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 | 1351.5 | ||
Root | \(0.445042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1351 |
Dual form | 5070.2.b.w.1351.2 |
$q$-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 | ||||||||
\(7\) | 3.44504i | 1.30210i | 0.759033 | + | 0.651052i | \(0.225672\pi\) | ||||
−0.759033 | + | 0.651052i | \(0.774328\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 4.24698i | 1.28051i | 0.768161 | + | 0.640256i | \(0.221172\pi\) | ||||
−0.768161 | + | 0.640256i | \(0.778828\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.44504 | −0.920726 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.78986 | −1.64678 | −0.823391 | − | 0.567474i | \(-0.807921\pi\) | ||||
−0.823391 | + | 0.567474i | \(0.807921\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | − 6.26875i | − 1.43815i | −0.694933 | − | 0.719075i | \(-0.744566\pi\) | ||||
0.694933 | − | 0.719075i | \(-0.255434\pi\) | |||||||
\(20\) | − 1.00000i | − 0.223607i | ||||||||
\(21\) | 3.44504i | 0.751770i | ||||||||
\(22\) | −4.24698 | −0.905459 | ||||||||
\(23\) | 1.30798 | 0.272732 | 0.136366 | − | 0.990658i | \(-0.456458\pi\) | ||||
0.136366 | + | 0.990658i | \(0.456458\pi\) | |||||||
\(24\) | − 1.00000i | − 0.204124i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | − 3.44504i | − 0.651052i | ||||||||
\(29\) | −9.14675 | −1.69851 | −0.849255 | − | 0.527984i | \(-0.822948\pi\) | ||||
−0.849255 | + | 0.527984i | \(0.822948\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | − 3.75302i | − 0.674062i | −0.941493 | − | 0.337031i | \(-0.890577\pi\) | ||||
0.941493 | − | 0.337031i | \(-0.109423\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 4.24698i | 0.739304i | ||||||||
\(34\) | − 6.78986i | − 1.16445i | ||||||||
\(35\) | −3.44504 | −0.582318 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 6.82908i | 1.12269i | 0.827580 | + | 0.561347i | \(0.189717\pi\) | ||||
−0.827580 | + | 0.561347i | \(0.810283\pi\) | |||||||
\(38\) | 6.26875 | 1.01693 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | − 4.26875i | − 0.666667i | −0.942809 | − | 0.333333i | \(-0.891827\pi\) | ||||
0.942809 | − | 0.333333i | \(-0.108173\pi\) | |||||||
\(42\) | −3.44504 | −0.531582 | ||||||||
\(43\) | −3.07069 | −0.468275 | −0.234138 | − | 0.972203i | \(-0.575227\pi\) | ||||
−0.234138 | + | 0.972203i | \(0.575227\pi\) | |||||||
\(44\) | − 4.24698i | − 0.640256i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | 1.30798i | 0.192851i | ||||||||
\(47\) | 7.76809i | 1.13309i | 0.824030 | + | 0.566546i | \(0.191721\pi\) | ||||
−0.824030 | + | 0.566546i | \(0.808279\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −4.86831 | −0.695473 | ||||||||
\(50\) | − 1.00000i | − 0.141421i | ||||||||
\(51\) | −6.78986 | −0.950770 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.93900 | −1.22787 | −0.613933 | − | 0.789358i | \(-0.710414\pi\) | ||||
−0.613933 | + | 0.789358i | \(0.710414\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −4.24698 | −0.572663 | ||||||||
\(56\) | 3.44504 | 0.460363 | ||||||||
\(57\) | − 6.26875i | − 0.830316i | ||||||||
\(58\) | − 9.14675i | − 1.20103i | ||||||||
\(59\) | − 10.3327i | − 1.34521i | −0.740003 | − | 0.672604i | \(-0.765176\pi\) | ||||
0.740003 | − | 0.672604i | \(-0.234824\pi\) | |||||||
\(60\) | − 1.00000i | − 0.129099i | ||||||||
\(61\) | 2.53319 | 0.324341 | 0.162171 | − | 0.986763i | \(-0.448150\pi\) | ||||
0.162171 | + | 0.986763i | \(0.448150\pi\) | |||||||
\(62\) | 3.75302 | 0.476634 | ||||||||
\(63\) | 3.44504i | 0.434034i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.24698 | −0.522767 | ||||||||
\(67\) | 0.0760644i | 0.00929275i | 0.999989 | + | 0.00464637i | \(0.00147899\pi\) | ||||
−0.999989 | + | 0.00464637i | \(0.998521\pi\) | |||||||
\(68\) | 6.78986 | 0.823391 | ||||||||
\(69\) | 1.30798 | 0.157462 | ||||||||
\(70\) | − 3.44504i | − 0.411761i | ||||||||
\(71\) | − 0.374354i | − 0.0444277i | −0.999753 | − | 0.0222138i | \(-0.992929\pi\) | ||||
0.999753 | − | 0.0222138i | \(-0.00707147\pi\) | |||||||
\(72\) | − 1.00000i | − 0.117851i | ||||||||
\(73\) | − 16.7114i | − 1.95592i | −0.208789 | − | 0.977961i | \(-0.566952\pi\) | ||||
0.208789 | − | 0.977961i | \(-0.433048\pi\) | |||||||
\(74\) | −6.82908 | −0.793865 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 6.26875i | 0.719075i | ||||||||
\(77\) | −14.6310 | −1.66736 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.33513 | −0.150213 | −0.0751067 | − | 0.997176i | \(-0.523930\pi\) | ||||
−0.0751067 | + | 0.997176i | \(0.523930\pi\) | |||||||
\(80\) | 1.00000i | 0.111803i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.26875 | 0.471405 | ||||||||
\(83\) | 0.740939i | 0.0813286i | 0.999173 | + | 0.0406643i | \(0.0129474\pi\) | ||||
−0.999173 | + | 0.0406643i | \(0.987053\pi\) | |||||||
\(84\) | − 3.44504i | − 0.375885i | ||||||||
\(85\) | − 6.78986i | − 0.736463i | ||||||||
\(86\) | − 3.07069i | − 0.331121i | ||||||||
\(87\) | −9.14675 | −0.980635 | ||||||||
\(88\) | 4.24698 | 0.452730 | ||||||||
\(89\) | 13.3274i | 1.41270i | 0.707864 | + | 0.706348i | \(0.249659\pi\) | ||||
−0.707864 | + | 0.706348i | \(0.750341\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.30798 | −0.136366 | ||||||||
\(93\) | − 3.75302i | − 0.389170i | ||||||||
\(94\) | −7.76809 | −0.801217 | ||||||||
\(95\) | 6.26875 | 0.643160 | ||||||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 13.1903i | 1.33927i | 0.742690 | + | 0.669636i | \(0.233550\pi\) | ||||
−0.742690 | + | 0.669636i | \(0.766450\pi\) | |||||||
\(98\) | − 4.86831i | − 0.491774i | ||||||||
\(99\) | 4.24698i | 0.426838i | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 15.0422 | 1.49676 | 0.748378 | − | 0.663272i | \(-0.230833\pi\) | ||||
0.748378 | + | 0.663272i | \(0.230833\pi\) | |||||||
\(102\) | − 6.78986i | − 0.672296i | ||||||||
\(103\) | 8.92154 | 0.879066 | 0.439533 | − | 0.898227i | \(-0.355144\pi\) | ||||
0.439533 | + | 0.898227i | \(0.355144\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.44504 | −0.336202 | ||||||||
\(106\) | − 8.93900i | − 0.868233i | ||||||||
\(107\) | 14.6746 | 1.41864 | 0.709322 | − | 0.704885i | \(-0.249001\pi\) | ||||
0.709322 | + | 0.704885i | \(0.249001\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | − 9.66786i | − 0.926013i | −0.886355 | − | 0.463006i | \(-0.846771\pi\) | ||||
0.886355 | − | 0.463006i | \(-0.153229\pi\) | |||||||
\(110\) | − 4.24698i | − 0.404934i | ||||||||
\(111\) | 6.82908i | 0.648188i | ||||||||
\(112\) | 3.44504i | 0.325526i | ||||||||
\(113\) | −11.3448 | −1.06723 | −0.533615 | − | 0.845727i | \(-0.679167\pi\) | ||||
−0.533615 | + | 0.845727i | \(0.679167\pi\) | |||||||
\(114\) | 6.26875 | 0.587122 | ||||||||
\(115\) | 1.30798i | 0.121970i | ||||||||
\(116\) | 9.14675 | 0.849255 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.3327 | 0.951205 | ||||||||
\(119\) | − 23.3913i | − 2.14428i | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | −7.03684 | −0.639712 | ||||||||
\(122\) | 2.53319i | 0.229344i | ||||||||
\(123\) | − 4.26875i | − 0.384900i | ||||||||
\(124\) | 3.75302i | 0.337031i | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | −3.44504 | −0.306909 | ||||||||
\(127\) | 2.54288 | 0.225644 | 0.112822 | − | 0.993615i | \(-0.464011\pi\) | ||||
0.112822 | + | 0.993615i | \(0.464011\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −3.07069 | −0.270359 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.8509 | −0.948044 | −0.474022 | − | 0.880513i | \(-0.657198\pi\) | ||||
−0.474022 | + | 0.880513i | \(0.657198\pi\) | |||||||
\(132\) | − 4.24698i | − 0.369652i | ||||||||
\(133\) | 21.5961 | 1.87262 | ||||||||
\(134\) | −0.0760644 | −0.00657096 | ||||||||
\(135\) | 1.00000i | 0.0860663i | ||||||||
\(136\) | 6.78986i | 0.582225i | ||||||||
\(137\) | − 18.6407i | − 1.59258i | −0.604913 | − | 0.796292i | \(-0.706792\pi\) | ||||
0.604913 | − | 0.796292i | \(-0.293208\pi\) | |||||||
\(138\) | 1.30798i | 0.111343i | ||||||||
\(139\) | 3.53750 | 0.300047 | 0.150023 | − | 0.988682i | \(-0.452065\pi\) | ||||
0.150023 | + | 0.988682i | \(0.452065\pi\) | |||||||
\(140\) | 3.44504 | 0.291159 | ||||||||
\(141\) | 7.76809i | 0.654191i | ||||||||
\(142\) | 0.374354 | 0.0314151 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | − 9.14675i | − 0.759596i | ||||||||
\(146\) | 16.7114 | 1.38305 | ||||||||
\(147\) | −4.86831 | −0.401532 | ||||||||
\(148\) | − 6.82908i | − 0.561347i | ||||||||
\(149\) | 16.6843i | 1.36683i | 0.730031 | + | 0.683414i | \(0.239505\pi\) | ||||
−0.730031 | + | 0.683414i | \(0.760495\pi\) | |||||||
\(150\) | − 1.00000i | − 0.0816497i | ||||||||
\(151\) | 18.3327i | 1.49190i | 0.666004 | + | 0.745948i | \(0.268003\pi\) | ||||
−0.666004 | + | 0.745948i | \(0.731997\pi\) | |||||||
\(152\) | −6.26875 | −0.508463 | ||||||||
\(153\) | −6.78986 | −0.548927 | ||||||||
\(154\) | − 14.6310i | − 1.17900i | ||||||||
\(155\) | 3.75302 | 0.301450 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6015 | −1.48456 | −0.742280 | − | 0.670090i | \(-0.766256\pi\) | ||||
−0.742280 | + | 0.670090i | \(0.766256\pi\) | |||||||
\(158\) | − 1.33513i | − 0.106217i | ||||||||
\(159\) | −8.93900 | −0.708909 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 4.50604i | 0.355126i | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 18.8944i | 1.47992i | 0.672649 | + | 0.739962i | \(0.265156\pi\) | ||||
−0.672649 | + | 0.739962i | \(0.734844\pi\) | |||||||
\(164\) | 4.26875i | 0.333333i | ||||||||
\(165\) | −4.24698 | −0.330627 | ||||||||
\(166\) | −0.740939 | −0.0575080 | ||||||||
\(167\) | − 4.24698i | − 0.328641i | −0.986407 | − | 0.164321i | \(-0.947457\pi\) | ||||
0.986407 | − | 0.164321i | \(-0.0525432\pi\) | |||||||
\(168\) | 3.44504 | 0.265791 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 6.78986 | 0.520758 | ||||||||
\(171\) | − 6.26875i | − 0.479383i | ||||||||
\(172\) | 3.07069 | 0.234138 | ||||||||
\(173\) | −1.16852 | −0.0888411 | −0.0444206 | − | 0.999013i | \(-0.514144\pi\) | ||||
−0.0444206 | + | 0.999013i | \(0.514144\pi\) | |||||||
\(174\) | − 9.14675i | − 0.693413i | ||||||||
\(175\) | − 3.44504i | − 0.260421i | ||||||||
\(176\) | 4.24698i | 0.320128i | ||||||||
\(177\) | − 10.3327i | − 0.776656i | ||||||||
\(178\) | −13.3274 | −0.998928 | ||||||||
\(179\) | 10.1836 | 0.761157 | 0.380579 | − | 0.924749i | \(-0.375725\pi\) | ||||
0.380579 | + | 0.924749i | \(0.375725\pi\) | |||||||
\(180\) | − 1.00000i | − 0.0745356i | ||||||||
\(181\) | −10.3351 | −0.768204 | −0.384102 | − | 0.923291i | \(-0.625489\pi\) | ||||
−0.384102 | + | 0.923291i | \(0.625489\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.53319 | 0.187259 | ||||||||
\(184\) | − 1.30798i | − 0.0964255i | ||||||||
\(185\) | −6.82908 | −0.502084 | ||||||||
\(186\) | 3.75302 | 0.275185 | ||||||||
\(187\) | − 28.8364i | − 2.10872i | ||||||||
\(188\) | − 7.76809i | − 0.566546i | ||||||||
\(189\) | 3.44504i | 0.250590i | ||||||||
\(190\) | 6.26875i | 0.454783i | ||||||||
\(191\) | −9.43296 | −0.682545 | −0.341273 | − | 0.939964i | \(-0.610858\pi\) | ||||
−0.341273 | + | 0.939964i | \(0.610858\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 22.9191i | 1.64976i | 0.565310 | + | 0.824878i | \(0.308756\pi\) | ||||
−0.565310 | + | 0.824878i | \(0.691244\pi\) | |||||||
\(194\) | −13.1903 | −0.947008 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.86831 | 0.347737 | ||||||||
\(197\) | 14.3502i | 1.02241i | 0.859459 | + | 0.511204i | \(0.170800\pi\) | ||||
−0.859459 | + | 0.511204i | \(0.829200\pi\) | |||||||
\(198\) | −4.24698 | −0.301820 | ||||||||
\(199\) | −14.2524 | −1.01032 | −0.505161 | − | 0.863025i | \(-0.668567\pi\) | ||||
−0.505161 | + | 0.863025i | \(0.668567\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0.0760644i | 0.00536517i | ||||||||
\(202\) | 15.0422i | 1.05837i | ||||||||
\(203\) | − 31.5109i | − 2.21163i | ||||||||
\(204\) | 6.78986 | 0.475385 | ||||||||
\(205\) | 4.26875 | 0.298142 | ||||||||
\(206\) | 8.92154i | 0.621593i | ||||||||
\(207\) | 1.30798 | 0.0909108 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 26.6233 | 1.84157 | ||||||||
\(210\) | − 3.44504i | − 0.237730i | ||||||||
\(211\) | 0.396125 | 0.0272703 | 0.0136352 | − | 0.999907i | \(-0.495660\pi\) | ||||
0.0136352 | + | 0.999907i | \(0.495660\pi\) | |||||||
\(212\) | 8.93900 | 0.613933 | ||||||||
\(213\) | − 0.374354i | − 0.0256503i | ||||||||
\(214\) | 14.6746i | 1.00313i | ||||||||
\(215\) | − 3.07069i | − 0.209419i | ||||||||
\(216\) | − 1.00000i | − 0.0680414i | ||||||||
\(217\) | 12.9293 | 0.877699 | ||||||||
\(218\) | 9.66786 | 0.654790 | ||||||||
\(219\) | − 16.7114i | − 1.12925i | ||||||||
\(220\) | 4.24698 | 0.286331 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.82908 | −0.458338 | ||||||||
\(223\) | − 1.49635i | − 0.100203i | −0.998744 | − | 0.0501016i | \(-0.984045\pi\) | ||||
0.998744 | − | 0.0501016i | \(-0.0159545\pi\) | |||||||
\(224\) | −3.44504 | −0.230182 | ||||||||
\(225\) | −1.00000 | −0.0666667 | ||||||||
\(226\) | − 11.3448i | − 0.754646i | ||||||||
\(227\) | − 25.2150i | − 1.67358i | −0.547523 | − | 0.836791i | \(-0.684429\pi\) | ||||
0.547523 | − | 0.836791i | \(-0.315571\pi\) | |||||||
\(228\) | 6.26875i | 0.415158i | ||||||||
\(229\) | − 22.3666i | − 1.47803i | −0.673691 | − | 0.739013i | \(-0.735292\pi\) | ||||
0.673691 | − | 0.739013i | \(-0.264708\pi\) | |||||||
\(230\) | −1.30798 | −0.0862456 | ||||||||
\(231\) | −14.6310 | −0.962651 | ||||||||
\(232\) | 9.14675i | 0.600514i | ||||||||
\(233\) | −14.0858 | −0.922788 | −0.461394 | − | 0.887195i | \(-0.652651\pi\) | ||||
−0.461394 | + | 0.887195i | \(0.652651\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.76809 | −0.506734 | ||||||||
\(236\) | 10.3327i | 0.672604i | ||||||||
\(237\) | −1.33513 | −0.0867257 | ||||||||
\(238\) | 23.3913 | 1.51624 | ||||||||
\(239\) | − 5.38106i | − 0.348072i | −0.984739 | − | 0.174036i | \(-0.944319\pi\) | ||||
0.984739 | − | 0.174036i | \(-0.0556809\pi\) | |||||||
\(240\) | 1.00000i | 0.0645497i | ||||||||
\(241\) | − 29.9420i | − 1.92873i | −0.264570 | − | 0.964366i | \(-0.585230\pi\) | ||||
0.264570 | − | 0.964366i | \(-0.414770\pi\) | |||||||
\(242\) | − 7.03684i | − 0.452345i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.53319 | −0.162171 | ||||||||
\(245\) | − 4.86831i | − 0.311025i | ||||||||
\(246\) | 4.26875 | 0.272166 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.75302 | −0.238317 | ||||||||
\(249\) | 0.740939i | 0.0469551i | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 8.73556 | 0.551384 | 0.275692 | − | 0.961246i | \(-0.411093\pi\) | ||||
0.275692 | + | 0.961246i | \(0.411093\pi\) | |||||||
\(252\) | − 3.44504i | − 0.217017i | ||||||||
\(253\) | 5.55496i | 0.349237i | ||||||||
\(254\) | 2.54288i | 0.159554i | ||||||||
\(255\) | − 6.78986i | − 0.425197i | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −21.2717 | −1.32689 | −0.663447 | − | 0.748223i | \(-0.730907\pi\) | ||||
−0.663447 | + | 0.748223i | \(0.730907\pi\) | |||||||
\(258\) | − 3.07069i | − 0.191173i | ||||||||
\(259\) | −23.5265 | −1.46186 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.14675 | −0.566170 | ||||||||
\(262\) | − 10.8509i | − 0.670368i | ||||||||
\(263\) | −22.2325 | −1.37091 | −0.685457 | − | 0.728113i | \(-0.740398\pi\) | ||||
−0.685457 | + | 0.728113i | \(0.740398\pi\) | |||||||
\(264\) | 4.24698 | 0.261384 | ||||||||
\(265\) | − 8.93900i | − 0.549118i | ||||||||
\(266\) | 21.5961i | 1.32414i | ||||||||
\(267\) | 13.3274i | 0.815621i | ||||||||
\(268\) | − 0.0760644i | − 0.00464637i | ||||||||
\(269\) | −10.2241 | −0.623377 | −0.311689 | − | 0.950184i | \(-0.600895\pi\) | ||||
−0.311689 | + | 0.950184i | \(0.600895\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | 0.716185i | 0.0435051i | 0.999763 | + | 0.0217526i | \(0.00692460\pi\) | ||||
−0.999763 | + | 0.0217526i | \(0.993075\pi\) | |||||||
\(272\) | −6.78986 | −0.411696 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.6407 | 1.12613 | ||||||||
\(275\) | − 4.24698i | − 0.256103i | ||||||||
\(276\) | −1.30798 | −0.0787311 | ||||||||
\(277\) | 22.8713 | 1.37420 | 0.687102 | − | 0.726561i | \(-0.258883\pi\) | ||||
0.687102 | + | 0.726561i | \(0.258883\pi\) | |||||||
\(278\) | 3.53750i | 0.212165i | ||||||||
\(279\) | − 3.75302i | − 0.224687i | ||||||||
\(280\) | 3.44504i | 0.205881i | ||||||||
\(281\) | 4.13036i | 0.246397i | 0.992382 | + | 0.123198i | \(0.0393151\pi\) | ||||
−0.992382 | + | 0.123198i | \(0.960685\pi\) | |||||||
\(282\) | −7.76809 | −0.462583 | ||||||||
\(283\) | −16.2959 | −0.968691 | −0.484345 | − | 0.874877i | \(-0.660942\pi\) | ||||
−0.484345 | + | 0.874877i | \(0.660942\pi\) | |||||||
\(284\) | 0.374354i | 0.0222138i | ||||||||
\(285\) | 6.26875 | 0.371329 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 14.7060 | 0.868069 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 29.1021 | 1.71189 | ||||||||
\(290\) | 9.14675 | 0.537116 | ||||||||
\(291\) | 13.1903i | 0.773229i | ||||||||
\(292\) | 16.7114i | 0.977961i | ||||||||
\(293\) | 7.72587i | 0.451350i | 0.974203 | + | 0.225675i | \(0.0724588\pi\) | ||||
−0.974203 | + | 0.225675i | \(0.927541\pi\) | |||||||
\(294\) | − 4.86831i | − 0.283926i | ||||||||
\(295\) | 10.3327 | 0.601595 | ||||||||
\(296\) | 6.82908 | 0.396932 | ||||||||
\(297\) | 4.24698i | 0.246435i | ||||||||
\(298\) | −16.6843 | −0.966493 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | − 10.5786i | − 0.609743i | ||||||||
\(302\) | −18.3327 | −1.05493 | ||||||||
\(303\) | 15.0422 | 0.864153 | ||||||||
\(304\) | − 6.26875i | − 0.359537i | ||||||||
\(305\) | 2.53319i | 0.145050i | ||||||||
\(306\) | − 6.78986i | − 0.388150i | ||||||||
\(307\) | − 5.13036i | − 0.292805i | −0.989225 | − | 0.146403i | \(-0.953231\pi\) | ||||
0.989225 | − | 0.146403i | \(-0.0467695\pi\) | |||||||
\(308\) | 14.6310 | 0.833680 | ||||||||
\(309\) | 8.92154 | 0.507529 | ||||||||
\(310\) | 3.75302i | 0.213157i | ||||||||
\(311\) | −33.1987 | −1.88252 | −0.941261 | − | 0.337679i | \(-0.890358\pi\) | ||||
−0.941261 | + | 0.337679i | \(0.890358\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.0814412 | 0.00460333 | 0.00230167 | − | 0.999997i | \(-0.499267\pi\) | ||||
0.00230167 | + | 0.999997i | \(0.499267\pi\) | |||||||
\(314\) | − 18.6015i | − 1.04974i | ||||||||
\(315\) | −3.44504 | −0.194106 | ||||||||
\(316\) | 1.33513 | 0.0751067 | ||||||||
\(317\) | 19.4969i | 1.09506i | 0.836787 | + | 0.547529i | \(0.184431\pi\) | ||||
−0.836787 | + | 0.547529i | \(0.815569\pi\) | |||||||
\(318\) | − 8.93900i | − 0.501274i | ||||||||
\(319\) | − 38.8461i | − 2.17496i | ||||||||
\(320\) | − 1.00000i | − 0.0559017i | ||||||||
\(321\) | 14.6746 | 0.819054 | ||||||||
\(322\) | −4.50604 | −0.251112 | ||||||||
\(323\) | 42.5639i | 2.36832i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −18.8944 | −1.04646 | ||||||||
\(327\) | − 9.66786i | − 0.534634i | ||||||||
\(328\) | −4.26875 | −0.235702 | ||||||||
\(329\) | −26.7614 | −1.47540 | ||||||||
\(330\) | − 4.24698i | − 0.233789i | ||||||||
\(331\) | − 23.8049i | − 1.30844i | −0.756306 | − | 0.654218i | \(-0.772998\pi\) | ||||
0.756306 | − | 0.654218i | \(-0.227002\pi\) | |||||||
\(332\) | − 0.740939i | − 0.0406643i | ||||||||
\(333\) | 6.82908i | 0.374232i | ||||||||
\(334\) | 4.24698 | 0.232384 | ||||||||
\(335\) | −0.0760644 | −0.00415584 | ||||||||
\(336\) | 3.44504i | 0.187942i | ||||||||
\(337\) | −21.2064 | −1.15519 | −0.577594 | − | 0.816324i | \(-0.696008\pi\) | ||||
−0.577594 | + | 0.816324i | \(0.696008\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −11.3448 | −0.616166 | ||||||||
\(340\) | 6.78986i | 0.368232i | ||||||||
\(341\) | 15.9390 | 0.863145 | ||||||||
\(342\) | 6.26875 | 0.338975 | ||||||||
\(343\) | 7.34375i | 0.396525i | ||||||||
\(344\) | 3.07069i | 0.165560i | ||||||||
\(345\) | 1.30798i | 0.0704192i | ||||||||
\(346\) | − 1.16852i | − 0.0628201i | ||||||||
\(347\) | −16.5773 | −0.889917 | −0.444959 | − | 0.895551i | \(-0.646782\pi\) | ||||
−0.444959 | + | 0.895551i | \(0.646782\pi\) | |||||||
\(348\) | 9.14675 | 0.490317 | ||||||||
\(349\) | 2.51035i | 0.134376i | 0.997740 | + | 0.0671880i | \(0.0214027\pi\) | ||||
−0.997740 | + | 0.0671880i | \(0.978597\pi\) | |||||||
\(350\) | 3.44504 | 0.184145 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.24698 | −0.226365 | ||||||||
\(353\) | 20.8412i | 1.10926i | 0.832096 | + | 0.554632i | \(0.187141\pi\) | ||||
−0.832096 | + | 0.554632i | \(0.812859\pi\) | |||||||
\(354\) | 10.3327 | 0.549179 | ||||||||
\(355\) | 0.374354 | 0.0198687 | ||||||||
\(356\) | − 13.3274i | − 0.706348i | ||||||||
\(357\) | − 23.3913i | − 1.23800i | ||||||||
\(358\) | 10.1836i | 0.538219i | ||||||||
\(359\) | 2.42566i | 0.128022i | 0.997949 | + | 0.0640108i | \(0.0203892\pi\) | ||||
−0.997949 | + | 0.0640108i | \(0.979611\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −20.2972 | −1.06827 | ||||||||
\(362\) | − 10.3351i | − 0.543202i | ||||||||
\(363\) | −7.03684 | −0.369338 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.7114 | 0.874715 | ||||||||
\(366\) | 2.53319i | 0.132412i | ||||||||
\(367\) | 2.66248 | 0.138980 | 0.0694902 | − | 0.997583i | \(-0.477863\pi\) | ||||
0.0694902 | + | 0.997583i | \(0.477863\pi\) | |||||||
\(368\) | 1.30798 | 0.0681831 | ||||||||
\(369\) | − 4.26875i | − 0.222222i | ||||||||
\(370\) | − 6.82908i | − 0.355027i | ||||||||
\(371\) | − 30.7952i | − 1.59881i | ||||||||
\(372\) | 3.75302i | 0.194585i | ||||||||
\(373\) | 5.87800 | 0.304351 | 0.152176 | − | 0.988353i | \(-0.451372\pi\) | ||||
0.152176 | + | 0.988353i | \(0.451372\pi\) | |||||||
\(374\) | 28.8364 | 1.49109 | ||||||||
\(375\) | − 1.00000i | − 0.0516398i | ||||||||
\(376\) | 7.76809 | 0.400608 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.44504 | −0.177194 | ||||||||
\(379\) | − 36.1540i | − 1.85711i | −0.371196 | − | 0.928554i | \(-0.621052\pi\) | ||||
0.371196 | − | 0.928554i | \(-0.378948\pi\) | |||||||
\(380\) | −6.26875 | −0.321580 | ||||||||
\(381\) | 2.54288 | 0.130276 | ||||||||
\(382\) | − 9.43296i | − 0.482632i | ||||||||
\(383\) | 8.98361i | 0.459041i | 0.973304 | + | 0.229520i | \(0.0737158\pi\) | ||||
−0.973304 | + | 0.229520i | \(0.926284\pi\) | |||||||
\(384\) | − 1.00000i | − 0.0510310i | ||||||||
\(385\) | − 14.6310i | − 0.745666i | ||||||||
\(386\) | −22.9191 | −1.16655 | ||||||||
\(387\) | −3.07069 | −0.156092 | ||||||||
\(388\) | − 13.1903i | − 0.669636i | ||||||||
\(389\) | −0.655186 | −0.0332192 | −0.0166096 | − | 0.999862i | \(-0.505287\pi\) | ||||
−0.0166096 | + | 0.999862i | \(0.505287\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.88099 | −0.449131 | ||||||||
\(392\) | 4.86831i | 0.245887i | ||||||||
\(393\) | −10.8509 | −0.547353 | ||||||||
\(394\) | −14.3502 | −0.722952 | ||||||||
\(395\) | − 1.33513i | − 0.0671775i | ||||||||
\(396\) | − 4.24698i | − 0.213419i | ||||||||
\(397\) | 0.271143i | 0.0136083i | 0.999977 | + | 0.00680413i | \(0.00216584\pi\) | ||||
−0.999977 | + | 0.00680413i | \(0.997834\pi\) | |||||||
\(398\) | − 14.2524i | − 0.714406i | ||||||||
\(399\) | 21.5961 | 1.08116 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 0.344814i | 0.0172192i | 0.999963 | + | 0.00860960i | \(0.00274056\pi\) | ||||
−0.999963 | + | 0.00860960i | \(0.997259\pi\) | |||||||
\(402\) | −0.0760644 | −0.00379375 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −15.0422 | −0.748378 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 31.5109 | 1.56386 | ||||||||
\(407\) | −29.0030 | −1.43762 | ||||||||
\(408\) | 6.78986i | 0.336148i | ||||||||
\(409\) | − 27.0388i | − 1.33698i | −0.743721 | − | 0.668490i | \(-0.766941\pi\) | ||||
0.743721 | − | 0.668490i | \(-0.233059\pi\) | |||||||
\(410\) | 4.26875i | 0.210819i | ||||||||
\(411\) | − 18.6407i | − 0.919478i | ||||||||
\(412\) | −8.92154 | −0.439533 | ||||||||
\(413\) | 35.5967 | 1.75160 | ||||||||
\(414\) | 1.30798i | 0.0642836i | ||||||||
\(415\) | −0.740939 | −0.0363713 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.53750 | 0.173232 | ||||||||
\(418\) | 26.6233i | 1.30219i | ||||||||
\(419\) | 5.86533 | 0.286540 | 0.143270 | − | 0.989684i | \(-0.454238\pi\) | ||||
0.143270 | + | 0.989684i | \(0.454238\pi\) | |||||||
\(420\) | 3.44504 | 0.168101 | ||||||||
\(421\) | 28.9476i | 1.41082i | 0.708799 | + | 0.705410i | \(0.249237\pi\) | ||||
−0.708799 | + | 0.705410i | \(0.750763\pi\) | |||||||
\(422\) | 0.396125i | 0.0192830i | ||||||||
\(423\) | 7.76809i | 0.377697i | ||||||||
\(424\) | 8.93900i | 0.434116i | ||||||||
\(425\) | 6.78986 | 0.329356 | ||||||||
\(426\) | 0.374354 | 0.0181375 | ||||||||
\(427\) | 8.72694i | 0.422326i | ||||||||
\(428\) | −14.6746 | −0.709322 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.07069 | 0.148082 | ||||||||
\(431\) | − 4.87023i | − 0.234591i | −0.993097 | − | 0.117295i | \(-0.962578\pi\) | ||||
0.993097 | − | 0.117295i | \(-0.0374224\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 36.9788 | 1.77709 | 0.888544 | − | 0.458791i | \(-0.151717\pi\) | ||||
0.888544 | + | 0.458791i | \(0.151717\pi\) | |||||||
\(434\) | 12.9293i | 0.620627i | ||||||||
\(435\) | − 9.14675i | − 0.438553i | ||||||||
\(436\) | 9.66786i | 0.463006i | ||||||||
\(437\) | − 8.19939i | − 0.392230i | ||||||||
\(438\) | 16.7114 | 0.798502 | ||||||||
\(439\) | −22.8799 | −1.09200 | −0.546000 | − | 0.837785i | \(-0.683850\pi\) | ||||
−0.546000 | + | 0.837785i | \(0.683850\pi\) | |||||||
\(440\) | 4.24698i | 0.202467i | ||||||||
\(441\) | −4.86831 | −0.231824 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.5942 | −0.503345 | −0.251673 | − | 0.967812i | \(-0.580981\pi\) | ||||
−0.251673 | + | 0.967812i | \(0.580981\pi\) | |||||||
\(444\) | − 6.82908i | − 0.324094i | ||||||||
\(445\) | −13.3274 | −0.631777 | ||||||||
\(446\) | 1.49635 | 0.0708543 | ||||||||
\(447\) | 16.6843i | 0.789138i | ||||||||
\(448\) | − 3.44504i | − 0.162763i | ||||||||
\(449\) | 19.6485i | 0.927269i | 0.886027 | + | 0.463635i | \(0.153455\pi\) | ||||
−0.886027 | + | 0.463635i | \(0.846545\pi\) | |||||||
\(450\) | − 1.00000i | − 0.0471405i | ||||||||
\(451\) | 18.1293 | 0.853675 | ||||||||
\(452\) | 11.3448 | 0.533615 | ||||||||
\(453\) | 18.3327i | 0.861347i | ||||||||
\(454\) | 25.2150 | 1.18340 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.26875 | −0.293561 | ||||||||
\(457\) | 18.4239i | 0.861832i | 0.902392 | + | 0.430916i | \(0.141809\pi\) | ||||
−0.902392 | + | 0.430916i | \(0.858191\pi\) | |||||||
\(458\) | 22.3666 | 1.04512 | ||||||||
\(459\) | −6.78986 | −0.316923 | ||||||||
\(460\) | − 1.30798i | − 0.0609848i | ||||||||
\(461\) | 22.2446i | 1.03603i | 0.855370 | + | 0.518017i | \(0.173330\pi\) | ||||
−0.855370 | + | 0.518017i | \(0.826670\pi\) | |||||||
\(462\) | − 14.6310i | − 0.680697i | ||||||||
\(463\) | − 8.68532i | − 0.403641i | −0.979423 | − | 0.201820i | \(-0.935314\pi\) | ||||
0.979423 | − | 0.201820i | \(-0.0646857\pi\) | |||||||
\(464\) | −9.14675 | −0.424627 | ||||||||
\(465\) | 3.75302 | 0.174042 | ||||||||
\(466\) | − 14.0858i | − 0.652510i | ||||||||
\(467\) | −19.6136 | −0.907608 | −0.453804 | − | 0.891102i | \(-0.649933\pi\) | ||||
−0.453804 | + | 0.891102i | \(0.649933\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.262045 | −0.0121001 | ||||||||
\(470\) | − 7.76809i | − 0.358315i | ||||||||
\(471\) | −18.6015 | −0.857111 | ||||||||
\(472\) | −10.3327 | −0.475603 | ||||||||
\(473\) | − 13.0411i | − 0.599633i | ||||||||
\(474\) | − 1.33513i | − 0.0613243i | ||||||||
\(475\) | 6.26875i | 0.287630i | ||||||||
\(476\) | 23.3913i | 1.07214i | ||||||||
\(477\) | −8.93900 | −0.409289 | ||||||||
\(478\) | 5.38106 | 0.246124 | ||||||||
\(479\) | 31.4698i | 1.43789i | 0.695066 | + | 0.718946i | \(0.255375\pi\) | ||||
−0.695066 | + | 0.718946i | \(0.744625\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 29.9420 | 1.36382 | ||||||||
\(483\) | 4.50604i | 0.205032i | ||||||||
\(484\) | 7.03684 | 0.319856 | ||||||||
\(485\) | −13.1903 | −0.598940 | ||||||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | − 13.2644i | − 0.601069i | −0.953771 | − | 0.300535i | \(-0.902835\pi\) | ||||
0.953771 | − | 0.300535i | \(-0.0971651\pi\) | |||||||
\(488\) | − 2.53319i | − 0.114672i | ||||||||
\(489\) | 18.8944i | 0.854434i | ||||||||
\(490\) | 4.86831 | 0.219928 | ||||||||
\(491\) | −11.7259 | −0.529181 | −0.264591 | − | 0.964361i | \(-0.585237\pi\) | ||||
−0.264591 | + | 0.964361i | \(0.585237\pi\) | |||||||
\(492\) | 4.26875i | 0.192450i | ||||||||
\(493\) | 62.1051 | 2.79707 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.24698 | −0.190888 | ||||||||
\(496\) | − 3.75302i | − 0.168516i | ||||||||
\(497\) | 1.28967 | 0.0578494 | ||||||||
\(498\) | −0.740939 | −0.0332023 | ||||||||
\(499\) | 26.7633i | 1.19809i | 0.800715 | + | 0.599045i | \(0.204453\pi\) | ||||
−0.800715 | + | 0.599045i | \(0.795547\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | − 4.24698i | − 0.189741i | ||||||||
\(502\) | 8.73556i | 0.389887i | ||||||||
\(503\) | 17.2239 | 0.767975 | 0.383987 | − | 0.923338i | \(-0.374551\pi\) | ||||
0.383987 | + | 0.923338i | \(0.374551\pi\) | |||||||
\(504\) | 3.44504 | 0.153454 | ||||||||
\(505\) | 15.0422i | 0.669370i | ||||||||
\(506\) | −5.55496 | −0.246948 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.54288 | −0.112822 | ||||||||
\(509\) | 28.2737i | 1.25321i | 0.779338 | + | 0.626604i | \(0.215556\pi\) | ||||
−0.779338 | + | 0.626604i | \(0.784444\pi\) | |||||||
\(510\) | 6.78986 | 0.300660 | ||||||||
\(511\) | 57.5715 | 2.54681 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 6.26875i | − 0.276772i | ||||||||
\(514\) | − 21.2717i | − 0.938256i | ||||||||
\(515\) | 8.92154i | 0.393130i | ||||||||
\(516\) | 3.07069 | 0.135179 | ||||||||
\(517\) | −32.9909 | −1.45094 | ||||||||
\(518\) | − 23.5265i | − 1.03369i | ||||||||
\(519\) | −1.16852 | −0.0512924 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.47889 | 0.0647915 | 0.0323958 | − | 0.999475i | \(-0.489686\pi\) | ||||
0.0323958 | + | 0.999475i | \(0.489686\pi\) | |||||||
\(522\) | − 9.14675i | − 0.400342i | ||||||||
\(523\) | −28.2198 | −1.23397 | −0.616984 | − | 0.786976i | \(-0.711646\pi\) | ||||
−0.616984 | + | 0.786976i | \(0.711646\pi\) | |||||||
\(524\) | 10.8509 | 0.474022 | ||||||||
\(525\) | − 3.44504i | − 0.150354i | ||||||||
\(526\) | − 22.2325i | − 0.969383i | ||||||||
\(527\) | 25.4825i | 1.11003i | ||||||||
\(528\) | 4.24698i | 0.184826i | ||||||||
\(529\) | −21.2892 | −0.925617 | ||||||||
\(530\) | 8.93900 | 0.388285 | ||||||||
\(531\) | − 10.3327i | − 0.448402i | ||||||||
\(532\) | −21.5961 | −0.936310 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −13.3274 | −0.576731 | ||||||||
\(535\) | 14.6746i | 0.634437i | ||||||||
\(536\) | 0.0760644 | 0.00328548 | ||||||||
\(537\) | 10.1836 | 0.439454 | ||||||||
\(538\) | − 10.2241i | − 0.440794i | ||||||||
\(539\) | − 20.6756i | − 0.890562i | ||||||||
\(540\) | − 1.00000i | − 0.0430331i | ||||||||
\(541\) | 0.245915i | 0.0105727i | 0.999986 | + | 0.00528635i | \(0.00168270\pi\) | ||||
−0.999986 | + | 0.00528635i | \(0.998317\pi\) | |||||||
\(542\) | −0.716185 | −0.0307628 | ||||||||
\(543\) | −10.3351 | −0.443523 | ||||||||
\(544\) | − 6.78986i | − 0.291113i | ||||||||
\(545\) | 9.66786 | 0.414126 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.6407 | −0.583235 | −0.291617 | − | 0.956535i | \(-0.594193\pi\) | ||||
−0.291617 | + | 0.956535i | \(0.594193\pi\) | |||||||
\(548\) | 18.6407i | 0.796292i | ||||||||
\(549\) | 2.53319 | 0.108114 | ||||||||
\(550\) | 4.24698 | 0.181092 | ||||||||
\(551\) | 57.3387i | 2.44271i | ||||||||
\(552\) | − 1.30798i | − 0.0556713i | ||||||||
\(553\) | − 4.59956i | − 0.195593i | ||||||||
\(554\) | 22.8713i | 0.971708i | ||||||||
\(555\) | −6.82908 | −0.289879 | ||||||||
\(556\) | −3.53750 | −0.150023 | ||||||||
\(557\) | 14.0248i | 0.594248i | 0.954839 | + | 0.297124i | \(0.0960275\pi\) | ||||
−0.954839 | + | 0.297124i | \(0.903973\pi\) | |||||||
\(558\) | 3.75302 | 0.158878 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −3.44504 | −0.145580 | ||||||||
\(561\) | − 28.8364i | − 1.21747i | ||||||||
\(562\) | −4.13036 | −0.174229 | ||||||||
\(563\) | 3.26981 | 0.137806 | 0.0689031 | − | 0.997623i | \(-0.478050\pi\) | ||||
0.0689031 | + | 0.997623i | \(0.478050\pi\) | |||||||
\(564\) | − 7.76809i | − 0.327095i | ||||||||
\(565\) | − 11.3448i | − 0.477280i | ||||||||
\(566\) | − 16.2959i | − 0.684968i | ||||||||
\(567\) | 3.44504i | 0.144678i | ||||||||
\(568\) | −0.374354 | −0.0157076 | ||||||||
\(569\) | −4.10752 | −0.172196 | −0.0860982 | − | 0.996287i | \(-0.527440\pi\) | ||||
−0.0860982 | + | 0.996287i | \(0.527440\pi\) | |||||||
\(570\) | 6.26875i | 0.262569i | ||||||||
\(571\) | −9.18465 | −0.384366 | −0.192183 | − | 0.981359i | \(-0.561557\pi\) | ||||
−0.192183 | + | 0.981359i | \(0.561557\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.43296 | −0.394068 | ||||||||
\(574\) | 14.7060i | 0.613817i | ||||||||
\(575\) | −1.30798 | −0.0545465 | ||||||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | − 28.0000i | − 1.16566i | −0.812596 | − | 0.582828i | \(-0.801946\pi\) | ||||
0.812596 | − | 0.582828i | \(-0.198054\pi\) | |||||||
\(578\) | 29.1021i | 1.21049i | ||||||||
\(579\) | 22.9191i | 0.952487i | ||||||||
\(580\) | 9.14675i | 0.379798i | ||||||||
\(581\) | −2.55257 | −0.105898 | ||||||||
\(582\) | −13.1903 | −0.546755 | ||||||||
\(583\) | − 37.9638i | − 1.57230i | ||||||||
\(584\) | −16.7114 | −0.691523 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.72587 | −0.319153 | ||||||||
\(587\) | 47.6765i | 1.96782i | 0.178668 | + | 0.983910i | \(0.442821\pi\) | ||||
−0.178668 | + | 0.983910i | \(0.557179\pi\) | |||||||
\(588\) | 4.86831 | 0.200766 | ||||||||
\(589\) | −23.5267 | −0.969403 | ||||||||
\(590\) | 10.3327i | 0.425392i | ||||||||
\(591\) | 14.3502i | 0.590288i | ||||||||
\(592\) | 6.82908i | 0.280674i | ||||||||
\(593\) | − 16.7681i | − 0.688583i | −0.938863 | − | 0.344291i | \(-0.888119\pi\) | ||||
0.938863 | − | 0.344291i | \(-0.111881\pi\) | |||||||
\(594\) | −4.24698 | −0.174256 | ||||||||
\(595\) | 23.3913 | 0.958951 | ||||||||
\(596\) | − 16.6843i | − 0.683414i | ||||||||
\(597\) | −14.2524 | −0.583310 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.0157 | 1.79843 | 0.899215 | − | 0.437506i | \(-0.144138\pi\) | ||||
0.899215 | + | 0.437506i | \(0.144138\pi\) | |||||||
\(600\) | 1.00000i | 0.0408248i | ||||||||
\(601\) | 39.1299 | 1.59614 | 0.798071 | − | 0.602564i | \(-0.205854\pi\) | ||||
0.798071 | + | 0.602564i | \(0.205854\pi\) | |||||||
\(602\) | 10.5786 | 0.431153 | ||||||||
\(603\) | 0.0760644i | 0.00309758i | ||||||||
\(604\) | − 18.3327i | − 0.745948i | ||||||||
\(605\) | − 7.03684i | − 0.286088i | ||||||||
\(606\) | 15.0422i | 0.611048i | ||||||||
\(607\) | 6.33273 | 0.257038 | 0.128519 | − | 0.991707i | \(-0.458978\pi\) | ||||
0.128519 | + | 0.991707i | \(0.458978\pi\) | |||||||
\(608\) | 6.26875 | 0.254231 | ||||||||
\(609\) | − 31.5109i | − 1.27689i | ||||||||
\(610\) | −2.53319 | −0.102566 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.78986 | 0.274464 | ||||||||
\(613\) | − 29.1129i | − 1.17586i | −0.808912 | − | 0.587929i | \(-0.799943\pi\) | ||||
0.808912 | − | 0.587929i | \(-0.200057\pi\) | |||||||
\(614\) | 5.13036 | 0.207044 | ||||||||
\(615\) | 4.26875 | 0.172133 | ||||||||
\(616\) | 14.6310i | 0.589501i | ||||||||
\(617\) | 27.9933i | 1.12697i | 0.826127 | + | 0.563484i | \(0.190539\pi\) | ||||
−0.826127 | + | 0.563484i | \(0.809461\pi\) | |||||||
\(618\) | 8.92154i | 0.358877i | ||||||||
\(619\) | 23.0084i | 0.924784i | 0.886676 | + | 0.462392i | \(0.153009\pi\) | ||||
−0.886676 | + | 0.462392i | \(0.846991\pi\) | |||||||
\(620\) | −3.75302 | −0.150725 | ||||||||
\(621\) | 1.30798 | 0.0524874 | ||||||||
\(622\) | − 33.1987i | − 1.33114i | ||||||||
\(623\) | −45.9133 | −1.83948 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0.0814412i | 0.00325505i | ||||||||
\(627\) | 26.6233 | 1.06323 | ||||||||
\(628\) | 18.6015 | 0.742280 | ||||||||
\(629\) | − 46.3685i | − 1.84883i | ||||||||
\(630\) | − 3.44504i | − 0.137254i | ||||||||
\(631\) | − 6.18731i | − 0.246313i | −0.992387 | − | 0.123156i | \(-0.960698\pi\) | ||||
0.992387 | − | 0.123156i | \(-0.0393017\pi\) | |||||||
\(632\) | 1.33513i | 0.0531084i | ||||||||
\(633\) | 0.396125 | 0.0157445 | ||||||||
\(634\) | −19.4969 | −0.774323 | ||||||||
\(635\) | 2.54288i | 0.100911i | ||||||||
\(636\) | 8.93900 | 0.354454 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 38.8461 | 1.53793 | ||||||||
\(639\) | − 0.374354i | − 0.0148092i | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −39.1159 | −1.54498 | −0.772492 | − | 0.635024i | \(-0.780990\pi\) | ||||
−0.772492 | + | 0.635024i | \(0.780990\pi\) | |||||||
\(642\) | 14.6746i | 0.579159i | ||||||||
\(643\) | − 8.78209i | − 0.346332i | −0.984893 | − | 0.173166i | \(-0.944600\pi\) | ||||
0.984893 | − | 0.173166i | \(-0.0553997\pi\) | |||||||
\(644\) | − 4.50604i | − 0.177563i | ||||||||
\(645\) | − 3.07069i | − 0.120908i | ||||||||
\(646\) | −42.5639 | −1.67465 | ||||||||
\(647\) | 30.1333 | 1.18466 | 0.592332 | − | 0.805694i | \(-0.298207\pi\) | ||||
0.592332 | + | 0.805694i | \(0.298207\pi\) | |||||||
\(648\) | − 1.00000i | − 0.0392837i | ||||||||
\(649\) | 43.8829 | 1.72255 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.9293 | 0.506740 | ||||||||
\(652\) | − 18.8944i | − 0.739962i | ||||||||
\(653\) | −27.0858 | −1.05995 | −0.529974 | − | 0.848014i | \(-0.677798\pi\) | ||||
−0.529974 | + | 0.848014i | \(0.677798\pi\) | |||||||
\(654\) | 9.66786 | 0.378043 | ||||||||
\(655\) | − 10.8509i | − 0.423978i | ||||||||
\(656\) | − 4.26875i | − 0.166667i | ||||||||
\(657\) | − 16.7114i | − 0.651974i | ||||||||
\(658\) | − 26.7614i | − 1.04327i | ||||||||
\(659\) | 5.69681 | 0.221916 | 0.110958 | − | 0.993825i | \(-0.464608\pi\) | ||||
0.110958 | + | 0.993825i | \(0.464608\pi\) | |||||||
\(660\) | 4.24698 | 0.165313 | ||||||||
\(661\) | − 17.1008i | − 0.665145i | −0.943078 | − | 0.332572i | \(-0.892083\pi\) | ||||
0.943078 | − | 0.332572i | \(-0.107917\pi\) | |||||||
\(662\) | 23.8049 | 0.925205 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.740939 | 0.0287540 | ||||||||
\(665\) | 21.5961i | 0.837461i | ||||||||
\(666\) | −6.82908 | −0.264622 | ||||||||
\(667\) | −11.9638 | −0.463238 | ||||||||
\(668\) | 4.24698i | 0.164321i | ||||||||
\(669\) | − 1.49635i | − 0.0578523i | ||||||||
\(670\) | − 0.0760644i | − 0.00293862i | ||||||||
\(671\) | 10.7584i | 0.415323i | ||||||||
\(672\) | −3.44504 | −0.132895 | ||||||||
\(673\) | 43.1957 | 1.66507 | 0.832535 | − | 0.553972i | \(-0.186889\pi\) | ||||
0.832535 | + | 0.553972i | \(0.186889\pi\) | |||||||
\(674\) | − 21.2064i | − 0.816841i | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.78746 | −0.299297 | −0.149648 | − | 0.988739i | \(-0.547814\pi\) | ||||
−0.149648 | + | 0.988739i | \(0.547814\pi\) | |||||||
\(678\) | − 11.3448i | − 0.435695i | ||||||||
\(679\) | −45.4411 | −1.74387 | ||||||||
\(680\) | −6.78986 | −0.260379 | ||||||||
\(681\) | − 25.2150i | − 0.966243i | ||||||||
\(682\) | 15.9390i | 0.610336i | ||||||||
\(683\) | 30.9138i | 1.18288i | 0.806348 | + | 0.591441i | \(0.201441\pi\) | ||||
−0.806348 | + | 0.591441i | \(0.798559\pi\) | |||||||
\(684\) | 6.26875i | 0.239692i | ||||||||
\(685\) | 18.6407 | 0.712225 | ||||||||
\(686\) | −7.34375 | −0.280386 | ||||||||
\(687\) | − 22.3666i | − 0.853338i | ||||||||
\(688\) | −3.07069 | −0.117069 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.30798 | −0.0497939 | ||||||||
\(691\) | 6.20237i | 0.235949i | 0.993017 | + | 0.117975i | \(0.0376402\pi\) | ||||
−0.993017 | + | 0.117975i | \(0.962360\pi\) | |||||||
\(692\) | 1.16852 | 0.0444206 | ||||||||
\(693\) | −14.6310 | −0.555787 | ||||||||
\(694\) | − 16.5773i | − 0.629266i | ||||||||
\(695\) | 3.53750i | 0.134185i | ||||||||
\(696\) | 9.14675i | 0.346707i | ||||||||
\(697\) | 28.9842i | 1.09785i | ||||||||
\(698\) | −2.51035 | −0.0950182 | ||||||||
\(699\) | −14.0858 | −0.532772 | ||||||||
\(700\) | 3.44504i | 0.130210i | ||||||||
\(701\) | −26.3220 | −0.994167 | −0.497084 | − | 0.867703i | \(-0.665596\pi\) | ||||
−0.497084 | + | 0.867703i | \(0.665596\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 42.8098 | 1.61460 | ||||||||
\(704\) | − 4.24698i | − 0.160064i | ||||||||
\(705\) | −7.76809 | −0.292563 | ||||||||
\(706\) | −20.8412 | −0.784368 | ||||||||
\(707\) | 51.8211i | 1.94893i | ||||||||
\(708\) | 10.3327i | 0.388328i | ||||||||
\(709\) | 33.7429i | 1.26724i | 0.773645 | + | 0.633620i | \(0.218432\pi\) | ||||
−0.773645 | + | 0.633620i | \(0.781568\pi\) | |||||||
\(710\) | 0.374354i | 0.0140493i | ||||||||
\(711\) | −1.33513 | −0.0500711 | ||||||||
\(712\) | 13.3274 | 0.499464 | ||||||||
\(713\) | − 4.90887i | − 0.183839i | ||||||||
\(714\) | 23.3913 | 0.875399 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.1836 | −0.380579 | ||||||||
\(717\) | − 5.38106i | − 0.200959i | ||||||||
\(718\) | −2.42566 | −0.0905250 | ||||||||
\(719\) | 9.50173 | 0.354355 | 0.177177 | − | 0.984179i | \(-0.443303\pi\) | ||||
0.177177 | + | 0.984179i | \(0.443303\pi\) | |||||||
\(720\) | 1.00000i | 0.0372678i | ||||||||
\(721\) | 30.7351i | 1.14463i | ||||||||
\(722\) | − 20.2972i | − 0.755384i | ||||||||
\(723\) | − 29.9420i | − 1.11355i | ||||||||
\(724\) | 10.3351 | 0.384102 | ||||||||
\(725\) | 9.14675 | 0.339702 | ||||||||
\(726\) | − 7.03684i | − 0.261161i | ||||||||
\(727\) | 12.2631 | 0.454814 | 0.227407 | − | 0.973800i | \(-0.426975\pi\) | ||||
0.227407 | + | 0.973800i | \(0.426975\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 16.7114i | 0.618517i | ||||||||
\(731\) | 20.8495 | 0.771148 | ||||||||
\(732\) | −2.53319 | −0.0936293 | ||||||||
\(733\) | − 1.52217i | − 0.0562227i | −0.999605 | − | 0.0281113i | \(-0.991051\pi\) | ||||
0.999605 | − | 0.0281113i | \(-0.00894930\pi\) | |||||||
\(734\) | 2.66248i | 0.0982740i | ||||||||
\(735\) | − 4.86831i | − 0.179570i | ||||||||
\(736\) | 1.30798i | 0.0482127i | ||||||||
\(737\) | −0.323044 | −0.0118995 | ||||||||
\(738\) | 4.26875 | 0.157135 | ||||||||
\(739\) | 51.1075i | 1.88002i | 0.341146 | + | 0.940010i | \(0.389185\pi\) | ||||
−0.341146 | + | 0.940010i | \(0.610815\pi\) | |||||||
\(740\) | 6.82908 | 0.251042 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.7952 | 1.13053 | ||||||||
\(743\) | 9.08144i | 0.333166i | 0.986027 | + | 0.166583i | \(0.0532733\pi\) | ||||
−0.986027 | + | 0.166583i | \(0.946727\pi\) | |||||||
\(744\) | −3.75302 | −0.137592 | ||||||||
\(745\) | −16.6843 | −0.611264 | ||||||||
\(746\) | 5.87800i | 0.215209i | ||||||||
\(747\) | 0.740939i | 0.0271095i | ||||||||
\(748\) | 28.8364i | 1.05436i | ||||||||
\(749\) | 50.5545i | 1.84722i | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −31.7090 | −1.15708 | −0.578539 | − | 0.815655i | \(-0.696377\pi\) | ||||
−0.578539 | + | 0.815655i | \(0.696377\pi\) | |||||||
\(752\) | 7.76809i | 0.283273i | ||||||||
\(753\) | 8.73556 | 0.318342 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.3327 | −0.667196 | ||||||||
\(756\) | − 3.44504i | − 0.125295i | ||||||||
\(757\) | −8.49934 | −0.308914 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(758\) | 36.1540 | 1.31317 | ||||||||
\(759\) | 5.55496i | 0.201632i | ||||||||
\(760\) | − 6.26875i | − 0.227391i | ||||||||
\(761\) | − 16.4198i | − 0.595218i | −0.954688 | − | 0.297609i | \(-0.903811\pi\) | ||||
0.954688 | − | 0.297609i | \(-0.0961891\pi\) | |||||||
\(762\) | 2.54288i | 0.0921187i | ||||||||
\(763\) | 33.3062 | 1.20576 | ||||||||
\(764\) | 9.43296 | 0.341273 | ||||||||
\(765\) | − 6.78986i | − 0.245488i | ||||||||
\(766\) | −8.98361 | −0.324591 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 27.1011i | 0.977290i | 0.872483 | + | 0.488645i | \(0.162509\pi\) | ||||
−0.872483 | + | 0.488645i | \(0.837491\pi\) | |||||||
\(770\) | 14.6310 | 0.527265 | ||||||||
\(771\) | −21.2717 | −0.766083 | ||||||||
\(772\) | − 22.9191i | − 0.824878i | ||||||||
\(773\) | − 12.6297i | − 0.454259i | −0.973865 | − | 0.227129i | \(-0.927066\pi\) | ||||
0.973865 | − | 0.227129i | \(-0.0729340\pi\) | |||||||
\(774\) | − 3.07069i | − 0.110374i | ||||||||
\(775\) | 3.75302i | 0.134812i | ||||||||
\(776\) | 13.1903 | 0.473504 | ||||||||
\(777\) | −23.5265 | −0.844008 | ||||||||
\(778\) | − 0.655186i | − 0.0234895i | ||||||||
\(779\) | −26.7597 | −0.958767 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.58987 | 0.0568902 | ||||||||
\(782\) | − 8.88099i | − 0.317583i | ||||||||
\(783\) | −9.14675 | −0.326878 | ||||||||
\(784\) | −4.86831 | −0.173868 | ||||||||
\(785\) | − 18.6015i | − 0.663915i | ||||||||
\(786\) | − 10.8509i | − 0.387037i | ||||||||
\(787\) | 3.02954i | 0.107991i | 0.998541 | + | 0.0539957i | \(0.0171957\pi\) | ||||
−0.998541 | + | 0.0539957i | \(0.982804\pi\) | |||||||
\(788\) | − 14.3502i | − 0.511204i | ||||||||
\(789\) | −22.2325 | −0.791498 | ||||||||
\(790\) | 1.33513 | 0.0475016 | ||||||||
\(791\) | − 39.0834i | − 1.38964i | ||||||||
\(792\) | 4.24698 | 0.150910 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −0.271143 | −0.00962250 | ||||||||
\(795\) | − 8.93900i | − 0.317034i | ||||||||
\(796\) | 14.2524 | 0.505161 | ||||||||
\(797\) | −40.2218 | −1.42473 | −0.712364 | − | 0.701810i | \(-0.752375\pi\) | ||||
−0.712364 | + | 0.701810i | \(0.752375\pi\) | |||||||
\(798\) | 21.5961i | 0.764494i | ||||||||
\(799\) | − 52.7442i | − 1.86596i | ||||||||
\(800\) | − 1.00000i | − 0.0353553i | ||||||||
\(801\) | 13.3274i | 0.470899i | ||||||||
\(802\) | −0.344814 | −0.0121758 | ||||||||
\(803\) | 70.9730 | 2.50458 | ||||||||
\(804\) | − 0.0760644i | − 0.00268259i | ||||||||
\(805\) | −4.50604 | −0.158817 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.2241 | −0.359907 | ||||||||
\(808\) | − 15.0422i | − 0.529183i | ||||||||
\(809\) | 33.7918 | 1.18806 | 0.594028 | − | 0.804445i | \(-0.297537\pi\) | ||||
0.594028 | + | 0.804445i | \(0.297537\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | − 33.6534i | − 1.18173i | −0.806770 | − | 0.590865i | \(-0.798787\pi\) | ||||
0.806770 | − | 0.590865i | \(-0.201213\pi\) | |||||||
\(812\) | 31.5109i | 1.10582i | ||||||||
\(813\) | 0.716185i | 0.0251177i | ||||||||
\(814\) | − 29.0030i | − 1.01655i | ||||||||
\(815\) | −18.8944 | −0.661842 | ||||||||
\(816\) | −6.78986 | −0.237693 | ||||||||
\(817\) | 19.2494i | 0.673450i | ||||||||
\(818\) | 27.0388 | 0.945388 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.26875 | −0.149071 | ||||||||
\(821\) | − 12.6939i | − 0.443022i | −0.975158 | − | 0.221511i | \(-0.928901\pi\) | ||||
0.975158 | − | 0.221511i | \(-0.0710988\pi\) | |||||||
\(822\) | 18.6407 | 0.650169 | ||||||||
\(823\) | 8.79523 | 0.306583 | 0.153291 | − | 0.988181i | \(-0.451013\pi\) | ||||
0.153291 | + | 0.988181i | \(0.451013\pi\) | |||||||
\(824\) | − 8.92154i | − 0.310797i | ||||||||
\(825\) | − 4.24698i | − 0.147861i | ||||||||
\(826\) | 35.5967i | 1.23857i | ||||||||
\(827\) | 32.1758i | 1.11886i | 0.828877 | + | 0.559431i | \(0.188980\pi\) | ||||
−0.828877 | + | 0.559431i | \(0.811020\pi\) | |||||||
\(828\) | −1.30798 | −0.0454554 | ||||||||
\(829\) | −21.1812 | −0.735653 | −0.367827 | − | 0.929894i | \(-0.619898\pi\) | ||||
−0.367827 | + | 0.929894i | \(0.619898\pi\) | |||||||
\(830\) | − 0.740939i | − 0.0257184i | ||||||||
\(831\) | 22.8713 | 0.793397 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.0551 | 1.14529 | ||||||||
\(834\) | 3.53750i | 0.122494i | ||||||||
\(835\) | 4.24698 | 0.146973 | ||||||||
\(836\) | −26.6233 | −0.920784 | ||||||||
\(837\) | − 3.75302i | − 0.129723i | ||||||||
\(838\) | 5.86533i | 0.202614i | ||||||||
\(839\) | 26.5931i | 0.918097i | 0.888411 | + | 0.459048i | \(0.151810\pi\) | ||||
−0.888411 | + | 0.459048i | \(0.848190\pi\) | |||||||
\(840\) | 3.44504i | 0.118865i | ||||||||
\(841\) | 54.6631 | 1.88493 | ||||||||
\(842\) | −28.9476 | −0.997601 | ||||||||
\(843\) | 4.13036i | 0.142257i | ||||||||
\(844\) | −0.396125 | −0.0136352 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.76809 | −0.267072 | ||||||||
\(847\) | − 24.2422i | − 0.832972i | ||||||||
\(848\) | −8.93900 | −0.306967 | ||||||||
\(849\) | −16.2959 | −0.559274 | ||||||||
\(850\) | 6.78986i | 0.232890i | ||||||||
\(851\) | 8.93230i | 0.306195i | ||||||||
\(852\) | 0.374354i | 0.0128252i | ||||||||
\(853\) | − 32.2457i | − 1.10407i | −0.833821 | − | 0.552035i | \(-0.813851\pi\) | ||||
0.833821 | − | 0.552035i | \(-0.186149\pi\) | |||||||
\(854\) | −8.72694 | −0.298630 | ||||||||
\(855\) | 6.26875 | 0.214387 | ||||||||
\(856\) | − 14.6746i | − 0.501566i | ||||||||
\(857\) | 43.0176 | 1.46945 | 0.734726 | − | 0.678364i | \(-0.237311\pi\) | ||||
0.734726 | + | 0.678364i | \(0.237311\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.1997 | −1.06452 | −0.532260 | − | 0.846581i | \(-0.678657\pi\) | ||||
−0.532260 | + | 0.846581i | \(0.678657\pi\) | |||||||
\(860\) | 3.07069i | 0.104710i | ||||||||
\(861\) | 14.7060 | 0.501180 | ||||||||
\(862\) | 4.87023 | 0.165881 | ||||||||
\(863\) | 34.5424i | 1.17584i | 0.808920 | + | 0.587919i | \(0.200052\pi\) | ||||
−0.808920 | + | 0.587919i | \(0.799948\pi\) | |||||||
\(864\) | 1.00000i | 0.0340207i | ||||||||
\(865\) | − 1.16852i | − 0.0397309i | ||||||||
\(866\) | 36.9788i | 1.25659i | ||||||||
\(867\) | 29.1021 | 0.988361 | ||||||||
\(868\) | −12.9293 | −0.438849 | ||||||||
\(869\) | − 5.67025i | − 0.192350i | ||||||||
\(870\) | 9.14675 | 0.310104 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −9.66786 | −0.327395 | ||||||||
\(873\) | 13.1903i | 0.446424i | ||||||||
\(874\) | 8.19939 | 0.277349 | ||||||||
\(875\) | 3.44504 | 0.116464 | ||||||||
\(876\) | 16.7114i | 0.564626i | ||||||||
\(877\) | − 2.12093i | − 0.0716188i | −0.999359 | − | 0.0358094i | \(-0.988599\pi\) | ||||
0.999359 | − | 0.0358094i | \(-0.0114009\pi\) | |||||||
\(878\) | − 22.8799i | − 0.772160i | ||||||||
\(879\) | 7.72587i | 0.260587i | ||||||||
\(880\) | −4.24698 | −0.143166 | ||||||||
\(881\) | −27.3489 | −0.921407 | −0.460703 | − | 0.887554i | \(-0.652403\pi\) | ||||
−0.460703 | + | 0.887554i | \(0.652403\pi\) | |||||||
\(882\) | − 4.86831i | − 0.163925i | ||||||||
\(883\) | 48.2959 | 1.62529 | 0.812643 | − | 0.582762i | \(-0.198028\pi\) | ||||
0.812643 | + | 0.582762i | \(0.198028\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.3327 | 0.347331 | ||||||||
\(886\) | − 10.5942i | − 0.355919i | ||||||||
\(887\) | 25.1943 | 0.845943 | 0.422972 | − | 0.906143i | \(-0.360987\pi\) | ||||
0.422972 | + | 0.906143i | \(0.360987\pi\) | |||||||
\(888\) | 6.82908 | 0.229169 | ||||||||
\(889\) | 8.76032i | 0.293812i | ||||||||
\(890\) | − 13.3274i | − 0.446734i | ||||||||
\(891\) | 4.24698i | 0.142279i | ||||||||
\(892\) | 1.49635i | 0.0501016i | ||||||||
\(893\) | 48.6962 | 1.62956 | ||||||||
\(894\) | −16.6843 | −0.558005 | ||||||||
\(895\) | 10.1836i | 0.340400i | ||||||||
\(896\) | 3.44504 | 0.115091 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.6485 | −0.655678 | ||||||||
\(899\) | 34.3279i | 1.14490i | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 60.6945 | 2.02203 | ||||||||
\(902\) | 18.1293i | 0.603639i | ||||||||
\(903\) | − 10.5786i | − 0.352035i | ||||||||
\(904\) | 11.3448i | 0.377323i | ||||||||
\(905\) | − 10.3351i | − 0.343551i | ||||||||
\(906\) | −18.3327 | −0.609064 | ||||||||
\(907\) | 20.0949 | 0.667239 | 0.333619 | − | 0.942708i | \(-0.391730\pi\) | ||||
0.333619 | + | 0.942708i | \(0.391730\pi\) | |||||||
\(908\) | 25.2150i | 0.836791i | ||||||||
\(909\) | 15.0422 | 0.498919 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.44563 | −0.246685 | −0.123342 | − | 0.992364i | \(-0.539361\pi\) | ||||
−0.123342 | + | 0.992364i | \(0.539361\pi\) | |||||||
\(912\) | − 6.26875i | − 0.207579i | ||||||||
\(913\) | −3.14675 | −0.104142 | ||||||||
\(914\) | −18.4239 | −0.609407 | ||||||||
\(915\) | 2.53319i | 0.0837446i | ||||||||
\(916\) | 22.3666i | 0.739013i | ||||||||
\(917\) | − 37.3817i | − 1.23445i | ||||||||
\(918\) | − 6.78986i | − 0.224099i | ||||||||
\(919\) | −14.2765 | −0.470939 | −0.235469 | − | 0.971882i | \(-0.575663\pi\) | ||||
−0.235469 | + | 0.971882i | \(0.575663\pi\) | |||||||
\(920\) | 1.30798 | 0.0431228 | ||||||||
\(921\) | − 5.13036i | − 0.169051i | ||||||||
\(922\) | −22.2446 | −0.732586 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 14.6310 | 0.481325 | ||||||||
\(925\) | − 6.82908i | − 0.224539i | ||||||||
\(926\) | 8.68532 | 0.285417 | ||||||||
\(927\) | 8.92154 | 0.293022 | ||||||||
\(928\) | − 9.14675i | − 0.300257i | ||||||||
\(929\) | − 30.9148i | − 1.01428i | −0.861863 | − | 0.507141i | \(-0.830702\pi\) | ||||
0.861863 | − | 0.507141i | \(-0.169298\pi\) | |||||||
\(930\) | 3.75302i | 0.123066i | ||||||||
\(931\) | 30.5182i | 1.00019i | ||||||||
\(932\) | 14.0858 | 0.461394 | ||||||||
\(933\) | −33.1987 | −1.08688 | ||||||||
\(934\) | − 19.6136i | − 0.641775i | ||||||||
\(935\) | 28.8364 | 0.943050 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.7187 | −0.546176 | −0.273088 | − | 0.961989i | \(-0.588045\pi\) | ||||
−0.273088 | + | 0.961989i | \(0.588045\pi\) | |||||||
\(938\) | − 0.262045i | − 0.00855608i | ||||||||
\(939\) | 0.0814412 | 0.00265773 | ||||||||
\(940\) | 7.76809 | 0.253367 | ||||||||
\(941\) | − 36.9033i | − 1.20301i | −0.798867 | − | 0.601507i | \(-0.794567\pi\) | ||||
0.798867 | − | 0.601507i | \(-0.205433\pi\) | |||||||
\(942\) | − 18.6015i | − 0.606069i | ||||||||
\(943\) | − 5.58343i | − 0.181822i | ||||||||
\(944\) | − 10.3327i | − 0.336302i | ||||||||
\(945\) | −3.44504 | −0.112067 | ||||||||
\(946\) | 13.0411 | 0.424004 | ||||||||
\(947\) | − 39.1661i | − 1.27273i | −0.771389 | − | 0.636364i | \(-0.780438\pi\) | ||||
0.771389 | − | 0.636364i | \(-0.219562\pi\) | |||||||
\(948\) | 1.33513 | 0.0433629 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −6.26875 | −0.203385 | ||||||||
\(951\) | 19.4969i | 0.632232i | ||||||||
\(952\) | −23.3913 | −0.758118 | ||||||||
\(953\) | 19.6200 | 0.635554 | 0.317777 | − | 0.948165i | \(-0.397064\pi\) | ||||
0.317777 | + | 0.948165i | \(0.397064\pi\) | |||||||
\(954\) | − 8.93900i | − 0.289411i | ||||||||
\(955\) | − 9.43296i | − 0.305243i | ||||||||
\(956\) | 5.38106i | 0.174036i | ||||||||
\(957\) | − 38.8461i | − 1.25572i | ||||||||
\(958\) | −31.4698 | −1.01674 | ||||||||
\(959\) | 64.2180 | 2.07371 | ||||||||
\(960\) | − 1.00000i | − 0.0322749i | ||||||||
\(961\) | 16.9148 | 0.545640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.6746 | 0.472881 | ||||||||
\(964\) | 29.9420i | 0.964366i | ||||||||
\(965\) | −22.9191 | −0.737794 | ||||||||
\(966\) | −4.50604 | −0.144979 | ||||||||
\(967\) | 43.1564i | 1.38782i | 0.720063 | + | 0.693909i | \(0.244113\pi\) | ||||
−0.720063 | + | 0.693909i | \(0.755887\pi\) | |||||||
\(968\) | 7.03684i | 0.226172i | ||||||||
\(969\) | 42.5639i | 1.36735i | ||||||||
\(970\) | − 13.1903i | − 0.423515i | ||||||||
\(971\) | 39.5032 | 1.26772 | 0.633859 | − | 0.773449i | \(-0.281470\pi\) | ||||
0.633859 | + | 0.773449i | \(0.281470\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 12.1868i | 0.390692i | ||||||||
\(974\) | 13.2644 | 0.425020 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.53319 | 0.0810854 | ||||||||
\(977\) | 3.84117i | 0.122890i | 0.998110 | + | 0.0614449i | \(0.0195708\pi\) | ||||
−0.998110 | + | 0.0614449i | \(0.980429\pi\) | |||||||
\(978\) | −18.8944 | −0.604176 | ||||||||
\(979\) | −56.6010 | −1.80898 | ||||||||
\(980\) | 4.86831i | 0.155513i | ||||||||
\(981\) | − 9.66786i | − 0.308671i | ||||||||
\(982\) | − 11.7259i | − 0.374188i | ||||||||
\(983\) | − 32.4300i | − 1.03436i | −0.855878 | − | 0.517178i | \(-0.826983\pi\) | ||||
0.855878 | − | 0.517178i | \(-0.173017\pi\) | |||||||
\(984\) | −4.26875 | −0.136083 | ||||||||
\(985\) | −14.3502 | −0.457235 | ||||||||
\(986\) | 62.1051i | 1.97783i | ||||||||
\(987\) | −26.7614 | −0.851824 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.01639 | −0.127714 | ||||||||
\(990\) | − 4.24698i | − 0.134978i | ||||||||
\(991\) | −61.9807 | −1.96888 | −0.984442 | − | 0.175712i | \(-0.943777\pi\) | ||||
−0.984442 | + | 0.175712i | \(0.943777\pi\) | |||||||
\(992\) | 3.75302 | 0.119159 | ||||||||
\(993\) | − 23.8049i | − 0.755426i | ||||||||
\(994\) | 1.28967i | 0.0409057i | ||||||||
\(995\) | − 14.2524i | − 0.451830i | ||||||||
\(996\) | − 0.740939i | − 0.0234775i | ||||||||
\(997\) | 28.9162 | 0.915784 | 0.457892 | − | 0.889008i | \(-0.348605\pi\) | ||||
0.457892 | + | 0.889008i | \(0.348605\pi\) | |||||||
\(998\) | −26.7633 | −0.847177 | ||||||||
\(999\) | 6.82908i | 0.216063i |
(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.w.1351.5 | 6 | ||
13.5 | odd | 4 | 5070.2.a.bx.1.2 | yes | 3 | ||
13.8 | odd | 4 | 5070.2.a.bo.1.2 | ✓ | 3 | ||
13.12 | even | 2 | inner | 5070.2.b.w.1351.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5070.2.a.bo.1.2 | ✓ | 3 | 13.8 | odd | 4 | ||
5070.2.a.bx.1.2 | yes | 3 | 13.5 | odd | 4 | ||
5070.2.b.w.1351.2 | 6 | 13.12 | even | 2 | inner | ||
5070.2.b.w.1351.5 | 6 | 1.1 | even | 1 | trivial |