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 | 2.1 | ||
Root | \(-1.93649 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.2 |
Dual form | 21.3.h.b.11.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
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 | \(-0.522155\pi\) |
−0.898701 | + | 0.438562i | \(0.855488\pi\) | |||||||
\(3\) | 0.936492 | − | 2.85008i | 0.312164 | − | 0.950028i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(5\) | 1.93649 | + | 1.11803i | 0.387298 | + | 0.223607i | 0.680989 | − | 0.732294i | \(-0.261550\pi\) |
−0.293691 | + | 0.955901i | \(0.594884\pi\) | |||||||
\(6\) | −5.00000 | + | 4.47214i | −0.833333 | + | 0.745356i | ||||
\(7\) | 3.50000 | + | 6.06218i | 0.500000 | + | 0.866025i | ||||
\(8\) | 6.70820i | 0.838525i | ||||||||
\(9\) | −7.24597 | − | 5.33816i | −0.805107 | − | 0.593129i | ||||
\(10\) | −2.50000 | − | 4.33013i | −0.250000 | − | 0.433013i | ||||
\(11\) | 9.68246 | − | 5.59017i | 0.880223 | − | 0.508197i | 0.00949140 | − | 0.999955i | \(-0.496979\pi\) |
0.870732 | + | 0.491758i | \(0.163645\pi\) | |||||||
\(12\) | 2.93649 | − | 0.614017i | 0.244708 | − | 0.0511681i | ||||
\(13\) | −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 | \(-0.956171\pi\) |
−0.376400 | + | 0.926457i | \(0.622838\pi\) | |||||||
\(18\) | 8.06351 | + | 18.4385i | 0.447973 | + | 1.02436i | ||||
\(19\) | −8.00000 | + | 13.8564i | −0.421053 | + | 0.729285i | −0.996043 | − | 0.0888758i | \(-0.971673\pi\) |
0.574990 | + | 0.818160i | \(0.305006\pi\) | |||||||
\(20\) | 2.23607i | 0.111803i | ||||||||
\(21\) | 20.5554 | − | 4.29812i | 0.978831 | − | 0.204672i | ||||
\(22\) | −25.0000 | −1.13636 | ||||||||
\(23\) | 11.6190 | + | 6.70820i | 0.505172 | + | 0.291661i | 0.730847 | − | 0.682542i | \(-0.239125\pi\) |
−0.225675 | + | 0.974203i | \(0.572459\pi\) | |||||||
\(24\) | 19.1190 | + | 6.28218i | 0.796623 | + | 0.261757i | ||||
\(25\) | −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 | \(-0.0869808\pi\) | |||||||
\(30\) | −14.6825 | + | 3.07008i | −0.489415 | + | 0.102336i | ||||
\(31\) | 1.50000 | + | 2.59808i | 0.0483871 | + | 0.0838089i | 0.889205 | − | 0.457510i | \(-0.151259\pi\) |
−0.840817 | + | 0.541319i | \(0.817925\pi\) | |||||||
\(32\) | −13.5554 | + | 7.82624i | −0.423608 | + | 0.244570i | ||||
\(33\) | −6.86492 | − | 32.8310i | −0.208028 | − | 0.994878i | ||||
\(34\) | 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 | −0.935644 | − | 0.352946i | \(-0.885180\pi\) |
0.773482 | + | 0.633819i | \(0.218513\pi\) | |||||||
\(38\) | 30.9839 | − | 17.8885i | 0.815365 | − | 0.470751i | ||||
\(39\) | −1.87298 | + | 5.70017i | −0.0480252 | + | 0.146158i | ||||
\(40\) | −7.50000 | + | 12.9904i | −0.187500 | + | 0.324760i | ||||
\(41\) | − | 31.3050i | − | 0.763535i | −0.924258 | − | 0.381768i | \(-0.875315\pi\) | ||
0.924258 | − | 0.381768i | \(-0.124685\pi\) | |||||||
\(42\) | −44.6109 | − | 14.6584i | −1.06216 | − | 0.349010i | ||||
\(43\) | 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 | ||||
\(45\) | −8.06351 | − | 18.4385i | −0.179189 | − | 0.409745i | ||||
\(46\) | −15.0000 | − | 25.9808i | −0.326087 | − | 0.564799i | ||||
\(47\) | −11.6190 | − | 6.70820i | −0.247212 | − | 0.142728i | 0.371275 | − | 0.928523i | \(-0.378921\pi\) |
−0.618487 | + | 0.785795i | \(0.712254\pi\) | |||||||
\(48\) | −38.0000 | − | 42.4853i | −0.791667 | − | 0.885110i | ||||
\(49\) | −24.5000 | + | 42.4352i | −0.500000 | + | 0.866025i | ||||
\(50\) | 44.7214i | 0.894427i | ||||||||
\(51\) | 16.4758 | + | 78.7943i | 0.323055 | + | 1.54499i | ||||
\(52\) | −1.00000 | − | 1.73205i | −0.0192308 | − | 0.0333087i | ||||
\(53\) | −17.4284 | + | 10.0623i | −0.328838 | + | 0.189855i | −0.655325 | − | 0.755347i | \(-0.727468\pi\) |
0.326487 | + | 0.945202i | \(0.394135\pi\) | |||||||
\(54\) | 60.1028 | − | 5.71414i | 1.11302 | − | 0.105817i | ||||
\(55\) | 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 | \(-0.612113\pi\) |
0.640373 | + | 0.768064i | \(0.278780\pi\) | |||||||
\(60\) | 6.37298 | + | 2.09406i | 0.106216 | + | 0.0349010i | ||||
\(61\) | 13.0000 | − | 22.5167i | 0.213115 | − | 0.369126i | −0.739573 | − | 0.673076i | \(-0.764973\pi\) |
0.952688 | + | 0.303951i | \(0.0983058\pi\) | |||||||
\(62\) | − | 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 | ||||
\(66\) | −23.4123 | + | 71.2521i | −0.354732 | + | 1.07958i | ||||
\(67\) | −26.0000 | − | 45.0333i | −0.388060 | − | 0.672139i | 0.604129 | − | 0.796887i | \(-0.293521\pi\) |
−0.992189 | + | 0.124748i | \(0.960188\pi\) | |||||||
\(68\) | −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 | \(-0.230026\pi\) | |||||||
\(72\) | 35.8095 | − | 48.6074i | 0.497354 | − | 0.675103i | ||||
\(73\) | −9.00000 | − | 15.5885i | −0.123288 | − | 0.213541i | 0.797775 | − | 0.602956i | \(-0.206010\pi\) |
−0.921062 | + | 0.389415i | \(0.872677\pi\) | |||||||
\(74\) | 23.2379 | − | 13.4164i | 0.314026 | − | 0.181303i | ||||
\(75\) | −58.7298 | + | 12.2803i | −0.783064 | + | 0.163738i | ||||
\(76\) | −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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(80\) | 36.7933 | − | 21.2426i | 0.459917 | − | 0.265533i | ||||
\(81\) | 24.0081 | + | 77.3603i | 0.296396 | + | 0.955065i | ||||
\(82\) | −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 | ||||
\(87\) | −44.6109 | − | 14.6584i | −0.512769 | − | 0.168488i | ||||
\(88\) | 37.5000 | + | 64.9519i | 0.426136 | + | 0.738090i | ||||
\(89\) | 42.6028 | + | 24.5967i | 0.478683 | + | 0.276368i | 0.719868 | − | 0.694111i | \(-0.244202\pi\) |
−0.241184 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(90\) | −5.00000 | + | 44.7214i | −0.0555556 | + | 0.496904i | ||||
\(91\) | −7.00000 | − | 12.1244i | −0.0769231 | − | 0.133235i | ||||
\(92\) | 13.4164i | 0.145831i | ||||||||
\(93\) | 8.80948 | − | 1.84205i | 0.0947255 | − | 0.0198070i | ||||
\(94\) | 15.0000 | + | 25.9808i | 0.159574 | + | 0.276391i | ||||
\(95\) | −30.9839 | + | 17.8885i | −0.326146 | + | 0.188300i | ||||
\(96\) | 9.61088 | + | 45.9634i | 0.100113 | + | 0.478785i | ||||
\(97\) | −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 | \(-0.759594\pi\) |
0.229592 | + | 0.973287i | \(0.426261\pi\) | |||||||
\(102\) | 56.1895 | − | 171.005i | 0.550877 | − | 1.67652i | ||||
\(103\) | 41.0000 | − | 71.0141i | 0.398058 | − | 0.689457i | −0.595428 | − | 0.803409i | \(-0.703018\pi\) |
0.993486 | + | 0.113952i | \(0.0363509\pi\) | |||||||
\(104\) | − | 13.4164i | − | 0.129004i | ||||||
\(105\) | 44.6109 | + | 14.6584i | 0.424866 | + | 0.139604i | ||||
\(106\) | 45.0000 | 0.424528 | ||||||||
\(107\) | −56.1583 | − | 32.4230i | −0.524844 | − | 0.303019i | 0.214071 | − | 0.976818i | \(-0.431328\pi\) |
−0.738914 | + | 0.673800i | \(0.764661\pi\) | |||||||
\(108\) | −24.5554 | − | 11.2263i | −0.227365 | − | 0.103947i | ||||
\(109\) | 72.0000 | + | 124.708i | 0.660550 | + | 1.14411i | 0.980471 | + | 0.196663i | \(0.0630104\pi\) |
−0.319921 | + | 0.947444i | \(0.603656\pi\) | |||||||
\(110\) | −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 | \(0.955766\pi\) | |||||||
\(114\) | −21.9677 | − | 105.059i | −0.192699 | − | 0.921571i | ||||
\(115\) | 15.0000 | + | 25.9808i | 0.130435 | + | 0.225920i | ||||
\(116\) | 13.5554 | − | 7.82624i | 0.116857 | − | 0.0674676i | ||||
\(117\) | 14.4919 | + | 10.6763i | 0.123863 | + | 0.0912506i | ||||
\(118\) | −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 | ||||
\(123\) | −89.2218 | − | 29.3168i | −0.725380 | − | 0.238348i | ||||
\(124\) | −1.50000 | + | 2.59808i | −0.0120968 | + | 0.0209522i | ||||
\(125\) | − | 100.623i | − | 0.804984i | ||||||
\(126\) | −83.5554 | + | 113.417i | −0.663138 | + | 0.900137i | ||||
\(127\) | 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 | ||||
\(129\) | 41.2056 | − | 125.404i | 0.319424 | − | 0.972122i | ||||
\(130\) | 5.00000 | + | 8.66025i | 0.0384615 | + | 0.0666173i | ||||
\(131\) | 164.602 | + | 95.0329i | 1.25650 | + | 0.725442i | 0.972393 | − | 0.233350i | \(-0.0749688\pi\) |
0.284109 | + | 0.958792i | \(0.408302\pi\) | |||||||
\(132\) | 25.0000 | − | 22.3607i | 0.189394 | − | 0.169399i | ||||
\(133\) | −112.000 | −0.842105 | ||||||||
\(134\) | 116.276i | 0.867728i | ||||||||
\(135\) | −60.1028 | + | 5.71414i | −0.445206 | + | 0.0423270i | ||||
\(136\) | −90.0000 | − | 155.885i | −0.661765 | − | 1.14621i | ||||
\(137\) | 185.903 | − | 107.331i | 1.35696 | − | 0.783440i | 0.367745 | − | 0.929927i | \(-0.380130\pi\) |
0.989213 | + | 0.146487i | \(0.0467966\pi\) | |||||||
\(138\) | −88.0948 | + | 18.4205i | −0.638368 | + | 0.133482i | ||||
\(139\) | −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 | ||||
\(144\) | −156.673 | + | 68.5161i | −1.08801 | + | 0.475806i | ||||
\(145\) | 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 | \(-0.318998\pi\) |
−0.460503 | + | 0.887658i | \(0.652331\pi\) | |||||||
\(150\) | 127.460 | + | 41.8812i | 0.849731 | + | 0.279208i | ||||
\(151\) | −29.5000 | − | 51.0955i | −0.195364 | − | 0.338381i | 0.751656 | − | 0.659556i | \(-0.229256\pi\) |
−0.947020 | + | 0.321175i | \(0.895922\pi\) | |||||||
\(152\) | −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 | ||||||||
\(156\) | −5.87298 | + | 1.22803i | −0.0376473 | + | 0.00787201i | ||||
\(157\) | 124.000 | + | 214.774i | 0.789809 | + | 1.36799i | 0.926084 | + | 0.377318i | \(0.123154\pi\) |
−0.136275 | + | 0.990671i | \(0.543513\pi\) | |||||||
\(158\) | −152.983 | + | 88.3247i | −0.968246 | + | 0.559017i | ||||
\(159\) | 12.3569 | + | 59.0958i | 0.0777160 | + | 0.371671i | ||||
\(160\) | −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 | −0.862942 | − | 0.505304i | \(-0.831380\pi\) |
0.869077 | + | 0.494678i | \(0.164714\pi\) | |||||||
\(164\) | 27.1109 | − | 15.6525i | 0.165310 | − | 0.0954419i | ||||
\(165\) | 23.4123 | − | 71.2521i | 0.141893 | − | 0.431831i | ||||
\(166\) | 157.500 | − | 272.798i | 0.948795 | − | 1.64336i | ||||
\(167\) | − | 250.440i | − | 1.49964i | −0.661643 | − | 0.749819i | \(-0.730140\pi\) | ||
0.661643 | − | 0.749819i | \(-0.269860\pi\) | |||||||
\(168\) | 28.8327 | + | 137.890i | 0.171623 | + | 0.820774i | ||||
\(169\) | −165.000 | −0.976331 | ||||||||
\(170\) | 116.190 | + | 67.0820i | 0.683468 | + | 0.394600i | ||||
\(171\) | 131.935 | − | 57.6978i | 0.771552 | − | 0.337414i | ||||
\(172\) | 22.0000 | + | 38.1051i | 0.127907 | + | 0.221541i | ||||
\(173\) | −228.506 | − | 131.928i | −1.32084 | − | 0.762590i | −0.336981 | − | 0.941512i | \(-0.609406\pi\) |
−0.983863 | + | 0.178922i | \(0.942739\pi\) | |||||||
\(174\) | 70.0000 | + | 78.2624i | 0.402299 | + | 0.449784i | ||||
\(175\) | 70.0000 | − | 121.244i | 0.400000 | − | 0.692820i | ||||
\(176\) | − | 212.426i | − | 1.20697i | ||||||
\(177\) | −12.3569 | − | 59.0958i | −0.0698127 | − | 0.333874i | ||||
\(178\) | −55.0000 | − | 95.2628i | −0.308989 | − | 0.535184i | ||||
\(179\) | −166.538 | + | 96.1509i | −0.930381 | + | 0.537156i | −0.886932 | − | 0.461900i | \(-0.847168\pi\) |
−0.0434493 | + | 0.999056i | \(0.513835\pi\) | |||||||
\(180\) | 11.9365 | − | 16.2025i | 0.0663138 | − | 0.0900137i | ||||
\(181\) | 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 | ||||
\(186\) | −19.1190 | − | 6.28218i | −0.102790 | − | 0.0337751i | ||||
\(187\) | −150.000 | + | 259.808i | −0.802139 | + | 1.38935i | ||||
\(188\) | − | 13.4164i | − | 0.0713639i | ||||||
\(189\) | −171.888 | − | 78.5842i | −0.909461 | − | 0.415790i | ||||
\(190\) | 80.0000 | 0.421053 | ||||||||
\(191\) | 147.173 | + | 84.9706i | 0.770541 | + | 0.444872i | 0.833068 | − | 0.553171i | \(-0.186582\pi\) |
−0.0625264 | + | 0.998043i | \(0.519916\pi\) | |||||||
\(192\) | −38.3962 | + | 116.853i | −0.199980 | + | 0.608612i | ||||
\(193\) | −29.5000 | − | 51.0955i | −0.152850 | − | 0.264744i | 0.779424 | − | 0.626496i | \(-0.215512\pi\) |
−0.932274 | + | 0.361753i | \(0.882178\pi\) | |||||||
\(194\) | 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 | \(0.812267\pi\) | |||||||
\(198\) | 181.149 | + | 133.454i | 0.914895 | + | 0.674010i | ||||
\(199\) | 117.000 | + | 202.650i | 0.587940 | + | 1.01834i | 0.994502 | + | 0.104718i | \(0.0333941\pi\) |
−0.406562 | + | 0.913623i | \(0.633273\pi\) | |||||||
\(200\) | 116.190 | − | 67.0820i | 0.580948 | − | 0.335410i | ||||
\(201\) | −152.698 | + | 31.9289i | −0.759689 | + | 0.158850i | ||||
\(202\) | 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 | ||||
\(207\) | −48.3810 | − | 110.631i | −0.233725 | − | 0.534450i | ||||
\(208\) | −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 | ||||
\(213\) | −267.665 | − | 87.9505i | −1.25664 | − | 0.412913i | ||||
\(214\) | 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 | ||||||
\(219\) | −52.8569 | + | 11.0523i | −0.241355 | + | 0.0504671i | ||||
\(220\) | 12.5000 | + | 21.6506i | 0.0568182 | + | 0.0984120i | ||||
\(221\) | 46.4758 | − | 26.8328i | 0.210298 | − | 0.121415i | ||||
\(222\) | −16.4758 | − | 78.7943i | −0.0742153 | − | 0.354929i | ||||
\(223\) | −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 | \(-0.435137\pi\) |
0.949291 | + | 0.314400i | \(0.101803\pi\) | |||||||
\(228\) | −14.9839 | + | 45.6014i | −0.0657187 | + | 0.200006i | ||||
\(229\) | 167.000 | − | 289.252i | 0.729258 | − | 1.26311i | −0.227940 | − | 0.973675i | \(-0.573199\pi\) |
0.957197 | − | 0.289436i | \(-0.0934678\pi\) | |||||||
\(230\) | − | 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 | \(-0.528647\pi\) |
−0.907459 | + | 0.420141i | \(0.861980\pi\) | |||||||
\(234\) | −16.1270 | − | 36.8771i | −0.0689189 | − | 0.157594i | ||||
\(235\) | −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 | \(0.799355\pi\) | |||||||
\(240\) | −26.0867 | − | 124.758i | −0.108695 | − | 0.519824i | ||||
\(241\) | −89.5000 | − | 155.019i | −0.371369 | − | 0.643230i | 0.618407 | − | 0.785858i | \(-0.287778\pi\) |
−0.989776 | + | 0.142627i | \(0.954445\pi\) | |||||||
\(242\) | −7.74597 | + | 4.47214i | −0.0320081 | + | 0.0184799i | ||||
\(243\) | 242.967 | + | 4.02223i | 0.999863 | + | 0.0165524i | ||||
\(244\) | 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 | ||||
\(249\) | 401.498 | + | 131.926i | 1.61244 | + | 0.529822i | ||||
\(250\) | −112.500 | + | 194.856i | −0.450000 | + | 0.779423i | ||||
\(251\) | 172.177i | 0.685965i | 0.939342 | + | 0.342983i | \(0.111437\pi\) | ||||
−0.939342 | + | 0.342983i | \(0.888563\pi\) | |||||||
\(252\) | 57.7218 | − | 25.2428i | 0.229055 | − | 0.100170i | ||||
\(253\) | 150.000 | 0.592885 | ||||||||
\(254\) | −342.759 | − | 197.892i | −1.34944 | − | 0.779102i | ||||
\(255\) | −56.1895 | + | 171.005i | −0.220351 | + | 0.670608i | ||||
\(256\) | −90.5000 | − | 156.751i | −0.353516 | − | 0.612307i | ||||
\(257\) | −228.506 | − | 131.928i | −0.889128 | − | 0.513339i | −0.0154711 | − | 0.999880i | \(-0.504925\pi\) |
−0.873657 | + | 0.486542i | \(0.838258\pi\) | |||||||
\(258\) | −220.000 | + | 196.774i | −0.852713 | + | 0.762690i | ||||
\(259\) | −84.0000 | −0.324324 | ||||||||
\(260\) | − | 4.47214i | − | 0.0172005i | ||||||
\(261\) | −83.5554 | + | 113.417i | −0.320136 | + | 0.434549i | ||||
\(262\) | −212.500 | − | 368.061i | −0.811069 | − | 1.40481i | ||||
\(263\) | −30.9839 | + | 17.8885i | −0.117809 | + | 0.0680173i | −0.557747 | − | 0.830011i | \(-0.688334\pi\) |
0.439937 | + | 0.898028i | \(0.355001\pi\) | |||||||
\(264\) | 220.237 | − | 46.0513i | 0.834231 | − | 0.174437i | ||||
\(265\) | −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 | \(-0.403540\pi\) |
0.975775 | + | 0.218776i | \(0.0702064\pi\) | |||||||
\(270\) | 122.777 | + | 56.1316i | 0.454730 | + | 0.207895i | ||||
\(271\) | −228.500 | + | 395.774i | −0.843173 | + | 1.46042i | 0.0440246 | + | 0.999030i | \(0.485982\pi\) |
−0.887198 | + | 0.461389i | \(0.847351\pi\) | |||||||
\(272\) | 509.823i | 1.87435i | ||||||||
\(273\) | −41.1109 | + | 8.59624i | −0.150589 | + | 0.0314880i | ||||
\(274\) | −480.000 | −1.75182 | ||||||||
\(275\) | −193.649 | − | 111.803i | −0.704179 | − | 0.406558i | ||||
\(276\) | 38.2379 | + | 12.5644i | 0.138543 | + | 0.0455230i | ||||
\(277\) | −26.0000 | − | 45.0333i | −0.0938628 | − | 0.162575i | 0.815271 | − | 0.579080i | \(-0.196588\pi\) |
−0.909133 | + | 0.416505i | \(0.863255\pi\) | |||||||
\(278\) | 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 | \(-0.0715233\pi\) | |||||||
\(282\) | 88.0948 | − | 18.4205i | 0.312393 | − | 0.0653209i | ||||
\(283\) | −44.0000 | − | 76.2102i | −0.155477 | − | 0.269294i | 0.777756 | − | 0.628567i | \(-0.216358\pi\) |
−0.933233 | + | 0.359273i | \(0.883025\pi\) | |||||||
\(284\) | 81.3327 | − | 46.9574i | 0.286383 | − | 0.165343i | ||||
\(285\) | 21.9677 | + | 105.059i | 0.0770798 | + | 0.368628i | ||||
\(286\) | 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 | ||||
\(291\) | −87.0937 | + | 265.058i | −0.299291 | + | 0.910852i | ||||
\(292\) | 9.00000 | − | 15.5885i | 0.0308219 | − | 0.0533851i | ||||
\(293\) | 15.6525i | 0.0534214i | 0.999643 | + | 0.0267107i | \(0.00850329\pi\) | ||||
−0.999643 | + | 0.0267107i | \(0.991497\pi\) | |||||||
\(294\) | −67.2762 | − | 321.744i | −0.228831 | − | 1.09437i | ||||
\(295\) | 45.0000 | 0.152542 | ||||||||
\(296\) | −69.7137 | − | 40.2492i | −0.235519 | − | 0.135977i | ||||
\(297\) | −125.514 | + | 274.538i | −0.422606 | + | 0.924371i | ||||
\(298\) | −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 | ||||||||
\(303\) | 35.6976 | + | 170.721i | 0.117814 | + | 0.563436i | ||||
\(304\) | 152.000 | + | 263.272i | 0.500000 | + | 0.866025i | ||||
\(305\) | 50.3488 | − | 29.0689i | 0.165078 | − | 0.0953078i | ||||
\(306\) | −434.758 | − | 320.290i | −1.42078 | − | 1.04670i | ||||
\(307\) | 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 | \(-0.831904\pi\) |
0.00449160 | + | 0.999990i | \(0.498570\pi\) | |||||||
\(312\) | −38.2379 | − | 12.5644i | −0.122557 | − | 0.0402704i | ||||
\(313\) | 135.500 | − | 234.693i | 0.432907 | − | 0.749818i | −0.564215 | − | 0.825628i | \(-0.690821\pi\) |
0.997122 | + | 0.0758104i | \(0.0241544\pi\) | |||||||
\(314\) | − | 554.545i | − | 1.76607i | ||||||
\(315\) | 83.5554 | − | 113.417i | 0.265255 | − | 0.360055i | ||||
\(316\) | 79.0000 | 0.250000 | ||||||||
\(317\) | 377.616 | + | 218.017i | 1.19122 | + | 0.687750i | 0.958583 | − | 0.284815i | \(-0.0919320\pi\) |
0.232635 | + | 0.972564i | \(0.425265\pi\) | |||||||
\(318\) | 42.1421 | − | 128.254i | 0.132522 | − | 0.403314i | ||||
\(319\) | −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 | ||||||
\(324\) | −54.9919 | + | 59.4717i | −0.169728 | + | 0.183555i | ||||
\(325\) | 20.0000 | + | 34.6410i | 0.0615385 | + | 0.106588i | ||||
\(326\) | −3.87298 | + | 2.23607i | −0.0118803 | + | 0.00685910i | ||||
\(327\) | 422.855 | − | 88.4184i | 1.29313 | − | 0.270393i | ||||
\(328\) | 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 | −0.853688 | − | 0.520785i | \(-0.825639\pi\) |
0.877857 | + | 0.478923i | \(0.158973\pi\) | |||||||
\(332\) | −121.999 | + | 70.4361i | −0.367467 | + | 0.212157i | ||||
\(333\) | 98.9516 | − | 43.2733i | 0.297152 | − | 0.129950i | ||||
\(334\) | −280.000 | + | 484.974i | −0.838323 | + | 1.45202i | ||||
\(335\) | − | 116.276i | − | 0.347091i | ||||||
\(336\) | 124.553 | − | 379.061i | 0.370695 | − | 1.12816i | ||||
\(337\) | −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 | ||||
\(339\) | 89.2218 | + | 29.3168i | 0.263191 | + | 0.0864803i | ||||
\(340\) | −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 | ||||||||
\(345\) | 88.0948 | − | 18.4205i | 0.255347 | − | 0.0533928i | ||||
\(346\) | 295.000 | + | 510.955i | 0.852601 | + | 1.47675i | ||||
\(347\) | −329.204 | + | 190.066i | −0.948713 | + | 0.547740i | −0.892681 | − | 0.450689i | \(-0.851178\pi\) |
−0.0560324 | + | 0.998429i | \(0.517845\pi\) | |||||||
\(348\) | −9.61088 | − | 45.9634i | −0.0276175 | − | 0.132079i | ||||
\(349\) | 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 | \(-0.895596\pi\) |
−0.194359 | + | 0.980931i | \(0.562263\pi\) | |||||||
\(354\) | −42.1421 | + | 128.254i | −0.119046 | + | 0.362299i | ||||
\(355\) | 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 | \(-0.228343\pi\) |
−0.192553 | + | 0.981287i | \(0.561677\pi\) | |||||||
\(360\) | 123.690 | − | 54.0917i | 0.343582 | − | 0.150255i | ||||
\(361\) | 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 | ||||||
\(366\) | 35.6976 | + | 170.721i | 0.0975343 | + | 0.466451i | ||||
\(367\) | −250.500 | − | 433.879i | −0.682561 | − | 1.18223i | −0.974197 | − | 0.225701i | \(-0.927533\pi\) |
0.291635 | − | 0.956530i | \(-0.405801\pi\) | |||||||
\(368\) | 220.760 | − | 127.456i | 0.599891 | − | 0.346347i | ||||
\(369\) | −167.111 | + | 226.835i | −0.452875 | + | 0.614728i | ||||
\(370\) | 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 | −0.162198 | + | 0.986758i | \(0.551858\pi\) |
−0.773458 | + | 0.633847i | \(0.781475\pi\) | |||||||
\(374\) | 580.948 | − | 335.410i | 1.55334 | − | 0.896819i | ||||
\(375\) | −286.784 | − | 94.2327i | −0.764758 | − | 0.251287i | ||||
\(376\) | 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 | ||||
\(381\) | 165.759 | − | 504.465i | 0.435063 | − | 1.32406i | ||||
\(382\) | −190.000 | − | 329.090i | −0.497382 | − | 0.861491i | ||||
\(383\) | −11.6190 | − | 6.70820i | −0.0303367 | − | 0.0175149i | 0.484755 | − | 0.874650i | \(-0.338909\pi\) |
−0.515092 | + | 0.857135i | \(0.672242\pi\) | |||||||
\(384\) | 345.000 | − | 308.577i | 0.898438 | − | 0.803587i | ||||
\(385\) | 87.5000 | + | 151.554i | 0.227273 | + | 0.393648i | ||||
\(386\) | 131.928i | 0.341782i | ||||||||
\(387\) | −318.823 | − | 234.879i | −0.823831 | − | 0.606923i | ||||
\(388\) | −46.5000 | − | 80.5404i | −0.119845 | − | 0.207578i | ||||
\(389\) | −58.0948 | + | 33.5410i | −0.149344 | + | 0.0862237i | −0.572810 | − | 0.819688i | \(-0.694147\pi\) |
0.423466 | + | 0.905912i | \(0.360813\pi\) | |||||||
\(390\) | 29.3649 | − | 6.14017i | 0.0752947 | − | 0.0157440i | ||||
\(391\) | −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 | ||||
\(396\) | −40.3175 | − | 92.1927i | −0.101812 | − | 0.232810i | ||||
\(397\) | 132.000 | − | 228.631i | 0.332494 | − | 0.575896i | −0.650506 | − | 0.759501i | \(-0.725443\pi\) |
0.983000 | + | 0.183605i | \(0.0587766\pi\) | |||||||
\(398\) | − | 523.240i | − | 1.31467i | ||||||
\(399\) | −104.887 | + | 319.209i | −0.262875 | + | 0.800024i | ||||
\(400\) | −380.000 | −0.950000 | ||||||||
\(401\) | 92.9516 | + | 53.6656i | 0.231800 | + | 0.133830i | 0.611402 | − | 0.791320i | \(-0.290606\pi\) |
−0.379602 | + | 0.925150i | \(0.623939\pi\) | |||||||
\(402\) | 331.395 | + | 108.891i | 0.824366 | + | 0.270873i | ||||
\(403\) | −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 | ||||||||
\(408\) | −528.569 | + | 110.523i | −1.29551 | + | 0.270890i | ||||
\(409\) | 99.5000 | + | 172.339i | 0.243276 | + | 0.421367i | 0.961646 | − | 0.274295i | \(-0.0884445\pi\) |
−0.718369 | + | 0.695662i | \(0.755111\pi\) | |||||||
\(410\) | −135.554 | + | 78.2624i | −0.330621 | + | 0.190884i | ||||
\(411\) | −131.806 | − | 630.355i | −0.320697 | − | 1.53371i | ||||
\(412\) | 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 | ||||
\(417\) | −106.760 | + | 324.910i | −0.256019 | + | 0.779160i | ||||
\(418\) | 200.000 | − | 346.410i | 0.478469 | − | 0.828732i | ||||
\(419\) | 93.9149i | 0.224140i | 0.993700 | + | 0.112070i | \(0.0357482\pi\) | ||||
−0.993700 | + | 0.112070i | \(0.964252\pi\) | |||||||
\(420\) | 9.61088 | + | 45.9634i | 0.0228831 | + | 0.109437i | ||||
\(421\) | 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 | ||||
\(423\) | 48.3810 | + | 110.631i | 0.114376 | + | 0.261540i | ||||
\(424\) | −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 | ||||||
\(429\) | 13.7298 | + | 65.6619i | 0.0320043 | + | 0.153058i | ||||
\(430\) | −110.000 | − | 190.526i | −0.255814 | − | 0.443083i | ||||
\(431\) | 104.571 | − | 60.3738i | 0.242623 | − | 0.140079i | −0.373759 | − | 0.927526i | \(-0.621931\pi\) |
0.616382 | + | 0.787447i | \(0.288598\pi\) | |||||||
\(432\) | 48.5534 | + | 510.697i | 0.112392 | + | 1.18217i | ||||
\(433\) | −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 | ||||
\(438\) | 114.714 | + | 37.6931i | 0.261903 | + | 0.0860572i | ||||
\(439\) | −235.500 | + | 407.898i | −0.536446 | + | 0.929153i | 0.462645 | + | 0.886543i | \(0.346900\pi\) |
−0.999092 | + | 0.0426091i | \(0.986433\pi\) | |||||||
\(440\) | 167.705i | 0.381148i | ||||||||
\(441\) | 404.052 | − | 176.699i | 0.916219 | − | 0.400679i | ||||
\(442\) | −120.000 | −0.271493 | ||||||||
\(443\) | 52.2853 | + | 30.1869i | 0.118025 | + | 0.0681420i | 0.557851 | − | 0.829941i | \(-0.311626\pi\) |
−0.439825 | + | 0.898083i | \(0.644960\pi\) | |||||||
\(444\) | −11.2379 | + | 34.2010i | −0.0253106 | + | 0.0770293i | ||||
\(445\) | 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 | \(0.898416\pi\) | |||||||
\(450\) | 238.730 | − | 324.049i | 0.530511 | − | 0.720110i | ||||
\(451\) | −175.000 | − | 303.109i | −0.388027 | − | 0.672082i | ||||
\(452\) | −27.1109 | + | 15.6525i | −0.0599798 | + | 0.0346294i | ||||
\(453\) | −173.253 | + | 36.2270i | −0.382457 | + | 0.0799713i | ||||
\(454\) | −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 | −0.853169 | − | 0.521634i | \(-0.825323\pi\) |
0.878333 | + | 0.478049i | \(0.158656\pi\) | |||||||
\(458\) | −646.788 | + | 373.423i | −1.41220 | + | 0.815335i | ||||
\(459\) | 301.234 | − | 658.892i | 0.656283 | − | 1.43549i | ||||
\(460\) | −15.0000 | + | 25.9808i | −0.0326087 | + | 0.0564799i | ||||
\(461\) | − | 594.794i | − | 1.29023i | −0.764087 | − | 0.645113i | \(-0.776810\pi\) | ||
0.764087 | − | 0.645113i | \(-0.223190\pi\) | |||||||
\(462\) | −513.886 | + | 107.453i | −1.11231 | + | 0.232582i | ||||
\(463\) | 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 | ||||
\(465\) | 19.1190 | + | 6.28218i | 0.0411160 | + | 0.0135101i | ||||
\(466\) | 300.000 | + | 519.615i | 0.643777 | + | 1.11505i | ||||
\(467\) | −499.615 | − | 288.453i | −1.06984 | − | 0.617672i | −0.141702 | − | 0.989909i | \(-0.545257\pi\) |
−0.928137 | + | 0.372238i | \(0.878591\pi\) | |||||||
\(468\) | −2.00000 | + | 17.8885i | −0.00427350 | + | 0.0382234i | ||||
\(469\) | 182.000 | − | 315.233i | 0.388060 | − | 0.672139i | ||||
\(470\) | 67.0820i | 0.142728i | ||||||||
\(471\) | 728.250 | − | 152.276i | 1.54618 | − | 0.323304i | ||||
\(472\) | 67.5000 | + | 116.913i | 0.143008 | + | 0.247698i | ||||
\(473\) | 426.028 | − | 245.967i | 0.900694 | − | 0.520016i | ||||
\(474\) | 108.466 | + | 518.729i | 0.228831 | + | 1.09437i | ||||
\(475\) | 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 | \(-0.782112\pi\) |
0.160223 | + | 0.987081i | \(0.448779\pi\) | |||||||
\(480\) | −32.7772 | + | 99.7530i | −0.0682859 | + | 0.207819i | ||||
\(481\) | 12.0000 | − | 20.7846i | 0.0249480 | − | 0.0432112i | ||||
\(482\) | 400.256i | 0.830407i | ||||||||
\(483\) | 267.665 | + | 87.9505i | 0.554172 | + | 0.182092i | ||||
\(484\) | 4.00000 | 0.00826446 | ||||||||
\(485\) | −180.094 | − | 103.977i | −0.371327 | − | 0.214386i | ||||
\(486\) | −466.006 | − | 279.434i | −0.958860 | − | 0.574967i | ||||
\(487\) | 404.500 | + | 700.615i | 0.830595 | + | 1.43863i | 0.897567 | + | 0.440879i | \(0.145333\pi\) |
−0.0669712 | + | 0.997755i | \(0.521334\pi\) | |||||||
\(488\) | 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 | \(-0.152955\pi\) | |||||||
\(492\) | −19.2218 | − | 91.9267i | −0.0390686 | − | 0.186843i | ||||
\(493\) | 210.000 | + | 363.731i | 0.425963 | + | 0.737790i | ||||
\(494\) | −61.9677 | + | 35.7771i | −0.125441 | + | 0.0724233i | ||||
\(495\) | −181.149 | − | 133.454i | −0.365958 | − | 0.269604i | ||||
\(496\) | 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 | −0.710253 | − | 0.703946i | \(-0.751419\pi\) |
0.964762 | + | 0.263124i | \(0.0847528\pi\) | |||||||
\(500\) | 87.1421 | − | 50.3115i | 0.174284 | − | 0.100623i | ||||
\(501\) | −713.774 | − | 234.535i | −1.42470 | − | 0.468133i | ||||
\(502\) | 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 | ||||
\(507\) | −154.521 | + | 470.264i | −0.304775 | + | 0.927542i | ||||
\(508\) | 88.5000 | + | 153.286i | 0.174213 | + | 0.301745i | ||||
\(509\) | −350.505 | − | 202.364i | −0.688615 | − | 0.397572i | 0.114478 | − | 0.993426i | \(-0.463480\pi\) |
−0.803093 | + | 0.595854i | \(0.796814\pi\) | |||||||
\(510\) | 300.000 | − | 268.328i | 0.588235 | − | 0.526134i | ||||
\(511\) | 63.0000 | − | 109.119i | 0.123288 | − | 0.213541i | ||||
\(512\) | − | 212.426i | − | 0.414895i | ||||||
\(513\) | −40.8871 | − | 430.061i | −0.0797019 | − | 0.838325i | ||||
\(514\) | 295.000 | + | 510.955i | 0.573930 | + | 0.994076i | ||||
\(515\) | 158.792 | − | 91.6788i | 0.308335 | − | 0.178017i | ||||
\(516\) | 129.206 | − | 27.0167i | 0.250399 | − | 0.0523580i | ||||
\(517\) | −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 | \(-0.558009\pi\) |
0.761067 | + | 0.648674i | \(0.224676\pi\) | |||||||
\(522\) | 288.609 | − | 126.214i | 0.552890 | − | 0.241789i | ||||
\(523\) | −197.000 | + | 341.214i | −0.376673 | + | 0.652417i | −0.990576 | − | 0.136965i | \(-0.956265\pi\) |
0.613903 | + | 0.789382i | \(0.289599\pi\) | |||||||
\(524\) | 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 | ||||
\(528\) | −605.433 | − | 198.936i | −1.14665 | − | 0.376772i | ||||
\(529\) | −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 | ||||||||
\(534\) | −323.014 | + | 67.5419i | −0.604895 | + | 0.126483i | ||||
\(535\) | −72.5000 | − | 125.574i | −0.135514 | − | 0.234717i | ||||
\(536\) | 302.093 | − | 174.413i | 0.563606 | − | 0.325398i | ||||
\(537\) | 118.077 | + | 564.693i | 0.219882 | + | 1.05157i | ||||
\(538\) | −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 | −0.990084 | − | 0.140480i | \(-0.955135\pi\) |
0.616701 | + | 0.787198i | \(0.288469\pi\) | |||||||
\(542\) | 884.977 | − | 510.942i | 1.63280 | − | 0.942697i | ||||
\(543\) | 76.7923 | − | 233.707i | 0.141422 | − | 0.430400i | ||||
\(544\) | 210.000 | − | 363.731i | 0.386029 | − | 0.668623i | ||||
\(545\) | 321.994i | 0.590814i | ||||||||
\(546\) | 89.2218 | + | 29.3168i | 0.163410 | + | 0.0536938i | ||||
\(547\) | 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 | ||||
\(549\) | −214.395 | + | 93.7589i | −0.390519 | + | 0.170781i | ||||
\(550\) | 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 | ||||||||
\(555\) | 16.4758 | + | 78.7943i | 0.0296861 | + | 0.141972i | ||||
\(556\) | −57.0000 | − | 98.7269i | −0.102518 | − | 0.177566i | ||||
\(557\) | −640.979 | + | 370.069i | −1.15077 | + | 0.664397i | −0.949075 | − | 0.315051i | \(-0.897978\pi\) |
−0.201695 | + | 0.979448i | \(0.564645\pi\) | |||||||
\(558\) | −35.8095 | + | 48.6074i | −0.0641747 | + | 0.0871101i | ||||
\(559\) | −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 | \(-0.598511\pi\) |
0.672600 | + | 0.740006i | \(0.265177\pi\) | |||||||
\(564\) | −38.2379 | − | 12.5644i | −0.0677977 | − | 0.0222772i | ||||
\(565\) | −35.0000 | + | 60.6218i | −0.0619469 | + | 0.107295i | ||||
\(566\) | 196.774i | 0.347657i | ||||||||
\(567\) | −384.944 | + | 416.302i | −0.678913 | + | 0.734219i | ||||
\(568\) | 630.000 | 1.10915 | ||||||||
\(569\) | −828.818 | − | 478.519i | −1.45662 | − | 0.840982i | −0.457780 | − | 0.889066i | \(-0.651355\pi\) |
−0.998843 | + | 0.0480841i | \(0.984688\pi\) | |||||||
\(570\) | 74.9193 | − | 228.007i | 0.131437 | − | 0.400012i | ||||
\(571\) | 23.0000 | + | 39.8372i | 0.0402802 | + | 0.0697674i | 0.885463 | − | 0.464711i | \(-0.153842\pi\) |
−0.845182 | + | 0.534478i | \(0.820508\pi\) | |||||||
\(572\) | −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 | ||||||
\(576\) | 297.085 | + | 218.865i | 0.515772 | + | 0.379973i | ||||
\(577\) | −495.500 | − | 858.231i | −0.858752 | − | 1.48740i | −0.873120 | − | 0.487506i | \(-0.837907\pi\) |
0.0143677 | − | 0.999897i | \(-0.495426\pi\) | |||||||
\(578\) | −834.628 | + | 481.873i | −1.44399 | + | 0.833690i | ||||
\(579\) | −173.253 | + | 36.2270i | −0.299228 | + | 0.0625682i | ||||
\(580\) | 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 | ||||
\(585\) | 16.1270 | + | 36.8771i | 0.0275675 | + | 0.0630378i | ||||
\(586\) | 17.5000 | − | 30.3109i | 0.0298635 | − | 0.0517251i | ||||
\(587\) | − | 766.971i | − | 1.30660i | −0.757101 | − | 0.653298i | \(-0.773385\pi\) | ||
0.757101 | − | 0.653298i | \(-0.226615\pi\) | |||||||
\(588\) | −45.8881 | + | 139.654i | −0.0780410 | + | 0.237507i | ||||
\(589\) | −48.0000 | −0.0814941 | ||||||||
\(590\) | −87.1421 | − | 50.3115i | −0.147699 | − | 0.0852738i | ||||
\(591\) | 624.552 | + | 205.218i | 1.05677 | + | 0.347238i | ||||
\(592\) | 114.000 | + | 197.454i | 0.192568 | + | 0.333537i | ||||
\(593\) | 151.046 | + | 87.2067i | 0.254716 | + | 0.147060i | 0.621922 | − | 0.783080i | \(-0.286352\pi\) |
−0.367206 | + | 0.930140i | \(0.619686\pi\) | |||||||
\(594\) | 550.000 | − | 391.312i | 0.925926 | − | 0.658774i | ||||
\(595\) | −210.000 | − | 363.731i | −0.352941 | − | 0.611312i | ||||
\(596\) | 13.4164i | 0.0225108i | ||||||||
\(597\) | 687.139 | − | 143.680i | 1.15099 | − | 0.240670i | ||||
\(598\) | 30.0000 | + | 51.9615i | 0.0501672 | + | 0.0868922i | ||||
\(599\) | 836.564 | − | 482.991i | 1.39660 | − | 0.806328i | 0.402567 | − | 0.915391i | \(-0.368118\pi\) |
0.994035 | + | 0.109062i | \(0.0347848\pi\) | |||||||
\(600\) | −82.3790 | − | 393.972i | −0.137298 | − | 0.656619i | ||||
\(601\) | −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 | ||||
\(606\) | 121.744 | − | 370.511i | 0.200898 | − | 0.611404i | ||||
\(607\) | 471.500 | − | 816.662i | 0.776771 | − | 1.34541i | −0.157023 | − | 0.987595i | \(-0.550190\pi\) |
0.933794 | − | 0.357812i | \(-0.116477\pi\) | |||||||
\(608\) | − | 250.440i | − | 0.411907i | ||||||
\(609\) | −67.2762 | − | 321.744i | −0.110470 | − | 0.528315i | ||||
\(610\) | −130.000 | −0.213115 | ||||||||
\(611\) | 23.2379 | + | 13.4164i | 0.0380326 | + | 0.0219581i | ||||
\(612\) | 96.7621 | + | 221.263i | 0.158108 | + | 0.361540i | ||||
\(613\) | −467.000 | − | 808.868i | −0.761827 | − | 1.31952i | −0.941908 | − | 0.335871i | \(-0.890969\pi\) |
0.180081 | − | 0.983652i | \(-0.442364\pi\) | |||||||
\(614\) | −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 | \(-0.0242488\pi\) | |||||||
\(618\) | 112.585 | + | 538.428i | 0.182176 | + | 0.871243i | ||||
\(619\) | 61.0000 | + | 105.655i | 0.0985460 | + | 0.170687i | 0.911083 | − | 0.412223i | \(-0.135247\pi\) |
−0.812537 | + | 0.582910i | \(0.801914\pi\) | |||||||
\(620\) | −5.80948 | + | 3.35410i | −0.00937012 | + | 0.00540984i | ||||
\(621\) | −360.617 | + | 34.2848i | −0.580704 | + | 0.0552091i | ||||
\(622\) | 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 | ||||
\(627\) | 509.839 | + | 167.525i | 0.813140 | + | 0.267185i | ||||
\(628\) | −124.000 | + | 214.774i | −0.197452 | + | 0.341997i | ||||
\(629\) | − | 321.994i | − | 0.511914i | ||||||
\(630\) | −288.609 | + | 126.214i | −0.458109 | + | 0.200339i | ||||
\(631\) | −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 | ||||
\(633\) | −24.3488 | + | 74.1022i | −0.0384657 | + | 0.117065i | ||||
\(634\) | −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 | ||||||||
\(639\) | −501.333 | + | 680.504i | −0.784558 | + | 1.06495i | ||||
\(640\) | 172.500 | + | 298.779i | 0.269531 | + | 0.466842i | ||||
\(641\) | −708.756 | + | 409.200i | −1.10570 | + | 0.638378i | −0.937713 | − | 0.347410i | \(-0.887061\pi\) |
−0.167990 | + | 0.985789i | \(0.553728\pi\) | |||||||
\(642\) | 425.791 | − | 89.0324i | 0.663226 | − | 0.138680i | ||||
\(643\) | 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 | \(-0.587754\pi\) |
0.697219 | + | 0.716858i | \(0.254421\pi\) | |||||||
\(648\) | −518.949 | + | 161.051i | −0.800846 | + | 0.248536i | ||||
\(649\) | 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 | \(-0.0559086\pi\) |
0.340978 | + | 0.940071i | \(0.389242\pi\) | |||||||
\(654\) | −917.710 | − | 301.545i | −1.40323 | − | 0.461077i | ||||
\(655\) | 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 | \(0.833778\pi\) | |||||||
\(660\) | 73.4123 | − | 15.3504i | 0.111231 | − | 0.0232582i | ||||
\(661\) | 418.000 | + | 723.997i | 0.632375 | + | 1.09531i | 0.987065 | + | 0.160322i | \(0.0512532\pi\) |
−0.354690 | + | 0.934984i | \(0.615413\pi\) | |||||||
\(662\) | −30.9839 | + | 17.8885i | −0.0468034 | + | 0.0270220i | ||||
\(663\) | −32.9516 | − | 157.589i | −0.0497008 | − | 0.237690i | ||||
\(664\) | −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 | ||||
\(669\) | −100.205 | + | 304.959i | −0.149783 | + | 0.455843i | ||||
\(670\) | −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 | ||||
\(675\) | 491.109 | + | 224.526i | 0.727569 | + | 0.332632i | ||||
\(676\) | −82.5000 | − | 142.894i | −0.122041 | − | 0.211382i | ||||
\(677\) | 923.707 | + | 533.302i | 1.36441 | + | 0.787743i | 0.990208 | − | 0.139603i | \(-0.0445827\pi\) |
0.374204 | + | 0.927346i | \(0.377916\pi\) | |||||||
\(678\) | −140.000 | − | 156.525i | −0.206490 | − | 0.230862i | ||||
\(679\) | −325.500 | − | 563.783i | −0.479381 | − | 0.830313i | ||||
\(680\) | − | 402.492i | − | 0.591900i | ||||||
\(681\) | −185.353 | − | 886.436i | −0.272177 | − | 1.30167i | ||||
\(682\) | −37.5000 | − | 64.9519i | −0.0549853 | − | 0.0952374i | ||||
\(683\) | 551.900 | − | 318.640i | 0.808053 | − | 0.466530i | −0.0382264 | − | 0.999269i | \(-0.512171\pi\) |
0.846279 | + | 0.532740i | \(0.178837\pi\) | |||||||
\(684\) | 115.935 | + | 85.4106i | 0.169496 | + | 0.124869i | ||||
\(685\) | 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 | ||||
\(690\) | −191.190 | − | 62.8218i | −0.277086 | − | 0.0910460i | ||||
\(691\) | −337.000 | + | 583.701i | −0.487699 | + | 0.844719i | −0.999900 | − | 0.0141462i | \(-0.995497\pi\) |
0.512201 | + | 0.858866i | \(0.328830\pi\) | |||||||
\(692\) | − | 263.856i | − | 0.381295i | ||||||
\(693\) | −282.223 | − | 645.349i | −0.407248 | − | 0.931239i | ||||
\(694\) | 850.000 | 1.22478 | ||||||||
\(695\) | −220.760 | − | 127.456i | −0.317640 | − | 0.183390i | ||||
\(696\) | 98.3316 | − | 299.259i | 0.141281 | − | 0.429970i | ||||
\(697\) | 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 | \(-0.279915\pi\) | |||||||
\(702\) | −120.206 | + | 11.4283i | −0.171233 | + | 0.0162796i | ||||
\(703\) | −96.0000 | − | 166.277i | −0.136558 | − | 0.236525i | ||||
\(704\) | −396.981 | + | 229.197i | −0.563893 | + | 0.325564i | ||||
\(705\) | −88.0948 | + | 18.4205i | −0.124957 | + | 0.0261284i | ||||
\(706\) | 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 | −0.823025 | − | 0.568006i | \(-0.807715\pi\) |
0.903420 | + | 0.428757i | \(0.141049\pi\) | |||||||
\(710\) | −406.663 | + | 234.787i | −0.572765 | + | 0.330686i | ||||
\(711\) | −651.431 | + | 284.883i | −0.916219 | + | 0.400679i | ||||
\(712\) | −165.000 | + | 285.788i | −0.231742 | + | 0.401388i | ||||
\(713\) | 40.2492i | 0.0564505i | ||||||||
\(714\) | 1233.33 | − | 257.887i | 1.72735 | − | 0.361186i | ||||
\(715\) | −50.0000 | −0.0699301 | ||||||||
\(716\) | −166.538 | − | 96.1509i | −0.232595 | − | 0.134289i | ||||
\(717\) | 802.996 | + | 263.851i | 1.11994 | + | 0.367994i | ||||
\(718\) | −260.000 | − | 450.333i | −0.362117 | − | 0.627205i | ||||
\(719\) | −336.950 | − | 194.538i | −0.468636 | − | 0.270567i | 0.247032 | − | 0.969007i | \(-0.420545\pi\) |
−0.715669 | + | 0.698440i | \(0.753878\pi\) | |||||||
\(720\) | −380.000 | − | 42.4853i | −0.527778 | − | 0.0590073i | ||||
\(721\) | 574.000 | 0.796117 | ||||||||
\(722\) | − | 234.787i | − | 0.325190i | ||||||
\(723\) | −525.632 | + | 109.909i | −0.727015 | + | 0.152018i | ||||
\(724\) | 41.0000 | + | 71.0141i | 0.0566298 | + | 0.0980858i | ||||
\(725\) | −271.109 | + | 156.525i | −0.373943 | + | 0.215896i | ||||
\(726\) | 5.49193 | + | 26.2648i | 0.00756465 | + | 0.0361774i | ||||
\(727\) | 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 | ||||
\(732\) | 24.3488 | − | 74.1022i | 0.0332634 | − | 0.101233i | ||||
\(733\) | −204.000 | + | 353.338i | −0.278308 | + | 0.482044i | −0.970964 | − | 0.239224i | \(-0.923107\pi\) |
0.692656 | + | 0.721268i | \(0.256440\pi\) | |||||||
\(734\) | 1120.27i | 1.52625i | ||||||||
\(735\) | 67.2762 | + | 321.744i | 0.0915322 | + | 0.437746i | ||||
\(736\) | −210.000 | −0.285326 | ||||||||
\(737\) | −503.488 | − | 290.689i | −0.683159 | − | 0.394422i | ||||
\(738\) | 577.218 | − | 252.428i | 0.782138 | − | 0.342043i | ||||
\(739\) | 177.000 | + | 306.573i | 0.239513 | + | 0.414848i | 0.960575 | − | 0.278022i | \(-0.0896789\pi\) |
−0.721062 | + | 0.692871i | \(0.756346\pi\) | |||||||
\(740\) | −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 | \(0.831272\pi\) | |||||||
\(744\) | 12.3569 | + | 59.0958i | 0.0166087 | + | 0.0794298i | ||||
\(745\) | 15.0000 | + | 25.9808i | 0.0201342 | + | 0.0348735i | ||||
\(746\) | 1351.67 | − | 780.388i | 1.81189 | − | 1.04610i | ||||
\(747\) | 751.999 | − | 1020.76i | 1.00669 | − | 1.36647i | ||||
\(748\) | −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 | −0.286571 | − | 0.958059i | \(-0.592515\pi\) |
0.972989 | − | 0.230852i | \(-0.0741513\pi\) | |||||||
\(752\) | −220.760 | + | 127.456i | −0.293564 | + | 0.169489i | ||||
\(753\) | 490.720 | + | 161.243i | 0.651686 | + | 0.214134i | ||||
\(754\) | 35.0000 | − | 60.6218i | 0.0464191 | − | 0.0804002i | ||||
\(755\) | − | 131.928i | − | 0.174739i | ||||||
\(756\) | −17.8881 | − | 188.152i | −0.0236615 | − | 0.248878i | ||||
\(757\) | −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 | ||||
\(759\) | 140.474 | − | 427.513i | 0.185077 | − | 0.563258i | ||||
\(760\) | −120.000 | − | 207.846i | −0.157895 | − | 0.273482i | ||||
\(761\) | 801.708 | + | 462.866i | 1.05349 | + | 0.608234i | 0.923625 | − | 0.383297i | \(-0.125212\pi\) |
0.129867 | + | 0.991531i | \(0.458545\pi\) | |||||||
\(762\) | −885.000 | + | 791.568i | −1.16142 | + | 1.03880i | ||||
\(763\) | −504.000 | + | 872.954i | −0.660550 | + | 1.14411i | ||||
\(764\) | 169.941i | 0.222436i | ||||||||
\(765\) | 434.758 | + | 320.290i | 0.568311 | + | 0.418679i | ||||
\(766\) | 15.0000 | + | 25.9808i | 0.0195822 | + | 0.0339174i | ||||
\(767\) | −34.8569 | + | 20.1246i | −0.0454457 | + | 0.0262381i | ||||
\(768\) | −531.505 | + | 111.137i | −0.692064 | + | 0.144710i | ||||
\(769\) | −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 | \(-0.560670\pi\) |
0.755617 | + | 0.655014i | \(0.227337\pi\) | |||||||
\(774\) | 354.794 | + | 811.296i | 0.458391 | + | 1.04819i | ||||
\(775\) | 30.0000 | − | 51.9615i | 0.0387097 | − | 0.0670471i | ||||
\(776\) | − | 623.863i | − | 0.803947i | ||||||
\(777\) | −78.6653 | + | 239.407i | −0.101242 | + | 0.308117i | ||||
\(778\) | 150.000 | 0.192802 | ||||||||
\(779\) | 433.774 | + | 250.440i | 0.556835 | + | 0.321489i | ||||
\(780\) | −12.7460 | − | 4.18812i | −0.0163410 | − | 0.00536938i | ||||
\(781\) | −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 | ||||||||
\(786\) | −1248.01 | + | 260.957i | −1.58780 | + | 0.332007i | ||||
\(787\) | −611.000 | − | 1058.28i | −0.776366 | − | 1.34471i | −0.934024 | − | 0.357211i | \(-0.883728\pi\) |
0.157658 | − | 0.987494i | \(-0.449606\pi\) | |||||||
\(788\) | −189.776 | + | 109.567i | −0.240833 | + | 0.139045i | ||||
\(789\) | 21.9677 | + | 105.059i | 0.0278425 | + | 0.133155i | ||||
\(790\) | −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 | ||||
\(795\) | −42.1421 | + | 128.254i | −0.0530090 | + | 0.161326i | ||||
\(796\) | −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 | ||||
\(801\) | −177.397 | − | 405.648i | −0.221470 | − | 0.506427i | ||||
\(802\) | −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 | ||||||||
\(807\) | −243.018 | − | 1162.22i | −0.301138 | − | 1.44017i | ||||
\(808\) | −195.000 | − | 337.750i | −0.241337 | − | 0.418007i | ||||
\(809\) | 185.903 | − | 107.331i | 0.229794 | − | 0.132672i | −0.380683 | − | 0.924706i | \(-0.624311\pi\) |
0.610477 | + | 0.792034i | \(0.290978\pi\) | |||||||
\(810\) | 274.960 | − | 297.359i | 0.339456 | − | 0.367109i | ||||
\(811\) | −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 | ||||
\(816\) | 1453.04 | + | 477.445i | 1.78069 | + | 0.585105i | ||||
\(817\) | −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 | \(-0.241467\pi\) |
−0.232837 | + | 0.972516i | \(0.574801\pi\) | |||||||
\(822\) | −449.516 | + | 1368.04i | −0.546856 | + | 1.66428i | ||||
\(823\) | 261.000 | + | 452.065i | 0.317132 | + | 0.549290i | 0.979888 | − | 0.199546i | \(-0.0639467\pi\) |
−0.662756 | + | 0.748835i | \(0.730613\pi\) | |||||||
\(824\) | 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 | \(0.796679\pi\) | |||||||
\(828\) | 71.6190 | − | 97.2148i | 0.0864963 | − | 0.117409i | ||||
\(829\) | 152.000 | + | 263.272i | 0.183353 | + | 0.317577i | 0.943020 | − | 0.332735i | \(-0.107971\pi\) |
−0.759667 | + | 0.650312i | \(0.774638\pi\) | |||||||
\(830\) | 609.995 | − | 352.181i | 0.734934 | − | 0.424314i | ||||
\(831\) | −152.698 | + | 31.9289i | −0.183752 | + | 0.0384222i | ||||
\(832\) | 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 | ||||
\(837\) | −73.6663 | − | 33.6790i | −0.0880123 | − | 0.0402377i | ||||
\(838\) | 105.000 | − | 181.865i | 0.125298 | − | 0.217023i | ||||
\(839\) | − | 1001.76i | − | 1.19399i | −0.802245 | − | 0.596996i | \(-0.796361\pi\) | ||
0.802245 | − | 0.596996i | \(-0.203639\pi\) | |||||||
\(840\) | −98.3316 | + | 299.259i | −0.117061 | + | 0.356261i | ||||
\(841\) | 596.000 | 0.708680 | ||||||||
\(842\) | −491.869 | − | 283.981i | −0.584167 | − | 0.337269i | ||||
\(843\) | −356.887 | − | 117.267i | −0.423354 | − | 0.139107i | ||||
\(844\) | −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 | ||||||||
\(849\) | −258.411 | + | 54.0335i | −0.304371 | + | 0.0636437i | ||||
\(850\) | −600.000 | − | 1039.23i | −0.705882 | − | 1.22262i | ||||
\(851\) | −139.427 | + | 80.4984i | −0.163839 | + | 0.0945928i | ||||
\(852\) | −57.6653 | − | 275.780i | −0.0676823 | − | 0.323686i | ||||
\(853\) | 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 | \(-0.665836\pi\) |
0.502258 | + | 0.864718i | \(0.332503\pi\) | |||||||
\(858\) | 46.8246 | − | 142.504i | 0.0545741 | − | 0.166089i | ||||
\(859\) | −64.0000 | + | 110.851i | −0.0745052 | + | 0.129047i | −0.900871 | − | 0.434087i | \(-0.857071\pi\) |
0.826366 | + | 0.563134i | \(0.190404\pi\) | |||||||
\(860\) | 98.3870i | 0.114403i | ||||||||
\(861\) | −134.552 | − | 643.487i | −0.156275 | − | 0.747372i | ||||
\(862\) | −270.000 | −0.313225 | ||||||||
\(863\) | −1289.70 | − | 744.611i | −1.49444 | − | 0.862816i | −0.494462 | − | 0.869199i | \(-0.664635\pi\) |
−0.999980 | + | 0.00638254i | \(0.997968\pi\) | |||||||
\(864\) | 175.720 | − | 384.353i | 0.203379 | − | 0.444854i | ||||
\(865\) | −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 | ||||||
\(870\) | 48.0544 | + | 229.817i | 0.0552350 | + | 0.264157i | ||||
\(871\) | 52.0000 | + | 90.0666i | 0.0597015 | + | 0.103406i | ||||
\(872\) | −836.564 | + | 482.991i | −0.959363 | + | 0.553888i | ||||
\(873\) | 673.875 | + | 496.449i | 0.771907 | + | 0.568670i | ||||
\(874\) | 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 | −0.0389316 | + | 0.999242i | \(0.512395\pi\) |
−0.845903 | + | 0.533337i | \(0.820938\pi\) | |||||||
\(878\) | 912.088 | − | 526.594i | 1.03882 | − | 0.599765i | ||||
\(879\) | 44.6109 | + | 14.6584i | 0.0507519 | + | 0.0166762i | ||||
\(880\) | 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 | ||||
\(885\) | 42.1421 | − | 128.254i | 0.0476182 | − | 0.144920i | ||||
\(886\) | −67.5000 | − | 116.913i | −0.0761851 | − | 0.131956i | ||||
\(887\) | −1204.50 | − | 695.417i | −1.35795 | − | 0.784010i | −0.368599 | − | 0.929589i | \(-0.620162\pi\) |
−0.989347 | + | 0.145578i | \(0.953496\pi\) | |||||||
\(888\) | −180.000 | + | 160.997i | −0.202703 | + | 0.181303i | ||||
\(889\) | 619.500 | + | 1073.01i | 0.696850 | + | 1.20698i | ||||
\(890\) | − | 245.967i | − | 0.276368i | ||||||
\(891\) | 664.914 | + | 614.829i | 0.746256 | + | 0.690043i | ||||
\(892\) | −53.5000 | − | 92.6647i | −0.0599776 | − | 0.103884i | ||||
\(893\) | 185.903 | − | 107.331i | 0.208178 | − | 0.120192i | ||||
\(894\) | −88.0948 | + | 18.4205i | −0.0985400 | + | 0.0206046i | ||||
\(895\) | −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 | ||||
\(900\) | −164.919 | + | 72.1222i | −0.183244 | + | 0.0801358i | ||||
\(901\) | 270.000 | − | 467.654i | 0.299667 | − | 0.519039i | ||||
\(902\) | 782.624i | 0.867654i | ||||||||
\(903\) | 904.439 | − | 189.117i | 1.00159 | − | 0.209432i | ||||
\(904\) | −210.000 | −0.232301 | ||||||||
\(905\) | 158.792 | + | 91.6788i | 0.175461 | + | 0.101303i | ||||
\(906\) | 376.006 | + | 123.549i | 0.415018 | + | 0.136368i | ||||
\(907\) | 149.000 | + | 258.076i | 0.164278 | + | 0.284538i | 0.936399 | − | 0.350938i | \(-0.114137\pi\) |
−0.772121 | + | 0.635476i | \(0.780804\pi\) | |||||||
\(908\) | 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 | \(-0.117501\pi\) | |||||||
\(912\) | 892.693 | − | 186.661i | 0.978831 | − | 0.204672i | ||||
\(913\) | 787.500 | + | 1363.99i | 0.862541 | + | 1.49396i | ||||
\(914\) | −44.5393 | + | 25.7148i | −0.0487301 | + | 0.0281343i | ||||
\(915\) | −35.6976 | − | 170.721i | −0.0390137 | − | 0.186580i | ||||
\(916\) | 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 | −0.931688 | − | 0.363260i | \(-0.881664\pi\) |
0.780436 | + | 0.625235i | \(0.214997\pi\) | |||||||
\(920\) | −174.284 | + | 100.623i | −0.189439 | + | 0.109373i | ||||
\(921\) | 155.458 | − | 473.114i | 0.168792 | − | 0.513696i | ||||
\(922\) | −665.000 | + | 1151.81i | −0.721258 | + | 1.24926i | ||||
\(923\) | 187.830i | 0.203499i | ||||||||
\(924\) | 223.054 | + | 73.2921i | 0.241401 | + | 0.0793204i | ||||
\(925\) | 240.000 | 0.259459 | ||||||||
\(926\) | −112.317 | − | 64.8460i | −0.121292 | − | 0.0700280i | ||||
\(927\) | −676.169 | + | 295.701i | −0.729417 | + | 0.318987i | ||||
\(928\) | 122.500 | + | 212.176i | 0.132004 | + | 0.228638i | ||||
\(929\) | −960.500 | − | 554.545i | −1.03391 | − | 0.596927i | −0.115806 | − | 0.993272i | \(-0.536945\pi\) |
−0.918102 | + | 0.396345i | \(0.870278\pi\) | |||||||
\(930\) | −30.0000 | − | 33.5410i | −0.0322581 | − | 0.0360656i | ||||
\(931\) | −392.000 | − | 678.964i | −0.421053 | − | 0.729285i | ||||
\(932\) | − | 268.328i | − | 0.287906i | ||||||
\(933\) | 189.472 | + | 906.135i | 0.203078 | + | 0.971206i | ||||
\(934\) | 645.000 | + | 1117.17i | 0.690578 | + | 1.19612i | ||||
\(935\) | −580.948 | + | 335.410i | −0.621334 | + | 0.358727i | ||||
\(936\) | −71.6190 | + | 97.2148i | −0.0765160 | + | 0.103862i | ||||
\(937\) | −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 | \(-0.483964\pi\) |
0.890106 | + | 0.455754i | \(0.150630\pi\) | |||||||
\(942\) | −1580.50 | − | 519.327i | −1.67781 | − | 0.551302i | ||||
\(943\) | 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 | \(-0.177630\pi\) |
−0.0344357 | + | 0.999407i | \(0.510963\pi\) | |||||||
\(948\) | 73.9828 | − | 225.157i | 0.0780410 | − | 0.237507i | ||||
\(949\) | 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 | \(-0.0846429\pi\) | |||||||
\(954\) | −326.069 | − | 240.217i | −0.341791 | − | 0.251800i | ||||
\(955\) | 190.000 | + | 329.090i | 0.198953 | + | 0.344596i | ||||
\(956\) | −243.998 | + | 140.872i | −0.255228 | + | 0.147356i | ||||
\(957\) | −513.886 | + | 107.453i | −0.536976 | + | 0.112281i | ||||
\(958\) | 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 | ||||
\(963\) | 233.842 | + | 534.718i | 0.242826 | + | 0.555262i | ||||
\(964\) | 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 | ||||
\(969\) | −1223.61 | − | 402.059i | −1.26276 | − | 0.414922i | ||||
\(970\) | 232.500 | + | 402.702i | 0.239691 | + | 0.415157i | ||||
\(971\) | 517.043 | + | 298.515i | 0.532485 | + | 0.307431i | 0.742028 | − | 0.670369i | \(-0.233864\pi\) |
−0.209543 | + | 0.977800i | \(0.567197\pi\) | |||||||
\(972\) | 118.000 | + | 212.426i | 0.121399 | + | 0.218546i | ||||
\(973\) | −399.000 | − | 691.088i | −0.410072 | − | 0.710265i | ||||
\(974\) | − | 1808.98i | − | 1.85727i | ||||||
\(975\) | 117.460 | − | 24.5607i | 0.120471 | − | 0.0251904i | ||||
\(976\) | −247.000 | − | 427.817i | −0.253074 | − | 0.438337i | ||||
\(977\) | 511.234 | − | 295.161i | 0.523269 | − | 0.302109i | −0.215002 | − | 0.976614i | \(-0.568976\pi\) |
0.738271 | + | 0.674504i | \(0.235643\pi\) | |||||||
\(978\) | 2.74597 | + | 13.1324i | 0.00280774 | + | 0.0134278i | ||||
\(979\) | 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 | \(-0.495640\pi\) |
0.872793 | + | 0.488090i | \(0.162306\pi\) | |||||||
\(984\) | 196.663 | − | 598.518i | 0.199861 | − | 0.608250i | ||||
\(985\) | −245.000 | + | 424.352i | −0.248731 | + | 0.430815i | ||||
\(986\) | − | 939.149i | − | 0.952483i | ||||||
\(987\) | −267.665 | − | 87.9505i | −0.271191 | − | 0.0891089i | ||||
\(988\) | 32.0000 | 0.0323887 | ||||||||
\(989\) | 511.234 | + | 295.161i | 0.516920 | + | 0.298444i | ||||
\(990\) | 201.588 | + | 460.964i | 0.203624 | + | 0.465620i | ||||
\(991\) | −8.50000 | − | 14.7224i | −0.00857719 | − | 0.0148561i | 0.861705 | − | 0.507410i | \(-0.169397\pi\) |
−0.870282 | + | 0.492554i | \(0.836064\pi\) | |||||||
\(992\) | −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 | ||||||||
\(996\) | 86.4980 | + | 413.670i | 0.0868453 | + | 0.415332i | ||||
\(997\) | −296.000 | − | 512.687i | −0.296891 | − | 0.514230i | 0.678532 | − | 0.734571i | \(-0.262616\pi\) |
−0.975423 | + | 0.220341i | \(0.929283\pi\) | |||||||
\(998\) | −491.869 | + | 283.981i | −0.492855 | + | 0.284550i | ||||
\(999\) | −30.6653 | − | 322.546i | −0.0306960 | − | 0.322868i |
(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.2.1 | ✓ | 4 | |
3.2 | odd | 2 | inner | 21.3.h.b.2.2 | yes | 4 | |
4.3 | odd | 2 | 336.3.bn.f.65.1 | 4 | |||
7.2 | even | 3 | 147.3.b.d.50.2 | 2 | |||
7.3 | odd | 6 | 147.3.h.b.116.2 | 4 | |||
7.4 | even | 3 | inner | 21.3.h.b.11.2 | yes | 4 | |
7.5 | odd | 6 | 147.3.b.c.50.2 | 2 | |||
7.6 | odd | 2 | 147.3.h.b.128.1 | 4 | |||
12.11 | even | 2 | 336.3.bn.f.65.2 | 4 | |||
21.2 | odd | 6 | 147.3.b.d.50.1 | 2 | |||
21.5 | even | 6 | 147.3.b.c.50.1 | 2 | |||
21.11 | odd | 6 | inner | 21.3.h.b.11.1 | yes | 4 | |
21.17 | even | 6 | 147.3.h.b.116.1 | 4 | |||
21.20 | even | 2 | 147.3.h.b.128.2 | 4 | |||
28.11 | odd | 6 | 336.3.bn.f.305.2 | 4 | |||
84.11 | even | 6 | 336.3.bn.f.305.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.h.b.2.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
21.3.h.b.2.2 | yes | 4 | 3.2 | odd | 2 | inner | |
21.3.h.b.11.1 | yes | 4 | 21.11 | odd | 6 | inner | |
21.3.h.b.11.2 | yes | 4 | 7.4 | even | 3 | inner | |
147.3.b.c.50.1 | 2 | 21.5 | even | 6 | |||
147.3.b.c.50.2 | 2 | 7.5 | odd | 6 | |||
147.3.b.d.50.1 | 2 | 21.2 | odd | 6 | |||
147.3.b.d.50.2 | 2 | 7.2 | even | 3 | |||
147.3.h.b.116.1 | 4 | 21.17 | even | 6 | |||
147.3.h.b.116.2 | 4 | 7.3 | odd | 6 | |||
147.3.h.b.128.1 | 4 | 7.6 | odd | 2 | |||
147.3.h.b.128.2 | 4 | 21.20 | even | 2 | |||
336.3.bn.f.65.1 | 4 | 4.3 | odd | 2 | |||
336.3.bn.f.65.2 | 4 | 12.11 | even | 2 | |||
336.3.bn.f.305.1 | 4 | 84.11 | even | 6 | |||
336.3.bn.f.305.2 | 4 | 28.11 | odd | 6 |