Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,4,Mod(16,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.e (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: | \(2.65508595026\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(1.68614 - 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.16 |
Dual form | 45.4.e.a.31.2 |
$q$-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 \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.68614 | − | 2.92048i | 0.596141 | − | 1.03255i | −0.397244 | − | 0.917713i | \(-0.630033\pi\) |
0.993385 | − | 0.114833i | \(-0.0366333\pi\) | |||||||
\(3\) | −1.50000 | − | 4.97494i | −0.288675 | − | 0.957427i | ||||
\(4\) | −1.68614 | − | 2.92048i | −0.210768 | − | 0.365060i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | −17.0584 | − | 4.00772i | −1.16068 | − | 0.272691i | ||||
\(7\) | −0.813859 | + | 1.40965i | −0.0439443 | + | 0.0761137i | −0.887161 | − | 0.461460i | \(-0.847326\pi\) |
0.843217 | + | 0.537574i | \(0.180659\pi\) | |||||||
\(8\) | 15.6060 | 0.689693 | ||||||||
\(9\) | −22.5000 | + | 14.9248i | −0.833333 | + | 0.552771i | ||||
\(10\) | −16.8614 | −0.533204 | ||||||||
\(11\) | 16.4307 | − | 28.4588i | 0.450368 | − | 0.780060i | −0.548041 | − | 0.836451i | \(-0.684626\pi\) |
0.998409 | + | 0.0563918i | \(0.0179596\pi\) | |||||||
\(12\) | −12.0000 | + | 12.7692i | −0.288675 | + | 0.307178i | ||||
\(13\) | 16.5109 | + | 28.5977i | 0.352253 | + | 0.610121i | 0.986644 | − | 0.162892i | \(-0.0520822\pi\) |
−0.634391 | + | 0.773013i | \(0.718749\pi\) | |||||||
\(14\) | 2.74456 | + | 4.75372i | 0.0523939 | + | 0.0907490i | ||||
\(15\) | −17.7921 | + | 18.9325i | −0.306260 | + | 0.325891i | ||||
\(16\) | 39.8030 | − | 68.9408i | 0.621922 | − | 1.07720i | ||||
\(17\) | 110.307 | 1.57373 | 0.786864 | − | 0.617126i | \(-0.211703\pi\) | ||||
0.786864 | + | 0.617126i | \(0.211703\pi\) | |||||||
\(18\) | 5.64947 | + | 90.8762i | 0.0739774 | + | 1.18998i | ||||
\(19\) | −54.3070 | −0.655731 | −0.327865 | − | 0.944724i | \(-0.606329\pi\) | ||||
−0.327865 | + | 0.944724i | \(0.606329\pi\) | |||||||
\(20\) | −8.43070 | + | 14.6024i | −0.0942581 | + | 0.163260i | ||||
\(21\) | 8.23369 | + | 1.93443i | 0.0855590 | + | 0.0201013i | ||||
\(22\) | −55.4090 | − | 95.9711i | −0.536965 | − | 0.930051i | ||||
\(23\) | 33.7188 | + | 58.4026i | 0.305689 | + | 0.529469i | 0.977415 | − | 0.211331i | \(-0.0677799\pi\) |
−0.671725 | + | 0.740800i | \(0.734447\pi\) | |||||||
\(24\) | −23.4090 | − | 77.6387i | −0.199097 | − | 0.660331i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | 111.359 | 0.839970 | ||||||||
\(27\) | 108.000 | + | 89.5489i | 0.769800 | + | 0.638285i | ||||
\(28\) | 5.48913 | 0.0370481 | ||||||||
\(29\) | −137.259 | + | 237.740i | −0.878912 | + | 1.52232i | −0.0263757 | + | 0.999652i | \(0.508397\pi\) |
−0.852536 | + | 0.522668i | \(0.824937\pi\) | |||||||
\(30\) | 25.2921 | + | 83.8844i | 0.153923 | + | 0.510504i | ||||
\(31\) | 3.00000 | + | 5.19615i | 0.0173812 | + | 0.0301050i | 0.874585 | − | 0.484872i | \(-0.161134\pi\) |
−0.857204 | + | 0.514977i | \(0.827800\pi\) | |||||||
\(32\) | −71.8030 | − | 124.366i | −0.396659 | − | 0.687034i | ||||
\(33\) | −166.227 | − | 39.0535i | −0.876860 | − | 0.206010i | ||||
\(34\) | 185.993 | − | 322.150i | 0.938164 | − | 1.62495i | ||||
\(35\) | 8.13859 | 0.0393050 | ||||||||
\(36\) | 81.5258 | + | 40.5455i | 0.377434 | + | 0.187711i | ||||
\(37\) | −347.723 | −1.54501 | −0.772504 | − | 0.635010i | \(-0.780996\pi\) | ||||
−0.772504 | + | 0.635010i | \(0.780996\pi\) | |||||||
\(38\) | −91.5693 | + | 158.603i | −0.390908 | + | 0.677072i | ||||
\(39\) | 117.505 | − | 125.037i | 0.482459 | − | 0.513383i | ||||
\(40\) | −39.0149 | − | 67.5758i | −0.154220 | − | 0.267117i | ||||
\(41\) | −145.668 | − | 252.305i | −0.554868 | − | 0.961060i | −0.997914 | − | 0.0645606i | \(-0.979435\pi\) |
0.443046 | − | 0.896499i | \(-0.353898\pi\) | |||||||
\(42\) | 19.5326 | − | 20.7846i | 0.0717607 | − | 0.0763604i | ||||
\(43\) | −100.694 | + | 174.408i | −0.357110 | + | 0.618533i | −0.987477 | − | 0.157765i | \(-0.949571\pi\) |
0.630367 | + | 0.776297i | \(0.282905\pi\) | |||||||
\(44\) | −110.818 | −0.379692 | ||||||||
\(45\) | 120.876 | + | 60.1158i | 0.400426 | + | 0.199145i | ||||
\(46\) | 227.418 | 0.728935 | ||||||||
\(47\) | 241.048 | − | 417.507i | 0.748094 | − | 1.29574i | −0.200642 | − | 0.979665i | \(-0.564303\pi\) |
0.948735 | − | 0.316071i | \(-0.102364\pi\) | |||||||
\(48\) | −402.681 | − | 94.6062i | −1.21087 | − | 0.284484i | ||||
\(49\) | 170.175 | + | 294.752i | 0.496138 | + | 0.859336i | ||||
\(50\) | 42.1535 | + | 73.0120i | 0.119228 | + | 0.206509i | ||||
\(51\) | −165.461 | − | 548.771i | −0.454296 | − | 1.50673i | ||||
\(52\) | 55.6793 | − | 96.4394i | 0.148487 | − | 0.257187i | ||||
\(53\) | −175.228 | −0.454140 | −0.227070 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227070 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(54\) | 443.629 | − | 164.420i | 1.11797 | − | 0.414347i | ||||
\(55\) | −164.307 | −0.402821 | ||||||||
\(56\) | −12.7011 | + | 21.9989i | −0.0303081 | + | 0.0524951i | ||||
\(57\) | 81.4605 | + | 270.174i | 0.189293 | + | 0.627815i | ||||
\(58\) | 462.878 | + | 801.728i | 1.04791 | + | 1.81503i | ||||
\(59\) | 91.6209 | + | 158.692i | 0.202170 | + | 0.350169i | 0.949227 | − | 0.314591i | \(-0.101867\pi\) |
−0.747057 | + | 0.664760i | \(0.768534\pi\) | |||||||
\(60\) | 85.2921 | + | 20.0386i | 0.183519 | + | 0.0431162i | ||||
\(61\) | −218.297 | + | 378.102i | −0.458199 | + | 0.793623i | −0.998866 | − | 0.0476132i | \(-0.984839\pi\) |
0.540667 | + | 0.841237i | \(0.318172\pi\) | |||||||
\(62\) | 20.2337 | 0.0414465 | ||||||||
\(63\) | −2.72686 | − | 43.8637i | −0.00545321 | − | 0.0877192i | ||||
\(64\) | 152.568 | 0.297984 | ||||||||
\(65\) | 82.5544 | − | 142.988i | 0.157532 | − | 0.272854i | ||||
\(66\) | −394.337 | + | 419.613i | −0.735447 | + | 0.782587i | ||||
\(67\) | 415.750 | + | 720.100i | 0.758089 | + | 1.31305i | 0.943824 | + | 0.330448i | \(0.107200\pi\) |
−0.185736 | + | 0.982600i | \(0.559467\pi\) | |||||||
\(68\) | −185.993 | − | 322.150i | −0.331691 | − | 0.574506i | ||||
\(69\) | 239.971 | − | 255.353i | 0.418683 | − | 0.445520i | ||||
\(70\) | 13.7228 | − | 23.7686i | 0.0234313 | − | 0.0405842i | ||||
\(71\) | −118.951 | −0.198829 | −0.0994146 | − | 0.995046i | \(-0.531697\pi\) | ||||
−0.0994146 | + | 0.995046i | \(0.531697\pi\) | |||||||
\(72\) | −351.134 | + | 232.916i | −0.574744 | + | 0.381242i | ||||
\(73\) | 183.318 | 0.293914 | 0.146957 | − | 0.989143i | \(-0.453052\pi\) | ||||
0.146957 | + | 0.989143i | \(0.453052\pi\) | |||||||
\(74\) | −586.310 | + | 1015.52i | −0.921042 | + | 1.59529i | ||||
\(75\) | 126.461 | + | 29.7108i | 0.194699 | + | 0.0457427i | ||||
\(76\) | 91.5693 | + | 158.603i | 0.138207 | + | 0.239381i | ||||
\(77\) | 26.7446 | + | 46.3229i | 0.0395822 | + | 0.0685583i | ||||
\(78\) | −167.038 | − | 554.002i | −0.242478 | − | 0.804210i | ||||
\(79\) | 319.147 | − | 552.778i | 0.454517 | − | 0.787246i | −0.544144 | − | 0.838992i | \(-0.683145\pi\) |
0.998660 | + | 0.0517463i | \(0.0164787\pi\) | |||||||
\(80\) | −398.030 | −0.556264 | ||||||||
\(81\) | 283.500 | − | 671.617i | 0.388889 | − | 0.921285i | ||||
\(82\) | −982.470 | −1.32312 | ||||||||
\(83\) | 747.322 | − | 1294.40i | 0.988304 | − | 1.71179i | 0.362085 | − | 0.932145i | \(-0.382065\pi\) |
0.626219 | − | 0.779647i | \(-0.284602\pi\) | |||||||
\(84\) | −8.23369 | − | 27.3081i | −0.0106949 | − | 0.0354709i | ||||
\(85\) | −275.768 | − | 477.643i | −0.351896 | − | 0.609502i | ||||
\(86\) | 339.569 | + | 588.151i | 0.425776 | + | 0.737465i | ||||
\(87\) | 1388.63 | + | 326.247i | 1.71123 | + | 0.402038i | ||||
\(88\) | 256.417 | − | 444.127i | 0.310615 | − | 0.538002i | ||||
\(89\) | −1437.27 | −1.71180 | −0.855900 | − | 0.517142i | \(-0.826996\pi\) | ||||
−0.855900 | + | 0.517142i | \(0.826996\pi\) | |||||||
\(90\) | 379.382 | − | 251.653i | 0.444337 | − | 0.294740i | ||||
\(91\) | −53.7501 | −0.0619181 | ||||||||
\(92\) | 113.709 | − | 196.950i | 0.128859 | − | 0.223190i | ||||
\(93\) | 21.3505 | − | 22.7190i | 0.0238059 | − | 0.0253318i | ||||
\(94\) | −812.880 | − | 1407.95i | −0.891938 | − | 1.54488i | ||||
\(95\) | 135.768 | + | 235.156i | 0.146626 | + | 0.253964i | ||||
\(96\) | −511.011 | + | 543.765i | −0.543279 | + | 0.578102i | ||||
\(97\) | 445.884 | − | 772.294i | 0.466729 | − | 0.808398i | −0.532549 | − | 0.846399i | \(-0.678766\pi\) |
0.999278 | + | 0.0380011i | \(0.0120990\pi\) | |||||||
\(98\) | 1147.76 | 1.18307 | ||||||||
\(99\) | 55.0516 | + | 885.548i | 0.0558878 | + | 0.899000i | ||||
\(100\) | 84.3070 | 0.0843070 | ||||||||
\(101\) | 76.8720 | − | 133.146i | 0.0757332 | − | 0.131174i | −0.825672 | − | 0.564151i | \(-0.809204\pi\) |
0.901405 | + | 0.432977i | \(0.142537\pi\) | |||||||
\(102\) | −1881.66 | − | 442.080i | −1.82659 | − | 0.429142i | ||||
\(103\) | −67.6469 | − | 117.168i | −0.0647131 | − | 0.112086i | 0.831854 | − | 0.554995i | \(-0.187280\pi\) |
−0.896567 | + | 0.442909i | \(0.853947\pi\) | |||||||
\(104\) | 257.668 | + | 446.294i | 0.242947 | + | 0.420796i | ||||
\(105\) | −12.2079 | − | 40.4890i | −0.0113464 | − | 0.0376316i | ||||
\(106\) | −295.459 | + | 511.750i | −0.270732 | + | 0.468921i | ||||
\(107\) | −718.783 | −0.649414 | −0.324707 | − | 0.945815i | \(-0.605266\pi\) | ||||
−0.324707 | + | 0.945815i | \(0.605266\pi\) | |||||||
\(108\) | 79.4226 | − | 466.404i | 0.0707634 | − | 0.415553i | ||||
\(109\) | −2010.56 | −1.76676 | −0.883378 | − | 0.468661i | \(-0.844736\pi\) | ||||
−0.883378 | + | 0.468661i | \(0.844736\pi\) | |||||||
\(110\) | −277.045 | + | 479.856i | −0.240138 | + | 0.415931i | ||||
\(111\) | 521.584 | + | 1729.90i | 0.446005 | + | 1.47923i | ||||
\(112\) | 64.7881 | + | 112.216i | 0.0546598 | + | 0.0946735i | ||||
\(113\) | 113.372 | + | 196.367i | 0.0943820 | + | 0.163474i | 0.909351 | − | 0.416031i | \(-0.136579\pi\) |
−0.814969 | + | 0.579505i | \(0.803246\pi\) | |||||||
\(114\) | 926.392 | + | 217.647i | 0.761093 | + | 0.178812i | ||||
\(115\) | 168.594 | − | 292.013i | 0.136708 | − | 0.236786i | ||||
\(116\) | 925.755 | 0.740985 | ||||||||
\(117\) | −798.310 | − | 397.026i | −0.630801 | − | 0.313718i | ||||
\(118\) | 617.943 | 0.482087 | ||||||||
\(119\) | −89.7744 | + | 155.494i | −0.0691564 | + | 0.119782i | ||||
\(120\) | −277.663 | + | 295.461i | −0.211225 | + | 0.224764i | ||||
\(121\) | 125.564 | + | 217.483i | 0.0943381 | + | 0.163398i | ||||
\(122\) | 736.160 | + | 1275.07i | 0.546302 | + | 0.946223i | ||||
\(123\) | −1036.70 | + | 1103.15i | −0.759968 | + | 0.808680i | ||||
\(124\) | 10.1168 | − | 17.5229i | 0.00732677 | − | 0.0126903i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −132.701 | − | 65.9967i | −0.0938250 | − | 0.0466623i | ||||
\(127\) | 1132.24 | 0.791100 | 0.395550 | − | 0.918444i | \(-0.370554\pi\) | ||||
0.395550 | + | 0.918444i | \(0.370554\pi\) | |||||||
\(128\) | 831.675 | − | 1440.50i | 0.574300 | − | 0.994717i | ||||
\(129\) | 1018.71 | + | 239.336i | 0.695289 | + | 0.163352i | ||||
\(130\) | −278.397 | − | 482.197i | −0.187823 | − | 0.325319i | ||||
\(131\) | −388.753 | − | 673.339i | −0.259278 | − | 0.449083i | 0.706770 | − | 0.707443i | \(-0.250151\pi\) |
−0.966049 | + | 0.258360i | \(0.916818\pi\) | |||||||
\(132\) | 166.227 | + | 551.312i | 0.109608 | + | 0.363527i | ||||
\(133\) | 44.1983 | − | 76.5537i | 0.0288156 | − | 0.0499101i | ||||
\(134\) | 2804.05 | 1.80771 | ||||||||
\(135\) | 117.758 | − | 691.526i | 0.0750740 | − | 0.440867i | ||||
\(136\) | 1721.45 | 1.08539 | ||||||||
\(137\) | −311.819 | + | 540.087i | −0.194456 | + | 0.336808i | −0.946722 | − | 0.322052i | \(-0.895628\pi\) |
0.752266 | + | 0.658860i | \(0.228961\pi\) | |||||||
\(138\) | −341.127 | − | 1131.39i | −0.210425 | − | 0.697902i | ||||
\(139\) | −641.341 | − | 1110.83i | −0.391351 | − | 0.677840i | 0.601277 | − | 0.799041i | \(-0.294659\pi\) |
−0.992628 | + | 0.121201i | \(0.961326\pi\) | |||||||
\(140\) | −13.7228 | − | 23.7686i | −0.00828421 | − | 0.0143487i | ||||
\(141\) | −2438.64 | − | 572.937i | −1.45653 | − | 0.342198i | ||||
\(142\) | −200.568 | + | 347.394i | −0.118530 | + | 0.205300i | ||||
\(143\) | 1085.14 | 0.634574 | ||||||||
\(144\) | 133.361 | + | 2145.22i | 0.0771766 | + | 1.24145i | ||||
\(145\) | 1372.59 | 0.786123 | ||||||||
\(146\) | 309.099 | − | 535.376i | 0.175214 | − | 0.303480i | ||||
\(147\) | 1211.11 | − | 1288.74i | 0.679529 | − | 0.723085i | ||||
\(148\) | 586.310 | + | 1015.52i | 0.325638 | + | 0.564021i | ||||
\(149\) | −762.156 | − | 1320.09i | −0.419049 | − | 0.725814i | 0.576795 | − | 0.816889i | \(-0.304303\pi\) |
−0.995844 | + | 0.0910749i | \(0.970970\pi\) | |||||||
\(150\) | 300.000 | − | 319.229i | 0.163299 | − | 0.173766i | ||||
\(151\) | −1581.28 | + | 2738.86i | −0.852203 | + | 1.47606i | 0.0270124 | + | 0.999635i | \(0.491401\pi\) |
−0.879216 | + | 0.476424i | \(0.841933\pi\) | |||||||
\(152\) | −847.514 | −0.452253 | ||||||||
\(153\) | −2481.91 | + | 1646.31i | −1.31144 | + | 0.869911i | ||||
\(154\) | 180.380 | 0.0943861 | ||||||||
\(155\) | 15.0000 | − | 25.9808i | 0.00777309 | − | 0.0134634i | ||||
\(156\) | −563.299 | − | 132.342i | −0.289103 | − | 0.0679220i | ||||
\(157\) | 1194.35 | + | 2068.67i | 0.607131 | + | 1.05158i | 0.991711 | + | 0.128490i | \(0.0410129\pi\) |
−0.384580 | + | 0.923092i | \(0.625654\pi\) | |||||||
\(158\) | −1076.25 | − | 1864.12i | −0.541912 | − | 0.938619i | ||||
\(159\) | 262.842 | + | 871.749i | 0.131099 | + | 0.434806i | ||||
\(160\) | −359.015 | + | 621.832i | −0.177391 | + | 0.307251i | ||||
\(161\) | −109.769 | −0.0537331 | ||||||||
\(162\) | −1483.42 | − | 1960.40i | −0.719436 | − | 0.950761i | ||||
\(163\) | −2544.79 | −1.22284 | −0.611422 | − | 0.791305i | \(-0.709402\pi\) | ||||
−0.611422 | + | 0.791305i | \(0.709402\pi\) | |||||||
\(164\) | −491.235 | + | 850.844i | −0.233896 | + | 0.405120i | ||||
\(165\) | 246.461 | + | 817.417i | 0.116284 | + | 0.385672i | ||||
\(166\) | −2520.18 | − | 4365.08i | −1.17834 | − | 2.04094i | ||||
\(167\) | 687.279 | + | 1190.40i | 0.318462 | + | 0.551593i | 0.980167 | − | 0.198171i | \(-0.0635002\pi\) |
−0.661705 | + | 0.749764i | \(0.730167\pi\) | |||||||
\(168\) | 128.495 | + | 30.1887i | 0.0590094 | + | 0.0138637i | ||||
\(169\) | 553.282 | − | 958.313i | 0.251835 | − | 0.436191i | ||||
\(170\) | −1859.93 | −0.839119 | ||||||||
\(171\) | 1221.91 | − | 810.522i | 0.546442 | − | 0.362469i | ||||
\(172\) | 679.139 | 0.301069 | ||||||||
\(173\) | −1180.23 | + | 2044.21i | −0.518675 | + | 0.898372i | 0.481089 | + | 0.876672i | \(0.340241\pi\) |
−0.999765 | + | 0.0217005i | \(0.993092\pi\) | |||||||
\(174\) | 3294.23 | − | 3505.38i | 1.43526 | − | 1.52725i | ||||
\(175\) | −20.3465 | − | 35.2411i | −0.00878885 | − | 0.0152227i | ||||
\(176\) | −1307.98 | − | 2265.49i | −0.560187 | − | 0.970272i | ||||
\(177\) | 652.052 | − | 693.846i | 0.276899 | − | 0.294648i | ||||
\(178\) | −2423.44 | + | 4197.52i | −1.02047 | + | 1.76751i | ||||
\(179\) | 1305.11 | 0.544963 | 0.272482 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272482 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(180\) | −28.2473 | − | 454.381i | −0.0116968 | − | 0.188153i | ||||
\(181\) | 3099.43 | 1.27281 | 0.636406 | − | 0.771355i | \(-0.280420\pi\) | ||||
0.636406 | + | 0.771355i | \(0.280420\pi\) | |||||||
\(182\) | −90.6303 | + | 156.976i | −0.0369119 | + | 0.0639332i | ||||
\(183\) | 2208.48 | + | 518.863i | 0.892107 | + | 0.209593i | ||||
\(184\) | 526.214 | + | 911.429i | 0.210832 | + | 0.365171i | ||||
\(185\) | 869.307 | + | 1505.68i | 0.345474 | + | 0.598379i | ||||
\(186\) | −30.3505 | − | 100.661i | −0.0119646 | − | 0.0396820i | ||||
\(187\) | 1812.42 | − | 3139.21i | 0.708756 | − | 1.22760i | ||||
\(188\) | −1625.76 | −0.630696 | ||||||||
\(189\) | −214.129 | + | 79.3616i | −0.0824105 | + | 0.0305434i | ||||
\(190\) | 915.693 | 0.349639 | ||||||||
\(191\) | −190.356 | + | 329.706i | −0.0721135 | + | 0.124904i | −0.899827 | − | 0.436246i | \(-0.856308\pi\) |
0.827714 | + | 0.561150i | \(0.189641\pi\) | |||||||
\(192\) | −228.852 | − | 759.016i | −0.0860207 | − | 0.285298i | ||||
\(193\) | −773.020 | − | 1338.91i | −0.288307 | − | 0.499362i | 0.685099 | − | 0.728450i | \(-0.259759\pi\) |
−0.973406 | + | 0.229088i | \(0.926426\pi\) | |||||||
\(194\) | −1503.65 | − | 2604.39i | −0.556472 | − | 0.963838i | ||||
\(195\) | −835.190 | − | 196.220i | −0.306714 | − | 0.0720596i | ||||
\(196\) | 573.879 | − | 993.987i | 0.209140 | − | 0.362240i | ||||
\(197\) | −4284.60 | −1.54957 | −0.774784 | − | 0.632226i | \(-0.782141\pi\) | ||||
−0.774784 | + | 0.632226i | \(0.782141\pi\) | |||||||
\(198\) | 2679.05 | + | 1332.38i | 0.961576 | + | 0.478224i | ||||
\(199\) | −1402.85 | −0.499727 | −0.249863 | − | 0.968281i | \(-0.580386\pi\) | ||||
−0.249863 | + | 0.968281i | \(0.580386\pi\) | |||||||
\(200\) | −195.075 | + | 337.879i | −0.0689693 | + | 0.119458i | ||||
\(201\) | 2958.83 | − | 3148.48i | 1.03831 | − | 1.10486i | ||||
\(202\) | −259.234 | − | 449.007i | −0.0902953 | − | 0.156396i | ||||
\(203\) | −223.420 | − | 386.974i | −0.0772463 | − | 0.133795i | ||||
\(204\) | −1323.68 | + | 1408.53i | −0.454296 | + | 0.483415i | ||||
\(205\) | −728.342 | + | 1261.53i | −0.248145 | + | 0.429799i | ||||
\(206\) | −456.249 | −0.154312 | ||||||||
\(207\) | −1630.32 | − | 810.813i | −0.547416 | − | 0.272248i | ||||
\(208\) | 2628.73 | 0.876296 | ||||||||
\(209\) | −892.303 | + | 1545.51i | −0.295320 | + | 0.511509i | ||||
\(210\) | −138.832 | − | 32.6172i | −0.0456204 | − | 0.0107181i | ||||
\(211\) | 1075.23 | + | 1862.35i | 0.350814 | + | 0.607628i | 0.986392 | − | 0.164409i | \(-0.0525716\pi\) |
−0.635578 | + | 0.772036i | \(0.719238\pi\) | |||||||
\(212\) | 295.459 | + | 511.750i | 0.0957180 | + | 0.165789i | ||||
\(213\) | 178.426 | + | 591.773i | 0.0573971 | + | 0.190365i | ||||
\(214\) | −1211.97 | + | 2099.19i | −0.387142 | + | 0.670550i | ||||
\(215\) | 1006.94 | 0.319409 | ||||||||
\(216\) | 1685.44 | + | 1397.50i | 0.530926 | + | 0.440220i | ||||
\(217\) | −9.76631 | −0.00305521 | ||||||||
\(218\) | −3390.08 | + | 5871.79i | −1.05324 | + | 1.82426i | ||||
\(219\) | −274.977 | − | 911.994i | −0.0848456 | − | 0.281401i | ||||
\(220\) | 277.045 | + | 479.856i | 0.0849016 | + | 0.147054i | ||||
\(221\) | 1821.27 | + | 3154.52i | 0.554351 | + | 0.960164i | ||||
\(222\) | 5931.60 | + | 1393.58i | 1.79326 | + | 0.421310i | ||||
\(223\) | 1279.07 | − | 2215.42i | 0.384095 | − | 0.665272i | −0.607548 | − | 0.794283i | \(-0.707847\pi\) |
0.991643 | + | 0.129011i | \(0.0411802\pi\) | |||||||
\(224\) | 233.750 | 0.0697236 | ||||||||
\(225\) | −41.8816 | − | 673.699i | −0.0124094 | − | 0.199615i | ||||
\(226\) | 764.646 | 0.225060 | ||||||||
\(227\) | 2042.27 | − | 3537.32i | 0.597138 | − | 1.03427i | −0.396104 | − | 0.918206i | \(-0.629638\pi\) |
0.993241 | − | 0.116067i | \(-0.0370287\pi\) | |||||||
\(228\) | 651.684 | − | 693.456i | 0.189293 | − | 0.201426i | ||||
\(229\) | 1370.95 | + | 2374.56i | 0.395612 | + | 0.685221i | 0.993179 | − | 0.116598i | \(-0.0371991\pi\) |
−0.597567 | + | 0.801819i | \(0.703866\pi\) | |||||||
\(230\) | −568.546 | − | 984.750i | −0.162995 | − | 0.282315i | ||||
\(231\) | 190.337 | − | 202.537i | 0.0542132 | − | 0.0576881i | ||||
\(232\) | −2142.07 | + | 3710.17i | −0.606179 | + | 1.04993i | ||||
\(233\) | 5084.70 | 1.42966 | 0.714828 | − | 0.699300i | \(-0.246505\pi\) | ||||
0.714828 | + | 0.699300i | \(0.246505\pi\) | |||||||
\(234\) | −2505.57 | + | 1662.01i | −0.699975 | + | 0.464311i | ||||
\(235\) | −2410.48 | −0.669115 | ||||||||
\(236\) | 308.971 | − | 535.154i | 0.0852217 | − | 0.147608i | ||||
\(237\) | −3228.76 | − | 758.567i | −0.884938 | − | 0.207908i | ||||
\(238\) | 302.745 | + | 524.369i | 0.0824538 | + | 0.142814i | ||||
\(239\) | −738.236 | − | 1278.66i | −0.199801 | − | 0.346066i | 0.748663 | − | 0.662951i | \(-0.230696\pi\) |
−0.948464 | + | 0.316885i | \(0.897363\pi\) | |||||||
\(240\) | 597.045 | + | 1980.17i | 0.160579 | + | 0.532582i | ||||
\(241\) | −881.728 | + | 1527.20i | −0.235673 | + | 0.408197i | −0.959468 | − | 0.281818i | \(-0.909063\pi\) |
0.723795 | + | 0.690015i | \(0.242396\pi\) | |||||||
\(242\) | 846.874 | 0.224955 | ||||||||
\(243\) | −3766.50 | − | 402.970i | −0.994325 | − | 0.106381i | ||||
\(244\) | 1472.32 | 0.386294 | ||||||||
\(245\) | 850.876 | − | 1473.76i | 0.221880 | − | 0.384307i | ||||
\(246\) | 1473.70 | + | 4887.73i | 0.381951 | + | 1.26679i | ||||
\(247\) | −896.657 | − | 1553.05i | −0.230983 | − | 0.400075i | ||||
\(248\) | 46.8179 | + | 81.0910i | 0.0119877 | + | 0.0207632i | ||||
\(249\) | −7560.54 | − | 1776.28i | −1.92422 | − | 0.452077i | ||||
\(250\) | 210.768 | − | 365.060i | 0.0533204 | − | 0.0923537i | ||||
\(251\) | 1705.16 | 0.428801 | 0.214400 | − | 0.976746i | \(-0.431220\pi\) | ||||
0.214400 | + | 0.976746i | \(0.431220\pi\) | |||||||
\(252\) | −123.505 | + | 81.9242i | −0.0308734 | + | 0.0204791i | ||||
\(253\) | 2216.09 | 0.550690 | ||||||||
\(254\) | 1909.11 | − | 3306.68i | 0.471607 | − | 0.816848i | ||||
\(255\) | −1962.59 | + | 2088.39i | −0.481970 | + | 0.512863i | ||||
\(256\) | −2194.37 | − | 3800.76i | −0.535735 | − | 0.927920i | ||||
\(257\) | −114.298 | − | 197.970i | −0.0277421 | − | 0.0480507i | 0.851821 | − | 0.523833i | \(-0.175498\pi\) |
−0.879563 | + | 0.475782i | \(0.842165\pi\) | |||||||
\(258\) | 2416.66 | − | 2571.56i | 0.583158 | − | 0.620537i | ||||
\(259\) | 282.997 | − | 490.166i | 0.0678942 | − | 0.117596i | ||||
\(260\) | −556.793 | −0.132811 | ||||||||
\(261\) | −459.892 | − | 7397.73i | −0.109068 | − | 1.75444i | ||||
\(262\) | −2621.97 | −0.618266 | ||||||||
\(263\) | 644.380 | − | 1116.10i | 0.151081 | − | 0.261679i | −0.780544 | − | 0.625100i | \(-0.785058\pi\) |
0.931625 | + | 0.363421i | \(0.118391\pi\) | |||||||
\(264\) | −2594.13 | − | 609.468i | −0.604764 | − | 0.142084i | ||||
\(265\) | 438.070 | + | 758.760i | 0.101549 | + | 0.175888i | ||||
\(266\) | −149.049 | − | 258.161i | −0.0343563 | − | 0.0595069i | ||||
\(267\) | 2155.90 | + | 7150.32i | 0.494154 | + | 1.63892i | ||||
\(268\) | 1402.03 | − | 2428.38i | 0.319561 | − | 0.553496i | ||||
\(269\) | 973.981 | 0.220761 | 0.110380 | − | 0.993889i | \(-0.464793\pi\) | ||||
0.110380 | + | 0.993889i | \(0.464793\pi\) | |||||||
\(270\) | −1821.03 | − | 1509.92i | −0.410461 | − | 0.340336i | ||||
\(271\) | −4021.83 | −0.901508 | −0.450754 | − | 0.892648i | \(-0.648845\pi\) | ||||
−0.450754 | + | 0.892648i | \(0.648845\pi\) | |||||||
\(272\) | 4390.55 | − | 7604.65i | 0.978736 | − | 1.69522i | ||||
\(273\) | 80.6252 | + | 267.403i | 0.0178742 | + | 0.0592820i | ||||
\(274\) | 1051.54 | + | 1821.32i | 0.231847 | + | 0.401570i | ||||
\(275\) | 410.768 | + | 711.470i | 0.0900735 | + | 0.156012i | ||||
\(276\) | −1150.38 | − | 270.271i | −0.250886 | − | 0.0589435i | ||||
\(277\) | 1689.59 | − | 2926.45i | 0.366489 | − | 0.634777i | −0.622525 | − | 0.782600i | \(-0.713893\pi\) |
0.989014 | + | 0.147823i | \(0.0472265\pi\) | |||||||
\(278\) | −4325.56 | −0.933201 | ||||||||
\(279\) | −145.052 | − | 72.1390i | −0.0311255 | − | 0.0154797i | ||||
\(280\) | 127.011 | 0.0271083 | ||||||||
\(281\) | −366.654 | + | 635.063i | −0.0778388 | + | 0.134821i | −0.902317 | − | 0.431073i | \(-0.858135\pi\) |
0.824478 | + | 0.565893i | \(0.191469\pi\) | |||||||
\(282\) | −5785.14 | + | 6155.95i | −1.22163 | + | 1.29993i | ||||
\(283\) | −3454.51 | − | 5983.39i | −0.725617 | − | 1.25680i | −0.958720 | − | 0.284353i | \(-0.908221\pi\) |
0.233103 | − | 0.972452i | \(-0.425112\pi\) | |||||||
\(284\) | 200.568 | + | 347.394i | 0.0419068 | + | 0.0725847i | ||||
\(285\) | 966.237 | − | 1028.17i | 0.200824 | − | 0.213697i | ||||
\(286\) | 1829.70 | − | 3169.13i | 0.378295 | − | 0.655227i | ||||
\(287\) | 474.214 | 0.0975331 | ||||||||
\(288\) | 3471.71 | + | 1726.60i | 0.710322 | + | 0.353267i | ||||
\(289\) | 7254.64 | 1.47662 | ||||||||
\(290\) | 2314.39 | − | 4008.64i | 0.468640 | − | 0.811708i | ||||
\(291\) | −4510.94 | − | 1059.81i | −0.908715 | − | 0.213494i | ||||
\(292\) | −309.099 | − | 535.376i | −0.0619475 | − | 0.107296i | ||||
\(293\) | 2324.74 | + | 4026.57i | 0.463525 | + | 0.802850i | 0.999134 | − | 0.0416170i | \(-0.0132509\pi\) |
−0.535608 | + | 0.844467i | \(0.679918\pi\) | |||||||
\(294\) | −1721.64 | − | 5710.02i | −0.341523 | − | 1.13271i | ||||
\(295\) | 458.104 | − | 793.460i | 0.0904131 | − | 0.156600i | ||||
\(296\) | −5426.55 | −1.06558 | ||||||||
\(297\) | 4322.97 | − | 1602.20i | 0.844593 | − | 0.313027i | ||||
\(298\) | −5140.41 | −0.999248 | ||||||||
\(299\) | −1113.45 | + | 1928.56i | −0.215360 | + | 0.373014i | ||||
\(300\) | −126.461 | − | 419.422i | −0.0243373 | − | 0.0807178i | ||||
\(301\) | −163.902 | − | 283.886i | −0.0313859 | − | 0.0543619i | ||||
\(302\) | 5332.52 | + | 9236.19i | 1.01607 | + | 1.75988i | ||||
\(303\) | −777.702 | − | 182.714i | −0.147452 | − | 0.0346424i | ||||
\(304\) | −2161.58 | + | 3743.97i | −0.407813 | + | 0.706353i | ||||
\(305\) | 2182.97 | 0.409825 | ||||||||
\(306\) | 623.176 | + | 10024.3i | 0.116420 | + | 1.87271i | ||||
\(307\) | −7361.42 | −1.36853 | −0.684264 | − | 0.729234i | \(-0.739877\pi\) | ||||
−0.684264 | + | 0.729234i | \(0.739877\pi\) | |||||||
\(308\) | 90.1902 | − | 156.214i | 0.0166853 | − | 0.0288997i | ||||
\(309\) | −481.433 | + | 512.291i | −0.0886335 | + | 0.0943146i | ||||
\(310\) | −50.5842 | − | 87.6144i | −0.00926771 | − | 0.0160521i | ||||
\(311\) | 1354.60 | + | 2346.24i | 0.246986 | + | 0.427792i | 0.962688 | − | 0.270614i | \(-0.0872266\pi\) |
−0.715702 | + | 0.698405i | \(0.753893\pi\) | |||||||
\(312\) | 1833.78 | − | 1951.32i | 0.332749 | − | 0.354077i | ||||
\(313\) | 3121.86 | − | 5407.22i | 0.563763 | − | 0.976467i | −0.433400 | − | 0.901202i | \(-0.642686\pi\) |
0.997164 | − | 0.0752653i | \(-0.0239804\pi\) | |||||||
\(314\) | 8055.37 | 1.44774 | ||||||||
\(315\) | −183.118 | + | 121.467i | −0.0327541 | + | 0.0217266i | ||||
\(316\) | −2152.50 | −0.383189 | ||||||||
\(317\) | −1042.02 | + | 1804.82i | −0.184623 | + | 0.319776i | −0.943449 | − | 0.331517i | \(-0.892440\pi\) |
0.758827 | + | 0.651293i | \(0.225773\pi\) | |||||||
\(318\) | 2989.12 | + | 702.266i | 0.527111 | + | 0.123840i | ||||
\(319\) | 4510.54 | + | 7812.48i | 0.791667 | + | 1.37121i | ||||
\(320\) | −381.420 | − | 660.639i | −0.0666313 | − | 0.115409i | ||||
\(321\) | 1078.17 | + | 3575.90i | 0.187470 | + | 0.621767i | ||||
\(322\) | −185.087 | + | 320.579i | −0.0320325 | + | 0.0554819i | ||||
\(323\) | −5990.45 | −1.03194 | ||||||||
\(324\) | −2439.46 | + | 304.483i | −0.418289 | + | 0.0522091i | ||||
\(325\) | −825.544 | −0.140901 | ||||||||
\(326\) | −4290.88 | + | 7432.02i | −0.728987 | + | 1.26264i | ||||
\(327\) | 3015.83 | + | 10002.4i | 0.510018 | + | 1.69154i | ||||
\(328\) | −2273.30 | − | 3937.47i | −0.382689 | − | 0.662836i | ||||
\(329\) | 392.358 | + | 679.583i | 0.0657489 | + | 0.113880i | ||||
\(330\) | 2802.82 | + | 658.497i | 0.467546 | + | 0.109846i | ||||
\(331\) | 113.938 | − | 197.347i | 0.0189203 | − | 0.0327709i | −0.856410 | − | 0.516296i | \(-0.827310\pi\) |
0.875331 | + | 0.483525i | \(0.160644\pi\) | |||||||
\(332\) | −5040.36 | −0.833210 | ||||||||
\(333\) | 7823.76 | − | 5189.70i | 1.28751 | − | 0.854035i | ||||
\(334\) | 4635.39 | 0.759394 | ||||||||
\(335\) | 2078.75 | − | 3600.50i | 0.339028 | − | 0.587213i | ||||
\(336\) | 461.087 | − | 490.641i | 0.0748641 | − | 0.0796627i | ||||
\(337\) | −1708.74 | − | 2959.62i | −0.276205 | − | 0.478400i | 0.694234 | − | 0.719750i | \(-0.255743\pi\) |
−0.970438 | + | 0.241349i | \(0.922410\pi\) | |||||||
\(338\) | −1865.82 | − | 3231.70i | −0.300259 | − | 0.520063i | ||||
\(339\) | 806.853 | − | 858.570i | 0.129269 | − | 0.137555i | ||||
\(340\) | −929.966 | + | 1610.75i | −0.148337 | + | 0.256927i | ||||
\(341\) | 197.168 | 0.0313116 | ||||||||
\(342\) | −306.806 | − | 4935.21i | −0.0485092 | − | 0.780309i | ||||
\(343\) | −1112.30 | −0.175098 | ||||||||
\(344\) | −1571.43 | + | 2721.80i | −0.246296 | + | 0.426598i | ||||
\(345\) | −1705.64 | − | 400.724i | −0.266169 | − | 0.0625341i | ||||
\(346\) | 3980.05 | + | 6893.65i | 0.618407 | + | 1.07111i | ||||
\(347\) | −1804.80 | − | 3126.00i | −0.279212 | − | 0.483610i | 0.691977 | − | 0.721920i | \(-0.256740\pi\) |
−0.971189 | + | 0.238310i | \(0.923407\pi\) | |||||||
\(348\) | −1388.63 | − | 4605.57i | −0.213904 | − | 0.709439i | ||||
\(349\) | 4400.42 | − | 7621.74i | 0.674925 | − | 1.16900i | −0.301566 | − | 0.953445i | \(-0.597509\pi\) |
0.976491 | − | 0.215559i | \(-0.0691574\pi\) | |||||||
\(350\) | −137.228 | −0.0209576 | ||||||||
\(351\) | −777.715 | + | 4567.08i | −0.118266 | + | 0.694509i | ||||
\(352\) | −4719.09 | −0.714570 | ||||||||
\(353\) | −4255.24 | + | 7370.30i | −0.641597 | + | 1.11128i | 0.343479 | + | 0.939160i | \(0.388395\pi\) |
−0.985076 | + | 0.172119i | \(0.944939\pi\) | |||||||
\(354\) | −926.914 | − | 3074.23i | −0.139166 | − | 0.461563i | ||||
\(355\) | 297.377 | + | 515.073i | 0.0444596 | + | 0.0770063i | ||||
\(356\) | 2423.44 | + | 4197.52i | 0.360792 | + | 0.624910i | ||||
\(357\) | 908.234 | + | 213.381i | 0.134647 | + | 0.0316340i | ||||
\(358\) | 2200.60 | − | 3811.55i | 0.324875 | − | 0.562700i | ||||
\(359\) | 4320.35 | 0.635152 | 0.317576 | − | 0.948233i | \(-0.397131\pi\) | ||||
0.317576 | + | 0.948233i | \(0.397131\pi\) | |||||||
\(360\) | 1886.39 | + | 938.166i | 0.276171 | + | 0.137349i | ||||
\(361\) | −3909.75 | −0.570017 | ||||||||
\(362\) | 5226.08 | − | 9051.83i | 0.758775 | − | 1.31424i | ||||
\(363\) | 893.619 | − | 950.898i | 0.129209 | − | 0.137491i | ||||
\(364\) | 90.6303 | + | 156.976i | 0.0130503 | + | 0.0226038i | ||||
\(365\) | −458.294 | − | 793.789i | −0.0657211 | − | 0.113832i | ||||
\(366\) | 5239.14 | − | 5574.95i | 0.748235 | − | 0.796195i | ||||
\(367\) | −3300.19 | + | 5716.10i | −0.469397 | + | 0.813020i | −0.999388 | − | 0.0349838i | \(-0.988862\pi\) |
0.529991 | + | 0.848003i | \(0.322195\pi\) | |||||||
\(368\) | 5368.43 | 0.760459 | ||||||||
\(369\) | 7043.15 | + | 3502.79i | 0.993636 | + | 0.494168i | ||||
\(370\) | 5863.10 | 0.823805 | ||||||||
\(371\) | 142.611 | − | 247.010i | 0.0199569 | − | 0.0345663i | ||||
\(372\) | −102.351 | − | 24.0463i | −0.0142651 | − | 0.00335146i | ||||
\(373\) | 4304.23 | + | 7455.14i | 0.597492 | + | 1.03489i | 0.993190 | + | 0.116506i | \(0.0371693\pi\) |
−0.395698 | + | 0.918381i | \(0.629497\pi\) | |||||||
\(374\) | −6112.00 | − | 10586.3i | −0.845037 | − | 1.46365i | ||||
\(375\) | −187.500 | − | 621.867i | −0.0258199 | − | 0.0856349i | ||||
\(376\) | 3761.78 | − | 6515.60i | 0.515955 | − | 0.893660i | ||||
\(377\) | −9065.10 | −1.23840 | ||||||||
\(378\) | −129.278 | + | 759.174i | −0.0175908 | + | 0.103301i | ||||
\(379\) | −7129.80 | −0.966314 | −0.483157 | − | 0.875534i | \(-0.660510\pi\) | ||||
−0.483157 | + | 0.875534i | \(0.660510\pi\) | |||||||
\(380\) | 457.846 | − | 793.013i | 0.0618080 | − | 0.107055i | ||||
\(381\) | −1698.36 | − | 5632.81i | −0.228371 | − | 0.757421i | ||||
\(382\) | 641.934 | + | 1111.86i | 0.0859796 | + | 0.148921i | ||||
\(383\) | −2963.73 | − | 5133.33i | −0.395404 | − | 0.684859i | 0.597749 | − | 0.801683i | \(-0.296062\pi\) |
−0.993153 | + | 0.116824i | \(0.962729\pi\) | |||||||
\(384\) | −8413.93 | − | 1976.78i | −1.11815 | − | 0.262700i | ||||
\(385\) | 133.723 | − | 231.615i | 0.0177017 | − | 0.0306602i | ||||
\(386\) | −5213.68 | −0.687486 | ||||||||
\(387\) | −337.379 | − | 5427.01i | −0.0443151 | − | 0.712844i | ||||
\(388\) | −3007.30 | −0.393485 | ||||||||
\(389\) | −519.432 | + | 899.683i | −0.0677024 | + | 0.117264i | −0.897890 | − | 0.440221i | \(-0.854900\pi\) |
0.830187 | + | 0.557485i | \(0.188234\pi\) | |||||||
\(390\) | −1981.30 | + | 2108.30i | −0.257249 | + | 0.273738i | ||||
\(391\) | 3719.42 | + | 6442.22i | 0.481072 | + | 0.833240i | ||||
\(392\) | 2655.75 | + | 4599.89i | 0.342183 | + | 0.592678i | ||||
\(393\) | −2766.69 | + | 2944.03i | −0.355117 | + | 0.377879i | ||||
\(394\) | −7224.43 | + | 12513.1i | −0.923761 | + | 1.60000i | ||||
\(395\) | −3191.47 | −0.406532 | ||||||||
\(396\) | 2493.40 | − | 1653.94i | 0.316410 | − | 0.209882i | ||||
\(397\) | 13441.4 | 1.69926 | 0.849628 | − | 0.527382i | \(-0.176826\pi\) | ||||
0.849628 | + | 0.527382i | \(0.176826\pi\) | |||||||
\(398\) | −2365.41 | + | 4097.01i | −0.297907 | + | 0.515991i | ||||
\(399\) | −447.147 | − | 105.053i | −0.0561037 | − | 0.0131810i | ||||
\(400\) | 995.075 | + | 1723.52i | 0.124384 | + | 0.215440i | ||||
\(401\) | −6537.70 | − | 11323.6i | −0.814157 | − | 1.41016i | −0.909931 | − | 0.414759i | \(-0.863866\pi\) |
0.0957739 | − | 0.995403i | \(-0.469467\pi\) | |||||||
\(402\) | −4206.08 | − | 13950.0i | −0.521841 | − | 1.73075i | ||||
\(403\) | −99.0652 | + | 171.586i | −0.0122451 | + | 0.0212092i | ||||
\(404\) | −518.468 | −0.0638484 | ||||||||
\(405\) | −3616.93 | + | 451.450i | −0.443770 | + | 0.0553895i | ||||
\(406\) | −1506.87 | −0.184199 | ||||||||
\(407\) | −5713.33 | + | 9895.78i | −0.695821 | + | 1.20520i | ||||
\(408\) | −2582.17 | − | 8564.10i | −0.313325 | − | 1.03918i | ||||
\(409\) | 2636.59 | + | 4566.71i | 0.318756 | + | 0.552101i | 0.980229 | − | 0.197868i | \(-0.0634017\pi\) |
−0.661473 | + | 0.749969i | \(0.730068\pi\) | |||||||
\(410\) | 2456.17 | + | 4254.22i | 0.295858 | + | 0.512441i | ||||
\(411\) | 3154.63 | + | 741.151i | 0.378604 | + | 0.0889496i | ||||
\(412\) | −228.124 | + | 395.123i | −0.0272788 | + | 0.0472484i | ||||
\(413\) | −298.266 | −0.0355368 | ||||||||
\(414\) | −5116.91 | + | 3394.18i | −0.607446 | + | 0.402934i | ||||
\(415\) | −7473.22 | −0.883966 | ||||||||
\(416\) | 2371.06 | − | 4106.80i | 0.279449 | − | 0.484020i | ||||
\(417\) | −4564.32 | + | 4856.88i | −0.536009 | + | 0.570366i | ||||
\(418\) | 3009.10 | + | 5211.91i | 0.352105 | + | 0.609863i | ||||
\(419\) | −6923.06 | − | 11991.1i | −0.807192 | − | 1.39810i | −0.914801 | − | 0.403905i | \(-0.867653\pi\) |
0.107609 | − | 0.994193i | \(-0.465681\pi\) | |||||||
\(420\) | −97.6631 | + | 103.923i | −0.0113464 | + | 0.0120736i | ||||
\(421\) | −548.684 | + | 950.349i | −0.0635184 | + | 0.110017i | −0.896036 | − | 0.443982i | \(-0.853565\pi\) |
0.832517 | + | 0.553999i | \(0.186899\pi\) | |||||||
\(422\) | 7251.94 | 0.836538 | ||||||||
\(423\) | 807.637 | + | 12991.5i | 0.0928338 | + | 1.49330i | ||||
\(424\) | −2734.60 | −0.313217 | ||||||||
\(425\) | −1378.84 | + | 2388.22i | −0.157373 | + | 0.272578i | ||||
\(426\) | 2029.12 | + | 476.722i | 0.230777 | + | 0.0542189i | ||||
\(427\) | −355.327 | − | 615.444i | −0.0402704 | − | 0.0697504i | ||||
\(428\) | 1211.97 | + | 2099.19i | 0.136875 | + | 0.237075i | ||||
\(429\) | −1627.71 | − | 5398.51i | −0.183186 | − | 0.607558i | ||||
\(430\) | 1697.85 | − | 2940.76i | 0.190413 | − | 0.329804i | ||||
\(431\) | 15912.8 | 1.77841 | 0.889205 | − | 0.457509i | \(-0.151258\pi\) | ||||
0.889205 | + | 0.457509i | \(0.151258\pi\) | |||||||
\(432\) | 10472.3 | − | 3881.29i | 1.16632 | − | 0.432266i | ||||
\(433\) | 3566.31 | 0.395810 | 0.197905 | − | 0.980221i | \(-0.436586\pi\) | ||||
0.197905 | + | 0.980221i | \(0.436586\pi\) | |||||||
\(434\) | −16.4674 | + | 28.5223i | −0.00182133 | + | 0.00315464i | ||||
\(435\) | −2058.89 | − | 6828.57i | −0.226934 | − | 0.752655i | ||||
\(436\) | 3390.08 | + | 5871.79i | 0.372375 | + | 0.644972i | ||||
\(437\) | −1831.17 | − | 3171.67i | −0.200450 | − | 0.347189i | ||||
\(438\) | −3127.11 | − | 734.686i | −0.341140 | − | 0.0801476i | ||||
\(439\) | 290.411 | − | 503.007i | 0.0315730 | − | 0.0546861i | −0.849807 | − | 0.527094i | \(-0.823282\pi\) |
0.881380 | + | 0.472408i | \(0.156615\pi\) | |||||||
\(440\) | −2564.17 | −0.277823 | ||||||||
\(441\) | −8228.06 | − | 4092.09i | −0.888464 | − | 0.441863i | ||||
\(442\) | 12283.6 | 1.32188 | ||||||||
\(443\) | 5396.39 | − | 9346.82i | 0.578759 | − | 1.00244i | −0.416863 | − | 0.908969i | \(-0.636871\pi\) |
0.995622 | − | 0.0934706i | \(-0.0297961\pi\) | |||||||
\(444\) | 4172.67 | − | 4440.13i | 0.446005 | − | 0.474593i | ||||
\(445\) | 3593.17 | + | 6223.56i | 0.382770 | + | 0.662977i | ||||
\(446\) | −4313.40 | − | 7471.03i | −0.457949 | − | 0.793191i | ||||
\(447\) | −5424.15 | + | 5771.82i | −0.573945 | + | 0.610733i | ||||
\(448\) | −124.169 | + | 215.067i | −0.0130947 | + | 0.0226807i | ||||
\(449\) | 2894.01 | 0.304180 | 0.152090 | − | 0.988367i | \(-0.451400\pi\) | ||||
0.152090 | + | 0.988367i | \(0.451400\pi\) | |||||||
\(450\) | −2038.14 | − | 1013.64i | −0.213509 | − | 0.106185i | ||||
\(451\) | −9573.74 | −0.999578 | ||||||||
\(452\) | 382.323 | − | 662.203i | 0.0397853 | − | 0.0689102i | ||||
\(453\) | 15997.6 | + | 3758.48i | 1.65923 | + | 0.389821i | ||||
\(454\) | −6887.11 | − | 11928.8i | −0.711956 | − | 1.23314i | ||||
\(455\) | 134.375 | + | 232.745i | 0.0138453 | + | 0.0239808i | ||||
\(456\) | 1271.27 | + | 4216.33i | 0.130554 | + | 0.432999i | ||||
\(457\) | −1599.96 | + | 2771.21i | −0.163770 | + | 0.283658i | −0.936218 | − | 0.351420i | \(-0.885699\pi\) |
0.772448 | + | 0.635078i | \(0.219032\pi\) | |||||||
\(458\) | 9246.49 | 0.943363 | ||||||||
\(459\) | 11913.2 | + | 9877.87i | 1.21146 | + | 1.00449i | ||||
\(460\) | −1137.09 | −0.115255 | ||||||||
\(461\) | −3658.19 | + | 6336.17i | −0.369585 | + | 0.640141i | −0.989501 | − | 0.144528i | \(-0.953834\pi\) |
0.619915 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(462\) | −270.571 | − | 897.381i | −0.0272469 | − | 0.0903678i | ||||
\(463\) | −3505.99 | − | 6072.55i | −0.351916 | − | 0.609536i | 0.634669 | − | 0.772784i | \(-0.281136\pi\) |
−0.986585 | + | 0.163248i | \(0.947803\pi\) | |||||||
\(464\) | 10926.7 | + | 18925.6i | 1.09323 | + | 1.89353i | ||||
\(465\) | −151.753 | − | 35.6529i | −0.0151341 | − | 0.00355562i | ||||
\(466\) | 8573.53 | − | 14849.8i | 0.852277 | − | 1.47619i | ||||
\(467\) | −8002.63 | −0.792971 | −0.396485 | − | 0.918041i | \(-0.629770\pi\) | ||||
−0.396485 | + | 0.918041i | \(0.629770\pi\) | |||||||
\(468\) | 186.555 | + | 3000.89i | 0.0184263 | + | 0.296402i | ||||
\(469\) | −1353.45 | −0.133255 | ||||||||
\(470\) | −4064.40 | + | 7039.75i | −0.398887 | + | 0.690892i | ||||
\(471\) | 8500.00 | − | 9044.83i | 0.831549 | − | 0.884849i | ||||
\(472\) | 1429.83 | + | 2476.54i | 0.139435 | + | 0.241509i | ||||
\(473\) | 3308.95 | + | 5731.28i | 0.321661 | + | 0.557134i | ||||
\(474\) | −7659.52 | + | 8150.47i | −0.742222 | + | 0.789797i | ||||
\(475\) | 678.838 | − | 1175.78i | 0.0655731 | − | 0.113576i | ||||
\(476\) | 605.489 | 0.0583037 | ||||||||
\(477\) | 3942.63 | − | 2615.25i | 0.378450 | − | 0.251035i | ||||
\(478\) | −4979.08 | −0.476439 | ||||||||
\(479\) | 1589.42 | − | 2752.96i | 0.151613 | − | 0.262601i | −0.780208 | − | 0.625520i | \(-0.784887\pi\) |
0.931820 | + | 0.362920i | \(0.118220\pi\) | |||||||
\(480\) | 3632.10 | + | 853.329i | 0.345379 | + | 0.0811436i | ||||
\(481\) | −5741.21 | − | 9944.06i | −0.544234 | − | 0.942641i | ||||
\(482\) | 2973.44 | + | 5150.14i | 0.280988 | + | 0.486686i | ||||
\(483\) | 164.654 | + | 546.096i | 0.0155114 | + | 0.0514456i | ||||
\(484\) | 423.437 | − | 733.414i | 0.0397668 | − | 0.0688781i | ||||
\(485\) | −4458.84 | −0.417455 | ||||||||
\(486\) | −7527.71 | + | 10320.5i | −0.702601 | + | 0.963269i | ||||
\(487\) | 13060.3 | 1.21523 | 0.607615 | − | 0.794232i | \(-0.292126\pi\) | ||||
0.607615 | + | 0.794232i | \(0.292126\pi\) | |||||||
\(488\) | −3406.74 | + | 5900.65i | −0.316016 | + | 0.547356i | ||||
\(489\) | 3817.19 | + | 12660.2i | 0.353005 | + | 1.17078i | ||||
\(490\) | −2869.39 | − | 4969.94i | −0.264543 | − | 0.458202i | ||||
\(491\) | 2200.81 | + | 3811.91i | 0.202283 | + | 0.350365i | 0.949264 | − | 0.314481i | \(-0.101831\pi\) |
−0.746981 | + | 0.664846i | \(0.768497\pi\) | |||||||
\(492\) | 4969.75 | + | 1167.60i | 0.455393 | + | 0.106991i | ||||
\(493\) | −15140.7 | + | 26224.4i | −1.38317 | + | 2.39572i | ||||
\(494\) | −6047.56 | −0.550794 | ||||||||
\(495\) | 3696.91 | − | 2452.25i | 0.335684 | − | 0.222668i | ||||
\(496\) | 477.636 | 0.0432389 | ||||||||
\(497\) | 96.8093 | − | 167.679i | 0.00873741 | − | 0.0151336i | ||||
\(498\) | −17935.7 | + | 19085.3i | −1.61389 | + | 1.71734i | ||||
\(499\) | −9362.60 | − | 16216.5i | −0.839935 | − | 1.45481i | −0.889948 | − | 0.456062i | \(-0.849260\pi\) |
0.0500129 | − | 0.998749i | \(-0.484074\pi\) | |||||||
\(500\) | −210.768 | − | 365.060i | −0.0188516 | − | 0.0326520i | ||||
\(501\) | 4891.26 | − | 5204.77i | 0.436178 | − | 0.464136i | ||||
\(502\) | 2875.15 | − | 4979.90i | 0.255626 | − | 0.442757i | ||||
\(503\) | −3811.68 | −0.337882 | −0.168941 | − | 0.985626i | \(-0.554035\pi\) | ||||
−0.168941 | + | 0.985626i | \(0.554035\pi\) | |||||||
\(504\) | −42.5553 | − | 684.536i | −0.00376104 | − | 0.0604993i | ||||
\(505\) | −768.720 | −0.0677378 | ||||||||
\(506\) | 3736.64 | − | 6472.06i | 0.328289 | − | 0.568613i | ||||
\(507\) | −5597.47 | − | 1315.07i | −0.490320 | − | 0.115196i | ||||
\(508\) | −1909.11 | − | 3306.68i | −0.166738 | − | 0.288799i | ||||
\(509\) | −2247.74 | − | 3893.20i | −0.195735 | − | 0.339024i | 0.751406 | − | 0.659840i | \(-0.229376\pi\) |
−0.947141 | + | 0.320816i | \(0.896043\pi\) | |||||||
\(510\) | 2789.90 | + | 9253.04i | 0.242233 | + | 0.803395i | ||||
\(511\) | −149.195 | + | 258.413i | −0.0129158 | + | 0.0223709i | ||||
\(512\) | −1493.27 | −0.128894 | ||||||||
\(513\) | −5865.16 | − | 4863.13i | −0.504782 | − | 0.418543i | ||||
\(514\) | −770.891 | −0.0661528 | ||||||||
\(515\) | −338.235 | + | 585.840i | −0.0289406 | + | 0.0501266i | ||||
\(516\) | −1018.71 | − | 3378.67i | −0.0869111 | − | 0.288251i | ||||
\(517\) | −7921.16 | − | 13719.9i | −0.673834 | − | 1.16712i | ||||
\(518\) | −954.347 | − | 1652.98i | −0.0809490 | − | 0.140208i | ||||
\(519\) | 11940.2 | + | 2805.23i | 1.00985 | + | 0.237256i | ||||
\(520\) | 1288.34 | − | 2231.47i | 0.108649 | − | 0.188186i | ||||
\(521\) | 12095.0 | 1.01706 | 0.508531 | − | 0.861043i | \(-0.330189\pi\) | ||||
0.508531 | + | 0.861043i | \(0.330189\pi\) | |||||||
\(522\) | −22380.4 | − | 11130.5i | −1.87656 | − | 0.933274i | ||||
\(523\) | 7385.38 | 0.617476 | 0.308738 | − | 0.951147i | \(-0.400093\pi\) | ||||
0.308738 | + | 0.951147i | \(0.400093\pi\) | |||||||
\(524\) | −1310.98 | + | 2270.69i | −0.109295 | + | 0.189304i | ||||
\(525\) | −144.803 | + | 154.084i | −0.0120375 | + | 0.0128091i | ||||
\(526\) | −2173.03 | − | 3763.80i | −0.180131 | − | 0.311995i | ||||
\(527\) | 330.921 | + | 573.172i | 0.0273532 | + | 0.0473772i | ||||
\(528\) | −9308.70 | + | 9905.37i | −0.767253 | + | 0.816431i | ||||
\(529\) | 3809.59 | − | 6598.40i | 0.313108 | − | 0.542320i | ||||
\(530\) | 2954.59 | 0.242150 | ||||||||
\(531\) | −4429.92 | − | 2203.15i | −0.362038 | − | 0.180054i | ||||
\(532\) | −298.098 | −0.0242936 | ||||||||
\(533\) | 4810.23 | − | 8331.56i | 0.390908 | − | 0.677073i | ||||
\(534\) | 24517.5 | + | 5760.17i | 1.98685 | + | 0.466792i | ||||
\(535\) | 1796.96 | + | 3112.42i | 0.145213 | + | 0.251517i | ||||
\(536\) | 6488.18 | + | 11237.9i | 0.522848 | + | 0.905600i | ||||
\(537\) | −1957.66 | − | 6492.83i | −0.157317 | − | 0.521763i | ||||
\(538\) | 1642.27 | − | 2844.49i | 0.131605 | − | 0.227946i | ||||
\(539\) | 11184.4 | 0.893778 | ||||||||
\(540\) | −2218.14 | + | 822.100i | −0.176766 | + | 0.0655140i | ||||
\(541\) | −5935.19 | −0.471670 | −0.235835 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235835 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(542\) | −6781.37 | + | 11745.7i | −0.537426 | + | 0.930849i | ||||
\(543\) | −4649.15 | − | 15419.5i | −0.367429 | − | 1.21862i | ||||
\(544\) | −7920.37 | − | 13718.5i | −0.624234 | − | 1.08120i | ||||
\(545\) | 5026.39 | + | 8705.96i | 0.395059 | + | 0.684262i | ||||
\(546\) | 916.892 | + | 215.416i | 0.0718670 | + | 0.0168845i | ||||
\(547\) | 5078.61 | − | 8796.41i | 0.396976 | − | 0.687582i | −0.596376 | − | 0.802705i | \(-0.703393\pi\) |
0.993351 | + | 0.115124i | \(0.0367264\pi\) | |||||||
\(548\) | 2103.08 | 0.163940 | ||||||||
\(549\) | −731.413 | − | 11765.3i | −0.0568596 | − | 0.914632i | ||||
\(550\) | 2770.45 | 0.214786 | ||||||||
\(551\) | 7454.16 | − | 12911.0i | 0.576330 | − | 0.998232i | ||||
\(552\) | 3744.98 | − | 3985.03i | 0.288763 | − | 0.307272i | ||||
\(553\) | 519.481 | + | 899.768i | 0.0399468 | + | 0.0691899i | ||||
\(554\) | −5697.76 | − | 9868.81i | −0.436958 | − | 0.756833i | ||||
\(555\) | 6186.72 | − | 6583.27i | 0.473174 | − | 0.503503i | ||||
\(556\) | −2162.78 | + | 3746.05i | −0.164968 | + | 0.285733i | ||||
\(557\) | 5709.62 | 0.434334 | 0.217167 | − | 0.976134i | \(-0.430318\pi\) | ||||
0.217167 | + | 0.976134i | \(0.430318\pi\) | |||||||
\(558\) | −455.258 | + | 301.984i | −0.0345387 | + | 0.0229104i | ||||
\(559\) | −6650.20 | −0.503173 | ||||||||
\(560\) | 323.940 | − | 561.081i | 0.0244446 | − | 0.0423393i | ||||
\(561\) | −18336.0 | − | 4307.88i | −1.37994 | − | 0.324204i | ||||
\(562\) | 1236.46 | + | 2141.61i | 0.0928058 | + | 0.160744i | ||||
\(563\) | −6469.56 | − | 11205.6i | −0.484297 | − | 0.838828i | 0.515540 | − | 0.856866i | \(-0.327591\pi\) |
−0.999837 | + | 0.0180378i | \(0.994258\pi\) | |||||||
\(564\) | 2438.64 | + | 8088.06i | 0.182066 | + | 0.603845i | ||||
\(565\) | 566.861 | − | 981.833i | 0.0422089 | − | 0.0731080i | ||||
\(566\) | −23299.2 | −1.73028 | ||||||||
\(567\) | 716.012 | + | 946.236i | 0.0530330 | + | 0.0700850i | ||||
\(568\) | −1856.34 | −0.137131 | ||||||||
\(569\) | 3062.71 | − | 5304.77i | 0.225651 | − | 0.390839i | −0.730863 | − | 0.682524i | \(-0.760882\pi\) |
0.956515 | + | 0.291684i | \(0.0942157\pi\) | |||||||
\(570\) | −1373.54 | − | 4555.51i | −0.100932 | − | 0.334754i | ||||
\(571\) | 9641.20 | + | 16699.0i | 0.706605 | + | 1.22388i | 0.966109 | + | 0.258134i | \(0.0831076\pi\) |
−0.259504 | + | 0.965742i | \(0.583559\pi\) | |||||||
\(572\) | −1829.70 | − | 3169.13i | −0.133748 | − | 0.231658i | ||||
\(573\) | 1925.80 | + | 452.450i | 0.140404 | + | 0.0329867i | ||||
\(574\) | 799.592 | − | 1384.93i | 0.0581434 | − | 0.100707i | ||||
\(575\) | −1685.94 | −0.122276 | ||||||||
\(576\) | −3432.78 | + | 2277.05i | −0.248320 | + | 0.164717i | ||||
\(577\) | −4988.14 | −0.359894 | −0.179947 | − | 0.983676i | \(-0.557593\pi\) | ||||
−0.179947 | + | 0.983676i | \(0.557593\pi\) | |||||||
\(578\) | 12232.3 | − | 21187.0i | 0.880274 | − | 1.52468i | ||||
\(579\) | −5501.46 | + | 5854.09i | −0.394876 | + | 0.420186i | ||||
\(580\) | −2314.39 | − | 4008.64i | −0.165689 | − | 0.286982i | ||||
\(581\) | 1216.43 | + | 2106.92i | 0.0868606 | + | 0.150447i | ||||
\(582\) | −10701.2 | + | 11387.1i | −0.762165 | + | 0.811018i | ||||
\(583\) | −2879.12 | + | 4986.78i | −0.204530 | + | 0.354256i | ||||
\(584\) | 2860.85 | 0.202710 | ||||||||
\(585\) | 276.601 | + | 4449.35i | 0.0195488 | + | 0.314458i | ||||
\(586\) | 15679.4 | 1.10531 | ||||||||
\(587\) | 7647.00 | − | 13245.0i | 0.537693 | − | 0.931311i | −0.461335 | − | 0.887226i | \(-0.652629\pi\) |
0.999028 | − | 0.0440852i | \(-0.0140373\pi\) | |||||||
\(588\) | −5805.84 | − | 1364.03i | −0.407192 | − | 0.0956661i | ||||
\(589\) | −162.921 | − | 282.188i | −0.0113974 | − | 0.0197408i | ||||
\(590\) | −1544.86 | − | 2675.77i | −0.107798 | − | 0.186711i | ||||
\(591\) | 6426.90 | + | 21315.6i | 0.447322 | + | 1.48360i | ||||
\(592\) | −13840.4 | + | 23972.3i | −0.960874 | + | 1.66428i | ||||
\(593\) | −11090.9 | −0.768040 | −0.384020 | − | 0.923325i | \(-0.625461\pi\) | ||||
−0.384020 | + | 0.923325i | \(0.625461\pi\) | |||||||
\(594\) | 2609.94 | − | 15326.7i | 0.180281 | − | 1.05869i | ||||
\(595\) | 897.744 | 0.0618553 | ||||||||
\(596\) | −2570.21 | + | 4451.73i | −0.176644 | + | 0.305956i | ||||
\(597\) | 2104.28 | + | 6979.10i | 0.144259 | + | 0.478452i | ||||
\(598\) | 3754.88 | + | 6503.63i | 0.256770 | + | 0.444738i | ||||
\(599\) | 14100.8 | + | 24423.3i | 0.961840 | + | 1.66596i | 0.717875 | + | 0.696172i | \(0.245115\pi\) |
0.243965 | + | 0.969784i | \(0.421552\pi\) | |||||||
\(600\) | 1973.54 | + | 463.665i | 0.134282 | + | 0.0315484i | ||||
\(601\) | −10572.0 | + | 18311.3i | −0.717539 | + | 1.24281i | 0.244433 | + | 0.969666i | \(0.421398\pi\) |
−0.961972 | + | 0.273148i | \(0.911935\pi\) | |||||||
\(602\) | −1105.45 | −0.0748416 | ||||||||
\(603\) | −20101.7 | − | 9997.26i | −1.35755 | − | 0.675157i | ||||
\(604\) | 10665.0 | 0.718467 | ||||||||
\(605\) | 627.820 | − | 1087.42i | 0.0421893 | − | 0.0730740i | ||||
\(606\) | −1844.93 | + | 1963.18i | −0.123672 | + | 0.131599i | ||||
\(607\) | 4399.49 | + | 7620.14i | 0.294184 | + | 0.509542i | 0.974795 | − | 0.223103i | \(-0.0716187\pi\) |
−0.680611 | + | 0.732645i | \(0.738285\pi\) | |||||||
\(608\) | 3899.41 | + | 6753.97i | 0.260102 | + | 0.450509i | ||||
\(609\) | −1590.04 | + | 1691.96i | −0.105799 | + | 0.112581i | ||||
\(610\) | 3680.80 | − | 6375.34i | 0.244314 | − | 0.423164i | ||||
\(611\) | 15919.6 | 1.05407 | ||||||||
\(612\) | 8992.87 | + | 4472.45i | 0.593979 | + | 0.295406i | ||||
\(613\) | 19539.8 | 1.28745 | 0.643724 | − | 0.765257i | \(-0.277388\pi\) | ||||
0.643724 | + | 0.765257i | \(0.277388\pi\) | |||||||
\(614\) | −12412.4 | + | 21498.9i | −0.815836 | + | 1.41307i | ||||
\(615\) | 7368.52 | + | 1731.17i | 0.483134 | + | 0.113508i | ||||
\(616\) | 417.375 | + | 722.914i | 0.0272995 | + | 0.0472842i | ||||
\(617\) | 1636.94 | + | 2835.26i | 0.106808 | + | 0.184997i | 0.914475 | − | 0.404641i | \(-0.132604\pi\) |
−0.807667 | + | 0.589638i | \(0.799270\pi\) | |||||||
\(618\) | 684.373 | + | 2269.81i | 0.0445462 | + | 0.147743i | ||||
\(619\) | −4693.24 | + | 8128.92i | −0.304745 | + | 0.527834i | −0.977205 | − | 0.212300i | \(-0.931905\pi\) |
0.672460 | + | 0.740134i | \(0.265238\pi\) | |||||||
\(620\) | −101.168 | −0.00655326 | ||||||||
\(621\) | −1588.26 | + | 9326.96i | −0.102632 | + | 0.602702i | ||||
\(622\) | 9136.21 | 0.588953 | ||||||||
\(623\) | 1169.73 | − | 2026.04i | 0.0752238 | − | 0.130291i | ||||
\(624\) | −3943.09 | − | 13077.8i | −0.252965 | − | 0.838989i | ||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −10527.8 | − | 18234.7i | −0.672165 | − | 1.16422i | ||||
\(627\) | 9027.29 | + | 2120.88i | 0.574984 | + | 0.135087i | ||||
\(628\) | 4027.68 | − | 6976.15i | 0.255927 | − | 0.443278i | ||||
\(629\) | −38356.3 | −2.43142 | ||||||||
\(630\) | 45.9787 | + | 739.604i | 0.00290768 | + | 0.0467723i | ||||
\(631\) | 9647.08 | 0.608628 | 0.304314 | − | 0.952572i | \(-0.401573\pi\) | ||||
0.304314 | + | 0.952572i | \(0.401573\pi\) | |||||||
\(632\) | 4980.59 | − | 8626.64i | 0.313477 | − | 0.542958i | ||||
\(633\) | 7652.23 | − | 8142.72i | 0.480488 | − | 0.511286i | ||||
\(634\) | 3513.97 | + | 6086.37i | 0.220122 | + | 0.381263i | ||||
\(635\) | −2830.59 | − | 4902.73i | −0.176895 | − | 0.306392i | ||||
\(636\) | 2102.74 | − | 2237.52i | 0.131099 | − | 0.139502i | ||||
\(637\) | −5619.48 | + | 9733.23i | −0.349532 | + | 0.605408i | ||||
\(638\) | 30421.6 | 1.88778 | ||||||||
\(639\) | 2676.40 | − | 1775.32i | 0.165691 | − | 0.109907i | ||||
\(640\) | −8316.75 | −0.513669 | ||||||||
\(641\) | 3501.88 | − | 6065.44i | 0.215782 | − | 0.373745i | −0.737732 | − | 0.675093i | \(-0.764103\pi\) |
0.953514 | + | 0.301348i | \(0.0974367\pi\) | |||||||
\(642\) | 12261.3 | + | 2880.68i | 0.753761 | + | 0.177089i | ||||
\(643\) | 3144.44 | + | 5446.34i | 0.192853 | + | 0.334032i | 0.946195 | − | 0.323598i | \(-0.104892\pi\) |
−0.753341 | + | 0.657630i | \(0.771559\pi\) | |||||||
\(644\) | 185.087 | + | 320.579i | 0.0113252 | + | 0.0196158i | ||||
\(645\) | −1510.41 | − | 5009.48i | −0.0922054 | − | 0.305811i | ||||
\(646\) | −10100.7 | + | 17495.0i | −0.615183 | + | 1.06553i | ||||
\(647\) | −5900.85 | −0.358557 | −0.179279 | − | 0.983798i | \(-0.557376\pi\) | ||||
−0.179279 | + | 0.983798i | \(0.557376\pi\) | |||||||
\(648\) | 4424.29 | − | 10481.2i | 0.268214 | − | 0.635404i | ||||
\(649\) | 6021.58 | 0.364203 | ||||||||
\(650\) | −1391.98 | + | 2410.99i | −0.0839970 | + | 0.145487i | ||||
\(651\) | 14.6495 | + | 48.5868i | 0.000881963 | + | 0.00292514i | ||||
\(652\) | 4290.88 | + | 7432.02i | 0.257736 | + | 0.446412i | ||||
\(653\) | 3942.57 | + | 6828.74i | 0.236271 | + | 0.409233i | 0.959641 | − | 0.281227i | \(-0.0907414\pi\) |
−0.723370 | + | 0.690460i | \(0.757408\pi\) | |||||||
\(654\) | 34296.9 | + | 8057.75i | 2.05064 | + | 0.481778i | ||||
\(655\) | −1943.76 | + | 3366.70i | −0.115953 | + | 0.200836i | ||||
\(656\) | −23192.2 | −1.38034 | ||||||||
\(657\) | −4124.65 | + | 2735.98i | −0.244928 | + | 0.162467i | ||||
\(658\) | 2646.28 | 0.156782 | ||||||||
\(659\) | −14378.9 | + | 24905.0i | −0.849959 | + | 1.47217i | 0.0312845 | + | 0.999511i | \(0.490040\pi\) |
−0.881244 | + | 0.472662i | \(0.843293\pi\) | |||||||
\(660\) | 1971.68 | − | 2098.06i | 0.116284 | − | 0.123738i | ||||
\(661\) | −4130.11 | − | 7153.57i | −0.243030 | − | 0.420940i | 0.718546 | − | 0.695479i | \(-0.244808\pi\) |
−0.961576 | + | 0.274539i | \(0.911475\pi\) | |||||||
\(662\) | −384.232 | − | 665.509i | −0.0225583 | − | 0.0390721i | ||||
\(663\) | 12961.7 | − | 13792.5i | 0.759260 | − | 0.807926i | ||||
\(664\) | 11662.7 | − | 20200.4i | 0.681626 | − | 1.18061i | ||||
\(665\) | −441.983 | −0.0257735 | ||||||||
\(666\) | −1964.45 | − | 31599.7i | −0.114296 | − | 1.83853i | ||||
\(667\) | −18512.9 | −1.07470 | ||||||||
\(668\) | 2317.70 | − | 4014.37i | 0.134243 | − | 0.232516i | ||||
\(669\) | −12940.2 | − | 3040.18i | −0.747828 | − | 0.175695i | ||||
\(670\) | −7010.13 | − | 12141.9i | −0.404216 | − | 0.700123i | ||||
\(671\) | 7173.56 | + | 12425.0i | 0.412716 | + | 0.714845i | ||||
\(672\) | −350.625 | − | 1162.89i | −0.0201275 | − | 0.0667553i | ||||
\(673\) | −402.481 | + | 697.118i | −0.0230528 | + | 0.0399285i | −0.877322 | − | 0.479903i | \(-0.840672\pi\) |
0.854269 | + | 0.519831i | \(0.174005\pi\) | |||||||
\(674\) | −11524.7 | −0.658627 | ||||||||
\(675\) | −3288.79 | + | 1218.91i | −0.187534 | + | 0.0695049i | ||||
\(676\) | −3731.65 | −0.212315 | ||||||||
\(677\) | −681.636 | + | 1180.63i | −0.0386963 | + | 0.0670240i | −0.884725 | − | 0.466114i | \(-0.845654\pi\) |
0.846029 | + | 0.533137i | \(0.178987\pi\) | |||||||
\(678\) | −1146.97 | − | 3804.07i | −0.0649692 | − | 0.215478i | ||||
\(679\) | 725.774 | + | 1257.08i | 0.0410201 | + | 0.0710489i | ||||
\(680\) | −4303.62 | − | 7454.09i | −0.242700 | − | 0.420370i | ||||
\(681\) | −20661.3 | − | 4854.19i | −1.16262 | − | 0.273147i | ||||
\(682\) | 332.454 | − | 575.827i | 0.0186661 | − | 0.0323307i | ||||
\(683\) | −11434.6 | −0.640604 | −0.320302 | − | 0.947315i | \(-0.603784\pi\) | ||||
−0.320302 | + | 0.947315i | \(0.603784\pi\) | |||||||
\(684\) | −4427.42 | − | 2201.91i | −0.247495 | − | 0.123088i | ||||
\(685\) | 3118.19 | 0.173927 | ||||||||
\(686\) | −1875.50 | + | 3248.46i | −0.104383 | + | 0.180797i | ||||
\(687\) | 9756.87 | − | 10382.3i | 0.541845 | − | 0.576576i | ||||
\(688\) | 8015.86 | + | 13883.9i | 0.444189 | + | 0.769358i | ||||
\(689\) | −2893.17 | − | 5011.12i | −0.159972 | − | 0.277080i | ||||
\(690\) | −4046.25 | + | 4305.60i | −0.223244 | + | 0.237553i | ||||
\(691\) | 9765.29 | − | 16914.0i | 0.537611 | − | 0.931170i | −0.461421 | − | 0.887181i | \(-0.652660\pi\) |
0.999032 | − | 0.0439884i | \(-0.0140065\pi\) | |||||||
\(692\) | 7960.10 | 0.437280 | ||||||||
\(693\) | −1293.11 | − | 643.109i | −0.0708822 | − | 0.0352521i | ||||
\(694\) | −12172.6 | −0.665799 | ||||||||
\(695\) | −3206.70 | + | 5554.17i | −0.175018 | + | 0.303139i | ||||
\(696\) | 21671.0 | + | 5091.40i | 1.18022 | + | 0.277283i | ||||
\(697\) | −16068.3 | − | 27831.0i | −0.873212 | − | 1.51245i | ||||
\(698\) | −14839.4 | − | 25702.7i | −0.804701 | − | 1.39378i | ||||
\(699\) | −7627.06 | − | 25296.1i | −0.412706 | − | 1.36879i | ||||
\(700\) | −68.6141 | + | 118.843i | −0.00370481 | + | 0.00641692i | ||||
\(701\) | −11041.4 | −0.594903 | −0.297452 | − | 0.954737i | \(-0.596137\pi\) | ||||
−0.297452 | + | 0.954737i | \(0.596137\pi\) | |||||||
\(702\) | 12026.7 | + | 9972.04i | 0.646609 | + | 0.536140i | ||||
\(703\) | 18883.8 | 1.01311 | ||||||||
\(704\) | 2506.80 | − | 4341.90i | 0.134203 | − | 0.232446i | ||||
\(705\) | 3615.71 | + | 11992.0i | 0.193157 | + | 0.640629i | ||||
\(706\) | 14349.9 | + | 24854.7i | 0.764964 | + | 1.32496i | ||||
\(707\) | 125.126 | + | 216.725i | 0.00665608 | + | 0.0115287i | ||||
\(708\) | −3125.82 | − | 734.382i | −0.165926 | − | 0.0389827i | ||||
\(709\) | −1969.54 | + | 3411.34i | −0.104327 | + | 0.180699i | −0.913463 | − | 0.406922i | \(-0.866602\pi\) |
0.809136 | + | 0.587621i | \(0.199935\pi\) | |||||||
\(710\) | 2005.68 | 0.106017 | ||||||||
\(711\) | 1069.31 | + | 17200.7i | 0.0564027 | + | 0.907282i | ||||
\(712\) | −22430.0 | −1.18062 | ||||||||
\(713\) | −202.313 | + | 350.416i | −0.0106265 | + | 0.0184056i | ||||
\(714\) | 2154.59 | − | 2292.69i | 0.112932 | − | 0.120170i | ||||
\(715\) | −2712.85 | − | 4698.80i | −0.141895 | − | 0.245769i | ||||
\(716\) | −2200.60 | − | 3811.55i | −0.114861 | − | 0.198944i | ||||
\(717\) | −5253.91 | + | 5590.67i | −0.273655 | + | 0.291196i | ||||
\(718\) | 7284.72 | − | 12617.5i | 0.378640 | − | 0.655824i | ||||
\(719\) | −23298.2 | −1.20845 | −0.604225 | − | 0.796814i | \(-0.706517\pi\) | ||||
−0.604225 | + | 0.796814i | \(0.706517\pi\) | |||||||
\(720\) | 8955.67 | − | 5940.52i | 0.463553 | − | 0.307486i | ||||
\(721\) | 220.220 | 0.0113751 | ||||||||
\(722\) | −6592.38 | + | 11418.3i | −0.339810 | + | 0.588569i | ||||
\(723\) | 8920.31 | + | 2095.75i | 0.458852 | + | 0.107803i | ||||
\(724\) | −5226.08 | − | 9051.83i | −0.268267 | − | 0.464653i | ||||
\(725\) | −3431.49 | − | 5943.51i | −0.175782 | − | 0.304464i | ||||
\(726\) | −1270.31 | − | 4213.15i | −0.0649389 | − | 0.215378i | ||||
\(727\) | 4752.24 | − | 8231.12i | 0.242436 | − | 0.419911i | −0.718972 | − | 0.695039i | \(-0.755387\pi\) |
0.961408 | + | 0.275128i | \(0.0887203\pi\) | |||||||
\(728\) | −838.823 | −0.0427044 | ||||||||
\(729\) | 3645.00 | + | 19342.6i | 0.185185 | + | 0.982704i | ||||
\(730\) | −3090.99 | −0.156716 | ||||||||
\(731\) | −11107.3 | + | 19238.4i | −0.561994 | + | 0.973402i | ||||
\(732\) | −2208.48 | − | 7324.70i | −0.111513 | − | 0.369848i | ||||
\(733\) | −3660.40 | − | 6340.01i | −0.184448 | − | 0.319473i | 0.758943 | − | 0.651157i | \(-0.225716\pi\) |
−0.943390 | + | 0.331685i | \(0.892383\pi\) | |||||||
\(734\) | 11129.2 | + | 19276.3i | 0.559653 | + | 0.969348i | ||||
\(735\) | −8608.18 | − | 2022.41i | −0.431997 | − | 0.101494i | ||||
\(736\) | 4842.22 | − | 8386.96i | 0.242509 | − | 0.420037i | ||||
\(737\) | 27324.3 | 1.36567 | ||||||||
\(738\) | 22105.6 | − | 14663.2i | 1.10260 | − | 0.731381i | ||||
\(739\) | −1274.52 | −0.0634424 | −0.0317212 | − | 0.999497i | \(-0.510099\pi\) | ||||
−0.0317212 | + | 0.999497i | \(0.510099\pi\) | |||||||
\(740\) | 2931.55 | − | 5077.59i | 0.145630 | − | 0.252238i | ||||
\(741\) | −6381.37 | + | 6790.39i | −0.316363 | + | 0.336641i | ||||
\(742\) | −480.925 | − | 832.986i | −0.0237942 | − | 0.0412128i | ||||
\(743\) | −970.576 | − | 1681.09i | −0.0479232 | − | 0.0830055i | 0.841069 | − | 0.540928i | \(-0.181927\pi\) |
−0.888992 | + | 0.457923i | \(0.848594\pi\) | |||||||
\(744\) | 333.196 | − | 354.553i | 0.0164187 | − | 0.0174711i | ||||
\(745\) | −3810.78 | + | 6600.47i | −0.187404 | + | 0.324594i | ||||
\(746\) | 29030.1 | 1.42476 | ||||||||
\(747\) | 2503.93 | + | 40277.6i | 0.122642 | + | 1.97280i | ||||
\(748\) | −12224.0 | −0.597531 | ||||||||
\(749\) | 584.988 | − | 1013.23i | 0.0285380 | − | 0.0494293i | ||||
\(750\) | −2132.30 | − | 500.965i | −0.103814 | − | 0.0243902i | ||||
\(751\) | −8270.01 | − | 14324.1i | −0.401834 | − | 0.695996i | 0.592114 | − | 0.805854i | \(-0.298294\pi\) |
−0.993947 | + | 0.109858i | \(0.964960\pi\) | |||||||
\(752\) | −19188.8 | − | 33236.0i | −0.930511 | − | 1.61169i | ||||
\(753\) | −2557.75 | − | 8483.08i | −0.123784 | − | 0.410545i | ||||
\(754\) | −15285.0 | + | 26474.4i | −0.738260 | + | 1.27870i | ||||
\(755\) | 15812.8 | 0.762234 | ||||||||
\(756\) | 592.826 | + | 491.545i | 0.0285197 | + | 0.0236472i | ||||
\(757\) | 21145.7 | 1.01526 | 0.507631 | − | 0.861575i | \(-0.330521\pi\) | ||||
0.507631 | + | 0.861575i | \(0.330521\pi\) | |||||||
\(758\) | −12021.8 | + | 20822.4i | −0.576059 | + | 0.997764i | ||||
\(759\) | −3324.14 | − | 11024.9i | −0.158970 | − | 0.527245i | ||||
\(760\) | 2118.78 | + | 3669.84i | 0.101127 | + | 0.175157i | ||||
\(761\) | 10067.1 | + | 17436.7i | 0.479543 | + | 0.830593i | 0.999725 | − | 0.0234624i | \(-0.00746901\pi\) |
−0.520181 | + | 0.854056i | \(0.674136\pi\) | |||||||
\(762\) | −19314.2 | − | 4537.69i | −0.918213 | − | 0.215726i | ||||
\(763\) | 1636.31 | − | 2834.17i | 0.0776388 | − | 0.134474i | ||||
\(764\) | 1283.87 | 0.0607968 | ||||||||
\(765\) | 13333.5 | + | 6631.20i | 0.630162 | + | 0.313401i | ||||
\(766\) | −19989.1 | −0.942865 | ||||||||
\(767\) | −3025.48 | + | 5240.29i | −0.142430 | + | 0.246696i | ||||
\(768\) | −15617.0 | + | 16618.0i | −0.733762 | + | 0.780795i | ||||
\(769\) | −1097.36 | − | 1900.68i | −0.0514587 | − | 0.0891291i | 0.839149 | − | 0.543902i | \(-0.183054\pi\) |
−0.890607 | + | 0.454773i | \(0.849720\pi\) | |||||||
\(770\) | −450.951 | − | 781.070i | −0.0211054 | − | 0.0365556i | ||||
\(771\) | −813.442 | + | 865.581i | −0.0379966 | + | 0.0404321i | ||||
\(772\) | −2606.84 | + | 4515.18i | −0.121531 | + | 0.210499i | ||||
\(773\) | −8327.70 | −0.387486 | −0.193743 | − | 0.981052i | \(-0.562063\pi\) | ||||
−0.193743 | + | 0.981052i | \(0.562063\pi\) | |||||||
\(774\) | −16418.4 | − | 8165.40i | −0.762462 | − | 0.379198i | ||||
\(775\) | −150.000 | −0.00695246 | ||||||||
\(776\) | 6958.46 | − | 12052.4i | 0.321900 | − | 0.557547i | ||||
\(777\) | −2863.04 | − | 672.646i | −0.132189 | − | 0.0310567i | ||||
\(778\) | 1751.67 | + | 3033.98i | 0.0807204 | + | 0.139812i | ||||
\(779\) | 7910.82 | + | 13701.9i | 0.363844 | + | 0.630196i | ||||
\(780\) | 835.190 | + | 2770.01i | 0.0383392 | + | 0.127157i | ||||
\(781\) | −1954.45 | + | 3385.20i | −0.0895463 | + | 0.155099i | ||||
\(782\) | 25085.8 | 1.14715 | ||||||||
\(783\) | −36113.4 | + | 13384.5i | −1.64826 | + | 0.610887i | ||||
\(784\) | 27093.9 | 1.23424 | ||||||||
\(785\) | 5971.75 | − | 10343.4i | 0.271517 | − | 0.470281i | ||||
\(786\) | 3932.95 | + | 13044.1i | 0.178478 | + | 0.591944i | ||||
\(787\) | 9481.64 | + | 16422.7i | 0.429459 | + | 0.743845i | 0.996825 | − | 0.0796209i | \(-0.0253710\pi\) |
−0.567366 | + | 0.823465i | \(0.692038\pi\) | |||||||
\(788\) | 7224.43 | + | 12513.1i | 0.326599 | + | 0.565686i | ||||
\(789\) | −6519.10 | − | 1531.60i | −0.294152 | − | 0.0691084i | ||||
\(790\) | −5381.26 | + | 9320.62i | −0.242350 | + | 0.419763i | ||||
\(791\) | −369.076 | −0.0165902 | ||||||||
\(792\) | 859.134 | + | 13819.8i | 0.0385454 | + | 0.620034i | ||||
\(793\) | −14417.1 | −0.645608 | ||||||||
\(794\) | 22664.1 | − | 39255.4i | 1.01300 | − | 1.75456i | ||||
\(795\) | 3117.68 | − | 3317.51i | 0.139085 | − | 0.148000i | ||||
\(796\) | 2365.41 | + | 4097.01i | 0.105326 | + | 0.182430i | ||||
\(797\) | −17132.6 | − | 29674.5i | −0.761439 | − | 1.31885i | −0.942109 | − | 0.335307i | \(-0.891160\pi\) |
0.180670 | − | 0.983544i | \(-0.442173\pi\) | |||||||
\(798\) | −1060.76 | + | 1128.75i | −0.0470557 | + | 0.0500718i | ||||
\(799\) | 26589.2 | − | 46053.9i | 1.17730 | − | 2.03914i | ||||
\(800\) | 3590.15 | 0.158664 | ||||||||
\(801\) | 32338.5 | − | 21451.0i | 1.42650 | − | 0.946233i | ||||
\(802\) | −44093.9 | −1.94141 | ||||||||
\(803\) | 3012.04 | − | 5217.00i | 0.132369 | − | 0.229270i | ||||
\(804\) | −14184.1 | − | 3332.42i | −0.622181 | − | 0.146176i | ||||
\(805\) | 274.423 | + | 475.315i | 0.0120151 | + | 0.0208108i | ||||
\(806\) | 334.076 | + | 578.636i | 0.0145997 | + | 0.0252873i | ||||
\(807\) | −1460.97 | − | 4845.49i | −0.0637282 | − | 0.211362i | ||||
\(808\) | 1199.66 | − | 2077.88i | 0.0522327 | − | 0.0904696i | ||||
\(809\) | 36425.5 | 1.58300 | 0.791502 | − | 0.611166i | \(-0.209299\pi\) | ||||
0.791502 | + | 0.611166i | \(0.209299\pi\) | |||||||
\(810\) | −4780.21 | + | 11324.4i | −0.207357 | + | 0.491233i | ||||
\(811\) | 45174.0 | 1.95595 | 0.977973 | − | 0.208732i | \(-0.0669335\pi\) | ||||
0.977973 | + | 0.208732i | \(0.0669335\pi\) | |||||||
\(812\) | −753.435 | + | 1304.99i | −0.0325620 | + | 0.0563991i | ||||
\(813\) | 6032.74 | + | 20008.3i | 0.260243 | + | 0.863128i | ||||
\(814\) | 19267.0 | + | 33371.3i | 0.829615 | + | 1.43694i | ||||
\(815\) | 6361.98 | + | 11019.3i | 0.273436 | + | 0.473605i | ||||
\(816\) | −44418.5 | − | 10435.7i | −1.90559 | − | 0.447700i | ||||
\(817\) | 5468.41 | − | 9471.56i | 0.234168 | − | 0.405591i | ||||
\(818\) | 17782.7 | 0.760093 | ||||||||
\(819\) | 1209.38 | − | 802.210i | 0.0515984 | − | 0.0342265i | ||||
\(820\) | 4912.35 | 0.209203 | ||||||||
\(821\) | 3459.65 | − | 5992.29i | 0.147068 | − | 0.254729i | −0.783075 | − | 0.621928i | \(-0.786350\pi\) |
0.930143 | + | 0.367199i | \(0.119683\pi\) | |||||||
\(822\) | 7483.66 | − | 7963.34i | 0.317546 | − | 0.337900i | ||||
\(823\) | 5699.26 | + | 9871.42i | 0.241390 | + | 0.418100i | 0.961110 | − | 0.276164i | \(-0.0890634\pi\) |
−0.719721 | + | 0.694264i | \(0.755730\pi\) | |||||||
\(824\) | −1055.70 | − | 1828.52i | −0.0446322 | − | 0.0773052i | ||||
\(825\) | 2923.37 | − | 3110.75i | 0.123368 | − | 0.131276i | ||||
\(826\) | −502.919 | + | 871.080i | −0.0211850 | + | 0.0366934i | ||||
\(827\) | 34712.0 | 1.45956 | 0.729779 | − | 0.683683i | \(-0.239623\pi\) | ||||
0.729779 | + | 0.683683i | \(0.239623\pi\) | |||||||
\(828\) | 380.986 | + | 6128.46i | 0.0159906 | + | 0.257221i | ||||
\(829\) | 2732.97 | 0.114500 | 0.0572498 | − | 0.998360i | \(-0.481767\pi\) | ||||
0.0572498 | + | 0.998360i | \(0.481767\pi\) | |||||||
\(830\) | −12600.9 | + | 21825.4i | −0.526968 | + | 0.912735i | ||||
\(831\) | −17093.3 | − | 4015.91i | −0.713549 | − | 0.167642i | ||||
\(832\) | 2519.03 | + | 4363.09i | 0.104966 | + | 0.181806i | ||||
\(833\) | 18771.5 | + | 32513.2i | 0.780786 | + | 1.35236i | ||||
\(834\) | 6488.34 | + | 21519.4i | 0.269392 | + | 0.893472i | ||||
\(835\) | 3436.39 | − | 5952.01i | 0.142421 | − | 0.246680i | ||||
\(836\) | 6018.19 | 0.248975 | ||||||||
\(837\) | −141.310 | + | 829.831i | −0.00583557 | + | 0.0342690i | ||||
\(838\) | −46693.0 | −1.92480 | ||||||||
\(839\) | 4787.89 | − | 8292.87i | 0.197016 | − | 0.341242i | −0.750544 | − | 0.660821i | \(-0.770208\pi\) |
0.947560 | + | 0.319579i | \(0.103542\pi\) | |||||||
\(840\) | −190.516 | − | 631.870i | −0.00782551 | − | 0.0259543i | ||||
\(841\) | −25485.8 | − | 44142.8i | −1.04497 | − | 1.80995i | ||||
\(842\) | 1850.32 | + | 3204.85i | 0.0757318 | + | 0.131171i | ||||
\(843\) | 3709.38 | + | 871.484i | 0.151551 | + | 0.0356056i | ||||
\(844\) | 3625.97 | − | 6280.37i | 0.147880 | − | 0.256136i | ||||
\(845\) | −5532.82 | −0.225248 | ||||||||
\(846\) | 39303.2 | + | 19546.8i | 1.59725 | + | 0.794364i | ||||
\(847\) | −408.766 | −0.0165825 | ||||||||
\(848\) | −6974.60 | + | 12080.4i | −0.282440 | + | 0.489200i | ||||
\(849\) | −24585.2 | + | 26161.1i | −0.993832 | + | 1.05753i | ||||
\(850\) | 4649.83 | + | 8053.74i | 0.187633 | + | 0.324989i | ||||
\(851\) | −11724.8 | − | 20307.9i | −0.472292 | − | 0.818034i | ||||
\(852\) | 1427.41 | − | 1518.90i | 0.0573971 | − | 0.0610761i | ||||
\(853\) | −4520.95 | + | 7830.51i | −0.181470 | + | 0.314316i | −0.942381 | − | 0.334540i | \(-0.891419\pi\) |
0.760911 | + | 0.648856i | \(0.224752\pi\) | |||||||
\(854\) | −2396.52 | −0.0960274 | ||||||||
\(855\) | −6564.43 | − | 3264.71i | −0.262572 | − | 0.130586i | ||||
\(856\) | −11217.3 | −0.447896 | ||||||||
\(857\) | 1157.64 | − | 2005.09i | 0.0461426 | − | 0.0799213i | −0.842032 | − | 0.539428i | \(-0.818640\pi\) |
0.888174 | + | 0.459507i | \(0.151974\pi\) | |||||||
\(858\) | −18510.8 | − | 4348.94i | −0.736536 | − | 0.173043i | ||||
\(859\) | 15701.6 | + | 27195.9i | 0.623667 | + | 1.08022i | 0.988797 | + | 0.149266i | \(0.0476912\pi\) |
−0.365130 | + | 0.930957i | \(0.618975\pi\) | |||||||
\(860\) | −1697.85 | − | 2940.76i | −0.0673210 | − | 0.116603i | ||||
\(861\) | −711.322 | − | 2359.19i | −0.0281554 | − | 0.0933808i | ||||
\(862\) | 26831.3 | − | 46473.2i | 1.06018 | − | 1.83629i | ||||
\(863\) | −40883.5 | −1.61262 | −0.806310 | − | 0.591493i | \(-0.798539\pi\) | ||||
−0.806310 | + | 0.591493i | \(0.798539\pi\) | |||||||
\(864\) | 3382.15 | − | 19861.4i | 0.133175 | − | 0.782060i | ||||
\(865\) | 11802.3 | 0.463917 | ||||||||
\(866\) | 6013.30 | − | 10415.3i | 0.235959 | − | 0.408692i | ||||
\(867\) | −10882.0 | − | 36091.4i | −0.426264 | − | 1.41376i | ||||
\(868\) | 16.4674 | + | 28.5223i | 0.000643939 | + | 0.00111534i | ||||
\(869\) | −10487.6 | − | 18165.1i | −0.409399 | − | 0.709100i | ||||
\(870\) | −23414.3 | − | 5500.98i | −0.912436 | − | 0.214369i | ||||
\(871\) | −13728.8 | + | 23779.0i | −0.534078 | + | 0.925051i | ||||
\(872\) | −31376.7 | −1.21852 | ||||||||
\(873\) | 1493.95 | + | 24031.4i | 0.0579182 | + | 0.931659i | ||||
\(874\) | −12350.4 | −0.477985 | ||||||||
\(875\) | −101.732 | + | 176.206i | −0.00393050 | + | 0.00680782i | ||||
\(876\) | −2199.81 | + | 2340.81i | −0.0848456 | + | 0.0902840i | ||||
\(877\) | 14157.3 | + | 24521.2i | 0.545107 | + | 0.944154i | 0.998600 | + | 0.0528937i | \(0.0168444\pi\) |
−0.453493 | + | 0.891260i | \(0.649822\pi\) | |||||||
\(878\) | −979.348 | − | 1696.28i | −0.0376440 | − | 0.0652013i | ||||
\(879\) | 16544.8 | − | 17605.3i | 0.634862 | − | 0.675554i | ||||
\(880\) | −6539.91 | + | 11327.5i | −0.250523 | + | 0.433919i | ||||
\(881\) | 6479.51 | 0.247787 | 0.123893 | − | 0.992296i | \(-0.460462\pi\) | ||||
0.123893 | + | 0.992296i | \(0.460462\pi\) | |||||||
\(882\) | −25824.5 | + | 17130.1i | −0.985893 | + | 0.653968i | ||||
\(883\) | −17769.0 | −0.677208 | −0.338604 | − | 0.940929i | \(-0.609955\pi\) | ||||
−0.338604 | + | 0.940929i | \(0.609955\pi\) | |||||||
\(884\) | 6141.82 | − | 10637.9i | 0.233678 | − | 0.404743i | ||||
\(885\) | −4634.57 | − | 1088.85i | −0.176033 | − | 0.0413574i | ||||
\(886\) | −18198.1 | − | 31520.1i | −0.690044 | − | 1.19519i | ||||
\(887\) | 12944.1 | + | 22419.8i | 0.489988 | + | 0.848684i | 0.999934 | − | 0.0115224i | \(-0.00366776\pi\) |
−0.509945 | + | 0.860207i | \(0.670334\pi\) | |||||||
\(888\) | 8139.83 | + | 26996.8i | 0.307607 | + | 1.02022i | ||||
\(889\) | −921.481 | + | 1596.05i | −0.0347643 | + | 0.0602136i | ||||
\(890\) | 24234.4 | 0.912739 | ||||||||
\(891\) | −14455.3 | − | 19103.2i | −0.543514 | − | 0.718273i | ||||
\(892\) | −8626.80 | −0.323819 | ||||||||
\(893\) | −13090.6 | + | 22673.5i | −0.490548 | + | 0.849654i | ||||
\(894\) | 7710.62 | + | 25573.2i | 0.288458 | + | 0.956707i | ||||
\(895\) | −3262.77 | − | 5651.29i | −0.121857 | − | 0.211063i | ||||
\(896\) | 1353.73 | + | 2344.73i | 0.0504744 | + | 0.0874242i | ||||
\(897\) | 11264.6 | + | 2646.52i | 0.419303 | + | 0.0985115i | ||||
\(898\) | 4879.71 | − | 8451.90i | 0.181334 | − | 0.314080i | ||||
\(899\) | −1647.11 | −0.0611060 | ||||||||
\(900\) | −1896.91 | + | 1258.27i | −0.0702559 | + | 0.0466025i | ||||
\(901\) | −19328.9 | −0.714694 | ||||||||
\(902\) | −16142.7 | + | 27959.9i | −0.595889 | + | 1.03211i | ||||
\(903\) | −1166.46 | + | 1241.23i | −0.0429873 | + | 0.0457426i | ||||
\(904\) | 1769.28 | + | 3064.49i | 0.0650946 | + | 0.112747i | ||||
\(905\) | −7748.58 | − | 13420.9i | −0.284609 | − | 0.492958i | ||||
\(906\) | 37950.7 | − | 40383.2i | 1.39164 | − | 1.48084i | ||||
\(907\) | 22594.1 | − | 39134.2i | 0.827150 | − | 1.43267i | −0.0731143 | − | 0.997324i | \(-0.523294\pi\) |
0.900265 | − | 0.435343i | \(-0.143373\pi\) | |||||||
\(908\) | −13774.2 | −0.503429 | ||||||||
\(909\) | 257.562 | + | 4143.09i | 0.00939802 | + | 0.151175i | ||||
\(910\) | 906.303 | 0.0330150 | ||||||||
\(911\) | −6587.08 | + | 11409.2i | −0.239560 | + | 0.414931i | −0.960588 | − | 0.277975i | \(-0.910337\pi\) |
0.721028 | + | 0.692906i | \(0.243670\pi\) | |||||||
\(912\) | 21868.4 | + | 5137.78i | 0.794007 | + | 0.186545i | ||||
\(913\) | −24558.0 | − | 42535.8i | −0.890200 | − | 1.54187i | ||||
\(914\) | 5395.51 | + | 9345.29i | 0.195260 | + | 0.338200i | ||||
\(915\) | −3274.46 | − | 10860.2i | −0.118306 | − | 0.392378i | ||||
\(916\) | 4623.24 | − | 8007.69i | 0.166765 | − | 0.288845i | ||||
\(917\) | 1265.56 | 0.0455752 | ||||||||
\(918\) | 48935.4 | − | 18136.7i | 1.75938 | − | 0.652069i | ||||
\(919\) | −54078.5 | −1.94112 | −0.970558 | − | 0.240867i | \(-0.922568\pi\) | ||||
−0.970558 | + | 0.240867i | \(0.922568\pi\) | |||||||
\(920\) | 2631.07 | − | 4557.15i | 0.0942868 | − | 0.163309i | ||||
\(921\) | 11042.1 | + | 36622.6i | 0.395060 | + | 1.31027i | ||||
\(922\) | 12336.4 | + | 21367.3i | 0.440650 | + | 0.763228i | ||||
\(923\) | −1963.98 | − | 3401.72i | −0.0700383 | − | 0.121310i | ||||
\(924\) | −912.440 | − | 214.370i | −0.0324860 | − | 0.00763229i | ||||
\(925\) | 4346.54 | − | 7528.42i | 0.154501 | − | 0.267603i | ||||
\(926\) | −23646.4 | −0.839166 | ||||||||
\(927\) | 3270.76 | + | 1626.66i | 0.115886 | + | 0.0576338i | ||||
\(928\) | 39422.6 | 1.39451 | ||||||||
\(929\) | 22858.9 | − | 39592.8i | 0.807294 | − | 1.39827i | −0.107438 | − | 0.994212i | \(-0.534265\pi\) |
0.914732 | − | 0.404062i | \(-0.132402\pi\) | |||||||
\(930\) | −360.000 | + | 383.075i | −0.0126934 | + | 0.0135070i | ||||
\(931\) | −9241.71 | − | 16007.1i | −0.325333 | − | 0.563493i | ||||
\(932\) | −8573.53 | − | 14849.8i | −0.301325 | − | 0.521911i | ||||
\(933\) | 9640.50 | − | 10258.4i | 0.338281 | − | 0.359963i | ||||
\(934\) | −13493.6 | + | 23371.5i | −0.472722 | + | 0.818779i | ||||
\(935\) | −18124.2 | −0.633931 | ||||||||
\(936\) | −12458.4 | − | 6195.98i | −0.435059 | − | 0.216369i | ||||
\(937\) | −5055.54 | −0.176262 | −0.0881309 | − | 0.996109i | \(-0.528089\pi\) | ||||
−0.0881309 | + | 0.996109i | \(0.528089\pi\) | |||||||
\(938\) | −2282.10 | + | 3952.72i | −0.0794385 | + | 0.137592i | ||||
\(939\) | −31583.4 | − | 7420.23i | −1.09764 | − | 0.257881i | ||||
\(940\) | 4064.40 | + | 7039.75i | 0.141028 | + | 0.244267i | ||||
\(941\) | −14056.0 | − | 24345.7i | −0.486942 | − | 0.843407i | 0.512946 | − | 0.858421i | \(-0.328554\pi\) |
−0.999887 | + | 0.0150136i | \(0.995221\pi\) | |||||||
\(942\) | −12083.1 | − | 40075.0i | −0.417927 | − | 1.38611i | ||||
\(943\) | 9823.52 | − | 17014.8i | 0.339234 | − | 0.587571i | ||||
\(944\) | 14587.1 | 0.502935 | ||||||||
\(945\) | 878.968 | + | 728.802i | 0.0302570 | + | 0.0250878i | ||||
\(946\) | 22317.4 | 0.767022 | ||||||||
\(947\) | −15060.2 | + | 26085.0i | −0.516780 | + | 0.895090i | 0.483030 | + | 0.875604i | \(0.339536\pi\) |
−0.999810 | + | 0.0194859i | \(0.993797\pi\) | |||||||
\(948\) | 3228.76 | + | 10708.6i | 0.110617 | + | 0.366876i | ||||
\(949\) | 3026.74 | + | 5242.46i | 0.103532 | + | 0.179323i | ||||
\(950\) | −2289.23 | − | 3965.07i | −0.0781816 | − | 0.135414i | ||||
\(951\) | 10541.9 | + | 2476.73i | 0.359458 | + | 0.0844514i | ||||
\(952\) | −1401.02 | + | 2426.63i | −0.0476967 | + | 0.0826130i | ||||
\(953\) | 19362.7 | 0.658154 | 0.329077 | − | 0.944303i | \(-0.393262\pi\) | ||||
0.329077 | + | 0.944303i | \(0.393262\pi\) | |||||||
\(954\) | −989.946 | − | 15924.1i | −0.0335961 | − | 0.540420i | ||||
\(955\) | 1903.56 | 0.0645003 | ||||||||
\(956\) | −2489.54 | + | 4312.01i | −0.0842233 | + | 0.145879i | ||||
\(957\) | 32100.8 | − | 34158.4i | 1.08430 | − | 1.15380i | ||||
\(958\) | −5359.97 | − | 9283.74i | −0.180765 | − | 0.313094i | ||||
\(959\) | −507.554 | − | 879.109i | −0.0170905 | − | 0.0296016i | ||||
\(960\) | −2714.51 | + | 2888.50i | −0.0912608 | + | 0.0971103i | ||||
\(961\) | 14877.5 | − | 25768.6i | 0.499396 | − | 0.864979i | ||||
\(962\) | −38721.9 | −1.29776 | ||||||||
\(963\) | 16172.6 | − | 10727.7i | 0.541179 | − | 0.358977i | ||||
\(964\) | 5946.87 | 0.198689 | ||||||||
\(965\) | −3865.10 | + | 6694.55i | −0.128935 | + | 0.223321i | ||||
\(966\) | 1872.49 | + | 439.925i | 0.0623669 | + | 0.0146525i | ||||
\(967\) | 15362.3 | + | 26608.2i | 0.510876 | + | 0.884863i | 0.999921 | + | 0.0126043i | \(0.00401218\pi\) |
−0.489045 | + | 0.872259i | \(0.662654\pi\) | |||||||
\(968\) | 1959.55 | + | 3394.04i | 0.0650643 | + | 0.112695i | ||||
\(969\) | 8985.67 | + | 29802.1i | 0.297896 | + | 0.988010i | ||||
\(970\) | −7518.24 | + | 13022.0i | −0.248862 | + | 0.431042i | ||||
\(971\) | −49791.0 | −1.64559 | −0.822796 | − | 0.568336i | \(-0.807587\pi\) | ||||
−0.822796 | + | 0.568336i | \(0.807587\pi\) | |||||||
\(972\) | 5173.98 | + | 11679.5i | 0.170736 | + | 0.385410i | ||||
\(973\) | 2087.84 | 0.0687906 | ||||||||
\(974\) | 22021.4 | − | 38142.3i | 0.724448 | − | 1.25478i | ||||
\(975\) | 1238.32 | + | 4107.03i | 0.0406747 | + | 0.134903i | ||||
\(976\) | 17377.8 | + | 30099.2i | 0.569927 | + | 0.987143i | ||||
\(977\) | 11195.9 | + | 19391.9i | 0.366622 | + | 0.635008i | 0.989035 | − | 0.147681i | \(-0.0471808\pi\) |
−0.622413 | + | 0.782689i | \(0.713847\pi\) | |||||||
\(978\) | 43410.2 | + | 10198.8i | 1.41933 | + | 0.333458i | ||||
\(979\) | −23615.3 | + | 40903.0i | −0.770939 | + | 1.33531i | ||||
\(980\) | −5738.79 | −0.187060 | ||||||||
\(981\) | 45237.5 | − | 30007.2i | 1.47230 | − | 0.976611i | ||||
\(982\) | 14843.5 | 0.482357 | ||||||||
\(983\) | 12309.7 | − | 21321.0i | 0.399408 | − | 0.691794i | −0.594245 | − | 0.804284i | \(-0.702549\pi\) |
0.993653 | + | 0.112490i | \(0.0358825\pi\) | |||||||
\(984\) | −16178.7 | + | 17215.7i | −0.524144 | + | 0.557741i | ||||
\(985\) | 10711.5 | + | 18552.8i | 0.346494 | + | 0.600145i | ||||
\(986\) | 51058.7 | + | 88436.2i | 1.64913 | + | 2.85637i | ||||
\(987\) | 2792.35 | − | 2971.33i | 0.0900521 | − | 0.0958242i | ||||
\(988\) | −3023.78 | + | 5237.34i | −0.0973676 | + | 0.168646i | ||||
\(989\) | −13581.1 | −0.436658 | ||||||||
\(990\) | −928.247 | − | 14931.6i | −0.0297996 | − | 0.479351i | ||||
\(991\) | 24540.3 | 0.786629 | 0.393314 | − | 0.919404i | \(-0.371328\pi\) | ||||
0.393314 | + | 0.919404i | \(0.371328\pi\) | |||||||
\(992\) | 430.818 | − | 746.199i | 0.0137888 | − | 0.0238829i | ||||
\(993\) | −1152.70 | − | 270.815i | −0.0368375 | − | 0.00865465i | ||||
\(994\) | −326.468 | − | 565.460i | −0.0104175 | − | 0.0180436i | ||||
\(995\) | 3507.13 | + | 6074.53i | 0.111742 | + | 0.193543i | ||||
\(996\) | 7560.54 | + | 25075.5i | 0.240527 | + | 0.797737i | ||||
\(997\) | −22978.0 | + | 39799.1i | −0.729912 | + | 1.26424i | 0.227008 | + | 0.973893i | \(0.427105\pi\) |
−0.956920 | + | 0.290351i | \(0.906228\pi\) | |||||||
\(998\) | −63146.7 | −2.00288 | ||||||||
\(999\) | −37554.1 | − | 31138.2i | −1.18935 | − | 0.986155i |
(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 | 45.4.e.a.16.2 | ✓ | 4 | |
3.2 | odd | 2 | 135.4.e.a.46.1 | 4 | |||
5.2 | odd | 4 | 225.4.k.a.124.4 | 8 | |||
5.3 | odd | 4 | 225.4.k.a.124.1 | 8 | |||
5.4 | even | 2 | 225.4.e.a.151.1 | 4 | |||
9.2 | odd | 6 | 405.4.a.e.1.2 | 2 | |||
9.4 | even | 3 | inner | 45.4.e.a.31.2 | yes | 4 | |
9.5 | odd | 6 | 135.4.e.a.91.1 | 4 | |||
9.7 | even | 3 | 405.4.a.d.1.1 | 2 | |||
45.4 | even | 6 | 225.4.e.a.76.1 | 4 | |||
45.13 | odd | 12 | 225.4.k.a.49.4 | 8 | |||
45.22 | odd | 12 | 225.4.k.a.49.1 | 8 | |||
45.29 | odd | 6 | 2025.4.a.j.1.1 | 2 | |||
45.34 | even | 6 | 2025.4.a.l.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.a.16.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
45.4.e.a.31.2 | yes | 4 | 9.4 | even | 3 | inner | |
135.4.e.a.46.1 | 4 | 3.2 | odd | 2 | |||
135.4.e.a.91.1 | 4 | 9.5 | odd | 6 | |||
225.4.e.a.76.1 | 4 | 45.4 | even | 6 | |||
225.4.e.a.151.1 | 4 | 5.4 | even | 2 | |||
225.4.k.a.49.1 | 8 | 45.22 | odd | 12 | |||
225.4.k.a.49.4 | 8 | 45.13 | odd | 12 | |||
225.4.k.a.124.1 | 8 | 5.3 | odd | 4 | |||
225.4.k.a.124.4 | 8 | 5.2 | odd | 4 | |||
405.4.a.d.1.1 | 2 | 9.7 | even | 3 | |||
405.4.a.e.1.2 | 2 | 9.2 | odd | 6 | |||
2025.4.a.j.1.1 | 2 | 45.29 | odd | 6 | |||
2025.4.a.l.1.2 | 2 | 45.34 | even | 6 |