Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(311,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.311");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 311.32 | ||
Character | \(\chi\) | \(=\) | 403.311 |
Dual form | 403.2.c.b.311.1 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.71381i | 1.91895i | 0.281790 | + | 0.959476i | \(0.409072\pi\) | ||||
−0.281790 | + | 0.959476i | \(0.590928\pi\) | |||||||
\(3\) | 0.265781 | 0.153449 | 0.0767245 | − | 0.997052i | \(-0.475554\pi\) | ||||
0.0767245 | + | 0.997052i | \(0.475554\pi\) | |||||||
\(4\) | −5.36475 | −2.68238 | ||||||||
\(5\) | − | 0.954130i | − | 0.426700i | −0.976976 | − | 0.213350i | \(-0.931563\pi\) | ||
0.976976 | − | 0.213350i | \(-0.0684375\pi\) | |||||||
\(6\) | 0.721280i | 0.294461i | ||||||||
\(7\) | − | 4.28452i | − | 1.61940i | −0.586847 | − | 0.809698i | \(-0.699631\pi\) | ||
0.586847 | − | 0.809698i | \(-0.300369\pi\) | |||||||
\(8\) | − | 9.13130i | − | 3.22840i | ||||||
\(9\) | −2.92936 | −0.976453 | ||||||||
\(10\) | 2.58933 | 0.818817 | ||||||||
\(11\) | − | 0.0225126i | − | 0.00678782i | −0.999994 | − | 0.00339391i | \(-0.998920\pi\) | ||
0.999994 | − | 0.00339391i | \(-0.00108032\pi\) | |||||||
\(12\) | −1.42585 | −0.411608 | ||||||||
\(13\) | 0.755896 | − | 3.52543i | 0.209648 | − | 0.977777i | ||||
\(14\) | 11.6274 | 3.10754 | ||||||||
\(15\) | − | 0.253590i | − | 0.0654767i | ||||||
\(16\) | 14.0511 | 3.51277 | ||||||||
\(17\) | −4.73883 | −1.14933 | −0.574667 | − | 0.818387i | \(-0.694869\pi\) | ||||
−0.574667 | + | 0.818387i | \(0.694869\pi\) | |||||||
\(18\) | − | 7.94972i | − | 1.87377i | ||||||
\(19\) | 1.51732i | 0.348097i | 0.984737 | + | 0.174048i | \(0.0556849\pi\) | ||||
−0.984737 | + | 0.174048i | \(0.944315\pi\) | |||||||
\(20\) | 5.11868i | 1.14457i | ||||||||
\(21\) | − | 1.13875i | − | 0.248495i | ||||||
\(22\) | 0.0610950 | 0.0130255 | ||||||||
\(23\) | −7.63808 | −1.59265 | −0.796325 | − | 0.604869i | \(-0.793226\pi\) | ||||
−0.796325 | + | 0.604869i | \(0.793226\pi\) | |||||||
\(24\) | − | 2.42693i | − | 0.495395i | ||||||
\(25\) | 4.08964 | 0.817927 | ||||||||
\(26\) | 9.56733 | + | 2.05136i | 1.87631 | + | 0.402304i | ||||
\(27\) | −1.57591 | −0.303285 | ||||||||
\(28\) | 22.9854i | 4.34383i | ||||||||
\(29\) | −2.41622 | −0.448681 | −0.224341 | − | 0.974511i | \(-0.572023\pi\) | ||||
−0.224341 | + | 0.974511i | \(0.572023\pi\) | |||||||
\(30\) | 0.688195 | 0.125647 | ||||||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | 19.8694i | 3.51244i | ||||||||
\(33\) | − | 0.00598344i | − | 0.00104158i | ||||||
\(34\) | − | 12.8603i | − | 2.20552i | ||||||
\(35\) | −4.08799 | −0.690996 | ||||||||
\(36\) | 15.7153 | 2.61922 | ||||||||
\(37\) | 2.46547i | 0.405321i | 0.979249 | + | 0.202660i | \(0.0649587\pi\) | ||||
−0.979249 | + | 0.202660i | \(0.935041\pi\) | |||||||
\(38\) | −4.11771 | −0.667981 | ||||||||
\(39\) | 0.200903 | − | 0.936992i | 0.0321702 | − | 0.150039i | ||||
\(40\) | −8.71245 | −1.37756 | ||||||||
\(41\) | − | 6.00514i | − | 0.937845i | −0.883239 | − | 0.468922i | \(-0.844642\pi\) | ||
0.883239 | − | 0.468922i | \(-0.155358\pi\) | |||||||
\(42\) | 3.09034 | 0.476849 | ||||||||
\(43\) | 9.18930 | 1.40136 | 0.700678 | − | 0.713478i | \(-0.252881\pi\) | ||||
0.700678 | + | 0.713478i | \(0.252881\pi\) | |||||||
\(44\) | 0.120775i | 0.0182075i | ||||||||
\(45\) | 2.79499i | 0.416653i | ||||||||
\(46\) | − | 20.7283i | − | 3.05622i | ||||||
\(47\) | 6.05875i | 0.883759i | 0.897074 | + | 0.441880i | \(0.145688\pi\) | ||||
−0.897074 | + | 0.441880i | \(0.854312\pi\) | |||||||
\(48\) | 3.73452 | 0.539031 | ||||||||
\(49\) | −11.3571 | −1.62244 | ||||||||
\(50\) | 11.0985i | 1.56956i | ||||||||
\(51\) | −1.25949 | −0.176364 | ||||||||
\(52\) | −4.05519 | + | 18.9130i | −0.562354 | + | 2.62277i | ||||
\(53\) | −5.67923 | −0.780103 | −0.390051 | − | 0.920793i | \(-0.627543\pi\) | ||||
−0.390051 | + | 0.920793i | \(0.627543\pi\) | |||||||
\(54\) | − | 4.27673i | − | 0.581989i | ||||||
\(55\) | −0.0214800 | −0.00289636 | ||||||||
\(56\) | −39.1232 | −5.22806 | ||||||||
\(57\) | 0.403275i | 0.0534151i | ||||||||
\(58\) | − | 6.55717i | − | 0.860998i | ||||||
\(59\) | − | 8.26538i | − | 1.07606i | −0.842926 | − | 0.538030i | \(-0.819169\pi\) | ||
0.842926 | − | 0.538030i | \(-0.180831\pi\) | |||||||
\(60\) | 1.36045i | 0.175633i | ||||||||
\(61\) | 9.28373 | 1.18866 | 0.594330 | − | 0.804221i | \(-0.297417\pi\) | ||||
0.594330 | + | 0.804221i | \(0.297417\pi\) | |||||||
\(62\) | 2.71381 | 0.344654 | ||||||||
\(63\) | 12.5509i | 1.58126i | ||||||||
\(64\) | −25.8194 | −3.22743 | ||||||||
\(65\) | −3.36371 | − | 0.721223i | −0.417217 | − | 0.0894567i | ||||
\(66\) | 0.0162379 | 0.00199875 | ||||||||
\(67\) | − | 7.52898i | − | 0.919812i | −0.887968 | − | 0.459906i | \(-0.847883\pi\) | ||
0.887968 | − | 0.459906i | \(-0.152117\pi\) | |||||||
\(68\) | 25.4227 | 3.08295 | ||||||||
\(69\) | −2.03006 | −0.244391 | ||||||||
\(70\) | − | 11.0940i | − | 1.32599i | ||||||
\(71\) | 13.2469i | 1.57212i | 0.618151 | + | 0.786060i | \(0.287882\pi\) | ||||
−0.618151 | + | 0.786060i | \(0.712118\pi\) | |||||||
\(72\) | 26.7489i | 3.15238i | ||||||||
\(73\) | − | 1.76582i | − | 0.206673i | −0.994646 | − | 0.103337i | \(-0.967048\pi\) | ||
0.994646 | − | 0.103337i | \(-0.0329519\pi\) | |||||||
\(74\) | −6.69081 | −0.777791 | ||||||||
\(75\) | 1.08695 | 0.125510 | ||||||||
\(76\) | − | 8.14005i | − | 0.933727i | ||||||
\(77\) | −0.0964559 | −0.0109922 | ||||||||
\(78\) | 2.54282 | + | 0.545212i | 0.287917 | + | 0.0617331i | ||||
\(79\) | 10.0714 | 1.13312 | 0.566559 | − | 0.824021i | \(-0.308274\pi\) | ||||
0.566559 | + | 0.824021i | \(0.308274\pi\) | |||||||
\(80\) | − | 13.4066i | − | 1.49890i | ||||||
\(81\) | 8.36923 | 0.929915 | ||||||||
\(82\) | 16.2968 | 1.79968 | ||||||||
\(83\) | − | 13.3518i | − | 1.46555i | −0.680469 | − | 0.732777i | \(-0.738224\pi\) | ||
0.680469 | − | 0.732777i | \(-0.261776\pi\) | |||||||
\(84\) | 6.10909i | 0.666556i | ||||||||
\(85\) | 4.52146i | 0.490421i | ||||||||
\(86\) | 24.9380i | 2.68913i | ||||||||
\(87\) | −0.642187 | −0.0688497 | ||||||||
\(88\) | −0.205570 | −0.0219138 | ||||||||
\(89\) | − | 6.66565i | − | 0.706558i | −0.935518 | − | 0.353279i | \(-0.885067\pi\) | ||
0.935518 | − | 0.353279i | \(-0.114933\pi\) | |||||||
\(90\) | −7.58507 | −0.799537 | ||||||||
\(91\) | −15.1048 | − | 3.23865i | −1.58341 | − | 0.339503i | ||||
\(92\) | 40.9764 | 4.27209 | ||||||||
\(93\) | − | 0.265781i | − | 0.0275602i | ||||||
\(94\) | −16.4423 | −1.69589 | ||||||||
\(95\) | 1.44772 | 0.148533 | ||||||||
\(96\) | 5.28090i | 0.538980i | ||||||||
\(97\) | − | 10.9110i | − | 1.10784i | −0.832568 | − | 0.553922i | \(-0.813130\pi\) | ||
0.832568 | − | 0.553922i | \(-0.186870\pi\) | |||||||
\(98\) | − | 30.8210i | − | 3.11339i | ||||||
\(99\) | 0.0659476i | 0.00662799i | ||||||||
\(100\) | −21.9399 | −2.19399 | ||||||||
\(101\) | 14.9766 | 1.49022 | 0.745111 | − | 0.666940i | \(-0.232396\pi\) | ||||
0.745111 | + | 0.666940i | \(0.232396\pi\) | |||||||
\(102\) | − | 3.41802i | − | 0.338435i | ||||||
\(103\) | −15.9516 | −1.57176 | −0.785880 | − | 0.618379i | \(-0.787790\pi\) | ||||
−0.785880 | + | 0.618379i | \(0.787790\pi\) | |||||||
\(104\) | −32.1917 | − | 6.90231i | −3.15666 | − | 0.676827i | ||||
\(105\) | −1.08651 | −0.106033 | ||||||||
\(106\) | − | 15.4124i | − | 1.49698i | ||||||
\(107\) | 0.382486 | 0.0369763 | 0.0184882 | − | 0.999829i | \(-0.494115\pi\) | ||||
0.0184882 | + | 0.999829i | \(0.494115\pi\) | |||||||
\(108\) | 8.45439 | 0.813524 | ||||||||
\(109\) | − | 1.44742i | − | 0.138638i | −0.997595 | − | 0.0693188i | \(-0.977917\pi\) | ||
0.997595 | − | 0.0693188i | \(-0.0220826\pi\) | |||||||
\(110\) | − | 0.0582926i | − | 0.00555798i | ||||||
\(111\) | 0.655276i | 0.0621960i | ||||||||
\(112\) | − | 60.2021i | − | 5.68857i | ||||||
\(113\) | −3.43980 | −0.323589 | −0.161795 | − | 0.986824i | \(-0.551728\pi\) | ||||
−0.161795 | + | 0.986824i | \(0.551728\pi\) | |||||||
\(114\) | −1.09441 | −0.102501 | ||||||||
\(115\) | 7.28773i | 0.679584i | ||||||||
\(116\) | 12.9624 | 1.20353 | ||||||||
\(117\) | −2.21429 | + | 10.3272i | −0.204711 | + | 0.954754i | ||||
\(118\) | 22.4306 | 2.06491 | ||||||||
\(119\) | 20.3036i | 1.86123i | ||||||||
\(120\) | −2.31561 | −0.211385 | ||||||||
\(121\) | 10.9995 | 0.999954 | ||||||||
\(122\) | 25.1943i | 2.28098i | ||||||||
\(123\) | − | 1.59605i | − | 0.143911i | ||||||
\(124\) | 5.36475i | 0.481769i | ||||||||
\(125\) | − | 8.67270i | − | 0.775710i | ||||||
\(126\) | −34.0607 | −3.03437 | ||||||||
\(127\) | −16.2398 | −1.44105 | −0.720525 | − | 0.693429i | \(-0.756099\pi\) | ||||
−0.720525 | + | 0.693429i | \(0.756099\pi\) | |||||||
\(128\) | − | 30.3303i | − | 2.68085i | ||||||
\(129\) | 2.44235 | 0.215036 | ||||||||
\(130\) | 1.95726 | − | 9.12848i | 0.171663 | − | 0.800620i | ||||
\(131\) | −4.33413 | −0.378675 | −0.189338 | − | 0.981912i | \(-0.560634\pi\) | ||||
−0.189338 | + | 0.981912i | \(0.560634\pi\) | |||||||
\(132\) | 0.0320997i | 0.00279392i | ||||||||
\(133\) | 6.50098 | 0.563707 | ||||||||
\(134\) | 20.4322 | 1.76507 | ||||||||
\(135\) | 1.50363i | 0.129412i | ||||||||
\(136\) | 43.2717i | 3.71051i | ||||||||
\(137\) | − | 5.03448i | − | 0.430124i | −0.976600 | − | 0.215062i | \(-0.931005\pi\) | ||
0.976600 | − | 0.215062i | \(-0.0689954\pi\) | |||||||
\(138\) | − | 5.50919i | − | 0.468974i | ||||||
\(139\) | −6.21851 | −0.527447 | −0.263724 | − | 0.964598i | \(-0.584951\pi\) | ||||
−0.263724 | + | 0.964598i | \(0.584951\pi\) | |||||||
\(140\) | 21.9311 | 1.85351 | ||||||||
\(141\) | 1.61030i | 0.135612i | ||||||||
\(142\) | −35.9496 | −3.01682 | ||||||||
\(143\) | −0.0793666 | − | 0.0170172i | −0.00663697 | − | 0.00142305i | ||||
\(144\) | −41.1607 | −3.43006 | ||||||||
\(145\) | 2.30539i | 0.191452i | ||||||||
\(146\) | 4.79209 | 0.396596 | ||||||||
\(147\) | −3.01851 | −0.248962 | ||||||||
\(148\) | − | 13.2266i | − | 1.08722i | ||||||
\(149\) | 16.2180i | 1.32863i | 0.747451 | + | 0.664317i | \(0.231278\pi\) | ||||
−0.747451 | + | 0.664317i | \(0.768722\pi\) | |||||||
\(150\) | 2.94977i | 0.240848i | ||||||||
\(151\) | − | 12.8028i | − | 1.04187i | −0.853595 | − | 0.520937i | \(-0.825583\pi\) | ||
0.853595 | − | 0.520937i | \(-0.174417\pi\) | |||||||
\(152\) | 13.8551 | 1.12380 | ||||||||
\(153\) | 13.8817 | 1.12227 | ||||||||
\(154\) | − | 0.261763i | − | 0.0210934i | ||||||
\(155\) | −0.954130 | −0.0766376 | ||||||||
\(156\) | −1.07780 | + | 5.02673i | −0.0862927 | + | 0.402461i | ||||
\(157\) | −6.29883 | −0.502701 | −0.251351 | − | 0.967896i | \(-0.580875\pi\) | ||||
−0.251351 | + | 0.967896i | \(0.580875\pi\) | |||||||
\(158\) | 27.3318i | 2.17440i | ||||||||
\(159\) | −1.50943 | −0.119706 | ||||||||
\(160\) | 18.9580 | 1.49876 | ||||||||
\(161\) | 32.7255i | 2.57913i | ||||||||
\(162\) | 22.7125i | 1.78446i | ||||||||
\(163\) | 17.1448i | 1.34288i | 0.741058 | + | 0.671441i | \(0.234325\pi\) | ||||
−0.741058 | + | 0.671441i | \(0.765675\pi\) | |||||||
\(164\) | 32.2161i | 2.51565i | ||||||||
\(165\) | −0.00570898 | −0.000444444 | ||||||||
\(166\) | 36.2343 | 2.81233 | ||||||||
\(167\) | − | 1.18249i | − | 0.0915038i | −0.998953 | − | 0.0457519i | \(-0.985432\pi\) | ||
0.998953 | − | 0.0457519i | \(-0.0145684\pi\) | |||||||
\(168\) | −10.3982 | −0.802241 | ||||||||
\(169\) | −11.8572 | − | 5.32971i | −0.912096 | − | 0.409977i | ||||
\(170\) | −12.2704 | −0.941095 | ||||||||
\(171\) | − | 4.44478i | − | 0.339900i | ||||||
\(172\) | −49.2983 | −3.75896 | ||||||||
\(173\) | 24.0917 | 1.83166 | 0.915828 | − | 0.401571i | \(-0.131536\pi\) | ||||
0.915828 | + | 0.401571i | \(0.131536\pi\) | |||||||
\(174\) | − | 1.74277i | − | 0.132119i | ||||||
\(175\) | − | 17.5221i | − | 1.32455i | ||||||
\(176\) | − | 0.316327i | − | 0.0238441i | ||||||
\(177\) | − | 2.19678i | − | 0.165120i | ||||||
\(178\) | 18.0893 | 1.35585 | ||||||||
\(179\) | −15.1454 | −1.13202 | −0.566009 | − | 0.824399i | \(-0.691513\pi\) | ||||
−0.566009 | + | 0.824399i | \(0.691513\pi\) | |||||||
\(180\) | − | 14.9944i | − | 1.11762i | ||||||
\(181\) | 6.94767 | 0.516416 | 0.258208 | − | 0.966089i | \(-0.416868\pi\) | ||||
0.258208 | + | 0.966089i | \(0.416868\pi\) | |||||||
\(182\) | 8.78907 | − | 40.9914i | 0.651489 | − | 3.03848i | ||||
\(183\) | 2.46744 | 0.182399 | ||||||||
\(184\) | 69.7456i | 5.14172i | ||||||||
\(185\) | 2.35238 | 0.172950 | ||||||||
\(186\) | 0.721280 | 0.0528868 | ||||||||
\(187\) | 0.106684i | 0.00780148i | ||||||||
\(188\) | − | 32.5037i | − | 2.37058i | ||||||
\(189\) | 6.75203i | 0.491138i | ||||||||
\(190\) | 3.92884i | 0.285028i | ||||||||
\(191\) | 0.202104 | 0.0146237 | 0.00731187 | − | 0.999973i | \(-0.497673\pi\) | ||||
0.00731187 | + | 0.999973i | \(0.497673\pi\) | |||||||
\(192\) | −6.86233 | −0.495246 | ||||||||
\(193\) | − | 2.83360i | − | 0.203967i | −0.994786 | − | 0.101983i | \(-0.967481\pi\) | ||
0.994786 | − | 0.101983i | \(-0.0325189\pi\) | |||||||
\(194\) | 29.6104 | 2.12590 | ||||||||
\(195\) | −0.894013 | − | 0.191688i | −0.0640216 | − | 0.0137270i | ||||
\(196\) | 60.9281 | 4.35201 | ||||||||
\(197\) | − | 17.4170i | − | 1.24091i | −0.784241 | − | 0.620456i | \(-0.786947\pi\) | ||
0.784241 | − | 0.620456i | \(-0.213053\pi\) | |||||||
\(198\) | −0.178969 | −0.0127188 | ||||||||
\(199\) | 0.880069 | 0.0623865 | 0.0311932 | − | 0.999513i | \(-0.490069\pi\) | ||||
0.0311932 | + | 0.999513i | \(0.490069\pi\) | |||||||
\(200\) | − | 37.3437i | − | 2.64060i | ||||||
\(201\) | − | 2.00106i | − | 0.141144i | ||||||
\(202\) | 40.6435i | 2.85967i | ||||||||
\(203\) | 10.3524i | 0.726593i | ||||||||
\(204\) | 6.75687 | 0.473075 | ||||||||
\(205\) | −5.72968 | −0.400178 | ||||||||
\(206\) | − | 43.2897i | − | 3.01613i | ||||||
\(207\) | 22.3747 | 1.55515 | ||||||||
\(208\) | 10.6212 | − | 49.5360i | 0.736444 | − | 3.43471i | ||||
\(209\) | 0.0341589 | 0.00236282 | ||||||||
\(210\) | − | 2.94858i | − | 0.203472i | ||||||
\(211\) | −5.82491 | −0.401003 | −0.200502 | − | 0.979693i | \(-0.564257\pi\) | ||||
−0.200502 | + | 0.979693i | \(0.564257\pi\) | |||||||
\(212\) | 30.4677 | 2.09253 | ||||||||
\(213\) | 3.52078i | 0.241240i | ||||||||
\(214\) | 1.03799i | 0.0709558i | ||||||||
\(215\) | − | 8.76779i | − | 0.597958i | ||||||
\(216\) | 14.3901i | 0.979125i | ||||||||
\(217\) | −4.28452 | −0.290852 | ||||||||
\(218\) | 3.92802 | 0.266039 | ||||||||
\(219\) | − | 0.469321i | − | 0.0317138i | ||||||
\(220\) | 0.115235 | 0.00776914 | ||||||||
\(221\) | −3.58206 | + | 16.7064i | −0.240955 | + | 1.12379i | ||||
\(222\) | −1.77829 | −0.119351 | ||||||||
\(223\) | 13.5018i | 0.904151i | 0.891980 | + | 0.452075i | \(0.149316\pi\) | ||||
−0.891980 | + | 0.452075i | \(0.850684\pi\) | |||||||
\(224\) | 85.1306 | 5.68803 | ||||||||
\(225\) | −11.9800 | −0.798668 | ||||||||
\(226\) | − | 9.33496i | − | 0.620952i | ||||||
\(227\) | − | 12.9771i | − | 0.861322i | −0.902514 | − | 0.430661i | \(-0.858280\pi\) | ||
0.902514 | − | 0.430661i | \(-0.141720\pi\) | |||||||
\(228\) | − | 2.16347i | − | 0.143280i | ||||||
\(229\) | 20.8066i | 1.37494i | 0.726212 | + | 0.687470i | \(0.241279\pi\) | ||||
−0.726212 | + | 0.687470i | \(0.758721\pi\) | |||||||
\(230\) | −19.7775 | −1.30409 | ||||||||
\(231\) | −0.0256362 | −0.00168674 | ||||||||
\(232\) | 22.0633i | 1.44852i | ||||||||
\(233\) | 14.1051 | 0.924057 | 0.462028 | − | 0.886865i | \(-0.347122\pi\) | ||||
0.462028 | + | 0.886865i | \(0.347122\pi\) | |||||||
\(234\) | −28.0261 | − | 6.00916i | −1.83213 | − | 0.392831i | ||||
\(235\) | 5.78083 | 0.377100 | ||||||||
\(236\) | 44.3417i | 2.88640i | ||||||||
\(237\) | 2.67678 | 0.173876 | ||||||||
\(238\) | −55.1001 | −3.57161 | ||||||||
\(239\) | 23.8483i | 1.54262i | 0.636459 | + | 0.771310i | \(0.280398\pi\) | ||||
−0.636459 | + | 0.771310i | \(0.719602\pi\) | |||||||
\(240\) | − | 3.56322i | − | 0.230005i | ||||||
\(241\) | 16.4903i | 1.06224i | 0.847298 | + | 0.531118i | \(0.178228\pi\) | ||||
−0.847298 | + | 0.531118i | \(0.821772\pi\) | |||||||
\(242\) | 29.8505i | 1.91886i | ||||||||
\(243\) | 6.95213 | 0.445979 | ||||||||
\(244\) | −49.8049 | −3.18843 | ||||||||
\(245\) | 10.8362i | 0.692297i | ||||||||
\(246\) | 4.33138 | 0.276159 | ||||||||
\(247\) | 5.34920 | + | 1.14694i | 0.340361 | + | 0.0729777i | ||||
\(248\) | −9.13130 | −0.579838 | ||||||||
\(249\) | − | 3.54867i | − | 0.224888i | ||||||
\(250\) | 23.5360 | 1.48855 | ||||||||
\(251\) | −9.32651 | −0.588684 | −0.294342 | − | 0.955700i | \(-0.595100\pi\) | ||||
−0.294342 | + | 0.955700i | \(0.595100\pi\) | |||||||
\(252\) | − | 67.3325i | − | 4.24155i | ||||||
\(253\) | 0.171953i | 0.0108106i | ||||||||
\(254\) | − | 44.0717i | − | 2.76531i | ||||||
\(255\) | 1.20172i | 0.0752546i | ||||||||
\(256\) | 30.6717 | 1.91698 | ||||||||
\(257\) | 21.1698 | 1.32054 | 0.660269 | − | 0.751029i | \(-0.270442\pi\) | ||||
0.660269 | + | 0.751029i | \(0.270442\pi\) | |||||||
\(258\) | 6.62806i | 0.412645i | ||||||||
\(259\) | 10.5633 | 0.656375 | ||||||||
\(260\) | 18.0455 | + | 3.86918i | 1.11913 | + | 0.239957i | ||||
\(261\) | 7.07799 | 0.438116 | ||||||||
\(262\) | − | 11.7620i | − | 0.726659i | ||||||
\(263\) | −15.0683 | −0.929150 | −0.464575 | − | 0.885534i | \(-0.653793\pi\) | ||||
−0.464575 | + | 0.885534i | \(0.653793\pi\) | |||||||
\(264\) | −0.0546366 | −0.00336265 | ||||||||
\(265\) | 5.41873i | 0.332870i | ||||||||
\(266\) | 17.6424i | 1.08173i | ||||||||
\(267\) | − | 1.77161i | − | 0.108421i | ||||||
\(268\) | 40.3912i | 2.46728i | ||||||||
\(269\) | −3.39090 | −0.206747 | −0.103373 | − | 0.994643i | \(-0.532964\pi\) | ||||
−0.103373 | + | 0.994643i | \(0.532964\pi\) | |||||||
\(270\) | −4.08056 | −0.248335 | ||||||||
\(271\) | − | 21.0667i | − | 1.27971i | −0.768494 | − | 0.639857i | \(-0.778994\pi\) | ||
0.768494 | − | 0.639857i | \(-0.221006\pi\) | |||||||
\(272\) | −66.5857 | −4.03735 | ||||||||
\(273\) | −4.01456 | − | 0.860773i | −0.242972 | − | 0.0520963i | ||||
\(274\) | 13.6626 | 0.825388 | ||||||||
\(275\) | − | 0.0920685i | − | 0.00555194i | ||||||
\(276\) | 10.8908 | 0.655548 | ||||||||
\(277\) | −2.38224 | −0.143135 | −0.0715675 | − | 0.997436i | \(-0.522800\pi\) | ||||
−0.0715675 | + | 0.997436i | \(0.522800\pi\) | |||||||
\(278\) | − | 16.8758i | − | 1.01215i | ||||||
\(279\) | 2.92936i | 0.175376i | ||||||||
\(280\) | 37.3287i | 2.23081i | ||||||||
\(281\) | − | 6.89508i | − | 0.411326i | −0.978623 | − | 0.205663i | \(-0.934065\pi\) | ||
0.978623 | − | 0.205663i | \(-0.0659350\pi\) | |||||||
\(282\) | −4.37005 | −0.260233 | ||||||||
\(283\) | 8.31358 | 0.494191 | 0.247095 | − | 0.968991i | \(-0.420524\pi\) | ||||
0.247095 | + | 0.968991i | \(0.420524\pi\) | |||||||
\(284\) | − | 71.0664i | − | 4.21702i | ||||||
\(285\) | 0.384777 | 0.0227922 | ||||||||
\(286\) | 0.0461814 | − | 0.215386i | 0.00273077 | − | 0.0127360i | ||||
\(287\) | −25.7291 | −1.51874 | ||||||||
\(288\) | − | 58.2045i | − | 3.42973i | ||||||
\(289\) | 5.45650 | 0.320971 | ||||||||
\(290\) | −6.25639 | −0.367388 | ||||||||
\(291\) | − | 2.89994i | − | 0.169998i | ||||||
\(292\) | 9.47317i | 0.554375i | ||||||||
\(293\) | 8.52889i | 0.498263i | 0.968470 | + | 0.249132i | \(0.0801451\pi\) | ||||
−0.968470 | + | 0.249132i | \(0.919855\pi\) | |||||||
\(294\) | − | 8.19165i | − | 0.477747i | ||||||
\(295\) | −7.88625 | −0.459155 | ||||||||
\(296\) | 22.5129 | 1.30854 | ||||||||
\(297\) | 0.0354780i | 0.00205864i | ||||||||
\(298\) | −44.0127 | −2.54959 | ||||||||
\(299\) | −5.77359 | + | 26.9275i | −0.333895 | + | 1.55726i | ||||
\(300\) | −5.83122 | −0.336665 | ||||||||
\(301\) | − | 39.3717i | − | 2.26935i | ||||||
\(302\) | 34.7442 | 1.99931 | ||||||||
\(303\) | 3.98049 | 0.228673 | ||||||||
\(304\) | 21.3200i | 1.22279i | ||||||||
\(305\) | − | 8.85789i | − | 0.507201i | ||||||
\(306\) | 37.6724i | 2.15359i | ||||||||
\(307\) | − | 27.0437i | − | 1.54346i | −0.635949 | − | 0.771731i | \(-0.719391\pi\) | ||
0.635949 | − | 0.771731i | \(-0.280609\pi\) | |||||||
\(308\) | 0.517462 | 0.0294851 | ||||||||
\(309\) | −4.23965 | −0.241185 | ||||||||
\(310\) | − | 2.58933i | − | 0.147064i | ||||||
\(311\) | 13.0421 | 0.739547 | 0.369773 | − | 0.929122i | \(-0.379435\pi\) | ||||
0.369773 | + | 0.929122i | \(0.379435\pi\) | |||||||
\(312\) | −8.55596 | − | 1.83451i | −0.484386 | − | 0.103858i | ||||
\(313\) | 8.35791 | 0.472417 | 0.236208 | − | 0.971702i | \(-0.424095\pi\) | ||||
0.236208 | + | 0.971702i | \(0.424095\pi\) | |||||||
\(314\) | − | 17.0938i | − | 0.964660i | ||||||
\(315\) | 11.9752 | 0.674726 | ||||||||
\(316\) | −54.0304 | −3.03945 | ||||||||
\(317\) | − | 17.9533i | − | 1.00836i | −0.863599 | − | 0.504180i | \(-0.831795\pi\) | ||
0.863599 | − | 0.504180i | \(-0.168205\pi\) | |||||||
\(318\) | − | 4.09632i | − | 0.229710i | ||||||
\(319\) | 0.0543956i | 0.00304557i | ||||||||
\(320\) | 24.6351i | 1.37714i | ||||||||
\(321\) | 0.101658 | 0.00567398 | ||||||||
\(322\) | −88.8108 | −4.94923 | ||||||||
\(323\) | − | 7.19032i | − | 0.400080i | ||||||
\(324\) | −44.8989 | −2.49438 | ||||||||
\(325\) | 3.09134 | − | 14.4177i | 0.171477 | − | 0.799750i | ||||
\(326\) | −46.5277 | −2.57693 | ||||||||
\(327\) | − | 0.384697i | − | 0.0212738i | ||||||
\(328\) | −54.8347 | −3.02774 | ||||||||
\(329\) | 25.9588 | 1.43116 | ||||||||
\(330\) | − | 0.0154931i | − | 0.000852866i | ||||||
\(331\) | − | 21.7321i | − | 1.19450i | −0.802054 | − | 0.597252i | \(-0.796259\pi\) | ||
0.802054 | − | 0.597252i | \(-0.203741\pi\) | |||||||
\(332\) | 71.6293i | 3.93117i | ||||||||
\(333\) | − | 7.22225i | − | 0.395777i | ||||||
\(334\) | 3.20905 | 0.175591 | ||||||||
\(335\) | −7.18363 | −0.392484 | ||||||||
\(336\) | − | 16.0006i | − | 0.872905i | ||||||
\(337\) | 35.0375 | 1.90862 | 0.954308 | − | 0.298824i | \(-0.0965945\pi\) | ||||
0.954308 | + | 0.298824i | \(0.0965945\pi\) | |||||||
\(338\) | 14.4638 | − | 32.1783i | 0.786727 | − | 1.75027i | ||||
\(339\) | −0.914235 | −0.0496544 | ||||||||
\(340\) | − | 24.2565i | − | 1.31549i | ||||||
\(341\) | −0.0225126 | −0.00121913 | ||||||||
\(342\) | 12.0623 | 0.652253 | ||||||||
\(343\) | 18.6681i | 1.00798i | ||||||||
\(344\) | − | 83.9102i | − | 4.52414i | ||||||
\(345\) | 1.93694i | 0.104281i | ||||||||
\(346\) | 65.3802i | 3.51486i | ||||||||
\(347\) | −25.4611 | −1.36682 | −0.683412 | − | 0.730033i | \(-0.739504\pi\) | ||||
−0.683412 | + | 0.730033i | \(0.739504\pi\) | |||||||
\(348\) | 3.44518 | 0.184681 | ||||||||
\(349\) | − | 17.4958i | − | 0.936531i | −0.883588 | − | 0.468265i | \(-0.844879\pi\) | ||
0.883588 | − | 0.468265i | \(-0.155121\pi\) | |||||||
\(350\) | 47.5517 | 2.54174 | ||||||||
\(351\) | −1.19123 | + | 5.55577i | −0.0635829 | + | 0.296545i | ||||
\(352\) | 0.447312 | 0.0238418 | ||||||||
\(353\) | − | 32.1393i | − | 1.71060i | −0.518132 | − | 0.855301i | \(-0.673372\pi\) | ||
0.518132 | − | 0.855301i | \(-0.326628\pi\) | |||||||
\(354\) | 5.96165 | 0.316858 | ||||||||
\(355\) | 12.6393 | 0.670823 | ||||||||
\(356\) | 35.7596i | 1.89525i | ||||||||
\(357\) | 5.39632i | 0.285604i | ||||||||
\(358\) | − | 41.1016i | − | 2.17229i | ||||||
\(359\) | − | 11.0850i | − | 0.585042i | −0.956259 | − | 0.292521i | \(-0.905506\pi\) | ||
0.956259 | − | 0.292521i | \(-0.0944941\pi\) | |||||||
\(360\) | 25.5219 | 1.34512 | ||||||||
\(361\) | 16.6977 | 0.878829 | ||||||||
\(362\) | 18.8546i | 0.990978i | ||||||||
\(363\) | 2.92346 | 0.153442 | ||||||||
\(364\) | 81.0333 | + | 17.3746i | 4.24730 | + | 0.910674i | ||||
\(365\) | −1.68482 | −0.0881874 | ||||||||
\(366\) | 6.69617i | 0.350014i | ||||||||
\(367\) | −9.66148 | −0.504325 | −0.252163 | − | 0.967685i | \(-0.581142\pi\) | ||||
−0.252163 | + | 0.967685i | \(0.581142\pi\) | |||||||
\(368\) | −107.323 | −5.59462 | ||||||||
\(369\) | 17.5912i | 0.915762i | ||||||||
\(370\) | 6.38390i | 0.331883i | ||||||||
\(371\) | 24.3328i | 1.26330i | ||||||||
\(372\) | 1.42585i | 0.0739270i | ||||||||
\(373\) | −21.0438 | −1.08961 | −0.544804 | − | 0.838564i | \(-0.683396\pi\) | ||||
−0.544804 | + | 0.838564i | \(0.683396\pi\) | |||||||
\(374\) | −0.289519 | −0.0149707 | ||||||||
\(375\) | − | 2.30504i | − | 0.119032i | ||||||
\(376\) | 55.3242 | 2.85313 | ||||||||
\(377\) | −1.82641 | + | 8.51821i | −0.0940650 | + | 0.438710i | ||||
\(378\) | −18.3237 | −0.942471 | ||||||||
\(379\) | 4.22803i | 0.217179i | 0.994087 | + | 0.108590i | \(0.0346334\pi\) | ||||
−0.994087 | + | 0.108590i | \(0.965367\pi\) | |||||||
\(380\) | −7.76667 | −0.398422 | ||||||||
\(381\) | −4.31624 | −0.221128 | ||||||||
\(382\) | 0.548472i | 0.0280623i | ||||||||
\(383\) | 2.50461i | 0.127979i | 0.997951 | + | 0.0639897i | \(0.0203825\pi\) | ||||
−0.997951 | + | 0.0639897i | \(0.979618\pi\) | |||||||
\(384\) | − | 8.06123i | − | 0.411373i | ||||||
\(385\) | 0.0920315i | 0.00469036i | ||||||||
\(386\) | 7.68984 | 0.391403 | ||||||||
\(387\) | −26.9188 | −1.36836 | ||||||||
\(388\) | 58.5349i | 2.97166i | ||||||||
\(389\) | 11.6085 | 0.588575 | 0.294288 | − | 0.955717i | \(-0.404918\pi\) | ||||
0.294288 | + | 0.955717i | \(0.404918\pi\) | |||||||
\(390\) | 0.520203 | − | 2.42618i | 0.0263415 | − | 0.122854i | ||||
\(391\) | 36.1956 | 1.83049 | ||||||||
\(392\) | 103.705i | 5.23790i | ||||||||
\(393\) | −1.15193 | −0.0581073 | ||||||||
\(394\) | 47.2665 | 2.38125 | ||||||||
\(395\) | − | 9.60940i | − | 0.483501i | ||||||
\(396\) | − | 0.353793i | − | 0.0177788i | ||||||
\(397\) | − | 9.50682i | − | 0.477134i | −0.971126 | − | 0.238567i | \(-0.923322\pi\) | ||
0.971126 | − | 0.238567i | \(-0.0766776\pi\) | |||||||
\(398\) | 2.38834i | 0.119717i | ||||||||
\(399\) | 1.72784 | 0.0865002 | ||||||||
\(400\) | 57.4638 | 2.87319 | ||||||||
\(401\) | − | 30.7755i | − | 1.53685i | −0.639937 | − | 0.768427i | \(-0.721040\pi\) | ||
0.639937 | − | 0.768427i | \(-0.278960\pi\) | |||||||
\(402\) | 5.43050 | 0.270849 | ||||||||
\(403\) | −3.52543 | − | 0.755896i | −0.175614 | − | 0.0376538i | ||||
\(404\) | −80.3456 | −3.99734 | ||||||||
\(405\) | − | 7.98534i | − | 0.396795i | ||||||
\(406\) | −28.0943 | −1.39430 | ||||||||
\(407\) | 0.0555042 | 0.00275124 | ||||||||
\(408\) | 11.5008i | 0.569375i | ||||||||
\(409\) | − | 13.7197i | − | 0.678395i | −0.940715 | − | 0.339197i | \(-0.889845\pi\) | ||
0.940715 | − | 0.339197i | \(-0.110155\pi\) | |||||||
\(410\) | − | 15.5493i | − | 0.767923i | ||||||
\(411\) | − | 1.33807i | − | 0.0660021i | ||||||
\(412\) | 85.5766 | 4.21606 | ||||||||
\(413\) | −35.4132 | −1.74257 | ||||||||
\(414\) | 60.7206i | 2.98426i | ||||||||
\(415\) | −12.7394 | −0.625352 | ||||||||
\(416\) | 70.0479 | + | 15.0192i | 3.43438 | + | 0.736375i | ||||
\(417\) | −1.65276 | −0.0809362 | ||||||||
\(418\) | 0.0927006i | 0.00453414i | ||||||||
\(419\) | 8.82161 | 0.430964 | 0.215482 | − | 0.976508i | \(-0.430868\pi\) | ||||
0.215482 | + | 0.976508i | \(0.430868\pi\) | |||||||
\(420\) | 5.82887 | 0.284420 | ||||||||
\(421\) | − | 9.49222i | − | 0.462623i | −0.972880 | − | 0.231311i | \(-0.925698\pi\) | ||
0.972880 | − | 0.231311i | \(-0.0743016\pi\) | |||||||
\(422\) | − | 15.8077i | − | 0.769506i | ||||||
\(423\) | − | 17.7483i | − | 0.862949i | ||||||
\(424\) | 51.8588i | 2.51849i | ||||||||
\(425\) | −19.3801 | −0.940072 | ||||||||
\(426\) | −9.55473 | −0.462928 | ||||||||
\(427\) | − | 39.7763i | − | 1.92491i | ||||||
\(428\) | −2.05194 | −0.0991845 | ||||||||
\(429\) | −0.0210942 | − | 0.00452286i | −0.00101844 | − | 0.000218366i | ||||
\(430\) | 23.7941 | 1.14745 | ||||||||
\(431\) | 24.5182i | 1.18100i | 0.807038 | + | 0.590499i | \(0.201069\pi\) | ||||
−0.807038 | + | 0.590499i | \(0.798931\pi\) | |||||||
\(432\) | −22.1433 | −1.06537 | ||||||||
\(433\) | 24.3795 | 1.17160 | 0.585801 | − | 0.810455i | \(-0.300780\pi\) | ||||
0.585801 | + | 0.810455i | \(0.300780\pi\) | |||||||
\(434\) | − | 11.6274i | − | 0.558131i | ||||||
\(435\) | 0.612730i | 0.0293782i | ||||||||
\(436\) | 7.76505i | 0.371878i | ||||||||
\(437\) | − | 11.5894i | − | 0.554397i | ||||||
\(438\) | 1.27365 | 0.0608572 | ||||||||
\(439\) | 6.37491 | 0.304258 | 0.152129 | − | 0.988361i | \(-0.451387\pi\) | ||||
0.152129 | + | 0.988361i | \(0.451387\pi\) | |||||||
\(440\) | 0.196140i | 0.00935062i | ||||||||
\(441\) | 33.2691 | 1.58424 | ||||||||
\(442\) | −45.3379 | − | 9.72102i | −2.15651 | − | 0.462382i | ||||
\(443\) | 20.4425 | 0.971252 | 0.485626 | − | 0.874167i | \(-0.338592\pi\) | ||||
0.485626 | + | 0.874167i | \(0.338592\pi\) | |||||||
\(444\) | − | 3.51539i | − | 0.166833i | ||||||
\(445\) | −6.35990 | −0.301488 | ||||||||
\(446\) | −36.6414 | −1.73502 | ||||||||
\(447\) | 4.31045i | 0.203878i | ||||||||
\(448\) | 110.624i | 5.22649i | ||||||||
\(449\) | 0.809817i | 0.0382176i | 0.999817 | + | 0.0191088i | \(0.00608289\pi\) | ||||
−0.999817 | + | 0.0191088i | \(0.993917\pi\) | |||||||
\(450\) | − | 32.5115i | − | 1.53261i | ||||||
\(451\) | −0.135192 | −0.00636592 | ||||||||
\(452\) | 18.4537 | 0.867988 | ||||||||
\(453\) | − | 3.40273i | − | 0.159874i | ||||||
\(454\) | 35.2174 | 1.65284 | ||||||||
\(455\) | −3.09009 | + | 14.4119i | −0.144866 | + | 0.675640i | ||||
\(456\) | 3.68243 | 0.172445 | ||||||||
\(457\) | 3.62678i | 0.169654i | 0.996396 | + | 0.0848269i | \(0.0270337\pi\) | ||||
−0.996396 | + | 0.0848269i | \(0.972966\pi\) | |||||||
\(458\) | −56.4652 | −2.63845 | ||||||||
\(459\) | 7.46799 | 0.348576 | ||||||||
\(460\) | − | 39.0969i | − | 1.82290i | ||||||
\(461\) | 31.7766i | 1.47998i | 0.672615 | + | 0.739992i | \(0.265171\pi\) | ||||
−0.672615 | + | 0.739992i | \(0.734829\pi\) | |||||||
\(462\) | − | 0.0695717i | − | 0.00323677i | ||||||
\(463\) | − | 7.74173i | − | 0.359788i | −0.983686 | − | 0.179894i | \(-0.942424\pi\) | ||
0.983686 | − | 0.179894i | \(-0.0575756\pi\) | |||||||
\(464\) | −33.9506 | −1.57612 | ||||||||
\(465\) | −0.253590 | −0.0117600 | ||||||||
\(466\) | 38.2786i | 1.77322i | ||||||||
\(467\) | −12.1610 | −0.562746 | −0.281373 | − | 0.959598i | \(-0.590790\pi\) | ||||
−0.281373 | + | 0.959598i | \(0.590790\pi\) | |||||||
\(468\) | 11.8791 | − | 55.4031i | 0.549113 | − | 2.56101i | ||||
\(469\) | −32.2581 | −1.48954 | ||||||||
\(470\) | 15.6881i | 0.723637i | ||||||||
\(471\) | −1.67411 | −0.0771390 | ||||||||
\(472\) | −75.4736 | −3.47396 | ||||||||
\(473\) | − | 0.206875i | − | 0.00951214i | ||||||
\(474\) | 7.26427i | 0.333659i | ||||||||
\(475\) | 6.20528i | 0.284718i | ||||||||
\(476\) | − | 108.924i | − | 4.99252i | ||||||
\(477\) | 16.6365 | 0.761734 | ||||||||
\(478\) | −64.7198 | −2.96022 | ||||||||
\(479\) | 15.1807i | 0.693624i | 0.937935 | + | 0.346812i | \(0.112736\pi\) | ||||
−0.937935 | + | 0.346812i | \(0.887264\pi\) | |||||||
\(480\) | 5.03867 | 0.229983 | ||||||||
\(481\) | 8.69183 | + | 1.86364i | 0.396313 | + | 0.0849745i | ||||
\(482\) | −44.7516 | −2.03838 | ||||||||
\(483\) | 8.69783i | 0.395765i | ||||||||
\(484\) | −59.0096 | −2.68225 | ||||||||
\(485\) | −10.4105 | −0.472717 | ||||||||
\(486\) | 18.8667i | 0.855813i | ||||||||
\(487\) | − | 12.5401i | − | 0.568246i | −0.958788 | − | 0.284123i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284123i | \(-0.0917024\pi\) | |||||||
\(488\) | − | 84.7725i | − | 3.83747i | ||||||
\(489\) | 4.55676i | 0.206064i | ||||||||
\(490\) | −29.4073 | −1.32848 | ||||||||
\(491\) | −34.6948 | −1.56576 | −0.782878 | − | 0.622175i | \(-0.786249\pi\) | ||||
−0.782878 | + | 0.622175i | \(0.786249\pi\) | |||||||
\(492\) | 8.56244i | 0.386024i | ||||||||
\(493\) | 11.4501 | 0.515685 | ||||||||
\(494\) | −3.11256 | + | 14.5167i | −0.140041 | + | 0.653137i | ||||
\(495\) | 0.0629226 | 0.00282816 | ||||||||
\(496\) | − | 14.0511i | − | 0.630912i | ||||||
\(497\) | 56.7567 | 2.54588 | ||||||||
\(498\) | 9.63041 | 0.431549 | ||||||||
\(499\) | 26.7370i | 1.19691i | 0.801156 | + | 0.598456i | \(0.204219\pi\) | ||||
−0.801156 | + | 0.598456i | \(0.795781\pi\) | |||||||
\(500\) | 46.5269i | 2.08075i | ||||||||
\(501\) | − | 0.314284i | − | 0.0140412i | ||||||
\(502\) | − | 25.3104i | − | 1.12966i | ||||||
\(503\) | −4.00119 | −0.178404 | −0.0892021 | − | 0.996014i | \(-0.528432\pi\) | ||||
−0.0892021 | + | 0.996014i | \(0.528432\pi\) | |||||||
\(504\) | 114.606 | 5.10496 | ||||||||
\(505\) | − | 14.2896i | − | 0.635878i | ||||||
\(506\) | −0.466649 | −0.0207451 | ||||||||
\(507\) | −3.15143 | − | 1.41654i | −0.139960 | − | 0.0629106i | ||||
\(508\) | 87.1226 | 3.86544 | ||||||||
\(509\) | 20.2683i | 0.898379i | 0.893437 | + | 0.449189i | \(0.148287\pi\) | ||||
−0.893437 | + | 0.449189i | \(0.851713\pi\) | |||||||
\(510\) | −3.26124 | −0.144410 | ||||||||
\(511\) | −7.56567 | −0.334686 | ||||||||
\(512\) | 22.5766i | 0.997755i | ||||||||
\(513\) | − | 2.39116i | − | 0.105572i | ||||||
\(514\) | 57.4509i | 2.53405i | ||||||||
\(515\) | 15.2199i | 0.670670i | ||||||||
\(516\) | −13.1026 | −0.576809 | ||||||||
\(517\) | 0.136398 | 0.00599880 | ||||||||
\(518\) | 28.6669i | 1.25955i | ||||||||
\(519\) | 6.40312 | 0.281066 | ||||||||
\(520\) | −6.58570 | + | 30.7151i | −0.288802 | + | 1.34695i | ||||
\(521\) | −14.2096 | −0.622532 | −0.311266 | − | 0.950323i | \(-0.600753\pi\) | ||||
−0.311266 | + | 0.950323i | \(0.600753\pi\) | |||||||
\(522\) | 19.2083i | 0.840725i | ||||||||
\(523\) | −4.58600 | −0.200532 | −0.100266 | − | 0.994961i | \(-0.531969\pi\) | ||||
−0.100266 | + | 0.994961i | \(0.531969\pi\) | |||||||
\(524\) | 23.2516 | 1.01575 | ||||||||
\(525\) | − | 4.65705i | − | 0.203251i | ||||||
\(526\) | − | 40.8924i | − | 1.78299i | ||||||
\(527\) | 4.73883i | 0.206427i | ||||||||
\(528\) | − | 0.0840739i | − | 0.00365885i | ||||||
\(529\) | 35.3403 | 1.53654 | ||||||||
\(530\) | −14.7054 | −0.638761 | ||||||||
\(531\) | 24.2123i | 1.05072i | ||||||||
\(532\) | −34.8762 | −1.51207 | ||||||||
\(533\) | −21.1707 | − | 4.53926i | −0.917003 | − | 0.196617i | ||||
\(534\) | 4.80780 | 0.208054 | ||||||||
\(535\) | − | 0.364942i | − | 0.0157778i | ||||||
\(536\) | −68.7494 | −2.96952 | ||||||||
\(537\) | −4.02536 | −0.173707 | ||||||||
\(538\) | − | 9.20225i | − | 0.396737i | ||||||
\(539\) | 0.255678i | 0.0110129i | ||||||||
\(540\) | − | 8.06659i | − | 0.347131i | ||||||
\(541\) | − | 9.43063i | − | 0.405454i | −0.979235 | − | 0.202727i | \(-0.935020\pi\) | ||
0.979235 | − | 0.202727i | \(-0.0649805\pi\) | |||||||
\(542\) | 57.1711 | 2.45571 | ||||||||
\(543\) | 1.84656 | 0.0792435 | ||||||||
\(544\) | − | 94.1575i | − | 4.03697i | ||||||
\(545\) | −1.38103 | −0.0591567 | ||||||||
\(546\) | 2.33597 | − | 10.8948i | 0.0999704 | − | 0.466252i | ||||
\(547\) | 33.3713 | 1.42686 | 0.713428 | − | 0.700729i | \(-0.247142\pi\) | ||||
0.713428 | + | 0.700729i | \(0.247142\pi\) | |||||||
\(548\) | 27.0087i | 1.15376i | ||||||||
\(549\) | −27.1954 | −1.16067 | ||||||||
\(550\) | 0.249856 | 0.0106539 | ||||||||
\(551\) | − | 3.66618i | − | 0.156185i | ||||||
\(552\) | 18.5371i | 0.788991i | ||||||||
\(553\) | − | 43.1510i | − | 1.83497i | ||||||
\(554\) | − | 6.46494i | − | 0.274669i | ||||||
\(555\) | 0.625218 | 0.0265390 | ||||||||
\(556\) | 33.3608 | 1.41481 | ||||||||
\(557\) | − | 27.1006i | − | 1.14829i | −0.818754 | − | 0.574144i | \(-0.805335\pi\) | ||
0.818754 | − | 0.574144i | \(-0.194665\pi\) | |||||||
\(558\) | −7.94972 | −0.336539 | ||||||||
\(559\) | 6.94615 | − | 32.3962i | 0.293791 | − | 1.37021i | ||||
\(560\) | −57.4407 | −2.42731 | ||||||||
\(561\) | 0.0283545i | 0.00119713i | ||||||||
\(562\) | 18.7119 | 0.789315 | ||||||||
\(563\) | 40.6775 | 1.71435 | 0.857176 | − | 0.515023i | \(-0.172217\pi\) | ||||
0.857176 | + | 0.515023i | \(0.172217\pi\) | |||||||
\(564\) | − | 8.63888i | − | 0.363762i | ||||||
\(565\) | 3.28202i | 0.138076i | ||||||||
\(566\) | 22.5615i | 0.948329i | ||||||||
\(567\) | − | 35.8581i | − | 1.50590i | ||||||
\(568\) | 120.962 | 5.07543 | ||||||||
\(569\) | 29.6678 | 1.24374 | 0.621870 | − | 0.783120i | \(-0.286373\pi\) | ||||
0.621870 | + | 0.783120i | \(0.286373\pi\) | |||||||
\(570\) | 1.04421i | 0.0437372i | ||||||||
\(571\) | −31.9473 | −1.33695 | −0.668476 | − | 0.743733i | \(-0.733053\pi\) | ||||
−0.668476 | + | 0.743733i | \(0.733053\pi\) | |||||||
\(572\) | 0.425783 | + | 0.0912932i | 0.0178029 | + | 0.00381716i | ||||
\(573\) | 0.0537155 | 0.00224400 | ||||||||
\(574\) | − | 69.8239i | − | 2.91439i | ||||||
\(575\) | −31.2370 | −1.30267 | ||||||||
\(576\) | 75.6344 | 3.15143 | ||||||||
\(577\) | − | 3.17220i | − | 0.132061i | −0.997818 | − | 0.0660303i | \(-0.978967\pi\) | ||
0.997818 | − | 0.0660303i | \(-0.0210334\pi\) | |||||||
\(578\) | 14.8079i | 0.615927i | ||||||||
\(579\) | − | 0.753118i | − | 0.0312985i | ||||||
\(580\) | − | 12.3679i | − | 0.513547i | ||||||
\(581\) | −57.2062 | −2.37331 | ||||||||
\(582\) | 7.86988 | 0.326217 | ||||||||
\(583\) | 0.127855i | 0.00529520i | ||||||||
\(584\) | −16.1242 | −0.667224 | ||||||||
\(585\) | 9.85353 | + | 2.11272i | 0.407393 | + | 0.0873503i | ||||
\(586\) | −23.1458 | −0.956143 | ||||||||
\(587\) | 18.0414i | 0.744650i | 0.928102 | + | 0.372325i | \(0.121439\pi\) | ||||
−0.928102 | + | 0.372325i | \(0.878561\pi\) | |||||||
\(588\) | 16.1936 | 0.667811 | ||||||||
\(589\) | 1.51732 | 0.0625201 | ||||||||
\(590\) | − | 21.4018i | − | 0.881097i | ||||||
\(591\) | − | 4.62912i | − | 0.190417i | ||||||
\(592\) | 34.6425i | 1.42380i | ||||||||
\(593\) | 4.22088i | 0.173331i | 0.996237 | + | 0.0866653i | \(0.0276211\pi\) | ||||
−0.996237 | + | 0.0866653i | \(0.972379\pi\) | |||||||
\(594\) | −0.0962805 | −0.00395043 | ||||||||
\(595\) | 19.3723 | 0.794186 | ||||||||
\(596\) | − | 87.0058i | − | 3.56390i | ||||||
\(597\) | 0.233906 | 0.00957314 | ||||||||
\(598\) | −73.0760 | − | 15.6684i | −2.98830 | − | 0.640729i | ||||
\(599\) | 46.9779 | 1.91947 | 0.959733 | − | 0.280915i | \(-0.0906380\pi\) | ||||
0.959733 | + | 0.280915i | \(0.0906380\pi\) | |||||||
\(600\) | − | 9.92526i | − | 0.405197i | ||||||
\(601\) | −32.9398 | −1.34364 | −0.671821 | − | 0.740713i | \(-0.734488\pi\) | ||||
−0.671821 | + | 0.740713i | \(0.734488\pi\) | |||||||
\(602\) | 106.847 | 4.35477 | ||||||||
\(603\) | 22.0551i | 0.898153i | ||||||||
\(604\) | 68.6837i | 2.79470i | ||||||||
\(605\) | − | 10.4949i | − | 0.426680i | ||||||
\(606\) | 10.8023i | 0.438813i | ||||||||
\(607\) | −27.8658 | −1.13104 | −0.565518 | − | 0.824736i | \(-0.691324\pi\) | ||||
−0.565518 | + | 0.824736i | \(0.691324\pi\) | |||||||
\(608\) | −30.1482 | −1.22267 | ||||||||
\(609\) | 2.75146i | 0.111495i | ||||||||
\(610\) | 24.0386 | 0.973295 | ||||||||
\(611\) | 21.3597 | + | 4.57978i | 0.864119 | + | 0.185278i | ||||
\(612\) | −74.4721 | −3.01036 | ||||||||
\(613\) | 40.6326i | 1.64114i | 0.571548 | + | 0.820568i | \(0.306343\pi\) | ||||
−0.571548 | + | 0.820568i | \(0.693657\pi\) | |||||||
\(614\) | 73.3913 | 2.96183 | ||||||||
\(615\) | −1.52284 | −0.0614070 | ||||||||
\(616\) | 0.880767i | 0.0354871i | ||||||||
\(617\) | − | 14.7457i | − | 0.593641i | −0.954933 | − | 0.296820i | \(-0.904074\pi\) | ||
0.954933 | − | 0.296820i | \(-0.0959263\pi\) | |||||||
\(618\) | − | 11.5056i | − | 0.462823i | ||||||
\(619\) | 0.164280i | 0.00660296i | 0.999995 | + | 0.00330148i | \(0.00105090\pi\) | ||||
−0.999995 | + | 0.00330148i | \(0.998949\pi\) | |||||||
\(620\) | 5.11868 | 0.205571 | ||||||||
\(621\) | 12.0370 | 0.483027 | ||||||||
\(622\) | 35.3936i | 1.41916i | ||||||||
\(623\) | −28.5591 | −1.14420 | ||||||||
\(624\) | 2.82290 | − | 13.1658i | 0.113007 | − | 0.527052i | ||||
\(625\) | 12.1733 | 0.486932 | ||||||||
\(626\) | 22.6818i | 0.906545i | ||||||||
\(627\) | 0.00907879 | 0.000362572 | ||||||||
\(628\) | 33.7917 | 1.34843 | ||||||||
\(629\) | − | 11.6834i | − | 0.465849i | ||||||
\(630\) | 32.4984i | 1.29477i | ||||||||
\(631\) | 13.1950i | 0.525284i | 0.964893 | + | 0.262642i | \(0.0845938\pi\) | ||||
−0.964893 | + | 0.262642i | \(0.915406\pi\) | |||||||
\(632\) | − | 91.9647i | − | 3.65816i | ||||||
\(633\) | −1.54815 | −0.0615336 | ||||||||
\(634\) | 48.7219 | 1.93499 | ||||||||
\(635\) | 15.4949i | 0.614896i | ||||||||
\(636\) | 8.09775 | 0.321097 | ||||||||
\(637\) | −8.58478 | + | 40.0386i | −0.340142 | + | 1.58639i | ||||
\(638\) | −0.147619 | −0.00584430 | ||||||||
\(639\) | − | 38.8050i | − | 1.53510i | ||||||
\(640\) | −28.9391 | −1.14392 | ||||||||
\(641\) | −18.4650 | −0.729324 | −0.364662 | − | 0.931140i | \(-0.618816\pi\) | ||||
−0.364662 | + | 0.931140i | \(0.618816\pi\) | |||||||
\(642\) | 0.275880i | 0.0108881i | ||||||||
\(643\) | 26.0213i | 1.02618i | 0.858335 | + | 0.513090i | \(0.171499\pi\) | ||||
−0.858335 | + | 0.513090i | \(0.828501\pi\) | |||||||
\(644\) | − | 175.564i | − | 6.91820i | ||||||
\(645\) | − | 2.33032i | − | 0.0917561i | ||||||
\(646\) | 19.5131 | 0.767734 | ||||||||
\(647\) | 2.83219 | 0.111345 | 0.0556724 | − | 0.998449i | \(-0.482270\pi\) | ||||
0.0556724 | + | 0.998449i | \(0.482270\pi\) | |||||||
\(648\) | − | 76.4220i | − | 3.00214i | ||||||
\(649\) | −0.186076 | −0.00730410 | ||||||||
\(650\) | 39.1269 | + | 8.38930i | 1.53468 | + | 0.329055i | ||||
\(651\) | −1.13875 | −0.0446310 | ||||||||
\(652\) | − | 91.9776i | − | 3.60212i | ||||||
\(653\) | −9.50505 | −0.371961 | −0.185981 | − | 0.982553i | \(-0.559546\pi\) | ||||
−0.185981 | + | 0.982553i | \(0.559546\pi\) | |||||||
\(654\) | 1.04399 | 0.0408234 | ||||||||
\(655\) | 4.13533i | 0.161581i | ||||||||
\(656\) | − | 84.3787i | − | 3.29443i | ||||||
\(657\) | 5.17271i | 0.201807i | ||||||||
\(658\) | 70.4472i | 2.74632i | ||||||||
\(659\) | −5.62723 | −0.219206 | −0.109603 | − | 0.993975i | \(-0.534958\pi\) | ||||
−0.109603 | + | 0.993975i | \(0.534958\pi\) | |||||||
\(660\) | 0.0306273 | 0.00119217 | ||||||||
\(661\) | 39.1535i | 1.52289i | 0.648228 | + | 0.761447i | \(0.275511\pi\) | ||||
−0.648228 | + | 0.761447i | \(0.724489\pi\) | |||||||
\(662\) | 58.9767 | 2.29219 | ||||||||
\(663\) | −0.952045 | + | 4.44025i | −0.0369744 | + | 0.172445i | ||||
\(664\) | −121.920 | −4.73140 | ||||||||
\(665\) | − | 6.20279i | − | 0.240534i | ||||||
\(666\) | 19.5998 | 0.759476 | ||||||||
\(667\) | 18.4553 | 0.714593 | ||||||||
\(668\) | 6.34376i | 0.245448i | ||||||||
\(669\) | 3.58854i | 0.138741i | ||||||||
\(670\) | − | 19.4950i | − | 0.753158i | ||||||
\(671\) | − | 0.209001i | − | 0.00806841i | ||||||
\(672\) | 22.6261 | 0.872822 | ||||||||
\(673\) | −28.2120 | −1.08749 | −0.543747 | − | 0.839249i | \(-0.682995\pi\) | ||||
−0.543747 | + | 0.839249i | \(0.682995\pi\) | |||||||
\(674\) | 95.0852i | 3.66254i | ||||||||
\(675\) | −6.44491 | −0.248065 | ||||||||
\(676\) | 63.6112 | + | 28.5926i | 2.44658 | + | 1.09971i | ||||
\(677\) | 26.9041 | 1.03401 | 0.517004 | − | 0.855983i | \(-0.327047\pi\) | ||||
0.517004 | + | 0.855983i | \(0.327047\pi\) | |||||||
\(678\) | − | 2.48106i | − | 0.0952845i | ||||||
\(679\) | −46.7484 | −1.79404 | ||||||||
\(680\) | 41.2868 | 1.58328 | ||||||||
\(681\) | − | 3.44908i | − | 0.132169i | ||||||
\(682\) | − | 0.0610950i | − | 0.00233945i | ||||||
\(683\) | 0.580132i | 0.0221981i | 0.999938 | + | 0.0110991i | \(0.00353301\pi\) | ||||
−0.999938 | + | 0.0110991i | \(0.996467\pi\) | |||||||
\(684\) | 23.8451i | 0.911741i | ||||||||
\(685\) | −4.80355 | −0.183534 | ||||||||
\(686\) | −50.6616 | −1.93427 | ||||||||
\(687\) | 5.53002i | 0.210983i | ||||||||
\(688\) | 129.120 | 4.92264 | ||||||||
\(689\) | −4.29291 | + | 20.0217i | −0.163547 | + | 0.762767i | ||||
\(690\) | −5.25649 | −0.200111 | ||||||||
\(691\) | − | 25.1489i | − | 0.956708i | −0.878167 | − | 0.478354i | \(-0.841234\pi\) | ||
0.878167 | − | 0.478354i | \(-0.158766\pi\) | |||||||
\(692\) | −129.246 | −4.91319 | ||||||||
\(693\) | 0.282554 | 0.0107333 | ||||||||
\(694\) | − | 69.0965i | − | 2.62287i | ||||||
\(695\) | 5.93327i | 0.225062i | ||||||||
\(696\) | 5.86400i | 0.222274i | ||||||||
\(697\) | 28.4573i | 1.07790i | ||||||||
\(698\) | 47.4804 | 1.79716 | ||||||||
\(699\) | 3.74888 | 0.141796 | ||||||||
\(700\) | 94.0019i | 3.55294i | ||||||||
\(701\) | 14.5697 | 0.550289 | 0.275144 | − | 0.961403i | \(-0.411274\pi\) | ||||
0.275144 | + | 0.961403i | \(0.411274\pi\) | |||||||
\(702\) | −15.0773 | − | 3.23276i | −0.569055 | − | 0.122013i | ||||
\(703\) | −3.74090 | −0.141091 | ||||||||
\(704\) | 0.581264i | 0.0219072i | ||||||||
\(705\) | 1.53644 | 0.0578656 | ||||||||
\(706\) | 87.2198 | 3.28256 | ||||||||
\(707\) | − | 64.1673i | − | 2.41326i | ||||||
\(708\) | 11.7852i | 0.442915i | ||||||||
\(709\) | 16.7626i | 0.629531i | 0.949169 | + | 0.314766i | \(0.101926\pi\) | ||||
−0.949169 | + | 0.314766i | \(0.898074\pi\) | |||||||
\(710\) | 34.3006i | 1.28728i | ||||||||
\(711\) | −29.5027 | −1.10644 | ||||||||
\(712\) | −60.8661 | −2.28105 | ||||||||
\(713\) | 7.63808i | 0.286048i | ||||||||
\(714\) | −14.6446 | −0.548060 | ||||||||
\(715\) | −0.0162366 | + | 0.0757261i | −0.000607216 | + | 0.00283200i | ||||
\(716\) | 81.2512 | 3.03650 | ||||||||
\(717\) | 6.33845i | 0.236714i | ||||||||
\(718\) | 30.0825 | 1.12267 | ||||||||
\(719\) | −17.1883 | −0.641016 | −0.320508 | − | 0.947246i | \(-0.603854\pi\) | ||||
−0.320508 | + | 0.947246i | \(0.603854\pi\) | |||||||
\(720\) | 39.2727i | 1.46361i | ||||||||
\(721\) | 68.3451i | 2.54530i | ||||||||
\(722\) | 45.3145i | 1.68643i | ||||||||
\(723\) | 4.38282i | 0.162999i | ||||||||
\(724\) | −37.2726 | −1.38522 | ||||||||
\(725\) | −9.88147 | −0.366989 | ||||||||
\(726\) | 7.93371i | 0.294448i | ||||||||
\(727\) | 37.3532 | 1.38535 | 0.692676 | − | 0.721249i | \(-0.256431\pi\) | ||||
0.692676 | + | 0.721249i | \(0.256431\pi\) | |||||||
\(728\) | −29.5731 | + | 137.926i | −1.09605 | + | 5.11188i | ||||
\(729\) | −23.2600 | −0.861480 | ||||||||
\(730\) | − | 4.57227i | − | 0.169227i | ||||||
\(731\) | −43.5465 | −1.61063 | ||||||||
\(732\) | −13.2372 | −0.489262 | ||||||||
\(733\) | 2.21871i | 0.0819498i | 0.999160 | + | 0.0409749i | \(0.0130464\pi\) | ||||
−0.999160 | + | 0.0409749i | \(0.986954\pi\) | |||||||
\(734\) | − | 26.2194i | − | 0.967776i | ||||||
\(735\) | 2.88005i | 0.106232i | ||||||||
\(736\) | − | 151.764i | − | 5.59409i | ||||||
\(737\) | −0.169497 | −0.00624352 | ||||||||
\(738\) | −47.7392 | −1.75730 | ||||||||
\(739\) | − | 34.3388i | − | 1.26317i | −0.775306 | − | 0.631586i | \(-0.782404\pi\) | ||
0.775306 | − | 0.631586i | \(-0.217596\pi\) | |||||||
\(740\) | −12.6199 | −0.463918 | ||||||||
\(741\) | 1.42172 | + | 0.304834i | 0.0522281 | + | 0.0111984i | ||||
\(742\) | −66.0345 | −2.42420 | ||||||||
\(743\) | 25.2755i | 0.927268i | 0.886027 | + | 0.463634i | \(0.153455\pi\) | ||||
−0.886027 | + | 0.463634i | \(0.846545\pi\) | |||||||
\(744\) | −2.42693 | −0.0889756 | ||||||||
\(745\) | 15.4741 | 0.566928 | ||||||||
\(746\) | − | 57.1089i | − | 2.09090i | ||||||
\(747\) | 39.1123i | 1.43105i | ||||||||
\(748\) | − | 0.572331i | − | 0.0209265i | ||||||
\(749\) | − | 1.63877i | − | 0.0598793i | ||||||
\(750\) | 6.25544 | 0.228416 | ||||||||
\(751\) | −24.0110 | −0.876172 | −0.438086 | − | 0.898933i | \(-0.644343\pi\) | ||||
−0.438086 | + | 0.898933i | \(0.644343\pi\) | |||||||
\(752\) | 85.1320i | 3.10444i | ||||||||
\(753\) | −2.47881 | −0.0903330 | ||||||||
\(754\) | −23.1168 | − | 4.95653i | −0.841864 | − | 0.180506i | ||||
\(755\) | −12.2155 | −0.444567 | ||||||||
\(756\) | − | 36.2230i | − | 1.31742i | ||||||
\(757\) | 25.2359 | 0.917214 | 0.458607 | − | 0.888639i | \(-0.348349\pi\) | ||||
0.458607 | + | 0.888639i | \(0.348349\pi\) | |||||||
\(758\) | −11.4741 | −0.416756 | ||||||||
\(759\) | 0.0457020i | 0.00165888i | ||||||||
\(760\) | − | 13.2196i | − | 0.479524i | ||||||
\(761\) | − | 38.2689i | − | 1.38725i | −0.720338 | − | 0.693623i | \(-0.756013\pi\) | ||
0.720338 | − | 0.693623i | \(-0.243987\pi\) | |||||||
\(762\) | − | 11.7134i | − | 0.424333i | ||||||
\(763\) | −6.20149 | −0.224509 | ||||||||
\(764\) | −1.08424 | −0.0392264 | ||||||||
\(765\) | − | 13.2450i | − | 0.478873i | ||||||
\(766\) | −6.79702 | −0.245586 | ||||||||
\(767\) | −29.1390 | − | 6.24776i | −1.05215 | − | 0.225594i | ||||
\(768\) | 8.15198 | 0.294159 | ||||||||
\(769\) | 2.61840i | 0.0944220i | 0.998885 | + | 0.0472110i | \(0.0150333\pi\) | ||||
−0.998885 | + | 0.0472110i | \(0.984967\pi\) | |||||||
\(770\) | −0.249756 | −0.00900057 | ||||||||
\(771\) | 5.62655 | 0.202635 | ||||||||
\(772\) | 15.2016i | 0.547116i | ||||||||
\(773\) | 6.45442i | 0.232149i | 0.993240 | + | 0.116075i | \(0.0370312\pi\) | ||||
−0.993240 | + | 0.116075i | \(0.962969\pi\) | |||||||
\(774\) | − | 73.0524i | − | 2.62581i | ||||||
\(775\) | − | 4.08964i | − | 0.146904i | ||||||
\(776\) | −99.6316 | −3.57657 | ||||||||
\(777\) | 2.80754 | 0.100720 | ||||||||
\(778\) | 31.5033i | 1.12945i | ||||||||
\(779\) | 9.11171 | 0.326461 | ||||||||
\(780\) | 4.79616 | + | 1.02836i | 0.171730 | + | 0.0368211i | ||||
\(781\) | 0.298223 | 0.0106713 | ||||||||
\(782\) | 98.2278i | 3.51262i | ||||||||
\(783\) | 3.80776 | 0.136078 | ||||||||
\(784\) | −159.580 | −5.69927 | ||||||||
\(785\) | 6.00991i | 0.214503i | ||||||||
\(786\) | − | 3.12612i | − | 0.111505i | ||||||
\(787\) | 54.8881i | 1.95655i | 0.207316 | + | 0.978274i | \(0.433527\pi\) | ||||
−0.207316 | + | 0.978274i | \(0.566473\pi\) | |||||||
\(788\) | 93.4381i | 3.32860i | ||||||||
\(789\) | −4.00487 | −0.142577 | ||||||||
\(790\) | 26.0781 | 0.927816 | ||||||||
\(791\) | 14.7379i | 0.524019i | ||||||||
\(792\) | 0.602188 | 0.0213978 | ||||||||
\(793\) | 7.01753 | − | 32.7291i | 0.249200 | − | 1.16224i | ||||
\(794\) | 25.7997 | 0.915597 | ||||||||
\(795\) | 1.44020i | 0.0510785i | ||||||||
\(796\) | −4.72136 | −0.167344 | ||||||||
\(797\) | −27.5639 | −0.976363 | −0.488182 | − | 0.872742i | \(-0.662340\pi\) | ||||
−0.488182 | + | 0.872742i | \(0.662340\pi\) | |||||||
\(798\) | 4.68903i | 0.165990i | ||||||||
\(799\) | − | 28.7114i | − | 1.01574i | ||||||
\(800\) | 81.2584i | 2.87292i | ||||||||
\(801\) | 19.5261i | 0.689921i | ||||||||
\(802\) | 83.5187 | 2.94915 | ||||||||
\(803\) | −0.0397532 | −0.00140286 | ||||||||
\(804\) | 10.7352i | 0.378602i | ||||||||
\(805\) | 31.2244 | 1.10052 | ||||||||
\(806\) | 2.05136 | − | 9.56733i | 0.0722559 | − | 0.336995i | ||||
\(807\) | −0.901238 | −0.0317251 | ||||||||
\(808\) | − | 136.755i | − | 4.81104i | ||||||
\(809\) | 26.5683 | 0.934090 | 0.467045 | − | 0.884234i | \(-0.345319\pi\) | ||||
0.467045 | + | 0.884234i | \(0.345319\pi\) | |||||||
\(810\) | 21.6707 | 0.761430 | ||||||||
\(811\) | 1.96642i | 0.0690503i | 0.999404 | + | 0.0345251i | \(0.0109919\pi\) | ||||
−0.999404 | + | 0.0345251i | \(0.989008\pi\) | |||||||
\(812\) | − | 55.5378i | − | 1.94900i | ||||||
\(813\) | − | 5.59915i | − | 0.196371i | ||||||
\(814\) | 0.150628i | 0.00527950i | ||||||||
\(815\) | 16.3584 | 0.573008 | ||||||||
\(816\) | −17.6972 | −0.619527 | ||||||||
\(817\) | 13.9431i | 0.487807i | ||||||||
\(818\) | 37.2326 | 1.30181 | ||||||||
\(819\) | 44.2473 | + | 9.48717i | 1.54612 | + | 0.331509i | ||||
\(820\) | 30.7383 | 1.07343 | ||||||||
\(821\) | 36.5850i | 1.27683i | 0.769694 | + | 0.638413i | \(0.220409\pi\) | ||||
−0.769694 | + | 0.638413i | \(0.779591\pi\) | |||||||
\(822\) | 3.63127 | 0.126655 | ||||||||
\(823\) | −8.10139 | −0.282397 | −0.141198 | − | 0.989981i | \(-0.545096\pi\) | ||||
−0.141198 | + | 0.989981i | \(0.545096\pi\) | |||||||
\(824\) | 145.659i | 5.07427i | ||||||||
\(825\) | − | 0.0244701i | − | 0.000851939i | ||||||
\(826\) | − | 96.1045i | − | 3.34390i | ||||||
\(827\) | 3.67207i | 0.127690i | 0.997960 | + | 0.0638452i | \(0.0203364\pi\) | ||||
−0.997960 | + | 0.0638452i | \(0.979664\pi\) | |||||||
\(828\) | −120.035 | −4.17150 | ||||||||
\(829\) | 17.4359 | 0.605574 | 0.302787 | − | 0.953058i | \(-0.402083\pi\) | ||||
0.302787 | + | 0.953058i | \(0.402083\pi\) | |||||||
\(830\) | − | 34.5723i | − | 1.20002i | ||||||
\(831\) | −0.633155 | −0.0219639 | ||||||||
\(832\) | −19.5168 | + | 91.0245i | −0.676623 | + | 3.15571i | ||||
\(833\) | 53.8194 | 1.86473 | ||||||||
\(834\) | − | 4.48529i | − | 0.155313i | ||||||
\(835\) | −1.12825 | −0.0390447 | ||||||||
\(836\) | −0.183254 | −0.00633797 | ||||||||
\(837\) | 1.57591i | 0.0544715i | ||||||||
\(838\) | 23.9402i | 0.826999i | ||||||||
\(839\) | 11.9615i | 0.412957i | 0.978451 | + | 0.206479i | \(0.0662004\pi\) | ||||
−0.978451 | + | 0.206479i | \(0.933800\pi\) | |||||||
\(840\) | 9.92126i | 0.342316i | ||||||||
\(841\) | −23.1619 | −0.798685 | ||||||||
\(842\) | 25.7601 | 0.887751 | ||||||||
\(843\) | − | 1.83258i | − | 0.0631175i | ||||||
\(844\) | 31.2492 | 1.07564 | ||||||||
\(845\) | −5.08523 | + | 11.3134i | −0.174937 | + | 0.389191i | ||||
\(846\) | 48.1653 | 1.65596 | ||||||||
\(847\) | − | 47.1275i | − | 1.61932i | ||||||
\(848\) | −79.7994 | −2.74032 | ||||||||
\(849\) | 2.20959 | 0.0758331 | ||||||||
\(850\) | − | 52.5938i | − | 1.80395i | ||||||
\(851\) | − | 18.8315i | − | 0.645534i | ||||||
\(852\) | − | 18.8881i | − | 0.647097i | ||||||
\(853\) | − | 9.54956i | − | 0.326971i | −0.986546 | − | 0.163485i | \(-0.947726\pi\) | ||
0.986546 | − | 0.163485i | \(-0.0522736\pi\) | |||||||
\(854\) | 107.945 | 3.69381 | ||||||||
\(855\) | −4.24089 | −0.145036 | ||||||||
\(856\) | − | 3.49260i | − | 0.119374i | ||||||
\(857\) | 8.24273 | 0.281566 | 0.140783 | − | 0.990040i | \(-0.455038\pi\) | ||||
0.140783 | + | 0.990040i | \(0.455038\pi\) | |||||||
\(858\) | 0.0122742 | − | 0.0572456i | 0.000419033 | − | 0.00195433i | ||||
\(859\) | −38.2968 | −1.30667 | −0.653336 | − | 0.757068i | \(-0.726631\pi\) | ||||
−0.653336 | + | 0.757068i | \(0.726631\pi\) | |||||||
\(860\) | 47.0370i | 1.60395i | ||||||||
\(861\) | −6.83832 | −0.233049 | ||||||||
\(862\) | −66.5376 | −2.26628 | ||||||||
\(863\) | 16.9988i | 0.578647i | 0.957231 | + | 0.289324i | \(0.0934304\pi\) | ||||
−0.957231 | + | 0.289324i | \(0.906570\pi\) | |||||||
\(864\) | − | 31.3124i | − | 1.06527i | ||||||
\(865\) | − | 22.9866i | − | 0.781568i | ||||||
\(866\) | 66.1612i | 2.24825i | ||||||||
\(867\) | 1.45024 | 0.0492526 | ||||||||
\(868\) | 22.9854 | 0.780175 | ||||||||
\(869\) | − | 0.226733i | − | 0.00769140i | ||||||
\(870\) | −1.66283 | −0.0563753 | ||||||||
\(871\) | −26.5429 | − | 5.69113i | −0.899371 | − | 0.192836i | ||||
\(872\) | −13.2168 | −0.447578 | ||||||||
\(873\) | 31.9623i | 1.08176i | ||||||||
\(874\) | 31.4514 | 1.06386 | ||||||||
\(875\) | −37.1583 | −1.25618 | ||||||||
\(876\) | 2.51779i | 0.0850683i | ||||||||
\(877\) | − | 41.8776i | − | 1.41411i | −0.707160 | − | 0.707054i | \(-0.750024\pi\) | ||
0.707160 | − | 0.707054i | \(-0.249976\pi\) | |||||||
\(878\) | 17.3003i | 0.583857i | ||||||||
\(879\) | 2.26682i | 0.0764579i | ||||||||
\(880\) | −0.301817 | −0.0101743 | ||||||||
\(881\) | 32.4570 | 1.09350 | 0.546752 | − | 0.837294i | \(-0.315864\pi\) | ||||
0.546752 | + | 0.837294i | \(0.315864\pi\) | |||||||
\(882\) | 90.2858i | 3.04008i | ||||||||
\(883\) | 29.1513 | 0.981020 | 0.490510 | − | 0.871436i | \(-0.336811\pi\) | ||||
0.490510 | + | 0.871436i | \(0.336811\pi\) | |||||||
\(884\) | 19.2169 | − | 89.6257i | 0.646333 | − | 3.01444i | ||||
\(885\) | −2.09602 | −0.0704569 | ||||||||
\(886\) | 55.4770i | 1.86379i | ||||||||
\(887\) | 27.8071 | 0.933670 | 0.466835 | − | 0.884344i | \(-0.345394\pi\) | ||||
0.466835 | + | 0.884344i | \(0.345394\pi\) | |||||||
\(888\) | 5.98352 | 0.200794 | ||||||||
\(889\) | 69.5798i | 2.33363i | ||||||||
\(890\) | − | 17.2595i | − | 0.578541i | ||||||
\(891\) | − | 0.188414i | − | 0.00631209i | ||||||
\(892\) | − | 72.4341i | − | 2.42527i | ||||||
\(893\) | −9.19305 | −0.307634 | ||||||||
\(894\) | −11.6977 | −0.391231 | ||||||||
\(895\) | 14.4507i | 0.483032i | ||||||||
\(896\) | −129.951 | −4.34135 | ||||||||
\(897\) | −1.53451 | + | 7.15683i | −0.0512359 | + | 0.238959i | ||||
\(898\) | −2.19769 | −0.0733378 | ||||||||
\(899\) | 2.41622i | 0.0805856i | ||||||||
\(900\) | 64.2698 | 2.14233 | ||||||||
\(901\) | 26.9129 | 0.896599 | ||||||||
\(902\) | − | 0.366884i | − | 0.0122159i | ||||||
\(903\) | − | 10.4643i | − | 0.348229i | ||||||
\(904\) | 31.4098i | 1.04468i | ||||||||
\(905\) | − | 6.62898i | − | 0.220355i | ||||||
\(906\) | 9.23437 | 0.306791 | ||||||||
\(907\) | −52.4054 | −1.74009 | −0.870046 | − | 0.492971i | \(-0.835911\pi\) | ||||
−0.870046 | + | 0.492971i | \(0.835911\pi\) | |||||||
\(908\) | 69.6191i | 2.31039i | ||||||||
\(909\) | −43.8717 | −1.45513 | ||||||||
\(910\) | −39.1111 | − | 8.38592i | −1.29652 | − | 0.277991i | ||||
\(911\) | 37.7982 | 1.25231 | 0.626155 | − | 0.779698i | \(-0.284628\pi\) | ||||
0.626155 | + | 0.779698i | \(0.284628\pi\) | |||||||
\(912\) | 5.66646i | 0.187635i | ||||||||
\(913\) | −0.300585 | −0.00994791 | ||||||||
\(914\) | −9.84240 | −0.325558 | ||||||||
\(915\) | − | 2.35426i | − | 0.0778295i | ||||||
\(916\) | − | 111.622i | − | 3.68811i | ||||||
\(917\) | 18.5697i | 0.613225i | ||||||||
\(918\) | 20.2667i | 0.668900i | ||||||||
\(919\) | 31.9123 | 1.05269 | 0.526345 | − | 0.850271i | \(-0.323562\pi\) | ||||
0.526345 | + | 0.850271i | \(0.323562\pi\) | |||||||
\(920\) | 66.5464 | 2.19397 | ||||||||
\(921\) | − | 7.18770i | − | 0.236843i | ||||||
\(922\) | −86.2356 | −2.84002 | ||||||||
\(923\) | 46.7010 | + | 10.0133i | 1.53718 | + | 0.329591i | ||||
\(924\) | 0.137532 | 0.00452446 | ||||||||
\(925\) | 10.0829i | 0.331523i | ||||||||
\(926\) | 21.0096 | 0.690417 | ||||||||
\(927\) | 46.7281 | 1.53475 | ||||||||
\(928\) | − | 48.0088i | − | 1.57597i | ||||||
\(929\) | 32.3509i | 1.06140i | 0.847560 | + | 0.530699i | \(0.178071\pi\) | ||||
−0.847560 | + | 0.530699i | \(0.821929\pi\) | |||||||
\(930\) | − | 0.688195i | − | 0.0225668i | ||||||
\(931\) | − | 17.2324i | − | 0.564768i | ||||||
\(932\) | −75.6705 | −2.47867 | ||||||||
\(933\) | 3.46634 | 0.113483 | ||||||||
\(934\) | − | 33.0027i | − | 1.07988i | ||||||
\(935\) | 0.101790 | 0.00332889 | ||||||||
\(936\) | 94.3011 | + | 20.2193i | 3.08233 | + | 0.660890i | ||||
\(937\) | −54.2649 | −1.77276 | −0.886379 | − | 0.462960i | \(-0.846787\pi\) | ||||
−0.886379 | + | 0.462960i | \(0.846787\pi\) | |||||||
\(938\) | − | 87.5422i | − | 2.85836i | ||||||
\(939\) | 2.22138 | 0.0724919 | ||||||||
\(940\) | −31.0128 | −1.01152 | ||||||||
\(941\) | 1.34366i | 0.0438021i | 0.999760 | + | 0.0219010i | \(0.00697187\pi\) | ||||
−0.999760 | + | 0.0219010i | \(0.993028\pi\) | |||||||
\(942\) | − | 4.54322i | − | 0.148026i | ||||||
\(943\) | 45.8677i | 1.49366i | ||||||||
\(944\) | − | 116.138i | − | 3.77995i | ||||||
\(945\) | 6.44232 | 0.209569 | ||||||||
\(946\) | 0.561420 | 0.0182533 | ||||||||
\(947\) | − | 15.5470i | − | 0.505208i | −0.967570 | − | 0.252604i | \(-0.918713\pi\) | ||
0.967570 | − | 0.252604i | \(-0.0812871\pi\) | |||||||
\(948\) | −14.3603 | −0.466400 | ||||||||
\(949\) | −6.22525 | − | 1.33477i | −0.202080 | − | 0.0433285i | ||||
\(950\) | −16.8399 | −0.546360 | ||||||||
\(951\) | − | 4.77166i | − | 0.154732i | ||||||
\(952\) | 185.398 | 6.00879 | ||||||||
\(953\) | 19.1043 | 0.618849 | 0.309425 | − | 0.950924i | \(-0.399864\pi\) | ||||
0.309425 | + | 0.950924i | \(0.399864\pi\) | |||||||
\(954\) | 45.1483i | 1.46173i | ||||||||
\(955\) | − | 0.192834i | − | 0.00623995i | ||||||
\(956\) | − | 127.941i | − | 4.13789i | ||||||
\(957\) | 0.0144573i | 0.000467339i | ||||||||
\(958\) | −41.1975 | −1.33103 | ||||||||
\(959\) | −21.5703 | −0.696541 | ||||||||
\(960\) | 6.54755i | 0.211321i | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −5.05755 | + | 23.5879i | −0.163062 | + | 0.760506i | ||||
\(963\) | −1.12044 | −0.0361057 | ||||||||
\(964\) | − | 88.4666i | − | 2.84932i | ||||||
\(965\) | −2.70362 | −0.0870327 | ||||||||
\(966\) | −23.6042 | −0.759454 | ||||||||
\(967\) | − | 25.9054i | − | 0.833061i | −0.909122 | − | 0.416530i | \(-0.863246\pi\) | ||
0.909122 | − | 0.416530i | \(-0.136754\pi\) | |||||||
\(968\) | − | 100.440i | − | 3.22825i | ||||||
\(969\) | − | 1.91105i | − | 0.0613919i | ||||||
\(970\) | − | 28.2521i | − | 0.907122i | ||||||
\(971\) | −28.1587 | −0.903657 | −0.451828 | − | 0.892105i | \(-0.649228\pi\) | ||||
−0.451828 | + | 0.892105i | \(0.649228\pi\) | |||||||
\(972\) | −37.2965 | −1.19628 | ||||||||
\(973\) | 26.6433i | 0.854146i | ||||||||
\(974\) | 34.0314 | 1.09044 | ||||||||
\(975\) | 0.821620 | − | 3.83196i | 0.0263129 | − | 0.122721i | ||||
\(976\) | 130.447 | 4.17549 | ||||||||
\(977\) | − | 42.3816i | − | 1.35591i | −0.735104 | − | 0.677954i | \(-0.762867\pi\) | ||
0.735104 | − | 0.677954i | \(-0.237133\pi\) | |||||||
\(978\) | −12.3662 | −0.395427 | ||||||||
\(979\) | −0.150061 | −0.00479598 | ||||||||
\(980\) | − | 58.1333i | − | 1.85700i | ||||||
\(981\) | 4.24001i | 0.135373i | ||||||||
\(982\) | − | 94.1551i | − | 3.00461i | ||||||
\(983\) | − | 59.8132i | − | 1.90774i | −0.300214 | − | 0.953872i | \(-0.597058\pi\) | ||
0.300214 | − | 0.953872i | \(-0.402942\pi\) | |||||||
\(984\) | −14.5740 | −0.464604 | ||||||||
\(985\) | −16.6181 | −0.529497 | ||||||||
\(986\) | 31.0733i | 0.989575i | ||||||||
\(987\) | 6.89937 | 0.219609 | ||||||||
\(988\) | −28.6971 | − | 6.15303i | −0.912977 | − | 0.195754i | ||||
\(989\) | −70.1886 | −2.23187 | ||||||||
\(990\) | 0.170760i | 0.00542711i | ||||||||
\(991\) | −12.1016 | −0.384420 | −0.192210 | − | 0.981354i | \(-0.561566\pi\) | ||||
−0.192210 | + | 0.981354i | \(0.561566\pi\) | |||||||
\(992\) | 19.8694 | 0.630853 | ||||||||
\(993\) | − | 5.77598i | − | 0.183295i | ||||||
\(994\) | 154.027i | 4.88543i | ||||||||
\(995\) | − | 0.839701i | − | 0.0266203i | ||||||
\(996\) | 19.0377i | 0.603234i | ||||||||
\(997\) | −35.4880 | −1.12392 | −0.561958 | − | 0.827166i | \(-0.689952\pi\) | ||||
−0.561958 | + | 0.827166i | \(0.689952\pi\) | |||||||
\(998\) | −72.5590 | −2.29682 | ||||||||
\(999\) | − | 3.88537i | − | 0.122928i |
(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 | 403.2.c.b.311.32 | yes | 32 | |
13.5 | odd | 4 | 5239.2.a.l.1.16 | 16 | |||
13.8 | odd | 4 | 5239.2.a.k.1.1 | 16 | |||
13.12 | even | 2 | inner | 403.2.c.b.311.1 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.c.b.311.1 | ✓ | 32 | 13.12 | even | 2 | inner | |
403.2.c.b.311.32 | yes | 32 | 1.1 | even | 1 | trivial | |
5239.2.a.k.1.1 | 16 | 13.8 | odd | 4 | |||
5239.2.a.l.1.16 | 16 | 13.5 | odd | 4 |