Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(229,690)]
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, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.229");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.33 | ||
Character | \(\chi\) | \(=\) | 690.229 |
Dual form | 690.3.f.a.229.35 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | −4.51156 | − | 2.15543i | −0.902311 | − | 0.431086i | ||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −9.45027 | −1.35004 | −0.675019 | − | 0.737800i | \(-0.735865\pi\) | ||||
−0.675019 | + | 0.737800i | \(0.735865\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | −3.04824 | + | 6.38030i | −0.304824 | + | 0.638030i | ||||
\(11\) | 0.168957i | 0.0153598i | 0.999971 | + | 0.00767988i | \(0.00244461\pi\) | ||||
−0.999971 | + | 0.00767988i | \(0.997555\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − | 0.410015i | − | 0.0315396i | −0.999876 | − | 0.0157698i | \(-0.994980\pi\) | ||
0.999876 | − | 0.0157698i | \(-0.00501989\pi\) | |||||||
\(14\) | 13.3647i | 0.954621i | ||||||||
\(15\) | −3.73331 | + | 7.81424i | −0.248887 | + | 0.520950i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −1.40721 | −0.0827770 | −0.0413885 | − | 0.999143i | \(-0.513178\pi\) | ||||
−0.0413885 | + | 0.999143i | \(0.513178\pi\) | |||||||
\(18\) | 4.24264i | 0.235702i | ||||||||
\(19\) | − | 13.0341i | − | 0.686004i | −0.939335 | − | 0.343002i | \(-0.888556\pi\) | ||
0.939335 | − | 0.343002i | \(-0.111444\pi\) | |||||||
\(20\) | 9.02311 | + | 4.31086i | 0.451156 | + | 0.215543i | ||||
\(21\) | 16.3683i | 0.779445i | ||||||||
\(22\) | 0.238942 | 0.0108610 | ||||||||
\(23\) | −19.0387 | + | 12.9045i | −0.827771 | + | 0.561067i | ||||
\(24\) | 4.89898 | 0.204124 | ||||||||
\(25\) | 15.7083 | + | 19.4487i | 0.628330 | + | 0.777947i | ||||
\(26\) | −0.579849 | −0.0223019 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 18.9005 | 0.675019 | ||||||||
\(29\) | 3.27423 | 0.112904 | 0.0564522 | − | 0.998405i | \(-0.482021\pi\) | ||||
0.0564522 | + | 0.998405i | \(0.482021\pi\) | |||||||
\(30\) | 11.0510 | + | 5.27970i | 0.368367 | + | 0.175990i | ||||
\(31\) | 46.3652 | 1.49565 | 0.747825 | − | 0.663896i | \(-0.231098\pi\) | ||||
0.747825 | + | 0.663896i | \(0.231098\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 0.292643 | 0.00886796 | ||||||||
\(34\) | 1.99009i | 0.0585322i | ||||||||
\(35\) | 42.6354 | + | 20.3694i | 1.21815 | + | 0.581982i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −8.23316 | −0.222518 | −0.111259 | − | 0.993791i | \(-0.535488\pi\) | ||||
−0.111259 | + | 0.993791i | \(0.535488\pi\) | |||||||
\(38\) | −18.4330 | −0.485078 | ||||||||
\(39\) | −0.710167 | −0.0182094 | ||||||||
\(40\) | 6.09647 | − | 12.7606i | 0.152412 | − | 0.319015i | ||||
\(41\) | 22.2032 | 0.541541 | 0.270770 | − | 0.962644i | \(-0.412722\pi\) | ||||
0.270770 | + | 0.962644i | \(0.412722\pi\) | |||||||
\(42\) | 23.1483 | 0.551151 | ||||||||
\(43\) | 27.5809 | 0.641417 | 0.320709 | − | 0.947178i | \(-0.396079\pi\) | ||||
0.320709 | + | 0.947178i | \(0.396079\pi\) | |||||||
\(44\) | − | 0.337915i | − | 0.00767988i | ||||||
\(45\) | 13.5347 | + | 6.46628i | 0.300770 | + | 0.143695i | ||||
\(46\) | 18.2498 | + | 26.9248i | 0.396734 | + | 0.585322i | ||||
\(47\) | − | 24.8110i | − | 0.527893i | −0.964537 | − | 0.263947i | \(-0.914976\pi\) | ||
0.964537 | − | 0.263947i | \(-0.0850243\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | 40.3076 | 0.822604 | ||||||||
\(50\) | 27.5046 | − | 22.2148i | 0.550091 | − | 0.444297i | ||||
\(51\) | 2.43736i | 0.0477913i | ||||||||
\(52\) | 0.820030i | 0.0157698i | ||||||||
\(53\) | 5.90213 | 0.111361 | 0.0556805 | − | 0.998449i | \(-0.482267\pi\) | ||||
0.0556805 | + | 0.998449i | \(0.482267\pi\) | |||||||
\(54\) | 7.34847 | 0.136083 | ||||||||
\(55\) | 0.364176 | − | 0.762261i | 0.00662137 | − | 0.0138593i | ||||
\(56\) | − | 26.7294i | − | 0.477311i | ||||||
\(57\) | −22.5757 | −0.396064 | ||||||||
\(58\) | − | 4.63046i | − | 0.0798355i | ||||||
\(59\) | −69.0614 | −1.17053 | −0.585266 | − | 0.810841i | \(-0.699010\pi\) | ||||
−0.585266 | + | 0.810841i | \(0.699010\pi\) | |||||||
\(60\) | 7.46662 | − | 15.6285i | 0.124444 | − | 0.260475i | ||||
\(61\) | 106.523i | 1.74628i | 0.487468 | + | 0.873141i | \(0.337921\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662079\pi\) | |||||||
\(62\) | − | 65.5703i | − | 1.05758i | ||||||
\(63\) | 28.3508 | 0.450013 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | −0.883758 | + | 1.84980i | −0.0135963 | + | 0.0284585i | ||||
\(66\) | − | 0.413859i | − | 0.00627060i | ||||||
\(67\) | −19.7414 | −0.294648 | −0.147324 | − | 0.989088i | \(-0.547066\pi\) | ||||
−0.147324 | + | 0.989088i | \(0.547066\pi\) | |||||||
\(68\) | 2.81442 | 0.0413885 | ||||||||
\(69\) | 22.3513 | + | 32.9760i | 0.323932 | + | 0.477914i | ||||
\(70\) | 28.8067 | − | 60.2956i | 0.411524 | − | 0.861365i | ||||
\(71\) | 10.3118 | 0.145237 | 0.0726185 | − | 0.997360i | \(-0.476864\pi\) | ||||
0.0726185 | + | 0.997360i | \(0.476864\pi\) | |||||||
\(72\) | − | 8.48528i | − | 0.117851i | ||||||
\(73\) | 8.92696i | 0.122287i | 0.998129 | + | 0.0611436i | \(0.0194748\pi\) | ||||
−0.998129 | + | 0.0611436i | \(0.980525\pi\) | |||||||
\(74\) | 11.6434i | 0.157344i | ||||||||
\(75\) | 33.6861 | − | 27.2075i | 0.449148 | − | 0.362767i | ||||
\(76\) | 26.0681i | 0.343002i | ||||||||
\(77\) | − | 1.59669i | − | 0.0207363i | ||||||
\(78\) | 1.00433i | 0.0128760i | ||||||||
\(79\) | 84.6198i | 1.07114i | 0.844492 | + | 0.535568i | \(0.179903\pi\) | ||||
−0.844492 | + | 0.535568i | \(0.820097\pi\) | |||||||
\(80\) | −18.0462 | − | 8.62171i | −0.225578 | − | 0.107771i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 31.4000i | − | 0.382927i | ||||||
\(83\) | 60.8352 | 0.732955 | 0.366477 | − | 0.930427i | \(-0.380564\pi\) | ||||
0.366477 | + | 0.930427i | \(0.380564\pi\) | |||||||
\(84\) | − | 32.7367i | − | 0.389723i | ||||||
\(85\) | 6.34870 | + | 3.03314i | 0.0746906 | + | 0.0356840i | ||||
\(86\) | − | 39.0053i | − | 0.453551i | ||||||
\(87\) | − | 5.67113i | − | 0.0651854i | ||||||
\(88\) | −0.477884 | −0.00543050 | ||||||||
\(89\) | − | 9.16191i | − | 0.102943i | −0.998674 | − | 0.0514714i | \(-0.983609\pi\) | ||
0.998674 | − | 0.0514714i | \(-0.0163911\pi\) | |||||||
\(90\) | 9.14471 | − | 19.1409i | 0.101608 | − | 0.212677i | ||||
\(91\) | 3.87475i | 0.0425797i | ||||||||
\(92\) | 38.0774 | − | 25.8091i | 0.413885 | − | 0.280533i | ||||
\(93\) | − | 80.3068i | − | 0.863514i | ||||||
\(94\) | −35.0880 | −0.373277 | ||||||||
\(95\) | −28.0940 | + | 58.8039i | −0.295726 | + | 0.618989i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | −86.3970 | −0.890691 | −0.445345 | − | 0.895359i | \(-0.646919\pi\) | ||||
−0.445345 | + | 0.895359i | \(0.646919\pi\) | |||||||
\(98\) | − | 57.0036i | − | 0.581669i | ||||||
\(99\) | − | 0.506872i | − | 0.00511992i | ||||||
\(100\) | −31.4165 | − | 38.8973i | −0.314165 | − | 0.388973i | ||||
\(101\) | −64.2539 | −0.636177 | −0.318088 | − | 0.948061i | \(-0.603041\pi\) | ||||
−0.318088 | + | 0.948061i | \(0.603041\pi\) | |||||||
\(102\) | 3.44694 | 0.0337936 | ||||||||
\(103\) | 74.5544 | 0.723829 | 0.361915 | − | 0.932211i | \(-0.382123\pi\) | ||||
0.361915 | + | 0.932211i | \(0.382123\pi\) | |||||||
\(104\) | 1.15970 | 0.0111509 | ||||||||
\(105\) | 35.2808 | − | 73.8467i | 0.336008 | − | 0.703302i | ||||
\(106\) | − | 8.34687i | − | 0.0787441i | ||||||
\(107\) | −49.4322 | −0.461983 | −0.230992 | − | 0.972956i | \(-0.574197\pi\) | ||||
−0.230992 | + | 0.972956i | \(0.574197\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | 90.4875i | 0.830161i | 0.909785 | + | 0.415080i | \(0.136247\pi\) | ||||
−0.909785 | + | 0.415080i | \(0.863753\pi\) | |||||||
\(110\) | −1.07800 | − | 0.515022i | −0.00979999 | − | 0.00468202i | ||||
\(111\) | 14.2602i | 0.128471i | ||||||||
\(112\) | −37.8011 | −0.337510 | ||||||||
\(113\) | 100.086 | 0.885713 | 0.442856 | − | 0.896593i | \(-0.353965\pi\) | ||||
0.442856 | + | 0.896593i | \(0.353965\pi\) | |||||||
\(114\) | 31.9268i | 0.280060i | ||||||||
\(115\) | 113.709 | − | 17.1829i | 0.988774 | − | 0.149417i | ||||
\(116\) | −6.54846 | −0.0564522 | ||||||||
\(117\) | 1.23004i | 0.0105132i | ||||||||
\(118\) | 97.6676i | 0.827691i | ||||||||
\(119\) | 13.2985 | 0.111752 | ||||||||
\(120\) | −22.1020 | − | 10.5594i | −0.184183 | − | 0.0879950i | ||||
\(121\) | 120.971 | 0.999764 | ||||||||
\(122\) | 150.647 | 1.23481 | ||||||||
\(123\) | − | 38.4570i | − | 0.312659i | ||||||
\(124\) | −92.7303 | −0.747825 | ||||||||
\(125\) | −28.9485 | − | 121.602i | −0.231588 | − | 0.972814i | ||||
\(126\) | − | 40.0941i | − | 0.318207i | ||||||
\(127\) | 158.414i | 1.24735i | 0.781683 | + | 0.623676i | \(0.214362\pi\) | ||||
−0.781683 | + | 0.623676i | \(0.785638\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | − | 47.7716i | − | 0.370322i | ||||||
\(130\) | 2.61602 | + | 1.24982i | 0.0201232 | + | 0.00961402i | ||||
\(131\) | −228.138 | −1.74151 | −0.870757 | − | 0.491713i | \(-0.836371\pi\) | ||||
−0.870757 | + | 0.491713i | \(0.836371\pi\) | |||||||
\(132\) | −0.585286 | −0.00443398 | ||||||||
\(133\) | 123.175i | 0.926131i | ||||||||
\(134\) | 27.9185i | 0.208347i | ||||||||
\(135\) | 11.1999 | − | 23.4427i | 0.0829625 | − | 0.173650i | ||||
\(136\) | − | 3.98019i | − | 0.0292661i | ||||||
\(137\) | 19.1955 | 0.140113 | 0.0700564 | − | 0.997543i | \(-0.477682\pi\) | ||||
0.0700564 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(138\) | 46.6352 | − | 31.6095i | 0.337936 | − | 0.229055i | ||||
\(139\) | 226.280 | 1.62791 | 0.813956 | − | 0.580926i | \(-0.197310\pi\) | ||||
0.813956 | + | 0.580926i | \(0.197310\pi\) | |||||||
\(140\) | −85.2708 | − | 40.7388i | −0.609077 | − | 0.290991i | ||||
\(141\) | −42.9739 | −0.304779 | ||||||||
\(142\) | − | 14.5831i | − | 0.102698i | ||||||
\(143\) | 0.0692751 | 0.000484441 | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | −14.7719 | − | 7.05737i | −0.101875 | − | 0.0486715i | ||||
\(146\) | 12.6246 | 0.0864701 | ||||||||
\(147\) | − | 69.8148i | − | 0.474931i | ||||||
\(148\) | 16.4663 | 0.111259 | ||||||||
\(149\) | 138.045i | 0.926474i | 0.886235 | + | 0.463237i | \(0.153312\pi\) | ||||
−0.886235 | + | 0.463237i | \(0.846688\pi\) | |||||||
\(150\) | −38.4772 | − | 47.6393i | −0.256515 | − | 0.317595i | ||||
\(151\) | −111.059 | −0.735490 | −0.367745 | − | 0.929927i | \(-0.619870\pi\) | ||||
−0.367745 | + | 0.929927i | \(0.619870\pi\) | |||||||
\(152\) | 36.8659 | 0.242539 | ||||||||
\(153\) | 4.22163 | 0.0275923 | ||||||||
\(154\) | −2.25807 | −0.0146628 | ||||||||
\(155\) | −209.179 | − | 99.9368i | −1.34954 | − | 0.644754i | ||||
\(156\) | 1.42033 | 0.00910470 | ||||||||
\(157\) | −208.561 | −1.32842 | −0.664208 | − | 0.747548i | \(-0.731231\pi\) | ||||
−0.664208 | + | 0.747548i | \(0.731231\pi\) | |||||||
\(158\) | 119.670 | 0.757408 | ||||||||
\(159\) | − | 10.2228i | − | 0.0642943i | ||||||
\(160\) | −12.1929 | + | 25.5212i | −0.0762059 | + | 0.159508i | ||||
\(161\) | 179.921 | − | 121.951i | 1.11752 | − | 0.757462i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 128.025i | 0.785427i | 0.919661 | + | 0.392713i | \(0.128464\pi\) | ||||
−0.919661 | + | 0.392713i | \(0.871536\pi\) | |||||||
\(164\) | −44.4063 | −0.270770 | ||||||||
\(165\) | −1.32027 | − | 0.630771i | −0.00800166 | − | 0.00382285i | ||||
\(166\) | − | 86.0340i | − | 0.518277i | ||||||
\(167\) | − | 313.129i | − | 1.87503i | −0.347950 | − | 0.937513i | \(-0.613122\pi\) | ||
0.347950 | − | 0.937513i | \(-0.386878\pi\) | |||||||
\(168\) | −46.2967 | −0.275575 | ||||||||
\(169\) | 168.832 | 0.999005 | ||||||||
\(170\) | 4.28950 | − | 8.97842i | 0.0252324 | − | 0.0528142i | ||||
\(171\) | 39.1022i | 0.228668i | ||||||||
\(172\) | −55.1619 | −0.320709 | ||||||||
\(173\) | 271.648i | 1.57022i | 0.619355 | + | 0.785111i | \(0.287394\pi\) | ||||
−0.619355 | + | 0.785111i | \(0.712606\pi\) | |||||||
\(174\) | −8.02019 | −0.0460931 | ||||||||
\(175\) | −148.447 | − | 183.795i | −0.848270 | − | 1.05026i | ||||
\(176\) | 0.675830i | 0.00383994i | ||||||||
\(177\) | 119.618i | 0.675807i | ||||||||
\(178\) | −12.9569 | −0.0727916 | ||||||||
\(179\) | −237.537 | −1.32702 | −0.663510 | − | 0.748167i | \(-0.730934\pi\) | ||||
−0.663510 | + | 0.748167i | \(0.730934\pi\) | |||||||
\(180\) | −27.0693 | − | 12.9326i | −0.150385 | − | 0.0718476i | ||||
\(181\) | 40.7017i | 0.224871i | 0.993659 | + | 0.112436i | \(0.0358652\pi\) | ||||
−0.993659 | + | 0.112436i | \(0.964135\pi\) | |||||||
\(182\) | 5.47973 | 0.0301084 | ||||||||
\(183\) | 184.504 | 1.00822 | ||||||||
\(184\) | −36.4995 | − | 53.8496i | −0.198367 | − | 0.292661i | ||||
\(185\) | 37.1443 | + | 17.7460i | 0.200780 | + | 0.0959242i | ||||
\(186\) | −113.571 | −0.610597 | ||||||||
\(187\) | − | 0.237758i | − | 0.00127143i | ||||||
\(188\) | 49.6220i | 0.263947i | ||||||||
\(189\) | − | 49.1050i | − | 0.259815i | ||||||
\(190\) | 83.1613 | + | 39.7309i | 0.437691 | + | 0.209110i | ||||
\(191\) | 202.716i | 1.06134i | 0.847578 | + | 0.530671i | \(0.178060\pi\) | ||||
−0.847578 | + | 0.530671i | \(0.821940\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | 185.008i | 0.958589i | 0.877654 | + | 0.479294i | \(0.159107\pi\) | ||||
−0.877654 | + | 0.479294i | \(0.840893\pi\) | |||||||
\(194\) | 122.184i | 0.629813i | ||||||||
\(195\) | 3.20396 | + | 1.53071i | 0.0164305 | + | 0.00784981i | ||||
\(196\) | −80.6152 | −0.411302 | ||||||||
\(197\) | 54.1067i | 0.274653i | 0.990526 | + | 0.137327i | \(0.0438510\pi\) | ||||
−0.990526 | + | 0.137327i | \(0.956149\pi\) | |||||||
\(198\) | −0.716826 | −0.00362033 | ||||||||
\(199\) | − | 40.4530i | − | 0.203281i | −0.994821 | − | 0.101641i | \(-0.967591\pi\) | ||
0.994821 | − | 0.101641i | \(-0.0324092\pi\) | |||||||
\(200\) | −55.0091 | + | 44.4297i | −0.275046 | + | 0.222148i | ||||
\(201\) | 34.1931i | 0.170115i | ||||||||
\(202\) | 90.8687i | 0.449845i | ||||||||
\(203\) | −30.9424 | −0.152425 | ||||||||
\(204\) | − | 4.87471i | − | 0.0238957i | ||||||
\(205\) | −100.171 | − | 47.8573i | −0.488638 | − | 0.233450i | ||||
\(206\) | − | 105.436i | − | 0.511824i | ||||||
\(207\) | 57.1162 | − | 38.7136i | 0.275924 | − | 0.187022i | ||||
\(208\) | − | 1.64006i | − | 0.00788490i | ||||||
\(209\) | 2.20220 | 0.0105369 | ||||||||
\(210\) | −104.435 | − | 49.8946i | −0.497310 | − | 0.237593i | ||||
\(211\) | −93.1211 | −0.441332 | −0.220666 | − | 0.975349i | \(-0.570823\pi\) | ||||
−0.220666 | + | 0.975349i | \(0.570823\pi\) | |||||||
\(212\) | −11.8043 | −0.0556805 | ||||||||
\(213\) | − | 17.8606i | − | 0.0838526i | ||||||
\(214\) | 69.9077i | 0.326672i | ||||||||
\(215\) | −124.433 | − | 59.4487i | −0.578758 | − | 0.276506i | ||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | −438.163 | −2.01919 | ||||||||
\(218\) | 127.969 | 0.587012 | ||||||||
\(219\) | 15.4620 | 0.0706025 | ||||||||
\(220\) | −0.728351 | + | 1.52452i | −0.00331069 | + | 0.00692964i | ||||
\(221\) | 0.576976i | 0.00261075i | ||||||||
\(222\) | 20.1670 | 0.0908425 | ||||||||
\(223\) | 326.830i | 1.46560i | 0.680441 | + | 0.732802i | \(0.261788\pi\) | ||||
−0.680441 | + | 0.732802i | \(0.738212\pi\) | |||||||
\(224\) | 53.4588i | 0.238655i | ||||||||
\(225\) | −47.1248 | − | 58.3460i | −0.209443 | − | 0.259316i | ||||
\(226\) | − | 141.542i | − | 0.626293i | ||||||
\(227\) | 130.957 | 0.576902 | 0.288451 | − | 0.957495i | \(-0.406860\pi\) | ||||
0.288451 | + | 0.957495i | \(0.406860\pi\) | |||||||
\(228\) | 45.1513 | 0.198032 | ||||||||
\(229\) | 169.709i | 0.741088i | 0.928815 | + | 0.370544i | \(0.120829\pi\) | ||||
−0.928815 | + | 0.370544i | \(0.879171\pi\) | |||||||
\(230\) | −24.3003 | − | 160.809i | −0.105654 | − | 0.699169i | ||||
\(231\) | −2.76555 | −0.0119721 | ||||||||
\(232\) | 9.26092i | 0.0399178i | ||||||||
\(233\) | 63.2641i | 0.271520i | 0.990742 | + | 0.135760i | \(0.0433476\pi\) | ||||
−0.990742 | + | 0.135760i | \(0.956652\pi\) | |||||||
\(234\) | 1.73955 | 0.00743396 | ||||||||
\(235\) | −53.4783 | + | 111.936i | −0.227567 | + | 0.476324i | ||||
\(236\) | 138.123 | 0.585266 | ||||||||
\(237\) | 146.566 | 0.618421 | ||||||||
\(238\) | − | 18.8069i | − | 0.0790207i | ||||||
\(239\) | −415.109 | −1.73686 | −0.868429 | − | 0.495814i | \(-0.834870\pi\) | ||||
−0.868429 | + | 0.495814i | \(0.834870\pi\) | |||||||
\(240\) | −14.9332 | + | 31.2570i | −0.0622219 | + | 0.130237i | ||||
\(241\) | 112.766i | 0.467910i | 0.972247 | + | 0.233955i | \(0.0751669\pi\) | ||||
−0.972247 | + | 0.233955i | \(0.924833\pi\) | |||||||
\(242\) | − | 171.079i | − | 0.706940i | ||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | − | 213.046i | − | 0.873141i | ||||||
\(245\) | −181.850 | − | 86.8801i | −0.742245 | − | 0.354613i | ||||
\(246\) | −54.3864 | −0.221083 | ||||||||
\(247\) | −5.34416 | −0.0216363 | ||||||||
\(248\) | 131.141i | 0.528792i | ||||||||
\(249\) | − | 105.370i | − | 0.423172i | ||||||
\(250\) | −171.971 | + | 40.9393i | −0.687883 | + | 0.163757i | ||||
\(251\) | − | 361.428i | − | 1.43995i | −0.693998 | − | 0.719977i | \(-0.744152\pi\) | ||
0.693998 | − | 0.719977i | \(-0.255848\pi\) | |||||||
\(252\) | −56.7016 | −0.225006 | ||||||||
\(253\) | −2.18032 | − | 3.21673i | −0.00861785 | − | 0.0127144i | ||||
\(254\) | 224.031 | 0.882011 | ||||||||
\(255\) | 5.25355 | − | 10.9963i | 0.0206021 | − | 0.0431226i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 139.253i | 0.541840i | 0.962602 | + | 0.270920i | \(0.0873279\pi\) | ||||
−0.962602 | + | 0.270920i | \(0.912672\pi\) | |||||||
\(258\) | −67.5592 | −0.261858 | ||||||||
\(259\) | 77.8055 | 0.300408 | ||||||||
\(260\) | 1.76752 | − | 3.69961i | 0.00679814 | − | 0.0142293i | ||||
\(261\) | −9.82269 | −0.0376348 | ||||||||
\(262\) | 322.636i | 1.23144i | ||||||||
\(263\) | 10.0975 | 0.0383934 | 0.0191967 | − | 0.999816i | \(-0.493889\pi\) | ||||
0.0191967 | + | 0.999816i | \(0.493889\pi\) | |||||||
\(264\) | 0.827719i | 0.00313530i | ||||||||
\(265\) | −26.6278 | − | 12.7216i | −0.100482 | − | 0.0480061i | ||||
\(266\) | 174.196 | 0.654874 | ||||||||
\(267\) | −15.8689 | −0.0594341 | ||||||||
\(268\) | 39.4828 | 0.147324 | ||||||||
\(269\) | −182.893 | −0.679900 | −0.339950 | − | 0.940444i | \(-0.610410\pi\) | ||||
−0.339950 | + | 0.940444i | \(0.610410\pi\) | |||||||
\(270\) | −33.1530 | − | 15.8391i | −0.122789 | − | 0.0586633i | ||||
\(271\) | −132.990 | −0.490739 | −0.245369 | − | 0.969430i | \(-0.578909\pi\) | ||||
−0.245369 | + | 0.969430i | \(0.578909\pi\) | |||||||
\(272\) | −5.62883 | −0.0206942 | ||||||||
\(273\) | 6.71127 | 0.0245834 | ||||||||
\(274\) | − | 27.1465i | − | 0.0990747i | ||||||
\(275\) | −3.28600 | + | 2.65403i | −0.0119491 | + | 0.00965101i | ||||
\(276\) | −44.7026 | − | 65.9521i | −0.161966 | − | 0.238957i | ||||
\(277\) | 76.3745i | 0.275720i | 0.990452 | + | 0.137860i | \(0.0440225\pi\) | ||||
−0.990452 | + | 0.137860i | \(0.955978\pi\) | |||||||
\(278\) | − | 320.008i | − | 1.15111i | ||||||
\(279\) | −139.096 | −0.498550 | ||||||||
\(280\) | −57.6133 | + | 120.591i | −0.205762 | + | 0.430683i | ||||
\(281\) | − | 389.767i | − | 1.38707i | −0.720423 | − | 0.693535i | \(-0.756052\pi\) | ||
0.720423 | − | 0.693535i | \(-0.243948\pi\) | |||||||
\(282\) | 60.7743i | 0.215512i | ||||||||
\(283\) | 95.1971 | 0.336385 | 0.168193 | − | 0.985754i | \(-0.446207\pi\) | ||||
0.168193 | + | 0.985754i | \(0.446207\pi\) | |||||||
\(284\) | −20.6237 | −0.0726185 | ||||||||
\(285\) | 101.851 | + | 48.6602i | 0.357373 | + | 0.170738i | ||||
\(286\) | − | 0.0979697i | − | 0.000342551i | ||||||
\(287\) | −209.826 | −0.731101 | ||||||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | −287.020 | −0.993148 | ||||||||
\(290\) | −9.98062 | + | 20.8906i | −0.0344159 | + | 0.0720365i | ||||
\(291\) | 149.644i | 0.514240i | ||||||||
\(292\) | − | 17.8539i | − | 0.0611436i | ||||||
\(293\) | 197.320 | 0.673448 | 0.336724 | − | 0.941603i | \(-0.390681\pi\) | ||||
0.336724 | + | 0.941603i | \(0.390681\pi\) | |||||||
\(294\) | −98.7331 | −0.335827 | ||||||||
\(295\) | 311.574 | + | 148.857i | 1.05618 | + | 0.504600i | ||||
\(296\) | − | 23.2869i | − | 0.0786719i | ||||||
\(297\) | −0.877928 | −0.00295599 | ||||||||
\(298\) | 195.225 | 0.655116 | ||||||||
\(299\) | 5.29105 | + | 7.80616i | 0.0176958 | + | 0.0261076i | ||||
\(300\) | −67.3722 | + | 54.4150i | −0.224574 | + | 0.181383i | ||||
\(301\) | −260.647 | −0.865938 | ||||||||
\(302\) | 157.061i | 0.520070i | ||||||||
\(303\) | 111.291i | 0.367297i | ||||||||
\(304\) | − | 52.1363i | − | 0.171501i | ||||||
\(305\) | 229.603 | − | 480.585i | 0.752797 | − | 1.57569i | ||||
\(306\) | − | 5.97028i | − | 0.0195107i | ||||||
\(307\) | − | 238.130i | − | 0.775669i | −0.921729 | − | 0.387835i | \(-0.873223\pi\) | ||
0.921729 | − | 0.387835i | \(-0.126777\pi\) | |||||||
\(308\) | 3.19339i | 0.0103681i | ||||||||
\(309\) | − | 129.132i | − | 0.417903i | ||||||
\(310\) | −141.332 | + | 295.824i | −0.455910 | + | 0.954270i | ||||
\(311\) | 48.8991 | 0.157232 | 0.0786158 | − | 0.996905i | \(-0.474950\pi\) | ||||
0.0786158 | + | 0.996905i | \(0.474950\pi\) | |||||||
\(312\) | − | 2.00865i | − | 0.00643800i | ||||||
\(313\) | 386.351 | 1.23435 | 0.617175 | − | 0.786826i | \(-0.288277\pi\) | ||||
0.617175 | + | 0.786826i | \(0.288277\pi\) | |||||||
\(314\) | 294.950i | 0.939332i | ||||||||
\(315\) | −127.906 | − | 61.1081i | −0.406052 | − | 0.193994i | ||||
\(316\) | − | 169.240i | − | 0.535568i | ||||||
\(317\) | 326.284i | 1.02929i | 0.857404 | + | 0.514644i | \(0.172076\pi\) | ||||
−0.857404 | + | 0.514644i | \(0.827924\pi\) | |||||||
\(318\) | −14.4572 | −0.0454629 | ||||||||
\(319\) | 0.553205i | 0.00173419i | ||||||||
\(320\) | 36.0924 | + | 17.2434i | 0.112789 | + | 0.0538857i | ||||
\(321\) | 85.6191i | 0.266726i | ||||||||
\(322\) | −172.465 | − | 254.447i | −0.535606 | − | 0.790208i | ||||
\(323\) | 18.3417i | 0.0567853i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 7.97424 | − | 6.44062i | 0.0245361 | − | 0.0198173i | ||||
\(326\) | 181.054 | 0.555381 | ||||||||
\(327\) | 156.729 | 0.479294 | ||||||||
\(328\) | 62.8000i | 0.191464i | ||||||||
\(329\) | 234.471i | 0.712677i | ||||||||
\(330\) | −0.892044 | + | 1.86715i | −0.00270316 | + | 0.00565803i | ||||
\(331\) | −45.7276 | −0.138150 | −0.0690750 | − | 0.997611i | \(-0.522005\pi\) | ||||
−0.0690750 | + | 0.997611i | \(0.522005\pi\) | |||||||
\(332\) | −121.670 | −0.366477 | ||||||||
\(333\) | 24.6995 | 0.0741726 | ||||||||
\(334\) | −442.832 | −1.32584 | ||||||||
\(335\) | 89.0644 | + | 42.5512i | 0.265864 | + | 0.127018i | ||||
\(336\) | 65.4734i | 0.194861i | ||||||||
\(337\) | −547.693 | −1.62520 | −0.812602 | − | 0.582820i | \(-0.801949\pi\) | ||||
−0.812602 | + | 0.582820i | \(0.801949\pi\) | |||||||
\(338\) | − | 238.764i | − | 0.706403i | ||||||
\(339\) | − | 173.353i | − | 0.511366i | ||||||
\(340\) | −12.6974 | − | 6.06627i | −0.0373453 | − | 0.0178420i | ||||
\(341\) | 7.83374i | 0.0229728i | ||||||||
\(342\) | 55.2989 | 0.161693 | ||||||||
\(343\) | 82.1455 | 0.239491 | ||||||||
\(344\) | 78.0107i | 0.226775i | ||||||||
\(345\) | −29.7617 | − | 196.950i | −0.0862657 | − | 0.570869i | ||||
\(346\) | 384.169 | 1.11031 | ||||||||
\(347\) | − | 430.247i | − | 1.23991i | −0.784639 | − | 0.619953i | \(-0.787152\pi\) | ||
0.784639 | − | 0.619953i | \(-0.212848\pi\) | |||||||
\(348\) | 11.3423i | 0.0325927i | ||||||||
\(349\) | −32.7928 | −0.0939623 | −0.0469811 | − | 0.998896i | \(-0.514960\pi\) | ||||
−0.0469811 | + | 0.998896i | \(0.514960\pi\) | |||||||
\(350\) | −259.926 | + | 209.936i | −0.742645 | + | 0.599818i | ||||
\(351\) | 2.13050 | 0.00606980 | ||||||||
\(352\) | 0.955767 | 0.00271525 | ||||||||
\(353\) | 228.526i | 0.647383i | 0.946163 | + | 0.323692i | \(0.104924\pi\) | ||||
−0.946163 | + | 0.323692i | \(0.895076\pi\) | |||||||
\(354\) | 169.165 | 0.477868 | ||||||||
\(355\) | −46.5224 | − | 22.2264i | −0.131049 | − | 0.0626096i | ||||
\(356\) | 18.3238i | 0.0514714i | ||||||||
\(357\) | − | 23.0337i | − | 0.0645201i | ||||||
\(358\) | 335.928i | 0.938345i | ||||||||
\(359\) | − | 687.674i | − | 1.91553i | −0.287559 | − | 0.957763i | \(-0.592844\pi\) | ||
0.287559 | − | 0.957763i | \(-0.407156\pi\) | |||||||
\(360\) | −18.2894 | + | 38.2818i | −0.0508039 | + | 0.106338i | ||||
\(361\) | 191.113 | 0.529399 | ||||||||
\(362\) | 57.5609 | 0.159008 | ||||||||
\(363\) | − | 209.529i | − | 0.577214i | ||||||
\(364\) | − | 7.74950i | − | 0.0212898i | ||||||
\(365\) | 19.2414 | − | 40.2745i | 0.0527162 | − | 0.110341i | ||||
\(366\) | − | 260.927i | − | 0.712917i | ||||||
\(367\) | 595.848 | 1.62356 | 0.811782 | − | 0.583960i | \(-0.198498\pi\) | ||||
0.811782 | + | 0.583960i | \(0.198498\pi\) | |||||||
\(368\) | −76.1549 | + | 51.6181i | −0.206943 | + | 0.140267i | ||||
\(369\) | −66.6095 | −0.180514 | ||||||||
\(370\) | 25.0966 | − | 52.5300i | 0.0678287 | − | 0.141973i | ||||
\(371\) | −55.7767 | −0.150342 | ||||||||
\(372\) | 160.614i | 0.431757i | ||||||||
\(373\) | −79.0781 | −0.212006 | −0.106003 | − | 0.994366i | \(-0.533805\pi\) | ||||
−0.106003 | + | 0.994366i | \(0.533805\pi\) | |||||||
\(374\) | −0.336241 | −0.000899040 | ||||||||
\(375\) | −210.620 | + | 50.1402i | −0.561654 | + | 0.133707i | ||||
\(376\) | 70.1761 | 0.186639 | ||||||||
\(377\) | − | 1.34248i | − | 0.00356096i | ||||||
\(378\) | −69.4450 | −0.183717 | ||||||||
\(379\) | − | 397.595i | − | 1.04906i | −0.851391 | − | 0.524532i | \(-0.824240\pi\) | ||
0.851391 | − | 0.524532i | \(-0.175760\pi\) | |||||||
\(380\) | 56.1880 | − | 117.608i | 0.147863 | − | 0.309494i | ||||
\(381\) | 274.381 | 0.720159 | ||||||||
\(382\) | 286.684 | 0.750482 | ||||||||
\(383\) | 37.8458 | 0.0988140 | 0.0494070 | − | 0.998779i | \(-0.484267\pi\) | ||||
0.0494070 | + | 0.998779i | \(0.484267\pi\) | |||||||
\(384\) | 19.5959 | 0.0510310 | ||||||||
\(385\) | −3.44156 | + | 7.20357i | −0.00893911 | + | 0.0187106i | ||||
\(386\) | 261.640 | 0.677825 | ||||||||
\(387\) | −82.7428 | −0.213806 | ||||||||
\(388\) | 172.794 | 0.445345 | ||||||||
\(389\) | 223.018i | 0.573310i | 0.958034 | + | 0.286655i | \(0.0925433\pi\) | ||||
−0.958034 | + | 0.286655i | \(0.907457\pi\) | |||||||
\(390\) | 2.16476 | − | 4.53108i | 0.00555065 | − | 0.0116181i | ||||
\(391\) | 26.7915 | − | 18.1594i | 0.0685203 | − | 0.0464434i | ||||
\(392\) | 114.007i | 0.290834i | ||||||||
\(393\) | 395.147i | 1.00546i | ||||||||
\(394\) | 76.5184 | 0.194209 | ||||||||
\(395\) | 182.392 | − | 381.767i | 0.461752 | − | 0.966499i | ||||
\(396\) | 1.01374i | 0.00255996i | ||||||||
\(397\) | 95.2611i | 0.239952i | 0.992777 | + | 0.119976i | \(0.0382818\pi\) | ||||
−0.992777 | + | 0.119976i | \(0.961718\pi\) | |||||||
\(398\) | −57.2091 | −0.143742 | ||||||||
\(399\) | 213.346 | 0.534702 | ||||||||
\(400\) | 62.8330 | + | 77.7947i | 0.157083 | + | 0.194487i | ||||
\(401\) | 91.8537i | 0.229062i | 0.993420 | + | 0.114531i | \(0.0365365\pi\) | ||||
−0.993420 | + | 0.114531i | \(0.963464\pi\) | |||||||
\(402\) | 48.3563 | 0.120289 | ||||||||
\(403\) | − | 19.0104i | − | 0.0471722i | ||||||
\(404\) | 128.508 | 0.318088 | ||||||||
\(405\) | −40.6040 | − | 19.3989i | −0.100257 | − | 0.0478984i | ||||
\(406\) | 43.7591i | 0.107781i | ||||||||
\(407\) | − | 1.39105i | − | 0.00341782i | ||||||
\(408\) | −6.89389 | −0.0168968 | ||||||||
\(409\) | 89.3154 | 0.218375 | 0.109188 | − | 0.994021i | \(-0.465175\pi\) | ||||
0.109188 | + | 0.994021i | \(0.465175\pi\) | |||||||
\(410\) | −67.6805 | + | 141.663i | −0.165074 | + | 0.345519i | ||||
\(411\) | − | 33.2475i | − | 0.0808942i | ||||||
\(412\) | −149.109 | −0.361915 | ||||||||
\(413\) | 652.649 | 1.58026 | ||||||||
\(414\) | −54.7493 | − | 80.7745i | −0.132245 | − | 0.195107i | ||||
\(415\) | −274.462 | − | 131.126i | −0.661353 | − | 0.315966i | ||||
\(416\) | −2.31939 | −0.00557547 | ||||||||
\(417\) | − | 391.928i | − | 0.939876i | ||||||
\(418\) | − | 3.11438i | − | 0.00745068i | ||||||
\(419\) | 9.33638i | 0.0222825i | 0.999938 | + | 0.0111413i | \(0.00354645\pi\) | ||||
−0.999938 | + | 0.0111413i | \(0.996454\pi\) | |||||||
\(420\) | −70.5616 | + | 147.693i | −0.168004 | + | 0.351651i | ||||
\(421\) | 737.189i | 1.75104i | 0.483179 | + | 0.875522i | \(0.339482\pi\) | ||||
−0.483179 | + | 0.875522i | \(0.660518\pi\) | |||||||
\(422\) | 131.693i | 0.312069i | ||||||||
\(423\) | 74.4330i | 0.175964i | ||||||||
\(424\) | 16.6937i | 0.0393720i | ||||||||
\(425\) | −22.1048 | − | 27.3683i | −0.0520113 | − | 0.0643961i | ||||
\(426\) | −25.2587 | −0.0592928 | ||||||||
\(427\) | − | 1006.67i | − | 2.35755i | ||||||
\(428\) | 98.8644 | 0.230992 | ||||||||
\(429\) | − | 0.119988i | − | 0.000279692i | ||||||
\(430\) | −84.0732 | + | 175.975i | −0.195519 | + | 0.409244i | ||||
\(431\) | 280.844i | 0.651611i | 0.945437 | + | 0.325805i | \(0.105635\pi\) | ||||
−0.945437 | + | 0.325805i | \(0.894365\pi\) | |||||||
\(432\) | 20.7846i | 0.0481125i | ||||||||
\(433\) | 145.165 | 0.335254 | 0.167627 | − | 0.985851i | \(-0.446390\pi\) | ||||
0.167627 | + | 0.985851i | \(0.446390\pi\) | |||||||
\(434\) | 619.657i | 1.42778i | ||||||||
\(435\) | −12.2237 | + | 25.5856i | −0.0281005 | + | 0.0588175i | ||||
\(436\) | − | 180.975i | − | 0.415080i | ||||||
\(437\) | 168.199 | + | 248.152i | 0.384894 | + | 0.567854i | ||||
\(438\) | − | 21.8665i | − | 0.0499235i | ||||||
\(439\) | 345.256 | 0.786460 | 0.393230 | − | 0.919440i | \(-0.371358\pi\) | ||||
0.393230 | + | 0.919440i | \(0.371358\pi\) | |||||||
\(440\) | 2.15600 | + | 1.03004i | 0.00490000 | + | 0.00234101i | ||||
\(441\) | −120.923 | −0.274201 | ||||||||
\(442\) | 0.815968 | 0.00184608 | ||||||||
\(443\) | − | 78.3990i | − | 0.176973i | −0.996077 | − | 0.0884864i | \(-0.971797\pi\) | ||
0.996077 | − | 0.0884864i | \(-0.0282030\pi\) | |||||||
\(444\) | − | 28.5205i | − | 0.0642353i | ||||||
\(445\) | −19.7478 | + | 41.3345i | −0.0443772 | + | 0.0928865i | ||||
\(446\) | 462.207 | 1.03634 | ||||||||
\(447\) | 239.100 | 0.534900 | ||||||||
\(448\) | 75.6022 | 0.168755 | ||||||||
\(449\) | 56.5141 | 0.125867 | 0.0629333 | − | 0.998018i | \(-0.479954\pi\) | ||||
0.0629333 | + | 0.998018i | \(0.479954\pi\) | |||||||
\(450\) | −82.5137 | + | 66.6445i | −0.183364 | + | 0.148099i | ||||
\(451\) | 3.75139i | 0.00831794i | ||||||||
\(452\) | −200.171 | −0.442856 | ||||||||
\(453\) | 192.360i | 0.424635i | ||||||||
\(454\) | − | 185.201i | − | 0.407931i | ||||||
\(455\) | 8.35175 | − | 17.4812i | 0.0183555 | − | 0.0384201i | ||||
\(456\) | − | 63.8536i | − | 0.140030i | ||||||
\(457\) | 312.960 | 0.684813 | 0.342407 | − | 0.939552i | \(-0.388758\pi\) | ||||
0.342407 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(458\) | 240.005 | 0.524029 | ||||||||
\(459\) | − | 7.31207i | − | 0.0159304i | ||||||
\(460\) | −227.418 | + | 34.3658i | −0.494387 | + | 0.0747083i | ||||
\(461\) | 101.113 | 0.219335 | 0.109667 | − | 0.993968i | \(-0.465021\pi\) | ||||
0.109667 | + | 0.993968i | \(0.465021\pi\) | |||||||
\(462\) | 3.91108i | 0.00846555i | ||||||||
\(463\) | − | 674.719i | − | 1.45728i | −0.684899 | − | 0.728638i | \(-0.740154\pi\) | ||
0.684899 | − | 0.728638i | \(-0.259846\pi\) | |||||||
\(464\) | 13.0969 | 0.0282261 | ||||||||
\(465\) | −173.096 | + | 362.309i | −0.372249 | + | 0.779158i | ||||
\(466\) | 89.4690 | 0.191994 | ||||||||
\(467\) | 205.659 | 0.440384 | 0.220192 | − | 0.975457i | \(-0.429332\pi\) | ||||
0.220192 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(468\) | − | 2.46009i | − | 0.00525660i | ||||||
\(469\) | 186.561 | 0.397786 | ||||||||
\(470\) | 158.302 | + | 75.6298i | 0.336812 | + | 0.160914i | ||||
\(471\) | 361.239i | 0.766961i | ||||||||
\(472\) | − | 195.335i | − | 0.413846i | ||||||
\(473\) | 4.66000i | 0.00985202i | ||||||||
\(474\) | − | 207.275i | − | 0.437290i | ||||||
\(475\) | 253.495 | − | 204.743i | 0.533674 | − | 0.431037i | ||||
\(476\) | −26.5970 | −0.0558761 | ||||||||
\(477\) | −17.7064 | −0.0371203 | ||||||||
\(478\) | 587.053i | 1.22814i | ||||||||
\(479\) | 647.140i | 1.35102i | 0.737349 | + | 0.675512i | \(0.236077\pi\) | ||||
−0.737349 | + | 0.675512i | \(0.763923\pi\) | |||||||
\(480\) | 44.2040 | + | 21.1188i | 0.0920917 | + | 0.0439975i | ||||
\(481\) | 3.37572i | 0.00701812i | ||||||||
\(482\) | 159.476 | 0.330862 | ||||||||
\(483\) | −211.226 | − | 311.632i | −0.437321 | − | 0.645202i | ||||
\(484\) | −241.943 | −0.499882 | ||||||||
\(485\) | 389.785 | + | 186.223i | 0.803680 | + | 0.383964i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | − | 605.672i | − | 1.24368i | −0.783144 | − | 0.621840i | \(-0.786385\pi\) | ||
0.783144 | − | 0.621840i | \(-0.213615\pi\) | |||||||
\(488\) | −301.293 | −0.617404 | ||||||||
\(489\) | 221.745 | 0.453466 | ||||||||
\(490\) | −122.867 | + | 257.175i | −0.250749 | + | 0.524846i | ||||
\(491\) | −276.372 | −0.562876 | −0.281438 | − | 0.959579i | \(-0.590811\pi\) | ||||
−0.281438 | + | 0.959579i | \(0.590811\pi\) | |||||||
\(492\) | 76.9140i | 0.156329i | ||||||||
\(493\) | −4.60752 | −0.00934589 | ||||||||
\(494\) | 7.55779i | 0.0152992i | ||||||||
\(495\) | −1.09253 | + | 2.28678i | −0.00220712 | + | 0.00461976i | ||||
\(496\) | 185.461 | 0.373913 | ||||||||
\(497\) | −97.4496 | −0.196076 | ||||||||
\(498\) | −149.015 | −0.299228 | ||||||||
\(499\) | 836.089 | 1.67553 | 0.837765 | − | 0.546031i | \(-0.183862\pi\) | ||||
0.837765 | + | 0.546031i | \(0.183862\pi\) | |||||||
\(500\) | 57.8969 | + | 243.204i | 0.115794 | + | 0.486407i | ||||
\(501\) | −542.356 | −1.08255 | ||||||||
\(502\) | −511.137 | −1.01820 | ||||||||
\(503\) | 395.531 | 0.786343 | 0.393172 | − | 0.919465i | \(-0.371378\pi\) | ||||
0.393172 | + | 0.919465i | \(0.371378\pi\) | |||||||
\(504\) | 80.1882i | 0.159104i | ||||||||
\(505\) | 289.885 | + | 138.495i | 0.574029 | + | 0.274247i | ||||
\(506\) | −4.54915 | + | 3.08343i | −0.00899041 | + | 0.00609374i | ||||
\(507\) | − | 292.425i | − | 0.576776i | ||||||
\(508\) | − | 316.827i | − | 0.623676i | ||||||
\(509\) | −7.74137 | −0.0152090 | −0.00760449 | − | 0.999971i | \(-0.502421\pi\) | ||||
−0.00760449 | + | 0.999971i | \(0.502421\pi\) | |||||||
\(510\) | −15.5511 | − | 7.42964i | −0.0304923 | − | 0.0145679i | ||||
\(511\) | − | 84.3622i | − | 0.165092i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 67.7270 | 0.132021 | ||||||||
\(514\) | 196.933 | 0.383139 | ||||||||
\(515\) | −336.356 | − | 160.697i | −0.653119 | − | 0.312032i | ||||
\(516\) | 95.5432i | 0.185161i | ||||||||
\(517\) | 4.19200 | 0.00810832 | ||||||||
\(518\) | − | 110.034i | − | 0.212420i | ||||||
\(519\) | 470.509 | 0.906568 | ||||||||
\(520\) | −5.23204 | − | 2.49964i | −0.0100616 | − | 0.00480701i | ||||
\(521\) | 186.274i | 0.357531i | 0.983892 | + | 0.178765i | \(0.0572103\pi\) | ||||
−0.983892 | + | 0.178765i | \(0.942790\pi\) | |||||||
\(522\) | 13.8914i | 0.0266118i | ||||||||
\(523\) | −561.122 | −1.07289 | −0.536445 | − | 0.843935i | \(-0.680233\pi\) | ||||
−0.536445 | + | 0.843935i | \(0.680233\pi\) | |||||||
\(524\) | 456.277 | 0.870757 | ||||||||
\(525\) | −318.343 | + | 257.118i | −0.606367 | + | 0.489749i | ||||
\(526\) | − | 14.2800i | − | 0.0271482i | ||||||
\(527\) | −65.2455 | −0.123805 | ||||||||
\(528\) | 1.17057 | 0.00221699 | ||||||||
\(529\) | 195.946 | − | 491.372i | 0.370408 | − | 0.928869i | ||||
\(530\) | −17.9911 | + | 37.6574i | −0.0339454 | + | 0.0710516i | ||||
\(531\) | 207.184 | 0.390177 | ||||||||
\(532\) | − | 246.351i | − | 0.463066i | ||||||
\(533\) | − | 9.10363i | − | 0.0170800i | ||||||
\(534\) | 22.4420i | 0.0420262i | ||||||||
\(535\) | 223.016 | + | 106.548i | 0.416853 | + | 0.199154i | ||||
\(536\) | − | 55.8371i | − | 0.104174i | ||||||
\(537\) | 411.425i | 0.766155i | ||||||||
\(538\) | 258.650i | 0.480762i | ||||||||
\(539\) | 6.81027i | 0.0126350i | ||||||||
\(540\) | −22.3999 | + | 46.8855i | −0.0414812 | + | 0.0868249i | ||||
\(541\) | −284.239 | −0.525396 | −0.262698 | − | 0.964878i | \(-0.584612\pi\) | ||||
−0.262698 | + | 0.964878i | \(0.584612\pi\) | |||||||
\(542\) | 188.077i | 0.347005i | ||||||||
\(543\) | 70.4974 | 0.129830 | ||||||||
\(544\) | 7.96037i | 0.0146330i | ||||||||
\(545\) | 195.039 | − | 408.239i | 0.357870 | − | 0.749063i | ||||
\(546\) | − | 9.49116i | − | 0.0173831i | ||||||
\(547\) | − | 588.955i | − | 1.07670i | −0.842721 | − | 0.538351i | \(-0.819048\pi\) | ||
0.842721 | − | 0.538351i | \(-0.180952\pi\) | |||||||
\(548\) | −38.3909 | −0.0700564 | ||||||||
\(549\) | − | 319.570i | − | 0.582094i | ||||||
\(550\) | 3.75336 | + | 4.64710i | 0.00682429 | + | 0.00844927i | ||||
\(551\) | − | 42.6765i | − | 0.0774529i | ||||||
\(552\) | −93.2703 | + | 63.2190i | −0.168968 | + | 0.114527i | ||||
\(553\) | − | 799.680i | − | 1.44608i | ||||||
\(554\) | 108.010 | 0.194964 | ||||||||
\(555\) | 30.7369 | − | 64.3359i | 0.0553819 | − | 0.115921i | ||||
\(556\) | −452.560 | −0.813956 | ||||||||
\(557\) | −29.3491 | −0.0526914 | −0.0263457 | − | 0.999653i | \(-0.508387\pi\) | ||||
−0.0263457 | + | 0.999653i | \(0.508387\pi\) | |||||||
\(558\) | 196.711i | 0.352528i | ||||||||
\(559\) | − | 11.3086i | − | 0.0202301i | ||||||
\(560\) | 170.542 | + | 81.4775i | 0.304539 | + | 0.145496i | ||||
\(561\) | −0.411809 | −0.000734063 | ||||||||
\(562\) | −551.213 | −0.980807 | ||||||||
\(563\) | 335.437 | 0.595802 | 0.297901 | − | 0.954597i | \(-0.403713\pi\) | ||||
0.297901 | + | 0.954597i | \(0.403713\pi\) | |||||||
\(564\) | 85.9478 | 0.152390 | ||||||||
\(565\) | −451.541 | − | 215.727i | −0.799188 | − | 0.381818i | ||||
\(566\) | − | 134.629i | − | 0.237860i | ||||||
\(567\) | −85.0524 | −0.150004 | ||||||||
\(568\) | 29.1663i | 0.0513490i | ||||||||
\(569\) | 874.221i | 1.53642i | 0.640200 | + | 0.768208i | \(0.278851\pi\) | ||||
−0.640200 | + | 0.768208i | \(0.721149\pi\) | |||||||
\(570\) | 68.8160 | − | 144.040i | 0.120730 | − | 0.252701i | ||||
\(571\) | 296.172i | 0.518689i | 0.965785 | + | 0.259345i | \(0.0835066\pi\) | ||||
−0.965785 | + | 0.259345i | \(0.916493\pi\) | |||||||
\(572\) | −0.138550 | −0.000242220 | ||||||||
\(573\) | 351.115 | 0.612766 | ||||||||
\(574\) | 296.739i | 0.516966i | ||||||||
\(575\) | −550.041 | − | 167.570i | −0.956593 | − | 0.291426i | ||||
\(576\) | 24.0000 | 0.0416667 | ||||||||
\(577\) | 309.659i | 0.536670i | 0.963326 | + | 0.268335i | \(0.0864734\pi\) | ||||
−0.963326 | + | 0.268335i | \(0.913527\pi\) | |||||||
\(578\) | 405.907i | 0.702262i | ||||||||
\(579\) | 320.443 | 0.553442 | ||||||||
\(580\) | 29.5437 | + | 14.1147i | 0.0509375 | + | 0.0243357i | ||||
\(581\) | −574.909 | −0.989517 | ||||||||
\(582\) | 211.629 | 0.363623 | ||||||||
\(583\) | 0.997208i | 0.00171048i | ||||||||
\(584\) | −25.2493 | −0.0432350 | ||||||||
\(585\) | 2.65127 | − | 5.54941i | 0.00453209 | − | 0.00948618i | ||||
\(586\) | − | 279.053i | − | 0.476200i | ||||||
\(587\) | 892.095i | 1.51975i | 0.650068 | + | 0.759876i | \(0.274740\pi\) | ||||
−0.650068 | + | 0.759876i | \(0.725260\pi\) | |||||||
\(588\) | 139.630i | 0.237465i | ||||||||
\(589\) | − | 604.327i | − | 1.02602i | ||||||
\(590\) | 210.515 | − | 440.633i | 0.356806 | − | 0.746835i | ||||
\(591\) | 93.7156 | 0.158571 | ||||||||
\(592\) | −32.9326 | −0.0556294 | ||||||||
\(593\) | 109.141i | 0.184049i | 0.995757 | + | 0.0920244i | \(0.0293338\pi\) | ||||
−0.995757 | + | 0.0920244i | \(0.970666\pi\) | |||||||
\(594\) | 1.24158i | 0.00209020i | ||||||||
\(595\) | −59.9969 | − | 28.6640i | −0.100835 | − | 0.0481747i | ||||
\(596\) | − | 276.089i | − | 0.463237i | ||||||
\(597\) | −70.0666 | −0.117364 | ||||||||
\(598\) | 11.0396 | − | 7.48268i | 0.0184608 | − | 0.0125128i | ||||
\(599\) | −184.005 | −0.307187 | −0.153594 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153594 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(600\) | 76.9544 | + | 95.2786i | 0.128257 | + | 0.158798i | ||||
\(601\) | 819.863 | 1.36417 | 0.682083 | − | 0.731275i | \(-0.261074\pi\) | ||||
0.682083 | + | 0.731275i | \(0.261074\pi\) | |||||||
\(602\) | 368.611i | 0.612311i | ||||||||
\(603\) | 59.2242 | 0.0982159 | ||||||||
\(604\) | 222.118 | 0.367745 | ||||||||
\(605\) | −545.769 | − | 260.745i | −0.902098 | − | 0.430984i | ||||
\(606\) | 157.389 | 0.259718 | ||||||||
\(607\) | 51.0051i | 0.0840281i | 0.999117 | + | 0.0420141i | \(0.0133774\pi\) | ||||
−0.999117 | + | 0.0420141i | \(0.986623\pi\) | |||||||
\(608\) | −73.7318 | −0.121269 | ||||||||
\(609\) | 53.5937i | 0.0880028i | ||||||||
\(610\) | −679.650 | − | 324.708i | −1.11418 | − | 0.532308i | ||||
\(611\) | −10.1729 | −0.0166496 | ||||||||
\(612\) | −8.44325 | −0.0137962 | ||||||||
\(613\) | 290.239 | 0.473474 | 0.236737 | − | 0.971574i | \(-0.423922\pi\) | ||||
0.236737 | + | 0.971574i | \(0.423922\pi\) | |||||||
\(614\) | −336.767 | −0.548481 | ||||||||
\(615\) | −82.8913 | + | 173.501i | −0.134783 | + | 0.282115i | ||||
\(616\) | 4.51613 | 0.00733138 | ||||||||
\(617\) | −901.299 | −1.46078 | −0.730388 | − | 0.683032i | \(-0.760661\pi\) | ||||
−0.730388 | + | 0.683032i | \(0.760661\pi\) | |||||||
\(618\) | −182.620 | −0.295502 | ||||||||
\(619\) | − | 898.463i | − | 1.45147i | −0.687972 | − | 0.725737i | \(-0.741499\pi\) | ||
0.687972 | − | 0.725737i | \(-0.258501\pi\) | |||||||
\(620\) | 418.358 | + | 199.874i | 0.674771 | + | 0.322377i | ||||
\(621\) | −67.0539 | − | 98.9281i | −0.107977 | − | 0.159305i | ||||
\(622\) | − | 69.1537i | − | 0.111180i | ||||||
\(623\) | 86.5826i | 0.138977i | ||||||||
\(624\) | −2.84067 | −0.00455235 | ||||||||
\(625\) | −131.501 | + | 611.009i | −0.210402 | + | 0.977615i | ||||
\(626\) | − | 546.383i | − | 0.872817i | ||||||
\(627\) | − | 3.81433i | − | 0.00608346i | ||||||
\(628\) | 417.123 | 0.664208 | ||||||||
\(629\) | 11.5858 | 0.0184193 | ||||||||
\(630\) | −86.4200 | + | 180.887i | −0.137175 | + | 0.287122i | ||||
\(631\) | 234.478i | 0.371598i | 0.982588 | + | 0.185799i | \(0.0594874\pi\) | ||||
−0.982588 | + | 0.185799i | \(0.940513\pi\) | |||||||
\(632\) | −239.341 | −0.378704 | ||||||||
\(633\) | 161.290i | 0.254803i | ||||||||
\(634\) | 461.435 | 0.727816 | ||||||||
\(635\) | 341.449 | − | 714.692i | 0.537716 | − | 1.12550i | ||||
\(636\) | 20.4456i | 0.0321471i | ||||||||
\(637\) | − | 16.5267i | − | 0.0259446i | ||||||
\(638\) | 0.782350 | 0.00122625 | ||||||||
\(639\) | −30.9355 | −0.0484123 | ||||||||
\(640\) | 24.3859 | − | 51.0424i | 0.0381029 | − | 0.0797538i | ||||
\(641\) | 859.266i | 1.34051i | 0.742132 | + | 0.670254i | \(0.233815\pi\) | ||||
−0.742132 | + | 0.670254i | \(0.766185\pi\) | |||||||
\(642\) | 121.084 | 0.188604 | ||||||||
\(643\) | 1213.71 | 1.88758 | 0.943789 | − | 0.330548i | \(-0.107234\pi\) | ||||
0.943789 | + | 0.330548i | \(0.107234\pi\) | |||||||
\(644\) | −359.842 | + | 243.903i | −0.558761 | + | 0.378731i | ||||
\(645\) | −102.968 | + | 215.524i | −0.159641 | + | 0.334146i | ||||
\(646\) | 25.9390 | 0.0401533 | ||||||||
\(647\) | 514.525i | 0.795247i | 0.917549 | + | 0.397624i | \(0.130165\pi\) | ||||
−0.917549 | + | 0.397624i | \(0.869835\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | − | 11.6684i | − | 0.0179791i | ||||||
\(650\) | −9.10841 | − | 11.2773i | −0.0140129 | − | 0.0173497i | ||||
\(651\) | 758.921i | 1.16578i | ||||||||
\(652\) | − | 256.049i | − | 0.392713i | ||||||
\(653\) | − | 129.367i | − | 0.198111i | −0.995082 | − | 0.0990556i | \(-0.968418\pi\) | ||
0.995082 | − | 0.0990556i | \(-0.0315822\pi\) | |||||||
\(654\) | − | 221.648i | − | 0.338912i | ||||||
\(655\) | 1029.26 | + | 491.736i | 1.57139 | + | 0.750742i | ||||
\(656\) | 88.8127 | 0.135385 | ||||||||
\(657\) | − | 26.7809i | − | 0.0407624i | ||||||
\(658\) | 331.591 | 0.503938 | ||||||||
\(659\) | − | 871.444i | − | 1.32237i | −0.750221 | − | 0.661187i | \(-0.770053\pi\) | ||
0.750221 | − | 0.661187i | \(-0.229947\pi\) | |||||||
\(660\) | 2.64055 | + | 1.26154i | 0.00400083 | + | 0.00191143i | ||||
\(661\) | 35.3844i | 0.0535317i | 0.999642 | + | 0.0267658i | \(0.00852085\pi\) | ||||
−0.999642 | + | 0.0267658i | \(0.991479\pi\) | |||||||
\(662\) | 64.6686i | 0.0976867i | ||||||||
\(663\) | 0.999353 | 0.00150732 | ||||||||
\(664\) | 172.068i | 0.259139i | ||||||||
\(665\) | 265.496 | − | 555.713i | 0.399242 | − | 0.835659i | ||||
\(666\) | − | 34.9303i | − | 0.0524479i | ||||||
\(667\) | −62.3372 | + | 42.2524i | −0.0934590 | + | 0.0633469i | ||||
\(668\) | 626.259i | 0.937513i | ||||||||
\(669\) | 566.086 | 0.846167 | ||||||||
\(670\) | 60.1764 | − | 125.956i | 0.0898156 | − | 0.187994i | ||||
\(671\) | −17.9979 | −0.0268225 | ||||||||
\(672\) | 92.5934 | 0.137788 | ||||||||
\(673\) | 1068.82i | 1.58815i | 0.607822 | + | 0.794074i | \(0.292044\pi\) | ||||
−0.607822 | + | 0.794074i | \(0.707956\pi\) | |||||||
\(674\) | 774.555i | 1.14919i | ||||||||
\(675\) | −101.058 | + | 81.6225i | −0.149716 | + | 0.120922i | ||||
\(676\) | −337.664 | −0.499503 | ||||||||
\(677\) | −870.438 | −1.28573 | −0.642864 | − | 0.765980i | \(-0.722254\pi\) | ||||
−0.642864 | + | 0.765980i | \(0.722254\pi\) | |||||||
\(678\) | −245.158 | −0.361591 | ||||||||
\(679\) | 816.475 | 1.20247 | ||||||||
\(680\) | −8.57901 | + | 17.9568i | −0.0126162 | + | 0.0264071i | ||||
\(681\) | − | 226.824i | − | 0.333074i | ||||||
\(682\) | 11.0786 | 0.0162443 | ||||||||
\(683\) | − | 711.510i | − | 1.04174i | −0.853635 | − | 0.520871i | \(-0.825607\pi\) | ||
0.853635 | − | 0.520871i | \(-0.174393\pi\) | |||||||
\(684\) | − | 78.2044i | − | 0.114334i | ||||||
\(685\) | −86.6013 | − | 41.3744i | −0.126425 | − | 0.0604006i | ||||
\(686\) | − | 116.171i | − | 0.169346i | ||||||
\(687\) | 293.945 | 0.427868 | ||||||||
\(688\) | 110.324 | 0.160354 | ||||||||
\(689\) | − | 2.41996i | − | 0.00351228i | ||||||
\(690\) | −278.529 | + | 42.0894i | −0.403665 | + | 0.0609991i | ||||
\(691\) | −958.657 | −1.38735 | −0.693674 | − | 0.720289i | \(-0.744009\pi\) | ||||
−0.693674 | + | 0.720289i | \(0.744009\pi\) | |||||||
\(692\) | − | 543.297i | − | 0.785111i | ||||||
\(693\) | 4.79008i | 0.00691209i | ||||||||
\(694\) | −608.461 | −0.876745 | ||||||||
\(695\) | −1020.87 | − | 487.730i | −1.46888 | − | 0.701770i | ||||
\(696\) | 16.0404 | 0.0230465 | ||||||||
\(697\) | −31.2445 | −0.0448271 | ||||||||
\(698\) | 46.3761i | 0.0664413i | ||||||||
\(699\) | 109.577 | 0.156762 | ||||||||
\(700\) | 296.895 | + | 367.590i | 0.424135 | + | 0.525129i | ||||
\(701\) | − | 94.5797i | − | 0.134921i | −0.997722 | − | 0.0674606i | \(-0.978510\pi\) | ||
0.997722 | − | 0.0674606i | \(-0.0214897\pi\) | |||||||
\(702\) | − | 3.01298i | − | 0.00429200i | ||||||
\(703\) | 107.312i | 0.152648i | ||||||||
\(704\) | − | 1.35166i | − | 0.00191997i | ||||||
\(705\) | 193.879 | + | 92.6272i | 0.275006 | + | 0.131386i | ||||
\(706\) | 323.185 | 0.457769 | ||||||||
\(707\) | 607.216 | 0.858863 | ||||||||
\(708\) | − | 239.236i | − | 0.337904i | ||||||
\(709\) | − | 340.569i | − | 0.480352i | −0.970729 | − | 0.240176i | \(-0.922795\pi\) | ||
0.970729 | − | 0.240176i | \(-0.0772051\pi\) | |||||||
\(710\) | −31.4329 | + | 65.7926i | −0.0442717 | + | 0.0926656i | ||||
\(711\) | − | 253.859i | − | 0.357046i | ||||||
\(712\) | 25.9138 | 0.0363958 | ||||||||
\(713\) | −882.734 | + | 598.321i | −1.23806 | + | 0.839160i | ||||
\(714\) | −32.5745 | −0.0456226 | ||||||||
\(715\) | −0.312538 | − | 0.149317i | −0.000437116 | − | 0.000208836i | ||||
\(716\) | 475.073 | 0.663510 | ||||||||
\(717\) | 718.990i | 1.00277i | ||||||||
\(718\) | −972.518 | −1.35448 | ||||||||
\(719\) | −1054.77 | −1.46700 | −0.733499 | − | 0.679690i | \(-0.762114\pi\) | ||||
−0.733499 | + | 0.679690i | \(0.762114\pi\) | |||||||
\(720\) | 54.1387 | + | 25.8651i | 0.0751926 | + | 0.0359238i | ||||
\(721\) | −704.559 | −0.977197 | ||||||||
\(722\) | − | 270.275i | − | 0.374342i | ||||||
\(723\) | 195.317 | 0.270148 | ||||||||
\(724\) | − | 81.4034i | − | 0.112436i | ||||||
\(725\) | 51.4324 | + | 63.6794i | 0.0709413 | + | 0.0878337i | ||||
\(726\) | −296.318 | −0.408152 | ||||||||
\(727\) | 230.764 | 0.317419 | 0.158709 | − | 0.987325i | \(-0.449267\pi\) | ||||
0.158709 | + | 0.987325i | \(0.449267\pi\) | |||||||
\(728\) | −10.9595 | −0.0150542 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −56.9567 | − | 27.2115i | −0.0780229 | − | 0.0372760i | ||||
\(731\) | −38.8121 | −0.0530946 | ||||||||
\(732\) | −369.007 | −0.504108 | ||||||||
\(733\) | −220.528 | −0.300857 | −0.150428 | − | 0.988621i | \(-0.548065\pi\) | ||||
−0.150428 | + | 0.988621i | \(0.548065\pi\) | |||||||
\(734\) | − | 842.657i | − | 1.14803i | ||||||
\(735\) | −150.481 | + | 314.973i | −0.204736 | + | 0.428535i | ||||
\(736\) | 72.9991 | + | 107.699i | 0.0991835 | + | 0.146331i | ||||
\(737\) | − | 3.33545i | − | 0.00452572i | ||||||
\(738\) | 94.2001i | 0.127642i | ||||||||
\(739\) | −839.593 | −1.13612 | −0.568060 | − | 0.822987i | \(-0.692306\pi\) | ||||
−0.568060 | + | 0.822987i | \(0.692306\pi\) | |||||||
\(740\) | −74.2887 | − | 35.4920i | −0.100390 | − | 0.0479621i | ||||
\(741\) | 9.25636i | 0.0124917i | ||||||||
\(742\) | 78.8802i | 0.106308i | ||||||||
\(743\) | −1143.07 | −1.53846 | −0.769229 | − | 0.638973i | \(-0.779360\pi\) | ||||
−0.769229 | + | 0.638973i | \(0.779360\pi\) | |||||||
\(744\) | 227.142 | 0.305298 | ||||||||
\(745\) | 297.545 | − | 622.796i | 0.399390 | − | 0.835967i | ||||
\(746\) | 111.833i | 0.149911i | ||||||||
\(747\) | −182.506 | −0.244318 | ||||||||
\(748\) | 0.475517i | 0.000635717i | ||||||||
\(749\) | 467.148 | 0.623695 | ||||||||
\(750\) | 70.9090 | + | 297.862i | 0.0945453 | + | 0.397150i | ||||
\(751\) | 672.056i | 0.894881i | 0.894314 | + | 0.447441i | \(0.147664\pi\) | ||||
−0.894314 | + | 0.447441i | \(0.852336\pi\) | |||||||
\(752\) | − | 99.2440i | − | 0.131973i | ||||||
\(753\) | −626.012 | −0.831357 | ||||||||
\(754\) | −1.89856 | −0.00251798 | ||||||||
\(755\) | 501.049 | + | 239.380i | 0.663641 | + | 0.317059i | ||||
\(756\) | 98.2101i | 0.129908i | ||||||||
\(757\) | 236.448 | 0.312349 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(758\) | −562.284 | −0.741800 | ||||||||
\(759\) | −5.57155 | + | 3.77642i | −0.00734064 | + | 0.00497552i | ||||
\(760\) | −166.323 | − | 79.4618i | −0.218846 | − | 0.104555i | ||||
\(761\) | 251.349 | 0.330288 | 0.165144 | − | 0.986269i | \(-0.447191\pi\) | ||||
0.165144 | + | 0.986269i | \(0.447191\pi\) | |||||||
\(762\) | − | 388.033i | − | 0.509229i | ||||||
\(763\) | − | 855.131i | − | 1.12075i | ||||||
\(764\) | − | 405.433i | − | 0.530671i | ||||||
\(765\) | −19.0461 | − | 9.09941i | −0.0248969 | − | 0.0118947i | ||||
\(766\) | − | 53.5220i | − | 0.0698721i | ||||||
\(767\) | 28.3162i | 0.0369181i | ||||||||
\(768\) | − | 27.7128i | − | 0.0360844i | ||||||
\(769\) | 770.703i | 1.00221i | 0.865385 | + | 0.501107i | \(0.167074\pi\) | ||||
−0.865385 | + | 0.501107i | \(0.832926\pi\) | |||||||
\(770\) | 10.1874 | + | 4.86710i | 0.0132304 | + | 0.00632091i | ||||
\(771\) | 241.193 | 0.312831 | ||||||||
\(772\) | − | 370.015i | − | 0.479294i | ||||||
\(773\) | −552.417 | −0.714640 | −0.357320 | − | 0.933982i | \(-0.616309\pi\) | ||||
−0.357320 | + | 0.933982i | \(0.616309\pi\) | |||||||
\(774\) | 117.016i | 0.151184i | ||||||||
\(775\) | 728.316 | + | 901.741i | 0.939763 | + | 1.16354i | ||||
\(776\) | − | 244.368i | − | 0.314907i | ||||||
\(777\) | − | 134.763i | − | 0.173440i | ||||||
\(778\) | 315.394 | 0.405391 | ||||||||
\(779\) | − | 289.398i | − | 0.371499i | ||||||
\(780\) | −6.40791 | − | 3.06143i | −0.00821527 | − | 0.00392491i | ||||
\(781\) | 1.74226i | 0.00223081i | ||||||||
\(782\) | −25.6812 | − | 37.8888i | −0.0328404 | − | 0.0484512i | ||||
\(783\) | 17.0134i | 0.0217285i | ||||||||
\(784\) | 161.230 | 0.205651 | ||||||||
\(785\) | 940.936 | + | 449.539i | 1.19864 | + | 0.572661i | ||||
\(786\) | 558.823 | 0.710970 | ||||||||
\(787\) | 805.038 | 1.02292 | 0.511460 | − | 0.859307i | \(-0.329105\pi\) | ||||
0.511460 | + | 0.859307i | \(0.329105\pi\) | |||||||
\(788\) | − | 108.213i | − | 0.137327i | ||||||
\(789\) | − | 17.4893i | − | 0.0221664i | ||||||
\(790\) | −539.900 | − | 257.941i | −0.683418 | − | 0.326508i | ||||
\(791\) | −945.835 | −1.19575 | ||||||||
\(792\) | 1.43365 | 0.00181017 | ||||||||
\(793\) | 43.6761 | 0.0550770 | ||||||||
\(794\) | 134.719 | 0.169672 | ||||||||
\(795\) | −22.0345 | + | 46.1207i | −0.0277163 | + | 0.0580134i | ||||
\(796\) | 80.9059i | 0.101641i | ||||||||
\(797\) | −1385.63 | −1.73855 | −0.869276 | − | 0.494327i | \(-0.835415\pi\) | ||||
−0.869276 | + | 0.494327i | \(0.835415\pi\) | |||||||
\(798\) | − | 301.717i | − | 0.378092i | ||||||
\(799\) | 34.9142i | 0.0436974i | ||||||||
\(800\) | 110.018 | − | 88.8593i | 0.137523 | − | 0.111074i | ||||
\(801\) | 27.4857i | 0.0343143i | ||||||||
\(802\) | 129.901 | 0.161971 | ||||||||
\(803\) | −1.50828 | −0.00187830 | ||||||||
\(804\) | − | 68.3862i | − | 0.0850575i | ||||||
\(805\) | −1074.58 | + | 162.383i | −1.33488 | + | 0.201718i | ||||
\(806\) | −26.8848 | −0.0333558 | ||||||||
\(807\) | 316.780i | 0.392540i | ||||||||
\(808\) | − | 181.737i | − | 0.224922i | ||||||
\(809\) | −802.124 | −0.991500 | −0.495750 | − | 0.868465i | \(-0.665107\pi\) | ||||
−0.495750 | + | 0.868465i | \(0.665107\pi\) | |||||||
\(810\) | −27.4341 | + | 57.4227i | −0.0338693 | + | 0.0708922i | ||||
\(811\) | −995.142 | −1.22706 | −0.613528 | − | 0.789673i | \(-0.710250\pi\) | ||||
−0.613528 | + | 0.789673i | \(0.710250\pi\) | |||||||
\(812\) | 61.8847 | 0.0762127 | ||||||||
\(813\) | 230.346i | 0.283328i | ||||||||
\(814\) | −1.96725 | −0.00241676 | ||||||||
\(815\) | 275.948 | − | 577.590i | 0.338586 | − | 0.708699i | ||||
\(816\) | 9.74943i | 0.0119478i | ||||||||
\(817\) | − | 359.492i | − | 0.440015i | ||||||
\(818\) | − | 126.311i | − | 0.154415i | ||||||
\(819\) | − | 11.6243i | − | 0.0141932i | ||||||
\(820\) | 200.342 | + | 95.7147i | 0.244319 | + | 0.116725i | ||||
\(821\) | −414.760 | −0.505189 | −0.252595 | − | 0.967572i | \(-0.581284\pi\) | ||||
−0.252595 | + | 0.967572i | \(0.581284\pi\) | |||||||
\(822\) | −47.0191 | −0.0572008 | ||||||||
\(823\) | − | 804.054i | − | 0.976979i | −0.872570 | − | 0.488489i | \(-0.837548\pi\) | ||
0.872570 | − | 0.488489i | \(-0.162452\pi\) | |||||||
\(824\) | 210.872i | 0.255912i | ||||||||
\(825\) | 4.59691 | + | 5.69151i | 0.00557201 | + | 0.00689880i | ||||
\(826\) | − | 922.985i | − | 1.11742i | ||||||
\(827\) | 1317.07 | 1.59259 | 0.796296 | − | 0.604907i | \(-0.206790\pi\) | ||||
0.796296 | + | 0.604907i | \(0.206790\pi\) | |||||||
\(828\) | −114.232 | + | 77.4272i | −0.137962 | + | 0.0935111i | ||||
\(829\) | −921.119 | −1.11112 | −0.555560 | − | 0.831476i | \(-0.687496\pi\) | ||||
−0.555560 | + | 0.831476i | \(0.687496\pi\) | |||||||
\(830\) | −185.440 | + | 388.147i | −0.223422 | + | 0.467647i | ||||
\(831\) | 132.285 | 0.159187 | ||||||||
\(832\) | 3.28012i | 0.00394245i | ||||||||
\(833\) | −56.7212 | −0.0680927 | ||||||||
\(834\) | −554.270 | −0.664592 | ||||||||
\(835\) | −674.928 | + | 1412.70i | −0.808297 | + | 1.69186i | ||||
\(836\) | −4.40440 | −0.00526843 | ||||||||
\(837\) | 240.920i | 0.287838i | ||||||||
\(838\) | 13.2036 | 0.0157561 | ||||||||
\(839\) | 703.790i | 0.838844i | 0.907791 | + | 0.419422i | \(0.137767\pi\) | ||||
−0.907791 | + | 0.419422i | \(0.862233\pi\) | |||||||
\(840\) | 208.870 | + | 99.7892i | 0.248655 | + | 0.118797i | ||||
\(841\) | −830.279 | −0.987253 | ||||||||
\(842\) | 1042.54 | 1.23817 | ||||||||
\(843\) | −675.096 | −0.800825 | ||||||||
\(844\) | 186.242 | 0.220666 | ||||||||
\(845\) | −761.694 | − | 363.905i | −0.901413 | − | 0.430657i | ||||
\(846\) | 105.264 | 0.124426 | ||||||||
\(847\) | −1143.21 | −1.34972 | ||||||||
\(848\) | 23.6085 | 0.0278402 | ||||||||
\(849\) | − | 164.886i | − | 0.194212i | ||||||
\(850\) | −38.7047 | + | 31.2609i | −0.0455349 | + | 0.0367775i | ||||
\(851\) | 156.749 | − | 106.245i | 0.184194 | − | 0.124847i | ||||
\(852\) | 35.7212i | 0.0419263i | ||||||||
\(853\) | − | 272.939i | − | 0.319976i | −0.987119 | − | 0.159988i | \(-0.948854\pi\) | ||
0.987119 | − | 0.159988i | \(-0.0511455\pi\) | |||||||
\(854\) | −1423.65 | −1.66704 | ||||||||
\(855\) | 84.2820 | − | 176.412i | 0.0985754 | − | 0.206330i | ||||
\(856\) | − | 139.815i | − | 0.163336i | ||||||
\(857\) | − | 66.8210i | − | 0.0779708i | −0.999240 | − | 0.0389854i | \(-0.987587\pi\) | ||
0.999240 | − | 0.0389854i | \(-0.0124126\pi\) | |||||||
\(858\) | −0.169689 | −0.000197772 | ||||||||
\(859\) | −1370.46 | −1.59541 | −0.797704 | − | 0.603049i | \(-0.793952\pi\) | ||||
−0.797704 | + | 0.603049i | \(0.793952\pi\) | |||||||
\(860\) | 248.866 | + | 118.897i | 0.289379 | + | 0.138253i | ||||
\(861\) | 363.429i | 0.422101i | ||||||||
\(862\) | 397.174 | 0.460758 | ||||||||
\(863\) | 1271.82i | 1.47372i | 0.676044 | + | 0.736861i | \(0.263693\pi\) | ||||
−0.676044 | + | 0.736861i | \(0.736307\pi\) | |||||||
\(864\) | 29.3939 | 0.0340207 | ||||||||
\(865\) | 585.518 | − | 1225.56i | 0.676900 | − | 1.41683i | ||||
\(866\) | − | 205.294i | − | 0.237060i | ||||||
\(867\) | 497.133i | 0.573394i | ||||||||
\(868\) | 876.327 | 1.00959 | ||||||||
\(869\) | −14.2971 | −0.0164524 | ||||||||
\(870\) | 36.1835 | + | 17.2869i | 0.0415903 | + | 0.0198701i | ||||
\(871\) | 8.09427i | 0.00929307i | ||||||||
\(872\) | −255.937 | −0.293506 | ||||||||
\(873\) | 259.191 | 0.296897 | ||||||||
\(874\) | 350.940 | − | 237.869i | 0.401533 | − | 0.272161i | ||||
\(875\) | 273.571 | + | 1149.17i | 0.312652 | + | 1.31334i | ||||
\(876\) | −30.9239 | −0.0353013 | ||||||||
\(877\) | 419.885i | 0.478774i | 0.970924 | + | 0.239387i | \(0.0769465\pi\) | ||||
−0.970924 | + | 0.239387i | \(0.923054\pi\) | |||||||
\(878\) | − | 488.266i | − | 0.556111i | ||||||
\(879\) | − | 341.769i | − | 0.388815i | ||||||
\(880\) | 1.45670 | − | 3.04904i | 0.00165534 | − | 0.00346482i | ||||
\(881\) | 723.901i | 0.821681i | 0.911707 | + | 0.410841i | \(0.134765\pi\) | ||||
−0.911707 | + | 0.410841i | \(0.865235\pi\) | |||||||
\(882\) | 171.011i | 0.193890i | ||||||||
\(883\) | − | 1279.17i | − | 1.44867i | −0.689449 | − | 0.724334i | \(-0.742147\pi\) | ||
0.689449 | − | 0.724334i | \(-0.257853\pi\) | |||||||
\(884\) | − | 1.15395i | − | 0.00130538i | ||||||
\(885\) | 257.828 | − | 539.663i | 0.291331 | − | 0.609788i | ||||
\(886\) | −110.873 | −0.125139 | ||||||||
\(887\) | − | 29.8132i | − | 0.0336112i | −0.999859 | − | 0.0168056i | \(-0.994650\pi\) | ||
0.999859 | − | 0.0168056i | \(-0.00534965\pi\) | |||||||
\(888\) | −40.3341 | −0.0454212 | ||||||||
\(889\) | − | 1497.05i | − | 1.68397i | ||||||
\(890\) | 58.4558 | + | 27.9277i | 0.0656807 | + | 0.0313794i | ||||
\(891\) | 1.52062i | 0.00170664i | ||||||||
\(892\) | − | 653.660i | − | 0.732802i | ||||||
\(893\) | −323.388 | −0.362137 | ||||||||
\(894\) | − | 338.139i | − | 0.378231i | ||||||
\(895\) | 1071.66 | + | 511.993i | 1.19738 | + | 0.572059i | ||||
\(896\) | − | 106.918i | − | 0.119328i | ||||||
\(897\) | 13.5207 | − | 9.16437i | 0.0150732 | − | 0.0102167i | ||||
\(898\) | − | 79.9231i | − | 0.0890012i | ||||||
\(899\) | 151.810 | 0.168866 | ||||||||
\(900\) | 94.2496 | + | 116.692i | 0.104722 | + | 0.129658i | ||||
\(901\) | −8.30553 | −0.00921812 | ||||||||
\(902\) | 5.30527 | 0.00588167 | ||||||||
\(903\) | 451.454i | 0.499950i | ||||||||
\(904\) | 283.085i | 0.313147i | ||||||||
\(905\) | 87.7296 | − | 183.628i | 0.0969388 | − | 0.202904i | ||||
\(906\) | 272.038 | 0.300262 | ||||||||
\(907\) | −981.810 | −1.08248 | −0.541240 | − | 0.840868i | \(-0.682045\pi\) | ||||
−0.541240 | + | 0.840868i | \(0.682045\pi\) | |||||||
\(908\) | −261.913 | −0.288451 | ||||||||
\(909\) | 192.762 | 0.212059 | ||||||||
\(910\) | −24.7221 | − | 11.8112i | −0.0271671 | − | 0.0129793i | ||||
\(911\) | − | 336.604i | − | 0.369488i | −0.982787 | − | 0.184744i | \(-0.940854\pi\) | ||
0.982787 | − | 0.184744i | \(-0.0591456\pi\) | |||||||
\(912\) | −90.3027 | −0.0990161 | ||||||||
\(913\) | 10.2786i | 0.0112580i | ||||||||
\(914\) | − | 442.592i | − | 0.484236i | ||||||
\(915\) | −832.398 | − | 397.684i | −0.909725 | − | 0.434628i | ||||
\(916\) | − | 339.419i | − | 0.370544i | ||||||
\(917\) | 2155.97 | 2.35111 | ||||||||
\(918\) | −10.3408 | −0.0112645 | ||||||||
\(919\) | − | 765.748i | − | 0.833240i | −0.909081 | − | 0.416620i | \(-0.863215\pi\) | ||
0.909081 | − | 0.416620i | \(-0.136785\pi\) | |||||||
\(920\) | 48.6006 | + | 321.618i | 0.0528268 | + | 0.349585i | ||||
\(921\) | −412.454 | −0.447833 | ||||||||
\(922\) | − | 142.996i | − | 0.155093i | ||||||
\(923\) | − | 4.22800i | − | 0.00458072i | ||||||
\(924\) | 5.53111 | 0.00598605 | ||||||||
\(925\) | −129.329 | − | 160.124i | −0.139815 | − | 0.173107i | ||||
\(926\) | −954.197 | −1.03045 | ||||||||
\(927\) | −223.663 | −0.241276 | ||||||||
\(928\) | − | 18.5218i | − | 0.0199589i | ||||||
\(929\) | 655.769 | 0.705887 | 0.352944 | − | 0.935645i | \(-0.385181\pi\) | ||||
0.352944 | + | 0.935645i | \(0.385181\pi\) | |||||||
\(930\) | 512.382 | + | 244.794i | 0.550948 | + | 0.263220i | ||||
\(931\) | − | 525.372i | − | 0.564309i | ||||||
\(932\) | − | 126.528i | − | 0.135760i | ||||||
\(933\) | − | 84.6956i | − | 0.0907778i | ||||||
\(934\) | − | 290.846i | − | 0.311398i | ||||||
\(935\) | −0.512471 | + | 1.07266i | −0.000548097 | + | 0.00114723i | ||||
\(936\) | −3.47909 | −0.00371698 | ||||||||
\(937\) | 1549.41 | 1.65359 | 0.826795 | − | 0.562503i | \(-0.190162\pi\) | ||||
0.826795 | + | 0.562503i | \(0.190162\pi\) | |||||||
\(938\) | − | 263.838i | − | 0.281277i | ||||||
\(939\) | − | 669.180i | − | 0.712652i | ||||||
\(940\) | 106.957 | − | 223.872i | 0.113784 | − | 0.238162i | ||||
\(941\) | − | 1106.87i | − | 1.17627i | −0.808762 | − | 0.588136i | \(-0.799862\pi\) | ||
0.808762 | − | 0.588136i | \(-0.200138\pi\) | |||||||
\(942\) | 510.869 | 0.542324 | ||||||||
\(943\) | −422.720 | + | 286.522i | −0.448271 | + | 0.303840i | ||||
\(944\) | −276.246 | −0.292633 | ||||||||
\(945\) | −105.842 | + | 221.540i | −0.112003 | + | 0.234434i | ||||
\(946\) | 6.59024 | 0.00696643 | ||||||||
\(947\) | 739.050i | 0.780411i | 0.920728 | + | 0.390206i | \(0.127596\pi\) | ||||
−0.920728 | + | 0.390206i | \(0.872404\pi\) | |||||||
\(948\) | −293.132 | −0.309211 | ||||||||
\(949\) | 3.66019 | 0.00385689 | ||||||||
\(950\) | −289.550 | − | 358.496i | −0.304789 | − | 0.377365i | ||||
\(951\) | 565.141 | 0.594259 | ||||||||
\(952\) | 37.6138i | 0.0395103i | ||||||||
\(953\) | 89.7360 | 0.0941616 | 0.0470808 | − | 0.998891i | \(-0.485008\pi\) | ||||
0.0470808 | + | 0.998891i | \(0.485008\pi\) | |||||||
\(954\) | 25.0406i | 0.0262480i | ||||||||
\(955\) | 436.941 | − | 914.566i | 0.457529 | − | 0.957661i | ||||
\(956\) | 830.218 | 0.868429 | ||||||||
\(957\) | 0.958180 | 0.00100123 | ||||||||
\(958\) | 915.195 | 0.955318 | ||||||||
\(959\) | −181.402 | −0.189158 | ||||||||
\(960\) | 29.8665 | − | 62.5139i | 0.0311109 | − | 0.0651187i | ||||
\(961\) | 1188.73 | 1.23697 | ||||||||
\(962\) | 4.77398 | 0.00496256 | ||||||||
\(963\) | 148.297 | 0.153994 | ||||||||
\(964\) | − | 225.533i | − | 0.233955i | ||||||
\(965\) | 398.771 | − | 834.672i | 0.413234 | − | 0.864945i | ||||
\(966\) | −440.715 | + | 298.719i | −0.456227 | + | 0.309232i | ||||
\(967\) | 1704.43i | 1.76260i | 0.472560 | + | 0.881299i | \(0.343330\pi\) | ||||
−0.472560 | + | 0.881299i | \(0.656670\pi\) | |||||||
\(968\) | 342.159i | 0.353470i | ||||||||
\(969\) | 31.7687 | 0.0327850 | ||||||||
\(970\) | 263.358 | − | 551.239i | 0.271503 | − | 0.568288i | ||||
\(971\) | 141.413i | 0.145637i | 0.997345 | + | 0.0728184i | \(0.0231994\pi\) | ||||
−0.997345 | + | 0.0728184i | \(0.976801\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −2138.41 | −2.19774 | ||||||||
\(974\) | −856.550 | −0.879414 | ||||||||
\(975\) | −11.1555 | − | 13.8118i | −0.0114415 | − | 0.0141659i | ||||
\(976\) | 426.093i | 0.436570i | ||||||||
\(977\) | 689.166 | 0.705390 | 0.352695 | − | 0.935738i | \(-0.385265\pi\) | ||||
0.352695 | + | 0.935738i | \(0.385265\pi\) | |||||||
\(978\) | − | 313.595i | − | 0.320649i | ||||||
\(979\) | 1.54797 | 0.00158118 | ||||||||
\(980\) | 363.700 | + | 173.760i | 0.371122 | + | 0.177306i | ||||
\(981\) | − | 271.463i | − | 0.276720i | ||||||
\(982\) | 390.849i | 0.398014i | ||||||||
\(983\) | −166.044 | −0.168915 | −0.0844577 | − | 0.996427i | \(-0.526916\pi\) | ||||
−0.0844577 | + | 0.996427i | \(0.526916\pi\) | |||||||
\(984\) | 108.773 | 0.110542 | ||||||||
\(985\) | 116.623 | − | 244.105i | 0.118399 | − | 0.247823i | ||||
\(986\) | 6.51602i | 0.00660854i | ||||||||
\(987\) | 406.115 | 0.411464 | ||||||||
\(988\) | 10.6883 | 0.0108181 | ||||||||
\(989\) | −525.106 | + | 355.919i | −0.530946 | + | 0.359878i | ||||
\(990\) | 3.23400 | + | 1.54507i | 0.00326666 | + | 0.00156067i | ||||
\(991\) | −694.830 | −0.701141 | −0.350570 | − | 0.936536i | \(-0.614012\pi\) | ||||
−0.350570 | + | 0.936536i | \(0.614012\pi\) | |||||||
\(992\) | − | 262.281i | − | 0.264396i | ||||||
\(993\) | 79.2026i | 0.0797609i | ||||||||
\(994\) | 137.815i | 0.138646i | ||||||||
\(995\) | −87.1935 | + | 182.506i | −0.0876316 | + | 0.183423i | ||||
\(996\) | 210.739i | 0.211586i | ||||||||
\(997\) | 302.519i | 0.303429i | 0.988424 | + | 0.151714i | \(0.0484794\pi\) | ||||
−0.988424 | + | 0.151714i | \(0.951521\pi\) | |||||||
\(998\) | − | 1182.41i | − | 1.18478i | ||||||
\(999\) | − | 42.7807i | − | 0.0428236i |
(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.f.a.229.33 | ✓ | 48 | |
5.4 | even | 2 | inner | 690.3.f.a.229.36 | yes | 48 | |
23.22 | odd | 2 | inner | 690.3.f.a.229.34 | yes | 48 | |
115.114 | odd | 2 | inner | 690.3.f.a.229.35 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.f.a.229.33 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.f.a.229.34 | yes | 48 | 23.22 | odd | 2 | inner | |
690.3.f.a.229.35 | yes | 48 | 115.114 | odd | 2 | inner | |
690.3.f.a.229.36 | yes | 48 | 5.4 | even | 2 | inner |