Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.9924270768.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 25x^{4} + 12x^{3} + 582x^{2} - 144x + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 21) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(2.65415 - 4.59712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.79 |
Dual form | 147.4.e.n.67.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65415 | + | 4.59712i | −0.938383 | + | 1.62533i | −0.169895 | + | 0.985462i | \(0.554343\pi\) |
−0.768488 | + | 0.639864i | \(0.778991\pi\) | |||||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | −10.0890 | − | 17.4746i | −1.26112 | − | 2.18433i | ||||
\(5\) | 2.78070 | − | 4.81631i | 0.248713 | − | 0.430784i | −0.714456 | − | 0.699681i | \(-0.753326\pi\) |
0.963169 | + | 0.268897i | \(0.0866590\pi\) | |||||||
\(6\) | 15.9249 | 1.08355 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 64.6443 | 2.85690 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | 14.7608 | + | 25.5664i | 0.466777 | + | 0.808481i | ||||
\(11\) | 6.95869 | + | 12.0528i | 0.190738 | + | 0.330369i | 0.945495 | − | 0.325636i | \(-0.105578\pi\) |
−0.754757 | + | 0.656005i | \(0.772245\pi\) | |||||||
\(12\) | −30.2670 | + | 52.4239i | −0.728110 | + | 1.26112i | ||||
\(13\) | −38.6718 | −0.825048 | −0.412524 | − | 0.910947i | \(-0.635353\pi\) | ||||
−0.412524 | + | 0.910947i | \(0.635353\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −16.6842 | −0.287189 | ||||||||
\(16\) | −90.8636 | + | 157.380i | −1.41974 | + | 2.45907i | ||||
\(17\) | 21.7394 | + | 37.6537i | 0.310152 | + | 0.537198i | 0.978395 | − | 0.206744i | \(-0.0662869\pi\) |
−0.668243 | + | 0.743943i | \(0.732954\pi\) | |||||||
\(18\) | −23.8873 | − | 41.3741i | −0.312794 | − | 0.541776i | ||||
\(19\) | −54.5139 | + | 94.4208i | −0.658228 | + | 1.14009i | 0.322845 | + | 0.946452i | \(0.395361\pi\) |
−0.981074 | + | 0.193633i | \(0.937973\pi\) | |||||||
\(20\) | −112.218 | −1.25463 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −73.8775 | −0.715943 | ||||||||
\(23\) | 37.4389 | − | 64.8461i | 0.339415 | − | 0.587885i | −0.644907 | − | 0.764261i | \(-0.723104\pi\) |
0.984323 | + | 0.176376i | \(0.0564374\pi\) | |||||||
\(24\) | −96.9665 | − | 167.951i | −0.824717 | − | 1.42845i | ||||
\(25\) | 47.0354 | + | 81.4677i | 0.376283 | + | 0.651742i | ||||
\(26\) | 102.641 | − | 177.779i | 0.774211 | − | 1.34097i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −72.3589 | −0.463335 | −0.231667 | − | 0.972795i | \(-0.574418\pi\) | ||||
−0.231667 | + | 0.972795i | \(0.574418\pi\) | |||||||
\(30\) | 44.2823 | − | 76.6992i | 0.269494 | − | 0.466777i | ||||
\(31\) | 32.0215 | + | 55.4629i | 0.185524 | + | 0.321337i | 0.943753 | − | 0.330652i | \(-0.107268\pi\) |
−0.758229 | + | 0.651988i | \(0.773935\pi\) | |||||||
\(32\) | −223.754 | − | 387.553i | −1.23608 | − | 2.14095i | ||||
\(33\) | 20.8761 | − | 36.1584i | 0.110123 | − | 0.190738i | ||||
\(34\) | −230.798 | −1.16416 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 181.602 | 0.840749 | ||||||||
\(37\) | −94.3636 | + | 163.443i | −0.419278 | + | 0.726211i | −0.995867 | − | 0.0908235i | \(-0.971050\pi\) |
0.576589 | + | 0.817034i | \(0.304383\pi\) | |||||||
\(38\) | −289.376 | − | 501.213i | −1.23534 | − | 2.13967i | ||||
\(39\) | 58.0077 | + | 100.472i | 0.238171 | + | 0.412524i | ||||
\(40\) | 179.756 | − | 311.347i | 0.710550 | − | 1.23071i | ||||
\(41\) | 24.7923 | 0.0944367 | 0.0472184 | − | 0.998885i | \(-0.484964\pi\) | ||||
0.0472184 | + | 0.998885i | \(0.484964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −243.881 | −0.864920 | −0.432460 | − | 0.901653i | \(-0.642354\pi\) | ||||
−0.432460 | + | 0.901653i | \(0.642354\pi\) | |||||||
\(44\) | 140.412 | − | 243.201i | 0.481090 | − | 0.833272i | ||||
\(45\) | 25.0263 | + | 43.3468i | 0.0829044 | + | 0.143595i | ||||
\(46\) | 198.737 | + | 344.222i | 0.637003 | + | 1.10332i | ||||
\(47\) | −310.274 | + | 537.411i | −0.962940 | + | 1.66786i | −0.247888 | + | 0.968789i | \(0.579736\pi\) |
−0.715052 | + | 0.699071i | \(0.753597\pi\) | |||||||
\(48\) | 545.182 | 1.63938 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −499.356 | −1.41239 | ||||||||
\(51\) | 65.2182 | − | 112.961i | 0.179066 | − | 0.310152i | ||||
\(52\) | 390.159 | + | 675.776i | 1.04049 | + | 1.80218i | ||||
\(53\) | 143.919 | + | 249.276i | 0.372997 | + | 0.646050i | 0.990025 | − | 0.140891i | \(-0.0449967\pi\) |
−0.617028 | + | 0.786941i | \(0.711663\pi\) | |||||||
\(54\) | −71.6620 | + | 124.122i | −0.180592 | + | 0.312794i | ||||
\(55\) | 77.4001 | 0.189757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 327.083 | 0.760057 | ||||||||
\(58\) | 192.051 | − | 332.642i | 0.434785 | − | 0.753070i | ||||
\(59\) | 262.526 | + | 454.708i | 0.579287 | + | 1.00335i | 0.995561 | + | 0.0941152i | \(0.0300022\pi\) |
−0.416275 | + | 0.909239i | \(0.636664\pi\) | |||||||
\(60\) | 168.327 | + | 291.551i | 0.362182 | + | 0.627317i | ||||
\(61\) | −191.718 | + | 332.065i | −0.402409 | + | 0.696993i | −0.994016 | − | 0.109234i | \(-0.965160\pi\) |
0.591607 | + | 0.806226i | \(0.298494\pi\) | |||||||
\(62\) | −339.960 | −0.696369 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 921.681 | 1.80016 | ||||||||
\(65\) | −107.535 | + | 186.255i | −0.205200 | + | 0.355417i | ||||
\(66\) | 110.816 | + | 191.939i | 0.206675 | + | 0.357971i | ||||
\(67\) | −99.0583 | − | 171.574i | −0.180625 | − | 0.312852i | 0.761468 | − | 0.648202i | \(-0.224479\pi\) |
−0.942094 | + | 0.335350i | \(0.891145\pi\) | |||||||
\(68\) | 438.657 | − | 759.776i | 0.782279 | − | 1.35495i | ||||
\(69\) | −224.634 | −0.391923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 785.432 | 1.31287 | 0.656434 | − | 0.754384i | \(-0.272064\pi\) | ||||
0.656434 | + | 0.754384i | \(0.272064\pi\) | |||||||
\(72\) | −290.900 | + | 503.853i | −0.476151 | + | 0.824717i | ||||
\(73\) | −165.570 | − | 286.776i | −0.265459 | − | 0.459789i | 0.702224 | − | 0.711956i | \(-0.252190\pi\) |
−0.967684 | + | 0.252166i | \(0.918857\pi\) | |||||||
\(74\) | −500.910 | − | 867.602i | −0.786887 | − | 1.36293i | ||||
\(75\) | 141.106 | − | 244.403i | 0.217247 | − | 0.376283i | ||||
\(76\) | 2199.96 | 3.32043 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −615.844 | −0.893981 | ||||||||
\(79\) | −218.823 | + | 379.013i | −0.311640 | + | 0.539776i | −0.978718 | − | 0.205212i | \(-0.934212\pi\) |
0.667078 | + | 0.744988i | \(0.267545\pi\) | |||||||
\(80\) | 505.329 | + | 875.255i | 0.706219 | + | 1.22321i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −65.8024 | + | 113.973i | −0.0886178 | + | 0.153491i | ||||
\(83\) | −241.241 | −0.319032 | −0.159516 | − | 0.987195i | \(-0.550993\pi\) | ||||
−0.159516 | + | 0.987195i | \(0.550993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 241.803 | 0.308555 | ||||||||
\(86\) | 647.297 | − | 1121.15i | 0.811626 | − | 1.40578i | ||||
\(87\) | 108.538 | + | 187.994i | 0.133753 | + | 0.231667i | ||||
\(88\) | 449.840 | + | 779.145i | 0.544921 | + | 0.943831i | ||||
\(89\) | 792.772 | − | 1373.12i | 0.944198 | − | 1.63540i | 0.186849 | − | 0.982389i | \(-0.440172\pi\) |
0.757349 | − | 0.653010i | \(-0.226494\pi\) | |||||||
\(90\) | −265.694 | −0.311184 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1510.88 | −1.71218 | ||||||||
\(93\) | 96.0646 | − | 166.389i | 0.107112 | − | 0.185524i | ||||
\(94\) | −1647.03 | − | 2852.73i | −1.80721 | − | 3.13018i | ||||
\(95\) | 303.173 | + | 525.112i | 0.327420 | + | 0.567109i | ||||
\(96\) | −671.261 | + | 1162.66i | −0.713649 | + | 1.23608i | ||||
\(97\) | −79.2754 | −0.0829814 | −0.0414907 | − | 0.999139i | \(-0.513211\pi\) | ||||
−0.0414907 | + | 0.999139i | \(0.513211\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −125.256 | −0.127159 | ||||||||
\(100\) | 949.080 | − | 1643.85i | 0.949080 | − | 1.64385i | ||||
\(101\) | 577.487 | + | 1000.24i | 0.568931 | + | 0.985418i | 0.996672 | + | 0.0815165i | \(0.0259763\pi\) |
−0.427741 | + | 0.903902i | \(0.640690\pi\) | |||||||
\(102\) | 346.197 | + | 599.631i | 0.336065 | + | 0.582082i | ||||
\(103\) | −722.430 | + | 1251.28i | −0.691098 | + | 1.19702i | 0.280380 | + | 0.959889i | \(0.409539\pi\) |
−0.971478 | + | 0.237128i | \(0.923794\pi\) | |||||||
\(104\) | −2499.91 | −2.35708 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1527.93 | −1.40006 | ||||||||
\(107\) | −495.480 | + | 858.197i | −0.447662 | + | 0.775374i | −0.998233 | − | 0.0594143i | \(-0.981077\pi\) |
0.550571 | + | 0.834788i | \(0.314410\pi\) | |||||||
\(108\) | −272.403 | − | 471.816i | −0.242703 | − | 0.420375i | ||||
\(109\) | −976.585 | − | 1691.49i | −0.858164 | − | 1.48638i | −0.873678 | − | 0.486504i | \(-0.838272\pi\) |
0.0155145 | − | 0.999880i | \(-0.495061\pi\) | |||||||
\(110\) | −205.431 | + | 355.817i | −0.178064 | + | 0.308417i | ||||
\(111\) | 566.182 | 0.484141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 672.882 | 0.560172 | 0.280086 | − | 0.959975i | \(-0.409637\pi\) | ||||
0.280086 | + | 0.959975i | \(0.409637\pi\) | |||||||
\(114\) | −868.127 | + | 1503.64i | −0.713224 | + | 1.23534i | ||||
\(115\) | −208.213 | − | 360.635i | −0.168834 | − | 0.292430i | ||||
\(116\) | 730.028 | + | 1264.45i | 0.584323 | + | 1.01208i | ||||
\(117\) | 174.023 | − | 301.417i | 0.137508 | − | 0.238171i | ||||
\(118\) | −2787.13 | −2.17437 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1078.54 | −0.820472 | ||||||||
\(121\) | 568.653 | − | 984.936i | 0.427238 | − | 0.739997i | ||||
\(122\) | −1017.69 | − | 1762.70i | −0.755227 | − | 1.30809i | ||||
\(123\) | −37.1884 | − | 64.4123i | −0.0272615 | − | 0.0472184i | ||||
\(124\) | 646.130 | − | 1119.13i | 0.467937 | − | 0.810491i | ||||
\(125\) | 1218.34 | 0.871773 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 175.815 | 0.122843 | 0.0614216 | − | 0.998112i | \(-0.480437\pi\) | ||||
0.0614216 | + | 0.998112i | \(0.480437\pi\) | |||||||
\(128\) | −656.249 | + | 1136.66i | −0.453163 | + | 0.784900i | ||||
\(129\) | 365.822 | + | 633.622i | 0.249681 | + | 0.432460i | ||||
\(130\) | −570.825 | − | 988.698i | −0.385113 | − | 0.667035i | ||||
\(131\) | 562.965 | − | 975.085i | 0.375470 | − | 0.650332i | −0.614928 | − | 0.788584i | \(-0.710815\pi\) |
0.990397 | + | 0.138251i | \(0.0441481\pi\) | |||||||
\(132\) | −842.474 | −0.555515 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1051.66 | 0.677983 | ||||||||
\(135\) | 75.0789 | − | 130.040i | 0.0478649 | − | 0.0829044i | ||||
\(136\) | 1405.33 | + | 2434.10i | 0.886073 | + | 1.53472i | ||||
\(137\) | −934.350 | − | 1618.34i | −0.582678 | − | 1.00923i | −0.995161 | − | 0.0982624i | \(-0.968672\pi\) |
0.412483 | − | 0.910966i | \(-0.364662\pi\) | |||||||
\(138\) | 596.210 | − | 1032.67i | 0.367774 | − | 0.637003i | ||||
\(139\) | 2817.19 | 1.71907 | 0.859537 | − | 0.511074i | \(-0.170752\pi\) | ||||
0.859537 | + | 0.511074i | \(0.170752\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1861.65 | 1.11191 | ||||||||
\(142\) | −2084.65 | + | 3610.72i | −1.23197 | + | 2.13384i | ||||
\(143\) | −269.105 | − | 466.103i | −0.157368 | − | 0.272570i | ||||
\(144\) | −817.773 | − | 1416.42i | −0.473248 | − | 0.819690i | ||||
\(145\) | −201.208 | + | 348.503i | −0.115238 | + | 0.199597i | ||||
\(146\) | 1757.79 | 0.996410 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3808.14 | 2.11505 | ||||||||
\(149\) | −900.163 | + | 1559.13i | −0.494928 | + | 0.857240i | −0.999983 | − | 0.00584714i | \(-0.998139\pi\) |
0.505055 | + | 0.863087i | \(0.331472\pi\) | |||||||
\(150\) | 749.034 | + | 1297.36i | 0.407722 | + | 0.706196i | ||||
\(151\) | 226.492 | + | 392.296i | 0.122064 | + | 0.211421i | 0.920581 | − | 0.390551i | \(-0.127715\pi\) |
−0.798517 | + | 0.601972i | \(0.794382\pi\) | |||||||
\(152\) | −3524.01 | + | 6103.77i | −1.88050 | + | 3.25711i | ||||
\(153\) | −391.309 | −0.206768 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 356.169 | 0.184569 | ||||||||
\(156\) | 1170.48 | − | 2027.33i | 0.600726 | − | 1.04049i | ||||
\(157\) | −931.829 | − | 1613.98i | −0.473682 | − | 0.820441i | 0.525864 | − | 0.850569i | \(-0.323742\pi\) |
−0.999546 | + | 0.0301273i | \(0.990409\pi\) | |||||||
\(158\) | −1161.58 | − | 2011.91i | −0.584875 | − | 1.01303i | ||||
\(159\) | 431.758 | − | 747.827i | 0.215350 | − | 0.372997i | ||||
\(160\) | −2488.77 | −1.22971 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 429.972 | 0.208529 | ||||||||
\(163\) | −1160.57 | + | 2010.16i | −0.557686 | + | 0.965940i | 0.440004 | + | 0.897996i | \(0.354977\pi\) |
−0.997689 | + | 0.0679437i | \(0.978356\pi\) | |||||||
\(164\) | −250.129 | − | 433.237i | −0.119096 | − | 0.206281i | ||||
\(165\) | −116.100 | − | 201.091i | −0.0547781 | − | 0.0948784i | ||||
\(166\) | 640.290 | − | 1109.01i | 0.299374 | − | 0.518531i | ||||
\(167\) | −3211.62 | −1.48816 | −0.744079 | − | 0.668092i | \(-0.767111\pi\) | ||||
−0.744079 | + | 0.668092i | \(0.767111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −701.494 | −0.319296 | ||||||||
\(170\) | −641.780 | + | 1111.60i | −0.289543 | + | 0.501503i | ||||
\(171\) | −490.625 | − | 849.787i | −0.219409 | − | 0.380028i | ||||
\(172\) | 2460.52 | + | 4261.74i | 1.09077 | + | 1.88927i | ||||
\(173\) | 107.139 | − | 185.569i | 0.0470844 | − | 0.0815525i | −0.841523 | − | 0.540222i | \(-0.818340\pi\) |
0.888607 | + | 0.458669i | \(0.151674\pi\) | |||||||
\(174\) | −1152.31 | −0.502047 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2529.17 | −1.08320 | ||||||||
\(177\) | 787.577 | − | 1364.12i | 0.334451 | − | 0.579287i | ||||
\(178\) | 4208.27 | + | 7288.93i | 1.77204 | + | 3.06926i | ||||
\(179\) | 1218.61 | + | 2110.70i | 0.508845 | + | 0.881345i | 0.999948 | + | 0.0102437i | \(0.00326072\pi\) |
−0.491102 | + | 0.871102i | \(0.663406\pi\) | |||||||
\(180\) | 504.980 | − | 874.652i | 0.209106 | − | 0.362182i | ||||
\(181\) | 248.631 | 0.102103 | 0.0510514 | − | 0.998696i | \(-0.483743\pi\) | ||||
0.0510514 | + | 0.998696i | \(0.483743\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1150.31 | 0.464662 | ||||||||
\(184\) | 2420.21 | − | 4191.93i | 0.969677 | − | 1.67953i | ||||
\(185\) | 524.794 | + | 908.970i | 0.208560 | + | 0.361237i | ||||
\(186\) | 509.939 | + | 883.241i | 0.201025 | + | 0.348185i | ||||
\(187\) | −302.555 | + | 524.041i | −0.118316 | + | 0.204929i | ||||
\(188\) | 12521.4 | 4.85755 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3218.67 | −1.22898 | ||||||||
\(191\) | 2156.54 | − | 3735.24i | 0.816972 | − | 1.41504i | −0.0909306 | − | 0.995857i | \(-0.528984\pi\) |
0.907903 | − | 0.419180i | \(-0.137683\pi\) | |||||||
\(192\) | −1382.52 | − | 2394.60i | −0.519661 | − | 0.900079i | ||||
\(193\) | −1030.43 | − | 1784.75i | −0.384309 | − | 0.665643i | 0.607364 | − | 0.794424i | \(-0.292227\pi\) |
−0.991673 | + | 0.128781i | \(0.958894\pi\) | |||||||
\(194\) | 210.409 | − | 364.438i | 0.0778683 | − | 0.134872i | ||||
\(195\) | 645.208 | 0.236945 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1666.09 | −0.602557 | −0.301279 | − | 0.953536i | \(-0.597413\pi\) | ||||
−0.301279 | + | 0.953536i | \(0.597413\pi\) | |||||||
\(198\) | 332.449 | − | 575.818i | 0.119324 | − | 0.206675i | ||||
\(199\) | −543.767 | − | 941.832i | −0.193702 | − | 0.335501i | 0.752773 | − | 0.658281i | \(-0.228716\pi\) |
−0.946474 | + | 0.322780i | \(0.895383\pi\) | |||||||
\(200\) | 3040.57 | + | 5266.43i | 1.07501 | + | 1.86196i | ||||
\(201\) | −297.175 | + | 514.722i | −0.104284 | + | 0.180625i | ||||
\(202\) | −6130.94 | −2.13550 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2631.94 | −0.903298 | ||||||||
\(205\) | 68.9399 | − | 119.407i | 0.0234877 | − | 0.0406818i | ||||
\(206\) | −3834.87 | − | 6642.19i | −1.29703 | − | 2.24652i | ||||
\(207\) | 336.950 | + | 583.615i | 0.113138 | + | 0.195962i | ||||
\(208\) | 3513.86 | − | 6086.18i | 1.17136 | − | 2.02885i | ||||
\(209\) | −1517.38 | −0.502198 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4676.47 | −1.52579 | −0.762895 | − | 0.646522i | \(-0.776223\pi\) | ||||
−0.762895 | + | 0.646522i | \(0.776223\pi\) | |||||||
\(212\) | 2904.01 | − | 5029.88i | 0.940792 | − | 1.62950i | ||||
\(213\) | −1178.15 | − | 2040.61i | −0.378992 | − | 0.656434i | ||||
\(214\) | −2630.15 | − | 4555.56i | −0.840157 | − | 1.45520i | ||||
\(215\) | −678.161 | + | 1174.61i | −0.215117 | + | 0.372594i | ||||
\(216\) | 1745.40 | 0.549811 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10368.0 | 3.22114 | ||||||||
\(219\) | −496.711 | + | 860.329i | −0.153263 | + | 0.265459i | ||||
\(220\) | −780.889 | − | 1352.54i | −0.239307 | − | 0.414492i | ||||
\(221\) | −840.701 | − | 1456.14i | −0.255890 | − | 0.443214i | ||||
\(222\) | −1502.73 | + | 2602.80i | −0.454309 | + | 0.786887i | ||||
\(223\) | −3246.03 | −0.974754 | −0.487377 | − | 0.873192i | \(-0.662046\pi\) | ||||
−0.487377 | + | 0.873192i | \(0.662046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −846.638 | −0.250856 | ||||||||
\(226\) | −1785.93 | + | 3093.32i | −0.525656 | + | 0.910463i | ||||
\(227\) | 2569.08 | + | 4449.77i | 0.751171 | + | 1.30107i | 0.947256 | + | 0.320479i | \(0.103844\pi\) |
−0.196085 | + | 0.980587i | \(0.562823\pi\) | |||||||
\(228\) | −3299.94 | − | 5715.67i | −0.958526 | − | 1.66022i | ||||
\(229\) | 307.403 | − | 532.438i | 0.0887064 | − | 0.153644i | −0.818258 | − | 0.574851i | \(-0.805060\pi\) |
0.906965 | + | 0.421207i | \(0.138393\pi\) | |||||||
\(230\) | 2210.51 | 0.633725 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4677.59 | −1.32370 | ||||||||
\(233\) | −1413.71 | + | 2448.61i | −0.397490 | + | 0.688472i | −0.993415 | − | 0.114567i | \(-0.963452\pi\) |
0.595926 | + | 0.803039i | \(0.296785\pi\) | |||||||
\(234\) | 923.765 | + | 1600.01i | 0.258070 | + | 0.446991i | ||||
\(235\) | 1725.56 | + | 2988.76i | 0.478992 | + | 0.829638i | ||||
\(236\) | 5297.24 | − | 9175.09i | 1.46111 | − | 2.53071i | ||||
\(237\) | 1312.94 | 0.359851 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3432.45 | −0.928983 | −0.464491 | − | 0.885578i | \(-0.653763\pi\) | ||||
−0.464491 | + | 0.885578i | \(0.653763\pi\) | |||||||
\(240\) | 1515.99 | − | 2625.77i | 0.407736 | − | 0.706219i | ||||
\(241\) | −1318.06 | − | 2282.94i | −0.352296 | − | 0.610195i | 0.634355 | − | 0.773042i | \(-0.281266\pi\) |
−0.986651 | + | 0.162847i | \(0.947932\pi\) | |||||||
\(242\) | 3018.58 | + | 5228.33i | 0.801825 | + | 1.38880i | ||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 7736.96 | 2.02995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 394.814 | 0.102327 | ||||||||
\(247\) | 2108.15 | − | 3651.42i | 0.543070 | − | 0.940625i | ||||
\(248\) | 2070.01 | + | 3585.37i | 0.530024 | + | 0.918028i | ||||
\(249\) | 361.862 | + | 626.763i | 0.0920967 | + | 0.159516i | ||||
\(250\) | −3233.65 | + | 5600.85i | −0.818057 | + | 1.41692i | ||||
\(251\) | −2057.57 | −0.517422 | −0.258711 | − | 0.965955i | \(-0.583298\pi\) | ||||
−0.258711 | + | 0.965955i | \(0.583298\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1042.10 | 0.258958 | ||||||||
\(254\) | −466.639 | + | 808.243i | −0.115274 | + | 0.199660i | ||||
\(255\) | −362.704 | − | 628.222i | −0.0890722 | − | 0.154278i | ||||
\(256\) | 203.161 | + | 351.885i | 0.0495998 | + | 0.0859093i | ||||
\(257\) | 1075.10 | − | 1862.13i | 0.260946 | − | 0.451972i | −0.705548 | − | 0.708663i | \(-0.749299\pi\) |
0.966494 | + | 0.256691i | \(0.0826322\pi\) | |||||||
\(258\) | −3883.78 | −0.937185 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4339.66 | 1.03513 | ||||||||
\(261\) | 325.615 | − | 563.982i | 0.0772225 | − | 0.133753i | ||||
\(262\) | 2988.39 | + | 5176.04i | 0.704668 | + | 1.22052i | ||||
\(263\) | 2295.08 | + | 3975.19i | 0.538100 | + | 0.932017i | 0.999006 | + | 0.0445683i | \(0.0141912\pi\) |
−0.460906 | + | 0.887449i | \(0.652475\pi\) | |||||||
\(264\) | 1349.52 | − | 2337.44i | 0.314610 | − | 0.544921i | ||||
\(265\) | 1600.79 | 0.371078 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4756.63 | −1.09027 | ||||||||
\(268\) | −1998.80 | + | 3462.02i | −0.455582 | + | 0.789091i | ||||
\(269\) | −189.689 | − | 328.551i | −0.0429945 | − | 0.0744687i | 0.843727 | − | 0.536772i | \(-0.180356\pi\) |
−0.886722 | + | 0.462303i | \(0.847023\pi\) | |||||||
\(270\) | 398.541 | + | 690.293i | 0.0898312 | + | 0.155592i | ||||
\(271\) | −2684.42 | + | 4649.55i | −0.601723 | + | 1.04221i | 0.390837 | + | 0.920460i | \(0.372185\pi\) |
−0.992560 | + | 0.121755i | \(0.961148\pi\) | |||||||
\(272\) | −7901.28 | −1.76134 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9919.61 | 2.18710 | ||||||||
\(275\) | −654.610 | + | 1133.82i | −0.143543 | + | 0.248624i | ||||
\(276\) | 2266.33 | + | 3925.39i | 0.494264 | + | 0.856090i | ||||
\(277\) | 2390.80 | + | 4140.99i | 0.518590 | + | 0.898224i | 0.999767 | + | 0.0216003i | \(0.00687613\pi\) |
−0.481177 | + | 0.876624i | \(0.659791\pi\) | |||||||
\(278\) | −7477.25 | + | 12951.0i | −1.61315 | + | 2.79406i | ||||
\(279\) | −576.388 | −0.123683 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2076.57 | −0.440845 | −0.220423 | − | 0.975404i | \(-0.570744\pi\) | ||||
−0.220423 | + | 0.975404i | \(0.570744\pi\) | |||||||
\(282\) | −4941.08 | + | 8558.20i | −1.04339 | + | 1.80721i | ||||
\(283\) | 1278.81 | + | 2214.96i | 0.268612 | + | 0.465250i | 0.968504 | − | 0.248999i | \(-0.0801017\pi\) |
−0.699892 | + | 0.714249i | \(0.746768\pi\) | |||||||
\(284\) | −7924.21 | − | 13725.1i | −1.65569 | − | 2.86774i | ||||
\(285\) | 909.520 | − | 1575.34i | 0.189036 | − | 0.327420i | ||||
\(286\) | 2856.97 | 0.590687 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4027.56 | 0.824050 | ||||||||
\(289\) | 1511.30 | − | 2617.65i | 0.307612 | − | 0.532800i | ||||
\(290\) | −1068.07 | − | 1849.96i | −0.216274 | − | 0.374597i | ||||
\(291\) | 118.913 | + | 205.963i | 0.0239547 | + | 0.0414907i | ||||
\(292\) | −3340.88 | + | 5786.57i | −0.669555 | + | 1.15970i | ||||
\(293\) | −560.049 | −0.111667 | −0.0558335 | − | 0.998440i | \(-0.517782\pi\) | ||||
−0.0558335 | + | 0.998440i | \(0.517782\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2920.02 | 0.576305 | ||||||||
\(296\) | −6100.08 | + | 10565.6i | −1.19784 | + | 2.07471i | ||||
\(297\) | 187.885 | + | 325.426i | 0.0367076 | + | 0.0635795i | ||||
\(298\) | −4778.33 | − | 8276.31i | −0.928863 | − | 1.60884i | ||||
\(299\) | −1447.83 | + | 2507.71i | −0.280034 | + | 0.485033i | ||||
\(300\) | −5694.48 | −1.09590 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2404.57 | −0.458171 | ||||||||
\(303\) | 1732.46 | − | 3000.71i | 0.328473 | − | 0.568931i | ||||
\(304\) | −9906.66 | − | 17158.8i | −1.86903 | − | 3.23726i | ||||
\(305\) | 1066.22 | + | 1846.75i | 0.200169 | + | 0.346703i | ||||
\(306\) | 1038.59 | − | 1798.89i | 0.194027 | − | 0.336065i | ||||
\(307\) | −3653.02 | −0.679117 | −0.339558 | − | 0.940585i | \(-0.610278\pi\) | ||||
−0.339558 | + | 0.940585i | \(0.610278\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4334.58 | 0.798011 | ||||||||
\(310\) | −945.325 | + | 1637.35i | −0.173196 | + | 0.299985i | ||||
\(311\) | 1746.13 | + | 3024.39i | 0.318374 | + | 0.551439i | 0.980149 | − | 0.198263i | \(-0.0635300\pi\) |
−0.661775 | + | 0.749702i | \(0.730197\pi\) | |||||||
\(312\) | 3749.87 | + | 6494.96i | 0.680431 | + | 1.17854i | ||||
\(313\) | 4356.05 | − | 7544.90i | 0.786640 | − | 1.36250i | −0.141374 | − | 0.989956i | \(-0.545152\pi\) |
0.928014 | − | 0.372544i | \(-0.121515\pi\) | |||||||
\(314\) | 9892.85 | 1.77798 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8830.83 | 1.57207 | ||||||||
\(317\) | −970.165 | + | 1680.37i | −0.171892 | + | 0.297726i | −0.939081 | − | 0.343695i | \(-0.888321\pi\) |
0.767189 | + | 0.641421i | \(0.221655\pi\) | |||||||
\(318\) | 2291.90 | + | 3969.69i | 0.404162 | + | 0.700029i | ||||
\(319\) | −503.523 | − | 872.127i | −0.0883758 | − | 0.153071i | ||||
\(320\) | 2562.92 | − | 4439.11i | 0.447724 | − | 0.775480i | ||||
\(321\) | 2972.88 | 0.516916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4740.39 | −0.816602 | ||||||||
\(324\) | −817.208 | + | 1415.45i | −0.140125 | + | 0.242703i | ||||
\(325\) | −1818.94 | − | 3150.50i | −0.310452 | − | 0.537718i | ||||
\(326\) | −6160.64 | − | 10670.5i | −1.04665 | − | 1.81284i | ||||
\(327\) | −2929.75 | + | 5074.48i | −0.495461 | + | 0.858164i | ||||
\(328\) | 1602.68 | 0.269797 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1232.59 | 0.205611 | ||||||||
\(331\) | 2865.75 | − | 4963.63i | 0.475879 | − | 0.824247i | −0.523739 | − | 0.851879i | \(-0.675463\pi\) |
0.999618 | + | 0.0276315i | \(0.00879650\pi\) | |||||||
\(332\) | 2433.88 | + | 4215.61i | 0.402339 | + | 0.696872i | ||||
\(333\) | −849.273 | − | 1470.98i | −0.139759 | − | 0.242070i | ||||
\(334\) | 8524.10 | − | 14764.2i | 1.39646 | − | 2.41874i | ||||
\(335\) | −1101.81 | −0.179696 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2403.74 | 0.388547 | 0.194273 | − | 0.980947i | \(-0.437765\pi\) | ||||
0.194273 | + | 0.980947i | \(0.437765\pi\) | |||||||
\(338\) | 1861.87 | − | 3224.85i | 0.299622 | − | 0.518960i | ||||
\(339\) | −1009.32 | − | 1748.20i | −0.161708 | − | 0.280086i | ||||
\(340\) | −2439.55 | − | 4225.42i | −0.389127 | − | 0.673987i | ||||
\(341\) | −445.656 | + | 771.898i | −0.0707731 | + | 0.122583i | ||||
\(342\) | 5208.76 | 0.823560 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −15765.6 | −2.47099 | ||||||||
\(345\) | −624.638 | + | 1081.91i | −0.0974765 | + | 0.168834i | ||||
\(346\) | 568.723 | + | 985.057i | 0.0883663 | + | 0.153055i | ||||
\(347\) | 1668.22 | + | 2889.45i | 0.258083 | + | 0.447013i | 0.965728 | − | 0.259555i | \(-0.0835758\pi\) |
−0.707645 | + | 0.706568i | \(0.750242\pi\) | |||||||
\(348\) | 2190.09 | − | 3793.34i | 0.337359 | − | 0.584323i | ||||
\(349\) | 2424.54 | 0.371870 | 0.185935 | − | 0.982562i | \(-0.440469\pi\) | ||||
0.185935 | + | 0.982562i | \(0.440469\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1044.14 | −0.158781 | ||||||||
\(352\) | 3114.06 | − | 5393.71i | 0.471534 | − | 0.816721i | ||||
\(353\) | −6201.56 | − | 10741.4i | −0.935059 | − | 1.61957i | −0.774528 | − | 0.632540i | \(-0.782013\pi\) |
−0.160531 | − | 0.987031i | \(-0.551321\pi\) | |||||||
\(354\) | 4180.69 | + | 7241.17i | 0.627687 | + | 1.08719i | ||||
\(355\) | 2184.05 | − | 3782.88i | 0.326528 | − | 0.565562i | ||||
\(356\) | −31993.1 | −4.76300 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12937.5 | −1.90997 | ||||||||
\(359\) | −676.921 | + | 1172.46i | −0.0995168 | + | 0.172368i | −0.911485 | − | 0.411334i | \(-0.865063\pi\) |
0.811968 | + | 0.583702i | \(0.198396\pi\) | |||||||
\(360\) | 1617.81 | + | 2802.13i | 0.236850 | + | 0.410236i | ||||
\(361\) | −2514.03 | − | 4354.42i | −0.366529 | − | 0.634848i | ||||
\(362\) | −659.903 | + | 1142.99i | −0.0958114 | + | 0.165950i | ||||
\(363\) | −3411.92 | −0.493332 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1841.61 | −0.264093 | ||||||||
\(366\) | −3053.08 | + | 5288.10i | −0.436031 | + | 0.755227i | ||||
\(367\) | −689.031 | − | 1193.44i | −0.0980031 | − | 0.169746i | 0.812855 | − | 0.582466i | \(-0.197912\pi\) |
−0.910858 | + | 0.412720i | \(0.864579\pi\) | |||||||
\(368\) | 6803.67 | + | 11784.3i | 0.963766 | + | 1.66929i | ||||
\(369\) | −111.565 | + | 193.237i | −0.0157395 | + | 0.0272615i | ||||
\(370\) | −5571.52 | −0.782837 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3876.78 | −0.540327 | ||||||||
\(373\) | −2728.46 | + | 4725.83i | −0.378752 | + | 0.656017i | −0.990881 | − | 0.134741i | \(-0.956980\pi\) |
0.612129 | + | 0.790758i | \(0.290313\pi\) | |||||||
\(374\) | −1606.05 | − | 2781.76i | −0.222051 | − | 0.384603i | ||||
\(375\) | −1827.51 | − | 3165.34i | −0.251659 | − | 0.435887i | ||||
\(376\) | −20057.5 | + | 34740.6i | −2.75103 | + | 4.76492i | ||||
\(377\) | 2798.25 | 0.382273 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 554.675 | 0.0751761 | 0.0375881 | − | 0.999293i | \(-0.488033\pi\) | ||||
0.0375881 | + | 0.999293i | \(0.488033\pi\) | |||||||
\(380\) | 6117.43 | − | 10595.7i | 0.825836 | − | 1.43039i | ||||
\(381\) | −263.723 | − | 456.781i | −0.0354618 | − | 0.0614216i | ||||
\(382\) | 11447.5 | + | 19827.7i | 1.53327 | + | 2.65569i | ||||
\(383\) | 2930.33 | − | 5075.48i | 0.390948 | − | 0.677141i | −0.601627 | − | 0.798777i | \(-0.705481\pi\) |
0.992575 | + | 0.121636i | \(0.0388140\pi\) | |||||||
\(384\) | 3937.50 | 0.523267 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 10939.6 | 1.44252 | ||||||||
\(387\) | 1097.47 | − | 1900.87i | 0.144153 | − | 0.249681i | ||||
\(388\) | 799.809 | + | 1385.31i | 0.104650 | + | 0.181259i | ||||
\(389\) | −3889.43 | − | 6736.69i | −0.506946 | − | 0.878056i | −0.999968 | − | 0.00803932i | \(-0.997441\pi\) |
0.493022 | − | 0.870017i | \(-0.335892\pi\) | |||||||
\(390\) | −1712.48 | + | 2966.10i | −0.222345 | + | 0.385113i | ||||
\(391\) | 3255.60 | 0.421081 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3377.79 | −0.433555 | ||||||||
\(394\) | 4422.04 | − | 7659.20i | 0.565429 | − | 0.979352i | ||||
\(395\) | 1216.96 | + | 2107.84i | 0.155018 | + | 0.268499i | ||||
\(396\) | 1263.71 | + | 2188.81i | 0.160363 | + | 0.277757i | ||||
\(397\) | 4013.94 | − | 6952.35i | 0.507440 | − | 0.878912i | −0.492523 | − | 0.870300i | \(-0.663925\pi\) |
0.999963 | − | 0.00861270i | \(-0.00274154\pi\) | |||||||
\(398\) | 5772.95 | 0.727065 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17095.2 | −2.13690 | ||||||||
\(401\) | −389.990 | + | 675.482i | −0.0485665 | + | 0.0841196i | −0.889287 | − | 0.457350i | \(-0.848799\pi\) |
0.840720 | + | 0.541470i | \(0.182132\pi\) | |||||||
\(402\) | −1577.49 | − | 2732.30i | −0.195717 | − | 0.338991i | ||||
\(403\) | −1238.33 | − | 2144.85i | −0.153066 | − | 0.265118i | ||||
\(404\) | 11652.5 | − | 20182.8i | 1.43499 | − | 2.48547i | ||||
\(405\) | −450.473 | −0.0552696 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2626.59 | −0.319890 | ||||||||
\(408\) | 4215.99 | − | 7302.30i | 0.511574 | − | 0.886073i | ||||
\(409\) | 7346.25 | + | 12724.1i | 0.888139 | + | 1.53830i | 0.842073 | + | 0.539363i | \(0.181335\pi\) |
0.0460654 | + | 0.998938i | \(0.485332\pi\) | |||||||
\(410\) | 365.953 | + | 633.850i | 0.0440809 | + | 0.0763503i | ||||
\(411\) | −2803.05 | + | 4855.02i | −0.336409 | + | 0.582678i | ||||
\(412\) | 29154.4 | 3.48624 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3577.26 | −0.424669 | ||||||||
\(415\) | −670.820 | + | 1161.89i | −0.0793476 | + | 0.137434i | ||||
\(416\) | 8652.95 | + | 14987.3i | 1.01982 | + | 1.76638i | ||||
\(417\) | −4225.79 | − | 7319.28i | −0.496254 | − | 0.859537i | ||||
\(418\) | 4027.35 | − | 6975.57i | 0.471254 | − | 0.816236i | ||||
\(419\) | −3370.31 | −0.392960 | −0.196480 | − | 0.980508i | \(-0.562951\pi\) | ||||
−0.196480 | + | 0.980508i | \(0.562951\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15651.0 | 1.81184 | 0.905919 | − | 0.423450i | \(-0.139181\pi\) | ||||
0.905919 | + | 0.423450i | \(0.139181\pi\) | |||||||
\(422\) | 12412.0 | − | 21498.3i | 1.43178 | − | 2.47991i | ||||
\(423\) | −2792.47 | − | 4836.70i | −0.320980 | − | 0.555953i | ||||
\(424\) | 9303.58 | + | 16114.3i | 1.06562 | + | 1.84570i | ||||
\(425\) | −2045.04 | + | 3542.12i | −0.233410 | + | 0.404277i | ||||
\(426\) | 12507.9 | 1.42256 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 19995.6 | 2.25823 | ||||||||
\(429\) | −807.314 | + | 1398.31i | −0.0908567 | + | 0.157368i | ||||
\(430\) | −3599.88 | − | 6235.17i | −0.403724 | − | 0.699271i | ||||
\(431\) | −2444.06 | − | 4233.24i | −0.273147 | − | 0.473104i | 0.696519 | − | 0.717538i | \(-0.254731\pi\) |
−0.969666 | + | 0.244434i | \(0.921398\pi\) | |||||||
\(432\) | −2453.32 | + | 4249.27i | −0.273230 | + | 0.473248i | ||||
\(433\) | 5255.73 | 0.583313 | 0.291656 | − | 0.956523i | \(-0.405794\pi\) | ||||
0.291656 | + | 0.956523i | \(0.405794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1207.25 | 0.133065 | ||||||||
\(436\) | −19705.5 | + | 34131.0i | −2.16450 | + | 3.74903i | ||||
\(437\) | 4081.88 | + | 7070.03i | 0.446826 | + | 0.773925i | ||||
\(438\) | −2636.69 | − | 4566.88i | −0.287639 | − | 0.498205i | ||||
\(439\) | −412.488 | + | 714.451i | −0.0448451 | + | 0.0776740i | −0.887577 | − | 0.460660i | \(-0.847613\pi\) |
0.842732 | + | 0.538334i | \(0.180946\pi\) | |||||||
\(440\) | 5003.48 | 0.542117 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8925.37 | 0.960490 | ||||||||
\(443\) | −6513.64 | + | 11281.9i | −0.698583 | + | 1.20998i | 0.270375 | + | 0.962755i | \(0.412852\pi\) |
−0.968958 | + | 0.247226i | \(0.920481\pi\) | |||||||
\(444\) | −5712.21 | − | 9893.83i | −0.610561 | − | 1.05752i | ||||
\(445\) | −4408.92 | − | 7636.47i | −0.469669 | − | 0.813491i | ||||
\(446\) | 8615.44 | − | 14922.4i | 0.914693 | − | 1.58429i | ||||
\(447\) | 5400.98 | 0.571493 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16526.1 | 1.73700 | 0.868500 | − | 0.495689i | \(-0.165084\pi\) | ||||
0.868500 | + | 0.495689i | \(0.165084\pi\) | |||||||
\(450\) | 2247.10 | − | 3892.09i | 0.235399 | − | 0.407722i | ||||
\(451\) | 172.522 | + | 298.817i | 0.0180127 | + | 0.0311989i | ||||
\(452\) | −6788.71 | − | 11758.4i | −0.706447 | − | 1.22360i | ||||
\(453\) | 679.476 | − | 1176.89i | 0.0704737 | − | 0.122064i | ||||
\(454\) | −27274.9 | −2.81954 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 21144.1 | 2.17141 | ||||||||
\(457\) | 1855.41 | − | 3213.67i | 0.189918 | − | 0.328947i | −0.755305 | − | 0.655374i | \(-0.772511\pi\) |
0.945223 | + | 0.326426i | \(0.105844\pi\) | |||||||
\(458\) | 1631.79 | + | 2826.34i | 0.166481 | + | 0.288354i | ||||
\(459\) | 586.963 | + | 1016.65i | 0.0596887 | + | 0.103384i | ||||
\(460\) | −4201.31 | + | 7276.89i | −0.425842 | + | 0.737580i | ||||
\(461\) | 9714.00 | 0.981401 | 0.490701 | − | 0.871328i | \(-0.336741\pi\) | ||||
0.490701 | + | 0.871328i | \(0.336741\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −43.2780 | −0.00434406 | −0.00217203 | − | 0.999998i | \(-0.500691\pi\) | ||||
−0.00217203 | + | 0.999998i | \(0.500691\pi\) | |||||||
\(464\) | 6574.79 | − | 11387.9i | 0.657817 | − | 1.13937i | ||||
\(465\) | −534.254 | − | 925.355i | −0.0532805 | − | 0.0922845i | ||||
\(466\) | −7504.38 | − | 12998.0i | −0.745995 | − | 1.29210i | ||||
\(467\) | −766.618 | + | 1327.82i | −0.0759633 | + | 0.131572i | −0.901505 | − | 0.432769i | \(-0.857537\pi\) |
0.825541 | + | 0.564341i | \(0.190870\pi\) | |||||||
\(468\) | −7022.87 | −0.693659 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −18319.6 | −1.79791 | ||||||||
\(471\) | −2795.49 | + | 4841.93i | −0.273480 | + | 0.473682i | ||||
\(472\) | 16970.8 | + | 29394.3i | 1.65497 | + | 2.86649i | ||||
\(473\) | −1697.09 | − | 2939.45i | −0.164974 | − | 0.285743i | ||||
\(474\) | −3484.74 | + | 6035.74i | −0.337678 | + | 0.584875i | ||||
\(475\) | −10256.3 | −0.990722 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2590.55 | −0.248665 | ||||||||
\(478\) | 9110.23 | − | 15779.4i | 0.871741 | − | 1.50990i | ||||
\(479\) | −3517.69 | − | 6092.81i | −0.335547 | − | 0.581185i | 0.648042 | − | 0.761604i | \(-0.275588\pi\) |
−0.983590 | + | 0.180419i | \(0.942255\pi\) | |||||||
\(480\) | 3733.15 | + | 6466.00i | 0.354988 | + | 0.614857i | ||||
\(481\) | 3649.21 | − | 6320.62i | 0.345924 | − | 0.599159i | ||||
\(482\) | 13993.3 | 1.32236 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −22948.6 | −2.15520 | ||||||||
\(485\) | −220.441 | + | 381.815i | −0.0206386 | + | 0.0357471i | ||||
\(486\) | −644.958 | − | 1117.10i | −0.0601973 | − | 0.104265i | ||||
\(487\) | 7685.64 | + | 13311.9i | 0.715132 | + | 1.23865i | 0.962908 | + | 0.269828i | \(0.0869669\pi\) |
−0.247776 | + | 0.968817i | \(0.579700\pi\) | |||||||
\(488\) | −12393.5 | + | 21466.1i | −1.14964 | + | 1.99124i | ||||
\(489\) | 6963.41 | 0.643960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2393.35 | −0.219980 | −0.109990 | − | 0.993933i | \(-0.535082\pi\) | ||||
−0.109990 | + | 0.993933i | \(0.535082\pi\) | |||||||
\(492\) | −750.388 | + | 1299.71i | −0.0687604 | + | 0.119096i | ||||
\(493\) | −1573.04 | − | 2724.58i | −0.143704 | − | 0.248903i | ||||
\(494\) | 11190.7 | + | 19382.8i | 1.01921 | + | 1.76533i | ||||
\(495\) | −348.300 | + | 603.274i | −0.0316261 | + | 0.0547781i | ||||
\(496\) | −11638.4 | −1.05359 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −3841.74 | −0.345688 | ||||||||
\(499\) | −346.760 | + | 600.606i | −0.0311084 | + | 0.0538814i | −0.881160 | − | 0.472817i | \(-0.843237\pi\) |
0.850052 | + | 0.526699i | \(0.176570\pi\) | |||||||
\(500\) | −12291.8 | − | 21290.1i | −1.09941 | − | 1.90424i | ||||
\(501\) | 4817.43 | + | 8344.03i | 0.429594 | + | 0.744079i | ||||
\(502\) | 5461.10 | − | 9458.91i | 0.485540 | − | 0.840979i | ||||
\(503\) | 8646.95 | 0.766498 | 0.383249 | − | 0.923645i | \(-0.374805\pi\) | ||||
0.383249 | + | 0.923645i | \(0.374805\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6423.27 | 0.566003 | ||||||||
\(506\) | −2765.89 | + | 4790.67i | −0.243002 | + | 0.420892i | ||||
\(507\) | 1052.24 | + | 1822.53i | 0.0921729 | + | 0.159648i | ||||
\(508\) | −1773.80 | − | 3072.31i | −0.154920 | − | 0.268330i | ||||
\(509\) | −7750.44 | + | 13424.1i | −0.674916 | + | 1.16899i | 0.301578 | + | 0.953441i | \(0.402487\pi\) |
−0.976494 | + | 0.215546i | \(0.930847\pi\) | |||||||
\(510\) | 3850.68 | 0.334335 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −12656.9 | −1.09250 | ||||||||
\(513\) | −1471.87 | + | 2549.36i | −0.126676 | + | 0.219409i | ||||
\(514\) | 5706.96 | + | 9884.75i | 0.489734 | + | 0.848245i | ||||
\(515\) | 4017.72 | + | 6958.89i | 0.343771 | + | 0.595428i | ||||
\(516\) | 7381.55 | − | 12785.2i | 0.629757 | − | 1.09077i | ||||
\(517\) | −8636.41 | −0.734678 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −642.831 | −0.0543683 | ||||||||
\(520\) | −6951.50 | + | 12040.4i | −0.586238 | + | 1.01539i | ||||
\(521\) | 432.354 | + | 748.858i | 0.0363565 | + | 0.0629714i | 0.883631 | − | 0.468184i | \(-0.155091\pi\) |
−0.847275 | + | 0.531155i | \(0.821758\pi\) | |||||||
\(522\) | 1728.46 | + | 2993.78i | 0.144928 | + | 0.251023i | ||||
\(523\) | −3127.81 | + | 5417.52i | −0.261509 | + | 0.452947i | −0.966643 | − | 0.256127i | \(-0.917554\pi\) |
0.705134 | + | 0.709074i | \(0.250887\pi\) | |||||||
\(524\) | −22719.0 | −1.89406 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24365.9 | −2.01978 | ||||||||
\(527\) | −1392.26 | + | 2411.46i | −0.115081 | + | 0.199326i | ||||
\(528\) | 3793.75 | + | 6570.97i | 0.312693 | + | 0.541600i | ||||
\(529\) | 3280.15 | + | 5681.39i | 0.269594 | + | 0.466951i | ||||
\(530\) | −4248.72 | + | 7359.01i | −0.348213 | + | 0.603122i | ||||
\(531\) | −4725.46 | −0.386191 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −958.762 | −0.0779148 | ||||||||
\(534\) | 12624.8 | − | 21866.8i | 1.02309 | − | 1.77204i | ||||
\(535\) | 2755.56 | + | 4772.78i | 0.222679 | + | 0.385692i | ||||
\(536\) | −6403.56 | − | 11091.3i | −0.516029 | − | 0.893789i | ||||
\(537\) | 3655.83 | − | 6332.09i | 0.293782 | − | 0.508845i | ||||
\(538\) | 2013.85 | 0.161381 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3029.88 | −0.241454 | ||||||||
\(541\) | −71.9353 | + | 124.596i | −0.00571671 | + | 0.00990164i | −0.868870 | − | 0.495041i | \(-0.835153\pi\) |
0.863153 | + | 0.504943i | \(0.168486\pi\) | |||||||
\(542\) | −14249.7 | − | 24681.2i | −1.12929 | − | 1.95599i | ||||
\(543\) | −372.946 | − | 645.962i | −0.0294745 | − | 0.0510514i | ||||
\(544\) | 9728.53 | − | 16850.3i | 0.766741 | − | 1.32804i | ||||
\(545\) | −10862.4 | −0.853747 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5455.65 | 0.426448 | 0.213224 | − | 0.977003i | \(-0.431604\pi\) | ||||
0.213224 | + | 0.977003i | \(0.431604\pi\) | |||||||
\(548\) | −18853.3 | + | 32654.9i | −1.46966 | + | 2.54552i | ||||
\(549\) | −1725.46 | − | 2988.58i | −0.134136 | − | 0.232331i | ||||
\(550\) | −3474.86 | − | 6018.63i | −0.269397 | − | 0.466610i | ||||
\(551\) | 3944.56 | − | 6832.18i | 0.304980 | − | 0.528241i | ||||
\(552\) | −14521.3 | −1.11969 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −25382.2 | −1.94654 | ||||||||
\(555\) | 1574.38 | − | 2726.91i | 0.120412 | − | 0.208560i | ||||
\(556\) | −28422.7 | − | 49229.5i | −2.16797 | − | 3.75503i | ||||
\(557\) | −12404.9 | − | 21486.0i | −0.943652 | − | 1.63445i | −0.758428 | − | 0.651756i | \(-0.774032\pi\) |
−0.185223 | − | 0.982696i | \(-0.559301\pi\) | |||||||
\(558\) | 1529.82 | − | 2649.72i | 0.116062 | − | 0.201025i | ||||
\(559\) | 9431.33 | 0.713600 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1815.33 | 0.136619 | ||||||||
\(562\) | 5511.51 | − | 9546.22i | 0.413682 | − | 0.716517i | ||||
\(563\) | 8184.91 | + | 14176.7i | 0.612705 | + | 1.06124i | 0.990782 | + | 0.135462i | \(0.0432520\pi\) |
−0.378077 | + | 0.925774i | \(0.623415\pi\) | |||||||
\(564\) | −18782.1 | − | 32531.6i | −1.40225 | − | 2.42877i | ||||
\(565\) | 1871.08 | − | 3240.81i | 0.139322 | − | 0.241313i | ||||
\(566\) | −13576.6 | −1.00824 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 50773.7 | 3.75074 | ||||||||
\(569\) | 9225.29 | − | 15978.7i | 0.679691 | − | 1.17726i | −0.295383 | − | 0.955379i | \(-0.595447\pi\) |
0.975074 | − | 0.221881i | \(-0.0712195\pi\) | |||||||
\(570\) | 4828.00 | + | 8362.34i | 0.354777 | + | 0.614491i | ||||
\(571\) | 3554.34 | + | 6156.30i | 0.260499 | + | 0.451197i | 0.966374 | − | 0.257139i | \(-0.0827797\pi\) |
−0.705876 | + | 0.708335i | \(0.749446\pi\) | |||||||
\(572\) | −5429.99 | + | 9405.02i | −0.396922 | + | 0.687489i | ||||
\(573\) | −12939.2 | −0.943358 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7043.82 | 0.510865 | ||||||||
\(576\) | −4147.57 | + | 7183.80i | −0.300026 | + | 0.519661i | ||||
\(577\) | 3797.09 | + | 6576.75i | 0.273960 | + | 0.474512i | 0.969872 | − | 0.243615i | \(-0.0783332\pi\) |
−0.695912 | + | 0.718127i | \(0.745000\pi\) | |||||||
\(578\) | 8022.42 | + | 13895.2i | 0.577316 | + | 0.999940i | ||||
\(579\) | −3091.28 | + | 5354.25i | −0.221881 | + | 0.384309i | ||||
\(580\) | 8119.96 | 0.581315 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1262.45 | −0.0899146 | ||||||||
\(583\) | −2002.98 | + | 3469.26i | −0.142290 | + | 0.246453i | ||||
\(584\) | −10703.2 | − | 18538.5i | −0.758392 | − | 1.31357i | ||||
\(585\) | −967.811 | − | 1676.30i | −0.0684001 | − | 0.118472i | ||||
\(586\) | 1486.45 | − | 2574.61i | 0.104786 | − | 0.181495i | ||||
\(587\) | 1763.34 | 0.123988 | 0.0619939 | − | 0.998077i | \(-0.480254\pi\) | ||||
0.0619939 | + | 0.998077i | \(0.480254\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6982.47 | −0.488468 | ||||||||
\(590\) | −7750.16 | + | 13423.7i | −0.540795 | + | 0.936684i | ||||
\(591\) | 2499.13 | + | 4328.62i | 0.173943 | + | 0.301279i | ||||
\(592\) | −17148.4 | − | 29702.0i | −1.19054 | − | 2.06207i | ||||
\(593\) | −6158.07 | + | 10666.1i | −0.426445 | + | 0.738624i | −0.996554 | − | 0.0829448i | \(-0.973567\pi\) |
0.570109 | + | 0.821569i | \(0.306901\pi\) | |||||||
\(594\) | −1994.69 | −0.137783 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36327.0 | 2.49666 | ||||||||
\(597\) | −1631.30 | + | 2825.49i | −0.111834 | + | 0.193702i | ||||
\(598\) | −7685.50 | − | 13311.7i | −0.525558 | − | 0.910293i | ||||
\(599\) | 4451.70 | + | 7710.57i | 0.303659 | + | 0.525952i | 0.976962 | − | 0.213414i | \(-0.0684584\pi\) |
−0.673303 | + | 0.739367i | \(0.735125\pi\) | |||||||
\(600\) | 9121.72 | − | 15799.3i | 0.620655 | − | 1.07501i | ||||
\(601\) | 19157.1 | 1.30022 | 0.650112 | − | 0.759838i | \(-0.274722\pi\) | ||||
0.650112 | + | 0.759838i | \(0.274722\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1783.05 | 0.120417 | ||||||||
\(604\) | 4570.15 | − | 7915.74i | 0.307876 | − | 0.533256i | ||||
\(605\) | −3162.51 | − | 5477.62i | −0.212519 | − | 0.368094i | ||||
\(606\) | 9196.41 | + | 15928.6i | 0.616466 | + | 1.06775i | ||||
\(607\) | −3784.96 | + | 6555.75i | −0.253092 | + | 0.438369i | −0.964376 | − | 0.264537i | \(-0.914781\pi\) |
0.711283 | + | 0.702905i | \(0.248114\pi\) | |||||||
\(608\) | 48790.7 | 3.25448 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11319.6 | −0.751340 | ||||||||
\(611\) | 11998.9 | − | 20782.6i | 0.794471 | − | 1.37606i | ||||
\(612\) | 3947.91 | + | 6837.99i | 0.260760 | + | 0.451649i | ||||
\(613\) | −1453.56 | − | 2517.65i | −0.0957730 | − | 0.165884i | 0.814158 | − | 0.580643i | \(-0.197199\pi\) |
−0.909931 | + | 0.414760i | \(0.863866\pi\) | |||||||
\(614\) | 9695.65 | − | 16793.4i | 0.637272 | − | 1.10379i | ||||
\(615\) | −413.640 | −0.0271212 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12510.9 | −0.816320 | −0.408160 | − | 0.912910i | \(-0.633829\pi\) | ||||
−0.408160 | + | 0.912910i | \(0.633829\pi\) | |||||||
\(618\) | −11504.6 | + | 19926.6i | −0.748840 | + | 1.29703i | ||||
\(619\) | 5032.78 | + | 8717.03i | 0.326792 | + | 0.566021i | 0.981873 | − | 0.189538i | \(-0.0606989\pi\) |
−0.655081 | + | 0.755558i | \(0.727366\pi\) | |||||||
\(620\) | −3593.39 | − | 6223.93i | −0.232764 | − | 0.403160i | ||||
\(621\) | 1010.85 | − | 1750.84i | 0.0653205 | − | 0.113138i | ||||
\(622\) | −18538.0 | −1.19503 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −21083.2 | −1.35257 | ||||||||
\(625\) | −2491.59 | + | 4315.56i | −0.159462 | + | 0.276196i | ||||
\(626\) | 23123.2 | + | 40050.5i | 1.47634 | + | 2.55709i | ||||
\(627\) | 2276.07 | + | 3942.27i | 0.144972 | + | 0.251099i | ||||
\(628\) | −18802.4 | + | 32566.8i | −1.19474 | + | 2.06936i | ||||
\(629\) | −8205.63 | −0.520159 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25146.6 | −1.58648 | −0.793242 | − | 0.608907i | \(-0.791608\pi\) | ||||
−0.793242 | + | 0.608907i | \(0.791608\pi\) | |||||||
\(632\) | −14145.7 | + | 24501.1i | −0.890325 | + | 1.54209i | ||||
\(633\) | 7014.71 | + | 12149.8i | 0.440458 | + | 0.762895i | ||||
\(634\) | −5149.92 | − | 8919.92i | −0.322602 | − | 0.558762i | ||||
\(635\) | 488.889 | − | 846.781i | 0.0305527 | − | 0.0529189i | ||||
\(636\) | −17424.0 | −1.08633 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5345.70 | 0.331721 | ||||||||
\(639\) | −3534.44 | + | 6121.83i | −0.218811 | + | 0.378992i | ||||
\(640\) | 3649.66 | + | 6321.41i | 0.225415 | + | 0.390430i | ||||
\(641\) | 14479.5 | + | 25079.1i | 0.892206 | + | 1.54535i | 0.837225 | + | 0.546859i | \(0.184176\pi\) |
0.0549809 | + | 0.998487i | \(0.482490\pi\) | |||||||
\(642\) | −7890.46 | + | 13666.7i | −0.485065 | + | 0.840157i | ||||
\(643\) | −7341.90 | −0.450290 | −0.225145 | − | 0.974325i | \(-0.572286\pi\) | ||||
−0.225145 | + | 0.974325i | \(0.572286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4068.97 | 0.248396 | ||||||||
\(646\) | 12581.7 | − | 21792.1i | 0.766285 | − | 1.32725i | ||||
\(647\) | 3035.99 | + | 5258.49i | 0.184478 | + | 0.319525i | 0.943400 | − | 0.331656i | \(-0.107607\pi\) |
−0.758923 | + | 0.651181i | \(0.774274\pi\) | |||||||
\(648\) | −2618.10 | − | 4534.67i | −0.158717 | − | 0.274906i | ||||
\(649\) | −3653.67 | + | 6328.34i | −0.220985 | + | 0.382756i | ||||
\(650\) | 19311.0 | 1.16529 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 46835.9 | 2.81324 | ||||||||
\(653\) | −13131.1 | + | 22743.7i | −0.786920 | + | 1.36298i | 0.140926 | + | 0.990020i | \(0.454992\pi\) |
−0.927846 | + | 0.372965i | \(0.878341\pi\) | |||||||
\(654\) | −15552.0 | − | 26936.9i | −0.929864 | − | 1.61057i | ||||
\(655\) | −3130.88 | − | 5422.84i | −0.186769 | − | 0.323493i | ||||
\(656\) | −2252.72 | + | 3901.82i | −0.134076 | + | 0.232226i | ||||
\(657\) | 2980.27 | 0.176973 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 26130.1 | 1.54459 | 0.772296 | − | 0.635263i | \(-0.219108\pi\) | ||||
0.772296 | + | 0.635263i | \(0.219108\pi\) | |||||||
\(660\) | −2342.67 | + | 4057.62i | −0.138164 | + | 0.239307i | ||||
\(661\) | −5962.75 | − | 10327.8i | −0.350868 | − | 0.607722i | 0.635533 | − | 0.772073i | \(-0.280780\pi\) |
−0.986402 | + | 0.164351i | \(0.947447\pi\) | |||||||
\(662\) | 15212.3 | + | 26348.4i | 0.893114 | + | 1.54692i | ||||
\(663\) | −2522.10 | + | 4368.41i | −0.147738 | + | 0.255890i | ||||
\(664\) | −15594.9 | −0.911444 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9016.38 | 0.524591 | ||||||||
\(667\) | −2709.04 | + | 4692.19i | −0.157263 | + | 0.272387i | ||||
\(668\) | 32402.0 | + | 56121.9i | 1.87675 | + | 3.25063i | ||||
\(669\) | 4869.04 | + | 8433.43i | 0.281387 | + | 0.487377i | ||||
\(670\) | 2924.35 | − | 5065.13i | 0.168623 | − | 0.292064i | ||||
\(671\) | −5336.42 | −0.307019 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6359.85 | −0.364271 | −0.182135 | − | 0.983273i | \(-0.558301\pi\) | ||||
−0.182135 | + | 0.983273i | \(0.558301\pi\) | |||||||
\(674\) | −6379.89 | + | 11050.3i | −0.364606 | + | 0.631516i | ||||
\(675\) | 1269.96 | + | 2199.63i | 0.0724158 | + | 0.125428i | ||||
\(676\) | 7077.36 | + | 12258.4i | 0.402672 | + | 0.697449i | ||||
\(677\) | 4280.81 | − | 7414.57i | 0.243020 | − | 0.420924i | −0.718553 | − | 0.695472i | \(-0.755195\pi\) |
0.961573 | + | 0.274549i | \(0.0885285\pi\) | |||||||
\(678\) | 10715.6 | 0.606975 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 15631.2 | 0.881513 | ||||||||
\(681\) | 7707.24 | − | 13349.3i | 0.433689 | − | 0.751171i | ||||
\(682\) | −2365.67 | − | 4097.46i | −0.132824 | − | 0.230059i | ||||
\(683\) | 3352.94 | + | 5807.47i | 0.187843 | + | 0.325354i | 0.944531 | − | 0.328423i | \(-0.106517\pi\) |
−0.756688 | + | 0.653776i | \(0.773184\pi\) | |||||||
\(684\) | −9899.82 | + | 17147.0i | −0.553405 | + | 0.958526i | ||||
\(685\) | −10392.6 | −0.579679 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1844.42 | −0.102429 | ||||||||
\(688\) | 22160.0 | − | 38382.2i | 1.22797 | − | 2.12690i | ||||
\(689\) | −5565.62 | − | 9639.94i | −0.307741 | − | 0.533022i | ||||
\(690\) | −3315.76 | − | 5743.07i | −0.182941 | − | 0.316862i | ||||
\(691\) | −12665.3 | + | 21937.0i | −0.697267 | + | 1.20770i | 0.272143 | + | 0.962257i | \(0.412268\pi\) |
−0.969410 | + | 0.245445i | \(0.921066\pi\) | |||||||
\(692\) | −4323.68 | −0.237517 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17710.8 | −0.968723 | ||||||||
\(695\) | 7833.77 | − | 13568.5i | 0.427557 | − | 0.740550i | ||||
\(696\) | 7016.39 | + | 12152.7i | 0.382120 | + | 0.661851i | ||||
\(697\) | 538.969 | + | 933.522i | 0.0292897 | + | 0.0507312i | ||||
\(698\) | −6435.08 | + | 11145.9i | −0.348956 | + | 0.604410i | ||||
\(699\) | 8482.25 | 0.458981 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27184.1 | −1.46467 | −0.732333 | − | 0.680947i | \(-0.761568\pi\) | ||||
−0.732333 | + | 0.680947i | \(0.761568\pi\) | |||||||
\(702\) | 2771.30 | − | 4800.03i | 0.148997 | − | 0.258070i | ||||
\(703\) | −10288.3 | − | 17819.8i | −0.551961 | − | 0.956025i | ||||
\(704\) | 6413.69 | + | 11108.8i | 0.343360 | + | 0.594716i | ||||
\(705\) | 5176.68 | − | 8966.27i | 0.276546 | − | 0.478992i | ||||
\(706\) | 65839.5 | 3.50977 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −31783.4 | −1.68714 | ||||||||
\(709\) | −8072.75 | + | 13982.4i | −0.427614 | + | 0.740649i | −0.996661 | − | 0.0816561i | \(-0.973979\pi\) |
0.569047 | + | 0.822305i | \(0.307312\pi\) | |||||||
\(710\) | 11593.6 | + | 20080.7i | 0.612816 | + | 1.06143i | ||||
\(711\) | −1969.41 | − | 3411.12i | −0.103880 | − | 0.179925i | ||||
\(712\) | 51248.2 | − | 88764.5i | 2.69748 | − | 4.67218i | ||||
\(713\) | 4795.41 | 0.251879 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2993.20 | −0.156558 | ||||||||
\(716\) | 24589.1 | − | 42589.6i | 1.28343 | − | 2.22297i | ||||
\(717\) | 5148.68 | + | 8917.77i | 0.268174 | + | 0.464491i | ||||
\(718\) | −3593.30 | − | 6223.77i | −0.186770 | − | 0.323494i | ||||
\(719\) | 8648.74 | − | 14980.0i | 0.448600 | − | 0.776998i | −0.549695 | − | 0.835365i | \(-0.685256\pi\) |
0.998295 | + | 0.0583673i | \(0.0185895\pi\) | |||||||
\(720\) | −9095.92 | −0.470812 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26690.4 | 1.37578 | ||||||||
\(723\) | −3954.17 | + | 6848.82i | −0.203398 | + | 0.352296i | ||||
\(724\) | −2508.44 | − | 4344.74i | −0.128764 | − | 0.223026i | ||||
\(725\) | −3403.43 | − | 5894.91i | −0.174345 | − | 0.301975i | ||||
\(726\) | 9055.74 | − | 15685.0i | 0.462934 | − | 0.801825i | ||||
\(727\) | −3514.71 | −0.179303 | −0.0896516 | − | 0.995973i | \(-0.528575\pi\) | ||||
−0.0896516 | + | 0.995973i | \(0.528575\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 4887.89 | − | 8466.08i | 0.247821 | − | 0.429238i | ||||
\(731\) | −5301.83 | − | 9183.04i | −0.268256 | − | 0.464633i | ||||
\(732\) | −11605.4 | − | 20101.2i | −0.585996 | − | 1.01498i | ||||
\(733\) | −13755.6 | + | 23825.4i | −0.693144 | + | 1.20056i | 0.277658 | + | 0.960680i | \(0.410442\pi\) |
−0.970802 | + | 0.239881i | \(0.922892\pi\) | |||||||
\(734\) | 7315.16 | 0.367858 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33508.4 | −1.67817 | ||||||||
\(737\) | 1378.63 | − | 2387.86i | 0.0689044 | − | 0.119346i | ||||
\(738\) | −592.222 | − | 1025.76i | −0.0295393 | − | 0.0511635i | ||||
\(739\) | −8050.80 | − | 13944.4i | −0.400749 | − | 0.694117i | 0.593068 | − | 0.805153i | \(-0.297917\pi\) |
−0.993816 | + | 0.111035i | \(0.964583\pi\) | |||||||
\(740\) | 10589.3 | − | 18341.2i | 0.526040 | − | 0.911129i | ||||
\(741\) | −12648.9 | −0.627083 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14682.4 | 0.724961 | 0.362480 | − | 0.931991i | \(-0.381930\pi\) | ||||
0.362480 | + | 0.931991i | \(0.381930\pi\) | |||||||
\(744\) | 6210.03 | − | 10756.1i | 0.306009 | − | 0.530024i | ||||
\(745\) | 5006.17 | + | 8670.93i | 0.246190 | + | 0.426414i | ||||
\(746\) | −14483.5 | − | 25086.1i | −0.710828 | − | 1.23119i | ||||
\(747\) | 1085.59 | − | 1880.29i | 0.0531720 | − | 0.0920967i | ||||
\(748\) | 12209.9 | 0.596843 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 19401.9 | 0.944611 | ||||||||
\(751\) | 3636.53 | − | 6298.66i | 0.176696 | − | 0.306047i | −0.764051 | − | 0.645156i | \(-0.776792\pi\) |
0.940747 | + | 0.339109i | \(0.110126\pi\) | |||||||
\(752\) | −56385.3 | − | 97662.2i | −2.73426 | − | 4.73587i | ||||
\(753\) | 3086.36 | + | 5345.73i | 0.149367 | + | 0.258711i | ||||
\(754\) | −7426.96 | + | 12863.9i | −0.358719 | + | 0.621319i | ||||
\(755\) | 2519.23 | 0.121436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8505.93 | 0.408393 | 0.204196 | − | 0.978930i | \(-0.434542\pi\) | ||||
0.204196 | + | 0.978930i | \(0.434542\pi\) | |||||||
\(758\) | −1472.19 | + | 2549.91i | −0.0705440 | + | 0.122186i | ||||
\(759\) | −1563.15 | − | 2707.46i | −0.0747548 | − | 0.129479i | ||||
\(760\) | 19598.4 | + | 33945.5i | 0.935408 | + | 1.62017i | ||||
\(761\) | 7108.86 | − | 12312.9i | 0.338628 | − | 0.586521i | −0.645547 | − | 0.763721i | \(-0.723370\pi\) |
0.984175 | + | 0.177200i | \(0.0567038\pi\) | |||||||
\(762\) | 2799.84 | 0.133107 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −87029.3 | −4.12121 | ||||||||
\(765\) | −1088.11 | + | 1884.67i | −0.0514259 | + | 0.0890722i | ||||
\(766\) | 15555.1 | + | 26942.2i | 0.733717 | + | 1.27084i | ||||
\(767\) | −10152.3 | − | 17584.4i | −0.477939 | − | 0.827815i | ||||
\(768\) | 609.482 | − | 1055.65i | 0.0286364 | − | 0.0495998i | ||||
\(769\) | −16379.1 | −0.768068 | −0.384034 | − | 0.923319i | \(-0.625466\pi\) | ||||
−0.384034 | + | 0.923319i | \(0.625466\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6450.62 | −0.301314 | ||||||||
\(772\) | −20791.9 | + | 36012.6i | −0.969323 | + | 1.67892i | ||||
\(773\) | −19948.3 | − | 34551.6i | −0.928192 | − | 1.60768i | −0.786346 | − | 0.617787i | \(-0.788030\pi\) |
−0.141846 | − | 0.989889i | \(-0.545304\pi\) | |||||||
\(774\) | 5825.67 | + | 10090.4i | 0.270542 | + | 0.468593i | ||||
\(775\) | −3012.29 | + | 5217.45i | −0.139619 | + | 0.241827i | ||||
\(776\) | −5124.70 | −0.237070 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 41292.5 | 1.90284 | ||||||||
\(779\) | −1351.52 | + | 2340.91i | −0.0621609 | + | 0.107666i | ||||
\(780\) | −6509.50 | − | 11274.8i | −0.298817 | − | 0.517566i | ||||
\(781\) | 5465.57 | + | 9466.65i | 0.250414 | + | 0.433730i | ||||
\(782\) | −8640.83 | + | 14966.4i | −0.395135 | + | 0.684394i | ||||
\(783\) | −1953.69 | −0.0891688 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10364.5 | −0.471244 | ||||||||
\(786\) | 8965.16 | − | 15528.1i | 0.406840 | − | 0.704668i | ||||
\(787\) | −16564.3 | − | 28690.2i | −0.750257 | − | 1.29948i | −0.947698 | − | 0.319169i | \(-0.896596\pi\) |
0.197440 | − | 0.980315i | \(-0.436737\pi\) | |||||||
\(788\) | 16809.1 | + | 29114.3i | 0.759899 | + | 1.31618i | ||||
\(789\) | 6885.23 | − | 11925.6i | 0.310672 | − | 0.538100i | ||||
\(790\) | −12920.0 | −0.581865 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8097.12 | −0.363281 | ||||||||
\(793\) | 7414.07 | − | 12841.5i | 0.332007 | − | 0.575052i | ||||
\(794\) | 21307.2 | + | 36905.1i | 0.952346 | + | 1.64951i | ||||
\(795\) | −2401.18 | − | 4158.97i | −0.107121 | − | 0.185539i | ||||
\(796\) | −10972.1 | + | 19004.3i | −0.488563 | + | 0.846216i | ||||
\(797\) | 17851.5 | 0.793390 | 0.396695 | − | 0.917951i | \(-0.370157\pi\) | ||||
0.396695 | + | 0.917951i | \(0.370157\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26980.7 | −1.19463 | ||||||||
\(800\) | 21048.7 | − | 36457.4i | 0.930229 | − | 1.61120i | ||||
\(801\) | 7134.94 | + | 12358.1i | 0.314733 | + | 0.545133i | ||||
\(802\) | −2070.18 | − | 3585.66i | −0.0911479 | − | 0.157873i | ||||
\(803\) | 2304.30 | − | 3991.17i | 0.101267 | − | 0.175399i | ||||
\(804\) | 11992.8 | 0.526061 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13146.8 | 0.574538 | ||||||||
\(807\) | −569.066 | + | 985.652i | −0.0248229 | + | 0.0429945i | ||||
\(808\) | 37331.2 | + | 64659.6i | 1.62538 | + | 2.81524i | ||||
\(809\) | 2528.52 | + | 4379.52i | 0.109886 | + | 0.190328i | 0.915724 | − | 0.401808i | \(-0.131618\pi\) |
−0.805838 | + | 0.592136i | \(0.798285\pi\) | |||||||
\(810\) | 1195.62 | − | 2070.88i | 0.0518641 | − | 0.0898312i | ||||
\(811\) | 17535.4 | 0.759251 | 0.379626 | − | 0.925140i | \(-0.376053\pi\) | ||||
0.379626 | + | 0.925140i | \(0.376053\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16106.5 | 0.694810 | ||||||||
\(814\) | 6971.35 | − | 12074.7i | 0.300179 | − | 0.519925i | ||||
\(815\) | 6454.39 | + | 11179.3i | 0.277408 | + | 0.480484i | ||||
\(816\) | 11851.9 | + | 20528.1i | 0.508456 | + | 0.880672i | ||||
\(817\) | 13294.9 | − | 23027.5i | 0.569315 | − | 0.986083i | ||||
\(818\) | −77992.1 | −3.33366 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2782.14 | −0.118484 | ||||||||
\(821\) | 9350.39 | − | 16195.3i | 0.397480 | − | 0.688455i | −0.595935 | − | 0.803033i | \(-0.703218\pi\) |
0.993414 | + | 0.114578i | \(0.0365516\pi\) | |||||||
\(822\) | −14879.4 | − | 25771.9i | −0.631361 | − | 1.09355i | ||||
\(823\) | −11111.3 | − | 19245.4i | −0.470615 | − | 0.815129i | 0.528820 | − | 0.848734i | \(-0.322635\pi\) |
−0.999435 | + | 0.0336046i | \(0.989301\pi\) | |||||||
\(824\) | −46701.0 | + | 80888.5i | −1.97440 | + | 3.41976i | ||||
\(825\) | 3927.66 | 0.165750 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25178.9 | 1.05872 | 0.529358 | − | 0.848399i | \(-0.322433\pi\) | ||||
0.529358 | + | 0.848399i | \(0.322433\pi\) | |||||||
\(828\) | 6798.98 | − | 11776.2i | 0.285363 | − | 0.494264i | ||||
\(829\) | 6139.45 | + | 10633.8i | 0.257216 | + | 0.445511i | 0.965495 | − | 0.260421i | \(-0.0838615\pi\) |
−0.708279 | + | 0.705933i | \(0.750528\pi\) | |||||||
\(830\) | −3560.91 | − | 6167.67i | −0.148917 | − | 0.257931i | ||||
\(831\) | 7172.41 | − | 12423.0i | 0.299408 | − | 0.518590i | ||||
\(832\) | −35643.1 | −1.48522 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 44863.5 | 1.86270 | ||||||||
\(835\) | −8930.54 | + | 15468.2i | −0.370125 | + | 0.641075i | ||||
\(836\) | 15308.8 | + | 26515.7i | 0.633334 | + | 1.09697i | ||||
\(837\) | 864.582 | + | 1497.50i | 0.0357041 | + | 0.0618413i | ||||
\(838\) | 8945.30 | − | 15493.7i | 0.368747 | − | 0.638689i | ||||
\(839\) | 25765.0 | 1.06020 | 0.530098 | − | 0.847936i | \(-0.322155\pi\) | ||||
0.530098 | + | 0.847936i | \(0.322155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19153.2 | −0.785321 | ||||||||
\(842\) | −41540.1 | + | 71949.6i | −1.70020 | + | 2.94483i | ||||
\(843\) | 3114.85 | + | 5395.08i | 0.127261 | + | 0.220423i | ||||
\(844\) | 47180.9 | + | 81719.7i | 1.92421 | + | 3.33283i | ||||
\(845\) | −1950.64 | + | 3378.61i | −0.0794132 | + | 0.137548i | ||||
\(846\) | 29646.5 | 1.20481 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −52308.2 | −2.11824 | ||||||||
\(849\) | 3836.42 | − | 6644.88i | 0.155083 | − | 0.268612i | ||||
\(850\) | −10855.7 | − | 18802.6i | −0.438055 | − | 0.758734i | ||||
\(851\) | 7065.75 | + | 12238.2i | 0.284619 | + | 0.492974i | ||||
\(852\) | −23772.6 | + | 41175.4i | −0.955912 | + | 1.65569i | ||||
\(853\) | −37864.5 | −1.51988 | −0.759939 | − | 0.649995i | \(-0.774771\pi\) | ||||
−0.759939 | + | 0.649995i | \(0.774771\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5457.12 | −0.218280 | ||||||||
\(856\) | −32030.0 | + | 55477.6i | −1.27893 | + | 2.21517i | ||||
\(857\) | −14604.4 | − | 25295.5i | −0.582118 | − | 1.00826i | −0.995228 | − | 0.0975771i | \(-0.968891\pi\) |
0.413110 | − | 0.910681i | \(-0.364443\pi\) | |||||||
\(858\) | −4285.46 | − | 7422.64i | −0.170517 | − | 0.295343i | ||||
\(859\) | 17451.5 | − | 30226.8i | 0.693173 | − | 1.20061i | −0.277619 | − | 0.960691i | \(-0.589545\pi\) |
0.970793 | − | 0.239920i | \(-0.0771213\pi\) | |||||||
\(860\) | 27367.8 | 1.08516 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25947.6 | 1.02527 | ||||||||
\(863\) | 6794.67 | − | 11768.7i | 0.268011 | − | 0.464208i | −0.700337 | − | 0.713812i | \(-0.746967\pi\) |
0.968348 | + | 0.249604i | \(0.0803004\pi\) | |||||||
\(864\) | −6041.35 | − | 10463.9i | −0.237883 | − | 0.412025i | ||||
\(865\) | −595.840 | − | 1032.03i | −0.0234210 | − | 0.0405664i | ||||
\(866\) | −13949.5 | + | 24161.2i | −0.547371 | + | 0.948074i | ||||
\(867\) | −9067.79 | −0.355200 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6090.89 | −0.237767 | ||||||||
\(870\) | −3204.22 | + | 5549.87i | −0.124866 | + | 0.216274i | ||||
\(871\) | 3830.76 | + | 6635.07i | 0.149025 | + | 0.258118i | ||||
\(872\) | −63130.7 | − | 109346.i | −2.45169 | − | 4.24645i | ||||
\(873\) | 356.739 | − | 617.890i | 0.0138302 | − | 0.0239547i | ||||
\(874\) | −43335.7 | −1.67717 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20045.3 | 0.773135 | ||||||||
\(877\) | 1189.87 | − | 2060.92i | 0.0458144 | − | 0.0793528i | −0.842209 | − | 0.539151i | \(-0.818745\pi\) |
0.888023 | + | 0.459799i | \(0.152078\pi\) | |||||||
\(878\) | −2189.61 | − | 3792.51i | −0.0841637 | − | 0.145776i | ||||
\(879\) | 840.074 | + | 1455.05i | 0.0322355 | + | 0.0558335i | ||||
\(880\) | −7032.85 | + | 12181.3i | −0.269406 | + | 0.466625i | ||||
\(881\) | 24235.5 | 0.926803 | 0.463401 | − | 0.886148i | \(-0.346629\pi\) | ||||
0.463401 | + | 0.886148i | \(0.346629\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9844.13 | −0.375177 | −0.187589 | − | 0.982248i | \(-0.560067\pi\) | ||||
−0.187589 | + | 0.982248i | \(0.560067\pi\) | |||||||
\(884\) | −16963.6 | + | 29381.9i | −0.645418 | + | 1.11790i | ||||
\(885\) | −4380.03 | − | 7586.43i | −0.166365 | − | 0.288153i | ||||
\(886\) | −34576.3 | − | 59887.9i | −1.31108 | − | 2.27085i | ||||
\(887\) | 14304.9 | − | 24776.9i | 0.541502 | − | 0.937910i | −0.457316 | − | 0.889304i | \(-0.651189\pi\) |
0.998818 | − | 0.0486051i | \(-0.0154776\pi\) | |||||||
\(888\) | 36600.5 | 1.38314 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 46807.7 | 1.76292 | ||||||||
\(891\) | 563.654 | − | 976.277i | 0.0211932 | − | 0.0367076i | ||||
\(892\) | 32749.2 | + | 56723.2i | 1.22929 | + | 2.12919i | ||||
\(893\) | −33828.5 | − | 58592.7i | −1.26767 | − | 2.19567i | ||||
\(894\) | −14335.0 | + | 24828.9i | −0.536279 | + | 0.928863i | ||||
\(895\) | 13554.4 | 0.506226 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8686.98 | 0.323355 | ||||||||
\(898\) | −43862.6 | + | 75972.2i | −1.62997 | + | 2.82319i | ||||
\(899\) | −2317.04 | − | 4013.24i | −0.0859596 | − | 0.148886i | ||||
\(900\) | 8541.72 | + | 14794.7i | 0.316360 | + | 0.547952i | ||||
\(901\) | −6257.44 | + | 10838.2i | −0.231371 | + | 0.400747i | ||||
\(902\) | −1831.59 | −0.0676113 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 43498.0 | 1.60036 | ||||||||
\(905\) | 691.368 | − | 1197.48i | 0.0253943 | − | 0.0439842i | ||||
\(906\) | 3606.86 | + | 6247.26i | 0.132263 | + | 0.229086i | ||||
\(907\) | −22289.2 | − | 38606.0i | −0.815986 | − | 1.41333i | −0.908618 | − | 0.417629i | \(-0.862861\pi\) |
0.0926313 | − | 0.995700i | \(-0.470472\pi\) | |||||||
\(908\) | 51838.8 | − | 89787.5i | 1.89464 | − | 3.28161i | ||||
\(909\) | −10394.8 | −0.379288 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45870.6 | 1.66823 | 0.834116 | − | 0.551589i | \(-0.185978\pi\) | ||||
0.834116 | + | 0.551589i | \(0.185978\pi\) | |||||||
\(912\) | −29720.0 | + | 51476.5i | −1.07909 | + | 1.86903i | ||||
\(913\) | −1678.72 | − | 2907.63i | −0.0608517 | − | 0.105398i | ||||
\(914\) | 9849.07 | + | 17059.1i | 0.356431 | + | 0.617357i | ||||
\(915\) | 3198.66 | − | 5540.24i | 0.115568 | − | 0.200169i | ||||
\(916\) | −12405.6 | −0.447479 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6231.55 | −0.224043 | ||||||||
\(919\) | −15544.1 | + | 26923.3i | −0.557948 | + | 0.966394i | 0.439720 | + | 0.898135i | \(0.355078\pi\) |
−0.997668 | + | 0.0682590i | \(0.978256\pi\) | |||||||
\(920\) | −13459.8 | − | 23313.0i | −0.482343 | − | 0.835443i | ||||
\(921\) | 5479.53 | + | 9490.83i | 0.196044 | + | 0.339558i | ||||
\(922\) | −25782.4 | + | 44656.4i | −0.920930 | + | 1.59510i | ||||
\(923\) | −30374.0 | −1.08318 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17753.7 | −0.631069 | ||||||||
\(926\) | 114.866 | − | 198.954i | 0.00407639 | − | 0.00706052i | ||||
\(927\) | −6501.87 | − | 11261.6i | −0.230366 | − | 0.399006i | ||||
\(928\) | 16190.6 | + | 28042.9i | 0.572717 | + | 0.991975i | ||||
\(929\) | −21047.3 | + | 36454.9i | −0.743313 | + | 1.28746i | 0.207665 | + | 0.978200i | \(0.433414\pi\) |
−0.950979 | + | 0.309257i | \(0.899920\pi\) | |||||||
\(930\) | 5671.95 | 0.199990 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 57051.5 | 2.00513 | ||||||||
\(933\) | 5238.40 | − | 9073.18i | 0.183813 | − | 0.318374i | ||||
\(934\) | −4069.43 | − | 7048.47i | −0.142565 | − | 0.246930i | ||||
\(935\) | 1682.63 | + | 2914.40i | 0.0588534 | + | 0.101937i | ||||
\(936\) | 11249.6 | − | 19484.9i | 0.392847 | − | 0.680431i | ||||
\(937\) | 44385.1 | 1.54749 | 0.773745 | − | 0.633497i | \(-0.218381\pi\) | ||||
0.773745 | + | 0.633497i | \(0.218381\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26136.3 | −0.908334 | ||||||||
\(940\) | 34818.3 | − | 60307.1i | 1.20814 | − | 2.09255i | ||||
\(941\) | 20495.8 | + | 35499.8i | 0.710036 | + | 1.22982i | 0.964843 | + | 0.262827i | \(0.0846547\pi\) |
−0.254807 | + | 0.966992i | \(0.582012\pi\) | |||||||
\(942\) | −14839.3 | − | 25702.4i | −0.513259 | − | 0.888990i | ||||
\(943\) | 928.197 | − | 1607.68i | 0.0320533 | − | 0.0555179i | ||||
\(944\) | −95416.1 | −3.28976 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18017.4 | 0.619233 | ||||||||
\(947\) | 26311.2 | − | 45572.4i | 0.902851 | − | 1.56378i | 0.0790737 | − | 0.996869i | \(-0.474804\pi\) |
0.823777 | − | 0.566914i | \(-0.191863\pi\) | |||||||
\(948\) | −13246.2 | − | 22943.2i | −0.453816 | − | 0.786033i | ||||
\(949\) | 6402.90 | + | 11090.1i | 0.219017 | + | 0.379348i | ||||
\(950\) | 27221.8 | − | 47149.6i | 0.929676 | − | 1.61025i | ||||
\(951\) | 5820.99 | 0.198484 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10798.1 | −0.367035 | −0.183517 | − | 0.983016i | \(-0.558748\pi\) | ||||
−0.183517 | + | 0.983016i | \(0.558748\pi\) | |||||||
\(954\) | 6875.70 | − | 11909.1i | 0.233343 | − | 0.404162i | ||||
\(955\) | −11993.4 | − | 20773.1i | −0.406384 | − | 0.703877i | ||||
\(956\) | 34630.0 | + | 59980.9i | 1.17156 | + | 2.02921i | ||||
\(957\) | −1510.57 | + | 2616.38i | −0.0510238 | + | 0.0883758i | ||||
\(958\) | 37345.8 | 1.25949 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −15377.5 | −0.516987 | ||||||||
\(961\) | 12844.7 | − | 22247.7i | 0.431162 | − | 0.746794i | ||||
\(962\) | 19371.1 | + | 33551.7i | 0.649219 | + | 1.12448i | ||||
\(963\) | −4459.32 | − | 7723.77i | −0.149221 | − | 0.258458i | ||||
\(964\) | −26595.7 | + | 46065.1i | −0.888579 | + | 1.53906i | ||||
\(965\) | −11461.2 | −0.382331 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15648.9 | 0.520408 | 0.260204 | − | 0.965554i | \(-0.416210\pi\) | ||||
0.260204 | + | 0.965554i | \(0.416210\pi\) | |||||||
\(968\) | 36760.2 | − | 63670.6i | 1.22058 | − | 2.11410i | ||||
\(969\) | 7110.59 | + | 12315.9i | 0.235733 | + | 0.408301i | ||||
\(970\) | −1170.17 | − | 2026.79i | −0.0387338 | − | 0.0670889i | ||||
\(971\) | 23629.9 | − | 40928.2i | 0.780968 | − | 1.35268i | −0.150411 | − | 0.988624i | \(-0.548060\pi\) |
0.931379 | − | 0.364052i | \(-0.118607\pi\) | |||||||
\(972\) | 4903.25 | 0.161802 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −81595.2 | −2.68427 | ||||||||
\(975\) | −5456.83 | + | 9451.51i | −0.179239 | + | 0.310452i | ||||
\(976\) | −34840.4 | − | 60345.3i | −1.14264 | − | 1.97910i | ||||
\(977\) | 24483.2 | + | 42406.2i | 0.801728 | + | 1.38863i | 0.918478 | + | 0.395473i | \(0.129419\pi\) |
−0.116749 | + | 0.993161i | \(0.537247\pi\) | |||||||
\(978\) | −18481.9 | + | 32011.6i | −0.604281 | + | 1.04665i | ||||
\(979\) | 22066.6 | 0.720380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17578.5 | 0.572109 | ||||||||
\(982\) | 6352.29 | − | 11002.5i | 0.206426 | − | 0.357540i | ||||
\(983\) | −9555.64 | − | 16550.9i | −0.310049 | − | 0.537020i | 0.668324 | − | 0.743870i | \(-0.267012\pi\) |
−0.978373 | + | 0.206850i | \(0.933679\pi\) | |||||||
\(984\) | −2404.02 | − | 4163.89i | −0.0778836 | − | 0.134898i | ||||
\(985\) | −4632.89 | + | 8024.39i | −0.149864 | + | 0.259572i | ||||
\(986\) | 16700.3 | 0.539397 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −85076.4 | −2.73951 | ||||||||
\(989\) | −9130.65 | + | 15814.8i | −0.293567 | + | 0.508473i | ||||
\(990\) | −1848.88 | − | 3202.36i | −0.0593548 | − | 0.102806i | ||||
\(991\) | 27051.3 | + | 46854.1i | 0.867115 | + | 1.50189i | 0.864931 | + | 0.501890i | \(0.167362\pi\) |
0.00218424 | + | 0.999998i | \(0.499305\pi\) | |||||||
\(992\) | 14329.9 | − | 24820.1i | 0.458643 | − | 0.794393i | ||||
\(993\) | −17194.5 | −0.549498 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6048.21 | −0.192705 | ||||||||
\(996\) | 7301.65 | − | 12646.8i | 0.232291 | − | 0.402339i | ||||
\(997\) | 4596.40 | + | 7961.20i | 0.146008 | + | 0.252892i | 0.929748 | − | 0.368196i | \(-0.120024\pi\) |
−0.783741 | + | 0.621088i | \(0.786691\pi\) | |||||||
\(998\) | −1840.70 | − | 3188.19i | −0.0583832 | − | 0.101123i | ||||
\(999\) | −2547.82 | + | 4412.95i | −0.0806901 | + | 0.139759i |
(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 | 147.4.e.n.79.1 | 6 | ||
3.2 | odd | 2 | 441.4.e.w.226.3 | 6 | |||
7.2 | even | 3 | 147.4.a.m.1.3 | 3 | |||
7.3 | odd | 6 | 21.4.e.b.4.1 | ✓ | 6 | ||
7.4 | even | 3 | inner | 147.4.e.n.67.1 | 6 | ||
7.5 | odd | 6 | 147.4.a.l.1.3 | 3 | |||
7.6 | odd | 2 | 21.4.e.b.16.1 | yes | 6 | ||
21.2 | odd | 6 | 441.4.a.t.1.1 | 3 | |||
21.5 | even | 6 | 441.4.a.s.1.1 | 3 | |||
21.11 | odd | 6 | 441.4.e.w.361.3 | 6 | |||
21.17 | even | 6 | 63.4.e.c.46.3 | 6 | |||
21.20 | even | 2 | 63.4.e.c.37.3 | 6 | |||
28.3 | even | 6 | 336.4.q.k.193.2 | 6 | |||
28.19 | even | 6 | 2352.4.a.ci.1.2 | 3 | |||
28.23 | odd | 6 | 2352.4.a.cg.1.2 | 3 | |||
28.27 | even | 2 | 336.4.q.k.289.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.1 | ✓ | 6 | 7.3 | odd | 6 | ||
21.4.e.b.16.1 | yes | 6 | 7.6 | odd | 2 | ||
63.4.e.c.37.3 | 6 | 21.20 | even | 2 | |||
63.4.e.c.46.3 | 6 | 21.17 | even | 6 | |||
147.4.a.l.1.3 | 3 | 7.5 | odd | 6 | |||
147.4.a.m.1.3 | 3 | 7.2 | even | 3 | |||
147.4.e.n.67.1 | 6 | 7.4 | even | 3 | inner | ||
147.4.e.n.79.1 | 6 | 1.1 | even | 1 | trivial | ||
336.4.q.k.193.2 | 6 | 28.3 | even | 6 | |||
336.4.q.k.289.2 | 6 | 28.27 | even | 2 | |||
441.4.a.s.1.1 | 3 | 21.5 | even | 6 | |||
441.4.a.t.1.1 | 3 | 21.2 | odd | 6 | |||
441.4.e.w.226.3 | 6 | 3.2 | odd | 2 | |||
441.4.e.w.361.3 | 6 | 21.11 | odd | 6 | |||
2352.4.a.cg.1.2 | 3 | 28.23 | odd | 6 | |||
2352.4.a.ci.1.2 | 3 | 28.19 | even | 6 |