Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(91,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, 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("690.91");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.2 | ||
Character | \(\chi\) | \(=\) | 690.91 |
Dual form | 690.3.c.a.91.7 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | − | 8.87387i | − | 1.26770i | −0.773458 | − | 0.633848i | \(-0.781474\pi\) | ||
0.773458 | − | 0.633848i | \(-0.218526\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 3.16228i | 0.316228i | ||||||||
\(11\) | 6.26975i | 0.569977i | 0.958531 | + | 0.284989i | \(0.0919898\pi\) | ||||
−0.958531 | + | 0.284989i | \(0.908010\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | 22.5219 | 1.73245 | 0.866227 | − | 0.499650i | \(-0.166538\pi\) | ||||
0.866227 | + | 0.499650i | \(0.166538\pi\) | |||||||
\(14\) | 12.5496i | 0.896396i | ||||||||
\(15\) | 3.87298i | 0.258199i | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 9.43891i | 0.555230i | 0.960692 | + | 0.277615i | \(0.0895440\pi\) | ||||
−0.960692 | + | 0.277615i | \(0.910456\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | − | 10.5287i | − | 0.554145i | −0.960849 | − | 0.277072i | \(-0.910636\pi\) | ||
0.960849 | − | 0.277072i | \(-0.0893642\pi\) | |||||||
\(20\) | − | 4.47214i | − | 0.223607i | ||||||
\(21\) | 15.3700i | 0.731905i | ||||||||
\(22\) | − | 8.86676i | − | 0.403035i | ||||||
\(23\) | 22.7674 | − | 3.26244i | 0.989889 | − | 0.141845i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −31.8508 | −1.22503 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | − | 17.7477i | − | 0.633848i | ||||||
\(29\) | −7.04808 | −0.243037 | −0.121519 | − | 0.992589i | \(-0.538776\pi\) | ||||
−0.121519 | + | 0.992589i | \(0.538776\pi\) | |||||||
\(30\) | − | 5.47723i | − | 0.182574i | ||||||
\(31\) | −18.9154 | −0.610174 | −0.305087 | − | 0.952324i | \(-0.598686\pi\) | ||||
−0.305087 | + | 0.952324i | \(0.598686\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − | 10.8595i | − | 0.329076i | ||||||
\(34\) | − | 13.3486i | − | 0.392607i | ||||||
\(35\) | −19.8426 | −0.566931 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 39.6300i | 1.07108i | 0.844510 | + | 0.535540i | \(0.179892\pi\) | ||||
−0.844510 | + | 0.535540i | \(0.820108\pi\) | |||||||
\(38\) | 14.8899i | 0.391839i | ||||||||
\(39\) | −39.0091 | −1.00023 | ||||||||
\(40\) | 6.32456i | 0.158114i | ||||||||
\(41\) | −2.96787 | −0.0723872 | −0.0361936 | − | 0.999345i | \(-0.511523\pi\) | ||||
−0.0361936 | + | 0.999345i | \(0.511523\pi\) | |||||||
\(42\) | − | 21.7365i | − | 0.517535i | ||||||
\(43\) | − | 73.5577i | − | 1.71064i | −0.518097 | − | 0.855322i | \(-0.673359\pi\) | ||
0.518097 | − | 0.855322i | \(-0.326641\pi\) | |||||||
\(44\) | 12.5395i | 0.284989i | ||||||||
\(45\) | − | 6.70820i | − | 0.149071i | ||||||
\(46\) | −32.1980 | + | 4.61379i | −0.699957 | + | 0.100300i | ||||
\(47\) | 64.8976 | 1.38080 | 0.690400 | − | 0.723428i | \(-0.257435\pi\) | ||||
0.690400 | + | 0.723428i | \(0.257435\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | −29.7456 | −0.607053 | ||||||||
\(50\) | 7.07107 | 0.141421 | ||||||||
\(51\) | − | 16.3487i | − | 0.320562i | ||||||
\(52\) | 45.0438 | 0.866227 | ||||||||
\(53\) | 14.0544i | 0.265177i | 0.991171 | + | 0.132589i | \(0.0423290\pi\) | ||||
−0.991171 | + | 0.132589i | \(0.957671\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | 14.0196 | 0.254901 | ||||||||
\(56\) | 25.0991i | 0.448198i | ||||||||
\(57\) | 18.2363i | 0.319936i | ||||||||
\(58\) | 9.96748 | 0.171853 | ||||||||
\(59\) | 19.3254 | 0.327548 | 0.163774 | − | 0.986498i | \(-0.447633\pi\) | ||||
0.163774 | + | 0.986498i | \(0.447633\pi\) | |||||||
\(60\) | 7.74597i | 0.129099i | ||||||||
\(61\) | − | 55.1446i | − | 0.904010i | −0.892015 | − | 0.452005i | \(-0.850709\pi\) | ||
0.892015 | − | 0.452005i | \(-0.149291\pi\) | |||||||
\(62\) | 26.7504 | 0.431458 | ||||||||
\(63\) | − | 26.6216i | − | 0.422565i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | − | 50.3605i | − | 0.774777i | ||||||
\(66\) | 15.3577i | 0.232692i | ||||||||
\(67\) | − | 41.0130i | − | 0.612134i | −0.952010 | − | 0.306067i | \(-0.900987\pi\) | ||
0.952010 | − | 0.306067i | \(-0.0990132\pi\) | |||||||
\(68\) | 18.8778i | 0.277615i | ||||||||
\(69\) | −39.4344 | + | 5.65071i | −0.571513 | + | 0.0818944i | ||||
\(70\) | 28.0616 | 0.400881 | ||||||||
\(71\) | −33.4246 | −0.470769 | −0.235384 | − | 0.971902i | \(-0.575635\pi\) | ||||
−0.235384 | + | 0.971902i | \(0.575635\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | 40.7761 | 0.558576 | 0.279288 | − | 0.960207i | \(-0.409902\pi\) | ||||
0.279288 | + | 0.960207i | \(0.409902\pi\) | |||||||
\(74\) | − | 56.0452i | − | 0.757368i | ||||||
\(75\) | 8.66025 | 0.115470 | ||||||||
\(76\) | − | 21.0575i | − | 0.277072i | ||||||
\(77\) | 55.6369 | 0.722558 | ||||||||
\(78\) | 55.1672 | 0.707272 | ||||||||
\(79\) | − | 49.8081i | − | 0.630482i | −0.949012 | − | 0.315241i | \(-0.897915\pi\) | ||
0.949012 | − | 0.315241i | \(-0.102085\pi\) | |||||||
\(80\) | − | 8.94427i | − | 0.111803i | ||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 4.19721 | 0.0511855 | ||||||||
\(83\) | − | 36.6835i | − | 0.441969i | −0.975277 | − | 0.220985i | \(-0.929073\pi\) | ||
0.975277 | − | 0.220985i | \(-0.0709271\pi\) | |||||||
\(84\) | 30.7400i | 0.365952i | ||||||||
\(85\) | 21.1060 | 0.248306 | ||||||||
\(86\) | 104.026i | 1.20961i | ||||||||
\(87\) | 12.2076 | 0.140318 | ||||||||
\(88\) | − | 17.7335i | − | 0.201517i | ||||||
\(89\) | − | 129.178i | − | 1.45144i | −0.687992 | − | 0.725718i | \(-0.741508\pi\) | ||
0.687992 | − | 0.725718i | \(-0.258492\pi\) | |||||||
\(90\) | 9.48683i | 0.105409i | ||||||||
\(91\) | − | 199.857i | − | 2.19623i | ||||||
\(92\) | 45.5349 | − | 6.52488i | 0.494944 | − | 0.0709226i | ||||
\(93\) | 32.7624 | 0.352284 | ||||||||
\(94\) | −91.7790 | −0.976372 | ||||||||
\(95\) | −23.5430 | −0.247821 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | − | 101.382i | − | 1.04518i | −0.852585 | − | 0.522588i | \(-0.824967\pi\) | ||
0.852585 | − | 0.522588i | \(-0.175033\pi\) | |||||||
\(98\) | 42.0666 | 0.429252 | ||||||||
\(99\) | 18.8092i | 0.189992i | ||||||||
\(100\) | −10.0000 | −0.100000 | ||||||||
\(101\) | −162.334 | −1.60726 | −0.803632 | − | 0.595127i | \(-0.797102\pi\) | ||||
−0.803632 | + | 0.595127i | \(0.797102\pi\) | |||||||
\(102\) | 23.1205i | 0.226672i | ||||||||
\(103\) | − | 131.572i | − | 1.27740i | −0.769456 | − | 0.638699i | \(-0.779473\pi\) | ||
0.769456 | − | 0.638699i | \(-0.220527\pi\) | |||||||
\(104\) | −63.7016 | −0.612515 | ||||||||
\(105\) | 34.3684 | 0.327318 | ||||||||
\(106\) | − | 19.8759i | − | 0.187509i | ||||||
\(107\) | 15.7264i | 0.146976i | 0.997296 | + | 0.0734878i | \(0.0234130\pi\) | ||||
−0.997296 | + | 0.0734878i | \(0.976587\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | − | 99.8298i | − | 0.915870i | −0.888986 | − | 0.457935i | \(-0.848589\pi\) | ||
0.888986 | − | 0.457935i | \(-0.151411\pi\) | |||||||
\(110\) | −19.8267 | −0.180243 | ||||||||
\(111\) | − | 68.6411i | − | 0.618388i | ||||||
\(112\) | − | 35.4955i | − | 0.316924i | ||||||
\(113\) | 139.012i | 1.23020i | 0.788450 | + | 0.615099i | \(0.210884\pi\) | ||||
−0.788450 | + | 0.615099i | \(0.789116\pi\) | |||||||
\(114\) | − | 25.7901i | − | 0.226229i | ||||||
\(115\) | −7.29504 | − | 50.9096i | −0.0634351 | − | 0.442692i | ||||
\(116\) | −14.0962 | −0.121519 | ||||||||
\(117\) | 67.5657 | 0.577485 | ||||||||
\(118\) | −27.3302 | −0.231612 | ||||||||
\(119\) | 83.7597 | 0.703863 | ||||||||
\(120\) | − | 10.9545i | − | 0.0912871i | ||||||
\(121\) | 81.6903 | 0.675126 | ||||||||
\(122\) | 77.9863i | 0.639232i | ||||||||
\(123\) | 5.14051 | 0.0417928 | ||||||||
\(124\) | −37.8308 | −0.305087 | ||||||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | 37.6487i | 0.298799i | ||||||||
\(127\) | −9.57946 | −0.0754288 | −0.0377144 | − | 0.999289i | \(-0.512008\pi\) | ||||
−0.0377144 | + | 0.999289i | \(0.512008\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 127.406i | 0.987641i | ||||||||
\(130\) | 71.2205i | 0.547850i | ||||||||
\(131\) | −50.3313 | −0.384209 | −0.192104 | − | 0.981375i | \(-0.561531\pi\) | ||||
−0.192104 | + | 0.981375i | \(0.561531\pi\) | |||||||
\(132\) | − | 21.7190i | − | 0.164538i | ||||||
\(133\) | −93.4308 | −0.702487 | ||||||||
\(134\) | 58.0011i | 0.432844i | ||||||||
\(135\) | 11.6190i | 0.0860663i | ||||||||
\(136\) | − | 26.6973i | − | 0.196303i | ||||||
\(137\) | − | 56.8530i | − | 0.414985i | −0.978237 | − | 0.207493i | \(-0.933470\pi\) | ||
0.978237 | − | 0.207493i | \(-0.0665303\pi\) | |||||||
\(138\) | 55.7686 | − | 7.99132i | 0.404120 | − | 0.0579081i | ||||
\(139\) | 106.054 | 0.762976 | 0.381488 | − | 0.924374i | \(-0.375412\pi\) | ||||
0.381488 | + | 0.924374i | \(0.375412\pi\) | |||||||
\(140\) | −39.6852 | −0.283465 | ||||||||
\(141\) | −112.406 | −0.797205 | ||||||||
\(142\) | 47.2695 | 0.332884 | ||||||||
\(143\) | 141.207i | 0.987459i | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 15.7600i | 0.108689i | ||||||||
\(146\) | −57.6660 | −0.394973 | ||||||||
\(147\) | 51.5209 | 0.350482 | ||||||||
\(148\) | 79.2599i | 0.535540i | ||||||||
\(149\) | 50.9174i | 0.341728i | 0.985295 | + | 0.170864i | \(0.0546558\pi\) | ||||
−0.985295 | + | 0.170864i | \(0.945344\pi\) | |||||||
\(150\) | −12.2474 | −0.0816497 | ||||||||
\(151\) | −214.536 | −1.42077 | −0.710383 | − | 0.703815i | \(-0.751478\pi\) | ||||
−0.710383 | + | 0.703815i | \(0.751478\pi\) | |||||||
\(152\) | 29.7798i | 0.195920i | ||||||||
\(153\) | 28.3167i | 0.185077i | ||||||||
\(154\) | −78.6825 | −0.510925 | ||||||||
\(155\) | 42.2961i | 0.272878i | ||||||||
\(156\) | −78.0182 | −0.500117 | ||||||||
\(157\) | 33.5167i | 0.213482i | 0.994287 | + | 0.106741i | \(0.0340416\pi\) | ||||
−0.994287 | + | 0.106741i | \(0.965958\pi\) | |||||||
\(158\) | 70.4393i | 0.445818i | ||||||||
\(159\) | − | 24.3429i | − | 0.153100i | ||||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | −28.9505 | − | 202.035i | −0.179817 | − | 1.25488i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 173.861 | 1.06663 | 0.533317 | − | 0.845915i | \(-0.320945\pi\) | ||||
0.533317 | + | 0.845915i | \(0.320945\pi\) | |||||||
\(164\) | −5.93575 | −0.0361936 | ||||||||
\(165\) | −24.2826 | −0.147167 | ||||||||
\(166\) | 51.8782i | 0.312519i | ||||||||
\(167\) | 73.4751 | 0.439971 | 0.219985 | − | 0.975503i | \(-0.429399\pi\) | ||||
0.219985 | + | 0.975503i | \(0.429399\pi\) | |||||||
\(168\) | − | 43.4729i | − | 0.258767i | ||||||
\(169\) | 338.237 | 2.00140 | ||||||||
\(170\) | −29.8485 | −0.175579 | ||||||||
\(171\) | − | 31.5862i | − | 0.184715i | ||||||
\(172\) | − | 147.115i | − | 0.855322i | ||||||
\(173\) | 85.3858 | 0.493559 | 0.246780 | − | 0.969072i | \(-0.420628\pi\) | ||||
0.246780 | + | 0.969072i | \(0.420628\pi\) | |||||||
\(174\) | −17.2642 | −0.0992195 | ||||||||
\(175\) | 44.3694i | 0.253539i | ||||||||
\(176\) | 25.0790i | 0.142494i | ||||||||
\(177\) | −33.4725 | −0.189110 | ||||||||
\(178\) | 182.685i | 1.02632i | ||||||||
\(179\) | 49.1221 | 0.274425 | 0.137213 | − | 0.990542i | \(-0.456186\pi\) | ||||
0.137213 | + | 0.990542i | \(0.456186\pi\) | |||||||
\(180\) | − | 13.4164i | − | 0.0745356i | ||||||
\(181\) | − | 6.70433i | − | 0.0370405i | −0.999828 | − | 0.0185203i | \(-0.994104\pi\) | ||
0.999828 | − | 0.0185203i | \(-0.00589552\pi\) | |||||||
\(182\) | 282.640i | 1.55297i | ||||||||
\(183\) | 95.5133i | 0.521931i | ||||||||
\(184\) | −64.3961 | + | 9.22758i | −0.349979 | + | 0.0501499i | ||||
\(185\) | 88.6153 | 0.479002 | ||||||||
\(186\) | −46.3331 | −0.249103 | ||||||||
\(187\) | −59.1796 | −0.316468 | ||||||||
\(188\) | 129.795 | 0.690400 | ||||||||
\(189\) | 46.1100i | 0.243968i | ||||||||
\(190\) | 33.2948 | 0.175236 | ||||||||
\(191\) | − | 155.274i | − | 0.812954i | −0.913661 | − | 0.406477i | \(-0.866757\pi\) | ||
0.913661 | − | 0.406477i | \(-0.133243\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | −29.0926 | −0.150739 | −0.0753695 | − | 0.997156i | \(-0.524014\pi\) | ||||
−0.0753695 | + | 0.997156i | \(0.524014\pi\) | |||||||
\(194\) | 143.376i | 0.739051i | ||||||||
\(195\) | 87.2270i | 0.447318i | ||||||||
\(196\) | −59.4912 | −0.303527 | ||||||||
\(197\) | −323.403 | −1.64164 | −0.820820 | − | 0.571187i | \(-0.806483\pi\) | ||||
−0.820820 | + | 0.571187i | \(0.806483\pi\) | |||||||
\(198\) | − | 26.6003i | − | 0.134345i | ||||||
\(199\) | 317.291i | 1.59443i | 0.603697 | + | 0.797214i | \(0.293694\pi\) | ||||
−0.603697 | + | 0.797214i | \(0.706306\pi\) | |||||||
\(200\) | 14.1421 | 0.0707107 | ||||||||
\(201\) | 71.0366i | 0.353416i | ||||||||
\(202\) | 229.574 | 1.13651 | ||||||||
\(203\) | 62.5437i | 0.308097i | ||||||||
\(204\) | − | 32.6973i | − | 0.160281i | ||||||
\(205\) | 6.63637i | 0.0323725i | ||||||||
\(206\) | 186.071i | 0.903257i | ||||||||
\(207\) | 68.3023 | − | 9.78732i | 0.329963 | − | 0.0472818i | ||||
\(208\) | 90.0876 | 0.433114 | ||||||||
\(209\) | 66.0126 | 0.315850 | ||||||||
\(210\) | −48.6042 | −0.231449 | ||||||||
\(211\) | −254.286 | −1.20515 | −0.602573 | − | 0.798064i | \(-0.705858\pi\) | ||||
−0.602573 | + | 0.798064i | \(0.705858\pi\) | |||||||
\(212\) | 28.1088i | 0.132589i | ||||||||
\(213\) | 57.8931 | 0.271799 | ||||||||
\(214\) | − | 22.2405i | − | 0.103927i | ||||||
\(215\) | −164.480 | −0.765023 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | 167.853i | 0.773516i | ||||||||
\(218\) | 141.181i | 0.647618i | ||||||||
\(219\) | −70.6262 | −0.322494 | ||||||||
\(220\) | 28.0392 | 0.127451 | ||||||||
\(221\) | 212.582i | 0.961911i | ||||||||
\(222\) | 97.0732i | 0.437267i | ||||||||
\(223\) | 82.8200 | 0.371390 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(224\) | 50.1982i | 0.224099i | ||||||||
\(225\) | −15.0000 | −0.0666667 | ||||||||
\(226\) | − | 196.593i | − | 0.869882i | ||||||
\(227\) | − | 89.4993i | − | 0.394270i | −0.980376 | − | 0.197135i | \(-0.936836\pi\) | ||
0.980376 | − | 0.197135i | \(-0.0631637\pi\) | |||||||
\(228\) | 36.4727i | 0.159968i | ||||||||
\(229\) | 32.1076i | 0.140208i | 0.997540 | + | 0.0701040i | \(0.0223331\pi\) | ||||
−0.997540 | + | 0.0701040i | \(0.977667\pi\) | |||||||
\(230\) | 10.3167 | + | 71.9970i | 0.0448554 | + | 0.313030i | ||||
\(231\) | −96.3660 | −0.417169 | ||||||||
\(232\) | 19.9350 | 0.0859266 | ||||||||
\(233\) | −167.955 | −0.720837 | −0.360418 | − | 0.932791i | \(-0.617366\pi\) | ||||
−0.360418 | + | 0.932791i | \(0.617366\pi\) | |||||||
\(234\) | −95.5524 | −0.408344 | ||||||||
\(235\) | − | 145.115i | − | 0.617512i | ||||||
\(236\) | 38.6507 | 0.163774 | ||||||||
\(237\) | 86.2702i | 0.364009i | ||||||||
\(238\) | −118.454 | −0.497706 | ||||||||
\(239\) | 96.4681 | 0.403632 | 0.201816 | − | 0.979423i | \(-0.435316\pi\) | ||||
0.201816 | + | 0.979423i | \(0.435316\pi\) | |||||||
\(240\) | 15.4919i | 0.0645497i | ||||||||
\(241\) | 428.477i | 1.77791i | 0.457991 | + | 0.888957i | \(0.348569\pi\) | ||||
−0.457991 | + | 0.888957i | \(0.651431\pi\) | |||||||
\(242\) | −115.527 | −0.477386 | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 110.289i | − | 0.452005i | ||||||
\(245\) | 66.5132i | 0.271482i | ||||||||
\(246\) | −7.26978 | −0.0295519 | ||||||||
\(247\) | − | 237.128i | − | 0.960031i | ||||||
\(248\) | 53.5008 | 0.215729 | ||||||||
\(249\) | 63.5376i | 0.255171i | ||||||||
\(250\) | − | 15.8114i | − | 0.0632456i | ||||||
\(251\) | 62.3046i | 0.248226i | 0.992268 | + | 0.124113i | \(0.0396085\pi\) | ||||
−0.992268 | + | 0.124113i | \(0.960392\pi\) | |||||||
\(252\) | − | 53.2432i | − | 0.211283i | ||||||
\(253\) | 20.4547 | + | 142.746i | 0.0808485 | + | 0.564214i | ||||
\(254\) | 13.5474 | 0.0533362 | ||||||||
\(255\) | −36.5567 | −0.143360 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −89.4115 | −0.347905 | −0.173952 | − | 0.984754i | \(-0.555654\pi\) | ||||
−0.173952 | + | 0.984754i | \(0.555654\pi\) | |||||||
\(258\) | − | 180.179i | − | 0.698368i | ||||||
\(259\) | 351.671 | 1.35780 | ||||||||
\(260\) | − | 100.721i | − | 0.387389i | ||||||
\(261\) | −21.1442 | −0.0810124 | ||||||||
\(262\) | 71.1792 | 0.271676 | ||||||||
\(263\) | − | 373.027i | − | 1.41835i | −0.705030 | − | 0.709177i | \(-0.749067\pi\) | ||
0.705030 | − | 0.709177i | \(-0.250933\pi\) | |||||||
\(264\) | 30.7154i | 0.116346i | ||||||||
\(265\) | 31.4266 | 0.118591 | ||||||||
\(266\) | 132.131 | 0.496733 | ||||||||
\(267\) | 223.743i | 0.837987i | ||||||||
\(268\) | − | 82.0260i | − | 0.306067i | ||||||
\(269\) | −329.332 | −1.22428 | −0.612141 | − | 0.790748i | \(-0.709692\pi\) | ||||
−0.612141 | + | 0.790748i | \(0.709692\pi\) | |||||||
\(270\) | − | 16.4317i | − | 0.0608581i | ||||||
\(271\) | −474.870 | −1.75229 | −0.876144 | − | 0.482049i | \(-0.839893\pi\) | ||||
−0.876144 | + | 0.482049i | \(0.839893\pi\) | |||||||
\(272\) | 37.7556i | 0.138808i | ||||||||
\(273\) | 346.162i | 1.26799i | ||||||||
\(274\) | 80.4023i | 0.293439i | ||||||||
\(275\) | − | 31.3487i | − | 0.113995i | ||||||
\(276\) | −78.8687 | + | 11.3014i | −0.285756 | + | 0.0409472i | ||||
\(277\) | −65.9751 | −0.238177 | −0.119089 | − | 0.992884i | \(-0.537997\pi\) | ||||
−0.119089 | + | 0.992884i | \(0.537997\pi\) | |||||||
\(278\) | −149.983 | −0.539506 | ||||||||
\(279\) | −56.7462 | −0.203391 | ||||||||
\(280\) | 56.1233 | 0.200440 | ||||||||
\(281\) | 414.508i | 1.47512i | 0.675284 | + | 0.737558i | \(0.264021\pi\) | ||||
−0.675284 | + | 0.737558i | \(0.735979\pi\) | |||||||
\(282\) | 158.966 | 0.563709 | ||||||||
\(283\) | − | 447.429i | − | 1.58102i | −0.612448 | − | 0.790511i | \(-0.709815\pi\) | ||
0.612448 | − | 0.790511i | \(-0.290185\pi\) | |||||||
\(284\) | −66.8492 | −0.235384 | ||||||||
\(285\) | 40.7777 | 0.143080 | ||||||||
\(286\) | − | 199.696i | − | 0.698239i | ||||||
\(287\) | 26.3365i | 0.0917649i | ||||||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | 199.907 | 0.691720 | ||||||||
\(290\) | − | 22.2880i | − | 0.0768551i | ||||||
\(291\) | 175.599i | 0.603433i | ||||||||
\(292\) | 81.5521 | 0.279288 | ||||||||
\(293\) | 346.420i | 1.18232i | 0.806554 | + | 0.591160i | \(0.201330\pi\) | ||||
−0.806554 | + | 0.591160i | \(0.798670\pi\) | |||||||
\(294\) | −72.8616 | −0.247828 | ||||||||
\(295\) | − | 43.2128i | − | 0.146484i | ||||||
\(296\) | − | 112.090i | − | 0.378684i | ||||||
\(297\) | − | 32.5786i | − | 0.109692i | ||||||
\(298\) | − | 72.0081i | − | 0.241638i | ||||||
\(299\) | 512.766 | − | 73.4764i | 1.71494 | − | 0.245740i | ||||
\(300\) | 17.3205 | 0.0577350 | ||||||||
\(301\) | −652.742 | −2.16858 | ||||||||
\(302\) | 303.399 | 1.00463 | ||||||||
\(303\) | 281.170 | 0.927954 | ||||||||
\(304\) | − | 42.1150i | − | 0.138536i | ||||||
\(305\) | −123.307 | −0.404286 | ||||||||
\(306\) | − | 40.0459i | − | 0.130869i | ||||||
\(307\) | 531.509 | 1.73130 | 0.865650 | − | 0.500649i | \(-0.166905\pi\) | ||||
0.865650 | + | 0.500649i | \(0.166905\pi\) | |||||||
\(308\) | 111.274 | 0.361279 | ||||||||
\(309\) | 227.890i | 0.737507i | ||||||||
\(310\) | − | 59.8158i | − | 0.192954i | ||||||
\(311\) | 423.951 | 1.36319 | 0.681594 | − | 0.731731i | \(-0.261287\pi\) | ||||
0.681594 | + | 0.731731i | \(0.261287\pi\) | |||||||
\(312\) | 110.334 | 0.353636 | ||||||||
\(313\) | − | 3.36548i | − | 0.0107523i | −0.999986 | − | 0.00537616i | \(-0.998289\pi\) | ||
0.999986 | − | 0.00537616i | \(-0.00171129\pi\) | |||||||
\(314\) | − | 47.3998i | − | 0.150955i | ||||||
\(315\) | −59.5277 | −0.188977 | ||||||||
\(316\) | − | 99.6162i | − | 0.315241i | ||||||
\(317\) | 162.592 | 0.512910 | 0.256455 | − | 0.966556i | \(-0.417445\pi\) | ||||
0.256455 | + | 0.966556i | \(0.417445\pi\) | |||||||
\(318\) | 34.4261i | 0.108258i | ||||||||
\(319\) | − | 44.1897i | − | 0.138526i | ||||||
\(320\) | − | 17.8885i | − | 0.0559017i | ||||||
\(321\) | − | 27.2389i | − | 0.0848564i | ||||||
\(322\) | 40.9422 | + | 285.721i | 0.127150 | + | 0.887333i | ||||
\(323\) | 99.3799 | 0.307678 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | −112.610 | −0.346491 | ||||||||
\(326\) | −245.877 | −0.754225 | ||||||||
\(327\) | 172.910i | 0.528778i | ||||||||
\(328\) | 8.39442 | 0.0255927 | ||||||||
\(329\) | − | 575.893i | − | 1.75043i | ||||||
\(330\) | 34.3408 | 0.104063 | ||||||||
\(331\) | −610.713 | −1.84505 | −0.922527 | − | 0.385933i | \(-0.873880\pi\) | ||||
−0.922527 | + | 0.385933i | \(0.873880\pi\) | |||||||
\(332\) | − | 73.3669i | − | 0.220985i | ||||||
\(333\) | 118.890i | 0.357027i | ||||||||
\(334\) | −103.910 | −0.311106 | ||||||||
\(335\) | −91.7079 | −0.273755 | ||||||||
\(336\) | 61.4800i | 0.182976i | ||||||||
\(337\) | 103.172i | 0.306148i | 0.988215 | + | 0.153074i | \(0.0489174\pi\) | ||||
−0.988215 | + | 0.153074i | \(0.951083\pi\) | |||||||
\(338\) | −478.339 | −1.41520 | ||||||||
\(339\) | − | 240.777i | − | 0.710256i | ||||||
\(340\) | 42.2121 | 0.124153 | ||||||||
\(341\) | − | 118.595i | − | 0.347785i | ||||||
\(342\) | 44.6697i | 0.130613i | ||||||||
\(343\) | − | 170.861i | − | 0.498137i | ||||||
\(344\) | 208.053i | 0.604804i | ||||||||
\(345\) | 12.6354 | + | 88.1779i | 0.0366243 | + | 0.255588i | ||||
\(346\) | −120.754 | −0.348999 | ||||||||
\(347\) | 589.976 | 1.70022 | 0.850109 | − | 0.526606i | \(-0.176536\pi\) | ||||
0.850109 | + | 0.526606i | \(0.176536\pi\) | |||||||
\(348\) | 24.4153 | 0.0701588 | ||||||||
\(349\) | 90.7968 | 0.260163 | 0.130081 | − | 0.991503i | \(-0.458476\pi\) | ||||
0.130081 | + | 0.991503i | \(0.458476\pi\) | |||||||
\(350\) | − | 62.7478i | − | 0.179279i | ||||||
\(351\) | −117.027 | −0.333411 | ||||||||
\(352\) | − | 35.4670i | − | 0.100759i | ||||||
\(353\) | −41.1499 | −0.116572 | −0.0582859 | − | 0.998300i | \(-0.518564\pi\) | ||||
−0.0582859 | + | 0.998300i | \(0.518564\pi\) | |||||||
\(354\) | 47.3373 | 0.133721 | ||||||||
\(355\) | 74.7397i | 0.210534i | ||||||||
\(356\) | − | 258.356i | − | 0.725718i | ||||||
\(357\) | −145.076 | −0.406375 | ||||||||
\(358\) | −69.4692 | −0.194048 | ||||||||
\(359\) | − | 227.208i | − | 0.632892i | −0.948610 | − | 0.316446i | \(-0.897510\pi\) | ||
0.948610 | − | 0.316446i | \(-0.102490\pi\) | |||||||
\(360\) | 18.9737i | 0.0527046i | ||||||||
\(361\) | 250.145 | 0.692924 | ||||||||
\(362\) | 9.48136i | 0.0261916i | ||||||||
\(363\) | −141.492 | −0.389784 | ||||||||
\(364\) | − | 399.713i | − | 1.09811i | ||||||
\(365\) | − | 91.1780i | − | 0.249803i | ||||||
\(366\) | − | 135.076i | − | 0.369061i | ||||||
\(367\) | − | 47.5374i | − | 0.129530i | −0.997901 | − | 0.0647648i | \(-0.979370\pi\) | ||
0.997901 | − | 0.0647648i | \(-0.0206297\pi\) | |||||||
\(368\) | 91.0698 | − | 13.0498i | 0.247472 | − | 0.0354613i | ||||
\(369\) | −8.90362 | −0.0241291 | ||||||||
\(370\) | −125.321 | −0.338705 | ||||||||
\(371\) | 124.717 | 0.336164 | ||||||||
\(372\) | 65.5249 | 0.176142 | ||||||||
\(373\) | 436.640i | 1.17062i | 0.810811 | + | 0.585308i | \(0.199026\pi\) | ||||
−0.810811 | + | 0.585308i | \(0.800974\pi\) | |||||||
\(374\) | 83.6926 | 0.223777 | ||||||||
\(375\) | − | 19.3649i | − | 0.0516398i | ||||||
\(376\) | −183.558 | −0.488186 | ||||||||
\(377\) | −158.736 | −0.421051 | ||||||||
\(378\) | − | 65.2094i | − | 0.172512i | ||||||
\(379\) | 430.461i | 1.13578i | 0.823104 | + | 0.567891i | \(0.192240\pi\) | ||||
−0.823104 | + | 0.567891i | \(0.807760\pi\) | |||||||
\(380\) | −47.0860 | −0.123911 | ||||||||
\(381\) | 16.5921 | 0.0435489 | ||||||||
\(382\) | 219.591i | 0.574846i | ||||||||
\(383\) | − | 625.629i | − | 1.63350i | −0.576994 | − | 0.816748i | \(-0.695774\pi\) | ||
0.576994 | − | 0.816748i | \(-0.304226\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | − | 124.408i | − | 0.323138i | ||||||
\(386\) | 41.1432 | 0.106589 | ||||||||
\(387\) | − | 220.673i | − | 0.570215i | ||||||
\(388\) | − | 202.764i | − | 0.522588i | ||||||
\(389\) | 499.976i | 1.28529i | 0.766166 | + | 0.642643i | \(0.222162\pi\) | ||||
−0.766166 | + | 0.642643i | \(0.777838\pi\) | |||||||
\(390\) | − | 123.358i | − | 0.316302i | ||||||
\(391\) | 30.7939 | + | 214.900i | 0.0787567 | + | 0.549616i | ||||
\(392\) | 84.1333 | 0.214626 | ||||||||
\(393\) | 87.1764 | 0.221823 | ||||||||
\(394\) | 457.361 | 1.16081 | ||||||||
\(395\) | −111.374 | −0.281960 | ||||||||
\(396\) | 37.6185i | 0.0949962i | ||||||||
\(397\) | 212.359 | 0.534909 | 0.267455 | − | 0.963570i | \(-0.413817\pi\) | ||||
0.267455 | + | 0.963570i | \(0.413817\pi\) | |||||||
\(398\) | − | 448.718i | − | 1.12743i | ||||||
\(399\) | 161.827 | 0.405581 | ||||||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | − | 109.048i | − | 0.271940i | −0.990713 | − | 0.135970i | \(-0.956585\pi\) | ||
0.990713 | − | 0.135970i | \(-0.0434150\pi\) | |||||||
\(402\) | − | 100.461i | − | 0.249903i | ||||||
\(403\) | −426.011 | −1.05710 | ||||||||
\(404\) | −324.667 | −0.803632 | ||||||||
\(405\) | − | 20.1246i | − | 0.0496904i | ||||||
\(406\) | − | 88.4502i | − | 0.217858i | ||||||
\(407\) | −248.470 | −0.610491 | ||||||||
\(408\) | 46.2410i | 0.113336i | ||||||||
\(409\) | 43.2954 | 0.105857 | 0.0529283 | − | 0.998598i | \(-0.483145\pi\) | ||||
0.0529283 | + | 0.998598i | \(0.483145\pi\) | |||||||
\(410\) | − | 9.38524i | − | 0.0228908i | ||||||
\(411\) | 98.4723i | 0.239592i | ||||||||
\(412\) | − | 263.144i | − | 0.638699i | ||||||
\(413\) | − | 171.491i | − | 0.415232i | ||||||
\(414\) | −96.5941 | + | 13.8414i | −0.233319 | + | 0.0334332i | ||||
\(415\) | −82.0267 | −0.197655 | ||||||||
\(416\) | −127.403 | −0.306258 | ||||||||
\(417\) | −183.690 | −0.440504 | ||||||||
\(418\) | −93.3559 | −0.223339 | ||||||||
\(419\) | 705.421i | 1.68358i | 0.539804 | + | 0.841791i | \(0.318498\pi\) | ||||
−0.539804 | + | 0.841791i | \(0.681502\pi\) | |||||||
\(420\) | 68.7367 | 0.163659 | ||||||||
\(421\) | − | 519.578i | − | 1.23415i | −0.786904 | − | 0.617076i | \(-0.788317\pi\) | ||
0.786904 | − | 0.617076i | \(-0.211683\pi\) | |||||||
\(422\) | 359.614 | 0.852166 | ||||||||
\(423\) | 194.693 | 0.460266 | ||||||||
\(424\) | − | 39.7519i | − | 0.0937544i | ||||||
\(425\) | − | 47.1946i | − | 0.111046i | ||||||
\(426\) | −81.8732 | −0.192191 | ||||||||
\(427\) | −489.347 | −1.14601 | ||||||||
\(428\) | 31.4528i | 0.0734878i | ||||||||
\(429\) | − | 244.577i | − | 0.570110i | ||||||
\(430\) | 232.610 | 0.540953 | ||||||||
\(431\) | − | 482.538i | − | 1.11958i | −0.828635 | − | 0.559789i | \(-0.810882\pi\) | ||
0.828635 | − | 0.559789i | \(-0.189118\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | − | 431.177i | − | 0.995789i | −0.867238 | − | 0.497894i | \(-0.834107\pi\) | ||
0.867238 | − | 0.497894i | \(-0.165893\pi\) | |||||||
\(434\) | − | 237.380i | − | 0.546958i | ||||||
\(435\) | − | 27.2971i | − | 0.0627519i | ||||||
\(436\) | − | 199.660i | − | 0.457935i | ||||||
\(437\) | −34.3494 | − | 239.713i | −0.0786028 | − | 0.548542i | ||||
\(438\) | 99.8805 | 0.228038 | ||||||||
\(439\) | 354.292 | 0.807044 | 0.403522 | − | 0.914970i | \(-0.367786\pi\) | ||||
0.403522 | + | 0.914970i | \(0.367786\pi\) | |||||||
\(440\) | −39.6534 | −0.0901213 | ||||||||
\(441\) | −89.2368 | −0.202351 | ||||||||
\(442\) | − | 300.637i | − | 0.680174i | ||||||
\(443\) | −602.448 | −1.35993 | −0.679964 | − | 0.733246i | \(-0.738004\pi\) | ||||
−0.679964 | + | 0.733246i | \(0.738004\pi\) | |||||||
\(444\) | − | 137.282i | − | 0.309194i | ||||||
\(445\) | −288.850 | −0.649102 | ||||||||
\(446\) | −117.125 | −0.262612 | ||||||||
\(447\) | − | 88.1916i | − | 0.197297i | ||||||
\(448\) | − | 70.9910i | − | 0.158462i | ||||||
\(449\) | 780.691 | 1.73873 | 0.869366 | − | 0.494169i | \(-0.164528\pi\) | ||||
0.869366 | + | 0.494169i | \(0.164528\pi\) | |||||||
\(450\) | 21.2132 | 0.0471405 | ||||||||
\(451\) | − | 18.6078i | − | 0.0412590i | ||||||
\(452\) | 278.025i | 0.615099i | ||||||||
\(453\) | 371.587 | 0.820280 | ||||||||
\(454\) | 126.571i | 0.278791i | ||||||||
\(455\) | −446.893 | −0.982182 | ||||||||
\(456\) | − | 51.5801i | − | 0.113114i | ||||||
\(457\) | 504.211i | 1.10331i | 0.834073 | + | 0.551654i | \(0.186003\pi\) | ||||
−0.834073 | + | 0.551654i | \(0.813997\pi\) | |||||||
\(458\) | − | 45.4070i | − | 0.0991420i | ||||||
\(459\) | − | 49.0460i | − | 0.106854i | ||||||
\(460\) | −14.5901 | − | 101.819i | −0.0317176 | − | 0.221346i | ||||
\(461\) | 533.437 | 1.15713 | 0.578565 | − | 0.815636i | \(-0.303613\pi\) | ||||
0.578565 | + | 0.815636i | \(0.303613\pi\) | |||||||
\(462\) | 136.282 | 0.294983 | ||||||||
\(463\) | 614.183 | 1.32653 | 0.663265 | − | 0.748385i | \(-0.269170\pi\) | ||||
0.663265 | + | 0.748385i | \(0.269170\pi\) | |||||||
\(464\) | −28.1923 | −0.0607593 | ||||||||
\(465\) | − | 73.2590i | − | 0.157546i | ||||||
\(466\) | 237.524 | 0.509709 | ||||||||
\(467\) | − | 725.648i | − | 1.55385i | −0.629593 | − | 0.776925i | \(-0.716778\pi\) | ||
0.629593 | − | 0.776925i | \(-0.283222\pi\) | |||||||
\(468\) | 135.131 | 0.288742 | ||||||||
\(469\) | −363.944 | −0.776000 | ||||||||
\(470\) | 205.224i | 0.436647i | ||||||||
\(471\) | − | 58.0527i | − | 0.123254i | ||||||
\(472\) | −54.6604 | −0.115806 | ||||||||
\(473\) | 461.188 | 0.975028 | ||||||||
\(474\) | − | 122.004i | − | 0.257393i | ||||||
\(475\) | 52.6437i | 0.110829i | ||||||||
\(476\) | 167.519 | 0.351931 | ||||||||
\(477\) | 42.1632i | 0.0883925i | ||||||||
\(478\) | −136.426 | −0.285411 | ||||||||
\(479\) | 344.695i | 0.719613i | 0.933027 | + | 0.359807i | \(0.117157\pi\) | ||||
−0.933027 | + | 0.359807i | \(0.882843\pi\) | |||||||
\(480\) | − | 21.9089i | − | 0.0456435i | ||||||
\(481\) | 892.542i | 1.85560i | ||||||||
\(482\) | − | 605.958i | − | 1.25717i | ||||||
\(483\) | 50.1437 | + | 349.936i | 0.103817 | + | 0.724504i | ||||
\(484\) | 163.381 | 0.337563 | ||||||||
\(485\) | −226.697 | −0.467417 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | −358.665 | −0.736479 | −0.368239 | − | 0.929731i | \(-0.620039\pi\) | ||||
−0.368239 | + | 0.929731i | \(0.620039\pi\) | |||||||
\(488\) | 155.973i | 0.319616i | ||||||||
\(489\) | −301.137 | −0.615822 | ||||||||
\(490\) | − | 94.0639i | − | 0.191967i | ||||||
\(491\) | −614.809 | −1.25216 | −0.626079 | − | 0.779760i | \(-0.715341\pi\) | ||||
−0.626079 | + | 0.779760i | \(0.715341\pi\) | |||||||
\(492\) | 10.2810 | 0.0208964 | ||||||||
\(493\) | − | 66.5262i | − | 0.134941i | ||||||
\(494\) | 335.349i | 0.678844i | ||||||||
\(495\) | 42.0587 | 0.0849672 | ||||||||
\(496\) | −75.6616 | −0.152544 | ||||||||
\(497\) | 296.606i | 0.596792i | ||||||||
\(498\) | − | 89.8557i | − | 0.180433i | ||||||
\(499\) | 800.923 | 1.60506 | 0.802528 | − | 0.596614i | \(-0.203488\pi\) | ||||
0.802528 | + | 0.596614i | \(0.203488\pi\) | |||||||
\(500\) | 22.3607i | 0.0447214i | ||||||||
\(501\) | −127.263 | −0.254017 | ||||||||
\(502\) | − | 88.1121i | − | 0.175522i | ||||||
\(503\) | − | 167.203i | − | 0.332412i | −0.986091 | − | 0.166206i | \(-0.946848\pi\) | ||
0.986091 | − | 0.166206i | \(-0.0531517\pi\) | |||||||
\(504\) | 75.2973i | 0.149399i | ||||||||
\(505\) | 362.989i | 0.718790i | ||||||||
\(506\) | −28.9273 | − | 201.873i | −0.0571685 | − | 0.398959i | ||||
\(507\) | −585.843 | −1.15551 | ||||||||
\(508\) | −19.1589 | −0.0377144 | ||||||||
\(509\) | 458.839 | 0.901451 | 0.450726 | − | 0.892663i | \(-0.351165\pi\) | ||||
0.450726 | + | 0.892663i | \(0.351165\pi\) | |||||||
\(510\) | 51.6990 | 0.101371 | ||||||||
\(511\) | − | 361.841i | − | 0.708105i | ||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 54.7090i | 0.106645i | ||||||||
\(514\) | 126.447 | 0.246006 | ||||||||
\(515\) | −294.204 | −0.571270 | ||||||||
\(516\) | 254.811i | 0.493820i | ||||||||
\(517\) | 406.891i | 0.787024i | ||||||||
\(518\) | −497.338 | −0.960112 | ||||||||
\(519\) | −147.893 | −0.284957 | ||||||||
\(520\) | 142.441i | 0.273925i | ||||||||
\(521\) | − | 993.025i | − | 1.90600i | −0.302974 | − | 0.952999i | \(-0.597980\pi\) | ||
0.302974 | − | 0.952999i | \(-0.402020\pi\) | |||||||
\(522\) | 29.9025 | 0.0572844 | ||||||||
\(523\) | 742.227i | 1.41917i | 0.704619 | + | 0.709586i | \(0.251118\pi\) | ||||
−0.704619 | + | 0.709586i | \(0.748882\pi\) | |||||||
\(524\) | −100.663 | −0.192104 | ||||||||
\(525\) | − | 76.8500i | − | 0.146381i | ||||||
\(526\) | 527.540i | 1.00293i | ||||||||
\(527\) | − | 178.541i | − | 0.338787i | ||||||
\(528\) | − | 43.4381i | − | 0.0822691i | ||||||
\(529\) | 507.713 | − | 148.555i | 0.959760 | − | 0.280822i | ||||
\(530\) | −44.4439 | −0.0838565 | ||||||||
\(531\) | 57.9761 | 0.109183 | ||||||||
\(532\) | −186.862 | −0.351244 | ||||||||
\(533\) | −66.8422 | −0.125407 | ||||||||
\(534\) | − | 316.420i | − | 0.592546i | ||||||
\(535\) | 35.1653 | 0.0657295 | ||||||||
\(536\) | 116.002i | 0.216422i | ||||||||
\(537\) | −85.0820 | −0.158440 | ||||||||
\(538\) | 465.746 | 0.865698 | ||||||||
\(539\) | − | 186.497i | − | 0.346006i | ||||||
\(540\) | 23.2379i | 0.0430331i | ||||||||
\(541\) | 718.623 | 1.32832 | 0.664162 | − | 0.747589i | \(-0.268788\pi\) | ||||
0.664162 | + | 0.747589i | \(0.268788\pi\) | |||||||
\(542\) | 671.568 | 1.23906 | ||||||||
\(543\) | 11.6122i | 0.0213853i | ||||||||
\(544\) | − | 53.3945i | − | 0.0981517i | ||||||
\(545\) | −223.226 | −0.409589 | ||||||||
\(546\) | − | 489.547i | − | 0.896606i | ||||||
\(547\) | −59.5405 | −0.108849 | −0.0544245 | − | 0.998518i | \(-0.517332\pi\) | ||||
−0.0544245 | + | 0.998518i | \(0.517332\pi\) | |||||||
\(548\) | − | 113.706i | − | 0.207493i | ||||||
\(549\) | − | 165.434i | − | 0.301337i | ||||||
\(550\) | 44.3338i | 0.0806069i | ||||||||
\(551\) | 74.2074i | 0.134678i | ||||||||
\(552\) | 111.537 | − | 15.9826i | 0.202060 | − | 0.0289540i | ||||
\(553\) | −441.991 | −0.799260 | ||||||||
\(554\) | 93.3028 | 0.168417 | ||||||||
\(555\) | −153.486 | −0.276552 | ||||||||
\(556\) | 212.107 | 0.381488 | ||||||||
\(557\) | 426.547i | 0.765793i | 0.923791 | + | 0.382896i | \(0.125073\pi\) | ||||
−0.923791 | + | 0.382896i | \(0.874927\pi\) | |||||||
\(558\) | 80.2513 | 0.143819 | ||||||||
\(559\) | − | 1656.66i | − | 2.96361i | ||||||
\(560\) | −79.3703 | −0.141733 | ||||||||
\(561\) | 102.502 | 0.182713 | ||||||||
\(562\) | − | 586.202i | − | 1.04306i | ||||||
\(563\) | − | 664.896i | − | 1.18099i | −0.807042 | − | 0.590494i | \(-0.798933\pi\) | ||
0.807042 | − | 0.590494i | \(-0.201067\pi\) | |||||||
\(564\) | −224.812 | −0.398602 | ||||||||
\(565\) | 310.841 | 0.550162 | ||||||||
\(566\) | 632.760i | 1.11795i | ||||||||
\(567\) | − | 79.8649i | − | 0.140855i | ||||||
\(568\) | 94.5390 | 0.166442 | ||||||||
\(569\) | − | 532.599i | − | 0.936026i | −0.883722 | − | 0.468013i | \(-0.844970\pi\) | ||
0.883722 | − | 0.468013i | \(-0.155030\pi\) | |||||||
\(570\) | −57.6683 | −0.101173 | ||||||||
\(571\) | 61.1738i | 0.107135i | 0.998564 | + | 0.0535673i | \(0.0170592\pi\) | ||||
−0.998564 | + | 0.0535673i | \(0.982941\pi\) | |||||||
\(572\) | 282.413i | 0.493730i | ||||||||
\(573\) | 268.943i | 0.469359i | ||||||||
\(574\) | − | 37.2455i | − | 0.0648876i | ||||||
\(575\) | −113.837 | + | 16.3122i | −0.197978 | + | 0.0283691i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 753.571 | 1.30602 | 0.653008 | − | 0.757351i | \(-0.273507\pi\) | ||||
0.653008 | + | 0.757351i | \(0.273507\pi\) | |||||||
\(578\) | −282.711 | −0.489120 | ||||||||
\(579\) | 50.3899 | 0.0870292 | ||||||||
\(580\) | 31.5200i | 0.0543447i | ||||||||
\(581\) | −325.524 | −0.560283 | ||||||||
\(582\) | − | 248.334i | − | 0.426691i | ||||||
\(583\) | −88.1176 | −0.151145 | ||||||||
\(584\) | −115.332 | −0.197486 | ||||||||
\(585\) | − | 151.082i | − | 0.258259i | ||||||
\(586\) | − | 489.912i | − | 0.836027i | ||||||
\(587\) | 38.5168 | 0.0656164 | 0.0328082 | − | 0.999462i | \(-0.489555\pi\) | ||||
0.0328082 | + | 0.999462i | \(0.489555\pi\) | |||||||
\(588\) | 103.042 | 0.175241 | ||||||||
\(589\) | 199.156i | 0.338125i | ||||||||
\(590\) | 61.1122i | 0.103580i | ||||||||
\(591\) | 560.150 | 0.947801 | ||||||||
\(592\) | 158.520i | 0.267770i | ||||||||
\(593\) | 499.235 | 0.841880 | 0.420940 | − | 0.907089i | \(-0.361700\pi\) | ||||
0.420940 | + | 0.907089i | \(0.361700\pi\) | |||||||
\(594\) | 46.0730i | 0.0775641i | ||||||||
\(595\) | − | 187.292i | − | 0.314777i | ||||||
\(596\) | 101.835i | 0.170864i | ||||||||
\(597\) | − | 549.565i | − | 0.920544i | ||||||
\(598\) | −725.161 | + | 103.911i | −1.21264 | + | 0.173765i | ||||
\(599\) | −649.431 | −1.08419 | −0.542096 | − | 0.840317i | \(-0.682369\pi\) | ||||
−0.542096 | + | 0.840317i | \(0.682369\pi\) | |||||||
\(600\) | −24.4949 | −0.0408248 | ||||||||
\(601\) | −552.930 | −0.920017 | −0.460009 | − | 0.887914i | \(-0.652154\pi\) | ||||
−0.460009 | + | 0.887914i | \(0.652154\pi\) | |||||||
\(602\) | 923.116 | 1.53342 | ||||||||
\(603\) | − | 123.039i | − | 0.204045i | ||||||
\(604\) | −429.072 | −0.710383 | ||||||||
\(605\) | − | 182.665i | − | 0.301926i | ||||||
\(606\) | −397.635 | −0.656163 | ||||||||
\(607\) | 483.183 | 0.796017 | 0.398009 | − | 0.917382i | \(-0.369701\pi\) | ||||
0.398009 | + | 0.917382i | \(0.369701\pi\) | |||||||
\(608\) | 59.5596i | 0.0979599i | ||||||||
\(609\) | − | 108.329i | − | 0.177880i | ||||||
\(610\) | 174.383 | 0.285873 | ||||||||
\(611\) | 1461.62 | 2.39217 | ||||||||
\(612\) | 56.6335i | 0.0925383i | ||||||||
\(613\) | 562.528i | 0.917664i | 0.888523 | + | 0.458832i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458832i | \(0.848268\pi\) | |||||||
\(614\) | −751.668 | −1.22421 | ||||||||
\(615\) | − | 11.4945i | − | 0.0186903i | ||||||
\(616\) | −157.365 | −0.255463 | ||||||||
\(617\) | − | 1185.68i | − | 1.92169i | −0.277090 | − | 0.960844i | \(-0.589370\pi\) | ||
0.277090 | − | 0.960844i | \(-0.410630\pi\) | |||||||
\(618\) | − | 322.284i | − | 0.521496i | ||||||
\(619\) | 1214.46i | 1.96197i | 0.194072 | + | 0.980987i | \(0.437830\pi\) | ||||
−0.194072 | + | 0.980987i | \(0.562170\pi\) | |||||||
\(620\) | 84.5922i | 0.136439i | ||||||||
\(621\) | −118.303 | + | 16.9521i | −0.190504 | + | 0.0272981i | ||||
\(622\) | −599.558 | −0.963919 | ||||||||
\(623\) | −1146.31 | −1.83998 | ||||||||
\(624\) | −156.036 | −0.250058 | ||||||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 4.75951i | 0.00760305i | ||||||||
\(627\) | −114.337 | −0.182356 | ||||||||
\(628\) | 67.0335i | 0.106741i | ||||||||
\(629\) | −374.064 | −0.594696 | ||||||||
\(630\) | 84.1849 | 0.133627 | ||||||||
\(631\) | − | 578.694i | − | 0.917106i | −0.888667 | − | 0.458553i | \(-0.848368\pi\) | ||
0.888667 | − | 0.458553i | \(-0.151632\pi\) | |||||||
\(632\) | 140.879i | 0.222909i | ||||||||
\(633\) | 440.436 | 0.695791 | ||||||||
\(634\) | −229.940 | −0.362682 | ||||||||
\(635\) | 21.4203i | 0.0337328i | ||||||||
\(636\) | − | 48.6859i | − | 0.0765501i | ||||||
\(637\) | −669.928 | −1.05169 | ||||||||
\(638\) | 62.4936i | 0.0979524i | ||||||||
\(639\) | −100.274 | −0.156923 | ||||||||
\(640\) | 25.2982i | 0.0395285i | ||||||||
\(641\) | 742.212i | 1.15790i | 0.815364 | + | 0.578949i | \(0.196537\pi\) | ||||
−0.815364 | + | 0.578949i | \(0.803463\pi\) | |||||||
\(642\) | 38.5216i | 0.0600025i | ||||||||
\(643\) | 1108.65i | 1.72418i | 0.506759 | + | 0.862088i | \(0.330843\pi\) | ||||
−0.506759 | + | 0.862088i | \(0.669157\pi\) | |||||||
\(644\) | −57.9010 | − | 404.071i | −0.0899083 | − | 0.627439i | ||||
\(645\) | 284.888 | 0.441686 | ||||||||
\(646\) | −140.544 | −0.217561 | ||||||||
\(647\) | 313.155 | 0.484011 | 0.242005 | − | 0.970275i | \(-0.422195\pi\) | ||||
0.242005 | + | 0.970275i | \(0.422195\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | 121.165i | 0.186695i | ||||||||
\(650\) | 159.254 | 0.245006 | ||||||||
\(651\) | − | 290.730i | − | 0.446589i | ||||||
\(652\) | 347.723 | 0.533317 | ||||||||
\(653\) | −328.562 | −0.503158 | −0.251579 | − | 0.967837i | \(-0.580950\pi\) | ||||
−0.251579 | + | 0.967837i | \(0.580950\pi\) | |||||||
\(654\) | − | 244.532i | − | 0.373902i | ||||||
\(655\) | 112.544i | 0.171823i | ||||||||
\(656\) | −11.8715 | −0.0180968 | ||||||||
\(657\) | 122.328 | 0.186192 | ||||||||
\(658\) | 814.435i | 1.23774i | ||||||||
\(659\) | 216.986i | 0.329266i | 0.986355 | + | 0.164633i | \(0.0526440\pi\) | ||||
−0.986355 | + | 0.164633i | \(0.947356\pi\) | |||||||
\(660\) | −48.5653 | −0.0735837 | ||||||||
\(661\) | 867.631i | 1.31260i | 0.754498 | + | 0.656302i | \(0.227880\pi\) | ||||
−0.754498 | + | 0.656302i | \(0.772120\pi\) | |||||||
\(662\) | 863.678 | 1.30465 | ||||||||
\(663\) | − | 368.203i | − | 0.555360i | ||||||
\(664\) | 103.756i | 0.156260i | ||||||||
\(665\) | 208.918i | 0.314162i | ||||||||
\(666\) | − | 168.136i | − | 0.252456i | ||||||
\(667\) | −160.467 | + | 22.9939i | −0.240580 | + | 0.0344737i | ||||
\(668\) | 146.950 | 0.219985 | ||||||||
\(669\) | −143.448 | −0.214422 | ||||||||
\(670\) | 129.695 | 0.193574 | ||||||||
\(671\) | 345.743 | 0.515265 | ||||||||
\(672\) | − | 86.9458i | − | 0.129384i | ||||||
\(673\) | −445.497 | −0.661957 | −0.330978 | − | 0.943638i | \(-0.607379\pi\) | ||||
−0.330978 | + | 0.943638i | \(0.607379\pi\) | |||||||
\(674\) | − | 145.907i | − | 0.216480i | ||||||
\(675\) | 25.9808 | 0.0384900 | ||||||||
\(676\) | 676.473 | 1.00070 | ||||||||
\(677\) | 568.893i | 0.840314i | 0.907451 | + | 0.420157i | \(0.138025\pi\) | ||||
−0.907451 | + | 0.420157i | \(0.861975\pi\) | |||||||
\(678\) | 340.510i | 0.502227i | ||||||||
\(679\) | −899.652 | −1.32497 | ||||||||
\(680\) | −59.6969 | −0.0877896 | ||||||||
\(681\) | 155.017i | 0.227632i | ||||||||
\(682\) | 167.718i | 0.245921i | ||||||||
\(683\) | −452.155 | −0.662013 | −0.331007 | − | 0.943628i | \(-0.607388\pi\) | ||||
−0.331007 | + | 0.943628i | \(0.607388\pi\) | |||||||
\(684\) | − | 63.1725i | − | 0.0923574i | ||||||
\(685\) | −127.127 | −0.185587 | ||||||||
\(686\) | 241.634i | 0.352236i | ||||||||
\(687\) | − | 55.6120i | − | 0.0809491i | ||||||
\(688\) | − | 294.231i | − | 0.427661i | ||||||
\(689\) | 316.532i | 0.459408i | ||||||||
\(690\) | −17.8691 | − | 124.702i | −0.0258973 | − | 0.180728i | ||||
\(691\) | 271.476 | 0.392874 | 0.196437 | − | 0.980516i | \(-0.437063\pi\) | ||||
0.196437 | + | 0.980516i | \(0.437063\pi\) | |||||||
\(692\) | 170.772 | 0.246780 | ||||||||
\(693\) | 166.911 | 0.240853 | ||||||||
\(694\) | −834.352 | −1.20224 | ||||||||
\(695\) | − | 237.143i | − | 0.341213i | ||||||
\(696\) | −34.5284 | −0.0496097 | ||||||||
\(697\) | − | 28.0135i | − | 0.0401915i | ||||||
\(698\) | −128.406 | −0.183963 | ||||||||
\(699\) | 290.907 | 0.416175 | ||||||||
\(700\) | 88.7387i | 0.126770i | ||||||||
\(701\) | − | 629.831i | − | 0.898474i | −0.893413 | − | 0.449237i | \(-0.851696\pi\) | ||
0.893413 | − | 0.449237i | \(-0.148304\pi\) | |||||||
\(702\) | 165.502 | 0.235757 | ||||||||
\(703\) | 417.254 | 0.593533 | ||||||||
\(704\) | 50.1580i | 0.0712471i | ||||||||
\(705\) | 251.347i | 0.356521i | ||||||||
\(706\) | 58.1947 | 0.0824288 | ||||||||
\(707\) | 1440.53i | 2.03752i | ||||||||
\(708\) | −66.9450 | −0.0945551 | ||||||||
\(709\) | 525.929i | 0.741790i | 0.928675 | + | 0.370895i | \(0.120949\pi\) | ||||
−0.928675 | + | 0.370895i | \(0.879051\pi\) | |||||||
\(710\) | − | 105.698i | − | 0.148870i | ||||||
\(711\) | − | 149.424i | − | 0.210161i | ||||||
\(712\) | 365.370i | 0.513160i | ||||||||
\(713\) | −430.655 | + | 61.7104i | −0.604005 | + | 0.0865503i | ||||
\(714\) | 205.168 | 0.287351 | ||||||||
\(715\) | 315.748 | 0.441605 | ||||||||
\(716\) | 98.2443 | 0.137213 | ||||||||
\(717\) | −167.088 | −0.233037 | ||||||||
\(718\) | 321.321i | 0.447522i | ||||||||
\(719\) | −632.328 | −0.879455 | −0.439727 | − | 0.898131i | \(-0.644925\pi\) | ||||
−0.439727 | + | 0.898131i | \(0.644925\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | −1167.55 | −1.61935 | ||||||||
\(722\) | −353.759 | −0.489971 | ||||||||
\(723\) | − | 742.144i | − | 1.02648i | ||||||
\(724\) | − | 13.4087i | − | 0.0185203i | ||||||
\(725\) | 35.2404 | 0.0486074 | ||||||||
\(726\) | 200.099 | 0.275619 | ||||||||
\(727\) | 1047.57i | 1.44095i | 0.693481 | + | 0.720475i | \(0.256076\pi\) | ||||
−0.693481 | + | 0.720475i | \(0.743924\pi\) | |||||||
\(728\) | 565.280i | 0.776483i | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 128.945i | 0.176637i | ||||||||
\(731\) | 694.304 | 0.949801 | ||||||||
\(732\) | 191.027i | 0.260965i | ||||||||
\(733\) | 1084.08i | 1.47896i | 0.673180 | + | 0.739479i | \(0.264928\pi\) | ||||
−0.673180 | + | 0.739479i | \(0.735072\pi\) | |||||||
\(734\) | 67.2280i | 0.0915913i | ||||||||
\(735\) | − | 115.204i | − | 0.156740i | ||||||
\(736\) | −128.792 | + | 18.4552i | −0.174989 | + | 0.0250749i | ||||
\(737\) | 257.141 | 0.348903 | ||||||||
\(738\) | 12.5916 | 0.0170618 | ||||||||
\(739\) | −219.665 | −0.297246 | −0.148623 | − | 0.988894i | \(-0.547484\pi\) | ||||
−0.148623 | + | 0.988894i | \(0.547484\pi\) | |||||||
\(740\) | 177.231 | 0.239501 | ||||||||
\(741\) | 410.717i | 0.554274i | ||||||||
\(742\) | −176.376 | −0.237704 | ||||||||
\(743\) | 498.194i | 0.670517i | 0.942126 | + | 0.335259i | \(0.108824\pi\) | ||||
−0.942126 | + | 0.335259i | \(0.891176\pi\) | |||||||
\(744\) | −92.6662 | −0.124551 | ||||||||
\(745\) | 113.855 | 0.152825 | ||||||||
\(746\) | − | 617.502i | − | 0.827750i | ||||||
\(747\) | − | 110.050i | − | 0.147323i | ||||||
\(748\) | −118.359 | −0.158234 | ||||||||
\(749\) | 139.554 | 0.186320 | ||||||||
\(750\) | 27.3861i | 0.0365148i | ||||||||
\(751\) | 102.191i | 0.136074i | 0.997683 | + | 0.0680368i | \(0.0216735\pi\) | ||||
−0.997683 | + | 0.0680368i | \(0.978326\pi\) | |||||||
\(752\) | 259.590 | 0.345200 | ||||||||
\(753\) | − | 107.915i | − | 0.143313i | ||||||
\(754\) | 224.487 | 0.297728 | ||||||||
\(755\) | 479.717i | 0.635386i | ||||||||
\(756\) | 92.2200i | 0.121984i | ||||||||
\(757\) | 657.156i | 0.868106i | 0.900887 | + | 0.434053i | \(0.142917\pi\) | ||||
−0.900887 | + | 0.434053i | \(0.857083\pi\) | |||||||
\(758\) | − | 608.764i | − | 0.803119i | ||||||
\(759\) | −35.4285 | − | 247.244i | −0.0466779 | − | 0.325749i | ||||
\(760\) | 66.5897 | 0.0876180 | ||||||||
\(761\) | 26.7073 | 0.0350950 | 0.0175475 | − | 0.999846i | \(-0.494414\pi\) | ||||
0.0175475 | + | 0.999846i | \(0.494414\pi\) | |||||||
\(762\) | −23.4648 | −0.0307937 | ||||||||
\(763\) | −885.877 | −1.16104 | ||||||||
\(764\) | − | 310.549i | − | 0.406477i | ||||||
\(765\) | 63.3181 | 0.0827688 | ||||||||
\(766\) | 884.773i | 1.15506i | ||||||||
\(767\) | 435.244 | 0.567463 | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 614.585i | 0.799200i | 0.916690 | + | 0.399600i | \(0.130851\pi\) | ||||
−0.916690 | + | 0.399600i | \(0.869149\pi\) | |||||||
\(770\) | 175.939i | 0.228493i | ||||||||
\(771\) | 154.865 | 0.200863 | ||||||||
\(772\) | −58.1853 | −0.0753695 | ||||||||
\(773\) | 537.714i | 0.695619i | 0.937565 | + | 0.347810i | \(0.113074\pi\) | ||||
−0.937565 | + | 0.347810i | \(0.886926\pi\) | |||||||
\(774\) | 312.079i | 0.403203i | ||||||||
\(775\) | 94.5770 | 0.122035 | ||||||||
\(776\) | 286.752i | 0.369526i | ||||||||
\(777\) | −609.112 | −0.783928 | ||||||||
\(778\) | − | 707.073i | − | 0.908834i | ||||||
\(779\) | 31.2480i | 0.0401130i | ||||||||
\(780\) | 174.454i | 0.223659i | ||||||||
\(781\) | − | 209.564i | − | 0.268327i | ||||||
\(782\) | −43.5491 | − | 303.914i | −0.0556894 | − | 0.388637i | ||||
\(783\) | 36.6229 | 0.0467725 | ||||||||
\(784\) | −118.982 | −0.151763 | ||||||||
\(785\) | 74.9457 | 0.0954722 | ||||||||
\(786\) | −123.286 | −0.156852 | ||||||||
\(787\) | − | 974.561i | − | 1.23832i | −0.785263 | − | 0.619162i | \(-0.787473\pi\) | ||
0.785263 | − | 0.619162i | \(-0.212527\pi\) | |||||||
\(788\) | −646.806 | −0.820820 | ||||||||
\(789\) | 646.102i | 0.818887i | ||||||||
\(790\) | 157.507 | 0.199376 | ||||||||
\(791\) | 1233.58 | 1.55952 | ||||||||
\(792\) | − | 53.2006i | − | 0.0671724i | ||||||
\(793\) | − | 1241.96i | − | 1.56616i | ||||||
\(794\) | −300.321 | −0.378238 | ||||||||
\(795\) | −54.4325 | −0.0684685 | ||||||||
\(796\) | 634.582i | 0.797214i | ||||||||
\(797\) | 347.580i | 0.436110i | 0.975936 | + | 0.218055i | \(0.0699712\pi\) | ||||
−0.975936 | + | 0.218055i | \(0.930029\pi\) | |||||||
\(798\) | −228.858 | −0.286789 | ||||||||
\(799\) | 612.562i | 0.766661i | ||||||||
\(800\) | 28.2843 | 0.0353553 | ||||||||
\(801\) | − | 387.534i | − | 0.483812i | ||||||
\(802\) | 154.217i | 0.192290i | ||||||||
\(803\) | 255.656i | 0.318376i | ||||||||
\(804\) | 142.073i | 0.176708i | ||||||||
\(805\) | −451.765 | + | 64.7352i | −0.561199 | + | 0.0804165i | ||||
\(806\) | 602.471 | 0.747482 | ||||||||
\(807\) | 570.420 | 0.706840 | ||||||||
\(808\) | 459.149 | 0.568254 | ||||||||
\(809\) | 37.9753 | 0.0469411 | 0.0234705 | − | 0.999725i | \(-0.492528\pi\) | ||||
0.0234705 | + | 0.999725i | \(0.492528\pi\) | |||||||
\(810\) | 28.4605i | 0.0351364i | ||||||||
\(811\) | −61.1194 | −0.0753630 | −0.0376815 | − | 0.999290i | \(-0.511997\pi\) | ||||
−0.0376815 | + | 0.999290i | \(0.511997\pi\) | |||||||
\(812\) | 125.087i | 0.154049i | ||||||||
\(813\) | 822.499 | 1.01168 | ||||||||
\(814\) | 351.389 | 0.431682 | ||||||||
\(815\) | − | 388.766i | − | 0.477014i | ||||||
\(816\) | − | 65.3947i | − | 0.0801405i | ||||||
\(817\) | −774.471 | −0.947944 | ||||||||
\(818\) | −61.2289 | −0.0748520 | ||||||||
\(819\) | − | 599.570i | − | 0.732075i | ||||||
\(820\) | 13.2727i | 0.0161863i | ||||||||
\(821\) | 1623.87 | 1.97792 | 0.988961 | − | 0.148176i | \(-0.0473403\pi\) | ||||
0.988961 | + | 0.148176i | \(0.0473403\pi\) | |||||||
\(822\) | − | 139.261i | − | 0.169417i | ||||||
\(823\) | 1525.91 | 1.85408 | 0.927042 | − | 0.374957i | \(-0.122342\pi\) | ||||
0.927042 | + | 0.374957i | \(0.122342\pi\) | |||||||
\(824\) | 372.142i | 0.451629i | ||||||||
\(825\) | 54.2976i | 0.0658153i | ||||||||
\(826\) | 242.525i | 0.293613i | ||||||||
\(827\) | 385.983i | 0.466727i | 0.972390 | + | 0.233363i | \(0.0749732\pi\) | ||||
−0.972390 | + | 0.233363i | \(0.925027\pi\) | |||||||
\(828\) | 136.605 | − | 19.5746i | 0.164981 | − | 0.0236409i | ||||
\(829\) | −70.2842 | −0.0847819 | −0.0423910 | − | 0.999101i | \(-0.513498\pi\) | ||||
−0.0423910 | + | 0.999101i | \(0.513498\pi\) | |||||||
\(830\) | 116.003 | 0.139763 | ||||||||
\(831\) | 114.272 | 0.137512 | ||||||||
\(832\) | 180.175 | 0.216557 | ||||||||
\(833\) | − | 280.766i | − | 0.337054i | ||||||
\(834\) | 259.777 | 0.311484 | ||||||||
\(835\) | − | 164.295i | − | 0.196761i | ||||||
\(836\) | 132.025 | 0.157925 | ||||||||
\(837\) | 98.2873 | 0.117428 | ||||||||
\(838\) | − | 997.616i | − | 1.19047i | ||||||
\(839\) | 200.173i | 0.238585i | 0.992859 | + | 0.119293i | \(0.0380626\pi\) | ||||
−0.992859 | + | 0.119293i | \(0.961937\pi\) | |||||||
\(840\) | −97.2084 | −0.115724 | ||||||||
\(841\) | −791.325 | −0.940933 | ||||||||
\(842\) | 734.794i | 0.872677i | ||||||||
\(843\) | − | 717.948i | − | 0.851659i | ||||||
\(844\) | −508.571 | −0.602573 | ||||||||
\(845\) | − | 756.320i | − | 0.895053i | ||||||
\(846\) | −275.337 | −0.325457 | ||||||||
\(847\) | − | 724.909i | − | 0.855855i | ||||||
\(848\) | 56.2176i | 0.0662944i | ||||||||
\(849\) | 774.970i | 0.912803i | ||||||||
\(850\) | 66.7432i | 0.0785214i | ||||||||
\(851\) | 129.290 | + | 902.273i | 0.151928 | + | 1.06025i | ||||
\(852\) | 115.786 | 0.135899 | ||||||||
\(853\) | 1050.86 | 1.23196 | 0.615980 | − | 0.787762i | \(-0.288760\pi\) | ||||
0.615980 | + | 0.787762i | \(0.288760\pi\) | |||||||
\(854\) | 692.040 | 0.810352 | ||||||||
\(855\) | −70.6290 | −0.0826070 | ||||||||
\(856\) | − | 44.4809i | − | 0.0519637i | ||||||
\(857\) | −1130.51 | −1.31914 | −0.659572 | − | 0.751642i | \(-0.729262\pi\) | ||||
−0.659572 | + | 0.751642i | \(0.729262\pi\) | |||||||
\(858\) | 345.884i | 0.403129i | ||||||||
\(859\) | 605.995 | 0.705465 | 0.352733 | − | 0.935724i | \(-0.385253\pi\) | ||||
0.352733 | + | 0.935724i | \(0.385253\pi\) | |||||||
\(860\) | −328.960 | −0.382512 | ||||||||
\(861\) | − | 45.6162i | − | 0.0529805i | ||||||
\(862\) | 682.412i | 0.791662i | ||||||||
\(863\) | −1029.98 | −1.19349 | −0.596746 | − | 0.802430i | \(-0.703540\pi\) | ||||
−0.596746 | + | 0.802430i | \(0.703540\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | − | 190.928i | − | 0.220726i | ||||||
\(866\) | 609.776i | 0.704129i | ||||||||
\(867\) | −346.249 | −0.399365 | ||||||||
\(868\) | 335.706i | 0.386758i | ||||||||
\(869\) | 312.284 | 0.359360 | ||||||||
\(870\) | 38.6039i | 0.0443723i | ||||||||
\(871\) | − | 923.691i | − | 1.06050i | ||||||
\(872\) | 282.361i | 0.323809i | ||||||||
\(873\) | − | 304.146i | − | 0.348392i | ||||||
\(874\) | 48.5774 | + | 339.005i | 0.0555806 | + | 0.387878i | ||||
\(875\) | 99.2129 | 0.113386 | ||||||||
\(876\) | −141.252 | −0.161247 | ||||||||
\(877\) | −132.885 | −0.151523 | −0.0757614 | − | 0.997126i | \(-0.524139\pi\) | ||||
−0.0757614 | + | 0.997126i | \(0.524139\pi\) | |||||||
\(878\) | −501.045 | −0.570666 | ||||||||
\(879\) | − | 600.017i | − | 0.682613i | ||||||
\(880\) | 56.0783 | 0.0637254 | ||||||||
\(881\) | 241.842i | 0.274508i | 0.990536 | + | 0.137254i | \(0.0438277\pi\) | ||||
−0.990536 | + | 0.137254i | \(0.956172\pi\) | |||||||
\(882\) | 126.200 | 0.143084 | ||||||||
\(883\) | 456.152 | 0.516594 | 0.258297 | − | 0.966066i | \(-0.416839\pi\) | ||||
0.258297 | + | 0.966066i | \(0.416839\pi\) | |||||||
\(884\) | 425.165i | 0.480955i | ||||||||
\(885\) | 74.8468i | 0.0845726i | ||||||||
\(886\) | 851.990 | 0.961614 | ||||||||
\(887\) | −1205.12 | −1.35865 | −0.679326 | − | 0.733836i | \(-0.737728\pi\) | ||||
−0.679326 | + | 0.733836i | \(0.737728\pi\) | |||||||
\(888\) | 194.146i | 0.218633i | ||||||||
\(889\) | 85.0069i | 0.0956208i | ||||||||
\(890\) | 408.496 | 0.458985 | ||||||||
\(891\) | 56.4277i | 0.0633308i | ||||||||
\(892\) | 165.640 | 0.185695 | ||||||||
\(893\) | − | 683.290i | − | 0.765163i | ||||||
\(894\) | 124.722i | 0.139510i | ||||||||
\(895\) | − | 109.840i | − | 0.122727i | ||||||
\(896\) | 100.396i | 0.112050i | ||||||||
\(897\) | −888.137 | + | 127.265i | −0.990120 | + | 0.141878i | ||||
\(898\) | −1104.06 | −1.22947 | ||||||||
\(899\) | 133.317 | 0.148295 | ||||||||
\(900\) | −30.0000 | −0.0333333 | ||||||||
\(901\) | −132.658 | −0.147234 | ||||||||
\(902\) | 26.3154i | 0.0291745i | ||||||||
\(903\) | 1130.58 | 1.25203 | ||||||||
\(904\) | − | 393.187i | − | 0.434941i | ||||||
\(905\) | −14.9913 | −0.0165650 | ||||||||
\(906\) | −525.503 | −0.580026 | ||||||||
\(907\) | − | 978.507i | − | 1.07884i | −0.842037 | − | 0.539420i | \(-0.818644\pi\) | ||
0.842037 | − | 0.539420i | \(-0.181356\pi\) | |||||||
\(908\) | − | 178.999i | − | 0.197135i | ||||||
\(909\) | −487.001 | −0.535755 | ||||||||
\(910\) | 632.002 | 0.694508 | ||||||||
\(911\) | 1443.03i | 1.58401i | 0.610515 | + | 0.792004i | \(0.290962\pi\) | ||||
−0.610515 | + | 0.792004i | \(0.709038\pi\) | |||||||
\(912\) | 72.9453i | 0.0799839i | ||||||||
\(913\) | 229.996 | 0.251912 | ||||||||
\(914\) | − | 713.063i | − | 0.780156i | ||||||
\(915\) | 213.574 | 0.233415 | ||||||||
\(916\) | 64.2153i | 0.0701040i | ||||||||
\(917\) | 446.634i | 0.487060i | ||||||||
\(918\) | 69.3615i | 0.0755572i | ||||||||
\(919\) | − | 311.006i | − | 0.338418i | −0.985580 | − | 0.169209i | \(-0.945879\pi\) | ||
0.985580 | − | 0.169209i | \(-0.0541213\pi\) | |||||||
\(920\) | 20.6335 | + | 143.994i | 0.0224277 | + | 0.156515i | ||||
\(921\) | −920.601 | −0.999567 | ||||||||
\(922\) | −754.394 | −0.818215 | ||||||||
\(923\) | −752.786 | −0.815586 | ||||||||
\(924\) | −192.732 | −0.208584 | ||||||||
\(925\) | − | 198.150i | − | 0.214216i | ||||||
\(926\) | −868.586 | −0.937998 | ||||||||
\(927\) | − | 394.716i | − | 0.425800i | ||||||
\(928\) | 39.8699 | 0.0429633 | ||||||||
\(929\) | −1541.65 | −1.65947 | −0.829734 | − | 0.558159i | \(-0.811508\pi\) | ||||
−0.829734 | + | 0.558159i | \(0.811508\pi\) | |||||||
\(930\) | 103.604i | 0.111402i | ||||||||
\(931\) | 313.184i | 0.336395i | ||||||||
\(932\) | −335.910 | −0.360418 | ||||||||
\(933\) | −734.305 | −0.787036 | ||||||||
\(934\) | 1026.22i | 1.09874i | ||||||||
\(935\) | 132.330i | 0.141529i | ||||||||
\(936\) | −191.105 | −0.204172 | ||||||||
\(937\) | − | 981.947i | − | 1.04797i | −0.851728 | − | 0.523984i | \(-0.824445\pi\) | ||
0.851728 | − | 0.523984i | \(-0.175555\pi\) | |||||||
\(938\) | 514.695 | 0.548715 | ||||||||
\(939\) | 5.82918i | 0.00620786i | ||||||||
\(940\) | − | 290.231i | − | 0.308756i | ||||||
\(941\) | 860.582i | 0.914540i | 0.889328 | + | 0.457270i | \(0.151173\pi\) | ||||
−0.889328 | + | 0.457270i | \(0.848827\pi\) | |||||||
\(942\) | 82.0989i | 0.0871538i | ||||||||
\(943\) | −67.5709 | + | 9.68251i | −0.0716553 | + | 0.0102678i | ||||
\(944\) | 77.3014 | 0.0818871 | ||||||||
\(945\) | 103.105 | 0.109106 | ||||||||
\(946\) | −652.219 | −0.689449 | ||||||||
\(947\) | −489.464 | −0.516858 | −0.258429 | − | 0.966030i | \(-0.583205\pi\) | ||||
−0.258429 | + | 0.966030i | \(0.583205\pi\) | |||||||
\(948\) | 172.540i | 0.182005i | ||||||||
\(949\) | 918.355 | 0.967708 | ||||||||
\(950\) | − | 74.4495i | − | 0.0783679i | ||||||
\(951\) | −281.618 | −0.296129 | ||||||||
\(952\) | −236.908 | −0.248853 | ||||||||
\(953\) | − | 1252.07i | − | 1.31382i | −0.753969 | − | 0.656910i | \(-0.771863\pi\) | ||
0.753969 | − | 0.656910i | \(-0.228137\pi\) | |||||||
\(954\) | − | 59.6278i | − | 0.0625029i | ||||||
\(955\) | −347.204 | −0.363564 | ||||||||
\(956\) | 192.936 | 0.201816 | ||||||||
\(957\) | 76.5387i | 0.0799778i | ||||||||
\(958\) | − | 487.472i | − | 0.508843i | ||||||
\(959\) | −504.506 | −0.526075 | ||||||||
\(960\) | 30.9839i | 0.0322749i | ||||||||
\(961\) | −603.208 | −0.627687 | ||||||||
\(962\) | − | 1262.25i | − | 1.31211i | ||||||
\(963\) | 47.1792i | 0.0489919i | ||||||||
\(964\) | 856.954i | 0.888957i | ||||||||
\(965\) | 65.0531i | 0.0674125i | ||||||||
\(966\) | −70.9139 | − | 494.884i | −0.0734098 | − | 0.512302i | ||||
\(967\) | −922.303 | −0.953778 | −0.476889 | − | 0.878963i | \(-0.658236\pi\) | ||||
−0.476889 | + | 0.878963i | \(0.658236\pi\) | |||||||
\(968\) | −231.055 | −0.238693 | ||||||||
\(969\) | −172.131 | −0.177638 | ||||||||
\(970\) | 320.598 | 0.330514 | ||||||||
\(971\) | 30.0774i | 0.0309757i | 0.999880 | + | 0.0154879i | \(0.00493014\pi\) | ||||
−0.999880 | + | 0.0154879i | \(0.995070\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | − | 941.107i | − | 0.967222i | ||||||
\(974\) | 507.229 | 0.520769 | ||||||||
\(975\) | 195.045 | 0.200047 | ||||||||
\(976\) | − | 220.579i | − | 0.226003i | ||||||
\(977\) | − | 1890.76i | − | 1.93527i | −0.252345 | − | 0.967637i | \(-0.581202\pi\) | ||
0.252345 | − | 0.967637i | \(-0.418798\pi\) | |||||||
\(978\) | 425.872 | 0.435452 | ||||||||
\(979\) | 809.913 | 0.827286 | ||||||||
\(980\) | 133.026i | 0.135741i | ||||||||
\(981\) | − | 299.489i | − | 0.305290i | ||||||
\(982\) | 869.472 | 0.885409 | ||||||||
\(983\) | 508.242i | 0.517031i | 0.966007 | + | 0.258516i | \(0.0832334\pi\) | ||||
−0.966007 | + | 0.258516i | \(0.916767\pi\) | |||||||
\(984\) | −14.5396 | −0.0147760 | ||||||||
\(985\) | 723.151i | 0.734164i | ||||||||
\(986\) | 94.0822i | 0.0954180i | ||||||||
\(987\) | 997.475i | 1.01061i | ||||||||
\(988\) | − | 474.255i | − | 0.480015i | ||||||
\(989\) | −239.978 | − | 1674.72i | −0.242647 | − | 1.69335i | ||||
\(990\) | −59.4800 | −0.0600809 | ||||||||
\(991\) | 800.204 | 0.807472 | 0.403736 | − | 0.914876i | \(-0.367711\pi\) | ||||
0.403736 | + | 0.914876i | \(0.367711\pi\) | |||||||
\(992\) | 107.002 | 0.107865 | ||||||||
\(993\) | 1057.79 | 1.06524 | ||||||||
\(994\) | − | 419.464i | − | 0.421996i | ||||||
\(995\) | 709.485 | 0.713050 | ||||||||
\(996\) | 127.075i | 0.127586i | ||||||||
\(997\) | −1003.69 | −1.00671 | −0.503354 | − | 0.864081i | \(-0.667901\pi\) | ||||
−0.503354 | + | 0.864081i | \(0.667901\pi\) | |||||||
\(998\) | −1132.68 | −1.13495 | ||||||||
\(999\) | − | 205.923i | − | 0.206129i |
(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 | 690.3.c.a.91.2 | ✓ | 32 | |
3.2 | odd | 2 | 2070.3.c.b.91.26 | 32 | |||
23.22 | odd | 2 | inner | 690.3.c.a.91.7 | yes | 32 | |
69.68 | even | 2 | 2070.3.c.b.91.23 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.c.a.91.2 | ✓ | 32 | 1.1 | even | 1 | trivial | |
690.3.c.a.91.7 | yes | 32 | 23.22 | odd | 2 | inner | |
2070.3.c.b.91.23 | 32 | 69.68 | even | 2 | |||
2070.3.c.b.91.26 | 32 | 3.2 | odd | 2 |