Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1351,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1351");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.b (of order \(2\), degree \(1\), not 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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.153664.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 5x^{4} + 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1351.3 | ||
Root | \(1.80194i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.v.1351.4 |
$q$-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 \(\left(\mathbb{Z}/5070\mathbb{Z}\right)^\times\).
\(n\) | \(1691\) | \(1861\) | \(4057\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.00000i | − 0.707107i | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | − 1.19806i | − 0.452825i | −0.974032 | − | 0.226412i | \(-0.927300\pi\) | ||||
0.974032 | − | 0.226412i | \(-0.0726997\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 3.93900i | 1.18765i | 0.804593 | + | 0.593827i | \(0.202384\pi\) | ||||
−0.804593 | + | 0.593827i | \(0.797616\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.19806 | −0.320196 | ||||||||
\(15\) | − 1.00000i | − 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.74094 | −0.422240 | −0.211120 | − | 0.977460i | \(-0.567711\pi\) | ||||
−0.211120 | + | 0.977460i | \(0.567711\pi\) | |||||||
\(18\) | − 1.00000i | − 0.235702i | ||||||||
\(19\) | − 0.911854i | − 0.209194i | −0.994515 | − | 0.104597i | \(-0.966645\pi\) | ||||
0.994515 | − | 0.104597i | \(-0.0333552\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 1.19806i | 0.261439i | ||||||||
\(22\) | 3.93900 | 0.839798 | ||||||||
\(23\) | −1.24698 | −0.260013 | −0.130007 | − | 0.991513i | \(-0.541500\pi\) | ||||
−0.130007 | + | 0.991513i | \(0.541500\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.19806i | 0.226412i | ||||||||
\(29\) | −3.47219 | −0.644769 | −0.322385 | − | 0.946609i | \(-0.604484\pi\) | ||||
−0.322385 | + | 0.946609i | \(0.604484\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 2.15883i | 0.387738i | 0.981027 | + | 0.193869i | \(0.0621037\pi\) | ||||
−0.981027 | + | 0.193869i | \(0.937896\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | − 3.93900i | − 0.685692i | ||||||||
\(34\) | 1.74094i | 0.298569i | ||||||||
\(35\) | 1.19806 | 0.202509 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 4.80194i | 0.789434i | 0.918803 | + | 0.394717i | \(0.129157\pi\) | ||||
−0.918803 | + | 0.394717i | \(0.870843\pi\) | |||||||
\(38\) | −0.911854 | −0.147922 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | − 0.198062i | − 0.0309321i | −0.999880 | − | 0.0154661i | \(-0.995077\pi\) | ||||
0.999880 | − | 0.0154661i | \(-0.00492320\pi\) | |||||||
\(42\) | 1.19806 | 0.184865 | ||||||||
\(43\) | −3.43296 | −0.523522 | −0.261761 | − | 0.965133i | \(-0.584303\pi\) | ||||
−0.261761 | + | 0.965133i | \(0.584303\pi\) | |||||||
\(44\) | − 3.93900i | − 0.593827i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 1.24698i | 0.183857i | ||||||||
\(47\) | 0.902165i | 0.131594i | 0.997833 | + | 0.0657972i | \(0.0209590\pi\) | ||||
−0.997833 | + | 0.0657972i | \(0.979041\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 5.56465 | 0.794950 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 1.74094 | 0.243780 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.91185 | −0.949416 | −0.474708 | − | 0.880143i | \(-0.657446\pi\) | ||||
−0.474708 | + | 0.880143i | \(0.657446\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −3.93900 | −0.531135 | ||||||||
\(56\) | 1.19806 | 0.160098 | ||||||||
\(57\) | 0.911854i | 0.120778i | ||||||||
\(58\) | 3.47219i | 0.455921i | ||||||||
\(59\) | − 10.2446i | − 1.33373i | −0.745178 | − | 0.666866i | \(-0.767635\pi\) | ||||
0.745178 | − | 0.666866i | \(-0.232365\pi\) | |||||||
\(60\) | 1.00000i | 0.129099i | ||||||||
\(61\) | 9.92692 | 1.27101 | 0.635506 | − | 0.772096i | \(-0.280792\pi\) | ||||
0.635506 | + | 0.772096i | \(0.280792\pi\) | |||||||
\(62\) | 2.15883 | 0.274172 | ||||||||
\(63\) | − 1.19806i | − 0.150942i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3.93900 | −0.484858 | ||||||||
\(67\) | 9.16852i | 1.12011i | 0.828454 | + | 0.560057i | \(0.189221\pi\) | ||||
−0.828454 | + | 0.560057i | \(0.810779\pi\) | |||||||
\(68\) | 1.74094 | 0.211120 | ||||||||
\(69\) | 1.24698 | 0.150119 | ||||||||
\(70\) | − 1.19806i | − 0.143196i | ||||||||
\(71\) | − 11.0707i | − 1.31385i | −0.753956 | − | 0.656924i | \(-0.771857\pi\) | ||||
0.753956 | − | 0.656924i | \(-0.228143\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 4.13706i | 0.484207i | 0.970250 | + | 0.242103i | \(0.0778373\pi\) | ||||
−0.970250 | + | 0.242103i | \(0.922163\pi\) | |||||||
\(74\) | 4.80194 | 0.558214 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 0.911854i | 0.104597i | ||||||||
\(77\) | 4.71917 | 0.537799 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.73556 | 0.307775 | 0.153887 | − | 0.988088i | \(-0.450821\pi\) | ||||
0.153887 | + | 0.988088i | \(0.450821\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.198062 | −0.0218723 | ||||||||
\(83\) | − 15.5864i | − 1.71083i | −0.517942 | − | 0.855416i | \(-0.673302\pi\) | ||||
0.517942 | − | 0.855416i | \(-0.326698\pi\) | |||||||
\(84\) | − 1.19806i | − 0.130719i | ||||||||
\(85\) | − 1.74094i | − 0.188831i | ||||||||
\(86\) | 3.43296i | 0.370186i | ||||||||
\(87\) | 3.47219 | 0.372258 | ||||||||
\(88\) | −3.93900 | −0.419899 | ||||||||
\(89\) | 8.57673i | 0.909131i | 0.890713 | + | 0.454566i | \(0.150206\pi\) | ||||
−0.890713 | + | 0.454566i | \(0.849794\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.24698 | 0.130007 | ||||||||
\(93\) | − 2.15883i | − 0.223861i | ||||||||
\(94\) | 0.902165 | 0.0930512 | ||||||||
\(95\) | 0.911854 | 0.0935542 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | − 16.9976i | − 1.72585i | −0.505336 | − | 0.862923i | \(-0.668631\pi\) | ||||
0.505336 | − | 0.862923i | \(-0.331369\pi\) | |||||||
\(98\) | − 5.56465i | − 0.562114i | ||||||||
\(99\) | 3.93900i | 0.395885i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −6.67025 | −0.663715 | −0.331857 | − | 0.943330i | \(-0.607675\pi\) | ||||
−0.331857 | + | 0.943330i | \(0.607675\pi\) | |||||||
\(102\) | − 1.74094i | − 0.172379i | ||||||||
\(103\) | −10.0315 | −0.988429 | −0.494215 | − | 0.869340i | \(-0.664544\pi\) | ||||
−0.494215 | + | 0.869340i | \(0.664544\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.19806 | −0.116919 | ||||||||
\(106\) | 6.91185i | 0.671339i | ||||||||
\(107\) | −10.1032 | −0.976714 | −0.488357 | − | 0.872644i | \(-0.662404\pi\) | ||||
−0.488357 | + | 0.872644i | \(0.662404\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | − 10.5211i | − 1.00774i | −0.863780 | − | 0.503870i | \(-0.831909\pi\) | ||||
0.863780 | − | 0.503870i | \(-0.168091\pi\) | |||||||
\(110\) | 3.93900i | 0.375569i | ||||||||
\(111\) | − 4.80194i | − 0.455780i | ||||||||
\(112\) | − 1.19806i | − 0.113206i | ||||||||
\(113\) | −11.2131 | −1.05484 | −0.527421 | − | 0.849604i | \(-0.676841\pi\) | ||||
−0.527421 | + | 0.849604i | \(0.676841\pi\) | |||||||
\(114\) | 0.911854 | 0.0854030 | ||||||||
\(115\) | − 1.24698i | − 0.116281i | ||||||||
\(116\) | 3.47219 | 0.322385 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.2446 | −0.943091 | ||||||||
\(119\) | 2.08575i | 0.191201i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −4.51573 | −0.410521 | ||||||||
\(122\) | − 9.92692i | − 0.898741i | ||||||||
\(123\) | 0.198062i | 0.0178587i | ||||||||
\(124\) | − 2.15883i | − 0.193869i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | −1.19806 | −0.106732 | ||||||||
\(127\) | 9.32736 | 0.827669 | 0.413834 | − | 0.910352i | \(-0.364189\pi\) | ||||
0.413834 | + | 0.910352i | \(0.364189\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 3.43296 | 0.302255 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.62133 | 0.403768 | 0.201884 | − | 0.979409i | \(-0.435294\pi\) | ||||
0.201884 | + | 0.979409i | \(0.435294\pi\) | |||||||
\(132\) | 3.93900i | 0.342846i | ||||||||
\(133\) | −1.09246 | −0.0947281 | ||||||||
\(134\) | 9.16852 | 0.792040 | ||||||||
\(135\) | − 1.00000i | − 0.0860663i | ||||||||
\(136\) | − 1.74094i | − 0.149284i | ||||||||
\(137\) | 0.0760644i | 0.00649862i | 0.999995 | + | 0.00324931i | \(0.00103429\pi\) | ||||
−0.999995 | + | 0.00324931i | \(0.998966\pi\) | |||||||
\(138\) | − 1.24698i | − 0.106150i | ||||||||
\(139\) | 18.7017 | 1.58626 | 0.793129 | − | 0.609053i | \(-0.208451\pi\) | ||||
0.793129 | + | 0.609053i | \(0.208451\pi\) | |||||||
\(140\) | −1.19806 | −0.101255 | ||||||||
\(141\) | − 0.902165i | − 0.0759760i | ||||||||
\(142\) | −11.0707 | −0.929031 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 3.47219i | − 0.288350i | ||||||||
\(146\) | 4.13706 | 0.342386 | ||||||||
\(147\) | −5.56465 | −0.458964 | ||||||||
\(148\) | − 4.80194i | − 0.394717i | ||||||||
\(149\) | − 13.6799i | − 1.12070i | −0.828254 | − | 0.560352i | \(-0.810666\pi\) | ||||
0.828254 | − | 0.560352i | \(-0.189334\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | − 1.15883i | − 0.0943045i | −0.998888 | − | 0.0471523i | \(-0.984985\pi\) | ||||
0.998888 | − | 0.0471523i | \(-0.0150146\pi\) | |||||||
\(152\) | 0.911854 | 0.0739611 | ||||||||
\(153\) | −1.74094 | −0.140747 | ||||||||
\(154\) | − 4.71917i | − 0.380281i | ||||||||
\(155\) | −2.15883 | −0.173402 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.2664 | −0.978962 | −0.489481 | − | 0.872014i | \(-0.662814\pi\) | ||||
−0.489481 | + | 0.872014i | \(0.662814\pi\) | |||||||
\(158\) | − 2.73556i | − 0.217630i | ||||||||
\(159\) | 6.91185 | 0.548146 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 1.49396i | 0.117740i | ||||||||
\(162\) | − 1.00000i | − 0.0785674i | ||||||||
\(163\) | − 2.48858i | − 0.194921i | −0.995239 | − | 0.0974604i | \(-0.968928\pi\) | ||||
0.995239 | − | 0.0974604i | \(-0.0310719\pi\) | |||||||
\(164\) | 0.198062i | 0.0154661i | ||||||||
\(165\) | 3.93900 | 0.306651 | ||||||||
\(166\) | −15.5864 | −1.20974 | ||||||||
\(167\) | 7.27950i | 0.563305i | 0.959516 | + | 0.281652i | \(0.0908825\pi\) | ||||
−0.959516 | + | 0.281652i | \(0.909117\pi\) | |||||||
\(168\) | −1.19806 | −0.0924325 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.74094 | −0.133524 | ||||||||
\(171\) | − 0.911854i | − 0.0697312i | ||||||||
\(172\) | 3.43296 | 0.261761 | ||||||||
\(173\) | −15.8485 | −1.20494 | −0.602468 | − | 0.798143i | \(-0.705816\pi\) | ||||
−0.602468 | + | 0.798143i | \(0.705816\pi\) | |||||||
\(174\) | − 3.47219i | − 0.263226i | ||||||||
\(175\) | 1.19806i | 0.0905650i | ||||||||
\(176\) | 3.93900i | 0.296913i | ||||||||
\(177\) | 10.2446i | 0.770030i | ||||||||
\(178\) | 8.57673 | 0.642853 | ||||||||
\(179\) | −18.4819 | −1.38140 | −0.690700 | − | 0.723141i | \(-0.742698\pi\) | ||||
−0.690700 | + | 0.723141i | \(0.742698\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −10.7041 | −0.795630 | −0.397815 | − | 0.917466i | \(-0.630231\pi\) | ||||
−0.397815 | + | 0.917466i | \(0.630231\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.92692 | −0.733819 | ||||||||
\(184\) | − 1.24698i | − 0.0919286i | ||||||||
\(185\) | −4.80194 | −0.353045 | ||||||||
\(186\) | −2.15883 | −0.158293 | ||||||||
\(187\) | − 6.85756i | − 0.501474i | ||||||||
\(188\) | − 0.902165i | − 0.0657972i | ||||||||
\(189\) | 1.19806i | 0.0871462i | ||||||||
\(190\) | − 0.911854i | − 0.0661528i | ||||||||
\(191\) | 15.3623 | 1.11158 | 0.555788 | − | 0.831324i | \(-0.312417\pi\) | ||||
0.555788 | + | 0.831324i | \(0.312417\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | − 18.3207i | − 1.31875i | −0.751815 | − | 0.659375i | \(-0.770821\pi\) | ||||
0.751815 | − | 0.659375i | \(-0.229179\pi\) | |||||||
\(194\) | −16.9976 | −1.22036 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.56465 | −0.397475 | ||||||||
\(197\) | 2.31336i | 0.164820i | 0.996599 | + | 0.0824099i | \(0.0262617\pi\) | ||||
−0.996599 | + | 0.0824099i | \(0.973738\pi\) | |||||||
\(198\) | 3.93900 | 0.279933 | ||||||||
\(199\) | −6.36765 | −0.451391 | −0.225695 | − | 0.974198i | \(-0.572465\pi\) | ||||
−0.225695 | + | 0.974198i | \(0.572465\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | − 9.16852i | − 0.646698i | ||||||||
\(202\) | 6.67025i | 0.469317i | ||||||||
\(203\) | 4.15990i | 0.291968i | ||||||||
\(204\) | −1.74094 | −0.121890 | ||||||||
\(205\) | 0.198062 | 0.0138333 | ||||||||
\(206\) | 10.0315i | 0.698925i | ||||||||
\(207\) | −1.24698 | −0.0866711 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.59179 | 0.248450 | ||||||||
\(210\) | 1.19806i | 0.0826742i | ||||||||
\(211\) | −11.6775 | −0.803915 | −0.401958 | − | 0.915658i | \(-0.631670\pi\) | ||||
−0.401958 | + | 0.915658i | \(0.631670\pi\) | |||||||
\(212\) | 6.91185 | 0.474708 | ||||||||
\(213\) | 11.0707i | 0.758551i | ||||||||
\(214\) | 10.1032i | 0.690641i | ||||||||
\(215\) | − 3.43296i | − 0.234126i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 2.58642 | 0.175577 | ||||||||
\(218\) | −10.5211 | −0.712579 | ||||||||
\(219\) | − 4.13706i | − 0.279557i | ||||||||
\(220\) | 3.93900 | 0.265567 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.80194 | −0.322285 | ||||||||
\(223\) | − 11.4004i | − 0.763430i | −0.924280 | − | 0.381715i | \(-0.875334\pi\) | ||||
0.924280 | − | 0.381715i | \(-0.124666\pi\) | |||||||
\(224\) | −1.19806 | −0.0800489 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | 11.2131i | 0.745886i | ||||||||
\(227\) | − 8.86725i | − 0.588540i | −0.955722 | − | 0.294270i | \(-0.904924\pi\) | ||||
0.955722 | − | 0.294270i | \(-0.0950765\pi\) | |||||||
\(228\) | − 0.911854i | − 0.0603890i | ||||||||
\(229\) | 12.6136i | 0.833528i | 0.909015 | + | 0.416764i | \(0.136836\pi\) | ||||
−0.909015 | + | 0.416764i | \(0.863164\pi\) | |||||||
\(230\) | −1.24698 | −0.0822234 | ||||||||
\(231\) | −4.71917 | −0.310498 | ||||||||
\(232\) | − 3.47219i | − 0.227960i | ||||||||
\(233\) | 23.4155 | 1.53400 | 0.767000 | − | 0.641647i | \(-0.221748\pi\) | ||||
0.767000 | + | 0.641647i | \(0.221748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.902165 | −0.0588508 | ||||||||
\(236\) | 10.2446i | 0.666866i | ||||||||
\(237\) | −2.73556 | −0.177694 | ||||||||
\(238\) | 2.08575 | 0.135199 | ||||||||
\(239\) | − 8.87263i | − 0.573922i | −0.957942 | − | 0.286961i | \(-0.907355\pi\) | ||||
0.957942 | − | 0.286961i | \(-0.0926451\pi\) | |||||||
\(240\) | − 1.00000i | − 0.0645497i | ||||||||
\(241\) | 9.72886i | 0.626691i | 0.949639 | + | 0.313345i | \(0.101450\pi\) | ||||
−0.949639 | + | 0.313345i | \(0.898550\pi\) | |||||||
\(242\) | 4.51573i | 0.290282i | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −9.92692 | −0.635506 | ||||||||
\(245\) | 5.56465i | 0.355512i | ||||||||
\(246\) | 0.198062 | 0.0126280 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.15883 | −0.137086 | ||||||||
\(249\) | 15.5864i | 0.987749i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −29.8823 | −1.88615 | −0.943077 | − | 0.332573i | \(-0.892083\pi\) | ||||
−0.943077 | + | 0.332573i | \(0.892083\pi\) | |||||||
\(252\) | 1.19806i | 0.0754708i | ||||||||
\(253\) | − 4.91185i | − 0.308806i | ||||||||
\(254\) | − 9.32736i | − 0.585250i | ||||||||
\(255\) | 1.74094i | 0.109022i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.52111 | 0.531532 | 0.265766 | − | 0.964038i | \(-0.414375\pi\) | ||||
0.265766 | + | 0.964038i | \(0.414375\pi\) | |||||||
\(258\) | − 3.43296i | − 0.213727i | ||||||||
\(259\) | 5.75302 | 0.357475 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.47219 | −0.214923 | ||||||||
\(262\) | − 4.62133i | − 0.285507i | ||||||||
\(263\) | −22.6450 | −1.39635 | −0.698176 | − | 0.715926i | \(-0.746005\pi\) | ||||
−0.698176 | + | 0.715926i | \(0.746005\pi\) | |||||||
\(264\) | 3.93900 | 0.242429 | ||||||||
\(265\) | − 6.91185i | − 0.424592i | ||||||||
\(266\) | 1.09246i | 0.0669829i | ||||||||
\(267\) | − 8.57673i | − 0.524887i | ||||||||
\(268\) | − 9.16852i | − 0.560057i | ||||||||
\(269\) | −9.02608 | −0.550330 | −0.275165 | − | 0.961397i | \(-0.588732\pi\) | ||||
−0.275165 | + | 0.961397i | \(0.588732\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | − 8.59611i | − 0.522176i | −0.965315 | − | 0.261088i | \(-0.915919\pi\) | ||||
0.965315 | − | 0.261088i | \(-0.0840813\pi\) | |||||||
\(272\) | −1.74094 | −0.105560 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0760644 | 0.00459522 | ||||||||
\(275\) | − 3.93900i | − 0.237531i | ||||||||
\(276\) | −1.24698 | −0.0750594 | ||||||||
\(277\) | −6.31527 | −0.379448 | −0.189724 | − | 0.981837i | \(-0.560759\pi\) | ||||
−0.189724 | + | 0.981837i | \(0.560759\pi\) | |||||||
\(278\) | − 18.7017i | − 1.12165i | ||||||||
\(279\) | 2.15883i | 0.129246i | ||||||||
\(280\) | 1.19806i | 0.0715979i | ||||||||
\(281\) | 21.7409i | 1.29696i | 0.761234 | + | 0.648478i | \(0.224594\pi\) | ||||
−0.761234 | + | 0.648478i | \(0.775406\pi\) | |||||||
\(282\) | −0.902165 | −0.0537232 | ||||||||
\(283\) | −12.9487 | −0.769720 | −0.384860 | − | 0.922975i | \(-0.625750\pi\) | ||||
−0.384860 | + | 0.922975i | \(0.625750\pi\) | |||||||
\(284\) | 11.0707i | 0.656924i | ||||||||
\(285\) | −0.911854 | −0.0540136 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.237291 | −0.0140068 | ||||||||
\(288\) | − 1.00000i | − 0.0589256i | ||||||||
\(289\) | −13.9691 | −0.821714 | ||||||||
\(290\) | −3.47219 | −0.203894 | ||||||||
\(291\) | 16.9976i | 0.996417i | ||||||||
\(292\) | − 4.13706i | − 0.242103i | ||||||||
\(293\) | 27.3056i | 1.59521i | 0.603181 | + | 0.797605i | \(0.293900\pi\) | ||||
−0.603181 | + | 0.797605i | \(0.706100\pi\) | |||||||
\(294\) | 5.56465i | 0.324537i | ||||||||
\(295\) | 10.2446 | 0.596463 | ||||||||
\(296\) | −4.80194 | −0.279107 | ||||||||
\(297\) | − 3.93900i | − 0.228564i | ||||||||
\(298\) | −13.6799 | −0.792458 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 4.11290i | 0.237064i | ||||||||
\(302\) | −1.15883 | −0.0666834 | ||||||||
\(303\) | 6.67025 | 0.383196 | ||||||||
\(304\) | − 0.911854i | − 0.0522984i | ||||||||
\(305\) | 9.92692i | 0.568414i | ||||||||
\(306\) | 1.74094i | 0.0995228i | ||||||||
\(307\) | − 24.9124i | − 1.42183i | −0.703279 | − | 0.710914i | \(-0.748281\pi\) | ||||
0.703279 | − | 0.710914i | \(-0.251719\pi\) | |||||||
\(308\) | −4.71917 | −0.268900 | ||||||||
\(309\) | 10.0315 | 0.570670 | ||||||||
\(310\) | 2.15883i | 0.122614i | ||||||||
\(311\) | −21.3787 | −1.21227 | −0.606136 | − | 0.795361i | \(-0.707281\pi\) | ||||
−0.606136 | + | 0.795361i | \(0.707281\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.8713 | −1.34929 | −0.674643 | − | 0.738144i | \(-0.735702\pi\) | ||||
−0.674643 | + | 0.738144i | \(0.735702\pi\) | |||||||
\(314\) | 12.2664i | 0.692231i | ||||||||
\(315\) | 1.19806 | 0.0675032 | ||||||||
\(316\) | −2.73556 | −0.153887 | ||||||||
\(317\) | 12.6407i | 0.709973i | 0.934871 | + | 0.354987i | \(0.115515\pi\) | ||||
−0.934871 | + | 0.354987i | \(0.884485\pi\) | |||||||
\(318\) | − 6.91185i | − 0.387598i | ||||||||
\(319\) | − 13.6770i | − 0.765763i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 10.1032 | 0.563906 | ||||||||
\(322\) | 1.49396 | 0.0832551 | ||||||||
\(323\) | 1.58748i | 0.0883299i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.48858 | −0.137830 | ||||||||
\(327\) | 10.5211i | 0.581819i | ||||||||
\(328\) | 0.198062 | 0.0109362 | ||||||||
\(329\) | 1.08085 | 0.0595892 | ||||||||
\(330\) | − 3.93900i | − 0.216835i | ||||||||
\(331\) | − 20.5109i | − 1.12738i | −0.825985 | − | 0.563692i | \(-0.809381\pi\) | ||||
0.825985 | − | 0.563692i | \(-0.190619\pi\) | |||||||
\(332\) | 15.5864i | 0.855416i | ||||||||
\(333\) | 4.80194i | 0.263145i | ||||||||
\(334\) | 7.27950 | 0.398317 | ||||||||
\(335\) | −9.16852 | −0.500930 | ||||||||
\(336\) | 1.19806i | 0.0653597i | ||||||||
\(337\) | −6.82371 | −0.371711 | −0.185856 | − | 0.982577i | \(-0.559506\pi\) | ||||
−0.185856 | + | 0.982577i | \(0.559506\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.2131 | 0.609014 | ||||||||
\(340\) | 1.74094i | 0.0944157i | ||||||||
\(341\) | −8.50365 | −0.460498 | ||||||||
\(342\) | −0.911854 | −0.0493074 | ||||||||
\(343\) | − 15.0532i | − 0.812798i | ||||||||
\(344\) | − 3.43296i | − 0.185093i | ||||||||
\(345\) | 1.24698i | 0.0671351i | ||||||||
\(346\) | 15.8485i | 0.852019i | ||||||||
\(347\) | −29.4741 | −1.58225 | −0.791127 | − | 0.611653i | \(-0.790505\pi\) | ||||
−0.791127 | + | 0.611653i | \(0.790505\pi\) | |||||||
\(348\) | −3.47219 | −0.186129 | ||||||||
\(349\) | − 34.5394i | − 1.84885i | −0.381361 | − | 0.924426i | \(-0.624544\pi\) | ||||
0.381361 | − | 0.924426i | \(-0.375456\pi\) | |||||||
\(350\) | 1.19806 | 0.0640391 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.93900 | 0.209949 | ||||||||
\(353\) | − 31.2295i | − 1.66218i | −0.556138 | − | 0.831090i | \(-0.687717\pi\) | ||||
0.556138 | − | 0.831090i | \(-0.312283\pi\) | |||||||
\(354\) | 10.2446 | 0.544494 | ||||||||
\(355\) | 11.0707 | 0.587571 | ||||||||
\(356\) | − 8.57673i | − 0.454566i | ||||||||
\(357\) | − 2.08575i | − 0.110390i | ||||||||
\(358\) | 18.4819i | 0.976798i | ||||||||
\(359\) | 18.2524i | 0.963323i | 0.876357 | + | 0.481661i | \(0.159966\pi\) | ||||
−0.876357 | + | 0.481661i | \(0.840034\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 18.1685 | 0.956238 | ||||||||
\(362\) | 10.7041i | 0.562595i | ||||||||
\(363\) | 4.51573 | 0.237014 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.13706 | −0.216544 | ||||||||
\(366\) | 9.92692i | 0.518888i | ||||||||
\(367\) | −19.3773 | −1.01149 | −0.505744 | − | 0.862683i | \(-0.668782\pi\) | ||||
−0.505744 | + | 0.862683i | \(0.668782\pi\) | |||||||
\(368\) | −1.24698 | −0.0650033 | ||||||||
\(369\) | − 0.198062i | − 0.0103107i | ||||||||
\(370\) | 4.80194i | 0.249641i | ||||||||
\(371\) | 8.28083i | 0.429919i | ||||||||
\(372\) | 2.15883i | 0.111930i | ||||||||
\(373\) | −13.6280 | −0.705633 | −0.352817 | − | 0.935693i | \(-0.614776\pi\) | ||||
−0.352817 | + | 0.935693i | \(0.614776\pi\) | |||||||
\(374\) | −6.85756 | −0.354596 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | −0.902165 | −0.0465256 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.19806 | 0.0616217 | ||||||||
\(379\) | 1.32006i | 0.0678069i | 0.999425 | + | 0.0339035i | \(0.0107939\pi\) | ||||
−0.999425 | + | 0.0339035i | \(0.989206\pi\) | |||||||
\(380\) | −0.911854 | −0.0467771 | ||||||||
\(381\) | −9.32736 | −0.477855 | ||||||||
\(382\) | − 15.3623i | − 0.786002i | ||||||||
\(383\) | − 25.5308i | − 1.30456i | −0.757977 | − | 0.652281i | \(-0.773812\pi\) | ||||
0.757977 | − | 0.652281i | \(-0.226188\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | 4.71917i | 0.240511i | ||||||||
\(386\) | −18.3207 | −0.932497 | ||||||||
\(387\) | −3.43296 | −0.174507 | ||||||||
\(388\) | 16.9976i | 0.862923i | ||||||||
\(389\) | 6.05967 | 0.307238 | 0.153619 | − | 0.988130i | \(-0.450907\pi\) | ||||
0.153619 | + | 0.988130i | \(0.450907\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.17092 | 0.109788 | ||||||||
\(392\) | 5.56465i | 0.281057i | ||||||||
\(393\) | −4.62133 | −0.233115 | ||||||||
\(394\) | 2.31336 | 0.116545 | ||||||||
\(395\) | 2.73556i | 0.137641i | ||||||||
\(396\) | − 3.93900i | − 0.197942i | ||||||||
\(397\) | 5.99330i | 0.300795i | 0.988626 | + | 0.150397i | \(0.0480553\pi\) | ||||
−0.988626 | + | 0.150397i | \(0.951945\pi\) | |||||||
\(398\) | 6.36765i | 0.319181i | ||||||||
\(399\) | 1.09246 | 0.0546913 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 17.3773i | 0.867783i | 0.900965 | + | 0.433891i | \(0.142860\pi\) | ||||
−0.900965 | + | 0.433891i | \(0.857140\pi\) | |||||||
\(402\) | −9.16852 | −0.457284 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 6.67025 | 0.331857 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 4.15990 | 0.206452 | ||||||||
\(407\) | −18.9148 | −0.937574 | ||||||||
\(408\) | 1.74094i | 0.0861893i | ||||||||
\(409\) | − 29.3672i | − 1.45211i | −0.687635 | − | 0.726057i | \(-0.741351\pi\) | ||||
0.687635 | − | 0.726057i | \(-0.258649\pi\) | |||||||
\(410\) | − 0.198062i | − 0.00978160i | ||||||||
\(411\) | − 0.0760644i | − 0.00375198i | ||||||||
\(412\) | 10.0315 | 0.494215 | ||||||||
\(413\) | −12.2737 | −0.603947 | ||||||||
\(414\) | 1.24698i | 0.0612857i | ||||||||
\(415\) | 15.5864 | 0.765107 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.7017 | −0.915827 | ||||||||
\(418\) | − 3.59179i | − 0.175680i | ||||||||
\(419\) | −26.5472 | −1.29692 | −0.648458 | − | 0.761251i | \(-0.724586\pi\) | ||||
−0.648458 | + | 0.761251i | \(0.724586\pi\) | |||||||
\(420\) | 1.19806 | 0.0584595 | ||||||||
\(421\) | 31.0834i | 1.51491i | 0.652887 | + | 0.757455i | \(0.273558\pi\) | ||||
−0.652887 | + | 0.757455i | \(0.726442\pi\) | |||||||
\(422\) | 11.6775i | 0.568454i | ||||||||
\(423\) | 0.902165i | 0.0438648i | ||||||||
\(424\) | − 6.91185i | − 0.335669i | ||||||||
\(425\) | 1.74094 | 0.0844479 | ||||||||
\(426\) | 11.0707 | 0.536377 | ||||||||
\(427\) | − 11.8931i | − 0.575546i | ||||||||
\(428\) | 10.1032 | 0.488357 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.43296 | −0.165552 | ||||||||
\(431\) | − 36.1226i | − 1.73996i | −0.493084 | − | 0.869982i | \(-0.664130\pi\) | ||||
0.493084 | − | 0.869982i | \(-0.335870\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 35.2868 | 1.69578 | 0.847888 | − | 0.530176i | \(-0.177874\pi\) | ||||
0.847888 | + | 0.530176i | \(0.177874\pi\) | |||||||
\(434\) | − 2.58642i | − 0.124152i | ||||||||
\(435\) | 3.47219i | 0.166479i | ||||||||
\(436\) | 10.5211i | 0.503870i | ||||||||
\(437\) | 1.13706i | 0.0543931i | ||||||||
\(438\) | −4.13706 | −0.197677 | ||||||||
\(439\) | 32.0170 | 1.52809 | 0.764044 | − | 0.645165i | \(-0.223211\pi\) | ||||
0.764044 | + | 0.645165i | \(0.223211\pi\) | |||||||
\(440\) | − 3.93900i | − 0.187785i | ||||||||
\(441\) | 5.56465 | 0.264983 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.5948 | −1.12102 | −0.560511 | − | 0.828147i | \(-0.689395\pi\) | ||||
−0.560511 | + | 0.828147i | \(0.689395\pi\) | |||||||
\(444\) | 4.80194i | 0.227890i | ||||||||
\(445\) | −8.57673 | −0.406576 | ||||||||
\(446\) | −11.4004 | −0.539826 | ||||||||
\(447\) | 13.6799i | 0.647039i | ||||||||
\(448\) | 1.19806i | 0.0566031i | ||||||||
\(449\) | − 19.8374i | − 0.936187i | −0.883679 | − | 0.468093i | \(-0.844941\pi\) | ||||
0.883679 | − | 0.468093i | \(-0.155059\pi\) | |||||||
\(450\) | 1.00000i | 0.0471405i | ||||||||
\(451\) | 0.780167 | 0.0367367 | ||||||||
\(452\) | 11.2131 | 0.527421 | ||||||||
\(453\) | 1.15883i | 0.0544468i | ||||||||
\(454\) | −8.86725 | −0.416161 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.911854 | −0.0427015 | ||||||||
\(457\) | 26.5284i | 1.24095i | 0.784228 | + | 0.620473i | \(0.213059\pi\) | ||||
−0.784228 | + | 0.620473i | \(0.786941\pi\) | |||||||
\(458\) | 12.6136 | 0.589393 | ||||||||
\(459\) | 1.74094 | 0.0812601 | ||||||||
\(460\) | 1.24698i | 0.0581407i | ||||||||
\(461\) | 12.2717i | 0.571552i | 0.958297 | + | 0.285776i | \(0.0922513\pi\) | ||||
−0.958297 | + | 0.285776i | \(0.907749\pi\) | |||||||
\(462\) | 4.71917i | 0.219556i | ||||||||
\(463\) | − 12.6455i | − 0.587686i | −0.955854 | − | 0.293843i | \(-0.905066\pi\) | ||||
0.955854 | − | 0.293843i | \(-0.0949343\pi\) | |||||||
\(464\) | −3.47219 | −0.161192 | ||||||||
\(465\) | 2.15883 | 0.100114 | ||||||||
\(466\) | − 23.4155i | − 1.08470i | ||||||||
\(467\) | −11.3870 | −0.526929 | −0.263464 | − | 0.964669i | \(-0.584865\pi\) | ||||
−0.263464 | + | 0.964669i | \(0.584865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.9845 | 0.507215 | ||||||||
\(470\) | 0.902165i | 0.0416138i | ||||||||
\(471\) | 12.2664 | 0.565204 | ||||||||
\(472\) | 10.2446 | 0.471545 | ||||||||
\(473\) | − 13.5224i | − 0.621762i | ||||||||
\(474\) | 2.73556i | 0.125649i | ||||||||
\(475\) | 0.911854i | 0.0418387i | ||||||||
\(476\) | − 2.08575i | − 0.0956003i | ||||||||
\(477\) | −6.91185 | −0.316472 | ||||||||
\(478\) | −8.87263 | −0.405824 | ||||||||
\(479\) | 18.8431i | 0.860963i | 0.902600 | + | 0.430481i | \(0.141656\pi\) | ||||
−0.902600 | + | 0.430481i | \(0.858344\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 9.72886 | 0.443137 | ||||||||
\(483\) | − 1.49396i | − 0.0679775i | ||||||||
\(484\) | 4.51573 | 0.205260 | ||||||||
\(485\) | 16.9976 | 0.771822 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − 27.6383i | − 1.25241i | −0.779658 | − | 0.626206i | \(-0.784607\pi\) | ||||
0.779658 | − | 0.626206i | \(-0.215393\pi\) | |||||||
\(488\) | 9.92692i | 0.449371i | ||||||||
\(489\) | 2.48858i | 0.112538i | ||||||||
\(490\) | 5.56465 | 0.251385 | ||||||||
\(491\) | 13.9866 | 0.631206 | 0.315603 | − | 0.948891i | \(-0.397793\pi\) | ||||
0.315603 | + | 0.948891i | \(0.397793\pi\) | |||||||
\(492\) | − 0.198062i | − 0.00892934i | ||||||||
\(493\) | 6.04487 | 0.272247 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.93900 | −0.177045 | ||||||||
\(496\) | 2.15883i | 0.0969345i | ||||||||
\(497\) | −13.2634 | −0.594944 | ||||||||
\(498\) | 15.5864 | 0.698444 | ||||||||
\(499\) | 8.87071i | 0.397107i | 0.980090 | + | 0.198554i | \(0.0636244\pi\) | ||||
−0.980090 | + | 0.198554i | \(0.936376\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | − 7.27950i | − 0.325224i | ||||||||
\(502\) | 29.8823i | 1.33371i | ||||||||
\(503\) | 1.99761 | 0.0890689 | 0.0445344 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445344 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(504\) | 1.19806 | 0.0533659 | ||||||||
\(505\) | − 6.67025i | − 0.296822i | ||||||||
\(506\) | −4.91185 | −0.218359 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.32736 | −0.413834 | ||||||||
\(509\) | 21.7023i | 0.961938i | 0.876738 | + | 0.480969i | \(0.159715\pi\) | ||||
−0.876738 | + | 0.480969i | \(0.840285\pi\) | |||||||
\(510\) | 1.74094 | 0.0770901 | ||||||||
\(511\) | 4.95646 | 0.219261 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0.911854i | 0.0402593i | ||||||||
\(514\) | − 8.52111i | − 0.375850i | ||||||||
\(515\) | − 10.0315i | − 0.442039i | ||||||||
\(516\) | −3.43296 | −0.151128 | ||||||||
\(517\) | −3.55363 | −0.156288 | ||||||||
\(518\) | − 5.75302i | − 0.252773i | ||||||||
\(519\) | 15.8485 | 0.695670 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8364 | 0.518561 | 0.259281 | − | 0.965802i | \(-0.416515\pi\) | ||||
0.259281 | + | 0.965802i | \(0.416515\pi\) | |||||||
\(522\) | 3.47219i | 0.151974i | ||||||||
\(523\) | 24.6112 | 1.07617 | 0.538086 | − | 0.842890i | \(-0.319148\pi\) | ||||
0.538086 | + | 0.842890i | \(0.319148\pi\) | |||||||
\(524\) | −4.62133 | −0.201884 | ||||||||
\(525\) | − 1.19806i | − 0.0522877i | ||||||||
\(526\) | 22.6450i | 0.987370i | ||||||||
\(527\) | − 3.75840i | − 0.163718i | ||||||||
\(528\) | − 3.93900i | − 0.171423i | ||||||||
\(529\) | −21.4450 | −0.932393 | ||||||||
\(530\) | −6.91185 | −0.300232 | ||||||||
\(531\) | − 10.2446i | − 0.444577i | ||||||||
\(532\) | 1.09246 | 0.0473641 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −8.57673 | −0.371151 | ||||||||
\(535\) | − 10.1032i | − 0.436800i | ||||||||
\(536\) | −9.16852 | −0.396020 | ||||||||
\(537\) | 18.4819 | 0.797552 | ||||||||
\(538\) | 9.02608i | 0.389142i | ||||||||
\(539\) | 21.9191i | 0.944125i | ||||||||
\(540\) | 1.00000i | 0.0430331i | ||||||||
\(541\) | 29.1282i | 1.25232i | 0.779694 | + | 0.626160i | \(0.215374\pi\) | ||||
−0.779694 | + | 0.626160i | \(0.784626\pi\) | |||||||
\(542\) | −8.59611 | −0.369234 | ||||||||
\(543\) | 10.7041 | 0.459357 | ||||||||
\(544\) | 1.74094i | 0.0746421i | ||||||||
\(545\) | 10.5211 | 0.450675 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.1752 | −0.435061 | −0.217531 | − | 0.976053i | \(-0.569800\pi\) | ||||
−0.217531 | + | 0.976053i | \(0.569800\pi\) | |||||||
\(548\) | − 0.0760644i | − 0.00324931i | ||||||||
\(549\) | 9.92692 | 0.423671 | ||||||||
\(550\) | −3.93900 | −0.167960 | ||||||||
\(551\) | 3.16613i | 0.134882i | ||||||||
\(552\) | 1.24698i | 0.0530750i | ||||||||
\(553\) | − 3.27737i | − 0.139368i | ||||||||
\(554\) | 6.31527i | 0.268310i | ||||||||
\(555\) | 4.80194 | 0.203831 | ||||||||
\(556\) | −18.7017 | −0.793129 | ||||||||
\(557\) | 13.0398i | 0.552515i | 0.961084 | + | 0.276257i | \(0.0890942\pi\) | ||||
−0.961084 | + | 0.276257i | \(0.910906\pi\) | |||||||
\(558\) | 2.15883 | 0.0913907 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.19806 | 0.0506274 | ||||||||
\(561\) | 6.85756i | 0.289526i | ||||||||
\(562\) | 21.7409 | 0.917086 | ||||||||
\(563\) | 32.9221 | 1.38750 | 0.693751 | − | 0.720215i | \(-0.255957\pi\) | ||||
0.693751 | + | 0.720215i | \(0.255957\pi\) | |||||||
\(564\) | 0.902165i | 0.0379880i | ||||||||
\(565\) | − 11.2131i | − 0.471740i | ||||||||
\(566\) | 12.9487i | 0.544274i | ||||||||
\(567\) | − 1.19806i | − 0.0503139i | ||||||||
\(568\) | 11.0707 | 0.464516 | ||||||||
\(569\) | −7.53319 | −0.315808 | −0.157904 | − | 0.987454i | \(-0.550474\pi\) | ||||
−0.157904 | + | 0.987454i | \(0.550474\pi\) | |||||||
\(570\) | 0.911854i | 0.0381934i | ||||||||
\(571\) | −36.2422 | −1.51669 | −0.758344 | − | 0.651854i | \(-0.773991\pi\) | ||||
−0.758344 | + | 0.651854i | \(0.773991\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.3623 | −0.641768 | ||||||||
\(574\) | 0.237291i | 0.00990433i | ||||||||
\(575\) | 1.24698 | 0.0520026 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 14.2198i | 0.591979i | 0.955191 | + | 0.295990i | \(0.0956494\pi\) | ||||
−0.955191 | + | 0.295990i | \(0.904351\pi\) | |||||||
\(578\) | 13.9691i | 0.581039i | ||||||||
\(579\) | 18.3207i | 0.761380i | ||||||||
\(580\) | 3.47219i | 0.144175i | ||||||||
\(581\) | −18.6735 | −0.774707 | ||||||||
\(582\) | 16.9976 | 0.704573 | ||||||||
\(583\) | − 27.2258i | − 1.12758i | ||||||||
\(584\) | −4.13706 | −0.171193 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.3056 | 1.12798 | ||||||||
\(587\) | − 22.3207i | − 0.921272i | −0.887589 | − | 0.460636i | \(-0.847621\pi\) | ||||
0.887589 | − | 0.460636i | \(-0.152379\pi\) | |||||||
\(588\) | 5.56465 | 0.229482 | ||||||||
\(589\) | 1.96854 | 0.0811123 | ||||||||
\(590\) | − 10.2446i | − 0.421763i | ||||||||
\(591\) | − 2.31336i | − 0.0951587i | ||||||||
\(592\) | 4.80194i | 0.197358i | ||||||||
\(593\) | − 1.64742i | − 0.0676513i | −0.999428 | − | 0.0338256i | \(-0.989231\pi\) | ||||
0.999428 | − | 0.0338256i | \(-0.0107691\pi\) | |||||||
\(594\) | −3.93900 | −0.161619 | ||||||||
\(595\) | −2.08575 | −0.0855075 | ||||||||
\(596\) | 13.6799i | 0.560352i | ||||||||
\(597\) | 6.36765 | 0.260611 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.41119 | 0.384531 | 0.192265 | − | 0.981343i | \(-0.438417\pi\) | ||||
0.192265 | + | 0.981343i | \(0.438417\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | 1.62565 | 0.0663115 | 0.0331557 | − | 0.999450i | \(-0.489444\pi\) | ||||
0.0331557 | + | 0.999450i | \(0.489444\pi\) | |||||||
\(602\) | 4.11290 | 0.167629 | ||||||||
\(603\) | 9.16852i | 0.373371i | ||||||||
\(604\) | 1.15883i | 0.0471523i | ||||||||
\(605\) | − 4.51573i | − 0.183591i | ||||||||
\(606\) | − 6.67025i | − 0.270960i | ||||||||
\(607\) | 14.9282 | 0.605919 | 0.302959 | − | 0.953003i | \(-0.402025\pi\) | ||||
0.302959 | + | 0.953003i | \(0.402025\pi\) | |||||||
\(608\) | −0.911854 | −0.0369806 | ||||||||
\(609\) | − 4.15990i | − 0.168568i | ||||||||
\(610\) | 9.92692 | 0.401929 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 1.74094 | 0.0703733 | ||||||||
\(613\) | − 28.8437i | − 1.16499i | −0.812836 | − | 0.582493i | \(-0.802078\pi\) | ||||
0.812836 | − | 0.582493i | \(-0.197922\pi\) | |||||||
\(614\) | −24.9124 | −1.00538 | ||||||||
\(615\) | −0.198062 | −0.00798664 | ||||||||
\(616\) | 4.71917i | 0.190141i | ||||||||
\(617\) | 39.7985i | 1.60223i | 0.598513 | + | 0.801113i | \(0.295759\pi\) | ||||
−0.598513 | + | 0.801113i | \(0.704241\pi\) | |||||||
\(618\) | − 10.0315i | − 0.403524i | ||||||||
\(619\) | − 38.0465i | − 1.52922i | −0.644494 | − | 0.764609i | \(-0.722932\pi\) | ||||
0.644494 | − | 0.764609i | \(-0.277068\pi\) | |||||||
\(620\) | 2.15883 | 0.0867008 | ||||||||
\(621\) | 1.24698 | 0.0500396 | ||||||||
\(622\) | 21.3787i | 0.857206i | ||||||||
\(623\) | 10.2755 | 0.411677 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 23.8713i | 0.954089i | ||||||||
\(627\) | −3.59179 | −0.143442 | ||||||||
\(628\) | 12.2664 | 0.489481 | ||||||||
\(629\) | − 8.35988i | − 0.333330i | ||||||||
\(630\) | − 1.19806i | − 0.0477319i | ||||||||
\(631\) | 23.0901i | 0.919201i | 0.888126 | + | 0.459600i | \(0.152007\pi\) | ||||
−0.888126 | + | 0.459600i | \(0.847993\pi\) | |||||||
\(632\) | 2.73556i | 0.108815i | ||||||||
\(633\) | 11.6775 | 0.464141 | ||||||||
\(634\) | 12.6407 | 0.502027 | ||||||||
\(635\) | 9.32736i | 0.370145i | ||||||||
\(636\) | −6.91185 | −0.274073 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13.6770 | −0.541476 | ||||||||
\(639\) | − 11.0707i | − 0.437950i | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −23.3948 | −0.924039 | −0.462019 | − | 0.886870i | \(-0.652875\pi\) | ||||
−0.462019 | + | 0.886870i | \(0.652875\pi\) | |||||||
\(642\) | − 10.1032i | − 0.398742i | ||||||||
\(643\) | 6.00836i | 0.236947i | 0.992957 | + | 0.118473i | \(0.0378000\pi\) | ||||
−0.992957 | + | 0.118473i | \(0.962200\pi\) | |||||||
\(644\) | − 1.49396i | − 0.0588702i | ||||||||
\(645\) | 3.43296i | 0.135173i | ||||||||
\(646\) | 1.58748 | 0.0624586 | ||||||||
\(647\) | 4.38511 | 0.172396 | 0.0861982 | − | 0.996278i | \(-0.472528\pi\) | ||||
0.0861982 | + | 0.996278i | \(0.472528\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 40.3534 | 1.58401 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.58642 | −0.101370 | ||||||||
\(652\) | 2.48858i | 0.0974604i | ||||||||
\(653\) | −20.6160 | −0.806765 | −0.403382 | − | 0.915032i | \(-0.632166\pi\) | ||||
−0.403382 | + | 0.915032i | \(0.632166\pi\) | |||||||
\(654\) | 10.5211 | 0.411408 | ||||||||
\(655\) | 4.62133i | 0.180570i | ||||||||
\(656\) | − 0.198062i | − 0.00773303i | ||||||||
\(657\) | 4.13706i | 0.161402i | ||||||||
\(658\) | − 1.08085i | − 0.0421359i | ||||||||
\(659\) | 18.4910 | 0.720306 | 0.360153 | − | 0.932893i | \(-0.382724\pi\) | ||||
0.360153 | + | 0.932893i | \(0.382724\pi\) | |||||||
\(660\) | −3.93900 | −0.153325 | ||||||||
\(661\) | 17.6420i | 0.686196i | 0.939300 | + | 0.343098i | \(0.111476\pi\) | ||||
−0.939300 | + | 0.343098i | \(0.888524\pi\) | |||||||
\(662\) | −20.5109 | −0.797180 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.5864 | 0.604870 | ||||||||
\(665\) | − 1.09246i | − 0.0423637i | ||||||||
\(666\) | 4.80194 | 0.186071 | ||||||||
\(667\) | 4.32975 | 0.167649 | ||||||||
\(668\) | − 7.27950i | − 0.281652i | ||||||||
\(669\) | 11.4004i | 0.440766i | ||||||||
\(670\) | 9.16852i | 0.354211i | ||||||||
\(671\) | 39.1021i | 1.50952i | ||||||||
\(672\) | 1.19806 | 0.0462163 | ||||||||
\(673\) | −17.1473 | −0.660981 | −0.330491 | − | 0.943809i | \(-0.607214\pi\) | ||||
−0.330491 | + | 0.943809i | \(0.607214\pi\) | |||||||
\(674\) | 6.82371i | 0.262839i | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.7982 | 1.22210 | 0.611052 | − | 0.791590i | \(-0.290746\pi\) | ||||
0.611052 | + | 0.791590i | \(0.290746\pi\) | |||||||
\(678\) | − 11.2131i | − 0.430638i | ||||||||
\(679\) | −20.3642 | −0.781506 | ||||||||
\(680\) | 1.74094 | 0.0667620 | ||||||||
\(681\) | 8.86725i | 0.339794i | ||||||||
\(682\) | 8.50365i | 0.325622i | ||||||||
\(683\) | 6.32783i | 0.242128i | 0.992645 | + | 0.121064i | \(0.0386306\pi\) | ||||
−0.992645 | + | 0.121064i | \(0.961369\pi\) | |||||||
\(684\) | 0.911854i | 0.0348656i | ||||||||
\(685\) | −0.0760644 | −0.00290627 | ||||||||
\(686\) | −15.0532 | −0.574735 | ||||||||
\(687\) | − 12.6136i | − 0.481237i | ||||||||
\(688\) | −3.43296 | −0.130880 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.24698 | 0.0474717 | ||||||||
\(691\) | 15.1825i | 0.577570i | 0.957394 | + | 0.288785i | \(0.0932513\pi\) | ||||
−0.957394 | + | 0.288785i | \(0.906749\pi\) | |||||||
\(692\) | 15.8485 | 0.602468 | ||||||||
\(693\) | 4.71917 | 0.179266 | ||||||||
\(694\) | 29.4741i | 1.11882i | ||||||||
\(695\) | 18.7017i | 0.709396i | ||||||||
\(696\) | 3.47219i | 0.131613i | ||||||||
\(697\) | 0.344814i | 0.0130608i | ||||||||
\(698\) | −34.5394 | −1.30734 | ||||||||
\(699\) | −23.4155 | −0.885656 | ||||||||
\(700\) | − 1.19806i | − 0.0452825i | ||||||||
\(701\) | 23.6528 | 0.893354 | 0.446677 | − | 0.894695i | \(-0.352607\pi\) | ||||
0.446677 | + | 0.894695i | \(0.352607\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.37867 | 0.165145 | ||||||||
\(704\) | − 3.93900i | − 0.148457i | ||||||||
\(705\) | 0.902165 | 0.0339775 | ||||||||
\(706\) | −31.2295 | −1.17534 | ||||||||
\(707\) | 7.99138i | 0.300547i | ||||||||
\(708\) | − 10.2446i | − 0.385015i | ||||||||
\(709\) | − 40.9353i | − 1.53736i | −0.639636 | − | 0.768678i | \(-0.720915\pi\) | ||||
0.639636 | − | 0.768678i | \(-0.279085\pi\) | |||||||
\(710\) | − 11.0707i | − 0.415476i | ||||||||
\(711\) | 2.73556 | 0.102592 | ||||||||
\(712\) | −8.57673 | −0.321426 | ||||||||
\(713\) | − 2.69202i | − 0.100817i | ||||||||
\(714\) | −2.08575 | −0.0780573 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18.4819 | 0.690700 | ||||||||
\(717\) | 8.87263i | 0.331354i | ||||||||
\(718\) | 18.2524 | 0.681172 | ||||||||
\(719\) | −4.55363 | −0.169822 | −0.0849109 | − | 0.996389i | \(-0.527061\pi\) | ||||
−0.0849109 | + | 0.996389i | \(0.527061\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 12.0183i | 0.447585i | ||||||||
\(722\) | − 18.1685i | − 0.676162i | ||||||||
\(723\) | − 9.72886i | − 0.361820i | ||||||||
\(724\) | 10.7041 | 0.397815 | ||||||||
\(725\) | 3.47219 | 0.128954 | ||||||||
\(726\) | − 4.51573i | − 0.167594i | ||||||||
\(727\) | −18.1612 | −0.673563 | −0.336781 | − | 0.941583i | \(-0.609338\pi\) | ||||
−0.336781 | + | 0.941583i | \(0.609338\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 4.13706i | 0.153120i | ||||||||
\(731\) | 5.97657 | 0.221052 | ||||||||
\(732\) | 9.92692 | 0.366910 | ||||||||
\(733\) | − 9.89115i | − 0.365338i | −0.983174 | − | 0.182669i | \(-0.941526\pi\) | ||||
0.983174 | − | 0.182669i | \(-0.0584737\pi\) | |||||||
\(734\) | 19.3773i | 0.715231i | ||||||||
\(735\) | − 5.56465i | − 0.205255i | ||||||||
\(736\) | 1.24698i | 0.0459643i | ||||||||
\(737\) | −36.1148 | −1.33031 | ||||||||
\(738\) | −0.198062 | −0.00729077 | ||||||||
\(739\) | − 23.9608i | − 0.881411i | −0.897652 | − | 0.440706i | \(-0.854728\pi\) | ||||
0.897652 | − | 0.440706i | \(-0.145272\pi\) | |||||||
\(740\) | 4.80194 | 0.176523 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.28083 | 0.303999 | ||||||||
\(743\) | − 46.6708i | − 1.71219i | −0.516821 | − | 0.856094i | \(-0.672885\pi\) | ||||
0.516821 | − | 0.856094i | \(-0.327115\pi\) | |||||||
\(744\) | 2.15883 | 0.0791467 | ||||||||
\(745\) | 13.6799 | 0.501194 | ||||||||
\(746\) | 13.6280i | 0.498958i | ||||||||
\(747\) | − 15.5864i | − 0.570277i | ||||||||
\(748\) | 6.85756i | 0.250737i | ||||||||
\(749\) | 12.1043i | 0.442281i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 30.9168 | 1.12817 | 0.564084 | − | 0.825717i | \(-0.309229\pi\) | ||||
0.564084 | + | 0.825717i | \(0.309229\pi\) | |||||||
\(752\) | 0.902165i | 0.0328986i | ||||||||
\(753\) | 29.8823 | 1.08897 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.15883 | 0.0421743 | ||||||||
\(756\) | − 1.19806i | − 0.0435731i | ||||||||
\(757\) | 24.4566 | 0.888892 | 0.444446 | − | 0.895806i | \(-0.353401\pi\) | ||||
0.444446 | + | 0.895806i | \(0.353401\pi\) | |||||||
\(758\) | 1.32006 | 0.0479467 | ||||||||
\(759\) | 4.91185i | 0.178289i | ||||||||
\(760\) | 0.911854i | 0.0330764i | ||||||||
\(761\) | − 20.5536i | − 0.745069i | −0.928018 | − | 0.372534i | \(-0.878489\pi\) | ||||
0.928018 | − | 0.372534i | \(-0.121511\pi\) | |||||||
\(762\) | 9.32736i | 0.337894i | ||||||||
\(763\) | −12.6049 | −0.456329 | ||||||||
\(764\) | −15.3623 | −0.555788 | ||||||||
\(765\) | − 1.74094i | − 0.0629438i | ||||||||
\(766\) | −25.5308 | −0.922465 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 21.0084i | 0.757581i | 0.925482 | + | 0.378790i | \(0.123660\pi\) | ||||
−0.925482 | + | 0.378790i | \(0.876340\pi\) | |||||||
\(770\) | 4.71917 | 0.170067 | ||||||||
\(771\) | −8.52111 | −0.306880 | ||||||||
\(772\) | 18.3207i | 0.659375i | ||||||||
\(773\) | 36.2626i | 1.30428i | 0.758100 | + | 0.652138i | \(0.226128\pi\) | ||||
−0.758100 | + | 0.652138i | \(0.773872\pi\) | |||||||
\(774\) | 3.43296i | 0.123395i | ||||||||
\(775\) | − 2.15883i | − 0.0775476i | ||||||||
\(776\) | 16.9976 | 0.610179 | ||||||||
\(777\) | −5.75302 | −0.206388 | ||||||||
\(778\) | − 6.05967i | − 0.217250i | ||||||||
\(779\) | −0.180604 | −0.00647081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.6075 | 1.56040 | ||||||||
\(782\) | − 2.17092i | − 0.0776318i | ||||||||
\(783\) | 3.47219 | 0.124086 | ||||||||
\(784\) | 5.56465 | 0.198737 | ||||||||
\(785\) | − 12.2664i | − 0.437805i | ||||||||
\(786\) | 4.62133i | 0.164838i | ||||||||
\(787\) | − 1.55927i | − 0.0555820i | −0.999614 | − | 0.0277910i | \(-0.991153\pi\) | ||||
0.999614 | − | 0.0277910i | \(-0.00884728\pi\) | |||||||
\(788\) | − 2.31336i | − 0.0824099i | ||||||||
\(789\) | 22.6450 | 0.806184 | ||||||||
\(790\) | 2.73556 | 0.0973269 | ||||||||
\(791\) | 13.4340i | 0.477659i | ||||||||
\(792\) | −3.93900 | −0.139966 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 5.99330 | 0.212694 | ||||||||
\(795\) | 6.91185i | 0.245138i | ||||||||
\(796\) | 6.36765 | 0.225695 | ||||||||
\(797\) | −5.16793 | −0.183058 | −0.0915288 | − | 0.995802i | \(-0.529175\pi\) | ||||
−0.0915288 | + | 0.995802i | \(0.529175\pi\) | |||||||
\(798\) | − 1.09246i | − 0.0386726i | ||||||||
\(799\) | − 1.57061i | − 0.0555644i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 8.57673i | 0.303044i | ||||||||
\(802\) | 17.3773 | 0.613615 | ||||||||
\(803\) | −16.2959 | −0.575070 | ||||||||
\(804\) | 9.16852i | 0.323349i | ||||||||
\(805\) | −1.49396 | −0.0526551 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.02608 | 0.317733 | ||||||||
\(808\) | − 6.67025i | − 0.234659i | ||||||||
\(809\) | −31.8605 | −1.12016 | −0.560079 | − | 0.828440i | \(-0.689229\pi\) | ||||
−0.560079 | + | 0.828440i | \(0.689229\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | 15.3056i | 0.537452i | 0.963217 | + | 0.268726i | \(0.0866026\pi\) | ||||
−0.963217 | + | 0.268726i | \(0.913397\pi\) | |||||||
\(812\) | − 4.15990i | − 0.145984i | ||||||||
\(813\) | 8.59611i | 0.301479i | ||||||||
\(814\) | 18.9148i | 0.662965i | ||||||||
\(815\) | 2.48858 | 0.0871712 | ||||||||
\(816\) | 1.74094 | 0.0609450 | ||||||||
\(817\) | 3.13036i | 0.109517i | ||||||||
\(818\) | −29.3672 | −1.02680 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.198062 | −0.00691663 | ||||||||
\(821\) | − 32.0248i | − 1.11767i | −0.829278 | − | 0.558836i | \(-0.811248\pi\) | ||||
0.829278 | − | 0.558836i | \(-0.188752\pi\) | |||||||
\(822\) | −0.0760644 | −0.00265305 | ||||||||
\(823\) | 36.8571 | 1.28476 | 0.642379 | − | 0.766387i | \(-0.277948\pi\) | ||||
0.642379 | + | 0.766387i | \(0.277948\pi\) | |||||||
\(824\) | − 10.0315i | − 0.349462i | ||||||||
\(825\) | 3.93900i | 0.137138i | ||||||||
\(826\) | 12.2737i | 0.427055i | ||||||||
\(827\) | − 37.9269i | − 1.31885i | −0.751771 | − | 0.659424i | \(-0.770800\pi\) | ||||
0.751771 | − | 0.659424i | \(-0.229200\pi\) | |||||||
\(828\) | 1.24698 | 0.0433355 | ||||||||
\(829\) | 34.2349 | 1.18903 | 0.594514 | − | 0.804086i | \(-0.297345\pi\) | ||||
0.594514 | + | 0.804086i | \(0.297345\pi\) | |||||||
\(830\) | − 15.5864i | − 0.541012i | ||||||||
\(831\) | 6.31527 | 0.219074 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.68771 | −0.335659 | ||||||||
\(834\) | 18.7017i | 0.647587i | ||||||||
\(835\) | −7.27950 | −0.251918 | ||||||||
\(836\) | −3.59179 | −0.124225 | ||||||||
\(837\) | − 2.15883i | − 0.0746202i | ||||||||
\(838\) | 26.5472i | 0.917057i | ||||||||
\(839\) | 18.7318i | 0.646695i | 0.946280 | + | 0.323347i | \(0.104808\pi\) | ||||
−0.946280 | + | 0.323347i | \(0.895192\pi\) | |||||||
\(840\) | − 1.19806i | − 0.0413371i | ||||||||
\(841\) | −16.9439 | −0.584273 | ||||||||
\(842\) | 31.0834 | 1.07120 | ||||||||
\(843\) | − 21.7409i | − 0.748798i | ||||||||
\(844\) | 11.6775 | 0.401958 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.902165 | 0.0310171 | ||||||||
\(847\) | 5.41013i | 0.185894i | ||||||||
\(848\) | −6.91185 | −0.237354 | ||||||||
\(849\) | 12.9487 | 0.444398 | ||||||||
\(850\) | − 1.74094i | − 0.0597137i | ||||||||
\(851\) | − 5.98792i | − 0.205263i | ||||||||
\(852\) | − 11.0707i | − 0.379276i | ||||||||
\(853\) | − 4.64071i | − 0.158895i | −0.996839 | − | 0.0794475i | \(-0.974684\pi\) | ||||
0.996839 | − | 0.0794475i | \(-0.0253156\pi\) | |||||||
\(854\) | −11.8931 | −0.406972 | ||||||||
\(855\) | 0.911854 | 0.0311847 | ||||||||
\(856\) | − 10.1032i | − 0.345321i | ||||||||
\(857\) | −11.1347 | −0.380353 | −0.190177 | − | 0.981750i | \(-0.560906\pi\) | ||||
−0.190177 | + | 0.981750i | \(0.560906\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.9661 | 0.988312 | 0.494156 | − | 0.869373i | \(-0.335477\pi\) | ||||
0.494156 | + | 0.869373i | \(0.335477\pi\) | |||||||
\(860\) | 3.43296i | 0.117063i | ||||||||
\(861\) | 0.237291 | 0.00808685 | ||||||||
\(862\) | −36.1226 | −1.23034 | ||||||||
\(863\) | − 33.1371i | − 1.12800i | −0.825775 | − | 0.563999i | \(-0.809262\pi\) | ||||
0.825775 | − | 0.563999i | \(-0.190738\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − 15.8485i | − 0.538864i | ||||||||
\(866\) | − 35.2868i | − 1.19909i | ||||||||
\(867\) | 13.9691 | 0.474417 | ||||||||
\(868\) | −2.58642 | −0.0877887 | ||||||||
\(869\) | 10.7754i | 0.365530i | ||||||||
\(870\) | 3.47219 | 0.117718 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.5211 | 0.356290 | ||||||||
\(873\) | − 16.9976i | − 0.575282i | ||||||||
\(874\) | 1.13706 | 0.0384617 | ||||||||
\(875\) | −1.19806 | −0.0405019 | ||||||||
\(876\) | 4.13706i | 0.139778i | ||||||||
\(877\) | − 19.1371i | − 0.646213i | −0.946363 | − | 0.323106i | \(-0.895273\pi\) | ||||
0.946363 | − | 0.323106i | \(-0.104727\pi\) | |||||||
\(878\) | − 32.0170i | − 1.08052i | ||||||||
\(879\) | − 27.3056i | − 0.920995i | ||||||||
\(880\) | −3.93900 | −0.132784 | ||||||||
\(881\) | 40.3387 | 1.35905 | 0.679523 | − | 0.733655i | \(-0.262187\pi\) | ||||
0.679523 | + | 0.733655i | \(0.262187\pi\) | |||||||
\(882\) | − 5.56465i | − 0.187371i | ||||||||
\(883\) | 4.31336 | 0.145156 | 0.0725780 | − | 0.997363i | \(-0.476877\pi\) | ||||
0.0725780 | + | 0.997363i | \(0.476877\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.2446 | −0.344368 | ||||||||
\(886\) | 23.5948i | 0.792682i | ||||||||
\(887\) | −9.38404 | −0.315085 | −0.157543 | − | 0.987512i | \(-0.550357\pi\) | ||||
−0.157543 | + | 0.987512i | \(0.550357\pi\) | |||||||
\(888\) | 4.80194 | 0.161142 | ||||||||
\(889\) | − 11.1748i | − 0.374789i | ||||||||
\(890\) | 8.57673i | 0.287493i | ||||||||
\(891\) | 3.93900i | 0.131962i | ||||||||
\(892\) | 11.4004i | 0.381715i | ||||||||
\(893\) | 0.822643 | 0.0275287 | ||||||||
\(894\) | 13.6799 | 0.457526 | ||||||||
\(895\) | − 18.4819i | − 0.617781i | ||||||||
\(896\) | 1.19806 | 0.0400245 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.8374 | −0.661984 | ||||||||
\(899\) | − 7.49588i | − 0.250002i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 12.0331 | 0.400881 | ||||||||
\(902\) | − 0.780167i | − 0.0259767i | ||||||||
\(903\) | − 4.11290i | − 0.136869i | ||||||||
\(904\) | − 11.2131i | − 0.372943i | ||||||||
\(905\) | − 10.7041i | − 0.355816i | ||||||||
\(906\) | 1.15883 | 0.0384997 | ||||||||
\(907\) | −14.2131 | −0.471939 | −0.235970 | − | 0.971760i | \(-0.575827\pi\) | ||||
−0.235970 | + | 0.971760i | \(0.575827\pi\) | |||||||
\(908\) | 8.86725i | 0.294270i | ||||||||
\(909\) | −6.67025 | −0.221238 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.2707 | 1.33423 | 0.667113 | − | 0.744956i | \(-0.267530\pi\) | ||||
0.667113 | + | 0.744956i | \(0.267530\pi\) | |||||||
\(912\) | 0.911854i | 0.0301945i | ||||||||
\(913\) | 61.3949 | 2.03188 | ||||||||
\(914\) | 26.5284 | 0.877482 | ||||||||
\(915\) | − 9.92692i | − 0.328174i | ||||||||
\(916\) | − 12.6136i | − 0.416764i | ||||||||
\(917\) | − 5.53665i | − 0.182836i | ||||||||
\(918\) | − 1.74094i | − 0.0574595i | ||||||||
\(919\) | 7.03577 | 0.232089 | 0.116044 | − | 0.993244i | \(-0.462979\pi\) | ||||
0.116044 | + | 0.993244i | \(0.462979\pi\) | |||||||
\(920\) | 1.24698 | 0.0411117 | ||||||||
\(921\) | 24.9124i | 0.820893i | ||||||||
\(922\) | 12.2717 | 0.404148 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 4.71917 | 0.155249 | ||||||||
\(925\) | − 4.80194i | − 0.157887i | ||||||||
\(926\) | −12.6455 | −0.415557 | ||||||||
\(927\) | −10.0315 | −0.329476 | ||||||||
\(928\) | 3.47219i | 0.113980i | ||||||||
\(929\) | 21.3575i | 0.700716i | 0.936616 | + | 0.350358i | \(0.113940\pi\) | ||||
−0.936616 | + | 0.350358i | \(0.886060\pi\) | |||||||
\(930\) | − 2.15883i | − 0.0707909i | ||||||||
\(931\) | − 5.07415i | − 0.166298i | ||||||||
\(932\) | −23.4155 | −0.767000 | ||||||||
\(933\) | 21.3787 | 0.699906 | ||||||||
\(934\) | 11.3870i | 0.372595i | ||||||||
\(935\) | 6.85756 | 0.224266 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.7396 | 1.36357 | 0.681787 | − | 0.731551i | \(-0.261203\pi\) | ||||
0.681787 | + | 0.731551i | \(0.261203\pi\) | |||||||
\(938\) | − 10.9845i | − 0.358655i | ||||||||
\(939\) | 23.8713 | 0.779010 | ||||||||
\(940\) | 0.902165 | 0.0294254 | ||||||||
\(941\) | 26.2078i | 0.854348i | 0.904169 | + | 0.427174i | \(0.140491\pi\) | ||||
−0.904169 | + | 0.427174i | \(0.859509\pi\) | |||||||
\(942\) | − 12.2664i | − 0.399660i | ||||||||
\(943\) | 0.246980i | 0.00804276i | ||||||||
\(944\) | − 10.2446i | − 0.333433i | ||||||||
\(945\) | −1.19806 | −0.0389730 | ||||||||
\(946\) | −13.5224 | −0.439652 | ||||||||
\(947\) | − 3.15239i | − 0.102439i | −0.998687 | − | 0.0512195i | \(-0.983689\pi\) | ||||
0.998687 | − | 0.0512195i | \(-0.0163108\pi\) | |||||||
\(948\) | 2.73556 | 0.0888469 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.911854 | 0.0295845 | ||||||||
\(951\) | − 12.6407i | − 0.409903i | ||||||||
\(952\) | −2.08575 | −0.0675996 | ||||||||
\(953\) | 3.56060 | 0.115339 | 0.0576695 | − | 0.998336i | \(-0.481633\pi\) | ||||
0.0576695 | + | 0.998336i | \(0.481633\pi\) | |||||||
\(954\) | 6.91185i | 0.223780i | ||||||||
\(955\) | 15.3623i | 0.497111i | ||||||||
\(956\) | 8.87263i | 0.286961i | ||||||||
\(957\) | 13.6770i | 0.442113i | ||||||||
\(958\) | 18.8431 | 0.608792 | ||||||||
\(959\) | 0.0911299 | 0.00294274 | ||||||||
\(960\) | 1.00000i | 0.0322749i | ||||||||
\(961\) | 26.3394 | 0.849659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −10.1032 | −0.325571 | ||||||||
\(964\) | − 9.72886i | − 0.313345i | ||||||||
\(965\) | 18.3207 | 0.589763 | ||||||||
\(966\) | −1.49396 | −0.0480673 | ||||||||
\(967\) | 7.26875i | 0.233747i | 0.993147 | + | 0.116874i | \(0.0372872\pi\) | ||||
−0.993147 | + | 0.116874i | \(0.962713\pi\) | |||||||
\(968\) | − 4.51573i | − 0.145141i | ||||||||
\(969\) | − 1.58748i | − 0.0509973i | ||||||||
\(970\) | − 16.9976i | − 0.545760i | ||||||||
\(971\) | −9.53511 | −0.305996 | −0.152998 | − | 0.988226i | \(-0.548893\pi\) | ||||
−0.152998 | + | 0.988226i | \(0.548893\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | − 22.4058i | − 0.718297i | ||||||||
\(974\) | −27.6383 | −0.885589 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.92692 | 0.317753 | ||||||||
\(977\) | 17.5700i | 0.562115i | 0.959691 | + | 0.281057i | \(0.0906851\pi\) | ||||
−0.959691 | + | 0.281057i | \(0.909315\pi\) | |||||||
\(978\) | 2.48858 | 0.0795761 | ||||||||
\(979\) | −33.7837 | −1.07973 | ||||||||
\(980\) | − 5.56465i | − 0.177756i | ||||||||
\(981\) | − 10.5211i | − 0.335913i | ||||||||
\(982\) | − 13.9866i | − 0.446330i | ||||||||
\(983\) | − 43.4935i | − 1.38723i | −0.720347 | − | 0.693613i | \(-0.756018\pi\) | ||||
0.720347 | − | 0.693613i | \(-0.243982\pi\) | |||||||
\(984\) | −0.198062 | −0.00631399 | ||||||||
\(985\) | −2.31336 | −0.0737096 | ||||||||
\(986\) | − 6.04487i | − 0.192508i | ||||||||
\(987\) | −1.08085 | −0.0344038 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.28083 | 0.136123 | ||||||||
\(990\) | 3.93900i | 0.125190i | ||||||||
\(991\) | 38.8232 | 1.23326 | 0.616630 | − | 0.787253i | \(-0.288497\pi\) | ||||
0.616630 | + | 0.787253i | \(0.288497\pi\) | |||||||
\(992\) | 2.15883 | 0.0685430 | ||||||||
\(993\) | 20.5109i | 0.650895i | ||||||||
\(994\) | 13.2634i | 0.420689i | ||||||||
\(995\) | − 6.36765i | − 0.201868i | ||||||||
\(996\) | − 15.5864i | − 0.493875i | ||||||||
\(997\) | −21.9807 | −0.696137 | −0.348069 | − | 0.937469i | \(-0.613162\pi\) | ||||
−0.348069 | + | 0.937469i | \(0.613162\pi\) | |||||||
\(998\) | 8.87071 | 0.280797 | ||||||||
\(999\) | − 4.80194i | − 0.151927i |
(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 | 5070.2.b.v.1351.3 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bl.1.1 | ✓ | 3 | ||
13.8 | odd | 4 | 5070.2.a.bs.1.3 | yes | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.v.1351.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bl.1.1 | ✓ | 3 | 13.5 | odd | 4 | ||
5070.2.a.bs.1.3 | yes | 3 | 13.8 | odd | 4 | ||
5070.2.b.v.1351.3 | 6 | 1.1 | even | 1 | trivial | ||
5070.2.b.v.1351.4 | 6 | 13.12 | even | 2 | inner |