Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,4,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (of order \(3\), 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: | \(4.36614134042\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 84 x^{8} - 140 x^{7} + 6309 x^{6} - 5214 x^{5} + 67648 x^{4} + 164178 x^{3} + 511389 x^{2} + \cdots + 443556 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(-0.858393 - 1.48678i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.47 |
Dual form | 74.4.c.b.63.2 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.35839 | − | 2.35281i | −0.261423 | − | 0.452798i | 0.705197 | − | 0.709011i | \(-0.250858\pi\) |
−0.966620 | + | 0.256213i | \(0.917525\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.388081 | + | 0.672176i | 0.0347110 | + | 0.0601213i | 0.882859 | − | 0.469638i | \(-0.155616\pi\) |
−0.848148 | + | 0.529759i | \(0.822282\pi\) | |||||||
\(6\) | 5.43357 | 0.369708 | ||||||||
\(7\) | 11.9492 | + | 20.6965i | 0.645194 | + | 1.11751i | 0.984257 | + | 0.176745i | \(0.0565567\pi\) |
−0.339063 | + | 0.940764i | \(0.610110\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 9.80954 | − | 16.9906i | 0.363316 | − | 0.629282i | ||||
\(10\) | −1.55232 | −0.0490888 | ||||||||
\(11\) | 52.4685 | 1.43817 | 0.719084 | − | 0.694923i | \(-0.244561\pi\) | ||||
0.719084 | + | 0.694923i | \(0.244561\pi\) | |||||||
\(12\) | −5.43357 | + | 9.41122i | −0.130711 | + | 0.226399i | ||||
\(13\) | 34.3127 | + | 59.4314i | 0.732049 | + | 1.26795i | 0.956006 | + | 0.293347i | \(0.0947692\pi\) |
−0.223957 | + | 0.974599i | \(0.571897\pi\) | |||||||
\(14\) | −47.7966 | −0.912442 | ||||||||
\(15\) | 1.05433 | − | 1.82616i | 0.0181485 | − | 0.0314341i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −44.7302 | + | 77.4750i | −0.638157 | + | 1.10532i | 0.347680 | + | 0.937613i | \(0.386969\pi\) |
−0.985837 | + | 0.167707i | \(0.946364\pi\) | |||||||
\(18\) | 19.6191 | + | 33.9812i | 0.256903 | + | 0.444970i | ||||
\(19\) | −47.2533 | − | 81.8450i | −0.570560 | − | 0.988239i | −0.996508 | − | 0.0834915i | \(-0.973393\pi\) |
0.425948 | − | 0.904747i | \(-0.359940\pi\) | |||||||
\(20\) | 1.55232 | − | 2.68870i | 0.0173555 | − | 0.0300606i | ||||
\(21\) | 32.4633 | − | 56.2281i | 0.337337 | − | 0.584284i | ||||
\(22\) | −52.4685 | + | 90.8782i | −0.508469 | + | 0.880695i | ||||
\(23\) | 135.523 | 1.22863 | 0.614317 | − | 0.789059i | \(-0.289432\pi\) | ||||
0.614317 | + | 0.789059i | \(0.289432\pi\) | |||||||
\(24\) | −10.8671 | − | 18.8224i | −0.0924269 | − | 0.160088i | ||||
\(25\) | 62.1988 | − | 107.731i | 0.497590 | − | 0.861852i | ||||
\(26\) | −137.251 | −1.03527 | ||||||||
\(27\) | −126.654 | −0.902762 | ||||||||
\(28\) | 47.7966 | − | 82.7862i | 0.322597 | − | 0.558754i | ||||
\(29\) | 172.177 | 1.10250 | 0.551248 | − | 0.834341i | \(-0.314152\pi\) | ||||
0.551248 | + | 0.834341i | \(0.314152\pi\) | |||||||
\(30\) | 2.10867 | + | 3.65232i | 0.0128329 | + | 0.0222273i | ||||
\(31\) | −286.679 | −1.66094 | −0.830468 | − | 0.557066i | \(-0.811927\pi\) | ||||
−0.830468 | + | 0.557066i | \(0.811927\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −71.2729 | − | 123.448i | −0.375970 | − | 0.651199i | ||||
\(34\) | −89.4604 | − | 154.950i | −0.451245 | − | 0.781579i | ||||
\(35\) | −9.27448 | + | 16.0639i | −0.0447907 | + | 0.0775797i | ||||
\(36\) | −78.4763 | −0.363316 | ||||||||
\(37\) | 184.044 | − | 129.541i | 0.817748 | − | 0.575577i | ||||
\(38\) | 189.013 | 0.806894 | ||||||||
\(39\) | 93.2203 | − | 161.462i | 0.382749 | − | 0.662940i | ||||
\(40\) | 3.10465 | + | 5.37741i | 0.0122722 | + | 0.0212561i | ||||
\(41\) | 80.2235 | + | 138.951i | 0.305581 | + | 0.529281i | 0.977390 | − | 0.211443i | \(-0.0678161\pi\) |
−0.671810 | + | 0.740724i | \(0.734483\pi\) | |||||||
\(42\) | 64.9266 | + | 112.456i | 0.238533 | + | 0.413151i | ||||
\(43\) | −459.761 | −1.63053 | −0.815266 | − | 0.579087i | \(-0.803409\pi\) | ||||
−0.815266 | + | 0.579087i | \(0.803409\pi\) | |||||||
\(44\) | −104.937 | − | 181.756i | −0.359542 | − | 0.622745i | ||||
\(45\) | 15.2276 | 0.0504443 | ||||||||
\(46\) | −135.523 | + | 234.733i | −0.434388 | + | 0.752381i | ||||
\(47\) | −57.4596 | −0.178326 | −0.0891632 | − | 0.996017i | \(-0.528419\pi\) | ||||
−0.0891632 | + | 0.996017i | \(0.528419\pi\) | |||||||
\(48\) | 43.4686 | 0.130711 | ||||||||
\(49\) | −114.065 | + | 197.566i | −0.332550 | + | 0.575993i | ||||
\(50\) | 124.398 | + | 215.463i | 0.351849 | + | 0.609421i | ||||
\(51\) | 243.045 | 0.667315 | ||||||||
\(52\) | 137.251 | − | 237.726i | 0.366025 | − | 0.633973i | ||||
\(53\) | −153.743 | + | 266.290i | −0.398457 | + | 0.690147i | −0.993536 | − | 0.113520i | \(-0.963787\pi\) |
0.595079 | + | 0.803667i | \(0.297121\pi\) | |||||||
\(54\) | 126.654 | − | 219.371i | 0.319175 | − | 0.552827i | ||||
\(55\) | 20.3620 | + | 35.2681i | 0.0499203 | + | 0.0864645i | ||||
\(56\) | 95.5932 | + | 165.572i | 0.228110 | + | 0.395099i | ||||
\(57\) | −128.377 | + | 222.355i | −0.298315 | + | 0.516696i | ||||
\(58\) | −172.177 | + | 298.219i | −0.389791 | + | 0.675138i | ||||
\(59\) | −93.4414 | + | 161.845i | −0.206187 | + | 0.357126i | −0.950510 | − | 0.310693i | \(-0.899439\pi\) |
0.744323 | + | 0.667819i | \(0.232772\pi\) | |||||||
\(60\) | −8.43466 | −0.0181485 | ||||||||
\(61\) | 266.755 | + | 462.034i | 0.559910 | + | 0.969793i | 0.997503 | + | 0.0706199i | \(0.0224977\pi\) |
−0.437593 | + | 0.899173i | \(0.644169\pi\) | |||||||
\(62\) | 286.679 | − | 496.542i | 0.587230 | − | 1.01711i | ||||
\(63\) | 468.863 | 0.937637 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −26.6322 | + | 46.1284i | −0.0508204 | + | 0.0880234i | ||||
\(66\) | 285.091 | 0.531702 | ||||||||
\(67\) | −92.1029 | − | 159.527i | −0.167943 | − | 0.290885i | 0.769754 | − | 0.638341i | \(-0.220379\pi\) |
−0.937696 | + | 0.347456i | \(0.887046\pi\) | |||||||
\(68\) | 357.841 | 0.638157 | ||||||||
\(69\) | −184.094 | − | 318.860i | −0.321193 | − | 0.556322i | ||||
\(70\) | −18.5490 | − | 32.1277i | −0.0316718 | − | 0.0548571i | ||||
\(71\) | −98.9525 | − | 171.391i | −0.165401 | − | 0.286484i | 0.771396 | − | 0.636355i | \(-0.219559\pi\) |
−0.936798 | + | 0.349871i | \(0.886225\pi\) | |||||||
\(72\) | 78.4763 | − | 135.925i | 0.128452 | − | 0.222485i | ||||
\(73\) | 62.7530 | 0.100612 | 0.0503061 | − | 0.998734i | \(-0.483980\pi\) | ||||
0.0503061 | + | 0.998734i | \(0.483980\pi\) | |||||||
\(74\) | 40.3269 | + | 448.314i | 0.0633501 | + | 0.704263i | ||||
\(75\) | −337.962 | −0.520326 | ||||||||
\(76\) | −189.013 | + | 327.380i | −0.285280 | + | 0.494119i | ||||
\(77\) | 626.955 | + | 1085.92i | 0.927897 | + | 1.60717i | ||||
\(78\) | 186.441 | + | 322.925i | 0.270644 | + | 0.468769i | ||||
\(79\) | −418.243 | − | 724.419i | −0.595646 | − | 1.03169i | −0.993455 | − | 0.114221i | \(-0.963563\pi\) |
0.397809 | − | 0.917468i | \(-0.369771\pi\) | |||||||
\(80\) | −12.4186 | −0.0173555 | ||||||||
\(81\) | −92.8116 | − | 160.754i | −0.127314 | − | 0.220514i | ||||
\(82\) | −320.894 | −0.432156 | ||||||||
\(83\) | 438.007 | − | 758.650i | 0.579247 | − | 1.00328i | −0.416319 | − | 0.909218i | \(-0.636680\pi\) |
0.995566 | − | 0.0940662i | \(-0.0299865\pi\) | |||||||
\(84\) | −259.706 | −0.337337 | ||||||||
\(85\) | −69.4358 | −0.0886043 | ||||||||
\(86\) | 459.761 | − | 796.329i | 0.576480 | − | 0.998493i | ||||
\(87\) | −233.883 | − | 405.098i | −0.288218 | − | 0.499208i | ||||
\(88\) | 419.748 | 0.508469 | ||||||||
\(89\) | 545.438 | − | 944.727i | 0.649622 | − | 1.12518i | −0.333591 | − | 0.942718i | \(-0.608260\pi\) |
0.983213 | − | 0.182461i | \(-0.0584062\pi\) | |||||||
\(90\) | −15.2276 | + | 26.3750i | −0.0178348 | + | 0.0308907i | ||||
\(91\) | −820.016 | + | 1420.31i | −0.944627 | + | 1.63614i | ||||
\(92\) | −271.047 | − | 469.467i | −0.307158 | − | 0.532014i | ||||
\(93\) | 389.422 | + | 674.499i | 0.434207 | + | 0.752068i | ||||
\(94\) | 57.4596 | − | 99.5230i | 0.0630479 | − | 0.109202i | ||||
\(95\) | 36.6762 | − | 63.5250i | 0.0396095 | − | 0.0686056i | ||||
\(96\) | −43.4686 | + | 75.2898i | −0.0462135 | + | 0.0800441i | ||||
\(97\) | −1433.73 | −1.50075 | −0.750377 | − | 0.661010i | \(-0.770128\pi\) | ||||
−0.750377 | + | 0.661010i | \(0.770128\pi\) | |||||||
\(98\) | −228.129 | − | 395.131i | −0.235148 | − | 0.407289i | ||||
\(99\) | 514.692 | − | 891.473i | 0.522510 | − | 0.905014i | ||||
\(100\) | −497.590 | −0.497590 | ||||||||
\(101\) | −483.484 | −0.476322 | −0.238161 | − | 0.971226i | \(-0.576545\pi\) | ||||
−0.238161 | + | 0.971226i | \(0.576545\pi\) | |||||||
\(102\) | −243.045 | + | 420.966i | −0.235931 | + | 0.408645i | ||||
\(103\) | −701.463 | −0.671041 | −0.335520 | − | 0.942033i | \(-0.608912\pi\) | ||||
−0.335520 | + | 0.942033i | \(0.608912\pi\) | |||||||
\(104\) | 274.502 | + | 475.451i | 0.258818 | + | 0.448287i | ||||
\(105\) | 50.3936 | 0.0468372 | ||||||||
\(106\) | −307.486 | − | 532.581i | −0.281751 | − | 0.488008i | ||||
\(107\) | 445.364 | + | 771.393i | 0.402383 | + | 0.696947i | 0.994013 | − | 0.109262i | \(-0.0348488\pi\) |
−0.591630 | + | 0.806209i | \(0.701515\pi\) | |||||||
\(108\) | 253.308 | + | 438.742i | 0.225691 | + | 0.390907i | ||||
\(109\) | −736.798 | + | 1276.17i | −0.647453 | + | 1.12142i | 0.336276 | + | 0.941764i | \(0.390833\pi\) |
−0.983729 | + | 0.179658i | \(0.942501\pi\) | |||||||
\(110\) | −81.4482 | −0.0705980 | ||||||||
\(111\) | −554.788 | − | 257.053i | −0.474398 | − | 0.219805i | ||||
\(112\) | −382.373 | −0.322597 | ||||||||
\(113\) | 829.553 | − | 1436.83i | 0.690600 | − | 1.19615i | −0.281041 | − | 0.959696i | \(-0.590680\pi\) |
0.971642 | − | 0.236459i | \(-0.0759868\pi\) | |||||||
\(114\) | −256.754 | − | 444.711i | −0.210940 | − | 0.365360i | ||||
\(115\) | 52.5941 | + | 91.0956i | 0.0426471 | + | 0.0738670i | ||||
\(116\) | −344.353 | − | 596.437i | −0.275624 | − | 0.477395i | ||||
\(117\) | 1346.37 | 1.06386 | ||||||||
\(118\) | −186.883 | − | 323.690i | −0.145796 | − | 0.252526i | ||||
\(119\) | −2137.95 | −1.64694 | ||||||||
\(120\) | 8.43466 | − | 14.6093i | 0.00641647 | − | 0.0111136i | ||||
\(121\) | 1421.95 | 1.06833 | ||||||||
\(122\) | −1067.02 | −0.791833 | ||||||||
\(123\) | 217.950 | − | 377.500i | 0.159771 | − | 0.276732i | ||||
\(124\) | 573.358 | + | 993.085i | 0.415234 | + | 0.719207i | ||||
\(125\) | 193.573 | 0.138510 | ||||||||
\(126\) | −468.863 | + | 812.094i | −0.331505 | + | 0.574183i | ||||
\(127\) | 1203.87 | − | 2085.17i | 0.841152 | − | 1.45692i | −0.0477695 | − | 0.998858i | \(-0.515211\pi\) |
0.888922 | − | 0.458060i | \(-0.151455\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 624.536 | + | 1081.73i | 0.426258 | + | 0.738301i | ||||
\(130\) | −53.2645 | − | 92.2568i | −0.0359354 | − | 0.0622420i | ||||
\(131\) | 129.574 | − | 224.430i | 0.0864196 | − | 0.149683i | −0.819576 | − | 0.572971i | \(-0.805791\pi\) |
0.905995 | + | 0.423288i | \(0.139124\pi\) | |||||||
\(132\) | −285.091 | + | 493.793i | −0.187985 | + | 0.325600i | ||||
\(133\) | 1129.27 | − | 1955.96i | 0.736243 | − | 1.27521i | ||||
\(134\) | 368.412 | 0.237507 | ||||||||
\(135\) | −49.1520 | − | 85.1338i | −0.0313358 | − | 0.0542752i | ||||
\(136\) | −357.841 | + | 619.800i | −0.225622 | + | 0.390790i | ||||
\(137\) | −933.443 | −0.582112 | −0.291056 | − | 0.956706i | \(-0.594007\pi\) | ||||
−0.291056 | + | 0.956706i | \(0.594007\pi\) | |||||||
\(138\) | 736.376 | 0.454235 | ||||||||
\(139\) | 344.347 | − | 596.427i | 0.210123 | − | 0.363944i | −0.741630 | − | 0.670810i | \(-0.765947\pi\) |
0.951753 | + | 0.306865i | \(0.0992801\pi\) | |||||||
\(140\) | 74.1959 | 0.0447907 | ||||||||
\(141\) | 78.0527 | + | 135.191i | 0.0466186 | + | 0.0807458i | ||||
\(142\) | 395.810 | 0.233913 | ||||||||
\(143\) | 1800.34 | + | 3118.28i | 1.05281 | + | 1.82352i | ||||
\(144\) | 156.953 | + | 271.850i | 0.0908291 | + | 0.157321i | ||||
\(145\) | 66.8185 | + | 115.733i | 0.0382688 | + | 0.0662835i | ||||
\(146\) | −62.7530 | + | 108.691i | −0.0355718 | + | 0.0616121i | ||||
\(147\) | 619.778 | 0.347744 | ||||||||
\(148\) | −816.830 | − | 378.466i | −0.453669 | − | 0.210201i | ||||
\(149\) | −1001.72 | −0.550765 | −0.275383 | − | 0.961335i | \(-0.588805\pi\) | ||||
−0.275383 | + | 0.961335i | \(0.588805\pi\) | |||||||
\(150\) | 337.962 | − | 585.366i | 0.183963 | − | 0.318633i | ||||
\(151\) | −928.781 | − | 1608.70i | −0.500550 | − | 0.866979i | −1.00000 | 0.000635608i | \(-0.999798\pi\) | |
0.499449 | − | 0.866343i | \(-0.333536\pi\) | |||||||
\(152\) | −378.026 | − | 654.760i | −0.201723 | − | 0.349395i | ||||
\(153\) | 877.565 | + | 1519.99i | 0.463705 | + | 0.803161i | ||||
\(154\) | −2507.82 | −1.31225 | ||||||||
\(155\) | −111.255 | − | 192.699i | −0.0576528 | − | 0.0998576i | ||||
\(156\) | −745.763 | −0.382749 | ||||||||
\(157\) | −203.348 | + | 352.210i | −0.103369 | + | 0.179041i | −0.913071 | − | 0.407801i | \(-0.866296\pi\) |
0.809702 | + | 0.586842i | \(0.199629\pi\) | |||||||
\(158\) | 1672.97 | 0.842371 | ||||||||
\(159\) | 835.373 | 0.416663 | ||||||||
\(160\) | 12.4186 | − | 21.5096i | 0.00613610 | − | 0.0106280i | ||||
\(161\) | 1619.39 | + | 2804.86i | 0.792707 | + | 1.37301i | ||||
\(162\) | 371.247 | 0.180049 | ||||||||
\(163\) | −122.787 | + | 212.672i | −0.0590023 | + | 0.102195i | −0.894018 | − | 0.448031i | \(-0.852125\pi\) |
0.835015 | + | 0.550226i | \(0.185459\pi\) | |||||||
\(164\) | 320.894 | − | 555.805i | 0.152790 | − | 0.264641i | ||||
\(165\) | 55.3193 | − | 95.8159i | 0.0261006 | − | 0.0452076i | ||||
\(166\) | 876.013 | + | 1517.30i | 0.409589 | + | 0.709429i | ||||
\(167\) | 443.342 | + | 767.892i | 0.205430 | + | 0.355816i | 0.950270 | − | 0.311428i | \(-0.100807\pi\) |
−0.744839 | + | 0.667244i | \(0.767474\pi\) | |||||||
\(168\) | 259.706 | − | 449.824i | 0.119267 | − | 0.206576i | ||||
\(169\) | −1256.23 | + | 2175.85i | −0.571792 | + | 0.990373i | ||||
\(170\) | 69.4358 | − | 120.266i | 0.0313264 | − | 0.0542588i | ||||
\(171\) | −1854.13 | −0.829175 | ||||||||
\(172\) | 919.522 | + | 1592.66i | 0.407633 | + | 0.706041i | ||||
\(173\) | 1970.08 | − | 3412.27i | 0.865793 | − | 1.49960i | −0.000464763 | − | 1.00000i | \(-0.500148\pi\) |
0.866258 | − | 0.499597i | \(-0.166519\pi\) | |||||||
\(174\) | 935.534 | 0.407601 | ||||||||
\(175\) | 2972.89 | 1.28417 | ||||||||
\(176\) | −419.748 | + | 727.025i | −0.179771 | + | 0.311373i | ||||
\(177\) | 507.720 | 0.215608 | ||||||||
\(178\) | 1090.88 | + | 1889.45i | 0.459352 | + | 0.795621i | ||||
\(179\) | −3033.79 | −1.26680 | −0.633398 | − | 0.773826i | \(-0.718340\pi\) | ||||
−0.633398 | + | 0.773826i | \(0.718340\pi\) | |||||||
\(180\) | −30.4552 | − | 52.7499i | −0.0126111 | − | 0.0218430i | ||||
\(181\) | −420.366 | − | 728.095i | −0.172627 | − | 0.299000i | 0.766710 | − | 0.641993i | \(-0.221892\pi\) |
−0.939338 | + | 0.342994i | \(0.888559\pi\) | |||||||
\(182\) | −1640.03 | − | 2840.62i | −0.667952 | − | 1.15693i | ||||
\(183\) | 724.717 | − | 1255.25i | 0.292747 | − | 0.507052i | ||||
\(184\) | 1084.19 | 0.434388 | ||||||||
\(185\) | 158.498 | + | 73.4378i | 0.0629893 | + | 0.0291851i | ||||
\(186\) | −1557.69 | −0.614061 | ||||||||
\(187\) | −2346.93 | + | 4065.00i | −0.917777 | + | 1.58964i | ||||
\(188\) | 114.919 | + | 199.046i | 0.0445816 | + | 0.0772176i | ||||
\(189\) | −1513.41 | − | 2621.30i | −0.582456 | − | 1.00884i | ||||
\(190\) | 73.3524 | + | 127.050i | 0.0280081 | + | 0.0485115i | ||||
\(191\) | −2187.61 | −0.828742 | −0.414371 | − | 0.910108i | \(-0.635998\pi\) | ||||
−0.414371 | + | 0.910108i | \(0.635998\pi\) | |||||||
\(192\) | −86.9371 | − | 150.580i | −0.0326778 | − | 0.0565997i | ||||
\(193\) | −809.935 | −0.302075 | −0.151037 | − | 0.988528i | \(-0.548261\pi\) | ||||
−0.151037 | + | 0.988528i | \(0.548261\pi\) | |||||||
\(194\) | 1433.73 | − | 2483.29i | 0.530597 | − | 0.919021i | ||||
\(195\) | 144.708 | 0.0531424 | ||||||||
\(196\) | 912.517 | 0.332550 | ||||||||
\(197\) | −1574.13 | + | 2726.47i | −0.569299 | + | 0.986054i | 0.427337 | + | 0.904093i | \(0.359452\pi\) |
−0.996635 | + | 0.0819617i | \(0.973881\pi\) | |||||||
\(198\) | 1029.38 | + | 1782.95i | 0.369470 | + | 0.639942i | ||||
\(199\) | 2211.71 | 0.787861 | 0.393930 | − | 0.919140i | \(-0.371115\pi\) | ||||
0.393930 | + | 0.919140i | \(0.371115\pi\) | |||||||
\(200\) | 497.590 | − | 861.852i | 0.175925 | − | 0.304711i | ||||
\(201\) | −250.224 | + | 433.401i | −0.0878081 | + | 0.152088i | ||||
\(202\) | 483.484 | − | 837.420i | 0.168405 | − | 0.291686i | ||||
\(203\) | 2057.36 | + | 3563.46i | 0.711323 | + | 1.23205i | ||||
\(204\) | −486.089 | − | 841.931i | −0.166829 | − | 0.288956i | ||||
\(205\) | −62.2664 | + | 107.849i | −0.0212140 | + | 0.0367438i | ||||
\(206\) | 701.463 | − | 1214.97i | 0.237249 | − | 0.410927i | ||||
\(207\) | 1329.42 | − | 2302.63i | 0.446383 | − | 0.773157i | ||||
\(208\) | −1098.01 | −0.366025 | ||||||||
\(209\) | −2479.31 | − | 4294.29i | −0.820562 | − | 1.42125i | ||||
\(210\) | −50.3936 | + | 87.2842i | −0.0165595 | + | 0.0286818i | ||||
\(211\) | −632.160 | −0.206254 | −0.103127 | − | 0.994668i | \(-0.532885\pi\) | ||||
−0.103127 | + | 0.994668i | \(0.532885\pi\) | |||||||
\(212\) | 1229.94 | 0.398457 | ||||||||
\(213\) | −268.833 | + | 465.632i | −0.0864794 | + | 0.149787i | ||||
\(214\) | −1781.46 | −0.569055 | ||||||||
\(215\) | −178.425 | − | 309.040i | −0.0565974 | − | 0.0980297i | ||||
\(216\) | −1013.23 | −0.319175 | ||||||||
\(217\) | −3425.57 | − | 5933.26i | −1.07163 | − | 1.85611i | ||||
\(218\) | −1473.60 | − | 2552.34i | −0.457819 | − | 0.792965i | ||||
\(219\) | −85.2432 | − | 147.646i | −0.0263023 | − | 0.0455569i | ||||
\(220\) | 81.4482 | − | 141.072i | 0.0249602 | − | 0.0432323i | ||||
\(221\) | −6139.26 | −1.86865 | ||||||||
\(222\) | 1000.02 | − | 703.868i | 0.302328 | − | 0.212795i | ||||
\(223\) | −4755.80 | −1.42813 | −0.714063 | − | 0.700081i | \(-0.753147\pi\) | ||||
−0.714063 | + | 0.700081i | \(0.753147\pi\) | |||||||
\(224\) | 382.373 | − | 662.289i | 0.114055 | − | 0.197549i | ||||
\(225\) | −1220.28 | − | 2113.59i | −0.361565 | − | 0.626249i | ||||
\(226\) | 1659.11 | + | 2873.66i | 0.488328 | + | 0.845809i | ||||
\(227\) | 1537.87 | + | 2663.67i | 0.449657 | + | 0.778829i | 0.998364 | − | 0.0571860i | \(-0.0182128\pi\) |
−0.548706 | + | 0.836015i | \(0.684879\pi\) | |||||||
\(228\) | 1027.02 | 0.298315 | ||||||||
\(229\) | −358.860 | − | 621.564i | −0.103555 | − | 0.179363i | 0.809592 | − | 0.586993i | \(-0.199689\pi\) |
−0.913147 | + | 0.407630i | \(0.866355\pi\) | |||||||
\(230\) | −210.376 | −0.0603122 | ||||||||
\(231\) | 1703.30 | − | 2950.20i | 0.485147 | − | 0.840299i | ||||
\(232\) | 1377.41 | 0.389791 | ||||||||
\(233\) | 3630.44 | 1.02076 | 0.510382 | − | 0.859948i | \(-0.329504\pi\) | ||||
0.510382 | + | 0.859948i | \(0.329504\pi\) | |||||||
\(234\) | −1346.37 | + | 2331.98i | −0.376132 | + | 0.651479i | ||||
\(235\) | −22.2990 | − | 38.6230i | −0.00618990 | − | 0.0107212i | ||||
\(236\) | 747.531 | 0.206187 | ||||||||
\(237\) | −1136.28 | + | 1968.09i | −0.311431 | + | 0.539414i | ||||
\(238\) | 2137.95 | − | 3703.04i | 0.582281 | − | 1.00854i | ||||
\(239\) | −205.221 | + | 355.454i | −0.0555425 | + | 0.0962024i | −0.892460 | − | 0.451127i | \(-0.851022\pi\) |
0.836917 | + | 0.547329i | \(0.184355\pi\) | |||||||
\(240\) | 16.8693 | + | 29.2185i | 0.00453713 | + | 0.00785854i | ||||
\(241\) | 1122.13 | + | 1943.59i | 0.299929 | + | 0.519492i | 0.976119 | − | 0.217235i | \(-0.0697037\pi\) |
−0.676190 | + | 0.736727i | \(0.736370\pi\) | |||||||
\(242\) | −1421.95 | + | 2462.88i | −0.377712 | + | 0.654216i | ||||
\(243\) | −1961.98 | + | 3398.25i | −0.517946 | + | 0.897110i | ||||
\(244\) | 1067.02 | − | 1848.14i | 0.279955 | − | 0.484897i | ||||
\(245\) | −177.065 | −0.0461726 | ||||||||
\(246\) | 435.900 | + | 755.001i | 0.112975 | + | 0.195679i | ||||
\(247\) | 3242.78 | − | 5616.65i | 0.835356 | − | 1.44688i | ||||
\(248\) | −2293.43 | −0.587230 | ||||||||
\(249\) | −2379.94 | −0.605713 | ||||||||
\(250\) | −193.573 | + | 335.278i | −0.0489705 | + | 0.0848194i | ||||
\(251\) | −1176.80 | −0.295932 | −0.147966 | − | 0.988992i | \(-0.547273\pi\) | ||||
−0.147966 | + | 0.988992i | \(0.547273\pi\) | |||||||
\(252\) | −937.726 | − | 1624.19i | −0.234409 | − | 0.406009i | ||||
\(253\) | 7110.71 | 1.76698 | ||||||||
\(254\) | 2407.74 | + | 4170.33i | 0.594784 | + | 1.03020i | ||||
\(255\) | 94.3210 | + | 163.369i | 0.0231632 | + | 0.0401198i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1642.03 | + | 2844.09i | −0.398550 | + | 0.690308i | −0.993547 | − | 0.113419i | \(-0.963820\pi\) |
0.594998 | + | 0.803727i | \(0.297153\pi\) | |||||||
\(258\) | −2498.14 | −0.602820 | ||||||||
\(259\) | 4880.21 | + | 2261.17i | 1.17082 | + | 0.542481i | ||||
\(260\) | 213.058 | 0.0508204 | ||||||||
\(261\) | 1688.97 | − | 2925.39i | 0.400555 | − | 0.693781i | ||||
\(262\) | 259.149 | + | 448.859i | 0.0611079 | + | 0.105842i | ||||
\(263\) | −239.738 | − | 415.238i | −0.0562086 | − | 0.0973561i | 0.836552 | − | 0.547888i | \(-0.184568\pi\) |
−0.892761 | + | 0.450531i | \(0.851235\pi\) | |||||||
\(264\) | −570.183 | − | 987.586i | −0.132926 | − | 0.230234i | ||||
\(265\) | −238.659 | −0.0553234 | ||||||||
\(266\) | 2258.55 | + | 3911.92i | 0.520603 | + | 0.901710i | ||||
\(267\) | −2963.68 | −0.679304 | ||||||||
\(268\) | −368.412 | + | 638.108i | −0.0839714 | + | 0.145443i | ||||
\(269\) | 1408.00 | 0.319134 | 0.159567 | − | 0.987187i | \(-0.448990\pi\) | ||||
0.159567 | + | 0.987187i | \(0.448990\pi\) | |||||||
\(270\) | 196.608 | 0.0443155 | ||||||||
\(271\) | 809.175 | − | 1401.53i | 0.181380 | − | 0.314159i | −0.760971 | − | 0.648786i | \(-0.775277\pi\) |
0.942351 | + | 0.334627i | \(0.108610\pi\) | |||||||
\(272\) | −715.683 | − | 1239.60i | −0.159539 | − | 0.276330i | ||||
\(273\) | 4455.62 | 0.987788 | ||||||||
\(274\) | 933.443 | − | 1616.77i | 0.205808 | − | 0.356469i | ||||
\(275\) | 3263.48 | − | 5652.51i | 0.715619 | − | 1.23949i | ||||
\(276\) | −736.376 | + | 1275.44i | −0.160596 | + | 0.278161i | ||||
\(277\) | 3653.07 | + | 6327.31i | 0.792389 | + | 1.37246i | 0.924484 | + | 0.381221i | \(0.124496\pi\) |
−0.132094 | + | 0.991237i | \(0.542170\pi\) | |||||||
\(278\) | 688.694 | + | 1192.85i | 0.148580 | + | 0.257348i | ||||
\(279\) | −2812.19 | + | 4870.85i | −0.603445 | + | 1.04520i | ||||
\(280\) | −74.1959 | + | 128.511i | −0.0158359 | + | 0.0274286i | ||||
\(281\) | −2299.27 | + | 3982.46i | −0.488125 | + | 0.845458i | −0.999907 | − | 0.0136580i | \(-0.995652\pi\) |
0.511782 | + | 0.859116i | \(0.328986\pi\) | |||||||
\(282\) | −312.211 | −0.0659287 | ||||||||
\(283\) | 4279.73 | + | 7412.71i | 0.898953 | + | 1.55703i | 0.828835 | + | 0.559493i | \(0.189004\pi\) |
0.0701175 | + | 0.997539i | \(0.477663\pi\) | |||||||
\(284\) | −395.810 | + | 685.563i | −0.0827007 | + | 0.143242i | ||||
\(285\) | −199.283 | −0.0414193 | ||||||||
\(286\) | −7201.35 | −1.48890 | ||||||||
\(287\) | −1917.21 | + | 3320.70i | −0.394317 | + | 0.682978i | ||||
\(288\) | −627.810 | −0.128452 | ||||||||
\(289\) | −1545.08 | − | 2676.16i | −0.314488 | − | 0.544709i | ||||
\(290\) | −267.274 | −0.0541202 | ||||||||
\(291\) | 1947.57 | + | 3373.29i | 0.392331 | + | 0.679538i | ||||
\(292\) | −125.506 | − | 217.383i | −0.0251530 | − | 0.0435663i | ||||
\(293\) | −1087.91 | − | 1884.32i | −0.216916 | − | 0.375710i | 0.736947 | − | 0.675950i | \(-0.236266\pi\) |
−0.953864 | + | 0.300240i | \(0.902933\pi\) | |||||||
\(294\) | −619.778 | + | 1073.49i | −0.122946 | + | 0.212949i | ||||
\(295\) | −145.051 | −0.0286279 | ||||||||
\(296\) | 1472.35 | − | 1036.33i | 0.289117 | − | 0.203497i | ||||
\(297\) | −6645.35 | −1.29832 | ||||||||
\(298\) | 1001.72 | − | 1735.03i | 0.194725 | − | 0.337273i | ||||
\(299\) | 4650.18 | + | 8054.34i | 0.899420 | + | 1.55784i | ||||
\(300\) | 675.923 | + | 1170.73i | 0.130081 | + | 0.225308i | ||||
\(301\) | −5493.75 | − | 9515.46i | −1.05201 | − | 1.82213i | ||||
\(302\) | 3715.12 | 0.707885 | ||||||||
\(303\) | 656.762 | + | 1137.54i | 0.124521 | + | 0.215677i | ||||
\(304\) | 1512.10 | 0.285280 | ||||||||
\(305\) | −207.045 | + | 358.613i | −0.0388701 | + | 0.0673250i | ||||
\(306\) | −3510.26 | −0.655778 | ||||||||
\(307\) | −3546.01 | −0.659223 | −0.329612 | − | 0.944117i | \(-0.606918\pi\) | ||||
−0.329612 | + | 0.944117i | \(0.606918\pi\) | |||||||
\(308\) | 2507.82 | − | 4343.67i | 0.463949 | − | 0.803583i | ||||
\(309\) | 952.862 | + | 1650.41i | 0.175425 | + | 0.303846i | ||||
\(310\) | 445.019 | 0.0815334 | ||||||||
\(311\) | 5032.15 | − | 8715.93i | 0.917514 | − | 1.58918i | 0.114335 | − | 0.993442i | \(-0.463526\pi\) |
0.803179 | − | 0.595738i | \(-0.203140\pi\) | |||||||
\(312\) | 745.763 | − | 1291.70i | 0.135322 | − | 0.234385i | ||||
\(313\) | 3854.56 | − | 6676.29i | 0.696078 | − | 1.20564i | −0.273738 | − | 0.961804i | \(-0.588260\pi\) |
0.969816 | − | 0.243839i | \(-0.0784067\pi\) | |||||||
\(314\) | −406.697 | − | 704.420i | −0.0730931 | − | 0.126601i | ||||
\(315\) | 181.957 | + | 315.158i | 0.0325464 | + | 0.0563719i | ||||
\(316\) | −1672.97 | + | 2897.68i | −0.297823 | + | 0.515845i | ||||
\(317\) | −4863.44 | + | 8423.72i | −0.861696 | + | 1.49250i | 0.00859393 | + | 0.999963i | \(0.497264\pi\) |
−0.870290 | + | 0.492539i | \(0.836069\pi\) | |||||||
\(318\) | −835.373 | + | 1446.91i | −0.147312 | + | 0.255153i | ||||
\(319\) | 9033.85 | 1.58558 | ||||||||
\(320\) | 24.8372 | + | 43.0193i | 0.00433888 | + | 0.00751516i | ||||
\(321\) | 1209.96 | − | 2095.71i | 0.210384 | − | 0.364396i | ||||
\(322\) | −6477.56 | −1.12106 | ||||||||
\(323\) | 8454.59 | 1.45643 | ||||||||
\(324\) | −371.247 | + | 643.018i | −0.0636568 | + | 0.110257i | ||||
\(325\) | 8536.84 | 1.45704 | ||||||||
\(326\) | −245.573 | − | 425.345i | −0.0417210 | − | 0.0722628i | ||||
\(327\) | 4003.44 | 0.677036 | ||||||||
\(328\) | 641.788 | + | 1111.61i | 0.108039 | + | 0.187129i | ||||
\(329\) | −686.594 | − | 1189.22i | −0.115055 | − | 0.199281i | ||||
\(330\) | 110.639 | + | 191.632i | 0.0184559 | + | 0.0319666i | ||||
\(331\) | 2150.24 | − | 3724.32i | 0.357062 | − | 0.618450i | −0.630406 | − | 0.776265i | \(-0.717112\pi\) |
0.987469 | + | 0.157815i | \(0.0504450\pi\) | |||||||
\(332\) | −3504.05 | −0.579247 | ||||||||
\(333\) | −395.588 | − | 4397.76i | −0.0650994 | − | 0.723710i | ||||
\(334\) | −1773.37 | −0.290522 | ||||||||
\(335\) | 71.4868 | − | 123.819i | 0.0116589 | − | 0.0201939i | ||||
\(336\) | 519.413 | + | 899.649i | 0.0843342 | + | 0.146071i | ||||
\(337\) | −4687.63 | − | 8119.21i | −0.757719 | − | 1.31241i | −0.944011 | − | 0.329913i | \(-0.892980\pi\) |
0.186292 | − | 0.982494i | \(-0.440353\pi\) | |||||||
\(338\) | −2512.45 | − | 4351.70i | −0.404318 | − | 0.700299i | ||||
\(339\) | −4507.44 | −0.722154 | ||||||||
\(340\) | 138.872 | + | 240.533i | 0.0221511 | + | 0.0383668i | ||||
\(341\) | −15041.6 | −2.38871 | ||||||||
\(342\) | 1854.13 | − | 3211.45i | 0.293158 | − | 0.507764i | ||||
\(343\) | 2745.22 | 0.432151 | ||||||||
\(344\) | −3678.09 | −0.576480 | ||||||||
\(345\) | 142.887 | − | 247.487i | 0.0222979 | − | 0.0386210i | ||||
\(346\) | 3940.15 | + | 6824.55i | 0.612208 | + | 1.06038i | ||||
\(347\) | −2361.85 | −0.365391 | −0.182695 | − | 0.983170i | \(-0.558482\pi\) | ||||
−0.182695 | + | 0.983170i | \(0.558482\pi\) | |||||||
\(348\) | −935.534 | + | 1620.39i | −0.144109 | + | 0.249604i | ||||
\(349\) | −1058.43 | + | 1833.25i | −0.162339 | + | 0.281180i | −0.935707 | − | 0.352777i | \(-0.885237\pi\) |
0.773368 | + | 0.633958i | \(0.218571\pi\) | |||||||
\(350\) | −2972.89 | + | 5149.20i | −0.454022 | + | 0.786389i | ||||
\(351\) | −4345.85 | − | 7527.23i | −0.660866 | − | 1.14465i | ||||
\(352\) | −839.497 | − | 1454.05i | −0.127117 | − | 0.220174i | ||||
\(353\) | 1964.66 | − | 3402.89i | 0.296227 | − | 0.513081i | −0.679042 | − | 0.734099i | \(-0.737605\pi\) |
0.975270 | + | 0.221018i | \(0.0709381\pi\) | |||||||
\(354\) | −507.720 | + | 879.397i | −0.0762289 | + | 0.132032i | ||||
\(355\) | 76.8032 | − | 133.027i | 0.0114825 | − | 0.0198883i | ||||
\(356\) | −4363.51 | −0.649622 | ||||||||
\(357\) | 2904.18 | + | 5030.18i | 0.430547 | + | 0.745730i | ||||
\(358\) | 3033.79 | − | 5254.68i | 0.447880 | − | 0.775751i | ||||
\(359\) | 1087.17 | 0.159829 | 0.0799143 | − | 0.996802i | \(-0.474535\pi\) | ||||
0.0799143 | + | 0.996802i | \(0.474535\pi\) | |||||||
\(360\) | 121.821 | 0.0178348 | ||||||||
\(361\) | −1036.24 | + | 1794.82i | −0.151078 | + | 0.261674i | ||||
\(362\) | 1681.46 | 0.244132 | ||||||||
\(363\) | −1931.56 | − | 3345.56i | −0.279286 | − | 0.483737i | ||||
\(364\) | 6560.13 | 0.944627 | ||||||||
\(365\) | 24.3533 | + | 42.1811i | 0.00349235 | + | 0.00604893i | ||||
\(366\) | 1449.43 | + | 2510.49i | 0.207003 | + | 0.358540i | ||||
\(367\) | −2223.20 | − | 3850.69i | −0.316213 | − | 0.547696i | 0.663482 | − | 0.748192i | \(-0.269078\pi\) |
−0.979695 | + | 0.200496i | \(0.935745\pi\) | |||||||
\(368\) | −1084.19 | + | 1877.87i | −0.153579 | + | 0.266007i | ||||
\(369\) | 3147.82 | 0.444090 | ||||||||
\(370\) | −285.696 | + | 201.089i | −0.0401423 | + | 0.0282544i | ||||
\(371\) | −7348.39 | −1.02833 | ||||||||
\(372\) | 1557.69 | − | 2698.00i | 0.217103 | − | 0.376034i | ||||
\(373\) | −1089.61 | − | 1887.26i | −0.151254 | − | 0.261980i | 0.780435 | − | 0.625237i | \(-0.214998\pi\) |
−0.931689 | + | 0.363258i | \(0.881665\pi\) | |||||||
\(374\) | −4693.85 | − | 8129.99i | −0.648966 | − | 1.12404i | ||||
\(375\) | −262.948 | − | 455.440i | −0.0362096 | − | 0.0627168i | ||||
\(376\) | −459.677 | −0.0630479 | ||||||||
\(377\) | 5907.85 | + | 10232.7i | 0.807081 | + | 1.39791i | ||||
\(378\) | 6053.63 | 0.823718 | ||||||||
\(379\) | −5269.65 | + | 9127.30i | −0.714205 | + | 1.23704i | 0.249061 | + | 0.968488i | \(0.419878\pi\) |
−0.963265 | + | 0.268551i | \(0.913455\pi\) | |||||||
\(380\) | −293.410 | −0.0396095 | ||||||||
\(381\) | −6541.32 | −0.879585 | ||||||||
\(382\) | 2187.61 | − | 3789.05i | 0.293005 | − | 0.507499i | ||||
\(383\) | −2792.81 | − | 4837.29i | −0.372600 | − | 0.645363i | 0.617364 | − | 0.786677i | \(-0.288200\pi\) |
−0.989965 | + | 0.141314i | \(0.954867\pi\) | |||||||
\(384\) | 347.749 | 0.0462135 | ||||||||
\(385\) | −486.618 | + | 842.848i | −0.0644166 | + | 0.111573i | ||||
\(386\) | 809.935 | − | 1402.85i | 0.106800 | − | 0.184982i | ||||
\(387\) | −4510.04 | + | 7811.62i | −0.592399 | + | 1.02606i | ||||
\(388\) | 2867.46 | + | 4966.58i | 0.375189 | + | 0.649846i | ||||
\(389\) | −1487.31 | − | 2576.09i | −0.193855 | − | 0.335766i | 0.752670 | − | 0.658398i | \(-0.228766\pi\) |
−0.946524 | + | 0.322632i | \(0.895432\pi\) | |||||||
\(390\) | −144.708 | + | 250.642i | −0.0187887 | + | 0.0325429i | ||||
\(391\) | −6061.99 | + | 10499.7i | −0.784061 | + | 1.35803i | ||||
\(392\) | −912.517 | + | 1580.52i | −0.117574 | + | 0.203644i | ||||
\(393\) | −704.052 | −0.0903683 | ||||||||
\(394\) | −3148.25 | − | 5452.93i | −0.402555 | − | 0.697246i | ||||
\(395\) | 324.625 | − | 562.266i | 0.0413510 | − | 0.0716220i | ||||
\(396\) | −4117.54 | −0.522510 | ||||||||
\(397\) | 11005.6 | 1.39133 | 0.695663 | − | 0.718369i | \(-0.255111\pi\) | ||||
0.695663 | + | 0.718369i | \(0.255111\pi\) | |||||||
\(398\) | −2211.71 | + | 3830.80i | −0.278551 | + | 0.482464i | ||||
\(399\) | −6135.98 | −0.769883 | ||||||||
\(400\) | 995.181 | + | 1723.70i | 0.124398 | + | 0.215463i | ||||
\(401\) | 11819.7 | 1.47194 | 0.735971 | − | 0.677013i | \(-0.236726\pi\) | ||||
0.735971 | + | 0.677013i | \(0.236726\pi\) | |||||||
\(402\) | −500.448 | − | 866.801i | −0.0620897 | − | 0.107543i | ||||
\(403\) | −9836.73 | − | 17037.7i | −1.21589 | − | 2.10598i | ||||
\(404\) | 966.969 | + | 1674.84i | 0.119080 | + | 0.206253i | ||||
\(405\) | 72.0369 | − | 124.772i | 0.00883838 | − | 0.0153085i | ||||
\(406\) | −8229.46 | −1.00596 | ||||||||
\(407\) | 9656.52 | − | 6796.81i | 1.17606 | − | 0.827777i | ||||
\(408\) | 1944.36 | 0.235931 | ||||||||
\(409\) | −1155.34 | + | 2001.11i | −0.139677 | + | 0.241928i | −0.927375 | − | 0.374134i | \(-0.877940\pi\) |
0.787697 | + | 0.616063i | \(0.211273\pi\) | |||||||
\(410\) | −124.533 | − | 215.697i | −0.0150006 | − | 0.0259818i | ||||
\(411\) | 1267.98 | + | 2196.21i | 0.152177 | + | 0.263579i | ||||
\(412\) | 1402.93 | + | 2429.94i | 0.167760 | + | 0.290569i | ||||
\(413\) | −4466.18 | −0.532122 | ||||||||
\(414\) | 2658.84 | + | 4605.25i | 0.315640 | + | 0.546705i | ||||
\(415\) | 679.928 | 0.0804250 | ||||||||
\(416\) | 1098.01 | − | 1901.80i | 0.129409 | − | 0.224143i | ||||
\(417\) | −1871.03 | −0.219724 | ||||||||
\(418\) | 9917.24 | 1.16045 | ||||||||
\(419\) | −5214.15 | + | 9031.16i | −0.607942 | + | 1.05299i | 0.383637 | + | 0.923484i | \(0.374671\pi\) |
−0.991579 | + | 0.129502i | \(0.958662\pi\) | |||||||
\(420\) | −100.787 | − | 174.568i | −0.0117093 | − | 0.0202811i | ||||
\(421\) | 12564.4 | 1.45451 | 0.727257 | − | 0.686366i | \(-0.240795\pi\) | ||||
0.727257 | + | 0.686366i | \(0.240795\pi\) | |||||||
\(422\) | 632.160 | − | 1094.93i | 0.0729219 | − | 0.126305i | ||||
\(423\) | −563.652 | + | 976.274i | −0.0647889 | + | 0.112218i | ||||
\(424\) | −1229.94 | + | 2130.32i | −0.140876 | + | 0.244004i | ||||
\(425\) | 5564.33 | + | 9637.70i | 0.635081 | + | 1.09999i | ||||
\(426\) | −537.666 | − | 931.264i | −0.0611502 | − | 0.105915i | ||||
\(427\) | −6375.00 | + | 11041.8i | −0.722501 | + | 1.25141i | ||||
\(428\) | 1781.46 | − | 3085.57i | 0.201191 | − | 0.348474i | ||||
\(429\) | 4891.13 | − | 8471.69i | 0.550457 | − | 0.953420i | ||||
\(430\) | 713.698 | 0.0800409 | ||||||||
\(431\) | −4556.08 | − | 7891.37i | −0.509185 | − | 0.881935i | −0.999943 | − | 0.0106388i | \(-0.996614\pi\) |
0.490758 | − | 0.871296i | \(-0.336720\pi\) | |||||||
\(432\) | 1013.23 | − | 1754.97i | 0.112845 | − | 0.195454i | ||||
\(433\) | −8620.44 | −0.956748 | −0.478374 | − | 0.878156i | \(-0.658774\pi\) | ||||
−0.478374 | + | 0.878156i | \(0.658774\pi\) | |||||||
\(434\) | 13702.3 | 1.51551 | ||||||||
\(435\) | 181.531 | − | 314.422i | 0.0200087 | − | 0.0346560i | ||||
\(436\) | 5894.38 | 0.647453 | ||||||||
\(437\) | −6403.92 | − | 11091.9i | −0.701009 | − | 1.21418i | ||||
\(438\) | 340.973 | 0.0371971 | ||||||||
\(439\) | 653.694 | + | 1132.23i | 0.0710686 | + | 0.123094i | 0.899370 | − | 0.437188i | \(-0.144026\pi\) |
−0.828301 | + | 0.560283i | \(0.810692\pi\) | |||||||
\(440\) | 162.896 | + | 282.145i | 0.0176495 | + | 0.0305698i | ||||
\(441\) | 2237.84 | + | 3876.06i | 0.241641 | + | 0.418535i | ||||
\(442\) | 6139.26 | − | 10633.5i | 0.660667 | − | 1.14431i | ||||
\(443\) | 13166.5 | 1.41209 | 0.706046 | − | 0.708166i | \(-0.250477\pi\) | ||||
0.706046 | + | 0.708166i | \(0.250477\pi\) | |||||||
\(444\) | 219.119 | + | 2435.95i | 0.0234210 | + | 0.260372i | ||||
\(445\) | 846.697 | 0.0901962 | ||||||||
\(446\) | 4755.80 | − | 8237.30i | 0.504919 | − | 0.874545i | ||||
\(447\) | 1360.73 | + | 2356.85i | 0.143983 | + | 0.249385i | ||||
\(448\) | 764.746 | + | 1324.58i | 0.0806492 | + | 0.139689i | ||||
\(449\) | 6928.66 | + | 12000.8i | 0.728249 | + | 1.26136i | 0.957623 | + | 0.288026i | \(0.0929989\pi\) |
−0.229373 | + | 0.973338i | \(0.573668\pi\) | |||||||
\(450\) | 4881.13 | 0.511331 | ||||||||
\(451\) | 4209.21 | + | 7290.56i | 0.439477 | + | 0.761196i | ||||
\(452\) | −6636.43 | −0.690600 | ||||||||
\(453\) | −2523.30 | + | 4370.48i | −0.261711 | + | 0.453296i | ||||
\(454\) | −6151.49 | −0.635911 | ||||||||
\(455\) | −1272.93 | −0.131156 | ||||||||
\(456\) | −1027.02 | + | 1778.84i | −0.105470 | + | 0.182680i | ||||
\(457\) | 3569.12 | + | 6181.89i | 0.365331 | + | 0.632772i | 0.988829 | − | 0.149053i | \(-0.0476225\pi\) |
−0.623498 | + | 0.781825i | \(0.714289\pi\) | |||||||
\(458\) | 1435.44 | 0.146449 | ||||||||
\(459\) | 5665.26 | − | 9812.52i | 0.576104 | − | 0.997841i | ||||
\(460\) | 210.376 | − | 364.382i | 0.0213236 | − | 0.0369335i | ||||
\(461\) | 173.069 | − | 299.764i | 0.0174851 | − | 0.0302851i | −0.857150 | − | 0.515066i | \(-0.827767\pi\) |
0.874636 | + | 0.484781i | \(0.161101\pi\) | |||||||
\(462\) | 3406.60 | + | 5900.41i | 0.343051 | + | 0.594181i | ||||
\(463\) | −296.192 | − | 513.020i | −0.0297305 | − | 0.0514947i | 0.850777 | − | 0.525526i | \(-0.176132\pi\) |
−0.880508 | + | 0.474032i | \(0.842798\pi\) | |||||||
\(464\) | −1377.41 | + | 2385.75i | −0.137812 | + | 0.238697i | ||||
\(465\) | −302.255 | + | 523.521i | −0.0301435 | + | 0.0522101i | ||||
\(466\) | −3630.44 | + | 6288.11i | −0.360895 | + | 0.625088i | ||||
\(467\) | −7407.74 | −0.734024 | −0.367012 | − | 0.930216i | \(-0.619619\pi\) | ||||
−0.367012 | + | 0.930216i | \(0.619619\pi\) | |||||||
\(468\) | −2692.74 | − | 4663.96i | −0.265965 | − | 0.460666i | ||||
\(469\) | 2201.10 | − | 3812.42i | 0.216711 | − | 0.375355i | ||||
\(470\) | 89.1959 | 0.00875383 | ||||||||
\(471\) | 1104.91 | 0.108092 | ||||||||
\(472\) | −747.531 | + | 1294.76i | −0.0728981 | + | 0.126263i | ||||
\(473\) | −24123.0 | −2.34498 | ||||||||
\(474\) | −2272.55 | − | 3936.18i | −0.220215 | − | 0.381424i | ||||
\(475\) | −11756.4 | −1.13562 | ||||||||
\(476\) | 4275.90 | + | 7406.08i | 0.411735 | + | 0.713145i | ||||
\(477\) | 3016.29 | + | 5224.37i | 0.289532 | + | 0.501483i | ||||
\(478\) | −410.442 | − | 710.907i | −0.0392745 | − | 0.0680254i | ||||
\(479\) | 3755.62 | − | 6504.93i | 0.358244 | − | 0.620496i | −0.629424 | − | 0.777062i | \(-0.716709\pi\) |
0.987668 | + | 0.156566i | \(0.0500424\pi\) | |||||||
\(480\) | −67.4773 | −0.00641647 | ||||||||
\(481\) | 14013.8 | + | 6493.10i | 1.32843 | + | 0.615509i | ||||
\(482\) | −4488.53 | −0.424164 | ||||||||
\(483\) | 4399.53 | − | 7620.22i | 0.414463 | − | 0.717871i | ||||
\(484\) | −2843.89 | − | 4925.77i | −0.267082 | − | 0.462600i | ||||
\(485\) | −556.403 | − | 963.719i | −0.0520927 | − | 0.0902273i | ||||
\(486\) | −3923.96 | − | 6796.49i | −0.366243 | − | 0.634352i | ||||
\(487\) | −10382.4 | −0.966057 | −0.483029 | − | 0.875605i | \(-0.660463\pi\) | ||||
−0.483029 | + | 0.875605i | \(0.660463\pi\) | |||||||
\(488\) | 2134.04 | + | 3696.27i | 0.197958 | + | 0.342874i | ||||
\(489\) | 667.169 | 0.0616982 | ||||||||
\(490\) | 177.065 | − | 306.686i | 0.0163245 | − | 0.0282748i | ||||
\(491\) | 789.050 | 0.0725241 | 0.0362620 | − | 0.999342i | \(-0.488455\pi\) | ||||
0.0362620 | + | 0.999342i | \(0.488455\pi\) | |||||||
\(492\) | −1743.60 | −0.159771 | ||||||||
\(493\) | −7701.49 | + | 13339.4i | −0.703565 | + | 1.21861i | ||||
\(494\) | 6485.55 | + | 11233.3i | 0.590686 | + | 1.02310i | ||||
\(495\) | 798.969 | 0.0725475 | ||||||||
\(496\) | 2293.43 | − | 3972.34i | 0.207617 | − | 0.359603i | ||||
\(497\) | 2364.80 | − | 4095.95i | 0.213432 | − | 0.369675i | ||||
\(498\) | 2379.94 | − | 4122.18i | 0.214152 | − | 0.370922i | ||||
\(499\) | 6298.52 | + | 10909.4i | 0.565051 | + | 0.978697i | 0.997045 | + | 0.0768202i | \(0.0244768\pi\) |
−0.431994 | + | 0.901876i | \(0.642190\pi\) | |||||||
\(500\) | −387.146 | − | 670.556i | −0.0346274 | − | 0.0599764i | ||||
\(501\) | 1204.47 | − | 2086.20i | 0.107408 | − | 0.186037i | ||||
\(502\) | 1176.80 | − | 2038.28i | 0.104628 | − | 0.181221i | ||||
\(503\) | −54.7405 | + | 94.8133i | −0.00485240 | + | 0.00840461i | −0.868441 | − | 0.495792i | \(-0.834878\pi\) |
0.863589 | + | 0.504196i | \(0.168211\pi\) | |||||||
\(504\) | 3750.90 | 0.331505 | ||||||||
\(505\) | −187.631 | − | 324.987i | −0.0165336 | − | 0.0286371i | ||||
\(506\) | −7110.71 | + | 12316.1i | −0.624723 | + | 1.08205i | ||||
\(507\) | 6825.80 | 0.597918 | ||||||||
\(508\) | −9630.97 | −0.841152 | ||||||||
\(509\) | 8335.62 | − | 14437.7i | 0.725874 | − | 1.25725i | −0.232740 | − | 0.972539i | \(-0.574769\pi\) |
0.958613 | − | 0.284711i | \(-0.0918977\pi\) | |||||||
\(510\) | −377.284 | −0.0327577 | ||||||||
\(511\) | 749.845 | + | 1298.77i | 0.0649143 | + | 0.112435i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 5984.82 | + | 10366.0i | 0.515080 | + | 0.892145i | ||||
\(514\) | −3284.07 | − | 5688.17i | −0.281817 | − | 0.488122i | ||||
\(515\) | −272.225 | − | 471.507i | −0.0232925 | − | 0.0403438i | ||||
\(516\) | 2498.14 | − | 4326.91i | 0.213129 | − | 0.369150i | ||||
\(517\) | −3014.82 | −0.256464 | ||||||||
\(518\) | −8796.68 | + | 6191.60i | −0.746147 | + | 0.525180i | ||||
\(519\) | −10704.6 | −0.905352 | ||||||||
\(520\) | −213.058 | + | 369.027i | −0.0179677 | + | 0.0311210i | ||||
\(521\) | −9189.88 | − | 15917.3i | −0.772775 | − | 1.33849i | −0.936036 | − | 0.351903i | \(-0.885535\pi\) |
0.163261 | − | 0.986583i | \(-0.447799\pi\) | |||||||
\(522\) | 3377.95 | + | 5850.77i | 0.283235 | + | 0.490577i | ||||
\(523\) | −1343.48 | − | 2326.97i | −0.112325 | − | 0.194553i | 0.804382 | − | 0.594112i | \(-0.202497\pi\) |
−0.916707 | + | 0.399559i | \(0.869163\pi\) | |||||||
\(524\) | −1036.60 | −0.0864196 | ||||||||
\(525\) | −4038.35 | − | 6994.63i | −0.335711 | − | 0.581468i | ||||
\(526\) | 958.950 | 0.0794909 | ||||||||
\(527\) | 12823.2 | − | 22210.4i | 1.05994 | − | 1.83587i | ||||
\(528\) | 2280.73 | 0.187985 | ||||||||
\(529\) | 6199.58 | 0.509541 | ||||||||
\(530\) | 238.659 | − | 413.369i | 0.0195598 | − | 0.0338785i | ||||
\(531\) | 1833.23 | + | 3175.25i | 0.149822 | + | 0.259500i | ||||
\(532\) | −9034.18 | −0.736243 | ||||||||
\(533\) | −5505.37 | + | 9535.59i | −0.447400 | + | 0.774920i | ||||
\(534\) | 2963.68 | − | 5133.24i | 0.240170 | − | 0.415987i | ||||
\(535\) | −345.675 | + | 598.726i | −0.0279342 | + | 0.0483835i | ||||
\(536\) | −736.823 | − | 1276.22i | −0.0593767 | − | 0.102844i | ||||
\(537\) | 4121.08 | + | 7137.92i | 0.331169 | + | 0.573602i | ||||
\(538\) | −1408.00 | + | 2438.72i | −0.112831 | + | 0.195429i | ||||
\(539\) | −5984.80 | + | 10366.0i | −0.478263 | + | 0.828375i | ||||
\(540\) | −196.608 | + | 340.535i | −0.0156679 | + | 0.0271376i | ||||
\(541\) | −13884.4 | −1.10339 | −0.551697 | − | 0.834045i | \(-0.686020\pi\) | ||||
−0.551697 | + | 0.834045i | \(0.686020\pi\) | |||||||
\(542\) | 1618.35 | + | 2803.06i | 0.128255 | + | 0.222144i | ||||
\(543\) | −1142.04 | + | 1978.08i | −0.0902575 | + | 0.156331i | ||||
\(544\) | 2862.73 | 0.225622 | ||||||||
\(545\) | −1143.75 | −0.0898951 | ||||||||
\(546\) | −4455.62 | + | 7717.35i | −0.349236 | + | 0.604894i | ||||
\(547\) | −10032.0 | −0.784161 | −0.392080 | − | 0.919931i | \(-0.628245\pi\) | ||||
−0.392080 | + | 0.919931i | \(0.628245\pi\) | |||||||
\(548\) | 1866.89 | + | 3233.54i | 0.145528 | + | 0.252062i | ||||
\(549\) | 10467.0 | 0.813698 | ||||||||
\(550\) | 6526.96 | + | 11305.0i | 0.506019 | + | 0.876451i | ||||
\(551\) | −8135.90 | − | 14091.8i | −0.629040 | − | 1.08953i | ||||
\(552\) | −1472.75 | − | 2550.88i | −0.113559 | − | 0.196690i | ||||
\(553\) | 9995.31 | − | 17312.4i | 0.768614 | − | 1.33128i | ||||
\(554\) | −14612.3 | −1.12061 | ||||||||
\(555\) | −42.5180 | − | 472.673i | −0.00325187 | − | 0.0361511i | ||||
\(556\) | −2754.78 | −0.210123 | ||||||||
\(557\) | −3402.32 | + | 5892.99i | −0.258817 | + | 0.448284i | −0.965925 | − | 0.258821i | \(-0.916666\pi\) |
0.707108 | + | 0.707105i | \(0.249999\pi\) | |||||||
\(558\) | −5624.37 | − | 9741.70i | −0.426700 | − | 0.739066i | ||||
\(559\) | −15775.7 | − | 27324.2i | −1.19363 | − | 2.06743i | ||||
\(560\) | −148.392 | − | 257.022i | −0.0111977 | − | 0.0193949i | ||||
\(561\) | 12752.2 | 0.959711 | ||||||||
\(562\) | −4598.55 | − | 7964.92i | −0.345157 | − | 0.597829i | ||||
\(563\) | 6070.28 | 0.454409 | 0.227204 | − | 0.973847i | \(-0.427041\pi\) | ||||
0.227204 | + | 0.973847i | \(0.427041\pi\) | |||||||
\(564\) | 312.211 | − | 540.765i | 0.0233093 | − | 0.0403729i | ||||
\(565\) | 1287.74 | 0.0958858 | ||||||||
\(566\) | −17118.9 | −1.27131 | ||||||||
\(567\) | 2218.04 | − | 3841.76i | 0.164284 | − | 0.284548i | ||||
\(568\) | −791.620 | − | 1371.13i | −0.0584783 | − | 0.101287i | ||||
\(569\) | −3086.82 | −0.227428 | −0.113714 | − | 0.993514i | \(-0.536275\pi\) | ||||
−0.113714 | + | 0.993514i | \(0.536275\pi\) | |||||||
\(570\) | 199.283 | − | 345.168i | 0.0146439 | − | 0.0253640i | ||||
\(571\) | 6743.89 | − | 11680.8i | 0.494261 | − | 0.856086i | −0.505717 | − | 0.862700i | \(-0.668772\pi\) |
0.999978 | + | 0.00661383i | \(0.00210526\pi\) | |||||||
\(572\) | 7201.35 | − | 12473.1i | 0.526405 | − | 0.911760i | ||||
\(573\) | 2971.63 | + | 5147.01i | 0.216652 | + | 0.375252i | ||||
\(574\) | −3834.41 | − | 6641.40i | −0.278824 | − | 0.482938i | ||||
\(575\) | 8429.39 | − | 14600.1i | 0.611356 | − | 1.05890i | ||||
\(576\) | 627.810 | − | 1087.40i | 0.0454145 | − | 0.0786603i | ||||
\(577\) | −11779.0 | + | 20401.8i | −0.849855 | + | 1.47199i | 0.0314832 | + | 0.999504i | \(0.489977\pi\) |
−0.881338 | + | 0.472487i | \(0.843356\pi\) | |||||||
\(578\) | 6180.32 | 0.444753 | ||||||||
\(579\) | 1100.21 | + | 1905.62i | 0.0789692 | + | 0.136779i | ||||
\(580\) | 267.274 | − | 462.932i | 0.0191344 | − | 0.0331417i | ||||
\(581\) | 20935.2 | 1.49491 | ||||||||
\(582\) | −7790.27 | −0.554840 | ||||||||
\(583\) | −8066.66 | + | 13971.9i | −0.573048 | + | 0.992548i | ||||
\(584\) | 502.024 | 0.0355718 | ||||||||
\(585\) | 522.500 | + | 904.997i | 0.0369277 | + | 0.0639607i | ||||
\(586\) | 4351.64 | 0.306766 | ||||||||
\(587\) | −7994.37 | − | 13846.7i | −0.562118 | − | 0.973616i | −0.997311 | − | 0.0732795i | \(-0.976653\pi\) |
0.435194 | − | 0.900337i | \(-0.356680\pi\) | |||||||
\(588\) | −1239.56 | − | 2146.97i | −0.0869361 | − | 0.150578i | ||||
\(589\) | 13546.5 | + | 23463.2i | 0.947664 | + | 1.64140i | ||||
\(590\) | 145.051 | − | 251.236i | 0.0101215 | − | 0.0175309i | ||||
\(591\) | 8553.13 | 0.595311 | ||||||||
\(592\) | 322.615 | + | 3586.51i | 0.0223976 | + | 0.248995i | ||||
\(593\) | −1694.48 | −0.117342 | −0.0586710 | − | 0.998277i | \(-0.518686\pi\) | ||||
−0.0586710 | + | 0.998277i | \(0.518686\pi\) | |||||||
\(594\) | 6645.35 | − | 11510.1i | 0.459027 | − | 0.795058i | ||||
\(595\) | −829.699 | − | 1437.08i | −0.0571669 | − | 0.0990160i | ||||
\(596\) | 2003.44 | + | 3470.06i | 0.137691 | + | 0.238488i | ||||
\(597\) | −3004.38 | − | 5203.73i | −0.205965 | − | 0.356741i | ||||
\(598\) | −18600.7 | −1.27197 | ||||||||
\(599\) | 12696.6 | + | 21991.1i | 0.866058 | + | 1.50006i | 0.865993 | + | 0.500056i | \(0.166687\pi\) |
6.47628e−5 | 1.00000i | \(0.499979\pi\) | ||||||||
\(600\) | −2703.69 | −0.183963 | ||||||||
\(601\) | −6109.34 | + | 10581.7i | −0.414651 | + | 0.718196i | −0.995392 | − | 0.0958920i | \(-0.969430\pi\) |
0.580741 | + | 0.814089i | \(0.302763\pi\) | |||||||
\(602\) | 21975.0 | 1.48777 | ||||||||
\(603\) | −3613.95 | −0.244065 | ||||||||
\(604\) | −3715.12 | + | 6434.78i | −0.250275 | + | 0.433489i | ||||
\(605\) | 551.831 | + | 955.799i | 0.0370828 | + | 0.0642293i | ||||
\(606\) | −2627.05 | −0.176100 | ||||||||
\(607\) | −3601.10 | + | 6237.29i | −0.240798 | + | 0.417074i | −0.960942 | − | 0.276751i | \(-0.910742\pi\) |
0.720144 | + | 0.693825i | \(0.244076\pi\) | |||||||
\(608\) | −1512.10 | + | 2619.04i | −0.100862 | + | 0.174698i | ||||
\(609\) | 5589.42 | − | 9681.15i | 0.371912 | − | 0.644171i | ||||
\(610\) | −414.091 | − | 717.227i | −0.0274853 | − | 0.0476060i | ||||
\(611\) | −1971.60 | − | 3414.90i | −0.130544 | − | 0.226108i | ||||
\(612\) | 3510.26 | − | 6079.95i | 0.231853 | − | 0.401581i | ||||
\(613\) | 3085.53 | − | 5344.29i | 0.203301 | − | 0.352127i | −0.746289 | − | 0.665622i | \(-0.768166\pi\) |
0.949590 | + | 0.313495i | \(0.101500\pi\) | |||||||
\(614\) | 3546.01 | − | 6141.87i | 0.233071 | − | 0.403690i | ||||
\(615\) | 338.329 | 0.0221833 | ||||||||
\(616\) | 5015.64 | + | 8687.34i | 0.328061 | + | 0.568219i | ||||
\(617\) | 14814.9 | − | 25660.1i | 0.966652 | − | 1.67429i | 0.261542 | − | 0.965192i | \(-0.415769\pi\) |
0.705110 | − | 0.709098i | \(-0.250898\pi\) | |||||||
\(618\) | −3811.45 | −0.248089 | ||||||||
\(619\) | −11685.8 | −0.758793 | −0.379397 | − | 0.925234i | \(-0.623868\pi\) | ||||
−0.379397 | + | 0.925234i | \(0.623868\pi\) | |||||||
\(620\) | −445.019 | + | 770.795i | −0.0288264 | + | 0.0499288i | ||||
\(621\) | −17164.6 | −1.10916 | ||||||||
\(622\) | 10064.3 | + | 17431.9i | 0.648780 | + | 1.12372i | ||||
\(623\) | 26070.1 | 1.67653 | ||||||||
\(624\) | 1491.53 | + | 2583.40i | 0.0956872 | + | 0.165735i | ||||
\(625\) | −7699.73 | − | 13336.3i | −0.492782 | − | 0.853524i | ||||
\(626\) | 7709.12 | + | 13352.6i | 0.492202 | + | 0.852518i | ||||
\(627\) | −6735.75 | + | 11666.7i | −0.429027 | + | 0.743097i | ||||
\(628\) | 1626.79 | 0.103369 | ||||||||
\(629\) | 1803.83 | + | 20053.2i | 0.114346 | + | 1.27118i | ||||
\(630\) | −727.827 | −0.0460275 | ||||||||
\(631\) | −180.276 | + | 312.247i | −0.0113735 | + | 0.0196995i | −0.871656 | − | 0.490118i | \(-0.836954\pi\) |
0.860283 | + | 0.509817i | \(0.170287\pi\) | |||||||
\(632\) | −3345.95 | − | 5795.35i | −0.210593 | − | 0.364757i | ||||
\(633\) | 858.721 | + | 1487.35i | 0.0539196 | + | 0.0933915i | ||||
\(634\) | −9726.87 | − | 16847.4i | −0.609311 | − | 1.05536i | ||||
\(635\) | 1868.80 | 0.116789 | ||||||||
\(636\) | −1670.75 | − | 2893.82i | −0.104166 | − | 0.180420i | ||||
\(637\) | −15655.5 | −0.973771 | ||||||||
\(638\) | −9033.85 | + | 15647.1i | −0.560586 | + | 0.970963i | ||||
\(639\) | −3882.71 | −0.240372 | ||||||||
\(640\) | −99.3488 | −0.00613610 | ||||||||
\(641\) | 6689.77 | − | 11587.0i | 0.412215 | − | 0.713977i | −0.582917 | − | 0.812532i | \(-0.698089\pi\) |
0.995132 | + | 0.0985545i | \(0.0314219\pi\) | |||||||
\(642\) | 2419.92 | + | 4191.42i | 0.148764 | + | 0.257667i | ||||
\(643\) | 15878.5 | 0.973850 | 0.486925 | − | 0.873444i | \(-0.338118\pi\) | ||||
0.486925 | + | 0.873444i | \(0.338118\pi\) | |||||||
\(644\) | 6477.56 | − | 11219.5i | 0.396353 | − | 0.686504i | ||||
\(645\) | −484.741 | + | 839.596i | −0.0295917 | + | 0.0512544i | ||||
\(646\) | −8454.59 | + | 14643.8i | −0.514925 | + | 0.891876i | ||||
\(647\) | 2787.95 | + | 4828.87i | 0.169406 | + | 0.293419i | 0.938211 | − | 0.346064i | \(-0.112482\pi\) |
−0.768805 | + | 0.639483i | \(0.779149\pi\) | |||||||
\(648\) | −742.493 | − | 1286.04i | −0.0450122 | − | 0.0779634i | ||||
\(649\) | −4902.73 | + | 8491.78i | −0.296532 | + | 0.513608i | ||||
\(650\) | −8536.84 | + | 14786.2i | −0.515142 | + | 0.892252i | ||||
\(651\) | −9306.54 | + | 16119.4i | −0.560295 | + | 0.970459i | ||||
\(652\) | 982.292 | 0.0590023 | ||||||||
\(653\) | 733.239 | + | 1270.01i | 0.0439416 | + | 0.0761091i | 0.887160 | − | 0.461462i | \(-0.152675\pi\) |
−0.843218 | + | 0.537572i | \(0.819342\pi\) | |||||||
\(654\) | −4003.44 | + | 6934.16i | −0.239368 | + | 0.414598i | ||||
\(655\) | 201.142 | 0.0119989 | ||||||||
\(656\) | −2567.15 | −0.152790 | ||||||||
\(657\) | 615.578 | − | 1066.21i | 0.0365540 | − | 0.0633134i | ||||
\(658\) | 2746.37 | 0.162713 | ||||||||
\(659\) | −3421.40 | − | 5926.05i | −0.202244 | − | 0.350297i | 0.747007 | − | 0.664816i | \(-0.231490\pi\) |
−0.949251 | + | 0.314519i | \(0.898157\pi\) | |||||||
\(660\) | −442.554 | −0.0261006 | ||||||||
\(661\) | 526.840 | + | 912.514i | 0.0310011 | + | 0.0536954i | 0.881110 | − | 0.472912i | \(-0.156797\pi\) |
−0.850109 | + | 0.526607i | \(0.823464\pi\) | |||||||
\(662\) | 4300.47 | + | 7448.64i | 0.252481 | + | 0.437310i | ||||
\(663\) | 8339.52 | + | 14444.5i | 0.488507 | + | 0.846119i | ||||
\(664\) | 3504.05 | − | 6069.20i | 0.204795 | − | 0.354715i | ||||
\(665\) | 1753.00 | 0.102223 | ||||||||
\(666\) | 8012.73 | + | 3712.58i | 0.466196 | + | 0.216005i | ||||
\(667\) | 23333.9 | 1.35456 | ||||||||
\(668\) | 1773.37 | − | 3071.57i | 0.102715 | − | 0.177908i | ||||
\(669\) | 6460.25 | + | 11189.5i | 0.373345 | + | 0.646652i | ||||
\(670\) | 142.974 | + | 247.638i | 0.00824411 | + | 0.0142792i | ||||
\(671\) | 13996.3 | + | 24242.2i | 0.805246 | + | 1.39473i | ||||
\(672\) | −2077.65 | −0.119267 | ||||||||
\(673\) | 5661.86 | + | 9806.62i | 0.324292 | + | 0.561690i | 0.981369 | − | 0.192133i | \(-0.0615406\pi\) |
−0.657077 | + | 0.753824i | \(0.728207\pi\) | |||||||
\(674\) | 18750.5 | 1.07158 | ||||||||
\(675\) | −7877.73 | + | 13644.6i | −0.449206 | + | 0.778047i | ||||
\(676\) | 10049.8 | 0.571792 | ||||||||
\(677\) | 19446.7 | 1.10399 | 0.551993 | − | 0.833849i | \(-0.313867\pi\) | ||||
0.551993 | + | 0.833849i | \(0.313867\pi\) | |||||||
\(678\) | 4507.44 | − | 7807.11i | 0.255320 | − | 0.442227i | ||||
\(679\) | −17131.9 | − | 29673.2i | −0.968277 | − | 1.67711i | ||||
\(680\) | −555.486 | −0.0313264 | ||||||||
\(681\) | 4178.07 | − | 7236.63i | 0.235101 | − | 0.407207i | ||||
\(682\) | 15041.6 | − | 26052.8i | 0.844536 | − | 1.46278i | ||||
\(683\) | −10174.1 | + | 17622.1i | −0.569989 | + | 0.987249i | 0.426578 | + | 0.904451i | \(0.359719\pi\) |
−0.996566 | + | 0.0827984i | \(0.973614\pi\) | |||||||
\(684\) | 3708.26 | + | 6422.90i | 0.207294 | + | 0.359043i | ||||
\(685\) | −362.251 | − | 627.438i | −0.0202057 | − | 0.0349973i | ||||
\(686\) | −2745.22 | + | 4754.86i | −0.152789 | + | 0.264638i | ||||
\(687\) | −974.946 | + | 1688.66i | −0.0541434 | + | 0.0937792i | ||||
\(688\) | 3678.09 | − | 6370.63i | 0.203817 | − | 0.353021i | ||||
\(689\) | −21101.3 | −1.16676 | ||||||||
\(690\) | 285.774 | + | 494.974i | 0.0157670 | + | 0.0273092i | ||||
\(691\) | 4149.78 | − | 7187.63i | 0.228459 | − | 0.395702i | −0.728893 | − | 0.684628i | \(-0.759965\pi\) |
0.957352 | + | 0.288926i | \(0.0932980\pi\) | |||||||
\(692\) | −15760.6 | −0.865793 | ||||||||
\(693\) | 24600.5 | 1.34848 | ||||||||
\(694\) | 2361.85 | − | 4090.84i | 0.129185 | − | 0.223755i | ||||
\(695\) | 534.539 | 0.0291744 | ||||||||
\(696\) | −1871.07 | − | 3240.78i | −0.101900 | − | 0.176497i | ||||
\(697\) | −14353.6 | −0.780033 | ||||||||
\(698\) | −2116.86 | − | 3666.51i | −0.114791 | − | 0.198824i | ||||
\(699\) | −4931.57 | − | 8541.72i | −0.266851 | − | 0.462200i | ||||
\(700\) | −5945.78 | − | 10298.4i | −0.321042 | − | 0.556061i | ||||
\(701\) | −4691.48 | + | 8125.88i | −0.252774 | + | 0.437818i | −0.964289 | − | 0.264854i | \(-0.914676\pi\) |
0.711514 | + | 0.702672i | \(0.248010\pi\) | |||||||
\(702\) | 17383.4 | 0.934606 | ||||||||
\(703\) | −19298.9 | − | 8941.88i | −1.03538 | − | 0.479729i | ||||
\(704\) | 3357.99 | 0.179771 | ||||||||
\(705\) | −60.5816 | + | 104.930i | −0.00323636 | + | 0.00560554i | ||||
\(706\) | 3929.32 | + | 6805.78i | 0.209464 | + | 0.362803i | ||||
\(707\) | −5777.23 | − | 10006.5i | −0.307320 | − | 0.532293i | ||||
\(708\) | −1015.44 | − | 1758.79i | −0.0539020 | − | 0.0933610i | ||||
\(709\) | 10322.1 | 0.546764 | 0.273382 | − | 0.961906i | \(-0.411858\pi\) | ||||
0.273382 | + | 0.961906i | \(0.411858\pi\) | |||||||
\(710\) | 153.606 | + | 266.054i | 0.00811936 | + | 0.0140631i | ||||
\(711\) | −16411.1 | −0.865632 | ||||||||
\(712\) | 4363.51 | − | 7557.82i | 0.229676 | − | 0.397811i | ||||
\(713\) | −38851.7 | −2.04068 | ||||||||
\(714\) | −11616.7 | −0.608886 | ||||||||
\(715\) | −1397.35 | + | 2420.29i | −0.0730883 | + | 0.126593i | ||||
\(716\) | 6067.59 | + | 10509.4i | 0.316699 | + | 0.548538i | ||||
\(717\) | 1115.08 | 0.0580803 | ||||||||
\(718\) | −1087.17 | + | 1883.03i | −0.0565079 | + | 0.0978746i | ||||
\(719\) | −16150.9 | + | 27974.3i | −0.837731 | + | 1.45099i | 0.0540560 | + | 0.998538i | \(0.482785\pi\) |
−0.891787 | + | 0.452455i | \(0.850548\pi\) | |||||||
\(720\) | −121.821 | + | 211.000i | −0.00630554 | + | 0.0109215i | ||||
\(721\) | −8381.89 | − | 14517.9i | −0.432951 | − | 0.749894i | ||||
\(722\) | −2072.48 | − | 3589.64i | −0.106828 | − | 0.185031i | ||||
\(723\) | 3048.59 | − | 5280.32i | 0.156817 | − | 0.271614i | ||||
\(724\) | −1681.46 | + | 2912.38i | −0.0863137 | + | 0.149500i | ||||
\(725\) | 10709.2 | − | 18548.8i | 0.548591 | − | 0.950188i | ||||
\(726\) | 7726.25 | 0.394970 | ||||||||
\(727\) | 10968.0 | + | 18997.2i | 0.559535 | + | 0.969143i | 0.997535 | + | 0.0701684i | \(0.0223537\pi\) |
−0.438000 | + | 0.898975i | \(0.644313\pi\) | |||||||
\(728\) | −6560.13 | + | 11362.5i | −0.333976 | + | 0.578464i | ||||
\(729\) | 5648.72 | 0.286985 | ||||||||
\(730\) | −97.4130 | −0.00493893 | ||||||||
\(731\) | 20565.2 | − | 35620.0i | 1.04053 | − | 1.80226i | ||||
\(732\) | −5797.74 | −0.292747 | ||||||||
\(733\) | −12123.5 | − | 20998.6i | −0.610905 | − | 1.05812i | −0.991088 | − | 0.133207i | \(-0.957472\pi\) |
0.380183 | − | 0.924911i | \(-0.375861\pi\) | |||||||
\(734\) | 8892.79 | 0.447192 | ||||||||
\(735\) | 240.524 | + | 416.600i | 0.0120706 | + | 0.0209068i | ||||
\(736\) | −2168.37 | − | 3755.73i | −0.108597 | − | 0.188095i | ||||
\(737\) | −4832.51 | − | 8370.15i | −0.241530 | − | 0.418342i | ||||
\(738\) | −3147.82 | + | 5452.19i | −0.157009 | + | 0.271948i | ||||
\(739\) | 5870.01 | 0.292195 | 0.146097 | − | 0.989270i | \(-0.453329\pi\) | ||||
0.146097 | + | 0.989270i | \(0.453329\pi\) | |||||||
\(740\) | −62.6005 | − | 695.929i | −0.00310978 | − | 0.0345714i | ||||
\(741\) | −17619.9 | −0.873524 | ||||||||
\(742\) | 7348.39 | − | 12727.8i | 0.363568 | − | 0.629719i | ||||
\(743\) | 1730.82 | + | 2997.87i | 0.0854611 | + | 0.148023i | 0.905588 | − | 0.424159i | \(-0.139430\pi\) |
−0.820127 | + | 0.572182i | \(0.806097\pi\) | |||||||
\(744\) | 3115.38 | + | 5396.00i | 0.153515 | + | 0.265896i | ||||
\(745\) | −388.748 | − | 673.331i | −0.0191176 | − | 0.0331127i | ||||
\(746\) | 4358.43 | 0.213906 | ||||||||
\(747\) | −8593.29 | − | 14884.0i | −0.420899 | − | 0.729019i | ||||
\(748\) | 18775.4 | 0.917777 | ||||||||
\(749\) | −10643.4 | + | 18435.0i | −0.519230 | + | 0.899332i | ||||
\(750\) | 1051.79 | 0.0512080 | ||||||||
\(751\) | 24153.8 | 1.17362 | 0.586808 | − | 0.809726i | \(-0.300384\pi\) | ||||
0.586808 | + | 0.809726i | \(0.300384\pi\) | |||||||
\(752\) | 459.677 | − | 796.184i | 0.0222908 | − | 0.0386088i | ||||
\(753\) | 1598.56 | + | 2768.78i | 0.0773634 | + | 0.133997i | ||||
\(754\) | −23631.4 | −1.14139 | ||||||||
\(755\) | 720.885 | − | 1248.61i | 0.0347492 | − | 0.0601874i | ||||
\(756\) | −6053.63 | + | 10485.2i | −0.291228 | + | 0.504422i | ||||
\(757\) | 1640.07 | − | 2840.68i | 0.0787441 | − | 0.136389i | −0.823964 | − | 0.566642i | \(-0.808242\pi\) |
0.902708 | + | 0.430253i | \(0.141576\pi\) | |||||||
\(758\) | −10539.3 | − | 18254.6i | −0.505019 | − | 0.874719i | ||||
\(759\) | −9659.14 | − | 16730.1i | −0.461930 | − | 0.800085i | ||||
\(760\) | 293.410 | − | 508.200i | 0.0140041 | − | 0.0242557i | ||||
\(761\) | 11208.5 | − | 19413.7i | 0.533914 | − | 0.924766i | −0.465301 | − | 0.885152i | \(-0.654054\pi\) |
0.999215 | − | 0.0396137i | \(-0.0126127\pi\) | |||||||
\(762\) | 6541.32 | − | 11329.9i | 0.310980 | − | 0.538634i | ||||
\(763\) | −35216.4 | −1.67093 | ||||||||
\(764\) | 4375.22 | + | 7578.10i | 0.207186 | + | 0.358856i | ||||
\(765\) | −681.133 | + | 1179.76i | −0.0321914 | + | 0.0557571i | ||||
\(766\) | 11171.2 | 0.526937 | ||||||||
\(767\) | −12824.9 | −0.603756 | ||||||||
\(768\) | −347.749 | + | 602.318i | −0.0163389 | + | 0.0282998i | ||||
\(769\) | −11280.2 | −0.528965 | −0.264483 | − | 0.964390i | \(-0.585201\pi\) | ||||
−0.264483 | + | 0.964390i | \(0.585201\pi\) | |||||||
\(770\) | −973.237 | − | 1685.70i | −0.0455494 | − | 0.0788938i | ||||
\(771\) | 8922.10 | 0.416760 | ||||||||
\(772\) | 1619.87 | + | 2805.70i | 0.0755187 | + | 0.130802i | ||||
\(773\) | 3037.07 | + | 5260.36i | 0.141314 | + | 0.244763i | 0.927992 | − | 0.372601i | \(-0.121534\pi\) |
−0.786678 | + | 0.617364i | \(0.788201\pi\) | |||||||
\(774\) | −9020.08 | − | 15623.2i | −0.418889 | − | 0.725537i | ||||
\(775\) | −17831.1 | + | 30884.3i | −0.826466 | + | 1.43148i | ||||
\(776\) | −11469.8 | −0.530597 | ||||||||
\(777\) | −1309.14 | − | 14553.8i | −0.0604444 | − | 0.671960i | ||||
\(778\) | 5949.23 | 0.274152 | ||||||||
\(779\) | 7581.64 | − | 13131.8i | 0.348704 | − | 0.603973i | ||||
\(780\) | −289.416 | − | 501.284i | −0.0132856 | − | 0.0230113i | ||||
\(781\) | −5191.89 | − | 8992.62i | −0.237875 | − | 0.412012i | ||||
\(782\) | −12124.0 | − | 20999.3i | −0.554415 | − | 0.960274i | ||||
\(783\) | −21806.9 | −0.995292 | ||||||||
\(784\) | −1825.03 | − | 3161.05i | −0.0831374 | − | 0.143998i | ||||
\(785\) | −315.663 | −0.0143522 | ||||||||
\(786\) | 704.052 | − | 1219.45i | 0.0319500 | − | 0.0553390i | ||||
\(787\) | 8222.13 | 0.372411 | 0.186205 | − | 0.982511i | \(-0.440381\pi\) | ||||
0.186205 | + | 0.982511i | \(0.440381\pi\) | |||||||
\(788\) | 12593.0 | 0.569299 | ||||||||
\(789\) | −651.315 | + | 1128.11i | −0.0293884 | + | 0.0509022i | ||||
\(790\) | 649.249 | + | 1124.53i | 0.0292396 | + | 0.0506444i | ||||
\(791\) | 39649.8 | 1.78228 | ||||||||
\(792\) | 4117.54 | − | 7131.78i | 0.184735 | − | 0.319971i | ||||
\(793\) | −18306.2 | + | 31707.3i | −0.819764 | + | 1.41987i | ||||
\(794\) | −11005.6 | + | 19062.3i | −0.491908 | + | 0.852009i | ||||
\(795\) | 324.192 | + | 561.518i | 0.0144628 | + | 0.0250503i | ||||
\(796\) | −4423.43 | − | 7661.60i | −0.196965 | − | 0.341154i | ||||
\(797\) | −15865.7 | + | 27480.2i | −0.705134 | + | 1.22133i | 0.261509 | + | 0.965201i | \(0.415780\pi\) |
−0.966643 | + | 0.256127i | \(0.917553\pi\) | |||||||
\(798\) | 6135.98 | − | 10627.8i | 0.272195 | − | 0.471455i | ||||
\(799\) | 2570.18 | − | 4451.68i | 0.113800 | − | 0.197108i | ||||
\(800\) | −3980.72 | −0.175925 | ||||||||
\(801\) | −10701.0 | − | 18534.7i | −0.472036 | − | 0.817591i | ||||
\(802\) | −11819.7 | + | 20472.4i | −0.520410 | + | 0.901377i | ||||
\(803\) | 3292.56 | 0.144697 | ||||||||
\(804\) | 2001.79 | 0.0878081 | ||||||||
\(805\) | −1256.91 | + | 2177.03i | −0.0550313 | + | 0.0953171i | ||||
\(806\) | 39346.9 | 1.71952 | ||||||||
\(807\) | −1912.61 | − | 3312.74i | −0.0834289 | − | 0.144503i | ||||
\(808\) | −3867.87 | −0.168405 | ||||||||
\(809\) | −4286.25 | − | 7424.01i | −0.186275 | − | 0.322638i | 0.757730 | − | 0.652568i | \(-0.226308\pi\) |
−0.944006 | + | 0.329930i | \(0.892975\pi\) | |||||||
\(810\) | 144.074 | + | 249.543i | 0.00624967 | + | 0.0108248i | ||||
\(811\) | −4034.56 | − | 6988.06i | −0.174689 | − | 0.302570i | 0.765365 | − | 0.643597i | \(-0.222559\pi\) |
−0.940054 | + | 0.341027i | \(0.889225\pi\) | |||||||
\(812\) | 8229.46 | − | 14253.8i | 0.355662 | − | 0.616024i | ||||
\(813\) | −4396.71 | −0.189667 | ||||||||
\(814\) | 2115.89 | + | 23522.4i | 0.0911082 | + | 1.01285i | ||||
\(815\) | −190.604 | −0.00819213 | ||||||||
\(816\) | −1944.36 | + | 3367.73i | −0.0834144 | + | 0.144478i | ||||
\(817\) | 21725.2 | + | 37629.1i | 0.930316 | + | 1.61136i | ||||
\(818\) | −2310.69 | − | 4002.23i | −0.0987669 | − | 0.171069i | ||||
\(819\) | 16088.0 | + | 27865.2i | 0.686397 | + | 1.18887i | ||||
\(820\) | 498.132 | 0.0212140 | ||||||||
\(821\) | −8924.58 | − | 15457.8i | −0.379379 | − | 0.657103i | 0.611593 | − | 0.791172i | \(-0.290529\pi\) |
−0.990972 | + | 0.134069i | \(0.957196\pi\) | |||||||
\(822\) | −5071.93 | −0.215211 | ||||||||
\(823\) | −3987.27 | + | 6906.16i | −0.168879 | + | 0.292508i | −0.938026 | − | 0.346565i | \(-0.887348\pi\) |
0.769147 | + | 0.639072i | \(0.220681\pi\) | |||||||
\(824\) | −5611.71 | −0.237249 | ||||||||
\(825\) | −17732.3 | −0.748316 | ||||||||
\(826\) | 4466.18 | − | 7735.65i | 0.188134 | − | 0.325857i | ||||
\(827\) | 19717.5 | + | 34151.7i | 0.829074 | + | 1.43600i | 0.898765 | + | 0.438430i | \(0.144465\pi\) |
−0.0696912 | + | 0.997569i | \(0.522201\pi\) | |||||||
\(828\) | −10635.4 | −0.446383 | ||||||||
\(829\) | 13596.0 | − | 23549.0i | 0.569614 | − | 0.986601i | −0.426990 | − | 0.904256i | \(-0.640426\pi\) |
0.996604 | − | 0.0823441i | \(-0.0262407\pi\) | |||||||
\(830\) | −679.928 | + | 1177.67i | −0.0284345 | + | 0.0492501i | ||||
\(831\) | 9924.61 | − | 17189.9i | 0.414297 | − | 0.717584i | ||||
\(832\) | 2196.01 | + | 3803.61i | 0.0915061 | + | 0.158493i | ||||
\(833\) | −10204.3 | − | 17674.3i | −0.424438 | − | 0.735148i | ||||
\(834\) | 1871.03 | − | 3240.73i | 0.0776842 | − | 0.134553i | ||||
\(835\) | −344.106 | + | 596.008i | −0.0142614 | + | 0.0247015i | ||||
\(836\) | −9917.24 | + | 17177.2i | −0.410281 | + | 0.710627i | ||||
\(837\) | 36309.0 | 1.49943 | ||||||||
\(838\) | −10428.3 | − | 18062.3i | −0.429880 | − | 0.744574i | ||||
\(839\) | −8976.25 | + | 15547.3i | −0.369362 | + | 0.639753i | −0.989466 | − | 0.144766i | \(-0.953757\pi\) |
0.620104 | + | 0.784519i | \(0.287090\pi\) | |||||||
\(840\) | 403.148 | 0.0165595 | ||||||||
\(841\) | 5255.77 | 0.215498 | ||||||||
\(842\) | −12564.4 | + | 21762.1i | −0.514248 | + | 0.890704i | ||||
\(843\) | 12493.3 | 0.510428 | ||||||||
\(844\) | 1264.32 | + | 2189.87i | 0.0515636 | + | 0.0893108i | ||||
\(845\) | −1950.07 | −0.0793899 | ||||||||
\(846\) | −1127.30 | − | 1952.55i | −0.0458127 | − | 0.0793499i | ||||
\(847\) | 16991.1 | + | 29429.4i | 0.689280 | + | 1.19387i | ||||
\(848\) | −2459.89 | − | 4260.65i | −0.0996142 | − | 0.172537i | ||||
\(849\) | 11627.1 | − | 20138.7i | 0.470013 | − | 0.814087i | ||||
\(850\) | −22257.3 | −0.898140 | ||||||||
\(851\) | 24942.3 | − | 17555.8i | 1.00471 | − | 0.707173i | ||||
\(852\) | 2150.66 | 0.0864794 | ||||||||
\(853\) | 2459.38 | − | 4259.77i | 0.0987194 | − | 0.170987i | −0.812435 | − | 0.583051i | \(-0.801859\pi\) |
0.911155 | + | 0.412064i | \(0.135192\pi\) | |||||||
\(854\) | −12750.0 | − | 22083.7i | −0.510885 | − | 0.884880i | ||||
\(855\) | −719.553 | − | 1246.30i | −0.0287815 | − | 0.0498510i | ||||
\(856\) | 3562.91 | + | 6171.14i | 0.142264 | + | 0.246408i | ||||
\(857\) | −34168.0 | −1.36191 | −0.680956 | − | 0.732325i | \(-0.738435\pi\) | ||||
−0.680956 | + | 0.732325i | \(0.738435\pi\) | |||||||
\(858\) | 9782.27 | + | 16943.4i | 0.389232 | + | 0.674170i | ||||
\(859\) | 31471.2 | 1.25004 | 0.625020 | − | 0.780608i | \(-0.285091\pi\) | ||||
0.625020 | + | 0.780608i | \(0.285091\pi\) | |||||||
\(860\) | −713.698 | + | 1236.16i | −0.0282987 | + | 0.0490148i | ||||
\(861\) | 10417.3 | 0.412334 | ||||||||
\(862\) | 18224.3 | 0.720097 | ||||||||
\(863\) | −4633.23 | + | 8024.99i | −0.182754 | + | 0.316540i | −0.942818 | − | 0.333309i | \(-0.891835\pi\) |
0.760063 | + | 0.649849i | \(0.225168\pi\) | |||||||
\(864\) | 2026.46 | + | 3509.94i | 0.0797937 | + | 0.138207i | ||||
\(865\) | 3058.20 | 0.120210 | ||||||||
\(866\) | 8620.44 | − | 14931.0i | 0.338262 | − | 0.585886i | ||||
\(867\) | −4197.65 | + | 7270.54i | −0.164429 | + | 0.284799i | ||||
\(868\) | −13702.3 | + | 23733.0i | −0.535813 | + | 0.928055i | ||||
\(869\) | −21944.6 | − | 38009.2i | −0.856640 | − | 1.48374i | ||||
\(870\) | 363.063 | + | 628.843i | 0.0141483 | + | 0.0245055i | ||||
\(871\) | 6320.61 | − | 10947.6i | 0.245885 | − | 0.425885i | ||||
\(872\) | −5894.38 | + | 10209.4i | −0.228909 | + | 0.396483i | ||||
\(873\) | −14064.2 | + | 24360.0i | −0.545248 | + | 0.944398i | ||||
\(874\) | 25615.7 | 0.991377 | ||||||||
\(875\) | 2313.03 | + | 4006.29i | 0.0893655 | + | 0.154786i | ||||
\(876\) | −340.973 | + | 590.582i | −0.0131512 | + | 0.0227785i | ||||
\(877\) | 7585.58 | 0.292072 | 0.146036 | − | 0.989279i | \(-0.453349\pi\) | ||||
0.146036 | + | 0.989279i | \(0.453349\pi\) | |||||||
\(878\) | −2614.78 | −0.100506 | ||||||||
\(879\) | −2955.62 | + | 5119.29i | −0.113414 | + | 0.196438i | ||||
\(880\) | −651.585 | −0.0249602 | ||||||||
\(881\) | 13118.8 | + | 22722.4i | 0.501684 | + | 0.868943i | 0.999998 | + | 0.00194607i | \(0.000619455\pi\) |
−0.498314 | + | 0.866997i | \(0.666047\pi\) | |||||||
\(882\) | −8951.37 | −0.341733 | ||||||||
\(883\) | 2316.25 | + | 4011.86i | 0.0882763 | + | 0.152899i | 0.906783 | − | 0.421599i | \(-0.138531\pi\) |
−0.818506 | + | 0.574498i | \(0.805197\pi\) | |||||||
\(884\) | 12278.5 | + | 21267.0i | 0.467162 | + | 0.809148i | ||||
\(885\) | 197.037 | + | 341.278i | 0.00748397 | + | 0.0129626i | ||||
\(886\) | −13166.5 | + | 22805.0i | −0.499250 | + | 0.864727i | ||||
\(887\) | 937.723 | 0.0354968 | 0.0177484 | − | 0.999842i | \(-0.494350\pi\) | ||||
0.0177484 | + | 0.999842i | \(0.494350\pi\) | |||||||
\(888\) | −4438.30 | − | 2056.42i | −0.167725 | − | 0.0777128i | ||||
\(889\) | 57541.0 | 2.17082 | ||||||||
\(890\) | −846.697 | + | 1466.52i | −0.0318892 | + | 0.0552337i | ||||
\(891\) | −4869.69 | − | 8434.55i | −0.183099 | − | 0.317136i | ||||
\(892\) | 9511.61 | + | 16474.6i | 0.357032 | + | 0.618397i | ||||
\(893\) | 2715.15 | + | 4702.78i | 0.101746 | + | 0.176229i | ||||
\(894\) | −5442.91 | −0.203622 | ||||||||
\(895\) | −1177.36 | − | 2039.24i | −0.0439718 | − | 0.0761613i | ||||
\(896\) | −3058.98 | −0.114055 | ||||||||
\(897\) | 12633.5 | − | 21881.9i | 0.470258 | − | 0.814511i | ||||
\(898\) | −27714.7 | −1.02990 | ||||||||
\(899\) | −49359.4 | −1.83118 | ||||||||
\(900\) | −4881.13 | + | 8454.37i | −0.180783 | + | 0.313125i | ||||
\(901\) | −13753.9 | − | 23822.4i | −0.508556 | − | 0.880844i | ||||
\(902\) | −16836.8 | −0.621514 | ||||||||
\(903\) | −14925.3 | + | 25851.5i | −0.550038 | + | 0.952694i | ||||
\(904\) | 6636.43 | − | 11494.6i | 0.244164 | − | 0.422904i | ||||
\(905\) | 326.272 | − | 565.120i | 0.0119842 | − | 0.0207572i | ||||
\(906\) | −5046.60 | − | 8740.96i | −0.185057 | − | 0.320529i | ||||
\(907\) | 12354.0 | + | 21397.8i | 0.452269 | + | 0.783353i | 0.998527 | − | 0.0542640i | \(-0.0172813\pi\) |
−0.546257 | + | 0.837617i | \(0.683948\pi\) | |||||||
\(908\) | 6151.49 | − | 10654.7i | 0.224829 | − | 0.389415i | ||||
\(909\) | −4742.76 | + | 8214.70i | −0.173055 | + | 0.299741i | ||||
\(910\) | 1272.93 | − | 2204.78i | 0.0463706 | − | 0.0803163i | ||||
\(911\) | 43065.2 | 1.56621 | 0.783103 | − | 0.621892i | \(-0.213636\pi\) | ||||
0.783103 | + | 0.621892i | \(0.213636\pi\) | |||||||
\(912\) | −2054.03 | − | 3557.69i | −0.0745787 | − | 0.129174i | ||||
\(913\) | 22981.6 | − | 39805.2i | 0.833055 | − | 1.44289i | ||||
\(914\) | −14276.5 | −0.516656 | ||||||||
\(915\) | 1125.00 | 0.0406461 | ||||||||
\(916\) | −1435.44 | + | 2486.26i | −0.0517776 | + | 0.0896815i | ||||
\(917\) | 6193.22 | 0.223030 | ||||||||
\(918\) | 11330.5 | + | 19625.0i | 0.407367 | + | 0.705580i | ||||
\(919\) | −10234.4 | −0.367356 | −0.183678 | − | 0.982986i | \(-0.558800\pi\) | ||||
−0.183678 | + | 0.982986i | \(0.558800\pi\) | |||||||
\(920\) | 420.752 | + | 728.765i | 0.0150780 | + | 0.0261159i | ||||
\(921\) | 4816.87 | + | 8343.07i | 0.172336 | + | 0.298495i | ||||
\(922\) | 346.138 | + | 599.528i | 0.0123638 | + | 0.0214148i | ||||
\(923\) | 6790.66 | − | 11761.8i | 0.242164 | − | 0.419440i | ||||
\(924\) | −13626.4 | −0.485147 | ||||||||
\(925\) | −2508.28 | − | 27884.6i | −0.0891588 | − | 0.991179i | ||||
\(926\) | 1184.77 | 0.0420452 | ||||||||
\(927\) | −6881.03 | + | 11918.3i | −0.243800 | + | 0.422274i | ||||
\(928\) | −2754.83 | − | 4771.50i | −0.0974478 | − | 0.168785i | ||||
\(929\) | 21571.9 | + | 37363.6i | 0.761841 | + | 1.31955i | 0.941900 | + | 0.335892i | \(0.109038\pi\) |
−0.180059 | + | 0.983656i | \(0.557629\pi\) | |||||||
\(930\) | −604.510 | − | 1047.04i | −0.0213147 | − | 0.0369181i | ||||
\(931\) | 21559.7 | 0.758958 | ||||||||
\(932\) | −7260.88 | − | 12576.2i | −0.255191 | − | 0.442004i | ||||
\(933\) | −27342.5 | −0.959436 | ||||||||
\(934\) | 7407.74 | − | 12830.6i | 0.259517 | − | 0.449496i | ||||
\(935\) | −3643.19 | −0.127428 | ||||||||
\(936\) | 10770.9 | 0.376132 | ||||||||
\(937\) | 6452.89 | − | 11176.7i | 0.224981 | − | 0.389678i | −0.731333 | − | 0.682021i | \(-0.761101\pi\) |
0.956314 | + | 0.292343i | \(0.0944348\pi\) | |||||||
\(938\) | 4402.21 | + | 7624.85i | 0.153238 | + | 0.265416i | ||||
\(939\) | −20944.0 | −0.727883 | ||||||||
\(940\) | −89.1959 | + | 154.492i | −0.00309495 | + | 0.00536061i | ||||
\(941\) | 2572.99 | − | 4456.55i | 0.0891361 | − | 0.154388i | −0.818010 | − | 0.575204i | \(-0.804923\pi\) |
0.907146 | + | 0.420816i | \(0.138256\pi\) | |||||||
\(942\) | −1104.91 | + | 1913.76i | −0.0382164 | + | 0.0661927i | ||||
\(943\) | 10872.2 | + | 18831.1i | 0.375447 | + | 0.650293i | ||||
\(944\) | −1495.06 | − | 2589.52i | −0.0515467 | − | 0.0892816i | ||||
\(945\) | 1174.65 | − | 2034.55i | 0.0404353 | − | 0.0700360i | ||||
\(946\) | 24123.0 | − | 41782.2i | 0.829076 | − | 1.43600i | ||||
\(947\) | 17452.0 | − | 30227.8i | 0.598855 | − | 1.03725i | −0.394136 | − | 0.919052i | \(-0.628956\pi\) |
0.992990 | − | 0.118194i | \(-0.0377106\pi\) | |||||||
\(948\) | 9090.22 | 0.311431 | ||||||||
\(949\) | 2153.23 | + | 3729.50i | 0.0736530 | + | 0.127571i | ||||
\(950\) | 11756.4 | − | 20362.6i | 0.401502 | − | 0.695423i | ||||
\(951\) | 26425.8 | 0.901068 | ||||||||
\(952\) | −17103.6 | −0.582281 | ||||||||
\(953\) | −26126.3 | + | 45252.1i | −0.888053 | + | 1.53815i | −0.0458792 | + | 0.998947i | \(0.514609\pi\) |
−0.842174 | + | 0.539206i | \(0.818724\pi\) | |||||||
\(954\) | −12065.2 | −0.409459 | ||||||||
\(955\) | −848.969 | − | 1470.46i | −0.0287665 | − | 0.0498250i | ||||
\(956\) | 1641.77 | 0.0555425 | ||||||||
\(957\) | −12271.5 | − | 21254.9i | −0.414506 | − | 0.717945i | ||||
\(958\) | 7511.24 | + | 13009.9i | 0.253317 | + | 0.438757i | ||||
\(959\) | −11153.8 | − | 19319.0i | −0.375575 | − | 0.650515i | ||||
\(960\) | 67.4773 | − | 116.874i | 0.00226856 | − | 0.00392927i | ||||
\(961\) | 52393.7 | 1.75871 | ||||||||
\(962\) | −25260.2 | + | 17779.6i | −0.846593 | + | 0.595880i | ||||
\(963\) | 17475.3 | 0.584769 | ||||||||
\(964\) | 4488.53 | − | 7774.36i | 0.149964 | − | 0.259746i | ||||
\(965\) | −314.321 | − | 544.419i | −0.0104853 | − | 0.0181611i | ||||
\(966\) | 8799.07 | + | 15240.4i | 0.293070 | + | 0.507612i | ||||
\(967\) | 9804.84 | + | 16982.5i | 0.326063 | + | 0.564757i | 0.981727 | − | 0.190296i | \(-0.0609446\pi\) |
−0.655664 | + | 0.755053i | \(0.727611\pi\) | |||||||
\(968\) | 11375.6 | 0.377712 | ||||||||
\(969\) | −11484.7 | − | 19892.0i | −0.380743 | − | 0.659467i | ||||
\(970\) | 2225.61 | 0.0736703 | ||||||||
\(971\) | 948.820 | − | 1643.40i | 0.0313585 | − | 0.0543145i | −0.849920 | − | 0.526911i | \(-0.823350\pi\) |
0.881279 | + | 0.472597i | \(0.156683\pi\) | |||||||
\(972\) | 15695.8 | 0.517946 | ||||||||
\(973\) | 16458.6 | 0.542281 | ||||||||
\(974\) | 10382.4 | − | 17982.8i | 0.341553 | − | 0.591587i | ||||
\(975\) | −11596.4 | − | 20085.5i | −0.380904 | − | 0.659745i | ||||
\(976\) | −8536.17 | −0.279955 | ||||||||
\(977\) | −10786.8 | + | 18683.3i | −0.353225 | + | 0.611804i | −0.986813 | − | 0.161867i | \(-0.948248\pi\) |
0.633587 | + | 0.773671i | \(0.281582\pi\) | |||||||
\(978\) | −667.169 | + | 1155.57i | −0.0218136 | + | 0.0377823i | ||||
\(979\) | 28618.4 | − | 49568.4i | 0.934266 | − | 1.61820i | ||||
\(980\) | 354.130 | + | 613.372i | 0.0115431 | + | 0.0199933i | ||||
\(981\) | 14455.3 | + | 25037.3i | 0.470461 | + | 0.814862i | ||||
\(982\) | −789.050 | + | 1366.67i | −0.0256411 | + | 0.0444117i | ||||
\(983\) | −8544.27 | + | 14799.1i | −0.277233 | + | 0.480181i | −0.970696 | − | 0.240311i | \(-0.922751\pi\) |
0.693463 | + | 0.720492i | \(0.256084\pi\) | |||||||
\(984\) | 1743.60 | − | 3020.00i | 0.0564877 | − | 0.0978396i | ||||
\(985\) | −2443.55 | −0.0790438 | ||||||||
\(986\) | −15403.0 | − | 26678.7i | −0.497496 | − | 0.861688i | ||||
\(987\) | −1865.33 | + | 3230.84i | −0.0601561 | + | 0.104193i | ||||
\(988\) | −25942.2 | −0.835356 | ||||||||
\(989\) | −62308.3 | −2.00333 | ||||||||
\(990\) | −798.969 | + | 1383.86i | −0.0256494 | + | 0.0444261i | ||||
\(991\) | −48873.0 | −1.56660 | −0.783301 | − | 0.621642i | \(-0.786466\pi\) | ||||
−0.783301 | + | 0.621642i | \(0.786466\pi\) | |||||||
\(992\) | 4586.86 | + | 7944.68i | 0.146807 | + | 0.254278i | ||||
\(993\) | −11683.5 | −0.373377 | ||||||||
\(994\) | 4729.60 | + | 8191.90i | 0.150919 | + | 0.261400i | ||||
\(995\) | 858.324 | + | 1486.66i | 0.0273475 | + | 0.0473672i | ||||
\(996\) | 4759.88 | + | 8244.35i | 0.151428 | + | 0.262281i | ||||
\(997\) | −9047.11 | + | 15670.0i | −0.287387 | + | 0.497769i | −0.973185 | − | 0.230023i | \(-0.926120\pi\) |
0.685798 | + | 0.727792i | \(0.259453\pi\) | |||||||
\(998\) | −25194.1 | −0.799102 | ||||||||
\(999\) | −23309.9 | + | 16406.8i | −0.738232 | + | 0.519609i |
(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 | 74.4.c.b.47.2 | ✓ | 10 | |
3.2 | odd | 2 | 666.4.f.d.343.4 | 10 | |||
37.26 | even | 3 | inner | 74.4.c.b.63.2 | yes | 10 | |
111.26 | odd | 6 | 666.4.f.d.433.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.4.c.b.47.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
74.4.c.b.63.2 | yes | 10 | 37.26 | even | 3 | inner | |
666.4.f.d.343.4 | 10 | 3.2 | odd | 2 | |||
666.4.f.d.433.4 | 10 | 111.26 | odd | 6 |