Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [198,4,Mod(37,198)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(198, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("198.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 198 = 2 \cdot 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 198.f (of order \(5\), 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: | \(11.6823781811\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 71x^{6} - 141x^{5} + 2911x^{4} + 2710x^{3} + 75340x^{2} + 169400x + 5856400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 22) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(-4.79501 - 3.48378i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 198.37 |
Dual form | 198.4.f.d.91.2 |
$q$-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 \(\left(\mathbb{Z}/198\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(155\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.61803 | − | 1.17557i | −0.572061 | − | 0.415627i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.23607 | + | 3.80423i | 0.154508 | + | 0.475528i | ||||
\(5\) | 10.3036 | − | 7.48598i | 0.921579 | − | 0.669566i | −0.0223375 | − | 0.999750i | \(-0.507111\pi\) |
0.943917 | + | 0.330184i | \(0.107111\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.24988 | + | 22.3128i | 0.391457 | + | 1.20478i | 0.931687 | + | 0.363263i | \(0.118337\pi\) |
−0.540230 | + | 0.841518i | \(0.681663\pi\) | |||||||
\(8\) | 2.47214 | − | 7.60845i | 0.109254 | − | 0.336249i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −25.4718 | −0.805490 | ||||||||
\(11\) | 3.69653 | + | 36.2951i | 0.101322 | + | 0.994854i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.27574 | − | 6.73922i | −0.197894 | − | 0.143779i | 0.484425 | − | 0.874833i | \(-0.339029\pi\) |
−0.682320 | + | 0.731054i | \(0.739029\pi\) | |||||||
\(14\) | 14.4998 | − | 44.6257i | 0.276802 | − | 0.851908i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −12.9443 | + | 9.40456i | −0.202254 | + | 0.146946i | ||||
\(17\) | −52.9924 | + | 38.5012i | −0.756032 | + | 0.549289i | −0.897691 | − | 0.440626i | \(-0.854756\pi\) |
0.141659 | + | 0.989916i | \(0.454756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.24041 | + | 6.89528i | −0.0270519 | + | 0.0832571i | −0.963671 | − | 0.267092i | \(-0.913937\pi\) |
0.936619 | + | 0.350349i | \(0.113937\pi\) | |||||||
\(20\) | 41.2143 | + | 29.9439i | 0.460790 | + | 0.334783i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 36.6864 | − | 63.0723i | 0.355525 | − | 0.611230i | ||||
\(23\) | 104.072 | 0.943504 | 0.471752 | − | 0.881731i | \(-0.343622\pi\) | ||||
0.471752 | + | 0.881731i | \(0.343622\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.4965 | − | 35.3825i | 0.0919719 | − | 0.283060i | ||||
\(26\) | 7.08604 | + | 21.8086i | 0.0534495 | + | 0.164501i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −75.9218 | + | 55.1604i | −0.512424 | + | 0.372298i | ||||
\(29\) | 39.3536 | + | 121.118i | 0.251993 | + | 0.775554i | 0.994407 | + | 0.105613i | \(0.0336805\pi\) |
−0.742415 | + | 0.669941i | \(0.766319\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 233.653 | + | 169.759i | 1.35372 | + | 0.983536i | 0.998817 | + | 0.0486336i | \(0.0154867\pi\) |
0.354905 | + | 0.934903i | \(0.384513\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 131.004 | 0.660796 | ||||||||
\(35\) | 241.733 | + | 175.629i | 1.16744 | + | 0.848194i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −26.3908 | − | 81.2224i | −0.117260 | − | 0.360889i | 0.875152 | − | 0.483849i | \(-0.160761\pi\) |
−0.992412 | + | 0.122960i | \(0.960761\pi\) | |||||||
\(38\) | 11.7310 | − | 8.52303i | 0.0500792 | − | 0.0363847i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −31.4849 | − | 96.9006i | −0.124455 | − | 0.383033i | ||||
\(41\) | 41.8544 | − | 128.815i | 0.159428 | − | 0.490670i | −0.839154 | − | 0.543893i | \(-0.816950\pi\) |
0.998583 | + | 0.0532236i | \(0.0169496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 353.691 | 1.25436 | 0.627178 | − | 0.778876i | \(-0.284210\pi\) | ||||
0.627178 | + | 0.778876i | \(0.284210\pi\) | |||||||
\(44\) | −133.506 | + | 58.9257i | −0.457426 | + | 0.201895i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −168.393 | − | 122.344i | −0.539742 | − | 0.392146i | ||||
\(47\) | 41.5948 | − | 128.016i | 0.129090 | − | 0.397298i | −0.865534 | − | 0.500850i | \(-0.833021\pi\) |
0.994624 | + | 0.103552i | \(0.0330208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −167.810 | + | 121.921i | −0.489241 | + | 0.355454i | ||||
\(50\) | −60.1964 | + | 43.7352i | −0.170261 | + | 0.123702i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14.1721 | − | 43.6171i | 0.0377945 | − | 0.116319i | ||||
\(53\) | 405.666 | + | 294.734i | 1.05137 | + | 0.763864i | 0.972472 | − | 0.233019i | \(-0.0748603\pi\) |
0.0788966 | + | 0.996883i | \(0.474860\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 309.792 | + | 346.297i | 0.759497 | + | 0.848994i | ||||
\(56\) | 187.689 | 0.447875 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 78.7073 | − | 242.236i | 0.178186 | − | 0.548399i | ||||
\(59\) | −201.373 | − | 619.763i | −0.444349 | − | 1.36756i | −0.883196 | − | 0.469003i | \(-0.844613\pi\) |
0.438848 | − | 0.898561i | \(-0.355387\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −295.928 | + | 215.004i | −0.621143 | + | 0.451287i | −0.853320 | − | 0.521387i | \(-0.825415\pi\) |
0.232178 | + | 0.972673i | \(0.425415\pi\) | |||||||
\(62\) | −178.495 | − | 549.352i | −0.365628 | − | 1.12529i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −51.7771 | − | 37.6183i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −146.023 | −0.278645 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −294.576 | −0.537136 | −0.268568 | − | 0.963261i | \(-0.586550\pi\) | ||||
−0.268568 | + | 0.963261i | \(0.586550\pi\) | |||||||
\(68\) | −211.969 | − | 154.005i | −0.378016 | − | 0.274645i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −184.668 | − | 568.349i | −0.315315 | − | 0.970438i | ||||
\(71\) | 107.151 | − | 77.8500i | 0.179106 | − | 0.130128i | −0.494620 | − | 0.869109i | \(-0.664693\pi\) |
0.673726 | + | 0.738981i | \(0.264693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 145.080 | + | 446.511i | 0.232607 | + | 0.715892i | 0.997430 | + | 0.0716507i | \(0.0228267\pi\) |
−0.764822 | + | 0.644241i | \(0.777173\pi\) | |||||||
\(74\) | −52.7815 | + | 162.445i | −0.0829153 | + | 0.255187i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −29.0005 | −0.0437709 | ||||||||
\(77\) | −783.048 | + | 345.616i | −1.15892 | + | 0.511514i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −330.105 | − | 239.836i | −0.470124 | − | 0.341565i | 0.327366 | − | 0.944898i | \(-0.393839\pi\) |
−0.797489 | + | 0.603333i | \(0.793839\pi\) | |||||||
\(80\) | −62.9698 | + | 193.801i | −0.0880030 | + | 0.270845i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −219.152 | + | 159.224i | −0.295138 | + | 0.214431i | ||||
\(83\) | −1099.89 | + | 799.119i | −1.45457 | + | 1.05680i | −0.469827 | + | 0.882758i | \(0.655684\pi\) |
−0.984738 | + | 0.174045i | \(0.944316\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −257.791 | + | 793.400i | −0.328957 | + | 1.01243i | ||||
\(86\) | −572.283 | − | 415.788i | −0.717569 | − | 0.521344i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 285.288 | + | 61.6016i | 0.345589 | + | 0.0746222i | ||||
\(89\) | 260.255 | 0.309966 | 0.154983 | − | 0.987917i | \(-0.450468\pi\) | ||||
0.154983 | + | 0.987917i | \(0.450468\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 83.1232 | − | 255.827i | 0.0957547 | − | 0.294703i | ||||
\(92\) | 128.641 | + | 395.915i | 0.145779 | + | 0.448663i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −217.793 | + | 158.236i | −0.238975 | + | 0.173626i | ||||
\(95\) | 28.5337 | + | 87.8177i | 0.0308157 | + | 0.0948411i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1144.38 | − | 831.440i | −1.19788 | − | 0.870309i | −0.203803 | − | 0.979012i | \(-0.565330\pi\) |
−0.994074 | + | 0.108703i | \(0.965330\pi\) | |||||||
\(98\) | 414.848 | 0.427612 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 148.814 | 0.148814 | ||||||||
\(101\) | −150.976 | − | 109.691i | −0.148740 | − | 0.108066i | 0.510927 | − | 0.859624i | \(-0.329302\pi\) |
−0.659666 | + | 0.751559i | \(0.729302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −362.450 | − | 1115.51i | −0.346731 | − | 1.06713i | −0.960651 | − | 0.277760i | \(-0.910408\pi\) |
0.613919 | − | 0.789369i | \(-0.289592\pi\) | |||||||
\(104\) | −74.2059 | + | 53.9138i | −0.0699662 | + | 0.0508335i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −309.901 | − | 953.779i | −0.283965 | − | 0.873954i | ||||
\(107\) | 220.241 | − | 677.831i | 0.198986 | − | 0.612415i | −0.800921 | − | 0.598770i | \(-0.795656\pi\) |
0.999907 | − | 0.0136452i | \(-0.00434354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1247.22 | 1.09598 | 0.547989 | − | 0.836486i | \(-0.315394\pi\) | ||||
0.547989 | + | 0.836486i | \(0.315394\pi\) | |||||||
\(110\) | −94.1574 | − | 924.503i | −0.0816141 | − | 0.801344i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −303.687 | − | 220.642i | −0.256212 | − | 0.186149i | ||||
\(113\) | 303.455 | − | 933.939i | 0.252625 | − | 0.777501i | −0.741663 | − | 0.670773i | \(-0.765963\pi\) |
0.994288 | − | 0.106728i | \(-0.0340374\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1072.32 | − | 779.084i | 0.869513 | − | 0.631739i | ||||
\(116\) | −412.117 | + | 299.420i | −0.329863 | + | 0.239659i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −402.747 | + | 1239.53i | −0.314202 | + | 0.967014i | ||||
\(119\) | −1243.26 | − | 903.281i | −0.957727 | − | 0.695829i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1303.67 | + | 268.332i | −0.979468 | + | 0.201602i | ||||
\(122\) | 731.574 | 0.542899 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −356.990 | + | 1098.70i | −0.258538 | + | 0.795697i | ||||
\(125\) | 345.533 | + | 1063.44i | 0.247244 | + | 0.760937i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1254.52 | − | 911.460i | 0.876538 | − | 0.636842i | −0.0557950 | − | 0.998442i | \(-0.517769\pi\) |
0.932333 | + | 0.361600i | \(0.117769\pi\) | |||||||
\(128\) | 39.5542 | + | 121.735i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 236.270 | + | 171.660i | 0.159402 | + | 0.115812i | ||||
\(131\) | −742.114 | −0.494953 | −0.247476 | − | 0.968894i | \(-0.579601\pi\) | ||||
−0.247476 | + | 0.968894i | \(0.579601\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −170.096 | −0.110896 | ||||||||
\(134\) | 476.633 | + | 346.294i | 0.307275 | + | 0.223248i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 161.930 | + | 498.370i | 0.102099 | + | 0.314227i | ||||
\(137\) | 417.192 | − | 303.108i | 0.260169 | − | 0.189024i | −0.450053 | − | 0.893002i | \(-0.648595\pi\) |
0.710222 | + | 0.703978i | \(0.248595\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 761.160 | + | 2342.61i | 0.464466 | + | 1.42948i | 0.859653 | + | 0.510878i | \(0.170680\pi\) |
−0.395187 | + | 0.918601i | \(0.629320\pi\) | |||||||
\(140\) | −369.335 | + | 1136.70i | −0.222961 | + | 0.686203i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −264.893 | −0.156544 | ||||||||
\(143\) | 210.313 | − | 361.576i | 0.122988 | − | 0.211444i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1312.17 | + | 953.348i | 0.751516 | + | 0.546008i | ||||
\(146\) | 290.160 | − | 893.021i | 0.164478 | − | 0.506212i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 276.368 | − | 200.793i | 0.153495 | − | 0.111521i | ||||
\(149\) | −351.726 | + | 255.544i | −0.193386 | + | 0.140503i | −0.680265 | − | 0.732966i | \(-0.738135\pi\) |
0.486879 | + | 0.873469i | \(0.338135\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −241.340 | + | 742.768i | −0.130066 | + | 0.400302i | −0.994790 | − | 0.101945i | \(-0.967493\pi\) |
0.864724 | + | 0.502247i | \(0.167493\pi\) | |||||||
\(152\) | 46.9238 | + | 34.0921i | 0.0250396 | + | 0.0181924i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1673.29 | + | 361.311i | 0.875570 | + | 0.189060i | ||||
\(155\) | 3678.27 | 1.90610 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 161.425 | − | 496.815i | 0.0820580 | − | 0.252549i | −0.901607 | − | 0.432555i | \(-0.857612\pi\) |
0.983665 | + | 0.180007i | \(0.0576120\pi\) | |||||||
\(158\) | 252.178 | + | 776.124i | 0.126976 | + | 0.390792i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 329.714 | − | 239.551i | 0.162914 | − | 0.118364i | ||||
\(161\) | 754.513 | + | 2322.15i | 0.369341 | + | 1.13672i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2057.56 | − | 1494.91i | −0.988716 | − | 0.718344i | −0.0290761 | − | 0.999577i | \(-0.509257\pi\) |
−0.959639 | + | 0.281233i | \(0.909257\pi\) | |||||||
\(164\) | 541.775 | 0.257960 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2719.08 | 1.27134 | ||||||||
\(167\) | 1120.85 | + | 814.342i | 0.519363 | + | 0.377339i | 0.816364 | − | 0.577538i | \(-0.195986\pi\) |
−0.297001 | + | 0.954877i | \(0.595986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −638.288 | − | 1964.45i | −0.290527 | − | 0.894150i | ||||
\(170\) | 1349.81 | − | 980.696i | 0.608976 | − | 0.442447i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 437.186 | + | 1345.52i | 0.193809 | + | 0.596482i | ||||
\(173\) | 137.052 | − | 421.804i | 0.0602307 | − | 0.185371i | −0.916414 | − | 0.400232i | \(-0.868930\pi\) |
0.976645 | + | 0.214861i | \(0.0689297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 872.833 | 0.377029 | ||||||||
\(176\) | −389.189 | − | 435.050i | −0.166683 | − | 0.186324i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −421.101 | − | 305.948i | −0.177319 | − | 0.128830i | ||||
\(179\) | −116.388 | + | 358.205i | −0.0485991 | + | 0.149573i | −0.972411 | − | 0.233274i | \(-0.925056\pi\) |
0.923812 | + | 0.382846i | \(0.125056\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2664.71 | + | 1936.02i | −1.09429 | + | 0.795047i | −0.980118 | − | 0.198414i | \(-0.936421\pi\) |
−0.114170 | + | 0.993461i | \(0.536421\pi\) | |||||||
\(182\) | −435.238 | + | 316.219i | −0.177264 | + | 0.128790i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 257.281 | − | 791.830i | 0.103082 | − | 0.317252i | ||||
\(185\) | −879.949 | − | 639.320i | −0.349703 | − | 0.254074i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1593.29 | − | 1781.04i | −0.623065 | − | 0.696486i | ||||
\(188\) | 538.415 | 0.208872 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 57.0674 | − | 175.635i | 0.0217900 | − | 0.0670628i | ||||
\(191\) | −707.730 | − | 2178.17i | −0.268113 | − | 0.825166i | −0.990960 | − | 0.134158i | \(-0.957167\pi\) |
0.722847 | − | 0.691008i | \(-0.242833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1863.49 | − | 1353.90i | 0.695010 | − | 0.504954i | −0.183293 | − | 0.983058i | \(-0.558676\pi\) |
0.878303 | + | 0.478104i | \(0.158676\pi\) | |||||||
\(194\) | 874.228 | + | 2690.60i | 0.323536 | + | 0.995740i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −671.238 | − | 487.683i | −0.244620 | − | 0.177727i | ||||
\(197\) | 1041.86 | 0.376801 | 0.188400 | − | 0.982092i | \(-0.439670\pi\) | ||||
0.188400 | + | 0.982092i | \(0.439670\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3463.83 | 1.23389 | 0.616946 | − | 0.787005i | \(-0.288370\pi\) | ||||
0.616946 | + | 0.787005i | \(0.288370\pi\) | |||||||
\(200\) | −240.785 | − | 174.941i | −0.0851305 | − | 0.0618509i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 115.336 | + | 354.966i | 0.0401732 | + | 0.123640i | ||||
\(203\) | −2417.18 | + | 1756.18i | −0.835728 | + | 0.607192i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −533.054 | − | 1640.57i | −0.181610 | − | 0.558939i | ||||
\(206\) | −724.901 | + | 2231.02i | −0.245176 | + | 0.754574i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 183.447 | 0.0611527 | ||||||||
\(209\) | −258.547 | − | 55.8274i | −0.0855696 | − | 0.0184769i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1692.45 | − | 1229.63i | −0.552193 | − | 0.401192i | 0.276400 | − | 0.961043i | \(-0.410858\pi\) |
−0.828593 | + | 0.559851i | \(0.810858\pi\) | |||||||
\(212\) | −619.803 | + | 1907.56i | −0.200794 | + | 0.617979i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1153.20 | + | 837.845i | −0.368368 | + | 0.267635i | ||||
\(215\) | 3644.28 | − | 2647.72i | 1.15599 | − | 0.839875i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2093.85 | + | 6444.20i | −0.655022 | + | 2.01595i | ||||
\(218\) | −2018.04 | − | 1466.19i | −0.626967 | − | 0.455518i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −934.468 | + | 1606.57i | −0.286372 | + | 0.492339i | ||||
\(221\) | 751.012 | 0.228591 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1144.45 | − | 3522.26i | 0.343669 | − | 1.05770i | −0.618623 | − | 0.785688i | \(-0.712309\pi\) |
0.962292 | − | 0.272017i | \(-0.0876906\pi\) | |||||||
\(224\) | 231.996 | + | 714.011i | 0.0692005 | + | 0.212977i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1588.91 | + | 1154.41i | −0.467667 | + | 0.339780i | ||||
\(227\) | 1499.81 | + | 4615.95i | 0.438529 | + | 1.34965i | 0.889426 | + | 0.457079i | \(0.151104\pi\) |
−0.450897 | + | 0.892576i | \(0.648896\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1081.53 | + | 785.778i | 0.312094 | + | 0.226750i | 0.732795 | − | 0.680450i | \(-0.238216\pi\) |
−0.420700 | + | 0.907200i | \(0.638216\pi\) | |||||||
\(230\) | −2650.91 | −0.759983 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1018.81 | 0.288311 | ||||||||
\(233\) | −4776.36 | − | 3470.23i | −1.34296 | − | 0.975718i | −0.999330 | − | 0.0366132i | \(-0.988343\pi\) |
−0.343631 | − | 0.939105i | \(-0.611657\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −529.748 | − | 1630.40i | −0.147051 | − | 0.452576i | ||||
\(236\) | 2108.81 | − | 1532.14i | 0.581660 | − | 0.422601i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 949.766 | + | 2923.08i | 0.258673 | + | 0.796114i | ||||
\(239\) | 1025.87 | − | 3157.30i | 0.277649 | − | 0.854515i | −0.710858 | − | 0.703336i | \(-0.751693\pi\) |
0.988506 | − | 0.151179i | \(-0.0483070\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5275.95 | −1.41018 | −0.705091 | − | 0.709116i | \(-0.749094\pi\) | ||||
−0.705091 | + | 0.709116i | \(0.749094\pi\) | |||||||
\(242\) | 2424.83 | + | 1098.39i | 0.644107 | + | 0.291764i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1183.71 | − | 860.017i | −0.310571 | − | 0.225643i | ||||
\(245\) | −816.340 | + | 2512.44i | −0.212874 | + | 0.655158i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 67.2503 | − | 48.8602i | 0.0173240 | − | 0.0125866i | ||||
\(248\) | 1869.23 | − | 1358.07i | 0.478613 | − | 0.347733i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 691.067 | − | 2126.88i | 0.174828 | − | 0.538064i | ||||
\(251\) | −1587.17 | − | 1153.15i | −0.399129 | − | 0.289984i | 0.370057 | − | 0.929009i | \(-0.379338\pi\) |
−0.769186 | + | 0.639025i | \(0.779338\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 384.707 | + | 3777.32i | 0.0955980 | + | 0.938648i | ||||
\(254\) | −3101.34 | −0.766123 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 79.1084 | − | 243.470i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −1836.17 | − | 5651.15i | −0.445669 | − | 1.37163i | −0.881748 | − | 0.471721i | \(-0.843633\pi\) |
0.436078 | − | 0.899909i | \(-0.356367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1620.97 | − | 1177.71i | 0.388890 | − | 0.282545i | ||||
\(260\) | −180.494 | − | 555.504i | −0.0430530 | − | 0.132503i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1200.77 | + | 872.408i | 0.283143 | + | 0.205716i | ||||
\(263\) | 1704.11 | 0.399544 | 0.199772 | − | 0.979842i | \(-0.435980\pi\) | ||||
0.199772 | + | 0.979842i | \(0.435980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6386.18 | 1.48038 | ||||||||
\(266\) | 275.221 | + | 199.960i | 0.0634395 | + | 0.0460915i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −364.115 | − | 1120.63i | −0.0829921 | − | 0.255423i | ||||
\(269\) | −4728.97 | + | 3435.80i | −1.07186 | + | 0.778752i | −0.976246 | − | 0.216666i | \(-0.930482\pi\) |
−0.0956148 | + | 0.995418i | \(0.530482\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1825.00 | + | 5616.79i | 0.409082 | + | 1.25902i | 0.917439 | + | 0.397877i | \(0.130253\pi\) |
−0.508357 | + | 0.861146i | \(0.669747\pi\) | |||||||
\(272\) | 323.861 | − | 996.740i | 0.0721946 | − | 0.222192i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1031.36 | −0.227396 | ||||||||
\(275\) | 1326.71 | + | 286.474i | 0.290922 | + | 0.0628182i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7186.00 | − | 5220.93i | −1.55872 | − | 1.13247i | −0.937051 | − | 0.349193i | \(-0.886456\pi\) |
−0.621667 | − | 0.783281i | \(-0.713544\pi\) | |||||||
\(278\) | 1522.32 | − | 4685.22i | 0.328427 | − | 1.01079i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1933.87 | − | 1405.04i | 0.412752 | − | 0.299882i | ||||
\(281\) | −6594.92 | + | 4791.49i | −1.40007 | + | 1.01721i | −0.405397 | + | 0.914141i | \(0.632867\pi\) |
−0.994674 | + | 0.103070i | \(0.967133\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1812.06 | − | 5576.96i | 0.380622 | − | 1.17143i | −0.558985 | − | 0.829178i | \(-0.688809\pi\) |
0.939607 | − | 0.342256i | \(-0.111191\pi\) | |||||||
\(284\) | 428.605 | + | 311.400i | 0.0895529 | + | 0.0650640i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −765.351 | + | 337.805i | −0.158238 | + | 0.0698420i | ||||
\(287\) | 3177.66 | 0.653559 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −192.352 | + | 592.000i | −0.0391517 | + | 0.120497i | ||||
\(290\) | −1002.41 | − | 3085.10i | −0.202978 | − | 0.624701i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1519.30 | + | 1103.83i | −0.304487 | + | 0.221223i | ||||
\(293\) | −2353.65 | − | 7243.79i | −0.469289 | − | 1.44432i | −0.853507 | − | 0.521081i | \(-0.825529\pi\) |
0.384218 | − | 0.923242i | \(-0.374471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6714.40 | − | 4878.30i | −1.32518 | − | 0.962798i | ||||
\(296\) | −683.219 | −0.134160 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 869.515 | 0.169026 | ||||||||
\(299\) | −965.348 | − | 701.367i | −0.186714 | − | 0.135656i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2564.22 | + | 7891.85i | 0.491026 | + | 1.51122i | ||||
\(302\) | 1263.67 | − | 918.112i | 0.240782 | − | 0.174938i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −35.8466 | − | 110.324i | −0.00676297 | − | 0.0208143i | ||||
\(305\) | −1439.60 | + | 4430.62i | −0.270266 | + | 0.831792i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4100.68 | 0.762339 | 0.381170 | − | 0.924505i | \(-0.375521\pi\) | ||||
0.381170 | + | 0.924505i | \(0.375521\pi\) | |||||||
\(308\) | −2282.70 | − | 2551.69i | −0.422302 | − | 0.472065i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5951.57 | − | 4324.07i | −1.09041 | − | 0.792228i | ||||
\(311\) | −449.969 | + | 1384.86i | −0.0820432 | + | 0.252503i | −0.983661 | − | 0.180031i | \(-0.942380\pi\) |
0.901618 | + | 0.432534i | \(0.142380\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2800.56 | − | 2034.72i | 0.505740 | − | 0.367442i | −0.305465 | − | 0.952203i | \(-0.598812\pi\) |
0.811205 | + | 0.584761i | \(0.198812\pi\) | |||||||
\(314\) | −845.232 | + | 614.097i | −0.151908 | + | 0.110368i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 504.356 | − | 1552.25i | 0.0897856 | − | 0.276332i | ||||
\(317\) | 4038.86 | + | 2934.41i | 0.715600 | + | 0.519914i | 0.884975 | − | 0.465638i | \(-0.154175\pi\) |
−0.169375 | + | 0.985552i | \(0.554175\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4250.52 | + | 1876.06i | −0.746030 | + | 0.329277i | ||||
\(320\) | −815.098 | −0.142392 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1509.03 | − | 4644.30i | 0.261164 | − | 0.803779i | ||||
\(323\) | −146.752 | − | 451.656i | −0.0252802 | − | 0.0778043i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −345.089 | + | 250.722i | −0.0588988 | + | 0.0427925i | ||||
\(326\) | 1571.84 | + | 4837.62i | 0.267043 | + | 0.821874i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −876.610 | − | 636.894i | −0.147569 | − | 0.107215i | ||||
\(329\) | 3157.95 | 0.529190 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10199.3 | 1.69366 | 0.846832 | − | 0.531861i | \(-0.178507\pi\) | ||||
0.846832 | + | 0.531861i | \(0.178507\pi\) | |||||||
\(332\) | −4399.57 | − | 3196.48i | −0.727283 | − | 0.528402i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −856.250 | − | 2635.27i | −0.140275 | − | 0.431723i | ||||
\(335\) | −3035.18 | + | 2205.19i | −0.495014 | + | 0.359648i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −519.376 | − | 1598.48i | −0.0839532 | − | 0.258381i | 0.900264 | − | 0.435343i | \(-0.143373\pi\) |
−0.984218 | + | 0.176962i | \(0.943373\pi\) | |||||||
\(338\) | −1276.58 | + | 3928.90i | −0.205434 | + | 0.632260i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3336.92 | −0.532264 | ||||||||
\(341\) | −5297.72 | + | 9107.99i | −0.841312 | + | 1.44641i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2573.29 | + | 1869.61i | 0.405087 | + | 0.294313i | ||||
\(344\) | 874.371 | − | 2691.04i | 0.137043 | − | 0.421776i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −717.616 | + | 521.378i | −0.111501 | + | 0.0810101i | ||||
\(347\) | 8515.93 | − | 6187.19i | 1.31746 | − | 0.957192i | 0.317501 | − | 0.948258i | \(-0.397156\pi\) |
0.999960 | − | 0.00893386i | \(-0.00284377\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1637.90 | + | 5040.94i | −0.251217 | + | 0.773168i | 0.743334 | + | 0.668920i | \(0.233243\pi\) |
−0.994551 | + | 0.104247i | \(0.966757\pi\) | |||||||
\(350\) | −1412.27 | − | 1026.08i | −0.215683 | − | 0.156703i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 118.289 | + | 1161.44i | 0.0179114 | + | 0.175867i | ||||
\(353\) | 7438.40 | 1.12155 | 0.560773 | − | 0.827969i | \(-0.310504\pi\) | ||||
0.560773 | + | 0.827969i | \(0.310504\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 521.257 | − | 1604.26i | 0.0779309 | − | 0.239847i | ||||
\(356\) | 321.693 | + | 990.068i | 0.0478923 | + | 0.147397i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 609.414 | − | 442.765i | 0.0899680 | − | 0.0653656i | ||||
\(359\) | −3136.93 | − | 9654.47i | −0.461172 | − | 1.41934i | −0.863734 | − | 0.503948i | \(-0.831880\pi\) |
0.402562 | − | 0.915393i | \(-0.368120\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5506.52 | + | 4000.72i | 0.802817 | + | 0.583281i | ||||
\(362\) | 6587.52 | 0.956443 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1075.97 | 0.154934 | ||||||||
\(365\) | 4837.41 | + | 3514.59i | 0.693703 | + | 0.504005i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 147.340 | + | 453.466i | 0.0209567 | + | 0.0644980i | 0.960988 | − | 0.276590i | \(-0.0892045\pi\) |
−0.940031 | + | 0.341088i | \(0.889204\pi\) | |||||||
\(368\) | −1347.14 | + | 978.755i | −0.190828 | + | 0.138644i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 672.221 | + | 2068.88i | 0.0944516 | + | 0.290692i | ||||
\(371\) | −3635.32 | + | 11188.4i | −0.508723 | + | 1.56569i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12738.5 | −1.76829 | −0.884146 | − | 0.467210i | \(-0.845259\pi\) | ||||
−0.884146 | + | 0.467210i | \(0.845259\pi\) | |||||||
\(374\) | 484.262 | + | 4754.82i | 0.0669534 | + | 0.657395i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −871.173 | − | 632.944i | −0.119488 | − | 0.0868128i | ||||
\(377\) | 451.207 | − | 1388.67i | 0.0616402 | − | 0.189709i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1050.66 | − | 763.349i | 0.142398 | − | 0.103458i | −0.514306 | − | 0.857607i | \(-0.671950\pi\) |
0.656704 | + | 0.754149i | \(0.271950\pi\) | |||||||
\(380\) | −298.809 | + | 217.097i | −0.0403383 | + | 0.0293075i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1415.46 | + | 4356.34i | −0.189584 | + | 0.583481i | ||||
\(383\) | −542.501 | − | 394.150i | −0.0723772 | − | 0.0525851i | 0.551008 | − | 0.834500i | \(-0.314243\pi\) |
−0.623386 | + | 0.781915i | \(0.714243\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5480.92 | + | 9422.95i | −0.725541 | + | 1.24737i | ||||
\(386\) | −4606.80 | −0.607461 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1748.46 | − | 5381.20i | 0.228774 | − | 0.704095i | ||||
\(389\) | −1617.98 | − | 4979.64i | −0.210887 | − | 0.649043i | −0.999420 | − | 0.0340509i | \(-0.989159\pi\) |
0.788533 | − | 0.614992i | \(-0.210841\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5515.04 | + | 4006.91i | −0.713319 | + | 0.518256i | ||||
\(392\) | 512.780 | + | 1578.18i | 0.0660697 | + | 0.203342i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1685.77 | − | 1224.79i | −0.215553 | − | 0.156609i | ||||
\(395\) | −5196.67 | −0.661956 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1751.64 | 0.221442 | 0.110721 | − | 0.993852i | \(-0.464684\pi\) | ||||
0.110721 | + | 0.993852i | \(0.464684\pi\) | |||||||
\(398\) | −5604.60 | − | 4071.98i | −0.705862 | − | 0.512839i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 183.944 | + | 566.121i | 0.0229930 | + | 0.0707651i | ||||
\(401\) | 2922.80 | − | 2123.54i | 0.363984 | − | 0.264450i | −0.390728 | − | 0.920506i | \(-0.627777\pi\) |
0.754712 | + | 0.656056i | \(0.227777\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1023.26 | − | 3149.28i | −0.126482 | − | 0.389273i | ||||
\(404\) | 230.671 | − | 709.933i | 0.0284067 | − | 0.0874269i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5975.60 | 0.730453 | ||||||||
\(407\) | 2850.42 | − | 1258.10i | 0.347151 | − | 0.153223i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9137.83 | + | 6639.02i | 1.10473 | + | 0.802637i | 0.981826 | − | 0.189781i | \(-0.0607779\pi\) |
0.122908 | + | 0.992418i | \(0.460778\pi\) | |||||||
\(410\) | −1066.11 | + | 3281.14i | −0.128418 | + | 0.395229i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3795.63 | − | 2757.69i | 0.453877 | − | 0.329761i | ||||
\(413\) | 12368.8 | − | 8986.42i | 1.47367 | − | 1.07069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5350.63 | + | 16467.5i | −0.632897 | + | 1.94786i | ||||
\(416\) | −296.824 | − | 215.655i | −0.0349831 | − | 0.0254167i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 352.708 | + | 394.271i | 0.0412716 | + | 0.0461349i | ||||
\(419\) | 3680.45 | 0.429121 | 0.214560 | − | 0.976711i | \(-0.431168\pi\) | ||||
0.214560 | + | 0.976711i | \(0.431168\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2860.31 | − | 8803.14i | 0.331124 | − | 1.01909i | −0.637476 | − | 0.770470i | \(-0.720021\pi\) |
0.968600 | − | 0.248625i | \(-0.0799786\pi\) | |||||||
\(422\) | 1292.91 | + | 3979.18i | 0.149142 | + | 0.459013i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3245.33 | − | 2357.87i | 0.371715 | − | 0.270067i | ||||
\(425\) | 753.045 | + | 2317.63i | 0.0859483 | + | 0.264522i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6942.80 | − | 5044.24i | −0.786852 | − | 0.571681i | ||||
\(428\) | 2850.85 | 0.321966 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −9009.14 | −1.01037 | ||||||||
\(431\) | 2899.55 | + | 2106.64i | 0.324052 | + | 0.235437i | 0.737902 | − | 0.674907i | \(-0.235816\pi\) |
−0.413851 | + | 0.910345i | \(0.635816\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2566.94 | − | 7900.24i | −0.284895 | − | 0.876816i | −0.986430 | − | 0.164181i | \(-0.947502\pi\) |
0.701535 | − | 0.712635i | \(-0.252498\pi\) | |||||||
\(434\) | 10963.5 | − | 7965.47i | 1.21260 | − | 0.881002i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1541.64 | + | 4744.69i | 0.169338 | + | 0.521168i | ||||
\(437\) | −233.165 | + | 717.608i | −0.0255236 | + | 0.0785534i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11932.4 | 1.29727 | 0.648634 | − | 0.761101i | \(-0.275341\pi\) | ||||
0.648634 | + | 0.761101i | \(0.275341\pi\) | |||||||
\(440\) | 3400.63 | − | 1500.94i | 0.368452 | − | 0.162624i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1215.16 | − | 882.867i | −0.130768 | − | 0.0950084i | ||||
\(443\) | −333.374 | + | 1026.02i | −0.0357541 | + | 0.110040i | −0.967341 | − | 0.253480i | \(-0.918425\pi\) |
0.931587 | + | 0.363519i | \(0.118425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2681.55 | − | 1948.26i | 0.285658 | − | 0.207543i | ||||
\(446\) | −5992.43 | + | 4353.75i | −0.636210 | + | 0.462234i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 463.993 | − | 1428.02i | 0.0489321 | − | 0.150598i | ||||
\(449\) | 10327.9 | + | 7503.63i | 1.08553 | + | 0.788682i | 0.978638 | − | 0.205589i | \(-0.0659111\pi\) |
0.106889 | + | 0.994271i | \(0.465911\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4830.06 | + | 1042.94i | 0.504298 | + | 0.108892i | ||||
\(452\) | 3928.01 | 0.408756 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2999.63 | − | 9231.91i | 0.310087 | − | 0.954350i | ||||
\(455\) | −1058.65 | − | 3258.19i | −0.109077 | − | 0.335706i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9082.69 | − | 6598.96i | 0.929695 | − | 0.675463i | −0.0162235 | − | 0.999868i | \(-0.505164\pi\) |
0.945918 | + | 0.324406i | \(0.105164\pi\) | |||||||
\(458\) | −826.216 | − | 2542.83i | −0.0842938 | − | 0.259430i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4289.27 | + | 3116.33i | 0.434757 | + | 0.315869i | ||||
\(461\) | 2160.58 | 0.218283 | 0.109141 | − | 0.994026i | \(-0.465190\pi\) | ||||
0.109141 | + | 0.994026i | \(0.465190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11469.5 | 1.15125 | 0.575627 | − | 0.817712i | \(-0.304758\pi\) | ||||
0.575627 | + | 0.817712i | \(0.304758\pi\) | |||||||
\(464\) | −1648.47 | − | 1197.68i | −0.164931 | − | 0.119830i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3648.81 | + | 11229.9i | 0.362721 | + | 1.11634i | ||||
\(467\) | 1632.91 | − | 1186.38i | 0.161803 | − | 0.117557i | −0.503937 | − | 0.863740i | \(-0.668116\pi\) |
0.665741 | + | 0.746183i | \(0.268116\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2135.64 | − | 6572.82i | −0.210266 | − | 0.647131i | ||||
\(470\) | −1059.50 | + | 3260.79i | −0.103981 | + | 0.320019i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5213.26 | −0.508389 | ||||||||
\(473\) | 1307.43 | + | 12837.2i | 0.127094 | + | 1.24790i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 218.216 | + | 158.543i | 0.0210788 | + | 0.0153146i | ||||
\(476\) | 1899.53 | − | 5846.16i | 0.182910 | − | 0.562938i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5371.53 | + | 3902.64i | −0.513991 | + | 0.373437i | ||||
\(479\) | −5927.67 | + | 4306.71i | −0.565433 | + | 0.410811i | −0.833443 | − | 0.552605i | \(-0.813634\pi\) |
0.268011 | + | 0.963416i | \(0.413634\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −302.582 | + | 931.252i | −0.0286831 | + | 0.0882774i | ||||
\(482\) | 8536.67 | + | 6202.26i | 0.806711 | + | 0.586110i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2632.22 | − | 4627.78i | −0.247203 | − | 0.434615i | ||||
\(485\) | −18015.3 | −1.68667 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1912.75 | + | 5886.85i | −0.177978 | + | 0.547759i | −0.999757 | − | 0.0220470i | \(-0.992982\pi\) |
0.821779 | + | 0.569806i | \(0.192982\pi\) | |||||||
\(488\) | 904.276 | + | 2783.07i | 0.0838824 | + | 0.258164i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4274.41 | − | 3105.54i | 0.394078 | − | 0.286315i | ||||
\(491\) | 3127.54 | + | 9625.57i | 0.287462 | + | 0.884717i | 0.985650 | + | 0.168802i | \(0.0539900\pi\) |
−0.698188 | + | 0.715914i | \(0.746010\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6748.64 | − | 4903.17i | −0.616518 | − | 0.447926i | ||||
\(494\) | −166.252 | −0.0151418 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4620.98 | −0.418323 | ||||||||
\(497\) | 2513.89 | + | 1826.45i | 0.226888 | + | 0.164844i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 791.952 | + | 2437.38i | 0.0710474 | + | 0.218661i | 0.980275 | − | 0.197638i | \(-0.0633269\pi\) |
−0.909228 | + | 0.416299i | \(0.863327\pi\) | |||||||
\(500\) | −3618.47 | + | 2628.97i | −0.323646 | + | 0.235143i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1212.49 | + | 3731.66i | 0.107801 | + | 0.331777i | ||||
\(503\) | −2658.01 | + | 8180.53i | −0.235616 | + | 0.725152i | 0.761423 | + | 0.648256i | \(0.224501\pi\) |
−0.997039 | + | 0.0768967i | \(0.975499\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2376.74 | −0.209432 | ||||||||
\(506\) | 3818.04 | − | 6564.08i | 0.335440 | − | 0.576698i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5018.07 | + | 3645.84i | 0.438269 | + | 0.318421i | ||||
\(509\) | 4309.27 | − | 13262.6i | 0.375255 | − | 1.15492i | −0.568051 | − | 0.822993i | \(-0.692302\pi\) |
0.943306 | − | 0.331924i | \(-0.107698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8911.11 | + | 6474.30i | −0.771437 | + | 0.560482i | ||||
\(512\) | −414.217 | + | 300.946i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3672.34 | + | 11302.3i | −0.315136 | + | 0.969889i | ||||
\(515\) | −12085.2 | − | 8780.41i | −1.03405 | − | 0.751284i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4800.10 | + | 1036.47i | 0.408333 | + | 0.0881704i | ||||
\(518\) | −4007.27 | −0.339902 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −360.988 | + | 1111.01i | −0.0304431 | + | 0.0936941i | ||||
\(521\) | 3736.89 | + | 11501.0i | 0.314234 | + | 0.967113i | 0.976069 | + | 0.217463i | \(0.0697782\pi\) |
−0.661834 | + | 0.749650i | \(0.730222\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13504.0 | − | 9811.21i | 1.12904 | − | 0.820295i | 0.143484 | − | 0.989653i | \(-0.454169\pi\) |
0.985555 | + | 0.169358i | \(0.0541693\pi\) | |||||||
\(524\) | −917.304 | − | 2823.17i | −0.0764744 | − | 0.235364i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2757.31 | − | 2003.30i | −0.228564 | − | 0.166061i | ||||
\(527\) | −18917.8 | −1.56370 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1335.94 | −0.109800 | ||||||||
\(530\) | −10333.1 | − | 7507.41i | −0.846867 | − | 0.615285i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −210.250 | − | 647.084i | −0.0171344 | − | 0.0527343i | ||||
\(533\) | −1256.34 | + | 912.785i | −0.102098 | + | 0.0741784i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2804.97 | − | 8632.79i | −0.226671 | − | 0.697623i | ||||
\(536\) | −728.231 | + | 2241.26i | −0.0586843 | + | 0.180612i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11690.7 | 0.936840 | ||||||||
\(539\) | −5045.44 | − | 5639.98i | −0.403196 | − | 0.450707i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16725.1 | − | 12151.5i | −1.32914 | − | 0.965679i | −0.999769 | − | 0.0214796i | \(-0.993162\pi\) |
−0.329374 | − | 0.944200i | \(-0.606838\pi\) | |||||||
\(542\) | 3650.01 | − | 11233.6i | 0.289264 | − | 0.890264i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1695.76 | + | 1232.04i | −0.133649 | + | 0.0971015i | ||||
\(545\) | 12850.8 | − | 9336.63i | 1.01003 | − | 0.733830i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2833.62 | − | 8721.00i | 0.221494 | − | 0.681687i | −0.777135 | − | 0.629334i | \(-0.783328\pi\) |
0.998629 | − | 0.0523532i | \(-0.0166722\pi\) | |||||||
\(548\) | 1668.77 | + | 1212.43i | 0.130084 | + | 0.0945119i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1809.89 | − | 2023.17i | −0.140317 | − | 0.156851i | ||||
\(551\) | −923.311 | −0.0713873 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2958.19 | − | 9104.37i | 0.227477 | − | 0.700104i | ||||
\(554\) | 5489.62 | + | 16895.3i | 0.420995 | + | 1.29569i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7970.97 | + | 5791.25i | −0.607994 | + | 0.441733i | ||||
\(557\) | −6276.38 | − | 19316.7i | −0.477449 | − | 1.46944i | −0.842627 | − | 0.538498i | \(-0.818992\pi\) |
0.365178 | − | 0.930938i | \(-0.381008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3280.74 | − | 2383.60i | −0.248230 | − | 0.180350i | ||||
\(560\) | −4780.78 | −0.360759 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16303.5 | 1.22371 | ||||||||
\(563\) | 4500.68 | + | 3269.94i | 0.336911 | + | 0.244780i | 0.743357 | − | 0.668894i | \(-0.233232\pi\) |
−0.406446 | + | 0.913675i | \(0.633232\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3864.78 | − | 11894.6i | −0.287774 | − | 0.885678i | ||||
\(566\) | −9488.08 | + | 6893.50i | −0.704618 | + | 0.511935i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −327.425 | − | 1007.71i | −0.0241874 | − | 0.0744412i | ||||
\(569\) | 7041.09 | − | 21670.3i | 0.518766 | − | 1.59660i | −0.257557 | − | 0.966263i | \(-0.582917\pi\) |
0.776323 | − | 0.630335i | \(-0.217083\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11157.6 | −0.817743 | −0.408871 | − | 0.912592i | \(-0.634078\pi\) | ||||
−0.408871 | + | 0.912592i | \(0.634078\pi\) | |||||||
\(572\) | 1635.48 | + | 353.145i | 0.119550 | + | 0.0258142i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5141.56 | − | 3735.56i | −0.373876 | − | 0.271637i | ||||
\(575\) | 1196.47 | − | 3682.34i | 0.0867758 | − | 0.267068i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10055.4 | + | 7305.64i | −0.725494 | + | 0.527102i | −0.888135 | − | 0.459583i | \(-0.847999\pi\) |
0.162641 | + | 0.986685i | \(0.447999\pi\) | |||||||
\(578\) | 1007.17 | − | 731.752i | 0.0724788 | − | 0.0526589i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2004.82 | + | 6170.20i | −0.143527 | + | 0.441730i | ||||
\(581\) | −25804.7 | − | 18748.2i | −1.84262 | − | 1.33874i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −9197.84 | + | 15813.2i | −0.653406 | + | 1.12335i | ||||
\(584\) | 3755.91 | 0.266131 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4707.30 | + | 14487.6i | −0.331837 | + | 1.02129i | ||||
\(587\) | −1889.62 | − | 5815.66i | −0.132867 | − | 0.408923i | 0.862385 | − | 0.506253i | \(-0.168970\pi\) |
−0.995252 | + | 0.0973299i | \(0.968970\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1694.02 | + | 1230.77i | −0.118507 | + | 0.0861005i | ||||
\(590\) | 5129.35 | + | 15786.5i | 0.357918 | + | 1.10156i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1105.47 | + | 803.172i | 0.0767476 | + | 0.0557604i | ||||
\(593\) | −7188.32 | −0.497789 | −0.248894 | − | 0.968531i | \(-0.580067\pi\) | ||||
−0.248894 | + | 0.968531i | \(0.580067\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −19572.0 | −1.34852 | ||||||||
\(596\) | −1406.90 | − | 1022.18i | −0.0966930 | − | 0.0702516i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 737.461 | + | 2269.67i | 0.0504298 | + | 0.155207i | ||||
\(599\) | −818.874 | + | 594.947i | −0.0558569 | + | 0.0405824i | −0.615363 | − | 0.788244i | \(-0.710991\pi\) |
0.559506 | + | 0.828826i | \(0.310991\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4134.93 | + | 12726.0i | 0.280644 | + | 0.863734i | 0.987671 | + | 0.156547i | \(0.0500362\pi\) |
−0.707026 | + | 0.707187i | \(0.749964\pi\) | |||||||
\(602\) | 5128.43 | − | 15783.7i | 0.347208 | − | 1.06860i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3123.97 | −0.210451 | ||||||||
\(605\) | −11423.7 | + | 12524.0i | −0.767671 | + | 0.841611i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −442.493 | − | 321.490i | −0.0295885 | − | 0.0214973i | 0.572893 | − | 0.819630i | \(-0.305821\pi\) |
−0.602481 | + | 0.798133i | \(0.705821\pi\) | |||||||
\(608\) | −71.6932 | + | 220.649i | −0.00478214 | + | 0.0147179i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7537.83 | − | 5476.55i | 0.500324 | − | 0.363507i | ||||
\(611\) | −1248.55 | + | 907.124i | −0.0826692 | + | 0.0600627i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4247.62 | − | 13072.8i | 0.279869 | − | 0.861349i | −0.708020 | − | 0.706192i | \(-0.750412\pi\) |
0.987890 | − | 0.155157i | \(-0.0495885\pi\) | |||||||
\(614\) | −6635.04 | − | 4820.64i | −0.436105 | − | 0.316849i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 693.798 | + | 6812.19i | 0.0453797 | + | 0.445570i | ||||
\(617\) | 3323.39 | 0.216847 | 0.108423 | − | 0.994105i | \(-0.465420\pi\) | ||||
0.108423 | + | 0.994105i | \(0.465420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6699.20 | + | 20618.0i | −0.434998 | + | 1.33879i | 0.458091 | + | 0.888905i | \(0.348533\pi\) |
−0.893089 | + | 0.449881i | \(0.851467\pi\) | |||||||
\(620\) | 4546.60 | + | 13993.0i | 0.294509 | + | 0.906406i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2356.07 | − | 1711.79i | 0.151881 | − | 0.110348i | ||||
\(623\) | 1886.82 | + | 5807.03i | 0.121338 | + | 0.373441i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15283.4 | + | 11104.0i | 0.978138 | + | 0.710659i | ||||
\(626\) | −6923.35 | −0.442033 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2089.53 | 0.132773 | ||||||||
\(629\) | 4525.67 | + | 3288.09i | 0.286885 | + | 0.208434i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9236.13 | − | 28425.9i | −0.582702 | − | 1.79337i | −0.608311 | − | 0.793699i | \(-0.708153\pi\) |
0.0256092 | − | 0.999672i | \(-0.491847\pi\) | |||||||
\(632\) | −2640.84 | + | 1918.68i | −0.166214 | + | 0.120761i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3085.42 | − | 9495.94i | −0.193277 | − | 0.594845i | ||||
\(635\) | 6102.83 | − | 18782.6i | 0.381391 | − | 1.17380i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2378.21 | 0.147925 | ||||||||
\(638\) | 9082.93 | + | 1961.26i | 0.563631 | + | 0.121704i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1318.86 | + | 958.205i | 0.0814569 | + | 0.0591819i | ||||
\(641\) | −8398.45 | + | 25847.8i | −0.517502 | + | 1.59271i | 0.261181 | + | 0.965290i | \(0.415888\pi\) |
−0.778683 | + | 0.627418i | \(0.784112\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13247.2 | + | 9624.69i | −0.812474 | + | 0.590297i | −0.914547 | − | 0.404480i | \(-0.867452\pi\) |
0.102073 | + | 0.994777i | \(0.467452\pi\) | |||||||
\(644\) | −7901.36 | + | 5740.67i | −0.483474 | + | 0.351264i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −293.504 | + | 903.312i | −0.0178758 | + | 0.0550160i | ||||
\(647\) | 1850.76 | + | 1344.66i | 0.112459 | + | 0.0817062i | 0.642593 | − | 0.766207i | \(-0.277859\pi\) |
−0.530134 | + | 0.847914i | \(0.677859\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 21750.0 | − | 9599.84i | 1.31550 | − | 0.580627i | ||||
\(650\) | 853.107 | 0.0514794 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3143.67 | − | 9675.23i | 0.188828 | − | 0.581152i | ||||
\(653\) | 354.419 | + | 1090.79i | 0.0212396 | + | 0.0653689i | 0.961115 | − | 0.276150i | \(-0.0890587\pi\) |
−0.939875 | + | 0.341519i | \(0.889059\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7646.43 | + | 5555.45i | −0.456138 | + | 0.331404i | ||||
\(656\) | 669.670 | + | 2061.03i | 0.0398571 | + | 0.122667i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5109.67 | − | 3712.40i | −0.302729 | − | 0.219946i | ||||
\(659\) | 377.923 | 0.0223396 | 0.0111698 | − | 0.999938i | \(-0.496444\pi\) | ||||
0.0111698 | + | 0.999938i | \(0.496444\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17500.4 | −1.02978 | −0.514892 | − | 0.857255i | \(-0.672168\pi\) | ||||
−0.514892 | + | 0.857255i | \(0.672168\pi\) | |||||||
\(662\) | −16502.8 | − | 11990.0i | −0.968880 | − | 0.703932i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3360.97 | + | 10344.0i | 0.196432 | + | 0.604556i | ||||
\(665\) | −1752.60 | + | 1273.34i | −0.102200 | + | 0.0742524i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4095.63 | + | 12605.0i | 0.237756 | + | 0.731738i | ||||
\(668\) | −1712.50 | + | 5270.53i | −0.0991895 | + | 0.305274i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 7503.38 | 0.432658 | ||||||||
\(671\) | −8897.51 | − | 9945.97i | −0.511900 | − | 0.572221i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11739.3 | + | 8529.08i | 0.672386 | + | 0.488517i | 0.870823 | − | 0.491597i | \(-0.163587\pi\) |
−0.198437 | + | 0.980114i | \(0.563587\pi\) | |||||||
\(674\) | −1038.75 | + | 3196.95i | −0.0593639 | + | 0.182703i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6684.24 | − | 4856.38i | 0.380305 | − | 0.276308i | ||||
\(677\) | 379.518 | − | 275.736i | 0.0215451 | − | 0.0156534i | −0.576961 | − | 0.816772i | \(-0.695761\pi\) |
0.598506 | + | 0.801119i | \(0.295761\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10255.2 | − | 31562.2i | 0.579614 | − | 1.78387i | ||||
\(680\) | 5399.25 | + | 3922.78i | 0.304488 | + | 0.221223i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19279.0 | − | 8509.20i | 1.08245 | − | 0.477763i | ||||
\(683\) | 15892.3 | 0.890342 | 0.445171 | − | 0.895446i | \(-0.353143\pi\) | ||||
0.445171 | + | 0.895446i | \(0.353143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2029.51 | − | 6246.19i | 0.113202 | − | 0.348401i | ||||
\(686\) | −1965.82 | − | 6050.17i | −0.109410 | − | 0.336730i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4578.27 | + | 3326.31i | −0.253699 | + | 0.184323i | ||||
\(689\) | −1776.58 | − | 5467.75i | −0.0982326 | − | 0.302329i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5020.47 | + | 3647.58i | 0.276393 | + | 0.200811i | 0.717343 | − | 0.696721i | \(-0.245358\pi\) |
−0.440950 | + | 0.897532i | \(0.645358\pi\) | |||||||
\(692\) | 1774.04 | 0.0974553 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21052.5 | −1.15150 | ||||||||
\(695\) | 25379.4 | + | 18439.2i | 1.38517 | + | 1.00639i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2741.55 | + | 8437.64i | 0.148987 | + | 0.458534i | ||||
\(698\) | 8576.16 | − | 6230.95i | 0.465061 | − | 0.337887i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1078.88 | + | 3320.46i | 0.0582541 | + | 0.179288i | ||||
\(701\) | −578.646 | + | 1780.89i | −0.0311771 | + | 0.0959533i | −0.965434 | − | 0.260647i | \(-0.916064\pi\) |
0.934257 | + | 0.356600i | \(0.116064\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 619.178 | 0.0332187 | ||||||||
\(704\) | 1173.96 | − | 2018.31i | 0.0628486 | − | 0.108051i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12035.6 | − | 8744.36i | −0.641594 | − | 0.466145i | ||||
\(707\) | 1352.95 | − | 4163.95i | 0.0719702 | − | 0.221502i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4236.02 | + | 3077.65i | −0.224383 | + | 0.163023i | −0.694297 | − | 0.719688i | \(-0.744285\pi\) |
0.469915 | + | 0.882712i | \(0.344285\pi\) | |||||||
\(710\) | −2729.34 | + | 1982.98i | −0.144268 | + | 0.104817i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 643.385 | − | 1980.14i | 0.0338650 | − | 0.104226i | ||||
\(713\) | 24316.8 | + | 17667.2i | 1.27724 | + | 0.927970i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −539.778 | − | 5299.92i | −0.0282329 | − | 0.277211i | ||||
\(716\) | −1506.56 | −0.0786349 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6273.85 | + | 19308.9i | −0.326098 | + | 1.00363i | ||||
\(719\) | 5338.20 | + | 16429.3i | 0.276886 | + | 0.852169i | 0.988714 | + | 0.149814i | \(0.0478676\pi\) |
−0.711828 | + | 0.702354i | \(0.752132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22262.4 | − | 16174.6i | 1.14993 | − | 0.835470i | ||||
\(722\) | −4206.61 | − | 12946.6i | −0.216833 | − | 0.667345i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10658.8 | − | 7744.09i | −0.547144 | − | 0.397523i | ||||
\(725\) | 4737.89 | 0.242705 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17292.7 | 0.882190 | 0.441095 | − | 0.897461i | \(-0.354590\pi\) | ||||
0.441095 | + | 0.897461i | \(0.354590\pi\) | |||||||
\(728\) | −1740.95 | − | 1264.88i | −0.0886319 | − | 0.0643949i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3695.45 | − | 11373.4i | −0.187363 | − | 0.576644i | ||||
\(731\) | −18742.9 | + | 13617.5i | −0.948333 | + | 0.689004i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4289.57 | − | 13201.9i | −0.216151 | − | 0.665245i | −0.999070 | − | 0.0431210i | \(-0.986270\pi\) |
0.782919 | − | 0.622124i | \(-0.213730\pi\) | |||||||
\(734\) | 294.680 | − | 906.933i | 0.0148186 | − | 0.0456069i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3330.32 | 0.166790 | ||||||||
\(737\) | −1088.91 | − | 10691.7i | −0.0544239 | − | 0.534372i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5160.93 | − | 3749.64i | −0.256898 | − | 0.186648i | 0.451880 | − | 0.892079i | \(-0.350753\pi\) |
−0.708779 | + | 0.705431i | \(0.750753\pi\) | |||||||
\(740\) | 1344.44 | − | 4137.77i | 0.0667874 | − | 0.205550i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19034.8 | − | 13829.6i | 0.941763 | − | 0.684231i | ||||
\(743\) | 18641.9 | − | 13544.2i | 0.920467 | − | 0.668758i | −0.0231734 | − | 0.999731i | \(-0.507377\pi\) |
0.943640 | + | 0.330973i | \(0.107377\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1711.04 | + | 5266.03i | −0.0841443 | + | 0.258970i | ||||
\(746\) | 20611.3 | + | 14975.0i | 1.01157 | + | 0.734950i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4806.07 | − | 8262.74i | 0.234930 | − | 0.403898i | ||||
\(749\) | 16721.1 | 0.815720 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6429.44 | + | 19787.8i | −0.312401 | + | 0.961473i | 0.664409 | + | 0.747369i | \(0.268683\pi\) |
−0.976811 | + | 0.214104i | \(0.931317\pi\) | |||||||
\(752\) | 665.517 | + | 2048.25i | 0.0322725 | + | 0.0993245i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2362.55 | + | 1716.49i | −0.114110 | + | 0.0829059i | ||||
\(755\) | 3073.68 | + | 9459.83i | 0.148163 | + | 0.455998i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17667.1 | + | 12835.9i | 0.848246 | + | 0.616287i | 0.924662 | − | 0.380789i | \(-0.124348\pi\) |
−0.0764161 | + | 0.997076i | \(0.524348\pi\) | |||||||
\(758\) | −2597.38 | −0.124460 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 738.696 | 0.0352570 | ||||||||
\(761\) | −5775.94 | − | 4196.47i | −0.275135 | − | 0.199897i | 0.441658 | − | 0.897184i | \(-0.354391\pi\) |
−0.716793 | + | 0.697286i | \(0.754391\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9042.17 | + | 27828.9i | 0.429028 | + | 1.32041i | ||||
\(764\) | 7411.45 | − | 5384.73i | 0.350964 | − | 0.254990i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 414.434 | + | 1275.50i | 0.0195484 | + | 0.0601639i | ||||
\(767\) | −2308.84 | + | 7105.86i | −0.108693 | + | 0.334521i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15473.8 | 0.725618 | 0.362809 | − | 0.931864i | \(-0.381818\pi\) | ||||
0.362809 | + | 0.931864i | \(0.381818\pi\) | |||||||
\(770\) | 19945.7 | − | 8803.46i | 0.933496 | − | 0.412019i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7453.96 | + | 5415.62i | 0.347505 | + | 0.252477i | ||||
\(773\) | −4709.69 | + | 14494.9i | −0.219141 | + | 0.674446i | 0.779693 | + | 0.626162i | \(0.215375\pi\) |
−0.998834 | + | 0.0482840i | \(0.984625\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8692.69 | − | 6315.61i | 0.402904 | − | 0.292727i | ||||
\(776\) | −9155.04 | + | 6651.52i | −0.423514 | + | 0.307701i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3235.97 | + | 9959.28i | −0.149120 | + | 0.458943i | ||||
\(779\) | 794.442 | + | 577.196i | 0.0365389 | + | 0.0265471i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3221.66 | + | 3601.29i | 0.147606 | + | 0.164999i | ||||
\(782\) | 13633.9 | 0.623464 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1025.56 | − | 3156.35i | 0.0467183 | − | 0.143784i | ||||
\(785\) | −2055.89 | − | 6327.39i | −0.0934751 | − | 0.287687i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29190.5 | + | 21208.1i | −1.32215 | + | 0.960595i | −0.322243 | + | 0.946657i | \(0.604437\pi\) |
−0.999903 | + | 0.0139380i | \(0.995563\pi\) | |||||||
\(788\) | 1287.82 | + | 3963.49i | 0.0582189 | + | 0.179179i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8408.39 | + | 6109.05i | 0.378680 | + | 0.275127i | ||||
\(791\) | 23038.9 | 1.03561 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4193.91 | 0.187806 | ||||||||
\(794\) | −2834.22 | − | 2059.18i | −0.126678 | − | 0.0920373i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4281.53 | + | 13177.2i | 0.190647 | + | 0.586751i | ||||
\(797\) | 2737.30 | − | 1988.76i | 0.121656 | − | 0.0883885i | −0.525293 | − | 0.850921i | \(-0.676044\pi\) |
0.646950 | + | 0.762533i | \(0.276044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2724.55 | + | 8385.31i | 0.120635 | + | 0.371278i | ||||
\(800\) | 367.887 | − | 1132.24i | 0.0162585 | − | 0.0500385i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7225.55 | −0.318134 | ||||||||
\(803\) | −15669.9 | + | 6916.24i | −0.688639 | + | 0.303946i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25157.7 | + | 18278.2i | 1.10148 | + | 0.800274i | ||||
\(806\) | −2046.53 | + | 6298.56i | −0.0894365 | + | 0.275257i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1207.81 | + | 877.525i | −0.0525874 | + | 0.0382070i | ||||
\(809\) | 10905.8 | − | 7923.49i | 0.473950 | − | 0.344345i | −0.325028 | − | 0.945704i | \(-0.605374\pi\) |
0.798979 | + | 0.601359i | \(0.205374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6620.10 | + | 20374.6i | −0.286638 | + | 0.882180i | 0.699265 | + | 0.714862i | \(0.253511\pi\) |
−0.985903 | + | 0.167318i | \(0.946489\pi\) | |||||||
\(812\) | −9668.72 | − | 7024.74i | −0.417864 | − | 0.303596i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6091.07 | − | 1315.23i | −0.262275 | − | 0.0566324i | ||||
\(815\) | −32391.1 | −1.39216 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −792.413 | + | 2438.80i | −0.0339327 | + | 0.104434i | ||||
\(818\) | −6980.68 | − | 21484.3i | −0.298379 | − | 0.918315i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5582.21 | − | 4055.71i | 0.237731 | − | 0.172722i | ||||
\(821\) | −3295.61 | − | 10142.8i | −0.140094 | − | 0.431166i | 0.856253 | − | 0.516556i | \(-0.172786\pi\) |
−0.996348 | + | 0.0853901i | \(0.972786\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9705.69 | + | 7051.60i | 0.411080 | + | 0.298667i | 0.774039 | − | 0.633138i | \(-0.218233\pi\) |
−0.362959 | + | 0.931805i | \(0.618233\pi\) | |||||||
\(824\) | −9383.31 | −0.396703 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30577.2 | −1.28804 | ||||||||
\(827\) | 33073.2 | + | 24029.1i | 1.39065 | + | 1.01037i | 0.995794 | + | 0.0916236i | \(0.0292057\pi\) |
0.394856 | + | 0.918743i | \(0.370794\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10270.8 | − | 31610.2i | −0.430301 | − | 1.32433i | −0.897826 | − | 0.440350i | \(-0.854855\pi\) |
0.467526 | − | 0.883979i | \(-0.345145\pi\) | |||||||
\(830\) | 28016.3 | − | 20355.0i | 1.17164 | − | 0.851244i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 226.753 | + | 697.874i | 0.00944862 | + | 0.0290799i | ||||
\(833\) | 4198.53 | − | 12921.7i | 0.174634 | − | 0.537469i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17644.9 | 0.731288 | ||||||||
\(836\) | −107.201 | − | 1052.58i | −0.00443497 | − | 0.0435456i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5955.09 | − | 4326.62i | −0.245483 | − | 0.178354i | ||||
\(839\) | 1968.00 | − | 6056.87i | 0.0809806 | − | 0.249233i | −0.902367 | − | 0.430969i | \(-0.858172\pi\) |
0.983347 | + | 0.181736i | \(0.0581718\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6610.24 | − | 4802.62i | 0.271034 | − | 0.196917i | ||||
\(842\) | −14976.8 | + | 10881.3i | −0.612987 | + | 0.445361i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2585.83 | − | 7958.36i | 0.105460 | − | 0.324571i | ||||
\(845\) | −21282.5 | − | 15462.6i | −0.866437 | − | 0.629503i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15438.7 | − | 27143.2i | −0.626305 | − | 1.10113i | ||||
\(848\) | −8022.90 | −0.324891 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1506.09 | − | 4635.27i | 0.0607746 | − | 0.187045i | ||||
\(851\) | −2746.55 | − | 8453.01i | −0.110635 | − | 0.340500i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2456.51 | + | 1784.76i | −0.0986040 | + | 0.0716400i | −0.635995 | − | 0.771693i | \(-0.719410\pi\) |
0.537391 | + | 0.843333i | \(0.319410\pi\) | |||||||
\(854\) | 5303.83 | + | 16323.5i | 0.212521 | + | 0.654074i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4612.78 | − | 3351.38i | −0.184184 | − | 0.133818i | ||||
\(857\) | 10184.8 | 0.405959 | 0.202979 | − | 0.979183i | \(-0.434938\pi\) | ||||
0.202979 | + | 0.979183i | \(0.434938\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34929.8 | −1.38742 | −0.693708 | − | 0.720256i | \(-0.744024\pi\) | ||||
−0.693708 | + | 0.720256i | \(0.744024\pi\) | |||||||
\(860\) | 14577.1 | + | 10590.9i | 0.577994 | + | 0.419937i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2215.06 | − | 6817.25i | −0.0875234 | − | 0.269369i | ||||
\(863\) | −9937.36 | + | 7219.91i | −0.391972 | + | 0.284784i | −0.766263 | − | 0.642527i | \(-0.777886\pi\) |
0.374291 | + | 0.927311i | \(0.377886\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1745.49 | − | 5372.06i | −0.0686108 | − | 0.211162i | ||||
\(866\) | −5133.89 | + | 15800.5i | −0.201451 | + | 0.620003i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −27103.3 | −1.05985 | ||||||||
\(869\) | 7484.62 | − | 12867.8i | 0.292173 | − | 0.502312i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2732.41 | + | 1985.21i | 0.106296 | + | 0.0772288i | ||||
\(872\) | 3083.29 | − | 9489.38i | 0.119740 | − | 0.368522i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1220.87 | − | 887.012i | 0.0472500 | − | 0.0343291i | ||||
\(875\) | −21223.4 | + | 15419.7i | −0.819977 | + | 0.595748i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5913.93 | − | 18201.2i | 0.227707 | − | 0.700811i | −0.770298 | − | 0.637684i | \(-0.779893\pi\) |
0.998005 | − | 0.0631273i | \(-0.0201074\pi\) | |||||||
\(878\) | −19307.0 | − | 14027.3i | −0.742117 | − | 0.539179i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7266.80 | − | 1569.10i | −0.278368 | − | 0.0601074i | ||||
\(881\) | 16737.0 | 0.640049 | 0.320024 | − | 0.947409i | \(-0.396309\pi\) | ||||
0.320024 | + | 0.947409i | \(0.396309\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −5749.02 | + | 17693.7i | −0.219105 | + | 0.674336i | 0.779731 | + | 0.626114i | \(0.215356\pi\) |
−0.998837 | + | 0.0482222i | \(0.984644\pi\) | |||||||
\(884\) | 928.301 | + | 2857.02i | 0.0353192 | + | 0.108701i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1745.57 | − | 1268.23i | 0.0661891 | − | 0.0480892i | ||||
\(887\) | −4917.33 | − | 15134.0i | −0.186142 | − | 0.572886i | 0.813824 | − | 0.581111i | \(-0.197382\pi\) |
−0.999966 | + | 0.00822537i | \(0.997382\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 29432.4 | + | 21383.9i | 1.11038 | + | 0.806740i | ||||
\(890\) | −6629.16 | −0.249674 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14814.1 | 0.556068 | ||||||||
\(893\) | 789.514 | + | 573.616i | 0.0295858 | + | 0.0214953i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1482.30 | + | 4562.06i | 0.0553609 | + | 0.170383i | ||||
\(896\) | −2429.50 | + | 1765.13i | −0.0905846 | + | 0.0658135i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7889.78 | − | 24282.3i | −0.293191 | − | 0.902349i | ||||
\(899\) | −11365.8 | + | 34980.3i | −0.421657 | + | 1.29773i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32844.8 | −1.21445 | ||||||||
\(902\) | −6589.14 | − | 7365.59i | −0.243231 | − | 0.271893i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6355.65 | − | 4617.65i | −0.233834 | − | 0.169890i | ||||
\(905\) | −12963.0 | + | 39895.9i | −0.476136 | + | 1.46540i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18247.6 | − | 13257.7i | 0.668029 | − | 0.485351i | −0.201336 | − | 0.979522i | \(-0.564528\pi\) |
0.869365 | + | 0.494171i | \(0.164528\pi\) | |||||||
\(908\) | −15706.3 | + | 11411.3i | −0.574042 | + | 0.417066i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2117.30 | + | 6516.37i | −0.0771294 | + | 0.237380i | ||||
\(911\) | 39123.8 | + | 28425.1i | 1.42286 | + | 1.03377i | 0.991291 | + | 0.131692i | \(0.0420410\pi\) |
0.431572 | + | 0.902078i | \(0.357959\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −33069.9 | − | 36966.8i | −1.19874 | − | 1.34000i | ||||
\(914\) | −22453.6 | −0.812583 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1652.43 | + | 5085.66i | −0.0596047 | + | 0.183444i | ||||
\(917\) | −5380.24 | − | 16558.7i | −0.193753 | − | 0.596310i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17000.9 | + | 12351.9i | −0.610238 | + | 0.443364i | −0.849498 | − | 0.527592i | \(-0.823095\pi\) |
0.239260 | + | 0.970955i | \(0.423095\pi\) | |||||||
\(920\) | −3276.71 | − | 10084.7i | −0.117424 | − | 0.361393i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3495.90 | − | 2539.92i | −0.124871 | − | 0.0907243i | ||||
\(923\) | −1518.56 | −0.0541537 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3177.26 | −0.112938 | ||||||||
\(926\) | −18558.0 | − | 13483.2i | −0.658588 | − | 0.478492i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1259.32 | + | 3875.78i | 0.0445464 | + | 0.137100i | ||||
\(929\) | 3980.09 | − | 2891.71i | 0.140563 | − | 0.102125i | −0.515282 | − | 0.857021i | \(-0.672313\pi\) |
0.655844 | + | 0.754896i | \(0.272313\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −464.715 | − | 1430.25i | −0.0163592 | − | 0.0503485i | ||||
\(932\) | 7297.63 | − | 22459.8i | 0.256483 | − | 0.789372i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4036.78 | −0.141421 | ||||||||
\(935\) | −29749.5 | − | 6423.74i | −1.04055 | − | 0.224683i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13899.1 | + | 10098.3i | 0.484594 | + | 0.352078i | 0.803102 | − | 0.595842i | \(-0.203182\pi\) |
−0.318507 | + | 0.947920i | \(0.603182\pi\) | |||||||
\(938\) | −4271.28 | + | 13145.6i | −0.148680 | + | 0.457591i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5547.59 | − | 4030.56i | 0.192492 | − | 0.139854i | ||||
\(941\) | −41653.8 | + | 30263.2i | −1.44301 | + | 1.04841i | −0.455609 | + | 0.890180i | \(0.650579\pi\) |
−0.987402 | + | 0.158230i | \(0.949421\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4355.89 | − | 13406.0i | 0.150421 | − | 0.462949i | ||||
\(944\) | 8435.24 | + | 6128.56i | 0.290830 | + | 0.211300i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12975.6 | − | 22308.1i | 0.445955 | − | 0.766700i | ||||
\(947\) | −45107.8 | −1.54784 | −0.773920 | − | 0.633283i | \(-0.781707\pi\) | ||||
−0.773920 | + | 0.633283i | \(0.781707\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1663.41 | − | 5119.44i | 0.0568983 | − | 0.175115i | ||||
\(950\) | −166.702 | − | 513.056i | −0.00569318 | − | 0.0175218i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9946.08 | + | 7226.25i | −0.338608 | + | 0.246013i | ||||
\(953\) | −7844.63 | − | 24143.3i | −0.266645 | − | 0.820648i | −0.991310 | − | 0.131547i | \(-0.958006\pi\) |
0.724665 | − | 0.689101i | \(-0.241994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23597.9 | − | 17144.9i | −0.799591 | − | 0.580937i | ||||
\(956\) | 13279.1 | 0.449245 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 14654.0 | 0.494206 | ||||||||
\(959\) | 9787.80 | + | 7111.25i | 0.329577 | + | 0.239452i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16569.8 | + | 50996.6i | 0.556201 | + | 1.71181i | ||||
\(962\) | 1584.34 | − | 1151.09i | 0.0530989 | − | 0.0385786i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6521.44 | − | 20070.9i | −0.217885 | − | 0.670582i | ||||
\(965\) | 9065.29 | − | 27900.1i | 0.302406 | − | 0.930710i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26837.3 | 0.892482 | 0.446241 | − | 0.894913i | \(-0.352762\pi\) | ||||
0.446241 | + | 0.894913i | \(0.352762\pi\) | |||||||
\(968\) | −1181.26 | + | 10582.3i | −0.0392223 | + | 0.351371i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 29149.4 | + | 21178.3i | 0.964878 | + | 0.701025i | ||||
\(971\) | 1684.71 | − | 5185.01i | 0.0556797 | − | 0.171364i | −0.919349 | − | 0.393443i | \(-0.871284\pi\) |
0.975029 | + | 0.222078i | \(0.0712840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −46752.0 | + | 33967.3i | −1.54039 | + | 1.11916i | ||||
\(974\) | 10015.3 | − | 7276.55i | 0.329478 | − | 0.239379i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1808.55 | − | 5566.15i | 0.0593138 | − | 0.182549i | ||||
\(977\) | −2919.12 | − | 2120.87i | −0.0955896 | − | 0.0694499i | 0.538964 | − | 0.842329i | \(-0.318816\pi\) |
−0.634553 | + | 0.772879i | \(0.718816\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 962.040 | + | 9445.98i | 0.0314065 | + | 0.308371i | ||||
\(980\) | −10566.9 | −0.344437 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6255.08 | − | 19251.1i | 0.203266 | − | 0.625589i | ||||
\(983\) | −17937.1 | − | 55204.6i | −0.581997 | − | 1.79120i | −0.611009 | − | 0.791624i | \(-0.709236\pi\) |
0.0290114 | − | 0.999579i | \(-0.490764\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10734.9 | − | 7799.38i | 0.347252 | − | 0.252293i | ||||
\(986\) | 5155.50 | + | 15867.0i | 0.166516 | + | 0.512483i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 269.001 | + | 195.441i | 0.00866201 | + | 0.00629332i | ||||
\(989\) | 36809.4 | 1.18349 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18977.5 | −0.608315 | −0.304157 | − | 0.952622i | \(-0.598375\pi\) | ||||
−0.304157 | + | 0.952622i | \(0.598375\pi\) | |||||||
\(992\) | 7476.90 | + | 5432.29i | 0.239306 | + | 0.173866i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1920.44 | − | 5910.51i | −0.0612803 | − | 0.188602i | ||||
\(995\) | 35689.8 | − | 25930.2i | 1.13713 | − | 0.826173i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7496.82 | − | 23072.8i | −0.238141 | − | 0.732923i | −0.996689 | − | 0.0813060i | \(-0.974091\pi\) |
0.758548 | − | 0.651617i | \(-0.225909\pi\) | |||||||
\(998\) | 1583.90 | − | 4874.76i | 0.0502381 | − | 0.154617i | ||||
\(999\) | 0 | 0 |
(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 | 198.4.f.d.37.2 | 8 | ||
3.2 | odd | 2 | 22.4.c.b.15.2 | yes | 8 | ||
11.3 | even | 5 | inner | 198.4.f.d.91.2 | 8 | ||
11.5 | even | 5 | 2178.4.a.by.1.2 | 4 | |||
11.6 | odd | 10 | 2178.4.a.bt.1.2 | 4 | |||
12.11 | even | 2 | 176.4.m.b.81.1 | 8 | |||
33.2 | even | 10 | 242.4.c.n.27.1 | 8 | |||
33.5 | odd | 10 | 242.4.a.n.1.4 | 4 | |||
33.8 | even | 10 | 242.4.c.q.3.2 | 8 | |||
33.14 | odd | 10 | 22.4.c.b.3.2 | ✓ | 8 | ||
33.17 | even | 10 | 242.4.a.o.1.4 | 4 | |||
33.20 | odd | 10 | 242.4.c.r.27.1 | 8 | |||
33.26 | odd | 10 | 242.4.c.r.9.1 | 8 | |||
33.29 | even | 10 | 242.4.c.n.9.1 | 8 | |||
33.32 | even | 2 | 242.4.c.q.81.2 | 8 | |||
132.47 | even | 10 | 176.4.m.b.113.1 | 8 | |||
132.71 | even | 10 | 1936.4.a.bn.1.1 | 4 | |||
132.83 | odd | 10 | 1936.4.a.bm.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.4.c.b.3.2 | ✓ | 8 | 33.14 | odd | 10 | ||
22.4.c.b.15.2 | yes | 8 | 3.2 | odd | 2 | ||
176.4.m.b.81.1 | 8 | 12.11 | even | 2 | |||
176.4.m.b.113.1 | 8 | 132.47 | even | 10 | |||
198.4.f.d.37.2 | 8 | 1.1 | even | 1 | trivial | ||
198.4.f.d.91.2 | 8 | 11.3 | even | 5 | inner | ||
242.4.a.n.1.4 | 4 | 33.5 | odd | 10 | |||
242.4.a.o.1.4 | 4 | 33.17 | even | 10 | |||
242.4.c.n.9.1 | 8 | 33.29 | even | 10 | |||
242.4.c.n.27.1 | 8 | 33.2 | even | 10 | |||
242.4.c.q.3.2 | 8 | 33.8 | even | 10 | |||
242.4.c.q.81.2 | 8 | 33.32 | even | 2 | |||
242.4.c.r.9.1 | 8 | 33.26 | odd | 10 | |||
242.4.c.r.27.1 | 8 | 33.20 | odd | 10 | |||
1936.4.a.bm.1.1 | 4 | 132.83 | odd | 10 | |||
1936.4.a.bn.1.1 | 4 | 132.71 | even | 10 | |||
2178.4.a.bt.1.2 | 4 | 11.6 | odd | 10 | |||
2178.4.a.by.1.2 | 4 | 11.5 | even | 5 |