
\(133\) | −208.909 | −1.57075 | ||||||||
\(134\) | − | 175.705i | − | 1.31123i | ||||||
\(135\) | − | 30.5999i | − | 0.226666i | ||||||
\(136\) | 4.61395i | 0.0339261i | ||||||||
\(137\) | − | 94.8211i | − | 0.692125i | −0.938212 | − | 0.346062i | \(-0.887519\pi\) | ||
0.938212 | − | 0.346062i | \(-0.112481\pi\) | |||||||
\(138\) | −107.455 | − | 60.6720i | −0.778659 | − | 0.439653i | ||||
\(139\) | 89.2774 | 0.642284 | 0.321142 | − | 0.947031i | \(-0.395933\pi\) | ||||
0.321142 | + | 0.947031i | \(0.395933\pi\) | |||||||
\(140\) | 31.7602 | 0.226859 | ||||||||
\(141\) | 24.3056 | 0.172380 | ||||||||
\(142\) | 61.6111 | 0.433881 | ||||||||
\(143\) | 225.960i | 1.58014i | ||||||||
\(144\) | 21.5715 | 0.149802 | ||||||||
\(145\) | 112.526i | 0.776044i | ||||||||
\(146\) | 68.0510 | 0.466103 | ||||||||
\(147\) | 5.44599 | 0.0370476 | ||||||||
\(148\) | 81.0857i | 0.547877i | ||||||||
\(149\) | − | 182.441i | − | 1.22443i | −0.790690 | − | 0.612217i | \(-0.790278\pi\) | ||
0.790690 | − | 0.612217i | \(-0.209722\pi\) | |||||||
\(150\) | 26.8262 | 0.178841 | ||||||||
\(151\) | 29.7608 | 0.197092 | 0.0985458 | − | 0.995133i | \(-0.468581\pi\) | ||||
0.0985458 | + | 0.995133i | \(0.468581\pi\) | |||||||
\(152\) | 83.2022i | 0.547383i | ||||||||
\(153\) | 8.79728i | 0.0574985i | ||||||||
\(154\) | −113.133 | −0.734631 | ||||||||
\(155\) | − | 24.8910i | − | 0.160587i | ||||||
\(156\) | −152.205 | −0.975673 | ||||||||
\(157\) | − | 64.1093i | − | 0.408340i | −0.978935 | − | 0.204170i | \(-0.934551\pi\) | ||
0.978935 | − | 0.204170i | \(-0.0654495\pi\) | |||||||
\(158\) | 142.873i | 0.904260i | ||||||||
\(159\) | 77.4494i | 0.487103i | ||||||||
\(160\) | − | 12.6491i | − | 0.0790569i | ||||||
\(161\) | −80.3097 | + | 142.235i | −0.498818 | + | 0.883446i | ||||
\(162\) | −142.062 | −0.876924 | ||||||||
\(163\) | −75.3328 | −0.462164 | −0.231082 | − | 0.972934i | \(-0.574227\pi\) | ||||
−0.231082 | + | 0.972934i | \(0.574227\pi\) | |||||||
\(164\) | −14.4808 | −0.0882975 | ||||||||
\(165\) | −95.5577 | −0.579137 | ||||||||
\(166\) | 144.828i | 0.872458i | ||||||||
\(167\) | 272.459 | 1.63149 | 0.815745 | − | 0.578412i | \(-0.196327\pi\) | ||||
0.815745 | + | 0.578412i | \(0.196327\pi\) | |||||||
\(168\) | − | 76.2056i | − | 0.453605i | ||||||
\(169\) | 233.393 | 1.38102 | ||||||||
\(170\) | 5.15855 | 0.0303444 | ||||||||
\(171\) | 158.639i | 0.927713i | ||||||||
\(172\) | − | 143.404i | − | 0.833745i | ||||||
\(173\) | 261.815 | 1.51338 | 0.756691 | − | 0.653773i | \(-0.226815\pi\) | ||||
0.756691 | + | 0.653773i | \(0.226815\pi\) | |||||||
\(174\) | 269.996 | 1.55170 | ||||||||
\(175\) | − | 35.5090i | − | 0.202908i | ||||||
\(176\) | 45.0575i | 0.256008i | ||||||||
\(177\) | 249.969 | 1.41225 | ||||||||
\(178\) | − | 13.6312i | − | 0.0765800i | ||||||
\(179\) | −184.406 | −1.03020 | −0.515101 | − | 0.857130i | \(-0.672246\pi\) | ||||
−0.515101 | + | 0.857130i | \(0.672246\pi\) | |||||||
\(180\) | − | 24.1177i | − | 0.133987i | ||||||
\(181\) | − | 191.867i | − | 1.06004i | −0.847986 | − | 0.530019i | \(-0.822185\pi\) | ||
0.847986 | − | 0.530019i | \(-0.177815\pi\) | |||||||
\(182\) | 201.469i | 1.10697i | ||||||||
\(183\) | 143.133i | 0.782145i | ||||||||
\(184\) | 56.6477 | + | 31.9849i | 0.307868 | + | 0.173831i | ||||
\(185\) | 90.6566 | 0.490036 | ||||||||
\(186\) | −59.7237 | −0.321095 | ||||||||
\(187\) | −18.3753 | −0.0982637 | ||||||||
\(188\) | −12.8133 | −0.0681560 | ||||||||
\(189\) | 97.1859i | 0.514211i | ||||||||
\(190\) | 93.0228 | 0.489594 | ||||||||
\(191\) | 32.6185i | 0.170778i | 0.996348 | + | 0.0853888i | \(0.0272132\pi\) | ||||
−0.996348 | + | 0.0853888i | \(0.972787\pi\) | |||||||
\(192\) | −30.3504 | −0.158075 | ||||||||
\(193\) | 316.748 | 1.64118 | 0.820592 | − | 0.571515i | \(-0.193644\pi\) | ||||
0.820592 | + | 0.571515i | \(0.193644\pi\) | |||||||
\(194\) | 203.125i | 1.04704i | ||||||||
\(195\) | 170.170i | 0.872669i | ||||||||
\(196\) | −2.87100 | −0.0146480 | ||||||||
\(197\) | −194.946 | −0.989573 | −0.494787 | − | 0.869015i | \(-0.664754\pi\) | ||||
−0.494787 | + | 0.869015i | \(0.664754\pi\) | |||||||
\(198\) | 85.9097i | 0.433887i | ||||||||
\(199\) | 74.0815i | 0.372269i | 0.982524 | + | 0.186134i | \(0.0595960\pi\) | ||||
−0.982524 | + | 0.186134i | \(0.940404\pi\) | |||||||
\(200\) | −14.1421 | −0.0707107 | ||||||||
\(201\) | 471.350i | 2.34503i | ||||||||
\(202\) | 145.804 | 0.721802 | ||||||||
\(203\) | − | 357.386i | − | 1.76052i | ||||||
\(204\) | − | 12.3775i | − | 0.0606739i | ||||||
\(205\) | 16.1900i | 0.0789757i | ||||||||
\(206\) | 139.814i | 0.678710i | ||||||||
\(207\) | 108.008 | + | 60.9846i | 0.521780 | + | 0.294612i | ||||
\(208\) | 80.2390 | 0.385764 | ||||||||
\(209\) | −331.357 | −1.58544 | ||||||||
\(210\) | −85.2005 | −0.405716 | ||||||||
\(211\) | −4.75017 | −0.0225126 | −0.0112563 | − | 0.999937i | \(-0.503583\pi\) | ||||
−0.0112563 | + | 0.999937i | \(0.503583\pi\) | |||||||
\(212\) | − | 40.8295i | − | 0.192592i | ||||||
\(213\) | −165.279 | −0.775958 | ||||||||
\(214\) | 31.8896i | 0.149017i | ||||||||
\(215\) | −160.331 | −0.745724 | ||||||||
\(216\) | 38.7062 | 0.179195 | ||||||||
\(217\) | 79.0544i | 0.364306i | ||||||||
\(218\) | − | 42.7643i | − | 0.196167i | ||||||
\(219\) | −182.555 | −0.833584 | ||||||||
\(220\) | 50.3758 | 0.228981 | ||||||||
\(221\) | 32.7230i | 0.148068i | ||||||||
\(222\) | − | 217.522i | − | 0.979829i | ||||||
\(223\) | 211.977 | 0.950571 | 0.475286 | − | 0.879832i | \(-0.342345\pi\) | ||||
0.475286 | + | 0.879832i | \(0.342345\pi\) | |||||||
\(224\) | 40.1738i | 0.179347i | ||||||||
\(225\) | −26.9644 | −0.119842 | ||||||||
\(226\) | − | 301.845i | − | 1.33560i | ||||||
\(227\) | − | 389.941i | − | 1.71780i | −0.512141 | − | 0.858901i | \(-0.671148\pi\) | ||
0.512141 | − | 0.858901i | \(-0.328852\pi\) | |||||||
\(228\) | − | 223.200i | − | 0.978945i | ||||||
\(229\) | 156.000i | 0.681224i | 0.940204 | + | 0.340612i | \(0.110634\pi\) | ||||
−0.940204 | + | 0.340612i | \(0.889366\pi\) | |||||||
\(230\) | 35.7602 | − | 63.3341i | 0.155479 | − | 0.275366i | ||||
\(231\) | 303.493 | 1.31382 | ||||||||
\(232\) | −142.336 | −0.613517 | ||||||||
\(233\) | −46.4968 | −0.199557 | −0.0997785 | − | 0.995010i | \(-0.531813\pi\) | ||||
−0.0997785 | + | 0.995010i | \(0.531813\pi\) | |||||||
\(234\) | 152.989 | 0.653800 | ||||||||
\(235\) | 14.3257i | 0.0609606i | ||||||||
\(236\) | −131.778 | −0.558381 | ||||||||
\(237\) | − | 383.274i | − | 1.61719i | ||||||
\(238\) | −16.3837 | −0.0688389 | ||||||||
\(239\) | −454.735 | −1.90266 | −0.951328 | − | 0.308181i | \(-0.900280\pi\) | ||||
−0.951328 | + | 0.308181i | \(0.900280\pi\) | |||||||
\(240\) | 33.9327i | 0.141386i | ||||||||
\(241\) | − | 149.357i | − | 0.619739i | −0.950779 | − | 0.309870i | \(-0.899715\pi\) | ||
0.950779 | − | 0.309870i | \(-0.100285\pi\) | |||||||
\(242\) | −8.32404 | −0.0343968 | ||||||||
\(243\) | 257.935 | 1.06146 | ||||||||
\(244\) | − | 75.4562i | − | 0.309247i | ||||||
\(245\) | 3.20988i | 0.0131015i | ||||||||
\(246\) | 38.8464 | 0.157912 | ||||||||
\(247\) | 590.085i | 2.38901i | ||||||||
\(248\) | 31.4849 | 0.126955 | ||||||||
\(249\) | − | 388.518i | − | 1.56031i | ||||||
\(250\) | 15.8114i | 0.0632456i | ||||||||
\(251\) | − | 364.513i | − | 1.45224i | −0.687567 | − | 0.726121i | \(-0.741321\pi\) | ||
0.687567 | − | 0.726121i | \(-0.258679\pi\) | |||||||
\(252\) | 76.5982i | 0.303961i | ||||||||
\(253\) | −127.382 | + | 225.603i | −0.503485 | + | 0.891711i | ||||
\(254\) | −42.3570 | −0.166760 | ||||||||
\(255\) | −13.8384 | −0.0542683 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 59.7088 | 0.232330 | 0.116165 | − | 0.993230i | \(-0.462940\pi\) | ||||
0.116165 | + | 0.993230i | \(0.462940\pi\) | |||||||
\(258\) | 384.698i | 1.49108i | ||||||||
\(259\) | −287.927 | −1.11169 | ||||||||
\(260\) | − | 89.7099i | − | 0.345038i | ||||||
\(261\) | −271.387 | −1.03980 | ||||||||
\(262\) | −164.736 | −0.628765 | ||||||||
\(263\) | − | 282.085i | − | 1.07257i | −0.844038 | − | 0.536284i | \(-0.819828\pi\) | ||
0.844038 | − | 0.536284i | \(-0.180172\pi\) | |||||||
\(264\) | − | 120.872i | − | 0.457848i | ||||||
\(265\) | −45.6488 | −0.172260 | ||||||||
\(266\) | −295.442 | −1.11069 | ||||||||
\(267\) | 36.5674i | 0.136957i | ||||||||
\(268\) | − | 248.485i | − | 0.927183i | ||||||
\(269\) | 14.7823 | 0.0549529 | 0.0274764 | − | 0.999622i | \(-0.491253\pi\) | ||||
0.0274764 | + | 0.999622i | \(0.491253\pi\) | |||||||
\(270\) | − | 43.2748i | − | 0.160277i | ||||||
\(271\) | −34.7150 | −0.128100 | −0.0640499 | − | 0.997947i | \(-0.520402\pi\) | ||||
−0.0640499 | + | 0.997947i | \(0.520402\pi\) | |||||||
\(272\) | 6.52511i | 0.0239894i | ||||||||
\(273\) | − | 540.465i | − | 1.97972i | ||||||
\(274\) | − | 134.097i | − | 0.489406i | ||||||
\(275\) | − | 56.3218i | − | 0.204807i | ||||||
\(276\) | −151.964 | − | 85.8032i | −0.550595 | − | 0.310881i | ||||
\(277\) | −191.042 | −0.689682 | −0.344841 | − | 0.938661i | \(-0.612067\pi\) | ||||
−0.344841 | + | 0.938661i | \(0.612067\pi\) | |||||||
\(278\) | 126.257 | 0.454163 | ||||||||
\(279\) | 60.0314 | 0.215166 | ||||||||
\(280\) | 44.9157 | 0.160413 | ||||||||
\(281\) | − | 471.349i | − | 1.67740i | −0.544596 | − | 0.838698i | \(-0.683317\pi\) | ||
0.544596 | − | 0.838698i | \(-0.316683\pi\) | |||||||
\(282\) | 34.3733 | 0.121891 | ||||||||
\(283\) | − | 23.4603i | − | 0.0828984i | −0.999141 | − | 0.0414492i | \(-0.986803\pi\) | ||
0.999141 | − | 0.0414492i | \(-0.0131975\pi\) | |||||||
\(284\) | 87.1312 | 0.306800 | ||||||||
\(285\) | −249.545 | −0.875595 | ||||||||
\(286\) | 319.556i | 1.11733i | ||||||||
\(287\) | − | 51.4198i | − | 0.179163i | ||||||
\(288\) | 30.5067 | 0.105926 | ||||||||
\(289\) | 286.339 | 0.990792 | ||||||||
\(290\) | 159.136i | 0.548746i | ||||||||
\(291\) | − | 544.908i | − | 1.87254i | ||||||
\(292\) | 96.2387 | 0.329585 | ||||||||
\(293\) | − | 289.288i | − | 0.987331i | −0.869652 | − | 0.493666i | \(-0.835657\pi\) | ||
0.869652 | − | 0.493666i | \(-0.164343\pi\) | |||||||
\(294\) | 7.70180 | 0.0261966 | ||||||||
\(295\) | 147.332i | 0.499431i | ||||||||
\(296\) | 114.673i | 0.387407i | ||||||||
\(297\) | 154.149i | 0.519022i | ||||||||
\(298\) | − | 258.010i | − | 0.865805i | ||||||
\(299\) | 401.756 | + | 226.843i | 1.34367 | + | 0.758672i | ||||
\(300\) | 37.9379 | 0.126460 | ||||||||
\(301\) | 509.213 | 1.69174 | ||||||||
\(302\) | 42.0882 | 0.139365 | ||||||||
\(303\) | −391.136 | −1.29088 | ||||||||
\(304\) | 117.666i | 0.387058i | ||||||||
\(305\) | −84.3625 | −0.276599 | ||||||||
\(306\) | 12.4412i | 0.0406576i | ||||||||
\(307\) | −563.775 | −1.83640 | −0.918200 | − | 0.396117i | \(-0.870358\pi\) | ||||
−0.918200 | + | 0.396117i | \(0.870358\pi\) | |||||||
\(308\) | −159.994 | −0.519463 | ||||||||
\(309\) | − | 375.068i | − | 1.21381i | ||||||
\(310\) | − | 35.2012i | − | 0.113552i | ||||||
\(311\) | 76.9428 | 0.247404 | 0.123702 | − | 0.992319i | \(-0.460523\pi\) | ||||
0.123702 | + | 0.992319i | \(0.460523\pi\) | |||||||
\(312\) | −215.250 | −0.689905 | ||||||||
\(313\) | 436.773i | 1.39544i | 0.716370 | + | 0.697721i | \(0.245802\pi\) | ||||
−0.716370 | + | 0.697721i | \(0.754198\pi\) | |||||||
\(314\) | − | 90.6643i | − | 0.288740i | ||||||
\(315\) | 85.6394 | 0.271871 | ||||||||
\(316\) | 202.053i | 0.639408i | ||||||||
\(317\) | 95.6774 | 0.301822 | 0.150911 | − | 0.988547i | \(-0.451779\pi\) | ||||
0.150911 | + | 0.988547i | \(0.451779\pi\) | |||||||
\(318\) | 109.530i | 0.344434i | ||||||||
\(319\) | − | 566.860i | − | 1.77699i | ||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | − | 85.5476i | − | 0.266503i | ||||||
\(322\) | −113.575 | + | 201.150i | −0.352718 | + | 0.624691i | ||||
\(323\) | −47.9863 | −0.148565 | ||||||||
\(324\) | −200.906 | −0.620079 | ||||||||
\(325\) | −100.299 | −0.308611 | ||||||||
\(326\) | −106.537 | −0.326799 | ||||||||
\(327\) | 114.720i | 0.350827i | ||||||||
\(328\) | −20.4789 | −0.0624357 | ||||||||
\(329\) | − | 45.4988i | − | 0.138294i | ||||||
\(330\) | −135.139 | −0.409512 | ||||||||
\(331\) | 515.137 | 1.55631 | 0.778153 | − | 0.628074i | \(-0.216157\pi\) | ||||
0.778153 | + | 0.628074i | \(0.216157\pi\) | |||||||
\(332\) | 204.818i | 0.616921i | ||||||||
\(333\) | 218.643i | 0.656584i | ||||||||
\(334\) | 385.315 | 1.15364 | ||||||||
\(335\) | −277.815 | −0.829297 | ||||||||
\(336\) | − | 107.771i | − | 0.320747i | ||||||
\(337\) | 251.793i | 0.747161i | 0.927598 | + | 0.373580i | \(0.121870\pi\) | ||||
−0.927598 | + | 0.373580i | \(0.878130\pi\) | |||||||
\(338\) | 330.068 | 0.976532 | ||||||||
\(339\) | 809.734i | 2.38860i | ||||||||
\(340\) | 7.29530 | 0.0214568 | ||||||||
\(341\) | 125.391i | 0.367714i | ||||||||
\(342\) | 224.349i | 0.655992i | ||||||||
\(343\) | 337.793i | 0.984820i | ||||||||
\(344\) | − | 202.804i | − | 0.589547i | ||||||
\(345\) | −95.9309 | + | 169.901i | −0.278061 | + | 0.492467i | ||||
\(346\) | 370.262 | 1.07012 | ||||||||
\(347\) | −167.899 | −0.483858 | −0.241929 | − | 0.970294i | \(-0.577780\pi\) | ||||
−0.241929 | + | 0.970294i | \(0.577780\pi\) | |||||||
\(348\) | 381.833 | 1.09722 | ||||||||
\(349\) | 131.699 | 0.377360 | 0.188680 | − | 0.982039i | \(-0.439579\pi\) | ||||
0.188680 | + | 0.982039i | \(0.439579\pi\) | |||||||
\(350\) | − | 50.2173i | − | 0.143478i | ||||||
\(351\) | 274.511 | 0.782084 | ||||||||
\(352\) | 63.7209i | 0.181025i | ||||||||
\(353\) | 232.683 | 0.659159 | 0.329580 | − | 0.944128i | \(-0.393093\pi\) | ||||
0.329580 | + | 0.944128i | \(0.393093\pi\) | |||||||
\(354\) | 353.510 | 0.998615 | ||||||||
\(355\) | − | 97.4157i | − | 0.274410i | ||||||
\(356\) | − | 19.2775i | − | 0.0541503i | ||||||
\(357\) | 43.9511 | 0.123112 | ||||||||
\(358\) | −260.790 | −0.728463 | ||||||||
\(359\) | 205.862i | 0.573432i | 0.958016 | + | 0.286716i | \(0.0925636\pi\) | ||||
−0.958016 | + | 0.286716i | \(0.907436\pi\) | |||||||
\(360\) | − | 34.1075i | − | 0.0947431i | ||||||
\(361\) | −504.325 | −1.39702 | ||||||||
\(362\) | − | 271.341i | − | 0.749560i | ||||||
\(363\) | 22.3302 | 0.0615157 | ||||||||
\(364\) | 284.920i | 0.782748i | ||||||||
\(365\) | − | 107.598i | − | 0.294789i | ||||||
\(366\) | 202.420i | 0.553060i | ||||||||
\(367\) | − | 158.406i | − | 0.431623i | −0.976435 | − | 0.215811i | \(-0.930760\pi\) | ||
0.976435 | − | 0.215811i | \(-0.0692396\pi\) | |||||||
\(368\) | 80.1120 | + | 45.2335i | 0.217696 | + | 0.122917i | ||||
\(369\) | −39.0465 | −0.105817 | ||||||||
\(370\) | 128.208 | 0.346508 | ||||||||
\(371\) | 144.981 | 0.390786 | ||||||||
\(372\) | −84.4621 | −0.227049 | ||||||||
\(373\) | − | 67.1037i | − | 0.179903i | −0.995946 | − | 0.0899513i | \(-0.971329\pi\) | ||
0.995946 | − | 0.0899513i | \(-0.0286712\pi\) | |||||||
\(374\) | −25.9866 | −0.0694829 | ||||||||
\(375\) | − | 42.4159i | − | 0.113109i | ||||||
\(376\) | −18.1208 | −0.0481936 | ||||||||
\(377\) | −1009.47 | −2.67765 | ||||||||
\(378\) | 137.442i | 0.363602i | ||||||||
\(379\) | 10.5032i | 0.0277128i | 0.999904 | + | 0.0138564i | \(0.00441078\pi\) | ||||
−0.999904 | + | 0.0138564i | \(0.995589\pi\) | |||||||
\(380\) | 131.554 | 0.346195 | ||||||||
\(381\) | 113.628 | 0.298235 | ||||||||
\(382\) | 46.1296i | 0.120758i | ||||||||
\(383\) | − | 360.978i | − | 0.942501i | −0.882000 | − | 0.471250i | \(-0.843803\pi\) | ||
0.882000 | − | 0.471250i | \(-0.156197\pi\) | |||||||
\(384\) | −42.9219 | −0.111776 | ||||||||
\(385\) | 178.879i | 0.464621i | ||||||||
\(386\) | 447.950 | 1.16049 | ||||||||
\(387\) | − | 386.680i | − | 0.999173i | ||||||
\(388\) | 287.263i | 0.740368i | ||||||||
\(389\) | 47.2280i | 0.121409i | 0.998156 | + | 0.0607044i | \(0.0193347\pi\) | ||||
−0.998156 | + | 0.0607044i | \(0.980665\pi\) | |||||||
\(390\) | 240.657i | 0.617070i | ||||||||
\(391\) | −18.4471 | + | 32.6712i | −0.0471793 | + | 0.0835582i | ||||
\(392\) | −4.06021 | −0.0103577 | ||||||||
\(393\) | 441.925 | 1.12449 | ||||||||
\(394\) | −275.695 | −0.699734 | ||||||||
\(395\) | 225.902 | 0.571904 | ||||||||
\(396\) | 121.495i | 0.306805i | ||||||||
\(397\) | 4.85826 | 0.0122374 | 0.00611872 | − | 0.999981i | \(-0.498052\pi\) | ||||
0.00611872 | + | 0.999981i | \(0.498052\pi\) | |||||||
\(398\) | 104.767i | 0.263234i | ||||||||
\(399\) | 792.559 | 1.98636 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 297.502i | 0.741900i | 0.928653 | + | 0.370950i | \(0.120968\pi\) | ||||
−0.928653 | + | 0.370950i | \(0.879032\pi\) | |||||||
\(402\) | 666.590i | 1.65818i | ||||||||
\(403\) | 223.297 | 0.554087 | ||||||||
\(404\) | 206.198 | 0.510391 | ||||||||
\(405\) | 224.619i | 0.554615i | ||||||||
\(406\) | − | 505.420i | − | 1.24488i | ||||||
\(407\) | −456.690 | −1.12209 | ||||||||
\(408\) | − | 17.5044i | − | 0.0429029i | ||||||
\(409\) | 238.943 | 0.584213 | 0.292106 | − | 0.956386i | \(-0.405644\pi\) | ||||
0.292106 | + | 0.956386i | \(0.405644\pi\) | |||||||
\(410\) | 22.8961i | 0.0558442i | ||||||||
\(411\) | 359.732i | 0.875259i | ||||||||
\(412\) | 197.727i | 0.479921i | ||||||||
\(413\) | − | 467.930i | − | 1.13300i | ||||||
\(414\) | 152.747 | + | 86.2452i | 0.368954 | + | 0.208322i | ||||
\(415\) | 228.993 | 0.551791 | ||||||||
\(416\) | 113.475 | 0.272776 | ||||||||
\(417\) | −338.700 | −0.812231 | ||||||||
\(418\) | −468.610 | −1.12108 | ||||||||
\(419\) | − | 197.316i | − | 0.470920i | −0.971884 | − | 0.235460i | \(-0.924340\pi\) | ||
0.971884 | − | 0.235460i | \(-0.0756597\pi\) | |||||||
\(420\) | −120.492 | −0.286885 | ||||||||
\(421\) | − | 459.256i | − | 1.09087i | −0.838153 | − | 0.545435i | \(-0.816365\pi\) | ||
0.838153 | − | 0.545435i | \(-0.183635\pi\) | |||||||
\(422\) | −6.71775 | −0.0159188 | ||||||||
\(423\) | −34.5503 | −0.0816793 | ||||||||
\(424\) | − | 57.7417i | − | 0.136183i | ||||||
\(425\) | − | 8.15639i | − | 0.0191915i | ||||||
\(426\) | −233.740 | −0.548685 | ||||||||
\(427\) | 267.937 | 0.627487 | ||||||||
\(428\) | 45.0987i | 0.105371i | ||||||||
\(429\) | − | 857.247i | − | 1.99824i | ||||||
\(430\) | −226.742 | −0.527306 | ||||||||
\(431\) | 475.283i | 1.10275i | 0.834259 | + | 0.551373i | \(0.185896\pi\) | ||||
−0.834259 | + | 0.551373i | \(0.814104\pi\) | |||||||
\(432\) | 54.7388 | 0.126710 | ||||||||
\(433\) | 694.309i | 1.60349i | 0.597669 | + | 0.801743i | \(0.296094\pi\) | ||||
−0.597669 | + | 0.801743i | \(0.703906\pi\) | |||||||
\(434\) | 111.800i | 0.257603i | ||||||||
\(435\) | − | 426.902i | − | 0.981384i | ||||||
\(436\) | − | 60.4779i | − | 0.138711i | ||||||
\(437\) | −332.651 | + | 589.152i | −0.761216 | + | 1.34817i | ||||
\(438\) | −258.172 | −0.589433 | ||||||||
\(439\) | −692.132 | −1.57661 | −0.788305 | − | 0.615284i | \(-0.789041\pi\) | ||||
−0.788305 | + | 0.615284i | \(0.789041\pi\) | |||||||
\(440\) | 71.2421 | 0.161914 | ||||||||
\(441\) | −7.74147 | −0.0175544 | ||||||||
\(442\) | 46.2773i | 0.104700i | ||||||||
\(443\) | −282.065 | −0.636716 | −0.318358 | − | 0.947971i | \(-0.603131\pi\) | ||||
−0.318358 | + | 0.947971i | \(0.603131\pi\) | |||||||
\(444\) | − | 307.623i | − | 0.692844i | ||||||
\(445\) | −21.5529 | −0.0484335 | ||||||||
\(446\) | 299.781 | 0.672155 | ||||||||
\(447\) | 692.142i | 1.54842i | ||||||||
\(448\) | 56.8144i | 0.126818i | ||||||||
\(449\) | −4.51574 | −0.0100573 | −0.00502866 | − | 0.999987i | \(-0.501601\pi\) | ||||
−0.00502866 | + | 0.999987i | \(0.501601\pi\) | |||||||
\(450\) | −38.1334 | −0.0847408 | ||||||||
\(451\) | − | 81.5584i | − | 0.180839i | ||||||
\(452\) | − | 426.873i | − | 0.944410i | ||||||
\(453\) | −112.907 | −0.249242 | ||||||||
\(454\) | − | 551.460i | − | 1.21467i | ||||||
\(455\) | 318.551 | 0.700111 | ||||||||
\(456\) | − | 315.652i | − | 0.692219i | ||||||
\(457\) | − | 399.040i | − | 0.873174i | −0.899662 | − | 0.436587i | \(-0.856187\pi\) | ||
0.899662 | − | 0.436587i | \(-0.143813\pi\) | |||||||
\(458\) | 220.618i | 0.481698i | ||||||||
\(459\) | 22.3235i | 0.0486352i | ||||||||
\(460\) | 50.5726 | − | 89.5679i | 0.109940 | − | 0.194713i | ||||
\(461\) | 44.2537 | 0.0959950 | 0.0479975 | − | 0.998847i | \(-0.484716\pi\) | ||||
0.0479975 | + | 0.998847i | \(0.484716\pi\) | |||||||
\(462\) | 429.204 | 0.929013 | ||||||||
\(463\) | −668.258 | −1.44332 | −0.721661 | − | 0.692247i | \(-0.756621\pi\) | ||||
−0.721661 | + | 0.692247i | \(0.756621\pi\) | |||||||
\(464\) | −201.293 | −0.433822 | ||||||||
\(465\) | 94.4315i | 0.203078i | ||||||||
\(466\) | −65.7564 | −0.141108 | ||||||||
\(467\) | 670.150i | 1.43501i | 0.696554 | + | 0.717505i | \(0.254716\pi\) | ||||
−0.696554 | + | 0.717505i | \(0.745284\pi\) | |||||||
\(468\) | 216.359 | 0.462306 | ||||||||
\(469\) | 882.345 | 1.88133 | ||||||||
\(470\) | 20.2597i | 0.0431056i | ||||||||
\(471\) | 243.218i | 0.516385i | ||||||||
\(472\) | −186.362 | −0.394835 | ||||||||
\(473\) | 807.678 | 1.70756 | ||||||||
\(474\) | − | 542.031i | − | 1.14352i | ||||||
\(475\) | − | 147.082i | − | 0.309646i | ||||||
\(476\) | −23.1700 | −0.0486765 | ||||||||
\(477\) | − | 110.094i | − | 0.230805i | ||||||
\(478\) | −643.092 | −1.34538 | ||||||||
\(479\) | 310.492i | 0.648209i | 0.946021 | + | 0.324105i | \(0.105063\pi\) | ||||
−0.946021 | + | 0.324105i | \(0.894937\pi\) | |||||||
\(480\) | 47.9881i | 0.0999753i | ||||||||
\(481\) | 813.279i | 1.69081i | ||||||||
\(482\) | − | 211.223i | − | 0.438222i | ||||||
\(483\) | 304.679 | − | 539.609i | 0.630804 | − | 1.11720i | ||||
\(484\) | −11.7720 | −0.0243222 | ||||||||
\(485\) | 321.169 | 0.662205 | ||||||||
\(486\) | 364.775 | 0.750566 | ||||||||
\(487\) | 829.644 | 1.70358 | 0.851790 | − | 0.523883i | \(-0.175517\pi\) | ||||
0.851790 | + | 0.523883i | \(0.175517\pi\) | |||||||
\(488\) | − | 106.711i | − | 0.218670i | ||||||
\(489\) | 285.797 | 0.584452 | ||||||||
\(490\) | 4.53945i | 0.00926419i | ||||||||
\(491\) | −123.794 | −0.252126 | −0.126063 | − | 0.992022i | \(-0.540234\pi\) | ||||
−0.126063 | + | 0.992022i | \(0.540234\pi\) | |||||||
\(492\) | 54.9371 | 0.111661 | ||||||||
\(493\) | − | 82.0913i | − | 0.166514i | ||||||
\(494\) | 834.507i | 1.68928i | ||||||||
\(495\) | 135.835 | 0.274414 | ||||||||
\(496\) | 44.5264 | 0.0897710 | ||||||||
\(497\) | 309.394i | 0.622523i | ||||||||
\(498\) | − | 549.448i | − | 1.10331i | ||||||
\(499\) | 757.919 | 1.51887 | 0.759437 | − | 0.650580i | \(-0.225474\pi\) | ||||
0.759437 | + | 0.650580i | \(0.225474\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −1033.65 | −2.06318 | ||||||||
\(502\) | − | 515.499i | − | 1.02689i | ||||||
\(503\) | − | 242.915i | − | 0.482933i | −0.970409 | − | 0.241467i | \(-0.922372\pi\) | ||
0.970409 | − | 0.241467i | \(-0.0776284\pi\) | |||||||
\(504\) | 108.326i | 0.214933i | ||||||||
\(505\) | − | 230.536i | − | 0.456507i | ||||||
\(506\) | −180.145 | + | 319.050i | −0.356017 | + | 0.630535i | ||||
\(507\) | −885.445 | −1.74644 | ||||||||
\(508\) | −59.9018 | −0.117917 | ||||||||
\(509\) | 822.585 | 1.61608 | 0.808040 | − | 0.589127i | \(-0.200528\pi\) | ||||
0.808040 | + | 0.589127i | \(0.200528\pi\) | |||||||
\(510\) | −19.5705 | −0.0383735 | ||||||||
\(511\) | 341.734i | 0.668755i | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 402.555i | 0.784707i | ||||||||
\(514\) | 84.4409 | 0.164282 | ||||||||
\(515\) | 221.066 | 0.429254 | ||||||||
\(516\) | 544.046i | 1.05435i | ||||||||
\(517\) | − | 72.1670i | − | 0.139588i | ||||||
\(518\) | −407.191 | −0.786082 | ||||||||
\(519\) | −993.273 | −1.91382 | ||||||||
\(520\) | − | 126.869i | − | 0.243979i | ||||||
\(521\) | − | 95.3538i | − | 0.183021i | −0.995804 | − | 0.0915103i | \(-0.970831\pi\) | ||
0.995804 | − | 0.0915103i | \(-0.0291694\pi\) | |||||||
\(522\) | −383.800 | −0.735248 | ||||||||
\(523\) | 277.463i | 0.530522i | 0.964177 | + | 0.265261i | \(0.0854581\pi\) | ||||
−0.964177 | + | 0.265261i | \(0.914542\pi\) | |||||||
\(524\) | −232.972 | −0.444604 | ||||||||
\(525\) | 134.714i | 0.256598i | ||||||||
\(526\) | − | 398.929i | − | 0.758420i | ||||||
\(527\) | 18.1588i | 0.0344568i | ||||||||
\(528\) | − | 170.939i | − | 0.323748i | ||||||
\(529\) | 273.242 | + | 452.968i | 0.516525 | + | 0.856272i | ||||
\(530\) | −64.5571 | −0.121806 | ||||||||
\(531\) | −355.331 | −0.669173 | ||||||||
\(532\) | −417.819 | −0.785373 | ||||||||
\(533\) | −145.240 | −0.272496 | ||||||||
\(534\) | 51.7141i | 0.0968430i | ||||||||
\(535\) | 50.4219 | 0.0942465 | ||||||||
\(536\) | − | 351.411i | − | 0.655617i | ||||||
\(537\) | 699.599 | 1.30279 | ||||||||
\(538\) | 20.9054 | 0.0388575 | ||||||||
\(539\) | − | 16.1700i | − | 0.0300000i | ||||||
\(540\) | − | 61.1998i | − | 0.113333i | ||||||
\(541\) | −666.108 | −1.23125 | −0.615627 | − | 0.788038i | \(-0.711097\pi\) | ||||
−0.615627 | + | 0.788038i | \(0.711097\pi\) | |||||||
\(542\) | −49.0945 | −0.0905802 | ||||||||
\(543\) | 727.903i | 1.34052i | ||||||||
\(544\) | 9.22790i | 0.0169631i | ||||||||
\(545\) | −67.6163 | −0.124067 | ||||||||
\(546\) | − | 764.332i | − | 1.39988i | ||||||
\(547\) | 349.611 | 0.639143 | 0.319571 | − | 0.947562i | \(-0.396461\pi\) | ||||
0.319571 | + | 0.947562i | \(0.396461\pi\) | |||||||
\(548\) | − | 189.642i | − | 0.346062i | ||||||
\(549\) | − | 203.463i | − | 0.370606i | ||||||
\(550\) | − | 79.6511i | − | 0.144820i | ||||||
\(551\) | − | 1480.33i | − | 2.68663i | ||||||
\(552\) | −214.910 | − | 121.344i | −0.389329 | − | 0.219826i | ||||
\(553\) | −717.469 | −1.29741 | ||||||||
\(554\) | −270.174 | −0.487679 | ||||||||
\(555\) | −343.933 | −0.619698 | ||||||||
\(556\) | 178.555 | 0.321142 | ||||||||
\(557\) | − | 8.96150i | − | 0.0160889i | −0.999968 | − | 0.00804443i | \(-0.997439\pi\) | ||
0.999968 | − | 0.00804443i | \(-0.00256065\pi\) | |||||||
\(558\) | 84.8972 | 0.152145 | ||||||||
\(559\) | − | 1438.32i | − | 2.57303i | ||||||
\(560\) | 63.5204 | 0.113429 | ||||||||
\(561\) | 69.7122 | 0.124264 | ||||||||
\(562\) | − | 666.587i | − | 1.18610i | ||||||
\(563\) | 732.683i | 1.30139i | 0.759339 | + | 0.650696i | \(0.225523\pi\) | ||||
−0.759339 | + | 0.650696i | \(0.774477\pi\) | |||||||
\(564\) | 48.6111 | 0.0861900 | ||||||||
\(565\) | −477.259 | −0.844706 | ||||||||
\(566\) | − | 33.1778i | − | 0.0586181i | ||||||
\(567\) | − | 713.395i | − | 1.25819i | ||||||
\(568\) | 123.222 | 0.216940 | ||||||||
\(569\) | − | 42.5363i | − | 0.0747563i | −0.999301 | − | 0.0373781i | \(-0.988099\pi\) | ||
0.999301 | − | 0.0373781i | \(-0.0119006\pi\) | |||||||
\(570\) | −352.909 | −0.619139 | ||||||||
\(571\) | 459.356i | 0.804476i | 0.915535 | + | 0.402238i | \(0.131768\pi\) | ||||
−0.915535 | + | 0.402238i | \(0.868232\pi\) | |||||||
\(572\) | 451.921i | 0.790071i | ||||||||
\(573\) | − | 123.748i | − | 0.215965i | ||||||
\(574\) | − | 72.7186i | − | 0.126687i | ||||||
\(575\) | −100.140 | − | 56.5418i | −0.174157 | − | 0.0983336i | ||||
\(576\) | 43.1430 | 0.0749010 | ||||||||
\(577\) | 831.608 | 1.44126 | 0.720630 | − | 0.693319i | \(-0.243852\pi\) | ||||
0.720630 | + | 0.693319i | \(0.243852\pi\) | |||||||
\(578\) | 404.944 | 0.700596 | ||||||||
\(579\) | −1201.68 | −2.07544 | ||||||||
\(580\) | 225.053i | 0.388022i | ||||||||
\(581\) | −727.287 | −1.25179 | ||||||||
\(582\) | − | 770.616i | − | 1.32408i | ||||||
\(583\) | 229.959 | 0.394441 | ||||||||
\(584\) | 136.102 | 0.233052 | ||||||||
\(585\) | − | 241.897i | − | 0.413499i | ||||||
\(586\) | − | 409.115i | − | 0.698149i | ||||||
\(587\) | −166.970 | −0.284447 | −0.142223 | − | 0.989835i | \(-0.545425\pi\) | ||||
−0.142223 | + | 0.989835i | \(0.545425\pi\) | |||||||
\(588\) | 10.8920 | 0.0185238 | ||||||||
\(589\) | 327.452i | 0.555945i | ||||||||
\(590\) | 208.359i | 0.353151i | ||||||||
\(591\) | 739.585 | 1.25141 | ||||||||
\(592\) | 162.171i | 0.273938i | ||||||||
\(593\) | 900.895 | 1.51922 | 0.759608 | − | 0.650381i | \(-0.225391\pi\) | ||||
0.759608 | + | 0.650381i | \(0.225391\pi\) | |||||||
\(594\) | 218.000i | 0.367004i | ||||||||
\(595\) | 25.9049i | 0.0435376i | ||||||||
\(596\) | − | 364.881i | − | 0.612217i | ||||||
\(597\) | − | 281.050i | − | 0.470771i | ||||||
\(598\) | 568.169 | + | 320.804i | 0.950116 | + | 0.536462i | ||||
\(599\) | −129.221 | −0.215727 | −0.107864 | − | 0.994166i | \(-0.534401\pi\) | ||||
−0.107864 | + | 0.994166i | \(0.534401\pi\) | |||||||
\(600\) | 53.6524 | 0.0894206 | ||||||||
\(601\) | 580.916 | 0.966582 | 0.483291 | − | 0.875460i | \(-0.339441\pi\) | ||||
0.483291 | + | 0.875460i | \(0.339441\pi\) | |||||||
\(602\) | 720.136 | 1.19624 | ||||||||
\(603\) | − | 670.024i | − | 1.11115i | ||||||
\(604\) | 59.5217 | 0.0985458 | ||||||||
\(605\) | 13.1615i | 0.0217545i | ||||||||
\(606\) | −553.150 | −0.912789 | ||||||||
\(607\) | −1063.36 | −1.75183 | −0.875915 | − | 0.482466i | \(-0.839741\pi\) | ||||
−0.875915 | + | 0.482466i | \(0.839741\pi\) | |||||||
\(608\) | 166.404i | 0.273691i | ||||||||
\(609\) | 1355.85i | 2.22635i | ||||||||
\(610\) | −119.307 | −0.195585 | ||||||||
\(611\) | −128.516 | −0.210337 | ||||||||
\(612\) | 17.5946i | 0.0287493i | ||||||||
\(613\) | − | 442.412i | − | 0.721715i | −0.932621 | − | 0.360858i | \(-0.882484\pi\) | ||
0.932621 | − | 0.360858i | \(-0.117516\pi\) | |||||||
\(614\) | −797.298 | −1.29853 | ||||||||
\(615\) | − | 61.4216i | − | 0.0998725i | ||||||
\(616\) | −226.266 | −0.367316 | ||||||||
\(617\) | 936.724i | 1.51819i | 0.650979 | + | 0.759095i | \(0.274358\pi\) | ||||
−0.650979 | + | 0.759095i | \(0.725642\pi\) | |||||||
\(618\) | − | 530.427i | − | 0.858296i | ||||||
\(619\) | − | 401.856i | − | 0.649202i | −0.945851 | − | 0.324601i | \(-0.894770\pi\) | ||
0.945851 | − | 0.324601i | \(-0.105230\pi\) | |||||||
\(620\) | − | 49.7821i | − | 0.0802937i | ||||||
\(621\) | 274.077 | + | 154.752i | 0.441348 | + | 0.249197i | ||||
\(622\) | 108.814 | 0.174941 | ||||||||
\(623\) | 68.4524 | 0.109875 | ||||||||
\(624\) | −304.410 | −0.487837 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 617.691i | 0.986726i | ||||||||
\(627\) | 1257.10 | 2.00495 | ||||||||
\(628\) | − | 128.219i | − | 0.204170i | ||||||
\(629\) | −66.1367 | −0.105146 | ||||||||
\(630\) | 121.112 | 0.192242 | ||||||||
\(631\) | − | 1033.92i | − | 1.63854i | −0.573411 | − | 0.819268i | \(-0.694380\pi\) | ||
0.573411 | − | 0.819268i | \(-0.305620\pi\) | |||||||
\(632\) | 285.746i | 0.452130i | ||||||||
\(633\) | 18.0212 | 0.0284694 | ||||||||
\(634\) | 135.308 | 0.213420 | ||||||||
\(635\) | 66.9722i | 0.105468i | ||||||||
\(636\) | 154.899i | 0.243552i | ||||||||
\(637\) | −28.7958 | −0.0452053 | ||||||||
\(638\) | − | 801.662i | − | 1.25652i | ||||||
\(639\) | 234.944 | 0.367674 | ||||||||
\(640\) | − | 25.2982i | − | 0.0395285i | ||||||
\(641\) | 188.175i | 0.293564i | 0.989169 | + | 0.146782i | \(0.0468916\pi\) | ||||
−0.989169 | + | 0.146782i | \(0.953108\pi\) | |||||||
\(642\) | − | 120.983i | − | 0.188446i | ||||||
\(643\) | − | 1055.82i | − | 1.64203i | −0.570909 | − | 0.821013i | \(-0.693409\pi\) | ||
0.570909 | − | 0.821013i | \(-0.306591\pi\) | |||||||
\(644\) | −160.619 | + | 284.470i | −0.249409 | + | 0.441723i | ||||
\(645\) | 608.261 | 0.943041 | ||||||||
\(646\) | −67.8629 | −0.105051 | ||||||||
\(647\) | −443.636 | −0.685681 | −0.342841 | − | 0.939394i | \(-0.611389\pi\) | ||||
−0.342841 | + | 0.939394i | \(0.611389\pi\) | |||||||
\(648\) | −284.123 | −0.438462 | ||||||||
\(649\) | − | 742.197i | − | 1.14360i | ||||||
\(650\) | −141.844 | −0.218221 | ||||||||
\(651\) | − | 299.916i | − | 0.460701i | ||||||
\(652\) | −150.666 | −0.231082 | ||||||||
\(653\) | 117.465 | 0.179886 | 0.0899429 | − | 0.995947i | \(-0.471332\pi\) | ||||
0.0899429 | + | 0.995947i | \(0.471332\pi\) | |||||||
\(654\) | 162.239i | 0.248072i | ||||||||
\(655\) | 260.471i | 0.397666i | ||||||||
\(656\) | −28.9616 | −0.0441487 | ||||||||
\(657\) | 259.502 | 0.394980 | ||||||||
\(658\) | − | 64.3451i | − | 0.0977888i | ||||||
\(659\) | 664.743i | 1.00871i | 0.863495 | + | 0.504357i | \(0.168270\pi\) | ||||
−0.863495 | + | 0.504357i | \(0.831730\pi\) | |||||||
\(660\) | −191.115 | −0.289569 | ||||||||
\(661\) | 426.231i | 0.644828i | 0.946599 | + | 0.322414i | \(0.104494\pi\) | ||||
−0.946599 | + | 0.322414i | \(0.895506\pi\) | |||||||
\(662\) | 728.514 | 1.10047 | ||||||||
\(663\) | − | 124.144i | − | 0.187246i | ||||||
\(664\) | 289.656i | 0.436229i | ||||||||
\(665\) | 467.135i | 0.702459i | ||||||||
\(666\) | 309.207i | 0.464275i | ||||||||
\(667\) | −1007.88 | − | 569.075i | −1.51106 | − | 0.853185i | ||||
\(668\) | 544.918 | 0.815745 | ||||||||
\(669\) | −804.198 | −1.20209 | ||||||||
\(670\) | −392.889 | −0.586402 | ||||||||
\(671\) | 424.983 | 0.633358 | ||||||||
\(672\) | − | 152.411i | − | 0.226802i | ||||||
\(673\) | −824.444 | −1.22503 | −0.612514 | − | 0.790460i | \(-0.709842\pi\) | ||||
−0.612514 | + | 0.790460i | \(0.709842\pi\) | |||||||
\(674\) | 356.089i | 0.528322i | ||||||||
\(675\) | −68.4235 | −0.101368 | ||||||||
\(676\) | 466.786 | 0.690512 | ||||||||
\(677\) | − | 530.039i | − | 0.782924i | −0.920194 | − | 0.391462i | \(-0.871969\pi\) | ||
0.920194 | − | 0.391462i | \(-0.128031\pi\) | |||||||
\(678\) | 1145.14i | 1.68899i | ||||||||
\(679\) | −1020.04 | −1.50227 | ||||||||
\(680\) | 10.3171 | 0.0151722 | ||||||||
\(681\) | 1479.36i | 2.17233i | ||||||||
\(682\) | 177.329i | 0.260013i | ||||||||
\(683\) | 414.954 | 0.607546 | 0.303773 | − | 0.952744i | \(-0.401754\pi\) | ||||
0.303773 | + | 0.952744i | \(0.401754\pi\) | |||||||
\(684\) | 317.278i | 0.463857i | ||||||||
\(685\) | −212.026 | −0.309527 | ||||||||
\(686\) | 477.712i | 0.696373i | ||||||||
\(687\) | − | 591.833i | − | 0.861475i | ||||||
\(688\) | − | 286.808i | − | 0.416872i | ||||||
\(689\) | − | 409.515i | − | 0.594361i | ||||||
\(690\) | −135.667 | + | 240.277i | −0.196619 | + | 0.348227i | ||||
\(691\) | −363.154 | −0.525548 | −0.262774 | − | 0.964857i | \(-0.584637\pi\) | ||||
−0.262774 | + | 0.964857i | \(0.584637\pi\) | |||||||
\(692\) | 523.630 | 0.756691 | ||||||||
\(693\) | −431.415 | −0.622532 | ||||||||
\(694\) | −237.445 | −0.342139 | ||||||||
\(695\) | − | 199.630i | − | 0.287238i | ||||||
\(696\) | 539.993 | 0.775852 | ||||||||
\(697\) | − | 11.8111i | − | 0.0169456i | ||||||
\(698\) | 186.250 | 0.266834 | ||||||||
\(699\) | 176.399 | 0.252360 | ||||||||
\(700\) | − | 71.0180i | − | 0.101454i | ||||||
\(701\) | 928.839i | 1.32502i | 0.749053 | + | 0.662510i | \(0.230509\pi\) | ||||
−0.749053 | + | 0.662510i | \(0.769491\pi\) | |||||||
\(702\) | 388.218 | 0.553017 | ||||||||
\(703\) | −1192.63 | −1.69648 | ||||||||
\(704\) | 90.1149i | 0.128004i | ||||||||
\(705\) | − | 54.3489i | − | 0.0770906i | ||||||
\(706\) | 329.064 | 0.466096 | ||||||||
\(707\) | 732.188i | 1.03563i | ||||||||
\(708\) | 499.938 | 0.706127 | ||||||||
\(709\) | − | 44.8088i | − | 0.0632000i | −0.999501 | − | 0.0316000i | \(-0.989940\pi\) | ||
0.999501 | − | 0.0316000i | \(-0.0100603\pi\) | |||||||
\(710\) | − | 137.767i | − | 0.194037i | ||||||
\(711\) | 544.823i | 0.766277i | ||||||||
\(712\) | − | 27.2625i | − | 0.0382900i | ||||||
\(713\) | 222.944 | + | 125.880i | 0.312684 | + | 0.176550i | ||||
\(714\) | 62.1563 | 0.0870536 | ||||||||
\(715\) | 505.263 | 0.706661 | ||||||||
\(716\) | −368.812 | −0.515101 | ||||||||
\(717\) | 1725.17 | 2.40609 | ||||||||
\(718\) | 291.133i | 0.405478i | ||||||||
\(719\) | 1308.36 | 1.81969 | 0.909844 | − | 0.414950i | \(-0.136201\pi\) | ||||
0.909844 | + | 0.414950i | \(0.136201\pi\) | |||||||
\(720\) | − | 48.2353i | − | 0.0669935i | ||||||
\(721\) | −702.110 | −0.973800 | ||||||||
\(722\) | −713.223 | −0.987843 | ||||||||
\(723\) | 566.630i | 0.783721i | ||||||||
\(724\) | − | 383.734i | − | 0.530019i | ||||||
\(725\) | 251.617 | 0.347057 | ||||||||
\(726\) | 31.5797 | 0.0434982 | ||||||||
\(727\) | − | 515.858i | − | 0.709570i | −0.934948 | − | 0.354785i | \(-0.884554\pi\) | ||
0.934948 | − | 0.354785i | \(-0.115446\pi\) | |||||||
\(728\) | 402.938i | 0.553487i | ||||||||
\(729\) | −74.4769 | −0.102163 | ||||||||
\(730\) | − | 152.167i | − | 0.208448i | ||||||
\(731\) | 116.966 | 0.160008 | ||||||||
\(732\) | 286.265i | 0.391073i | ||||||||
\(733\) | 405.638i | 0.553394i | 0.960957 | + | 0.276697i | \(0.0892398\pi\) | ||||
−0.960957 | + | 0.276697i | \(0.910760\pi\) | |||||||
\(734\) | − | 224.019i | − | 0.305203i | ||||||
\(735\) | − | 12.1776i | − | 0.0165682i | ||||||
\(736\) | 113.295 | + | 63.9698i | 0.153934 | + | 0.0869155i | ||||
\(737\) | 1399.51 | 1.89893 | ||||||||
\(738\) | −55.2201 | −0.0748240 | ||||||||
\(739\) | 601.397 | 0.813798 | 0.406899 | − | 0.913473i | \(-0.366610\pi\) | ||||
0.406899 | + | 0.913473i | \(0.366610\pi\) | |||||||
\(740\) | 181.313 | 0.245018 | ||||||||
\(741\) | − | 2238.66i | − | 3.02114i | ||||||
\(742\) | 205.035 | 0.276327 | ||||||||
\(743\) | − | 775.124i | − | 1.04324i | −0.853179 | − | 0.521618i | \(-0.825329\pi\) | ||
0.853179 | − | 0.521618i | \(-0.174671\pi\) | |||||||
\(744\) | −119.447 | −0.160548 | ||||||||
\(745\) | −407.950 | −0.547583 | ||||||||
\(746\) | − | 94.8990i | − | 0.127210i | ||||||
\(747\) | 552.278i | 0.739328i | ||||||||
\(748\) | −36.7506 | −0.0491319 | ||||||||
\(749\) | −160.141 | −0.213806 | ||||||||
\(750\) | − | 59.9852i | − | 0.0799802i | ||||||
\(751\) | 533.250i | 0.710054i | 0.934856 | + | 0.355027i | \(0.115528\pi\) | ||||
−0.934856 | + | 0.355027i | \(0.884472\pi\) | |||||||
\(752\) | −25.6267 | −0.0340780 | ||||||||
\(753\) | 1382.89i | 1.83650i | ||||||||
\(754\) | −1427.61 | −1.89338 | ||||||||
\(755\) | − | 66.5473i | − | 0.0881421i | ||||||
\(756\) | 194.372i | 0.257106i | ||||||||
\(757\) | − | 794.660i | − | 1.04975i | −0.851180 | − | 0.524875i | \(-0.824112\pi\) | ||
0.851180 | − | 0.524875i | \(-0.175888\pi\) | |||||||
\(758\) | 14.8537i | 0.0195959i | ||||||||
\(759\) | 483.260 | − | 855.890i | 0.636706 | − | 1.12766i | ||||
\(760\) | 186.046 | 0.244797 | ||||||||
\(761\) | −1322.01 | −1.73720 | −0.868599 | − | 0.495515i | \(-0.834979\pi\) | ||||
−0.868599 | + | 0.495515i | \(0.834979\pi\) | |||||||
\(762\) | 160.694 | 0.210884 | ||||||||
\(763\) | 214.751 | 0.281456 | ||||||||
\(764\) | 65.2371i | 0.0853888i | ||||||||
\(765\) | 19.6713 | 0.0257141 | ||||||||
\(766\) | − | 510.500i | − | 0.666449i | ||||||
\(767\) | −1321.71 | −1.72323 | ||||||||
\(768\) | −60.7007 | −0.0790374 | ||||||||
\(769\) | 1443.85i | 1.87757i | 0.344500 | + | 0.938786i | \(0.388048\pi\) | ||||
−0.344500 | + | 0.938786i | \(0.611952\pi\) | |||||||
\(770\) | 252.973i | 0.328537i | ||||||||
\(771\) | −226.523 | −0.293804 | ||||||||
\(772\) | 633.497 | 0.820592 | ||||||||
\(773\) | 64.8298i | 0.0838678i | 0.999120 | + | 0.0419339i | \(0.0133519\pi\) | ||||
−0.999120 | + | 0.0419339i | \(0.986648\pi\) | |||||||
\(774\) | − | 546.848i | − | 0.706522i | ||||||
\(775\) | −55.6580 | −0.0718168 | ||||||||
\(776\) | 406.251i | 0.523519i | ||||||||
\(777\) | 1092.34 | 1.40584 | ||||||||
\(778\) | 66.7905i | 0.0858490i | ||||||||
\(779\) | − | 212.986i | − | 0.273410i | ||||||
\(780\) | 340.341i | 0.436334i | ||||||||
\(781\) | 490.739i | 0.628347i | ||||||||
\(782\) | −26.0881 | + | 46.2041i | −0.0333608 | + | 0.0590845i | ||||
\(783\) | −688.659 | −0.879514 | ||||||||
\(784\) | −5.74200 | −0.00732398 | ||||||||
\(785\) | −143.353 | −0.182615 | ||||||||
\(786\) | 624.976 | 0.795135 | ||||||||
\(787\) | − | 1247.04i | − | 1.58455i | −0.610163 | − | 0.792276i | \(-0.708896\pi\) | ||
0.610163 | − | 0.792276i | \(-0.291104\pi\) | |||||||
\(788\) | −389.892 | −0.494787 | ||||||||
\(789\) | 1070.17i | 1.35637i | ||||||||
\(790\) | 319.474 | 0.404397 | ||||||||
\(791\) | 1515.78 | 1.91629 | ||||||||
\(792\) | 171.819i | 0.216944i | ||||||||
\(793\) | − | 756.815i | − | 0.954370i | ||||||
\(794\) | 6.87062 | 0.00865317 | ||||||||
\(795\) | 173.182 | 0.217839 | ||||||||
\(796\) | 148.163i | 0.186134i | ||||||||
\(797\) | − | 965.218i | − | 1.21106i | −0.795821 | − | 0.605532i | \(-0.792960\pi\) | ||
0.795821 | − | 0.605532i | \(-0.207040\pi\) | |||||||
\(798\) | 1120.85 | 1.40457 | ||||||||
\(799\) | − | 10.4511i | − | 0.0130802i | ||||||
\(800\) | −28.2843 | −0.0353553 | ||||||||
\(801\) | − | 51.9805i | − | 0.0648946i | ||||||
\(802\) | 420.731i | 0.524602i | ||||||||
\(803\) | 542.034i | 0.675011i | ||||||||
\(804\) | 942.701i | 1.17251i | ||||||||
\(805\) | 318.047 | + | 179.578i | 0.395089 | + | 0.223078i | ||||
\(806\) | 315.790 | 0.391799 | ||||||||
\(807\) | −56.0811 | −0.0694933 | ||||||||
\(808\) | 291.608 | 0.360901 | ||||||||
\(809\) | −1310.48 | −1.61988 | −0.809939 | − | 0.586514i | \(-0.800500\pi\) | ||||
−0.809939 | + | 0.586514i | \(0.800500\pi\) | |||||||
\(810\) | 317.660i | 0.392172i | ||||||||
\(811\) | −1174.00 | −1.44760 | −0.723799 | − | 0.690010i | \(-0.757606\pi\) | ||||
−0.723799 | + | 0.690010i | \(0.757606\pi\) | |||||||
\(812\) | − | 714.772i | − | 0.880261i | ||||||
\(813\) | 131.702 | 0.161995 | ||||||||
\(814\) | −645.857 | −0.793436 | ||||||||
\(815\) | 168.449i | 0.206686i | ||||||||
\(816\) | − | 24.7549i | − | 0.0303369i | ||||||
\(817\) | 2109.22 | 2.58166 | ||||||||
\(818\) | 337.917 | 0.413101 | ||||||||
\(819\) | 768.270i | 0.938058i | ||||||||
\(820\) | 32.3800i | 0.0394878i | ||||||||
\(821\) | −1238.00 | −1.50791 | −0.753956 | − | 0.656925i | \(-0.771857\pi\) | ||||
−0.753956 | + | 0.656925i | \(0.771857\pi\) | |||||||
\(822\) | 508.737i | 0.618902i | ||||||||
\(823\) | −937.653 | −1.13931 | −0.569656 | − | 0.821883i | \(-0.692923\pi\) | ||||
−0.569656 | + | 0.821883i | \(0.692923\pi\) | |||||||
\(824\) | 279.629i | 0.339355i | ||||||||
\(825\) | 213.673i | 0.258998i | ||||||||
\(826\) | − | 661.753i | − | 0.801153i | ||||||
\(827\) | 199.863i | 0.241672i | 0.992672 | + | 0.120836i | \(0.0385575\pi\) | ||||
−0.992672 | + | 0.120836i | \(0.961443\pi\) | |||||||
\(828\) | 216.017 | + | 121.969i | 0.260890 | + | 0.147306i | ||||
\(829\) | −892.787 | −1.07695 | −0.538473 | − | 0.842643i | \(-0.680998\pi\) | ||||
−0.538473 | + | 0.842643i | \(0.680998\pi\) | |||||||
\(830\) | 323.845 | 0.390175 | ||||||||
\(831\) | 724.774 | 0.872171 | ||||||||
\(832\) | 160.478 | 0.192882 | ||||||||
\(833\) | − | 2.34170i | − | 0.00281117i | ||||||
\(834\) | −478.994 | −0.574334 | ||||||||
\(835\) | − | 609.236i | − | 0.729624i | ||||||
\(836\) | −662.714 | −0.792721 | ||||||||
\(837\) | 152.333 | 0.181998 | ||||||||
\(838\) | − | 279.046i | − | 0.332991i | ||||||
\(839\) | − | 515.108i | − | 0.613955i | −0.951717 | − | 0.306977i | \(-0.900682\pi\) | ||
0.951717 | − | 0.306977i | \(-0.0993176\pi\) | |||||||
\(840\) | −170.401 | −0.202858 | ||||||||
\(841\) | 1691.44 | 2.01122 | ||||||||
\(842\) | − | 649.486i | − | 0.771361i | ||||||
\(843\) | 1788.20i | 2.12123i | ||||||||
\(844\) | −9.50033 | −0.0112563 | ||||||||
\(845\) | − | 521.883i | − | 0.617613i | ||||||
\(846\) | −48.8615 | −0.0577560 | ||||||||
\(847\) | − | 41.8010i | − | 0.0493519i | ||||||
\(848\) | − | 81.6590i | − | 0.0962960i | ||||||
\(849\) | 89.0034i | 0.104833i | ||||||||
\(850\) | − | 11.5349i | − | 0.0135704i | ||||||
\(851\) | −458.474 | + | 811.993i | −0.538747 | + | 0.954163i | ||||
\(852\) | −330.558 | −0.387979 | ||||||||
\(853\) | −483.197 | −0.566467 | −0.283234 | − | 0.959051i | \(-0.591407\pi\) | ||||
−0.283234 | + | 0.959051i | \(0.591407\pi\) | |||||||
\(854\) | 378.920 | 0.443701 | ||||||||
\(855\) | 354.727 | 0.414886 | ||||||||
\(856\) | 63.7792i | 0.0745084i | ||||||||
\(857\) | 920.413 | 1.07399 | 0.536997 | − | 0.843584i | \(-0.319559\pi\) | ||||
0.536997 | + | 0.843584i | \(0.319559\pi\) | |||||||
\(858\) | − | 1212.33i | − | 1.41297i | ||||||
\(859\) | 1173.30 | 1.36589 | 0.682947 | − | 0.730468i | \(-0.260698\pi\) | ||||
0.682947 | + | 0.730468i | \(0.260698\pi\) | |||||||
\(860\) | −320.661 | −0.372862 | ||||||||
\(861\) | 195.076i | 0.226569i | ||||||||
\(862\) | 672.152i | 0.779759i | ||||||||
\(863\) | 866.353 | 1.00388 | 0.501942 | − | 0.864901i | \(-0.332619\pi\) | ||||
0.501942 | + | 0.864901i | \(0.332619\pi\) | |||||||
\(864\) | 77.4123 | 0.0895976 | ||||||||
\(865\) | − | 585.436i | − | 0.676805i | ||||||
\(866\) | 981.901i | 1.13384i | ||||||||
\(867\) | −1086.31 | −1.25295 | ||||||||
\(868\) | 158.109i | 0.182153i | ||||||||
\(869\) | −1138.00 | −1.30955 | ||||||||
\(870\) | − | 603.730i | − | 0.693943i | ||||||
\(871\) | − | 2492.27i | − | 2.86139i | ||||||
\(872\) | − | 85.5286i | − | 0.0980833i | ||||||
\(873\) | 774.586i | 0.887269i | ||||||||
\(874\) | −470.440 | + | 833.186i | −0.538261 | + | 0.953303i | ||||
\(875\) | −79.4005 | −0.0907434 | ||||||||
\(876\) | −365.110 | −0.416792 | ||||||||
\(877\) | 281.590 | 0.321084 | 0.160542 | − | 0.987029i | \(-0.448676\pi\) | ||||
0.160542 | + | 0.987029i | \(0.448676\pi\) | |||||||
\(878\) | −978.823 | −1.11483 | ||||||||
\(879\) | 1097.50i | 1.24858i | ||||||||
\(880\) | 100.752 | 0.114490 | ||||||||
\(881\) | 919.123i | 1.04327i | 0.853168 | + | 0.521636i | \(0.174678\pi\) | ||||
−0.853168 | + | 0.521636i | \(0.825322\pi\) | |||||||
\(882\) | −10.9481 | −0.0124128 | ||||||||
\(883\) | −821.800 | −0.930691 | −0.465346 | − | 0.885129i | \(-0.654070\pi\) | ||||
−0.465346 | + | 0.885129i | \(0.654070\pi\) | |||||||
\(884\) | 65.4460i | 0.0740340i | ||||||||
\(885\) | − | 558.948i | − | 0.631579i | ||||||
\(886\) | −398.901 | −0.450226 | ||||||||
\(887\) | 1280.91 | 1.44409 | 0.722047 | − | 0.691844i | \(-0.243201\pi\) | ||||
0.722047 | + | 0.691844i | \(0.243201\pi\) | |||||||
\(888\) | − | 435.044i | − | 0.489915i | ||||||
\(889\) | − | 212.705i | − | 0.239263i | ||||||
\(890\) | −30.4804 | −0.0342476 | ||||||||
\(891\) | − | 1131.54i | − | 1.26996i | ||||||
\(892\) | 423.955 | 0.475286 | ||||||||
\(893\) | − | 188.461i | − | 0.211043i | ||||||
\(894\) | 978.837i | 1.09490i | ||||||||
\(895\) | 412.345i | 0.460720i | ||||||||
\(896\) | 80.3476i | 0.0896737i | ||||||||
\(897\) | −1524.18 | − | 860.595i | −1.69920 | − | 0.959415i | ||||
\(898\) | −6.38621 | −0.00711160 | ||||||||
\(899\) | −560.180 | −0.623114 | ||||||||
\(900\) | −53.9287 | −0.0599208 | ||||||||
\(901\) | 33.3022 | 0.0369613 | ||||||||
\(902\) | − | 115.341i | − | 0.127873i | ||||||
\(903\) | −1931.85 | −2.13937 | ||||||||
\(904\) | − | 603.690i | − | 0.667798i | ||||||
\(905\) | −429.027 | −0.474063 | ||||||||
\(906\) | −159.674 | −0.176241 | ||||||||
\(907\) | 1726.39i | 1.90341i | 0.307021 | + | 0.951703i | \(0.400668\pi\) | ||||
−0.307021 | + | 0.951703i | \(0.599332\pi\) | |||||||
\(908\) | − | 779.882i | − | 0.858901i | ||||||
\(909\) | 556.000 | 0.611661 | ||||||||
\(910\) | 450.499 | 0.495053 | ||||||||
\(911\) | − | 791.171i | − | 0.868464i | −0.900801 | − | 0.434232i | \(-0.857020\pi\) | ||
0.900801 | − | 0.434232i | \(-0.142980\pi\) | |||||||
\(912\) | − | 446.399i | − | 0.489473i | ||||||
\(913\) | −1153.57 | −1.26350 | ||||||||
\(914\) | − | 564.328i | − | 0.617427i | ||||||
\(915\) | 320.054 | 0.349786 | ||||||||
\(916\) | 312.001i | 0.340612i | ||||||||
\(917\) | − | 827.262i | − | 0.902139i | ||||||
\(918\) | 31.5703i | 0.0343903i | ||||||||
\(919\) | − | 1272.36i | − | 1.38451i | −0.721655 | − | 0.692253i | \(-0.756618\pi\) | ||
0.721655 | − | 0.692253i | \(-0.243382\pi\) | |||||||
\(920\) | 71.5204 | − | 126.668i | 0.0777396 | − | 0.137683i | ||||
\(921\) | 2138.85 | 2.32231 | ||||||||
\(922\) | 62.5842 | 0.0678787 | ||||||||
\(923\) | 873.915 | 0.946820 | ||||||||
\(924\) | 606.986 | 0.656911 | ||||||||
\(925\) | − | 202.714i | − | 0.219151i | ||||||
\(926\) | −945.060 | −1.02058 | ||||||||
\(927\) | 533.159i | 0.575145i | ||||||||
\(928\) | −284.672 | −0.306758 | ||||||||
\(929\) | 672.653 | 0.724062 | 0.362031 | − | 0.932166i | \(-0.382083\pi\) | ||||
0.362031 | + | 0.932166i | \(0.382083\pi\) | |||||||
\(930\) | 133.546i | 0.143598i | ||||||||
\(931\) | − | 42.2273i | − | 0.0453569i | ||||||
\(932\) | −92.9936 | −0.0997785 | ||||||||
\(933\) | −291.905 | −0.312867 | ||||||||
\(934\) | 947.735i | 1.01471i | ||||||||
\(935\) | 41.0885i | 0.0439449i | ||||||||
\(936\) | 305.978 | 0.326900 | ||||||||
\(937\) | − | 1599.57i | − | 1.70711i | −0.520999 | − | 0.853557i | \(-0.674440\pi\) | ||
0.520999 | − | 0.853557i | \(-0.325560\pi\) | |||||||
\(938\) | 1247.82 | 1.33030 | ||||||||
\(939\) | − | 1657.03i | − | 1.76467i | ||||||
\(940\) | 28.6515i | 0.0304803i | ||||||||
\(941\) | 1628.06i | 1.73014i | 0.501651 | + | 0.865070i | \(0.332726\pi\) | ||||
−0.501651 | + | 0.865070i | \(0.667274\pi\) | |||||||
\(942\) | 343.961i | 0.365140i | ||||||||
\(943\) | −145.011 | − | 81.8770i | −0.153776 | − | 0.0868261i | ||||
\(944\) | −263.556 | −0.279190 | ||||||||
\(945\) | 217.314 | 0.229962 | ||||||||
\(946\) | 1142.23 | 1.20743 | ||||||||
\(947\) | −1829.88 | −1.93229 | −0.966147 | − | 0.257992i | \(-0.916939\pi\) | ||||
−0.966147 | + | 0.257992i | \(0.916939\pi\) | |||||||
\(948\) | − | 766.547i | − | 0.808594i | ||||||
\(949\) | 965.262 | 1.01714 | ||||||||
\(950\) | − | 208.005i | − | 0.218953i | ||||||
\(951\) | −362.980 | −0.381683 | ||||||||
\(952\) | −32.7673 | −0.0344195 | ||||||||
\(953\) | 655.714i | 0.688053i | 0.938960 | + | 0.344026i | \(0.111791\pi\) | ||||
−0.938960 | + | 0.344026i | \(0.888209\pi\) | |||||||
\(954\) | − | 155.697i | − | 0.163204i | ||||||
\(955\) | 72.9373 | 0.0763741 | ||||||||
\(956\) | −909.469 | −0.951328 | ||||||||
\(957\) | 2150.55i | 2.24718i | ||||||||
\(958\) | 439.102i | 0.458353i | ||||||||
\(959\) | 673.400 | 0.702190 | ||||||||
\(960\) | 67.8655i | 0.0706932i | ||||||||
\(961\) | −837.087 | −0.871059 | ||||||||
\(962\) | 1150.15i | 1.19558i | ||||||||
\(963\) | 121.606i | 0.126278i | ||||||||
\(964\) | − | 298.714i | − | 0.309870i | ||||||
\(965\) | − | 708.271i | − | 0.733960i | ||||||
\(966\) | 430.880 | − | 763.123i | 0.446046 | − | 0.789982i | ||||
\(967\) | 143.641 | 0.148543 | 0.0742716 | − | 0.997238i | \(-0.476337\pi\) | ||||
0.0742716 | + | 0.997238i | \(0.476337\pi\) | |||||||
\(968\) | −16.6481 | −0.0171984 | ||||||||
\(969\) | 182.050 | 0.187874 | ||||||||
\(970\) | 454.202 | 0.468250 | ||||||||
\(971\) | 1107.60i | 1.14068i | 0.821408 | + | 0.570341i | \(0.193189\pi\) | ||||
−0.821408 | + | 0.570341i | \(0.806811\pi\) | |||||||
\(972\) | 515.870 | 0.530730 | ||||||||
\(973\) | 634.030i | 0.651624i | ||||||||
\(974\) | 1173.29 | 1.20461 | ||||||||
\(975\) | 380.513 | 0.390269 | ||||||||
\(976\) | − | 150.912i | − | 0.154623i | ||||||
\(977\) | − | 626.322i | − | 0.641066i | −0.947237 | − | 0.320533i | \(-0.896138\pi\) | ||
0.947237 | − | 0.320533i | \(-0.103862\pi\) | |||||||
\(978\) | 404.178 | 0.413270 | ||||||||
\(979\) | 108.574 | 0.110903 | ||||||||
\(980\) | 6.41976i | 0.00655077i | ||||||||
\(981\) | − | 163.075i | − | 0.166233i | ||||||
\(982\) | −175.071 | −0.178280 | ||||||||
\(983\) | 202.538i | 0.206041i | 0.994679 | + | 0.103020i | \(0.0328507\pi\) | ||||
−0.994679 | + | 0.103020i | \(0.967149\pi\) | |||||||
\(984\) | 77.6928 | 0.0789561 | ||||||||
\(985\) | 435.912i | 0.442551i | ||||||||
\(986\) | − | 116.095i | − | 0.117743i | ||||||
\(987\) | 172.613i | 0.174887i | ||||||||
\(988\) | 1180.17i | 1.19450i | ||||||||
\(989\) | 810.833 | − | 1436.05i | 0.819851 | − | 1.45202i | ||||
\(990\) | 192.100 | 0.194040 | ||||||||
\(991\) | 354.302 | 0.357520 | 0.178760 | − | 0.983893i | \(-0.442791\pi\) | ||||
0.178760 | + | 0.983893i | \(0.442791\pi\) | |||||||
\(992\) | 62.9699 | 0.0634777 | ||||||||
\(993\) | −1954.33 | −1.96810 | ||||||||
\(994\) | 437.549i | 0.440190i | ||||||||
\(995\) | 165.651 | 0.166484 | ||||||||
\(996\) | − | 777.037i | − | 0.780157i | ||||||
\(997\) | 184.596 | 0.185152 | 0.0925758 | − | 0.995706i | \(-0.470490\pi\) | ||||
0.0925758 | + | 0.995706i | \(0.470490\pi\) | |||||||
\(998\) | 1071.86 | 1.07401 | ||||||||
\(999\) | 554.817i | 0.555372i |
(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 | 230.3.d.a.91.9 | ✓ | 16 | |
3.2 | odd | 2 | 2070.3.c.a.91.8 | 16 | |||
4.3 | odd | 2 | 1840.3.k.d.321.13 | 16 | |||
5.2 | odd | 4 | 1150.3.c.c.1149.10 | 32 | |||
5.3 | odd | 4 | 1150.3.c.c.1149.23 | 32 | |||
5.4 | even | 2 | 1150.3.d.b.551.7 | 16 | |||
23.22 | odd | 2 | inner | 230.3.d.a.91.10 | yes | 16 | |
69.68 | even | 2 | 2070.3.c.a.91.1 | 16 | |||
92.91 | even | 2 | 1840.3.k.d.321.14 | 16 | |||
115.22 | even | 4 | 1150.3.c.c.1149.24 | 32 | |||
115.68 | even | 4 | 1150.3.c.c.1149.9 | 32 | |||
115.114 | odd | 2 | 1150.3.d.b.551.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.9 | ✓ | 16 | 1.1 | even | 1 | trivial | |
230.3.d.a.91.10 | yes | 16 | 23.22 | odd | 2 | inner | |
1150.3.c.c.1149.9 | 32 | 115.68 | even | 4 | |||
1150.3.c.c.1149.10 | 32 | 5.2 | odd | 4 | |||
1150.3.c.c.1149.23 | 32 | 5.3 | odd | 4 | |||
1150.3.c.c.1149.24 | 32 | 115.22 | even | 4 | |||
1150.3.d.b.551.7 | 16 | 5.4 | even | 2 | |||
1150.3.d.b.551.8 | 16 | 115.114 | odd | 2 | |||
1840.3.k.d.321.13 | 16 | 4.3 | odd | 2 | |||
1840.3.k.d.321.14 | 16 | 92.91 | even | 2 | |||
2070.3.c.a.91.1 | 16 | 69.68 | even | 2 | |||
2070.3.c.a.91.8 | 16 | 3.2 | odd | 2 |