Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,3,Mod(546,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.546");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.b (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: | \(14.9046704605\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 546.1 | ||
Character | \(\chi\) | \(=\) | 547.546 |
Dual form | 547.3.b.b.546.88 |
$q$-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 \(\left(\mathbb{Z}/547\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.90365i | − | 1.95183i | −0.218157 | − | 0.975914i | \(-0.570005\pi\) | ||
0.218157 | − | 0.975914i | \(-0.429995\pi\) | |||||||
\(3\) | 5.00487i | 1.66829i | 0.551546 | + | 0.834144i | \(0.314038\pi\) | ||||
−0.551546 | + | 0.834144i | \(0.685962\pi\) | |||||||
\(4\) | −11.2385 | −2.80963 | ||||||||
\(5\) | − | 3.32024i | − | 0.664049i | −0.943271 | − | 0.332024i | \(-0.892268\pi\) | ||
0.943271 | − | 0.332024i | \(-0.107732\pi\) | |||||||
\(6\) | 19.5373 | 3.25621 | ||||||||
\(7\) | 0.969581i | 0.138512i | 0.997599 | + | 0.0692558i | \(0.0220625\pi\) | ||||
−0.997599 | + | 0.0692558i | \(0.977938\pi\) | |||||||
\(8\) | 28.2567i | 3.53208i | ||||||||
\(9\) | −16.0487 | −1.78319 | ||||||||
\(10\) | −12.9611 | −1.29611 | ||||||||
\(11\) | 6.84519 | 0.622290 | 0.311145 | − | 0.950362i | \(-0.399287\pi\) | ||||
0.311145 | + | 0.950362i | \(0.399287\pi\) | |||||||
\(12\) | − | 56.2473i | − | 4.68727i | ||||||
\(13\) | 4.85135 | 0.373181 | 0.186591 | − | 0.982438i | \(-0.440256\pi\) | ||||
0.186591 | + | 0.982438i | \(0.440256\pi\) | |||||||
\(14\) | 3.78491 | 0.270351 | ||||||||
\(15\) | 16.6174 | 1.10782 | ||||||||
\(16\) | 65.3502 | 4.08439 | ||||||||
\(17\) | − | 0.703267i | − | 0.0413686i | −0.999786 | − | 0.0206843i | \(-0.993416\pi\) | ||
0.999786 | − | 0.0206843i | \(-0.00658449\pi\) | |||||||
\(18\) | 62.6485i | 3.48047i | ||||||||
\(19\) | −27.4439 | −1.44442 | −0.722209 | − | 0.691675i | \(-0.756873\pi\) | ||||
−0.722209 | + | 0.691675i | \(0.756873\pi\) | |||||||
\(20\) | 37.3146i | 1.86573i | ||||||||
\(21\) | −4.85262 | −0.231077 | ||||||||
\(22\) | − | 26.7213i | − | 1.21460i | ||||||
\(23\) | − | 33.5843i | − | 1.46019i | −0.683348 | − | 0.730093i | \(-0.739477\pi\) | ||
0.683348 | − | 0.730093i | \(-0.260523\pi\) | |||||||
\(24\) | −141.421 | −5.89254 | ||||||||
\(25\) | 13.9760 | 0.559040 | ||||||||
\(26\) | − | 18.9380i | − | 0.728385i | ||||||
\(27\) | − | 35.2777i | − | 1.30658i | ||||||
\(28\) | − | 10.8967i | − | 0.389166i | ||||||
\(29\) | 5.47585 | 0.188822 | 0.0944112 | − | 0.995533i | \(-0.469903\pi\) | ||||
0.0944112 | + | 0.995533i | \(0.469903\pi\) | |||||||
\(30\) | − | 64.8685i | − | 2.16228i | ||||||
\(31\) | − | 43.4294i | − | 1.40095i | −0.713678 | − | 0.700474i | \(-0.752972\pi\) | ||
0.713678 | − | 0.700474i | \(-0.247028\pi\) | |||||||
\(32\) | − | 142.078i | − | 4.43994i | ||||||
\(33\) | 34.2593i | 1.03816i | ||||||||
\(34\) | −2.74531 | −0.0807444 | ||||||||
\(35\) | 3.21924 | 0.0919784 | ||||||||
\(36\) | 180.363 | 5.01010 | ||||||||
\(37\) | − | 33.9385i | − | 0.917256i | −0.888628 | − | 0.458628i | \(-0.848341\pi\) | ||
0.888628 | − | 0.458628i | \(-0.151659\pi\) | |||||||
\(38\) | 107.132i | 2.81925i | ||||||||
\(39\) | 24.2804i | 0.622574i | ||||||||
\(40\) | 93.8190 | 2.34548 | ||||||||
\(41\) | − | 29.4683i | − | 0.718738i | −0.933196 | − | 0.359369i | \(-0.882992\pi\) | ||
0.933196 | − | 0.359369i | \(-0.117008\pi\) | |||||||
\(42\) | 18.9430i | 0.451023i | ||||||||
\(43\) | − | 34.3798i | − | 0.799531i | −0.916617 | − | 0.399765i | \(-0.869092\pi\) | ||
0.916617 | − | 0.399765i | \(-0.130908\pi\) | |||||||
\(44\) | −76.9298 | −1.74841 | ||||||||
\(45\) | 53.2855i | 1.18412i | ||||||||
\(46\) | −131.101 | −2.85003 | ||||||||
\(47\) | −78.9339 | −1.67944 | −0.839722 | − | 0.543016i | \(-0.817282\pi\) | ||||
−0.839722 | + | 0.543016i | \(0.817282\pi\) | |||||||
\(48\) | 327.069i | 6.81394i | ||||||||
\(49\) | 48.0599 | 0.980815 | ||||||||
\(50\) | − | 54.5574i | − | 1.09115i | ||||||
\(51\) | 3.51976 | 0.0690148 | ||||||||
\(52\) | −54.5220 | −1.04850 | ||||||||
\(53\) | −79.8474 | −1.50656 | −0.753278 | − | 0.657703i | \(-0.771528\pi\) | ||||
−0.753278 | + | 0.657703i | \(0.771528\pi\) | |||||||
\(54\) | −137.712 | −2.55022 | ||||||||
\(55\) | − | 22.7277i | − | 0.413231i | ||||||
\(56\) | −27.3971 | −0.489235 | ||||||||
\(57\) | − | 137.353i | − | 2.40971i | ||||||
\(58\) | − | 21.3758i | − | 0.368549i | ||||||
\(59\) | 33.1151i | 0.561272i | 0.959814 | + | 0.280636i | \(0.0905454\pi\) | ||||
−0.959814 | + | 0.280636i | \(0.909455\pi\) | |||||||
\(60\) | −186.755 | −3.11258 | ||||||||
\(61\) | − | 15.9587i | − | 0.261617i | −0.991408 | − | 0.130809i | \(-0.958243\pi\) | ||
0.991408 | − | 0.130809i | \(-0.0417574\pi\) | |||||||
\(62\) | −169.533 | −2.73441 | ||||||||
\(63\) | − | 15.5605i | − | 0.246992i | ||||||
\(64\) | −293.223 | −4.58160 | ||||||||
\(65\) | − | 16.1077i | − | 0.247810i | ||||||
\(66\) | 133.736 | 2.02631 | ||||||||
\(67\) | 49.9969 | 0.746222 | 0.373111 | − | 0.927787i | \(-0.378291\pi\) | ||||
0.373111 | + | 0.927787i | \(0.378291\pi\) | |||||||
\(68\) | 7.90368i | 0.116231i | ||||||||
\(69\) | 168.085 | 2.43601 | ||||||||
\(70\) | − | 12.5668i | − | 0.179526i | ||||||
\(71\) | 80.1855i | 1.12937i | 0.825305 | + | 0.564687i | \(0.191003\pi\) | ||||
−0.825305 | + | 0.564687i | \(0.808997\pi\) | |||||||
\(72\) | − | 453.482i | − | 6.29837i | ||||||
\(73\) | −25.7088 | −0.352175 | −0.176087 | − | 0.984375i | \(-0.556344\pi\) | ||||
−0.176087 | + | 0.984375i | \(0.556344\pi\) | |||||||
\(74\) | −132.484 | −1.79032 | ||||||||
\(75\) | 69.9480i | 0.932639i | ||||||||
\(76\) | 308.429 | 4.05828 | ||||||||
\(77\) | 6.63697i | 0.0861944i | ||||||||
\(78\) | 94.7822 | 1.21516 | ||||||||
\(79\) | − | 92.2999i | − | 1.16835i | −0.811627 | − | 0.584177i | \(-0.801418\pi\) | ||
0.811627 | − | 0.584177i | \(-0.198582\pi\) | |||||||
\(80\) | − | 216.979i | − | 2.71223i | ||||||
\(81\) | 32.1221 | 0.396570 | ||||||||
\(82\) | −115.034 | −1.40285 | ||||||||
\(83\) | − | 64.5112i | − | 0.777243i | −0.921398 | − | 0.388621i | \(-0.872951\pi\) | ||
0.921398 | − | 0.388621i | \(-0.127049\pi\) | |||||||
\(84\) | 54.5363 | 0.649242 | ||||||||
\(85\) | −2.33502 | −0.0274708 | ||||||||
\(86\) | −134.207 | −1.56055 | ||||||||
\(87\) | 27.4059i | 0.315010i | ||||||||
\(88\) | 193.422i | 2.19798i | ||||||||
\(89\) | − | 138.030i | − | 1.55090i | −0.631412 | − | 0.775448i | \(-0.717524\pi\) | ||
0.631412 | − | 0.775448i | \(-0.282476\pi\) | |||||||
\(90\) | 208.008 | 2.31120 | ||||||||
\(91\) | 4.70378i | 0.0516899i | ||||||||
\(92\) | 377.437i | 4.10258i | ||||||||
\(93\) | 217.358 | 2.33718 | ||||||||
\(94\) | 308.131i | 3.27799i | ||||||||
\(95\) | 91.1205i | 0.959163i | ||||||||
\(96\) | 711.081 | 7.40710 | ||||||||
\(97\) | 164.954 | 1.70056 | 0.850280 | − | 0.526330i | \(-0.176432\pi\) | ||||
0.850280 | + | 0.526330i | \(0.176432\pi\) | |||||||
\(98\) | − | 187.609i | − | 1.91438i | ||||||
\(99\) | −109.856 | −1.10966 | ||||||||
\(100\) | −157.069 | −1.57069 | ||||||||
\(101\) | − | 96.2354i | − | 0.952826i | −0.879222 | − | 0.476413i | \(-0.841937\pi\) | ||
0.879222 | − | 0.476413i | \(-0.158063\pi\) | |||||||
\(102\) | − | 13.7399i | − | 0.134705i | ||||||
\(103\) | 98.8378i | 0.959590i | 0.877381 | + | 0.479795i | \(0.159289\pi\) | ||||
−0.877381 | + | 0.479795i | \(0.840711\pi\) | |||||||
\(104\) | 137.083i | 1.31811i | ||||||||
\(105\) | 16.1119i | 0.153447i | ||||||||
\(106\) | 311.697i | 2.94054i | ||||||||
\(107\) | 57.3593i | 0.536068i | 0.963409 | + | 0.268034i | \(0.0863740\pi\) | ||||
−0.963409 | + | 0.268034i | \(0.913626\pi\) | |||||||
\(108\) | 396.469i | 3.67101i | ||||||||
\(109\) | − | 74.7904i | − | 0.686150i | −0.939308 | − | 0.343075i | \(-0.888531\pi\) | ||
0.939308 | − | 0.343075i | \(-0.111469\pi\) | |||||||
\(110\) | −88.7211 | −0.806556 | ||||||||
\(111\) | 169.857 | 1.53025 | ||||||||
\(112\) | 63.3623i | 0.565735i | ||||||||
\(113\) | 165.519 | 1.46477 | 0.732386 | − | 0.680890i | \(-0.238407\pi\) | ||||
0.732386 | + | 0.680890i | \(0.238407\pi\) | |||||||
\(114\) | −536.180 | −4.70333 | ||||||||
\(115\) | −111.508 | −0.969634 | ||||||||
\(116\) | −61.5404 | −0.530521 | ||||||||
\(117\) | −77.8579 | −0.665452 | ||||||||
\(118\) | 129.270 | 1.09551 | ||||||||
\(119\) | 0.681874 | 0.00573003 | ||||||||
\(120\) | 469.552i | 3.91293i | ||||||||
\(121\) | −74.1433 | −0.612755 | ||||||||
\(122\) | −62.2971 | −0.510632 | ||||||||
\(123\) | 147.485 | 1.19906 | ||||||||
\(124\) | 488.082i | 3.93614i | ||||||||
\(125\) | − | 129.410i | − | 1.03528i | ||||||
\(126\) | −60.7428 | −0.482086 | ||||||||
\(127\) | 84.3990 | 0.664559 | 0.332279 | − | 0.943181i | \(-0.392182\pi\) | ||||
0.332279 | + | 0.943181i | \(0.392182\pi\) | |||||||
\(128\) | 576.327i | 4.50256i | ||||||||
\(129\) | 172.066 | 1.33385 | ||||||||
\(130\) | −62.8788 | −0.483683 | ||||||||
\(131\) | −59.8237 | −0.456669 | −0.228335 | − | 0.973583i | \(-0.573328\pi\) | ||||
−0.228335 | + | 0.973583i | \(0.573328\pi\) | |||||||
\(132\) | − | 385.024i | − | 2.91685i | ||||||
\(133\) | − | 26.6091i | − | 0.200069i | ||||||
\(134\) | − | 195.170i | − | 1.45650i | ||||||
\(135\) | −117.131 | −0.867634 | ||||||||
\(136\) | 19.8720 | 0.146117 | ||||||||
\(137\) | 161.651 | 1.17993 | 0.589965 | − | 0.807428i | \(-0.299141\pi\) | ||||
0.589965 | + | 0.807428i | \(0.299141\pi\) | |||||||
\(138\) | − | 656.145i | − | 4.75467i | ||||||
\(139\) | 226.854 | 1.63204 | 0.816021 | − | 0.578022i | \(-0.196175\pi\) | ||||
0.816021 | + | 0.578022i | \(0.196175\pi\) | |||||||
\(140\) | −36.1795 | −0.258425 | ||||||||
\(141\) | − | 395.054i | − | 2.80180i | ||||||
\(142\) | 313.017 | 2.20434 | ||||||||
\(143\) | 33.2085 | 0.232227 | ||||||||
\(144\) | −1048.79 | −7.28323 | ||||||||
\(145\) | − | 18.1812i | − | 0.125387i | ||||||
\(146\) | 100.358i | 0.687385i | ||||||||
\(147\) | 240.533i | 1.63628i | ||||||||
\(148\) | 381.418i | 2.57715i | ||||||||
\(149\) | 120.427 | 0.808232 | 0.404116 | − | 0.914708i | \(-0.367579\pi\) | ||||
0.404116 | + | 0.914708i | \(0.367579\pi\) | |||||||
\(150\) | 273.053 | 1.82035 | ||||||||
\(151\) | − | 185.662i | − | 1.22955i | −0.788701 | − | 0.614776i | \(-0.789246\pi\) | ||
0.788701 | − | 0.614776i | \(-0.210754\pi\) | |||||||
\(152\) | − | 775.474i | − | 5.10181i | ||||||
\(153\) | 11.2865i | 0.0737680i | ||||||||
\(154\) | 25.9084 | 0.168237 | ||||||||
\(155\) | −144.196 | −0.930297 | ||||||||
\(156\) | − | 272.876i | − | 1.74920i | ||||||
\(157\) | −51.3979 | −0.327375 | −0.163688 | − | 0.986512i | \(-0.552339\pi\) | ||||
−0.163688 | + | 0.986512i | \(0.552339\pi\) | |||||||
\(158\) | −360.307 | −2.28042 | ||||||||
\(159\) | − | 399.626i | − | 2.51337i | ||||||
\(160\) | −471.733 | −2.94833 | ||||||||
\(161\) | 32.5627 | 0.202253 | ||||||||
\(162\) | − | 125.394i | − | 0.774035i | ||||||
\(163\) | 289.443i | 1.77572i | 0.460109 | + | 0.887862i | \(0.347810\pi\) | ||||
−0.460109 | + | 0.887862i | \(0.652190\pi\) | |||||||
\(164\) | 331.180i | 2.01939i | ||||||||
\(165\) | 113.749 | 0.689389 | ||||||||
\(166\) | −251.829 | −1.51704 | ||||||||
\(167\) | −280.016 | −1.67674 | −0.838372 | − | 0.545098i | \(-0.816492\pi\) | ||||
−0.838372 | + | 0.545098i | \(0.816492\pi\) | |||||||
\(168\) | − | 137.119i | − | 0.816185i | ||||||
\(169\) | −145.464 | −0.860736 | ||||||||
\(170\) | 9.11510i | 0.0536182i | ||||||||
\(171\) | 440.439 | 2.57567 | ||||||||
\(172\) | 386.378i | 2.24639i | ||||||||
\(173\) | − | 15.8385i | − | 0.0915523i | −0.998952 | − | 0.0457761i | \(-0.985424\pi\) | ||
0.998952 | − | 0.0457761i | \(-0.0145761\pi\) | |||||||
\(174\) | 106.983 | 0.614846 | ||||||||
\(175\) | 13.5509i | 0.0774334i | ||||||||
\(176\) | 447.335 | 2.54168 | ||||||||
\(177\) | −165.736 | −0.936364 | ||||||||
\(178\) | −538.820 | −3.02708 | ||||||||
\(179\) | −177.343 | −0.990742 | −0.495371 | − | 0.868681i | \(-0.664968\pi\) | ||||
−0.495371 | + | 0.868681i | \(0.664968\pi\) | |||||||
\(180\) | − | 598.850i | − | 3.32695i | ||||||
\(181\) | −146.264 | −0.808087 | −0.404044 | − | 0.914740i | \(-0.632396\pi\) | ||||
−0.404044 | + | 0.914740i | \(0.632396\pi\) | |||||||
\(182\) | 18.3619 | 0.100890 | ||||||||
\(183\) | 79.8710 | 0.436453 | ||||||||
\(184\) | 948.980 | 5.15750 | ||||||||
\(185\) | −112.684 | −0.609102 | ||||||||
\(186\) | − | 848.491i | − | 4.56178i | ||||||
\(187\) | − | 4.81400i | − | 0.0257433i | ||||||
\(188\) | 887.100 | 4.71862 | ||||||||
\(189\) | 34.2046 | 0.180977 | ||||||||
\(190\) | 355.703 | 1.87212 | ||||||||
\(191\) | 85.2771 | 0.446477 | 0.223238 | − | 0.974764i | \(-0.428337\pi\) | ||||
0.223238 | + | 0.974764i | \(0.428337\pi\) | |||||||
\(192\) | − | 1467.54i | − | 7.64343i | ||||||
\(193\) | −216.985 | −1.12427 | −0.562137 | − | 0.827044i | \(-0.690021\pi\) | ||||
−0.562137 | + | 0.827044i | \(0.690021\pi\) | |||||||
\(194\) | − | 643.925i | − | 3.31920i | ||||||
\(195\) | 80.6168 | 0.413419 | ||||||||
\(196\) | −540.122 | −2.75573 | ||||||||
\(197\) | 230.341i | 1.16924i | 0.811306 | + | 0.584622i | \(0.198757\pi\) | ||||
−0.811306 | + | 0.584622i | \(0.801243\pi\) | |||||||
\(198\) | 428.841i | 2.16587i | ||||||||
\(199\) | −105.453 | −0.529915 | −0.264958 | − | 0.964260i | \(-0.585358\pi\) | ||||
−0.264958 | + | 0.964260i | \(0.585358\pi\) | |||||||
\(200\) | 394.915i | 1.97457i | ||||||||
\(201\) | 250.228i | 1.24491i | ||||||||
\(202\) | −375.670 | −1.85975 | ||||||||
\(203\) | 5.30928i | 0.0261541i | ||||||||
\(204\) | −39.5568 | −0.193906 | ||||||||
\(205\) | −97.8418 | −0.477277 | ||||||||
\(206\) | 385.829 | 1.87295 | ||||||||
\(207\) | 538.983i | 2.60378i | ||||||||
\(208\) | 317.037 | 1.52422 | ||||||||
\(209\) | −187.859 | −0.898847 | ||||||||
\(210\) | 62.8952 | 0.299501 | ||||||||
\(211\) | 387.259i | 1.83535i | 0.397334 | + | 0.917674i | \(0.369936\pi\) | ||||
−0.397334 | + | 0.917674i | \(0.630064\pi\) | |||||||
\(212\) | 897.367 | 4.23286 | ||||||||
\(213\) | −401.318 | −1.88412 | ||||||||
\(214\) | 223.911 | 1.04631 | ||||||||
\(215\) | −114.149 | −0.530927 | ||||||||
\(216\) | 996.831 | 4.61496 | ||||||||
\(217\) | 42.1083 | 0.194047 | ||||||||
\(218\) | −291.956 | −1.33925 | ||||||||
\(219\) | − | 128.669i | − | 0.587530i | ||||||
\(220\) | 255.426i | 1.16103i | ||||||||
\(221\) | − | 3.41180i | − | 0.0154380i | ||||||
\(222\) | − | 663.065i | − | 2.98678i | ||||||
\(223\) | − | 11.6351i | − | 0.0521752i | −0.999660 | − | 0.0260876i | \(-0.991695\pi\) | ||
0.999660 | − | 0.0260876i | \(-0.00830488\pi\) | |||||||
\(224\) | 137.756 | 0.614983 | ||||||||
\(225\) | −224.296 | −0.996872 | ||||||||
\(226\) | − | 646.130i | − | 2.85898i | ||||||
\(227\) | 109.614 | 0.482881 | 0.241440 | − | 0.970416i | \(-0.422380\pi\) | ||||
0.241440 | + | 0.970416i | \(0.422380\pi\) | |||||||
\(228\) | 1543.65i | 6.77038i | ||||||||
\(229\) | − | 261.170i | − | 1.14048i | −0.821478 | − | 0.570240i | \(-0.806850\pi\) | ||
0.821478 | − | 0.570240i | \(-0.193150\pi\) | |||||||
\(230\) | 435.288i | 1.89256i | ||||||||
\(231\) | −33.2171 | −0.143797 | ||||||||
\(232\) | 154.729i | 0.666937i | ||||||||
\(233\) | 185.781 | 0.797343 | 0.398671 | − | 0.917094i | \(-0.369471\pi\) | ||||
0.398671 | + | 0.917094i | \(0.369471\pi\) | |||||||
\(234\) | 303.930i | 1.29885i | ||||||||
\(235\) | 262.080i | 1.11523i | ||||||||
\(236\) | − | 372.164i | − | 1.57697i | ||||||
\(237\) | 461.949 | 1.94915 | ||||||||
\(238\) | − | 2.66180i | − | 0.0111840i | ||||||
\(239\) | −335.028 | −1.40179 | −0.700896 | − | 0.713264i | \(-0.747216\pi\) | ||||
−0.700896 | + | 0.713264i | \(0.747216\pi\) | |||||||
\(240\) | 1085.95 | 4.52479 | ||||||||
\(241\) | 352.978i | 1.46464i | 0.680962 | + | 0.732319i | \(0.261562\pi\) | ||||
−0.680962 | + | 0.732319i | \(0.738438\pi\) | |||||||
\(242\) | 289.430i | 1.19599i | ||||||||
\(243\) | − | 156.733i | − | 0.644990i | ||||||
\(244\) | 179.352i | 0.735048i | ||||||||
\(245\) | − | 159.571i | − | 0.651308i | ||||||
\(246\) | − | 575.729i | − | 2.34036i | ||||||
\(247\) | −133.140 | −0.539029 | ||||||||
\(248\) | 1227.17 | 4.94826 | ||||||||
\(249\) | 322.870 | 1.29667 | ||||||||
\(250\) | −505.171 | −2.02068 | ||||||||
\(251\) | − | 156.474i | − | 0.623403i | −0.950180 | − | 0.311702i | \(-0.899101\pi\) | ||
0.950180 | − | 0.311702i | \(-0.100899\pi\) | |||||||
\(252\) | 174.877i | 0.693956i | ||||||||
\(253\) | − | 229.891i | − | 0.908659i | ||||||
\(254\) | − | 329.464i | − | 1.29710i | ||||||
\(255\) | − | 11.6864i | − | 0.0458292i | ||||||
\(256\) | 1076.89 | 4.20661 | ||||||||
\(257\) | − | 24.9264i | − | 0.0969898i | −0.998823 | − | 0.0484949i | \(-0.984558\pi\) | ||
0.998823 | − | 0.0484949i | \(-0.0154425\pi\) | |||||||
\(258\) | − | 671.688i | − | 2.60344i | ||||||
\(259\) | 32.9061 | 0.127051 | ||||||||
\(260\) | 181.026i | 0.696255i | ||||||||
\(261\) | −87.8802 | −0.336706 | ||||||||
\(262\) | 233.531i | 0.891339i | ||||||||
\(263\) | 21.0838 | 0.0801666 | 0.0400833 | − | 0.999196i | \(-0.487238\pi\) | ||||
0.0400833 | + | 0.999196i | \(0.487238\pi\) | |||||||
\(264\) | −968.053 | −3.66687 | ||||||||
\(265\) | 265.113i | 1.00043i | ||||||||
\(266\) | −103.873 | −0.390499 | ||||||||
\(267\) | 690.820 | 2.58734 | ||||||||
\(268\) | −561.891 | −2.09661 | ||||||||
\(269\) | −356.206 | −1.32419 | −0.662094 | − | 0.749421i | \(-0.730332\pi\) | ||||
−0.662094 | + | 0.749421i | \(0.730332\pi\) | |||||||
\(270\) | 457.237i | 1.69347i | ||||||||
\(271\) | 191.625i | 0.707103i | 0.935415 | + | 0.353552i | \(0.115026\pi\) | ||||
−0.935415 | + | 0.353552i | \(0.884974\pi\) | |||||||
\(272\) | − | 45.9586i | − | 0.168966i | ||||||
\(273\) | −23.5418 | −0.0862337 | ||||||||
\(274\) | − | 631.028i | − | 2.30302i | ||||||
\(275\) | 95.6684 | 0.347885 | ||||||||
\(276\) | −1889.02 | −6.84429 | ||||||||
\(277\) | −193.785 | −0.699585 | −0.349793 | − | 0.936827i | \(-0.613748\pi\) | ||||
−0.349793 | + | 0.936827i | \(0.613748\pi\) | |||||||
\(278\) | − | 885.559i | − | 3.18546i | ||||||
\(279\) | 696.984i | 2.49815i | ||||||||
\(280\) | 90.9651i | 0.324876i | ||||||||
\(281\) | − | 72.5495i | − | 0.258183i | −0.991633 | − | 0.129092i | \(-0.958794\pi\) | ||
0.991633 | − | 0.129092i | \(-0.0412061\pi\) | |||||||
\(282\) | −1542.15 | −5.46863 | ||||||||
\(283\) | − | 405.318i | − | 1.43222i | −0.697987 | − | 0.716110i | \(-0.745921\pi\) | ||
0.697987 | − | 0.716110i | \(-0.254079\pi\) | |||||||
\(284\) | − | 901.167i | − | 3.17312i | ||||||
\(285\) | −456.046 | −1.60016 | ||||||||
\(286\) | − | 129.634i | − | 0.453267i | ||||||
\(287\) | 28.5719 | 0.0995535 | ||||||||
\(288\) | 2280.17i | 7.91724i | ||||||||
\(289\) | 288.505 | 0.998289 | ||||||||
\(290\) | −70.9729 | −0.244734 | ||||||||
\(291\) | 825.575i | 2.83703i | ||||||||
\(292\) | 288.929 | 0.989481 | ||||||||
\(293\) | −223.354 | −0.762302 | −0.381151 | − | 0.924513i | \(-0.624472\pi\) | ||||
−0.381151 | + | 0.924513i | \(0.624472\pi\) | |||||||
\(294\) | 938.959 | 3.19374 | ||||||||
\(295\) | 109.950 | 0.372712 | ||||||||
\(296\) | 958.988 | 3.23982 | ||||||||
\(297\) | − | 241.483i | − | 0.813074i | ||||||
\(298\) | − | 470.104i | − | 1.57753i | ||||||
\(299\) | − | 162.929i | − | 0.544914i | ||||||
\(300\) | − | 786.111i | − | 2.62037i | ||||||
\(301\) | 33.3340 | 0.110744 | ||||||||
\(302\) | −724.762 | −2.39987 | ||||||||
\(303\) | 481.645 | 1.58959 | ||||||||
\(304\) | −1793.47 | −5.89956 | ||||||||
\(305\) | −52.9866 | −0.173727 | ||||||||
\(306\) | 44.0586 | 0.143982 | ||||||||
\(307\) | 186.097i | 0.606178i | 0.952962 | + | 0.303089i | \(0.0980180\pi\) | ||||
−0.952962 | + | 0.303089i | \(0.901982\pi\) | |||||||
\(308\) | − | 74.5897i | − | 0.242174i | ||||||
\(309\) | −494.670 | −1.60087 | ||||||||
\(310\) | 562.891i | 1.81578i | ||||||||
\(311\) | 109.411 | 0.351803 | 0.175902 | − | 0.984408i | \(-0.443716\pi\) | ||||
0.175902 | + | 0.984408i | \(0.443716\pi\) | |||||||
\(312\) | −686.083 | −2.19898 | ||||||||
\(313\) | 484.583 | 1.54819 | 0.774095 | − | 0.633070i | \(-0.218205\pi\) | ||||
0.774095 | + | 0.633070i | \(0.218205\pi\) | |||||||
\(314\) | 200.640i | 0.638980i | ||||||||
\(315\) | −51.6646 | −0.164015 | ||||||||
\(316\) | 1037.31i | 3.28264i | ||||||||
\(317\) | −225.140 | −0.710221 | −0.355111 | − | 0.934824i | \(-0.615557\pi\) | ||||
−0.355111 | + | 0.934824i | \(0.615557\pi\) | |||||||
\(318\) | −1560.00 | −4.90566 | ||||||||
\(319\) | 37.4833 | 0.117502 | ||||||||
\(320\) | 973.570i | 3.04241i | ||||||||
\(321\) | −287.076 | −0.894316 | ||||||||
\(322\) | − | 127.113i | − | 0.394762i | ||||||
\(323\) | 19.3004i | 0.0597536i | ||||||||
\(324\) | −361.005 | −1.11421 | ||||||||
\(325\) | 67.8025 | 0.208623 | ||||||||
\(326\) | 1129.89 | 3.46591 | ||||||||
\(327\) | 374.316 | 1.14470 | ||||||||
\(328\) | 832.675 | 2.53864 | ||||||||
\(329\) | − | 76.5328i | − | 0.232623i | ||||||
\(330\) | − | 444.037i | − | 1.34557i | ||||||
\(331\) | 551.970i | 1.66758i | 0.552080 | + | 0.833791i | \(0.313834\pi\) | ||||
−0.552080 | + | 0.833791i | \(0.686166\pi\) | |||||||
\(332\) | 725.010i | 2.18376i | ||||||||
\(333\) | 544.668i | 1.63564i | ||||||||
\(334\) | 1093.09i | 3.27272i | ||||||||
\(335\) | − | 166.002i | − | 0.495527i | ||||||
\(336\) | −317.120 | −0.943810 | ||||||||
\(337\) | − | 474.094i | − | 1.40681i | −0.710790 | − | 0.703404i | \(-0.751663\pi\) | ||
0.710790 | − | 0.703404i | \(-0.248337\pi\) | |||||||
\(338\) | 567.843i | 1.68001i | ||||||||
\(339\) | 828.401i | 2.44366i | ||||||||
\(340\) | 26.2421 | 0.0771827 | ||||||||
\(341\) | − | 297.282i | − | 0.871796i | ||||||
\(342\) | − | 1719.32i | − | 5.02726i | ||||||
\(343\) | 94.1075i | 0.274366i | ||||||||
\(344\) | 971.460 | 2.82401 | ||||||||
\(345\) | − | 558.082i | − | 1.61763i | ||||||
\(346\) | −61.8282 | −0.178694 | ||||||||
\(347\) | −207.655 | −0.598430 | −0.299215 | − | 0.954186i | \(-0.596725\pi\) | ||||
−0.299215 | + | 0.954186i | \(0.596725\pi\) | |||||||
\(348\) | − | 308.002i | − | 0.885062i | ||||||
\(349\) | −448.334 | −1.28462 | −0.642312 | − | 0.766443i | \(-0.722025\pi\) | ||||
−0.642312 | + | 0.766443i | \(0.722025\pi\) | |||||||
\(350\) | 52.8978 | 0.151137 | ||||||||
\(351\) | − | 171.145i | − | 0.487592i | ||||||
\(352\) | − | 972.552i | − | 2.76293i | ||||||
\(353\) | 129.045 | 0.365567 | 0.182783 | − | 0.983153i | \(-0.441489\pi\) | ||||
0.182783 | + | 0.983153i | \(0.441489\pi\) | |||||||
\(354\) | 646.978i | 1.82762i | ||||||||
\(355\) | 266.235 | 0.749959 | ||||||||
\(356\) | 1551.25i | 4.35744i | ||||||||
\(357\) | 3.41269i | 0.00955935i | ||||||||
\(358\) | 692.285i | 1.93376i | ||||||||
\(359\) | − | 286.030i | − | 0.796742i | −0.917224 | − | 0.398371i | \(-0.869576\pi\) | ||
0.917224 | − | 0.398371i | \(-0.130424\pi\) | |||||||
\(360\) | −1505.67 | −4.18242 | ||||||||
\(361\) | 392.170 | 1.08634 | ||||||||
\(362\) | 570.963i | 1.57725i | ||||||||
\(363\) | − | 371.077i | − | 1.02225i | ||||||
\(364\) | − | 52.8635i | − | 0.145230i | ||||||
\(365\) | 85.3594i | 0.233861i | ||||||||
\(366\) | − | 311.789i | − | 0.851882i | ||||||
\(367\) | −153.171 | −0.417359 | −0.208680 | − | 0.977984i | \(-0.566917\pi\) | ||||
−0.208680 | + | 0.977984i | \(0.566917\pi\) | |||||||
\(368\) | − | 2194.74i | − | 5.96397i | ||||||
\(369\) | 472.927i | 1.28164i | ||||||||
\(370\) | 439.879i | 1.18886i | ||||||||
\(371\) | − | 77.4186i | − | 0.208675i | ||||||
\(372\) | −2442.78 | −6.56662 | ||||||||
\(373\) | 422.859i | 1.13367i | 0.823832 | + | 0.566835i | \(0.191832\pi\) | ||||
−0.823832 | + | 0.566835i | \(0.808168\pi\) | |||||||
\(374\) | −18.7922 | −0.0502465 | ||||||||
\(375\) | 647.678 | 1.72714 | ||||||||
\(376\) | − | 2230.41i | − | 5.93194i | ||||||
\(377\) | 26.5653 | 0.0704650 | ||||||||
\(378\) | − | 133.523i | − | 0.353235i | ||||||
\(379\) | −106.386 | −0.280702 | −0.140351 | − | 0.990102i | \(-0.544823\pi\) | ||||
−0.140351 | + | 0.990102i | \(0.544823\pi\) | |||||||
\(380\) | − | 1024.06i | − | 2.69489i | ||||||
\(381\) | 422.406i | 1.10868i | ||||||||
\(382\) | − | 332.892i | − | 0.871446i | ||||||
\(383\) | −213.762 | −0.558125 | −0.279062 | − | 0.960273i | \(-0.590024\pi\) | ||||
−0.279062 | + | 0.960273i | \(0.590024\pi\) | |||||||
\(384\) | −2884.44 | −7.51157 | ||||||||
\(385\) | 22.0364 | 0.0572373 | ||||||||
\(386\) | 847.034i | 2.19439i | ||||||||
\(387\) | 551.751i | 1.42571i | ||||||||
\(388\) | −1853.84 | −4.77795 | ||||||||
\(389\) | − | 251.111i | − | 0.645529i | −0.946479 | − | 0.322764i | \(-0.895388\pi\) | ||
0.946479 | − | 0.322764i | \(-0.104612\pi\) | |||||||
\(390\) | − | 314.700i | − | 0.806923i | ||||||
\(391\) | −23.6187 | −0.0604059 | ||||||||
\(392\) | 1358.01i | 3.46432i | ||||||||
\(393\) | − | 299.409i | − | 0.761856i | ||||||
\(394\) | 899.171 | 2.28216 | ||||||||
\(395\) | −306.458 | −0.775843 | ||||||||
\(396\) | 1234.62 | 3.11773 | ||||||||
\(397\) | − | 377.872i | − | 0.951819i | −0.879494 | − | 0.475910i | \(-0.842119\pi\) | ||
0.879494 | − | 0.475910i | \(-0.157881\pi\) | |||||||
\(398\) | 411.653i | 1.03430i | ||||||||
\(399\) | 133.175 | 0.333772 | ||||||||
\(400\) | 913.334 | 2.28333 | ||||||||
\(401\) | −5.96869 | −0.0148845 | −0.00744225 | − | 0.999972i | \(-0.502369\pi\) | ||||
−0.00744225 | + | 0.999972i | \(0.502369\pi\) | |||||||
\(402\) | 976.802 | 2.42986 | ||||||||
\(403\) | − | 210.691i | − | 0.522807i | ||||||
\(404\) | 1081.54i | 2.67709i | ||||||||
\(405\) | − | 106.653i | − | 0.263341i | ||||||
\(406\) | 20.7256 | 0.0510483 | ||||||||
\(407\) | − | 232.315i | − | 0.570799i | ||||||
\(408\) | 99.4566i | 0.243766i | ||||||||
\(409\) | 362.692 | 0.886777 | 0.443389 | − | 0.896329i | \(-0.353776\pi\) | ||||
0.443389 | + | 0.896329i | \(0.353776\pi\) | |||||||
\(410\) | 381.940i | 0.931562i | ||||||||
\(411\) | 809.039i | 1.96847i | ||||||||
\(412\) | − | 1110.79i | − | 2.69609i | ||||||
\(413\) | −32.1077 | −0.0777427 | ||||||||
\(414\) | 2104.00 | 5.08214 | ||||||||
\(415\) | −214.193 | −0.516127 | ||||||||
\(416\) | − | 689.271i | − | 1.65690i | ||||||
\(417\) | 1135.37i | 2.72272i | ||||||||
\(418\) | 733.337i | 1.75439i | ||||||||
\(419\) | −249.142 | −0.594611 | −0.297305 | − | 0.954782i | \(-0.596088\pi\) | ||||
−0.297305 | + | 0.954782i | \(0.596088\pi\) | |||||||
\(420\) | − | 181.074i | − | 0.431128i | ||||||
\(421\) | − | 590.667i | − | 1.40301i | −0.712664 | − | 0.701505i | \(-0.752512\pi\) | ||
0.712664 | − | 0.701505i | \(-0.247488\pi\) | |||||||
\(422\) | 1511.72 | 3.58228 | ||||||||
\(423\) | 1266.79 | 2.99476 | ||||||||
\(424\) | − | 2256.22i | − | 5.32128i | ||||||
\(425\) | − | 9.82885i | − | 0.0231267i | ||||||
\(426\) | 1566.61i | 3.67748i | ||||||||
\(427\) | 15.4732 | 0.0362370 | ||||||||
\(428\) | − | 644.633i | − | 1.50615i | ||||||
\(429\) | 166.204i | 0.387422i | ||||||||
\(430\) | 445.600i | 1.03628i | ||||||||
\(431\) | 588.476i | 1.36537i | 0.730711 | + | 0.682687i | \(0.239189\pi\) | ||||
−0.730711 | + | 0.682687i | \(0.760811\pi\) | |||||||
\(432\) | − | 2305.41i | − | 5.33659i | ||||||
\(433\) | − | 704.427i | − | 1.62685i | −0.581668 | − | 0.813426i | \(-0.697600\pi\) | ||
0.581668 | − | 0.813426i | \(-0.302400\pi\) | |||||||
\(434\) | − | 164.376i | − | 0.378747i | ||||||
\(435\) | 90.9942 | 0.209182 | ||||||||
\(436\) | 840.533i | 1.92783i | ||||||||
\(437\) | 921.684i | 2.10912i | ||||||||
\(438\) | −502.279 | −1.14676 | ||||||||
\(439\) | −14.7433 | −0.0335839 | −0.0167919 | − | 0.999859i | \(-0.505345\pi\) | ||||
−0.0167919 | + | 0.999859i | \(0.505345\pi\) | |||||||
\(440\) | 642.209 | 1.45957 | ||||||||
\(441\) | −771.298 | −1.74898 | ||||||||
\(442\) | −13.3185 | −0.0301323 | ||||||||
\(443\) | 153.885 | 0.347369 | 0.173685 | − | 0.984801i | \(-0.444433\pi\) | ||||
0.173685 | + | 0.984801i | \(0.444433\pi\) | |||||||
\(444\) | −1908.95 | −4.29943 | ||||||||
\(445\) | −458.292 | −1.02987 | ||||||||
\(446\) | −45.4193 | −0.101837 | ||||||||
\(447\) | 602.719i | 1.34836i | ||||||||
\(448\) | − | 284.303i | − | 0.634605i | ||||||
\(449\) | 739.862 | 1.64780 | 0.823900 | − | 0.566735i | \(-0.191794\pi\) | ||||
0.823900 | + | 0.566735i | \(0.191794\pi\) | |||||||
\(450\) | 875.575i | 1.94572i | ||||||||
\(451\) | − | 201.716i | − | 0.447264i | ||||||
\(452\) | −1860.19 | −4.11546 | ||||||||
\(453\) | 929.216 | 2.05125 | ||||||||
\(454\) | − | 427.895i | − | 0.942499i | ||||||
\(455\) | 15.6177 | 0.0343246 | ||||||||
\(456\) | 3881.15 | 8.51128 | ||||||||
\(457\) | 631.065i | 1.38089i | 0.723387 | + | 0.690443i | \(0.242584\pi\) | ||||
−0.723387 | + | 0.690443i | \(0.757416\pi\) | |||||||
\(458\) | −1019.52 | −2.22602 | ||||||||
\(459\) | −24.8097 | −0.0540515 | ||||||||
\(460\) | 1253.18 | 2.72431 | ||||||||
\(461\) | − | 231.719i | − | 0.502645i | −0.967903 | − | 0.251322i | \(-0.919135\pi\) | ||
0.967903 | − | 0.251322i | \(-0.0808654\pi\) | |||||||
\(462\) | 129.668i | 0.280667i | ||||||||
\(463\) | − | 453.210i | − | 0.978855i | −0.872044 | − | 0.489427i | \(-0.837206\pi\) | ||
0.872044 | − | 0.489427i | \(-0.162794\pi\) | |||||||
\(464\) | 357.848 | 0.771224 | ||||||||
\(465\) | − | 721.682i | − | 1.55200i | ||||||
\(466\) | − | 725.224i | − | 1.55628i | ||||||
\(467\) | −802.518 | −1.71845 | −0.859227 | − | 0.511595i | \(-0.829055\pi\) | ||||
−0.859227 | + | 0.511595i | \(0.829055\pi\) | |||||||
\(468\) | 875.007 | 1.86967 | ||||||||
\(469\) | 48.4760i | 0.103360i | ||||||||
\(470\) | 1023.07 | 2.17674 | ||||||||
\(471\) | − | 257.240i | − | 0.546157i | ||||||
\(472\) | −935.721 | −1.98246 | ||||||||
\(473\) | − | 235.337i | − | 0.497540i | ||||||
\(474\) | − | 1803.29i | − | 3.80440i | ||||||
\(475\) | −383.556 | −0.807487 | ||||||||
\(476\) | −7.66325 | −0.0160993 | ||||||||
\(477\) | 1281.45 | 2.68647 | ||||||||
\(478\) | 1307.83i | 2.73606i | ||||||||
\(479\) | 550.111 | 1.14846 | 0.574228 | − | 0.818695i | \(-0.305302\pi\) | ||||
0.574228 | + | 0.818695i | \(0.305302\pi\) | |||||||
\(480\) | − | 2360.96i | − | 4.91867i | ||||||
\(481\) | − | 164.648i | − | 0.342303i | ||||||
\(482\) | 1377.90 | 2.85872 | ||||||||
\(483\) | 162.972i | 0.337416i | ||||||||
\(484\) | 833.261 | 1.72161 | ||||||||
\(485\) | − | 547.689i | − | 1.12925i | ||||||
\(486\) | −611.830 | −1.25891 | ||||||||
\(487\) | 400.505i | 0.822392i | 0.911547 | + | 0.411196i | \(0.134889\pi\) | ||||
−0.911547 | + | 0.411196i | \(0.865111\pi\) | |||||||
\(488\) | 450.939 | 0.924055 | ||||||||
\(489\) | −1448.62 | −2.96242 | ||||||||
\(490\) | −622.908 | −1.27124 | ||||||||
\(491\) | 233.743i | 0.476056i | 0.971258 | + | 0.238028i | \(0.0765009\pi\) | ||||
−0.971258 | + | 0.238028i | \(0.923499\pi\) | |||||||
\(492\) | −1657.51 | −3.36892 | ||||||||
\(493\) | − | 3.85098i | − | 0.00781132i | ||||||
\(494\) | 519.734i | 1.05209i | ||||||||
\(495\) | 364.750i | 0.736868i | ||||||||
\(496\) | − | 2838.12i | − | 5.72201i | ||||||
\(497\) | −77.7464 | −0.156431 | ||||||||
\(498\) | − | 1260.37i | − | 2.53087i | ||||||
\(499\) | −496.829 | −0.995648 | −0.497824 | − | 0.867278i | \(-0.665868\pi\) | ||||
−0.497824 | + | 0.867278i | \(0.665868\pi\) | |||||||
\(500\) | 1454.37i | 2.90875i | ||||||||
\(501\) | − | 1401.44i | − | 2.79729i | ||||||
\(502\) | −610.821 | −1.21678 | ||||||||
\(503\) | − | 713.303i | − | 1.41810i | −0.705160 | − | 0.709048i | \(-0.749125\pi\) | ||
0.705160 | − | 0.709048i | \(-0.250875\pi\) | |||||||
\(504\) | 439.688 | 0.872397 | ||||||||
\(505\) | −319.525 | −0.632723 | ||||||||
\(506\) | −897.414 | −1.77355 | ||||||||
\(507\) | − | 728.030i | − | 1.43596i | ||||||
\(508\) | −948.519 | −1.86716 | ||||||||
\(509\) | 364.570 | 0.716248 | 0.358124 | − | 0.933674i | \(-0.383417\pi\) | ||||
0.358124 | + | 0.933674i | \(0.383417\pi\) | |||||||
\(510\) | −45.6198 | −0.0894507 | ||||||||
\(511\) | − | 24.9267i | − | 0.0487803i | ||||||
\(512\) | − | 1898.51i | − | 3.70803i | ||||||
\(513\) | 968.160i | 1.88725i | ||||||||
\(514\) | −97.3039 | −0.189307 | ||||||||
\(515\) | 328.165 | 0.637215 | ||||||||
\(516\) | −1933.77 | −3.74762 | ||||||||
\(517\) | −540.318 | −1.04510 | ||||||||
\(518\) | − | 128.454i | − | 0.247981i | ||||||
\(519\) | 79.2698 | 0.152736 | ||||||||
\(520\) | 455.149 | 0.875287 | ||||||||
\(521\) | 919.984 | 1.76580 | 0.882902 | − | 0.469557i | \(-0.155586\pi\) | ||||
0.882902 | + | 0.469557i | \(0.155586\pi\) | |||||||
\(522\) | 343.054i | 0.657191i | ||||||||
\(523\) | − | 234.101i | − | 0.447611i | −0.974634 | − | 0.223806i | \(-0.928152\pi\) | ||
0.974634 | − | 0.223806i | \(-0.0718481\pi\) | |||||||
\(524\) | 672.329 | 1.28307 | ||||||||
\(525\) | −67.8202 | −0.129181 | ||||||||
\(526\) | − | 82.3039i | − | 0.156471i | ||||||
\(527\) | −30.5424 | −0.0579553 | ||||||||
\(528\) | 2238.85i | 4.24025i | ||||||||
\(529\) | −598.903 | −1.13214 | ||||||||
\(530\) | 1034.91 | 1.95266 | ||||||||
\(531\) | − | 531.453i | − | 1.00085i | ||||||
\(532\) | 299.047i | 0.562119i | ||||||||
\(533\) | − | 142.961i | − | 0.268219i | ||||||
\(534\) | − | 2696.72i | − | 5.05004i | ||||||
\(535\) | 190.447 | 0.355975 | ||||||||
\(536\) | 1412.74i | 2.63572i | ||||||||
\(537\) | − | 887.577i | − | 1.65284i | ||||||
\(538\) | 1390.51i | 2.58459i | ||||||||
\(539\) | 328.979 | 0.610351 | ||||||||
\(540\) | 1316.37 | 2.43773 | ||||||||
\(541\) | 599.817i | 1.10872i | 0.832277 | + | 0.554360i | \(0.187037\pi\) | ||||
−0.832277 | + | 0.554360i | \(0.812963\pi\) | |||||||
\(542\) | 748.038 | 1.38014 | ||||||||
\(543\) | − | 732.031i | − | 1.34812i | ||||||
\(544\) | −99.9187 | −0.183674 | ||||||||
\(545\) | −248.322 | −0.455637 | ||||||||
\(546\) | 91.8990i | 0.168313i | ||||||||
\(547\) | 530.243 | − | 134.356i | 0.969365 | − | 0.245624i | ||||
\(548\) | −1816.71 | −3.31517 | ||||||||
\(549\) | 256.116i | 0.466513i | ||||||||
\(550\) | − | 373.456i | − | 0.679011i | ||||||
\(551\) | −150.279 | −0.272738 | ||||||||
\(552\) | 4749.52i | 8.60420i | ||||||||
\(553\) | 89.4922 | 0.161830 | ||||||||
\(554\) | 756.470i | 1.36547i | ||||||||
\(555\) | − | 563.968i | − | 1.01616i | ||||||
\(556\) | −2549.50 | −4.58543 | ||||||||
\(557\) | −224.433 | −0.402932 | −0.201466 | − | 0.979496i | \(-0.564570\pi\) | ||||
−0.201466 | + | 0.979496i | \(0.564570\pi\) | |||||||
\(558\) | 2720.79 | 4.87596 | ||||||||
\(559\) | − | 166.789i | − | 0.298370i | ||||||
\(560\) | 210.378 | 0.375676 | ||||||||
\(561\) | 24.0934 | 0.0429473 | ||||||||
\(562\) | −283.208 | −0.503929 | ||||||||
\(563\) | −467.590 | −0.830533 | −0.415266 | − | 0.909700i | \(-0.636312\pi\) | ||||
−0.415266 | + | 0.909700i | \(0.636312\pi\) | |||||||
\(564\) | 4439.82i | 7.87202i | ||||||||
\(565\) | − | 549.564i | − | 0.972679i | ||||||
\(566\) | −1582.22 | −2.79545 | ||||||||
\(567\) | 31.1450i | 0.0549295i | ||||||||
\(568\) | −2265.78 | −3.98904 | ||||||||
\(569\) | 218.850i | 0.384622i | 0.981334 | + | 0.192311i | \(0.0615982\pi\) | ||||
−0.981334 | + | 0.192311i | \(0.938402\pi\) | |||||||
\(570\) | 1780.25i | 3.12324i | ||||||||
\(571\) | 500.613 | 0.876730 | 0.438365 | − | 0.898797i | \(-0.355558\pi\) | ||||
0.438365 | + | 0.898797i | \(0.355558\pi\) | |||||||
\(572\) | −373.214 | −0.652472 | ||||||||
\(573\) | 426.800i | 0.744852i | ||||||||
\(574\) | − | 111.535i | − | 0.194311i | ||||||
\(575\) | − | 469.373i | − | 0.816301i | ||||||
\(576\) | 4705.84 | 8.16985 | ||||||||
\(577\) | 286.318i | 0.496218i | 0.968732 | + | 0.248109i | \(0.0798091\pi\) | ||||
−0.968732 | + | 0.248109i | \(0.920191\pi\) | |||||||
\(578\) | − | 1126.23i | − | 1.94849i | ||||||
\(579\) | − | 1085.98i | − | 1.87561i | ||||||
\(580\) | 204.329i | 0.352292i | ||||||||
\(581\) | 62.5488 | 0.107657 | ||||||||
\(582\) | 3222.76 | 5.53738 | ||||||||
\(583\) | −546.571 | −0.937515 | ||||||||
\(584\) | − | 726.444i | − | 1.24391i | ||||||
\(585\) | 258.507i | 0.441892i | ||||||||
\(586\) | 871.898i | 1.48788i | ||||||||
\(587\) | −434.405 | −0.740042 | −0.370021 | − | 0.929023i | \(-0.620650\pi\) | ||||
−0.370021 | + | 0.929023i | \(0.620650\pi\) | |||||||
\(588\) | − | 2703.24i | − | 4.59735i | ||||||
\(589\) | 1191.87i | 2.02355i | ||||||||
\(590\) | − | 429.207i | − | 0.727469i | ||||||
\(591\) | −1152.83 | −1.95063 | ||||||||
\(592\) | − | 2217.89i | − | 3.74643i | ||||||
\(593\) | 998.651 | 1.68407 | 0.842033 | − | 0.539426i | \(-0.181359\pi\) | ||||
0.842033 | + | 0.539426i | \(0.181359\pi\) | |||||||
\(594\) | −942.666 | −1.58698 | ||||||||
\(595\) | − | 2.26399i | − | 0.00380502i | ||||||
\(596\) | −1353.42 | −2.27083 | ||||||||
\(597\) | − | 527.779i | − | 0.884052i | ||||||
\(598\) | −636.019 | −1.06358 | ||||||||
\(599\) | −98.2919 | −0.164093 | −0.0820467 | − | 0.996628i | \(-0.526146\pi\) | ||||
−0.0820467 | + | 0.996628i | \(0.526146\pi\) | |||||||
\(600\) | −1976.50 | −3.29416 | ||||||||
\(601\) | −1067.75 | −1.77661 | −0.888307 | − | 0.459250i | \(-0.848118\pi\) | ||||
−0.888307 | + | 0.459250i | \(0.848118\pi\) | |||||||
\(602\) | − | 130.125i | − | 0.216154i | ||||||
\(603\) | −802.384 | −1.33065 | ||||||||
\(604\) | 2086.57i | 3.45459i | ||||||||
\(605\) | 246.174i | 0.406899i | ||||||||
\(606\) | − | 1880.18i | − | 3.10260i | ||||||
\(607\) | 809.497 | 1.33360 | 0.666802 | − | 0.745235i | \(-0.267663\pi\) | ||||
0.666802 | + | 0.745235i | \(0.267663\pi\) | |||||||
\(608\) | 3899.18i | 6.41312i | ||||||||
\(609\) | −26.5722 | −0.0436326 | ||||||||
\(610\) | 206.842i | 0.339084i | ||||||||
\(611\) | −382.936 | −0.626737 | ||||||||
\(612\) | − | 126.844i | − | 0.207261i | ||||||
\(613\) | 174.436 | 0.284560 | 0.142280 | − | 0.989826i | \(-0.454557\pi\) | ||||
0.142280 | + | 0.989826i | \(0.454557\pi\) | |||||||
\(614\) | 726.457 | 1.18316 | ||||||||
\(615\) | − | 489.685i | − | 0.796236i | ||||||
\(616\) | −187.539 | −0.304446 | ||||||||
\(617\) | − | 578.735i | − | 0.937982i | −0.883203 | − | 0.468991i | \(-0.844618\pi\) | ||
0.883203 | − | 0.468991i | \(-0.155382\pi\) | |||||||
\(618\) | 1931.02i | 3.12463i | ||||||||
\(619\) | 580.916i | 0.938475i | 0.883072 | + | 0.469238i | \(0.155471\pi\) | ||||
−0.883072 | + | 0.469238i | \(0.844529\pi\) | |||||||
\(620\) | 1620.55 | 2.61379 | ||||||||
\(621\) | −1184.78 | −1.90785 | ||||||||
\(622\) | − | 427.102i | − | 0.686659i | ||||||
\(623\) | 133.831 | 0.214817 | ||||||||
\(624\) | 1586.73i | 2.54283i | ||||||||
\(625\) | −80.2720 | −0.128435 | ||||||||
\(626\) | − | 1891.65i | − | 3.02180i | ||||||
\(627\) | − | 940.210i | − | 1.49954i | ||||||
\(628\) | 577.637 | 0.919804 | ||||||||
\(629\) | −23.8678 | −0.0379456 | ||||||||
\(630\) | 201.681i | 0.320128i | ||||||||
\(631\) | −454.380 | −0.720096 | −0.360048 | − | 0.932934i | \(-0.617240\pi\) | ||||
−0.360048 | + | 0.932934i | \(0.617240\pi\) | |||||||
\(632\) | 2608.09 | 4.12672 | ||||||||
\(633\) | −1938.18 | −3.06189 | ||||||||
\(634\) | 878.869i | 1.38623i | ||||||||
\(635\) | − | 280.225i | − | 0.441299i | ||||||
\(636\) | 4491.20i | 7.06164i | ||||||||
\(637\) | 233.156 | 0.366022 | ||||||||
\(638\) | − | 146.322i | − | 0.229344i | ||||||
\(639\) | − | 1286.87i | − | 2.01388i | ||||||
\(640\) | 1913.55 | 2.98992 | ||||||||
\(641\) | 366.675i | 0.572035i | 0.958224 | + | 0.286018i | \(0.0923316\pi\) | ||||
−0.958224 | + | 0.286018i | \(0.907668\pi\) | |||||||
\(642\) | 1120.64i | 1.74555i | ||||||||
\(643\) | 1101.06 | 1.71239 | 0.856193 | − | 0.516657i | \(-0.172824\pi\) | ||||
0.856193 | + | 0.516657i | \(0.172824\pi\) | |||||||
\(644\) | −365.956 | −0.568255 | ||||||||
\(645\) | − | 571.302i | − | 0.885740i | ||||||
\(646\) | 75.3421 | 0.116629 | ||||||||
\(647\) | −471.671 | −0.729012 | −0.364506 | − | 0.931201i | \(-0.618762\pi\) | ||||
−0.364506 | + | 0.931201i | \(0.618762\pi\) | |||||||
\(648\) | 907.665i | 1.40072i | ||||||||
\(649\) | 226.679i | 0.349274i | ||||||||
\(650\) | − | 264.677i | − | 0.407196i | ||||||
\(651\) | 210.746i | 0.323727i | ||||||||
\(652\) | − | 3252.91i | − | 4.98913i | ||||||
\(653\) | 1097.71i | 1.68103i | 0.541791 | + | 0.840513i | \(0.317746\pi\) | ||||
−0.541791 | + | 0.840513i | \(0.682254\pi\) | |||||||
\(654\) | − | 1461.20i | − | 2.23425i | ||||||
\(655\) | 198.629i | 0.303250i | ||||||||
\(656\) | − | 1925.76i | − | 2.93561i | ||||||
\(657\) | 412.592 | 0.627994 | ||||||||
\(658\) | −298.758 | −0.454039 | ||||||||
\(659\) | − | 406.433i | − | 0.616742i | −0.951266 | − | 0.308371i | \(-0.900216\pi\) | ||
0.951266 | − | 0.308371i | \(-0.0997839\pi\) | |||||||
\(660\) | −1278.37 | −1.93693 | ||||||||
\(661\) | −594.616 | −0.899570 | −0.449785 | − | 0.893137i | \(-0.648499\pi\) | ||||
−0.449785 | + | 0.893137i | \(0.648499\pi\) | |||||||
\(662\) | 2154.70 | 3.25483 | ||||||||
\(663\) | 17.0756 | 0.0257550 | ||||||||
\(664\) | 1822.87 | 2.74529 | ||||||||
\(665\) | −88.3487 | −0.132855 | ||||||||
\(666\) | 2126.19 | 3.19248 | ||||||||
\(667\) | − | 183.902i | − | 0.275716i | ||||||
\(668\) | 3146.97 | 4.71103 | ||||||||
\(669\) | 58.2320 | 0.0870433 | ||||||||
\(670\) | −648.013 | −0.967184 | ||||||||
\(671\) | − | 109.240i | − | 0.162802i | ||||||
\(672\) | 689.451i | 1.02597i | ||||||||
\(673\) | 664.918 | 0.987992 | 0.493996 | − | 0.869464i | \(-0.335536\pi\) | ||||
0.493996 | + | 0.869464i | \(0.335536\pi\) | |||||||
\(674\) | −1850.70 | −2.74585 | ||||||||
\(675\) | − | 493.041i | − | 0.730431i | ||||||
\(676\) | 1634.80 | 2.41835 | ||||||||
\(677\) | −892.607 | −1.31847 | −0.659237 | − | 0.751935i | \(-0.729121\pi\) | ||||
−0.659237 | + | 0.751935i | \(0.729121\pi\) | |||||||
\(678\) | 3233.79 | 4.76961 | ||||||||
\(679\) | 159.937i | 0.235547i | ||||||||
\(680\) | − | 65.9798i | − | 0.0970291i | ||||||
\(681\) | 548.603i | 0.805584i | ||||||||
\(682\) | −1160.49 | −1.70160 | ||||||||
\(683\) | 364.405 | 0.533536 | 0.266768 | − | 0.963761i | \(-0.414044\pi\) | ||||
0.266768 | + | 0.963761i | \(0.414044\pi\) | |||||||
\(684\) | −4949.88 | −7.23667 | ||||||||
\(685\) | − | 536.719i | − | 0.783531i | ||||||
\(686\) | 367.363 | 0.535515 | ||||||||
\(687\) | 1307.12 | 1.90265 | ||||||||
\(688\) | − | 2246.73i | − | 3.26560i | ||||||
\(689\) | −387.368 | −0.562218 | ||||||||
\(690\) | −2178.56 | −3.15733 | ||||||||
\(691\) | 229.110 | 0.331564 | 0.165782 | − | 0.986162i | \(-0.446985\pi\) | ||||
0.165782 | + | 0.986162i | \(0.446985\pi\) | |||||||
\(692\) | 178.002i | 0.257228i | ||||||||
\(693\) | − | 106.515i | − | 0.153701i | ||||||
\(694\) | 810.614i | 1.16803i | ||||||||
\(695\) | − | 753.210i | − | 1.08375i | ||||||
\(696\) | −774.400 | −1.11264 | ||||||||
\(697\) | −20.7240 | −0.0297332 | ||||||||
\(698\) | 1750.14i | 2.50736i | ||||||||
\(699\) | 929.808i | 1.33020i | ||||||||
\(700\) | − | 152.292i | − | 0.217559i | ||||||
\(701\) | −157.823 | −0.225139 | −0.112570 | − | 0.993644i | \(-0.535908\pi\) | ||||
−0.112570 | + | 0.993644i | \(0.535908\pi\) | |||||||
\(702\) | −668.090 | −0.951695 | ||||||||
\(703\) | 931.405i | 1.32490i | ||||||||
\(704\) | −2007.17 | −2.85109 | ||||||||
\(705\) | −1311.67 | −1.86053 | ||||||||
\(706\) | − | 503.747i | − | 0.713523i | ||||||
\(707\) | 93.3080 | 0.131977 | ||||||||
\(708\) | 1862.63 | 2.63084 | ||||||||
\(709\) | 961.391i | 1.35598i | 0.735070 | + | 0.677991i | \(0.237149\pi\) | ||||
−0.735070 | + | 0.677991i | \(0.762851\pi\) | |||||||
\(710\) | − | 1039.29i | − | 1.46379i | ||||||
\(711\) | 1481.29i | 2.08339i | ||||||||
\(712\) | 3900.26 | 5.47789 | ||||||||
\(713\) | −1458.54 | −2.04564 | ||||||||
\(714\) | 13.3220 | 0.0186582 | ||||||||
\(715\) | − | 110.260i | − | 0.154210i | ||||||
\(716\) | 1993.07 | 2.78362 | ||||||||
\(717\) | − | 1676.77i | − | 2.33859i | ||||||
\(718\) | −1116.56 | −1.55510 | ||||||||
\(719\) | − | 42.2639i | − | 0.0587815i | −0.999568 | − | 0.0293907i | \(-0.990643\pi\) | ||
0.999568 | − | 0.0293907i | \(-0.00935671\pi\) | |||||||
\(720\) | 3482.22i | 4.83642i | ||||||||
\(721\) | −95.8313 | −0.132914 | ||||||||
\(722\) | − | 1530.89i | − | 2.12035i | ||||||
\(723\) | −1766.61 | −2.44344 | ||||||||
\(724\) | 1643.79 | 2.27043 | ||||||||
\(725\) | 76.5304 | 0.105559 | ||||||||
\(726\) | −1448.56 | −1.99526 | ||||||||
\(727\) | − | 1128.71i | − | 1.55256i | −0.630387 | − | 0.776281i | \(-0.717104\pi\) | ||
0.630387 | − | 0.776281i | \(-0.282896\pi\) | |||||||
\(728\) | −132.913 | −0.182573 | ||||||||
\(729\) | 1073.52 | 1.47260 | ||||||||
\(730\) | 333.213 | 0.456457 | ||||||||
\(731\) | −24.1782 | −0.0330755 | ||||||||
\(732\) | −897.631 | −1.22627 | ||||||||
\(733\) | − | 1014.33i | − | 1.38381i | −0.721988 | − | 0.691905i | \(-0.756772\pi\) | ||
0.721988 | − | 0.691905i | \(-0.243228\pi\) | |||||||
\(734\) | 597.926i | 0.814613i | ||||||||
\(735\) | 798.629 | 1.08657 | ||||||||
\(736\) | −4771.59 | −6.48313 | ||||||||
\(737\) | 342.238 | 0.464367 | ||||||||
\(738\) | 1846.14 | 2.50155 | ||||||||
\(739\) | 1091.99i | 1.47766i | 0.673894 | + | 0.738828i | \(0.264620\pi\) | ||||
−0.673894 | + | 0.738828i | \(0.735380\pi\) | |||||||
\(740\) | 1266.40 | 1.71135 | ||||||||
\(741\) | − | 666.349i | − | 0.899257i | ||||||
\(742\) | −302.215 | −0.407298 | ||||||||
\(743\) | 351.284 | 0.472791 | 0.236396 | − | 0.971657i | \(-0.424034\pi\) | ||||
0.236396 | + | 0.971657i | \(0.424034\pi\) | |||||||
\(744\) | 6141.82i | 8.25513i | ||||||||
\(745\) | − | 399.845i | − | 0.536705i | ||||||
\(746\) | 1650.69 | 2.21273 | ||||||||
\(747\) | 1035.32i | 1.38597i | ||||||||
\(748\) | 54.1022i | 0.0723291i | ||||||||
\(749\) | −55.6145 | −0.0742516 | ||||||||
\(750\) | − | 2528.31i | − | 3.37108i | ||||||
\(751\) | 143.419 | 0.190971 | 0.0954855 | − | 0.995431i | \(-0.469560\pi\) | ||||
0.0954855 | + | 0.995431i | \(0.469560\pi\) | |||||||
\(752\) | −5158.35 | −6.85950 | ||||||||
\(753\) | 783.132 | 1.04002 | ||||||||
\(754\) | − | 103.702i | − | 0.137535i | ||||||
\(755\) | −616.444 | −0.816483 | ||||||||
\(756\) | −384.409 | −0.508478 | ||||||||
\(757\) | 808.819 | 1.06845 | 0.534226 | − | 0.845341i | \(-0.320603\pi\) | ||||
0.534226 | + | 0.845341i | \(0.320603\pi\) | |||||||
\(758\) | 415.294i | 0.547881i | ||||||||
\(759\) | 1150.57 | 1.51591 | ||||||||
\(760\) | −2574.76 | −3.38785 | ||||||||
\(761\) | 36.9250 | 0.0485217 | 0.0242608 | − | 0.999706i | \(-0.492277\pi\) | ||||
0.0242608 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(762\) | 1648.93 | 2.16394 | ||||||||
\(763\) | 72.5153 | 0.0950397 | ||||||||
\(764\) | −958.388 | −1.25443 | ||||||||
\(765\) | 37.4739 | 0.0489855 | ||||||||
\(766\) | 834.452i | 1.08936i | ||||||||
\(767\) | 160.653i | 0.209456i | ||||||||
\(768\) | 5389.71i | 7.01785i | ||||||||
\(769\) | 1010.47i | 1.31400i | 0.753890 | + | 0.657001i | \(0.228175\pi\) | ||||
−0.753890 | + | 0.657001i | \(0.771825\pi\) | |||||||
\(770\) | − | 86.0223i | − | 0.111717i | ||||||
\(771\) | 124.753 | 0.161807 | ||||||||
\(772\) | 2438.59 | 3.15879 | ||||||||
\(773\) | − | 688.071i | − | 0.890130i | −0.895498 | − | 0.445065i | \(-0.853181\pi\) | ||
0.895498 | − | 0.445065i | \(-0.146819\pi\) | |||||||
\(774\) | 2153.85 | 2.78275 | ||||||||
\(775\) | − | 606.968i | − | 0.783185i | ||||||
\(776\) | 4661.06i | 6.00652i | ||||||||
\(777\) | 164.691i | 0.211957i | ||||||||
\(778\) | −980.249 | −1.25996 | ||||||||
\(779\) | 808.725i | 1.03816i | ||||||||
\(780\) | −906.013 | −1.16156 | ||||||||
\(781\) | 548.886i | 0.702798i | ||||||||
\(782\) | 92.1992i | 0.117902i | ||||||||
\(783\) | − | 193.176i | − | 0.246712i | ||||||
\(784\) | 3140.73 | 4.00603 | ||||||||
\(785\) | 170.654i | 0.217393i | ||||||||
\(786\) | −1168.79 | −1.48701 | ||||||||
\(787\) | 132.330 | 0.168145 | 0.0840726 | − | 0.996460i | \(-0.473207\pi\) | ||||
0.0840726 | + | 0.996460i | \(0.473207\pi\) | |||||||
\(788\) | − | 2588.69i | − | 3.28514i | ||||||
\(789\) | 105.522i | 0.133741i | ||||||||
\(790\) | 1196.31i | 1.51431i | ||||||||
\(791\) | 160.484i | 0.202888i | ||||||||
\(792\) | − | 3104.18i | − | 3.91941i | ||||||
\(793\) | − | 77.4211i | − | 0.0976307i | ||||||
\(794\) | −1475.08 | −1.85779 | ||||||||
\(795\) | −1326.85 | −1.66900 | ||||||||
\(796\) | 1185.14 | 1.48887 | ||||||||
\(797\) | −693.629 | −0.870300 | −0.435150 | − | 0.900358i | \(-0.643305\pi\) | ||||
−0.435150 | + | 0.900358i | \(0.643305\pi\) | |||||||
\(798\) | − | 519.870i | − | 0.651466i | ||||||
\(799\) | 55.5116i | 0.0694763i | ||||||||
\(800\) | − | 1985.68i | − | 2.48210i | ||||||
\(801\) | 2215.20i | 2.76554i | ||||||||
\(802\) | 23.2997i | 0.0290520i | ||||||||
\(803\) | −175.982 | −0.219155 | ||||||||
\(804\) | − | 2812.19i | − | 3.49775i | ||||||
\(805\) | − | 108.116i | − | 0.134306i | ||||||
\(806\) | −822.466 | −1.02043 | ||||||||
\(807\) | − | 1782.77i | − | 2.20913i | ||||||
\(808\) | 2719.29 | 3.36546 | ||||||||
\(809\) | − | 1579.45i | − | 1.95235i | −0.216974 | − | 0.976177i | \(-0.569619\pi\) | ||
0.216974 | − | 0.976177i | \(-0.430381\pi\) | |||||||
\(810\) | −416.338 | −0.513997 | ||||||||
\(811\) | 308.993 | 0.381003 | 0.190501 | − | 0.981687i | \(-0.438989\pi\) | ||||
0.190501 | + | 0.981687i | \(0.438989\pi\) | |||||||
\(812\) | − | 59.6684i | − | 0.0734833i | ||||||
\(813\) | −959.058 | −1.17965 | ||||||||
\(814\) | −906.879 | −1.11410 | ||||||||
\(815\) | 961.021 | 1.17917 | ||||||||
\(816\) | 230.017 | 0.281883 | ||||||||
\(817\) | 943.518i | 1.15486i | ||||||||
\(818\) | − | 1415.82i | − | 1.73084i | ||||||
\(819\) | − | 75.4895i | − | 0.0921728i | ||||||
\(820\) | 1099.60 | 1.34097 | ||||||||
\(821\) | − | 720.263i | − | 0.877300i | −0.898658 | − | 0.438650i | \(-0.855457\pi\) | ||
0.898658 | − | 0.438650i | \(-0.144543\pi\) | |||||||
\(822\) | 3158.21 | 3.84210 | ||||||||
\(823\) | −295.522 | −0.359078 | −0.179539 | − | 0.983751i | \(-0.557461\pi\) | ||||
−0.179539 | + | 0.983751i | \(0.557461\pi\) | |||||||
\(824\) | −2792.83 | −3.38935 | ||||||||
\(825\) | 478.807i | 0.580373i | ||||||||
\(826\) | 125.337i | 0.151740i | ||||||||
\(827\) | − | 487.477i | − | 0.589452i | −0.955582 | − | 0.294726i | \(-0.904772\pi\) | ||
0.955582 | − | 0.294726i | \(-0.0952284\pi\) | |||||||
\(828\) | − | 6057.37i | − | 7.31567i | ||||||
\(829\) | 135.412 | 0.163344 | 0.0816718 | − | 0.996659i | \(-0.473974\pi\) | ||||
0.0816718 | + | 0.996659i | \(0.473974\pi\) | |||||||
\(830\) | 836.134i | 1.00739i | ||||||||
\(831\) | − | 969.868i | − | 1.16711i | ||||||
\(832\) | −1422.53 | −1.70977 | ||||||||
\(833\) | − | 33.7989i | − | 0.0405750i | ||||||
\(834\) | 4432.10 | 5.31427 | ||||||||
\(835\) | 929.722i | 1.11344i | ||||||||
\(836\) | 2111.26 | 2.52543 | ||||||||
\(837\) | −1532.09 | −1.83045 | ||||||||
\(838\) | 972.564i | 1.16058i | ||||||||
\(839\) | −827.593 | −0.986405 | −0.493202 | − | 0.869915i | \(-0.664174\pi\) | ||||
−0.493202 | + | 0.869915i | \(0.664174\pi\) | |||||||
\(840\) | −455.268 | −0.541986 | ||||||||
\(841\) | −811.015 | −0.964346 | ||||||||
\(842\) | −2305.76 | −2.73843 | ||||||||
\(843\) | 363.100 | 0.430724 | ||||||||
\(844\) | − | 4352.21i | − | 5.15665i | ||||||
\(845\) | 482.977i | 0.571570i | ||||||||
\(846\) | − | 4945.09i | − | 5.84526i | ||||||
\(847\) | − | 71.8880i | − | 0.0848736i | ||||||
\(848\) | −5218.05 | −6.15336 | ||||||||
\(849\) | 2028.56 | 2.38936 | ||||||||
\(850\) | −38.3684 | −0.0451393 | ||||||||
\(851\) | −1139.80 | −1.33936 | ||||||||
\(852\) | 4510.22 | 5.29368 | ||||||||
\(853\) | 1611.25 | 1.88893 | 0.944463 | − | 0.328617i | \(-0.106583\pi\) | ||||
0.944463 | + | 0.328617i | \(0.106583\pi\) | |||||||
\(854\) | − | 60.4021i | − | 0.0707284i | ||||||
\(855\) | − | 1462.36i | − | 1.71037i | ||||||
\(856\) | −1620.78 | −1.89344 | ||||||||
\(857\) | − | 727.225i | − | 0.848571i | −0.905528 | − | 0.424286i | \(-0.860525\pi\) | ||
0.905528 | − | 0.424286i | \(-0.139475\pi\) | |||||||
\(858\) | 648.803 | 0.756180 | ||||||||
\(859\) | 1207.94 | 1.40622 | 0.703108 | − | 0.711083i | \(-0.251795\pi\) | ||||
0.703108 | + | 0.711083i | \(0.251795\pi\) | |||||||
\(860\) | 1282.87 | 1.49171 | ||||||||
\(861\) | 142.998i | 0.166084i | ||||||||
\(862\) | 2297.21 | 2.66497 | ||||||||
\(863\) | 503.549i | 0.583486i | 0.956497 | + | 0.291743i | \(0.0942353\pi\) | ||||
−0.956497 | + | 0.291743i | \(0.905765\pi\) | |||||||
\(864\) | −5012.19 | −5.80114 | ||||||||
\(865\) | −52.5878 | −0.0607951 | ||||||||
\(866\) | −2749.84 | −3.17533 | ||||||||
\(867\) | 1443.93i | 1.66543i | ||||||||
\(868\) | −473.235 | −0.545201 | ||||||||
\(869\) | − | 631.811i | − | 0.727055i | ||||||
\(870\) | − | 355.210i | − | 0.408287i | ||||||
\(871\) | 242.552 | 0.278476 | ||||||||
\(872\) | 2113.33 | 2.42354 | ||||||||
\(873\) | −2647.30 | −3.03242 | ||||||||
\(874\) | 3597.94 | 4.11663 | ||||||||
\(875\) | 125.473 | 0.143398 | ||||||||
\(876\) | 1446.05i | 1.65074i | ||||||||
\(877\) | − | 1097.38i | − | 1.25129i | −0.780109 | − | 0.625643i | \(-0.784837\pi\) | ||
0.780109 | − | 0.625643i | \(-0.215163\pi\) | |||||||
\(878\) | 57.5528i | 0.0655499i | ||||||||
\(879\) | − | 1117.86i | − | 1.27174i | ||||||
\(880\) | − | 1485.26i | − | 1.68780i | ||||||
\(881\) | − | 1117.59i | − | 1.26855i | −0.773108 | − | 0.634274i | \(-0.781299\pi\) | ||
0.773108 | − | 0.634274i | \(-0.218701\pi\) | |||||||
\(882\) | 3010.88i | 3.41370i | ||||||||
\(883\) | −533.431 | −0.604112 | −0.302056 | − | 0.953290i | \(-0.597673\pi\) | ||||
−0.302056 | + | 0.953290i | \(0.597673\pi\) | |||||||
\(884\) | 38.3435i | 0.0433750i | ||||||||
\(885\) | 550.285i | 0.621791i | ||||||||
\(886\) | − | 600.713i | − | 0.678005i | ||||||
\(887\) | 417.592 | 0.470791 | 0.235396 | − | 0.971900i | \(-0.424361\pi\) | ||||
0.235396 | + | 0.971900i | \(0.424361\pi\) | |||||||
\(888\) | 4799.61i | 5.40496i | ||||||||
\(889\) | 81.8316i | 0.0920491i | ||||||||
\(890\) | 1789.01i | 2.01013i | ||||||||
\(891\) | 219.882 | 0.246781 | ||||||||
\(892\) | 130.761i | 0.146593i | ||||||||
\(893\) | 2166.26 | 2.42582 | ||||||||
\(894\) | 2352.81 | 2.63177 | ||||||||
\(895\) | 588.821i | 0.657901i | ||||||||
\(896\) | −558.796 | −0.623656 | ||||||||
\(897\) | 815.439 | 0.909073 | ||||||||
\(898\) | − | 2888.17i | − | 3.21622i | ||||||
\(899\) | − | 237.813i | − | 0.264530i | ||||||
\(900\) | 2520.76 | 2.80084 | ||||||||
\(901\) | 56.1540i | 0.0623241i | ||||||||
\(902\) | −787.429 | −0.872982 | ||||||||
\(903\) | 166.832i | 0.184753i | ||||||||
\(904\) | 4677.02i | 5.17370i | ||||||||
\(905\) | 485.631i | 0.536609i | ||||||||
\(906\) | − | 3627.34i | − | 4.00368i | ||||||
\(907\) | 1770.66 | 1.95221 | 0.976107 | − | 0.217291i | \(-0.0697222\pi\) | ||||
0.976107 | + | 0.217291i | \(0.0697222\pi\) | |||||||
\(908\) | −1231.90 | −1.35672 | ||||||||
\(909\) | 1544.45i | 1.69907i | ||||||||
\(910\) | − | 60.9661i | − | 0.0669957i | ||||||
\(911\) | 307.188i | 0.337199i | 0.985685 | + | 0.168599i | \(0.0539244\pi\) | ||||
−0.985685 | + | 0.168599i | \(0.946076\pi\) | |||||||
\(912\) | − | 8976.06i | − | 9.84218i | ||||||
\(913\) | − | 441.591i | − | 0.483671i | ||||||
\(914\) | 2463.46 | 2.69525 | ||||||||
\(915\) | − | 265.191i | − | 0.289826i | ||||||
\(916\) | 2935.16i | 3.20433i | ||||||||
\(917\) | − | 58.0039i | − | 0.0632540i | ||||||
\(918\) | 96.8483i | 0.105499i | ||||||||
\(919\) | 134.435 | 0.146284 | 0.0731420 | − | 0.997322i | \(-0.476697\pi\) | ||||
0.0731420 | + | 0.997322i | \(0.476697\pi\) | |||||||
\(920\) | − | 3150.84i | − | 3.42483i | ||||||
\(921\) | −931.389 | −1.01128 | ||||||||
\(922\) | −904.551 | −0.981075 | ||||||||
\(923\) | 389.008i | 0.421461i | ||||||||
\(924\) | 373.312 | 0.404017 | ||||||||
\(925\) | − | 474.323i | − | 0.512782i | ||||||
\(926\) | −1769.17 | −1.91056 | ||||||||
\(927\) | − | 1586.22i | − | 1.71113i | ||||||
\(928\) | − | 777.998i | − | 0.838360i | ||||||
\(929\) | 1004.28i | 1.08103i | 0.841333 | + | 0.540517i | \(0.181771\pi\) | ||||
−0.841333 | + | 0.540517i | \(0.818229\pi\) | |||||||
\(930\) | −2817.20 | −3.02924 | ||||||||
\(931\) | −1318.95 | −1.41671 | ||||||||
\(932\) | −2087.90 | −2.24024 | ||||||||
\(933\) | 547.586i | 0.586909i | ||||||||
\(934\) | 3132.75i | 3.35412i | ||||||||
\(935\) | −15.9836 | −0.0170948 | ||||||||
\(936\) | − | 2200.00i | − | 2.35043i | ||||||
\(937\) | 721.788i | 0.770318i | 0.922850 | + | 0.385159i | \(0.125853\pi\) | ||||
−0.922850 | + | 0.385159i | \(0.874147\pi\) | |||||||
\(938\) | 189.234 | 0.201742 | ||||||||
\(939\) | 2425.28i | 2.58283i | ||||||||
\(940\) | − | 2945.39i | − | 3.13339i | ||||||
\(941\) | 732.588 | 0.778521 | 0.389260 | − | 0.921128i | \(-0.372731\pi\) | ||||
0.389260 | + | 0.921128i | \(0.372731\pi\) | |||||||
\(942\) | −1004.18 | −1.06600 | ||||||||
\(943\) | −989.670 | −1.04949 | ||||||||
\(944\) | 2164.08i | 2.29245i | ||||||||
\(945\) | − | 113.568i | − | 0.120177i | ||||||
\(946\) | −918.673 | −0.971113 | ||||||||
\(947\) | 898.921 | 0.949230 | 0.474615 | − | 0.880193i | \(-0.342587\pi\) | ||||
0.474615 | + | 0.880193i | \(0.342587\pi\) | |||||||
\(948\) | −5191.62 | −5.47639 | ||||||||
\(949\) | −124.722 | −0.131425 | ||||||||
\(950\) | 1497.27i | 1.57607i | ||||||||
\(951\) | − | 1126.80i | − | 1.18485i | ||||||
\(952\) | 19.2675i | 0.0202390i | ||||||||
\(953\) | −736.249 | −0.772559 | −0.386280 | − | 0.922382i | \(-0.626240\pi\) | ||||
−0.386280 | + | 0.922382i | \(0.626240\pi\) | |||||||
\(954\) | − | 5002.32i | − | 5.24353i | ||||||
\(955\) | − | 283.141i | − | 0.296482i | ||||||
\(956\) | 3765.22 | 3.93852 | ||||||||
\(957\) | 187.599i | 0.196028i | ||||||||
\(958\) | − | 2147.44i | − | 2.24159i | ||||||
\(959\) | 156.733i | 0.163434i | ||||||||
\(960\) | −4872.59 | −5.07561 | ||||||||
\(961\) | −925.109 | −0.962653 | ||||||||
\(962\) | −642.727 | −0.668115 | ||||||||
\(963\) | − | 920.541i | − | 0.955910i | ||||||
\(964\) | − | 3966.95i | − | 4.11509i | ||||||
\(965\) | 720.442i | 0.746572i | ||||||||
\(966\) | 636.186 | 0.658577 | ||||||||
\(967\) | 1378.98i | 1.42604i | 0.701142 | + | 0.713022i | \(0.252674\pi\) | ||||
−0.701142 | + | 0.713022i | \(0.747326\pi\) | |||||||
\(968\) | − | 2095.04i | − | 2.16430i | ||||||
\(969\) | −96.5960 | −0.0996862 | ||||||||
\(970\) | −2137.99 | −2.20411 | ||||||||
\(971\) | − | 125.504i | − | 0.129253i | −0.997910 | − | 0.0646264i | \(-0.979414\pi\) | ||
0.997910 | − | 0.0646264i | \(-0.0205856\pi\) | |||||||
\(972\) | 1761.44i | 1.81218i | ||||||||
\(973\) | 219.953i | 0.226057i | ||||||||
\(974\) | 1563.43 | 1.60517 | ||||||||
\(975\) | 339.342i | 0.348043i | ||||||||
\(976\) | − | 1042.90i | − | 1.06855i | ||||||
\(977\) | 735.470i | 0.752784i | 0.926461 | + | 0.376392i | \(0.122835\pi\) | ||||
−0.926461 | + | 0.376392i | \(0.877165\pi\) | |||||||
\(978\) | 5654.93i | 5.78213i | ||||||||
\(979\) | − | 944.840i | − | 0.965108i | ||||||
\(980\) | 1793.34i | 1.82994i | ||||||||
\(981\) | 1200.29i | 1.22353i | ||||||||
\(982\) | 912.453 | 0.929178 | ||||||||
\(983\) | 678.521i | 0.690256i | 0.938556 | + | 0.345128i | \(0.112164\pi\) | ||||
−0.938556 | + | 0.345128i | \(0.887836\pi\) | |||||||
\(984\) | 4167.43i | 4.23519i | ||||||||
\(985\) | 764.788 | 0.776434 | ||||||||
\(986\) | −15.0329 | −0.0152464 | ||||||||
\(987\) | 383.036 | 0.388082 | ||||||||
\(988\) | 1496.30 | 1.51447 | ||||||||
\(989\) | −1154.62 | −1.16746 | ||||||||
\(990\) | 1423.86 | 1.43824 | ||||||||
\(991\) | −1158.52 | −1.16905 | −0.584523 | − | 0.811377i | \(-0.698718\pi\) | ||||
−0.584523 | + | 0.811377i | \(0.698718\pi\) | |||||||
\(992\) | −6170.36 | −6.22012 | ||||||||
\(993\) | −2762.54 | −2.78201 | ||||||||
\(994\) | 303.495i | 0.305327i | ||||||||
\(995\) | 350.130i | 0.351889i | ||||||||
\(996\) | −3628.58 | −3.64315 | ||||||||
\(997\) | − | 819.959i | − | 0.822426i | −0.911539 | − | 0.411213i | \(-0.865105\pi\) | ||
0.911539 | − | 0.411213i | \(-0.134895\pi\) | |||||||
\(998\) | 1939.45i | 1.94333i | ||||||||
\(999\) | −1197.27 | −1.19847 |
(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 | 547.3.b.b.546.1 | ✓ | 88 | |
547.546 | odd | 2 | inner | 547.3.b.b.546.88 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.3.b.b.546.1 | ✓ | 88 | 1.1 | even | 1 | trivial | |
547.3.b.b.546.88 | yes | 88 | 547.546 | odd | 2 | inner |