Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,4,Mod(4,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, 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("21.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.23904011012\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 4.1 | ||
Root | \(2.65415 + 4.59712i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.4 |
Dual form | 21.4.e.b.16.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | −0.768488 | − | 0.639864i | \(-0.778991\pi\) |
−0.169895 | − | 0.985462i | \(-0.554343\pi\) | |||||||
\(3\) | 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 | \(-0.246674\pi\) |
−0.963169 | + | 0.268897i | \(0.913341\pi\) | |||||||
\(6\) | −15.9249 | −1.08355 | ||||||||
\(7\) | 9.67799 | − | 15.7904i | 0.522562 | − | 0.852601i | ||||
\(8\) | 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 | −0.754757 | − | 0.656005i | \(-0.772245\pi\) |
0.945495 | + | 0.325636i | \(0.105578\pi\) | |||||||
\(12\) | 30.2670 | + | 52.4239i | 0.728110 | + | 1.26112i | ||||
\(13\) | 38.6718 | 0.825048 | 0.412524 | − | 0.910947i | \(-0.364647\pi\) | ||||
0.412524 | + | 0.910947i | \(0.364647\pi\) | |||||||
\(14\) | −98.2771 | − | 2.58082i | −1.87612 | − | 0.0492680i | ||||
\(15\) | −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 | \(-0.933713\pi\) |
0.668243 | + | 0.743943i | \(0.267046\pi\) | |||||||
\(18\) | −23.8873 | + | 41.3741i | −0.312794 | + | 0.541776i | ||||
\(19\) | 54.5139 | + | 94.4208i | 0.658228 | + | 1.14009i | 0.981074 | + | 0.193633i | \(0.0620273\pi\) |
−0.322845 | + | 0.946452i | \(0.604639\pi\) | |||||||
\(20\) | 112.218 | 1.25463 | ||||||||
\(21\) | −26.5077 | − | 48.8297i | −0.275450 | − | 0.507406i | ||||
\(22\) | −73.8775 | −0.715943 | ||||||||
\(23\) | 37.4389 | + | 64.8461i | 0.339415 | + | 0.587885i | 0.984323 | − | 0.176376i | \(-0.0564374\pi\) |
−0.644907 | + | 0.764261i | \(0.723104\pi\) | |||||||
\(24\) | 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 | ||||||||
\(28\) | 178.290 | + | 328.429i | 1.20335 | + | 2.21668i | ||||
\(29\) | −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 | \(-0.892732\pi\) |
0.758229 | + | 0.651988i | \(0.226065\pi\) | |||||||
\(32\) | −223.754 | + | 387.553i | −1.23608 | + | 2.14095i | ||||
\(33\) | −20.8761 | − | 36.1584i | −0.110123 | − | 0.190738i | ||||
\(34\) | 230.798 | 1.16416 | ||||||||
\(35\) | −102.963 | − | 2.70387i | −0.497255 | − | 0.0130582i | ||||
\(36\) | 181.602 | 0.840749 | ||||||||
\(37\) | −94.3636 | − | 163.443i | −0.419278 | − | 0.726211i | 0.576589 | − | 0.817034i | \(-0.304383\pi\) |
−0.995867 | + | 0.0908235i | \(0.971050\pi\) | |||||||
\(38\) | 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 | \(-0.515036\pi\) | ||||
−0.0472184 | + | 0.998885i | \(0.515036\pi\) | |||||||
\(42\) | −154.121 | + | 251.460i | −0.566223 | + | 0.923837i | ||||
\(43\) | −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 | 0.715052 | + | 0.699071i | \(0.246403\pi\) |
0.247888 | + | 0.968789i | \(0.420264\pi\) | |||||||
\(48\) | −545.182 | −1.63938 | ||||||||
\(49\) | −155.673 | − | 305.638i | −0.453857 | − | 0.891074i | ||||
\(50\) | −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 | −0.617028 | − | 0.786941i | \(-0.711663\pi\) |
0.990025 | + | 0.140891i | \(0.0449967\pi\) | |||||||
\(54\) | 71.6620 | + | 124.122i | 0.180592 | + | 0.312794i | ||||
\(55\) | −77.4001 | −0.189757 | ||||||||
\(56\) | 625.627 | − | 1020.76i | 1.49291 | − | 2.43580i | ||||
\(57\) | 327.083 | 0.760057 | ||||||||
\(58\) | 192.051 | + | 332.642i | 0.434785 | + | 0.753070i | ||||
\(59\) | −262.526 | + | 454.708i | −0.579287 | + | 1.00335i | 0.416275 | + | 0.909239i | \(0.363336\pi\) |
−0.995561 | + | 0.0941152i | \(0.969998\pi\) | |||||||
\(60\) | 168.327 | − | 291.551i | 0.362182 | − | 0.627317i | ||||
\(61\) | 191.718 | + | 332.065i | 0.402409 | + | 0.696993i | 0.994016 | − | 0.109234i | \(-0.0348397\pi\) |
−0.591607 | + | 0.806226i | \(0.701506\pi\) | |||||||
\(62\) | 339.960 | 0.696369 | ||||||||
\(63\) | −166.625 | − | 4.37567i | −0.333218 | − | 0.00875052i | ||||
\(64\) | 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 | −0.942094 | − | 0.335350i | \(-0.891145\pi\) |
0.761468 | + | 0.648202i | \(0.224479\pi\) | |||||||
\(68\) | −438.657 | − | 759.776i | −0.782279 | − | 1.35495i | ||||
\(69\) | 224.634 | 0.391923 | ||||||||
\(70\) | 260.849 | + | 480.510i | 0.445392 | + | 0.820456i | ||||
\(71\) | 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 | \(-0.747810\pi\) |
0.967684 | + | 0.252166i | \(0.0811430\pi\) | |||||||
\(74\) | −500.910 | + | 867.602i | −0.786887 | + | 1.36293i | ||||
\(75\) | −141.106 | − | 244.403i | −0.217247 | − | 0.376283i | ||||
\(76\) | −2199.96 | −3.32043 | ||||||||
\(77\) | −122.972 | − | 226.527i | −0.182000 | − | 0.335262i | ||||
\(78\) | −615.844 | −0.893981 | ||||||||
\(79\) | −218.823 | − | 379.013i | −0.311640 | − | 0.539776i | 0.667078 | − | 0.744988i | \(-0.267545\pi\) |
−0.978718 | + | 0.205212i | \(0.934212\pi\) | |||||||
\(80\) | −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 | \(-0.449007\pi\) | ||||
0.159516 | + | 0.987195i | \(0.449007\pi\) | |||||||
\(84\) | 1120.72 | + | 29.4308i | 1.45572 | + | 0.0382281i | ||||
\(85\) | 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 | −0.757349 | − | 0.653010i | \(-0.773506\pi\) |
−0.186849 | − | 0.982389i | \(-0.559828\pi\) | |||||||
\(90\) | 265.694 | 0.311184 | ||||||||
\(91\) | 374.265 | − | 610.643i | 0.431139 | − | 0.703437i | ||||
\(92\) | −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 | \(-0.486789\pi\) | ||||
0.0414907 | + | 0.999139i | \(0.486789\pi\) | |||||||
\(98\) | −991.877 | + | 1526.86i | −1.02239 | + | 1.57384i | ||||
\(99\) | −125.256 | −0.127159 | ||||||||
\(100\) | 949.080 | + | 1643.85i | 0.949080 | + | 1.64385i | ||||
\(101\) | −577.487 | + | 1000.24i | −0.568931 | + | 0.985418i | 0.427741 | + | 0.903902i | \(0.359310\pi\) |
−0.996672 | + | 0.0815165i | \(0.974024\pi\) | |||||||
\(102\) | 346.197 | − | 599.631i | 0.336065 | − | 0.582082i | ||||
\(103\) | 722.430 | + | 1251.28i | 0.691098 | + | 1.19702i | 0.971478 | + | 0.237128i | \(0.0762061\pi\) |
−0.280380 | + | 0.959889i | \(0.590461\pi\) | |||||||
\(104\) | 2499.91 | 2.35708 | ||||||||
\(105\) | −161.469 | + | 263.450i | −0.150074 | + | 0.244858i | ||||
\(106\) | −1527.93 | −1.40006 | ||||||||
\(107\) | −495.480 | − | 858.197i | −0.447662 | − | 0.775374i | 0.550571 | − | 0.834788i | \(-0.314410\pi\) |
−0.998233 | + | 0.0594143i | \(0.981077\pi\) | |||||||
\(108\) | 272.403 | − | 471.816i | 0.242703 | − | 0.420375i | ||||
\(109\) | −976.585 | + | 1691.49i | −0.858164 | + | 1.48638i | 0.0155145 | + | 0.999880i | \(0.495061\pi\) |
−0.873678 | + | 0.486504i | \(0.838272\pi\) | |||||||
\(110\) | 205.431 | + | 355.817i | 0.178064 | + | 0.308417i | ||||
\(111\) | −566.182 | −0.484141 | ||||||||
\(112\) | −3364.48 | − | 88.3533i | −2.83851 | − | 0.0745410i | ||||
\(113\) | 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 | ||||||||
\(119\) | 384.174 | + | 707.686i | 0.295942 | + | 0.545155i | ||||
\(120\) | −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 | ||||||||
\(126\) | 422.131 | + | 777.608i | 0.298464 | + | 0.549800i | ||||
\(127\) | 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 | \(-0.289185\pi\) |
−0.990397 | + | 0.138251i | \(0.955852\pi\) | |||||||
\(132\) | 842.474 | 0.555515 | ||||||||
\(133\) | 2018.53 | + | 53.0078i | 1.31600 | + | 0.0345591i | ||||
\(134\) | 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 | 0.412483 | + | 0.910966i | \(0.364662\pi\) |
−0.995161 | + | 0.0982624i | \(0.968672\pi\) | |||||||
\(138\) | −596.210 | − | 1032.67i | −0.367774 | − | 0.637003i | ||||
\(139\) | −2817.19 | −1.71907 | −0.859537 | − | 0.511074i | \(-0.829248\pi\) | ||||
−0.859537 | + | 0.511074i | \(0.829248\pi\) | |||||||
\(140\) | 1086.04 | − | 1771.96i | 0.655624 | − | 1.06970i | ||||
\(141\) | 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 | ||||||||
\(147\) | −1027.58 | − | 54.0071i | −0.576555 | − | 0.0303023i | ||||
\(148\) | 3808.14 | 2.11505 | ||||||||
\(149\) | −900.163 | − | 1559.13i | −0.494928 | − | 0.857240i | 0.505055 | − | 0.863087i | \(-0.331472\pi\) |
−0.999983 | + | 0.00584714i | \(0.998139\pi\) | |||||||
\(150\) | −749.034 | + | 1297.36i | −0.407722 | + | 0.706196i | ||||
\(151\) | 226.492 | − | 392.296i | 0.122064 | − | 0.211421i | −0.798517 | − | 0.601972i | \(-0.794382\pi\) |
0.920581 | + | 0.390551i | \(0.127715\pi\) | |||||||
\(152\) | 3524.01 | + | 6103.77i | 1.88050 | + | 3.25711i | ||||
\(153\) | 391.309 | 0.206768 | ||||||||
\(154\) | −714.986 | + | 1166.56i | −0.374125 | + | 0.610414i | ||||
\(155\) | 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 | \(-0.676258\pi\) |
0.999546 | + | 0.0301273i | \(0.00959128\pi\) | |||||||
\(158\) | −1161.58 | + | 2011.91i | −0.584875 | + | 1.01303i | ||||
\(159\) | −431.758 | − | 747.827i | −0.215350 | − | 0.372997i | ||||
\(160\) | 2488.77 | 1.22971 | ||||||||
\(161\) | 1386.28 | + | 36.4046i | 0.678597 | + | 0.0178204i | ||||
\(162\) | 429.972 | 0.208529 | ||||||||
\(163\) | −1160.57 | − | 2010.16i | −0.557686 | − | 0.965940i | −0.997689 | − | 0.0679437i | \(-0.978356\pi\) |
0.440004 | − | 0.897996i | \(-0.354977\pi\) | |||||||
\(164\) | 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 | \(-0.232889\pi\) | ||||
0.744079 | + | 0.668092i | \(0.232889\pi\) | |||||||
\(168\) | −1713.57 | − | 3156.57i | −0.786934 | − | 1.44961i | ||||
\(169\) | −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 | \(-0.181660\pi\) |
−0.888607 | + | 0.458669i | \(0.848326\pi\) | |||||||
\(174\) | 1152.31 | 0.502047 | ||||||||
\(175\) | −831.199 | − | 1531.15i | −0.359044 | − | 0.661395i | ||||
\(176\) | −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 | −0.491102 | − | 0.871102i | \(-0.663406\pi\) |
0.999948 | − | 0.0102437i | \(-0.00326072\pi\) | |||||||
\(180\) | −504.980 | − | 874.652i | −0.209106 | − | 0.362182i | ||||
\(181\) | −248.631 | −0.102103 | −0.0510514 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510514 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(182\) | −3800.55 | − | 99.8048i | −1.54789 | − | 0.0406485i | ||||
\(183\) | 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 | ||||||||
\(189\) | −261.306 | + | 426.341i | −0.100567 | + | 0.164083i | ||||
\(190\) | −3218.67 | −1.22898 | ||||||||
\(191\) | 2156.54 | + | 3735.24i | 0.816972 | + | 1.41504i | 0.907903 | + | 0.419180i | \(0.137683\pi\) |
−0.0909306 | + | 0.995857i | \(0.528984\pi\) | |||||||
\(192\) | 1382.52 | − | 2394.60i | 0.519661 | − | 0.900079i | ||||
\(193\) | −1030.43 | + | 1784.75i | −0.384309 | + | 0.665643i | −0.991673 | − | 0.128781i | \(-0.958894\pi\) |
0.607364 | + | 0.794424i | \(0.292227\pi\) | |||||||
\(194\) | −210.409 | − | 364.438i | −0.0778683 | − | 0.134872i | ||||
\(195\) | −645.208 | −0.236945 | ||||||||
\(196\) | 6911.51 | + | 363.252i | 2.51877 | + | 0.132380i | ||||
\(197\) | −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 | \(-0.771284\pi\) |
0.946474 | + | 0.322780i | \(0.104617\pi\) | |||||||
\(200\) | 3040.57 | − | 5266.43i | 1.07501 | − | 1.86196i | ||||
\(201\) | 297.175 | + | 514.722i | 0.104284 | + | 0.180625i | ||||
\(202\) | 6130.94 | 2.13550 | ||||||||
\(203\) | −700.288 | + | 1142.58i | −0.242121 | + | 0.395040i | ||||
\(204\) | −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 | ||||||||
\(210\) | 1639.67 | + | 43.0589i | 0.538801 | + | 0.0141493i | ||||
\(211\) | −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 | ||||||||
\(217\) | 565.878 | + | 1042.40i | 0.177024 | + | 0.326096i | ||||
\(218\) | 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 | \(-0.337954\pi\) | ||||
0.487377 | + | 0.873192i | \(0.337954\pi\) | |||||||
\(224\) | 3954.12 | + | 7283.89i | 1.17945 | + | 2.17266i | ||||
\(225\) | −846.638 | −0.250856 | ||||||||
\(226\) | −1785.93 | − | 3093.32i | −0.525656 | − | 0.910463i | ||||
\(227\) | −2569.08 | + | 4449.77i | −0.751171 | + | 1.30107i | 0.196085 | + | 0.980587i | \(0.437177\pi\) |
−0.947256 | + | 0.320479i | \(0.896156\pi\) | |||||||
\(228\) | −3299.94 | + | 5715.67i | −0.958526 | + | 1.66022i | ||||
\(229\) | −307.403 | − | 532.438i | −0.0887064 | − | 0.153644i | 0.818258 | − | 0.574851i | \(-0.194940\pi\) |
−0.906965 | + | 0.421207i | \(0.861607\pi\) | |||||||
\(230\) | −2210.51 | −0.633725 | ||||||||
\(231\) | −772.994 | − | 20.2993i | −0.220170 | − | 0.00578180i | ||||
\(232\) | −4677.59 | −1.32370 | ||||||||
\(233\) | −1413.71 | − | 2448.61i | −0.397490 | − | 0.688472i | 0.595926 | − | 0.803039i | \(-0.296785\pi\) |
−0.993415 | + | 0.114567i | \(0.963452\pi\) | |||||||
\(234\) | −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 | ||||||||
\(238\) | 2233.66 | − | 3644.39i | 0.608348 | − | 0.992567i | ||||
\(239\) | −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 | \(-0.718734\pi\) |
0.986651 | + | 0.162847i | \(0.0520675\pi\) | |||||||
\(242\) | 3018.58 | − | 5228.33i | 0.801825 | − | 1.38880i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −7736.96 | −2.02995 | ||||||||
\(245\) | −1039.17 | + | 1599.66i | −0.270980 | + | 0.417137i | ||||
\(246\) | 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 | \(-0.416702\pi\) | ||||
0.258711 | + | 0.965955i | \(0.416702\pi\) | |||||||
\(252\) | 1757.54 | − | 2867.57i | 0.439344 | − | 0.716824i | ||||
\(253\) | 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 | \(-0.250701\pi\) |
−0.966494 | + | 0.256691i | \(0.917368\pi\) | |||||||
\(258\) | 3883.78 | 0.937185 | ||||||||
\(259\) | −3494.07 | − | 91.7566i | −0.838267 | − | 0.0220134i | ||||
\(260\) | 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 | −0.460906 | − | 0.887449i | \(-0.652475\pi\) |
0.999006 | − | 0.0445683i | \(-0.0141912\pi\) | |||||||
\(264\) | −1349.52 | − | 2337.44i | −0.314610 | − | 0.544921i | ||||
\(265\) | −1600.79 | −0.371078 | ||||||||
\(266\) | −5113.78 | − | 9420.09i | −1.17874 | − | 2.17136i | ||||
\(267\) | −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 | \(-0.819644\pi\) |
0.886722 | + | 0.462303i | \(0.152977\pi\) | |||||||
\(270\) | 398.541 | − | 690.293i | 0.0898312 | − | 0.155592i | ||||
\(271\) | 2684.42 | + | 4649.55i | 0.601723 | + | 1.04221i | 0.992560 | + | 0.121755i | \(0.0388521\pi\) |
−0.390837 | + | 0.920460i | \(0.627815\pi\) | |||||||
\(272\) | 7901.28 | 1.76134 | ||||||||
\(273\) | −1025.10 | − | 1888.33i | −0.227259 | − | 0.418634i | ||||
\(274\) | 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 | −0.481177 | − | 0.876624i | \(-0.659791\pi\) |
0.999767 | − | 0.0216003i | \(-0.00687613\pi\) | |||||||
\(278\) | 7477.25 | + | 12951.0i | 1.61315 | + | 2.79406i | ||||
\(279\) | 576.388 | 0.123683 | ||||||||
\(280\) | −6655.98 | − | 174.790i | −1.42061 | − | 0.0373061i | ||||
\(281\) | −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 | \(-0.919898\pi\) |
0.699892 | + | 0.714249i | \(0.253232\pi\) | |||||||
\(284\) | −7924.21 | + | 13725.1i | −1.65569 | + | 2.86774i | ||||
\(285\) | −909.520 | − | 1575.34i | −0.189036 | − | 0.327420i | ||||
\(286\) | −2856.97 | −0.590687 | ||||||||
\(287\) | −239.940 | + | 391.480i | −0.0493491 | + | 0.0805169i | ||||
\(288\) | 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 | \(-0.482218\pi\) | ||||
0.0558335 | + | 0.998440i | \(0.482218\pi\) | |||||||
\(294\) | 2479.08 | + | 4867.26i | 0.491778 | + | 0.965524i | ||||
\(295\) | 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 | ||||||||
\(301\) | −2360.28 | + | 3850.98i | −0.451975 | + | 0.737432i | ||||
\(302\) | −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 | \(-0.389722\pi\) | ||||
0.339558 | + | 0.940585i | \(0.389722\pi\) | |||||||
\(308\) | 5199.15 | + | 136.533i | 0.961848 | + | 0.0252587i | ||||
\(309\) | 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 | \(-0.936470\pi\) |
0.661775 | + | 0.749702i | \(0.269803\pi\) | |||||||
\(312\) | 3749.87 | − | 6494.96i | 0.680431 | − | 1.17854i | ||||
\(313\) | −4356.05 | − | 7544.90i | −0.786640 | − | 1.36250i | −0.928014 | − | 0.372544i | \(-0.878485\pi\) |
0.141374 | − | 0.989956i | \(-0.454848\pi\) | |||||||
\(314\) | −9892.85 | −1.77798 | ||||||||
\(315\) | 442.259 | + | 814.685i | 0.0791063 | + | 0.145722i | ||||
\(316\) | 8830.83 | 1.57207 | ||||||||
\(317\) | −970.165 | − | 1680.37i | −0.171892 | − | 0.297726i | 0.767189 | − | 0.641421i | \(-0.221655\pi\) |
−0.939081 | + | 0.343695i | \(0.888321\pi\) | |||||||
\(318\) | −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 | ||||||||
\(322\) | −3512.03 | − | 6469.51i | −0.607820 | − | 1.11966i | ||||
\(323\) | −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 | ||||||||
\(329\) | 11488.8 | + | 301.702i | 1.92522 | + | 0.0505574i | ||||
\(330\) | 1232.59 | 0.205611 | ||||||||
\(331\) | 2865.75 | + | 4963.63i | 0.475879 | + | 0.824247i | 0.999618 | − | 0.0276315i | \(-0.00879650\pi\) |
−0.523739 | + | 0.851879i | \(0.675463\pi\) | |||||||
\(332\) | −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 | ||||||||
\(336\) | −5276.26 | + | 8608.64i | −0.856678 | + | 1.39774i | ||||
\(337\) | 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 | ||||||||
\(343\) | −6332.75 | − | 499.826i | −0.996900 | − | 0.0786824i | ||||
\(344\) | −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 | −0.707645 | − | 0.706568i | \(-0.750242\pi\) |
0.965728 | + | 0.259555i | \(0.0835758\pi\) | |||||||
\(348\) | −2190.09 | − | 3793.34i | −0.337359 | − | 0.584323i | ||||
\(349\) | −2424.54 | −0.371870 | −0.185935 | − | 0.982562i | \(-0.559531\pi\) | ||||
−0.185935 | + | 0.982562i | \(0.559531\pi\) | |||||||
\(350\) | −4832.76 | + | 7885.02i | −0.738062 | + | 1.20421i | ||||
\(351\) | −1044.14 | −0.158781 | ||||||||
\(352\) | 3114.06 | + | 5393.71i | 0.471534 | + | 0.816721i | ||||
\(353\) | 6201.56 | − | 10741.4i | 0.935059 | − | 1.61957i | 0.160531 | − | 0.987031i | \(-0.448679\pi\) |
0.774528 | − | 0.632540i | \(-0.217987\pi\) | |||||||
\(354\) | 4180.69 | − | 7241.17i | 0.627687 | − | 1.08719i | ||||
\(355\) | −2184.05 | − | 3782.88i | −0.326528 | − | 0.565562i | ||||
\(356\) | 31993.1 | 4.76300 | ||||||||
\(357\) | 2414.88 | + | 63.4163i | 0.358009 | + | 0.00940153i | ||||
\(358\) | −12937.5 | −1.90997 | ||||||||
\(359\) | −676.921 | − | 1172.46i | −0.0995168 | − | 0.172368i | 0.811968 | − | 0.583702i | \(-0.198396\pi\) |
−0.911485 | + | 0.411334i | \(0.865063\pi\) | |||||||
\(360\) | −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 | ||||||||
\(364\) | 6894.81 | + | 12700.9i | 0.992819 | + | 1.82887i | ||||
\(365\) | −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 | \(-0.802088\pi\) |
0.910858 | + | 0.412720i | \(0.135421\pi\) | |||||||
\(368\) | 6803.67 | − | 11784.3i | 0.963766 | − | 1.66929i | ||||
\(369\) | 111.565 | + | 193.237i | 0.0157395 | + | 0.0272615i | ||||
\(370\) | 5571.52 | 0.782837 | ||||||||
\(371\) | −2543.31 | − | 4685.03i | −0.355909 | − | 0.655619i | ||||
\(372\) | −3876.78 | −0.540327 | ||||||||
\(373\) | −2728.46 | − | 4725.83i | −0.378752 | − | 0.656017i | 0.612129 | − | 0.790758i | \(-0.290313\pi\) |
−0.990881 | + | 0.134741i | \(0.956980\pi\) | |||||||
\(374\) | 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 | ||||||||
\(378\) | 2653.48 | + | 69.6821i | 0.361059 | + | 0.00948164i | ||||
\(379\) | 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 | \(-0.294519\pi\) |
−0.992575 | + | 0.121636i | \(0.961186\pi\) | |||||||
\(384\) | −3937.50 | −0.523267 | ||||||||
\(385\) | −749.077 | + | 1222.18i | −0.0991597 | + | 0.161787i | ||||
\(386\) | 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 | 0.493022 | + | 0.870017i | \(0.335892\pi\) |
−0.999968 | + | 0.00803932i | \(0.997441\pi\) | |||||||
\(390\) | 1712.48 | + | 2966.10i | 0.222345 | + | 0.385113i | ||||
\(391\) | −3255.60 | −0.421081 | ||||||||
\(392\) | −10063.4 | − | 19757.8i | −1.29663 | − | 2.54571i | ||||
\(393\) | −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 | −0.999963 | − | 0.00861270i | \(-0.997258\pi\) |
0.492523 | − | 0.870300i | \(-0.336075\pi\) | |||||||
\(398\) | −5772.95 | −0.727065 | ||||||||
\(399\) | 3165.51 | − | 5164.77i | 0.397177 | − | 0.648025i | ||||
\(400\) | −17095.2 | −2.13690 | ||||||||
\(401\) | −389.990 | − | 675.482i | −0.0485665 | − | 0.0841196i | 0.840720 | − | 0.541470i | \(-0.182132\pi\) |
−0.889287 | + | 0.457350i | \(0.848799\pi\) | |||||||
\(402\) | 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 | ||||||||
\(406\) | 7111.22 | + | 186.745i | 0.869271 | + | 0.0228276i | ||||
\(407\) | −2626.59 | −0.319890 | ||||||||
\(408\) | 4215.99 | + | 7302.30i | 0.511574 | + | 0.886073i | ||||
\(409\) | −7346.25 | + | 12724.1i | −0.888139 | + | 1.53830i | −0.0460654 | + | 0.998938i | \(0.514668\pi\) |
−0.842073 | + | 0.539363i | \(0.818665\pi\) | |||||||
\(410\) | 365.953 | − | 633.850i | 0.0440809 | − | 0.0763503i | ||||
\(411\) | 2803.05 | + | 4855.02i | 0.336409 | + | 0.582678i | ||||
\(412\) | −29154.4 | −3.48624 | ||||||||
\(413\) | 4639.29 | + | 8546.04i | 0.552748 | + | 1.01822i | ||||
\(414\) | −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 | \(-0.437049\pi\) | ||||
0.196480 | + | 0.980508i | \(0.437049\pi\) | |||||||
\(420\) | −2974.63 | − | 5479.57i | −0.345589 | − | 0.636608i | ||||
\(421\) | 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 | ||||||||
\(427\) | 7098.88 | + | 186.421i | 0.804541 | + | 0.0211277i | ||||
\(428\) | 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 | −0.969666 | − | 0.244434i | \(-0.921398\pi\) |
0.696519 | + | 0.717538i | \(0.254731\pi\) | |||||||
\(432\) | 2453.32 | + | 4249.27i | 0.273230 | + | 0.473248i | ||||
\(433\) | −5255.73 | −0.583313 | −0.291656 | − | 0.956523i | \(-0.594206\pi\) | ||||
−0.291656 | + | 0.956523i | \(0.594206\pi\) | |||||||
\(434\) | 3290.12 | − | 5368.10i | 0.363896 | − | 0.593725i | ||||
\(435\) | 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 | \(-0.152387\pi\) |
−0.842732 | + | 0.538334i | \(0.819054\pi\) | |||||||
\(440\) | −5003.48 | −0.542117 | ||||||||
\(441\) | −1681.69 | + | 2588.72i | −0.181588 | + | 0.279530i | ||||
\(442\) | 8925.37 | 0.960490 | ||||||||
\(443\) | −6513.64 | − | 11281.9i | −0.698583 | − | 1.20998i | −0.968958 | − | 0.247226i | \(-0.920481\pi\) |
0.270375 | − | 0.962755i | \(-0.412852\pi\) | |||||||
\(444\) | 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 | ||||||||
\(448\) | 8920.02 | − | 14553.7i | 0.940695 | − | 1.53482i | ||||
\(449\) | 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 | ||||||||
\(455\) | −3981.76 | − | 104.564i | −0.410259 | − | 0.0107737i | ||||
\(456\) | 21144.1 | 2.17141 | ||||||||
\(457\) | 1855.41 | + | 3213.67i | 0.189918 | + | 0.328947i | 0.945223 | − | 0.326426i | \(-0.105844\pi\) |
−0.755305 | + | 0.655374i | \(0.772511\pi\) | |||||||
\(458\) | −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 | \(-0.663259\pi\) | ||||
−0.490701 | + | 0.871328i | \(0.663259\pi\) | |||||||
\(462\) | 1958.32 | + | 3607.42i | 0.197206 | + | 0.363274i | ||||
\(463\) | −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 | \(-0.142463\pi\) |
−0.825541 | + | 0.564341i | \(0.809130\pi\) | |||||||
\(468\) | 7022.87 | 0.693659 | ||||||||
\(469\) | 1750.54 | + | 3224.66i | 0.172350 | + | 0.317486i | ||||
\(470\) | −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 | ||||||||
\(476\) | −16242.5 | − | 426.538i | −1.56402 | − | 0.0410721i | ||||
\(477\) | −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 | \(-0.724412\pi\) |
0.983590 | + | 0.180419i | \(0.0577454\pi\) | |||||||
\(480\) | 3733.15 | − | 6466.00i | 0.354988 | − | 0.614857i | ||||
\(481\) | −3649.21 | − | 6320.62i | −0.345924 | − | 0.599159i | ||||
\(482\) | −13993.3 | −1.32236 | ||||||||
\(483\) | 2174.00 | − | 3547.05i | 0.204804 | − | 0.334154i | ||||
\(484\) | −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 | −0.247776 | − | 0.968817i | \(-0.579700\pi\) |
0.962908 | − | 0.269828i | \(-0.0869669\pi\) | |||||||
\(488\) | 12393.5 | + | 21466.1i | 1.14964 | + | 1.99124i | ||||
\(489\) | −6963.41 | −0.643960 | ||||||||
\(490\) | 10111.9 | + | 531.458i | 0.932266 | + | 0.0489976i | ||||
\(491\) | −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 | ||||||||
\(497\) | 7601.40 | − | 12402.3i | 0.686055 | − | 1.11935i | ||||
\(498\) | −3841.74 | −0.345688 | ||||||||
\(499\) | −346.760 | − | 600.606i | −0.0311084 | − | 0.0538814i | 0.850052 | − | 0.526699i | \(-0.176570\pi\) |
−0.881160 | + | 0.472817i | \(0.843237\pi\) | |||||||
\(500\) | 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 | \(-0.625195\pi\) | ||||
−0.383249 | + | 0.923645i | \(0.625195\pi\) | |||||||
\(504\) | −10771.4 | − | 282.863i | −0.951973 | − | 0.0249994i | ||||
\(505\) | 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 | 0.976494 | + | 0.215546i | \(0.0691533\pi\) |
−0.301578 | + | 0.953441i | \(0.597513\pi\) | |||||||
\(510\) | −3850.68 | −0.334335 | ||||||||
\(511\) | −2925.92 | − | 5389.84i | −0.253298 | − | 0.466600i | ||||
\(512\) | −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 | ||||||||
\(518\) | 8851.97 | + | 16306.2i | 0.750836 | + | 1.38311i | ||||
\(519\) | −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 | \(-0.844909\pi\) |
0.847275 | + | 0.531155i | \(0.178242\pi\) | |||||||
\(522\) | 1728.46 | − | 2993.78i | 0.144928 | − | 0.251023i | ||||
\(523\) | 3127.81 | + | 5417.52i | 0.261509 | + | 0.452947i | 0.966643 | − | 0.256127i | \(-0.0824465\pi\) |
−0.705134 | + | 0.709074i | \(0.749113\pi\) | |||||||
\(524\) | 22719.0 | 1.89406 | ||||||||
\(525\) | −5224.85 | − | 137.208i | −0.434345 | − | 0.0114062i | ||||
\(526\) | −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 | ||||||||
\(532\) | −21291.2 | + | 34738.2i | −1.73513 | + | 2.83100i | ||||
\(533\) | −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 | ||||||||
\(539\) | −4767.08 | − | 250.546i | −0.380951 | − | 0.0200218i | ||||
\(540\) | −3029.88 | −0.241454 | ||||||||
\(541\) | −71.9353 | − | 124.596i | −0.00571671 | − | 0.00990164i | 0.863153 | − | 0.504943i | \(-0.168486\pi\) |
−0.868870 | + | 0.495041i | \(0.835153\pi\) | |||||||
\(542\) | 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 | ||||||||
\(546\) | −5960.13 | + | 9724.41i | −0.467161 | + | 0.762210i | ||||
\(547\) | 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 | ||||||||
\(553\) | −8102.54 | − | 212.778i | −0.623065 | − | 0.0163621i | ||||
\(554\) | −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 | −0.185223 | + | 0.982696i | \(0.559301\pi\) |
−0.758428 | + | 0.651756i | \(0.774032\pi\) | |||||||
\(558\) | −1529.82 | − | 2649.72i | −0.116062 | − | 0.201025i | ||||
\(559\) | −9431.33 | −0.713600 | ||||||||
\(560\) | 8930.06 | + | 16450.1i | 0.673864 | + | 1.24132i | ||||
\(561\) | 1815.33 | 0.136619 | ||||||||
\(562\) | 5511.51 | + | 9546.22i | 0.413682 | + | 0.716517i | ||||
\(563\) | −8184.91 | + | 14176.7i | −0.612705 | + | 1.06124i | 0.378077 | + | 0.925774i | \(0.376585\pi\) |
−0.990782 | + | 0.135462i | \(0.956748\pi\) | |||||||
\(564\) | −18782.1 | + | 32531.6i | −1.40225 | + | 2.42877i | ||||
\(565\) | −1871.08 | − | 3240.81i | −0.139322 | − | 0.241313i | ||||
\(566\) | 13576.6 | 1.00824 | ||||||||
\(567\) | 715.707 | + | 1318.40i | 0.0530104 | + | 0.0976503i | ||||
\(568\) | 50773.7 | 3.75074 | ||||||||
\(569\) | 9225.29 | + | 15978.7i | 0.679691 | + | 1.17726i | 0.975074 | + | 0.221881i | \(0.0712195\pi\) |
−0.295383 | + | 0.955379i | \(0.595447\pi\) | |||||||
\(570\) | −4828.00 | + | 8362.34i | −0.354777 | + | 0.614491i | ||||
\(571\) | 3554.34 | − | 6156.30i | 0.260499 | − | 0.451197i | −0.705876 | − | 0.708335i | \(-0.749446\pi\) |
0.966374 | + | 0.257139i | \(0.0827797\pi\) | |||||||
\(572\) | 5429.99 | + | 9405.02i | 0.396922 | + | 0.687489i | ||||
\(573\) | 12939.2 | 0.943358 | ||||||||
\(574\) | 2436.52 | + | 63.9844i | 0.177175 | + | 0.00465271i | ||||
\(575\) | 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 | \(-0.921667\pi\) |
0.695912 | + | 0.718127i | \(0.255000\pi\) | |||||||
\(578\) | 8022.42 | − | 13895.2i | 0.577316 | − | 0.999940i | ||||
\(579\) | 3091.28 | + | 5354.25i | 0.221881 | + | 0.384309i | ||||
\(580\) | −8119.96 | −0.581315 | ||||||||
\(581\) | 2334.73 | − | 3809.30i | 0.166714 | − | 0.272007i | ||||
\(582\) | −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 | \(-0.519746\pi\) | ||||
−0.0619939 | + | 0.998077i | \(0.519746\pi\) | |||||||
\(588\) | 11311.0 | − | 17411.8i | 0.793297 | − | 1.22117i | ||||
\(589\) | −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 | \(-0.0264325\pi\) |
−0.570109 | + | 0.821569i | \(0.693099\pi\) | |||||||
\(594\) | 1994.69 | 0.137783 | ||||||||
\(595\) | 2340.16 | − | 3818.16i | 0.161239 | − | 0.263075i | ||||
\(596\) | 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 | −0.673303 | − | 0.739367i | \(-0.735125\pi\) |
0.976962 | + | 0.213414i | \(0.0684584\pi\) | |||||||
\(600\) | −9121.72 | − | 15799.3i | −0.620655 | − | 1.07501i | ||||
\(601\) | −19157.1 | −1.30022 | −0.650112 | − | 0.759838i | \(-0.725278\pi\) | ||||
−0.650112 | + | 0.759838i | \(0.725278\pi\) | |||||||
\(602\) | 23968.0 | + | 629.413i | 1.62269 | + | 0.0426129i | ||||
\(603\) | 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 | \(-0.0852191\pi\) |
−0.711283 | + | 0.702905i | \(0.751886\pi\) | |||||||
\(608\) | −48790.7 | −3.25448 | ||||||||
\(609\) | 1918.07 | + | 3533.27i | 0.127625 | + | 0.235099i | ||||
\(610\) | −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 | −0.909931 | − | 0.414760i | \(-0.863866\pi\) |
0.814158 | + | 0.580643i | \(0.197199\pi\) | |||||||
\(614\) | −9695.65 | − | 16793.4i | −0.637272 | − | 1.10379i | ||||
\(615\) | 413.640 | 0.0271212 | ||||||||
\(616\) | −7949.47 | − | 14643.7i | −0.519956 | − | 0.957811i | ||||
\(617\) | −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 | \(-0.939301\pi\) |
0.655081 | + | 0.755558i | \(0.272634\pi\) | |||||||
\(620\) | −3593.39 | + | 6223.93i | −0.232764 | + | 0.403160i | ||||
\(621\) | −1010.85 | − | 1750.84i | −0.0653205 | − | 0.113138i | ||||
\(622\) | 18538.0 | 1.19503 | ||||||||
\(623\) | −29354.6 | − | 770.869i | −1.88775 | − | 0.0495734i | ||||
\(624\) | −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 | ||||||||
\(630\) | 2571.38 | − | 4195.41i | 0.162613 | − | 0.265316i | ||||
\(631\) | −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 | ||||||||
\(637\) | −6020.16 | − | 11819.6i | −0.374454 | − | 0.735179i | ||||
\(638\) | 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 | 0.0549809 | − | 0.998487i | \(-0.482490\pi\) |
0.837225 | − | 0.546859i | \(-0.184176\pi\) | |||||||
\(642\) | 7890.46 | + | 13666.7i | 0.485065 | + | 0.840157i | ||||
\(643\) | 7341.90 | 0.450290 | 0.225145 | − | 0.974325i | \(-0.427714\pi\) | ||||
0.225145 | + | 0.974325i | \(0.427714\pi\) | |||||||
\(644\) | −14622.3 | + | 23857.5i | −0.894721 | + | 1.45981i | ||||
\(645\) | 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 | \(-0.892393\pi\) |
0.758923 | + | 0.651181i | \(0.225726\pi\) | |||||||
\(648\) | −2618.10 | + | 4534.67i | −0.158717 | + | 0.274906i | ||||
\(649\) | 3653.67 | + | 6328.34i | 0.220985 | + | 0.382756i | ||||
\(650\) | −19311.0 | −1.16529 | ||||||||
\(651\) | 3557.06 | + | 93.4105i | 0.214151 | + | 0.00562373i | ||||
\(652\) | 46835.9 | 2.81324 | ||||||||
\(653\) | −13131.1 | − | 22743.7i | −0.786920 | − | 1.36298i | −0.927846 | − | 0.372965i | \(-0.878341\pi\) |
0.140926 | − | 0.990020i | \(-0.454992\pi\) | |||||||
\(654\) | 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 | ||||||||
\(658\) | −29105.9 | − | 53615.9i | −1.72442 | − | 3.17655i | ||||
\(659\) | 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 | \(-0.719220\pi\) |
0.986402 | + | 0.164351i | \(0.0525531\pi\) | |||||||
\(662\) | 15212.3 | − | 26348.4i | 0.893114 | − | 1.54692i | ||||
\(663\) | 2522.10 | + | 4368.41i | 0.147738 | + | 0.255890i | ||||
\(664\) | 15594.9 | 0.911444 | ||||||||
\(665\) | −5357.61 | − | 9869.25i | −0.312420 | − | 0.575509i | ||||
\(666\) | 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 | ||||||||
\(672\) | 24855.3 | + | 652.715i | 1.42681 | + | 0.0374688i | ||||
\(673\) | −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 | \(-0.244805\pi\) |
−0.961573 | + | 0.274549i | \(0.911472\pi\) | |||||||
\(678\) | −10715.6 | −0.606975 | ||||||||
\(679\) | 767.226 | − | 1251.79i | 0.0433629 | − | 0.0707500i | ||||
\(680\) | 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 | −0.756688 | − | 0.653776i | \(-0.773184\pi\) |
0.944531 | + | 0.328423i | \(0.106517\pi\) | |||||||
\(684\) | 9899.82 | + | 17147.0i | 0.553405 | + | 0.958526i | ||||
\(685\) | 10392.6 | 0.579679 | ||||||||
\(686\) | 14510.3 | + | 30439.0i | 0.807589 | + | 1.69412i | ||||
\(687\) | −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 | 0.969410 | + | 0.245445i | \(0.0789342\pi\) |
−0.272143 | + | 0.962257i | \(0.587732\pi\) | |||||||
\(692\) | 4323.68 | 0.237517 | ||||||||
\(693\) | −1212.23 | + | 1977.85i | −0.0664485 | + | 0.108416i | ||||
\(694\) | −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 | ||||||||
\(700\) | 35142.3 | + | 922.859i | 1.89751 | + | 0.0498297i | ||||
\(701\) | −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 | ||||||||
\(707\) | 10205.2 | + | 18799.0i | 0.542867 | + | 1.00001i | ||||
\(708\) | −31783.4 | −1.68714 | ||||||||
\(709\) | −8072.75 | − | 13982.4i | −0.427614 | − | 0.740649i | 0.569047 | − | 0.822305i | \(-0.307312\pi\) |
−0.996661 | + | 0.0816561i | \(0.973979\pi\) | |||||||
\(710\) | −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 | ||||||||
\(714\) | −6117.92 | − | 11269.8i | −0.320669 | − | 0.590703i | ||||
\(715\) | −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 | \(-0.314744\pi\) |
−0.998295 | + | 0.0583673i | \(0.981411\pi\) | |||||||
\(720\) | 9095.92 | 0.470812 | ||||||||
\(721\) | 26749.9 | + | 702.470i | 1.38172 | + | 0.0362848i | ||||
\(722\) | 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 | \(-0.471425\pi\) | ||||
0.0896516 | + | 0.995973i | \(0.471425\pi\) | |||||||
\(728\) | 24194.1 | − | 39474.6i | 1.23172 | − | 2.00965i | ||||
\(729\) | 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 | 0.970802 | + | 0.239881i | \(0.0771083\pi\) |
−0.277658 | + | 0.960680i | \(0.589558\pi\) | |||||||
\(734\) | −7315.16 | −0.367858 | ||||||||
\(735\) | 2597.28 | + | 5099.33i | 0.130343 | + | 0.255907i | ||||
\(736\) | −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 | −0.993816 | − | 0.111035i | \(-0.964583\pi\) |
0.593068 | + | 0.805153i | \(0.297917\pi\) | |||||||
\(740\) | −10589.3 | − | 18341.2i | −0.526040 | − | 0.911129i | ||||
\(741\) | 12648.9 | 0.627083 | ||||||||
\(742\) | −14787.3 | + | 24126.7i | −0.731617 | + | 1.19369i | ||||
\(743\) | 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 | ||||||||
\(749\) | −18346.5 | − | 481.791i | −0.895016 | − | 0.0235037i | ||||
\(750\) | 19401.9 | 0.944611 | ||||||||
\(751\) | 3636.53 | + | 6298.66i | 0.176696 | + | 0.306047i | 0.940747 | − | 0.339109i | \(-0.110126\pi\) |
−0.764051 | + | 0.645156i | \(0.776792\pi\) | |||||||
\(752\) | 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 | ||||||||
\(756\) | −4813.84 | − | 8867.57i | −0.231584 | − | 0.426601i | ||||
\(757\) | 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 | \(-0.276630\pi\) |
−0.984175 | + | 0.177200i | \(0.943296\pi\) | |||||||
\(762\) | −2799.84 | −0.133107 | ||||||||
\(763\) | 17258.0 | + | 31790.9i | 0.818848 | + | 1.50840i | ||||
\(764\) | −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 | \(-0.374534\pi\) | ||||
0.384034 | + | 0.923319i | \(0.374534\pi\) | |||||||
\(770\) | 7606.66 | + | 199.756i | 0.356006 | + | 0.00934895i | ||||
\(771\) | −6450.62 | −0.301314 | ||||||||
\(772\) | −20791.9 | − | 36012.6i | −0.969323 | − | 1.67892i | ||||
\(773\) | 19948.3 | − | 34551.6i | 0.928192 | − | 1.60768i | 0.141846 | − | 0.989889i | \(-0.454696\pi\) |
0.786346 | − | 0.617787i | \(-0.211970\pi\) | |||||||
\(774\) | 5825.67 | − | 10090.4i | 0.270542 | − | 0.468593i | ||||
\(775\) | 3012.29 | + | 5217.45i | 0.139619 | + | 0.241827i | ||||
\(776\) | 5124.70 | 0.237070 | ||||||||
\(777\) | −5479.50 | + | 8940.23i | −0.252994 | + | 0.412779i | ||||
\(778\) | 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 | ||||||||
\(784\) | −33956.5 | + | 52271.3i | −1.54685 | + | 2.38116i | ||||
\(785\) | −10364.5 | −0.471244 | ||||||||
\(786\) | 8965.16 | + | 15528.1i | 0.406840 | + | 0.704668i | ||||
\(787\) | 16564.3 | − | 28690.2i | 0.750257 | − | 1.29948i | −0.197440 | − | 0.980315i | \(-0.563263\pi\) |
0.947698 | − | 0.319169i | \(-0.103404\pi\) | |||||||
\(788\) | 16809.1 | − | 29114.3i | 0.759899 | − | 1.31618i | ||||
\(789\) | −6885.23 | − | 11925.6i | −0.310672 | − | 0.538100i | ||||
\(790\) | 12920.0 | 0.581865 | ||||||||
\(791\) | 6512.15 | − | 10625.1i | 0.292725 | − | 0.477603i | ||||
\(792\) | −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 | \(-0.629843\pi\) | ||||
−0.396695 | + | 0.917951i | \(0.629843\pi\) | |||||||
\(798\) | −32144.8 | − | 844.142i | −1.42596 | − | 0.0374465i | ||||
\(799\) | −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 | ||||||||
\(805\) | −3679.49 | − | 6777.98i | −0.161099 | − | 0.296761i | ||||
\(806\) | 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 | −0.805838 | − | 0.592136i | \(-0.798285\pi\) |
0.915724 | + | 0.401808i | \(0.131618\pi\) | |||||||
\(810\) | −1195.62 | − | 2070.88i | −0.0518641 | − | 0.0898312i | ||||
\(811\) | −17535.4 | −0.759251 | −0.379626 | − | 0.925140i | \(-0.623947\pi\) | ||||
−0.379626 | + | 0.925140i | \(0.623947\pi\) | |||||||
\(812\) | −12900.9 | − | 23764.7i | −0.557553 | − | 1.02707i | ||||
\(813\) | 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 | ||||||||
\(819\) | −6443.68 | − | 169.215i | −0.274921 | − | 0.00721960i | ||||
\(820\) | −2782.14 | −0.118484 | ||||||||
\(821\) | 9350.39 | + | 16195.3i | 0.397480 | + | 0.688455i | 0.993414 | − | 0.114578i | \(-0.0365516\pi\) |
−0.595935 | + | 0.803033i | \(0.703218\pi\) | |||||||
\(822\) | 14879.4 | − | 25771.9i | 0.631361 | − | 1.09355i | ||||
\(823\) | −11111.3 | + | 19245.4i | −0.470615 | + | 0.815129i | −0.999435 | − | 0.0336046i | \(-0.989301\pi\) |
0.528820 | + | 0.848734i | \(0.322635\pi\) | |||||||
\(824\) | 46701.0 | + | 80888.5i | 1.97440 | + | 3.41976i | ||||
\(825\) | −3927.66 | −0.165750 | ||||||||
\(826\) | 26973.8 | − | 44009.8i | 1.13624 | − | 1.85387i | ||||
\(827\) | 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 | \(-0.916139\pi\) |
0.708279 | + | 0.705933i | \(0.249472\pi\) | |||||||
\(830\) | −3560.91 | + | 6167.67i | −0.148917 | + | 0.257931i | ||||
\(831\) | −7172.41 | − | 12423.0i | −0.299408 | − | 0.518590i | ||||
\(832\) | 35643.1 | 1.48522 | ||||||||
\(833\) | 14892.7 | + | 782.721i | 0.619448 | + | 0.0325566i | ||||
\(834\) | 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 | \(-0.677845\pi\) | ||||
−0.530098 | + | 0.847936i | \(0.677845\pi\) | |||||||
\(840\) | −10438.1 | + | 17030.6i | −0.428748 | + | 0.699536i | ||||
\(841\) | −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 | ||||||||
\(847\) | 21056.0 | + | 552.943i | 0.854181 | + | 0.0224313i | ||||
\(848\) | −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 | \(-0.225229\pi\) | ||||
0.759939 | + | 0.649995i | \(0.225229\pi\) | |||||||
\(854\) | −17984.5 | − | 33129.2i | −0.720627 | − | 1.32747i | ||||
\(855\) | −5457.12 | −0.218280 | ||||||||
\(856\) | −32030.0 | − | 55477.6i | −1.27893 | − | 2.21517i | ||||
\(857\) | 14604.4 | − | 25295.5i | 0.582118 | − | 1.00826i | −0.413110 | − | 0.910681i | \(-0.635557\pi\) |
0.995228 | − | 0.0975771i | \(-0.0311093\pi\) | |||||||
\(858\) | −4285.46 | + | 7422.64i | −0.170517 | + | 0.295343i | ||||
\(859\) | −17451.5 | − | 30226.8i | −0.693173 | − | 1.20061i | −0.970793 | − | 0.239920i | \(-0.922879\pi\) |
0.277619 | − | 0.960691i | \(-0.410455\pi\) | |||||||
\(860\) | −27367.8 | −1.08516 | ||||||||
\(861\) | 657.186 | + | 1210.60i | 0.0260126 | + | 0.0479178i | ||||
\(862\) | 25947.6 | 1.02527 | ||||||||
\(863\) | 6794.67 | + | 11768.7i | 0.268011 | + | 0.464208i | 0.968348 | − | 0.249604i | \(-0.0803004\pi\) |
−0.700337 | + | 0.713812i | \(0.746967\pi\) | |||||||
\(864\) | 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 | ||||||||
\(868\) | −23924.8 | − | 628.279i | −0.935552 | − | 0.0245682i | ||||
\(869\) | −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 | ||||||||
\(875\) | −11791.1 | + | 19238.1i | −0.455556 | + | 0.743275i | ||||
\(876\) | 20045.3 | 0.773135 | ||||||||
\(877\) | 1189.87 | + | 2060.92i | 0.0458144 | + | 0.0793528i | 0.888023 | − | 0.459799i | \(-0.152078\pi\) |
−0.842209 | + | 0.539151i | \(0.818745\pi\) | |||||||
\(878\) | 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 | \(-0.653371\pi\) | ||||
−0.463401 | + | 0.886148i | \(0.653371\pi\) | |||||||
\(882\) | 16364.1 | + | 860.057i | 0.624726 | + | 0.0328340i | ||||
\(883\) | −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 | −0.998818 | − | 0.0486051i | \(-0.984522\pi\) |
0.457316 | − | 0.889304i | \(-0.348811\pi\) | |||||||
\(888\) | −36600.5 | −1.38314 | ||||||||
\(889\) | 1701.54 | − | 2776.19i | 0.0641932 | − | 0.104736i | ||||
\(890\) | 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 | ||||||||
\(896\) | −24299.4 | − | 638.118i | −0.906013 | − | 0.0237925i | ||||
\(897\) | 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 | ||||||||
\(903\) | 6464.73 | + | 11908.7i | 0.238242 | + | 0.438866i | ||||
\(904\) | 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 | 0.0926313 | + | 0.995700i | \(0.470472\pi\) |
−0.908618 | + | 0.417629i | \(0.862861\pi\) | |||||||
\(908\) | −51838.8 | − | 89787.5i | −1.89464 | − | 3.28161i | ||||
\(909\) | 10394.8 | 0.379288 | ||||||||
\(910\) | 10087.5 | + | 18582.2i | 0.367470 | + | 0.676915i | ||||
\(911\) | 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 | ||||||||
\(917\) | −20845.3 | − | 547.412i | −0.750680 | − | 0.0197133i | ||||
\(918\) | −6231.55 | −0.224043 | ||||||||
\(919\) | −15544.1 | − | 26923.3i | −0.557948 | − | 0.966394i | −0.997668 | − | 0.0682590i | \(-0.978256\pi\) |
0.439720 | − | 0.898135i | \(-0.355078\pi\) | |||||||
\(920\) | 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 | ||||||||
\(924\) | 8153.45 | − | 13303.0i | 0.290291 | − | 0.473632i | ||||
\(925\) | −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 | 0.950979 | + | 0.309257i | \(0.100080\pi\) |
−0.207665 | + | 0.978200i | \(0.566586\pi\) | |||||||
\(930\) | −5671.95 | −0.199990 | ||||||||
\(931\) | 20372.3 | − | 31360.3i | 0.717159 | − | 1.10397i | ||||
\(932\) | 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 | \(-0.781619\pi\) | ||||
−0.773745 | + | 0.633497i | \(0.781619\pi\) | |||||||
\(938\) | 10178.0 | − | 16606.1i | 0.354288 | − | 0.578049i | ||||
\(939\) | −26136.3 | −0.908334 | ||||||||
\(940\) | 34818.3 | + | 60307.1i | 1.20814 | + | 2.09255i | ||||
\(941\) | −20495.8 | + | 35499.8i | −0.710036 | + | 1.22982i | 0.254807 | + | 0.966992i | \(0.417988\pi\) |
−0.964843 | + | 0.262827i | \(0.915345\pi\) | |||||||
\(942\) | −14839.3 | + | 25702.4i | −0.513259 | + | 0.888990i | ||||
\(943\) | −928.197 | − | 1607.68i | −0.0320533 | − | 0.0555179i | ||||
\(944\) | 95416.1 | 3.28976 | ||||||||
\(945\) | 2780.00 | + | 73.0046i | 0.0956968 | + | 0.00251306i | ||||
\(946\) | 18017.4 | 0.619233 | ||||||||
\(947\) | 26311.2 | + | 45572.4i | 0.902851 | + | 1.56378i | 0.823777 | + | 0.566914i | \(0.191863\pi\) |
0.0790737 | + | 0.996869i | \(0.474804\pi\) | |||||||
\(948\) | 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 | ||||||||
\(952\) | 24834.7 | + | 45747.9i | 0.845479 | + | 1.55746i | ||||
\(953\) | −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 | ||||||||
\(959\) | 16511.6 | + | 30416.0i | 0.555983 | + | 1.02418i | ||||
\(960\) | −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 | ||||||||
\(966\) | −22076.3 | − | 579.738i | −0.735294 | − | 0.0193093i | ||||
\(967\) | 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 | −0.931379 | − | 0.364052i | \(-0.881393\pi\) |
0.150411 | − | 0.988624i | \(-0.451940\pi\) | |||||||
\(972\) | −4903.25 | −0.161802 | ||||||||
\(973\) | −27264.8 | + | 44484.6i | −0.898323 | + | 1.46568i | ||||
\(974\) | −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 | −0.116749 | − | 0.993161i | \(-0.537247\pi\) |
0.918478 | − | 0.395473i | \(-0.129419\pi\) | |||||||
\(978\) | 18481.9 | + | 32011.6i | 0.604281 | + | 1.04665i | ||||
\(979\) | −22066.6 | −0.720380 | ||||||||
\(980\) | −17469.3 | − | 34298.1i | −0.569425 | − | 1.11797i | ||||
\(981\) | 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 | \(-0.732988\pi\) |
0.978373 | + | 0.206850i | \(0.0663214\pi\) | |||||||
\(984\) | −2404.02 | + | 4163.89i | −0.0778836 | + | 0.134898i | ||||
\(985\) | 4632.89 | + | 8024.39i | 0.149864 | + | 0.259572i | ||||
\(986\) | −16700.3 | −0.539397 | ||||||||
\(987\) | 18017.0 | − | 29396.1i | 0.581040 | − | 0.948013i | ||||
\(988\) | −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 | 0.00218424 | − | 0.999998i | \(-0.499305\pi\) |
0.864931 | − | 0.501890i | \(-0.167362\pi\) | |||||||
\(992\) | −14329.9 | − | 24820.1i | −0.458643 | − | 0.794393i | ||||
\(993\) | 17194.5 | 0.549498 | ||||||||
\(994\) | −77189.9 | − | 2027.06i | −2.46309 | − | 0.0646824i | ||||
\(995\) | −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 | \(-0.879976\pi\) |
0.783741 | + | 0.621088i | \(0.213309\pi\) | |||||||
\(998\) | −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 | 21.4.e.b.4.1 | ✓ | 6 | |
3.2 | odd | 2 | 63.4.e.c.46.3 | 6 | |||
4.3 | odd | 2 | 336.4.q.k.193.2 | 6 | |||
7.2 | even | 3 | inner | 21.4.e.b.16.1 | yes | 6 | |
7.3 | odd | 6 | 147.4.a.m.1.3 | 3 | |||
7.4 | even | 3 | 147.4.a.l.1.3 | 3 | |||
7.5 | odd | 6 | 147.4.e.n.79.1 | 6 | |||
7.6 | odd | 2 | 147.4.e.n.67.1 | 6 | |||
21.2 | odd | 6 | 63.4.e.c.37.3 | 6 | |||
21.5 | even | 6 | 441.4.e.w.226.3 | 6 | |||
21.11 | odd | 6 | 441.4.a.s.1.1 | 3 | |||
21.17 | even | 6 | 441.4.a.t.1.1 | 3 | |||
21.20 | even | 2 | 441.4.e.w.361.3 | 6 | |||
28.3 | even | 6 | 2352.4.a.cg.1.2 | 3 | |||
28.11 | odd | 6 | 2352.4.a.ci.1.2 | 3 | |||
28.23 | odd | 6 | 336.4.q.k.289.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.4.e.b.4.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
21.4.e.b.16.1 | yes | 6 | 7.2 | even | 3 | inner | |
63.4.e.c.37.3 | 6 | 21.2 | odd | 6 | |||
63.4.e.c.46.3 | 6 | 3.2 | odd | 2 | |||
147.4.a.l.1.3 | 3 | 7.4 | even | 3 | |||
147.4.a.m.1.3 | 3 | 7.3 | odd | 6 | |||
147.4.e.n.67.1 | 6 | 7.6 | odd | 2 | |||
147.4.e.n.79.1 | 6 | 7.5 | odd | 6 | |||
336.4.q.k.193.2 | 6 | 4.3 | odd | 2 | |||
336.4.q.k.289.2 | 6 | 28.23 | odd | 6 | |||
441.4.a.s.1.1 | 3 | 21.11 | odd | 6 | |||
441.4.a.t.1.1 | 3 | 21.17 | even | 6 | |||
441.4.e.w.226.3 | 6 | 21.5 | even | 6 | |||
441.4.e.w.361.3 | 6 | 21.20 | even | 2 | |||
2352.4.a.cg.1.2 | 3 | 28.3 | even | 6 | |||
2352.4.a.ci.1.2 | 3 | 28.11 | odd | 6 |