Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,4,Mod(2,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.2");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.d (of order \(8\), degree \(4\), 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: | \(1.00303247010\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 9.2 | ||
Root | \(0.705468i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.9 |
Dual form | 17.4.d.a.2.2 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.20595 | + | 1.20595i | −0.426367 | + | 0.426367i | −0.887389 | − | 0.461022i | \(-0.847483\pi\) |
0.461022 | + | 0.887389i | \(0.347483\pi\) | |||||||
\(3\) | 4.10553 | + | 1.70057i | 0.790110 | + | 0.327274i | 0.740988 | − | 0.671519i | \(-0.234358\pi\) |
0.0491220 | + | 0.998793i | \(0.484358\pi\) | |||||||
\(4\) | 5.09138i | 0.636422i | ||||||||
\(5\) | 2.60601 | − | 6.29147i | 0.233089 | − | 0.562726i | −0.763449 | − | 0.645868i | \(-0.776496\pi\) |
0.996538 | + | 0.0831423i | \(0.0264956\pi\) | |||||||
\(6\) | −7.00185 | + | 2.90026i | −0.476416 | + | 0.197338i | ||||
\(7\) | −5.31013 | − | 12.8198i | −0.286720 | − | 0.692203i | 0.713242 | − | 0.700918i | \(-0.247226\pi\) |
−0.999962 | + | 0.00871466i | \(0.997226\pi\) | |||||||
\(8\) | −15.7875 | − | 15.7875i | −0.697716 | − | 0.697716i | ||||
\(9\) | −5.12843 | − | 5.12843i | −0.189942 | − | 0.189942i | ||||
\(10\) | 4.44447 | + | 10.7299i | 0.140546 | + | 0.339309i | ||||
\(11\) | 28.4888 | − | 11.8005i | 0.780882 | − | 0.323452i | 0.0436106 | − | 0.999049i | \(-0.486114\pi\) |
0.737271 | + | 0.675597i | \(0.236114\pi\) | |||||||
\(12\) | −8.65823 | + | 20.9028i | −0.208285 | + | 0.502844i | ||||
\(13\) | 66.0130i | 1.40836i | 0.710021 | + | 0.704181i | \(0.248686\pi\) | ||||
−0.710021 | + | 0.704181i | \(0.751314\pi\) | |||||||
\(14\) | 21.8637 | + | 9.05625i | 0.417380 | + | 0.172885i | ||||
\(15\) | 21.3981 | − | 21.3981i | 0.368331 | − | 0.368331i | ||||
\(16\) | −2.65318 | −0.0414559 | ||||||||
\(17\) | 3.91802 | − | 69.9832i | 0.0558976 | − | 0.998437i | ||||
\(18\) | 12.3692 | 0.161970 | ||||||||
\(19\) | −56.3670 | + | 56.3670i | −0.680604 | + | 0.680604i | −0.960136 | − | 0.279532i | \(-0.909821\pi\) |
0.279532 | + | 0.960136i | \(0.409821\pi\) | |||||||
\(20\) | 32.0322 | + | 13.2682i | 0.358131 | + | 0.148343i | ||||
\(21\) | − | 61.6622i | − | 0.640752i | ||||||
\(22\) | −20.1253 | + | 48.5868i | −0.195033 | + | 0.470852i | ||||
\(23\) | −26.6989 | + | 11.0590i | −0.242048 | + | 0.100259i | −0.500410 | − | 0.865789i | \(-0.666817\pi\) |
0.258362 | + | 0.966048i | \(0.416817\pi\) | |||||||
\(24\) | −37.9684 | − | 91.6639i | −0.322928 | − | 0.779617i | ||||
\(25\) | 55.5971 | + | 55.5971i | 0.444777 | + | 0.444777i | ||||
\(26\) | −79.6082 | − | 79.6082i | −0.600479 | − | 0.600479i | ||||
\(27\) | −58.2490 | − | 140.625i | −0.415186 | − | 1.00235i | ||||
\(28\) | 65.2704 | − | 27.0359i | 0.440534 | − | 0.182475i | ||||
\(29\) | −101.871 | + | 245.938i | −0.652308 | + | 1.57481i | 0.157113 | + | 0.987581i | \(0.449781\pi\) |
−0.809421 | + | 0.587229i | \(0.800219\pi\) | |||||||
\(30\) | 51.6100i | 0.314089i | ||||||||
\(31\) | −33.0662 | − | 13.6965i | −0.191576 | − | 0.0793534i | 0.284833 | − | 0.958577i | \(-0.408062\pi\) |
−0.476409 | + | 0.879224i | \(0.658062\pi\) | |||||||
\(32\) | 129.500 | − | 129.500i | 0.715392 | − | 0.715392i | ||||
\(33\) | 137.029 | 0.722840 | ||||||||
\(34\) | 79.6712 | + | 89.1210i | 0.401867 | + | 0.449533i | ||||
\(35\) | −94.4935 | −0.456352 | ||||||||
\(36\) | 26.1108 | − | 26.1108i | 0.120883 | − | 0.120883i | ||||
\(37\) | 330.633 | + | 136.953i | 1.46907 | + | 0.608510i | 0.966648 | − | 0.256110i | \(-0.0824409\pi\) |
0.502426 | + | 0.864620i | \(0.332441\pi\) | |||||||
\(38\) | − | 135.951i | − | 0.580374i | ||||||
\(39\) | −112.259 | + | 271.018i | −0.460920 | + | 1.11276i | ||||
\(40\) | −140.469 | + | 58.1842i | −0.555253 | + | 0.229993i | ||||
\(41\) | 12.5311 | + | 30.2527i | 0.0477323 | + | 0.115236i | 0.945947 | − | 0.324321i | \(-0.105136\pi\) |
−0.898215 | + | 0.439556i | \(0.855136\pi\) | |||||||
\(42\) | 74.3614 | + | 74.3614i | 0.273196 | + | 0.273196i | ||||
\(43\) | −364.978 | − | 364.978i | −1.29439 | − | 1.29439i | −0.932045 | − | 0.362342i | \(-0.881977\pi\) |
−0.362342 | − | 0.932045i | \(-0.618023\pi\) | |||||||
\(44\) | 60.0806 | + | 145.047i | 0.205852 | + | 0.496971i | ||||
\(45\) | −45.6301 | + | 18.9006i | −0.151158 | + | 0.0626119i | ||||
\(46\) | 18.8608 | − | 45.5340i | 0.0604538 | − | 0.145948i | ||||
\(47\) | − | 210.602i | − | 0.653606i | −0.945093 | − | 0.326803i | \(-0.894029\pi\) | ||
0.945093 | − | 0.326803i | \(-0.105971\pi\) | |||||||
\(48\) | −10.8927 | − | 4.51190i | −0.0327547 | − | 0.0135674i | ||||
\(49\) | 106.388 | − | 106.388i | 0.310170 | − | 0.310170i | ||||
\(50\) | −134.094 | −0.379276 | ||||||||
\(51\) | 135.097 | − | 280.655i | 0.370928 | − | 0.770581i | ||||
\(52\) | −336.097 | −0.896313 | ||||||||
\(53\) | 61.6826 | − | 61.6826i | 0.159863 | − | 0.159863i | −0.622643 | − | 0.782506i | \(-0.713941\pi\) |
0.782506 | + | 0.622643i | \(0.213941\pi\) | |||||||
\(54\) | 239.832 | + | 99.3418i | 0.604390 | + | 0.250346i | ||||
\(55\) | − | 209.989i | − | 0.514815i | ||||||
\(56\) | −118.559 | + | 286.226i | −0.282912 | + | 0.683011i | ||||
\(57\) | −327.272 | + | 135.561i | −0.760496 | + | 0.315008i | ||||
\(58\) | −173.737 | − | 419.439i | −0.393324 | − | 0.949569i | ||||
\(59\) | 219.718 | + | 219.718i | 0.484828 | + | 0.484828i | 0.906670 | − | 0.421841i | \(-0.138616\pi\) |
−0.421841 | + | 0.906670i | \(0.638616\pi\) | |||||||
\(60\) | 108.946 | + | 108.946i | 0.234414 | + | 0.234414i | ||||
\(61\) | 139.774 | + | 337.444i | 0.293381 | + | 0.708284i | 1.00000 | 0.000689814i | \(0.000219575\pi\) | |
−0.706619 | + | 0.707594i | \(0.749780\pi\) | |||||||
\(62\) | 56.3933 | − | 23.3589i | 0.115515 | − | 0.0478481i | ||||
\(63\) | −38.5127 | + | 92.9779i | −0.0770182 | + | 0.185938i | ||||
\(64\) | 291.115i | 0.568583i | ||||||||
\(65\) | 415.318 | + | 172.030i | 0.792521 | + | 0.328273i | ||||
\(66\) | −165.250 | + | 165.250i | −0.308195 | + | 0.308195i | ||||
\(67\) | 660.131 | 1.20370 | 0.601850 | − | 0.798609i | \(-0.294431\pi\) | ||||
0.601850 | + | 0.798609i | \(0.294431\pi\) | |||||||
\(68\) | 356.311 | + | 19.9481i | 0.635427 | + | 0.0355745i | ||||
\(69\) | −128.420 | −0.224056 | ||||||||
\(70\) | 113.954 | − | 113.954i | 0.194573 | − | 0.194573i | ||||
\(71\) | −367.732 | − | 152.319i | −0.614672 | − | 0.254605i | 0.0535526 | − | 0.998565i | \(-0.482946\pi\) |
−0.668225 | + | 0.743960i | \(0.732946\pi\) | |||||||
\(72\) | 161.930i | 0.265051i | ||||||||
\(73\) | 246.235 | − | 594.463i | 0.394789 | − | 0.953105i | −0.594092 | − | 0.804397i | \(-0.702489\pi\) |
0.988881 | − | 0.148708i | \(-0.0475115\pi\) | |||||||
\(74\) | −563.884 | + | 233.568i | −0.885813 | + | 0.366916i | ||||
\(75\) | 133.709 | + | 322.802i | 0.205859 | + | 0.496986i | ||||
\(76\) | −286.986 | − | 286.986i | −0.433152 | − | 0.433152i | ||||
\(77\) | −302.558 | − | 302.558i | −0.447789 | − | 0.447789i | ||||
\(78\) | −191.455 | − | 462.213i | −0.277923 | − | 0.670965i | ||||
\(79\) | −355.241 | + | 147.146i | −0.505921 | + | 0.209559i | −0.621020 | − | 0.783795i | \(-0.713282\pi\) |
0.115099 | + | 0.993354i | \(0.463282\pi\) | |||||||
\(80\) | −6.91421 | + | 16.6924i | −0.00966290 | + | 0.0233283i | ||||
\(81\) | − | 480.576i | − | 0.659226i | ||||||
\(82\) | −51.5949 | − | 21.3713i | −0.0694842 | − | 0.0287813i | ||||
\(83\) | 108.533 | − | 108.533i | 0.143530 | − | 0.143530i | −0.631690 | − | 0.775221i | \(-0.717639\pi\) |
0.775221 | + | 0.631690i | \(0.217639\pi\) | |||||||
\(84\) | 313.946 | 0.407789 | ||||||||
\(85\) | −430.087 | − | 207.027i | −0.548817 | − | 0.264179i | ||||
\(86\) | 880.289 | 1.10377 | ||||||||
\(87\) | −836.467 | + | 836.467i | −1.03079 | + | 1.03079i | ||||
\(88\) | −636.068 | − | 263.468i | −0.770512 | − | 0.319157i | ||||
\(89\) | 599.053i | 0.713477i | 0.934204 | + | 0.356738i | \(0.116111\pi\) | ||||
−0.934204 | + | 0.356738i | \(0.883889\pi\) | |||||||
\(90\) | 32.2344 | − | 77.8206i | 0.0377533 | − | 0.0911446i | ||||
\(91\) | 846.272 | − | 350.537i | 0.974872 | − | 0.403805i | ||||
\(92\) | −56.3057 | − | 135.934i | −0.0638073 | − | 0.154045i | ||||
\(93\) | −112.462 | − | 112.462i | −0.125396 | − | 0.125396i | ||||
\(94\) | 253.975 | + | 253.975i | 0.278676 | + | 0.278676i | ||||
\(95\) | 207.738 | + | 501.524i | 0.224352 | + | 0.541635i | ||||
\(96\) | 751.888 | − | 311.442i | 0.799367 | − | 0.331109i | ||||
\(97\) | −17.0560 | + | 41.1767i | −0.0178533 | + | 0.0431017i | −0.932555 | − | 0.361028i | \(-0.882426\pi\) |
0.914701 | + | 0.404130i | \(0.132426\pi\) | |||||||
\(98\) | 256.598i | 0.264492i | ||||||||
\(99\) | −206.621 | − | 85.5851i | −0.209759 | − | 0.0868851i | ||||
\(100\) | −283.066 | + | 283.066i | −0.283066 | + | 0.283066i | ||||
\(101\) | −1478.33 | −1.45643 | −0.728215 | − | 0.685348i | \(-0.759650\pi\) | ||||
−0.728215 | + | 0.685348i | \(0.759650\pi\) | |||||||
\(102\) | 175.536 | + | 501.375i | 0.170399 | + | 0.486701i | ||||
\(103\) | 618.133 | 0.591325 | 0.295662 | − | 0.955293i | \(-0.404460\pi\) | ||||
0.295662 | + | 0.955293i | \(0.404460\pi\) | |||||||
\(104\) | 1042.18 | − | 1042.18i | 0.982637 | − | 0.982637i | ||||
\(105\) | −387.946 | − | 160.692i | −0.360568 | − | 0.149352i | ||||
\(106\) | 148.772i | 0.136321i | ||||||||
\(107\) | 53.1850 | − | 128.400i | 0.0480522 | − | 0.116008i | −0.898031 | − | 0.439933i | \(-0.855002\pi\) |
0.946083 | + | 0.323924i | \(0.105002\pi\) | |||||||
\(108\) | 715.978 | − | 296.568i | 0.637916 | − | 0.264234i | ||||
\(109\) | 315.127 | + | 760.783i | 0.276914 | + | 0.668531i | 0.999747 | − | 0.0224926i | \(-0.00716024\pi\) |
−0.722833 | + | 0.691023i | \(0.757160\pi\) | |||||||
\(110\) | 253.235 | + | 253.235i | 0.219500 | + | 0.219500i | ||||
\(111\) | 1124.53 | + | 1124.53i | 0.961580 | + | 0.961580i | ||||
\(112\) | 14.0887 | + | 34.0132i | 0.0118862 | + | 0.0286959i | ||||
\(113\) | −556.614 | + | 230.557i | −0.463379 | + | 0.191938i | −0.602144 | − | 0.798387i | \(-0.705687\pi\) |
0.138765 | + | 0.990325i | \(0.455687\pi\) | |||||||
\(114\) | 231.194 | − | 558.152i | 0.189941 | − | 0.458559i | ||||
\(115\) | 196.795i | 0.159576i | ||||||||
\(116\) | −1252.16 | − | 518.663i | −1.00224 | − | 0.415143i | ||||
\(117\) | 338.543 | − | 338.543i | 0.267507 | − | 0.267507i | ||||
\(118\) | −529.937 | −0.413430 | ||||||||
\(119\) | −917.975 | + | 321.392i | −0.707148 | + | 0.247579i | ||||
\(120\) | −675.646 | −0.513982 | ||||||||
\(121\) | −268.797 | + | 268.797i | −0.201951 | + | 0.201951i | ||||
\(122\) | −575.501 | − | 238.380i | −0.427077 | − | 0.176901i | ||||
\(123\) | 145.513i | 0.106671i | ||||||||
\(124\) | 69.7339 | − | 168.352i | 0.0505023 | − | 0.121923i | ||||
\(125\) | 1281.11 | − | 530.652i | 0.916686 | − | 0.379704i | ||||
\(126\) | −65.6822 | − | 158.571i | −0.0464400 | − | 0.112116i | ||||
\(127\) | −1065.60 | − | 1065.60i | −0.744538 | − | 0.744538i | 0.228909 | − | 0.973448i | \(-0.426484\pi\) |
−0.973448 | + | 0.228909i | \(0.926484\pi\) | |||||||
\(128\) | 684.929 | + | 684.929i | 0.472967 | + | 0.472967i | ||||
\(129\) | −877.759 | − | 2119.10i | −0.599088 | − | 1.44633i | ||||
\(130\) | −708.312 | + | 293.392i | −0.477870 | + | 0.197940i | ||||
\(131\) | 1065.23 | − | 2571.69i | 0.710455 | − | 1.71519i | 0.0115939 | − | 0.999933i | \(-0.496309\pi\) |
0.698861 | − | 0.715257i | \(-0.253691\pi\) | |||||||
\(132\) | 697.667i | 0.460032i | ||||||||
\(133\) | 1021.93 | + | 423.297i | 0.666259 | + | 0.275974i | ||||
\(134\) | −796.084 | + | 796.084i | −0.513218 | + | 0.513218i | ||||
\(135\) | −1036.54 | −0.660822 | ||||||||
\(136\) | −1166.72 | + | 1043.01i | −0.735626 | + | 0.657625i | ||||
\(137\) | −629.783 | −0.392744 | −0.196372 | − | 0.980529i | \(-0.562916\pi\) | ||||
−0.196372 | + | 0.980529i | \(0.562916\pi\) | |||||||
\(138\) | 154.867 | − | 154.867i | 0.0955303 | − | 0.0955303i | ||||
\(139\) | 2452.07 | + | 1015.68i | 1.49627 | + | 0.619775i | 0.972671 | − | 0.232190i | \(-0.0745890\pi\) |
0.523599 | + | 0.851965i | \(0.324589\pi\) | |||||||
\(140\) | − | 481.102i | − | 0.290432i | ||||||
\(141\) | 358.143 | − | 864.633i | 0.213908 | − | 0.516420i | ||||
\(142\) | 627.154 | − | 259.776i | 0.370631 | − | 0.153520i | ||||
\(143\) | 778.983 | + | 1880.63i | 0.455537 | + | 1.09976i | ||||
\(144\) | 13.6066 | + | 13.6066i | 0.00787421 | + | 0.00787421i | ||||
\(145\) | 1281.83 | + | 1281.83i | 0.734141 | + | 0.734141i | ||||
\(146\) | 419.946 | + | 1013.84i | 0.238048 | + | 0.574698i | ||||
\(147\) | 617.701 | − | 255.860i | 0.346579 | − | 0.143558i | ||||
\(148\) | −697.278 | + | 1683.38i | −0.387270 | + | 0.934951i | ||||
\(149\) | − | 2216.30i | − | 1.21857i | −0.792953 | − | 0.609283i | \(-0.791457\pi\) | ||
0.792953 | − | 0.609283i | \(-0.208543\pi\) | |||||||
\(150\) | −550.529 | − | 228.036i | −0.299670 | − | 0.124127i | ||||
\(151\) | −1508.37 | + | 1508.37i | −0.812908 | + | 0.812908i | −0.985069 | − | 0.172161i | \(-0.944925\pi\) |
0.172161 | + | 0.985069i | \(0.444925\pi\) | |||||||
\(152\) | 1779.79 | 0.949737 | ||||||||
\(153\) | −378.997 | + | 338.811i | −0.200262 | + | 0.179028i | ||||
\(154\) | 729.740 | 0.381845 | ||||||||
\(155\) | −172.342 | + | 172.342i | −0.0893085 | + | 0.0893085i | ||||
\(156\) | −1379.86 | − | 571.555i | −0.708186 | − | 0.293340i | ||||
\(157\) | 345.107i | 0.175430i | 0.996146 | + | 0.0877152i | \(0.0279565\pi\) | ||||
−0.996146 | + | 0.0877152i | \(0.972043\pi\) | |||||||
\(158\) | 250.952 | − | 605.853i | 0.126359 | − | 0.305057i | ||||
\(159\) | 358.135 | − | 148.344i | 0.178629 | − | 0.0739904i | ||||
\(160\) | −477.266 | − | 1152.22i | −0.235820 | − | 0.569319i | ||||
\(161\) | 283.549 | + | 283.549i | 0.138800 | + | 0.138800i | ||||
\(162\) | 579.549 | + | 579.549i | 0.281072 | + | 0.281072i | ||||
\(163\) | 259.661 | + | 626.876i | 0.124774 | + | 0.301231i | 0.973907 | − | 0.226948i | \(-0.0728748\pi\) |
−0.849133 | + | 0.528180i | \(0.822875\pi\) | |||||||
\(164\) | −154.028 | + | 63.8004i | −0.0733387 | + | 0.0303779i | ||||
\(165\) | 357.099 | − | 862.114i | 0.168486 | − | 0.406761i | ||||
\(166\) | 261.770i | 0.122393i | ||||||||
\(167\) | −738.909 | − | 306.066i | −0.342386 | − | 0.141821i | 0.204863 | − | 0.978791i | \(-0.434325\pi\) |
−0.547249 | + | 0.836970i | \(0.684325\pi\) | |||||||
\(168\) | −973.494 | + | 973.494i | −0.447063 | + | 0.447063i | ||||
\(169\) | −2160.71 | −0.983483 | ||||||||
\(170\) | 768.326 | − | 268.998i | 0.346635 | − | 0.121360i | ||||
\(171\) | 578.148 | 0.258550 | ||||||||
\(172\) | 1858.24 | − | 1858.24i | 0.823777 | − | 0.823777i | ||||
\(173\) | −1741.96 | − | 721.542i | −0.765540 | − | 0.317097i | −0.0344756 | − | 0.999406i | \(-0.510976\pi\) |
−0.731064 | + | 0.682308i | \(0.760976\pi\) | |||||||
\(174\) | − | 2017.47i | − | 0.878989i | ||||||
\(175\) | 417.515 | − | 1007.97i | 0.180350 | − | 0.435402i | ||||
\(176\) | −75.5859 | + | 31.3087i | −0.0323722 | + | 0.0134090i | ||||
\(177\) | 528.414 | + | 1275.70i | 0.224396 | + | 0.541739i | ||||
\(178\) | −722.426 | − | 722.426i | −0.304203 | − | 0.304203i | ||||
\(179\) | −2537.71 | − | 2537.71i | −1.05965 | − | 1.05965i | −0.998104 | − | 0.0615460i | \(-0.980397\pi\) |
−0.0615460 | − | 0.998104i | \(-0.519603\pi\) | |||||||
\(180\) | −96.2301 | − | 232.320i | −0.0398476 | − | 0.0962006i | ||||
\(181\) | −426.229 | + | 176.550i | −0.175035 | + | 0.0725020i | −0.468480 | − | 0.883474i | \(-0.655198\pi\) |
0.293445 | + | 0.955976i | \(0.405198\pi\) | |||||||
\(182\) | −597.830 | + | 1443.29i | −0.243484 | + | 0.587823i | ||||
\(183\) | 1623.08i | 0.655638i | ||||||||
\(184\) | 596.103 | + | 246.914i | 0.238833 | + | 0.0989280i | ||||
\(185\) | 1723.27 | − | 1723.27i | 0.684849 | − | 0.684849i | ||||
\(186\) | 271.248 | 0.106929 | ||||||||
\(187\) | −714.214 | − | 2039.97i | −0.279297 | − | 0.797741i | ||||
\(188\) | 1072.26 | 0.415969 | ||||||||
\(189\) | −1493.48 | + | 1493.48i | −0.574786 | + | 0.574786i | ||||
\(190\) | −855.333 | − | 354.291i | −0.326592 | − | 0.135279i | ||||
\(191\) | 4519.91i | 1.71230i | 0.516728 | + | 0.856149i | \(0.327150\pi\) | ||||
−0.516728 | + | 0.856149i | \(0.672850\pi\) | |||||||
\(192\) | −495.060 | + | 1195.18i | −0.186083 | + | 0.449243i | ||||
\(193\) | −2705.97 | + | 1120.85i | −1.00922 | + | 0.418034i | −0.825171 | − | 0.564882i | \(-0.808922\pi\) |
−0.184052 | + | 0.982916i | \(0.558922\pi\) | |||||||
\(194\) | −29.0884 | − | 70.2256i | −0.0107651 | − | 0.0259892i | ||||
\(195\) | 1412.55 | + | 1412.55i | 0.518744 | + | 0.518744i | ||||
\(196\) | 541.663 | + | 541.663i | 0.197399 | + | 0.197399i | ||||
\(197\) | 737.100 | + | 1779.52i | 0.266580 | + | 0.643580i | 0.999318 | − | 0.0369306i | \(-0.0117581\pi\) |
−0.732738 | + | 0.680511i | \(0.761758\pi\) | |||||||
\(198\) | 352.385 | − | 145.963i | 0.126479 | − | 0.0523895i | ||||
\(199\) | 1181.20 | − | 2851.66i | 0.420767 | − | 1.01582i | −0.561354 | − | 0.827576i | \(-0.689720\pi\) |
0.982122 | − | 0.188247i | \(-0.0602805\pi\) | |||||||
\(200\) | − | 1755.48i | − | 0.620656i | ||||||
\(201\) | 2710.19 | + | 1122.60i | 0.951055 | + | 0.393940i | ||||
\(202\) | 1782.79 | − | 1782.79i | 0.620974 | − | 0.620974i | ||||
\(203\) | 3693.81 | 1.27712 | ||||||||
\(204\) | 1428.92 | + | 687.828i | 0.490415 | + | 0.236067i | ||||
\(205\) | 222.990 | 0.0759721 | ||||||||
\(206\) | −745.436 | + | 745.436i | −0.252121 | + | 0.252121i | ||||
\(207\) | 193.639 | + | 80.2077i | 0.0650184 | + | 0.0269315i | ||||
\(208\) | − | 175.144i | − | 0.0583849i | ||||||
\(209\) | −940.673 | + | 2270.99i | −0.311329 | + | 0.751614i | ||||
\(210\) | 661.629 | − | 274.056i | 0.217413 | − | 0.0900554i | ||||
\(211\) | −1378.58 | − | 3328.18i | −0.449787 | − | 1.08588i | −0.972402 | − | 0.233314i | \(-0.925043\pi\) |
0.522614 | − | 0.852569i | \(-0.324957\pi\) | |||||||
\(212\) | 314.050 | + | 314.050i | 0.101741 | + | 0.101741i | ||||
\(213\) | −1250.70 | − | 1250.70i | −0.402333 | − | 0.402333i | ||||
\(214\) | 90.7053 | + | 218.982i | 0.0289742 | + | 0.0699500i | ||||
\(215\) | −3247.38 | + | 1345.11i | −1.03009 | + | 0.426678i | ||||
\(216\) | −1300.52 | + | 3139.73i | −0.409672 | + | 0.989037i | ||||
\(217\) | 496.631i | 0.155362i | ||||||||
\(218\) | −1297.49 | − | 537.439i | −0.403106 | − | 0.166972i | ||||
\(219\) | 2021.85 | − | 2021.85i | 0.623853 | − | 0.623853i | ||||
\(220\) | 1069.13 | 0.327640 | ||||||||
\(221\) | 4619.80 | + | 258.640i | 1.40616 | + | 0.0787241i | ||||
\(222\) | −2712.24 | −0.819972 | ||||||||
\(223\) | −1115.41 | + | 1115.41i | −0.334948 | + | 0.334948i | −0.854462 | − | 0.519514i | \(-0.826113\pi\) |
0.519514 | + | 0.854462i | \(0.326113\pi\) | |||||||
\(224\) | −2347.82 | − | 972.498i | −0.700314 | − | 0.290079i | ||||
\(225\) | − | 570.252i | − | 0.168963i | ||||||
\(226\) | 393.208 | − | 949.287i | 0.115734 | − | 0.279405i | ||||
\(227\) | −3966.12 | + | 1642.82i | −1.15965 | + | 0.480343i | −0.877759 | − | 0.479103i | \(-0.840962\pi\) |
−0.281892 | + | 0.959446i | \(0.590962\pi\) | |||||||
\(228\) | −690.191 | − | 1666.27i | −0.200478 | − | 0.483997i | ||||
\(229\) | −410.753 | − | 410.753i | −0.118530 | − | 0.118530i | 0.645354 | − | 0.763884i | \(-0.276710\pi\) |
−0.763884 | + | 0.645354i | \(0.776710\pi\) | |||||||
\(230\) | −237.324 | − | 237.324i | −0.0680378 | − | 0.0680378i | ||||
\(231\) | −727.642 | − | 1756.68i | −0.207253 | − | 0.500352i | ||||
\(232\) | 5491.03 | − | 2274.46i | 1.55390 | − | 0.643645i | ||||
\(233\) | −257.078 | + | 620.642i | −0.0722823 | + | 0.174505i | −0.955891 | − | 0.293721i | \(-0.905106\pi\) |
0.883609 | + | 0.468225i | \(0.155106\pi\) | |||||||
\(234\) | 816.530i | 0.228112i | ||||||||
\(235\) | −1325.00 | − | 548.831i | −0.367801 | − | 0.152348i | ||||
\(236\) | −1118.67 | + | 1118.67i | −0.308556 | + | 0.308556i | ||||
\(237\) | −1708.69 | −0.468317 | ||||||||
\(238\) | 719.448 | − | 1494.61i | 0.195945 | − | 0.407064i | ||||
\(239\) | −273.635 | −0.0740584 | −0.0370292 | − | 0.999314i | \(-0.511789\pi\) | ||||
−0.0370292 | + | 0.999314i | \(0.511789\pi\) | |||||||
\(240\) | −56.7730 | + | 56.7730i | −0.0152695 | + | 0.0152695i | ||||
\(241\) | 5992.80 | + | 2482.30i | 1.60178 | + | 0.663481i | 0.991667 | − | 0.128831i | \(-0.0411223\pi\) |
0.610117 | + | 0.792311i | \(0.291122\pi\) | |||||||
\(242\) | − | 648.310i | − | 0.172211i | ||||||
\(243\) | −755.472 | + | 1823.87i | −0.199438 | + | 0.481487i | ||||
\(244\) | −1718.06 | + | 711.643i | −0.450768 | + | 0.186714i | ||||
\(245\) | −392.089 | − | 946.587i | −0.102244 | − | 0.246838i | ||||
\(246\) | −175.481 | − | 175.481i | −0.0454808 | − | 0.0454808i | ||||
\(247\) | −3720.95 | − | 3720.95i | −0.958537 | − | 0.958537i | ||||
\(248\) | 305.800 | + | 738.266i | 0.0782996 | + | 0.189032i | ||||
\(249\) | 630.152 | − | 261.017i | 0.160378 | − | 0.0664309i | ||||
\(250\) | −905.010 | + | 2184.89i | −0.228951 | + | 0.552738i | ||||
\(251\) | − | 2527.58i | − | 0.635615i | −0.948155 | − | 0.317808i | \(-0.897053\pi\) | ||
0.948155 | − | 0.317808i | \(-0.102947\pi\) | |||||||
\(252\) | −473.386 | − | 196.083i | −0.118335 | − | 0.0490161i | ||||
\(253\) | −630.117 | + | 630.117i | −0.156582 | + | 0.156582i | ||||
\(254\) | 2570.11 | 0.634893 | ||||||||
\(255\) | −1413.67 | − | 1581.35i | −0.347166 | − | 0.388344i | ||||
\(256\) | −3980.89 | −0.971898 | ||||||||
\(257\) | 1203.81 | − | 1203.81i | 0.292184 | − | 0.292184i | −0.545758 | − | 0.837943i | \(-0.683758\pi\) |
0.837943 | + | 0.545758i | \(0.183758\pi\) | |||||||
\(258\) | 3614.05 | + | 1496.99i | 0.872098 | + | 0.361235i | ||||
\(259\) | − | 4965.88i | − | 1.19137i | ||||||
\(260\) | −875.872 | + | 2114.54i | −0.208920 | + | 0.504378i | ||||
\(261\) | 1783.71 | − | 738.837i | 0.423023 | − | 0.175222i | ||||
\(262\) | 1816.72 | + | 4385.94i | 0.428386 | + | 1.03421i | ||||
\(263\) | 3022.46 | + | 3022.46i | 0.708641 | + | 0.708641i | 0.966249 | − | 0.257608i | \(-0.0829344\pi\) |
−0.257608 | + | 0.966249i | \(0.582934\pi\) | |||||||
\(264\) | −2163.35 | − | 2163.35i | −0.504337 | − | 0.504337i | ||||
\(265\) | −227.328 | − | 548.819i | −0.0526969 | − | 0.127222i | ||||
\(266\) | −1742.87 | + | 721.919i | −0.401737 | + | 0.166405i | ||||
\(267\) | −1018.73 | + | 2459.43i | −0.233503 | + | 0.563725i | ||||
\(268\) | 3360.98i | 0.766061i | ||||||||
\(269\) | 7387.65 | + | 3060.07i | 1.67447 | + | 0.693589i | 0.999039 | − | 0.0438311i | \(-0.0139563\pi\) |
0.675434 | + | 0.737420i | \(0.263956\pi\) | |||||||
\(270\) | 1250.01 | − | 1250.01i | 0.281753 | − | 0.281753i | ||||
\(271\) | −474.268 | −0.106309 | −0.0531545 | − | 0.998586i | \(-0.516928\pi\) | ||||
−0.0531545 | + | 0.998586i | \(0.516928\pi\) | |||||||
\(272\) | −10.3952 | + | 185.678i | −0.00231729 | + | 0.0413911i | ||||
\(273\) | 4070.51 | 0.902411 | ||||||||
\(274\) | 759.485 | − | 759.485i | 0.167453 | − | 0.167453i | ||||
\(275\) | 2239.97 | + | 927.825i | 0.491182 | + | 0.203454i | ||||
\(276\) | − | 653.833i | − | 0.142595i | ||||||
\(277\) | −1081.56 | + | 2611.11i | −0.234601 | + | 0.566378i | −0.996708 | − | 0.0810736i | \(-0.974165\pi\) |
0.762107 | + | 0.647451i | \(0.224165\pi\) | |||||||
\(278\) | −4181.92 | + | 1732.21i | −0.902212 | + | 0.373708i | ||||
\(279\) | 99.3362 | + | 239.819i | 0.0213158 | + | 0.0514609i | ||||
\(280\) | 1491.82 | + | 1491.82i | 0.318404 | + | 0.318404i | ||||
\(281\) | −1766.46 | − | 1766.46i | −0.375011 | − | 0.375011i | 0.494287 | − | 0.869299i | \(-0.335429\pi\) |
−0.869299 | + | 0.494287i | \(0.835429\pi\) | |||||||
\(282\) | 610.801 | + | 1474.60i | 0.128981 | + | 0.311388i | ||||
\(283\) | 2233.09 | − | 924.974i | 0.469057 | − | 0.194290i | −0.135619 | − | 0.990761i | \(-0.543302\pi\) |
0.604676 | + | 0.796471i | \(0.293302\pi\) | |||||||
\(284\) | 775.516 | − | 1872.26i | 0.162037 | − | 0.391191i | ||||
\(285\) | 2412.29i | 0.501375i | ||||||||
\(286\) | −3207.36 | − | 1328.53i | −0.663129 | − | 0.274677i | ||||
\(287\) | 321.291 | − | 321.291i | 0.0660808 | − | 0.0660808i | ||||
\(288\) | −1328.26 | −0.271766 | ||||||||
\(289\) | −4882.30 | − | 548.391i | −0.993751 | − | 0.111620i | ||||
\(290\) | −3091.65 | −0.626027 | ||||||||
\(291\) | −140.047 | + | 140.047i | −0.0282121 | + | 0.0282121i | ||||
\(292\) | 3026.64 | + | 1253.67i | 0.606577 | + | 0.251253i | ||||
\(293\) | − | 6652.17i | − | 1.32636i | −0.748459 | − | 0.663181i | \(-0.769206\pi\) | ||
0.748459 | − | 0.663181i | \(-0.230794\pi\) | |||||||
\(294\) | −436.361 | + | 1053.47i | −0.0865616 | + | 0.208978i | ||||
\(295\) | 1954.94 | − | 809.761i | 0.385833 | − | 0.159817i | ||||
\(296\) | −3057.73 | − | 7382.02i | −0.600429 | − | 1.44956i | ||||
\(297\) | −3318.89 | − | 3318.89i | −0.648423 | − | 0.648423i | ||||
\(298\) | 2672.74 | + | 2672.74i | 0.519557 | + | 0.519557i | ||||
\(299\) | −730.039 | − | 1762.47i | −0.141202 | − | 0.340891i | ||||
\(300\) | −1643.51 | + | 680.763i | −0.316293 | + | 0.131013i | ||||
\(301\) | −2740.86 | + | 6617.02i | −0.524852 | + | 1.26711i | ||||
\(302\) | − | 3638.02i | − | 0.693194i | ||||||
\(303\) | −6069.34 | − | 2514.00i | −1.15074 | − | 0.476652i | ||||
\(304\) | 149.552 | − | 149.552i | 0.0282151 | − | 0.0282151i | ||||
\(305\) | 2487.27 | 0.466954 | ||||||||
\(306\) | 48.4629 | − | 865.639i | 0.00905373 | − | 0.161717i | ||||
\(307\) | −2511.18 | −0.466842 | −0.233421 | − | 0.972376i | \(-0.574992\pi\) | ||||
−0.233421 | + | 0.972376i | \(0.574992\pi\) | |||||||
\(308\) | 1540.44 | − | 1540.44i | 0.284983 | − | 0.284983i | ||||
\(309\) | 2537.76 | + | 1051.18i | 0.467211 | + | 0.193525i | ||||
\(310\) | − | 415.670i | − | 0.0761563i | ||||||
\(311\) | 1371.96 | − | 3312.20i | 0.250150 | − | 0.603916i | −0.748066 | − | 0.663625i | \(-0.769017\pi\) |
0.998216 | + | 0.0597089i | \(0.0190172\pi\) | |||||||
\(312\) | 6051.00 | − | 2506.41i | 1.09798 | − | 0.454799i | ||||
\(313\) | −999.691 | − | 2413.47i | −0.180530 | − | 0.435838i | 0.807546 | − | 0.589804i | \(-0.200795\pi\) |
−0.988076 | + | 0.153967i | \(0.950795\pi\) | |||||||
\(314\) | −416.182 | − | 416.182i | −0.0747977 | − | 0.0747977i | ||||
\(315\) | 484.603 | + | 484.603i | 0.0866803 | + | 0.0866803i | ||||
\(316\) | −749.175 | − | 1808.67i | −0.133368 | − | 0.321980i | ||||
\(317\) | −3606.64 | + | 1493.92i | −0.639019 | + | 0.264690i | −0.678579 | − | 0.734527i | \(-0.737404\pi\) |
0.0395609 | + | 0.999217i | \(0.487404\pi\) | |||||||
\(318\) | −252.997 | + | 610.788i | −0.0446143 | + | 0.107708i | ||||
\(319\) | 8208.60i | 1.44073i | ||||||||
\(320\) | 1831.54 | + | 758.647i | 0.319956 | + | 0.132530i | ||||
\(321\) | 436.705 | − | 436.705i | 0.0759331 | − | 0.0759331i | ||||
\(322\) | −683.890 | −0.118359 | ||||||||
\(323\) | 3723.90 | + | 4165.59i | 0.641496 | + | 0.717584i | ||||
\(324\) | 2446.79 | 0.419546 | ||||||||
\(325\) | −3670.13 | + | 3670.13i | −0.626407 | + | 0.626407i | ||||
\(326\) | −1069.12 | − | 442.843i | −0.181635 | − | 0.0752355i | ||||
\(327\) | 3659.31i | 0.618839i | ||||||||
\(328\) | 279.780 | − | 675.449i | 0.0470984 | − | 0.113706i | ||||
\(329\) | −2699.87 | + | 1118.32i | −0.452428 | + | 0.187402i | ||||
\(330\) | 609.022 | + | 1470.31i | 0.101593 | + | 0.245266i | ||||
\(331\) | 4409.54 | + | 4409.54i | 0.732236 | + | 0.732236i | 0.971062 | − | 0.238826i | \(-0.0767626\pi\) |
−0.238826 | + | 0.971062i | \(0.576763\pi\) | |||||||
\(332\) | 552.581 | + | 552.581i | 0.0913459 | + | 0.0913459i | ||||
\(333\) | −993.276 | − | 2397.98i | −0.163457 | − | 0.394620i | ||||
\(334\) | 1260.19 | − | 521.986i | 0.206450 | − | 0.0855144i | ||||
\(335\) | 1720.31 | − | 4153.19i | 0.280569 | − | 0.677353i | ||||
\(336\) | 163.601i | 0.0265630i | ||||||||
\(337\) | 3549.62 | + | 1470.30i | 0.573769 | + | 0.237663i | 0.650650 | − | 0.759378i | \(-0.274496\pi\) |
−0.0768818 | + | 0.997040i | \(0.524496\pi\) | |||||||
\(338\) | 2605.71 | − | 2605.71i | 0.419325 | − | 0.419325i | ||||
\(339\) | −2677.27 | −0.428936 | ||||||||
\(340\) | 1054.05 | − | 2189.73i | 0.168130 | − | 0.349279i | ||||
\(341\) | −1103.64 | −0.175265 | ||||||||
\(342\) | −697.217 | + | 697.217i | −0.110237 | + | 0.110237i | ||||
\(343\) | −6325.99 | − | 2620.31i | −0.995836 | − | 0.412489i | ||||
\(344\) | 11524.2i | 1.80623i | ||||||||
\(345\) | −334.663 | + | 807.947i | −0.0522250 | + | 0.126082i | ||||
\(346\) | 2970.85 | − | 1230.57i | 0.461601 | − | 0.191201i | ||||
\(347\) | 3176.99 | + | 7669.92i | 0.491497 | + | 1.18658i | 0.953958 | + | 0.299940i | \(0.0969665\pi\) |
−0.462461 | + | 0.886640i | \(0.653034\pi\) | |||||||
\(348\) | −4258.77 | − | 4258.77i | −0.656017 | − | 0.656017i | ||||
\(349\) | 3485.45 | + | 3485.45i | 0.534590 | + | 0.534590i | 0.921935 | − | 0.387345i | \(-0.126608\pi\) |
−0.387345 | + | 0.921935i | \(0.626608\pi\) | |||||||
\(350\) | 712.058 | + | 1719.06i | 0.108746 | + | 0.262536i | ||||
\(351\) | 9283.10 | − | 3845.19i | 1.41167 | − | 0.584732i | ||||
\(352\) | 2161.14 | − | 5217.45i | 0.327242 | − | 0.790032i | ||||
\(353\) | − | 9607.54i | − | 1.44861i | −0.689482 | − | 0.724303i | \(-0.742162\pi\) | ||
0.689482 | − | 0.724303i | \(-0.257838\pi\) | |||||||
\(354\) | −2175.67 | − | 901.194i | −0.326655 | − | 0.135305i | ||||
\(355\) | −1916.62 | + | 1916.62i | −0.286546 | + | 0.286546i | ||||
\(356\) | −3050.00 | −0.454073 | ||||||||
\(357\) | −4315.32 | − | 241.594i | −0.639751 | − | 0.0358165i | ||||
\(358\) | 6120.69 | 0.903600 | ||||||||
\(359\) | −1387.88 | + | 1387.88i | −0.204038 | + | 0.204038i | −0.801728 | − | 0.597690i | \(-0.796085\pi\) |
0.597690 | + | 0.801728i | \(0.296085\pi\) | |||||||
\(360\) | 1018.78 | + | 421.992i | 0.149151 | + | 0.0617804i | ||||
\(361\) | 504.522i | 0.0735561i | ||||||||
\(362\) | 301.100 | − | 726.921i | 0.0437168 | − | 0.105542i | ||||
\(363\) | −1560.66 | + | 646.447i | −0.225657 | + | 0.0934702i | ||||
\(364\) | 1784.72 | + | 4308.69i | 0.256991 | + | 0.620431i | ||||
\(365\) | −3098.36 | − | 3098.36i | −0.444316 | − | 0.444316i | ||||
\(366\) | −1957.35 | − | 1957.35i | −0.279542 | − | 0.279542i | ||||
\(367\) | −1323.43 | − | 3195.04i | −0.188235 | − | 0.454441i | 0.801385 | − | 0.598149i | \(-0.204097\pi\) |
−0.989620 | + | 0.143709i | \(0.954097\pi\) | |||||||
\(368\) | 70.8368 | − | 29.3416i | 0.0100343 | − | 0.00415634i | ||||
\(369\) | 90.8840 | − | 219.413i | 0.0128218 | − | 0.0309545i | ||||
\(370\) | 4156.34i | 0.583994i | ||||||||
\(371\) | −1118.30 | − | 463.215i | −0.156494 | − | 0.0648219i | ||||
\(372\) | 572.589 | − | 572.589i | 0.0798047 | − | 0.0798047i | ||||
\(373\) | −2661.22 | −0.369418 | −0.184709 | − | 0.982793i | \(-0.559134\pi\) | ||||
−0.184709 | + | 0.982793i | \(0.559134\pi\) | |||||||
\(374\) | 3321.41 | + | 1598.80i | 0.459213 | + | 0.221048i | ||||
\(375\) | 6162.03 | 0.848549 | ||||||||
\(376\) | −3324.88 | + | 3324.88i | −0.456031 | + | 0.456031i | ||||
\(377\) | −16235.1 | − | 6724.79i | −2.21790 | − | 0.918685i | ||||
\(378\) | − | 3602.11i | − | 0.490140i | ||||||
\(379\) | 2136.53 | − | 5158.04i | 0.289568 | − | 0.699079i | −0.710421 | − | 0.703777i | \(-0.751495\pi\) |
0.999989 | + | 0.00469813i | \(0.00149547\pi\) | |||||||
\(380\) | −2553.45 | + | 1057.67i | −0.344708 | + | 0.142783i | ||||
\(381\) | −2562.72 | − | 6186.95i | −0.344599 | − | 0.831935i | ||||
\(382\) | −5450.77 | − | 5450.77i | −0.730068 | − | 0.730068i | ||||
\(383\) | 5538.16 | + | 5538.16i | 0.738868 | + | 0.738868i | 0.972359 | − | 0.233491i | \(-0.0750149\pi\) |
−0.233491 | + | 0.972359i | \(0.575015\pi\) | |||||||
\(384\) | 1647.23 | + | 3976.77i | 0.218906 | + | 0.528486i | ||||
\(385\) | −2692.01 | + | 1115.07i | −0.356357 | + | 0.147608i | ||||
\(386\) | 1911.57 | − | 4614.95i | 0.252064 | − | 0.608535i | ||||
\(387\) | 3743.53i | 0.491717i | ||||||||
\(388\) | −209.646 | − | 86.8383i | −0.0274309 | − | 0.0113622i | ||||
\(389\) | −5255.89 | + | 5255.89i | −0.685050 | + | 0.685050i | −0.961134 | − | 0.276084i | \(-0.910963\pi\) |
0.276084 | + | 0.961134i | \(0.410963\pi\) | |||||||
\(390\) | −3406.93 | −0.442350 | ||||||||
\(391\) | 669.339 | + | 1911.80i | 0.0865728 | + | 0.247273i | ||||
\(392\) | −3359.22 | −0.432821 | ||||||||
\(393\) | 8746.67 | − | 8746.67i | 1.12267 | − | 1.12267i | ||||
\(394\) | −3034.91 | − | 1257.10i | −0.388062 | − | 0.160741i | ||||
\(395\) | 2618.45i | 0.333541i | ||||||||
\(396\) | 435.746 | − | 1051.98i | 0.0552956 | − | 0.133495i | ||||
\(397\) | 8814.05 | − | 3650.90i | 1.11427 | − | 0.461545i | 0.251863 | − | 0.967763i | \(-0.418957\pi\) |
0.862406 | + | 0.506218i | \(0.168957\pi\) | |||||||
\(398\) | 2014.49 | + | 4863.41i | 0.253712 | + | 0.612514i | ||||
\(399\) | 3475.71 | + | 3475.71i | 0.436099 | + | 0.436099i | ||||
\(400\) | −147.509 | − | 147.509i | −0.0184386 | − | 0.0184386i | ||||
\(401\) | 3315.30 | + | 8003.85i | 0.412863 | + | 0.996741i | 0.984365 | + | 0.176140i | \(0.0563611\pi\) |
−0.571502 | + | 0.820601i | \(0.693639\pi\) | |||||||
\(402\) | −4622.14 | + | 1914.55i | −0.573461 | + | 0.237535i | ||||
\(403\) | 904.144 | − | 2182.80i | 0.111758 | − | 0.269808i | ||||
\(404\) | − | 7526.75i | − | 0.926905i | ||||||
\(405\) | −3023.53 | − | 1252.39i | −0.370963 | − | 0.153658i | ||||
\(406\) | −4454.55 | + | 4454.55i | −0.544521 | + | 0.544521i | ||||
\(407\) | 11035.4 | 1.34400 | ||||||||
\(408\) | −6563.69 | + | 2298.01i | −0.796449 | + | 0.278844i | ||||
\(409\) | 5279.17 | 0.638235 | 0.319117 | − | 0.947715i | \(-0.396614\pi\) | ||||
0.319117 | + | 0.947715i | \(0.396614\pi\) | |||||||
\(410\) | −268.914 | + | 268.914i | −0.0323920 | + | 0.0323920i | ||||
\(411\) | −2585.59 | − | 1070.99i | −0.310311 | − | 0.128535i | ||||
\(412\) | 3147.15i | 0.376332i | ||||||||
\(413\) | 1650.01 | − | 3983.47i | 0.196590 | − | 0.474610i | ||||
\(414\) | −330.244 | + | 136.792i | −0.0392044 | + | 0.0162390i | ||||
\(415\) | −399.993 | − | 965.668i | −0.0473129 | − | 0.114224i | ||||
\(416\) | 8548.66 | + | 8548.66i | 1.00753 | + | 1.00753i | ||||
\(417\) | 8339.80 | + | 8339.80i | 0.979381 | + | 0.979381i | ||||
\(418\) | −1604.29 | − | 3873.09i | −0.187723 | − | 0.453204i | ||||
\(419\) | −8692.08 | + | 3600.38i | −1.01345 | + | 0.419785i | −0.826713 | − | 0.562624i | \(-0.809792\pi\) |
−0.186738 | + | 0.982410i | \(0.559792\pi\) | |||||||
\(420\) | 818.146 | − | 1975.18i | 0.0950510 | − | 0.229473i | ||||
\(421\) | − | 8191.97i | − | 0.948343i | −0.880433 | − | 0.474171i | \(-0.842748\pi\) | ||
0.880433 | − | 0.474171i | \(-0.157252\pi\) | |||||||
\(422\) | 5676.10 | + | 2351.12i | 0.654759 | + | 0.271210i | ||||
\(423\) | −1080.06 | + | 1080.06i | −0.124147 | + | 0.124147i | ||||
\(424\) | −1947.63 | −0.223079 | ||||||||
\(425\) | 4108.69 | − | 3673.03i | 0.468943 | − | 0.419219i | ||||
\(426\) | 3016.57 | 0.343083 | ||||||||
\(427\) | 3583.75 | − | 3583.75i | 0.406158 | − | 0.406158i | ||||
\(428\) | 653.733 | + | 270.785i | 0.0738303 | + | 0.0305815i | ||||
\(429\) | 9045.70i | 1.01802i | ||||||||
\(430\) | 2294.04 | − | 5538.31i | 0.257276 | − | 0.621119i | ||||
\(431\) | 1801.84 | − | 746.345i | 0.201372 | − | 0.0834111i | −0.279718 | − | 0.960082i | \(-0.590241\pi\) |
0.481090 | + | 0.876671i | \(0.340241\pi\) | |||||||
\(432\) | 154.545 | + | 373.104i | 0.0172119 | + | 0.0415532i | ||||
\(433\) | −7885.88 | − | 7885.88i | −0.875223 | − | 0.875223i | 0.117813 | − | 0.993036i | \(-0.462412\pi\) |
−0.993036 | + | 0.117813i | \(0.962412\pi\) | |||||||
\(434\) | −598.911 | − | 598.911i | −0.0662411 | − | 0.0662411i | ||||
\(435\) | 3082.76 | + | 7442.44i | 0.339786 | + | 0.820317i | ||||
\(436\) | −3873.44 | + | 1604.43i | −0.425468 | + | 0.176235i | ||||
\(437\) | 881.570 | − | 2128.30i | 0.0965016 | − | 0.232976i | ||||
\(438\) | 4876.49i | 0.531981i | ||||||||
\(439\) | −434.369 | − | 179.922i | −0.0472240 | − | 0.0195608i | 0.358946 | − | 0.933358i | \(-0.383136\pi\) |
−0.406170 | + | 0.913797i | \(0.633136\pi\) | |||||||
\(440\) | −3315.20 | + | 3315.20i | −0.359195 | + | 0.359195i | ||||
\(441\) | −1091.21 | −0.117829 | ||||||||
\(442\) | −5883.14 | + | 5259.33i | −0.633105 | + | 0.565975i | ||||
\(443\) | −13132.9 | −1.40849 | −0.704246 | − | 0.709956i | \(-0.748715\pi\) | ||||
−0.704246 | + | 0.709956i | \(0.748715\pi\) | |||||||
\(444\) | −5725.39 | + | 5725.39i | −0.611971 | + | 0.611971i | ||||
\(445\) | 3768.92 | + | 1561.14i | 0.401492 | + | 0.166303i | ||||
\(446\) | − | 2690.25i | − | 0.285621i | ||||||
\(447\) | 3768.97 | − | 9099.09i | 0.398805 | − | 0.962801i | ||||
\(448\) | 3732.02 | − | 1545.86i | 0.393575 | − | 0.163024i | ||||
\(449\) | 3992.55 | + | 9638.87i | 0.419644 | + | 1.01311i | 0.982451 | + | 0.186522i | \(0.0597214\pi\) |
−0.562807 | + | 0.826588i | \(0.690279\pi\) | |||||||
\(450\) | 687.694 | + | 687.694i | 0.0720404 | + | 0.0720404i | ||||
\(451\) | 713.990 | + | 713.990i | 0.0745465 | + | 0.0745465i | ||||
\(452\) | −1173.85 | − | 2833.93i | −0.122154 | − | 0.294905i | ||||
\(453\) | −8757.72 | + | 3627.57i | −0.908330 | + | 0.376243i | ||||
\(454\) | 2801.78 | − | 6764.09i | 0.289634 | − | 0.699239i | ||||
\(455\) | − | 6237.79i | − | 0.642708i | ||||||
\(456\) | 7306.98 | + | 3026.65i | 0.750397 | + | 0.310824i | ||||
\(457\) | 179.170 | − | 179.170i | 0.0183397 | − | 0.0183397i | −0.697877 | − | 0.716217i | \(-0.745872\pi\) |
0.716217 | + | 0.697877i | \(0.245872\pi\) | |||||||
\(458\) | 990.694 | 0.101074 | ||||||||
\(459\) | −10069.6 | + | 3525.48i | −1.02399 | + | 0.358508i | ||||
\(460\) | −1001.96 | −0.101558 | ||||||||
\(461\) | 11002.7 | − | 11002.7i | 1.11160 | − | 1.11160i | 0.118665 | − | 0.992934i | \(-0.462139\pi\) |
0.992934 | − | 0.118665i | \(-0.0378613\pi\) | |||||||
\(462\) | 2995.97 | + | 1240.97i | 0.301699 | + | 0.124968i | ||||
\(463\) | − | 10727.9i | − | 1.07682i | −0.842684 | − | 0.538409i | \(-0.819026\pi\) | ||
0.842684 | − | 0.538409i | \(-0.180974\pi\) | |||||||
\(464\) | 270.281 | − | 652.516i | 0.0270420 | − | 0.0652852i | ||||
\(465\) | −1000.63 | + | 414.475i | −0.0997918 | + | 0.0413351i | ||||
\(466\) | −438.439 | − | 1058.49i | −0.0435843 | − | 0.105222i | ||||
\(467\) | 1386.27 | + | 1386.27i | 0.137364 | + | 0.137364i | 0.772445 | − | 0.635081i | \(-0.219033\pi\) |
−0.635081 | + | 0.772445i | \(0.719033\pi\) | |||||||
\(468\) | 1723.65 | + | 1723.65i | 0.170247 | + | 0.170247i | ||||
\(469\) | −3505.38 | − | 8462.74i | −0.345125 | − | 0.833205i | ||||
\(470\) | 2259.74 | − | 936.014i | 0.221774 | − | 0.0918619i | ||||
\(471\) | −586.878 | + | 1416.85i | −0.0574138 | + | 0.138609i | ||||
\(472\) | − | 6937.61i | − | 0.676545i | ||||||
\(473\) | −14704.7 | − | 6090.89i | −1.42944 | − | 0.592092i | ||||
\(474\) | 2060.59 | − | 2060.59i | 0.199675 | − | 0.199675i | ||||
\(475\) | −6267.68 | −0.605434 | ||||||||
\(476\) | −1636.33 | − | 4673.76i | −0.157565 | − | 0.450045i | ||||
\(477\) | −632.670 | −0.0607295 | ||||||||
\(478\) | 329.989 | − | 329.989i | 0.0315761 | − | 0.0315761i | ||||
\(479\) | −3967.31 | − | 1643.31i | −0.378436 | − | 0.156754i | 0.185353 | − | 0.982672i | \(-0.440657\pi\) |
−0.563790 | + | 0.825918i | \(0.690657\pi\) | |||||||
\(480\) | − | 5542.10i | − | 0.527002i | ||||||
\(481\) | −9040.65 | + | 21826.1i | −0.857002 | + | 2.06899i | ||||
\(482\) | −10220.5 | + | 4233.48i | −0.965834 | + | 0.400062i | ||||
\(483\) | 681.924 | + | 1646.31i | 0.0642415 | + | 0.155093i | ||||
\(484\) | −1368.55 | − | 1368.55i | −0.128526 | − | 0.128526i | ||||
\(485\) | 214.614 | + | 214.614i | 0.0200930 | + | 0.0200930i | ||||
\(486\) | −1288.43 | − | 3110.55i | −0.120256 | − | 0.290324i | ||||
\(487\) | 16642.3 | − | 6893.47i | 1.54853 | − | 0.641423i | 0.565483 | − | 0.824760i | \(-0.308690\pi\) |
0.983050 | + | 0.183337i | \(0.0586899\pi\) | |||||||
\(488\) | 3120.73 | − | 7534.10i | 0.289485 | − | 0.698878i | ||||
\(489\) | 3015.23i | 0.278841i | ||||||||
\(490\) | 1614.37 | + | 668.696i | 0.148837 | + | 0.0616502i | ||||
\(491\) | −9710.80 | + | 9710.80i | −0.892551 | + | 0.892551i | −0.994763 | − | 0.102212i | \(-0.967408\pi\) |
0.102212 | + | 0.994763i | \(0.467408\pi\) | |||||||
\(492\) | −740.862 | −0.0678875 | ||||||||
\(493\) | 16812.4 | + | 8092.83i | 1.53589 | + | 0.739316i | ||||
\(494\) | 8974.55 | 0.817377 | ||||||||
\(495\) | −1076.91 | + | 1076.91i | −0.0977850 | + | 0.0977850i | ||||
\(496\) | 87.7304 | + | 36.3391i | 0.00794196 | + | 0.00328967i | ||||
\(497\) | 5523.07i | 0.498478i | ||||||||
\(498\) | −445.157 | + | 1074.70i | −0.0400561 | + | 0.0967040i | ||||
\(499\) | 7157.95 | − | 2964.92i | 0.642152 | − | 0.265988i | −0.0377542 | − | 0.999287i | \(-0.512020\pi\) |
0.679906 | + | 0.733299i | \(0.262020\pi\) | |||||||
\(500\) | 2701.75 | + | 6522.60i | 0.241652 | + | 0.583399i | ||||
\(501\) | −2513.13 | − | 2513.13i | −0.224108 | − | 0.224108i | ||||
\(502\) | 3048.13 | + | 3048.13i | 0.271005 | + | 0.271005i | ||||
\(503\) | 7348.93 | + | 17741.9i | 0.651436 | + | 1.57271i | 0.810694 | + | 0.585470i | \(0.199090\pi\) |
−0.159258 | + | 0.987237i | \(0.550910\pi\) | |||||||
\(504\) | 2075.91 | − | 859.871i | 0.183469 | − | 0.0759954i | ||||
\(505\) | −3852.55 | + | 9300.87i | −0.339478 | + | 0.819571i | ||||
\(506\) | − | 1519.78i | − | 0.133522i | ||||||
\(507\) | −8870.87 | − | 3674.43i | −0.777059 | − | 0.321868i | ||||
\(508\) | 5425.35 | − | 5425.35i | 0.473841 | − | 0.473841i | ||||
\(509\) | −151.325 | −0.0131775 | −0.00658876 | − | 0.999978i | \(-0.502097\pi\) | ||||
−0.00658876 | + | 0.999978i | \(0.502097\pi\) | |||||||
\(510\) | 3611.83 | + | 202.209i | 0.313597 | + | 0.0175568i | ||||
\(511\) | −8928.43 | −0.772936 | ||||||||
\(512\) | −678.683 | + | 678.683i | −0.0585817 | + | 0.0585817i | ||||
\(513\) | 11210.0 | + | 4643.32i | 0.964779 | + | 0.399625i | ||||
\(514\) | 2903.45i | 0.249155i | ||||||||
\(515\) | 1610.86 | − | 3888.96i | 0.137831 | − | 0.332754i | ||||
\(516\) | 10789.1 | − | 4469.01i | 0.920475 | − | 0.381273i | ||||
\(517\) | −2485.20 | − | 5999.80i | −0.211410 | − | 0.510389i | ||||
\(518\) | 5988.59 | + | 5988.59i | 0.507961 | + | 0.507961i | ||||
\(519\) | −5924.62 | − | 5924.62i | −0.501083 | − | 0.501083i | ||||
\(520\) | −3840.91 | − | 9272.78i | −0.323914 | − | 0.781997i | ||||
\(521\) | 7897.89 | − | 3271.41i | 0.664133 | − | 0.275093i | −0.0250438 | − | 0.999686i | \(-0.507973\pi\) |
0.689176 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(522\) | −1260.06 | + | 3042.06i | −0.105654 | + | 0.255072i | ||||
\(523\) | 17874.0i | 1.49441i | 0.664593 | + | 0.747205i | \(0.268605\pi\) | ||||
−0.664593 | + | 0.747205i | \(0.731395\pi\) | |||||||
\(524\) | 13093.5 | + | 5423.49i | 1.09159 | + | 0.452150i | ||||
\(525\) | 3428.24 | − | 3428.24i | 0.284992 | − | 0.284992i | ||||
\(526\) | −7289.85 | −0.604283 | ||||||||
\(527\) | −1088.08 | + | 2260.41i | −0.0899380 | + | 0.186841i | ||||
\(528\) | −363.563 | −0.0299660 | ||||||||
\(529\) | −8012.84 | + | 8012.84i | −0.658572 | + | 0.658572i | ||||
\(530\) | 935.994 | + | 387.701i | 0.0767113 | + | 0.0317749i | ||||
\(531\) | − | 2253.62i | − | 0.184178i | ||||||
\(532\) | −2155.16 | + | 5203.03i | −0.175636 | + | 0.424022i | ||||
\(533\) | −1997.07 | + | 827.212i | −0.162294 | + | 0.0672243i | ||||
\(534\) | −1737.41 | − | 4194.48i | −0.140796 | − | 0.339911i | ||||
\(535\) | −669.223 | − | 669.223i | −0.0540805 | − | 0.0540805i | ||||
\(536\) | −10421.8 | − | 10421.8i | −0.839841 | − | 0.839841i | ||||
\(537\) | −6103.10 | − | 14734.2i | −0.490444 | − | 1.18404i | ||||
\(538\) | −12599.4 | + | 5218.85i | −1.00966 | + | 0.418216i | ||||
\(539\) | 1775.45 | − | 4286.31i | 0.141881 | − | 0.342531i | ||||
\(540\) | − | 5277.41i | − | 0.420562i | ||||||
\(541\) | −1960.69 | − | 812.146i | −0.155817 | − | 0.0645414i | 0.303412 | − | 0.952859i | \(-0.401874\pi\) |
−0.459229 | + | 0.888318i | \(0.651874\pi\) | |||||||
\(542\) | 571.942 | − | 571.942i | 0.0453266 | − | 0.0453266i | ||||
\(543\) | −2050.13 | −0.162025 | ||||||||
\(544\) | −8555.43 | − | 9570.19i | −0.674285 | − | 0.754262i | ||||
\(545\) | 5607.67 | 0.440745 | ||||||||
\(546\) | −4908.82 | + | 4908.82i | −0.384758 | + | 0.384758i | ||||
\(547\) | 262.443 | + | 108.707i | 0.0205141 | + | 0.00849724i | 0.392917 | − | 0.919574i | \(-0.371466\pi\) |
−0.372403 | + | 0.928071i | \(0.621466\pi\) | |||||||
\(548\) | − | 3206.46i | − | 0.249951i | ||||||
\(549\) | 1013.74 | − | 2447.38i | 0.0788075 | − | 0.190258i | ||||
\(550\) | −3820.19 | + | 1582.38i | −0.296170 | + | 0.122678i | ||||
\(551\) | −8120.62 | − | 19604.9i | −0.627859 | − | 1.51579i | ||||
\(552\) | 2027.43 | + | 2027.43i | 0.156328 | + | 0.156328i | ||||
\(553\) | 3772.75 | + | 3772.75i | 0.290115 | + | 0.290115i | ||||
\(554\) | −1844.56 | − | 4453.17i | −0.141459 | − | 0.341511i | ||||
\(555\) | 10005.4 | − | 4144.39i | 0.765239 | − | 0.316972i | ||||
\(556\) | −5171.21 | + | 12484.4i | −0.394439 | + | 0.952260i | ||||
\(557\) | 9915.36i | 0.754268i | 0.926159 | + | 0.377134i | \(0.123090\pi\) | ||||
−0.926159 | + | 0.377134i | \(0.876910\pi\) | |||||||
\(558\) | −409.003 | − | 169.415i | −0.0310296 | − | 0.0128529i | ||||
\(559\) | 24093.3 | − | 24093.3i | 1.82297 | − | 1.82297i | ||||
\(560\) | 250.708 | 0.0189185 | ||||||||
\(561\) | 536.883 | − | 9589.74i | 0.0404050 | − | 0.721710i | ||||
\(562\) | 4260.52 | 0.319785 | ||||||||
\(563\) | −3569.84 | + | 3569.84i | −0.267231 | + | 0.267231i | −0.827983 | − | 0.560753i | \(-0.810512\pi\) |
0.560753 | + | 0.827983i | \(0.310512\pi\) | |||||||
\(564\) | 4402.18 | + | 1823.44i | 0.328661 | + | 0.136136i | ||||
\(565\) | 4102.75i | 0.305494i | ||||||||
\(566\) | −1577.51 | + | 3808.46i | −0.117152 | + | 0.282829i | ||||
\(567\) | −6160.87 | + | 2551.92i | −0.456318 | + | 0.189013i | ||||
\(568\) | 3400.82 | + | 8210.32i | 0.251224 | + | 0.606509i | ||||
\(569\) | −7753.04 | − | 7753.04i | −0.571220 | − | 0.571220i | 0.361249 | − | 0.932469i | \(-0.382350\pi\) |
−0.932469 | + | 0.361249i | \(0.882350\pi\) | |||||||
\(570\) | −2909.10 | − | 2909.10i | −0.213770 | − | 0.213770i | ||||
\(571\) | 2586.01 | + | 6243.18i | 0.189529 | + | 0.457564i | 0.989869 | − | 0.141983i | \(-0.0453477\pi\) |
−0.800340 | + | 0.599546i | \(0.795348\pi\) | |||||||
\(572\) | −9575.01 | + | 3966.10i | −0.699915 | + | 0.289914i | ||||
\(573\) | −7686.40 | + | 18556.6i | −0.560391 | + | 1.35290i | ||||
\(574\) | 774.920i | 0.0563494i | ||||||||
\(575\) | −2099.23 | − | 869.529i | −0.152250 | − | 0.0630641i | ||||
\(576\) | 1492.96 | − | 1492.96i | 0.107998 | − | 0.107998i | ||||
\(577\) | 18050.9 | 1.30237 | 0.651187 | − | 0.758917i | \(-0.274271\pi\) | ||||
0.651187 | + | 0.758917i | \(0.274271\pi\) | |||||||
\(578\) | 6549.13 | − | 5226.47i | 0.471294 | − | 0.376111i | ||||
\(579\) | −13015.5 | −0.934209 | ||||||||
\(580\) | −6526.29 | + | 6526.29i | −0.467224 | + | 0.467224i | ||||
\(581\) | −1967.69 | − | 815.043i | −0.140505 | − | 0.0581991i | ||||
\(582\) | − | 337.780i | − | 0.0240574i | ||||||
\(583\) | 1029.38 | − | 2485.15i | 0.0731263 | − | 0.176543i | ||||
\(584\) | −13272.5 | + | 5497.67i | −0.940448 | + | 0.389546i | ||||
\(585\) | −1247.68 | − | 3012.18i | −0.0881802 | − | 0.212886i | ||||
\(586\) | 8022.17 | + | 8022.17i | 0.565517 | + | 0.565517i | ||||
\(587\) | −5265.87 | − | 5265.87i | −0.370265 | − | 0.370265i | 0.497309 | − | 0.867574i | \(-0.334322\pi\) |
−0.867574 | + | 0.497309i | \(0.834322\pi\) | |||||||
\(588\) | 1302.68 | + | 3144.95i | 0.0913633 | + | 0.220571i | ||||
\(589\) | 2635.87 | − | 1091.81i | 0.184396 | − | 0.0763792i | ||||
\(590\) | −1381.02 | + | 3334.08i | −0.0963657 | + | 0.232647i | ||||
\(591\) | 8559.34i | 0.595743i | ||||||||
\(592\) | −877.228 | − | 363.360i | −0.0609018 | − | 0.0252263i | ||||
\(593\) | 869.258 | − | 869.258i | 0.0601958 | − | 0.0601958i | −0.676368 | − | 0.736564i | \(-0.736447\pi\) |
0.736564 | + | 0.676368i | \(0.236447\pi\) | |||||||
\(594\) | 8004.82 | 0.552932 | ||||||||
\(595\) | −370.227 | + | 6612.95i | −0.0255090 | + | 0.455638i | ||||
\(596\) | 11284.0 | 0.775523 | ||||||||
\(597\) | 9698.87 | − | 9698.87i | 0.664905 | − | 0.664905i | ||||
\(598\) | 3005.84 | + | 1245.06i | 0.205548 | + | 0.0851408i | ||||
\(599\) | − | 10655.6i | − | 0.726840i | −0.931625 | − | 0.363420i | \(-0.881609\pi\) | ||
0.931625 | − | 0.363420i | \(-0.118391\pi\) | |||||||
\(600\) | 2985.31 | − | 7207.18i | 0.203125 | − | 0.490386i | ||||
\(601\) | 1972.01 | − | 816.833i | 0.133843 | − | 0.0554398i | −0.314756 | − | 0.949172i | \(-0.601923\pi\) |
0.448600 | + | 0.893733i | \(0.351923\pi\) | |||||||
\(602\) | −4674.45 | − | 11285.1i | −0.316472 | − | 0.764032i | ||||
\(603\) | −3385.44 | − | 3385.44i | −0.228633 | − | 0.228633i | ||||
\(604\) | −7679.66 | − | 7679.66i | −0.517353 | − | 0.517353i | ||||
\(605\) | 990.639 | + | 2391.62i | 0.0665706 | + | 0.160716i | ||||
\(606\) | 10351.1 | − | 4287.55i | 0.693866 | − | 0.287409i | ||||
\(607\) | −4731.84 | + | 11423.7i | −0.316407 | + | 0.763875i | 0.683032 | + | 0.730389i | \(0.260661\pi\) |
−0.999439 | + | 0.0334863i | \(0.989339\pi\) | |||||||
\(608\) | 14599.0i | 0.973797i | ||||||||
\(609\) | 15165.1 | + | 6281.58i | 1.00906 | + | 0.417968i | ||||
\(610\) | −2999.52 | + | 2999.52i | −0.199094 | + | 0.199094i | ||||
\(611\) | 13902.5 | 0.920513 | ||||||||
\(612\) | −1725.01 | − | 1929.62i | −0.113937 | − | 0.127451i | ||||
\(613\) | 4888.87 | 0.322120 | 0.161060 | − | 0.986945i | \(-0.448509\pi\) | ||||
0.161060 | + | 0.986945i | \(0.448509\pi\) | |||||||
\(614\) | 3028.35 | − | 3028.35i | 0.199046 | − | 0.199046i | ||||
\(615\) | 915.491 | + | 379.209i | 0.0600263 | + | 0.0248637i | ||||
\(616\) | 9553.30i | 0.624859i | ||||||||
\(617\) | −9471.41 | + | 22866.0i | −0.617998 | + | 1.49198i | 0.236027 | + | 0.971747i | \(0.424155\pi\) |
−0.854025 | + | 0.520232i | \(0.825845\pi\) | |||||||
\(618\) | −4328.07 | + | 1792.75i | −0.281716 | + | 0.116691i | ||||
\(619\) | −4131.00 | − | 9973.11i | −0.268237 | − | 0.647582i | 0.731163 | − | 0.682202i | \(-0.238978\pi\) |
−0.999401 | + | 0.0346207i | \(0.988978\pi\) | |||||||
\(620\) | −877.456 | − | 877.456i | −0.0568379 | − | 0.0568379i | ||||
\(621\) | 3110.36 | + | 3110.36i | 0.200990 | + | 0.200990i | ||||
\(622\) | 2339.83 | + | 5648.86i | 0.150834 | + | 0.364145i | ||||
\(623\) | 7679.72 | − | 3181.05i | 0.493871 | − | 0.204568i | ||||
\(624\) | 297.844 | − | 719.059i | 0.0191079 | − | 0.0461305i | ||||
\(625\) | 385.346i | 0.0246621i | ||||||||
\(626\) | 4116.09 | + | 1704.94i | 0.262799 | + | 0.108855i | ||||
\(627\) | −7723.92 | + | 7723.92i | −0.491968 | + | 0.491968i | ||||
\(628\) | −1757.07 | −0.111648 | ||||||||
\(629\) | 10879.8 | − | 22602.2i | 0.689677 | − | 1.43276i | ||||
\(630\) | −1168.81 | −0.0739152 | ||||||||
\(631\) | −5359.80 | + | 5359.80i | −0.338146 | + | 0.338146i | −0.855669 | − | 0.517523i | \(-0.826854\pi\) |
0.517523 | + | 0.855669i | \(0.326854\pi\) | |||||||
\(632\) | 7931.45 | + | 3285.31i | 0.499203 | + | 0.206777i | ||||
\(633\) | − | 16008.3i | − | 1.00517i | ||||||
\(634\) | 2547.83 | − | 6151.00i | 0.159601 | − | 0.385312i | ||||
\(635\) | −9481.12 | + | 3927.21i | −0.592514 | + | 0.245427i | ||||
\(636\) | 755.278 | + | 1823.40i | 0.0470892 | + | 0.113683i | ||||
\(637\) | 7023.01 | + | 7023.01i | 0.436832 | + | 0.436832i | ||||
\(638\) | −9899.14 | − | 9899.14i | −0.614280 | − | 0.614280i | ||||
\(639\) | 1104.73 | + | 2667.05i | 0.0683917 | + | 0.165112i | ||||
\(640\) | 6094.14 | − | 2524.28i | 0.376394 | − | 0.155907i | ||||
\(641\) | −1217.52 | + | 2939.35i | −0.0750219 | + | 0.181119i | −0.956941 | − | 0.290281i | \(-0.906251\pi\) |
0.881920 | + | 0.471400i | \(0.156251\pi\) | |||||||
\(642\) | 1053.29i | 0.0647507i | ||||||||
\(643\) | −9749.51 | − | 4038.38i | −0.597952 | − | 0.247680i | 0.0631154 | − | 0.998006i | \(-0.479896\pi\) |
−0.661068 | + | 0.750326i | \(0.729896\pi\) | |||||||
\(644\) | −1443.65 | + | 1443.65i | −0.0883353 | + | 0.0883353i | ||||
\(645\) | −15619.7 | −0.953526 | ||||||||
\(646\) | −9514.31 | − | 532.660i | −0.579467 | − | 0.0324415i | ||||
\(647\) | −10952.0 | −0.665483 | −0.332742 | − | 0.943018i | \(-0.607974\pi\) | ||||
−0.332742 | + | 0.943018i | \(0.607974\pi\) | |||||||
\(648\) | −7587.10 | + | 7587.10i | −0.459953 | + | 0.459953i | ||||
\(649\) | 8852.29 | + | 3666.74i | 0.535412 | + | 0.221775i | ||||
\(650\) | − | 8851.97i | − | 0.534158i | ||||||
\(651\) | −844.554 | + | 2038.93i | −0.0508459 | + | 0.122753i | ||||
\(652\) | −3191.66 | + | 1322.03i | −0.191710 | + | 0.0794090i | ||||
\(653\) | 2497.68 | + | 6029.94i | 0.149681 | + | 0.361362i | 0.980880 | − | 0.194613i | \(-0.0623450\pi\) |
−0.831199 | + | 0.555975i | \(0.812345\pi\) | |||||||
\(654\) | −4412.94 | − | 4412.94i | −0.263853 | − | 0.263853i | ||||
\(655\) | −13403.7 | − | 13403.7i | −0.799583 | − | 0.799583i | ||||
\(656\) | −33.2471 | − | 80.2657i | −0.00197878 | − | 0.00477721i | ||||
\(657\) | −4311.46 | + | 1785.87i | −0.256022 | + | 0.106048i | ||||
\(658\) | 1907.27 | − | 4604.55i | 0.112998 | − | 0.272802i | ||||
\(659\) | − | 25717.9i | − | 1.52022i | −0.649793 | − | 0.760111i | \(-0.725145\pi\) | ||
0.649793 | − | 0.760111i | \(-0.274855\pi\) | |||||||
\(660\) | 4389.35 | + | 1818.13i | 0.258872 | + | 0.107228i | ||||
\(661\) | −8350.18 | + | 8350.18i | −0.491353 | + | 0.491353i | −0.908732 | − | 0.417379i | \(-0.862949\pi\) |
0.417379 | + | 0.908732i | \(0.362949\pi\) | |||||||
\(662\) | −10635.3 | −0.624403 | ||||||||
\(663\) | 18526.9 | + | 8918.13i | 1.08526 | + | 0.522400i | ||||
\(664\) | −3426.93 | −0.200287 | ||||||||
\(665\) | 5326.31 | − | 5326.31i | 0.310595 | − | 0.310595i | ||||
\(666\) | 4089.68 | + | 1694.00i | 0.237946 | + | 0.0985603i | ||||
\(667\) | − | 7692.85i | − | 0.446579i | ||||||
\(668\) | 1558.30 | − | 3762.07i | 0.0902581 | − | 0.217902i | ||||
\(669\) | −6476.17 | + | 2682.52i | −0.374265 | + | 0.155026i | ||||
\(670\) | 2933.93 | + | 7083.14i | 0.169176 | + | 0.408426i | ||||
\(671\) | 7964.00 | + | 7964.00i | 0.458192 | + | 0.458192i | ||||
\(672\) | −7985.24 | − | 7985.24i | −0.458389 | − | 0.458389i | ||||
\(673\) | −2404.34 | − | 5804.60i | −0.137713 | − | 0.332468i | 0.839945 | − | 0.542672i | \(-0.182587\pi\) |
−0.977658 | + | 0.210204i | \(0.932587\pi\) | |||||||
\(674\) | −6053.76 | + | 2507.55i | −0.345967 | + | 0.143304i | ||||
\(675\) | 4579.89 | − | 11056.8i | 0.261156 | − | 0.630486i | ||||
\(676\) | − | 11001.0i | − | 0.625910i | ||||||
\(677\) | 17094.4 | + | 7080.72i | 0.970443 | + | 0.401970i | 0.810877 | − | 0.585217i | \(-0.198991\pi\) |
0.159566 | + | 0.987187i | \(0.448991\pi\) | |||||||
\(678\) | 3228.65 | − | 3228.65i | 0.182884 | − | 0.182884i | ||||
\(679\) | 618.446 | 0.0349540 | ||||||||
\(680\) | 3521.56 | + | 10058.4i | 0.198596 | + | 0.567241i | ||||
\(681\) | −19076.8 | −1.07346 | ||||||||
\(682\) | 1330.93 | − | 1330.93i | 0.0747274 | − | 0.0747274i | ||||
\(683\) | 127.050 | + | 52.6260i | 0.00711779 | + | 0.00294828i | 0.386239 | − | 0.922399i | \(-0.373774\pi\) |
−0.379122 | + | 0.925347i | \(0.623774\pi\) | |||||||
\(684\) | 2943.57i | 0.164547i | ||||||||
\(685\) | −1641.22 | + | 3962.26i | −0.0915442 | + | 0.221007i | ||||
\(686\) | 10788.8 | − | 4468.86i | 0.600463 | − | 0.248720i | ||||
\(687\) | −987.847 | − | 2384.87i | −0.0548598 | − | 0.132443i | ||||
\(688\) | 968.352 | + | 968.352i | 0.0536600 | + | 0.0536600i | ||||
\(689\) | 4071.85 | + | 4071.85i | 0.225145 | + | 0.225145i | ||||
\(690\) | −570.756 | − | 1377.93i | −0.0314903 | − | 0.0760244i | ||||
\(691\) | −280.152 | + | 116.043i | −0.0154233 | + | 0.00638854i | −0.390382 | − | 0.920653i | \(-0.627657\pi\) |
0.374958 | + | 0.927042i | \(0.377657\pi\) | |||||||
\(692\) | 3673.64 | − | 8868.96i | 0.201808 | − | 0.487207i | ||||
\(693\) | 3103.30i | 0.170108i | ||||||||
\(694\) | −13080.8 | − | 5418.25i | −0.715476 | − | 0.296360i | ||||
\(695\) | 12780.2 | − | 12780.2i | 0.697527 | − | 0.697527i | ||||
\(696\) | 26411.5 | 1.43840 | ||||||||
\(697\) | 2166.27 | − | 758.433i | 0.117724 | − | 0.0412162i | ||||
\(698\) | −8406.54 | −0.455863 | ||||||||
\(699\) | −2110.89 | + | 2110.89i | −0.114222 | + | 0.114222i | ||||
\(700\) | 5131.96 | + | 2125.73i | 0.277100 | + | 0.114778i | ||||
\(701\) | 23434.3i | 1.26263i | 0.775528 | + | 0.631313i | \(0.217484\pi\) | ||||
−0.775528 | + | 0.631313i | \(0.782516\pi\) | |||||||
\(702\) | −6557.84 | + | 15832.0i | −0.352578 | + | 0.851199i | ||||
\(703\) | −26356.4 | + | 10917.2i | −1.41401 | + | 0.585703i | ||||
\(704\) | 3435.28 | + | 8293.51i | 0.183909 | + | 0.443996i | ||||
\(705\) | −4506.49 | − | 4506.49i | −0.240743 | − | 0.240743i | ||||
\(706\) | 11586.2 | + | 11586.2i | 0.617638 | + | 0.617638i | ||||
\(707\) | 7850.13 | + | 18951.9i | 0.417588 | + | 1.00815i | ||||
\(708\) | −6495.10 | + | 2690.36i | −0.344775 | + | 0.142810i | ||||
\(709\) | 19.9707 | − | 48.2136i | 0.00105785 | − | 0.00255388i | −0.923350 | − | 0.383960i | \(-0.874560\pi\) |
0.924408 | + | 0.381406i | \(0.124560\pi\) | |||||||
\(710\) | − | 4622.70i | − | 0.244348i | ||||||
\(711\) | 2576.46 | + | 1067.20i | 0.135900 | + | 0.0562915i | ||||
\(712\) | 9457.56 | − | 9457.56i | 0.497805 | − | 0.497805i | ||||
\(713\) | 1034.30 | 0.0543265 | ||||||||
\(714\) | 5495.40 | − | 4912.70i | 0.288039 | − | 0.257498i | ||||
\(715\) | 13862.0 | 0.725046 | ||||||||
\(716\) | 12920.4 | − | 12920.4i | 0.674385 | − | 0.674385i | ||||
\(717\) | −1123.42 | − | 465.334i | −0.0585143 | − | 0.0242374i | ||||
\(718\) | − | 3347.43i | − | 0.173990i | ||||||
\(719\) | −859.046 | + | 2073.92i | −0.0445577 | + | 0.107572i | −0.944591 | − | 0.328248i | \(-0.893542\pi\) |
0.900034 | + | 0.435820i | \(0.143542\pi\) | |||||||
\(720\) | 121.065 | − | 50.1466i | 0.00626641 | − | 0.00259563i | ||||
\(721\) | −3282.36 | − | 7924.33i | −0.169545 | − | 0.409317i | ||||
\(722\) | −608.427 | − | 608.427i | −0.0313619 | − | 0.0313619i | ||||
\(723\) | 20382.3 | + | 20382.3i | 1.04844 | + | 1.04844i | ||||
\(724\) | −898.883 | − | 2170.10i | −0.0461419 | − | 0.111396i | ||||
\(725\) | −19337.1 | + | 8009.71i | −0.990570 | + | 0.410308i | ||||
\(726\) | 1102.49 | − | 2661.66i | 0.0563601 | − | 0.136065i | ||||
\(727\) | − | 2971.90i | − | 0.151612i | −0.997123 | − | 0.0758059i | \(-0.975847\pi\) | ||
0.997123 | − | 0.0758059i | \(-0.0241529\pi\) | |||||||
\(728\) | −18894.6 | − | 7826.42i | −0.961926 | − | 0.398443i | ||||
\(729\) | −15378.3 | + | 15378.3i | −0.781299 | + | 0.781299i | ||||
\(730\) | 7472.91 | 0.378883 | ||||||||
\(731\) | −26972.3 | + | 24112.4i | −1.36472 | + | 1.22001i | ||||
\(732\) | −8263.73 | −0.417263 | ||||||||
\(733\) | 22418.7 | − | 22418.7i | 1.12968 | − | 1.12968i | 0.139447 | − | 0.990230i | \(-0.455468\pi\) |
0.990230 | − | 0.139447i | \(-0.0445324\pi\) | |||||||
\(734\) | 5449.04 | + | 2257.07i | 0.274016 | + | 0.113501i | ||||
\(735\) | − | 4553.02i | − | 0.228491i | ||||||
\(736\) | −2025.35 | + | 4889.64i | −0.101434 | + | 0.244884i | ||||
\(737\) | 18806.4 | − | 7789.85i | 0.939947 | − | 0.389339i | ||||
\(738\) | 155.000 | + | 374.202i | 0.00773119 | + | 0.0186647i | ||||
\(739\) | 26152.8 | + | 26152.8i | 1.30182 | + | 1.30182i | 0.927163 | + | 0.374657i | \(0.122240\pi\) |
0.374657 | + | 0.927163i | \(0.377760\pi\) | |||||||
\(740\) | 8773.80 | + | 8773.80i | 0.435853 | + | 0.435853i | ||||
\(741\) | −8948.76 | − | 21604.2i | −0.443645 | − | 1.07105i | ||||
\(742\) | 1907.22 | − | 789.998i | 0.0943617 | − | 0.0390859i | ||||
\(743\) | −4057.18 | + | 9794.89i | −0.200328 | + | 0.483633i | −0.991835 | − | 0.127526i | \(-0.959296\pi\) |
0.791508 | + | 0.611159i | \(0.209296\pi\) | |||||||
\(744\) | 3551.01i | 0.174981i | ||||||||
\(745\) | −13943.8 | − | 5775.70i | −0.685719 | − | 0.284034i | ||||
\(746\) | 3209.30 | − | 3209.30i | 0.157508 | − | 0.157508i | ||||
\(747\) | −1113.21 | −0.0545248 | ||||||||
\(748\) | 10386.3 | − | 3636.33i | 0.507700 | − | 0.177751i | ||||
\(749\) | −1928.48 | −0.0940789 | ||||||||
\(750\) | −7431.09 | + | 7431.09i | −0.361793 | + | 0.361793i | ||||
\(751\) | −26941.7 | − | 11159.6i | −1.30908 | − | 0.542238i | −0.384463 | − | 0.923141i | \(-0.625613\pi\) |
−0.924615 | + | 0.380903i | \(0.875613\pi\) | |||||||
\(752\) | 558.765i | 0.0270958i | ||||||||
\(753\) | 4298.32 | − | 10377.1i | 0.208020 | − | 0.502206i | ||||
\(754\) | 27688.4 | − | 11468.9i | 1.33734 | − | 0.553943i | ||||
\(755\) | 5559.01 | + | 13420.6i | 0.267965 | + | 0.646924i | ||||
\(756\) | −7603.86 | − | 7603.86i | −0.365807 | − | 0.365807i | ||||
\(757\) | −24358.4 | − | 24358.4i | −1.16951 | − | 1.16951i | −0.982325 | − | 0.187186i | \(-0.940063\pi\) |
−0.187186 | − | 0.982325i | \(-0.559937\pi\) | |||||||
\(758\) | 3643.79 | + | 8796.88i | 0.174602 | + | 0.421526i | ||||
\(759\) | −3658.52 | + | 1515.41i | −0.174962 | + | 0.0724715i | ||||
\(760\) | 4638.15 | − | 11197.5i | 0.221373 | − | 0.534442i | ||||
\(761\) | − | 14414.5i | − | 0.686632i | −0.939220 | − | 0.343316i | \(-0.888450\pi\) | ||
0.939220 | − | 0.343316i | \(-0.111550\pi\) | |||||||
\(762\) | 10551.7 | + | 4370.64i | 0.501635 | + | 0.207784i | ||||
\(763\) | 8079.71 | − | 8079.71i | 0.383362 | − | 0.383362i | ||||
\(764\) | −23012.6 | −1.08975 | ||||||||
\(765\) | 1143.94 | + | 3267.39i | 0.0540646 | + | 0.154422i | ||||
\(766\) | −13357.5 | −0.630058 | ||||||||
\(767\) | −14504.2 | + | 14504.2i | −0.682814 | + | 0.682814i | ||||
\(768\) | −16343.7 | − | 6769.77i | −0.767906 | − | 0.318077i | ||||
\(769\) | 7049.33i | 0.330566i | 0.986246 | + | 0.165283i | \(0.0528537\pi\) | ||||
−0.986246 | + | 0.165283i | \(0.947146\pi\) | |||||||
\(770\) | 1901.71 | − | 4591.13i | 0.0890037 | − | 0.214874i | ||||
\(771\) | 6989.41 | − | 2895.11i | 0.326482 | − | 0.135233i | ||||
\(772\) | −5706.67 | − | 13777.1i | −0.266046 | − | 0.642292i | ||||
\(773\) | −18928.0 | − | 18928.0i | −0.880716 | − | 0.880716i | 0.112891 | − | 0.993607i | \(-0.463989\pi\) |
−0.993607 | + | 0.112891i | \(0.963989\pi\) | |||||||
\(774\) | −4514.50 | − | 4514.50i | −0.209652 | − | 0.209652i | ||||
\(775\) | −1076.90 | − | 2599.87i | −0.0499141 | − | 0.120503i | ||||
\(776\) | 919.349 | − | 380.807i | 0.0425293 | − | 0.0176162i | ||||
\(777\) | 8444.80 | − | 20387.6i | 0.389904 | − | 0.941312i | ||||
\(778\) | − | 12676.7i | − | 0.584165i | ||||||
\(779\) | −2411.59 | − | 998.913i | −0.110917 | − | 0.0459432i | ||||
\(780\) | −7191.84 | + | 7191.84i | −0.330140 | + | 0.330140i | ||||
\(781\) | −12273.7 | −0.562339 | ||||||||
\(782\) | −3112.72 | − | 1498.34i | −0.142341 | − | 0.0685175i | ||||
\(783\) | 40519.0 | 1.84934 | ||||||||
\(784\) | −282.267 | + | 282.267i | −0.0128584 | + | 0.0128584i | ||||
\(785\) | 2171.23 | + | 899.353i | 0.0987192 | + | 0.0408908i | ||||
\(786\) | 21096.1i | 0.957343i | ||||||||
\(787\) | 9982.50 | − | 24099.9i | 0.452144 | − | 1.09157i | −0.519361 | − | 0.854555i | \(-0.673830\pi\) |
0.971505 | − | 0.237018i | \(-0.0761700\pi\) | |||||||
\(788\) | −9060.19 | + | 3752.85i | −0.409589 | + | 0.169657i | ||||
\(789\) | 7268.90 | + | 17548.7i | 0.327984 | + | 0.791824i | ||||
\(790\) | −3157.72 | − | 3157.72i | −0.142211 | − | 0.142211i | ||||
\(791\) | 5911.38 | + | 5911.38i | 0.265720 | + | 0.265720i | ||||
\(792\) | 1910.85 | + | 4613.21i | 0.0857313 | + | 0.206974i | ||||
\(793\) | −22275.7 | + | 9226.90i | −0.997520 | + | 0.413186i | ||||
\(794\) | −6226.49 | + | 15032.1i | −0.278300 | + | 0.671875i | ||||
\(795\) | − | 2639.78i | − | 0.117765i | ||||||
\(796\) | 14518.9 | + | 6013.91i | 0.646492 | + | 0.267786i | ||||
\(797\) | −12804.7 | + | 12804.7i | −0.569092 | + | 0.569092i | −0.931874 | − | 0.362782i | \(-0.881827\pi\) |
0.362782 | + | 0.931874i | \(0.381827\pi\) | |||||||
\(798\) | −8383.06 | −0.371876 | ||||||||
\(799\) | −14738.6 | − | 825.143i | −0.652584 | − | 0.0365350i | ||||
\(800\) | 14399.6 | 0.636379 | ||||||||
\(801\) | 3072.20 | − | 3072.20i | 0.135519 | − | 0.135519i | ||||
\(802\) | −13650.3 | − | 5654.14i | −0.601009 | − | 0.248946i | ||||
\(803\) | − | 19841.2i | − | 0.871958i | ||||||
\(804\) | −5715.57 | + | 13798.6i | −0.250712 | + | 0.605273i | ||||
\(805\) | 2522.87 | − | 1045.01i | 0.110459 | − | 0.0457536i | ||||
\(806\) | 1541.99 | + | 3722.69i | 0.0673874 | + | 0.162687i | ||||
\(807\) | 25126.4 | + | 25126.4i | 1.09602 | + | 1.09602i | ||||
\(808\) | 23339.2 | + | 23339.2i | 1.01618 | + | 1.01618i | ||||
\(809\) | 2795.36 | + | 6748.59i | 0.121483 | + | 0.293285i | 0.972909 | − | 0.231189i | \(-0.0742617\pi\) |
−0.851426 | + | 0.524475i | \(0.824262\pi\) | |||||||
\(810\) | 5156.53 | − | 2135.90i | 0.223681 | − | 0.0926518i | ||||
\(811\) | 7466.79 | − | 18026.4i | 0.323298 | − | 0.780510i | −0.675761 | − | 0.737121i | \(-0.736185\pi\) |
0.999058 | − | 0.0433884i | \(-0.0138153\pi\) | |||||||
\(812\) | 18806.6i | 0.812786i | ||||||||
\(813\) | −1947.12 | − | 806.524i | −0.0839957 | − | 0.0347922i | ||||
\(814\) | −13308.2 | + | 13308.2i | −0.573036 | + | 0.573036i | ||||
\(815\) | 4620.65 | 0.198594 | ||||||||
\(816\) | −358.435 | + | 744.628i | −0.0153771 | + | 0.0319451i | ||||
\(817\) | 41145.5 | 1.76193 | ||||||||
\(818\) | −6366.40 | + | 6366.40i | −0.272122 | + | 0.272122i | ||||
\(819\) | −6137.75 | − | 2542.34i | −0.261869 | − | 0.108470i | ||||
\(820\) | 1135.32i | 0.0483503i | ||||||||
\(821\) | 11237.2 | − | 27129.1i | 0.477689 | − | 1.15324i | −0.483001 | − | 0.875620i | \(-0.660453\pi\) |
0.960690 | − | 0.277623i | \(-0.0895467\pi\) | |||||||
\(822\) | 4409.64 | − | 1826.53i | 0.187109 | − | 0.0775033i | ||||
\(823\) | 10758.2 | + | 25972.5i | 0.455657 | + | 1.10005i | 0.970138 | + | 0.242552i | \(0.0779846\pi\) |
−0.514481 | + | 0.857502i | \(0.672015\pi\) | |||||||
\(824\) | −9758.78 | − | 9758.78i | −0.412577 | − | 0.412577i | ||||
\(825\) | 7618.42 | + | 7618.42i | 0.321502 | + | 0.321502i | ||||
\(826\) | 2814.03 | + | 6793.68i | 0.118538 | + | 0.286177i | ||||
\(827\) | 36364.4 | − | 15062.6i | 1.52904 | − | 0.633348i | 0.549659 | − | 0.835389i | \(-0.314757\pi\) |
0.979377 | + | 0.202041i | \(0.0647575\pi\) | |||||||
\(828\) | −408.368 | + | 985.888i | −0.0171398 | + | 0.0413792i | ||||
\(829\) | 15525.3i | 0.650443i | 0.945638 | + | 0.325221i | \(0.105439\pi\) | ||||
−0.945638 | + | 0.325221i | \(0.894561\pi\) | |||||||
\(830\) | 1646.92 | + | 682.175i | 0.0688738 | + | 0.0285285i | ||||
\(831\) | −8880.75 | + | 8880.75i | −0.370722 | + | 0.370722i | ||||
\(832\) | −19217.3 | −0.800771 | ||||||||
\(833\) | −7028.56 | − | 7862.23i | −0.292347 | − | 0.327023i | ||||
\(834\) | −20114.7 | −0.835151 | ||||||||
\(835\) | −3851.21 | + | 3851.21i | −0.159613 | + | 0.159613i | ||||
\(836\) | −11562.4 | − | 4789.32i | −0.478344 | − | 0.198137i | ||||
\(837\) | 5447.75i | 0.224972i | ||||||||
\(838\) | 6140.33 | − | 14824.1i | 0.253120 | − | 0.611085i | ||||
\(839\) | 27723.7 | − | 11483.5i | 1.14079 | − | 0.472533i | 0.269358 | − | 0.963040i | \(-0.413189\pi\) |
0.871437 | + | 0.490508i | \(0.163189\pi\) | |||||||
\(840\) | 3587.77 | + | 8661.64i | 0.147369 | + | 0.355780i | ||||
\(841\) | −32862.1 | − | 32862.1i | −1.34741 | − | 1.34741i | ||||
\(842\) | 9879.09 | + | 9879.09i | 0.404342 | + | 0.404342i | ||||
\(843\) | −4248.27 | − | 10256.2i | −0.173568 | − | 0.419031i | ||||
\(844\) | 16945.0 | − | 7018.86i | 0.691080 | − | 0.286255i | ||||
\(845\) | −5630.84 | + | 13594.0i | −0.229239 | + | 0.553431i | ||||
\(846\) | − | 2604.99i | − | 0.105864i | ||||||
\(847\) | 4873.27 | + | 2018.57i | 0.197695 | + | 0.0818878i | ||||
\(848\) | −163.655 | + | 163.655i | −0.00662728 | + | 0.00662728i | ||||
\(849\) | 10741.0 | 0.434193 | ||||||||
\(850\) | −525.385 | + | 9384.36i | −0.0212006 | + | 0.378683i | ||||
\(851\) | −10342.1 | −0.416595 | ||||||||
\(852\) | 6367.81 | − | 6367.81i | 0.256053 | − | 0.256053i | ||||
\(853\) | −4020.20 | − | 1665.22i | −0.161371 | − | 0.0668419i | 0.300536 | − | 0.953770i | \(-0.402834\pi\) |
−0.461907 | + | 0.886929i | \(0.652834\pi\) | |||||||
\(854\) | 8643.62i | 0.346345i | ||||||||
\(855\) | 1506.66 | − | 3637.40i | 0.0602652 | − | 0.145493i | ||||
\(856\) | −2866.78 | + | 1187.46i | −0.114468 | + | 0.0474141i | ||||
\(857\) | −9896.77 | − | 23892.9i | −0.394478 | − | 0.952353i | −0.988952 | − | 0.148238i | \(-0.952640\pi\) |
0.594474 | − | 0.804115i | \(-0.297360\pi\) | |||||||
\(858\) | −10908.6 | − | 10908.6i | −0.434050 | − | 0.434050i | ||||
\(859\) | 13494.4 | + | 13494.4i | 0.535999 | + | 0.535999i | 0.922351 | − | 0.386352i | \(-0.126265\pi\) |
−0.386352 | + | 0.922351i | \(0.626265\pi\) | |||||||
\(860\) | −6848.47 | − | 16533.7i | −0.271548 | − | 0.655574i | ||||
\(861\) | 1865.45 | − | 772.693i | 0.0738377 | − | 0.0305846i | ||||
\(862\) | −1272.87 | + | 3072.97i | −0.0502947 | + | 0.121422i | ||||
\(863\) | 24790.2i | 0.977831i | 0.872331 | + | 0.488916i | \(0.162607\pi\) | ||||
−0.872331 | + | 0.488916i | \(0.837393\pi\) | |||||||
\(864\) | −25754.2 | − | 10667.7i | −1.01409 | − | 0.420051i | ||||
\(865\) | −9079.11 | + | 9079.11i | −0.356877 | + | 0.356877i | ||||
\(866\) | 19019.9 | 0.746332 | ||||||||
\(867\) | −19111.8 | − | 10554.1i | −0.748642 | − | 0.413421i | ||||
\(868\) | −2528.54 | −0.0988757 | ||||||||
\(869\) | −8384.02 | + | 8384.02i | −0.327282 | + | 0.327282i | ||||
\(870\) | −12692.8 | − | 5257.55i | −0.494630 | − | 0.204882i | ||||
\(871\) | 43577.2i | 1.69524i | ||||||||
\(872\) | 7035.81 | − | 16986.0i | 0.273237 | − | 0.659653i | ||||
\(873\) | 298.642 | − | 123.702i | 0.0115779 | − | 0.00479572i | ||||
\(874\) | 1503.49 | + | 3629.74i | 0.0581880 | + | 0.140478i | ||||
\(875\) | −13605.7 | − | 13605.7i | −0.525664 | − | 0.525664i | ||||
\(876\) | 10294.0 | + | 10294.0i | 0.397034 | + | 0.397034i | ||||
\(877\) | −5508.33 | − | 13298.3i | −0.212090 | − | 0.512031i | 0.781654 | − | 0.623713i | \(-0.214376\pi\) |
−0.993744 | + | 0.111681i | \(0.964376\pi\) | |||||||
\(878\) | 740.803 | − | 306.851i | 0.0284748 | − | 0.0117947i | ||||
\(879\) | 11312.5 | − | 27310.7i | 0.434084 | − | 1.04797i | ||||
\(880\) | 557.137i | 0.0213421i | ||||||||
\(881\) | 14161.8 | + | 5866.00i | 0.541569 | + | 0.224325i | 0.636662 | − | 0.771143i | \(-0.280315\pi\) |
−0.0950925 | + | 0.995468i | \(0.530315\pi\) | |||||||
\(882\) | 1315.94 | − | 1315.94i | 0.0502382 | − | 0.0502382i | ||||
\(883\) | −8385.90 | −0.319602 | −0.159801 | − | 0.987149i | \(-0.551085\pi\) | ||||
−0.159801 | + | 0.987149i | \(0.551085\pi\) | |||||||
\(884\) | −1316.84 | + | 23521.1i | −0.0501018 | + | 0.894912i | ||||
\(885\) | 9403.11 | 0.357155 | ||||||||
\(886\) | 15837.6 | − | 15837.6i | 0.600534 | − | 0.600534i | ||||
\(887\) | 8514.38 | + | 3526.77i | 0.322305 | + | 0.133503i | 0.537969 | − | 0.842964i | \(-0.319192\pi\) |
−0.215664 | + | 0.976468i | \(0.569192\pi\) | |||||||
\(888\) | − | 35507.0i | − | 1.34182i | ||||||
\(889\) | −8002.26 | + | 19319.2i | −0.301898 | + | 0.728846i | ||||
\(890\) | −6427.77 | + | 2662.47i | −0.242089 | + | 0.100277i | ||||
\(891\) | −5671.01 | − | 13691.0i | −0.213228 | − | 0.514778i | ||||
\(892\) | −5678.97 | − | 5678.97i | −0.213168 | − | 0.213168i | ||||
\(893\) | 11871.0 | + | 11871.0i | 0.444847 | + | 0.444847i | ||||
\(894\) | 6427.85 | + | 15518.2i | 0.240469 | + | 0.580544i | ||||
\(895\) | −22579.2 | + | 9352.62i | −0.843285 | + | 0.349300i | ||||
\(896\) | 5143.58 | − | 12417.7i | 0.191780 | − | 0.462998i | ||||
\(897\) | − | 8477.36i | − | 0.315553i | ||||||
\(898\) | −16438.8 | − | 6809.17i | −0.610879 | − | 0.253034i | ||||
\(899\) | 6736.95 | − | 6736.95i | 0.249933 | − | 0.249933i | ||||
\(900\) | 2903.37 | 0.107532 | ||||||||
\(901\) | −4075.07 | − | 4558.42i | −0.150677 | − | 0.168549i | ||||
\(902\) | −1722.07 | −0.0635684 | ||||||||
\(903\) | −22505.4 | + | 22505.4i | −0.829382 | + | 0.829382i | ||||
\(904\) | 12427.5 | + | 5147.63i | 0.457225 | + | 0.189389i | ||||
\(905\) | 3141.70i | 0.115396i | ||||||||
\(906\) | 6186.70 | − | 14936.0i | 0.226864 | − | 0.547699i | ||||
\(907\) | −6900.44 | + | 2858.25i | −0.252619 | + | 0.104638i | −0.505400 | − | 0.862885i | \(-0.668655\pi\) |
0.252781 | + | 0.967524i | \(0.418655\pi\) | |||||||
\(908\) | −8364.23 | − | 20193.0i | −0.305701 | − | 0.738028i | ||||
\(909\) | 7581.52 | + | 7581.52i | 0.276637 | + | 0.276637i | ||||
\(910\) | 7522.45 | + | 7522.45i | 0.274030 | + | 0.274030i | ||||
\(911\) | −11747.7 | − | 28361.5i | −0.427244 | − | 1.03146i | −0.980157 | − | 0.198220i | \(-0.936484\pi\) |
0.552913 | − | 0.833239i | \(-0.313516\pi\) | |||||||
\(912\) | 868.311 | − | 359.666i | 0.0315270 | − | 0.0130589i | ||||
\(913\) | 1811.23 | − | 4372.71i | 0.0656551 | − | 0.158505i | ||||
\(914\) | 432.140i | 0.0156389i | ||||||||
\(915\) | 10211.6 | + | 4229.77i | 0.368945 | + | 0.152822i | ||||
\(916\) | 2091.30 | − | 2091.30i | 0.0754351 | − | 0.0754351i | ||||
\(917\) | −38625.1 | −1.39096 | ||||||||
\(918\) | 7891.92 | − | 16395.0i | 0.283739 | − | 0.589451i | ||||
\(919\) | −24550.8 | −0.881237 | −0.440619 | − | 0.897694i | \(-0.645241\pi\) | ||||
−0.440619 | + | 0.897694i | \(0.645241\pi\) | |||||||
\(920\) | 3106.90 | − | 3106.90i | 0.111339 | − | 0.111339i | ||||
\(921\) | −10309.7 | − | 4270.42i | −0.368856 | − | 0.152785i | ||||
\(922\) | 26537.4i | 0.947898i | ||||||||
\(923\) | 10055.1 | − | 24275.1i | 0.358577 | − | 0.865681i | ||||
\(924\) | 8943.94 | − | 3704.70i | 0.318435 | − | 0.131900i | ||||
\(925\) | 10768.1 | + | 25996.4i | 0.382759 | + | 0.924061i | ||||
\(926\) | 12937.3 | + | 12937.3i | 0.459119 | + | 0.459119i | ||||
\(927\) | −3170.05 | − | 3170.05i | −0.112317 | − | 0.112317i | ||||
\(928\) | 18656.6 | + | 45041.1i | 0.659951 | + | 1.59326i | ||||
\(929\) | −38484.2 | + | 15940.7i | −1.35912 | + | 0.562967i | −0.938817 | − | 0.344415i | \(-0.888077\pi\) |
−0.420306 | + | 0.907383i | \(0.638077\pi\) | |||||||
\(930\) | 706.874 | − | 1706.55i | 0.0249240 | − | 0.0601719i | ||||
\(931\) | 11993.6i | 0.422206i | ||||||||
\(932\) | −3159.93 | − | 1308.88i | −0.111059 | − | 0.0460021i | ||||
\(933\) | 11265.2 | − | 11265.2i | 0.395292 | − | 0.395292i | ||||
\(934\) | −3343.54 | −0.117135 | ||||||||
\(935\) | −14695.7 | − | 822.739i | −0.514011 | − | 0.0287770i | ||||
\(936\) | −10689.5 | −0.373288 | ||||||||
\(937\) | 59.2109 | − | 59.2109i | 0.00206439 | − | 0.00206439i | −0.706074 | − | 0.708138i | \(-0.749535\pi\) |
0.708138 | + | 0.706074i | \(0.249535\pi\) | |||||||
\(938\) | 14432.9 | + | 5978.31i | 0.502401 | + | 0.208101i | ||||
\(939\) | − | 11608.6i | − | 0.403442i | ||||||
\(940\) | 2794.31 | − | 6746.06i | 0.0969577 | − | 0.234077i | ||||
\(941\) | 45541.8 | − | 18864.0i | 1.57770 | − | 0.653507i | 0.589657 | − | 0.807654i | \(-0.299263\pi\) |
0.988048 | + | 0.154147i | \(0.0492630\pi\) | |||||||
\(942\) | −1000.90 | − | 2416.39i | −0.0346190 | − | 0.0835778i | ||||
\(943\) | −669.130 | − | 669.130i | −0.0231070 | − | 0.0231070i | ||||
\(944\) | −582.951 | − | 582.951i | −0.0200990 | − | 0.0200990i | ||||
\(945\) | 5504.15 | + | 13288.2i | 0.189471 | + | 0.457423i | ||||
\(946\) | 25078.4 | − | 10387.8i | 0.861913 | − | 0.357016i | ||||
\(947\) | 3614.55 | − | 8726.29i | 0.124031 | − | 0.299436i | −0.849652 | − | 0.527343i | \(-0.823188\pi\) |
0.973683 | + | 0.227907i | \(0.0731882\pi\) | |||||||
\(948\) | − | 8699.57i | − | 0.298047i | ||||||
\(949\) | 39242.3 | + | 16254.7i | 1.34232 | + | 0.556006i | ||||
\(950\) | 7558.50 | − | 7558.50i | 0.258137 | − | 0.258137i | ||||
\(951\) | −17347.7 | −0.591521 | ||||||||
\(952\) | 19566.5 | + | 9418.57i | 0.666129 | + | 0.320649i | ||||
\(953\) | 41693.4 | 1.41719 | 0.708595 | − | 0.705616i | \(-0.249329\pi\) | ||||
0.708595 | + | 0.705616i | \(0.249329\pi\) | |||||||
\(954\) | 762.967 | − | 762.967i | 0.0258930 | − | 0.0258930i | ||||
\(955\) | 28436.8 | + | 11778.9i | 0.963555 | + | 0.399117i | ||||
\(956\) | − | 1393.18i | − | 0.0471324i | ||||||
\(957\) | −13959.3 | + | 33700.6i | −0.471514 | + | 1.13834i | ||||
\(958\) | 6766.12 | − | 2802.62i | 0.228187 | − | 0.0945183i | ||||
\(959\) | 3344.23 | + | 8073.68i | 0.112608 | + | 0.271859i | ||||
\(960\) | 6229.30 | + | 6229.30i | 0.209427 | + | 0.209427i | ||||
\(961\) | −20159.6 | − | 20159.6i | −0.676702 | − | 0.676702i | ||||
\(962\) | −15418.5 | − | 37223.6i | −0.516750 | − | 1.24755i | ||||
\(963\) | −931.246 | + | 385.735i | −0.0311620 | + | 0.0129077i | ||||
\(964\) | −12638.3 | + | 30511.6i | −0.422254 | + | 1.01941i | ||||
\(965\) | 19945.5i | 0.665355i | ||||||||
\(966\) | −2807.73 | − | 1163.00i | −0.0935168 | − | 0.0387359i | ||||
\(967\) | −22896.1 | + | 22896.1i | −0.761416 | + | 0.761416i | −0.976578 | − | 0.215162i | \(-0.930972\pi\) |
0.215162 | + | 0.976578i | \(0.430972\pi\) | |||||||
\(968\) | 8487.28 | 0.281809 | ||||||||
\(969\) | 8204.71 | + | 23434.7i | 0.272005 | + | 0.776915i | ||||
\(970\) | −517.626 | −0.0171340 | ||||||||
\(971\) | 3819.26 | − | 3819.26i | 0.126226 | − | 0.126226i | −0.641171 | − | 0.767398i | \(-0.721551\pi\) |
0.767398 | + | 0.641171i | \(0.221551\pi\) | |||||||
\(972\) | −9286.01 | − | 3846.39i | −0.306429 | − | 0.126927i | ||||
\(973\) | − | 36828.3i | − | 1.21342i | ||||||
\(974\) | −11756.6 | + | 28382.9i | −0.386762 | + | 0.933725i | ||||
\(975\) | −21309.1 | + | 8826.53i | −0.699937 | + | 0.289923i | ||||
\(976\) | −370.845 | − | 895.300i | −0.0121624 | − | 0.0293626i | ||||
\(977\) | 17738.6 | + | 17738.6i | 0.580869 | + | 0.580869i | 0.935142 | − | 0.354273i | \(-0.115272\pi\) |
−0.354273 | + | 0.935142i | \(0.615272\pi\) | |||||||
\(978\) | −3636.21 | − | 3636.21i | −0.118889 | − | 0.118889i | ||||
\(979\) | 7069.09 | + | 17066.3i | 0.230775 | + | 0.557141i | ||||
\(980\) | 4819.44 | − | 1996.28i | 0.157093 | − | 0.0650701i | ||||
\(981\) | 2285.52 | − | 5517.73i | 0.0743843 | − | 0.179580i | ||||
\(982\) | − | 23421.4i | − | 0.761108i | ||||||
\(983\) | −55092.4 | − | 22820.0i | −1.78756 | − | 0.740433i | −0.990665 | − | 0.136322i | \(-0.956472\pi\) |
−0.796900 | − | 0.604112i | \(-0.793528\pi\) | |||||||
\(984\) | 2297.29 | − | 2297.29i | 0.0744258 | − | 0.0744258i | ||||
\(985\) | 13116.7 | 0.424296 | ||||||||
\(986\) | −30034.4 | + | 10515.3i | −0.970071 | + | 0.339631i | ||||
\(987\) | −12986.2 | −0.418799 | ||||||||
\(988\) | 18944.8 | − | 18944.8i | 0.610034 | − | 0.610034i | ||||
\(989\) | 13780.8 | + | 5708.20i | 0.443078 | + | 0.183529i | ||||
\(990\) | − | 2597.40i | − | 0.0833846i | ||||||
\(991\) | −15331.8 | + | 37014.1i | −0.491452 | + | 1.18647i | 0.462529 | + | 0.886604i | \(0.346942\pi\) |
−0.953981 | + | 0.299867i | \(0.903058\pi\) | |||||||
\(992\) | −6055.75 | + | 2508.37i | −0.193821 | + | 0.0802832i | ||||
\(993\) | 10604.8 | + | 25602.2i | 0.338905 | + | 0.818189i | ||||
\(994\) | −6660.54 | − | 6660.54i | −0.212535 | − | 0.212535i | ||||
\(995\) | −14862.9 | − | 14862.9i | −0.473553 | − | 0.473553i | ||||
\(996\) | 1328.94 | + | 3208.34i | 0.0422781 | + | 0.102068i | ||||
\(997\) | −9994.87 | + | 4140.01i | −0.317493 | + | 0.131510i | −0.535738 | − | 0.844384i | \(-0.679967\pi\) |
0.218245 | + | 0.975894i | \(0.429967\pi\) | |||||||
\(998\) | −5056.58 | + | 12207.7i | −0.160384 | + | 0.387201i | ||||
\(999\) | − | 54472.8i | − | 1.72517i |
(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 | 17.4.d.a.9.2 | yes | 12 | |
3.2 | odd | 2 | 153.4.l.a.145.2 | 12 | |||
17.2 | even | 8 | inner | 17.4.d.a.2.2 | ✓ | 12 | |
17.6 | odd | 16 | 289.4.a.g.1.6 | 12 | |||
17.7 | odd | 16 | 289.4.b.e.288.7 | 12 | |||
17.10 | odd | 16 | 289.4.b.e.288.8 | 12 | |||
17.11 | odd | 16 | 289.4.a.g.1.5 | 12 | |||
51.2 | odd | 8 | 153.4.l.a.19.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.2.2 | ✓ | 12 | 17.2 | even | 8 | inner | |
17.4.d.a.9.2 | yes | 12 | 1.1 | even | 1 | trivial | |
153.4.l.a.19.2 | 12 | 51.2 | odd | 8 | |||
153.4.l.a.145.2 | 12 | 3.2 | odd | 2 | |||
289.4.a.g.1.5 | 12 | 17.11 | odd | 16 | |||
289.4.a.g.1.6 | 12 | 17.6 | odd | 16 | |||
289.4.b.e.288.7 | 12 | 17.7 | odd | 16 | |||
289.4.b.e.288.8 | 12 | 17.10 | odd | 16 |