Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,4,Mod(4,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.j (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.30107449022\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 70x^{8} + 1645x^{6} + 14700x^{4} + 44100x^{2} + 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 10.2 | ||
Root | \(2.04224i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.10 |
Dual form | 39.4.j.c.4.2 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.76863 | + | 1.02112i | −0.625307 | + | 0.361021i | −0.778932 | − | 0.627108i | \(-0.784238\pi\) |
0.153626 | + | 0.988129i | \(0.450905\pi\) | |||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | −1.91462 | + | 3.31622i | −0.239328 | + | 0.414528i | ||||
\(5\) | − | 12.0825i | − | 1.08069i | −0.841444 | − | 0.540344i | \(-0.818294\pi\) | ||
0.841444 | − | 0.540344i | \(-0.181706\pi\) | |||||||
\(6\) | 5.30590 | + | 3.06336i | 0.361021 | + | 0.208436i | ||||
\(7\) | −25.7533 | − | 14.8686i | −1.39055 | − | 0.802832i | −0.397170 | − | 0.917745i | \(-0.630008\pi\) |
−0.993375 | + | 0.114914i | \(0.963341\pi\) | |||||||
\(8\) | − | 24.1582i | − | 1.06765i | ||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 12.3377 | + | 21.3694i | 0.390151 | + | 0.675761i | ||||
\(11\) | 24.3038 | − | 14.0318i | 0.666169 | − | 0.384613i | −0.128454 | − | 0.991715i | \(-0.541002\pi\) |
0.794624 | + | 0.607102i | \(0.207668\pi\) | |||||||
\(12\) | 11.4877 | 0.276352 | ||||||||
\(13\) | −40.9717 | + | 22.7667i | −0.874115 | + | 0.485719i | ||||
\(14\) | 60.7308 | 1.15936 | ||||||||
\(15\) | −31.3911 | + | 18.1237i | −0.540344 | + | 0.311968i | ||||
\(16\) | 9.35146 | + | 16.1972i | 0.146117 | + | 0.253081i | ||||
\(17\) | −25.3278 | + | 43.8690i | −0.361347 | + | 0.625871i | −0.988183 | − | 0.153280i | \(-0.951016\pi\) |
0.626836 | + | 0.779151i | \(0.284350\pi\) | |||||||
\(18\) | − | 18.3802i | − | 0.240681i | ||||||
\(19\) | 91.0612 | + | 52.5742i | 1.09952 | + | 0.634808i | 0.936095 | − | 0.351748i | \(-0.114413\pi\) |
0.163425 | + | 0.986556i | \(0.447746\pi\) | |||||||
\(20\) | 40.0681 | + | 23.1333i | 0.447975 | + | 0.258639i | ||||
\(21\) | 89.2119i | 0.927030i | ||||||||
\(22\) | −28.6563 | + | 49.6342i | −0.277707 | + | 0.481002i | ||||
\(23\) | −80.2961 | − | 139.077i | −0.727951 | − | 1.26085i | −0.957748 | − | 0.287610i | \(-0.907139\pi\) |
0.229796 | − | 0.973239i | \(-0.426194\pi\) | |||||||
\(24\) | −62.7648 | + | 36.2373i | −0.533826 | + | 0.308204i | ||||
\(25\) | −20.9857 | −0.167886 | ||||||||
\(26\) | 49.2164 | − | 82.1030i | 0.371235 | − | 0.619297i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 98.6155 | − | 56.9357i | 0.665592 | − | 0.384280i | ||||
\(29\) | −70.0525 | − | 121.334i | −0.448566 | − | 0.776939i | 0.549727 | − | 0.835344i | \(-0.314732\pi\) |
−0.998293 | + | 0.0584051i | \(0.981398\pi\) | |||||||
\(30\) | 37.0130 | − | 64.1083i | 0.225254 | − | 0.390151i | ||||
\(31\) | − | 223.593i | − | 1.29544i | −0.761880 | − | 0.647718i | \(-0.775724\pi\) | ||
0.761880 | − | 0.647718i | \(-0.224276\pi\) | |||||||
\(32\) | 134.294 | + | 77.5348i | 0.741878 | + | 0.428323i | ||||
\(33\) | −72.9113 | − | 42.0954i | −0.384613 | − | 0.222056i | ||||
\(34\) | − | 103.451i | − | 0.521815i | ||||||
\(35\) | −179.650 | + | 311.163i | −0.867610 | + | 1.50274i | ||||
\(36\) | −17.2316 | − | 29.8460i | −0.0797759 | − | 0.138176i | ||||
\(37\) | −197.759 | + | 114.176i | −0.878684 | + | 0.507308i | −0.870224 | − | 0.492656i | \(-0.836026\pi\) |
−0.00845956 | + | 0.999964i | \(0.502693\pi\) | |||||||
\(38\) | −214.739 | −0.916716 | ||||||||
\(39\) | 120.607 | + | 72.2975i | 0.495195 | + | 0.296843i | ||||
\(40\) | −291.890 | −1.15380 | ||||||||
\(41\) | 256.259 | − | 147.951i | 0.976119 | − | 0.563563i | 0.0750227 | − | 0.997182i | \(-0.476097\pi\) |
0.901096 | + | 0.433619i | \(0.142764\pi\) | |||||||
\(42\) | −91.0962 | − | 157.783i | −0.334677 | − | 0.579678i | ||||
\(43\) | 96.0517 | − | 166.366i | 0.340645 | − | 0.590015i | −0.643907 | − | 0.765103i | \(-0.722688\pi\) |
0.984553 | + | 0.175088i | \(0.0560211\pi\) | |||||||
\(44\) | 107.462i | 0.368194i | ||||||||
\(45\) | 94.1734 | + | 54.3710i | 0.311968 | + | 0.180115i | ||||
\(46\) | 284.029 | + | 163.984i | 0.910386 | + | 0.525611i | ||||
\(47\) | 36.9300i | 0.114613i | 0.998357 | + | 0.0573063i | \(0.0182512\pi\) | ||||
−0.998357 | + | 0.0573063i | \(0.981749\pi\) | |||||||
\(48\) | 28.0544 | − | 48.5916i | 0.0843605 | − | 0.146117i | ||||
\(49\) | 270.653 | + | 468.785i | 0.789077 | + | 1.36672i | ||||
\(50\) | 37.1160 | − | 21.4289i | 0.104980 | − | 0.0606102i | ||||
\(51\) | 151.967 | 0.417247 | ||||||||
\(52\) | 2.94589 | − | 179.461i | 0.00785618 | − | 0.478591i | ||||
\(53\) | 149.102 | 0.386429 | 0.193214 | − | 0.981157i | \(-0.438109\pi\) | ||||
0.193214 | + | 0.981157i | \(0.438109\pi\) | |||||||
\(54\) | −47.7531 | + | 27.5703i | −0.120340 | + | 0.0694785i | ||||
\(55\) | −169.538 | − | 293.649i | −0.415647 | − | 0.719921i | ||||
\(56\) | −359.200 | + | 622.152i | −0.857144 | + | 1.48462i | ||||
\(57\) | − | 315.445i | − | 0.733013i | ||||||
\(58\) | 247.794 | + | 143.064i | 0.560983 | + | 0.323884i | ||||
\(59\) | −380.070 | − | 219.433i | −0.838659 | − | 0.484200i | 0.0181492 | − | 0.999835i | \(-0.494223\pi\) |
−0.856808 | + | 0.515635i | \(0.827556\pi\) | |||||||
\(60\) | − | 138.800i | − | 0.298650i | ||||||
\(61\) | −143.073 | + | 247.809i | −0.300305 | + | 0.520143i | −0.976205 | − | 0.216850i | \(-0.930422\pi\) |
0.675900 | + | 0.736993i | \(0.263755\pi\) | |||||||
\(62\) | 228.316 | + | 395.454i | 0.467679 | + | 0.810044i | ||||
\(63\) | 231.779 | − | 133.818i | 0.463515 | − | 0.267611i | ||||
\(64\) | −466.313 | −0.910768 | ||||||||
\(65\) | 275.077 | + | 495.038i | 0.524910 | + | 0.944645i | ||||
\(66\) | 171.938 | 0.320668 | ||||||||
\(67\) | 465.166 | − | 268.564i | 0.848195 | − | 0.489706i | −0.0118462 | − | 0.999930i | \(-0.503771\pi\) |
0.860042 | + | 0.510224i | \(0.170438\pi\) | |||||||
\(68\) | −96.9863 | − | 167.985i | −0.172961 | − | 0.299576i | ||||
\(69\) | −240.888 | + | 417.231i | −0.420283 | + | 0.727951i | ||||
\(70\) | − | 733.777i | − | 1.25290i | ||||||
\(71\) | 88.9656 | + | 51.3643i | 0.148708 | + | 0.0858567i | 0.572508 | − | 0.819899i | \(-0.305971\pi\) |
−0.423800 | + | 0.905756i | \(0.639304\pi\) | |||||||
\(72\) | 188.294 | + | 108.712i | 0.308204 | + | 0.177942i | ||||
\(73\) | − | 75.5209i | − | 0.121083i | −0.998166 | − | 0.0605414i | \(-0.980717\pi\) | ||
0.998166 | − | 0.0605414i | \(-0.0192827\pi\) | |||||||
\(74\) | 233.175 | − | 403.871i | 0.366298 | − | 0.634446i | ||||
\(75\) | 31.4786 | + | 54.5225i | 0.0484644 | + | 0.0839428i | ||||
\(76\) | −348.696 | + | 201.319i | −0.526291 | + | 0.303854i | ||||
\(77\) | −834.535 | −1.23512 | ||||||||
\(78\) | −287.134 | − | 4.71337i | −0.416815 | − | 0.00684211i | ||||
\(79\) | 17.5526 | 0.0249978 | 0.0124989 | − | 0.999922i | \(-0.496021\pi\) | ||||
0.0124989 | + | 0.999922i | \(0.496021\pi\) | |||||||
\(80\) | 195.702 | − | 112.989i | 0.273502 | − | 0.157906i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −302.152 | + | 523.342i | −0.406916 | + | 0.704799i | ||||
\(83\) | − | 1463.08i | − | 1.93487i | −0.253122 | − | 0.967434i | \(-0.581457\pi\) | ||
0.253122 | − | 0.967434i | \(-0.418543\pi\) | |||||||
\(84\) | −295.847 | − | 170.807i | −0.384280 | − | 0.221864i | ||||
\(85\) | 530.045 | + | 306.022i | 0.676371 | + | 0.390503i | ||||
\(86\) | 392.322i | 0.491920i | ||||||||
\(87\) | −210.157 | + | 364.003i | −0.258980 | + | 0.448566i | ||||
\(88\) | −338.983 | − | 587.135i | −0.410633 | − | 0.711236i | ||||
\(89\) | −290.036 | + | 167.453i | −0.345436 | + | 0.199438i | −0.662673 | − | 0.748909i | \(-0.730578\pi\) |
0.317237 | + | 0.948346i | \(0.397245\pi\) | |||||||
\(90\) | −222.078 | −0.260101 | ||||||||
\(91\) | 1393.66 | + | 22.8773i | 1.60545 | + | 0.0263538i | ||||
\(92\) | 614.946 | 0.696876 | ||||||||
\(93\) | −580.912 | + | 335.390i | −0.647718 | + | 0.373960i | ||||
\(94\) | −37.7100 | − | 65.3156i | −0.0413776 | − | 0.0716680i | ||||
\(95\) | 635.225 | − | 1100.24i | 0.686029 | − | 1.18824i | ||||
\(96\) | − | 465.209i | − | 0.494585i | ||||||
\(97\) | −648.442 | − | 374.378i | −0.678756 | − | 0.391880i | 0.120630 | − | 0.992697i | \(-0.461508\pi\) |
−0.799386 | + | 0.600818i | \(0.794842\pi\) | |||||||
\(98\) | −957.374 | − | 552.740i | −0.986830 | − | 0.569747i | ||||
\(99\) | 252.572i | 0.256409i | ||||||||
\(100\) | 40.1797 | − | 69.5933i | 0.0401797 | − | 0.0695933i | ||||
\(101\) | −392.001 | − | 678.966i | −0.386194 | − | 0.668907i | 0.605740 | − | 0.795662i | \(-0.292877\pi\) |
−0.991934 | + | 0.126755i | \(0.959544\pi\) | |||||||
\(102\) | −268.774 | + | 155.176i | −0.260907 | + | 0.150635i | ||||
\(103\) | −396.040 | −0.378864 | −0.189432 | − | 0.981894i | \(-0.560665\pi\) | ||||
−0.189432 | + | 0.981894i | \(0.560665\pi\) | |||||||
\(104\) | 550.002 | + | 989.801i | 0.518578 | + | 0.933250i | ||||
\(105\) | 1077.90 | 1.00183 | ||||||||
\(106\) | −263.707 | + | 152.251i | −0.241636 | + | 0.139509i | ||||
\(107\) | 718.296 | + | 1244.12i | 0.648974 | + | 1.12406i | 0.983368 | + | 0.181623i | \(0.0581351\pi\) |
−0.334394 | + | 0.942433i | \(0.608532\pi\) | |||||||
\(108\) | −51.6948 | + | 89.5380i | −0.0460587 | + | 0.0797759i | ||||
\(109\) | 1977.92i | 1.73807i | 0.494746 | + | 0.869037i | \(0.335261\pi\) | ||||
−0.494746 | + | 0.869037i | \(0.664739\pi\) | |||||||
\(110\) | 599.703 | + | 346.239i | 0.519813 | + | 0.300114i | ||||
\(111\) | 593.276 | + | 342.528i | 0.507308 | + | 0.292895i | ||||
\(112\) | − | 556.175i | − | 0.469228i | ||||||
\(113\) | −61.2026 | + | 106.006i | −0.0509509 | + | 0.0882496i | −0.890376 | − | 0.455226i | \(-0.849559\pi\) |
0.839425 | + | 0.543475i | \(0.182892\pi\) | |||||||
\(114\) | 322.108 | + | 557.907i | 0.264633 | + | 0.458358i | ||||
\(115\) | −1680.39 | + | 970.173i | −1.36258 | + | 0.786688i | ||||
\(116\) | 536.496 | 0.429417 | ||||||||
\(117\) | 6.92382 | − | 421.793i | 0.00547100 | − | 0.333288i | ||||
\(118\) | 896.273 | 0.699225 | ||||||||
\(119\) | 1304.55 | − | 753.180i | 1.00494 | − | 0.580201i | ||||
\(120\) | 437.835 | + | 758.353i | 0.333073 | + | 0.576899i | ||||
\(121\) | −271.718 | + | 470.629i | −0.204146 | + | 0.353591i | ||||
\(122\) | − | 584.379i | − | 0.433665i | ||||||
\(123\) | −768.776 | − | 443.853i | −0.563563 | − | 0.325373i | ||||
\(124\) | 741.484 | + | 428.096i | 0.536994 | + | 0.310034i | ||||
\(125\) | − | 1256.75i | − | 0.899256i | ||||||
\(126\) | −273.289 | + | 473.350i | −0.193226 | + | 0.334677i | ||||
\(127\) | 1154.80 | + | 2000.18i | 0.806868 | + | 1.39754i | 0.915022 | + | 0.403403i | \(0.132173\pi\) |
−0.108154 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(128\) | −249.616 | + | 144.116i | −0.172369 | + | 0.0995170i | ||||
\(129\) | −576.310 | −0.393343 | ||||||||
\(130\) | −992.006 | − | 594.654i | −0.669266 | − | 0.401190i | ||||
\(131\) | −1444.26 | −0.963250 | −0.481625 | − | 0.876377i | \(-0.659953\pi\) | ||||
−0.481625 | + | 0.876377i | \(0.659953\pi\) | |||||||
\(132\) | 279.195 | − | 161.193i | 0.184097 | − | 0.106289i | ||||
\(133\) | −1563.41 | − | 2707.91i | −1.01929 | − | 1.76546i | ||||
\(134\) | −548.472 | + | 949.982i | −0.353588 | + | 0.612433i | ||||
\(135\) | − | 326.226i | − | 0.207978i | ||||||
\(136\) | 1059.80 | + | 611.874i | 0.668212 | + | 0.385792i | ||||
\(137\) | 637.324 | + | 367.959i | 0.397447 | + | 0.229466i | 0.685382 | − | 0.728184i | \(-0.259635\pi\) |
−0.287935 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(138\) | − | 983.904i | − | 0.606924i | ||||||
\(139\) | 752.571 | − | 1303.49i | 0.459225 | − | 0.795400i | −0.539696 | − | 0.841860i | \(-0.681461\pi\) |
0.998920 | + | 0.0464599i | \(0.0147940\pi\) | |||||||
\(140\) | −687.923 | − | 1191.52i | −0.415286 | − | 0.719297i | ||||
\(141\) | 95.9469 | − | 55.3950i | 0.0573063 | − | 0.0330858i | ||||
\(142\) | −209.797 | −0.123984 | ||||||||
\(143\) | −676.309 | + | 1128.22i | −0.395495 | + | 0.659767i | ||||
\(144\) | −168.326 | −0.0974111 | ||||||||
\(145\) | −1466.02 | + | 846.406i | −0.839629 | + | 0.484760i | ||||
\(146\) | 77.1160 | + | 133.569i | 0.0437134 | + | 0.0757139i | ||||
\(147\) | 811.960 | − | 1406.36i | 0.455574 | − | 0.789077i | ||||
\(148\) | − | 874.415i | − | 0.485652i | ||||||
\(149\) | 370.523 | + | 213.921i | 0.203721 | + | 0.117618i | 0.598390 | − | 0.801205i | \(-0.295807\pi\) |
−0.394669 | + | 0.918823i | \(0.629141\pi\) | |||||||
\(150\) | −111.348 | − | 64.2868i | −0.0606102 | − | 0.0349933i | ||||
\(151\) | − | 1601.83i | − | 0.863278i | −0.902046 | − | 0.431639i | \(-0.857935\pi\) | ||
0.902046 | − | 0.431639i | \(-0.142065\pi\) | |||||||
\(152\) | 1270.10 | − | 2199.87i | 0.677753 | − | 1.17390i | ||||
\(153\) | −227.950 | − | 394.821i | −0.120449 | − | 0.208624i | ||||
\(154\) | 1475.99 | − | 852.161i | 0.772327 | − | 0.445903i | ||||
\(155\) | −2701.55 | −1.39996 | ||||||||
\(156\) | −470.672 | + | 261.538i | −0.241563 | + | 0.134229i | ||||
\(157\) | −730.346 | −0.371261 | −0.185631 | − | 0.982620i | \(-0.559433\pi\) | ||||
−0.185631 | + | 0.982620i | \(0.559433\pi\) | |||||||
\(158\) | −31.0442 | + | 17.9234i | −0.0156313 | + | 0.00902473i | ||||
\(159\) | −223.653 | − | 387.378i | −0.111552 | − | 0.193214i | ||||
\(160\) | 936.811 | − | 1622.60i | 0.462884 | − | 0.801738i | ||||
\(161\) | 4775.58i | 2.33769i | ||||||||
\(162\) | 143.259 | + | 82.7108i | 0.0694785 | + | 0.0401134i | ||||
\(163\) | −1644.03 | − | 949.180i | −0.790001 | − | 0.456107i | 0.0499619 | − | 0.998751i | \(-0.484090\pi\) |
−0.839963 | + | 0.542644i | \(0.817423\pi\) | |||||||
\(164\) | 1133.08i | 0.539505i | ||||||||
\(165\) | −508.615 | + | 880.948i | −0.239974 | + | 0.415647i | ||||
\(166\) | 1493.98 | + | 2587.66i | 0.698528 | + | 1.20989i | ||||
\(167\) | 1236.25 | − | 713.751i | 0.572839 | − | 0.330729i | −0.185444 | − | 0.982655i | \(-0.559372\pi\) |
0.758282 | + | 0.651926i | \(0.226039\pi\) | |||||||
\(168\) | 2155.20 | 0.989745 | ||||||||
\(169\) | 1160.36 | − | 1865.58i | 0.528155 | − | 0.849148i | ||||
\(170\) | −1249.94 | −0.563919 | ||||||||
\(171\) | −819.551 | + | 473.168i | −0.366507 | + | 0.211603i | ||||
\(172\) | 367.806 | + | 637.058i | 0.163052 | + | 0.282414i | ||||
\(173\) | −1022.20 | + | 1770.50i | −0.449227 | + | 0.778084i | −0.998336 | − | 0.0576667i | \(-0.981634\pi\) |
0.549109 | + | 0.835751i | \(0.314967\pi\) | |||||||
\(174\) | − | 858.385i | − | 0.373988i | ||||||
\(175\) | 540.450 | + | 312.029i | 0.233453 | + | 0.134784i | ||||
\(176\) | 454.552 | + | 262.436i | 0.194677 | + | 0.112397i | ||||
\(177\) | 1316.60i | 0.559106i | ||||||||
\(178\) | 341.979 | − | 592.325i | 0.144002 | − | 0.249419i | ||||
\(179\) | −1944.86 | − | 3368.59i | −0.812098 | − | 1.40660i | −0.911393 | − | 0.411537i | \(-0.864992\pi\) |
0.0992948 | − | 0.995058i | \(-0.468341\pi\) | |||||||
\(180\) | −360.613 | + | 208.200i | −0.149325 | + | 0.0862129i | ||||
\(181\) | 2477.02 | 1.01721 | 0.508606 | − | 0.861000i | \(-0.330161\pi\) | ||||
0.508606 | + | 0.861000i | \(0.330161\pi\) | |||||||
\(182\) | −2488.24 | + | 1382.64i | −1.01341 | + | 0.563121i | ||||
\(183\) | 858.437 | 0.346762 | ||||||||
\(184\) | −3359.84 | + | 1939.81i | −1.34615 | + | 0.777198i | ||||
\(185\) | 1379.53 | + | 2389.41i | 0.548242 | + | 0.949583i | ||||
\(186\) | 684.947 | − | 1186.36i | 0.270015 | − | 0.467679i | ||||
\(187\) | 1421.58i | 0.555914i | ||||||||
\(188\) | −122.468 | − | 70.7070i | −0.0475101 | − | 0.0274300i | ||||
\(189\) | −695.338 | − | 401.454i | −0.267611 | − | 0.154505i | ||||
\(190\) | 2594.57i | 0.990683i | ||||||||
\(191\) | −1138.40 | + | 1971.78i | −0.431267 | + | 0.746977i | −0.996983 | − | 0.0776235i | \(-0.975267\pi\) |
0.565715 | + | 0.824601i | \(0.308600\pi\) | |||||||
\(192\) | 699.470 | + | 1211.52i | 0.262916 | + | 0.455384i | ||||
\(193\) | 3396.92 | − | 1961.21i | 1.26692 | − | 0.731456i | 0.292515 | − | 0.956261i | \(-0.405508\pi\) |
0.974404 | + | 0.224805i | \(0.0721744\pi\) | |||||||
\(194\) | 1529.14 | 0.565907 | ||||||||
\(195\) | 873.531 | − | 1457.23i | 0.320794 | − | 0.535151i | ||||
\(196\) | −2072.80 | −0.755392 | ||||||||
\(197\) | 4384.88 | − | 2531.61i | 1.58584 | − | 0.915584i | 0.591855 | − | 0.806045i | \(-0.298396\pi\) |
0.993982 | − | 0.109539i | \(-0.0349375\pi\) | |||||||
\(198\) | −257.907 | − | 446.708i | −0.0925689 | − | 0.160334i | ||||
\(199\) | 1635.03 | − | 2831.95i | 0.582433 | − | 1.00880i | −0.412757 | − | 0.910841i | \(-0.635434\pi\) |
0.995190 | − | 0.0979624i | \(-0.0312325\pi\) | |||||||
\(200\) | 506.977i | 0.179243i | ||||||||
\(201\) | −1395.50 | − | 805.691i | −0.489706 | − | 0.282732i | ||||
\(202\) | 1386.61 | + | 800.561i | 0.482979 | + | 0.278848i | ||||
\(203\) | 4166.34i | 1.44049i | ||||||||
\(204\) | −290.959 | + | 503.956i | −0.0998588 | + | 0.172961i | ||||
\(205\) | −1787.61 | − | 3096.23i | −0.609035 | − | 1.05488i | ||||
\(206\) | 700.450 | − | 404.405i | 0.236906 | − | 0.136778i | ||||
\(207\) | 1445.33 | 0.485301 | ||||||||
\(208\) | −751.902 | − | 450.725i | −0.250649 | − | 0.150251i | ||||
\(209\) | 2950.84 | 0.976622 | ||||||||
\(210\) | −1906.41 | + | 1100.67i | −0.626451 | + | 0.361682i | ||||
\(211\) | 1406.09 | + | 2435.42i | 0.458764 | + | 0.794602i | 0.998896 | − | 0.0469781i | \(-0.0149591\pi\) |
−0.540132 | + | 0.841580i | \(0.681626\pi\) | |||||||
\(212\) | −285.474 | + | 494.455i | −0.0924831 | + | 0.160185i | ||||
\(213\) | − | 308.186i | − | 0.0991388i | ||||||
\(214\) | −2540.80 | − | 1466.93i | −0.811616 | − | 0.468587i | ||||
\(215\) | −2010.12 | − | 1160.54i | −0.637622 | − | 0.368131i | ||||
\(216\) | − | 652.271i | − | 0.205470i | ||||||
\(217\) | −3324.53 | + | 5758.25i | −1.04002 | + | 1.80136i | ||||
\(218\) | −2019.69 | − | 3498.21i | −0.627481 | − | 1.08683i | ||||
\(219\) | −196.209 | + | 113.281i | −0.0605414 | + | 0.0349536i | ||||
\(220\) | 1298.41 | 0.397903 | ||||||||
\(221\) | 38.9700 | − | 2374.02i | 0.0118616 | − | 0.722596i | ||||
\(222\) | −1399.05 | −0.422964 | ||||||||
\(223\) | 794.783 | − | 458.868i | 0.238666 | − | 0.137794i | −0.375897 | − | 0.926661i | \(-0.622665\pi\) |
0.614564 | + | 0.788867i | \(0.289332\pi\) | |||||||
\(224\) | −2305.68 | − | 3993.55i | −0.687743 | − | 1.19121i | ||||
\(225\) | 94.4357 | − | 163.567i | 0.0279809 | − | 0.0484644i | ||||
\(226\) | − | 249.981i | − | 0.0735774i | ||||||
\(227\) | −1157.35 | − | 668.194i | −0.338396 | − | 0.195373i | 0.321167 | − | 0.947023i | \(-0.395925\pi\) |
−0.659562 | + | 0.751650i | \(0.729258\pi\) | |||||||
\(228\) | 1046.09 | + | 603.958i | 0.303854 | + | 0.175430i | ||||
\(229\) | 164.820i | 0.0475617i | 0.999717 | + | 0.0237808i | \(0.00757039\pi\) | ||||
−0.999717 | + | 0.0237808i | \(0.992430\pi\) | |||||||
\(230\) | 1981.33 | − | 3431.76i | 0.568022 | − | 0.983843i | ||||
\(231\) | 1251.80 | + | 2168.19i | 0.356548 | + | 0.617559i | ||||
\(232\) | −2931.22 | + | 1692.34i | −0.829500 | + | 0.478912i | ||||
\(233\) | 4243.42 | 1.19312 | 0.596558 | − | 0.802570i | \(-0.296535\pi\) | ||||
0.596558 | + | 0.802570i | \(0.296535\pi\) | |||||||
\(234\) | 418.456 | + | 753.067i | 0.116903 | + | 0.210383i | ||||
\(235\) | 446.205 | 0.123860 | ||||||||
\(236\) | 1455.38 | − | 840.264i | 0.401429 | − | 0.231765i | ||||
\(237\) | −26.3289 | − | 45.6031i | −0.00721624 | − | 0.0124989i | ||||
\(238\) | −1538.18 | + | 2664.20i | −0.418929 | + | 0.725607i | ||||
\(239\) | 2491.07i | 0.674200i | 0.941469 | + | 0.337100i | \(0.109446\pi\) | ||||
−0.941469 | + | 0.337100i | \(0.890554\pi\) | |||||||
\(240\) | −587.106 | − | 338.966i | −0.157906 | − | 0.0911673i | ||||
\(241\) | −2526.54 | − | 1458.70i | −0.675306 | − | 0.389888i | 0.122778 | − | 0.992434i | \(-0.460820\pi\) |
−0.798084 | + | 0.602546i | \(0.794153\pi\) | |||||||
\(242\) | − | 1109.83i | − | 0.294803i | ||||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −547.861 | − | 948.922i | −0.143743 | − | 0.248969i | ||||
\(245\) | 5664.08 | − | 3270.16i | 1.47700 | − | 0.852746i | ||||
\(246\) | 1812.91 | 0.469866 | ||||||||
\(247\) | −4927.87 | − | 80.8921i | −1.26944 | − | 0.0208382i | ||||
\(248\) | −5401.60 | −1.38307 | ||||||||
\(249\) | −3801.20 | + | 2194.62i | −0.967434 | + | 0.558549i | ||||
\(250\) | 1283.29 | + | 2222.73i | 0.324650 | + | 0.562310i | ||||
\(251\) | −656.939 | + | 1137.85i | −0.165202 | + | 0.286138i | −0.936727 | − | 0.350061i | \(-0.886161\pi\) |
0.771525 | + | 0.636199i | \(0.219494\pi\) | |||||||
\(252\) | 1024.84i | 0.256187i | ||||||||
\(253\) | −3902.99 | − | 2253.39i | −0.969878 | − | 0.559959i | ||||
\(254\) | −4084.85 | − | 2358.39i | −1.00908 | − | 0.582593i | ||||
\(255\) | − | 1836.13i | − | 0.450914i | ||||||
\(256\) | 2159.57 | − | 3740.49i | 0.527239 | − | 0.913205i | ||||
\(257\) | −493.791 | − | 855.271i | −0.119851 | − | 0.207589i | 0.799857 | − | 0.600190i | \(-0.204909\pi\) |
−0.919709 | + | 0.392601i | \(0.871575\pi\) | |||||||
\(258\) | 1019.28 | − | 588.483i | 0.245960 | − | 0.142005i | ||||
\(259\) | 6790.57 | 1.62913 | ||||||||
\(260\) | −2168.33 | − | 35.5936i | −0.517207 | − | 0.00849007i | ||||
\(261\) | 1260.94 | 0.299044 | ||||||||
\(262\) | 2554.37 | − | 1474.77i | 0.602326 | − | 0.347753i | ||||
\(263\) | 3493.23 | + | 6050.44i | 0.819017 | + | 1.41858i | 0.906407 | + | 0.422405i | \(0.138814\pi\) |
−0.0873899 | + | 0.996174i | \(0.527853\pi\) | |||||||
\(264\) | −1016.95 | + | 1761.41i | −0.237079 | + | 0.410633i | ||||
\(265\) | − | 1801.52i | − | 0.417609i | ||||||
\(266\) | 5530.22 | + | 3192.87i | 1.27473 | + | 0.735968i | ||||
\(267\) | 870.109 | + | 502.358i | 0.199438 | + | 0.115145i | ||||
\(268\) | 2056.79i | 0.468801i | ||||||||
\(269\) | 2952.17 | − | 5113.31i | 0.669134 | − | 1.15897i | −0.309013 | − | 0.951058i | \(-0.599999\pi\) |
0.978147 | − | 0.207916i | \(-0.0666681\pi\) | |||||||
\(270\) | 333.117 | + | 576.975i | 0.0750846 | + | 0.130050i | ||||
\(271\) | −1845.97 | + | 1065.77i | −0.413781 | + | 0.238897i | −0.692413 | − | 0.721501i | \(-0.743452\pi\) |
0.278632 | + | 0.960398i | \(0.410119\pi\) | |||||||
\(272\) | −947.408 | −0.211195 | ||||||||
\(273\) | −2031.06 | − | 3655.16i | −0.450276 | − | 0.810331i | ||||
\(274\) | −1502.92 | −0.331368 | ||||||||
\(275\) | −510.032 | + | 294.467i | −0.111840 | + | 0.0645710i | ||||
\(276\) | −922.420 | − | 1597.68i | −0.201171 | − | 0.348438i | ||||
\(277\) | 2016.21 | − | 3492.17i | 0.437336 | − | 0.757489i | −0.560147 | − | 0.828393i | \(-0.689255\pi\) |
0.997483 | + | 0.0709046i | \(0.0225886\pi\) | |||||||
\(278\) | 3073.86i | 0.663159i | ||||||||
\(279\) | 1742.74 | + | 1006.17i | 0.373960 | + | 0.215906i | ||||
\(280\) | 7517.12 | + | 4340.01i | 1.60441 | + | 0.926305i | ||||
\(281\) | − | 2298.29i | − | 0.487916i | −0.969786 | − | 0.243958i | \(-0.921554\pi\) | ||
0.969786 | − | 0.243958i | \(-0.0784459\pi\) | |||||||
\(282\) | −113.130 | + | 195.947i | −0.0238893 | + | 0.0413776i | ||||
\(283\) | 3328.40 | + | 5764.96i | 0.699127 | + | 1.21092i | 0.968770 | + | 0.247963i | \(0.0797611\pi\) |
−0.269643 | + | 0.962960i | \(0.586906\pi\) | |||||||
\(284\) | −340.671 | + | 196.687i | −0.0711800 | + | 0.0410958i | ||||
\(285\) | −3811.35 | −0.792158 | ||||||||
\(286\) | 44.0914 | − | 2686.01i | 0.00911601 | − | 0.555339i | ||||
\(287\) | −8799.33 | −1.80978 | ||||||||
\(288\) | −1208.65 | + | 697.813i | −0.247293 | + | 0.142774i | ||||
\(289\) | 1173.51 | + | 2032.57i | 0.238857 | + | 0.413713i | ||||
\(290\) | 1728.57 | − | 2993.96i | 0.350017 | − | 0.606247i | ||||
\(291\) | 2246.27i | 0.452504i | ||||||||
\(292\) | 250.444 | + | 144.594i | 0.0501922 | + | 0.0289785i | ||||
\(293\) | −6466.60 | − | 3733.49i | −1.28936 | − | 0.744413i | −0.310821 | − | 0.950468i | \(-0.600604\pi\) |
−0.978540 | + | 0.206055i | \(0.933937\pi\) | |||||||
\(294\) | 3316.44i | 0.657887i | ||||||||
\(295\) | −2651.29 | + | 4592.18i | −0.523269 | + | 0.906328i | ||||
\(296\) | 2758.28 | + | 4777.49i | 0.541628 | + | 0.938128i | ||||
\(297\) | 656.202 | − | 378.858i | 0.128204 | − | 0.0740188i | ||||
\(298\) | −873.759 | −0.169851 | ||||||||
\(299\) | 6456.18 | + | 3870.14i | 1.24873 | + | 0.748548i | ||||
\(300\) | −241.078 | −0.0463955 | ||||||||
\(301\) | −4947.29 | + | 2856.32i | −0.947365 | + | 0.546962i | ||||
\(302\) | 1635.66 | + | 2833.05i | 0.311662 | + | 0.539814i | ||||
\(303\) | −1176.00 | + | 2036.90i | −0.222969 | + | 0.386194i | ||||
\(304\) | 1966.58i | 0.371024i | ||||||||
\(305\) | 2994.14 | + | 1728.67i | 0.562112 | + | 0.324536i | ||||
\(306\) | 806.321 | + | 465.529i | 0.150635 | + | 0.0869691i | ||||
\(307\) | − | 3965.99i | − | 0.737299i | −0.929568 | − | 0.368650i | \(-0.879820\pi\) | ||
0.929568 | − | 0.368650i | \(-0.120180\pi\) | |||||||
\(308\) | 1597.82 | − | 2767.50i | 0.295598 | − | 0.511991i | ||||
\(309\) | 594.060 | + | 1028.94i | 0.109369 | + | 0.189432i | ||||
\(310\) | 4778.06 | − | 2758.61i | 0.875405 | − | 0.505415i | ||||
\(311\) | −7372.29 | −1.34419 | −0.672097 | − | 0.740463i | \(-0.734606\pi\) | ||||
−0.672097 | + | 0.740463i | \(0.734606\pi\) | |||||||
\(312\) | 1746.58 | − | 2913.65i | 0.316925 | − | 0.528695i | ||||
\(313\) | 8249.55 | 1.48975 | 0.744875 | − | 0.667204i | \(-0.232509\pi\) | ||||
0.744875 | + | 0.667204i | \(0.232509\pi\) | |||||||
\(314\) | 1291.72 | − | 745.772i | 0.232152 | − | 0.134033i | ||||
\(315\) | −1616.85 | − | 2800.46i | −0.289203 | − | 0.500915i | ||||
\(316\) | −33.6067 | + | 58.2084i | −0.00598267 | + | 0.0103623i | ||||
\(317\) | 5575.26i | 0.987817i | 0.869514 | + | 0.493909i | \(0.164432\pi\) | ||||
−0.869514 | + | 0.493909i | \(0.835568\pi\) | |||||||
\(318\) | 791.120 | + | 456.753i | 0.139509 | + | 0.0805455i | ||||
\(319\) | −3405.08 | − | 1965.92i | −0.597642 | − | 0.345049i | ||||
\(320\) | 5634.21i | 0.984256i | ||||||||
\(321\) | 2154.89 | − | 3732.37i | 0.374686 | − | 0.648974i | ||||
\(322\) | −4876.44 | − | 8446.25i | −0.843955 | − | 1.46177i | ||||
\(323\) | −4612.76 | + | 2663.18i | −0.794615 | + | 0.458771i | ||||
\(324\) | 310.169 | 0.0531840 | ||||||||
\(325\) | 859.819 | − | 477.775i | 0.146751 | − | 0.0815452i | ||||
\(326\) | 3876.91 | 0.658657 | ||||||||
\(327\) | 5138.78 | − | 2966.88i | 0.869037 | − | 0.501739i | ||||
\(328\) | −3574.23 | − | 6190.74i | −0.601688 | − | 1.04215i | ||||
\(329\) | 549.099 | − | 951.068i | 0.0920146 | − | 0.159374i | ||||
\(330\) | − | 2077.43i | − | 0.346542i | ||||||
\(331\) | −3600.38 | − | 2078.68i | −0.597870 | − | 0.345180i | 0.170333 | − | 0.985387i | \(-0.445516\pi\) |
−0.768203 | + | 0.640206i | \(0.778849\pi\) | |||||||
\(332\) | 4851.91 | + | 2801.25i | 0.802057 | + | 0.463068i | ||||
\(333\) | − | 2055.17i | − | 0.338206i | ||||||
\(334\) | −1457.65 | + | 2524.73i | −0.238800 | + | 0.413614i | ||||
\(335\) | −3244.91 | − | 5620.35i | −0.529219 | − | 0.916634i | ||||
\(336\) | −1444.98 | + | 834.262i | −0.234614 | + | 0.135454i | ||||
\(337\) | −3225.18 | −0.521326 | −0.260663 | − | 0.965430i | \(-0.583941\pi\) | ||||
−0.260663 | + | 0.965430i | \(0.583941\pi\) | |||||||
\(338\) | −147.264 | + | 4484.39i | −0.0236986 | + | 0.721653i | ||||
\(339\) | 367.215 | 0.0588330 | ||||||||
\(340\) | −2029.67 | + | 1171.83i | −0.323749 | + | 0.186916i | ||||
\(341\) | −3137.41 | − | 5434.15i | −0.498241 | − | 0.862979i | ||||
\(342\) | 966.324 | − | 1673.72i | 0.152786 | − | 0.264633i | ||||
\(343\) | − | 5897.11i | − | 0.928321i | ||||||
\(344\) | −4019.11 | − | 2320.44i | −0.629930 | − | 0.363690i | ||||
\(345\) | 5041.17 | + | 2910.52i | 0.786688 | + | 0.454195i | ||||
\(346\) | − | 4175.15i | − | 0.648721i | ||||||
\(347\) | −1645.25 | + | 2849.65i | −0.254529 | + | 0.440856i | −0.964767 | − | 0.263104i | \(-0.915254\pi\) |
0.710239 | + | 0.703961i | \(0.248587\pi\) | |||||||
\(348\) | −804.744 | − | 1393.86i | −0.123962 | − | 0.214709i | ||||
\(349\) | −3889.77 | + | 2245.76i | −0.596604 | + | 0.344449i | −0.767704 | − | 0.640804i | \(-0.778601\pi\) |
0.171101 | + | 0.985254i | \(0.445268\pi\) | |||||||
\(350\) | −1274.48 | −0.194639 | ||||||||
\(351\) | −1106.24 | + | 614.700i | −0.168224 | + | 0.0934766i | ||||
\(352\) | 4351.81 | 0.658955 | ||||||||
\(353\) | −5107.71 | + | 2948.94i | −0.770130 | + | 0.444635i | −0.832921 | − | 0.553392i | \(-0.813333\pi\) |
0.0627907 | + | 0.998027i | \(0.480000\pi\) | |||||||
\(354\) | −1344.41 | − | 2328.58i | −0.201849 | − | 0.349613i | ||||
\(355\) | 620.607 | − | 1074.92i | 0.0927843 | − | 0.160707i | ||||
\(356\) | − | 1282.43i | − | 0.190924i | ||||||
\(357\) | −3913.64 | − | 2259.54i | −0.580201 | − | 0.334979i | ||||
\(358\) | 6879.49 | + | 3971.87i | 1.01562 | + | 0.586369i | ||||
\(359\) | − | 9277.20i | − | 1.36388i | −0.731410 | − | 0.681938i | \(-0.761137\pi\) | ||
0.731410 | − | 0.681938i | \(-0.238863\pi\) | |||||||
\(360\) | 1313.51 | − | 2275.06i | 0.192300 | − | 0.333073i | ||||
\(361\) | 2098.59 | + | 3634.87i | 0.305962 | + | 0.529942i | ||||
\(362\) | −4380.94 | + | 2529.33i | −0.636069 | + | 0.367234i | ||||
\(363\) | 1630.31 | 0.235727 | ||||||||
\(364\) | −2744.21 | + | 4577.90i | −0.395152 | + | 0.659195i | ||||
\(365\) | −912.477 | −0.130853 | ||||||||
\(366\) | −1518.26 | + | 876.568i | −0.216833 | + | 0.125188i | ||||
\(367\) | 3287.18 | + | 5693.56i | 0.467546 | + | 0.809814i | 0.999312 | − | 0.0370774i | \(-0.0118048\pi\) |
−0.531766 | + | 0.846891i | \(0.678471\pi\) | |||||||
\(368\) | 1501.77 | − | 2601.14i | 0.212732 | − | 0.368462i | ||||
\(369\) | 2663.12i | 0.375708i | ||||||||
\(370\) | −4879.75 | − | 2817.33i | −0.685638 | − | 0.395853i | ||||
\(371\) | −3839.86 | − | 2216.94i | −0.537347 | − | 0.310237i | ||||
\(372\) | − | 2568.58i | − | 0.357996i | ||||||
\(373\) | 2672.77 | − | 4629.38i | 0.371021 | − | 0.642628i | −0.618702 | − | 0.785626i | \(-0.712341\pi\) |
0.989723 | + | 0.142998i | \(0.0456743\pi\) | |||||||
\(374\) | −1451.60 | − | 2514.25i | −0.200697 | − | 0.347617i | ||||
\(375\) | −3265.13 | + | 1885.12i | −0.449628 | + | 0.259593i | ||||
\(376\) | 892.162 | 0.122366 | ||||||||
\(377\) | 5632.55 | + | 3376.41i | 0.769472 | + | 0.461258i | ||||
\(378\) | 1639.73 | 0.223118 | ||||||||
\(379\) | 899.378 | − | 519.256i | 0.121894 | − | 0.0703757i | −0.437813 | − | 0.899066i | \(-0.644247\pi\) |
0.559707 | + | 0.828690i | \(0.310914\pi\) | |||||||
\(380\) | 2432.43 | + | 4213.10i | 0.328372 | + | 0.568756i | ||||
\(381\) | 3464.41 | − | 6000.54i | 0.465846 | − | 0.806868i | ||||
\(382\) | − | 4649.80i | − | 0.622786i | ||||||
\(383\) | 5844.97 | + | 3374.59i | 0.779801 | + | 0.450219i | 0.836360 | − | 0.548181i | \(-0.184679\pi\) |
−0.0565585 | + | 0.998399i | \(0.518013\pi\) | |||||||
\(384\) | 748.849 | + | 432.348i | 0.0995170 | + | 0.0574562i | ||||
\(385\) | 10083.2i | 1.33478i | ||||||||
\(386\) | −4005.27 | + | 6937.33i | −0.528142 | + | 0.914769i | ||||
\(387\) | 864.465 | + | 1497.30i | 0.113548 | + | 0.196672i | ||||
\(388\) | 2483.04 | − | 1433.59i | 0.324890 | − | 0.187575i | ||||
\(389\) | 1246.11 | 0.162417 | 0.0812083 | − | 0.996697i | \(-0.474122\pi\) | ||||
0.0812083 | + | 0.996697i | \(0.474122\pi\) | |||||||
\(390\) | −56.9491 | + | 3469.29i | −0.00739418 | + | 0.450447i | ||||
\(391\) | 8134.89 | 1.05217 | ||||||||
\(392\) | 11325.0 | − | 6538.50i | 1.45918 | − | 0.842459i | ||||
\(393\) | 2166.39 | + | 3752.30i | 0.278066 | + | 0.481625i | ||||
\(394\) | −5170.17 | + | 8954.99i | −0.661090 | + | 1.14504i | ||||
\(395\) | − | 212.079i | − | 0.0270148i | ||||||
\(396\) | −837.586 | − | 483.580i | −0.106289 | − | 0.0613657i | ||||
\(397\) | −7236.24 | − | 4177.85i | −0.914802 | − | 0.528161i | −0.0328293 | − | 0.999461i | \(-0.510452\pi\) |
−0.881973 | + | 0.471300i | \(0.843785\pi\) | |||||||
\(398\) | 6678.25i | 0.841082i | ||||||||
\(399\) | −4690.24 | + | 8123.74i | −0.588486 | + | 1.01929i | ||||
\(400\) | −196.247 | − | 339.910i | −0.0245309 | − | 0.0424887i | ||||
\(401\) | 2843.73 | − | 1641.83i | 0.354137 | − | 0.204461i | −0.312369 | − | 0.949961i | \(-0.601122\pi\) |
0.666506 | + | 0.745500i | \(0.267789\pi\) | |||||||
\(402\) | 3290.83 | 0.408288 | ||||||||
\(403\) | 5090.47 | + | 9160.98i | 0.629217 | + | 1.13236i | ||||
\(404\) | 3002.14 | 0.369708 | ||||||||
\(405\) | −847.561 | + | 489.339i | −0.103989 | + | 0.0600382i | ||||
\(406\) | −4254.34 | − | 7368.74i | −0.520048 | − | 0.900749i | ||||
\(407\) | −3204.18 | + | 5549.81i | −0.390235 | + | 0.675906i | ||||
\(408\) | − | 3671.24i | − | 0.445474i | ||||||
\(409\) | 9464.72 | + | 5464.46i | 1.14426 | + | 0.660636i | 0.947481 | − | 0.319813i | \(-0.103620\pi\) |
0.196775 | + | 0.980449i | \(0.436953\pi\) | |||||||
\(410\) | 6323.26 | + | 3650.74i | 0.761667 | + | 0.439749i | ||||
\(411\) | − | 2207.75i | − | 0.264965i | ||||||
\(412\) | 758.267 | − | 1313.36i | 0.0906726 | − | 0.157050i | ||||
\(413\) | 6525.36 | + | 11302.3i | 0.777462 | + | 1.34660i | ||||
\(414\) | −2556.26 | + | 1475.86i | −0.303462 | + | 0.175204i | ||||
\(415\) | −17677.6 | −2.09099 | ||||||||
\(416\) | −7267.47 | − | 119.297i | −0.856531 | − | 0.0140601i | ||||
\(417\) | −4515.43 | −0.530267 | ||||||||
\(418\) | −5218.96 | + | 3013.17i | −0.610688 | + | 0.352581i | ||||
\(419\) | −3651.47 | − | 6324.53i | −0.425742 | − | 0.737407i | 0.570747 | − | 0.821126i | \(-0.306654\pi\) |
−0.996489 | + | 0.0837185i | \(0.973320\pi\) | |||||||
\(420\) | −2063.77 | + | 3574.55i | −0.239766 | + | 0.415286i | ||||
\(421\) | − | 7580.99i | − | 0.877612i | −0.898582 | − | 0.438806i | \(-0.855401\pi\) | ||
0.898582 | − | 0.438806i | \(-0.144599\pi\) | |||||||
\(422\) | −4973.71 | − | 2871.57i | −0.573736 | − | 0.331247i | ||||
\(423\) | −287.841 | − | 166.185i | −0.0330858 | − | 0.0191021i | ||||
\(424\) | − | 3602.03i | − | 0.412571i | ||||||
\(425\) | 531.521 | − | 920.622i | 0.0606649 | − | 0.105075i | ||||
\(426\) | 314.695 | + | 545.068i | 0.0357912 | + | 0.0619921i | ||||
\(427\) | 7369.18 | − | 4254.60i | 0.835175 | − | 0.482188i | ||||
\(428\) | −5501.06 | −0.621270 | ||||||||
\(429\) | 3945.67 | + | 64.7690i | 0.444053 | + | 0.00728923i | ||||
\(430\) | 4740.21 | 0.531612 | ||||||||
\(431\) | 8709.40 | − | 5028.37i | 0.973357 | − | 0.561968i | 0.0730993 | − | 0.997325i | \(-0.476711\pi\) |
0.900258 | + | 0.435357i | \(0.143378\pi\) | |||||||
\(432\) | 252.490 | + | 437.325i | 0.0281202 | + | 0.0487055i | ||||
\(433\) | 1366.69 | − | 2367.18i | 0.151683 | − | 0.262723i | −0.780163 | − | 0.625576i | \(-0.784864\pi\) |
0.931846 | + | 0.362853i | \(0.118197\pi\) | |||||||
\(434\) | − | 13579.0i | − | 1.50187i | ||||||
\(435\) | 4398.05 | + | 2539.22i | 0.484760 | + | 0.279876i | ||||
\(436\) | −6559.22 | − | 3786.97i | −0.720481 | − | 0.415970i | ||||
\(437\) | − | 16886.0i | − | 1.84844i | ||||||
\(438\) | 231.348 | − | 400.706i | 0.0252380 | − | 0.0437134i | ||||
\(439\) | 3372.12 | + | 5840.68i | 0.366611 | + | 0.634989i | 0.989033 | − | 0.147692i | \(-0.0471846\pi\) |
−0.622422 | + | 0.782682i | \(0.713851\pi\) | |||||||
\(440\) | −7094.03 | + | 4095.74i | −0.768624 | + | 0.443765i | ||||
\(441\) | −4871.76 | −0.526051 | ||||||||
\(442\) | 2355.24 | + | 4238.56i | 0.253455 | + | 0.456126i | ||||
\(443\) | 8655.69 | 0.928317 | 0.464158 | − | 0.885752i | \(-0.346357\pi\) | ||||
0.464158 | + | 0.885752i | \(0.346357\pi\) | |||||||
\(444\) | −2271.80 | + | 1311.62i | −0.242826 | + | 0.140196i | ||||
\(445\) | 2023.24 | + | 3504.35i | 0.215530 | + | 0.373308i | ||||
\(446\) | −937.120 | + | 1623.14i | −0.0994931 | + | 0.172327i | ||||
\(447\) | − | 1283.53i | − | 0.135814i | ||||||
\(448\) | 12009.1 | + | 6933.45i | 1.26646 | + | 0.731193i | ||||
\(449\) | 5648.62 | + | 3261.23i | 0.593708 | + | 0.342777i | 0.766562 | − | 0.642170i | \(-0.221966\pi\) |
−0.172854 | + | 0.984947i | \(0.555299\pi\) | |||||||
\(450\) | 385.721i | 0.0404068i | ||||||||
\(451\) | 4152.03 | − | 7191.53i | 0.433507 | − | 0.750856i | ||||
\(452\) | −234.360 | − | 405.923i | −0.0243879 | − | 0.0422411i | ||||
\(453\) | −4161.67 | + | 2402.74i | −0.431639 | + | 0.249207i | ||||
\(454\) | 2729.23 | 0.282135 | ||||||||
\(455\) | 276.414 | − | 16838.9i | 0.0284802 | − | 1.73499i | ||||
\(456\) | −7620.59 | −0.782602 | ||||||||
\(457\) | −1343.40 | + | 775.613i | −0.137509 | + | 0.0793909i | −0.567176 | − | 0.823596i | \(-0.691964\pi\) |
0.429667 | + | 0.902987i | \(0.358631\pi\) | |||||||
\(458\) | −168.301 | − | 291.507i | −0.0171708 | − | 0.0297406i | ||||
\(459\) | −683.850 | + | 1184.46i | −0.0695412 | + | 0.120449i | ||||
\(460\) | − | 7430.06i | − | 0.753105i | ||||||
\(461\) | −6725.77 | − | 3883.12i | −0.679501 | − | 0.392310i | 0.120166 | − | 0.992754i | \(-0.461657\pi\) |
−0.799667 | + | 0.600444i | \(0.794991\pi\) | |||||||
\(462\) | −4427.96 | − | 2556.48i | −0.445903 | − | 0.257442i | ||||
\(463\) | 2004.52i | 0.201205i | 0.994927 | + | 0.100603i | \(0.0320771\pi\) | ||||
−0.994927 | + | 0.100603i | \(0.967923\pi\) | |||||||
\(464\) | 1310.19 | − | 2269.31i | 0.131086 | − | 0.227048i | ||||
\(465\) | 4052.33 | + | 7018.84i | 0.404134 | + | 0.699980i | ||||
\(466\) | −7505.06 | + | 4333.05i | −0.746063 | + | 0.430739i | ||||
\(467\) | −18674.3 | −1.85042 | −0.925209 | − | 0.379458i | \(-0.876111\pi\) | ||||
−0.925209 | + | 0.379458i | \(0.876111\pi\) | |||||||
\(468\) | 1385.50 | + | 830.535i | 0.136848 | + | 0.0820331i | ||||
\(469\) | −15972.7 | −1.57261 | ||||||||
\(470\) | −789.173 | + | 455.629i | −0.0774507 | + | 0.0447162i | ||||
\(471\) | 1095.52 | + | 1897.50i | 0.107174 | + | 0.185631i | ||||
\(472\) | −5301.11 | + | 9181.80i | −0.516957 | + | 0.895395i | ||||
\(473\) | − | 5391.11i | − | 0.524067i | ||||||
\(474\) | 93.1326 | + | 53.7701i | 0.00902473 | + | 0.00521043i | ||||
\(475\) | −1910.98 | − | 1103.31i | −0.184594 | − | 0.106575i | ||||
\(476\) | 5768.22i | 0.555433i | ||||||||
\(477\) | −670.959 | + | 1162.13i | −0.0644048 | + | 0.111552i | ||||
\(478\) | −2543.68 | − | 4405.79i | −0.243400 | − | 0.421581i | ||||
\(479\) | 8065.31 | − | 4656.51i | 0.769340 | − | 0.444178i | −0.0632994 | − | 0.997995i | \(-0.520162\pi\) |
0.832639 | + | 0.553816i | \(0.186829\pi\) | |||||||
\(480\) | −5620.86 | −0.534492 | ||||||||
\(481\) | 5503.09 | − | 9180.28i | 0.521662 | − | 0.870239i | ||||
\(482\) | 5958.03 | 0.563031 | ||||||||
\(483\) | 12407.3 | − | 7163.36i | 1.16884 | − | 0.674833i | ||||
\(484\) | −1040.47 | − | 1802.15i | −0.0977155 | − | 0.169248i | ||||
\(485\) | −4523.41 | + | 7834.77i | −0.423500 | + | 0.733523i | ||||
\(486\) | − | 496.265i | − | 0.0463190i | ||||||
\(487\) | 3062.96 | + | 1768.40i | 0.285002 | + | 0.164546i | 0.635686 | − | 0.771948i | \(-0.280717\pi\) |
−0.350684 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(488\) | 5986.62 | + | 3456.38i | 0.555331 | + | 0.320621i | ||||
\(489\) | 5695.08i | 0.526667i | ||||||||
\(490\) | −6678.46 | + | 11567.4i | −0.615718 | + | 1.06646i | ||||
\(491\) | −1680.89 | − | 2911.39i | −0.154496 | − | 0.267595i | 0.778379 | − | 0.627794i | \(-0.216042\pi\) |
−0.932875 | + | 0.360199i | \(0.882709\pi\) | |||||||
\(492\) | 2943.83 | − | 1699.62i | 0.269752 | − | 0.155742i | ||||
\(493\) | 7097.10 | 0.648351 | ||||||||
\(494\) | 8798.20 | − | 4888.88i | 0.801315 | − | 0.445266i | ||||
\(495\) | 3051.69 | 0.277098 | ||||||||
\(496\) | 3621.58 | − | 2090.92i | 0.327851 | − | 0.189285i | ||||
\(497\) | −1527.44 | − | 2645.60i | −0.137857 | − | 0.238775i | ||||
\(498\) | 4481.95 | − | 7762.97i | 0.403295 | − | 0.698528i | ||||
\(499\) | 4027.43i | 0.361308i | 0.983547 | + | 0.180654i | \(0.0578214\pi\) | ||||
−0.983547 | + | 0.180654i | \(0.942179\pi\) | |||||||
\(500\) | 4167.66 | + | 2406.20i | 0.372767 | + | 0.215217i | ||||
\(501\) | −3708.76 | − | 2141.25i | −0.330729 | − | 0.190946i | ||||
\(502\) | − | 2683.26i | − | 0.238565i | ||||||
\(503\) | −883.336 | + | 1529.98i | −0.0783022 | + | 0.135623i | −0.902518 | − | 0.430653i | \(-0.858283\pi\) |
0.824215 | + | 0.566277i | \(0.191617\pi\) | |||||||
\(504\) | −3232.80 | − | 5599.37i | −0.285715 | − | 0.494872i | ||||
\(505\) | −8203.57 | + | 4736.33i | −0.722880 | + | 0.417355i | ||||
\(506\) | 9203.96 | 0.808628 | ||||||||
\(507\) | −6587.45 | − | 216.327i | −0.577039 | − | 0.0189496i | ||||
\(508\) | −8844.05 | −0.772424 | ||||||||
\(509\) | −5903.06 | + | 3408.13i | −0.514044 | + | 0.296784i | −0.734495 | − | 0.678615i | \(-0.762581\pi\) |
0.220450 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(510\) | 1874.91 | + | 3247.44i | 0.162789 | + | 0.281959i | ||||
\(511\) | −1122.89 | + | 1944.91i | −0.0972091 | + | 0.168371i | ||||
\(512\) | 6514.89i | 0.562344i | ||||||||
\(513\) | 2458.65 | + | 1419.50i | 0.211603 | + | 0.122169i | ||||
\(514\) | 1746.67 | + | 1008.44i | 0.149888 | + | 0.0865378i | ||||
\(515\) | 4785.13i | 0.409433i | ||||||||
\(516\) | 1103.42 | − | 1911.17i | 0.0941380 | − | 0.163052i | ||||
\(517\) | 518.194 | + | 897.538i | 0.0440815 | + | 0.0763514i | ||||
\(518\) | −12010.0 | + | 6933.99i | −1.01871 | + | 0.588151i | ||||
\(519\) | 6133.19 | 0.518723 | ||||||||
\(520\) | 11959.2 | − | 6645.37i | 1.00855 | − | 0.560421i | ||||
\(521\) | −5442.27 | −0.457640 | −0.228820 | − | 0.973469i | \(-0.573487\pi\) | ||||
−0.228820 | + | 0.973469i | \(0.573487\pi\) | |||||||
\(522\) | −2230.15 | + | 1287.58i | −0.186994 | + | 0.107961i | ||||
\(523\) | −10364.3 | − | 17951.4i | −0.866535 | − | 1.50088i | −0.865515 | − | 0.500883i | \(-0.833009\pi\) |
−0.00101984 | − | 0.999999i | \(-0.500325\pi\) | |||||||
\(524\) | 2765.22 | − | 4789.49i | 0.230532 | − | 0.399294i | ||||
\(525\) | − | 1872.17i | − | 0.155635i | ||||||
\(526\) | −12356.5 | − | 7134.01i | −1.02427 | − | 0.591365i | ||||
\(527\) | 9808.81 | + | 5663.12i | 0.810775 | + | 0.468101i | ||||
\(528\) | − | 1574.61i | − | 0.129785i | ||||||
\(529\) | −6811.41 | + | 11797.7i | −0.559827 | + | 0.969648i | ||||
\(530\) | 1839.57 | + | 3186.22i | 0.150765 | + | 0.261133i | ||||
\(531\) | 3420.63 | − | 1974.90i | 0.279553 | − | 0.161400i | ||||
\(532\) | 11973.4 | 0.975775 | ||||||||
\(533\) | −7130.99 | + | 11896.0i | −0.579508 | + | 0.966738i | ||||
\(534\) | −2051.87 | −0.166279 | ||||||||
\(535\) | 15032.1 | − | 8678.77i | 1.21475 | − | 0.701339i | ||||
\(536\) | −6488.01 | − | 11237.6i | −0.522835 | − | 0.905577i | ||||
\(537\) | −5834.58 | + | 10105.8i | −0.468865 | + | 0.812098i | ||||
\(538\) | 12058.1i | 0.966285i | ||||||||
\(539\) | 13155.8 | + | 7595.50i | 1.05132 | + | 0.606979i | ||||
\(540\) | 1081.84 | + | 624.600i | 0.0862129 | + | 0.0497750i | ||||
\(541\) | 8577.44i | 0.681651i | 0.940127 | + | 0.340825i | \(0.110706\pi\) | ||||
−0.940127 | + | 0.340825i | \(0.889294\pi\) | |||||||
\(542\) | 2176.56 | − | 3769.92i | 0.172493 | − | 0.298767i | ||||
\(543\) | −3715.53 | − | 6435.48i | −0.293644 | − | 0.508606i | ||||
\(544\) | −6802.75 | + | 3927.57i | −0.536150 | + | 0.309546i | ||||
\(545\) | 23898.1 | 1.87832 | ||||||||
\(546\) | 7324.56 | + | 4390.68i | 0.574107 | + | 0.344146i | ||||
\(547\) | 8723.99 | 0.681921 | 0.340961 | − | 0.940078i | \(-0.389248\pi\) | ||||
0.340961 | + | 0.940078i | \(0.389248\pi\) | |||||||
\(548\) | −2440.47 | + | 1409.01i | −0.190240 | + | 0.109835i | ||||
\(549\) | −1287.65 | − | 2230.28i | −0.100102 | − | 0.173381i | ||||
\(550\) | 601.373 | − | 1041.61i | 0.0466230 | − | 0.0807533i | ||||
\(551\) | − | 14731.8i | − | 1.13901i | ||||||
\(552\) | 10079.5 | + | 5819.42i | 0.777198 | + | 0.448716i | ||||
\(553\) | −452.037 | − | 260.984i | −0.0347606 | − | 0.0200690i | ||||
\(554\) | 8235.17i | 0.631550i | ||||||||
\(555\) | 4138.58 | − | 7168.22i | 0.316528 | − | 0.548242i | ||||
\(556\) | 2881.78 | + | 4991.39i | 0.219810 | + | 0.380723i | ||||
\(557\) | −835.720 | + | 482.503i | −0.0635738 | + | 0.0367043i | −0.531450 | − | 0.847090i | \(-0.678353\pi\) |
0.467876 | + | 0.883794i | \(0.345019\pi\) | |||||||
\(558\) | −4109.68 | −0.311786 | ||||||||
\(559\) | −147.788 | + | 9003.09i | −0.0111820 | + | 0.681199i | ||||
\(560\) | −6719.95 | −0.507089 | ||||||||
\(561\) | 3693.36 | − | 2132.37i | 0.277957 | − | 0.160479i | ||||
\(562\) | 2346.83 | + | 4064.83i | 0.176148 | + | 0.305097i | ||||
\(563\) | −7302.60 | + | 12648.5i | −0.546657 | + | 0.946837i | 0.451844 | + | 0.892097i | \(0.350766\pi\) |
−0.998501 | + | 0.0547402i | \(0.982567\pi\) | |||||||
\(564\) | 424.242i | 0.0316734i | ||||||||
\(565\) | 1280.81 | + | 739.477i | 0.0953702 | + | 0.0550620i | ||||
\(566\) | −11773.4 | − | 6797.40i | −0.874337 | − | 0.504799i | ||||
\(567\) | 2408.72i | 0.178407i | ||||||||
\(568\) | 1240.87 | − | 2149.25i | 0.0916650 | − | 0.158768i | ||||
\(569\) | 3901.24 | + | 6757.15i | 0.287432 | + | 0.497846i | 0.973196 | − | 0.229977i | \(-0.0738653\pi\) |
−0.685764 | + | 0.727824i | \(0.740532\pi\) | |||||||
\(570\) | 6740.89 | − | 3891.85i | 0.495342 | − | 0.285986i | ||||
\(571\) | −11988.2 | −0.878618 | −0.439309 | − | 0.898336i | \(-0.644777\pi\) | ||||
−0.439309 | + | 0.898336i | \(0.644777\pi\) | |||||||
\(572\) | −2446.56 | − | 4402.91i | −0.178839 | − | 0.321844i | ||||
\(573\) | 6830.43 | 0.497985 | ||||||||
\(574\) | 15562.8 | − | 8985.18i | 1.13167 | − | 0.653370i | ||||
\(575\) | 1685.07 | + | 2918.63i | 0.122213 | + | 0.211678i | ||||
\(576\) | 2098.41 | − | 3634.55i | 0.151795 | − | 0.262916i | ||||
\(577\) | − | 5576.90i | − | 0.402374i | −0.979553 | − | 0.201187i | \(-0.935520\pi\) | ||
0.979553 | − | 0.201187i | \(-0.0644798\pi\) | |||||||
\(578\) | −4151.01 | − | 2396.58i | −0.298718 | − | 0.172465i | ||||
\(579\) | −10190.8 | − | 5883.63i | −0.731456 | − | 0.422306i | ||||
\(580\) | − | 6482.19i | − | 0.464066i | ||||||
\(581\) | −21754.1 | + | 37679.1i | −1.55337 | + | 2.69052i | ||||
\(582\) | −2293.71 | − | 3972.83i | −0.163363 | − | 0.282954i | ||||
\(583\) | 3623.74 | − | 2092.17i | 0.257427 | − | 0.148626i | ||||
\(584\) | −1824.45 | −0.129274 | ||||||||
\(585\) | −5096.29 | − | 83.6567i | −0.360181 | − | 0.00591245i | ||||
\(586\) | 15249.4 | 1.07499 | ||||||||
\(587\) | −23169.7 | + | 13377.0i | −1.62916 | + | 0.940593i | −0.644810 | + | 0.764343i | \(0.723064\pi\) |
−0.984345 | + | 0.176251i | \(0.943603\pi\) | |||||||
\(588\) | 3109.19 | + | 5385.28i | 0.218063 | + | 0.377696i | ||||
\(589\) | 11755.2 | − | 20360.6i | 0.822353 | − | 1.42436i | ||||
\(590\) | − | 10829.2i | − | 0.755644i | ||||||
\(591\) | −13154.6 | − | 7594.84i | −0.915584 | − | 0.528612i | ||||
\(592\) | −3698.66 | − | 2135.42i | −0.256781 | − | 0.148252i | ||||
\(593\) | − | 3589.40i | − | 0.248565i | −0.992247 | − | 0.124283i | \(-0.960337\pi\) | ||
0.992247 | − | 0.124283i | \(-0.0396629\pi\) | |||||||
\(594\) | −773.721 | + | 1340.12i | −0.0534447 | + | 0.0925689i | ||||
\(595\) | −9100.26 | − | 15762.1i | −0.627016 | − | 1.08602i | ||||
\(596\) | −1418.82 | + | 819.158i | −0.0975122 | + | 0.0562987i | ||||
\(597\) | −9810.18 | −0.672536 | ||||||||
\(598\) | −15370.5 | − | 252.310i | −1.05108 | − | 0.0172537i | ||||
\(599\) | −7462.78 | −0.509050 | −0.254525 | − | 0.967066i | \(-0.581919\pi\) | ||||
−0.254525 | + | 0.967066i | \(0.581919\pi\) | |||||||
\(600\) | 1317.16 | − | 760.465i | 0.0896216 | − | 0.0517431i | ||||
\(601\) | 8255.52 | + | 14299.0i | 0.560316 | + | 0.970495i | 0.997469 | + | 0.0711081i | \(0.0226535\pi\) |
−0.437153 | + | 0.899387i | \(0.644013\pi\) | |||||||
\(602\) | 5833.30 | − | 10103.6i | 0.394929 | − | 0.684037i | ||||
\(603\) | 4834.15i | 0.326471i | ||||||||
\(604\) | 5312.02 | + | 3066.90i | 0.357853 | + | 0.206606i | ||||
\(605\) | 5686.35 | + | 3283.02i | 0.382121 | + | 0.220618i | ||||
\(606\) | − | 4803.37i | − | 0.321986i | ||||||
\(607\) | 5976.78 | − | 10352.1i | 0.399654 | − | 0.692222i | −0.594029 | − | 0.804444i | \(-0.702464\pi\) |
0.993683 | + | 0.112222i | \(0.0357968\pi\) | |||||||
\(608\) | 8152.66 | + | 14120.8i | 0.543806 | + | 0.941900i | ||||
\(609\) | 10824.5 | − | 6249.51i | 0.720246 | − | 0.415834i | ||||
\(610\) | −7060.73 | −0.468657 | ||||||||
\(611\) | −840.773 | − | 1513.08i | −0.0556695 | − | 0.100185i | ||||
\(612\) | 1745.75 | 0.115307 | ||||||||
\(613\) | 3962.63 | − | 2287.82i | 0.261091 | − | 0.150741i | −0.363741 | − | 0.931500i | \(-0.618501\pi\) |
0.624832 | + | 0.780759i | \(0.285167\pi\) | |||||||
\(614\) | 4049.76 | + | 7014.38i | 0.266181 | + | 0.461038i | ||||
\(615\) | −5362.83 | + | 9288.70i | −0.351627 | + | 0.609035i | ||||
\(616\) | 20160.9i | 1.31868i | ||||||||
\(617\) | −16654.6 | − | 9615.51i | −1.08669 | − | 0.627400i | −0.153996 | − | 0.988071i | \(-0.549214\pi\) |
−0.932693 | + | 0.360671i | \(0.882548\pi\) | |||||||
\(618\) | −2101.35 | − | 1213.21i | −0.136778 | − | 0.0789687i | ||||
\(619\) | − | 11715.6i | − | 0.760727i | −0.924837 | − | 0.380363i | \(-0.875799\pi\) | ||
0.924837 | − | 0.380363i | \(-0.124201\pi\) | |||||||
\(620\) | 5172.45 | − | 8958.95i | 0.335050 | − | 0.580323i | ||||
\(621\) | −2167.99 | − | 3755.07i | −0.140094 | − | 0.242650i | ||||
\(622\) | 13038.9 | − | 7528.00i | 0.840533 | − | 0.485282i | ||||
\(623\) | 9959.17 | 0.640459 | ||||||||
\(624\) | −43.1652 | + | 2629.59i | −0.00276922 | + | 0.168698i | ||||
\(625\) | −17807.8 | −1.13970 | ||||||||
\(626\) | −14590.4 | + | 8423.79i | −0.931551 | + | 0.537831i | ||||
\(627\) | −4426.26 | − | 7666.51i | −0.281926 | − | 0.488311i | ||||
\(628\) | 1398.34 | − | 2421.99i | 0.0888531 | − | 0.153898i | ||||
\(629\) | − | 11567.3i | − | 0.733256i | ||||||
\(630\) | 5719.22 | + | 3302.00i | 0.361682 | + | 0.208817i | ||||
\(631\) | 7603.78 | + | 4390.04i | 0.479717 | + | 0.276965i | 0.720299 | − | 0.693664i | \(-0.244005\pi\) |
−0.240581 | + | 0.970629i | \(0.577338\pi\) | |||||||
\(632\) | − | 424.040i | − | 0.0266889i | ||||||
\(633\) | 4218.27 | − | 7306.25i | 0.264867 | − | 0.458764i | ||||
\(634\) | −5693.02 | − | 9860.60i | −0.356623 | − | 0.617689i | ||||
\(635\) | 24167.1 | − | 13952.9i | 1.51030 | − | 0.871973i | ||||
\(636\) | 1712.84 | 0.106790 | ||||||||
\(637\) | −21761.8 | − | 13045.0i | −1.35359 | − | 0.811403i | ||||
\(638\) | 8029.78 | 0.498279 | ||||||||
\(639\) | −800.691 | + | 462.279i | −0.0495694 | + | 0.0286189i | ||||
\(640\) | 1741.28 | + | 3015.98i | 0.107547 | + | 0.186277i | ||||
\(641\) | 12495.9 | − | 21643.5i | 0.769980 | − | 1.33364i | −0.167593 | − | 0.985856i | \(-0.553599\pi\) |
0.937573 | − | 0.347789i | \(-0.113067\pi\) | |||||||
\(642\) | 8801.60i | 0.541077i | ||||||||
\(643\) | −2038.50 | − | 1176.93i | −0.125024 | − | 0.0721827i | 0.436184 | − | 0.899858i | \(-0.356330\pi\) |
−0.561208 | + | 0.827675i | \(0.689663\pi\) | |||||||
\(644\) | −15836.9 | − | 9143.42i | −0.969038 | − | 0.559474i | ||||
\(645\) | 6963.24i | 0.425081i | ||||||||
\(646\) | 5438.85 | − | 9420.37i | 0.331252 | − | 0.573745i | ||||
\(647\) | −2955.40 | − | 5118.90i | −0.179581 | − | 0.311043i | 0.762156 | − | 0.647393i | \(-0.224141\pi\) |
−0.941737 | + | 0.336350i | \(0.890807\pi\) | |||||||
\(648\) | −1694.65 | + | 978.407i | −0.102735 | + | 0.0593140i | ||||
\(649\) | −12316.2 | −0.744918 | ||||||||
\(650\) | −1032.84 | + | 1722.99i | −0.0623251 | + | 0.103971i | ||||
\(651\) | 19947.2 | 1.20091 | ||||||||
\(652\) | 6295.38 | − | 3634.64i | 0.378138 | − | 0.218318i | ||||
\(653\) | −2962.17 | − | 5130.63i | −0.177517 | − | 0.307469i | 0.763512 | − | 0.645793i | \(-0.223473\pi\) |
−0.941029 | + | 0.338325i | \(0.890140\pi\) | |||||||
\(654\) | −6059.08 | + | 10494.6i | −0.362277 | + | 0.627481i | ||||
\(655\) | 17450.2i | 1.04097i | ||||||||
\(656\) | 4792.79 | + | 2767.12i | 0.285254 | + | 0.164692i | ||||
\(657\) | 588.627 | + | 339.844i | 0.0349536 | + | 0.0201805i | ||||
\(658\) | 2242.79i | 0.132877i | ||||||||
\(659\) | 6419.77 | − | 11119.4i | 0.379482 | − | 0.657282i | −0.611505 | − | 0.791241i | \(-0.709436\pi\) |
0.990987 | + | 0.133958i | \(0.0427688\pi\) | |||||||
\(660\) | −1947.61 | − | 3373.36i | −0.114865 | − | 0.198952i | ||||
\(661\) | 8890.18 | − | 5132.75i | 0.523129 | − | 0.302028i | −0.215085 | − | 0.976595i | \(-0.569003\pi\) |
0.738214 | + | 0.674567i | \(0.235670\pi\) | |||||||
\(662\) | 8490.35 | 0.498469 | ||||||||
\(663\) | −6226.33 | + | 3459.78i | −0.364722 | + | 0.202665i | ||||
\(664\) | −35345.4 | −2.06577 | ||||||||
\(665\) | −32718.2 | + | 18889.9i | −1.90791 | + | 1.10153i | ||||
\(666\) | 2098.57 | + | 3634.84i | 0.122099 | + | 0.211482i | ||||
\(667\) | −11249.9 | + | 19485.4i | −0.653069 | + | 1.13115i | ||||
\(668\) | 5466.25i | 0.316610i | ||||||||
\(669\) | −2384.35 | − | 1376.60i | −0.137794 | − | 0.0795555i | ||||
\(670\) | 11478.1 | + | 6626.89i | 0.661848 | + | 0.382118i | ||||
\(671\) | 8030.27i | 0.462004i | ||||||||
\(672\) | −6917.03 | + | 11980.6i | −0.397069 | + | 0.687743i | ||||
\(673\) | 4931.41 | + | 8541.45i | 0.282454 | + | 0.489225i | 0.971989 | − | 0.235028i | \(-0.0755181\pi\) |
−0.689534 | + | 0.724253i | \(0.742185\pi\) | |||||||
\(674\) | 5704.17 | − | 3293.30i | 0.325989 | − | 0.188210i | ||||
\(675\) | −566.614 | −0.0323096 | ||||||||
\(676\) | 3965.03 | + | 7419.88i | 0.225593 | + | 0.422160i | ||||
\(677\) | 32615.5 | 1.85158 | 0.925788 | − | 0.378043i | \(-0.123403\pi\) | ||||
0.925788 | + | 0.378043i | \(0.123403\pi\) | |||||||
\(678\) | −649.470 | + | 374.971i | −0.0367887 | + | 0.0212400i | ||||
\(679\) | 11133.0 | + | 19282.9i | 0.629227 | + | 1.08985i | ||||
\(680\) | 7392.93 | − | 12804.9i | 0.416921 | − | 0.722128i | ||||
\(681\) | 4009.17i | 0.225597i | ||||||||
\(682\) | 11097.9 | + | 6407.35i | 0.623107 | + | 0.359751i | ||||
\(683\) | 18729.9 | + | 10813.7i | 1.04931 | + | 0.605820i | 0.922456 | − | 0.386102i | \(-0.126179\pi\) |
0.126854 | + | 0.991921i | \(0.459512\pi\) | |||||||
\(684\) | − | 3623.75i | − | 0.202570i | ||||||
\(685\) | 4445.85 | − | 7700.44i | 0.247981 | − | 0.429516i | ||||
\(686\) | 6021.66 | + | 10429.8i | 0.335143 | + | 0.580485i | ||||
\(687\) | 428.215 | − | 247.230i | 0.0237808 | − | 0.0137299i | ||||
\(688\) | 3592.90 | 0.199096 | ||||||||
\(689\) | −6108.95 | + | 3394.56i | −0.337783 | + | 0.187696i | ||||
\(690\) | −11888.0 | −0.655895 | ||||||||
\(691\) | −12326.3 | + | 7116.57i | −0.678601 | + | 0.391790i | −0.799328 | − | 0.600896i | \(-0.794811\pi\) |
0.120727 | + | 0.992686i | \(0.461477\pi\) | |||||||
\(692\) | −3914.25 | − | 6779.67i | −0.215025 | − | 0.372434i | ||||
\(693\) | 3755.41 | − | 6504.56i | 0.205853 | − | 0.356548i | ||||
\(694\) | − | 6719.98i | − | 0.367561i | ||||||
\(695\) | −15749.4 | − | 9092.90i | −0.859579 | − | 0.496278i | ||||
\(696\) | 8793.66 | + | 5077.02i | 0.478912 | + | 0.276500i | ||||
\(697\) | 14989.1i | 0.814566i | ||||||||
\(698\) | 4586.39 | − | 7943.86i | 0.248707 | − | 0.430773i | ||||
\(699\) | −6365.13 | − | 11024.7i | −0.344423 | − | 0.596558i | ||||
\(700\) | −2069.52 | + | 1194.84i | −0.111743 | + | 0.0645151i | ||||
\(701\) | 28747.0 | 1.54887 | 0.774437 | − | 0.632651i | \(-0.218033\pi\) | ||||
0.774437 | + | 0.632651i | \(0.218033\pi\) | |||||||
\(702\) | 1328.84 | − | 2216.78i | 0.0714443 | − | 0.119184i | ||||
\(703\) | −24010.8 | −1.28817 | ||||||||
\(704\) | −11333.2 | + | 6543.21i | −0.606726 | + | 0.350293i | ||||
\(705\) | −669.307 | − | 1159.27i | −0.0357554 | − | 0.0619302i | ||||
\(706\) | 6022.45 | − | 10431.2i | 0.321045 | − | 0.556066i | ||||
\(707\) | 23314.1i | 1.24019i | ||||||||
\(708\) | −4366.14 | − | 2520.79i | −0.231765 | − | 0.133810i | ||||
\(709\) | 1575.00 | + | 909.324i | 0.0834276 | + | 0.0481670i | 0.541133 | − | 0.840937i | \(-0.317995\pi\) |
−0.457706 | + | 0.889104i | \(0.651329\pi\) | |||||||
\(710\) | 2534.86i | 0.133988i | ||||||||
\(711\) | −78.9868 | + | 136.809i | −0.00416630 | + | 0.00721624i | ||||
\(712\) | 4045.35 | + | 7006.75i | 0.212930 | + | 0.368805i | ||||
\(713\) | −31096.6 | + | 17953.6i | −1.63335 | + | 0.943014i | ||||
\(714\) | 9229.06 | 0.483738 | ||||||||
\(715\) | 13631.7 | + | 8171.47i | 0.713002 | + | 0.427407i | ||||
\(716\) | 14894.7 | 0.777431 | ||||||||
\(717\) | 6471.98 | − | 3736.60i | 0.337100 | − | 0.194625i | ||||
\(718\) | 9473.15 | + | 16408.0i | 0.492388 | + | 0.852841i | ||||
\(719\) | 13070.9 | − | 22639.5i | 0.677973 | − | 1.17428i | −0.297617 | − | 0.954685i | \(-0.596192\pi\) |
0.975590 | − | 0.219599i | \(-0.0704748\pi\) | |||||||
\(720\) | 2033.80i | 0.105271i | ||||||||
\(721\) | 10199.3 | + | 5888.58i | 0.526827 | + | 0.304164i | ||||
\(722\) | −7423.29 | − | 4285.84i | −0.382640 | − | 0.220917i | ||||
\(723\) | 8752.19i | 0.450204i | ||||||||
\(724\) | −4742.55 | + | 8214.34i | −0.243447 | + | 0.421662i | ||||
\(725\) | 1470.10 | + | 2546.29i | 0.0753078 | + | 0.130437i | ||||
\(726\) | −2883.42 | + | 1664.74i | −0.147402 | + | 0.0851024i | ||||
\(727\) | 1340.10 | 0.0683652 | 0.0341826 | − | 0.999416i | \(-0.489117\pi\) | ||||
0.0341826 | + | 0.999416i | \(0.489117\pi\) | |||||||
\(728\) | 552.674 | − | 33668.4i | 0.0281366 | − | 1.71406i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 1613.84 | − | 931.750i | 0.0818231 | − | 0.0472406i | ||||
\(731\) | 4865.56 | + | 8427.39i | 0.246182 | + | 0.426400i | ||||
\(732\) | −1643.58 | + | 2846.77i | −0.0829898 | + | 0.143743i | ||||
\(733\) | 32517.1i | 1.63854i | 0.573409 | + | 0.819269i | \(0.305620\pi\) | ||||
−0.573409 | + | 0.819269i | \(0.694380\pi\) | |||||||
\(734\) | −11627.6 | − | 6713.22i | −0.584719 | − | 0.337588i | ||||
\(735\) | −16992.2 | − | 9810.47i | −0.852746 | − | 0.492333i | ||||
\(736\) | − | 24903.0i | − | 1.24719i | ||||||
\(737\) | 7536.86 | − | 13054.2i | 0.376694 | − | 0.652454i | ||||
\(738\) | −2719.37 | − | 4710.08i | −0.135639 | − | 0.234933i | ||||
\(739\) | −19200.2 | + | 11085.3i | −0.955741 | + | 0.551797i | −0.894860 | − | 0.446348i | \(-0.852724\pi\) |
−0.0608813 | + | 0.998145i | \(0.519391\pi\) | |||||||
\(740\) | −10565.1 | −0.524838 | ||||||||
\(741\) | 7181.64 | + | 12924.3i | 0.356038 | + | 0.640738i | ||||
\(742\) | 9055.07 | 0.448008 | ||||||||
\(743\) | 26316.6 | − | 15193.9i | 1.29941 | − | 0.750216i | 0.319110 | − | 0.947718i | \(-0.396616\pi\) |
0.980303 | + | 0.197502i | \(0.0632828\pi\) | |||||||
\(744\) | 8102.40 | + | 14033.8i | 0.399259 | + | 0.691536i | ||||
\(745\) | 2584.70 | − | 4476.83i | 0.127109 | − | 0.220159i | ||||
\(746\) | 10916.9i | 0.535786i | ||||||||
\(747\) | 11403.6 | + | 6583.87i | 0.558549 | + | 0.322478i | ||||
\(748\) | −4714.27 | − | 2721.78i | −0.230442 | − | 0.133046i | ||||
\(749\) | − | 42720.3i | − | 2.08407i | ||||||
\(750\) | 3849.88 | − | 6668.18i | 0.187437 | − | 0.324650i | ||||
\(751\) | −8449.17 | − | 14634.4i | −0.410539 | − | 0.711074i | 0.584410 | − | 0.811459i | \(-0.301326\pi\) |
−0.994949 | + | 0.100385i | \(0.967993\pi\) | |||||||
\(752\) | −598.163 | + | 345.350i | −0.0290063 | + | 0.0167468i | ||||
\(753\) | 3941.63 | 0.190758 | ||||||||
\(754\) | −13409.6 | − | 220.122i | −0.647680 | − | 0.0106318i | ||||
\(755\) | −19354.0 | −0.932934 | ||||||||
\(756\) | 2662.62 | − | 1537.26i | 0.128093 | − | 0.0739547i | ||||
\(757\) | −16462.9 | − | 28514.6i | −0.790428 | − | 1.36906i | −0.925702 | − | 0.378253i | \(-0.876525\pi\) |
0.135275 | − | 0.990808i | \(-0.456808\pi\) | |||||||
\(758\) | −1060.45 | + | 1836.75i | −0.0508142 | + | 0.0880128i | ||||
\(759\) | 13520.4i | 0.646585i | ||||||||
\(760\) | −26579.9 | − | 15345.9i | −1.26862 | − | 0.732440i | ||||
\(761\) | 14542.3 | + | 8396.01i | 0.692718 | + | 0.399941i | 0.804630 | − | 0.593777i | \(-0.202364\pi\) |
−0.111911 | + | 0.993718i | \(0.535697\pi\) | |||||||
\(762\) | 14150.3i | 0.672720i | ||||||||
\(763\) | 29409.0 | − | 50937.8i | 1.39538 | − | 2.41687i | ||||
\(764\) | −4359.23 | − | 7550.41i | −0.206429 | − | 0.357545i | ||||
\(765\) | −4770.41 | + | 2754.20i | −0.225457 | + | 0.130168i | ||||
\(766\) | −13783.5 | −0.650153 | ||||||||
\(767\) | 20567.9 | + | 337.626i | 0.968270 | + | 0.0158944i | ||||
\(768\) | −12957.4 | −0.608804 | ||||||||
\(769\) | 1335.04 | − | 770.783i | 0.0626042 | − | 0.0361445i | −0.468371 | − | 0.883532i | \(-0.655159\pi\) |
0.530975 | + | 0.847387i | \(0.321826\pi\) | |||||||
\(770\) | −10296.2 | − | 17833.5i | −0.481882 | − | 0.834645i | ||||
\(771\) | −1481.37 | + | 2565.81i | −0.0691963 | + | 0.119851i | ||||
\(772\) | 15019.9i | 0.700231i | ||||||||
\(773\) | −32970.6 | − | 19035.6i | −1.53411 | − | 0.885721i | −0.999166 | − | 0.0408357i | \(-0.986998\pi\) |
−0.534948 | − | 0.844885i | \(-0.679669\pi\) | |||||||
\(774\) | −3057.85 | − | 1765.45i | −0.142005 | − | 0.0819867i | ||||
\(775\) | 4692.26i | 0.217485i | ||||||||
\(776\) | −9044.30 | + | 15665.2i | −0.418391 | + | 0.724674i | ||||
\(777\) | −10185.9 | − | 17642.4i | −0.470290 | − | 0.814566i | ||||
\(778\) | −2203.91 | + | 1272.43i | −0.101560 | + | 0.0586358i | ||||
\(779\) | 31113.6 | 1.43102 | ||||||||
\(780\) | 3160.02 | + | 5686.87i | 0.145060 | + | 0.261055i | ||||
\(781\) | 2882.93 | 0.132086 | ||||||||
\(782\) | −14387.6 | + | 8306.71i | −0.657930 | + | 0.379856i | ||||
\(783\) | −1891.42 | − | 3276.03i | −0.0863266 | − | 0.149522i | ||||
\(784\) | −5062.01 | + | 8767.66i | −0.230595 | + | 0.399401i | ||||
\(785\) | 8824.38i | 0.401217i | ||||||||
\(786\) | −7663.11 | − | 4424.30i | −0.347753 | − | 0.200775i | ||||
\(787\) | −17363.6 | − | 10024.9i | −0.786463 | − | 0.454065i | 0.0522528 | − | 0.998634i | \(-0.483360\pi\) |
−0.838716 | + | 0.544569i | \(0.816693\pi\) | |||||||
\(788\) | 19388.3i | 0.876498i | ||||||||
\(789\) | 10479.7 | − | 18151.3i | 0.472860 | − | 0.819017i | ||||
\(790\) | 216.558 | + | 375.090i | 0.00975291 | + | 0.0168925i | ||||
\(791\) | 3152.33 | − | 1820.00i | 0.141699 | − | 0.0818100i | ||||
\(792\) | 6101.69 | 0.273755 | ||||||||
\(793\) | 220.136 | − | 13410.5i | 0.00985781 | − | 0.600529i | ||||
\(794\) | 17064.4 | 0.762709 | ||||||||
\(795\) | −4680.48 | + | 2702.28i | −0.208804 | + | 0.120553i | ||||
\(796\) | 6260.93 | + | 10844.2i | 0.278785 | + | 0.482869i | ||||
\(797\) | −11200.9 | + | 19400.6i | −0.497813 | + | 0.862238i | −0.999997 | − | 0.00252302i | \(-0.999197\pi\) |
0.502183 | + | 0.864761i | \(0.332530\pi\) | |||||||
\(798\) | − | 19157.2i | − | 0.849823i | ||||||
\(799\) | −1620.08 | − | 935.355i | −0.0717327 | − | 0.0414149i | ||||
\(800\) | −2818.26 | − | 1627.12i | −0.124551 | − | 0.0719093i | ||||
\(801\) | − | 3014.15i | − | 0.132958i | ||||||
\(802\) | −3353.01 | + | 5807.59i | −0.147630 | + | 0.255702i | ||||
\(803\) | −1059.69 | − | 1835.44i | −0.0465700 | − | 0.0806617i | ||||
\(804\) | 5343.70 | − | 3085.19i | 0.234400 | − | 0.135331i | ||||
\(805\) | 57700.7 | 2.52631 | ||||||||
\(806\) | −18357.7 | − | 11004.4i | −0.802259 | − | 0.480911i | ||||
\(807\) | −17713.0 | −0.772649 | ||||||||
\(808\) | −16402.6 | + | 9470.04i | −0.714159 | + | 0.412320i | ||||
\(809\) | 20983.2 | + | 36343.9i | 0.911903 | + | 1.57946i | 0.811373 | + | 0.584528i | \(0.198720\pi\) |
0.100530 | + | 0.994934i | \(0.467946\pi\) | |||||||
\(810\) | 999.350 | − | 1730.92i | 0.0433501 | − | 0.0750846i | ||||
\(811\) | 13029.1i | 0.564133i | 0.959395 | + | 0.282067i | \(0.0910199\pi\) | ||||
−0.959395 | + | 0.282067i | \(0.908980\pi\) | |||||||
\(812\) | −13816.5 | − | 7976.97i | −0.597124 | − | 0.344750i | ||||
\(813\) | 5537.91 | + | 3197.31i | 0.238897 | + | 0.137927i | ||||
\(814\) | − | 13087.4i | − | 0.563532i | ||||||
\(815\) | −11468.4 | + | 19863.9i | −0.492909 | + | 0.853744i | ||||
\(816\) | 1421.11 | + | 2461.44i | 0.0609667 | + | 0.105597i | ||||
\(817\) | 17493.2 | − | 10099.7i | 0.749092 | − | 0.432489i | ||||
\(818\) | −22319.5 | −0.954014 | ||||||||
\(819\) | −6449.80 | + | 10759.6i | −0.275182 | + | 0.459060i | ||||
\(820\) | 13690.4 | 0.583036 | ||||||||
\(821\) | −7706.01 | + | 4449.07i | −0.327578 | + | 0.189127i | −0.654765 | − | 0.755832i | \(-0.727233\pi\) |
0.327187 | + | 0.944960i | \(0.393899\pi\) | |||||||
\(822\) | 2254.39 | + | 3904.71i | 0.0956578 | + | 0.165684i | ||||
\(823\) | 11361.8 | − | 19679.2i | 0.481224 | − | 0.833504i | −0.518544 | − | 0.855051i | \(-0.673526\pi\) |
0.999768 | + | 0.0215466i | \(0.00685902\pi\) | |||||||
\(824\) | 9567.61i | 0.404494i | ||||||||
\(825\) | 1530.09 | + | 883.401i | 0.0645710 | + | 0.0372801i | ||||
\(826\) | −23081.9 | − | 13326.4i | −0.972304 | − | 0.561360i | ||||
\(827\) | 19073.3i | 0.801989i | 0.916081 | + | 0.400994i | \(0.131335\pi\) | ||||
−0.916081 | + | 0.400994i | \(0.868665\pi\) | |||||||
\(828\) | −2767.26 | + | 4793.03i | −0.116146 | + | 0.201171i | ||||
\(829\) | 21251.9 | + | 36809.4i | 0.890361 | + | 1.54215i | 0.839443 | + | 0.543448i | \(0.182881\pi\) |
0.0509178 | + | 0.998703i | \(0.483785\pi\) | |||||||
\(830\) | 31265.2 | − | 18051.0i | 1.30751 | − | 0.754891i | ||||
\(831\) | −12097.2 | −0.504992 | ||||||||
\(832\) | 19105.6 | − | 10616.4i | 0.796116 | − | 0.442377i | ||||
\(833\) | −27420.2 | −1.14052 | ||||||||
\(834\) | 7986.13 | − | 4610.80i | 0.331579 | − | 0.191437i | ||||
\(835\) | −8623.86 | − | 14937.0i | −0.357414 | − | 0.619060i | ||||
\(836\) | −5649.74 | + | 9785.65i | −0.233733 | + | 0.404837i | ||||
\(837\) | − | 6037.01i | − | 0.249307i | ||||||
\(838\) | 12916.2 | + | 7457.19i | 0.532439 | + | 0.307404i | ||||
\(839\) | 16824.5 | + | 9713.62i | 0.692307 | + | 0.399704i | 0.804476 | − | 0.593985i | \(-0.202446\pi\) |
−0.112168 | + | 0.993689i | \(0.535780\pi\) | |||||||
\(840\) | − | 26040.1i | − | 1.06960i | ||||||
\(841\) | 2379.80 | − | 4121.94i | 0.0975768 | − | 0.169008i | ||||
\(842\) | 7741.11 | + | 13408.0i | 0.316836 | + | 0.548777i | ||||
\(843\) | −5971.13 | + | 3447.43i | −0.243958 | + | 0.140849i | ||||
\(844\) | −10768.5 | −0.439180 | ||||||||
\(845\) | −22540.8 | − | 14020.0i | −0.917664 | − | 0.570770i | ||||
\(846\) | 678.780 | 0.0275850 | ||||||||
\(847\) | 13995.2 | − | 8080.15i | 0.567747 | − | 0.327789i | ||||
\(848\) | 1394.32 | + | 2415.03i | 0.0564637 | + | 0.0977979i | ||||
\(849\) | 9985.20 | − | 17294.9i | 0.403641 | − | 0.699127i | ||||
\(850\) | 2170.99i | 0.0876052i | ||||||||
\(851\) | 31758.5 | + | 18335.8i | 1.27928 | + | 0.738592i | ||||
\(852\) | 1022.01 | + | 590.060i | 0.0410958 | + | 0.0237267i | ||||
\(853\) | 26851.8i | 1.07783i | 0.842361 | + | 0.538914i | \(0.181165\pi\) | ||||
−0.842361 | + | 0.538914i | \(0.818835\pi\) | |||||||
\(854\) | −8688.92 | + | 15049.7i | −0.348160 | + | 0.603031i | ||||
\(855\) | 5717.03 | + | 9902.18i | 0.228676 | + | 0.396079i | ||||
\(856\) | 30055.8 | − | 17352.7i | 1.20010 | − | 0.692878i | ||||
\(857\) | −41539.4 | −1.65573 | −0.827864 | − | 0.560929i | \(-0.810444\pi\) | ||||
−0.827864 | + | 0.560929i | \(0.810444\pi\) | |||||||
\(858\) | −7044.58 | + | 3914.46i | −0.280301 | + | 0.155754i | ||||
\(859\) | −11936.2 | −0.474107 | −0.237054 | − | 0.971497i | \(-0.576182\pi\) | ||||
−0.237054 | + | 0.971497i | \(0.576182\pi\) | |||||||
\(860\) | 7697.22 | − | 4443.99i | 0.305201 | − | 0.176208i | ||||
\(861\) | 13199.0 | + | 22861.3i | 0.522439 | + | 0.904892i | ||||
\(862\) | −10269.2 | + | 17786.7i | −0.405765 | + | 0.702805i | ||||
\(863\) | − | 41128.6i | − | 1.62229i | −0.584848 | − | 0.811143i | \(-0.698846\pi\) | ||
0.584848 | − | 0.811143i | \(-0.301154\pi\) | |||||||
\(864\) | 3625.94 | + | 2093.44i | 0.142774 | + | 0.0824309i | ||||
\(865\) | 21392.0 | + | 12350.7i | 0.840866 | + | 0.485474i | ||||
\(866\) | 5582.22i | 0.219043i | ||||||||
\(867\) | 3520.52 | − | 6097.72i | 0.137904 | − | 0.238857i | ||||
\(868\) | −12730.4 | − | 22049.7i | −0.497810 | − | 0.862232i | ||||
\(869\) | 426.595 | − | 246.295i | 0.0166528 | − | 0.00961448i | ||||
\(870\) | −10371.4 | −0.404165 | ||||||||
\(871\) | −12944.3 | + | 21593.8i | −0.503561 | + | 0.840044i | ||||
\(872\) | 47782.9 | 1.85566 | ||||||||
\(873\) | 5835.98 | − | 3369.40i | 0.226252 | − | 0.130627i | ||||
\(874\) | 17242.7 | + | 29865.2i | 0.667325 | + | 1.15584i | ||||
\(875\) | −18686.1 | + | 32365.4i | −0.721951 | + | 1.25046i | ||||
\(876\) | − | 867.564i | − | 0.0334615i | ||||||
\(877\) | −5548.50 | − | 3203.43i | −0.213637 | − | 0.123343i | 0.389364 | − | 0.921084i | \(-0.372695\pi\) |
−0.603001 | + | 0.797741i | \(0.706028\pi\) | |||||||
\(878\) | −11928.1 | − | 6886.68i | −0.458489 | − | 0.264709i | ||||
\(879\) | 22401.0i | 0.859574i | ||||||||
\(880\) | 3170.87 | − | 5492.10i | 0.121466 | − | 0.210385i | ||||
\(881\) | −1469.04 | − | 2544.45i | −0.0561783 | − | 0.0973037i | 0.836569 | − | 0.547862i | \(-0.184558\pi\) |
−0.892747 | + | 0.450559i | \(0.851225\pi\) | |||||||
\(882\) | 8616.36 | − | 4974.66i | 0.328943 | − | 0.189916i | ||||
\(883\) | −3022.06 | −0.115176 | −0.0575881 | − | 0.998340i | \(-0.518341\pi\) | ||||
−0.0575881 | + | 0.998340i | \(0.518341\pi\) | |||||||
\(884\) | 7798.16 | + | 4674.58i | 0.296697 | + | 0.177854i | ||||
\(885\) | 15907.8 | 0.604219 | ||||||||
\(886\) | −15308.8 | + | 8838.51i | −0.580483 | + | 0.335142i | ||||
\(887\) | 5030.22 | + | 8712.59i | 0.190415 | + | 0.329809i | 0.945388 | − | 0.325948i | \(-0.105683\pi\) |
−0.754973 | + | 0.655756i | \(0.772350\pi\) | |||||||
\(888\) | 8274.85 | − | 14332.5i | 0.312709 | − | 0.541628i | ||||
\(889\) | − | 68681.5i | − | 2.59112i | ||||||
\(890\) | −7156.74 | − | 4131.94i | −0.269544 | − | 0.155621i | ||||
\(891\) | −1968.61 | − | 1136.57i | −0.0740188 | − | 0.0427348i | ||||
\(892\) | 3514.24i | 0.131912i | ||||||||
\(893\) | −1941.57 | + | 3362.89i | −0.0727570 | + | 0.126019i | ||||
\(894\) | 1310.64 | + | 2270.09i | 0.0490317 | + | 0.0849254i | ||||
\(895\) | −40700.9 | + | 23498.7i | −1.52009 | + | 0.877624i | ||||
\(896\) | 8571.24 | 0.319582 | ||||||||
\(897\) | 370.637 | − | 22578.9i | 0.0137962 | − | 0.840453i | ||||
\(898\) | −13320.5 | −0.494999 | ||||||||
\(899\) | −27129.5 | + | 15663.2i | −1.00647 | + | 0.581088i | ||||
\(900\) | 361.617 | + | 626.339i | 0.0133932 | + | 0.0231978i | ||||
\(901\) | −3776.42 | + | 6540.95i | −0.139635 | + | 0.241854i | ||||
\(902\) | 16958.9i | 0.626020i | ||||||||
\(903\) | 14841.9 | + | 8568.96i | 0.546962 | + | 0.315788i | ||||
\(904\) | 2560.91 | + | 1478.54i | 0.0942197 | + | 0.0543978i | ||||
\(905\) | − | 29928.4i | − | 1.09929i | ||||||
\(906\) | 4906.99 | − | 8499.15i | 0.179938 | − | 0.311662i | ||||
\(907\) | −21579.3 | − | 37376.5i | −0.789999 | − | 1.36832i | −0.925967 | − | 0.377606i | \(-0.876748\pi\) |
0.135967 | − | 0.990713i | \(-0.456586\pi\) | |||||||
\(908\) | 4431.76 | − | 2558.68i | 0.161975 | − | 0.0935163i | ||||
\(909\) | 7056.02 | 0.257462 | ||||||||
\(910\) | 16705.7 | + | 30064.1i | 0.608558 | + | 1.09518i | ||||
\(911\) | −32665.9 | −1.18800 | −0.594001 | − | 0.804464i | \(-0.702453\pi\) | ||||
−0.594001 | + | 0.804464i | \(0.702453\pi\) | |||||||
\(912\) | 5109.33 | − | 2949.87i | 0.185512 | − | 0.107105i | ||||
\(913\) | −20529.7 | − | 35558.4i | −0.744176 | − | 1.28895i | ||||
\(914\) | 1583.99 | − | 2743.55i | 0.0573235 | − | 0.0992873i | ||||
\(915\) | − | 10372.0i | − | 0.374741i | ||||||
\(916\) | −546.581 | − | 315.568i | −0.0197156 | − | 0.0113828i | ||||
\(917\) | 37194.4 | + | 21474.2i | 1.33944 | + | 0.773327i | ||||
\(918\) | − | 2793.18i | − | 0.100423i | ||||||
\(919\) | −9494.97 | + | 16445.8i | −0.340816 | + | 0.590311i | −0.984585 | − | 0.174909i | \(-0.944037\pi\) |
0.643768 | + | 0.765221i | \(0.277370\pi\) | |||||||
\(920\) | 23437.6 | + | 40595.2i | 0.839909 | + | 1.45476i | ||||
\(921\) | −10303.9 | + | 5948.98i | −0.368650 | + | 0.212840i | ||||
\(922\) | 15860.6 | 0.566529 | ||||||||
\(923\) | −4814.47 | − | 79.0305i | −0.171690 | − | 0.00281833i | ||||
\(924\) | −9586.91 | −0.341327 | ||||||||
\(925\) | 4150.10 | − | 2396.06i | 0.147518 | − | 0.0851698i | ||||
\(926\) | −2046.86 | − | 3545.27i | −0.0726393 | − | 0.125815i | ||||
\(927\) | 1782.18 | − | 3086.83i | 0.0631440 | − | 0.109369i | ||||
\(928\) | − | 21726.0i | − | 0.768525i | ||||||
\(929\) | −4846.98 | − | 2798.40i | −0.171178 | − | 0.0988295i | 0.411963 | − | 0.911200i | \(-0.364843\pi\) |
−0.583141 | + | 0.812371i | \(0.698177\pi\) | |||||||
\(930\) | −14334.2 | − | 8275.84i | −0.505415 | − | 0.291802i | ||||
\(931\) | 56917.6i | 2.00365i | ||||||||
\(932\) | −8124.55 | + | 14072.1i | −0.285546 | + | 0.494579i | ||||
\(933\) | 11058.4 | + | 19153.8i | 0.388035 | + | 0.672097i | ||||
\(934\) | 33028.1 | − | 19068.8i | 1.15708 | − | 0.668040i | ||||
\(935\) | 17176.1 | 0.600770 | ||||||||
\(936\) | −10189.7 | − | 167.267i | −0.355836 | − | 0.00584112i | ||||
\(937\) | 40294.4 | 1.40487 | 0.702433 | − | 0.711750i | \(-0.252097\pi\) | ||||
0.702433 | + | 0.711750i | \(0.252097\pi\) | |||||||
\(938\) | 28249.9 | − | 16310.1i | 0.983360 | − | 0.567743i | ||||
\(939\) | −12374.3 | − | 21432.9i | −0.430054 | − | 0.744875i | ||||
\(940\) | −854.314 | + | 1479.72i | −0.0296432 | + | 0.0513436i | ||||
\(941\) | − | 43648.8i | − | 1.51213i | −0.654499 | − | 0.756063i | \(-0.727120\pi\) | ||
0.654499 | − | 0.756063i | \(-0.272880\pi\) | |||||||
\(942\) | −3875.15 | − | 2237.32i | −0.134033 | − | 0.0773840i | ||||
\(943\) | −41153.1 | − | 23759.8i | −1.42113 | − | 0.820492i | ||||
\(944\) | − | 8208.10i | − | 0.282999i | ||||||
\(945\) | −4850.54 | + | 8401.39i | −0.166972 | + | 0.289203i | ||||
\(946\) | 5504.98 | + | 9534.90i | 0.189199 | + | 0.327702i | ||||
\(947\) | −9081.62 | + | 5243.28i | −0.311629 | + | 0.179919i | −0.647655 | − | 0.761933i | \(-0.724250\pi\) |
0.336026 | + | 0.941853i | \(0.390917\pi\) | |||||||
\(948\) | 201.640 | 0.00690819 | ||||||||
\(949\) | 1719.36 | + | 3094.22i | 0.0588122 | + | 0.105840i | ||||
\(950\) | 4506.44 | 0.153903 | ||||||||
\(951\) | 14485.0 | − | 8362.90i | 0.493909 | − | 0.285158i | ||||
\(952\) | −18195.5 | − | 31515.5i | −0.619452 | − | 1.07292i | ||||
\(953\) | 16529.4 | − | 28629.7i | 0.561846 | − | 0.973145i | −0.435490 | − | 0.900194i | \(-0.643425\pi\) |
0.997335 | − | 0.0729517i | \(-0.0232419\pi\) | |||||||
\(954\) | − | 2740.52i | − | 0.0930059i | ||||||
\(955\) | 23823.9 | + | 13754.7i | 0.807249 | + | 0.466065i | ||||
\(956\) | −8260.93 | − | 4769.45i | −0.279475 | − | 0.161355i | ||||
\(957\) | 11795.5i | 0.398428i | ||||||||
\(958\) | −9509.73 | + | 16471.3i | −0.320715 | + | 0.555495i | ||||
\(959\) | −10942.1 | − | 18952.3i | −0.368445 | − | 0.638166i | ||||
\(960\) | 14638.1 | − | 8451.31i | 0.492128 | − | 0.284130i | ||||
\(961\) | −20202.8 | −0.678152 | ||||||||
\(962\) | −358.769 | + | 21855.9i | −0.0120241 | + | 0.732497i | ||||
\(963\) | −12929.3 | −0.432650 | ||||||||
\(964\) | 9674.74 | − | 5585.71i | 0.323239 | − | 0.186622i | ||||
\(965\) | −23696.2 | − | 41043.1i | −0.790476 | − | 1.36914i | ||||
\(966\) | −14629.3 | + | 25338.7i | −0.487258 | + | 0.843955i | ||||
\(967\) | 53634.9i | 1.78364i | 0.452389 | + | 0.891821i | \(0.350572\pi\) | ||||
−0.452389 | + | 0.891821i | \(0.649428\pi\) | |||||||
\(968\) | 11369.5 | + | 6564.21i | 0.377511 | + | 0.217956i | ||||
\(969\) | 13838.3 | + | 7989.53i | 0.458771 | + | 0.264872i | ||||
\(970\) | − | 18475.8i | − | 0.611569i | ||||||
\(971\) | 2043.40 | − | 3539.27i | 0.0675344 | − | 0.116973i | −0.830281 | − | 0.557345i | \(-0.811820\pi\) |
0.897815 | + | 0.440372i | \(0.145153\pi\) | |||||||
\(972\) | −465.253 | − | 805.842i | −0.0153529 | − | 0.0265920i | ||||
\(973\) | −38762.3 | + | 22379.4i | −1.27715 | + | 0.737360i | ||||
\(974\) | −7223.00 | −0.237618 | ||||||||
\(975\) | −2531.02 | − | 1517.21i | −0.0831361 | − | 0.0498356i | ||||
\(976\) | −5351.76 | −0.175518 | ||||||||
\(977\) | −12454.3 | + | 7190.48i | −0.407827 | + | 0.235459i | −0.689856 | − | 0.723947i | \(-0.742326\pi\) |
0.282028 | + | 0.959406i | \(0.408993\pi\) | |||||||
\(978\) | −5815.37 | − | 10072.5i | −0.190138 | − | 0.329329i | ||||
\(979\) | −4699.32 | + | 8139.46i | −0.153413 | + | 0.265718i | ||||
\(980\) | 25044.5i | 0.816343i | ||||||||
\(981\) | −15416.3 | − | 8900.63i | −0.501739 | − | 0.289679i | ||||
\(982\) | 5945.76 | + | 3432.79i | 0.193215 | + | 0.111553i | ||||
\(983\) | − | 12916.5i | − | 0.419099i | −0.977798 | − | 0.209549i | \(-0.932800\pi\) | ||
0.977798 | − | 0.209549i | \(-0.0671997\pi\) | |||||||
\(984\) | −10722.7 | + | 18572.2i | −0.347385 | + | 0.601688i | ||||
\(985\) | −30588.1 | − | 52980.1i | −0.989460 | − | 1.71379i | ||||
\(986\) | −12552.2 | + | 7247.00i | −0.405418 | + | 0.234068i | ||||
\(987\) | −3294.59 | −0.106249 | ||||||||
\(988\) | 9703.27 | − | 16187.0i | 0.312451 | − | 0.521233i | ||||
\(989\) | −30850.3 | −0.991893 | ||||||||
\(990\) | −5397.33 | + | 3116.15i | −0.173271 | + | 0.100038i | ||||
\(991\) | 2919.49 | + | 5056.71i | 0.0935829 | + | 0.162090i | 0.909016 | − | 0.416761i | \(-0.136835\pi\) |
−0.815433 | + | 0.578851i | \(0.803501\pi\) | |||||||
\(992\) | 17336.2 | − | 30027.2i | 0.554865 | − | 0.961055i | ||||
\(993\) | 12472.1i | 0.398580i | ||||||||
\(994\) | 5402.95 | + | 3119.40i | 0.172406 | + | 0.0995385i | ||||
\(995\) | −34217.0 | − | 19755.2i | −1.09020 | − | 0.629428i | ||||
\(996\) | − | 16807.5i | − | 0.534705i | ||||||
\(997\) | −22145.1 | + | 38356.4i | −0.703452 | + | 1.21841i | 0.263796 | + | 0.964579i | \(0.415026\pi\) |
−0.967247 | + | 0.253835i | \(0.918308\pi\) | |||||||
\(998\) | −4112.50 | − | 7123.05i | −0.130440 | − | 0.225928i | ||||
\(999\) | −5339.48 | + | 3082.75i | −0.169103 | + | 0.0976315i |
(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 | 39.4.j.c.10.2 | yes | 10 | |
3.2 | odd | 2 | 117.4.q.e.10.4 | 10 | |||
4.3 | odd | 2 | 624.4.bv.h.49.2 | 10 | |||
13.2 | odd | 12 | 507.4.a.r.1.4 | 10 | |||
13.3 | even | 3 | 507.4.b.i.337.4 | 10 | |||
13.4 | even | 6 | inner | 39.4.j.c.4.2 | ✓ | 10 | |
13.10 | even | 6 | 507.4.b.i.337.7 | 10 | |||
13.11 | odd | 12 | 507.4.a.r.1.7 | 10 | |||
39.2 | even | 12 | 1521.4.a.bk.1.7 | 10 | |||
39.11 | even | 12 | 1521.4.a.bk.1.4 | 10 | |||
39.17 | odd | 6 | 117.4.q.e.82.4 | 10 | |||
52.43 | odd | 6 | 624.4.bv.h.433.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.2 | ✓ | 10 | 13.4 | even | 6 | inner | |
39.4.j.c.10.2 | yes | 10 | 1.1 | even | 1 | trivial | |
117.4.q.e.10.4 | 10 | 3.2 | odd | 2 | |||
117.4.q.e.82.4 | 10 | 39.17 | odd | 6 | |||
507.4.a.r.1.4 | 10 | 13.2 | odd | 12 | |||
507.4.a.r.1.7 | 10 | 13.11 | odd | 12 | |||
507.4.b.i.337.4 | 10 | 13.3 | even | 3 | |||
507.4.b.i.337.7 | 10 | 13.10 | even | 6 | |||
624.4.bv.h.49.2 | 10 | 4.3 | odd | 2 | |||
624.4.bv.h.433.4 | 10 | 52.43 | odd | 6 | |||
1521.4.a.bk.1.4 | 10 | 39.11 | even | 12 | |||
1521.4.a.bk.1.7 | 10 | 39.2 | even | 12 |