Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,3,Mod(2,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.h (of order \(6\), degree \(2\), 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: | \(0.572208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(1.93649 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.11 |
Dual form | 21.3.h.b.2.2 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93649 | − | 1.11803i | 0.968246 | − | 0.559017i | 0.0695448 | − | 0.997579i | \(-0.477845\pi\) |
0.898701 | + | 0.438562i | \(0.144512\pi\) | |||||||
\(3\) | −2.93649 | + | 0.614017i | −0.978831 | + | 0.204672i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(5\) | −1.93649 | + | 1.11803i | −0.387298 | + | 0.223607i | −0.680989 | − | 0.732294i | \(-0.738450\pi\) |
0.293691 | + | 0.955901i | \(0.405116\pi\) | |||||||
\(6\) | −5.00000 | + | 4.47214i | −0.833333 | + | 0.745356i | ||||
\(7\) | 3.50000 | − | 6.06218i | 0.500000 | − | 0.866025i | ||||
\(8\) | 6.70820i | 0.838525i | ||||||||
\(9\) | 8.24597 | − | 3.60611i | 0.916219 | − | 0.400679i | ||||
\(10\) | −2.50000 | + | 4.33013i | −0.250000 | + | 0.433013i | ||||
\(11\) | −9.68246 | − | 5.59017i | −0.880223 | − | 0.508197i | −0.00949140 | − | 0.999955i | \(-0.503021\pi\) |
−0.870732 | + | 0.491758i | \(0.836355\pi\) | |||||||
\(12\) | −0.936492 | + | 2.85008i | −0.0780410 | + | 0.237507i | ||||
\(13\) | −2.00000 | −0.153846 | −0.0769231 | − | 0.997037i | \(-0.524510\pi\) | ||||
−0.0769231 | + | 0.997037i | \(0.524510\pi\) | |||||||
\(14\) | − | 15.6525i | − | 1.11803i | ||||||
\(15\) | 5.00000 | − | 4.47214i | 0.333333 | − | 0.298142i | ||||
\(16\) | 9.50000 | + | 16.4545i | 0.593750 | + | 1.02841i | ||||
\(17\) | 23.2379 | + | 13.4164i | 1.36694 | + | 0.789200i | 0.990535 | − | 0.137257i | \(-0.0438286\pi\) |
0.376400 | + | 0.926457i | \(0.377162\pi\) | |||||||
\(18\) | 11.9365 | − | 16.2025i | 0.663138 | − | 0.900137i | ||||
\(19\) | −8.00000 | − | 13.8564i | −0.421053 | − | 0.729285i | 0.574990 | − | 0.818160i | \(-0.305006\pi\) |
−0.996043 | + | 0.0888758i | \(0.971673\pi\) | |||||||
\(20\) | 2.23607i | 0.111803i | ||||||||
\(21\) | −6.55544 | + | 19.9506i | −0.312164 | + | 0.950028i | ||||
\(22\) | −25.0000 | −1.13636 | ||||||||
\(23\) | −11.6190 | + | 6.70820i | −0.505172 | + | 0.291661i | −0.730847 | − | 0.682542i | \(-0.760875\pi\) |
0.225675 | + | 0.974203i | \(0.427541\pi\) | |||||||
\(24\) | −4.11895 | − | 19.6986i | −0.171623 | − | 0.820774i | ||||
\(25\) | −10.0000 | + | 17.3205i | −0.400000 | + | 0.692820i | ||||
\(26\) | −3.87298 | + | 2.23607i | −0.148961 | + | 0.0860026i | ||||
\(27\) | −22.0000 | + | 15.6525i | −0.814815 | + | 0.579721i | ||||
\(28\) | −3.50000 | − | 6.06218i | −0.125000 | − | 0.216506i | ||||
\(29\) | − | 15.6525i | − | 0.539741i | −0.962897 | − | 0.269870i | \(-0.913019\pi\) | ||
0.962897 | − | 0.269870i | \(-0.0869808\pi\) | |||||||
\(30\) | 4.68246 | − | 14.2504i | 0.156082 | − | 0.475014i | ||||
\(31\) | 1.50000 | − | 2.59808i | 0.0483871 | − | 0.0838089i | −0.840817 | − | 0.541319i | \(-0.817925\pi\) |
0.889205 | + | 0.457510i | \(0.151259\pi\) | |||||||
\(32\) | 13.5554 | + | 7.82624i | 0.423608 | + | 0.244570i | ||||
\(33\) | 31.8649 | + | 10.4703i | 0.965604 | + | 0.317282i | ||||
\(34\) | 60.0000 | 1.76471 | ||||||||
\(35\) | 15.6525i | 0.447214i | ||||||||
\(36\) | 1.00000 | − | 8.94427i | 0.0277778 | − | 0.248452i | ||||
\(37\) | −6.00000 | − | 10.3923i | −0.162162 | − | 0.280873i | 0.773482 | − | 0.633819i | \(-0.218513\pi\) |
−0.935644 | + | 0.352946i | \(0.885180\pi\) | |||||||
\(38\) | −30.9839 | − | 17.8885i | −0.815365 | − | 0.470751i | ||||
\(39\) | 5.87298 | − | 1.22803i | 0.150589 | − | 0.0314880i | ||||
\(40\) | −7.50000 | − | 12.9904i | −0.187500 | − | 0.324760i | ||||
\(41\) | − | 31.3050i | − | 0.763535i | −0.924258 | − | 0.381768i | \(-0.875315\pi\) | ||
0.924258 | − | 0.381768i | \(-0.124685\pi\) | |||||||
\(42\) | 9.61088 | + | 45.9634i | 0.228831 | + | 1.09437i | ||||
\(43\) | 44.0000 | 1.02326 | 0.511628 | − | 0.859207i | \(-0.329043\pi\) | ||||
0.511628 | + | 0.859207i | \(0.329043\pi\) | |||||||
\(44\) | −9.68246 | + | 5.59017i | −0.220056 | + | 0.127049i | ||||
\(45\) | −11.9365 | + | 16.2025i | −0.265255 | + | 0.360055i | ||||
\(46\) | −15.0000 | + | 25.9808i | −0.326087 | + | 0.564799i | ||||
\(47\) | 11.6190 | − | 6.70820i | 0.247212 | − | 0.142728i | −0.371275 | − | 0.928523i | \(-0.621079\pi\) |
0.618487 | + | 0.785795i | \(0.287746\pi\) | |||||||
\(48\) | −38.0000 | − | 42.4853i | −0.791667 | − | 0.885110i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.500000 | − | 0.866025i | ||||
\(50\) | 44.7214i | 0.894427i | ||||||||
\(51\) | −76.4758 | − | 25.1287i | −1.49953 | − | 0.492720i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.0192308 | + | 0.0333087i | ||||
\(53\) | 17.4284 | + | 10.0623i | 0.328838 | + | 0.189855i | 0.655325 | − | 0.755347i | \(-0.272532\pi\) |
−0.326487 | + | 0.945202i | \(0.605865\pi\) | |||||||
\(54\) | −25.1028 | + | 54.9076i | −0.464867 | + | 1.01681i | ||||
\(55\) | 25.0000 | 0.454545 | ||||||||
\(56\) | 40.6663 | + | 23.4787i | 0.726184 | + | 0.419263i | ||||
\(57\) | 32.0000 | + | 35.7771i | 0.561404 | + | 0.627668i | ||||
\(58\) | −17.5000 | − | 30.3109i | −0.301724 | − | 0.522602i | ||||
\(59\) | −17.4284 | − | 10.0623i | −0.295397 | − | 0.170548i | 0.344976 | − | 0.938611i | \(-0.387887\pi\) |
−0.640373 | + | 0.768064i | \(0.721220\pi\) | |||||||
\(60\) | −1.37298 | − | 6.56619i | −0.0228831 | − | 0.109437i | ||||
\(61\) | 13.0000 | + | 22.5167i | 0.213115 | + | 0.369126i | 0.952688 | − | 0.303951i | \(-0.0983058\pi\) |
−0.739573 | + | 0.673076i | \(0.764973\pi\) | |||||||
\(62\) | − | 6.70820i | − | 0.108197i | ||||||
\(63\) | 7.00000 | − | 62.6099i | 0.111111 | − | 0.993808i | ||||
\(64\) | −41.0000 | −0.640625 | ||||||||
\(65\) | 3.87298 | − | 2.23607i | 0.0595844 | − | 0.0344010i | ||||
\(66\) | 73.4123 | − | 15.3504i | 1.11231 | − | 0.232582i | ||||
\(67\) | −26.0000 | + | 45.0333i | −0.388060 | + | 0.672139i | −0.992189 | − | 0.124748i | \(-0.960188\pi\) |
0.604129 | + | 0.796887i | \(0.293521\pi\) | |||||||
\(68\) | 23.2379 | − | 13.4164i | 0.341734 | − | 0.197300i | ||||
\(69\) | 30.0000 | − | 26.8328i | 0.434783 | − | 0.388881i | ||||
\(70\) | 17.5000 | + | 30.3109i | 0.250000 | + | 0.433013i | ||||
\(71\) | − | 93.9149i | − | 1.32274i | −0.750058 | − | 0.661372i | \(-0.769974\pi\) | ||
0.750058 | − | 0.661372i | \(-0.230026\pi\) | |||||||
\(72\) | 24.1905 | + | 55.3156i | 0.335980 | + | 0.768273i | ||||
\(73\) | −9.00000 | + | 15.5885i | −0.123288 | + | 0.213541i | −0.921062 | − | 0.389415i | \(-0.872677\pi\) |
0.797775 | + | 0.602956i | \(0.206010\pi\) | |||||||
\(74\) | −23.2379 | − | 13.4164i | −0.314026 | − | 0.181303i | ||||
\(75\) | 18.7298 | − | 57.0017i | 0.249731 | − | 0.760023i | ||||
\(76\) | −16.0000 | −0.210526 | ||||||||
\(77\) | −67.7772 | + | 39.1312i | −0.880223 | + | 0.508197i | ||||
\(78\) | 10.0000 | − | 8.94427i | 0.128205 | − | 0.114670i | ||||
\(79\) | 39.5000 | + | 68.4160i | 0.500000 | + | 0.866025i | 1.00000 | \(0\) | ||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | −36.7933 | − | 21.2426i | −0.459917 | − | 0.265533i | ||||
\(81\) | 54.9919 | − | 59.4717i | 0.678913 | − | 0.734219i | ||||
\(82\) | −35.0000 | − | 60.6218i | −0.426829 | − | 0.739290i | ||||
\(83\) | 140.872i | 1.69726i | 0.528990 | + | 0.848628i | \(0.322571\pi\) | ||||
−0.528990 | + | 0.848628i | \(0.677429\pi\) | |||||||
\(84\) | 14.0000 | + | 15.6525i | 0.166667 | + | 0.186339i | ||||
\(85\) | −60.0000 | −0.705882 | ||||||||
\(86\) | 85.2056 | − | 49.1935i | 0.990763 | − | 0.572017i | ||||
\(87\) | 9.61088 | + | 45.9634i | 0.110470 | + | 0.528315i | ||||
\(88\) | 37.5000 | − | 64.9519i | 0.426136 | − | 0.738090i | ||||
\(89\) | −42.6028 | + | 24.5967i | −0.478683 | + | 0.276368i | −0.719868 | − | 0.694111i | \(-0.755798\pi\) |
0.241184 | + | 0.970479i | \(0.422464\pi\) | |||||||
\(90\) | −5.00000 | + | 44.7214i | −0.0555556 | + | 0.496904i | ||||
\(91\) | −7.00000 | + | 12.1244i | −0.0769231 | + | 0.133235i | ||||
\(92\) | 13.4164i | 0.145831i | ||||||||
\(93\) | −2.80948 | + | 8.55025i | −0.0302094 | + | 0.0919382i | ||||
\(94\) | 15.0000 | − | 25.9808i | 0.159574 | − | 0.276391i | ||||
\(95\) | 30.9839 | + | 17.8885i | 0.326146 | + | 0.188300i | ||||
\(96\) | −44.6109 | − | 14.6584i | −0.464697 | − | 0.152692i | ||||
\(97\) | −93.0000 | −0.958763 | −0.479381 | − | 0.877607i | \(-0.659139\pi\) | ||||
−0.479381 | + | 0.877607i | \(0.659139\pi\) | |||||||
\(98\) | −94.8881 | − | 54.7837i | −0.968246 | − | 0.559017i | ||||
\(99\) | −100.000 | − | 11.1803i | −1.01010 | − | 0.112933i | ||||
\(100\) | 10.0000 | + | 17.3205i | 0.100000 | + | 0.173205i | ||||
\(101\) | 50.3488 | + | 29.0689i | 0.498503 | + | 0.287811i | 0.728095 | − | 0.685476i | \(-0.240406\pi\) |
−0.229592 | + | 0.973287i | \(0.573739\pi\) | |||||||
\(102\) | −176.190 | + | 36.8410i | −1.72735 | + | 0.361186i | ||||
\(103\) | 41.0000 | + | 71.0141i | 0.398058 | + | 0.689457i | 0.993486 | − | 0.113952i | \(-0.0363509\pi\) |
−0.595428 | + | 0.803409i | \(0.703018\pi\) | |||||||
\(104\) | − | 13.4164i | − | 0.129004i | ||||||
\(105\) | −9.61088 | − | 45.9634i | −0.0915322 | − | 0.437746i | ||||
\(106\) | 45.0000 | 0.424528 | ||||||||
\(107\) | 56.1583 | − | 32.4230i | 0.524844 | − | 0.303019i | −0.214071 | − | 0.976818i | \(-0.568672\pi\) |
0.738914 | + | 0.673800i | \(0.235339\pi\) | |||||||
\(108\) | 2.55544 | + | 26.8788i | 0.0236615 | + | 0.248878i | ||||
\(109\) | 72.0000 | − | 124.708i | 0.660550 | − | 1.14411i | −0.319921 | − | 0.947444i | \(-0.603656\pi\) |
0.980471 | − | 0.196663i | \(-0.0630104\pi\) | |||||||
\(110\) | 48.4123 | − | 27.9508i | 0.440112 | − | 0.254099i | ||||
\(111\) | 24.0000 | + | 26.8328i | 0.216216 | + | 0.241737i | ||||
\(112\) | 133.000 | 1.18750 | ||||||||
\(113\) | 31.3050i | 0.277035i | 0.990360 | + | 0.138517i | \(0.0442337\pi\) | ||||
−0.990360 | + | 0.138517i | \(0.955766\pi\) | |||||||
\(114\) | 101.968 | + | 33.5049i | 0.894454 | + | 0.293903i | ||||
\(115\) | 15.0000 | − | 25.9808i | 0.130435 | − | 0.225920i | ||||
\(116\) | −13.5554 | − | 7.82624i | −0.116857 | − | 0.0674676i | ||||
\(117\) | −16.4919 | + | 7.21222i | −0.140957 | + | 0.0616429i | ||||
\(118\) | −45.0000 | −0.381356 | ||||||||
\(119\) | 162.665 | − | 93.9149i | 1.36694 | − | 0.789200i | ||||
\(120\) | 30.0000 | + | 33.5410i | 0.250000 | + | 0.279508i | ||||
\(121\) | 2.00000 | + | 3.46410i | 0.0165289 | + | 0.0286289i | ||||
\(122\) | 50.3488 | + | 29.0689i | 0.412695 | + | 0.238270i | ||||
\(123\) | 19.2218 | + | 91.9267i | 0.156275 | + | 0.747372i | ||||
\(124\) | −1.50000 | − | 2.59808i | −0.0120968 | − | 0.0209522i | ||||
\(125\) | − | 100.623i | − | 0.804984i | ||||||
\(126\) | −56.4446 | − | 129.070i | −0.447973 | − | 1.02436i | ||||
\(127\) | 177.000 | 1.39370 | 0.696850 | − | 0.717217i | \(-0.254584\pi\) | ||||
0.696850 | + | 0.717217i | \(0.254584\pi\) | |||||||
\(128\) | −133.618 | + | 77.1443i | −1.04389 | + | 0.602690i | ||||
\(129\) | −129.206 | + | 27.0167i | −1.00159 | + | 0.209432i | ||||
\(130\) | 5.00000 | − | 8.66025i | 0.0384615 | − | 0.0666173i | ||||
\(131\) | −164.602 | + | 95.0329i | −1.25650 | + | 0.725442i | −0.972393 | − | 0.233350i | \(-0.925031\pi\) |
−0.284109 | + | 0.958792i | \(0.591698\pi\) | |||||||
\(132\) | 25.0000 | − | 22.3607i | 0.189394 | − | 0.169399i | ||||
\(133\) | −112.000 | −0.842105 | ||||||||
\(134\) | 116.276i | 0.867728i | ||||||||
\(135\) | 25.1028 | − | 54.9076i | 0.185947 | − | 0.406723i | ||||
\(136\) | −90.0000 | + | 155.885i | −0.661765 | + | 1.14621i | ||||
\(137\) | −185.903 | − | 107.331i | −1.35696 | − | 0.783440i | −0.367745 | − | 0.929927i | \(-0.619870\pi\) |
−0.989213 | + | 0.146487i | \(0.953203\pi\) | |||||||
\(138\) | 28.0948 | − | 85.5025i | 0.203585 | − | 0.619584i | ||||
\(139\) | −114.000 | −0.820144 | −0.410072 | − | 0.912053i | \(-0.634496\pi\) | ||||
−0.410072 | + | 0.912053i | \(0.634496\pi\) | |||||||
\(140\) | 13.5554 | + | 7.82624i | 0.0968246 | + | 0.0559017i | ||||
\(141\) | −30.0000 | + | 26.8328i | −0.212766 | + | 0.190304i | ||||
\(142\) | −105.000 | − | 181.865i | −0.739437 | − | 1.28074i | ||||
\(143\) | 19.3649 | + | 11.1803i | 0.135419 | + | 0.0781842i | ||||
\(144\) | 137.673 | + | 101.425i | 0.956065 | + | 0.704341i | ||||
\(145\) | 17.5000 | + | 30.3109i | 0.120690 | + | 0.209041i | ||||
\(146\) | 40.2492i | 0.275680i | ||||||||
\(147\) | 98.0000 | + | 109.567i | 0.666667 | + | 0.745356i | ||||
\(148\) | −12.0000 | −0.0810811 | ||||||||
\(149\) | −11.6190 | + | 6.70820i | −0.0779795 | + | 0.0450215i | −0.538483 | − | 0.842637i | \(-0.681002\pi\) |
0.460503 | + | 0.887658i | \(0.347669\pi\) | |||||||
\(150\) | −27.4597 | − | 131.324i | −0.183064 | − | 0.875493i | ||||
\(151\) | −29.5000 | + | 51.0955i | −0.195364 | + | 0.338381i | −0.947020 | − | 0.321175i | \(-0.895922\pi\) |
0.751656 | + | 0.659556i | \(0.229256\pi\) | |||||||
\(152\) | 92.9516 | − | 53.6656i | 0.611524 | − | 0.353063i | ||||
\(153\) | 240.000 | + | 26.8328i | 1.56863 | + | 0.175378i | ||||
\(154\) | −87.5000 | + | 151.554i | −0.568182 | + | 0.984120i | ||||
\(155\) | 6.70820i | 0.0432787i | ||||||||
\(156\) | 1.87298 | − | 5.70017i | 0.0120063 | − | 0.0365395i | ||||
\(157\) | 124.000 | − | 214.774i | 0.789809 | − | 1.36799i | −0.136275 | − | 0.990671i | \(-0.543513\pi\) |
0.926084 | − | 0.377318i | \(-0.123154\pi\) | |||||||
\(158\) | 152.983 | + | 88.3247i | 0.968246 | + | 0.559017i | ||||
\(159\) | −57.3569 | − | 18.8465i | −0.360735 | − | 0.118532i | ||||
\(160\) | −35.0000 | −0.218750 | ||||||||
\(161\) | 93.9149i | 0.583322i | ||||||||
\(162\) | 40.0000 | − | 176.649i | 0.246914 | − | 1.09043i | ||||
\(163\) | 1.00000 | + | 1.73205i | 0.00613497 | + | 0.0106261i | 0.869077 | − | 0.494678i | \(-0.164714\pi\) |
−0.862942 | + | 0.505304i | \(0.831380\pi\) | |||||||
\(164\) | −27.1109 | − | 15.6525i | −0.165310 | − | 0.0954419i | ||||
\(165\) | −73.4123 | + | 15.3504i | −0.444923 | + | 0.0930329i | ||||
\(166\) | 157.500 | + | 272.798i | 0.948795 | + | 1.64336i | ||||
\(167\) | − | 250.440i | − | 1.49964i | −0.661643 | − | 0.749819i | \(-0.730140\pi\) | ||
0.661643 | − | 0.749819i | \(-0.269860\pi\) | |||||||
\(168\) | −133.833 | − | 43.9752i | −0.796623 | − | 0.261757i | ||||
\(169\) | −165.000 | −0.976331 | ||||||||
\(170\) | −116.190 | + | 67.0820i | −0.683468 | + | 0.394600i | ||||
\(171\) | −115.935 | − | 85.4106i | −0.677985 | − | 0.499477i | ||||
\(172\) | 22.0000 | − | 38.1051i | 0.127907 | − | 0.221541i | ||||
\(173\) | 228.506 | − | 131.928i | 1.32084 | − | 0.762590i | 0.336981 | − | 0.941512i | \(-0.390594\pi\) |
0.983863 | + | 0.178922i | \(0.0572609\pi\) | |||||||
\(174\) | 70.0000 | + | 78.2624i | 0.402299 | + | 0.449784i | ||||
\(175\) | 70.0000 | + | 121.244i | 0.400000 | + | 0.692820i | ||||
\(176\) | − | 212.426i | − | 1.20697i | ||||||
\(177\) | 57.3569 | + | 18.8465i | 0.324050 | + | 0.106478i | ||||
\(178\) | −55.0000 | + | 95.2628i | −0.308989 | + | 0.535184i | ||||
\(179\) | 166.538 | + | 96.1509i | 0.930381 | + | 0.537156i | 0.886932 | − | 0.461900i | \(-0.152832\pi\) |
0.0434493 | + | 0.999056i | \(0.486165\pi\) | |||||||
\(180\) | 8.06351 | + | 18.4385i | 0.0447973 | + | 0.102436i | ||||
\(181\) | 82.0000 | 0.453039 | 0.226519 | − | 0.974007i | \(-0.427265\pi\) | ||||
0.226519 | + | 0.974007i | \(0.427265\pi\) | |||||||
\(182\) | 31.3050i | 0.172005i | ||||||||
\(183\) | −52.0000 | − | 58.1378i | −0.284153 | − | 0.317693i | ||||
\(184\) | −45.0000 | − | 77.9423i | −0.244565 | − | 0.423599i | ||||
\(185\) | 23.2379 | + | 13.4164i | 0.125610 | + | 0.0725211i | ||||
\(186\) | 4.11895 | + | 19.6986i | 0.0221449 | + | 0.105906i | ||||
\(187\) | −150.000 | − | 259.808i | −0.802139 | − | 1.38935i | ||||
\(188\) | − | 13.4164i | − | 0.0713639i | ||||||
\(189\) | 17.8881 | + | 188.152i | 0.0946460 | + | 0.995511i | ||||
\(190\) | 80.0000 | 0.421053 | ||||||||
\(191\) | −147.173 | + | 84.9706i | −0.770541 | + | 0.444872i | −0.833068 | − | 0.553171i | \(-0.813418\pi\) |
0.0625264 | + | 0.998043i | \(0.480084\pi\) | |||||||
\(192\) | 120.396 | − | 25.1747i | 0.627063 | − | 0.131118i | ||||
\(193\) | −29.5000 | + | 51.0955i | −0.152850 | + | 0.264744i | −0.932274 | − | 0.361753i | \(-0.882178\pi\) |
0.779424 | + | 0.626496i | \(0.215512\pi\) | |||||||
\(194\) | −180.094 | + | 103.977i | −0.928318 | + | 0.535965i | ||||
\(195\) | −10.0000 | + | 8.94427i | −0.0512821 | + | 0.0458681i | ||||
\(196\) | −49.0000 | −0.250000 | ||||||||
\(197\) | 219.135i | 1.11236i | 0.831062 | + | 0.556179i | \(0.187733\pi\) | ||||
−0.831062 | + | 0.556179i | \(0.812267\pi\) | |||||||
\(198\) | −206.149 | + | 90.1528i | −1.04116 | + | 0.455317i | ||||
\(199\) | 117.000 | − | 202.650i | 0.587940 | − | 1.01834i | −0.406562 | − | 0.913623i | \(-0.633273\pi\) |
0.994502 | − | 0.104718i | \(-0.0333941\pi\) | |||||||
\(200\) | −116.190 | − | 67.0820i | −0.580948 | − | 0.335410i | ||||
\(201\) | 48.6976 | − | 148.204i | 0.242276 | − | 0.737335i | ||||
\(202\) | 130.000 | 0.643564 | ||||||||
\(203\) | −94.8881 | − | 54.7837i | −0.467429 | − | 0.269870i | ||||
\(204\) | −60.0000 | + | 53.6656i | −0.294118 | + | 0.263067i | ||||
\(205\) | 35.0000 | + | 60.6218i | 0.170732 | + | 0.295716i | ||||
\(206\) | 158.792 | + | 91.6788i | 0.770836 | + | 0.445043i | ||||
\(207\) | −71.6190 | + | 97.2148i | −0.345985 | + | 0.469637i | ||||
\(208\) | −19.0000 | − | 32.9090i | −0.0913462 | − | 0.158216i | ||||
\(209\) | 178.885i | 0.855911i | ||||||||
\(210\) | −70.0000 | − | 78.2624i | −0.333333 | − | 0.372678i | ||||
\(211\) | −26.0000 | −0.123223 | −0.0616114 | − | 0.998100i | \(-0.519624\pi\) | ||||
−0.0616114 | + | 0.998100i | \(0.519624\pi\) | |||||||
\(212\) | 17.4284 | − | 10.0623i | 0.0822096 | − | 0.0474637i | ||||
\(213\) | 57.6653 | + | 275.780i | 0.270729 | + | 1.29474i | ||||
\(214\) | 72.5000 | − | 125.574i | 0.338785 | − | 0.586793i | ||||
\(215\) | −85.2056 | + | 49.1935i | −0.396305 | + | 0.228807i | ||||
\(216\) | −105.000 | − | 147.580i | −0.486111 | − | 0.683243i | ||||
\(217\) | −10.5000 | − | 18.1865i | −0.0483871 | − | 0.0838089i | ||||
\(218\) | − | 321.994i | − | 1.47704i | ||||||
\(219\) | 16.8569 | − | 51.3015i | 0.0769719 | − | 0.234254i | ||||
\(220\) | 12.5000 | − | 21.6506i | 0.0568182 | − | 0.0984120i | ||||
\(221\) | −46.4758 | − | 26.8328i | −0.210298 | − | 0.121415i | ||||
\(222\) | 76.4758 | + | 25.1287i | 0.344486 | + | 0.113192i | ||||
\(223\) | −107.000 | −0.479821 | −0.239910 | − | 0.970795i | \(-0.577118\pi\) | ||||
−0.239910 | + | 0.970795i | \(0.577118\pi\) | |||||||
\(224\) | 94.8881 | − | 54.7837i | 0.423608 | − | 0.244570i | ||||
\(225\) | −20.0000 | + | 178.885i | −0.0888889 | + | 0.795046i | ||||
\(226\) | 35.0000 | + | 60.6218i | 0.154867 | + | 0.268238i | ||||
\(227\) | −261.426 | − | 150.935i | −1.15166 | − | 0.664910i | −0.202367 | − | 0.979310i | \(-0.564863\pi\) |
−0.949291 | + | 0.314400i | \(0.898197\pi\) | |||||||
\(228\) | 46.9839 | − | 9.82427i | 0.206070 | − | 0.0430889i | ||||
\(229\) | 167.000 | + | 289.252i | 0.729258 | + | 1.26311i | 0.957197 | + | 0.289436i | \(0.0934678\pi\) |
−0.227940 | + | 0.973675i | \(0.573199\pi\) | |||||||
\(230\) | − | 67.0820i | − | 0.291661i | ||||||
\(231\) | 175.000 | − | 156.525i | 0.757576 | − | 0.677596i | ||||
\(232\) | 105.000 | 0.452586 | ||||||||
\(233\) | 232.379 | − | 134.164i | 0.997335 | − | 0.575811i | 0.0898761 | − | 0.995953i | \(-0.471353\pi\) |
0.907459 | + | 0.420141i | \(0.138020\pi\) | |||||||
\(234\) | −23.8730 | + | 32.4049i | −0.102021 | + | 0.138483i | ||||
\(235\) | −15.0000 | + | 25.9808i | −0.0638298 | + | 0.110556i | ||||
\(236\) | −17.4284 | + | 10.0623i | −0.0738493 | + | 0.0426369i | ||||
\(237\) | −158.000 | − | 176.649i | −0.666667 | − | 0.745356i | ||||
\(238\) | 210.000 | − | 363.731i | 0.882353 | − | 1.52828i | ||||
\(239\) | 281.745i | 1.17885i | 0.807824 | + | 0.589424i | \(0.200645\pi\) | ||||
−0.807824 | + | 0.589424i | \(0.799355\pi\) | |||||||
\(240\) | 121.087 | + | 39.7871i | 0.504528 | + | 0.165780i | ||||
\(241\) | −89.5000 | + | 155.019i | −0.371369 | + | 0.643230i | −0.989776 | − | 0.142627i | \(-0.954445\pi\) |
0.618407 | + | 0.785858i | \(0.287778\pi\) | |||||||
\(242\) | 7.74597 | + | 4.47214i | 0.0320081 | + | 0.0184799i | ||||
\(243\) | −124.967 | + | 208.404i | −0.514266 | + | 0.857631i | ||||
\(244\) | 26.0000 | 0.106557 | ||||||||
\(245\) | 94.8881 | + | 54.7837i | 0.387298 | + | 0.223607i | ||||
\(246\) | 140.000 | + | 156.525i | 0.569106 | + | 0.636280i | ||||
\(247\) | 16.0000 | + | 27.7128i | 0.0647773 | + | 0.112198i | ||||
\(248\) | 17.4284 | + | 10.0623i | 0.0702759 | + | 0.0405738i | ||||
\(249\) | −86.4980 | − | 413.670i | −0.347381 | − | 1.66133i | ||||
\(250\) | −112.500 | − | 194.856i | −0.450000 | − | 0.779423i | ||||
\(251\) | 172.177i | 0.685965i | 0.939342 | + | 0.342983i | \(0.111437\pi\) | ||||
−0.939342 | + | 0.342983i | \(0.888563\pi\) | |||||||
\(252\) | −50.7218 | − | 37.3671i | −0.201277 | − | 0.148282i | ||||
\(253\) | 150.000 | 0.592885 | ||||||||
\(254\) | 342.759 | − | 197.892i | 1.34944 | − | 0.779102i | ||||
\(255\) | 176.190 | − | 36.8410i | 0.690939 | − | 0.144475i | ||||
\(256\) | −90.5000 | + | 156.751i | −0.353516 | + | 0.612307i | ||||
\(257\) | 228.506 | − | 131.928i | 0.889128 | − | 0.513339i | 0.0154711 | − | 0.999880i | \(-0.495075\pi\) |
0.873657 | + | 0.486542i | \(0.161742\pi\) | |||||||
\(258\) | −220.000 | + | 196.774i | −0.852713 | + | 0.762690i | ||||
\(259\) | −84.0000 | −0.324324 | ||||||||
\(260\) | − | 4.47214i | − | 0.0172005i | ||||||
\(261\) | −56.4446 | − | 129.070i | −0.216263 | − | 0.494520i | ||||
\(262\) | −212.500 | + | 368.061i | −0.811069 | + | 1.40481i | ||||
\(263\) | 30.9839 | + | 17.8885i | 0.117809 | + | 0.0680173i | 0.557747 | − | 0.830011i | \(-0.311666\pi\) |
−0.439937 | + | 0.898028i | \(0.644999\pi\) | |||||||
\(264\) | −70.2369 | + | 213.756i | −0.266049 | + | 0.809683i | ||||
\(265\) | −45.0000 | −0.169811 | ||||||||
\(266\) | −216.887 | + | 125.220i | −0.815365 | + | 0.470751i | ||||
\(267\) | 110.000 | − | 98.3870i | 0.411985 | − | 0.368491i | ||||
\(268\) | 26.0000 | + | 45.0333i | 0.0970149 | + | 0.168035i | ||||
\(269\) | −342.759 | − | 197.892i | −1.27420 | − | 0.735658i | −0.298422 | − | 0.954434i | \(-0.596460\pi\) |
−0.975775 | + | 0.218776i | \(0.929794\pi\) | |||||||
\(270\) | −12.7772 | − | 134.394i | −0.0473230 | − | 0.497755i | ||||
\(271\) | −228.500 | − | 395.774i | −0.843173 | − | 1.46042i | −0.887198 | − | 0.461389i | \(-0.847351\pi\) |
0.0440246 | − | 0.999030i | \(-0.485982\pi\) | |||||||
\(272\) | 509.823i | 1.87435i | ||||||||
\(273\) | 13.1109 | − | 39.9012i | 0.0480252 | − | 0.146158i | ||||
\(274\) | −480.000 | −1.75182 | ||||||||
\(275\) | 193.649 | − | 111.803i | 0.704179 | − | 0.406558i | ||||
\(276\) | −8.23790 | − | 39.3972i | −0.0298475 | − | 0.142743i | ||||
\(277\) | −26.0000 | + | 45.0333i | −0.0938628 | + | 0.162575i | −0.909133 | − | 0.416505i | \(-0.863255\pi\) |
0.815271 | + | 0.579080i | \(0.196588\pi\) | |||||||
\(278\) | −220.760 | + | 127.456i | −0.794101 | + | 0.458474i | ||||
\(279\) | 3.00000 | − | 26.8328i | 0.0107527 | − | 0.0961750i | ||||
\(280\) | −105.000 | −0.375000 | ||||||||
\(281\) | − | 125.220i | − | 0.445622i | −0.974862 | − | 0.222811i | \(-0.928477\pi\) | ||
0.974862 | − | 0.222811i | \(-0.0715233\pi\) | |||||||
\(282\) | −28.0948 | + | 85.5025i | −0.0996268 | + | 0.303201i | ||||
\(283\) | −44.0000 | + | 76.2102i | −0.155477 | + | 0.269294i | −0.933233 | − | 0.359273i | \(-0.883025\pi\) |
0.777756 | + | 0.628567i | \(0.216358\pi\) | |||||||
\(284\) | −81.3327 | − | 46.9574i | −0.286383 | − | 0.165343i | ||||
\(285\) | −101.968 | − | 33.5049i | −0.357782 | − | 0.117561i | ||||
\(286\) | 50.0000 | 0.174825 | ||||||||
\(287\) | −189.776 | − | 109.567i | −0.661241 | − | 0.381768i | ||||
\(288\) | 140.000 | + | 15.6525i | 0.486111 | + | 0.0543489i | ||||
\(289\) | 215.500 | + | 373.257i | 0.745675 | + | 1.29155i | ||||
\(290\) | 67.7772 | + | 39.1312i | 0.233715 | + | 0.134935i | ||||
\(291\) | 273.094 | − | 57.1036i | 0.938466 | − | 0.196232i | ||||
\(292\) | 9.00000 | + | 15.5885i | 0.0308219 | + | 0.0533851i | ||||
\(293\) | 15.6525i | 0.0534214i | 0.999643 | + | 0.0267107i | \(0.00850329\pi\) | ||||
−0.999643 | + | 0.0267107i | \(0.991497\pi\) | |||||||
\(294\) | 312.276 | + | 102.609i | 1.06216 | + | 0.349010i | ||||
\(295\) | 45.0000 | 0.152542 | ||||||||
\(296\) | 69.7137 | − | 40.2492i | 0.235519 | − | 0.135977i | ||||
\(297\) | 300.514 | − | 28.5707i | 1.01183 | − | 0.0961977i | ||||
\(298\) | −15.0000 | + | 25.9808i | −0.0503356 | + | 0.0871838i | ||||
\(299\) | 23.2379 | − | 13.4164i | 0.0777187 | − | 0.0448709i | ||||
\(300\) | −40.0000 | − | 44.7214i | −0.133333 | − | 0.149071i | ||||
\(301\) | 154.000 | − | 266.736i | 0.511628 | − | 0.886166i | ||||
\(302\) | 131.928i | 0.436848i | ||||||||
\(303\) | −165.698 | − | 54.4455i | −0.546857 | − | 0.179688i | ||||
\(304\) | 152.000 | − | 263.272i | 0.500000 | − | 0.866025i | ||||
\(305\) | −50.3488 | − | 29.0689i | −0.165078 | − | 0.0953078i | ||||
\(306\) | 494.758 | − | 216.367i | 1.61686 | − | 0.707081i | ||||
\(307\) | 166.000 | 0.540717 | 0.270358 | − | 0.962760i | \(-0.412858\pi\) | ||||
0.270358 | + | 0.962760i | \(0.412858\pi\) | |||||||
\(308\) | 78.2624i | 0.254099i | ||||||||
\(309\) | −164.000 | − | 183.358i | −0.530744 | − | 0.593390i | ||||
\(310\) | 7.50000 | + | 12.9904i | 0.0241935 | + | 0.0419045i | ||||
\(311\) | 267.236 | + | 154.289i | 0.859279 | + | 0.496105i | 0.863771 | − | 0.503885i | \(-0.168096\pi\) |
−0.00449160 | + | 0.999990i | \(0.501430\pi\) | |||||||
\(312\) | 8.23790 | + | 39.3972i | 0.0264035 | + | 0.126273i | ||||
\(313\) | 135.500 | + | 234.693i | 0.432907 | + | 0.749818i | 0.997122 | − | 0.0758104i | \(-0.0241544\pi\) |
−0.564215 | + | 0.825628i | \(0.690821\pi\) | |||||||
\(314\) | − | 554.545i | − | 1.76607i | ||||||
\(315\) | 56.4446 | + | 129.070i | 0.179189 | + | 0.409745i | ||||
\(316\) | 79.0000 | 0.250000 | ||||||||
\(317\) | −377.616 | + | 218.017i | −1.19122 | + | 0.687750i | −0.958583 | − | 0.284815i | \(-0.908068\pi\) |
−0.232635 | + | 0.972564i | \(0.574735\pi\) | |||||||
\(318\) | −132.142 | + | 27.6308i | −0.415541 | + | 0.0868892i | ||||
\(319\) | −87.5000 | + | 151.554i | −0.274295 | + | 0.475092i | ||||
\(320\) | 79.3962 | − | 45.8394i | 0.248113 | − | 0.143248i | ||||
\(321\) | −145.000 | + | 129.692i | −0.451713 | + | 0.404025i | ||||
\(322\) | 105.000 | + | 181.865i | 0.326087 | + | 0.564799i | ||||
\(323\) | − | 429.325i | − | 1.32918i | ||||||
\(324\) | −24.0081 | − | 77.3603i | −0.0740990 | − | 0.238766i | ||||
\(325\) | 20.0000 | − | 34.6410i | 0.0615385 | − | 0.106588i | ||||
\(326\) | 3.87298 | + | 2.23607i | 0.0118803 | + | 0.00685910i | ||||
\(327\) | −134.855 | + | 410.412i | −0.412400 | + | 1.25508i | ||||
\(328\) | 210.000 | 0.640244 | ||||||||
\(329\) | − | 93.9149i | − | 0.285455i | ||||||
\(330\) | −125.000 | + | 111.803i | −0.378788 | + | 0.338798i | ||||
\(331\) | 8.00000 | + | 13.8564i | 0.0241692 | + | 0.0418623i | 0.877857 | − | 0.478923i | \(-0.158973\pi\) |
−0.853688 | + | 0.520785i | \(0.825639\pi\) | |||||||
\(332\) | 121.999 | + | 70.4361i | 0.367467 | + | 0.212157i | ||||
\(333\) | −86.9516 | − | 64.0579i | −0.261116 | − | 0.192366i | ||||
\(334\) | −280.000 | − | 484.974i | −0.838323 | − | 1.45202i | ||||
\(335\) | − | 116.276i | − | 0.347091i | ||||||
\(336\) | −390.553 | + | 81.6642i | −1.16236 | + | 0.243048i | ||||
\(337\) | −509.000 | −1.51039 | −0.755193 | − | 0.655503i | \(-0.772457\pi\) | ||||
−0.755193 | + | 0.655503i | \(0.772457\pi\) | |||||||
\(338\) | −319.521 | + | 184.476i | −0.945329 | + | 0.545786i | ||||
\(339\) | −19.2218 | − | 91.9267i | −0.0567014 | − | 0.271170i | ||||
\(340\) | −30.0000 | + | 51.9615i | −0.0882353 | + | 0.152828i | ||||
\(341\) | −29.0474 | + | 16.7705i | −0.0851829 | + | 0.0491804i | ||||
\(342\) | −320.000 | − | 35.7771i | −0.935673 | − | 0.104611i | ||||
\(343\) | −343.000 | −1.00000 | ||||||||
\(344\) | 295.161i | 0.858026i | ||||||||
\(345\) | −28.0948 | + | 85.5025i | −0.0814341 | + | 0.247833i | ||||
\(346\) | 295.000 | − | 510.955i | 0.852601 | − | 1.47675i | ||||
\(347\) | 329.204 | + | 190.066i | 0.948713 | + | 0.547740i | 0.892681 | − | 0.450689i | \(-0.148822\pi\) |
0.0560324 | + | 0.998429i | \(0.482155\pi\) | |||||||
\(348\) | 44.6109 | + | 14.6584i | 0.128192 | + | 0.0421219i | ||||
\(349\) | 628.000 | 1.79943 | 0.899713 | − | 0.436481i | \(-0.143775\pi\) | ||||
0.899713 | + | 0.436481i | \(0.143775\pi\) | |||||||
\(350\) | 271.109 | + | 156.525i | 0.774597 | + | 0.447214i | ||||
\(351\) | 44.0000 | − | 31.3050i | 0.125356 | − | 0.0891879i | ||||
\(352\) | −87.5000 | − | 151.554i | −0.248580 | − | 0.430552i | ||||
\(353\) | 402.790 | + | 232.551i | 1.14105 | + | 0.658785i | 0.946690 | − | 0.322146i | \(-0.104404\pi\) |
0.194359 | + | 0.980931i | \(0.437737\pi\) | |||||||
\(354\) | 132.142 | − | 27.6308i | 0.373283 | − | 0.0780530i | ||||
\(355\) | 105.000 | + | 181.865i | 0.295775 | + | 0.512297i | ||||
\(356\) | 49.1935i | 0.138184i | ||||||||
\(357\) | −420.000 | + | 375.659i | −1.17647 | + | 1.05227i | ||||
\(358\) | 430.000 | 1.20112 | ||||||||
\(359\) | −201.395 | + | 116.276i | −0.560989 | + | 0.323887i | −0.753542 | − | 0.657399i | \(-0.771657\pi\) |
0.192553 | + | 0.981287i | \(0.438323\pi\) | |||||||
\(360\) | −108.690 | − | 80.0724i | −0.301915 | − | 0.222423i | ||||
\(361\) | 52.5000 | − | 90.9327i | 0.145429 | − | 0.251891i | ||||
\(362\) | 158.792 | − | 91.6788i | 0.438653 | − | 0.253256i | ||||
\(363\) | −8.00000 | − | 8.94427i | −0.0220386 | − | 0.0246399i | ||||
\(364\) | 7.00000 | + | 12.1244i | 0.0192308 | + | 0.0333087i | ||||
\(365\) | − | 40.2492i | − | 0.110272i | ||||||
\(366\) | −165.698 | − | 54.4455i | −0.452726 | − | 0.148758i | ||||
\(367\) | −250.500 | + | 433.879i | −0.682561 | + | 1.18223i | 0.291635 | + | 0.956530i | \(0.405801\pi\) |
−0.974197 | + | 0.225701i | \(0.927533\pi\) | |||||||
\(368\) | −220.760 | − | 127.456i | −0.599891 | − | 0.346347i | ||||
\(369\) | −112.889 | − | 258.140i | −0.305933 | − | 0.699565i | ||||
\(370\) | 60.0000 | 0.162162 | ||||||||
\(371\) | 121.999 | − | 70.4361i | 0.328838 | − | 0.189855i | ||||
\(372\) | 6.00000 | + | 6.70820i | 0.0161290 | + | 0.0180328i | ||||
\(373\) | −349.000 | − | 604.486i | −0.935657 | − | 1.62061i | −0.773458 | − | 0.633847i | \(-0.781475\pi\) |
−0.162198 | − | 0.986758i | \(-0.551858\pi\) | |||||||
\(374\) | −580.948 | − | 335.410i | −1.55334 | − | 0.896819i | ||||
\(375\) | 61.7843 | + | 295.479i | 0.164758 | + | 0.787943i | ||||
\(376\) | 45.0000 | + | 77.9423i | 0.119681 | + | 0.207293i | ||||
\(377\) | 31.3050i | 0.0830370i | ||||||||
\(378\) | 245.000 | + | 344.354i | 0.648148 | + | 0.910991i | ||||
\(379\) | 366.000 | 0.965699 | 0.482850 | − | 0.875703i | \(-0.339602\pi\) | ||||
0.482850 | + | 0.875703i | \(0.339602\pi\) | |||||||
\(380\) | 30.9839 | − | 17.8885i | 0.0815365 | − | 0.0470751i | ||||
\(381\) | −519.759 | + | 108.681i | −1.36420 | + | 0.285252i | ||||
\(382\) | −190.000 | + | 329.090i | −0.497382 | + | 0.861491i | ||||
\(383\) | 11.6190 | − | 6.70820i | 0.0303367 | − | 0.0175149i | −0.484755 | − | 0.874650i | \(-0.661091\pi\) |
0.515092 | + | 0.857135i | \(0.327758\pi\) | |||||||
\(384\) | 345.000 | − | 308.577i | 0.898438 | − | 0.803587i | ||||
\(385\) | 87.5000 | − | 151.554i | 0.227273 | − | 0.393648i | ||||
\(386\) | 131.928i | 0.341782i | ||||||||
\(387\) | 362.823 | − | 158.669i | 0.937526 | − | 0.409997i | ||||
\(388\) | −46.5000 | + | 80.5404i | −0.119845 | + | 0.207578i | ||||
\(389\) | 58.0948 | + | 33.5410i | 0.149344 | + | 0.0862237i | 0.572810 | − | 0.819688i | \(-0.305853\pi\) |
−0.423466 | + | 0.905912i | \(0.639187\pi\) | |||||||
\(390\) | −9.36492 | + | 28.5008i | −0.0240126 | + | 0.0730791i | ||||
\(391\) | −360.000 | −0.920716 | ||||||||
\(392\) | 284.664 | − | 164.351i | 0.726184 | − | 0.419263i | ||||
\(393\) | 425.000 | − | 380.132i | 1.08142 | − | 0.967256i | ||||
\(394\) | 245.000 | + | 424.352i | 0.621827 | + | 1.07704i | ||||
\(395\) | −152.983 | − | 88.3247i | −0.387298 | − | 0.223607i | ||||
\(396\) | −59.6825 | + | 81.0124i | −0.150713 | + | 0.204577i | ||||
\(397\) | 132.000 | + | 228.631i | 0.332494 | + | 0.575896i | 0.983000 | − | 0.183605i | \(-0.0587766\pi\) |
−0.650506 | + | 0.759501i | \(0.725443\pi\) | |||||||
\(398\) | − | 523.240i | − | 1.31467i | ||||||
\(399\) | 328.887 | − | 68.7699i | 0.824278 | − | 0.172356i | ||||
\(400\) | −380.000 | −0.950000 | ||||||||
\(401\) | −92.9516 | + | 53.6656i | −0.231800 | + | 0.133830i | −0.611402 | − | 0.791320i | \(-0.709394\pi\) |
0.379602 | + | 0.925150i | \(0.376061\pi\) | |||||||
\(402\) | −71.3951 | − | 341.442i | −0.177600 | − | 0.849359i | ||||
\(403\) | −3.00000 | + | 5.19615i | −0.00744417 | + | 0.0128937i | ||||
\(404\) | 50.3488 | − | 29.0689i | 0.124626 | − | 0.0719527i | ||||
\(405\) | −40.0000 | + | 176.649i | −0.0987654 | + | 0.436171i | ||||
\(406\) | −245.000 | −0.603448 | ||||||||
\(407\) | 134.164i | 0.329641i | ||||||||
\(408\) | 168.569 | − | 513.015i | 0.413158 | − | 1.25739i | ||||
\(409\) | 99.5000 | − | 172.339i | 0.243276 | − | 0.421367i | −0.718369 | − | 0.695662i | \(-0.755111\pi\) |
0.961646 | + | 0.274295i | \(0.0884445\pi\) | |||||||
\(410\) | 135.554 | + | 78.2624i | 0.330621 | + | 0.190884i | ||||
\(411\) | 611.806 | + | 201.030i | 1.48858 | + | 0.489123i | ||||
\(412\) | 82.0000 | 0.199029 | ||||||||
\(413\) | −121.999 | + | 70.4361i | −0.295397 | + | 0.170548i | ||||
\(414\) | −30.0000 | + | 268.328i | −0.0724638 | + | 0.648136i | ||||
\(415\) | −157.500 | − | 272.798i | −0.379518 | − | 0.657345i | ||||
\(416\) | −27.1109 | − | 15.6525i | −0.0651704 | − | 0.0376261i | ||||
\(417\) | 334.760 | − | 69.9979i | 0.802782 | − | 0.167861i | ||||
\(418\) | 200.000 | + | 346.410i | 0.478469 | + | 0.828732i | ||||
\(419\) | 93.9149i | 0.224140i | 0.993700 | + | 0.112070i | \(0.0357482\pi\) | ||||
−0.993700 | + | 0.112070i | \(0.964252\pi\) | |||||||
\(420\) | −44.6109 | − | 14.6584i | −0.106216 | − | 0.0349010i | ||||
\(421\) | 254.000 | 0.603325 | 0.301663 | − | 0.953415i | \(-0.402458\pi\) | ||||
0.301663 | + | 0.953415i | \(0.402458\pi\) | |||||||
\(422\) | −50.3488 | + | 29.0689i | −0.119310 | + | 0.0688836i | ||||
\(423\) | 71.6190 | − | 97.2148i | 0.169312 | − | 0.229822i | ||||
\(424\) | −67.5000 | + | 116.913i | −0.159198 | + | 0.275739i | ||||
\(425\) | −464.758 | + | 268.328i | −1.09355 | + | 0.631360i | ||||
\(426\) | 420.000 | + | 469.574i | 0.985915 | + | 1.10229i | ||||
\(427\) | 182.000 | 0.426230 | ||||||||
\(428\) | − | 64.8460i | − | 0.151509i | ||||||
\(429\) | −63.7298 | − | 20.9406i | −0.148554 | − | 0.0488126i | ||||
\(430\) | −110.000 | + | 190.526i | −0.255814 | + | 0.443083i | ||||
\(431\) | −104.571 | − | 60.3738i | −0.242623 | − | 0.140079i | 0.373759 | − | 0.927526i | \(-0.378069\pi\) |
−0.616382 | + | 0.787447i | \(0.711402\pi\) | |||||||
\(432\) | −466.553 | − | 213.300i | −1.07998 | − | 0.493750i | ||||
\(433\) | −506.000 | −1.16859 | −0.584296 | − | 0.811541i | \(-0.698629\pi\) | ||||
−0.584296 | + | 0.811541i | \(0.698629\pi\) | |||||||
\(434\) | −40.6663 | − | 23.4787i | −0.0937012 | − | 0.0540984i | ||||
\(435\) | −70.0000 | − | 78.2624i | −0.160920 | − | 0.179914i | ||||
\(436\) | −72.0000 | − | 124.708i | −0.165138 | − | 0.286027i | ||||
\(437\) | 185.903 | + | 107.331i | 0.425408 | + | 0.245609i | ||||
\(438\) | −24.7137 | − | 118.192i | −0.0564240 | − | 0.269844i | ||||
\(439\) | −235.500 | − | 407.898i | −0.536446 | − | 0.929153i | −0.999092 | − | 0.0426091i | \(-0.986433\pi\) |
0.462645 | − | 0.886543i | \(-0.346900\pi\) | |||||||
\(440\) | 167.705i | 0.381148i | ||||||||
\(441\) | −355.052 | − | 261.570i | −0.805107 | − | 0.593129i | ||||
\(442\) | −120.000 | −0.271493 | ||||||||
\(443\) | −52.2853 | + | 30.1869i | −0.118025 | + | 0.0681420i | −0.557851 | − | 0.829941i | \(-0.688374\pi\) |
0.439825 | + | 0.898083i | \(0.355040\pi\) | |||||||
\(444\) | 35.2379 | − | 7.36820i | 0.0793646 | − | 0.0165950i | ||||
\(445\) | 55.0000 | − | 95.2628i | 0.123596 | − | 0.214074i | ||||
\(446\) | −207.205 | + | 119.630i | −0.464584 | + | 0.268228i | ||||
\(447\) | 30.0000 | − | 26.8328i | 0.0671141 | − | 0.0600287i | ||||
\(448\) | −143.500 | + | 248.549i | −0.320312 | + | 0.554798i | ||||
\(449\) | 281.745i | 0.627493i | 0.949507 | + | 0.313747i | \(0.101584\pi\) | ||||
−0.949507 | + | 0.313747i | \(0.898416\pi\) | |||||||
\(450\) | 161.270 | + | 368.771i | 0.358378 | + | 0.819491i | ||||
\(451\) | −175.000 | + | 303.109i | −0.388027 | + | 0.672082i | ||||
\(452\) | 27.1109 | + | 15.6525i | 0.0599798 | + | 0.0346294i | ||||
\(453\) | 55.2530 | − | 168.155i | 0.121971 | − | 0.371203i | ||||
\(454\) | −675.000 | −1.48678 | ||||||||
\(455\) | − | 31.3050i | − | 0.0688021i | ||||||
\(456\) | −240.000 | + | 214.663i | −0.526316 | + | 0.470751i | ||||
\(457\) | 11.5000 | + | 19.9186i | 0.0251641 | + | 0.0435855i | 0.878333 | − | 0.478049i | \(-0.158656\pi\) |
−0.853169 | + | 0.521634i | \(0.825323\pi\) | |||||||
\(458\) | 646.788 | + | 373.423i | 1.41220 | + | 0.815335i | ||||
\(459\) | −721.234 | + | 68.5697i | −1.57132 | + | 0.149389i | ||||
\(460\) | −15.0000 | − | 25.9808i | −0.0326087 | − | 0.0564799i | ||||
\(461\) | − | 594.794i | − | 1.29023i | −0.764087 | − | 0.645113i | \(-0.776810\pi\) | ||
0.764087 | − | 0.645113i | \(-0.223190\pi\) | |||||||
\(462\) | 163.886 | − | 498.765i | 0.354732 | − | 1.07958i | ||||
\(463\) | 58.0000 | 0.125270 | 0.0626350 | − | 0.998037i | \(-0.480050\pi\) | ||||
0.0626350 | + | 0.998037i | \(0.480050\pi\) | |||||||
\(464\) | 257.553 | − | 148.699i | 0.555072 | − | 0.320471i | ||||
\(465\) | −4.11895 | − | 19.6986i | −0.00885796 | − | 0.0423625i | ||||
\(466\) | 300.000 | − | 519.615i | 0.643777 | − | 1.11505i | ||||
\(467\) | 499.615 | − | 288.453i | 1.06984 | − | 0.617672i | 0.141702 | − | 0.989909i | \(-0.454743\pi\) |
0.928137 | + | 0.372238i | \(0.121409\pi\) | |||||||
\(468\) | −2.00000 | + | 17.8885i | −0.00427350 | + | 0.0382234i | ||||
\(469\) | 182.000 | + | 315.233i | 0.388060 | + | 0.672139i | ||||
\(470\) | 67.0820i | 0.142728i | ||||||||
\(471\) | −232.250 | + | 706.821i | −0.493100 | + | 1.50068i | ||||
\(472\) | 67.5000 | − | 116.913i | 0.143008 | − | 0.247698i | ||||
\(473\) | −426.028 | − | 245.967i | −0.900694 | − | 0.520016i | ||||
\(474\) | −503.466 | − | 165.431i | −1.06216 | − | 0.349010i | ||||
\(475\) | 320.000 | 0.673684 | ||||||||
\(476\) | − | 187.830i | − | 0.394600i | ||||||
\(477\) | 180.000 | + | 20.1246i | 0.377358 | + | 0.0421900i | ||||
\(478\) | 315.000 | + | 545.596i | 0.658996 | + | 1.14141i | ||||
\(479\) | 294.347 | + | 169.941i | 0.614503 | + | 0.354783i | 0.774726 | − | 0.632298i | \(-0.217888\pi\) |
−0.160223 | + | 0.987081i | \(0.551221\pi\) | |||||||
\(480\) | 102.777 | − | 21.4906i | 0.214119 | − | 0.0447721i | ||||
\(481\) | 12.0000 | + | 20.7846i | 0.0249480 | + | 0.0432112i | ||||
\(482\) | 400.256i | 0.830407i | ||||||||
\(483\) | −57.6653 | − | 275.780i | −0.119390 | − | 0.570973i | ||||
\(484\) | 4.00000 | 0.00826446 | ||||||||
\(485\) | 180.094 | − | 103.977i | 0.371327 | − | 0.214386i | ||||
\(486\) | −8.99398 | + | 543.290i | −0.0185061 | + | 1.11788i | ||||
\(487\) | 404.500 | − | 700.615i | 0.830595 | − | 1.43863i | −0.0669712 | − | 0.997755i | \(-0.521334\pi\) |
0.897567 | − | 0.440879i | \(-0.145333\pi\) | |||||||
\(488\) | −151.046 | + | 87.2067i | −0.309521 | + | 0.178702i | ||||
\(489\) | −4.00000 | − | 4.47214i | −0.00817996 | − | 0.00914547i | ||||
\(490\) | 245.000 | 0.500000 | ||||||||
\(491\) | − | 453.922i | − | 0.924484i | −0.886754 | − | 0.462242i | \(-0.847045\pi\) | ||
0.886754 | − | 0.462242i | \(-0.152955\pi\) | |||||||
\(492\) | 89.2218 | + | 29.3168i | 0.181345 | + | 0.0595870i | ||||
\(493\) | 210.000 | − | 363.731i | 0.425963 | − | 0.737790i | ||||
\(494\) | 61.9677 | + | 35.7771i | 0.125441 | + | 0.0724233i | ||||
\(495\) | 206.149 | − | 90.1528i | 0.416463 | − | 0.182127i | ||||
\(496\) | 57.0000 | 0.114919 | ||||||||
\(497\) | −569.329 | − | 328.702i | −1.14553 | − | 0.661372i | ||||
\(498\) | −630.000 | − | 704.361i | −1.26506 | − | 1.41438i | ||||
\(499\) | 127.000 | + | 219.970i | 0.254509 | + | 0.440823i | 0.964762 | − | 0.263124i | \(-0.0847528\pi\) |
−0.710253 | + | 0.703946i | \(0.751419\pi\) | |||||||
\(500\) | −87.1421 | − | 50.3115i | −0.174284 | − | 0.100623i | ||||
\(501\) | 153.774 | + | 735.414i | 0.306934 | + | 1.46789i | ||||
\(502\) | 192.500 | + | 333.420i | 0.383466 | + | 0.664183i | ||||
\(503\) | 939.149i | 1.86709i | 0.358454 | + | 0.933547i | \(0.383304\pi\) | ||||
−0.358454 | + | 0.933547i | \(0.616696\pi\) | |||||||
\(504\) | 420.000 | + | 46.9574i | 0.833333 | + | 0.0931695i | ||||
\(505\) | −130.000 | −0.257426 | ||||||||
\(506\) | 290.474 | − | 167.705i | 0.574059 | − | 0.331433i | ||||
\(507\) | 484.521 | − | 101.313i | 0.955663 | − | 0.199828i | ||||
\(508\) | 88.5000 | − | 153.286i | 0.174213 | − | 0.301745i | ||||
\(509\) | 350.505 | − | 202.364i | 0.688615 | − | 0.397572i | −0.114478 | − | 0.993426i | \(-0.536520\pi\) |
0.803093 | + | 0.595854i | \(0.203186\pi\) | |||||||
\(510\) | 300.000 | − | 268.328i | 0.588235 | − | 0.526134i | ||||
\(511\) | 63.0000 | + | 109.119i | 0.123288 | + | 0.213541i | ||||
\(512\) | − | 212.426i | − | 0.414895i | ||||||
\(513\) | 392.887 | + | 179.621i | 0.765862 | + | 0.350139i | ||||
\(514\) | 295.000 | − | 510.955i | 0.573930 | − | 0.994076i | ||||
\(515\) | −158.792 | − | 91.6788i | −0.308335 | − | 0.178017i | ||||
\(516\) | −41.2056 | + | 125.404i | −0.0798559 | + | 0.243030i | ||||
\(517\) | −150.000 | −0.290135 | ||||||||
\(518\) | −162.665 | + | 93.9149i | −0.314026 | + | 0.181303i | ||||
\(519\) | −590.000 | + | 527.712i | −1.13680 | + | 1.01679i | ||||
\(520\) | 15.0000 | + | 25.9808i | 0.0288462 | + | 0.0499630i | ||||
\(521\) | −302.093 | − | 174.413i | −0.579832 | − | 0.334766i | 0.181234 | − | 0.983440i | \(-0.441991\pi\) |
−0.761067 | + | 0.648674i | \(0.775324\pi\) | |||||||
\(522\) | −253.609 | − | 186.836i | −0.485841 | − | 0.357923i | ||||
\(523\) | −197.000 | − | 341.214i | −0.376673 | − | 0.652417i | 0.613903 | − | 0.789382i | \(-0.289599\pi\) |
−0.990576 | + | 0.136965i | \(0.956265\pi\) | |||||||
\(524\) | 190.066i | 0.362721i | ||||||||
\(525\) | −280.000 | − | 313.050i | −0.533333 | − | 0.596285i | ||||
\(526\) | 80.0000 | 0.152091 | ||||||||
\(527\) | 69.7137 | − | 40.2492i | 0.132284 | − | 0.0763742i | ||||
\(528\) | 130.433 | + | 623.789i | 0.247033 | + | 1.18142i | ||||
\(529\) | −174.500 | + | 302.243i | −0.329868 | + | 0.571348i | ||||
\(530\) | −87.1421 | + | 50.3115i | −0.164419 | + | 0.0949274i | ||||
\(531\) | −180.000 | − | 20.1246i | −0.338983 | − | 0.0378995i | ||||
\(532\) | −56.0000 | + | 96.9948i | −0.105263 | + | 0.182321i | ||||
\(533\) | 62.6099i | 0.117467i | ||||||||
\(534\) | 103.014 | − | 313.509i | 0.192910 | − | 0.587096i | ||||
\(535\) | −72.5000 | + | 125.574i | −0.135514 | + | 0.234717i | ||||
\(536\) | −302.093 | − | 174.413i | −0.563606 | − | 0.325398i | ||||
\(537\) | −548.077 | − | 180.089i | −1.02063 | − | 0.335361i | ||||
\(538\) | −885.000 | −1.64498 | ||||||||
\(539\) | 547.837i | 1.01639i | ||||||||
\(540\) | −35.0000 | − | 49.1935i | −0.0648148 | − | 0.0910991i | ||||
\(541\) | −202.000 | − | 349.874i | −0.373383 | − | 0.646718i | 0.616701 | − | 0.787198i | \(-0.288469\pi\) |
−0.990084 | + | 0.140480i | \(0.955135\pi\) | |||||||
\(542\) | −884.977 | − | 510.942i | −1.63280 | − | 0.942697i | ||||
\(543\) | −240.792 | + | 50.3494i | −0.443448 | + | 0.0927245i | ||||
\(544\) | 210.000 | + | 363.731i | 0.386029 | + | 0.668623i | ||||
\(545\) | 321.994i | 0.590814i | ||||||||
\(546\) | −19.2218 | − | 91.9267i | −0.0352047 | − | 0.168364i | ||||
\(547\) | 16.0000 | 0.0292505 | 0.0146252 | − | 0.999893i | \(-0.495344\pi\) | ||||
0.0146252 | + | 0.999893i | \(0.495344\pi\) | |||||||
\(548\) | −185.903 | + | 107.331i | −0.339239 | + | 0.195860i | ||||
\(549\) | 188.395 | + | 138.792i | 0.343161 | + | 0.252809i | ||||
\(550\) | 250.000 | − | 433.013i | 0.454545 | − | 0.787296i | ||||
\(551\) | −216.887 | + | 125.220i | −0.393624 | + | 0.227259i | ||||
\(552\) | 180.000 | + | 201.246i | 0.326087 | + | 0.364576i | ||||
\(553\) | 553.000 | 1.00000 | ||||||||
\(554\) | 116.276i | 0.209884i | ||||||||
\(555\) | −76.4758 | − | 25.1287i | −0.137794 | − | 0.0452770i | ||||
\(556\) | −57.0000 | + | 98.7269i | −0.102518 | + | 0.177566i | ||||
\(557\) | 640.979 | + | 370.069i | 1.15077 | + | 0.664397i | 0.949075 | − | 0.315051i | \(-0.102022\pi\) |
0.201695 | + | 0.979448i | \(0.435355\pi\) | |||||||
\(558\) | −24.1905 | − | 55.3156i | −0.0433522 | − | 0.0991319i | ||||
\(559\) | −88.0000 | −0.157424 | ||||||||
\(560\) | −257.553 | + | 148.699i | −0.459917 | + | 0.265533i | ||||
\(561\) | 600.000 | + | 670.820i | 1.06952 | + | 1.19576i | ||||
\(562\) | −140.000 | − | 242.487i | −0.249110 | − | 0.431472i | ||||
\(563\) | −207.205 | − | 119.630i | −0.368037 | − | 0.212486i | 0.304564 | − | 0.952492i | \(-0.401489\pi\) |
−0.672600 | + | 0.740006i | \(0.734823\pi\) | |||||||
\(564\) | 8.23790 | + | 39.3972i | 0.0146062 | + | 0.0698531i | ||||
\(565\) | −35.0000 | − | 60.6218i | −0.0619469 | − | 0.107295i | ||||
\(566\) | 196.774i | 0.347657i | ||||||||
\(567\) | −168.056 | − | 541.522i | −0.296396 | − | 0.955065i | ||||
\(568\) | 630.000 | 1.10915 | ||||||||
\(569\) | 828.818 | − | 478.519i | 1.45662 | − | 0.840982i | 0.457780 | − | 0.889066i | \(-0.348645\pi\) |
0.998843 | + | 0.0480841i | \(0.0153115\pi\) | |||||||
\(570\) | −234.919 | + | 49.1213i | −0.412139 | + | 0.0861778i | ||||
\(571\) | 23.0000 | − | 39.8372i | 0.0402802 | − | 0.0697674i | −0.845182 | − | 0.534478i | \(-0.820508\pi\) |
0.885463 | + | 0.464711i | \(0.153842\pi\) | |||||||
\(572\) | 19.3649 | − | 11.1803i | 0.0338547 | − | 0.0195460i | ||||
\(573\) | 380.000 | − | 339.882i | 0.663176 | − | 0.593163i | ||||
\(574\) | −490.000 | −0.853659 | ||||||||
\(575\) | − | 268.328i | − | 0.466658i | ||||||
\(576\) | −338.085 | + | 147.851i | −0.586952 | + | 0.256685i | ||||
\(577\) | −495.500 | + | 858.231i | −0.858752 | + | 1.48740i | 0.0143677 | + | 0.999897i | \(0.495426\pi\) |
−0.873120 | + | 0.487506i | \(0.837907\pi\) | |||||||
\(578\) | 834.628 | + | 481.873i | 1.44399 | + | 0.833690i | ||||
\(579\) | 55.2530 | − | 168.155i | 0.0954283 | − | 0.290423i | ||||
\(580\) | 35.0000 | 0.0603448 | ||||||||
\(581\) | 853.993 | + | 493.053i | 1.46987 | + | 0.848628i | ||||
\(582\) | 465.000 | − | 415.909i | 0.798969 | − | 0.714620i | ||||
\(583\) | −112.500 | − | 194.856i | −0.192967 | − | 0.334229i | ||||
\(584\) | −104.571 | − | 60.3738i | −0.179059 | − | 0.103380i | ||||
\(585\) | 23.8730 | − | 32.4049i | 0.0408085 | − | 0.0553931i | ||||
\(586\) | 17.5000 | + | 30.3109i | 0.0298635 | + | 0.0517251i | ||||
\(587\) | − | 766.971i | − | 1.30660i | −0.757101 | − | 0.653298i | \(-0.773385\pi\) | ||
0.757101 | − | 0.653298i | \(-0.226615\pi\) | |||||||
\(588\) | 143.888 | − | 30.0868i | 0.244708 | − | 0.0511681i | ||||
\(589\) | −48.0000 | −0.0814941 | ||||||||
\(590\) | 87.1421 | − | 50.3115i | 0.147699 | − | 0.0852738i | ||||
\(591\) | −134.552 | − | 643.487i | −0.227669 | − | 1.08881i | ||||
\(592\) | 114.000 | − | 197.454i | 0.192568 | − | 0.333537i | ||||
\(593\) | −151.046 | + | 87.2067i | −0.254716 | + | 0.147060i | −0.621922 | − | 0.783080i | \(-0.713648\pi\) |
0.367206 | + | 0.930140i | \(0.380314\pi\) | |||||||
\(594\) | 550.000 | − | 391.312i | 0.925926 | − | 0.658774i | ||||
\(595\) | −210.000 | + | 363.731i | −0.352941 | + | 0.611312i | ||||
\(596\) | 13.4164i | 0.0225108i | ||||||||
\(597\) | −219.139 | + | 666.920i | −0.367067 | + | 1.11712i | ||||
\(598\) | 30.0000 | − | 51.9615i | 0.0501672 | − | 0.0868922i | ||||
\(599\) | −836.564 | − | 482.991i | −1.39660 | − | 0.806328i | −0.402567 | − | 0.915391i | \(-0.631882\pi\) |
−0.994035 | + | 0.109062i | \(0.965215\pi\) | |||||||
\(600\) | 382.379 | + | 125.644i | 0.637298 | + | 0.209406i | ||||
\(601\) | −471.000 | −0.783694 | −0.391847 | − | 0.920030i | \(-0.628164\pi\) | ||||
−0.391847 | + | 0.920030i | \(0.628164\pi\) | |||||||
\(602\) | − | 688.709i | − | 1.14403i | ||||||
\(603\) | −52.0000 | + | 465.102i | −0.0862355 | + | 0.771314i | ||||
\(604\) | 29.5000 | + | 51.0955i | 0.0488411 | + | 0.0845952i | ||||
\(605\) | −7.74597 | − | 4.47214i | −0.0128033 | − | 0.00739196i | ||||
\(606\) | −381.744 | + | 79.8222i | −0.629940 | + | 0.131720i | ||||
\(607\) | 471.500 | + | 816.662i | 0.776771 | + | 1.34541i | 0.933794 | + | 0.357812i | \(0.116477\pi\) |
−0.157023 | + | 0.987595i | \(0.550190\pi\) | |||||||
\(608\) | − | 250.440i | − | 0.411907i | ||||||
\(609\) | 312.276 | + | 102.609i | 0.512769 | + | 0.168488i | ||||
\(610\) | −130.000 | −0.213115 | ||||||||
\(611\) | −23.2379 | + | 13.4164i | −0.0380326 | + | 0.0219581i | ||||
\(612\) | 143.238 | − | 194.430i | 0.234049 | − | 0.317696i | ||||
\(613\) | −467.000 | + | 808.868i | −0.761827 | + | 1.31952i | 0.180081 | + | 0.983652i | \(0.442364\pi\) |
−0.941908 | + | 0.335871i | \(0.890969\pi\) | |||||||
\(614\) | 321.458 | − | 185.594i | 0.523547 | − | 0.302270i | ||||
\(615\) | −140.000 | − | 156.525i | −0.227642 | − | 0.254512i | ||||
\(616\) | −262.500 | − | 454.663i | −0.426136 | − | 0.738090i | ||||
\(617\) | − | 93.9149i | − | 0.152212i | −0.997100 | − | 0.0761060i | \(-0.975751\pi\) | ||
0.997100 | − | 0.0761060i | \(-0.0242488\pi\) | |||||||
\(618\) | −522.585 | − | 171.713i | −0.845606 | − | 0.277852i | ||||
\(619\) | 61.0000 | − | 105.655i | 0.0985460 | − | 0.170687i | −0.812537 | − | 0.582910i | \(-0.801914\pi\) |
0.911083 | + | 0.412223i | \(0.135247\pi\) | |||||||
\(620\) | 5.80948 | + | 3.35410i | 0.00937012 | + | 0.00540984i | ||||
\(621\) | 150.617 | − | 329.446i | 0.242539 | − | 0.530509i | ||||
\(622\) | 690.000 | 1.10932 | ||||||||
\(623\) | 344.354i | 0.552736i | ||||||||
\(624\) | 76.0000 | + | 84.9706i | 0.121795 | + | 0.136171i | ||||
\(625\) | −137.500 | − | 238.157i | −0.220000 | − | 0.381051i | ||||
\(626\) | 524.789 | + | 302.987i | 0.838321 | + | 0.484005i | ||||
\(627\) | −109.839 | − | 525.296i | −0.175181 | − | 0.837792i | ||||
\(628\) | −124.000 | − | 214.774i | −0.197452 | − | 0.341997i | ||||
\(629\) | − | 321.994i | − | 0.511914i | ||||||
\(630\) | 253.609 | + | 186.836i | 0.402554 | + | 0.296565i | ||||
\(631\) | −61.0000 | −0.0966719 | −0.0483360 | − | 0.998831i | \(-0.515392\pi\) | ||||
−0.0483360 | + | 0.998831i | \(0.515392\pi\) | |||||||
\(632\) | −458.949 | + | 264.974i | −0.726184 | + | 0.419263i | ||||
\(633\) | 76.3488 | − | 15.9644i | 0.120614 | − | 0.0252203i | ||||
\(634\) | −487.500 | + | 844.375i | −0.768927 | + | 1.33182i | ||||
\(635\) | −342.759 | + | 197.892i | −0.539778 | + | 0.311641i | ||||
\(636\) | −45.0000 | + | 40.2492i | −0.0707547 | + | 0.0632849i | ||||
\(637\) | 49.0000 | + | 84.8705i | 0.0769231 | + | 0.133235i | ||||
\(638\) | 391.312i | 0.613342i | ||||||||
\(639\) | −338.667 | − | 774.419i | −0.529996 | − | 1.21192i | ||||
\(640\) | 172.500 | − | 298.779i | 0.269531 | − | 0.466842i | ||||
\(641\) | 708.756 | + | 409.200i | 1.10570 | + | 0.638378i | 0.937713 | − | 0.347410i | \(-0.112939\pi\) |
0.167990 | + | 0.985789i | \(0.446272\pi\) | |||||||
\(642\) | −135.791 | + | 413.262i | −0.211513 | + | 0.643711i | ||||
\(643\) | 908.000 | 1.41213 | 0.706065 | − | 0.708147i | \(-0.250468\pi\) | ||||
0.706065 | + | 0.708147i | \(0.250468\pi\) | |||||||
\(644\) | 81.3327 | + | 46.9574i | 0.126293 | + | 0.0729153i | ||||
\(645\) | 220.000 | − | 196.774i | 0.341085 | − | 0.305076i | ||||
\(646\) | −480.000 | − | 831.384i | −0.743034 | − | 1.28697i | ||||
\(647\) | −274.982 | − | 158.761i | −0.425011 | − | 0.245380i | 0.272208 | − | 0.962238i | \(-0.412246\pi\) |
−0.697219 | + | 0.716858i | \(0.745579\pi\) | |||||||
\(648\) | 398.949 | + | 368.897i | 0.615661 | + | 0.569286i | ||||
\(649\) | 112.500 | + | 194.856i | 0.173344 | + | 0.300240i | ||||
\(650\) | − | 89.4427i | − | 0.137604i | ||||||
\(651\) | 42.0000 | + | 46.9574i | 0.0645161 | + | 0.0721312i | ||||
\(652\) | 2.00000 | 0.00306748 | ||||||||
\(653\) | −865.612 | + | 499.761i | −1.32559 | + | 0.765331i | −0.984615 | − | 0.174740i | \(-0.944091\pi\) |
−0.340978 | + | 0.940071i | \(0.610758\pi\) | |||||||
\(654\) | 197.710 | + | 945.532i | 0.302308 | + | 1.44577i | ||||
\(655\) | 212.500 | − | 368.061i | 0.324427 | − | 0.561925i | ||||
\(656\) | 515.107 | − | 297.397i | 0.785224 | − | 0.453349i | ||||
\(657\) | −18.0000 | + | 160.997i | −0.0273973 | + | 0.245049i | ||||
\(658\) | −105.000 | − | 181.865i | −0.159574 | − | 0.276391i | ||||
\(659\) | 657.404i | 0.997578i | 0.866723 | + | 0.498789i | \(0.166222\pi\) | ||||
−0.866723 | + | 0.498789i | \(0.833778\pi\) | |||||||
\(660\) | −23.4123 | + | 71.2521i | −0.0354732 | + | 0.107958i | ||||
\(661\) | 418.000 | − | 723.997i | 0.632375 | − | 1.09531i | −0.354690 | − | 0.934984i | \(-0.615413\pi\) |
0.987065 | − | 0.160322i | \(-0.0512532\pi\) | |||||||
\(662\) | 30.9839 | + | 17.8885i | 0.0468034 | + | 0.0270220i | ||||
\(663\) | 152.952 | + | 50.2574i | 0.230696 | + | 0.0758030i | ||||
\(664\) | −945.000 | −1.42319 | ||||||||
\(665\) | 216.887 | − | 125.220i | 0.326146 | − | 0.188300i | ||||
\(666\) | −240.000 | − | 26.8328i | −0.360360 | − | 0.0402895i | ||||
\(667\) | 105.000 | + | 181.865i | 0.157421 | + | 0.272662i | ||||
\(668\) | −216.887 | − | 125.220i | −0.324681 | − | 0.187455i | ||||
\(669\) | 314.205 | − | 65.6998i | 0.469663 | − | 0.0982060i | ||||
\(670\) | −130.000 | − | 225.167i | −0.194030 | − | 0.336070i | ||||
\(671\) | − | 290.689i | − | 0.433217i | ||||||
\(672\) | −245.000 | + | 219.135i | −0.364583 | + | 0.326093i | ||||
\(673\) | −677.000 | −1.00594 | −0.502972 | − | 0.864303i | \(-0.667760\pi\) | ||||
−0.502972 | + | 0.864303i | \(0.667760\pi\) | |||||||
\(674\) | −985.674 | + | 569.079i | −1.46242 | + | 0.844331i | ||||
\(675\) | −51.1088 | − | 537.576i | −0.0757168 | − | 0.796409i | ||||
\(676\) | −82.5000 | + | 142.894i | −0.122041 | + | 0.211382i | ||||
\(677\) | −923.707 | + | 533.302i | −1.36441 | + | 0.787743i | −0.990208 | − | 0.139603i | \(-0.955417\pi\) |
−0.374204 | + | 0.927346i | \(0.622084\pi\) | |||||||
\(678\) | −140.000 | − | 156.525i | −0.206490 | − | 0.230862i | ||||
\(679\) | −325.500 | + | 563.783i | −0.479381 | + | 0.830313i | ||||
\(680\) | − | 402.492i | − | 0.591900i | ||||||
\(681\) | 860.353 | + | 282.698i | 1.26337 | + | 0.415122i | ||||
\(682\) | −37.5000 | + | 64.9519i | −0.0549853 | + | 0.0952374i | ||||
\(683\) | −551.900 | − | 318.640i | −0.808053 | − | 0.466530i | 0.0382264 | − | 0.999269i | \(-0.487829\pi\) |
−0.846279 | + | 0.532740i | \(0.821163\pi\) | |||||||
\(684\) | −131.935 | + | 57.6978i | −0.192888 | + | 0.0843535i | ||||
\(685\) | 480.000 | 0.700730 | ||||||||
\(686\) | −664.217 | + | 383.486i | −0.968246 | + | 0.559017i | ||||
\(687\) | −668.000 | − | 746.847i | −0.972344 | − | 1.08711i | ||||
\(688\) | 418.000 | + | 723.997i | 0.607558 | + | 1.05232i | ||||
\(689\) | −34.8569 | − | 20.1246i | −0.0505905 | − | 0.0292084i | ||||
\(690\) | 41.1895 | + | 196.986i | 0.0596949 | + | 0.285487i | ||||
\(691\) | −337.000 | − | 583.701i | −0.487699 | − | 0.844719i | 0.512201 | − | 0.858866i | \(-0.328830\pi\) |
−0.999900 | + | 0.0141462i | \(0.995497\pi\) | |||||||
\(692\) | − | 263.856i | − | 0.381295i | ||||||
\(693\) | −417.777 | + | 567.087i | −0.602853 | + | 0.818307i | ||||
\(694\) | 850.000 | 1.22478 | ||||||||
\(695\) | 220.760 | − | 127.456i | 0.317640 | − | 0.183390i | ||||
\(696\) | −308.332 | + | 64.4718i | −0.443005 | + | 0.0926318i | ||||
\(697\) | 420.000 | − | 727.461i | 0.602582 | − | 1.04370i | ||||
\(698\) | 1216.12 | − | 702.125i | 1.74229 | − | 1.00591i | ||||
\(699\) | −600.000 | + | 536.656i | −0.858369 | + | 0.767749i | ||||
\(700\) | 140.000 | 0.200000 | ||||||||
\(701\) | − | 1080.02i | − | 1.54069i | −0.637630 | − | 0.770343i | \(-0.720085\pi\) | ||
0.637630 | − | 0.770343i | \(-0.279915\pi\) | |||||||
\(702\) | 50.2056 | − | 109.815i | 0.0715180 | − | 0.156432i | ||||
\(703\) | −96.0000 | + | 166.277i | −0.136558 | + | 0.236525i | ||||
\(704\) | 396.981 | + | 229.197i | 0.563893 | + | 0.325564i | ||||
\(705\) | 28.0948 | − | 85.5025i | 0.0398507 | − | 0.121280i | ||||
\(706\) | 1040.00 | 1.47309 | ||||||||
\(707\) | 352.441 | − | 203.482i | 0.498503 | − | 0.287811i | ||||
\(708\) | 45.0000 | − | 40.2492i | 0.0635593 | − | 0.0568492i | ||||
\(709\) | 57.0000 | + | 98.7269i | 0.0803949 | + | 0.139248i | 0.903420 | − | 0.428757i | \(-0.141049\pi\) |
−0.823025 | + | 0.568006i | \(0.807715\pi\) | |||||||
\(710\) | 406.663 | + | 234.787i | 0.572765 | + | 0.330686i | ||||
\(711\) | 572.431 | + | 421.715i | 0.805107 | + | 0.593129i | ||||
\(712\) | −165.000 | − | 285.788i | −0.231742 | − | 0.401388i | ||||
\(713\) | 40.2492i | 0.0564505i | ||||||||
\(714\) | −393.327 | + | 1197.04i | −0.550877 | + | 1.67652i | ||||
\(715\) | −50.0000 | −0.0699301 | ||||||||
\(716\) | 166.538 | − | 96.1509i | 0.232595 | − | 0.134289i | ||||
\(717\) | −172.996 | − | 827.341i | −0.241277 | − | 1.15389i | ||||
\(718\) | −260.000 | + | 450.333i | −0.362117 | + | 0.627205i | ||||
\(719\) | 336.950 | − | 194.538i | 0.468636 | − | 0.270567i | −0.247032 | − | 0.969007i | \(-0.579455\pi\) |
0.715669 | + | 0.698440i | \(0.246122\pi\) | |||||||
\(720\) | −380.000 | − | 42.4853i | −0.527778 | − | 0.0590073i | ||||
\(721\) | 574.000 | 0.796117 | ||||||||
\(722\) | − | 234.787i | − | 0.325190i | ||||||
\(723\) | 167.632 | − | 510.165i | 0.231856 | − | 0.705623i | ||||
\(724\) | 41.0000 | − | 71.0141i | 0.0566298 | − | 0.0980858i | ||||
\(725\) | 271.109 | + | 156.525i | 0.373943 | + | 0.215896i | ||||
\(726\) | −25.4919 | − | 8.37624i | −0.0351129 | − | 0.0115375i | ||||
\(727\) | 1307.00 | 1.79780 | 0.898900 | − | 0.438155i | \(-0.144368\pi\) | ||||
0.898900 | + | 0.438155i | \(0.144368\pi\) | |||||||
\(728\) | −81.3327 | − | 46.9574i | −0.111721 | − | 0.0645020i | ||||
\(729\) | 239.000 | − | 688.709i | 0.327846 | − | 0.944731i | ||||
\(730\) | −45.0000 | − | 77.9423i | −0.0616438 | − | 0.106770i | ||||
\(731\) | 1022.47 | + | 590.322i | 1.39872 | + | 0.807554i | ||||
\(732\) | −76.3488 | + | 15.9644i | −0.104302 | + | 0.0218093i | ||||
\(733\) | −204.000 | − | 353.338i | −0.278308 | − | 0.482044i | 0.692656 | − | 0.721268i | \(-0.256440\pi\) |
−0.970964 | + | 0.239224i | \(0.923107\pi\) | |||||||
\(734\) | 1120.27i | 1.52625i | ||||||||
\(735\) | −312.276 | − | 102.609i | −0.424866 | − | 0.139604i | ||||
\(736\) | −210.000 | −0.285326 | ||||||||
\(737\) | 503.488 | − | 290.689i | 0.683159 | − | 0.394422i | ||||
\(738\) | −507.218 | − | 373.671i | −0.687287 | − | 0.506330i | ||||
\(739\) | 177.000 | − | 306.573i | 0.239513 | − | 0.414848i | −0.721062 | − | 0.692871i | \(-0.756346\pi\) |
0.960575 | + | 0.278022i | \(0.0896789\pi\) | |||||||
\(740\) | 23.2379 | − | 13.4164i | 0.0314026 | − | 0.0181303i | ||||
\(741\) | −64.0000 | − | 71.5542i | −0.0863698 | − | 0.0965643i | ||||
\(742\) | 157.500 | − | 272.798i | 0.212264 | − | 0.367652i | ||||
\(743\) | 751.319i | 1.01120i | 0.862769 | + | 0.505598i | \(0.168728\pi\) | ||||
−0.862769 | + | 0.505598i | \(0.831272\pi\) | |||||||
\(744\) | −57.3569 | − | 18.8465i | −0.0770925 | − | 0.0253314i | ||||
\(745\) | 15.0000 | − | 25.9808i | 0.0201342 | − | 0.0348735i | ||||
\(746\) | −1351.67 | − | 780.388i | −1.81189 | − | 1.04610i | ||||
\(747\) | 508.001 | + | 1161.63i | 0.680055 | + | 1.55506i | ||||
\(748\) | −300.000 | −0.401070 | ||||||||
\(749\) | − | 453.922i | − | 0.606037i | ||||||
\(750\) | 450.000 | + | 503.115i | 0.600000 | + | 0.670820i | ||||
\(751\) | 515.500 | + | 892.872i | 0.686418 | + | 1.18891i | 0.972989 | + | 0.230852i | \(0.0741513\pi\) |
−0.286571 | + | 0.958059i | \(0.592515\pi\) | |||||||
\(752\) | 220.760 | + | 127.456i | 0.293564 | + | 0.169489i | ||||
\(753\) | −105.720 | − | 505.597i | −0.140398 | − | 0.671444i | ||||
\(754\) | 35.0000 | + | 60.6218i | 0.0464191 | + | 0.0804002i | ||||
\(755\) | − | 131.928i | − | 0.174739i | ||||||
\(756\) | 171.888 | + | 78.5842i | 0.227365 | + | 0.103947i | ||||
\(757\) | −1258.00 | −1.66182 | −0.830911 | − | 0.556405i | \(-0.812180\pi\) | ||||
−0.830911 | + | 0.556405i | \(0.812180\pi\) | |||||||
\(758\) | 708.756 | − | 409.200i | 0.935034 | − | 0.539842i | ||||
\(759\) | −440.474 | + | 92.1025i | −0.580334 | + | 0.121347i | ||||
\(760\) | −120.000 | + | 207.846i | −0.157895 | + | 0.273482i | ||||
\(761\) | −801.708 | + | 462.866i | −1.05349 | + | 0.608234i | −0.923625 | − | 0.383297i | \(-0.874788\pi\) |
−0.129867 | + | 0.991531i | \(0.541455\pi\) | |||||||
\(762\) | −885.000 | + | 791.568i | −1.16142 | + | 1.03880i | ||||
\(763\) | −504.000 | − | 872.954i | −0.660550 | − | 1.14411i | ||||
\(764\) | 169.941i | 0.222436i | ||||||||
\(765\) | −494.758 | + | 216.367i | −0.646742 | + | 0.282832i | ||||
\(766\) | 15.0000 | − | 25.9808i | 0.0195822 | − | 0.0339174i | ||||
\(767\) | 34.8569 | + | 20.1246i | 0.0454457 | + | 0.0262381i | ||||
\(768\) | 169.505 | − | 515.865i | 0.220710 | − | 0.671700i | ||||
\(769\) | −877.000 | −1.14044 | −0.570221 | − | 0.821491i | \(-0.693142\pi\) | ||||
−0.570221 | + | 0.821491i | \(0.693142\pi\) | |||||||
\(770\) | − | 391.312i | − | 0.508197i | ||||||
\(771\) | −590.000 | + | 527.712i | −0.765240 | + | 0.684451i | ||||
\(772\) | 29.5000 | + | 51.0955i | 0.0382124 | + | 0.0661859i | ||||
\(773\) | −437.647 | − | 252.676i | −0.566167 | − | 0.326877i | 0.189450 | − | 0.981890i | \(-0.439330\pi\) |
−0.755617 | + | 0.655014i | \(0.772663\pi\) | |||||||
\(774\) | 525.206 | − | 712.909i | 0.678560 | − | 0.921071i | ||||
\(775\) | 30.0000 | + | 51.9615i | 0.0387097 | + | 0.0670471i | ||||
\(776\) | − | 623.863i | − | 0.803947i | ||||||
\(777\) | 246.665 | − | 51.5774i | 0.317459 | − | 0.0663802i | ||||
\(778\) | 150.000 | 0.192802 | ||||||||
\(779\) | −433.774 | + | 250.440i | −0.556835 | + | 0.321489i | ||||
\(780\) | 2.74597 | + | 13.1324i | 0.00352047 | + | 0.0168364i | ||||
\(781\) | −525.000 | + | 909.327i | −0.672215 | + | 1.16431i | ||||
\(782\) | −697.137 | + | 402.492i | −0.891480 | + | 0.514696i | ||||
\(783\) | 245.000 | + | 344.354i | 0.312899 | + | 0.439789i | ||||
\(784\) | 465.500 | − | 806.270i | 0.593750 | − | 1.02841i | ||||
\(785\) | 554.545i | 0.706427i | ||||||||
\(786\) | 398.009 | − | 1211.29i | 0.506373 | − | 1.54108i | ||||
\(787\) | −611.000 | + | 1058.28i | −0.776366 | + | 1.34471i | 0.157658 | + | 0.987494i | \(0.449606\pi\) |
−0.934024 | + | 0.357211i | \(0.883728\pi\) | |||||||
\(788\) | 189.776 | + | 109.567i | 0.240833 | + | 0.139045i | ||||
\(789\) | −101.968 | − | 33.5049i | −0.129237 | − | 0.0424651i | ||||
\(790\) | −395.000 | −0.500000 | ||||||||
\(791\) | 189.776 | + | 109.567i | 0.239919 | + | 0.138517i | ||||
\(792\) | 75.0000 | − | 670.820i | 0.0946970 | − | 0.846995i | ||||
\(793\) | −26.0000 | − | 45.0333i | −0.0327869 | − | 0.0567886i | ||||
\(794\) | 511.234 | + | 295.161i | 0.643871 | + | 0.371739i | ||||
\(795\) | 132.142 | − | 27.6308i | 0.166217 | − | 0.0347557i | ||||
\(796\) | −117.000 | − | 202.650i | −0.146985 | − | 0.254585i | ||||
\(797\) | 547.837i | 0.687373i | 0.939084 | + | 0.343687i | \(0.111676\pi\) | ||||
−0.939084 | + | 0.343687i | \(0.888324\pi\) | |||||||
\(798\) | 560.000 | − | 500.879i | 0.701754 | − | 0.627668i | ||||
\(799\) | 360.000 | 0.450563 | ||||||||
\(800\) | −271.109 | + | 156.525i | −0.338886 | + | 0.195656i | ||||
\(801\) | −262.603 | + | 356.454i | −0.327844 | + | 0.445012i | ||||
\(802\) | −120.000 | + | 207.846i | −0.149626 | + | 0.259160i | ||||
\(803\) | 174.284 | − | 100.623i | 0.217041 | − | 0.125309i | ||||
\(804\) | −104.000 | − | 116.276i | −0.129353 | − | 0.144621i | ||||
\(805\) | −105.000 | − | 181.865i | −0.130435 | − | 0.225920i | ||||
\(806\) | 13.4164i | 0.0166457i | ||||||||
\(807\) | 1128.02 | + | 370.648i | 1.39779 | + | 0.459292i | ||||
\(808\) | −195.000 | + | 337.750i | −0.241337 | + | 0.418007i | ||||
\(809\) | −185.903 | − | 107.331i | −0.229794 | − | 0.132672i | 0.380683 | − | 0.924706i | \(-0.375689\pi\) |
−0.610477 | + | 0.792034i | \(0.709022\pi\) | |||||||
\(810\) | 120.040 | + | 386.801i | 0.148198 | + | 0.477533i | ||||
\(811\) | −436.000 | −0.537608 | −0.268804 | − | 0.963195i | \(-0.586628\pi\) | ||||
−0.268804 | + | 0.963195i | \(0.586628\pi\) | |||||||
\(812\) | −94.8881 | + | 54.7837i | −0.116857 | + | 0.0674676i | ||||
\(813\) | 914.000 | + | 1021.88i | 1.12423 | + | 1.25693i | ||||
\(814\) | 150.000 | + | 259.808i | 0.184275 | + | 0.319174i | ||||
\(815\) | −3.87298 | − | 2.23607i | −0.00475213 | − | 0.00274364i | ||||
\(816\) | −313.040 | − | 1497.09i | −0.383628 | − | 1.83467i | ||||
\(817\) | −352.000 | − | 609.682i | −0.430845 | − | 0.746245i | ||||
\(818\) | − | 444.978i | − | 0.543982i | ||||||
\(819\) | −14.0000 | + | 125.220i | −0.0170940 | + | 0.152894i | ||||
\(820\) | 70.0000 | 0.0853659 | ||||||||
\(821\) | −404.727 | + | 233.669i | −0.492968 | + | 0.284615i | −0.725805 | − | 0.687901i | \(-0.758533\pi\) |
0.232837 | + | 0.972516i | \(0.425199\pi\) | |||||||
\(822\) | 1409.52 | − | 294.728i | 1.71474 | − | 0.358550i | ||||
\(823\) | 261.000 | − | 452.065i | 0.317132 | − | 0.549290i | −0.662756 | − | 0.748835i | \(-0.730613\pi\) |
0.979888 | + | 0.199546i | \(0.0639467\pi\) | |||||||
\(824\) | −476.377 | + | 275.036i | −0.578127 | + | 0.333782i | ||||
\(825\) | −500.000 | + | 447.214i | −0.606061 | + | 0.542077i | ||||
\(826\) | −157.500 | + | 272.798i | −0.190678 | + | 0.330264i | ||||
\(827\) | 986.106i | 1.19239i | 0.802840 | + | 0.596195i | \(0.203321\pi\) | ||||
−0.802840 | + | 0.596195i | \(0.796679\pi\) | |||||||
\(828\) | 48.3810 | + | 110.631i | 0.0584312 | + | 0.133613i | ||||
\(829\) | 152.000 | − | 263.272i | 0.183353 | − | 0.317577i | −0.759667 | − | 0.650312i | \(-0.774638\pi\) |
0.943020 | + | 0.332735i | \(0.107971\pi\) | |||||||
\(830\) | −609.995 | − | 352.181i | −0.734934 | − | 0.424314i | ||||
\(831\) | 48.6976 | − | 148.204i | 0.0586012 | − | 0.178345i | ||||
\(832\) | 82.0000 | 0.0985577 | ||||||||
\(833\) | − | 1314.81i | − | 1.57840i | ||||||
\(834\) | 570.000 | − | 509.823i | 0.683453 | − | 0.611299i | ||||
\(835\) | 280.000 | + | 484.974i | 0.335329 | + | 0.580807i | ||||
\(836\) | 154.919 | + | 89.4427i | 0.185310 | + | 0.106989i | ||||
\(837\) | 7.66633 | + | 80.6364i | 0.00915929 | + | 0.0963398i | ||||
\(838\) | 105.000 | + | 181.865i | 0.125298 | + | 0.217023i | ||||
\(839\) | − | 1001.76i | − | 1.19399i | −0.802245 | − | 0.596996i | \(-0.796361\pi\) | ||
0.802245 | − | 0.596996i | \(-0.203639\pi\) | |||||||
\(840\) | 308.332 | − | 64.4718i | 0.367061 | − | 0.0767521i | ||||
\(841\) | 596.000 | 0.708680 | ||||||||
\(842\) | 491.869 | − | 283.981i | 0.584167 | − | 0.337269i | ||||
\(843\) | 76.8871 | + | 367.707i | 0.0912065 | + | 0.436189i | ||||
\(844\) | −13.0000 | + | 22.5167i | −0.0154028 | + | 0.0266785i | ||||
\(845\) | 319.521 | − | 184.476i | 0.378132 | − | 0.218314i | ||||
\(846\) | 30.0000 | − | 268.328i | 0.0354610 | − | 0.317173i | ||||
\(847\) | 28.0000 | 0.0330579 | ||||||||
\(848\) | 382.368i | 0.450905i | ||||||||
\(849\) | 82.4113 | − | 250.807i | 0.0970686 | − | 0.295415i | ||||
\(850\) | −600.000 | + | 1039.23i | −0.705882 | + | 1.22262i | ||||
\(851\) | 139.427 | + | 80.4984i | 0.163839 | + | 0.0945928i | ||||
\(852\) | 267.665 | + | 87.9505i | 0.314161 | + | 0.103228i | ||||
\(853\) | 824.000 | 0.966002 | 0.483001 | − | 0.875620i | \(-0.339547\pi\) | ||||
0.483001 | + | 0.875620i | \(0.339547\pi\) | |||||||
\(854\) | 352.441 | − | 203.482i | 0.412695 | − | 0.238270i | ||||
\(855\) | 320.000 | + | 35.7771i | 0.374269 | + | 0.0418445i | ||||
\(856\) | 217.500 | + | 376.721i | 0.254089 | + | 0.440095i | ||||
\(857\) | −3.87298 | − | 2.23607i | −0.00451923 | − | 0.00260918i | 0.497739 | − | 0.867327i | \(-0.334164\pi\) |
−0.502258 | + | 0.864718i | \(0.667497\pi\) | |||||||
\(858\) | −146.825 | + | 30.7008i | −0.171124 | + | 0.0357819i | ||||
\(859\) | −64.0000 | − | 110.851i | −0.0745052 | − | 0.129047i | 0.826366 | − | 0.563134i | \(-0.190404\pi\) |
−0.900871 | + | 0.434087i | \(0.857071\pi\) | |||||||
\(860\) | 98.3870i | 0.114403i | ||||||||
\(861\) | 624.552 | + | 205.218i | 0.725380 | + | 0.238348i | ||||
\(862\) | −270.000 | −0.313225 | ||||||||
\(863\) | 1289.70 | − | 744.611i | 1.49444 | − | 0.862816i | 0.494462 | − | 0.869199i | \(-0.335365\pi\) |
0.999980 | + | 0.00638254i | \(0.00203164\pi\) | |||||||
\(864\) | −420.720 | + | 39.9990i | −0.486944 | + | 0.0462951i | ||||
\(865\) | −295.000 | + | 510.955i | −0.341040 | + | 0.590699i | ||||
\(866\) | −979.865 | + | 565.725i | −1.13148 | + | 0.653262i | ||||
\(867\) | −862.000 | − | 963.745i | −0.994233 | − | 1.11159i | ||||
\(868\) | −21.0000 | −0.0241935 | ||||||||
\(869\) | − | 883.247i | − | 1.01639i | ||||||
\(870\) | −223.054 | − | 73.2921i | −0.256384 | − | 0.0842438i | ||||
\(871\) | 52.0000 | − | 90.0666i | 0.0597015 | − | 0.103406i | ||||
\(872\) | 836.564 | + | 482.991i | 0.959363 | + | 0.553888i | ||||
\(873\) | −766.875 | + | 335.368i | −0.878436 | + | 0.384156i | ||||
\(874\) | 480.000 | 0.549199 | ||||||||
\(875\) | −609.995 | − | 352.181i | −0.697137 | − | 0.402492i | ||||
\(876\) | −36.0000 | − | 40.2492i | −0.0410959 | − | 0.0459466i | ||||
\(877\) | −776.000 | − | 1344.07i | −0.884835 | − | 1.53258i | −0.845903 | − | 0.533337i | \(-0.820938\pi\) |
−0.0389316 | − | 0.999242i | \(-0.512395\pi\) | |||||||
\(878\) | −912.088 | − | 526.594i | −1.03882 | − | 0.599765i | ||||
\(879\) | −9.61088 | − | 45.9634i | −0.0109339 | − | 0.0522905i | ||||
\(880\) | 237.500 | + | 411.362i | 0.269886 | + | 0.467457i | ||||
\(881\) | 1690.47i | 1.91881i | 0.282040 | + | 0.959403i | \(0.408989\pi\) | ||||
−0.282040 | + | 0.959403i | \(0.591011\pi\) | |||||||
\(882\) | −980.000 | − | 109.567i | −1.11111 | − | 0.124226i | ||||
\(883\) | −502.000 | −0.568516 | −0.284258 | − | 0.958748i | \(-0.591747\pi\) | ||||
−0.284258 | + | 0.958748i | \(0.591747\pi\) | |||||||
\(884\) | −46.4758 | + | 26.8328i | −0.0525744 | + | 0.0303539i | ||||
\(885\) | −132.142 | + | 27.6308i | −0.149313 | + | 0.0312212i | ||||
\(886\) | −67.5000 | + | 116.913i | −0.0761851 | + | 0.131956i | ||||
\(887\) | 1204.50 | − | 695.417i | 1.35795 | − | 0.784010i | 0.368599 | − | 0.929589i | \(-0.379838\pi\) |
0.989347 | + | 0.145578i | \(0.0465042\pi\) | |||||||
\(888\) | −180.000 | + | 160.997i | −0.202703 | + | 0.181303i | ||||
\(889\) | 619.500 | − | 1073.01i | 0.696850 | − | 1.20698i | ||||
\(890\) | − | 245.967i | − | 0.276368i | ||||||
\(891\) | −864.914 | + | 268.418i | −0.970723 | + | 0.301255i | ||||
\(892\) | −53.5000 | + | 92.6647i | −0.0599776 | + | 0.103884i | ||||
\(893\) | −185.903 | − | 107.331i | −0.208178 | − | 0.120192i | ||||
\(894\) | 28.0948 | − | 85.5025i | 0.0314259 | − | 0.0956404i | ||||
\(895\) | −430.000 | −0.480447 | ||||||||
\(896\) | 1080.02i | 1.20538i | ||||||||
\(897\) | −60.0000 | + | 53.6656i | −0.0668896 | + | 0.0598279i | ||||
\(898\) | 315.000 | + | 545.596i | 0.350780 | + | 0.607568i | ||||
\(899\) | −40.6663 | − | 23.4787i | −0.0452351 | − | 0.0261165i | ||||
\(900\) | 144.919 | + | 106.763i | 0.161021 | + | 0.118626i | ||||
\(901\) | 270.000 | + | 467.654i | 0.299667 | + | 0.519039i | ||||
\(902\) | 782.624i | 0.867654i | ||||||||
\(903\) | −288.439 | + | 877.826i | −0.319424 | + | 0.972122i | ||||
\(904\) | −210.000 | −0.232301 | ||||||||
\(905\) | −158.792 | + | 91.6788i | −0.175461 | + | 0.101303i | ||||
\(906\) | −81.0060 | − | 387.406i | −0.0894106 | − | 0.427600i | ||||
\(907\) | 149.000 | − | 258.076i | 0.164278 | − | 0.284538i | −0.772121 | − | 0.635476i | \(-0.780804\pi\) |
0.936399 | + | 0.350938i | \(0.114137\pi\) | |||||||
\(908\) | −261.426 | + | 150.935i | −0.287915 | + | 0.166228i | ||||
\(909\) | 520.000 | + | 58.1378i | 0.572057 | + | 0.0639579i | ||||
\(910\) | −35.0000 | − | 60.6218i | −0.0384615 | − | 0.0666173i | ||||
\(911\) | − | 657.404i | − | 0.721629i | −0.932638 | − | 0.360814i | \(-0.882499\pi\) | ||
0.932638 | − | 0.360814i | \(-0.117501\pi\) | |||||||
\(912\) | −284.693 | + | 866.426i | −0.312164 | + | 0.950028i | ||||
\(913\) | 787.500 | − | 1363.99i | 0.862541 | − | 1.49396i | ||||
\(914\) | 44.5393 | + | 25.7148i | 0.0487301 | + | 0.0281343i | ||||
\(915\) | 165.698 | + | 54.4455i | 0.181090 | + | 0.0595033i | ||||
\(916\) | 334.000 | 0.364629 | ||||||||
\(917\) | 1330.46i | 1.45088i | ||||||||
\(918\) | −1320.00 | + | 939.149i | −1.43791 | + | 1.02304i | ||||
\(919\) | −139.000 | − | 240.755i | −0.151251 | − | 0.261975i | 0.780436 | − | 0.625235i | \(-0.214997\pi\) |
−0.931688 | + | 0.363260i | \(0.881664\pi\) | |||||||
\(920\) | 174.284 | + | 100.623i | 0.189439 | + | 0.109373i | ||||
\(921\) | −487.458 | + | 101.927i | −0.529270 | + | 0.110670i | ||||
\(922\) | −665.000 | − | 1151.81i | −0.721258 | − | 1.24926i | ||||
\(923\) | 187.830i | 0.203499i | ||||||||
\(924\) | −48.0544 | − | 229.817i | −0.0520069 | − | 0.248720i | ||||
\(925\) | 240.000 | 0.259459 | ||||||||
\(926\) | 112.317 | − | 64.8460i | 0.121292 | − | 0.0700280i | ||||
\(927\) | 594.169 | + | 437.729i | 0.640959 | + | 0.472200i | ||||
\(928\) | 122.500 | − | 212.176i | 0.132004 | − | 0.228638i | ||||
\(929\) | 960.500 | − | 554.545i | 1.03391 | − | 0.596927i | 0.115806 | − | 0.993272i | \(-0.463055\pi\) |
0.918102 | + | 0.396345i | \(0.129722\pi\) | |||||||
\(930\) | −30.0000 | − | 33.5410i | −0.0322581 | − | 0.0360656i | ||||
\(931\) | −392.000 | + | 678.964i | −0.421053 | + | 0.729285i | ||||
\(932\) | − | 268.328i | − | 0.287906i | ||||||
\(933\) | −879.472 | − | 288.980i | −0.942628 | − | 0.309732i | ||||
\(934\) | 645.000 | − | 1117.17i | 0.690578 | − | 1.19612i | ||||
\(935\) | 580.948 | + | 335.410i | 0.621334 | + | 0.358727i | ||||
\(936\) | −48.3810 | − | 110.631i | −0.0516892 | − | 0.118196i | ||||
\(937\) | −219.000 | −0.233725 | −0.116862 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116862 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(938\) | 704.883 | + | 406.964i | 0.751474 | + | 0.433864i | ||||
\(939\) | −542.000 | − | 605.974i | −0.577210 | − | 0.645340i | ||||
\(940\) | 15.0000 | + | 25.9808i | 0.0159574 | + | 0.0276391i | ||||
\(941\) | −884.977 | − | 510.942i | −0.940464 | − | 0.542977i | −0.0503583 | − | 0.998731i | \(-0.516036\pi\) |
−0.890106 | + | 0.455754i | \(0.849370\pi\) | |||||||
\(942\) | 340.500 | + | 1628.42i | 0.361465 | + | 1.72868i | ||||
\(943\) | 210.000 | + | 363.731i | 0.222694 | + | 0.385717i | ||||
\(944\) | − | 382.368i | − | 0.405050i | ||||||
\(945\) | −245.000 | − | 344.354i | −0.259259 | − | 0.364396i | ||||
\(946\) | −1100.00 | −1.16279 | ||||||||
\(947\) | −770.724 | + | 444.978i | −0.813858 | + | 0.469881i | −0.848294 | − | 0.529526i | \(-0.822370\pi\) |
0.0344357 | + | 0.999407i | \(0.489037\pi\) | |||||||
\(948\) | −231.983 | + | 48.5073i | −0.244708 | + | 0.0511681i | ||||
\(949\) | 18.0000 | − | 31.1769i | 0.0189673 | − | 0.0328524i | ||||
\(950\) | 619.677 | − | 357.771i | 0.652292 | − | 0.376601i | ||||
\(951\) | 975.000 | − | 872.067i | 1.02524 | − | 0.916999i | ||||
\(952\) | 630.000 | + | 1091.19i | 0.661765 | + | 1.14621i | ||||
\(953\) | − | 500.879i | − | 0.525582i | −0.964853 | − | 0.262791i | \(-0.915357\pi\) | ||
0.964853 | − | 0.262791i | \(-0.0846429\pi\) | |||||||
\(954\) | 371.069 | − | 162.275i | 0.388961 | − | 0.170100i | ||||
\(955\) | 190.000 | − | 329.090i | 0.198953 | − | 0.344596i | ||||
\(956\) | 243.998 | + | 140.872i | 0.255228 | + | 0.147356i | ||||
\(957\) | 163.886 | − | 498.765i | 0.171250 | − | 0.521175i | ||||
\(958\) | 760.000 | 0.793319 | ||||||||
\(959\) | −1301.32 | + | 751.319i | −1.35696 | + | 0.783440i | ||||
\(960\) | −205.000 | + | 183.358i | −0.213542 | + | 0.190997i | ||||
\(961\) | 476.000 | + | 824.456i | 0.495317 | + | 0.857915i | ||||
\(962\) | 46.4758 | + | 26.8328i | 0.0483116 | + | 0.0278927i | ||||
\(963\) | 346.158 | − | 469.872i | 0.359458 | − | 0.487925i | ||||
\(964\) | 89.5000 | + | 155.019i | 0.0928423 | + | 0.160808i | ||||
\(965\) | − | 131.928i | − | 0.136713i | ||||||
\(966\) | −420.000 | − | 469.574i | −0.434783 | − | 0.486102i | ||||
\(967\) | 1087.00 | 1.12410 | 0.562048 | − | 0.827105i | \(-0.310014\pi\) | ||||
0.562048 | + | 0.827105i | \(0.310014\pi\) | |||||||
\(968\) | −23.2379 | + | 13.4164i | −0.0240061 | + | 0.0138599i | ||||
\(969\) | 263.613 | + | 1260.71i | 0.272046 | + | 1.30104i | ||||
\(970\) | 232.500 | − | 402.702i | 0.239691 | − | 0.415157i | ||||
\(971\) | −517.043 | + | 298.515i | −0.532485 | + | 0.307431i | −0.742028 | − | 0.670369i | \(-0.766136\pi\) |
0.209543 | + | 0.977800i | \(0.432803\pi\) | |||||||
\(972\) | 118.000 | + | 212.426i | 0.121399 | + | 0.218546i | ||||
\(973\) | −399.000 | + | 691.088i | −0.410072 | + | 0.710265i | ||||
\(974\) | − | 1808.98i | − | 1.85727i | ||||||
\(975\) | −37.4597 | + | 114.003i | −0.0384202 | + | 0.116927i | ||||
\(976\) | −247.000 | + | 427.817i | −0.253074 | + | 0.438337i | ||||
\(977\) | −511.234 | − | 295.161i | −0.523269 | − | 0.302109i | 0.215002 | − | 0.976614i | \(-0.431024\pi\) |
−0.738271 | + | 0.674504i | \(0.764357\pi\) | |||||||
\(978\) | −12.7460 | − | 4.18812i | −0.0130327 | − | 0.00428233i | ||||
\(979\) | 550.000 | 0.561798 | ||||||||
\(980\) | 94.8881 | − | 54.7837i | 0.0968246 | − | 0.0559017i | ||||
\(981\) | 144.000 | − | 1287.98i | 0.146789 | − | 1.31292i | ||||
\(982\) | −507.500 | − | 879.016i | −0.516802 | − | 0.895128i | ||||
\(983\) | −871.421 | − | 503.115i | −0.886492 | − | 0.511816i | −0.0136983 | − | 0.999906i | \(-0.504360\pi\) |
−0.872793 | + | 0.488090i | \(0.837694\pi\) | |||||||
\(984\) | −616.663 | + | 128.944i | −0.626690 | + | 0.131040i | ||||
\(985\) | −245.000 | − | 424.352i | −0.248731 | − | 0.430815i | ||||
\(986\) | − | 939.149i | − | 0.952483i | ||||||
\(987\) | 57.6653 | + | 275.780i | 0.0584248 | + | 0.279413i | ||||
\(988\) | 32.0000 | 0.0323887 | ||||||||
\(989\) | −511.234 | + | 295.161i | −0.516920 | + | 0.298444i | ||||
\(990\) | 298.412 | − | 405.062i | 0.301427 | − | 0.409153i | ||||
\(991\) | −8.50000 | + | 14.7224i | −0.00857719 | + | 0.0148561i | −0.870282 | − | 0.492554i | \(-0.836064\pi\) |
0.861705 | + | 0.507410i | \(0.169397\pi\) | |||||||
\(992\) | 40.6663 | − | 23.4787i | 0.0409943 | − | 0.0236681i | ||||
\(993\) | −32.0000 | − | 35.7771i | −0.0322256 | − | 0.0360293i | ||||
\(994\) | −1470.00 | −1.47887 | ||||||||
\(995\) | 523.240i | 0.525869i | ||||||||
\(996\) | −401.498 | − | 131.926i | −0.403110 | − | 0.132456i | ||||
\(997\) | −296.000 | + | 512.687i | −0.296891 | + | 0.514230i | −0.975423 | − | 0.220341i | \(-0.929283\pi\) |
0.678532 | + | 0.734571i | \(0.262616\pi\) | |||||||
\(998\) | 491.869 | + | 283.981i | 0.492855 | + | 0.284550i | ||||
\(999\) | 294.665 | + | 134.716i | 0.294960 | + | 0.134851i |
(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 | 21.3.h.b.11.2 | yes | 4 | |
3.2 | odd | 2 | inner | 21.3.h.b.11.1 | yes | 4 | |
4.3 | odd | 2 | 336.3.bn.f.305.2 | 4 | |||
7.2 | even | 3 | inner | 21.3.h.b.2.1 | ✓ | 4 | |
7.3 | odd | 6 | 147.3.b.c.50.2 | 2 | |||
7.4 | even | 3 | 147.3.b.d.50.2 | 2 | |||
7.5 | odd | 6 | 147.3.h.b.128.1 | 4 | |||
7.6 | odd | 2 | 147.3.h.b.116.2 | 4 | |||
12.11 | even | 2 | 336.3.bn.f.305.1 | 4 | |||
21.2 | odd | 6 | inner | 21.3.h.b.2.2 | yes | 4 | |
21.5 | even | 6 | 147.3.h.b.128.2 | 4 | |||
21.11 | odd | 6 | 147.3.b.d.50.1 | 2 | |||
21.17 | even | 6 | 147.3.b.c.50.1 | 2 | |||
21.20 | even | 2 | 147.3.h.b.116.1 | 4 | |||
28.23 | odd | 6 | 336.3.bn.f.65.1 | 4 | |||
84.23 | even | 6 | 336.3.bn.f.65.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.h.b.2.1 | ✓ | 4 | 7.2 | even | 3 | inner | |
21.3.h.b.2.2 | yes | 4 | 21.2 | odd | 6 | inner | |
21.3.h.b.11.1 | yes | 4 | 3.2 | odd | 2 | inner | |
21.3.h.b.11.2 | yes | 4 | 1.1 | even | 1 | trivial | |
147.3.b.c.50.1 | 2 | 21.17 | even | 6 | |||
147.3.b.c.50.2 | 2 | 7.3 | odd | 6 | |||
147.3.b.d.50.1 | 2 | 21.11 | odd | 6 | |||
147.3.b.d.50.2 | 2 | 7.4 | even | 3 | |||
147.3.h.b.116.1 | 4 | 21.20 | even | 2 | |||
147.3.h.b.116.2 | 4 | 7.6 | odd | 2 | |||
147.3.h.b.128.1 | 4 | 7.5 | odd | 6 | |||
147.3.h.b.128.2 | 4 | 21.5 | even | 6 | |||
336.3.bn.f.65.1 | 4 | 28.23 | odd | 6 | |||
336.3.bn.f.65.2 | 4 | 84.23 | even | 6 | |||
336.3.bn.f.305.1 | 4 | 12.11 | even | 2 | |||
336.3.bn.f.305.2 | 4 | 4.3 | odd | 2 |