Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [65,4,Mod(16,65)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(65, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("65.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 65 = 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 65.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: | \(3.83512415037\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 2 x^{13} + 45 x^{12} - 52 x^{11} + 1311 x^{10} - 1336 x^{9} + 20343 x^{8} - 11166 x^{7} + \cdots + 1157776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 61.1 | ||
Root | \(2.45261 - 4.24804i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 65.61 |
Dual form | 65.4.e.a.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 \(\left(\mathbb{Z}/65\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.45261 | + | 4.24804i | −0.867127 | + | 1.50191i | −0.00220750 | + | 0.999998i | \(0.500703\pi\) |
−0.864920 | + | 0.501911i | \(0.832631\pi\) | |||||||
\(3\) | −3.39607 | + | 5.88216i | −0.653573 | + | 1.13202i | 0.328676 | + | 0.944443i | \(0.393397\pi\) |
−0.982249 | + | 0.187579i | \(0.939936\pi\) | |||||||
\(4\) | −8.03055 | − | 13.9093i | −1.00382 | − | 1.73866i | ||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −16.6584 | − | 28.8532i | −1.13346 | − | 1.96321i | ||||
\(7\) | 2.60104 | + | 4.50514i | 0.140443 | + | 0.243255i | 0.927664 | − | 0.373417i | \(-0.121814\pi\) |
−0.787220 | + | 0.616672i | \(0.788481\pi\) | |||||||
\(8\) | 39.5414 | 1.74750 | ||||||||
\(9\) | −9.56652 | − | 16.5697i | −0.354316 | − | 0.613692i | ||||
\(10\) | 12.2630 | − | 21.2402i | 0.387791 | − | 0.671674i | ||||
\(11\) | −20.9688 | + | 36.3191i | −0.574758 | + | 0.995511i | 0.421309 | + | 0.906917i | \(0.361571\pi\) |
−0.996068 | + | 0.0885938i | \(0.971763\pi\) | |||||||
\(12\) | 109.089 | 2.62428 | ||||||||
\(13\) | 46.1350 | − | 8.28002i | 0.984274 | − | 0.176651i | ||||
\(14\) | −25.5173 | −0.487128 | ||||||||
\(15\) | 16.9803 | − | 29.4108i | 0.292287 | − | 0.506256i | ||||
\(16\) | −32.7350 | + | 56.6988i | −0.511485 | + | 0.885918i | ||||
\(17\) | −19.1803 | − | 33.2212i | −0.273641 | − | 0.473961i | 0.696150 | − | 0.717896i | \(-0.254895\pi\) |
−0.969791 | + | 0.243935i | \(0.921562\pi\) | |||||||
\(18\) | 93.8516 | 1.22895 | ||||||||
\(19\) | −67.6145 | − | 117.112i | −0.816412 | − | 1.41407i | −0.908310 | − | 0.418298i | \(-0.862627\pi\) |
0.0918983 | − | 0.995768i | \(-0.470707\pi\) | |||||||
\(20\) | 40.1527 | + | 69.5466i | 0.448921 | + | 0.777555i | ||||
\(21\) | −35.3332 | −0.367159 | ||||||||
\(22\) | −102.857 | − | 178.153i | −0.996777 | − | 1.72647i | ||||
\(23\) | −73.9418 | + | 128.071i | −0.670345 | + | 1.16107i | 0.307462 | + | 0.951560i | \(0.400520\pi\) |
−0.977806 | + | 0.209511i | \(0.932813\pi\) | |||||||
\(24\) | −134.285 | + | 232.589i | −1.14212 | + | 1.97821i | ||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −77.9772 | + | 216.291i | −0.588176 | + | 1.63147i | ||||
\(27\) | −53.4334 | −0.380862 | ||||||||
\(28\) | 41.7756 | − | 72.3575i | 0.281959 | − | 0.488367i | ||||
\(29\) | 98.4740 | − | 170.562i | 0.630557 | − | 1.09216i | −0.356881 | − | 0.934150i | \(-0.616160\pi\) |
0.987438 | − | 0.158007i | \(-0.0505069\pi\) | |||||||
\(30\) | 83.2921 | + | 144.266i | 0.506900 | + | 0.877976i | ||||
\(31\) | −177.355 | −1.02754 | −0.513772 | − | 0.857927i | \(-0.671752\pi\) | ||||
−0.513772 | + | 0.857927i | \(0.671752\pi\) | |||||||
\(32\) | −2.40675 | − | 4.16861i | −0.0132955 | − | 0.0230285i | ||||
\(33\) | −142.423 | − | 246.684i | −0.751293 | − | 1.30128i | ||||
\(34\) | 188.167 | 0.949128 | ||||||||
\(35\) | −13.0052 | − | 22.5257i | −0.0628081 | − | 0.108787i | ||||
\(36\) | −153.649 | + | 266.128i | −0.711337 | + | 1.23207i | ||||
\(37\) | −156.728 | + | 271.461i | −0.696377 | + | 1.20616i | 0.273338 | + | 0.961918i | \(0.411872\pi\) |
−0.969714 | + | 0.244242i | \(0.921461\pi\) | |||||||
\(38\) | 663.326 | 2.83173 | ||||||||
\(39\) | −107.973 | + | 299.493i | −0.443322 | + | 1.22967i | ||||
\(40\) | −197.707 | −0.781505 | ||||||||
\(41\) | −72.0889 | + | 124.862i | −0.274595 | + | 0.475613i | −0.970033 | − | 0.242974i | \(-0.921877\pi\) |
0.695438 | + | 0.718586i | \(0.255210\pi\) | |||||||
\(42\) | 86.6585 | − | 150.097i | 0.318374 | − | 0.551440i | ||||
\(43\) | −36.6532 | − | 63.4852i | −0.129990 | − | 0.225149i | 0.793683 | − | 0.608332i | \(-0.208161\pi\) |
−0.923672 | + | 0.383183i | \(0.874828\pi\) | |||||||
\(44\) | 673.565 | 2.30781 | ||||||||
\(45\) | 47.8326 | + | 82.8485i | 0.158455 | + | 0.274452i | ||||
\(46\) | −362.700 | − | 628.215i | −1.16255 | − | 2.01359i | ||||
\(47\) | 194.126 | 0.602473 | 0.301236 | − | 0.953550i | \(-0.402601\pi\) | ||||
0.301236 | + | 0.953550i | \(0.402601\pi\) | |||||||
\(48\) | −222.341 | − | 385.105i | −0.668586 | − | 1.15802i | ||||
\(49\) | 157.969 | − | 273.611i | 0.460551 | − | 0.797699i | ||||
\(50\) | −61.3151 | + | 106.201i | −0.173425 | + | 0.300382i | ||||
\(51\) | 260.550 | 0.715379 | ||||||||
\(52\) | −485.659 | − | 575.214i | −1.29517 | − | 1.53400i | ||||
\(53\) | −751.545 | −1.94779 | −0.973893 | − | 0.227009i | \(-0.927105\pi\) | ||||
−0.973893 | + | 0.227009i | \(0.927105\pi\) | |||||||
\(54\) | 131.051 | − | 226.987i | 0.330256 | − | 0.572020i | ||||
\(55\) | 104.844 | − | 181.595i | 0.257040 | − | 0.445206i | ||||
\(56\) | 102.849 | + | 178.139i | 0.245424 | + | 0.425087i | ||||
\(57\) | 918.492 | 2.13434 | ||||||||
\(58\) | 483.036 | + | 836.642i | 1.09355 | + | 1.89408i | ||||
\(59\) | 226.456 | + | 392.233i | 0.499696 | + | 0.865499i | 1.00000 | 0.000351133i | \(-0.000111769\pi\) | |
−0.500304 | + | 0.865850i | \(0.666778\pi\) | |||||||
\(60\) | −545.445 | −1.17361 | ||||||||
\(61\) | 77.2358 | + | 133.776i | 0.162115 | + | 0.280792i | 0.935627 | − | 0.352990i | \(-0.114835\pi\) |
−0.773512 | + | 0.633782i | \(0.781502\pi\) | |||||||
\(62\) | 434.981 | − | 753.410i | 0.891011 | − | 1.54328i | ||||
\(63\) | 49.7659 | − | 86.1970i | 0.0995224 | − | 0.172378i | ||||
\(64\) | −500.149 | −0.976854 | ||||||||
\(65\) | −230.675 | + | 41.4001i | −0.440181 | + | 0.0790008i | ||||
\(66\) | 1397.23 | 2.60587 | ||||||||
\(67\) | −424.112 | + | 734.583i | −0.773336 | + | 1.33946i | 0.162389 | + | 0.986727i | \(0.448080\pi\) |
−0.935725 | + | 0.352730i | \(0.885253\pi\) | |||||||
\(68\) | −308.057 | + | 533.570i | −0.549373 | + | 0.951542i | ||||
\(69\) | −502.222 | − | 869.875i | −0.876239 | − | 1.51769i | ||||
\(70\) | 127.587 | 0.217850 | ||||||||
\(71\) | 379.816 | + | 657.860i | 0.634871 | + | 1.09963i | 0.986542 | + | 0.163505i | \(0.0522801\pi\) |
−0.351671 | + | 0.936124i | \(0.614387\pi\) | |||||||
\(72\) | −378.273 | − | 655.189i | −0.619166 | − | 1.07243i | ||||
\(73\) | 143.577 | 0.230197 | 0.115099 | − | 0.993354i | \(-0.463282\pi\) | ||||
0.115099 | + | 0.993354i | \(0.463282\pi\) | |||||||
\(74\) | −768.784 | − | 1331.57i | −1.20769 | − | 2.09179i | ||||
\(75\) | −84.9016 | + | 147.054i | −0.130715 | + | 0.226404i | ||||
\(76\) | −1085.96 | + | 1880.94i | −1.63906 | + | 2.83893i | ||||
\(77\) | −218.163 | −0.322883 | ||||||||
\(78\) | −1007.44 | − | 1193.21i | −1.46244 | − | 1.73211i | ||||
\(79\) | −133.740 | −0.190467 | −0.0952337 | − | 0.995455i | \(-0.530360\pi\) | ||||
−0.0952337 | + | 0.995455i | \(0.530360\pi\) | |||||||
\(80\) | 163.675 | − | 283.494i | 0.228743 | − | 0.396195i | ||||
\(81\) | 439.759 | − | 761.686i | 0.603237 | − | 1.04484i | ||||
\(82\) | −353.611 | − | 612.473i | −0.476218 | − | 0.824833i | ||||
\(83\) | −607.864 | −0.803877 | −0.401938 | − | 0.915667i | \(-0.631663\pi\) | ||||
−0.401938 | + | 0.915667i | \(0.631663\pi\) | |||||||
\(84\) | 283.745 | + | 491.461i | 0.368561 | + | 0.638367i | ||||
\(85\) | 95.9015 | + | 166.106i | 0.122376 | + | 0.211962i | ||||
\(86\) | 359.584 | 0.450871 | ||||||||
\(87\) | 668.848 | + | 1158.48i | 0.824231 | + | 1.42761i | ||||
\(88\) | −829.137 | + | 1436.11i | −1.00439 | + | 1.73965i | ||||
\(89\) | −74.0017 | + | 128.175i | −0.0881367 | + | 0.152657i | −0.906724 | − | 0.421726i | \(-0.861425\pi\) |
0.818587 | + | 0.574383i | \(0.194758\pi\) | |||||||
\(90\) | −469.258 | −0.549601 | ||||||||
\(91\) | 157.302 | + | 186.308i | 0.181206 | + | 0.214620i | ||||
\(92\) | 2375.17 | 2.69162 | ||||||||
\(93\) | 602.309 | − | 1043.23i | 0.671575 | − | 1.16320i | ||||
\(94\) | −476.115 | + | 824.655i | −0.522420 | + | 0.904858i | ||||
\(95\) | 338.072 | + | 585.558i | 0.365110 | + | 0.632390i | ||||
\(96\) | 32.6939 | 0.0347584 | ||||||||
\(97\) | 247.792 | + | 429.189i | 0.259376 | + | 0.449253i | 0.966075 | − | 0.258262i | \(-0.0831497\pi\) |
−0.706699 | + | 0.707515i | \(0.749816\pi\) | |||||||
\(98\) | 774.872 | + | 1342.12i | 0.798713 | + | 1.38341i | ||||
\(99\) | 802.395 | 0.814583 | ||||||||
\(100\) | −200.764 | − | 347.733i | −0.200764 | − | 0.347733i | ||||
\(101\) | −257.578 | + | 446.138i | −0.253762 | + | 0.439528i | −0.964558 | − | 0.263869i | \(-0.915001\pi\) |
0.710797 | + | 0.703398i | \(0.248335\pi\) | |||||||
\(102\) | −639.027 | + | 1106.83i | −0.620324 | + | 1.07443i | ||||
\(103\) | 140.957 | 0.134844 | 0.0674219 | − | 0.997725i | \(-0.478523\pi\) | ||||
0.0674219 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(104\) | 1824.24 | − | 327.404i | 1.72002 | − | 0.308698i | ||||
\(105\) | 176.666 | 0.164199 | ||||||||
\(106\) | 1843.24 | − | 3192.59i | 1.68898 | − | 2.92539i | ||||
\(107\) | 163.491 | − | 283.174i | 0.147713 | − | 0.255846i | −0.782669 | − | 0.622438i | \(-0.786142\pi\) |
0.930382 | + | 0.366592i | \(0.119476\pi\) | |||||||
\(108\) | 429.100 | + | 743.223i | 0.382316 | + | 0.662191i | ||||
\(109\) | −762.166 | −0.669745 | −0.334873 | − | 0.942263i | \(-0.608693\pi\) | ||||
−0.334873 | + | 0.942263i | \(0.608693\pi\) | |||||||
\(110\) | 514.283 | + | 890.764i | 0.445772 | + | 0.772100i | ||||
\(111\) | −1064.52 | − | 1843.80i | −0.910266 | − | 1.57663i | ||||
\(112\) | −340.581 | −0.287338 | ||||||||
\(113\) | −902.285 | − | 1562.80i | −0.751149 | − | 1.30103i | −0.947266 | − | 0.320448i | \(-0.896166\pi\) |
0.196117 | − | 0.980581i | \(-0.437167\pi\) | |||||||
\(114\) | −2252.70 | + | 3901.79i | −1.85074 | + | 3.20558i | ||||
\(115\) | 369.709 | − | 640.355i | 0.299787 | − | 0.519247i | ||||
\(116\) | −3163.20 | −2.53186 | ||||||||
\(117\) | −578.549 | − | 685.233i | −0.457153 | − | 0.541451i | ||||
\(118\) | −2221.63 | −1.73320 | ||||||||
\(119\) | 99.7776 | − | 172.820i | 0.0768621 | − | 0.133129i | ||||
\(120\) | 671.426 | − | 1162.94i | 0.510771 | − | 0.884681i | ||||
\(121\) | −213.884 | − | 370.459i | −0.160694 | − | 0.278331i | ||||
\(122\) | −757.716 | −0.562298 | ||||||||
\(123\) | −489.637 | − | 848.077i | −0.358936 | − | 0.621695i | ||||
\(124\) | 1424.26 | + | 2466.88i | 1.03147 | + | 1.78655i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 244.112 | + | 422.814i | 0.172597 | + | 0.298947i | ||||
\(127\) | 1321.40 | − | 2288.74i | 0.923273 | − | 1.59916i | 0.128959 | − | 0.991650i | \(-0.458837\pi\) |
0.794315 | − | 0.607506i | \(-0.207830\pi\) | |||||||
\(128\) | 1245.92 | − | 2158.00i | 0.860352 | − | 1.49017i | ||||
\(129\) | 497.907 | 0.339831 | ||||||||
\(130\) | 389.886 | − | 1081.45i | 0.263041 | − | 0.729614i | ||||
\(131\) | −467.861 | −0.312040 | −0.156020 | − | 0.987754i | \(-0.549866\pi\) | ||||
−0.156020 | + | 0.987754i | \(0.549866\pi\) | |||||||
\(132\) | −2287.47 | + | 3962.02i | −1.50832 | + | 2.61249i | ||||
\(133\) | 351.736 | − | 609.225i | 0.229319 | − | 0.397192i | ||||
\(134\) | −2080.36 | − | 3603.29i | −1.34116 | − | 2.32296i | ||||
\(135\) | 267.167 | 0.170327 | ||||||||
\(136\) | −758.416 | − | 1313.61i | −0.478188 | − | 0.828246i | ||||
\(137\) | 704.357 | + | 1219.98i | 0.439250 | + | 0.760803i | 0.997632 | − | 0.0687808i | \(-0.0219109\pi\) |
−0.558382 | + | 0.829584i | \(0.688578\pi\) | |||||||
\(138\) | 4927.01 | 3.03924 | ||||||||
\(139\) | 821.610 | + | 1423.07i | 0.501353 | + | 0.868368i | 0.999999 | + | 0.00156264i | \(0.000497404\pi\) |
−0.498646 | + | 0.866806i | \(0.666169\pi\) | |||||||
\(140\) | −208.878 | + | 361.787i | −0.126096 | + | 0.218404i | ||||
\(141\) | −659.265 | + | 1141.88i | −0.393760 | + | 0.682012i | ||||
\(142\) | −3726.15 | −2.20206 | ||||||||
\(143\) | −666.675 | + | 1849.20i | −0.389861 | + | 1.08139i | ||||
\(144\) | 1252.64 | 0.724908 | ||||||||
\(145\) | −492.370 | + | 852.810i | −0.281994 | + | 0.488428i | ||||
\(146\) | −352.137 | + | 609.920i | −0.199610 | + | 0.345735i | ||||
\(147\) | 1072.95 | + | 1858.40i | 0.602008 | + | 1.04271i | ||||
\(148\) | 5034.45 | 2.79614 | ||||||||
\(149\) | −1214.31 | − | 2103.25i | −0.667653 | − | 1.15641i | −0.978559 | − | 0.205968i | \(-0.933966\pi\) |
0.310906 | − | 0.950441i | \(-0.399368\pi\) | |||||||
\(150\) | −416.460 | − | 721.331i | −0.226692 | − | 0.392643i | ||||
\(151\) | 877.503 | 0.472915 | 0.236458 | − | 0.971642i | \(-0.424014\pi\) | ||||
0.236458 | + | 0.971642i | \(0.424014\pi\) | |||||||
\(152\) | −2673.57 | − | 4630.76i | −1.42668 | − | 2.47108i | ||||
\(153\) | −366.977 | + | 635.623i | −0.193911 | + | 0.335863i | ||||
\(154\) | 535.069 | − | 926.766i | 0.279981 | − | 0.484941i | ||||
\(155\) | 886.774 | 0.459532 | ||||||||
\(156\) | 5032.83 | − | 903.260i | 2.58300 | − | 0.463581i | ||||
\(157\) | −1961.12 | −0.996909 | −0.498454 | − | 0.866916i | \(-0.666099\pi\) | ||||
−0.498454 | + | 0.866916i | \(0.666099\pi\) | |||||||
\(158\) | 328.011 | − | 568.132i | 0.165159 | − | 0.286064i | ||||
\(159\) | 2552.30 | − | 4420.71i | 1.27302 | − | 2.20494i | ||||
\(160\) | 12.0337 | + | 20.8430i | 0.00594594 | + | 0.0102987i | ||||
\(161\) | −769.303 | −0.376581 | ||||||||
\(162\) | 2157.11 | + | 3736.23i | 1.04617 | + | 1.81201i | ||||
\(163\) | 799.568 | + | 1384.89i | 0.384215 | + | 0.665479i | 0.991660 | − | 0.128882i | \(-0.0411389\pi\) |
−0.607445 | + | 0.794362i | \(0.707806\pi\) | |||||||
\(164\) | 2315.65 | 1.10257 | ||||||||
\(165\) | 712.115 | + | 1233.42i | 0.335989 | + | 0.581949i | ||||
\(166\) | 1490.85 | − | 2582.23i | 0.697063 | − | 1.20735i | ||||
\(167\) | 28.0584 | − | 48.5986i | 0.0130013 | − | 0.0225190i | −0.859452 | − | 0.511217i | \(-0.829195\pi\) |
0.872453 | + | 0.488698i | \(0.162528\pi\) | |||||||
\(168\) | −1397.13 | −0.641611 | ||||||||
\(169\) | 2059.88 | − | 763.998i | 0.937589 | − | 0.347746i | ||||
\(170\) | −940.834 | −0.424463 | ||||||||
\(171\) | −1293.67 | + | 2240.70i | −0.578535 | + | 1.00205i | ||||
\(172\) | −588.691 | + | 1019.64i | −0.260972 | + | 0.452018i | ||||
\(173\) | 1836.03 | + | 3180.10i | 0.806883 | + | 1.39756i | 0.915013 | + | 0.403425i | \(0.132180\pi\) |
−0.108130 | + | 0.994137i | \(0.534486\pi\) | |||||||
\(174\) | −6561.68 | −2.85885 | ||||||||
\(175\) | 65.0261 | + | 112.628i | 0.0280886 | + | 0.0486509i | ||||
\(176\) | −1372.83 | − | 2377.81i | −0.587961 | − | 1.01838i | ||||
\(177\) | −3076.24 | −1.30635 | ||||||||
\(178\) | −362.994 | − | 628.724i | −0.152851 | − | 0.264746i | ||||
\(179\) | −1869.35 | + | 3237.82i | −0.780570 | + | 1.35199i | 0.151040 | + | 0.988528i | \(0.451738\pi\) |
−0.931610 | + | 0.363460i | \(0.881595\pi\) | |||||||
\(180\) | 768.244 | − | 1330.64i | 0.318120 | − | 0.550999i | ||||
\(181\) | 1800.89 | 0.739551 | 0.369776 | − | 0.929121i | \(-0.379435\pi\) | ||||
0.369776 | + | 0.929121i | \(0.379435\pi\) | |||||||
\(182\) | −1177.24 | + | 211.284i | −0.479467 | + | 0.0860517i | ||||
\(183\) | −1049.19 | −0.423817 | ||||||||
\(184\) | −2923.76 | + | 5064.10i | −1.17143 | + | 2.02897i | ||||
\(185\) | 783.640 | − | 1357.31i | 0.311429 | − | 0.539411i | ||||
\(186\) | 2954.45 | + | 5117.26i | 1.16468 | + | 2.01729i | ||||
\(187\) | 1608.75 | 0.629111 | ||||||||
\(188\) | −1558.94 | − | 2700.16i | −0.604773 | − | 1.04750i | ||||
\(189\) | −138.983 | − | 240.725i | −0.0534894 | − | 0.0926464i | ||||
\(190\) | −3316.63 | −1.26639 | ||||||||
\(191\) | 115.792 | + | 200.557i | 0.0438659 | + | 0.0759780i | 0.887125 | − | 0.461530i | \(-0.152699\pi\) |
−0.843259 | + | 0.537508i | \(0.819366\pi\) | |||||||
\(192\) | 1698.54 | − | 2941.96i | 0.638446 | − | 1.10582i | ||||
\(193\) | −1096.71 | + | 1899.57i | −0.409032 | + | 0.708465i | −0.994782 | − | 0.102028i | \(-0.967467\pi\) |
0.585749 | + | 0.810492i | \(0.300800\pi\) | |||||||
\(194\) | −2430.95 | −0.899649 | ||||||||
\(195\) | 539.866 | − | 1497.47i | 0.198260 | − | 0.549927i | ||||
\(196\) | −5074.32 | −1.84924 | ||||||||
\(197\) | −1466.70 | + | 2540.40i | −0.530447 | + | 0.918761i | 0.468922 | + | 0.883239i | \(0.344642\pi\) |
−0.999369 | + | 0.0355211i | \(0.988691\pi\) | |||||||
\(198\) | −1967.96 | + | 3408.60i | −0.706347 | + | 1.22343i | ||||
\(199\) | 1530.71 | + | 2651.27i | 0.545273 | + | 0.944440i | 0.998590 | + | 0.0530906i | \(0.0169072\pi\) |
−0.453317 | + | 0.891349i | \(0.649759\pi\) | |||||||
\(200\) | 988.535 | 0.349500 | ||||||||
\(201\) | −2880.62 | − | 4989.38i | −1.01086 | − | 1.75087i | ||||
\(202\) | −1263.47 | − | 2188.40i | −0.440088 | − | 0.762254i | ||||
\(203\) | 1024.54 | 0.354230 | ||||||||
\(204\) | −2092.36 | − | 3624.08i | −0.718111 | − | 1.24380i | ||||
\(205\) | 360.445 | − | 624.309i | 0.122803 | − | 0.212700i | ||||
\(206\) | −345.712 | + | 598.791i | −0.116927 | + | 0.202523i | ||||
\(207\) | 2829.46 | 0.950054 | ||||||||
\(208\) | −1040.77 | + | 2886.85i | −0.346943 | + | 0.962340i | ||||
\(209\) | 5671.19 | 1.87696 | ||||||||
\(210\) | −433.293 | + | 750.485i | −0.142381 | + | 0.246611i | ||||
\(211\) | −854.274 | + | 1479.65i | −0.278724 | + | 0.482763i | −0.971068 | − | 0.238804i | \(-0.923245\pi\) |
0.692344 | + | 0.721567i | \(0.256578\pi\) | |||||||
\(212\) | 6035.32 | + | 10453.5i | 1.95522 | + | 3.38655i | ||||
\(213\) | −5159.52 | −1.65974 | ||||||||
\(214\) | 801.956 | + | 1389.03i | 0.256171 | + | 0.443701i | ||||
\(215\) | 183.266 | + | 317.426i | 0.0581332 | + | 0.100690i | ||||
\(216\) | −2112.83 | −0.665556 | ||||||||
\(217\) | −461.308 | − | 799.008i | −0.144312 | − | 0.249955i | ||||
\(218\) | 1869.29 | − | 3237.71i | 0.580754 | − | 1.00590i | ||||
\(219\) | −487.596 | + | 844.541i | −0.150451 | + | 0.260588i | ||||
\(220\) | −3367.83 | −1.03209 | ||||||||
\(221\) | −1159.96 | − | 1373.85i | −0.353064 | − | 0.418168i | ||||
\(222\) | 10443.4 | 3.15727 | ||||||||
\(223\) | −809.512 | + | 1402.12i | −0.243089 | + | 0.421043i | −0.961593 | − | 0.274481i | \(-0.911494\pi\) |
0.718503 | + | 0.695523i | \(0.244827\pi\) | |||||||
\(224\) | 12.5201 | − | 21.6854i | 0.00373453 | − | 0.00646839i | ||||
\(225\) | −239.163 | − | 414.242i | −0.0708631 | − | 0.122738i | ||||
\(226\) | 8851.80 | 2.60537 | ||||||||
\(227\) | −2556.69 | − | 4428.32i | −0.747549 | − | 1.29479i | −0.948994 | − | 0.315293i | \(-0.897897\pi\) |
0.201445 | − | 0.979500i | \(-0.435436\pi\) | |||||||
\(228\) | −7376.00 | − | 12775.6i | −2.14249 | − | 3.71090i | ||||
\(229\) | 194.004 | 0.0559831 | 0.0279916 | − | 0.999608i | \(-0.491089\pi\) | ||||
0.0279916 | + | 0.999608i | \(0.491089\pi\) | |||||||
\(230\) | 1813.50 | + | 3141.08i | 0.519907 | + | 0.900506i | ||||
\(231\) | 740.897 | − | 1283.27i | 0.211028 | − | 0.365511i | ||||
\(232\) | 3893.80 | − | 6744.26i | 1.10190 | − | 1.90854i | ||||
\(233\) | −385.584 | −0.108414 | −0.0542070 | − | 0.998530i | \(-0.517263\pi\) | ||||
−0.0542070 | + | 0.998530i | \(0.517263\pi\) | |||||||
\(234\) | 4329.85 | − | 777.093i | 1.20962 | − | 0.217095i | ||||
\(235\) | −970.631 | −0.269434 | ||||||||
\(236\) | 3637.13 | − | 6299.70i | 1.00321 | − | 1.73761i | ||||
\(237\) | 454.190 | − | 786.679i | 0.124484 | − | 0.215613i | ||||
\(238\) | 489.430 | + | 847.718i | 0.133298 | + | 0.230880i | ||||
\(239\) | −2941.98 | −0.796238 | −0.398119 | − | 0.917334i | \(-0.630337\pi\) | ||||
−0.398119 | + | 0.917334i | \(0.630337\pi\) | |||||||
\(240\) | 1111.70 | + | 1925.53i | 0.299001 | + | 0.517884i | ||||
\(241\) | 2006.66 | + | 3475.63i | 0.536349 | + | 0.928983i | 0.999097 | + | 0.0424933i | \(0.0135301\pi\) |
−0.462748 | + | 0.886490i | \(0.653137\pi\) | |||||||
\(242\) | 2098.30 | 0.557370 | ||||||||
\(243\) | 2265.55 | + | 3924.05i | 0.598087 | + | 1.03592i | ||||
\(244\) | 1240.49 | − | 2148.60i | 0.325469 | − | 0.563728i | ||||
\(245\) | −789.846 | + | 1368.05i | −0.205965 | + | 0.356742i | ||||
\(246\) | 4803.55 | 1.24497 | ||||||||
\(247\) | −4089.08 | − | 4843.10i | −1.05337 | − | 1.24761i | ||||
\(248\) | −7012.86 | −1.79563 | ||||||||
\(249\) | 2064.35 | − | 3575.55i | 0.525392 | − | 0.910006i | ||||
\(250\) | 306.576 | − | 531.005i | 0.0775582 | − | 0.134335i | ||||
\(251\) | −1346.81 | − | 2332.74i | −0.338684 | − | 0.586618i | 0.645501 | − | 0.763759i | \(-0.276648\pi\) |
−0.984185 | + | 0.177141i | \(0.943315\pi\) | |||||||
\(252\) | −1598.59 | −0.399610 | ||||||||
\(253\) | −3100.95 | − | 5371.00i | −0.770573 | − | 1.33467i | ||||
\(254\) | 6481.77 | + | 11226.8i | 1.60119 | + | 2.77334i | ||||
\(255\) | −1302.75 | −0.319927 | ||||||||
\(256\) | 4110.92 | + | 7120.32i | 1.00364 | + | 1.73836i | ||||
\(257\) | −1805.94 | + | 3127.99i | −0.438333 | + | 0.759216i | −0.997561 | − | 0.0697984i | \(-0.977764\pi\) |
0.559228 | + | 0.829014i | \(0.311098\pi\) | |||||||
\(258\) | −1221.17 | + | 2115.13i | −0.294677 | + | 0.510396i | ||||
\(259\) | −1630.63 | −0.391205 | ||||||||
\(260\) | 2428.30 | + | 2876.07i | 0.579217 | + | 0.686024i | ||||
\(261\) | −3768.21 | −0.893665 | ||||||||
\(262\) | 1147.48 | − | 1987.49i | 0.270578 | − | 0.468655i | ||||
\(263\) | −967.940 | + | 1676.52i | −0.226942 | + | 0.393075i | −0.956900 | − | 0.290417i | \(-0.906206\pi\) |
0.729958 | + | 0.683492i | \(0.239539\pi\) | |||||||
\(264\) | −5631.61 | − | 9754.23i | −1.31288 | − | 2.27398i | ||||
\(265\) | 3757.72 | 0.871076 | ||||||||
\(266\) | 1725.34 | + | 2988.38i | 0.397697 | + | 0.688832i | ||||
\(267\) | −502.629 | − | 870.579i | −0.115208 | − | 0.199545i | ||||
\(268\) | 13623.4 | 3.10516 | ||||||||
\(269\) | 118.712 | + | 205.615i | 0.0269070 | + | 0.0466043i | 0.879165 | − | 0.476517i | \(-0.158101\pi\) |
−0.852258 | + | 0.523121i | \(0.824768\pi\) | |||||||
\(270\) | −655.256 | + | 1134.94i | −0.147695 | + | 0.255815i | ||||
\(271\) | −1277.70 | + | 2213.04i | −0.286401 | + | 0.496061i | −0.972948 | − | 0.231024i | \(-0.925792\pi\) |
0.686547 | + | 0.727085i | \(0.259126\pi\) | |||||||
\(272\) | 2511.47 | 0.559854 | ||||||||
\(273\) | −1630.10 | + | 292.560i | −0.361385 | + | 0.0648591i | ||||
\(274\) | −6910.04 | −1.52354 | ||||||||
\(275\) | −524.221 | + | 907.977i | −0.114952 | + | 0.199102i | ||||
\(276\) | −8066.24 | + | 13971.1i | −1.75917 | + | 3.04697i | ||||
\(277\) | −2593.65 | − | 4492.33i | −0.562590 | − | 0.974434i | −0.997269 | − | 0.0738488i | \(-0.976472\pi\) |
0.434680 | − | 0.900585i | \(-0.356862\pi\) | |||||||
\(278\) | −8060.34 | −1.73895 | ||||||||
\(279\) | 1696.67 | + | 2938.72i | 0.364075 | + | 0.630596i | ||||
\(280\) | −514.244 | − | 890.697i | −0.109757 | − | 0.190105i | ||||
\(281\) | 5148.13 | 1.09292 | 0.546462 | − | 0.837484i | \(-0.315974\pi\) | ||||
0.546462 | + | 0.837484i | \(0.315974\pi\) | |||||||
\(282\) | −3233.83 | − | 5601.17i | −0.682880 | − | 1.18278i | ||||
\(283\) | 1146.62 | − | 1986.00i | 0.240846 | − | 0.417157i | −0.720110 | − | 0.693860i | \(-0.755909\pi\) |
0.960955 | + | 0.276703i | \(0.0892418\pi\) | |||||||
\(284\) | 6100.26 | − | 10566.0i | 1.27459 | − | 2.20766i | ||||
\(285\) | −4592.46 | −0.954505 | ||||||||
\(286\) | −6220.40 | − | 7367.43i | −1.28608 | − | 1.52324i | ||||
\(287\) | −750.026 | −0.154260 | ||||||||
\(288\) | −46.0483 | + | 79.7581i | −0.00942161 | + | 0.0163187i | ||||
\(289\) | 1720.73 | − | 2980.40i | 0.350241 | − | 0.606635i | ||||
\(290\) | −2415.18 | − | 4183.21i | −0.489049 | − | 0.847058i | ||||
\(291\) | −3366.07 | −0.678085 | ||||||||
\(292\) | −1153.00 | − | 1997.06i | −0.231076 | − | 0.400236i | ||||
\(293\) | −2233.46 | − | 3868.47i | −0.445325 | − | 0.771326i | 0.552749 | − | 0.833347i | \(-0.313579\pi\) |
−0.998075 | + | 0.0620213i | \(0.980245\pi\) | |||||||
\(294\) | −10526.1 | −2.08807 | ||||||||
\(295\) | −1132.28 | − | 1961.17i | −0.223471 | − | 0.387063i | ||||
\(296\) | −6197.25 | + | 10733.9i | −1.21692 | + | 2.10776i | ||||
\(297\) | 1120.44 | − | 1940.65i | 0.218904 | − | 0.379152i | ||||
\(298\) | 11912.9 | 2.31576 | ||||||||
\(299\) | −2350.88 | + | 6520.80i | −0.454698 | + | 1.26123i | ||||
\(300\) | 2727.23 | 0.524855 | ||||||||
\(301\) | 190.673 | − | 330.256i | 0.0365124 | − | 0.0632413i | ||||
\(302\) | −2152.17 | + | 3727.67i | −0.410078 | + | 0.710275i | ||||
\(303\) | −1749.50 | − | 3030.23i | −0.331704 | − | 0.574528i | ||||
\(304\) | 8853.45 | 1.67033 | ||||||||
\(305\) | −386.179 | − | 668.882i | −0.0725002 | − | 0.125574i | ||||
\(306\) | −1800.10 | − | 3117.87i | −0.336291 | − | 0.582473i | ||||
\(307\) | 4456.35 | 0.828460 | 0.414230 | − | 0.910172i | \(-0.364051\pi\) | ||||
0.414230 | + | 0.910172i | \(0.364051\pi\) | |||||||
\(308\) | 1751.97 | + | 3034.50i | 0.324116 | + | 0.561386i | ||||
\(309\) | −478.699 | + | 829.131i | −0.0881303 | + | 0.152646i | ||||
\(310\) | −2174.91 | + | 3767.05i | −0.398472 | + | 0.690174i | ||||
\(311\) | 5351.54 | 0.975749 | 0.487875 | − | 0.872914i | \(-0.337772\pi\) | ||||
0.487875 | + | 0.872914i | \(0.337772\pi\) | |||||||
\(312\) | −4269.41 | + | 11842.4i | −0.774704 | + | 2.14885i | ||||
\(313\) | 8231.19 | 1.48644 | 0.743218 | − | 0.669050i | \(-0.233299\pi\) | ||||
0.743218 | + | 0.669050i | \(0.233299\pi\) | |||||||
\(314\) | 4809.86 | − | 8330.93i | 0.864447 | − | 1.49727i | ||||
\(315\) | −248.829 | + | 430.985i | −0.0445077 | + | 0.0770897i | ||||
\(316\) | 1074.01 | + | 1860.23i | 0.191195 | + | 0.331159i | ||||
\(317\) | −5173.89 | −0.916702 | −0.458351 | − | 0.888771i | \(-0.651560\pi\) | ||||
−0.458351 | + | 0.888771i | \(0.651560\pi\) | |||||||
\(318\) | 12519.5 | + | 21684.5i | 2.20774 | + | 3.82392i | ||||
\(319\) | 4129.77 | + | 7152.97i | 0.724836 | + | 1.25545i | ||||
\(320\) | 2500.75 | 0.436863 | ||||||||
\(321\) | 1110.45 | + | 1923.36i | 0.193082 | + | 0.334428i | ||||
\(322\) | 1886.80 | − | 3268.03i | 0.326544 | − | 0.565590i | ||||
\(323\) | −2593.73 | + | 4492.47i | −0.446808 | + | 0.773894i | ||||
\(324\) | −14126.0 | −2.42216 | ||||||||
\(325\) | 1153.38 | − | 207.001i | 0.196855 | − | 0.0353302i | ||||
\(326\) | −7844.10 | −1.33265 | ||||||||
\(327\) | 2588.37 | − | 4483.18i | 0.437728 | − | 0.758166i | ||||
\(328\) | −2850.50 | + | 4937.21i | −0.479855 | + | 0.831133i | ||||
\(329\) | 504.930 | + | 874.565i | 0.0846131 | + | 0.146554i | ||||
\(330\) | −6986.15 | −1.16538 | ||||||||
\(331\) | −1354.54 | − | 2346.13i | −0.224931 | − | 0.389592i | 0.731368 | − | 0.681983i | \(-0.238882\pi\) |
−0.956299 | + | 0.292392i | \(0.905549\pi\) | |||||||
\(332\) | 4881.48 | + | 8454.98i | 0.806946 | + | 1.39767i | ||||
\(333\) | 5997.37 | 0.986948 | ||||||||
\(334\) | 137.632 | + | 238.386i | 0.0225476 | + | 0.0390536i | ||||
\(335\) | 2120.56 | − | 3672.92i | 0.345846 | − | 0.599023i | ||||
\(336\) | 1156.64 | − | 2003.35i | 0.187797 | − | 0.325273i | ||||
\(337\) | −1289.00 | −0.208356 | −0.104178 | − | 0.994559i | \(-0.533221\pi\) | ||||
−0.104178 | + | 0.994559i | \(0.533221\pi\) | |||||||
\(338\) | −1806.59 | + | 10624.2i | −0.290726 | + | 1.70971i | ||||
\(339\) | 12256.9 | 1.96372 | ||||||||
\(340\) | 1540.28 | − | 2667.85i | 0.245687 | − | 0.425542i | ||||
\(341\) | 3718.92 | − | 6441.37i | 0.590590 | − | 1.02293i | ||||
\(342\) | −6345.72 | − | 10991.1i | −1.00333 | − | 1.73781i | ||||
\(343\) | 3427.85 | 0.539611 | ||||||||
\(344\) | −1449.32 | − | 2510.29i | −0.227157 | − | 0.393448i | ||||
\(345\) | 2511.11 | + | 4349.37i | 0.391866 | + | 0.678731i | ||||
\(346\) | −18012.2 | −2.79868 | ||||||||
\(347\) | 4471.64 | + | 7745.11i | 0.691787 | + | 1.19821i | 0.971252 | + | 0.238055i | \(0.0765098\pi\) |
−0.279464 | + | 0.960156i | \(0.590157\pi\) | |||||||
\(348\) | 10742.4 | − | 18606.4i | 1.65476 | − | 2.86612i | ||||
\(349\) | −851.482 | + | 1474.81i | −0.130598 | + | 0.226203i | −0.923907 | − | 0.382616i | \(-0.875023\pi\) |
0.793309 | + | 0.608819i | \(0.208356\pi\) | |||||||
\(350\) | −637.933 | −0.0974256 | ||||||||
\(351\) | −2465.15 | + | 442.430i | −0.374872 | + | 0.0672797i | ||||
\(352\) | 201.867 | 0.0305668 | ||||||||
\(353\) | 2917.43 | − | 5053.14i | 0.439884 | − | 0.761902i | −0.557796 | − | 0.829978i | \(-0.688353\pi\) |
0.997680 | + | 0.0680764i | \(0.0216862\pi\) | |||||||
\(354\) | 7544.80 | − | 13068.0i | 1.13277 | − | 1.96202i | ||||
\(355\) | −1899.08 | − | 3289.30i | −0.283923 | − | 0.491769i | ||||
\(356\) | 2377.10 | 0.353893 | ||||||||
\(357\) | 677.702 | + | 1173.81i | 0.100470 | + | 0.174019i | ||||
\(358\) | −9169.58 | − | 15882.2i | −1.35371 | − | 2.34469i | ||||
\(359\) | −11215.3 | −1.64881 | −0.824404 | − | 0.566001i | \(-0.808490\pi\) | ||||
−0.824404 | + | 0.566001i | \(0.808490\pi\) | |||||||
\(360\) | 1891.37 | + | 3275.94i | 0.276899 | + | 0.479604i | ||||
\(361\) | −5713.93 | + | 9896.82i | −0.833056 | + | 1.44289i | ||||
\(362\) | −4416.86 | + | 7650.23i | −0.641285 | + | 1.11074i | ||||
\(363\) | 2905.46 | 0.420102 | ||||||||
\(364\) | 1328.20 | − | 3684.12i | 0.191254 | − | 0.530495i | ||||
\(365\) | −717.884 | −0.102947 | ||||||||
\(366\) | 2573.25 | − | 4457.01i | 0.367503 | − | 0.636534i | ||||
\(367\) | −3223.76 | + | 5583.72i | −0.458526 | + | 0.794190i | −0.998883 | − | 0.0472454i | \(-0.984956\pi\) |
0.540357 | + | 0.841436i | \(0.318289\pi\) | |||||||
\(368\) | −4840.98 | − | 8384.82i | −0.685743 | − | 1.18774i | ||||
\(369\) | 2758.56 | 0.389173 | ||||||||
\(370\) | 3843.92 | + | 6657.87i | 0.540097 | + | 0.935476i | ||||
\(371\) | −1954.80 | − | 3385.81i | −0.273553 | − | 0.473808i | ||||
\(372\) | −19347.5 | −2.69656 | ||||||||
\(373\) | 1924.55 | + | 3333.42i | 0.267156 | + | 0.462728i | 0.968126 | − | 0.250462i | \(-0.0805826\pi\) |
−0.700970 | + | 0.713191i | \(0.747249\pi\) | |||||||
\(374\) | −3945.64 | + | 6834.05i | −0.545519 | + | 0.944867i | ||||
\(375\) | 424.508 | − | 735.270i | 0.0584574 | − | 0.101251i | ||||
\(376\) | 7676.02 | 1.05282 | ||||||||
\(377\) | 3130.84 | − | 8684.25i | 0.427710 | − | 1.18637i | ||||
\(378\) | 1363.48 | 0.185529 | ||||||||
\(379\) | −4440.40 | + | 7691.00i | −0.601815 | + | 1.04237i | 0.390731 | + | 0.920505i | \(0.372222\pi\) |
−0.992546 | + | 0.121869i | \(0.961111\pi\) | |||||||
\(380\) | 5429.81 | − | 9404.71i | 0.733009 | − | 1.26961i | ||||
\(381\) | 8975.15 | + | 15545.4i | 1.20685 | + | 2.09033i | ||||
\(382\) | −1135.97 | −0.152149 | ||||||||
\(383\) | −2148.54 | − | 3721.38i | −0.286645 | − | 0.496484i | 0.686362 | − | 0.727260i | \(-0.259207\pi\) |
−0.973007 | + | 0.230776i | \(0.925873\pi\) | |||||||
\(384\) | 8462.47 | + | 14657.4i | 1.12461 | + | 1.94788i | ||||
\(385\) | 1090.82 | 0.144398 | ||||||||
\(386\) | −5379.62 | − | 9317.77i | −0.709366 | − | 1.22866i | ||||
\(387\) | −701.287 | + | 1214.67i | −0.0921148 | + | 0.159548i | ||||
\(388\) | 3979.82 | − | 6893.24i | 0.520733 | − | 0.901937i | ||||
\(389\) | 1541.34 | 0.200897 | 0.100449 | − | 0.994942i | \(-0.467972\pi\) | ||||
0.100449 | + | 0.994942i | \(0.467972\pi\) | |||||||
\(390\) | 5037.21 | + | 5966.06i | 0.654023 | + | 0.774624i | ||||
\(391\) | 5672.90 | 0.733737 | ||||||||
\(392\) | 6246.32 | − | 10818.9i | 0.804813 | − | 1.39398i | ||||
\(393\) | 1588.89 | − | 2752.03i | 0.203941 | − | 0.353236i | ||||
\(394\) | −7194.47 | − | 12461.2i | −0.919929 | − | 1.59336i | ||||
\(395\) | 668.700 | 0.0851796 | ||||||||
\(396\) | −6443.67 | − | 11160.8i | −0.817694 | − | 1.41629i | ||||
\(397\) | 2370.42 | + | 4105.69i | 0.299668 | + | 0.519040i | 0.976060 | − | 0.217502i | \(-0.0697909\pi\) |
−0.676392 | + | 0.736542i | \(0.736458\pi\) | |||||||
\(398\) | −15016.9 | −1.89128 | ||||||||
\(399\) | 2389.04 | + | 4137.94i | 0.299753 | + | 0.519188i | ||||
\(400\) | −818.376 | + | 1417.47i | −0.102297 | + | 0.177184i | ||||
\(401\) | −310.131 | + | 537.162i | −0.0386214 | + | 0.0668943i | −0.884690 | − | 0.466180i | \(-0.845630\pi\) |
0.846069 | + | 0.533074i | \(0.178963\pi\) | |||||||
\(402\) | 28260.1 | 3.50619 | ||||||||
\(403\) | −8182.27 | + | 1468.50i | −1.01138 | + | 0.181517i | ||||
\(404\) | 8273.96 | 1.01892 | ||||||||
\(405\) | −2198.80 | + | 3808.43i | −0.269776 | + | 0.467265i | ||||
\(406\) | −2512.79 | + | 4352.29i | −0.307162 | + | 0.532021i | ||||
\(407\) | −6572.81 | − | 11384.4i | −0.800497 | − | 1.38650i | ||||
\(408\) | 10302.5 | 1.25012 | ||||||||
\(409\) | 6245.99 | + | 10818.4i | 0.755121 | + | 1.30791i | 0.945314 | + | 0.326161i | \(0.105755\pi\) |
−0.190193 | + | 0.981747i | \(0.560911\pi\) | |||||||
\(410\) | 1768.06 | + | 3062.37i | 0.212971 | + | 0.368877i | ||||
\(411\) | −9568.16 | −1.14833 | ||||||||
\(412\) | −1131.96 | − | 1960.62i | −0.135359 | − | 0.234448i | ||||
\(413\) | −1178.04 | + | 2040.43i | −0.140358 | + | 0.243107i | ||||
\(414\) | −6939.55 | + | 12019.7i | −0.823818 | + | 1.42689i | ||||
\(415\) | 3039.32 | 0.359505 | ||||||||
\(416\) | −145.551 | − | 172.391i | −0.0171544 | − | 0.0203177i | ||||
\(417\) | −11161.0 | −1.31068 | ||||||||
\(418\) | −13909.2 | + | 24091.4i | −1.62756 | + | 2.81902i | ||||
\(419\) | 4428.53 | − | 7670.43i | 0.516343 | − | 0.894332i | −0.483477 | − | 0.875357i | \(-0.660626\pi\) |
0.999820 | − | 0.0189750i | \(-0.00604030\pi\) | |||||||
\(420\) | −1418.73 | − | 2457.31i | −0.164826 | − | 0.285486i | ||||
\(421\) | 13928.2 | 1.61240 | 0.806198 | − | 0.591646i | \(-0.201522\pi\) | ||||
0.806198 | + | 0.591646i | \(0.201522\pi\) | |||||||
\(422\) | −4190.40 | − | 7257.98i | −0.483378 | − | 0.837234i | ||||
\(423\) | −1857.11 | − | 3216.61i | −0.213465 | − | 0.369733i | ||||
\(424\) | −29717.1 | −3.40375 | ||||||||
\(425\) | −479.507 | − | 830.531i | −0.0547283 | − | 0.0947922i | ||||
\(426\) | 12654.3 | − | 21917.8i | 1.43920 | − | 2.49277i | ||||
\(427\) | −401.787 | + | 695.916i | −0.0455360 | + | 0.0788706i | ||||
\(428\) | −5251.68 | −0.593106 | ||||||||
\(429\) | −8613.24 | − | 10201.5i | −0.969350 | − | 1.14810i | ||||
\(430\) | −1797.92 | −0.201636 | ||||||||
\(431\) | 4776.87 | − | 8273.78i | 0.533860 | − | 0.924673i | −0.465357 | − | 0.885123i | \(-0.654074\pi\) |
0.999218 | − | 0.0395500i | \(-0.0125924\pi\) | |||||||
\(432\) | 1749.15 | − | 3029.61i | 0.194805 | − | 0.337412i | ||||
\(433\) | 1273.19 | + | 2205.22i | 0.141306 | + | 0.244749i | 0.927989 | − | 0.372609i | \(-0.121537\pi\) |
−0.786683 | + | 0.617357i | \(0.788203\pi\) | |||||||
\(434\) | 4525.62 | 0.500546 | ||||||||
\(435\) | −3344.24 | − | 5792.40i | −0.368607 | − | 0.638446i | ||||
\(436\) | 6120.61 | + | 10601.2i | 0.672303 | + | 1.16446i | ||||
\(437\) | 19998.1 | 2.18911 | ||||||||
\(438\) | −2391.76 | − | 4142.65i | −0.260920 | − | 0.451926i | ||||
\(439\) | 7907.04 | − | 13695.4i | 0.859641 | − | 1.48894i | −0.0126310 | − | 0.999920i | \(-0.504021\pi\) |
0.872272 | − | 0.489021i | \(-0.162646\pi\) | |||||||
\(440\) | 4145.68 | − | 7180.54i | 0.449177 | − | 0.777997i | ||||
\(441\) | −6044.86 | −0.652722 | ||||||||
\(442\) | 8681.08 | − | 1558.03i | 0.934201 | − | 0.167664i | ||||
\(443\) | −10518.3 | −1.12808 | −0.564039 | − | 0.825748i | \(-0.690753\pi\) | ||||
−0.564039 | + | 0.825748i | \(0.690753\pi\) | |||||||
\(444\) | −17097.3 | + | 29613.4i | −1.82748 | + | 3.16530i | ||||
\(445\) | 370.009 | − | 640.874i | 0.0394159 | − | 0.0682704i | ||||
\(446\) | −3970.83 | − | 6877.67i | −0.421579 | − | 0.730195i | ||||
\(447\) | 16495.5 | 1.74544 | ||||||||
\(448\) | −1300.91 | − | 2253.24i | −0.137192 | − | 0.237624i | ||||
\(449\) | −7146.12 | − | 12377.4i | −0.751105 | − | 1.30095i | −0.947287 | − | 0.320385i | \(-0.896188\pi\) |
0.196182 | − | 0.980567i | \(-0.437146\pi\) | |||||||
\(450\) | 2346.29 | 0.245789 | ||||||||
\(451\) | −3023.24 | − | 5236.41i | −0.315652 | − | 0.546725i | ||||
\(452\) | −14491.7 | + | 25100.4i | −1.50804 | + | 2.61199i | ||||
\(453\) | −2980.06 | + | 5161.61i | −0.309085 | + | 0.535350i | ||||
\(454\) | 25082.2 | 2.59288 | ||||||||
\(455\) | −786.509 | − | 931.540i | −0.0810376 | − | 0.0959808i | ||||
\(456\) | 36318.5 | 3.72975 | ||||||||
\(457\) | −5794.14 | + | 10035.7i | −0.593082 | + | 1.02725i | 0.400732 | + | 0.916195i | \(0.368756\pi\) |
−0.993814 | + | 0.111053i | \(0.964578\pi\) | |||||||
\(458\) | −475.815 | + | 824.136i | −0.0485445 | + | 0.0840815i | ||||
\(459\) | 1024.87 | + | 1775.13i | 0.104220 | + | 0.180514i | ||||
\(460\) | −11875.9 | −1.20373 | ||||||||
\(461\) | 1357.61 | + | 2351.45i | 0.137159 | + | 0.237566i | 0.926420 | − | 0.376492i | \(-0.122870\pi\) |
−0.789261 | + | 0.614057i | \(0.789536\pi\) | |||||||
\(462\) | 3634.26 | + | 6294.72i | 0.365976 | + | 0.633889i | ||||
\(463\) | 3749.77 | 0.376386 | 0.188193 | − | 0.982132i | \(-0.439737\pi\) | ||||
0.188193 | + | 0.982132i | \(0.439737\pi\) | |||||||
\(464\) | 6447.10 | + | 11166.7i | 0.645041 | + | 1.11724i | ||||
\(465\) | −3011.54 | + | 5216.15i | −0.300338 | + | 0.520200i | ||||
\(466\) | 945.687 | − | 1637.98i | 0.0940088 | − | 0.162828i | ||||
\(467\) | −5440.29 | −0.539071 | −0.269536 | − | 0.962990i | \(-0.586870\pi\) | ||||
−0.269536 | + | 0.962990i | \(0.586870\pi\) | |||||||
\(468\) | −4885.05 | + | 13550.0i | −0.482503 | + | 1.33835i | ||||
\(469\) | −4412.53 | −0.434439 | ||||||||
\(470\) | 2380.57 | − | 4123.28i | 0.233633 | − | 0.404665i | ||||
\(471\) | 6660.10 | − | 11535.6i | 0.651553 | − | 1.12852i | ||||
\(472\) | 8954.38 | + | 15509.4i | 0.873218 | + | 1.51246i | ||||
\(473\) | 3074.30 | 0.298851 | ||||||||
\(474\) | 2227.90 | + | 3858.83i | 0.215887 | + | 0.373928i | ||||
\(475\) | −1690.36 | − | 2927.79i | −0.163282 | − | 0.282813i | ||||
\(476\) | −3205.07 | −0.308623 | ||||||||
\(477\) | 7189.67 | + | 12452.9i | 0.690131 | + | 1.19534i | ||||
\(478\) | 7215.52 | − | 12497.6i | 0.690439 | − | 1.19588i | ||||
\(479\) | 9431.46 | − | 16335.8i | 0.899655 | − | 1.55825i | 0.0717187 | − | 0.997425i | \(-0.477152\pi\) |
0.827936 | − | 0.560823i | \(-0.189515\pi\) | |||||||
\(480\) | −163.469 | −0.0155444 | ||||||||
\(481\) | −4982.95 | + | 13821.6i | −0.472356 | + | 1.31021i | ||||
\(482\) | −19686.1 | −1.86033 | ||||||||
\(483\) | 2612.60 | − | 4525.16i | 0.246123 | − | 0.426298i | ||||
\(484\) | −3435.22 | + | 5949.97i | −0.322616 | + | 0.558788i | ||||
\(485\) | −1238.96 | − | 2145.94i | −0.115997 | − | 0.200912i | ||||
\(486\) | −22226.0 | −2.07447 | ||||||||
\(487\) | −3394.98 | − | 5880.28i | −0.315896 | − | 0.547148i | 0.663731 | − | 0.747971i | \(-0.268972\pi\) |
−0.979628 | + | 0.200823i | \(0.935638\pi\) | |||||||
\(488\) | 3054.01 | + | 5289.70i | 0.283296 | + | 0.490684i | ||||
\(489\) | −10861.5 | −1.00445 | ||||||||
\(490\) | −3874.36 | − | 6710.59i | −0.357195 | − | 0.618681i | ||||
\(491\) | −1157.76 | + | 2005.30i | −0.106413 | + | 0.184313i | −0.914315 | − | 0.405004i | \(-0.867270\pi\) |
0.807902 | + | 0.589318i | \(0.200603\pi\) | |||||||
\(492\) | −7864.12 | + | 13621.0i | −0.720613 | + | 1.24814i | ||||
\(493\) | −7555.04 | −0.690187 | ||||||||
\(494\) | 30602.6 | − | 5492.36i | 2.78720 | − | 0.500228i | ||||
\(495\) | −4011.98 | −0.364293 | ||||||||
\(496\) | 5805.72 | − | 10055.8i | 0.525573 | − | 0.910320i | ||||
\(497\) | −1975.83 | + | 3422.25i | −0.178327 | + | 0.308871i | ||||
\(498\) | 10126.1 | + | 17538.8i | 0.911163 | + | 1.57818i | ||||
\(499\) | −19441.3 | −1.74411 | −0.872056 | − | 0.489407i | \(-0.837213\pi\) | ||||
−0.872056 | + | 0.489407i | \(0.837213\pi\) | |||||||
\(500\) | 1003.82 | + | 1738.66i | 0.0897843 | + | 0.155511i | ||||
\(501\) | 190.576 | + | 330.088i | 0.0169946 | + | 0.0294356i | ||||
\(502\) | 13212.7 | 1.17473 | ||||||||
\(503\) | 495.628 | + | 858.453i | 0.0439343 | + | 0.0760965i | 0.887156 | − | 0.461469i | \(-0.152677\pi\) |
−0.843222 | + | 0.537565i | \(0.819344\pi\) | |||||||
\(504\) | 1967.81 | − | 3408.35i | 0.173915 | − | 0.301230i | ||||
\(505\) | 1287.89 | − | 2230.69i | 0.113486 | − | 0.196563i | ||||
\(506\) | 30421.6 | 2.67274 | ||||||||
\(507\) | −2501.54 | + | 14711.1i | −0.219127 | + | 1.28865i | ||||
\(508\) | −42446.4 | −3.70720 | ||||||||
\(509\) | −10.9670 | + | 18.9953i | −0.000955014 | + | 0.00165413i | −0.866503 | − | 0.499173i | \(-0.833637\pi\) |
0.865548 | + | 0.500827i | \(0.166971\pi\) | |||||||
\(510\) | 3195.13 | − | 5534.13i | 0.277417 | − | 0.480501i | ||||
\(511\) | 373.449 | + | 646.833i | 0.0323296 | + | 0.0559965i | ||||
\(512\) | −20395.1 | −1.76044 | ||||||||
\(513\) | 3612.87 | + | 6257.68i | 0.310940 | + | 0.538564i | ||||
\(514\) | −8858.54 | − | 15343.4i | −0.760181 | − | 1.31667i | ||||
\(515\) | −704.785 | −0.0603040 | ||||||||
\(516\) | −3998.47 | − | 6925.54i | −0.341129 | − | 0.590853i | ||||
\(517\) | −4070.60 | + | 7050.49i | −0.346276 | + | 0.599768i | ||||
\(518\) | 3999.28 | − | 6926.96i | 0.339225 | − | 0.587554i | ||||
\(519\) | −24941.1 | −2.10943 | ||||||||
\(520\) | −9121.22 | + | 1637.02i | −0.769215 | + | 0.138054i | ||||
\(521\) | 4649.64 | 0.390987 | 0.195494 | − | 0.980705i | \(-0.437369\pi\) | ||||
0.195494 | + | 0.980705i | \(0.437369\pi\) | |||||||
\(522\) | 9241.94 | − | 16007.5i | 0.774921 | − | 1.34220i | ||||
\(523\) | 2344.42 | − | 4060.66i | 0.196012 | − | 0.339503i | −0.751220 | − | 0.660052i | \(-0.770534\pi\) |
0.947232 | + | 0.320549i | \(0.103867\pi\) | |||||||
\(524\) | 3757.18 | + | 6507.62i | 0.313231 | + | 0.542532i | ||||
\(525\) | −883.331 | −0.0734319 | ||||||||
\(526\) | −4747.95 | − | 8223.69i | −0.393575 | − | 0.681692i | ||||
\(527\) | 3401.72 | + | 5891.95i | 0.281179 | + | 0.487016i | ||||
\(528\) | 18648.9 | 1.53710 | ||||||||
\(529\) | −4851.28 | − | 8402.66i | −0.398724 | − | 0.690611i | ||||
\(530\) | −9216.22 | + | 15963.0i | −0.755334 | + | 1.30828i | ||||
\(531\) | 4332.79 | − | 7504.61i | 0.354100 | − | 0.613319i | ||||
\(532\) | −11298.5 | −0.920778 | ||||||||
\(533\) | −2291.97 | + | 6357.40i | −0.186259 | + | 0.516641i | ||||
\(534\) | 4931.01 | 0.399598 | ||||||||
\(535\) | −817.453 | + | 1415.87i | −0.0660591 | + | 0.114418i | ||||
\(536\) | −16770.0 | + | 29046.4i | −1.35140 | + | 2.34070i | ||||
\(537\) | −12696.9 | − | 21991.7i | −1.02032 | − | 1.76725i | ||||
\(538\) | −1164.61 | −0.0933272 | ||||||||
\(539\) | 6624.86 | + | 11474.6i | 0.529412 | + | 0.916968i | ||||
\(540\) | −2145.50 | − | 3716.11i | −0.170977 | − | 0.296141i | ||||
\(541\) | 14821.9 | 1.17790 | 0.588949 | − | 0.808170i | \(-0.299542\pi\) | ||||
0.588949 | + | 0.808170i | \(0.299542\pi\) | |||||||
\(542\) | −6267.38 | − | 10855.4i | −0.496692 | − | 0.860296i | ||||
\(543\) | −6115.93 | + | 10593.1i | −0.483351 | + | 0.837188i | ||||
\(544\) | −92.3242 | + | 159.910i | −0.00727641 | + | 0.0126031i | ||||
\(545\) | 3810.83 | 0.299519 | ||||||||
\(546\) | 2755.19 | − | 7642.26i | 0.215955 | − | 0.599009i | ||||
\(547\) | 8989.48 | 0.702673 | 0.351337 | − | 0.936249i | \(-0.385727\pi\) | ||||
0.351337 | + | 0.936249i | \(0.385727\pi\) | |||||||
\(548\) | 11312.7 | − | 19594.2i | 0.881855 | − | 1.52742i | ||||
\(549\) | 1477.76 | − | 2559.55i | 0.114880 | − | 0.198978i | ||||
\(550\) | −2571.41 | − | 4453.82i | −0.199355 | − | 0.345294i | ||||
\(551\) | −26633.1 | −2.05918 | ||||||||
\(552\) | −19858.6 | − | 34396.0i | −1.53123 | − | 2.65216i | ||||
\(553\) | −347.863 | − | 602.517i | −0.0267498 | − | 0.0463321i | ||||
\(554\) | 25444.8 | 1.95135 | ||||||||
\(555\) | 5322.59 | + | 9218.99i | 0.407083 | + | 0.705089i | ||||
\(556\) | 13196.0 | − | 22856.1i | 1.00653 | − | 1.74337i | ||||
\(557\) | 7720.12 | − | 13371.6i | 0.587275 | − | 1.01719i | −0.407313 | − | 0.913289i | \(-0.633534\pi\) |
0.994588 | − | 0.103901i | \(-0.0331325\pi\) | |||||||
\(558\) | −16645.0 | −1.26280 | ||||||||
\(559\) | −2216.66 | − | 2625.40i | −0.167718 | − | 0.198645i | ||||
\(560\) | 1702.91 | 0.128502 | ||||||||
\(561\) | −5463.43 | + | 9462.95i | −0.411170 | + | 0.712167i | ||||
\(562\) | −12626.3 | + | 21869.4i | −0.947704 | + | 1.64147i | ||||
\(563\) | −1781.58 | − | 3085.79i | −0.133365 | − | 0.230995i | 0.791607 | − | 0.611031i | \(-0.209245\pi\) |
−0.924972 | + | 0.380036i | \(0.875912\pi\) | |||||||
\(564\) | 21177.0 | 1.58105 | ||||||||
\(565\) | 4511.43 | + | 7814.02i | 0.335924 | + | 0.581838i | ||||
\(566\) | 5624.40 | + | 9741.75i | 0.417688 | + | 0.723457i | ||||
\(567\) | 4575.33 | 0.338882 | ||||||||
\(568\) | 15018.4 | + | 26012.7i | 1.10944 | + | 1.92160i | ||||
\(569\) | −8271.49 | + | 14326.6i | −0.609418 | + | 1.05554i | 0.381918 | + | 0.924196i | \(0.375264\pi\) |
−0.991336 | + | 0.131347i | \(0.958070\pi\) | |||||||
\(570\) | 11263.5 | − | 19509.0i | 0.827677 | − | 1.43358i | ||||
\(571\) | −596.812 | −0.0437404 | −0.0218702 | − | 0.999761i | \(-0.506962\pi\) | ||||
−0.0218702 | + | 0.999761i | \(0.506962\pi\) | |||||||
\(572\) | 31074.9 | − | 5577.13i | 2.27152 | − | 0.407678i | ||||
\(573\) | −1572.95 | −0.114678 | ||||||||
\(574\) | 1839.52 | − | 3186.14i | 0.133763 | − | 0.231684i | ||||
\(575\) | −1848.54 | + | 3201.77i | −0.134069 | + | 0.232214i | ||||
\(576\) | 4784.69 | + | 8287.33i | 0.346115 | + | 0.599488i | ||||
\(577\) | 4462.98 | 0.322004 | 0.161002 | − | 0.986954i | \(-0.448528\pi\) | ||||
0.161002 | + | 0.986954i | \(0.448528\pi\) | |||||||
\(578\) | 8440.56 | + | 14619.5i | 0.607406 | + | 1.05206i | ||||
\(579\) | −7449.03 | − | 12902.1i | −0.534665 | − | 0.926067i | ||||
\(580\) | 15816.0 | 1.13228 | ||||||||
\(581\) | −1581.08 | − | 2738.51i | −0.112899 | − | 0.195547i | ||||
\(582\) | 8255.65 | − | 14299.2i | 0.587986 | − | 1.01842i | ||||
\(583\) | 15759.0 | − | 27295.4i | 1.11951 | − | 1.93904i | ||||
\(584\) | 5677.23 | 0.402269 | ||||||||
\(585\) | 2892.75 | + | 3426.16i | 0.204445 | + | 0.242144i | ||||
\(586\) | 21911.2 | 1.54461 | ||||||||
\(587\) | 3818.39 | − | 6613.64i | 0.268487 | − | 0.465033i | −0.699984 | − | 0.714158i | \(-0.746810\pi\) |
0.968471 | + | 0.249125i | \(0.0801431\pi\) | |||||||
\(588\) | 17232.7 | − | 29847.9i | 1.20861 | − | 2.09338i | ||||
\(589\) | 11991.8 | + | 20770.3i | 0.838899 | + | 1.45302i | ||||
\(590\) | 11108.1 | 0.775110 | ||||||||
\(591\) | −9962.01 | − | 17254.7i | −0.693371 | − | 1.20095i | ||||
\(592\) | −10261.0 | − | 17772.6i | −0.712373 | − | 1.23387i | ||||
\(593\) | 20911.9 | 1.44814 | 0.724070 | − | 0.689726i | \(-0.242269\pi\) | ||||
0.724070 | + | 0.689726i | \(0.242269\pi\) | |||||||
\(594\) | 5495.98 | + | 9519.32i | 0.379634 | + | 0.657546i | ||||
\(595\) | −498.888 | + | 864.099i | −0.0343738 | + | 0.0595372i | ||||
\(596\) | −19503.2 | + | 33780.5i | −1.34040 | + | 2.32165i | ||||
\(597\) | −20793.6 | −1.42550 | ||||||||
\(598\) | −21934.8 | − | 25979.6i | −1.49997 | − | 1.77656i | ||||
\(599\) | 7395.85 | 0.504485 | 0.252242 | − | 0.967664i | \(-0.418832\pi\) | ||||
0.252242 | + | 0.967664i | \(0.418832\pi\) | |||||||
\(600\) | −3357.13 | + | 5814.72i | −0.228424 | + | 0.395641i | ||||
\(601\) | −6668.34 | + | 11549.9i | −0.452591 | + | 0.783911i | −0.998546 | − | 0.0539039i | \(-0.982834\pi\) |
0.545955 | + | 0.837814i | \(0.316167\pi\) | |||||||
\(602\) | 935.292 | + | 1619.97i | 0.0633217 | + | 0.109676i | ||||
\(603\) | 16229.1 | 1.09602 | ||||||||
\(604\) | −7046.83 | − | 12205.5i | −0.474721 | − | 0.822241i | ||||
\(605\) | 1069.42 | + | 1852.29i | 0.0718648 | + | 0.124473i | ||||
\(606\) | 17163.4 | 1.15052 | ||||||||
\(607\) | 12797.2 | + | 22165.3i | 0.855718 | + | 1.48215i | 0.875977 | + | 0.482352i | \(0.160217\pi\) |
−0.0202594 | + | 0.999795i | \(0.506449\pi\) | |||||||
\(608\) | −325.462 | + | 563.716i | −0.0217092 | + | 0.0376015i | ||||
\(609\) | −3479.41 | + | 6026.51i | −0.231515 | + | 0.400996i | ||||
\(610\) | 3788.58 | 0.251467 | ||||||||
\(611\) | 8956.02 | − | 1607.37i | 0.592998 | − | 0.106427i | ||||
\(612\) | 11788.1 | 0.778605 | ||||||||
\(613\) | 11104.0 | − | 19232.6i | 0.731623 | − | 1.26721i | −0.224566 | − | 0.974459i | \(-0.572097\pi\) |
0.956189 | − | 0.292749i | \(-0.0945701\pi\) | |||||||
\(614\) | −10929.7 | + | 18930.7i | −0.718380 | + | 1.24427i | ||||
\(615\) | 2448.19 | + | 4240.38i | 0.160521 | + | 0.278031i | ||||
\(616\) | −8626.48 | −0.564239 | ||||||||
\(617\) | 107.676 | + | 186.500i | 0.00702571 | + | 0.0121689i | 0.869517 | − | 0.493903i | \(-0.164430\pi\) |
−0.862491 | + | 0.506072i | \(0.831097\pi\) | |||||||
\(618\) | −2348.12 | − | 4067.07i | −0.152840 | − | 0.264727i | ||||
\(619\) | −26851.4 | −1.74353 | −0.871767 | − | 0.489921i | \(-0.837026\pi\) | ||||
−0.871767 | + | 0.489921i | \(0.837026\pi\) | |||||||
\(620\) | −7121.28 | − | 12334.4i | −0.461286 | − | 0.798972i | ||||
\(621\) | 3950.96 | − | 6843.27i | 0.255309 | − | 0.442208i | ||||
\(622\) | −13125.2 | + | 22733.5i | −0.846098 | + | 1.46549i | ||||
\(623\) | −769.927 | −0.0495128 | ||||||||
\(624\) | −13446.4 | − | 15925.9i | −0.862638 | − | 1.02171i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −20187.9 | + | 34966.4i | −1.28893 | + | 2.23249i | ||||
\(627\) | −19259.7 | + | 33358.8i | −1.22673 | + | 2.12476i | ||||
\(628\) | 15748.9 | + | 27277.9i | 1.00072 | + | 1.73329i | ||||
\(629\) | 12024.4 | 0.762230 | ||||||||
\(630\) | −1220.56 | − | 2114.07i | −0.0771877 | − | 0.133693i | ||||
\(631\) | −12877.7 | − | 22304.8i | −0.812446 | − | 1.40720i | −0.911148 | − | 0.412080i | \(-0.864802\pi\) |
0.0987017 | − | 0.995117i | \(-0.468531\pi\) | |||||||
\(632\) | −5288.26 | −0.332841 | ||||||||
\(633\) | −5802.34 | − | 10050.0i | −0.364332 | − | 0.631042i | ||||
\(634\) | 12689.5 | − | 21978.9i | 0.794897 | − | 1.37680i | ||||
\(635\) | −6607.02 | + | 11443.7i | −0.412900 | + | 0.715164i | ||||
\(636\) | −81985.3 | −5.11153 | ||||||||
\(637\) | 5022.41 | − | 13931.0i | 0.312394 | − | 0.866510i | ||||
\(638\) | −40514.8 | −2.51410 | ||||||||
\(639\) | 7267.03 | − | 12586.9i | 0.449889 | − | 0.779231i | ||||
\(640\) | −6229.62 | + | 10790.0i | −0.384761 | + | 0.666426i | ||||
\(641\) | −9471.69 | − | 16405.4i | −0.583634 | − | 1.01088i | −0.995044 | − | 0.0994332i | \(-0.968297\pi\) |
0.411410 | − | 0.911450i | \(-0.365036\pi\) | |||||||
\(642\) | −10894.0 | −0.669706 | ||||||||
\(643\) | −758.843 | − | 1314.35i | −0.0465410 | − | 0.0806113i | 0.841816 | − | 0.539764i | \(-0.181486\pi\) |
−0.888357 | + | 0.459153i | \(0.848153\pi\) | |||||||
\(644\) | 6177.93 | + | 10700.5i | 0.378019 | + | 0.654749i | ||||
\(645\) | −2489.53 | −0.151977 | ||||||||
\(646\) | −12722.8 | − | 22036.5i | −0.774879 | − | 1.34213i | ||||
\(647\) | 4795.78 | − | 8306.54i | 0.291409 | − | 0.504735i | −0.682734 | − | 0.730667i | \(-0.739209\pi\) |
0.974143 | + | 0.225932i | \(0.0725426\pi\) | |||||||
\(648\) | 17388.7 | − | 30118.1i | 1.05416 | − | 1.82585i | ||||
\(649\) | −18994.1 | −1.14882 | ||||||||
\(650\) | −1949.43 | + | 5407.27i | −0.117635 | + | 0.326293i | ||||
\(651\) | 6266.52 | 0.377272 | ||||||||
\(652\) | 12841.9 | − | 22242.9i | 0.771364 | − | 1.33604i | ||||
\(653\) | −8161.11 | + | 14135.5i | −0.489079 | + | 0.847110i | −0.999921 | − | 0.0125644i | \(-0.996001\pi\) |
0.510842 | + | 0.859675i | \(0.329334\pi\) | |||||||
\(654\) | 12696.5 | + | 21990.9i | 0.759131 | + | 1.31485i | ||||
\(655\) | 2339.30 | 0.139548 | ||||||||
\(656\) | −4719.67 | − | 8174.71i | −0.280903 | − | 0.486538i | ||||
\(657\) | −1373.53 | − | 2379.02i | −0.0815624 | − | 0.141270i | ||||
\(658\) | −4953.58 | −0.293481 | ||||||||
\(659\) | 8149.60 | + | 14115.5i | 0.481735 | + | 0.834389i | 0.999780 | − | 0.0209640i | \(-0.00667354\pi\) |
−0.518045 | + | 0.855353i | \(0.673340\pi\) | |||||||
\(660\) | 11437.4 | − | 19810.1i | 0.674543 | − | 1.16834i | ||||
\(661\) | −3890.65 | + | 6738.80i | −0.228939 | + | 0.396534i | −0.957494 | − | 0.288453i | \(-0.906859\pi\) |
0.728555 | + | 0.684987i | \(0.240192\pi\) | |||||||
\(662\) | 13288.6 | 0.780175 | ||||||||
\(663\) | 12020.5 | − | 2157.36i | 0.704128 | − | 0.126372i | ||||
\(664\) | −24035.8 | −1.40477 | ||||||||
\(665\) | −1758.68 | + | 3046.13i | −0.102554 | + | 0.177630i | ||||
\(666\) | −14709.2 | + | 25477.0i | −0.855810 | + | 1.48231i | ||||
\(667\) | 14562.7 | + | 25223.3i | 0.845382 | + | 1.46424i | ||||
\(668\) | −901.297 | −0.0522039 | ||||||||
\(669\) | −5498.31 | − | 9523.35i | −0.317753 | − | 0.550365i | ||||
\(670\) | 10401.8 | + | 18016.4i | 0.599785 | + | 1.03886i | ||||
\(671\) | −6478.18 | −0.372709 | ||||||||
\(672\) | 85.0381 | + | 147.290i | 0.00488157 | + | 0.00845513i | ||||
\(673\) | −14995.3 | + | 25972.7i | −0.858882 | + | 1.48763i | 0.0141152 | + | 0.999900i | \(0.495507\pi\) |
−0.872997 | + | 0.487726i | \(0.837826\pi\) | |||||||
\(674\) | 3161.40 | − | 5475.70i | 0.180671 | − | 0.312932i | ||||
\(675\) | −1335.84 | −0.0761724 | ||||||||
\(676\) | −27168.7 | − | 22516.2i | −1.54578 | − | 1.28108i | ||||
\(677\) | 17816.3 | 1.01143 | 0.505714 | − | 0.862701i | \(-0.331229\pi\) | ||||
0.505714 | + | 0.862701i | \(0.331229\pi\) | |||||||
\(678\) | −30061.3 | + | 52067.7i | −1.70280 | + | 2.94933i | ||||
\(679\) | −1289.04 | + | 2232.68i | −0.0728552 | + | 0.126189i | ||||
\(680\) | 3792.08 | + | 6568.07i | 0.213852 | + | 0.370403i | ||||
\(681\) | 34730.8 | 1.95431 | ||||||||
\(682\) | 18242.1 | + | 31596.3i | 1.02423 | + | 1.77402i | ||||
\(683\) | 13584.1 | + | 23528.3i | 0.761024 | + | 1.31813i | 0.942323 | + | 0.334705i | \(0.108637\pi\) |
−0.181299 | + | 0.983428i | \(0.558030\pi\) | |||||||
\(684\) | 41555.5 | 2.32298 | ||||||||
\(685\) | −3521.78 | − | 6099.91i | −0.196439 | − | 0.340242i | ||||
\(686\) | −8407.17 | + | 14561.7i | −0.467912 | + | 0.810447i | ||||
\(687\) | −658.850 | + | 1141.16i | −0.0365891 | + | 0.0633741i | ||||
\(688\) | 4799.38 | 0.265951 | ||||||||
\(689\) | −34672.5 | + | 6222.81i | −1.91715 | + | 0.344078i | ||||
\(690\) | −24635.1 | −1.35919 | ||||||||
\(691\) | −12073.4 | + | 20911.7i | −0.664680 | + | 1.15126i | 0.314692 | + | 0.949194i | \(0.398099\pi\) |
−0.979372 | + | 0.202065i | \(0.935235\pi\) | |||||||
\(692\) | 29488.6 | − | 51075.8i | 1.61993 | − | 2.80580i | ||||
\(693\) | 2087.06 | + | 3614.90i | 0.114403 | + | 0.198151i | ||||
\(694\) | −43868.7 | −2.39947 | ||||||||
\(695\) | −4108.05 | − | 7115.35i | −0.224212 | − | 0.388346i | ||||
\(696\) | 26447.2 | + | 45807.9i | 1.44034 | + | 2.49475i | ||||
\(697\) | 5530.75 | 0.300562 | ||||||||
\(698\) | −4176.70 | − | 7234.25i | −0.226490 | − | 0.392293i | ||||
\(699\) | 1309.47 | − | 2268.07i | 0.0708565 | − | 0.122727i | ||||
\(700\) | 1044.39 | − | 1808.94i | 0.0563918 | − | 0.0976734i | ||||
\(701\) | 22270.2 | 1.19991 | 0.599953 | − | 0.800035i | \(-0.295186\pi\) | ||||
0.599953 | + | 0.800035i | \(0.295186\pi\) | |||||||
\(702\) | 4166.59 | − | 11557.2i | 0.224014 | − | 0.621364i | ||||
\(703\) | 42388.3 | 2.27412 | ||||||||
\(704\) | 10487.6 | − | 18165.0i | 0.561455 | − | 0.972469i | ||||
\(705\) | 3296.33 | − | 5709.40i | 0.176095 | − | 0.305005i | ||||
\(706\) | 14310.6 | + | 24786.7i | 0.762871 | + | 1.32133i | ||||
\(707\) | −2679.88 | −0.142556 | ||||||||
\(708\) | 24703.9 | + | 42788.4i | 1.31134 | + | 2.27131i | ||||
\(709\) | −1811.20 | − | 3137.09i | −0.0959393 | − | 0.166172i | 0.814061 | − | 0.580779i | \(-0.197252\pi\) |
−0.910000 | + | 0.414608i | \(0.863919\pi\) | |||||||
\(710\) | 18630.8 | 0.984789 | ||||||||
\(711\) | 1279.43 | + | 2216.03i | 0.0674855 | + | 0.116888i | ||||
\(712\) | −2926.13 | + | 5068.21i | −0.154019 | + | 0.266768i | ||||
\(713\) | 13113.9 | − | 22714.0i | 0.688809 | − | 1.19305i | ||||
\(714\) | −6648.55 | −0.348481 | ||||||||
\(715\) | 3333.38 | − | 9246.02i | 0.174351 | − | 0.483611i | ||||
\(716\) | 60047.8 | 3.13420 | ||||||||
\(717\) | 9991.15 | − | 17305.2i | 0.520400 | − | 0.901359i | ||||
\(718\) | 27506.8 | − | 47643.1i | 1.42973 | − | 2.47636i | ||||
\(719\) | −6465.05 | − | 11197.8i | −0.335335 | − | 0.580817i | 0.648214 | − | 0.761458i | \(-0.275516\pi\) |
−0.983549 | + | 0.180641i | \(0.942183\pi\) | |||||||
\(720\) | −6263.21 | −0.324189 | ||||||||
\(721\) | 366.635 | + | 635.031i | 0.0189379 | + | 0.0328014i | ||||
\(722\) | −28028.0 | − | 48546.0i | −1.44473 | − | 2.50235i | ||||
\(723\) | −27258.9 | −1.40217 | ||||||||
\(724\) | −14462.1 | − | 25049.1i | −0.742375 | − | 1.28583i | ||||
\(725\) | 2461.85 | − | 4264.05i | 0.126111 | − | 0.218431i | ||||
\(726\) | −7125.95 | + | 12342.5i | −0.364282 | + | 0.630955i | ||||
\(727\) | −21574.3 | −1.10061 | −0.550307 | − | 0.834962i | \(-0.685489\pi\) | ||||
−0.550307 | + | 0.834962i | \(0.685489\pi\) | |||||||
\(728\) | 6219.93 | + | 7366.88i | 0.316657 | + | 0.375048i | ||||
\(729\) | −7028.84 | −0.357102 | ||||||||
\(730\) | 1760.69 | − | 3049.60i | 0.0892684 | − | 0.154617i | ||||
\(731\) | −1406.04 | + | 2435.33i | −0.0711412 | + | 0.123220i | ||||
\(732\) | 8425.59 | + | 14593.5i | 0.425435 | + | 0.736875i | ||||
\(733\) | −17320.0 | −0.872754 | −0.436377 | − | 0.899764i | \(-0.643739\pi\) | ||||
−0.436377 | + | 0.899764i | \(0.643739\pi\) | |||||||
\(734\) | −15813.2 | − | 27389.3i | −0.795201 | − | 1.37733i | ||||
\(735\) | −5364.74 | − | 9291.99i | −0.269226 | − | 0.466313i | ||||
\(736\) | 711.836 | 0.0356503 | ||||||||
\(737\) | −17786.3 | − | 30806.7i | −0.888963 | − | 1.53973i | ||||
\(738\) | −6765.66 | + | 11718.5i | −0.337463 | + | 0.584502i | ||||
\(739\) | −5485.97 | + | 9501.97i | −0.273078 | + | 0.472985i | −0.969648 | − | 0.244504i | \(-0.921375\pi\) |
0.696571 | + | 0.717488i | \(0.254708\pi\) | |||||||
\(740\) | −25172.3 | −1.25047 | ||||||||
\(741\) | 42374.7 | − | 7605.14i | 2.10077 | − | 0.377033i | ||||
\(742\) | 19177.4 | 0.948821 | ||||||||
\(743\) | −5775.29 | + | 10003.1i | −0.285161 | + | 0.493914i | −0.972648 | − | 0.232283i | \(-0.925380\pi\) |
0.687487 | + | 0.726197i | \(0.258714\pi\) | |||||||
\(744\) | 23816.1 | − | 41250.7i | 1.17358 | − | 2.03269i | ||||
\(745\) | 6071.56 | + | 10516.2i | 0.298583 | + | 0.517162i | ||||
\(746\) | −18880.6 | −0.926634 | ||||||||
\(747\) | 5815.14 | + | 10072.1i | 0.284826 | + | 0.493333i | ||||
\(748\) | −12919.2 | − | 22376.7i | −0.631513 | − | 1.09381i | ||||
\(749\) | 1700.99 | 0.0829808 | ||||||||
\(750\) | 2082.30 | + | 3606.65i | 0.101380 | + | 0.175595i | ||||
\(751\) | −10036.4 | + | 17383.5i | −0.487659 | + | 0.844650i | −0.999899 | − | 0.0141921i | \(-0.995482\pi\) |
0.512240 | + | 0.858842i | \(0.328816\pi\) | |||||||
\(752\) | −6354.73 | + | 11006.7i | −0.308156 | + | 0.533741i | ||||
\(753\) | 18295.4 | 0.885419 | ||||||||
\(754\) | 29212.3 | + | 34599.0i | 1.41094 | + | 1.67111i | ||||
\(755\) | −4387.52 | −0.211494 | ||||||||
\(756\) | −2232.21 | + | 3866.31i | −0.107387 | + | 0.186000i | ||||
\(757\) | 5686.88 | − | 9849.97i | 0.273043 | − | 0.472924i | −0.696597 | − | 0.717463i | \(-0.745303\pi\) |
0.969639 | + | 0.244539i | \(0.0786366\pi\) | |||||||
\(758\) | −21781.1 | − | 37726.0i | −1.04370 | − | 1.80774i | ||||
\(759\) | 42124.1 | 2.01450 | ||||||||
\(760\) | 13367.8 | + | 23153.8i | 0.638030 | + | 1.10510i | ||||
\(761\) | 566.510 | + | 981.223i | 0.0269855 | + | 0.0467402i | 0.879203 | − | 0.476448i | \(-0.158076\pi\) |
−0.852217 | + | 0.523188i | \(0.824743\pi\) | |||||||
\(762\) | −88050.1 | −4.18598 | ||||||||
\(763\) | −1982.43 | − | 3433.66i | −0.0940611 | − | 0.162919i | ||||
\(764\) | 1859.74 | − | 3221.17i | 0.0880669 | − | 0.152536i | ||||
\(765\) | 1834.89 | − | 3178.12i | 0.0867196 | − | 0.150203i | ||||
\(766\) | 21078.1 | 0.994231 | ||||||||
\(767\) | 13695.3 | + | 16220.6i | 0.644729 | + | 0.763616i | ||||
\(768\) | −55843.8 | −2.62381 | ||||||||
\(769\) | 10105.7 | − | 17503.6i | 0.473889 | − | 0.820800i | −0.525664 | − | 0.850692i | \(-0.676183\pi\) |
0.999553 | + | 0.0298925i | \(0.00951650\pi\) | |||||||
\(770\) | −2675.34 | + | 4633.83i | −0.125211 | + | 0.216872i | ||||
\(771\) | −12266.2 | − | 21245.7i | −0.572966 | − | 0.992406i | ||||
\(772\) | 35228.9 | 1.64238 | ||||||||
\(773\) | 3787.65 | + | 6560.41i | 0.176239 | + | 0.305254i | 0.940589 | − | 0.339547i | \(-0.110274\pi\) |
−0.764351 | + | 0.644801i | \(0.776940\pi\) | |||||||
\(774\) | −3439.96 | − | 5958.19i | −0.159751 | − | 0.276696i | ||||
\(775\) | −4433.87 | −0.205509 | ||||||||
\(776\) | 9798.05 | + | 16970.7i | 0.453260 | + | 0.785069i | ||||
\(777\) | 5537.71 | − | 9591.60i | 0.255681 | − | 0.442853i | ||||
\(778\) | −3780.29 | + | 6547.66i | −0.174203 | + | 0.301729i | ||||
\(779\) | 19497.0 | 0.896731 | ||||||||
\(780\) | −25164.1 | + | 4516.30i | −1.15515 | + | 0.207320i | ||||
\(781\) | −31857.2 | −1.45959 | ||||||||
\(782\) | −13913.4 | + | 24098.7i | −0.636243 | + | 1.10200i | ||||
\(783\) | −5261.80 | + | 9113.71i | −0.240155 | + | 0.415961i | ||||
\(784\) | 10342.3 | + | 17913.3i | 0.471130 | + | 0.816022i | ||||
\(785\) | 9805.62 | 0.445831 | ||||||||
\(786\) | 7793.82 | + | 13499.3i | 0.353685 | + | 0.612600i | ||||
\(787\) | −7232.41 | − | 12526.9i | −0.327583 | − | 0.567390i | 0.654449 | − | 0.756106i | \(-0.272901\pi\) |
−0.982032 | + | 0.188716i | \(0.939567\pi\) | |||||||
\(788\) | 47113.6 | 2.12989 | ||||||||
\(789\) | −6574.37 | − | 11387.1i | −0.296646 | − | 0.513806i | ||||
\(790\) | −1640.06 | + | 2840.66i | −0.0738615 | + | 0.127932i | ||||
\(791\) | 4693.77 | − | 8129.84i | 0.210988 | − | 0.365441i | ||||
\(792\) | 31727.8 | 1.42348 | ||||||||
\(793\) | 4670.95 | + | 5532.26i | 0.209168 | + | 0.247738i | ||||
\(794\) | −23254.8 | −1.03940 | ||||||||
\(795\) | −12761.5 | + | 22103.5i | −0.569312 | + | 0.986077i | ||||
\(796\) | 24584.9 | − | 42582.3i | 1.09471 | − | 1.89609i | ||||
\(797\) | −57.2099 | − | 99.0904i | −0.00254263 | − | 0.00440397i | 0.864751 | − | 0.502200i | \(-0.167476\pi\) |
−0.867294 | + | 0.497796i | \(0.834143\pi\) | |||||||
\(798\) | −23437.5 | −1.03970 | ||||||||
\(799\) | −3723.40 | − | 6449.11i | −0.164861 | − | 0.285548i | ||||
\(800\) | −60.1686 | − | 104.215i | −0.00265910 | − | 0.00460570i | ||||
\(801\) | 2831.75 | 0.124913 | ||||||||
\(802\) | −1521.26 | − | 2634.89i | −0.0669794 | − | 0.116012i | ||||
\(803\) | −3010.64 | + | 5214.58i | −0.132308 | + | 0.229164i | ||||
\(804\) | −46266.0 | + | 80135.0i | −2.02945 | + | 3.51510i | ||||
\(805\) | 3846.52 | 0.168412 | ||||||||
\(806\) | 13829.6 | − | 38360.3i | 0.604377 | − | 1.67640i | ||||
\(807\) | −1612.61 | −0.0703428 | ||||||||
\(808\) | −10185.0 | + | 17640.9i | −0.443449 | + | 0.768076i | ||||
\(809\) | −2254.04 | + | 3904.11i | −0.0979578 | + | 0.169668i | −0.910839 | − | 0.412761i | \(-0.864564\pi\) |
0.812881 | + | 0.582429i | \(0.197898\pi\) | |||||||
\(810\) | −10785.6 | − | 18681.1i | −0.467859 | − | 0.810356i | ||||
\(811\) | 34706.7 | 1.50273 | 0.751367 | − | 0.659885i | \(-0.229395\pi\) | ||||
0.751367 | + | 0.659885i | \(0.229395\pi\) | |||||||
\(812\) | −8227.62 | − | 14250.7i | −0.355582 | − | 0.615887i | ||||
\(813\) | −8678.29 | − | 15031.2i | −0.374368 | − | 0.648424i | ||||
\(814\) | 64482.1 | 2.77653 | ||||||||
\(815\) | −3997.84 | − | 6924.46i | −0.171826 | − | 0.297611i | ||||
\(816\) | −8529.12 | + | 14772.9i | −0.365906 | + | 0.633767i | ||||
\(817\) | −4956.57 | + | 8585.04i | −0.212250 | + | 0.367628i | ||||
\(818\) | −61275.8 | −2.61914 | ||||||||
\(819\) | 1582.24 | − | 4388.76i | 0.0675065 | − | 0.187248i | ||||
\(820\) | −11578.3 | −0.493086 | ||||||||
\(821\) | −17327.1 | + | 30011.4i | −0.736564 | + | 1.27577i | 0.217470 | + | 0.976067i | \(0.430220\pi\) |
−0.954034 | + | 0.299699i | \(0.903114\pi\) | |||||||
\(822\) | 23466.9 | − | 40645.9i | 0.995746 | − | 1.72468i | ||||
\(823\) | −23129.6 | − | 40061.6i | −0.979642 | − | 1.69679i | −0.663677 | − | 0.748019i | \(-0.731005\pi\) |
−0.315965 | − | 0.948771i | \(-0.602328\pi\) | |||||||
\(824\) | 5573.64 | 0.235639 | ||||||||
\(825\) | −3560.58 | − | 6167.10i | −0.150259 | − | 0.260256i | ||||
\(826\) | −5778.55 | − | 10008.7i | −0.243416 | − | 0.421609i | ||||
\(827\) | −2113.42 | −0.0888641 | −0.0444321 | − | 0.999012i | \(-0.514148\pi\) | ||||
−0.0444321 | + | 0.999012i | \(0.514148\pi\) | |||||||
\(828\) | −22722.1 | − | 39355.9i | −0.953682 | − | 1.65183i | ||||
\(829\) | 3048.19 | − | 5279.63i | 0.127706 | − | 0.221193i | −0.795082 | − | 0.606503i | \(-0.792572\pi\) |
0.922787 | + | 0.385310i | \(0.125905\pi\) | |||||||
\(830\) | −7454.26 | + | 12911.1i | −0.311736 | + | 0.539943i | ||||
\(831\) | 35232.8 | 1.47077 | ||||||||
\(832\) | −23074.4 | + | 4141.25i | −0.961492 | + | 0.172562i | ||||
\(833\) | −12119.6 | −0.504104 | ||||||||
\(834\) | 27373.4 | − | 47412.2i | 1.13653 | − | 1.96852i | ||||
\(835\) | −140.292 | + | 242.993i | −0.00581438 | + | 0.0100708i | ||||
\(836\) | −45542.7 | − | 78882.3i | −1.88413 | − | 3.26340i | ||||
\(837\) | 9476.68 | 0.391352 | ||||||||
\(838\) | 21722.9 | + | 37625.1i | 0.895470 | + | 1.55100i | ||||
\(839\) | 10782.9 | + | 18676.5i | 0.443703 | + | 0.768517i | 0.997961 | − | 0.0638285i | \(-0.0203311\pi\) |
−0.554258 | + | 0.832345i | \(0.686998\pi\) | |||||||
\(840\) | 6985.63 | 0.286937 | ||||||||
\(841\) | −7199.75 | − | 12470.3i | −0.295205 | − | 0.511310i | ||||
\(842\) | −34160.4 | + | 59167.5i | −1.39815 | + | 2.42167i | ||||
\(843\) | −17483.4 | + | 30282.1i | −0.714306 | + | 1.23721i | ||||
\(844\) | 27441.2 | 1.11915 | ||||||||
\(845\) | −10299.4 | + | 3819.99i | −0.419302 | + | 0.155517i | ||||
\(846\) | 18219.0 | 0.740406 | ||||||||
\(847\) | 1112.64 | − | 1927.16i | 0.0451369 | − | 0.0781794i | ||||
\(848\) | 24601.9 | − | 42611.7i | 0.996263 | − | 1.72558i | ||||
\(849\) | 7787.98 | + | 13489.2i | 0.314821 | + | 0.545286i | ||||
\(850\) | 4704.17 | 0.189826 | ||||||||
\(851\) | −23177.5 | − | 40144.6i | −0.933625 | − | 1.61709i | ||||
\(852\) | 41433.8 | + | 71765.4i | 1.66608 | + | 2.88573i | ||||
\(853\) | −26903.9 | −1.07992 | −0.539961 | − | 0.841690i | \(-0.681561\pi\) | ||||
−0.539961 | + | 0.841690i | \(0.681561\pi\) | |||||||
\(854\) | −1970.85 | − | 3413.62i | −0.0789709 | − | 0.136782i | ||||
\(855\) | 6468.35 | − | 11203.5i | 0.258729 | − | 0.448131i | ||||
\(856\) | 6464.65 | − | 11197.1i | 0.258128 | − | 0.447090i | ||||
\(857\) | −23634.8 | −0.942063 | −0.471031 | − | 0.882116i | \(-0.656118\pi\) | ||||
−0.471031 | + | 0.882116i | \(0.656118\pi\) | |||||||
\(858\) | 64461.3 | − | 11569.1i | 2.56489 | − | 0.460329i | ||||
\(859\) | 26252.0 | 1.04273 | 0.521365 | − | 0.853334i | \(-0.325423\pi\) | ||||
0.521365 | + | 0.853334i | \(0.325423\pi\) | |||||||
\(860\) | 2943.45 | − | 5098.21i | 0.116710 | − | 0.202148i | ||||
\(861\) | 2547.14 | − | 4411.77i | 0.100820 | − | 0.174626i | ||||
\(862\) | 23431.6 | + | 40584.6i | 0.925849 | + | 1.60362i | ||||
\(863\) | −21344.0 | −0.841898 | −0.420949 | − | 0.907084i | \(-0.638303\pi\) | ||||
−0.420949 | + | 0.907084i | \(0.638303\pi\) | |||||||
\(864\) | 128.601 | + | 222.743i | 0.00506375 | + | 0.00877068i | ||||
\(865\) | −9180.15 | − | 15900.5i | −0.360849 | − | 0.625009i | ||||
\(866\) | −12490.5 | −0.490120 | ||||||||
\(867\) | 11687.4 | + | 20243.2i | 0.457816 | + | 0.792960i | ||||
\(868\) | −7409.11 | + | 12832.9i | −0.289725 | + | 0.501819i | ||||
\(869\) | 2804.37 | − | 4857.31i | 0.109473 | − | 0.189612i | ||||
\(870\) | 32808.4 | 1.27852 | ||||||||
\(871\) | −13484.0 | + | 37401.7i | −0.524557 | + | 1.45500i | ||||
\(872\) | −30137.1 | −1.17038 | ||||||||
\(873\) | 4741.02 | − | 8211.69i | 0.183802 | − | 0.318354i | ||||
\(874\) | −49047.5 | + | 84952.8i | −1.89824 | + | 3.28784i | ||||
\(875\) | −325.130 | − | 563.142i | −0.0125616 | − | 0.0217574i | ||||
\(876\) | 15662.7 | 0.604101 | ||||||||
\(877\) | −14326.9 | − | 24815.0i | −0.551638 | − | 0.955464i | −0.998157 | − | 0.0606902i | \(-0.980670\pi\) |
0.446519 | − | 0.894774i | \(-0.352664\pi\) | |||||||
\(878\) | 38785.7 | + | 67178.8i | 1.49084 | + | 2.58220i | ||||
\(879\) | 30340.0 | 1.16421 | ||||||||
\(880\) | 6864.16 | + | 11889.1i | 0.262944 | + | 0.455432i | ||||
\(881\) | −9917.23 | + | 17177.1i | −0.379251 | + | 0.656881i | −0.990953 | − | 0.134206i | \(-0.957152\pi\) |
0.611703 | + | 0.791088i | \(0.290485\pi\) | |||||||
\(882\) | 14825.7 | − | 25678.8i | 0.565993 | − | 0.980329i | ||||
\(883\) | 34322.7 | 1.30810 | 0.654049 | − | 0.756453i | \(-0.273069\pi\) | ||||
0.654049 | + | 0.756453i | \(0.273069\pi\) | |||||||
\(884\) | −9794.23 | + | 27167.0i | −0.372642 | + | 1.03362i | ||||
\(885\) | 15381.2 | 0.584218 | ||||||||
\(886\) | 25797.2 | − | 44682.0i | 0.978187 | − | 1.69427i | ||||
\(887\) | −970.751 | + | 1681.39i | −0.0367470 | + | 0.0636477i | −0.883814 | − | 0.467838i | \(-0.845033\pi\) |
0.847067 | + | 0.531486i | \(0.178366\pi\) | |||||||
\(888\) | −42092.5 | − | 72906.4i | −1.59069 | − | 2.75515i | ||||
\(889\) | 13748.1 | 0.518670 | ||||||||
\(890\) | 1814.97 | + | 3143.62i | 0.0683572 | + | 0.118398i | ||||
\(891\) | 18442.5 | + | 31943.3i | 0.693431 | + | 1.20106i | ||||
\(892\) | 26003.3 | 0.976070 | ||||||||
\(893\) | −13125.7 | − | 22734.4i | −0.491866 | − | 0.851936i | ||||
\(894\) | −40457.0 | + | 70073.6i | −1.51352 | + | 2.62149i | ||||
\(895\) | 9346.77 | − | 16189.1i | 0.349082 | − | 0.604627i | ||||
\(896\) | 12962.8 | 0.483322 | ||||||||
\(897\) | −30372.6 | − | 35973.3i | −1.13056 | − | 1.33903i | ||||
\(898\) | 70106.5 | 2.60521 | ||||||||
\(899\) | −17464.8 | + | 30250.0i | −0.647925 | + | 1.12224i | ||||
\(900\) | −3841.22 | + | 6653.19i | −0.142267 | + | 0.246414i | ||||
\(901\) | 14414.9 | + | 24967.3i | 0.532995 | + | 0.923174i | ||||
\(902\) | 29659.3 | 1.09484 | ||||||||
\(903\) | 1295.08 | + | 2243.14i | 0.0477270 | + | 0.0826656i | ||||
\(904\) | −35677.6 | − | 61795.4i | −1.31263 | − | 2.27355i | ||||
\(905\) | −9004.43 | −0.330737 | ||||||||
\(906\) | −14617.8 | − | 25318.8i | −0.536031 | − | 0.928434i | ||||
\(907\) | 3037.11 | − | 5260.43i | 0.111186 | − | 0.192579i | −0.805063 | − | 0.593190i | \(-0.797868\pi\) |
0.916249 | + | 0.400610i | \(0.131202\pi\) | |||||||
\(908\) | −41063.3 | + | 71123.7i | −1.50081 | + | 2.59948i | ||||
\(909\) | 9856.49 | 0.359647 | ||||||||
\(910\) | 5886.21 | − | 1056.42i | 0.214424 | − | 0.0384835i | ||||
\(911\) | 1631.31 | 0.0593279 | 0.0296639 | − | 0.999560i | \(-0.490556\pi\) | ||||
0.0296639 | + | 0.999560i | \(0.490556\pi\) | |||||||
\(912\) | −30066.9 | + | 52077.4i | −1.09168 | + | 1.89085i | ||||
\(913\) | 12746.2 | − | 22077.1i | 0.462035 | − | 0.800268i | ||||
\(914\) | −28421.5 | − | 49227.5i | −1.02856 | − | 1.78151i | ||||
\(915\) | 5245.96 | 0.189537 | ||||||||
\(916\) | −1557.96 | − | 2698.46i | −0.0561969 | − | 0.0973359i | ||||
\(917\) | −1216.93 | − | 2107.78i | −0.0438238 | − | 0.0759051i | ||||
\(918\) | −10054.4 | −0.361487 | ||||||||
\(919\) | −9714.59 | − | 16826.2i | −0.348700 | − | 0.603965i | 0.637319 | − | 0.770600i | \(-0.280043\pi\) |
−0.986019 | + | 0.166635i | \(0.946710\pi\) | |||||||
\(920\) | 14618.8 | − | 25320.5i | 0.523878 | − | 0.907383i | ||||
\(921\) | −15134.1 | + | 26212.9i | −0.541459 | + | 0.937835i | ||||
\(922\) | −13318.7 | −0.475736 | ||||||||
\(923\) | 22969.9 | + | 27205.5i | 0.819137 | + | 0.970185i | ||||
\(924\) | −23799.2 | −0.847335 | ||||||||
\(925\) | −3918.20 | + | 6786.53i | −0.139275 | + | 0.241232i | ||||
\(926\) | −9196.72 | + | 15929.2i | −0.326375 | + | 0.565297i | ||||
\(927\) | −1348.47 | − | 2335.62i | −0.0477772 | − | 0.0827526i | ||||
\(928\) | −948.007 | −0.0335343 | ||||||||
\(929\) | 5816.90 | + | 10075.2i | 0.205432 | + | 0.355819i | 0.950270 | − | 0.311426i | \(-0.100807\pi\) |
−0.744838 | + | 0.667245i | \(0.767473\pi\) | |||||||
\(930\) | −14772.3 | − | 25586.3i | −0.520862 | − | 0.902159i | ||||
\(931\) | −42724.0 | −1.50400 | ||||||||
\(932\) | 3096.45 | + | 5363.22i | 0.108828 | + | 0.188496i | ||||
\(933\) | −18174.2 | + | 31478.6i | −0.637723 | + | 1.10457i | ||||
\(934\) | 13342.9 | − | 23110.5i | 0.467443 | − | 0.809636i | ||||
\(935\) | −8043.77 | −0.281347 | ||||||||
\(936\) | −22876.6 | − | 27095.0i | −0.798874 | − | 0.946185i | ||||
\(937\) | 52690.1 | 1.83704 | 0.918522 | − | 0.395370i | \(-0.129384\pi\) | ||||
0.918522 | + | 0.395370i | \(0.129384\pi\) | |||||||
\(938\) | 10822.2 | − | 18744.6i | 0.376714 | − | 0.652487i | ||||
\(939\) | −27953.7 | + | 48417.1i | −0.971494 | + | 1.68268i | ||||
\(940\) | 7794.70 | + | 13500.8i | 0.270463 | + | 0.468455i | ||||
\(941\) | 1968.02 | 0.0681781 | 0.0340890 | − | 0.999419i | \(-0.489147\pi\) | ||||
0.0340890 | + | 0.999419i | \(0.489147\pi\) | |||||||
\(942\) | 32669.2 | + | 56584.7i | 1.12996 | + | 1.95714i | ||||
\(943\) | −10660.8 | − | 18465.0i | −0.368147 | − | 0.637649i | ||||
\(944\) | −29652.2 | −1.02235 | ||||||||
\(945\) | 694.913 | + | 1203.63i | 0.0239212 | + | 0.0414327i | ||||
\(946\) | −7540.05 | + | 13059.7i | −0.259142 | + | 0.448847i | ||||
\(947\) | 5196.19 | − | 9000.07i | 0.178304 | − | 0.308831i | −0.762996 | − | 0.646403i | \(-0.776272\pi\) |
0.941300 | + | 0.337572i | \(0.109606\pi\) | |||||||
\(948\) | −14589.6 | −0.499839 | ||||||||
\(949\) | 6623.92 | − | 1188.82i | 0.226577 | − | 0.0406646i | ||||
\(950\) | 16583.2 | 0.566346 | ||||||||
\(951\) | 17570.9 | − | 30433.6i | 0.599131 | − | 1.03773i | ||||
\(952\) | 3945.34 | − | 6833.54i | 0.134317 | − | 0.232643i | ||||
\(953\) | 12589.2 | + | 21805.2i | 0.427917 | + | 0.741174i | 0.996688 | − | 0.0813218i | \(-0.0259141\pi\) |
−0.568771 | + | 0.822496i | \(0.692581\pi\) | |||||||
\(954\) | −70533.7 | −2.39372 | ||||||||
\(955\) | −578.959 | − | 1002.79i | −0.0196174 | − | 0.0339784i | ||||
\(956\) | 23625.7 | + | 40920.9i | 0.799278 | + | 1.38439i | ||||
\(957\) | −56099.9 | −1.89493 | ||||||||
\(958\) | 46263.3 | + | 80130.4i | 1.56023 | + | 2.70240i | ||||
\(959\) | −3664.12 | + | 6346.45i | −0.123379 | + | 0.213699i | ||||
\(960\) | −8492.70 | + | 14709.8i | −0.285522 | + | 0.494538i | ||||
\(961\) | 1663.74 | 0.0558470 | ||||||||
\(962\) | −46493.4 | − | 55066.6i | −1.55822 | − | 1.84555i | ||||
\(963\) | −6256.15 | −0.209347 | ||||||||
\(964\) | 32229.1 | − | 55822.4i | 1.07679 | − | 1.86506i | ||||
\(965\) | 5483.57 | − | 9497.83i | 0.182925 | − | 0.316835i | ||||
\(966\) | 12815.4 | + | 22196.9i | 0.426840 | + | 0.739309i | ||||
\(967\) | −31665.6 | −1.05305 | −0.526523 | − | 0.850161i | \(-0.676505\pi\) | ||||
−0.526523 | + | 0.850161i | \(0.676505\pi\) | |||||||
\(968\) | −8457.28 | − | 14648.4i | −0.280813 | − | 0.486383i | ||||
\(969\) | −17617.0 | − | 30513.5i | −0.584044 | − | 1.01159i | ||||
\(970\) | 12154.7 | 0.402335 | ||||||||
\(971\) | −16407.5 | − | 28418.7i | −0.542269 | − | 0.939237i | −0.998773 | − | 0.0495160i | \(-0.984232\pi\) |
0.456505 | − | 0.889721i | \(-0.349101\pi\) | |||||||
\(972\) | 36387.3 | − | 63024.6i | 1.20074 | − | 2.07975i | ||||
\(973\) | −4274.08 | + | 7402.93i | −0.140823 | + | 0.243913i | ||||
\(974\) | 33306.2 | 1.09569 | ||||||||
\(975\) | −2699.33 | + | 7487.33i | −0.0886644 | + | 0.245935i | ||||
\(976\) | −10113.3 | −0.331678 | ||||||||
\(977\) | 71.8349 | − | 124.422i | 0.00235231 | − | 0.00407431i | −0.864847 | − | 0.502036i | \(-0.832585\pi\) |
0.867199 | + | 0.497961i | \(0.165918\pi\) | |||||||
\(978\) | 26639.1 | − | 46140.2i | 0.870985 | − | 1.50859i | ||||
\(979\) | −3103.46 | − | 5375.35i | −0.101315 | − | 0.175482i | ||||
\(980\) | 25371.6 | 0.827006 | ||||||||
\(981\) | 7291.27 | + | 12628.9i | 0.237301 | + | 0.411018i | ||||
\(982\) | −5679.05 | − | 9836.40i | −0.184547 | − | 0.319646i | ||||
\(983\) | 39094.1 | 1.26847 | 0.634235 | − | 0.773140i | \(-0.281315\pi\) | ||||
0.634235 | + | 0.773140i | \(0.281315\pi\) | |||||||
\(984\) | −19360.9 | − | 33534.1i | −0.627240 | − | 1.08641i | ||||
\(985\) | 7333.50 | − | 12702.0i | 0.237223 | − | 0.410882i | ||||
\(986\) | 18529.5 | − | 32094.1i | 0.598479 | − | 1.03660i | ||||
\(987\) | −6859.11 | −0.221203 | ||||||||
\(988\) | −34526.7 | + | 95769.1i | −1.11178 | + | 3.08383i | ||||
\(989\) | 10840.8 | 0.348552 | ||||||||
\(990\) | 9839.79 | − | 17043.0i | 0.315888 | − | 0.547134i | ||||
\(991\) | 15672.6 | − | 27145.7i | 0.502378 | − | 0.870144i | −0.497618 | − | 0.867396i | \(-0.665792\pi\) |
0.999996 | − | 0.00274791i | \(-0.000874688\pi\) | |||||||
\(992\) | 426.848 | + | 739.322i | 0.0136617 | + | 0.0236628i | ||||
\(993\) | 18400.4 | 0.588035 | ||||||||
\(994\) | −9691.89 | − | 16786.8i | −0.309264 | − | 0.535660i | ||||
\(995\) | −7653.56 | − | 13256.4i | −0.243853 | − | 0.422366i | ||||
\(996\) | −66311.3 | −2.10959 | ||||||||
\(997\) | −24852.0 | − | 43044.9i | −0.789439 | − | 1.36735i | −0.926311 | − | 0.376760i | \(-0.877038\pi\) |
0.136872 | − | 0.990589i | \(-0.456295\pi\) | |||||||
\(998\) | 47681.8 | − | 82587.3i | 1.51237 | − | 2.61949i | ||||
\(999\) | 8374.52 | − | 14505.1i | 0.265223 | − | 0.459380i |
(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 | 65.4.e.a.61.1 | yes | 14 | |
13.3 | even | 3 | inner | 65.4.e.a.16.1 | ✓ | 14 | |
13.4 | even | 6 | 845.4.a.h.1.1 | 7 | |||
13.9 | even | 3 | 845.4.a.k.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.4.e.a.16.1 | ✓ | 14 | 13.3 | even | 3 | inner | |
65.4.e.a.61.1 | yes | 14 | 1.1 | even | 1 | trivial | |
845.4.a.h.1.1 | 7 | 13.4 | even | 6 | |||
845.4.a.k.1.7 | 7 | 13.9 | even | 3 |