Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + 22736 x^{3} + 18792 x^{2} + 4256 x + 784 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 116.3 | ||
Root | \(-1.02943 + 1.78303i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.116 |
Dual form | 245.4.e.q.226.3 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.322324 | − | 0.558282i | −0.113959 | − | 0.197382i | 0.803404 | − | 0.595434i | \(-0.203020\pi\) |
−0.917363 | + | 0.398052i | \(0.869687\pi\) | |||||||
\(3\) | −2.09344 | + | 3.62594i | −0.402882 | + | 0.697812i | −0.994072 | − | 0.108720i | \(-0.965325\pi\) |
0.591190 | + | 0.806532i | \(0.298658\pi\) | |||||||
\(4\) | 3.79221 | − | 6.56831i | 0.474027 | − | 0.821039i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 2.69906 | 0.183648 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −10.0465 | −0.443995 | ||||||||
\(9\) | 4.73504 | + | 8.20133i | 0.175372 | + | 0.303753i | ||||
\(10\) | −1.61162 | + | 2.79141i | −0.0509639 | + | 0.0882721i | ||||
\(11\) | 23.8507 | − | 41.3106i | 0.653750 | − | 1.13233i | −0.328456 | − | 0.944519i | \(-0.606528\pi\) |
0.982206 | − | 0.187808i | \(-0.0601383\pi\) | |||||||
\(12\) | 15.8775 | + | 27.5007i | 0.381954 | + | 0.661564i | ||||
\(13\) | −57.2256 | −1.22089 | −0.610443 | − | 0.792060i | \(-0.709009\pi\) | ||||
−0.610443 | + | 0.792060i | \(0.709009\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.9344 | 0.360349 | ||||||||
\(16\) | −27.0995 | − | 46.9377i | −0.423430 | − | 0.733402i | ||||
\(17\) | −18.4843 | + | 32.0157i | −0.263712 | + | 0.456762i | −0.967225 | − | 0.253920i | \(-0.918280\pi\) |
0.703514 | + | 0.710682i | \(0.251613\pi\) | |||||||
\(18\) | 3.05244 | − | 5.28697i | 0.0399703 | − | 0.0692306i | ||||
\(19\) | 15.3830 | + | 26.6441i | 0.185742 | + | 0.321714i | 0.943826 | − | 0.330442i | \(-0.107198\pi\) |
−0.758084 | + | 0.652156i | \(0.773865\pi\) | |||||||
\(20\) | −37.9221 | −0.423982 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −30.7506 | −0.298002 | ||||||||
\(23\) | −26.5641 | − | 46.0104i | −0.240826 | − | 0.417123i | 0.720124 | − | 0.693846i | \(-0.244085\pi\) |
−0.960950 | + | 0.276723i | \(0.910752\pi\) | |||||||
\(24\) | 21.0317 | − | 36.4279i | 0.178878 | − | 0.309826i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 18.4452 | + | 31.9480i | 0.139131 | + | 0.240981i | ||||
\(27\) | −152.696 | −1.08838 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −195.663 | −1.25288 | −0.626442 | − | 0.779468i | \(-0.715490\pi\) | ||||
−0.626442 | + | 0.779468i | \(0.715490\pi\) | |||||||
\(30\) | −6.74765 | − | 11.6873i | −0.0410649 | − | 0.0711265i | ||||
\(31\) | 128.935 | − | 223.322i | 0.747014 | − | 1.29387i | −0.202234 | − | 0.979337i | \(-0.564820\pi\) |
0.949248 | − | 0.314529i | \(-0.101846\pi\) | |||||||
\(32\) | −57.6555 | + | 99.8623i | −0.318505 | + | 0.551666i | ||||
\(33\) | 99.8597 | + | 172.962i | 0.526768 | + | 0.912389i | ||||
\(34\) | 23.8317 | 0.120209 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 71.8252 | 0.332524 | ||||||||
\(37\) | −173.212 | − | 300.011i | −0.769616 | − | 1.33301i | −0.937771 | − | 0.347254i | \(-0.887114\pi\) |
0.168155 | − | 0.985761i | \(-0.446219\pi\) | |||||||
\(38\) | 9.91660 | − | 17.1760i | 0.0423338 | − | 0.0733243i | ||||
\(39\) | 119.798 | − | 207.497i | 0.491873 | − | 0.851950i | ||||
\(40\) | 25.1162 | + | 43.5025i | 0.0992804 | + | 0.171959i | ||||
\(41\) | −267.050 | −1.01722 | −0.508611 | − | 0.860996i | \(-0.669841\pi\) | ||||
−0.508611 | + | 0.860996i | \(0.669841\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −176.859 | −0.627227 | −0.313614 | − | 0.949551i | \(-0.601540\pi\) | ||||
−0.313614 | + | 0.949551i | \(0.601540\pi\) | |||||||
\(44\) | −180.894 | − | 313.317i | −0.619790 | − | 1.07351i | ||||
\(45\) | 23.6752 | − | 41.0067i | 0.0784287 | − | 0.135843i | ||||
\(46\) | −17.1245 | + | 29.6605i | −0.0548884 | + | 0.0950696i | ||||
\(47\) | −155.799 | − | 269.852i | −0.483524 | − | 0.837489i | 0.516297 | − | 0.856410i | \(-0.327310\pi\) |
−0.999821 | + | 0.0189211i | \(0.993977\pi\) | |||||||
\(48\) | 226.924 | 0.682369 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 16.1162 | 0.0455835 | ||||||||
\(51\) | −77.3914 | − | 134.046i | −0.212489 | − | 0.368042i | ||||
\(52\) | −217.012 | + | 375.875i | −0.578733 | + | 1.00240i | ||||
\(53\) | 246.135 | − | 426.318i | 0.637910 | − | 1.10489i | −0.347980 | − | 0.937502i | \(-0.613132\pi\) |
0.985891 | − | 0.167391i | \(-0.0535343\pi\) | |||||||
\(54\) | 49.2175 | + | 85.2472i | 0.124031 | + | 0.214827i | ||||
\(55\) | −238.507 | −0.584731 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −128.813 | −0.299328 | ||||||||
\(58\) | 63.0668 | + | 109.235i | 0.142777 | + | 0.247297i | ||||
\(59\) | 49.3827 | − | 85.5333i | 0.108967 | − | 0.188737i | −0.806385 | − | 0.591391i | \(-0.798579\pi\) |
0.915352 | + | 0.402654i | \(0.131912\pi\) | |||||||
\(60\) | 79.3876 | − | 137.503i | 0.170815 | − | 0.295860i | ||||
\(61\) | 41.0841 | + | 71.1597i | 0.0862340 | + | 0.149362i | 0.905916 | − | 0.423457i | \(-0.139183\pi\) |
−0.819682 | + | 0.572818i | \(0.805850\pi\) | |||||||
\(62\) | −166.235 | −0.340515 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −359.257 | −0.701674 | ||||||||
\(65\) | 143.064 | + | 247.794i | 0.272999 | + | 0.472847i | ||||
\(66\) | 64.3744 | − | 111.500i | 0.120060 | − | 0.207949i | ||||
\(67\) | −327.334 | + | 566.959i | −0.596869 | + | 1.03381i | 0.396411 | + | 0.918073i | \(0.370255\pi\) |
−0.993280 | + | 0.115734i | \(0.963078\pi\) | |||||||
\(68\) | 140.193 | + | 242.821i | 0.250013 | + | 0.433035i | ||||
\(69\) | 222.441 | 0.388098 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 779.658 | 1.30322 | 0.651608 | − | 0.758556i | \(-0.274095\pi\) | ||||
0.651608 | + | 0.758556i | \(0.274095\pi\) | |||||||
\(72\) | −47.5705 | − | 82.3945i | −0.0778643 | − | 0.134865i | ||||
\(73\) | −414.836 | + | 718.518i | −0.665109 | + | 1.15200i | 0.314147 | + | 0.949374i | \(0.398281\pi\) |
−0.979256 | + | 0.202628i | \(0.935052\pi\) | |||||||
\(74\) | −111.660 | + | 193.402i | −0.175409 | + | 0.303817i | ||||
\(75\) | −52.3359 | − | 90.6485i | −0.0805764 | − | 0.139562i | ||||
\(76\) | 233.342 | 0.352186 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −154.455 | −0.224213 | ||||||||
\(79\) | 384.713 | + | 666.343i | 0.547894 | + | 0.948980i | 0.998419 | + | 0.0562159i | \(0.0179035\pi\) |
−0.450525 | + | 0.892764i | \(0.648763\pi\) | |||||||
\(80\) | −135.497 | + | 234.689i | −0.189363 | + | 0.327987i | ||||
\(81\) | 191.813 | − | 332.229i | 0.263117 | − | 0.455733i | ||||
\(82\) | 86.0765 | + | 149.089i | 0.115921 | + | 0.200782i | ||||
\(83\) | −613.203 | −0.810937 | −0.405469 | − | 0.914109i | \(-0.632892\pi\) | ||||
−0.405469 | + | 0.914109i | \(0.632892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 184.843 | 0.235871 | ||||||||
\(86\) | 57.0059 | + | 98.7372i | 0.0714780 | + | 0.123804i | ||||
\(87\) | 409.608 | − | 709.461i | 0.504765 | − | 0.874278i | ||||
\(88\) | −239.615 | + | 415.025i | −0.290262 | + | 0.502748i | ||||
\(89\) | −228.833 | − | 396.350i | −0.272542 | − | 0.472057i | 0.696970 | − | 0.717100i | \(-0.254531\pi\) |
−0.969512 | + | 0.245043i | \(0.921198\pi\) | |||||||
\(90\) | −30.5244 | −0.0357506 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −402.947 | −0.456632 | ||||||||
\(93\) | 539.835 | + | 935.022i | 0.601917 | + | 1.04255i | ||||
\(94\) | −100.436 | + | 173.960i | −0.110204 | + | 0.190878i | ||||
\(95\) | 76.9148 | − | 133.220i | 0.0830662 | − | 0.143875i | ||||
\(96\) | −241.396 | − | 418.111i | −0.256640 | − | 0.444513i | ||||
\(97\) | 1412.11 | 1.47813 | 0.739063 | − | 0.673636i | \(-0.235268\pi\) | ||||
0.739063 | + | 0.673636i | \(0.235268\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 451.736 | 0.458597 | ||||||||
\(100\) | 94.8054 | + | 164.208i | 0.0948054 | + | 0.164208i | ||||
\(101\) | 911.895 | − | 1579.45i | 0.898386 | − | 1.55605i | 0.0688279 | − | 0.997629i | \(-0.478074\pi\) |
0.829558 | − | 0.558421i | \(-0.188593\pi\) | |||||||
\(102\) | −49.8902 | + | 86.4124i | −0.0484301 | + | 0.0838833i | ||||
\(103\) | 203.887 | + | 353.143i | 0.195045 | + | 0.337828i | 0.946915 | − | 0.321483i | \(-0.104181\pi\) |
−0.751870 | + | 0.659311i | \(0.770848\pi\) | |||||||
\(104\) | 574.915 | 0.542068 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −317.341 | −0.290782 | ||||||||
\(107\) | 185.054 | + | 320.524i | 0.167195 | + | 0.289591i | 0.937433 | − | 0.348167i | \(-0.113196\pi\) |
−0.770237 | + | 0.637757i | \(0.779862\pi\) | |||||||
\(108\) | −579.055 | + | 1002.95i | −0.515922 | + | 0.893603i | ||||
\(109\) | −487.785 | + | 844.869i | −0.428636 | + | 0.742420i | −0.996752 | − | 0.0805287i | \(-0.974339\pi\) |
0.568116 | + | 0.822948i | \(0.307672\pi\) | |||||||
\(110\) | 76.8764 | + | 133.154i | 0.0666352 | + | 0.115416i | ||||
\(111\) | 1450.43 | 1.24026 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1978.85 | 1.64739 | 0.823693 | − | 0.567036i | \(-0.191910\pi\) | ||||
0.823693 | + | 0.567036i | \(0.191910\pi\) | |||||||
\(114\) | 41.5195 | + | 71.9139i | 0.0341111 | + | 0.0590821i | ||||
\(115\) | −132.820 | + | 230.052i | −0.107701 | + | 0.186543i | ||||
\(116\) | −741.995 | + | 1285.17i | −0.593901 | + | 1.02867i | ||||
\(117\) | −270.966 | − | 469.326i | −0.214109 | − | 0.370848i | ||||
\(118\) | −63.6689 | −0.0496711 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −210.317 | −0.159993 | ||||||||
\(121\) | −472.208 | − | 817.888i | −0.354777 | − | 0.614492i | ||||
\(122\) | 26.4848 | − | 45.8730i | 0.0196542 | − | 0.0340422i | ||||
\(123\) | 559.052 | − | 968.306i | 0.409821 | − | 0.709831i | ||||
\(124\) | −977.899 | − | 1693.77i | −0.708209 | − | 1.22665i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1392.38 | 0.972867 | 0.486433 | − | 0.873718i | \(-0.338298\pi\) | ||||
0.486433 | + | 0.873718i | \(0.338298\pi\) | |||||||
\(128\) | 577.041 | + | 999.465i | 0.398467 | + | 0.690164i | ||||
\(129\) | 370.243 | − | 641.280i | 0.252699 | − | 0.437687i | ||||
\(130\) | 92.2259 | − | 159.740i | 0.0622211 | − | 0.107770i | ||||
\(131\) | −888.509 | − | 1538.94i | −0.592591 | − | 1.02640i | −0.993882 | − | 0.110447i | \(-0.964772\pi\) |
0.401291 | − | 0.915951i | \(-0.368562\pi\) | |||||||
\(132\) | 1514.76 | 0.998809 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 422.031 | 0.272074 | ||||||||
\(135\) | 381.739 | + | 661.192i | 0.243369 | + | 0.421528i | ||||
\(136\) | 185.702 | − | 321.645i | 0.117087 | − | 0.202800i | ||||
\(137\) | 990.240 | − | 1715.15i | 0.617532 | − | 1.06960i | −0.372402 | − | 0.928071i | \(-0.621466\pi\) |
0.989935 | − | 0.141526i | \(-0.0452009\pi\) | |||||||
\(138\) | −71.6981 | − | 124.185i | −0.0442271 | − | 0.0766037i | ||||
\(139\) | −2182.09 | −1.33153 | −0.665763 | − | 0.746163i | \(-0.731894\pi\) | ||||
−0.665763 | + | 0.746163i | \(0.731894\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1304.62 | 0.779213 | ||||||||
\(142\) | −251.302 | − | 435.268i | −0.148513 | − | 0.257232i | ||||
\(143\) | −1364.87 | + | 2364.02i | −0.798154 | + | 1.38244i | ||||
\(144\) | 256.635 | − | 444.504i | 0.148515 | − | 0.257236i | ||||
\(145\) | 489.157 | + | 847.244i | 0.280153 | + | 0.485240i | ||||
\(146\) | 534.847 | 0.303180 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2627.42 | −1.45928 | ||||||||
\(149\) | −335.077 | − | 580.370i | −0.184232 | − | 0.319099i | 0.759085 | − | 0.650991i | \(-0.225646\pi\) |
−0.943317 | + | 0.331892i | \(0.892313\pi\) | |||||||
\(150\) | −33.7383 | + | 58.4364i | −0.0183648 | + | 0.0318087i | ||||
\(151\) | −1674.42 | + | 2900.18i | −0.902401 | + | 1.56300i | −0.0780315 | + | 0.996951i | \(0.524863\pi\) |
−0.824369 | + | 0.566053i | \(0.808470\pi\) | |||||||
\(152\) | −154.544 | − | 267.679i | −0.0824685 | − | 0.142840i | ||||
\(153\) | −350.096 | −0.184990 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1289.35 | −0.668149 | ||||||||
\(156\) | −908.601 | − | 1573.74i | −0.466322 | − | 0.807694i | ||||
\(157\) | 1204.20 | − | 2085.74i | 0.612140 | − | 1.06026i | −0.378739 | − | 0.925504i | \(-0.623642\pi\) |
0.990879 | − | 0.134754i | \(-0.0430245\pi\) | |||||||
\(158\) | 248.005 | − | 429.556i | 0.124875 | − | 0.216289i | ||||
\(159\) | 1030.54 | + | 1784.94i | 0.514005 | + | 0.890284i | ||||
\(160\) | 576.555 | 0.284879 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −247.303 | −0.119938 | ||||||||
\(163\) | 1905.52 | + | 3300.45i | 0.915654 | + | 1.58596i | 0.805942 | + | 0.591995i | \(0.201659\pi\) |
0.109712 | + | 0.993963i | \(0.465007\pi\) | |||||||
\(164\) | −1012.71 | + | 1754.06i | −0.482191 | + | 0.835179i | ||||
\(165\) | 499.299 | − | 864.810i | 0.235578 | − | 0.408033i | ||||
\(166\) | 197.650 | + | 342.340i | 0.0924134 | + | 0.160065i | ||||
\(167\) | −1207.15 | −0.559354 | −0.279677 | − | 0.960094i | \(-0.590227\pi\) | ||||
−0.279677 | + | 0.960094i | \(0.590227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1077.77 | 0.490564 | ||||||||
\(170\) | −59.5793 | − | 103.194i | −0.0268795 | − | 0.0465567i | ||||
\(171\) | −145.678 | + | 252.322i | −0.0651478 | + | 0.112839i | ||||
\(172\) | −670.688 | + | 1161.67i | −0.297322 | + | 0.514978i | ||||
\(173\) | 1621.64 | + | 2808.76i | 0.712665 | + | 1.23437i | 0.963853 | + | 0.266434i | \(0.0858454\pi\) |
−0.251188 | + | 0.967938i | \(0.580821\pi\) | |||||||
\(174\) | −528.105 | −0.230089 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2585.36 | −1.10727 | ||||||||
\(177\) | 206.759 | + | 358.117i | 0.0878020 | + | 0.152078i | ||||
\(178\) | −147.517 | + | 255.507i | −0.0621171 | + | 0.107590i | ||||
\(179\) | −429.864 | + | 744.546i | −0.179495 | + | 0.310894i | −0.941708 | − | 0.336433i | \(-0.890780\pi\) |
0.762213 | + | 0.647326i | \(0.224113\pi\) | |||||||
\(180\) | −179.563 | − | 311.012i | −0.0743546 | − | 0.128786i | ||||
\(181\) | 290.504 | 0.119298 | 0.0596491 | − | 0.998219i | \(-0.481002\pi\) | ||||
0.0596491 | + | 0.998219i | \(0.481002\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −344.028 | −0.138969 | ||||||||
\(184\) | 266.875 | + | 462.242i | 0.106926 | + | 0.185201i | ||||
\(185\) | −866.058 | + | 1500.06i | −0.344183 | + | 0.596142i | ||||
\(186\) | 348.004 | − | 602.760i | 0.137187 | − | 0.237616i | ||||
\(187\) | 881.725 | + | 1527.19i | 0.344803 | + | 0.597216i | ||||
\(188\) | −2363.30 | −0.916814 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −99.1660 | −0.0378645 | ||||||||
\(191\) | −2447.81 | − | 4239.73i | −0.927315 | − | 1.60616i | −0.787795 | − | 0.615937i | \(-0.788778\pi\) |
−0.139519 | − | 0.990219i | \(-0.544556\pi\) | |||||||
\(192\) | 752.082 | − | 1302.64i | 0.282692 | − | 0.489637i | ||||
\(193\) | 1774.36 | − | 3073.29i | 0.661770 | − | 1.14622i | −0.318381 | − | 0.947963i | \(-0.603139\pi\) |
0.980150 | − | 0.198256i | \(-0.0635276\pi\) | |||||||
\(194\) | −455.158 | − | 788.356i | −0.168445 | − | 0.291756i | ||||
\(195\) | −1197.98 | −0.439945 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −650.107 | −0.235118 | −0.117559 | − | 0.993066i | \(-0.537507\pi\) | ||||
−0.117559 | + | 0.993066i | \(0.537507\pi\) | |||||||
\(198\) | −145.605 | − | 252.196i | −0.0522612 | − | 0.0905190i | ||||
\(199\) | 2027.55 | − | 3511.81i | 0.722256 | − | 1.25098i | −0.237838 | − | 0.971305i | \(-0.576439\pi\) |
0.960094 | − | 0.279679i | \(-0.0902279\pi\) | |||||||
\(200\) | 125.581 | − | 217.512i | 0.0443995 | − | 0.0769023i | ||||
\(201\) | −1370.51 | − | 2373.79i | −0.480936 | − | 0.833005i | ||||
\(202\) | −1175.70 | −0.409516 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1173.94 | −0.402903 | ||||||||
\(205\) | 667.624 | + | 1156.36i | 0.227458 | + | 0.393969i | ||||
\(206\) | 131.436 | − | 227.653i | 0.0444541 | − | 0.0769968i | ||||
\(207\) | 251.564 | − | 435.722i | 0.0844682 | − | 0.146303i | ||||
\(208\) | 1550.79 | + | 2686.04i | 0.516960 | + | 0.895400i | ||||
\(209\) | 1467.58 | 0.485714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1569.67 | −0.512134 | −0.256067 | − | 0.966659i | \(-0.582427\pi\) | ||||
−0.256067 | + | 0.966659i | \(0.582427\pi\) | |||||||
\(212\) | −1866.79 | − | 3233.38i | −0.604773 | − | 1.04750i | ||||
\(213\) | −1632.16 | + | 2826.99i | −0.525042 | + | 0.909400i | ||||
\(214\) | 119.295 | − | 206.625i | 0.0381067 | − | 0.0660027i | ||||
\(215\) | 442.148 | + | 765.822i | 0.140252 | + | 0.242924i | ||||
\(216\) | 1534.05 | 0.483236 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 628.900 | 0.195387 | ||||||||
\(219\) | −1736.87 | − | 3008.34i | −0.535921 | − | 0.928242i | ||||
\(220\) | −904.468 | + | 1566.58i | −0.277178 | + | 0.480087i | ||||
\(221\) | 1057.77 | − | 1832.12i | 0.321962 | − | 0.557655i | ||||
\(222\) | −467.508 | − | 809.748i | −0.141338 | − | 0.244805i | ||||
\(223\) | −4723.86 | −1.41853 | −0.709267 | − | 0.704940i | \(-0.750974\pi\) | ||||
−0.709267 | + | 0.704940i | \(0.750974\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −236.752 | −0.0701488 | ||||||||
\(226\) | −637.831 | − | 1104.76i | −0.187734 | − | 0.325165i | ||||
\(227\) | 1842.51 | − | 3191.32i | 0.538730 | − | 0.933108i | −0.460243 | − | 0.887793i | \(-0.652238\pi\) |
0.998973 | − | 0.0453145i | \(-0.0144290\pi\) | |||||||
\(228\) | −488.487 | + | 846.084i | −0.141890 | + | 0.245760i | ||||
\(229\) | 1678.39 | + | 2907.05i | 0.484328 | + | 0.838880i | 0.999838 | − | 0.0180032i | \(-0.00573089\pi\) |
−0.515510 | + | 0.856883i | \(0.672398\pi\) | |||||||
\(230\) | 171.245 | 0.0490937 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1965.72 | 0.556275 | ||||||||
\(233\) | −1157.01 | − | 2004.00i | −0.325314 | − | 0.563460i | 0.656262 | − | 0.754533i | \(-0.272137\pi\) |
−0.981576 | + | 0.191073i | \(0.938803\pi\) | |||||||
\(234\) | −174.677 | + | 302.550i | −0.0487992 | + | 0.0845228i | ||||
\(235\) | −778.996 | + | 1349.26i | −0.216239 | + | 0.374536i | ||||
\(236\) | −374.539 | − | 648.721i | −0.103307 | − | 0.178933i | ||||
\(237\) | −3221.49 | −0.882946 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 941.179 | 0.254727 | 0.127364 | − | 0.991856i | \(-0.459348\pi\) | ||||
0.127364 | + | 0.991856i | \(0.459348\pi\) | |||||||
\(240\) | −567.311 | − | 982.611i | −0.152582 | − | 0.264280i | ||||
\(241\) | 2819.12 | − | 4882.86i | 0.753509 | − | 1.30512i | −0.192604 | − | 0.981277i | \(-0.561693\pi\) |
0.946112 | − | 0.323838i | \(-0.104973\pi\) | |||||||
\(242\) | −304.408 | + | 527.250i | −0.0808599 | + | 0.140053i | ||||
\(243\) | −1258.30 | − | 2179.43i | −0.332180 | − | 0.575353i | ||||
\(244\) | 623.199 | 0.163509 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −720.783 | −0.186811 | ||||||||
\(247\) | −880.299 | − | 1524.72i | −0.226770 | − | 0.392777i | ||||
\(248\) | −1295.34 | + | 2243.60i | −0.331671 | + | 0.574471i | ||||
\(249\) | 1283.70 | − | 2223.44i | 0.326712 | − | 0.565882i | ||||
\(250\) | −40.2905 | − | 69.7852i | −0.0101928 | − | 0.0176544i | ||||
\(251\) | −365.822 | −0.0919940 | −0.0459970 | − | 0.998942i | \(-0.514646\pi\) | ||||
−0.0459970 | + | 0.998942i | \(0.514646\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2534.28 | −0.629759 | ||||||||
\(254\) | −448.799 | − | 777.342i | −0.110867 | − | 0.192027i | ||||
\(255\) | −386.957 | + | 670.229i | −0.0950282 | + | 0.164594i | ||||
\(256\) | −1065.04 | + | 1844.70i | −0.260019 | + | 0.450367i | ||||
\(257\) | −3138.23 | − | 5435.57i | −0.761702 | − | 1.31931i | −0.941973 | − | 0.335689i | \(-0.891031\pi\) |
0.180271 | − | 0.983617i | \(-0.442303\pi\) | |||||||
\(258\) | −477.353 | −0.115189 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2170.12 | 0.517635 | ||||||||
\(261\) | −926.471 | − | 1604.69i | −0.219721 | − | 0.380568i | ||||
\(262\) | −572.776 | + | 992.076i | −0.135062 | + | 0.233934i | ||||
\(263\) | 2112.99 | − | 3659.80i | 0.495408 | − | 0.858072i | −0.504578 | − | 0.863366i | \(-0.668352\pi\) |
0.999986 | + | 0.00529397i | \(0.00168513\pi\) | |||||||
\(264\) | −1003.24 | − | 1737.66i | −0.233883 | − | 0.405097i | ||||
\(265\) | −2461.35 | −0.570564 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1916.19 | 0.439210 | ||||||||
\(268\) | 2482.64 | + | 4300.06i | 0.565864 | + | 0.980105i | ||||
\(269\) | 490.796 | − | 850.083i | 0.111243 | − | 0.192678i | −0.805029 | − | 0.593236i | \(-0.797850\pi\) |
0.916272 | + | 0.400557i | \(0.131184\pi\) | |||||||
\(270\) | 246.087 | − | 426.236i | 0.0554681 | − | 0.0960737i | ||||
\(271\) | 1942.21 | + | 3364.01i | 0.435354 | + | 0.754055i | 0.997324 | − | 0.0731021i | \(-0.0232899\pi\) |
−0.561971 | + | 0.827157i | \(0.689957\pi\) | |||||||
\(272\) | 2003.66 | 0.446653 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1276.71 | −0.281493 | ||||||||
\(275\) | 596.267 | + | 1032.76i | 0.130750 | + | 0.226465i | ||||
\(276\) | 843.544 | − | 1461.06i | 0.183969 | − | 0.318643i | ||||
\(277\) | −1807.46 | + | 3130.62i | −0.392058 | + | 0.679064i | −0.992721 | − | 0.120438i | \(-0.961570\pi\) |
0.600663 | + | 0.799502i | \(0.294903\pi\) | |||||||
\(278\) | 703.339 | + | 1218.22i | 0.151739 | + | 0.262820i | ||||
\(279\) | 2442.05 | 0.524021 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 72.6835 | 0.0154304 | 0.00771518 | − | 0.999970i | \(-0.497544\pi\) | ||||
0.00771518 | + | 0.999970i | \(0.497544\pi\) | |||||||
\(282\) | −420.511 | − | 728.347i | −0.0887982 | − | 0.153803i | ||||
\(283\) | 871.522 | − | 1509.52i | 0.183062 | − | 0.317073i | −0.759860 | − | 0.650087i | \(-0.774732\pi\) |
0.942922 | + | 0.333014i | \(0.108066\pi\) | |||||||
\(284\) | 2956.63 | − | 5121.03i | 0.617759 | − | 1.06999i | ||||
\(285\) | 322.033 | + | 557.777i | 0.0669318 | + | 0.115929i | ||||
\(286\) | 1759.72 | 0.363827 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1092.01 | −0.223427 | ||||||||
\(289\) | 1773.16 | + | 3071.21i | 0.360912 | + | 0.625119i | ||||
\(290\) | 315.334 | − | 546.174i | 0.0638519 | − | 0.110595i | ||||
\(291\) | −2956.17 | + | 5120.23i | −0.595511 | + | 1.03145i | ||||
\(292\) | 3146.30 | + | 5449.55i | 0.630559 | + | 1.09216i | ||||
\(293\) | 4989.29 | 0.994804 | 0.497402 | − | 0.867520i | \(-0.334287\pi\) | ||||
0.497402 | + | 0.867520i | \(0.334287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −493.827 | −0.0974634 | ||||||||
\(296\) | 1740.17 | + | 3014.05i | 0.341706 | + | 0.591853i | ||||
\(297\) | −3641.89 | + | 6307.94i | −0.711529 | + | 1.23240i | ||||
\(298\) | −216.007 | + | 374.135i | −0.0419897 | + | 0.0727283i | ||||
\(299\) | 1520.15 | + | 2632.97i | 0.294021 | + | 0.509260i | ||||
\(300\) | −793.876 | −0.152782 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2158.82 | 0.411346 | ||||||||
\(303\) | 3817.99 | + | 6612.95i | 0.723887 | + | 1.25381i | ||||
\(304\) | 833.741 | − | 1444.08i | 0.157297 | − | 0.272447i | ||||
\(305\) | 205.420 | − | 355.799i | 0.0385650 | − | 0.0667966i | ||||
\(306\) | 112.844 | + | 195.452i | 0.0210813 | + | 0.0365139i | ||||
\(307\) | −1664.61 | −0.309461 | −0.154731 | − | 0.987957i | \(-0.549451\pi\) | ||||
−0.154731 | + | 0.987957i | \(0.549451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1707.30 | −0.314320 | ||||||||
\(310\) | 415.589 | + | 719.821i | 0.0761415 | + | 0.131881i | ||||
\(311\) | 272.812 | − | 472.524i | 0.0497419 | − | 0.0861555i | −0.840082 | − | 0.542459i | \(-0.817493\pi\) |
0.889824 | + | 0.456303i | \(0.150827\pi\) | |||||||
\(312\) | −1203.55 | + | 2084.61i | −0.218390 | + | 0.378262i | ||||
\(313\) | 106.782 | + | 184.952i | 0.0192833 | + | 0.0333997i | 0.875506 | − | 0.483207i | \(-0.160528\pi\) |
−0.856223 | + | 0.516607i | \(0.827195\pi\) | |||||||
\(314\) | −1552.58 | −0.279035 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5835.66 | 1.03887 | ||||||||
\(317\) | 1341.97 | + | 2324.35i | 0.237767 | + | 0.411825i | 0.960073 | − | 0.279748i | \(-0.0902511\pi\) |
−0.722306 | + | 0.691574i | \(0.756918\pi\) | |||||||
\(318\) | 664.333 | − | 1150.66i | 0.117151 | − | 0.202911i | ||||
\(319\) | −4666.68 | + | 8082.93i | −0.819073 | + | 1.41868i | ||||
\(320\) | 898.142 | + | 1555.63i | 0.156899 | + | 0.271757i | ||||
\(321\) | −1549.60 | −0.269440 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1137.37 | −0.195929 | ||||||||
\(324\) | −1454.79 | − | 2519.77i | −0.249449 | − | 0.432059i | ||||
\(325\) | 715.320 | − | 1238.97i | 0.122089 | − | 0.211464i | ||||
\(326\) | 1228.39 | − | 2127.63i | 0.208693 | − | 0.361468i | ||||
\(327\) | −2042.30 | − | 3537.36i | −0.345380 | − | 0.598215i | ||||
\(328\) | 2682.91 | 0.451642 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −643.744 | −0.107385 | ||||||||
\(331\) | 2533.76 | + | 4388.61i | 0.420750 | + | 0.728760i | 0.996013 | − | 0.0892084i | \(-0.0284337\pi\) |
−0.575263 | + | 0.817968i | \(0.695100\pi\) | |||||||
\(332\) | −2325.40 | + | 4027.71i | −0.384406 | + | 0.665811i | ||||
\(333\) | 1640.33 | − | 2841.13i | 0.269938 | − | 0.467547i | ||||
\(334\) | 389.093 | + | 673.930i | 0.0637433 | + | 0.110407i | ||||
\(335\) | 3273.34 | 0.533856 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9353.21 | −1.51187 | −0.755937 | − | 0.654644i | \(-0.772818\pi\) | ||||
−0.755937 | + | 0.654644i | \(0.772818\pi\) | |||||||
\(338\) | −347.391 | − | 601.699i | −0.0559041 | − | 0.0968287i | ||||
\(339\) | −4142.60 | + | 7175.19i | −0.663703 | + | 1.14957i | ||||
\(340\) | 700.964 | − | 1214.10i | 0.111809 | − | 0.193659i | ||||
\(341\) | −6150.37 | − | 10652.8i | −0.976720 | − | 1.69173i | ||||
\(342\) | 187.822 | 0.0296966 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 1776.81 | 0.278486 | ||||||||
\(345\) | −556.103 | − | 963.198i | −0.0867813 | − | 0.150310i | ||||
\(346\) | 1045.39 | − | 1810.66i | 0.162429 | − | 0.281335i | ||||
\(347\) | −1174.67 | + | 2034.59i | −0.181728 | + | 0.314762i | −0.942469 | − | 0.334293i | \(-0.891502\pi\) |
0.760741 | + | 0.649055i | \(0.224836\pi\) | |||||||
\(348\) | −3106.64 | − | 5380.86i | −0.478544 | − | 0.828863i | ||||
\(349\) | 10472.6 | 1.60626 | 0.803128 | − | 0.595806i | \(-0.203167\pi\) | ||||
0.803128 | + | 0.595806i | \(0.203167\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8738.10 | 1.32879 | ||||||||
\(352\) | 2750.24 | + | 4763.56i | 0.416445 | + | 0.721303i | ||||
\(353\) | −3587.31 | + | 6213.41i | −0.540888 | + | 0.936845i | 0.457966 | + | 0.888970i | \(0.348578\pi\) |
−0.998853 | + | 0.0478752i | \(0.984755\pi\) | |||||||
\(354\) | 133.287 | − | 230.859i | 0.0200116 | − | 0.0346611i | ||||
\(355\) | −1949.14 | − | 3376.02i | −0.291408 | − | 0.504733i | ||||
\(356\) | −3471.14 | −0.516769 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 554.222 | 0.0818199 | ||||||||
\(359\) | 3767.06 | + | 6524.74i | 0.553811 | + | 0.959228i | 0.997995 | + | 0.0632926i | \(0.0201601\pi\) |
−0.444185 | + | 0.895935i | \(0.646507\pi\) | |||||||
\(360\) | −237.852 | + | 411.972i | −0.0348220 | + | 0.0603135i | ||||
\(361\) | 2956.23 | − | 5120.34i | 0.431000 | − | 0.746514i | ||||
\(362\) | −93.6364 | − | 162.183i | −0.0135951 | − | 0.0235474i | ||||
\(363\) | 3954.15 | 0.571733 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4148.36 | 0.594891 | ||||||||
\(366\) | 110.888 | + | 192.064i | 0.0158367 | + | 0.0274300i | ||||
\(367\) | 2726.53 | − | 4722.49i | 0.387803 | − | 0.671694i | −0.604351 | − | 0.796718i | \(-0.706567\pi\) |
0.992154 | + | 0.125024i | \(0.0399008\pi\) | |||||||
\(368\) | −1439.75 | + | 2493.71i | −0.203946 | + | 0.353244i | ||||
\(369\) | −1264.49 | − | 2190.16i | −0.178392 | − | 0.308985i | ||||
\(370\) | 1116.60 | 0.156891 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8188.68 | 1.14130 | ||||||||
\(373\) | −4115.65 | − | 7128.51i | −0.571314 | − | 0.989545i | −0.996431 | − | 0.0844067i | \(-0.973101\pi\) |
0.425117 | − | 0.905138i | \(-0.360233\pi\) | |||||||
\(374\) | 568.402 | − | 984.501i | 0.0785866 | − | 0.136116i | ||||
\(375\) | −261.680 | + | 453.242i | −0.0360349 | + | 0.0624142i | ||||
\(376\) | 1565.23 | + | 2711.06i | 0.214683 | + | 0.371841i | ||||
\(377\) | 11196.9 | 1.52963 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1670.06 | 0.226346 | 0.113173 | − | 0.993575i | \(-0.463898\pi\) | ||||
0.113173 | + | 0.993575i | \(0.463898\pi\) | |||||||
\(380\) | −583.355 | − | 1010.40i | −0.0787512 | − | 0.136401i | ||||
\(381\) | −2914.87 | + | 5048.70i | −0.391951 | + | 0.678879i | ||||
\(382\) | −1577.97 | + | 2733.13i | −0.211351 | + | 0.366071i | ||||
\(383\) | 1610.07 | + | 2788.72i | 0.214806 | + | 0.372055i | 0.953213 | − | 0.302301i | \(-0.0977548\pi\) |
−0.738407 | + | 0.674356i | \(0.764421\pi\) | |||||||
\(384\) | −4832.00 | −0.642140 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2287.68 | −0.301658 | ||||||||
\(387\) | −837.435 | − | 1450.48i | −0.109998 | − | 0.190522i | ||||
\(388\) | 5355.03 | − | 9275.19i | 0.700672 | − | 1.21360i | ||||
\(389\) | −1761.11 | + | 3050.34i | −0.229543 | + | 0.397579i | −0.957673 | − | 0.287860i | \(-0.907056\pi\) |
0.728130 | + | 0.685439i | \(0.240390\pi\) | |||||||
\(390\) | 386.138 | + | 668.811i | 0.0501356 | + | 0.0868374i | ||||
\(391\) | 1964.07 | 0.254034 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7440.15 | 0.954977 | ||||||||
\(394\) | 209.545 | + | 362.943i | 0.0267937 | + | 0.0464081i | ||||
\(395\) | 1923.57 | − | 3331.71i | 0.245026 | − | 0.424397i | ||||
\(396\) | 1713.08 | − | 2967.14i | 0.217387 | − | 0.376526i | ||||
\(397\) | −2727.58 | − | 4724.31i | −0.344819 | − | 0.597245i | 0.640502 | − | 0.767957i | \(-0.278726\pi\) |
−0.985321 | + | 0.170712i | \(0.945393\pi\) | |||||||
\(398\) | −2614.11 | −0.329229 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1354.97 | 0.169372 | ||||||||
\(401\) | 580.899 | + | 1006.15i | 0.0723409 | + | 0.125298i | 0.899927 | − | 0.436041i | \(-0.143620\pi\) |
−0.827586 | + | 0.561339i | \(0.810286\pi\) | |||||||
\(402\) | −883.494 | + | 1530.26i | −0.109614 | + | 0.189856i | ||||
\(403\) | −7378.39 | + | 12779.7i | −0.912019 | + | 1.57966i | ||||
\(404\) | −6916.20 | − | 11979.2i | −0.851718 | − | 1.47522i | ||||
\(405\) | −1918.13 | −0.235339 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −16524.8 | −2.01255 | ||||||||
\(408\) | 777.510 | + | 1346.69i | 0.0943443 | + | 0.163409i | ||||
\(409\) | −3699.32 | + | 6407.42i | −0.447237 | + | 0.774637i | −0.998205 | − | 0.0598896i | \(-0.980925\pi\) |
0.550968 | + | 0.834526i | \(0.314258\pi\) | |||||||
\(410\) | 430.382 | − | 745.444i | 0.0518416 | − | 0.0897924i | ||||
\(411\) | 4146.01 | + | 7181.10i | 0.497586 | + | 0.861843i | ||||
\(412\) | 3092.74 | 0.369826 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −324.341 | −0.0385036 | ||||||||
\(415\) | 1533.01 | + | 2655.25i | 0.181331 | + | 0.314075i | ||||
\(416\) | 3299.37 | − | 5714.68i | 0.388858 | − | 0.673522i | ||||
\(417\) | 4568.06 | − | 7912.11i | 0.536448 | − | 0.929155i | ||||
\(418\) | −473.035 | − | 819.320i | −0.0553514 | − | 0.0958714i | ||||
\(419\) | −2134.46 | −0.248867 | −0.124433 | − | 0.992228i | \(-0.539711\pi\) | ||||
−0.124433 | + | 0.992228i | \(0.539711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3902.36 | −0.451756 | −0.225878 | − | 0.974156i | \(-0.572525\pi\) | ||||
−0.225878 | + | 0.974156i | \(0.572525\pi\) | |||||||
\(422\) | 505.941 | + | 876.316i | 0.0583621 | + | 0.101086i | ||||
\(423\) | 1475.43 | − | 2555.52i | 0.169593 | − | 0.293744i | ||||
\(424\) | −2472.79 | + | 4283.00i | −0.283229 | + | 0.490568i | ||||
\(425\) | −462.107 | − | 800.393i | −0.0527423 | − | 0.0913524i | ||||
\(426\) | 2104.34 | 0.239333 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2807.06 | 0.317020 | ||||||||
\(429\) | −5714.53 | − | 9897.86i | −0.643124 | − | 1.11392i | ||||
\(430\) | 285.030 | − | 493.686i | 0.0319659 | − | 0.0553666i | ||||
\(431\) | 1809.07 | − | 3133.39i | 0.202180 | − | 0.350186i | −0.747050 | − | 0.664767i | \(-0.768531\pi\) |
0.949231 | + | 0.314581i | \(0.101864\pi\) | |||||||
\(432\) | 4137.98 | + | 7167.18i | 0.460853 | + | 0.798221i | ||||
\(433\) | −4222.37 | −0.468624 | −0.234312 | − | 0.972161i | \(-0.575284\pi\) | ||||
−0.234312 | + | 0.972161i | \(0.575284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4096.08 | −0.451475 | ||||||||
\(436\) | 3699.57 | + | 6407.85i | 0.406370 | + | 0.703854i | ||||
\(437\) | 817.269 | − | 1415.55i | 0.0894629 | − | 0.154954i | ||||
\(438\) | −1119.67 | + | 1939.32i | −0.122146 | + | 0.211563i | ||||
\(439\) | 6758.98 | + | 11706.9i | 0.734826 | + | 1.27276i | 0.954800 | + | 0.297250i | \(0.0960693\pi\) |
−0.219974 | + | 0.975506i | \(0.570597\pi\) | |||||||
\(440\) | 2396.15 | 0.259618 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1363.78 | −0.146762 | ||||||||
\(443\) | −8295.58 | − | 14368.4i | −0.889695 | − | 1.54100i | −0.840236 | − | 0.542222i | \(-0.817583\pi\) |
−0.0494599 | − | 0.998776i | \(-0.515750\pi\) | |||||||
\(444\) | 5500.34 | − | 9526.87i | 0.587916 | − | 1.01830i | ||||
\(445\) | −1144.17 | + | 1981.75i | −0.121885 | + | 0.211110i | ||||
\(446\) | 1522.61 | + | 2637.24i | 0.161654 | + | 0.279993i | ||||
\(447\) | 2805.85 | 0.296895 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8354.32 | 0.878095 | 0.439048 | − | 0.898464i | \(-0.355316\pi\) | ||||
0.439048 | + | 0.898464i | \(0.355316\pi\) | |||||||
\(450\) | 76.3109 | + | 132.174i | 0.00799407 | + | 0.0138461i | ||||
\(451\) | −6369.31 | + | 11032.0i | −0.665009 | + | 1.15183i | ||||
\(452\) | 7504.23 | − | 12997.7i | 0.780905 | − | 1.35257i | ||||
\(453\) | −7010.59 | − | 12142.7i | −0.727122 | − | 1.25941i | ||||
\(454\) | −2375.54 | −0.245572 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1294.12 | 0.132900 | ||||||||
\(457\) | 640.168 | + | 1108.80i | 0.0655269 | + | 0.113496i | 0.896928 | − | 0.442177i | \(-0.145794\pi\) |
−0.831401 | + | 0.555673i | \(0.812461\pi\) | |||||||
\(458\) | 1081.97 | − | 1874.03i | 0.110387 | − | 0.191195i | ||||
\(459\) | 2822.47 | − | 4888.66i | 0.287019 | − | 0.497131i | ||||
\(460\) | 1007.37 | + | 1744.81i | 0.102106 | + | 0.176853i | ||||
\(461\) | −6986.72 | −0.705865 | −0.352932 | − | 0.935649i | \(-0.614815\pi\) | ||||
−0.352932 | + | 0.935649i | \(0.614815\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5587.32 | −0.560831 | −0.280416 | − | 0.959879i | \(-0.590472\pi\) | ||||
−0.280416 | + | 0.959879i | \(0.590472\pi\) | |||||||
\(464\) | 5302.36 | + | 9183.96i | 0.530508 | + | 0.918867i | ||||
\(465\) | 2699.18 | − | 4675.11i | 0.269185 | − | 0.466243i | ||||
\(466\) | −745.863 | + | 1291.87i | −0.0741447 | + | 0.128422i | ||||
\(467\) | 4966.92 | + | 8602.95i | 0.492166 | + | 0.852456i | 0.999959 | − | 0.00902263i | \(-0.00287203\pi\) |
−0.507793 | + | 0.861479i | \(0.669539\pi\) | |||||||
\(468\) | −4110.24 | −0.405974 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1004.36 | 0.0985691 | ||||||||
\(471\) | 5041.85 | + | 8732.75i | 0.493241 | + | 0.854318i | ||||
\(472\) | −496.121 | + | 859.308i | −0.0483810 | + | 0.0837984i | ||||
\(473\) | −4218.21 | + | 7306.15i | −0.410049 | + | 0.710226i | ||||
\(474\) | 1038.36 | + | 1798.50i | 0.100619 | + | 0.174278i | ||||
\(475\) | −769.148 | −0.0742967 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4661.84 | 0.447486 | ||||||||
\(478\) | −303.365 | − | 525.443i | −0.0290284 | − | 0.0502787i | ||||
\(479\) | −2534.31 | + | 4389.55i | −0.241744 | + | 0.418714i | −0.961211 | − | 0.275813i | \(-0.911053\pi\) |
0.719467 | + | 0.694527i | \(0.244386\pi\) | |||||||
\(480\) | −1206.98 | + | 2090.55i | −0.114773 | + | 0.198792i | ||||
\(481\) | 9912.14 | + | 17168.3i | 0.939614 | + | 1.62746i | ||||
\(482\) | −3634.68 | −0.343476 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7162.86 | −0.672695 | ||||||||
\(485\) | −3530.28 | − | 6114.62i | −0.330519 | − | 0.572476i | ||||
\(486\) | −811.158 | + | 1404.97i | −0.0757096 | + | 0.131133i | ||||
\(487\) | −132.177 | + | 228.937i | −0.0122988 | + | 0.0213021i | −0.872109 | − | 0.489311i | \(-0.837248\pi\) |
0.859811 | + | 0.510613i | \(0.170582\pi\) | |||||||
\(488\) | −412.750 | − | 714.904i | −0.0382875 | − | 0.0663159i | ||||
\(489\) | −15956.3 | −1.47560 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7459.47 | −0.685623 | −0.342812 | − | 0.939404i | \(-0.611379\pi\) | ||||
−0.342812 | + | 0.939404i | \(0.611379\pi\) | |||||||
\(492\) | −4240.09 | − | 7344.05i | −0.388532 | − | 0.672958i | ||||
\(493\) | 3616.68 | − | 6264.28i | 0.330400 | − | 0.572270i | ||||
\(494\) | −567.483 | + | 982.910i | −0.0516848 | + | 0.0895206i | ||||
\(495\) | −1129.34 | − | 1956.07i | −0.102545 | − | 0.177614i | ||||
\(496\) | −13976.3 | −1.26523 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1655.07 | −0.148927 | ||||||||
\(499\) | −3603.34 | − | 6241.16i | −0.323261 | − | 0.559905i | 0.657897 | − | 0.753108i | \(-0.271446\pi\) |
−0.981159 | + | 0.193202i | \(0.938113\pi\) | |||||||
\(500\) | 474.027 | − | 821.039i | 0.0423982 | − | 0.0734359i | ||||
\(501\) | 2527.09 | − | 4377.05i | 0.225354 | − | 0.390324i | ||||
\(502\) | 117.913 | + | 204.232i | 0.0104835 | + | 0.0181580i | ||||
\(503\) | 10886.7 | 0.965037 | 0.482519 | − | 0.875886i | \(-0.339722\pi\) | ||||
0.482519 | + | 0.875886i | \(0.339722\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9118.95 | −0.803541 | ||||||||
\(506\) | 816.861 | + | 1414.84i | 0.0717666 | + | 0.124303i | ||||
\(507\) | −2256.24 | + | 3907.93i | −0.197640 | + | 0.342322i | ||||
\(508\) | 5280.22 | − | 9145.61i | 0.461165 | − | 0.798761i | ||||
\(509\) | −3752.48 | − | 6499.49i | −0.326770 | − | 0.565982i | 0.655099 | − | 0.755543i | \(-0.272627\pi\) |
−0.981869 | + | 0.189561i | \(0.939294\pi\) | |||||||
\(510\) | 498.902 | 0.0433172 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10605.8 | 0.915459 | ||||||||
\(513\) | −2348.91 | − | 4068.43i | −0.202158 | − | 0.350148i | ||||
\(514\) | −2023.05 | + | 3504.03i | −0.173605 | + | 0.300693i | ||||
\(515\) | 1019.44 | − | 1765.72i | 0.0872267 | − | 0.151081i | ||||
\(516\) | −2808.09 | − | 4863.75i | −0.239572 | − | 0.414951i | ||||
\(517\) | −14863.7 | −1.26442 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −13579.2 | −1.14848 | ||||||||
\(520\) | −1437.29 | − | 2489.46i | −0.121210 | − | 0.209942i | ||||
\(521\) | −11132.4 | + | 19281.8i | −0.936120 | + | 1.62141i | −0.163495 | + | 0.986544i | \(0.552277\pi\) |
−0.772625 | + | 0.634863i | \(0.781056\pi\) | |||||||
\(522\) | −597.248 | + | 1034.46i | −0.0500782 | + | 0.0867380i | ||||
\(523\) | 5643.33 | + | 9774.54i | 0.471828 | + | 0.817229i | 0.999480 | − | 0.0322308i | \(-0.0102612\pi\) |
−0.527653 | + | 0.849460i | \(0.676928\pi\) | |||||||
\(524\) | −13477.7 | −1.12362 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2724.27 | −0.225824 | ||||||||
\(527\) | 4766.55 | + | 8255.90i | 0.393992 | + | 0.682415i | ||||
\(528\) | 5412.30 | − | 9374.37i | 0.446098 | − | 0.772665i | ||||
\(529\) | 4672.20 | − | 8092.48i | 0.384006 | − | 0.665118i | ||||
\(530\) | 793.352 | + | 1374.13i | 0.0650208 | + | 0.112619i | ||||
\(531\) | 935.316 | 0.0764393 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15282.1 | 1.24191 | ||||||||
\(534\) | −617.634 | − | 1069.77i | −0.0500518 | − | 0.0866922i | ||||
\(535\) | 925.272 | − | 1602.62i | 0.0747720 | − | 0.129509i | ||||
\(536\) | 3288.55 | − | 5695.94i | 0.265007 | − | 0.459006i | ||||
\(537\) | −1799.79 | − | 3117.32i | −0.144630 | − | 0.250507i | ||||
\(538\) | −632.781 | −0.0507084 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5790.55 | 0.461455 | ||||||||
\(541\) | −8203.38 | − | 14208.7i | −0.651924 | − | 1.12917i | −0.982655 | − | 0.185440i | \(-0.940629\pi\) |
0.330732 | − | 0.943725i | \(-0.392705\pi\) | |||||||
\(542\) | 1252.04 | − | 2168.60i | 0.0992248 | − | 0.171862i | ||||
\(543\) | −608.152 | + | 1053.35i | −0.0480631 | + | 0.0832478i | ||||
\(544\) | −2131.44 | − | 3691.77i | −0.167987 | − | 0.290962i | ||||
\(545\) | 4877.85 | 0.383384 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8692.48 | −0.679458 | −0.339729 | − | 0.940523i | \(-0.610335\pi\) | ||||
−0.339729 | + | 0.940523i | \(0.610335\pi\) | |||||||
\(548\) | −7510.41 | − | 13008.4i | −0.585454 | − | 1.01404i | ||||
\(549\) | −389.070 | + | 673.888i | −0.0302461 | + | 0.0523877i | ||||
\(550\) | 384.382 | − | 665.769i | 0.0298002 | − | 0.0516154i | ||||
\(551\) | −3009.87 | − | 5213.25i | −0.232713 | − | 0.403071i | ||||
\(552\) | −2234.75 | −0.172314 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 2330.36 | 0.178714 | ||||||||
\(555\) | −3626.08 | − | 6280.55i | −0.277330 | − | 0.480350i | ||||
\(556\) | −8274.94 | + | 14332.6i | −0.631179 | + | 1.09323i | ||||
\(557\) | 6967.85 | − | 12068.7i | 0.530049 | − | 0.918071i | −0.469337 | − | 0.883019i | \(-0.655507\pi\) |
0.999385 | − | 0.0350521i | \(-0.0111597\pi\) | |||||||
\(558\) | −787.132 | − | 1363.35i | −0.0597168 | − | 0.103432i | ||||
\(559\) | 10120.9 | 0.765773 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7383.34 | −0.555659 | ||||||||
\(562\) | −23.4276 | − | 40.5778i | −0.00175843 | − | 0.00304568i | ||||
\(563\) | 11131.8 | − | 19280.9i | 0.833304 | − | 1.44332i | −0.0621002 | − | 0.998070i | \(-0.519780\pi\) |
0.895404 | − | 0.445255i | \(-0.146887\pi\) | |||||||
\(564\) | 4947.41 | − | 8569.17i | 0.369368 | − | 0.639764i | ||||
\(565\) | −4947.13 | − | 8568.68i | −0.368367 | − | 0.638030i | ||||
\(566\) | −1123.65 | −0.0834462 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7832.81 | −0.578622 | ||||||||
\(569\) | −4762.83 | − | 8249.47i | −0.350911 | − | 0.607795i | 0.635498 | − | 0.772102i | \(-0.280795\pi\) |
−0.986409 | + | 0.164307i | \(0.947461\pi\) | |||||||
\(570\) | 207.598 | − | 359.570i | 0.0152549 | − | 0.0264223i | ||||
\(571\) | −3835.00 | + | 6642.41i | −0.281068 | + | 0.486823i | −0.971648 | − | 0.236432i | \(-0.924022\pi\) |
0.690580 | + | 0.723256i | \(0.257355\pi\) | |||||||
\(572\) | 10351.7 | + | 17929.8i | 0.756693 | + | 1.31063i | ||||
\(573\) | 20497.3 | 1.49439 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1328.20 | 0.0963304 | ||||||||
\(576\) | −1701.10 | − | 2946.39i | −0.123054 | − | 0.213136i | ||||
\(577\) | −1953.57 | + | 3383.69i | −0.140950 | + | 0.244133i | −0.927855 | − | 0.372942i | \(-0.878349\pi\) |
0.786904 | + | 0.617075i | \(0.211682\pi\) | |||||||
\(578\) | 1143.07 | − | 1979.85i | 0.0822582 | − | 0.142475i | ||||
\(579\) | 7429.04 | + | 12867.5i | 0.533230 | + | 0.923582i | ||||
\(580\) | 7419.95 | 0.531201 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3811.38 | 0.271455 | ||||||||
\(583\) | −11741.0 | − | 20336.0i | −0.834067 | − | 1.44465i | ||||
\(584\) | 4167.64 | − | 7218.57i | 0.295305 | − | 0.511484i | ||||
\(585\) | −1354.83 | + | 2346.63i | −0.0957526 | + | 0.165848i | ||||
\(586\) | −1608.17 | − | 2785.43i | −0.113367 | − | 0.196357i | ||||
\(587\) | −19891.6 | −1.39866 | −0.699331 | − | 0.714798i | \(-0.746519\pi\) | ||||
−0.699331 | + | 0.714798i | \(0.746519\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7933.61 | 0.555007 | ||||||||
\(590\) | 159.172 | + | 275.694i | 0.0111068 | + | 0.0192375i | ||||
\(591\) | 1360.96 | − | 2357.25i | 0.0947248 | − | 0.164068i | ||||
\(592\) | −9387.89 | + | 16260.3i | −0.651757 | + | 1.12888i | ||||
\(593\) | −2390.18 | − | 4139.91i | −0.165519 | − | 0.286688i | 0.771320 | − | 0.636447i | \(-0.219597\pi\) |
−0.936840 | + | 0.349759i | \(0.886263\pi\) | |||||||
\(594\) | 4695.48 | 0.324340 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5082.74 | −0.349324 | ||||||||
\(597\) | 8489.08 | + | 14703.5i | 0.581968 | + | 1.00800i | ||||
\(598\) | 979.959 | − | 1697.34i | 0.0670126 | − | 0.116069i | ||||
\(599\) | −5542.80 | + | 9600.42i | −0.378085 | + | 0.654862i | −0.990784 | − | 0.135454i | \(-0.956751\pi\) |
0.612699 | + | 0.790317i | \(0.290084\pi\) | |||||||
\(600\) | 525.791 | + | 910.697i | 0.0357756 | + | 0.0619651i | ||||
\(601\) | −1573.44 | −0.106792 | −0.0533958 | − | 0.998573i | \(-0.517005\pi\) | ||||
−0.0533958 | + | 0.998573i | \(0.517005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6199.76 | −0.418696 | ||||||||
\(604\) | 12699.5 | + | 21996.2i | 0.855524 | + | 1.48181i | ||||
\(605\) | −2361.04 | + | 4089.44i | −0.158661 | + | 0.274809i | ||||
\(606\) | 2461.26 | − | 4263.03i | 0.164987 | − | 0.285765i | ||||
\(607\) | −4271.36 | − | 7398.22i | −0.285617 | − | 0.494702i | 0.687142 | − | 0.726523i | \(-0.258865\pi\) |
−0.972759 | + | 0.231821i | \(0.925532\pi\) | |||||||
\(608\) | −3547.65 | −0.236639 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −264.848 | −0.0175793 | ||||||||
\(611\) | 8915.70 | + | 15442.4i | 0.590328 | + | 1.02248i | ||||
\(612\) | −1327.64 | + | 2299.54i | −0.0876904 | + | 0.151884i | ||||
\(613\) | −7534.08 | + | 13049.4i | −0.496409 | + | 0.859805i | −0.999991 | − | 0.00414209i | \(-0.998682\pi\) |
0.503583 | + | 0.863947i | \(0.332015\pi\) | |||||||
\(614\) | 536.545 | + | 929.323i | 0.0352658 | + | 0.0610822i | ||||
\(615\) | −5590.52 | −0.366555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2524.58 | 0.164725 | 0.0823627 | − | 0.996602i | \(-0.473753\pi\) | ||||
0.0823627 | + | 0.996602i | \(0.473753\pi\) | |||||||
\(618\) | 550.304 | + | 953.155i | 0.0358196 | + | 0.0620413i | ||||
\(619\) | 10619.5 | − | 18393.4i | 0.689551 | − | 1.19434i | −0.282433 | − | 0.959287i | \(-0.591141\pi\) |
0.971983 | − | 0.235050i | \(-0.0755253\pi\) | |||||||
\(620\) | −4889.50 | + | 8468.85i | −0.316721 | + | 0.548576i | ||||
\(621\) | 4056.22 | + | 7025.58i | 0.262110 | + | 0.453988i | ||||
\(622\) | −351.735 | −0.0226741 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −12985.9 | −0.833095 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 68.8369 | − | 119.229i | 0.00439501 | − | 0.00761238i | ||||
\(627\) | −3072.28 | + | 5321.34i | −0.195686 | + | 0.338937i | ||||
\(628\) | −9133.21 | − | 15819.2i | −0.580342 | − | 1.00518i | ||||
\(629\) | 12806.8 | 0.811827 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8885.83 | −0.560601 | −0.280300 | − | 0.959912i | \(-0.590434\pi\) | ||||
−0.280300 | + | 0.959912i | \(0.590434\pi\) | |||||||
\(632\) | −3865.01 | − | 6694.39i | −0.243262 | − | 0.421343i | ||||
\(633\) | 3286.00 | − | 5691.51i | 0.206330 | − | 0.357373i | ||||
\(634\) | 865.095 | − | 1498.39i | 0.0541914 | − | 0.0938622i | ||||
\(635\) | −3480.96 | − | 6029.20i | −0.217540 | − | 0.376790i | ||||
\(636\) | 15632.1 | 0.974609 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 6016.74 | 0.373362 | ||||||||
\(639\) | 3691.71 | + | 6394.23i | 0.228547 | + | 0.395856i | ||||
\(640\) | 2885.21 | − | 4997.32i | 0.178200 | − | 0.308651i | ||||
\(641\) | −1827.82 | + | 3165.87i | −0.112628 | + | 0.195077i | −0.916829 | − | 0.399280i | \(-0.869260\pi\) |
0.804201 | + | 0.594357i | \(0.202593\pi\) | |||||||
\(642\) | 499.473 | + | 865.112i | 0.0307050 | + | 0.0531827i | ||||
\(643\) | 4221.22 | 0.258894 | 0.129447 | − | 0.991586i | \(-0.458680\pi\) | ||||
0.129447 | + | 0.991586i | \(0.458680\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3702.43 | −0.226020 | ||||||||
\(646\) | 366.602 | + | 634.974i | 0.0223278 | + | 0.0386729i | ||||
\(647\) | −51.8393 | + | 89.7884i | −0.00314995 | + | 0.00545587i | −0.867596 | − | 0.497270i | \(-0.834336\pi\) |
0.864446 | + | 0.502725i | \(0.167669\pi\) | |||||||
\(648\) | −1927.04 | + | 3337.73i | −0.116823 | + | 0.202343i | ||||
\(649\) | −2355.62 | − | 4080.05i | −0.142475 | − | 0.246773i | ||||
\(650\) | −922.259 | −0.0556523 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 28904.5 | 1.73618 | ||||||||
\(653\) | −2238.05 | − | 3876.42i | −0.134122 | − | 0.232307i | 0.791140 | − | 0.611636i | \(-0.209488\pi\) |
−0.925262 | + | 0.379329i | \(0.876155\pi\) | |||||||
\(654\) | −1316.56 | + | 2280.35i | −0.0787181 | + | 0.136344i | ||||
\(655\) | −4442.55 | + | 7694.71i | −0.265015 | + | 0.459019i | ||||
\(656\) | 7236.91 | + | 12534.7i | 0.430722 | + | 0.746033i | ||||
\(657\) | −7857.07 | −0.466566 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12022.0 | 0.710641 | 0.355321 | − | 0.934745i | \(-0.384372\pi\) | ||||
0.355321 | + | 0.934745i | \(0.384372\pi\) | |||||||
\(660\) | −3786.89 | − | 6559.09i | −0.223340 | − | 0.386837i | ||||
\(661\) | −6725.51 | + | 11648.9i | −0.395752 | + | 0.685462i | −0.993197 | − | 0.116448i | \(-0.962849\pi\) |
0.597445 | + | 0.801910i | \(0.296183\pi\) | |||||||
\(662\) | 1633.38 | − | 2829.11i | 0.0958962 | − | 0.166097i | ||||
\(663\) | 4428.77 | + | 7670.85i | 0.259426 | + | 0.449338i | ||||
\(664\) | 6160.53 | 0.360053 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2114.87 | −0.123047 | ||||||||
\(667\) | 5197.60 | + | 9002.51i | 0.301727 | + | 0.522606i | ||||
\(668\) | −4577.77 | + | 7928.93i | −0.265149 | + | 0.459251i | ||||
\(669\) | 9889.10 | − | 17128.4i | 0.571502 | − | 0.989870i | ||||
\(670\) | −1055.08 | − | 1827.45i | −0.0608375 | − | 0.105374i | ||||
\(671\) | 3919.53 | 0.225502 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9774.83 | 0.559869 | 0.279935 | − | 0.960019i | \(-0.409687\pi\) | ||||
0.279935 | + | 0.960019i | \(0.409687\pi\) | |||||||
\(674\) | 3014.76 | + | 5221.72i | 0.172291 | + | 0.298417i | ||||
\(675\) | 1908.70 | − | 3305.96i | 0.108838 | − | 0.188513i | ||||
\(676\) | 4087.13 | − | 7079.13i | 0.232541 | − | 0.402772i | ||||
\(677\) | −11928.7 | − | 20661.1i | −0.677190 | − | 1.17293i | −0.975824 | − | 0.218560i | \(-0.929864\pi\) |
0.298634 | − | 0.954368i | \(-0.403469\pi\) | |||||||
\(678\) | 5341.04 | 0.302539 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1857.02 | −0.104726 | ||||||||
\(681\) | 7714.36 | + | 13361.7i | 0.434089 | + | 0.751865i | ||||
\(682\) | −3964.83 | + | 6867.28i | −0.222612 | + | 0.385574i | ||||
\(683\) | −5959.68 | + | 10322.5i | −0.333881 | + | 0.578299i | −0.983269 | − | 0.182158i | \(-0.941692\pi\) |
0.649388 | + | 0.760457i | \(0.275025\pi\) | |||||||
\(684\) | 1104.88 | + | 1913.72i | 0.0617636 | + | 0.106978i | ||||
\(685\) | −9902.40 | −0.552338 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14054.4 | −0.780508 | ||||||||
\(688\) | 4792.79 | + | 8301.36i | 0.265587 | + | 0.460009i | ||||
\(689\) | −14085.2 | + | 24396.3i | −0.778816 | + | 1.34895i | ||||
\(690\) | −358.490 | + | 620.924i | −0.0197790 | + | 0.0342582i | ||||
\(691\) | 4101.79 | + | 7104.51i | 0.225817 | + | 0.391126i | 0.956564 | − | 0.291522i | \(-0.0941616\pi\) |
−0.730747 | + | 0.682648i | \(0.760828\pi\) | |||||||
\(692\) | 24598.4 | 1.35129 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1514.50 | 0.0828380 | ||||||||
\(695\) | 5455.21 | + | 9448.71i | 0.297738 | + | 0.515698i | ||||
\(696\) | −4115.11 | + | 7127.58i | −0.224113 | + | 0.388176i | ||||
\(697\) | 4936.22 | − | 8549.79i | 0.268254 | − | 0.464629i | ||||
\(698\) | −3375.56 | − | 5846.64i | −0.183047 | − | 0.317047i | ||||
\(699\) | 9688.49 | 0.524252 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 449.084 | 0.0241964 | 0.0120982 | − | 0.999927i | \(-0.496149\pi\) | ||||
0.0120982 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(702\) | −2816.50 | − | 4878.32i | −0.151427 | − | 0.262280i | ||||
\(703\) | 5329.01 | − | 9230.12i | 0.285900 | − | 0.495193i | ||||
\(704\) | −8568.51 | + | 14841.1i | −0.458719 | + | 0.794524i | ||||
\(705\) | −3261.56 | − | 5649.18i | −0.174237 | − | 0.301788i | ||||
\(706\) | 4625.11 | 0.246556 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3136.30 | 0.166482 | ||||||||
\(709\) | −948.819 | − | 1643.40i | −0.0502590 | − | 0.0870512i | 0.839801 | − | 0.542894i | \(-0.182671\pi\) |
−0.890060 | + | 0.455843i | \(0.849338\pi\) | |||||||
\(710\) | −1256.51 | + | 2176.34i | −0.0664170 | + | 0.115038i | ||||
\(711\) | −3643.27 | + | 6310.32i | −0.192170 | + | 0.332849i | ||||
\(712\) | 2298.96 | + | 3981.92i | 0.121007 | + | 0.209591i | ||||
\(713\) | −13700.2 | −0.719601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13648.7 | 0.713891 | ||||||||
\(716\) | 3260.27 | + | 5646.96i | 0.170171 | + | 0.294744i | ||||
\(717\) | −1970.30 | + | 3412.66i | −0.102625 | + | 0.177752i | ||||
\(718\) | 2428.43 | − | 4206.16i | 0.126223 | − | 0.218625i | ||||
\(719\) | −3247.35 | − | 5624.58i | −0.168436 | − | 0.291740i | 0.769434 | − | 0.638726i | \(-0.220538\pi\) |
−0.937870 | + | 0.346986i | \(0.887205\pi\) | |||||||
\(720\) | −2566.35 | −0.132836 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3811.45 | −0.196465 | ||||||||
\(723\) | 11803.3 | + | 20443.9i | 0.607150 | + | 1.05162i | ||||
\(724\) | 1101.65 | − | 1908.12i | 0.0565506 | − | 0.0979485i | ||||
\(725\) | 2445.78 | − | 4236.22i | 0.125288 | − | 0.217006i | ||||
\(726\) | −1274.52 | − | 2207.53i | −0.0651540 | − | 0.112850i | ||||
\(727\) | −18311.2 | −0.934148 | −0.467074 | − | 0.884218i | \(-0.654692\pi\) | ||||
−0.467074 | + | 0.884218i | \(0.654692\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20894.5 | 1.06155 | ||||||||
\(730\) | −1337.12 | − | 2315.96i | −0.0677931 | − | 0.117421i | ||||
\(731\) | 3269.11 | − | 5662.27i | 0.165407 | − | 0.286493i | ||||
\(732\) | −1304.63 | + | 2259.68i | −0.0658749 | + | 0.114099i | ||||
\(733\) | −10616.6 | − | 18388.5i | −0.534972 | − | 0.926598i | −0.999165 | − | 0.0408640i | \(-0.986989\pi\) |
0.464193 | − | 0.885734i | \(-0.346344\pi\) | |||||||
\(734\) | −3515.30 | −0.176774 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6126.27 | 0.306817 | ||||||||
\(737\) | 15614.3 | + | 27044.7i | 0.780406 | + | 1.35170i | ||||
\(738\) | −815.152 | + | 1411.88i | −0.0406587 | + | 0.0704230i | ||||
\(739\) | 11011.8 | − | 19072.9i | 0.548138 | − | 0.949404i | −0.450264 | − | 0.892896i | \(-0.648670\pi\) |
0.998402 | − | 0.0565080i | \(-0.0179966\pi\) | |||||||
\(740\) | 6568.55 | + | 11377.1i | 0.326304 | + | 0.565175i | ||||
\(741\) | 7371.40 | 0.365446 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9436.77 | 0.465951 | 0.232975 | − | 0.972483i | \(-0.425154\pi\) | ||||
0.232975 | + | 0.972483i | \(0.425154\pi\) | |||||||
\(744\) | −5423.44 | − | 9393.67i | −0.267248 | − | 0.462888i | ||||
\(745\) | −1675.38 | + | 2901.85i | −0.0823911 | + | 0.142706i | ||||
\(746\) | −2653.14 | + | 4595.38i | −0.130212 | + | 0.225535i | ||||
\(747\) | −2903.54 | − | 5029.08i | −0.142216 | − | 0.246325i | ||||
\(748\) | 13374.8 | 0.653783 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 337.383 | 0.0164260 | ||||||||
\(751\) | 19580.9 | + | 33915.1i | 0.951421 | + | 1.64791i | 0.742354 | + | 0.670008i | \(0.233709\pi\) |
0.209067 | + | 0.977901i | \(0.432957\pi\) | |||||||
\(752\) | −8444.16 | + | 14625.7i | −0.409477 | + | 0.709235i | ||||
\(753\) | 765.826 | − | 1326.45i | 0.0370627 | − | 0.0641946i | ||||
\(754\) | −3609.03 | − | 6251.03i | −0.174315 | − | 0.301922i | ||||
\(755\) | 16744.2 | 0.807132 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20340.6 | 0.976607 | 0.488303 | − | 0.872674i | \(-0.337616\pi\) | ||||
0.488303 | + | 0.872674i | \(0.337616\pi\) | |||||||
\(758\) | −538.301 | − | 932.365i | −0.0257942 | − | 0.0446768i | ||||
\(759\) | 5305.36 | − | 9189.16i | 0.253719 | − | 0.439454i | ||||
\(760\) | −772.722 | + | 1338.39i | −0.0368810 | + | 0.0638798i | ||||
\(761\) | −1653.95 | − | 2864.72i | −0.0787852 | − | 0.136460i | 0.823941 | − | 0.566676i | \(-0.191771\pi\) |
−0.902726 | + | 0.430216i | \(0.858437\pi\) | |||||||
\(762\) | 3758.13 | 0.178665 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −37130.4 | −1.75829 | ||||||||
\(765\) | 875.239 | + | 1515.96i | 0.0413651 | + | 0.0716465i | ||||
\(766\) | 1037.93 | − | 1797.74i | 0.0489580 | − | 0.0847978i | ||||
\(767\) | −2825.95 | + | 4894.69i | −0.133037 | + | 0.230427i | ||||
\(768\) | −4459.19 | − | 7723.54i | −0.209514 | − | 0.362889i | ||||
\(769\) | 17234.0 | 0.808159 | 0.404079 | − | 0.914724i | \(-0.367592\pi\) | ||||
0.404079 | + | 0.914724i | \(0.367592\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26278.7 | 1.22750 | ||||||||
\(772\) | −13457.5 | − | 23309.1i | −0.627393 | − | 1.08668i | ||||
\(773\) | 4363.17 | − | 7557.23i | 0.203017 | − | 0.351636i | −0.746482 | − | 0.665406i | \(-0.768259\pi\) |
0.949499 | + | 0.313770i | \(0.101592\pi\) | |||||||
\(774\) | −539.851 | + | 935.049i | −0.0250705 | + | 0.0434233i | ||||
\(775\) | 3223.38 | + | 5583.05i | 0.149403 | + | 0.258773i | ||||
\(776\) | −14186.7 | −0.656281 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2270.60 | 0.104634 | ||||||||
\(779\) | −4108.01 | − | 7115.29i | −0.188941 | − | 0.327255i | ||||
\(780\) | −4543.00 | + | 7868.72i | −0.208546 | + | 0.361212i | ||||
\(781\) | 18595.3 | − | 32208.1i | 0.851977 | − | 1.47567i | ||||
\(782\) | −633.068 | − | 1096.51i | −0.0289494 | − | 0.0501419i | ||||
\(783\) | 29876.8 | 1.36362 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12042.0 | −0.547515 | ||||||||
\(786\) | −2398.14 | − | 4153.70i | −0.108828 | − | 0.188496i | ||||
\(787\) | 5321.03 | − | 9216.30i | 0.241009 | − | 0.417440i | −0.719993 | − | 0.693982i | \(-0.755855\pi\) |
0.961002 | + | 0.276541i | \(0.0891883\pi\) | |||||||
\(788\) | −2465.35 | + | 4270.11i | −0.111452 | + | 0.193041i | ||||
\(789\) | 8846.81 | + | 15323.1i | 0.399182 | + | 0.691404i | ||||
\(790\) | −2480.05 | −0.111691 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4538.35 | −0.203615 | ||||||||
\(793\) | −2351.06 | − | 4072.16i | −0.105282 | − | 0.182354i | ||||
\(794\) | −1758.33 | + | 3045.51i | −0.0785904 | + | 0.136123i | ||||
\(795\) | 5152.68 | − | 8924.71i | 0.229870 | − | 0.398147i | ||||
\(796\) | −15377.8 | − | 26635.1i | −0.684737 | − | 1.18600i | ||||
\(797\) | 29234.1 | 1.29928 | 0.649640 | − | 0.760242i | \(-0.274920\pi\) | ||||
0.649640 | + | 0.760242i | \(0.274920\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11519.3 | 0.510044 | ||||||||
\(800\) | −1441.39 | − | 2496.56i | −0.0637010 | − | 0.110333i | ||||
\(801\) | 2167.07 | − | 3753.47i | 0.0955925 | − | 0.165571i | ||||
\(802\) | 374.475 | − | 648.610i | 0.0164878 | − | 0.0285576i | ||||
\(803\) | 19788.2 | + | 34274.2i | 0.869629 | + | 1.50624i | ||||
\(804\) | −20789.0 | −0.911906 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9512.93 | 0.415730 | ||||||||
\(807\) | 2054.90 | + | 3559.19i | 0.0896355 | + | 0.155253i | ||||
\(808\) | −9161.33 | + | 15867.9i | −0.398879 | + | 0.690879i | ||||
\(809\) | −18105.6 | + | 31359.8i | −0.786846 | + | 1.36286i | 0.141045 | + | 0.990003i | \(0.454954\pi\) |
−0.927890 | + | 0.372853i | \(0.878379\pi\) | |||||||
\(810\) | 618.258 | + | 1070.85i | 0.0268190 | + | 0.0464518i | ||||
\(811\) | −27995.2 | −1.21214 | −0.606069 | − | 0.795412i | \(-0.707254\pi\) | ||||
−0.606069 | + | 0.795412i | \(0.707254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16263.6 | −0.701585 | ||||||||
\(814\) | 5326.35 | + | 9225.51i | 0.229347 | + | 0.397241i | ||||
\(815\) | 9527.58 | − | 16502.3i | 0.409493 | − | 0.709262i | ||||
\(816\) | −4194.53 | + | 7265.15i | −0.179949 | + | 0.311680i | ||||
\(817\) | −2720.62 | − | 4712.25i | −0.116502 | − | 0.201788i | ||||
\(818\) | 4769.52 | 0.203866 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10127.1 | 0.431285 | ||||||||
\(821\) | −22402.9 | − | 38802.9i | −0.952333 | − | 1.64949i | −0.740356 | − | 0.672215i | \(-0.765343\pi\) |
−0.211977 | − | 0.977275i | \(-0.567990\pi\) | |||||||
\(822\) | 2672.72 | − | 4629.28i | 0.113408 | − | 0.196429i | ||||
\(823\) | 7925.47 | − | 13727.3i | 0.335680 | − | 0.581415i | −0.647935 | − | 0.761695i | \(-0.724367\pi\) |
0.983615 | + | 0.180281i | \(0.0577007\pi\) | |||||||
\(824\) | −2048.35 | − | 3547.85i | −0.0865991 | − | 0.149994i | ||||
\(825\) | −4992.99 | −0.210707 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −45013.9 | −1.89273 | −0.946363 | − | 0.323104i | \(-0.895274\pi\) | ||||
−0.946363 | + | 0.323104i | \(0.895274\pi\) | |||||||
\(828\) | −1907.97 | − | 3304.70i | −0.0800804 | − | 0.138703i | ||||
\(829\) | −2827.91 | + | 4898.09i | −0.118477 | + | 0.205208i | −0.919164 | − | 0.393874i | \(-0.871135\pi\) |
0.800687 | + | 0.599083i | \(0.204468\pi\) | |||||||
\(830\) | 988.251 | − | 1711.70i | 0.0413285 | − | 0.0715831i | ||||
\(831\) | −7567.63 | − | 13107.5i | −0.315906 | − | 0.547166i | ||||
\(832\) | 20558.7 | 0.856664 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −5889.58 | −0.244532 | ||||||||
\(835\) | 3017.88 | + | 5227.11i | 0.125075 | + | 0.216637i | ||||
\(836\) | 5565.36 | − | 9639.49i | 0.230242 | − | 0.398790i | ||||
\(837\) | −19687.8 | + | 34100.3i | −0.813036 | + | 1.40822i | ||||
\(838\) | 687.987 | + | 1191.63i | 0.0283605 | + | 0.0491219i | ||||
\(839\) | −22037.0 | −0.906797 | −0.453398 | − | 0.891308i | \(-0.649789\pi\) | ||||
−0.453398 | + | 0.891308i | \(0.649789\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13894.9 | 0.569719 | ||||||||
\(842\) | 1257.82 | + | 2178.62i | 0.0514816 | + | 0.0891687i | ||||
\(843\) | −152.158 | + | 263.546i | −0.00621662 | + | 0.0107675i | ||||
\(844\) | −5952.51 | + | 10310.1i | −0.242765 | + | 0.420482i | ||||
\(845\) | −2694.42 | − | 4666.88i | −0.109694 | − | 0.189995i | ||||
\(846\) | −1902.27 | −0.0773065 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −26680.5 | −1.08044 | ||||||||
\(849\) | 3648.95 | + | 6320.17i | 0.147505 | + | 0.255486i | ||||
\(850\) | −297.896 | + | 515.972i | −0.0120209 | + | 0.0208208i | ||||
\(851\) | −9202.42 | + | 15939.1i | −0.370687 | + | 0.642049i | ||||
\(852\) | 12379.0 | + | 21441.1i | 0.497768 | + | 0.862160i | ||||
\(853\) | −44486.7 | −1.78569 | −0.892846 | − | 0.450362i | \(-0.851295\pi\) | ||||
−0.892846 | + | 0.450362i | \(0.851295\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1456.78 | 0.0582699 | ||||||||
\(856\) | −1859.14 | − | 3220.13i | −0.0742339 | − | 0.128577i | ||||
\(857\) | 19279.8 | − | 33393.6i | 0.768478 | − | 1.33104i | −0.169910 | − | 0.985460i | \(-0.554348\pi\) |
0.938388 | − | 0.345583i | \(-0.112319\pi\) | |||||||
\(858\) | −3683.86 | + | 6380.64i | −0.146579 | + | 0.253883i | ||||
\(859\) | −4213.01 | − | 7297.14i | −0.167341 | − | 0.289843i | 0.770143 | − | 0.637871i | \(-0.220185\pi\) |
−0.937484 | + | 0.348028i | \(0.886851\pi\) | |||||||
\(860\) | 6706.88 | 0.265933 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2332.42 | −0.0921608 | ||||||||
\(863\) | 10027.2 | + | 17367.6i | 0.395514 | + | 0.685051i | 0.993167 | − | 0.116704i | \(-0.0372330\pi\) |
−0.597652 | + | 0.801755i | \(0.703900\pi\) | |||||||
\(864\) | 8803.75 | − | 15248.5i | 0.346655 | − | 0.600423i | ||||
\(865\) | 8108.20 | − | 14043.8i | 0.318713 | − | 0.552028i | ||||
\(866\) | 1360.97 | + | 2357.27i | 0.0534038 | + | 0.0924981i | ||||
\(867\) | −14848.0 | −0.581621 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36702.6 | 1.43274 | ||||||||
\(870\) | 1320.26 | + | 2286.76i | 0.0514496 | + | 0.0891133i | ||||
\(871\) | 18731.9 | − | 32444.6i | 0.728709 | − | 1.26216i | ||||
\(872\) | 4900.52 | − | 8487.95i | 0.190313 | − | 0.329631i | ||||
\(873\) | 6686.41 | + | 11581.2i | 0.259222 | + | 0.448985i | ||||
\(874\) | −1053.70 | −0.0407803 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −26346.3 | −1.01616 | ||||||||
\(877\) | −23541.1 | − | 40774.3i | −0.906414 | − | 1.56995i | −0.819008 | − | 0.573782i | \(-0.805476\pi\) |
−0.0874057 | − | 0.996173i | \(-0.527858\pi\) | |||||||
\(878\) | 4357.16 | − | 7546.83i | 0.167480 | − | 0.290083i | ||||
\(879\) | −10444.8 | + | 18090.9i | −0.400789 | + | 0.694186i | ||||
\(880\) | 6463.41 | + | 11195.0i | 0.247593 | + | 0.428843i | ||||
\(881\) | −9467.24 | −0.362042 | −0.181021 | − | 0.983479i | \(-0.557940\pi\) | ||||
−0.181021 | + | 0.983479i | \(0.557940\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3049.49 | −0.116221 | −0.0581106 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581106 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(884\) | −8022.62 | − | 13895.6i | −0.305237 | − | 0.528686i | ||||
\(885\) | 1033.79 | − | 1790.59i | 0.0392663 | − | 0.0680112i | ||||
\(886\) | −5347.73 | + | 9262.54i | −0.202777 | + | 0.351220i | ||||
\(887\) | 9734.29 | + | 16860.3i | 0.368484 | + | 0.638233i | 0.989329 | − | 0.145700i | \(-0.0465435\pi\) |
−0.620845 | + | 0.783934i | \(0.713210\pi\) | |||||||
\(888\) | −14571.7 | −0.550669 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1475.17 | 0.0555592 | ||||||||
\(891\) | −9149.71 | − | 15847.8i | −0.344026 | − | 0.595870i | ||||
\(892\) | −17913.9 | + | 31027.8i | −0.672423 | + | 1.16467i | ||||
\(893\) | 4793.30 | − | 8302.25i | 0.179621 | − | 0.311113i | ||||
\(894\) | −904.393 | − | 1566.45i | −0.0338338 | − | 0.0586019i | ||||
\(895\) | 4298.64 | 0.160545 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12729.3 | −0.473823 | ||||||||
\(898\) | −2692.80 | − | 4664.06i | −0.100067 | − | 0.173321i | ||||
\(899\) | −25227.8 | + | 43695.8i | −0.935922 | + | 1.62106i | ||||
\(900\) | −897.815 | + | 1555.06i | −0.0332524 | + | 0.0575948i | ||||
\(901\) | 9099.26 | + | 15760.4i | 0.336449 | + | 0.582746i | ||||
\(902\) | 8211.92 | 0.303134 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19880.5 | −0.731432 | ||||||||
\(905\) | −726.260 | − | 1257.92i | −0.0266759 | − | 0.0462040i | ||||
\(906\) | −4519.36 | + | 7827.77i | −0.165724 | + | 0.287042i | ||||
\(907\) | 16007.1 | − | 27725.1i | 0.586006 | − | 1.01499i | −0.408743 | − | 0.912649i | \(-0.634033\pi\) |
0.994749 | − | 0.102343i | \(-0.0326339\pi\) | |||||||
\(908\) | −13974.4 | − | 24204.3i | −0.510745 | − | 0.884636i | ||||
\(909\) | 17271.4 | 0.630206 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20921.1 | 0.760866 | 0.380433 | − | 0.924809i | \(-0.375775\pi\) | ||||
0.380433 | + | 0.924809i | \(0.375775\pi\) | |||||||
\(912\) | 3490.77 | + | 6046.19i | 0.126744 | + | 0.219528i | ||||
\(913\) | −14625.3 | + | 25331.8i | −0.530150 | + | 0.918247i | ||||
\(914\) | 412.683 | − | 714.788i | 0.0149347 | − | 0.0258677i | ||||
\(915\) | 860.069 | + | 1489.68i | 0.0310743 | + | 0.0538223i | ||||
\(916\) | 25459.2 | 0.918337 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3639.00 | −0.130833 | ||||||||
\(919\) | −21733.7 | − | 37643.9i | −0.780118 | − | 1.35120i | −0.931872 | − | 0.362786i | \(-0.881826\pi\) |
0.151754 | − | 0.988418i | \(-0.451508\pi\) | |||||||
\(920\) | 1334.38 | − | 2311.21i | 0.0478186 | − | 0.0828242i | ||||
\(921\) | 3484.77 | − | 6035.79i | 0.124676 | − | 0.215946i | ||||
\(922\) | 2251.99 | + | 3900.55i | 0.0804395 | + | 0.139325i | ||||
\(923\) | −44616.4 | −1.59108 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8660.58 | 0.307847 | ||||||||
\(926\) | 1800.93 | + | 3119.30i | 0.0639116 | + | 0.110698i | ||||
\(927\) | −1930.83 | + | 3344.30i | −0.0684108 | + | 0.118491i | ||||
\(928\) | 11281.0 | − | 19539.3i | 0.399050 | − | 0.691174i | ||||
\(929\) | 9271.05 | + | 16057.9i | 0.327420 | + | 0.567108i | 0.981999 | − | 0.188885i | \(-0.0604875\pi\) |
−0.654579 | + | 0.755993i | \(0.727154\pi\) | |||||||
\(930\) | −3480.04 | −0.122704 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −17550.5 | −0.616830 | ||||||||
\(933\) | 1142.23 | + | 1978.40i | 0.0400803 | + | 0.0694210i | ||||
\(934\) | 3201.91 | − | 5545.87i | 0.112173 | − | 0.194290i | ||||
\(935\) | 4408.62 | − | 7635.96i | 0.154200 | − | 0.267083i | ||||
\(936\) | 2722.25 | + | 4715.07i | 0.0950635 | + | 0.164655i | ||||
\(937\) | 13842.5 | 0.482619 | 0.241309 | − | 0.970448i | \(-0.422423\pi\) | ||||
0.241309 | + | 0.970448i | \(0.422423\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −894.167 | −0.0310757 | ||||||||
\(940\) | 5908.24 | + | 10233.4i | 0.205006 | + | 0.355081i | ||||
\(941\) | 26696.6 | − | 46239.8i | 0.924850 | − | 1.60189i | 0.133047 | − | 0.991110i | \(-0.457524\pi\) |
0.791803 | − | 0.610777i | \(-0.209143\pi\) | |||||||
\(942\) | 3250.22 | − | 5629.55i | 0.112418 | − | 0.194714i | ||||
\(943\) | 7093.93 | + | 12287.0i | 0.244974 | + | 0.424307i | ||||
\(944\) | −5352.98 | −0.184560 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5438.52 | 0.186915 | ||||||||
\(947\) | −11172.1 | − | 19350.7i | −0.383364 | − | 0.664005i | 0.608177 | − | 0.793801i | \(-0.291901\pi\) |
−0.991541 | + | 0.129796i | \(0.958568\pi\) | |||||||
\(948\) | −12216.6 | + | 21159.7i | −0.418540 | + | 0.724933i | ||||
\(949\) | 23739.3 | − | 41117.6i | 0.812022 | − | 1.40646i | ||||
\(950\) | 247.915 | + | 429.401i | 0.00846676 | + | 0.0146649i | ||||
\(951\) | −11237.3 | −0.383169 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8902.63 | −0.302607 | −0.151304 | − | 0.988487i | \(-0.548347\pi\) | ||||
−0.151304 | + | 0.988487i | \(0.548347\pi\) | |||||||
\(954\) | −1502.62 | − | 2602.62i | −0.0509950 | − | 0.0883259i | ||||
\(955\) | −12239.0 | + | 21198.6i | −0.414708 | + | 0.718295i | ||||
\(956\) | 3569.15 | − | 6181.96i | 0.120748 | − | 0.209141i | ||||
\(957\) | −19538.8 | − | 33842.2i | −0.659979 | − | 1.14312i | ||||
\(958\) | 3267.48 | 0.110196 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −7520.82 | −0.252847 | ||||||||
\(961\) | −18353.0 | − | 31788.4i | −0.616059 | − | 1.06705i | ||||
\(962\) | 6389.84 | − | 11067.5i | 0.214155 | − | 0.370927i | ||||
\(963\) | −1752.48 | + | 3035.39i | −0.0586427 | + | 0.101572i | ||||
\(964\) | −21381.4 | − | 37033.7i | −0.714366 | − | 1.23732i | ||||
\(965\) | −17743.6 | −0.591905 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2225.57 | −0.0740119 | −0.0370059 | − | 0.999315i | \(-0.511782\pi\) | ||||
−0.0370059 | + | 0.999315i | \(0.511782\pi\) | |||||||
\(968\) | 4744.02 | + | 8216.89i | 0.157519 | + | 0.272831i | ||||
\(969\) | 2381.02 | − | 4124.04i | 0.0789363 | − | 0.136722i | ||||
\(970\) | −2275.79 | + | 3941.78i | −0.0753311 | + | 0.130477i | ||||
\(971\) | 5662.41 | + | 9807.59i | 0.187143 | + | 0.324141i | 0.944296 | − | 0.329096i | \(-0.106744\pi\) |
−0.757154 | + | 0.653237i | \(0.773411\pi\) | |||||||
\(972\) | −19086.9 | −0.629849 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 170.415 | 0.00560621 | ||||||||
\(975\) | 2994.96 | + | 5187.41i | 0.0983747 | + | 0.170390i | ||||
\(976\) | 2226.72 | − | 3856.78i | 0.0730281 | − | 0.126488i | ||||
\(977\) | 28847.9 | − | 49966.1i | 0.944654 | − | 1.63619i | 0.188213 | − | 0.982128i | \(-0.439731\pi\) |
0.756442 | − | 0.654061i | \(-0.226936\pi\) | |||||||
\(978\) | 5143.10 | + | 8908.11i | 0.168158 | + | 0.291258i | ||||
\(979\) | −21831.3 | −0.712697 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9238.73 | −0.300683 | ||||||||
\(982\) | 2404.36 | + | 4164.48i | 0.0781328 | + | 0.135330i | ||||
\(983\) | −29828.6 | + | 51664.7i | −0.967839 | + | 1.67635i | −0.266054 | + | 0.963958i | \(0.585720\pi\) |
−0.701786 | + | 0.712388i | \(0.747614\pi\) | |||||||
\(984\) | −5616.49 | + | 9728.05i | −0.181959 | + | 0.315162i | ||||
\(985\) | 1625.27 | + | 2815.05i | 0.0525740 | + | 0.0910608i | ||||
\(986\) | −4662.98 | −0.150608 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13353.1 | −0.429980 | ||||||||
\(989\) | 4698.10 | + | 8137.35i | 0.151053 | + | 0.261631i | ||||
\(990\) | −728.026 | + | 1260.98i | −0.0233719 | + | 0.0404813i | ||||
\(991\) | −1445.30 | + | 2503.33i | −0.0463284 | + | 0.0802431i | −0.888260 | − | 0.459342i | \(-0.848085\pi\) |
0.841931 | + | 0.539585i | \(0.181419\pi\) | |||||||
\(992\) | 14867.6 | + | 25751.5i | 0.475855 | + | 0.824205i | ||||
\(993\) | −21217.1 | −0.678050 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −20275.5 | −0.646005 | ||||||||
\(996\) | −9736.15 | − | 16863.5i | −0.309741 | − | 0.536487i | ||||
\(997\) | 5309.79 | − | 9196.83i | 0.168669 | − | 0.292143i | −0.769283 | − | 0.638908i | \(-0.779387\pi\) |
0.937952 | + | 0.346765i | \(0.112720\pi\) | |||||||
\(998\) | −2322.88 | + | 4023.35i | −0.0736769 | + | 0.127612i | ||||
\(999\) | 26448.7 | + | 45810.4i | 0.837636 | + | 1.45083i |
(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 | 245.4.e.q.116.3 | 12 | ||
7.2 | even | 3 | inner | 245.4.e.q.226.3 | 12 | ||
7.3 | odd | 6 | 245.4.a.p.1.4 | yes | 6 | ||
7.4 | even | 3 | 245.4.a.o.1.4 | ✓ | 6 | ||
7.5 | odd | 6 | 245.4.e.p.226.3 | 12 | |||
7.6 | odd | 2 | 245.4.e.p.116.3 | 12 | |||
21.11 | odd | 6 | 2205.4.a.bz.1.3 | 6 | |||
21.17 | even | 6 | 2205.4.a.ca.1.3 | 6 | |||
35.4 | even | 6 | 1225.4.a.bj.1.3 | 6 | |||
35.24 | odd | 6 | 1225.4.a.bi.1.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.4 | ✓ | 6 | 7.4 | even | 3 | ||
245.4.a.p.1.4 | yes | 6 | 7.3 | odd | 6 | ||
245.4.e.p.116.3 | 12 | 7.6 | odd | 2 | |||
245.4.e.p.226.3 | 12 | 7.5 | odd | 6 | |||
245.4.e.q.116.3 | 12 | 1.1 | even | 1 | trivial | ||
245.4.e.q.226.3 | 12 | 7.2 | even | 3 | inner | ||
1225.4.a.bi.1.3 | 6 | 35.24 | odd | 6 | |||
1225.4.a.bj.1.3 | 6 | 35.4 | even | 6 | |||
2205.4.a.bz.1.3 | 6 | 21.11 | odd | 6 | |||
2205.4.a.ca.1.3 | 6 | 21.17 | even | 6 |