Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,4,Mod(67,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.78218718056\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.79 |
Dual form | 98.4.c.h.67.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.353553 | − | 0.612372i | ||||
\(3\) | −3.53553 | − | 6.12372i | −0.680414 | − | 1.17851i | −0.974855 | − | 0.222842i | \(-0.928467\pi\) |
0.294441 | − | 0.955670i | \(-0.404867\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −9.89949 | + | 17.1464i | −0.885438 | + | 1.53362i | −0.0402266 | + | 0.999191i | \(0.512808\pi\) |
−0.845211 | + | 0.534433i | \(0.820525\pi\) | |||||||
\(6\) | −14.1421 | −0.962250 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | −11.5000 | + | 19.9186i | −0.425926 | + | 0.737725i | ||||
\(10\) | 19.7990 | + | 34.2929i | 0.626099 | + | 1.08444i | ||||
\(11\) | 7.00000 | + | 12.1244i | 0.191871 | + | 0.332330i | 0.945870 | − | 0.324545i | \(-0.105211\pi\) |
−0.753999 | + | 0.656875i | \(0.771878\pi\) | |||||||
\(12\) | −14.1421 | + | 24.4949i | −0.340207 | + | 0.589256i | ||||
\(13\) | −50.9117 | −1.08618 | −0.543091 | − | 0.839674i | \(-0.682746\pi\) | ||||
−0.543091 | + | 0.839674i | \(0.682746\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 140.000 | 2.40986 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.707107 | + | 1.22474i | 0.0100882 | + | 0.0174732i | 0.871025 | − | 0.491238i | \(-0.163455\pi\) |
−0.860937 | + | 0.508711i | \(0.830122\pi\) | |||||||
\(18\) | 23.0000 | + | 39.8372i | 0.301175 | + | 0.521651i | ||||
\(19\) | −0.707107 | + | 1.22474i | −0.00853797 | + | 0.0147882i | −0.870263 | − | 0.492588i | \(-0.836051\pi\) |
0.861725 | + | 0.507376i | \(0.169384\pi\) | |||||||
\(20\) | 79.1960 | 0.885438 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 28.0000 | 0.271346 | ||||||||
\(23\) | −70.0000 | + | 121.244i | −0.634609 | + | 1.09918i | 0.351989 | + | 0.936004i | \(0.385506\pi\) |
−0.986598 | + | 0.163171i | \(0.947828\pi\) | |||||||
\(24\) | 28.2843 | + | 48.9898i | 0.240563 | + | 0.416667i | ||||
\(25\) | −133.500 | − | 231.229i | −1.06800 | − | 1.84983i | ||||
\(26\) | −50.9117 | + | 88.1816i | −0.384023 | + | 0.665148i | ||||
\(27\) | −28.2843 | −0.201604 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −286.000 | −1.83134 | −0.915670 | − | 0.401931i | \(-0.868339\pi\) | ||||
−0.915670 | + | 0.401931i | \(0.868339\pi\) | |||||||
\(30\) | 140.000 | − | 242.487i | 0.852013 | − | 1.47573i | ||||
\(31\) | −46.6690 | − | 80.8332i | −0.270387 | − | 0.468325i | 0.698574 | − | 0.715538i | \(-0.253818\pi\) |
−0.968961 | + | 0.247213i | \(0.920485\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 49.4975 | − | 85.7321i | 0.261103 | − | 0.452244i | ||||
\(34\) | 2.82843 | 0.0142668 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 92.0000 | 0.425926 | ||||||||
\(37\) | 19.0000 | − | 32.9090i | 0.0844211 | − | 0.146222i | −0.820723 | − | 0.571326i | \(-0.806429\pi\) |
0.905144 | + | 0.425104i | \(0.139763\pi\) | |||||||
\(38\) | 1.41421 | + | 2.44949i | 0.00603726 | + | 0.0104568i | ||||
\(39\) | 180.000 | + | 311.769i | 0.739053 | + | 1.28008i | ||||
\(40\) | 79.1960 | − | 137.171i | 0.313050 | − | 0.542218i | ||||
\(41\) | 125.865 | 0.479434 | 0.239717 | − | 0.970843i | \(-0.422945\pi\) | ||||
0.239717 | + | 0.970843i | \(0.422945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −34.0000 | −0.120580 | −0.0602901 | − | 0.998181i | \(-0.519203\pi\) | ||||
−0.0602901 | + | 0.998181i | \(0.519203\pi\) | |||||||
\(44\) | 28.0000 | − | 48.4974i | 0.0959354 | − | 0.166165i | ||||
\(45\) | −227.688 | − | 394.368i | −0.754262 | − | 1.30642i | ||||
\(46\) | 140.000 | + | 242.487i | 0.448736 | + | 0.777234i | ||||
\(47\) | 261.630 | − | 453.156i | 0.811970 | − | 1.40637i | −0.0995134 | − | 0.995036i | \(-0.531729\pi\) |
0.911483 | − | 0.411337i | \(-0.134938\pi\) | |||||||
\(48\) | 113.137 | 0.340207 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −534.000 | −1.51038 | ||||||||
\(51\) | 5.00000 | − | 8.66025i | 0.0137282 | − | 0.0237780i | ||||
\(52\) | 101.823 | + | 176.363i | 0.271545 | + | 0.470330i | ||||
\(53\) | 37.0000 | + | 64.0859i | 0.0958932 | + | 0.166092i | 0.909981 | − | 0.414650i | \(-0.136096\pi\) |
−0.814088 | + | 0.580742i | \(0.802763\pi\) | |||||||
\(54\) | −28.2843 | + | 48.9898i | −0.0712778 | + | 0.123457i | ||||
\(55\) | −277.186 | −0.679559 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.0000 | 0.0232374 | ||||||||
\(58\) | −286.000 | + | 495.367i | −0.647477 | + | 1.12146i | ||||
\(59\) | 217.082 | + | 375.997i | 0.479011 | + | 0.829671i | 0.999710 | − | 0.0240689i | \(-0.00766211\pi\) |
−0.520699 | + | 0.853740i | \(0.674329\pi\) | |||||||
\(60\) | −280.000 | − | 484.974i | −0.602464 | − | 1.04350i | ||||
\(61\) | 7.07107 | − | 12.2474i | 0.0148419 | − | 0.0257070i | −0.858509 | − | 0.512798i | \(-0.828609\pi\) |
0.873351 | + | 0.487091i | \(0.161942\pi\) | |||||||
\(62\) | −186.676 | −0.382385 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 504.000 | − | 872.954i | 0.961746 | − | 1.66579i | ||||
\(66\) | −98.9949 | − | 171.464i | −0.184628 | − | 0.319785i | ||||
\(67\) | −342.000 | − | 592.361i | −0.623611 | − | 1.08013i | −0.988808 | − | 0.149196i | \(-0.952332\pi\) |
0.365196 | − | 0.930930i | \(-0.381002\pi\) | |||||||
\(68\) | 2.82843 | − | 4.89898i | 0.00504408 | − | 0.00873660i | ||||
\(69\) | 989.949 | 1.72719 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 588.000 | 0.982856 | 0.491428 | − | 0.870918i | \(-0.336475\pi\) | ||||
0.491428 | + | 0.870918i | \(0.336475\pi\) | |||||||
\(72\) | 92.0000 | − | 159.349i | 0.150588 | − | 0.260825i | ||||
\(73\) | −135.057 | − | 233.926i | −0.216538 | − | 0.375055i | 0.737209 | − | 0.675664i | \(-0.236143\pi\) |
−0.953747 | + | 0.300610i | \(0.902810\pi\) | |||||||
\(74\) | −38.0000 | − | 65.8179i | −0.0596947 | − | 0.103394i | ||||
\(75\) | −943.988 | + | 1635.03i | −1.45336 | + | 2.51730i | ||||
\(76\) | 5.65685 | 0.00853797 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 720.000 | 1.04518 | ||||||||
\(79\) | −610.000 | + | 1056.55i | −0.868739 | + | 1.50470i | −0.00545246 | + | 0.999985i | \(0.501736\pi\) |
−0.863286 | + | 0.504715i | \(0.831598\pi\) | |||||||
\(80\) | −158.392 | − | 274.343i | −0.221359 | − | 0.383406i | ||||
\(81\) | 410.500 | + | 711.007i | 0.563100 | + | 0.975318i | ||||
\(82\) | 125.865 | − | 218.005i | 0.169506 | − | 0.293592i | ||||
\(83\) | −422.850 | −0.559202 | −0.279601 | − | 0.960116i | \(-0.590202\pi\) | ||||
−0.279601 | + | 0.960116i | \(0.590202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.0000 | −0.0357297 | ||||||||
\(86\) | −34.0000 | + | 58.8897i | −0.0426316 | + | 0.0738400i | ||||
\(87\) | 1011.16 | + | 1751.39i | 1.24607 | + | 2.15826i | ||||
\(88\) | −56.0000 | − | 96.9948i | −0.0678366 | − | 0.117496i | ||||
\(89\) | 309.006 | − | 535.214i | 0.368028 | − | 0.637444i | −0.621229 | − | 0.783629i | \(-0.713366\pi\) |
0.989257 | + | 0.146185i | \(0.0466996\pi\) | |||||||
\(90\) | −910.754 | −1.06669 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 560.000 | 0.634609 | ||||||||
\(93\) | −330.000 | + | 571.577i | −0.367951 | + | 0.637309i | ||||
\(94\) | −523.259 | − | 906.311i | −0.574149 | − | 0.994456i | ||||
\(95\) | −14.0000 | − | 24.2487i | −0.0151197 | − | 0.0261881i | ||||
\(96\) | 113.137 | − | 195.959i | 0.120281 | − | 0.208333i | ||||
\(97\) | −1483.51 | −1.55286 | −0.776431 | − | 0.630202i | \(-0.782972\pi\) | ||||
−0.776431 | + | 0.630202i | \(0.782972\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −322.000 | −0.326891 | ||||||||
\(100\) | −534.000 | + | 924.915i | −0.534000 | + | 0.924915i | ||||
\(101\) | 564.271 | + | 977.346i | 0.555912 | + | 0.962867i | 0.997832 | + | 0.0658130i | \(0.0209641\pi\) |
−0.441920 | + | 0.897054i | \(0.645703\pi\) | |||||||
\(102\) | −10.0000 | − | 17.3205i | −0.00970733 | − | 0.0168136i | ||||
\(103\) | −434.164 | + | 751.993i | −0.415334 | + | 0.719380i | −0.995463 | − | 0.0951446i | \(-0.969669\pi\) |
0.580129 | + | 0.814524i | \(0.303002\pi\) | |||||||
\(104\) | 407.294 | 0.384023 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 148.000 | 0.135613 | ||||||||
\(107\) | 842.000 | − | 1458.39i | 0.760740 | − | 1.31764i | −0.181729 | − | 0.983349i | \(-0.558169\pi\) |
0.942469 | − | 0.334292i | \(-0.108497\pi\) | |||||||
\(108\) | 56.5685 | + | 97.9796i | 0.0504010 | + | 0.0872971i | ||||
\(109\) | 409.000 | + | 708.409i | 0.359405 | + | 0.622507i | 0.987861 | − | 0.155337i | \(-0.0496465\pi\) |
−0.628457 | + | 0.777844i | \(0.716313\pi\) | |||||||
\(110\) | −277.186 | + | 480.100i | −0.240260 | + | 0.416143i | ||||
\(111\) | −268.701 | −0.229765 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −540.000 | −0.449548 | −0.224774 | − | 0.974411i | \(-0.572164\pi\) | ||||
−0.224774 | + | 0.974411i | \(0.572164\pi\) | |||||||
\(114\) | 10.0000 | − | 17.3205i | 0.00821567 | − | 0.0142299i | ||||
\(115\) | −1385.93 | − | 2400.50i | −1.12381 | − | 1.94650i | ||||
\(116\) | 572.000 | + | 990.733i | 0.457835 | + | 0.792994i | ||||
\(117\) | 585.484 | − | 1014.09i | 0.462633 | − | 0.801304i | ||||
\(118\) | 868.327 | 0.677424 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1120.00 | −0.852013 | ||||||||
\(121\) | 567.500 | − | 982.939i | 0.426371 | − | 0.738496i | ||||
\(122\) | −14.1421 | − | 24.4949i | −0.0104948 | − | 0.0181776i | ||||
\(123\) | −445.000 | − | 770.763i | −0.326214 | − | 0.565019i | ||||
\(124\) | −186.676 | + | 323.333i | −0.135194 | + | 0.234162i | ||||
\(125\) | 2811.46 | 2.01171 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1720.00 | 1.20177 | 0.600887 | − | 0.799334i | \(-0.294814\pi\) | ||||
0.600887 | + | 0.799334i | \(0.294814\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 120.208 | + | 208.207i | 0.0820445 | + | 0.142105i | ||||
\(130\) | −1008.00 | − | 1745.91i | −0.680057 | − | 1.17789i | ||||
\(131\) | −867.620 | + | 1502.76i | −0.578659 | + | 1.00227i | 0.416975 | + | 0.908918i | \(0.363090\pi\) |
−0.995634 | + | 0.0933484i | \(0.970243\pi\) | |||||||
\(132\) | −395.980 | −0.261103 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1368.00 | −0.881919 | ||||||||
\(135\) | 280.000 | − | 484.974i | 0.178508 | − | 0.309185i | ||||
\(136\) | −5.65685 | − | 9.79796i | −0.00356670 | − | 0.00617771i | ||||
\(137\) | −414.000 | − | 717.069i | −0.258178 | − | 0.447178i | 0.707576 | − | 0.706638i | \(-0.249789\pi\) |
−0.965754 | + | 0.259460i | \(0.916455\pi\) | |||||||
\(138\) | 989.949 | − | 1714.64i | 0.610653 | − | 1.05768i | ||||
\(139\) | 425.678 | 0.259752 | 0.129876 | − | 0.991530i | \(-0.458542\pi\) | ||||
0.129876 | + | 0.991530i | \(0.458542\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3700.00 | −2.20990 | ||||||||
\(142\) | 588.000 | − | 1018.45i | 0.347492 | − | 0.601874i | ||||
\(143\) | −356.382 | − | 617.271i | −0.208407 | − | 0.360971i | ||||
\(144\) | −184.000 | − | 318.697i | −0.106481 | − | 0.184431i | ||||
\(145\) | 2831.26 | − | 4903.88i | 1.62154 | − | 2.80859i | ||||
\(146\) | −540.230 | −0.306231 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −152.000 | −0.0844211 | ||||||||
\(149\) | −1025.00 | + | 1775.35i | −0.563566 | + | 0.976124i | 0.433616 | + | 0.901098i | \(0.357237\pi\) |
−0.997182 | + | 0.0750264i | \(0.976096\pi\) | |||||||
\(150\) | 1887.98 | + | 3270.07i | 1.02768 | + | 1.78000i | ||||
\(151\) | 236.000 | + | 408.764i | 0.127188 | + | 0.220296i | 0.922586 | − | 0.385791i | \(-0.126071\pi\) |
−0.795398 | + | 0.606087i | \(0.792738\pi\) | |||||||
\(152\) | 5.65685 | − | 9.79796i | 0.00301863 | − | 0.00522842i | ||||
\(153\) | −32.5269 | −0.0171872 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1848.00 | 0.957645 | ||||||||
\(156\) | 720.000 | − | 1247.08i | 0.369527 | − | 0.640039i | ||||
\(157\) | −1105.92 | − | 1915.50i | −0.562176 | − | 0.973717i | −0.997306 | − | 0.0733498i | \(-0.976631\pi\) |
0.435130 | − | 0.900367i | \(-0.356702\pi\) | |||||||
\(158\) | 1220.00 | + | 2113.10i | 0.614291 | + | 1.06398i | ||||
\(159\) | 261.630 | − | 453.156i | 0.130494 | − | 0.226022i | ||||
\(160\) | −633.568 | −0.313050 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1642.00 | 0.796344 | ||||||||
\(163\) | −1643.00 | + | 2845.76i | −0.789507 | + | 1.36747i | 0.136762 | + | 0.990604i | \(0.456331\pi\) |
−0.926269 | + | 0.376863i | \(0.877003\pi\) | |||||||
\(164\) | −251.730 | − | 436.009i | −0.119859 | − | 0.207601i | ||||
\(165\) | 980.000 | + | 1697.41i | 0.462381 | + | 0.800868i | ||||
\(166\) | −422.850 | + | 732.397i | −0.197708 | + | 0.342440i | ||||
\(167\) | 1490.58 | 0.690686 | 0.345343 | − | 0.938476i | \(-0.387763\pi\) | ||||
0.345343 | + | 0.938476i | \(0.387763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 395.000 | 0.179791 | ||||||||
\(170\) | −28.0000 | + | 48.4974i | −0.0126324 | + | 0.0218799i | ||||
\(171\) | −16.2635 | − | 28.1691i | −0.00727309 | − | 0.0125974i | ||||
\(172\) | 68.0000 | + | 117.779i | 0.0301451 | + | 0.0522128i | ||||
\(173\) | −1035.20 | + | 1793.03i | −0.454943 | + | 0.787984i | −0.998685 | − | 0.0512682i | \(-0.983674\pi\) |
0.543742 | + | 0.839252i | \(0.317007\pi\) | |||||||
\(174\) | 4044.65 | 1.76221 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −224.000 | −0.0959354 | ||||||||
\(177\) | 1535.00 | − | 2658.70i | 0.651851 | − | 1.12904i | ||||
\(178\) | −618.011 | − | 1070.43i | −0.260235 | − | 0.450741i | ||||
\(179\) | −270.000 | − | 467.654i | −0.112742 | − | 0.195274i | 0.804133 | − | 0.594449i | \(-0.202630\pi\) |
−0.916875 | + | 0.399175i | \(0.869297\pi\) | |||||||
\(180\) | −910.754 | + | 1577.47i | −0.377131 | + | 0.653210i | ||||
\(181\) | −3784.44 | −1.55412 | −0.777058 | − | 0.629429i | \(-0.783289\pi\) | ||||
−0.777058 | + | 0.629429i | \(0.783289\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −100.000 | −0.0403946 | ||||||||
\(184\) | 560.000 | − | 969.948i | 0.224368 | − | 0.388617i | ||||
\(185\) | 376.181 | + | 651.564i | 0.149499 | + | 0.258940i | ||||
\(186\) | 660.000 | + | 1143.15i | 0.260180 | + | 0.450646i | ||||
\(187\) | −9.89949 | + | 17.1464i | −0.00387124 | + | 0.00670519i | ||||
\(188\) | −2093.04 | −0.811970 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −56.0000 | −0.0213825 | ||||||||
\(191\) | −514.000 | + | 890.274i | −0.194721 | + | 0.337267i | −0.946809 | − | 0.321796i | \(-0.895714\pi\) |
0.752088 | + | 0.659063i | \(0.229047\pi\) | |||||||
\(192\) | −226.274 | − | 391.918i | −0.0850517 | − | 0.147314i | ||||
\(193\) | −2296.00 | − | 3976.79i | −0.856320 | − | 1.48319i | −0.875415 | − | 0.483372i | \(-0.839412\pi\) |
0.0190956 | − | 0.999818i | \(-0.493921\pi\) | |||||||
\(194\) | −1483.51 | + | 2569.51i | −0.549020 | + | 0.950930i | ||||
\(195\) | −7127.64 | −2.61754 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 794.000 | 0.287158 | 0.143579 | − | 0.989639i | \(-0.454139\pi\) | ||||
0.143579 | + | 0.989639i | \(0.454139\pi\) | |||||||
\(198\) | −322.000 | + | 557.720i | −0.115573 | + | 0.200179i | ||||
\(199\) | 1243.09 | + | 2153.10i | 0.442817 | + | 0.766981i | 0.997897 | − | 0.0648153i | \(-0.0206458\pi\) |
−0.555080 | + | 0.831797i | \(0.687312\pi\) | |||||||
\(200\) | 1068.00 | + | 1849.83i | 0.377595 | + | 0.654014i | ||||
\(201\) | −2418.31 | + | 4188.63i | −0.848627 | + | 1.46987i | ||||
\(202\) | 2257.08 | 0.786178 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −40.0000 | −0.0137282 | ||||||||
\(205\) | −1246.00 | + | 2158.14i | −0.424509 | + | 0.735272i | ||||
\(206\) | 868.327 | + | 1503.99i | 0.293686 | + | 0.508678i | ||||
\(207\) | −1610.00 | − | 2788.60i | −0.540593 | − | 0.936334i | ||||
\(208\) | 407.294 | − | 705.453i | 0.135773 | − | 0.235165i | ||||
\(209\) | −19.7990 | −0.00655275 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2748.00 | −0.896588 | −0.448294 | − | 0.893886i | \(-0.647968\pi\) | ||||
−0.448294 | + | 0.893886i | \(0.647968\pi\) | |||||||
\(212\) | 148.000 | − | 256.344i | 0.0479466 | − | 0.0830460i | ||||
\(213\) | −2078.89 | − | 3600.75i | −0.668749 | − | 1.15831i | ||||
\(214\) | −1684.00 | − | 2916.77i | −0.537925 | − | 0.931713i | ||||
\(215\) | 336.583 | − | 582.979i | 0.106766 | − | 0.184925i | ||||
\(216\) | 226.274 | 0.0712778 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1636.00 | 0.508275 | ||||||||
\(219\) | −955.000 | + | 1654.11i | −0.294671 | + | 0.510385i | ||||
\(220\) | 554.372 | + | 960.200i | 0.169890 | + | 0.294258i | ||||
\(221\) | −36.0000 | − | 62.3538i | −0.0109576 | − | 0.0189791i | ||||
\(222\) | −268.701 | + | 465.403i | −0.0812342 | + | 0.140702i | ||||
\(223\) | 3428.05 | 1.02941 | 0.514707 | − | 0.857366i | \(-0.327901\pi\) | ||||
0.514707 | + | 0.857366i | \(0.327901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6141.00 | 1.81956 | ||||||||
\(226\) | −540.000 | + | 935.307i | −0.158939 | + | 0.275291i | ||||
\(227\) | 2645.29 | + | 4581.77i | 0.773453 | + | 1.33966i | 0.935660 | + | 0.352903i | \(0.114805\pi\) |
−0.162207 | + | 0.986757i | \(0.551861\pi\) | |||||||
\(228\) | −20.0000 | − | 34.6410i | −0.00580935 | − | 0.0100621i | ||||
\(229\) | −1374.62 | + | 2380.90i | −0.396669 | + | 0.687051i | −0.993313 | − | 0.115456i | \(-0.963167\pi\) |
0.596644 | + | 0.802506i | \(0.296501\pi\) | |||||||
\(230\) | −5543.72 | −1.58931 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2288.00 | 0.647477 | ||||||||
\(233\) | −36.0000 | + | 62.3538i | −0.0101221 | + | 0.0175319i | −0.871042 | − | 0.491208i | \(-0.836555\pi\) |
0.860920 | + | 0.508740i | \(0.169889\pi\) | |||||||
\(234\) | −1170.97 | − | 2028.18i | −0.327131 | − | 0.566607i | ||||
\(235\) | 5180.00 | + | 8972.02i | 1.43790 | + | 2.49051i | ||||
\(236\) | 868.327 | − | 1503.99i | 0.239505 | − | 0.414836i | ||||
\(237\) | 8626.70 | 2.36441 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4308.00 | 1.16595 | 0.582974 | − | 0.812491i | \(-0.301889\pi\) | ||||
0.582974 | + | 0.812491i | \(0.301889\pi\) | |||||||
\(240\) | −1120.00 | + | 1939.90i | −0.301232 | + | 0.521749i | ||||
\(241\) | −770.039 | − | 1333.75i | −0.205820 | − | 0.356490i | 0.744574 | − | 0.667540i | \(-0.232653\pi\) |
−0.950394 | + | 0.311050i | \(0.899319\pi\) | |||||||
\(242\) | −1135.00 | − | 1965.88i | −0.301490 | − | 0.522196i | ||||
\(243\) | 2520.84 | − | 4366.22i | 0.665480 | − | 1.15265i | ||||
\(244\) | −56.5685 | −0.0148419 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1780.00 | −0.461336 | ||||||||
\(247\) | 36.0000 | − | 62.3538i | 0.00927379 | − | 0.0160627i | ||||
\(248\) | 373.352 | + | 646.665i | 0.0955964 | + | 0.165578i | ||||
\(249\) | 1495.00 | + | 2589.42i | 0.380489 | + | 0.659026i | ||||
\(250\) | 2811.46 | − | 4869.59i | 0.711249 | − | 1.23192i | ||||
\(251\) | −931.967 | −0.234363 | −0.117182 | − | 0.993110i | \(-0.537386\pi\) | ||||
−0.117182 | + | 0.993110i | \(0.537386\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1960.00 | −0.487052 | ||||||||
\(254\) | 1720.00 | − | 2979.13i | 0.424891 | − | 0.735933i | ||||
\(255\) | 98.9949 | + | 171.464i | 0.0243110 | + | 0.0421079i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 468.812 | − | 812.006i | 0.113789 | − | 0.197088i | −0.803506 | − | 0.595296i | \(-0.797035\pi\) |
0.917295 | + | 0.398209i | \(0.130368\pi\) | |||||||
\(258\) | 480.833 | 0.116028 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −4032.00 | −0.961746 | ||||||||
\(261\) | 3289.00 | − | 5696.72i | 0.780015 | − | 1.35103i | ||||
\(262\) | 1735.24 | + | 3005.52i | 0.409174 | + | 0.708709i | ||||
\(263\) | −3570.00 | − | 6183.42i | −0.837018 | − | 1.44976i | −0.892377 | − | 0.451291i | \(-0.850964\pi\) |
0.0553595 | − | 0.998466i | \(-0.482370\pi\) | |||||||
\(264\) | −395.980 | + | 685.857i | −0.0923139 | + | 0.159892i | ||||
\(265\) | −1465.13 | −0.339630 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4370.00 | −1.00165 | ||||||||
\(268\) | −1368.00 | + | 2369.45i | −0.311806 | + | 0.540063i | ||||
\(269\) | 2305.17 | + | 3992.67i | 0.522485 | + | 0.904971i | 0.999658 | + | 0.0261615i | \(0.00832843\pi\) |
−0.477172 | + | 0.878810i | \(0.658338\pi\) | |||||||
\(270\) | −560.000 | − | 969.948i | −0.126224 | − | 0.218627i | ||||
\(271\) | −1182.28 | + | 2047.77i | −0.265013 | + | 0.459016i | −0.967567 | − | 0.252614i | \(-0.918710\pi\) |
0.702554 | + | 0.711630i | \(0.252043\pi\) | |||||||
\(272\) | −22.6274 | −0.00504408 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1656.00 | −0.365119 | ||||||||
\(275\) | 1869.00 | − | 3237.20i | 0.409836 | − | 0.709857i | ||||
\(276\) | −1979.90 | − | 3429.29i | −0.431797 | − | 0.747894i | ||||
\(277\) | −2003.00 | − | 3469.30i | −0.434472 | − | 0.752527i | 0.562781 | − | 0.826606i | \(-0.309731\pi\) |
−0.997252 | + | 0.0740794i | \(0.976398\pi\) | |||||||
\(278\) | 425.678 | − | 737.296i | 0.0918363 | − | 0.159065i | ||||
\(279\) | 2146.78 | 0.460660 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5984.00 | −1.27038 | −0.635188 | − | 0.772358i | \(-0.719077\pi\) | ||||
−0.635188 | + | 0.772358i | \(0.719077\pi\) | |||||||
\(282\) | −3700.00 | + | 6408.59i | −0.781318 | + | 1.35328i | ||||
\(283\) | −2464.27 | − | 4268.24i | −0.517617 | − | 0.896538i | −0.999791 | − | 0.0204627i | \(-0.993486\pi\) |
0.482174 | − | 0.876075i | \(-0.339847\pi\) | |||||||
\(284\) | −1176.00 | − | 2036.89i | −0.245714 | − | 0.425589i | ||||
\(285\) | −98.9949 | + | 171.464i | −0.0205753 | + | 0.0356374i | ||||
\(286\) | −1425.53 | −0.294731 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −736.000 | −0.150588 | ||||||||
\(289\) | 2455.50 | − | 4253.05i | 0.499796 | − | 0.865673i | ||||
\(290\) | −5662.51 | − | 9807.76i | −1.14660 | − | 1.98597i | ||||
\(291\) | 5245.00 | + | 9084.61i | 1.05659 | + | 1.83007i | ||||
\(292\) | −540.230 | + | 935.705i | −0.108269 | + | 0.187527i | ||||
\(293\) | −1971.41 | −0.393076 | −0.196538 | − | 0.980496i | \(-0.562970\pi\) | ||||
−0.196538 | + | 0.980496i | \(0.562970\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8596.00 | −1.69654 | ||||||||
\(296\) | −152.000 | + | 263.272i | −0.0298474 | + | 0.0516972i | ||||
\(297\) | −197.990 | − | 342.929i | −0.0386820 | − | 0.0669991i | ||||
\(298\) | 2050.00 | + | 3550.70i | 0.398501 | + | 0.690224i | ||||
\(299\) | 3563.82 | − | 6172.71i | 0.689301 | − | 1.19390i | ||||
\(300\) | 7551.90 | 1.45336 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 944.000 | 0.179871 | ||||||||
\(303\) | 3990.00 | − | 6910.88i | 0.756500 | − | 1.31030i | ||||
\(304\) | −11.3137 | − | 19.5959i | −0.00213449 | − | 0.00369705i | ||||
\(305\) | 140.000 | + | 242.487i | 0.0262832 | + | 0.0455238i | ||||
\(306\) | −32.5269 | + | 56.3383i | −0.00607660 | + | 0.0105250i | ||||
\(307\) | 4767.31 | 0.886270 | 0.443135 | − | 0.896455i | \(-0.353866\pi\) | ||||
0.443135 | + | 0.896455i | \(0.353866\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6140.00 | 1.13040 | ||||||||
\(310\) | 1848.00 | − | 3200.83i | 0.338579 | − | 0.586435i | ||||
\(311\) | −3388.46 | − | 5868.98i | −0.617819 | − | 1.07009i | −0.989883 | − | 0.141887i | \(-0.954683\pi\) |
0.372064 | − | 0.928207i | \(-0.378650\pi\) | |||||||
\(312\) | −1440.00 | − | 2494.15i | −0.261295 | − | 0.452576i | ||||
\(313\) | −3095.01 | + | 5360.71i | −0.558914 | + | 0.968068i | 0.438673 | + | 0.898647i | \(0.355449\pi\) |
−0.997587 | + | 0.0694210i | \(0.977885\pi\) | |||||||
\(314\) | −4423.66 | −0.795037 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4880.00 | 0.868739 | ||||||||
\(317\) | −4913.00 | + | 8509.57i | −0.870478 | + | 1.50771i | −0.00897524 | + | 0.999960i | \(0.502857\pi\) |
−0.861503 | + | 0.507753i | \(0.830476\pi\) | |||||||
\(318\) | −523.259 | − | 906.311i | −0.0922733 | − | 0.159822i | ||||
\(319\) | −2002.00 | − | 3467.57i | −0.351381 | − | 0.608609i | ||||
\(320\) | −633.568 | + | 1097.37i | −0.110680 | + | 0.191703i | ||||
\(321\) | −11907.7 | −2.07047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | −0.000344529 | ||||||||
\(324\) | 1642.00 | − | 2844.03i | 0.281550 | − | 0.487659i | ||||
\(325\) | 6796.71 | + | 11772.2i | 1.16004 | + | 2.00925i | ||||
\(326\) | 3286.00 | + | 5691.52i | 0.558266 | + | 0.966945i | ||||
\(327\) | 2892.07 | − | 5009.21i | 0.489088 | − | 0.847125i | ||||
\(328\) | −1006.92 | −0.169506 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 3920.00 | 0.653906 | ||||||||
\(331\) | 2869.00 | − | 4969.25i | 0.476418 | − | 0.825181i | −0.523216 | − | 0.852200i | \(-0.675268\pi\) |
0.999635 | + | 0.0270189i | \(0.00860142\pi\) | |||||||
\(332\) | 845.700 | + | 1464.79i | 0.139801 | + | 0.242142i | ||||
\(333\) | 437.000 | + | 756.906i | 0.0719143 | + | 0.124559i | ||||
\(334\) | 1490.58 | − | 2581.76i | 0.244195 | − | 0.422957i | ||||
\(335\) | 13542.5 | 2.20868 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2254.00 | −0.364342 | −0.182171 | − | 0.983267i | \(-0.558312\pi\) | ||||
−0.182171 | + | 0.983267i | \(0.558312\pi\) | |||||||
\(338\) | 395.000 | − | 684.160i | 0.0635656 | − | 0.110099i | ||||
\(339\) | 1909.19 | + | 3306.81i | 0.305879 | + | 0.529797i | ||||
\(340\) | 56.0000 | + | 96.9948i | 0.00893243 | + | 0.0154714i | ||||
\(341\) | 653.367 | − | 1131.66i | 0.103759 | − | 0.179716i | ||||
\(342\) | −65.0538 | −0.0102857 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 272.000 | 0.0426316 | ||||||||
\(345\) | −9800.00 | + | 16974.1i | −1.52932 | + | 2.64885i | ||||
\(346\) | 2070.41 | + | 3586.05i | 0.321693 | + | 0.557189i | ||||
\(347\) | 993.000 | + | 1719.93i | 0.153623 | + | 0.266082i | 0.932557 | − | 0.361024i | \(-0.117573\pi\) |
−0.778934 | + | 0.627106i | \(0.784239\pi\) | |||||||
\(348\) | 4044.65 | − | 7005.54i | 0.623035 | − | 1.07913i | ||||
\(349\) | −6771.25 | −1.03856 | −0.519279 | − | 0.854605i | \(-0.673800\pi\) | ||||
−0.519279 | + | 0.854605i | \(0.673800\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1440.00 | 0.218979 | ||||||||
\(352\) | −224.000 | + | 387.979i | −0.0339183 | + | 0.0587482i | ||||
\(353\) | 3496.64 | + | 6056.36i | 0.527217 | + | 0.913166i | 0.999497 | + | 0.0317177i | \(0.0100978\pi\) |
−0.472280 | + | 0.881449i | \(0.656569\pi\) | |||||||
\(354\) | −3070.00 | − | 5317.40i | −0.460928 | − | 0.798351i | ||||
\(355\) | −5820.90 | + | 10082.1i | −0.870258 | + | 1.50733i | ||||
\(356\) | −2472.05 | −0.368028 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1080.00 | −0.159441 | ||||||||
\(359\) | −2972.00 | + | 5147.66i | −0.436925 | + | 0.756777i | −0.997451 | − | 0.0713606i | \(-0.977266\pi\) |
0.560525 | + | 0.828137i | \(0.310599\pi\) | |||||||
\(360\) | 1821.51 | + | 3154.94i | 0.266672 | + | 0.461889i | ||||
\(361\) | 3428.50 | + | 5938.34i | 0.499854 | + | 0.865773i | ||||
\(362\) | −3784.44 | + | 6554.83i | −0.549463 | + | 0.951697i | ||||
\(363\) | −8025.66 | −1.16044 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5348.00 | 0.766924 | ||||||||
\(366\) | −100.000 | + | 173.205i | −0.0142816 | + | 0.0247365i | ||||
\(367\) | −421.436 | − | 729.948i | −0.0599421 | − | 0.103823i | 0.834497 | − | 0.551012i | \(-0.185758\pi\) |
−0.894439 | + | 0.447190i | \(0.852425\pi\) | |||||||
\(368\) | −1120.00 | − | 1939.90i | −0.158652 | − | 0.274794i | ||||
\(369\) | −1447.45 | + | 2507.05i | −0.204204 | + | 0.353691i | ||||
\(370\) | 1504.72 | 0.211424 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2640.00 | 0.367951 | ||||||||
\(373\) | 2863.00 | − | 4958.86i | 0.397428 | − | 0.688365i | −0.595980 | − | 0.802999i | \(-0.703236\pi\) |
0.993408 | + | 0.114634i | \(0.0365696\pi\) | |||||||
\(374\) | 19.7990 | + | 34.2929i | 0.00273738 | + | 0.00474129i | ||||
\(375\) | −9940.00 | − | 17216.6i | −1.36880 | − | 2.37083i | ||||
\(376\) | −2093.04 | + | 3625.24i | −0.287075 | + | 0.497228i | ||||
\(377\) | 14560.7 | 1.98917 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10330.0 | 1.40004 | 0.700022 | − | 0.714122i | \(-0.253174\pi\) | ||||
0.700022 | + | 0.714122i | \(0.253174\pi\) | |||||||
\(380\) | −56.0000 | + | 96.9948i | −0.00755984 | + | 0.0130940i | ||||
\(381\) | −6081.12 | − | 10532.8i | −0.817704 | − | 1.41630i | ||||
\(382\) | 1028.00 | + | 1780.55i | 0.137689 | + | 0.238484i | ||||
\(383\) | 502.046 | − | 869.569i | 0.0669800 | − | 0.116013i | −0.830591 | − | 0.556884i | \(-0.811997\pi\) |
0.897571 | + | 0.440871i | \(0.145330\pi\) | |||||||
\(384\) | −905.097 | −0.120281 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9184.00 | −1.21102 | ||||||||
\(387\) | 391.000 | − | 677.232i | 0.0513583 | − | 0.0889551i | ||||
\(388\) | 2967.02 | + | 5139.03i | 0.388216 | + | 0.672409i | ||||
\(389\) | −2605.00 | − | 4511.99i | −0.339534 | − | 0.588090i | 0.644811 | − | 0.764342i | \(-0.276936\pi\) |
−0.984345 | + | 0.176252i | \(0.943603\pi\) | |||||||
\(390\) | −7127.64 | + | 12345.4i | −0.925441 | + | 1.60291i | ||||
\(391\) | −197.990 | −0.0256081 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12270.0 | 1.57491 | ||||||||
\(394\) | 794.000 | − | 1375.25i | 0.101526 | − | 0.175848i | ||||
\(395\) | −12077.4 | − | 20918.6i | −1.53843 | − | 2.66464i | ||||
\(396\) | 644.000 | + | 1115.44i | 0.0817228 | + | 0.141548i | ||||
\(397\) | −36.7696 | + | 63.6867i | −0.00464839 | + | 0.00805125i | −0.868340 | − | 0.495969i | \(-0.834813\pi\) |
0.863692 | + | 0.504020i | \(0.168146\pi\) | |||||||
\(398\) | 4972.37 | 0.626238 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4272.00 | 0.534000 | ||||||||
\(401\) | 249.000 | − | 431.281i | 0.0310086 | − | 0.0537085i | −0.850105 | − | 0.526614i | \(-0.823461\pi\) |
0.881113 | + | 0.472905i | \(0.156795\pi\) | |||||||
\(402\) | 4836.61 | + | 8377.25i | 0.600070 | + | 1.03935i | ||||
\(403\) | 2376.00 | + | 4115.35i | 0.293690 | + | 0.508686i | ||||
\(404\) | 2257.08 | − | 3909.39i | 0.277956 | − | 0.481434i | ||||
\(405\) | −16255.0 | −1.99436 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 532.000 | 0.0647918 | ||||||||
\(408\) | −40.0000 | + | 69.2820i | −0.00485366 | + | 0.00840679i | ||||
\(409\) | 1677.96 | + | 2906.32i | 0.202861 | + | 0.351365i | 0.949449 | − | 0.313921i | \(-0.101643\pi\) |
−0.746588 | + | 0.665286i | \(0.768309\pi\) | |||||||
\(410\) | 2492.00 | + | 4316.27i | 0.300173 | + | 0.519916i | ||||
\(411\) | −2927.42 | + | 5070.44i | −0.351336 | + | 0.608532i | ||||
\(412\) | 3473.31 | 0.415334 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6440.00 | −0.764514 | ||||||||
\(415\) | 4186.00 | − | 7250.36i | 0.495139 | − | 0.857606i | ||||
\(416\) | −814.587 | − | 1410.91i | −0.0960058 | − | 0.166287i | ||||
\(417\) | −1505.00 | − | 2606.74i | −0.176739 | − | 0.306121i | ||||
\(418\) | −19.7990 | + | 34.2929i | −0.00231675 | + | 0.00401272i | ||||
\(419\) | −14545.2 | −1.69589 | −0.847946 | − | 0.530082i | \(-0.822161\pi\) | ||||
−0.847946 | + | 0.530082i | \(0.822161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10854.0 | 1.25651 | 0.628256 | − | 0.778007i | \(-0.283769\pi\) | ||||
0.628256 | + | 0.778007i | \(0.283769\pi\) | |||||||
\(422\) | −2748.00 | + | 4759.68i | −0.316992 | + | 0.549046i | ||||
\(423\) | 6017.48 | + | 10422.6i | 0.691678 | + | 1.19802i | ||||
\(424\) | −296.000 | − | 512.687i | −0.0339034 | − | 0.0587224i | ||||
\(425\) | 188.798 | − | 327.007i | 0.0215483 | − | 0.0373227i | ||||
\(426\) | −8315.58 | −0.945753 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6736.00 | −0.760740 | ||||||||
\(429\) | −2520.00 | + | 4364.77i | −0.283605 | + | 0.491219i | ||||
\(430\) | −673.166 | − | 1165.96i | −0.0754952 | − | 0.130762i | ||||
\(431\) | 2682.00 | + | 4645.36i | 0.299739 | + | 0.519163i | 0.976076 | − | 0.217429i | \(-0.0697672\pi\) |
−0.676337 | + | 0.736592i | \(0.736434\pi\) | |||||||
\(432\) | 226.274 | − | 391.918i | 0.0252005 | − | 0.0436486i | ||||
\(433\) | 6487.00 | 0.719966 | 0.359983 | − | 0.932959i | \(-0.382783\pi\) | ||||
0.359983 | + | 0.932959i | \(0.382783\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −40040.0 | −4.41327 | ||||||||
\(436\) | 1636.00 | − | 2833.64i | 0.179702 | − | 0.311253i | ||||
\(437\) | −98.9949 | − | 171.464i | −0.0108365 | − | 0.0187694i | ||||
\(438\) | 1910.00 | + | 3308.22i | 0.208364 | + | 0.360897i | ||||
\(439\) | 6966.42 | − | 12066.2i | 0.757378 | − | 1.31182i | −0.186806 | − | 0.982397i | \(-0.559813\pi\) |
0.944183 | − | 0.329420i | \(-0.106853\pi\) | |||||||
\(440\) | 2217.49 | 0.240260 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −144.000 | −0.0154963 | ||||||||
\(443\) | −2998.00 | + | 5192.69i | −0.321533 | + | 0.556912i | −0.980805 | − | 0.194993i | \(-0.937532\pi\) |
0.659271 | + | 0.751905i | \(0.270865\pi\) | |||||||
\(444\) | 537.401 | + | 930.806i | 0.0574413 | + | 0.0994912i | ||||
\(445\) | 6118.00 | + | 10596.7i | 0.651733 | + | 1.12883i | ||||
\(446\) | 3428.05 | − | 5937.56i | 0.363953 | − | 0.630385i | ||||
\(447\) | 14495.7 | 1.53383 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2622.00 | 0.275590 | 0.137795 | − | 0.990461i | \(-0.455999\pi\) | ||||
0.137795 | + | 0.990461i | \(0.455999\pi\) | |||||||
\(450\) | 6141.00 | − | 10636.5i | 0.643310 | − | 1.11425i | ||||
\(451\) | 881.055 | + | 1526.03i | 0.0919895 | + | 0.159330i | ||||
\(452\) | 1080.00 | + | 1870.61i | 0.112387 | + | 0.194660i | ||||
\(453\) | 1668.77 | − | 2890.40i | 0.173081 | − | 0.299785i | ||||
\(454\) | 10581.1 | 1.09383 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −80.0000 | −0.00821567 | ||||||||
\(457\) | −5604.00 | + | 9706.41i | −0.573619 | + | 0.993538i | 0.422571 | + | 0.906330i | \(0.361128\pi\) |
−0.996190 | + | 0.0872080i | \(0.972206\pi\) | |||||||
\(458\) | 2749.23 | + | 4761.81i | 0.280487 | + | 0.485818i | ||||
\(459\) | −20.0000 | − | 34.6410i | −0.00203381 | − | 0.00352267i | ||||
\(460\) | −5543.72 | + | 9602.00i | −0.561907 | + | 0.973251i | ||||
\(461\) | −9786.36 | −0.988712 | −0.494356 | − | 0.869260i | \(-0.664596\pi\) | ||||
−0.494356 | + | 0.869260i | \(0.664596\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3952.00 | 0.396685 | 0.198342 | − | 0.980133i | \(-0.436444\pi\) | ||||
0.198342 | + | 0.980133i | \(0.436444\pi\) | |||||||
\(464\) | 2288.00 | − | 3962.93i | 0.228918 | − | 0.396497i | ||||
\(465\) | −6533.67 | − | 11316.6i | −0.651595 | − | 1.12860i | ||||
\(466\) | 72.0000 | + | 124.708i | 0.00715737 | + | 0.0123969i | ||||
\(467\) | 8753.27 | − | 15161.1i | 0.867352 | − | 1.50230i | 0.00265876 | − | 0.999996i | \(-0.499154\pi\) |
0.864693 | − | 0.502301i | \(-0.167513\pi\) | |||||||
\(468\) | −4683.88 | −0.462633 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 20720.0 | 2.03349 | ||||||||
\(471\) | −7820.00 | + | 13544.6i | −0.765025 | + | 1.32506i | ||||
\(472\) | −1736.65 | − | 3007.97i | −0.169356 | − | 0.293333i | ||||
\(473\) | −238.000 | − | 412.228i | −0.0231358 | − | 0.0400724i | ||||
\(474\) | 8626.70 | − | 14941.9i | 0.835944 | − | 1.44790i | ||||
\(475\) | 377.595 | 0.0364742 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1702.00 | −0.163374 | ||||||||
\(478\) | 4308.00 | − | 7461.67i | 0.412225 | − | 0.713994i | ||||
\(479\) | 1144.10 | + | 1981.64i | 0.109134 | + | 0.189026i | 0.915420 | − | 0.402501i | \(-0.131859\pi\) |
−0.806286 | + | 0.591526i | \(0.798526\pi\) | |||||||
\(480\) | 2240.00 | + | 3879.79i | 0.213003 | + | 0.368932i | ||||
\(481\) | −967.322 | + | 1675.45i | −0.0916967 | + | 0.158823i | ||||
\(482\) | −3080.16 | −0.291073 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4540.00 | −0.426371 | ||||||||
\(485\) | 14686.0 | − | 25436.9i | 1.37496 | − | 2.38151i | ||||
\(486\) | −5041.67 | − | 8732.43i | −0.470566 | − | 0.815043i | ||||
\(487\) | −486.000 | − | 841.777i | −0.0452213 | − | 0.0783256i | 0.842529 | − | 0.538651i | \(-0.181066\pi\) |
−0.887750 | + | 0.460326i | \(0.847733\pi\) | |||||||
\(488\) | −56.5685 | + | 97.9796i | −0.00524741 | + | 0.00908879i | ||||
\(489\) | 23235.5 | 2.14877 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7404.00 | −0.680525 | −0.340263 | − | 0.940330i | \(-0.610516\pi\) | ||||
−0.340263 | + | 0.940330i | \(0.610516\pi\) | |||||||
\(492\) | −1780.00 | + | 3083.05i | −0.163107 | + | 0.282509i | ||||
\(493\) | −202.233 | − | 350.277i | −0.0184748 | − | 0.0319994i | ||||
\(494\) | −72.0000 | − | 124.708i | −0.00655756 | − | 0.0113580i | ||||
\(495\) | 3187.64 | − | 5521.15i | 0.289442 | − | 0.501328i | ||||
\(496\) | 1493.41 | 0.135194 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5980.00 | 0.538093 | ||||||||
\(499\) | 6122.00 | − | 10603.6i | 0.549215 | − | 0.951269i | −0.449113 | − | 0.893475i | \(-0.648260\pi\) |
0.998329 | − | 0.0577938i | \(-0.0184066\pi\) | |||||||
\(500\) | −5622.91 | − | 9739.17i | −0.502929 | − | 0.871098i | ||||
\(501\) | −5270.00 | − | 9127.91i | −0.469953 | − | 0.813982i | ||||
\(502\) | −931.967 | + | 1614.21i | −0.0828600 | + | 0.143518i | ||||
\(503\) | 2415.48 | 0.214117 | 0.107058 | − | 0.994253i | \(-0.465857\pi\) | ||||
0.107058 | + | 0.994253i | \(0.465857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22344.0 | −1.96890 | ||||||||
\(506\) | −1960.00 | + | 3394.82i | −0.172199 | + | 0.298257i | ||||
\(507\) | −1396.54 | − | 2418.87i | −0.122332 | − | 0.211885i | ||||
\(508\) | −3440.00 | − | 5958.25i | −0.300444 | − | 0.520383i | ||||
\(509\) | −2853.88 | + | 4943.07i | −0.248519 | + | 0.430447i | −0.963115 | − | 0.269090i | \(-0.913277\pi\) |
0.714596 | + | 0.699537i | \(0.246610\pi\) | |||||||
\(510\) | 395.980 | 0.0343809 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 20.0000 | − | 34.6410i | 0.00172129 | − | 0.00298136i | ||||
\(514\) | −937.624 | − | 1624.01i | −0.0804607 | − | 0.139362i | ||||
\(515\) | −8596.00 | − | 14888.7i | −0.735505 | − | 1.27393i | ||||
\(516\) | 480.833 | − | 832.827i | 0.0410222 | − | 0.0710526i | ||||
\(517\) | 7325.63 | 0.623173 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14640.0 | 1.23820 | ||||||||
\(520\) | −4032.00 | + | 6983.63i | −0.340029 | + | 0.588947i | ||||
\(521\) | 0.707107 | + | 1.22474i | 5.94605e−5 | + | 0.000102989i | 0.866055 | − | 0.499949i | \(-0.166648\pi\) |
−0.865996 | + | 0.500051i | \(0.833314\pi\) | |||||||
\(522\) | −6578.00 | − | 11393.4i | −0.551554 | − | 0.955320i | ||||
\(523\) | −6128.49 | + | 10614.9i | −0.512391 | + | 0.887487i | 0.487506 | + | 0.873120i | \(0.337907\pi\) |
−0.999897 | + | 0.0143672i | \(0.995427\pi\) | |||||||
\(524\) | 6940.96 | 0.578659 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14280.0 | −1.18372 | ||||||||
\(527\) | 66.0000 | − | 114.315i | 0.00545542 | − | 0.00944906i | ||||
\(528\) | 791.960 | + | 1371.71i | 0.0652758 | + | 0.113061i | ||||
\(529\) | −3716.50 | − | 6437.17i | −0.305457 | − | 0.529068i | ||||
\(530\) | −1465.13 | + | 2537.67i | −0.120077 | + | 0.207980i | ||||
\(531\) | −9985.76 | −0.816093 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6408.00 | −0.520753 | ||||||||
\(534\) | −4370.00 | + | 7569.06i | −0.354136 | + | 0.613381i | ||||
\(535\) | 16670.7 | + | 28874.6i | 1.34718 | + | 2.33338i | ||||
\(536\) | 2736.00 | + | 4738.89i | 0.220480 | + | 0.381882i | ||||
\(537\) | −1909.19 | + | 3306.81i | −0.153422 | + | 0.265735i | ||||
\(538\) | 9220.67 | 0.738906 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2240.00 | −0.178508 | ||||||||
\(541\) | −1025.00 | + | 1775.35i | −0.0814569 | + | 0.141088i | −0.903876 | − | 0.427795i | \(-0.859291\pi\) |
0.822419 | + | 0.568882i | \(0.192624\pi\) | |||||||
\(542\) | 2364.57 | + | 4095.55i | 0.187393 | + | 0.324573i | ||||
\(543\) | 13380.0 | + | 23174.8i | 1.05744 | + | 1.83154i | ||||
\(544\) | −22.6274 | + | 39.1918i | −0.00178335 | + | 0.00308885i | ||||
\(545\) | −16195.6 | −1.27292 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14554.0 | 1.13763 | 0.568815 | − | 0.822465i | \(-0.307402\pi\) | ||||
0.568815 | + | 0.822465i | \(0.307402\pi\) | |||||||
\(548\) | −1656.00 | + | 2868.28i | −0.129089 | + | 0.223589i | ||||
\(549\) | 162.635 | + | 281.691i | 0.0126431 | + | 0.0218985i | ||||
\(550\) | −3738.00 | − | 6474.41i | −0.289798 | − | 0.501945i | ||||
\(551\) | 202.233 | − | 350.277i | 0.0156359 | − | 0.0270822i | ||||
\(552\) | −7919.60 | −0.610653 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8012.00 | −0.614435 | ||||||||
\(555\) | 2660.00 | − | 4607.26i | 0.203443 | − | 0.352373i | ||||
\(556\) | −851.357 | − | 1474.59i | −0.0649381 | − | 0.112476i | ||||
\(557\) | −3477.00 | − | 6022.34i | −0.264498 | − | 0.458123i | 0.702934 | − | 0.711255i | \(-0.251873\pi\) |
−0.967432 | + | 0.253131i | \(0.918539\pi\) | |||||||
\(558\) | 2146.78 | − | 3718.33i | 0.162868 | − | 0.282095i | ||||
\(559\) | 1731.00 | 0.130972 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 140.000 | 0.0105362 | ||||||||
\(562\) | −5984.00 | + | 10364.6i | −0.449146 | + | 0.777943i | ||||
\(563\) | −818.123 | − | 1417.03i | −0.0612429 | − | 0.106076i | 0.833778 | − | 0.552099i | \(-0.186173\pi\) |
−0.895021 | + | 0.446024i | \(0.852840\pi\) | |||||||
\(564\) | 7400.00 | + | 12817.2i | 0.552476 | + | 0.956916i | ||||
\(565\) | 5345.73 | − | 9259.07i | 0.398047 | − | 0.689437i | ||||
\(566\) | −9857.07 | −0.732020 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4704.00 | −0.347492 | ||||||||
\(569\) | 3571.00 | − | 6185.15i | 0.263100 | − | 0.455703i | −0.703964 | − | 0.710236i | \(-0.748588\pi\) |
0.967064 | + | 0.254533i | \(0.0819216\pi\) | |||||||
\(570\) | 197.990 | + | 342.929i | 0.0145489 | + | 0.0251995i | ||||
\(571\) | 10303.0 | + | 17845.3i | 0.755109 | + | 1.30789i | 0.945320 | + | 0.326144i | \(0.105749\pi\) |
−0.190211 | + | 0.981743i | \(0.560917\pi\) | |||||||
\(572\) | −1425.53 | + | 2469.09i | −0.104203 | + | 0.180485i | ||||
\(573\) | 7269.06 | 0.529964 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37380.0 | 2.71105 | ||||||||
\(576\) | −736.000 | + | 1274.79i | −0.0532407 | + | 0.0922157i | ||||
\(577\) | −4401.74 | − | 7624.04i | −0.317585 | − | 0.550074i | 0.662398 | − | 0.749152i | \(-0.269539\pi\) |
−0.979984 | + | 0.199078i | \(0.936205\pi\) | |||||||
\(578\) | −4911.00 | − | 8506.10i | −0.353409 | − | 0.612123i | ||||
\(579\) | −16235.2 | + | 28120.1i | −1.16530 | + | 2.01836i | ||||
\(580\) | −22650.0 | −1.62154 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20980.0 | 1.49424 | ||||||||
\(583\) | −518.000 | + | 897.202i | −0.0367982 | + | 0.0637364i | ||||
\(584\) | 1080.46 | + | 1871.41i | 0.0765577 | + | 0.132602i | ||||
\(585\) | 11592.0 | + | 20077.9i | 0.819265 | + | 1.41901i | ||||
\(586\) | −1971.41 | + | 3414.59i | −0.138973 | + | 0.240709i | ||||
\(587\) | −6503.97 | −0.457321 | −0.228661 | − | 0.973506i | \(-0.573435\pi\) | ||||
−0.228661 | + | 0.973506i | \(0.573435\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 132.000 | 0.00923424 | ||||||||
\(590\) | −8596.00 | + | 14888.7i | −0.599816 | + | 1.03891i | ||||
\(591\) | −2807.21 | − | 4862.24i | −0.195386 | − | 0.338419i | ||||
\(592\) | 304.000 | + | 526.543i | 0.0211053 | + | 0.0365554i | ||||
\(593\) | −11570.4 | + | 20040.5i | −0.801246 | + | 1.38780i | 0.117550 | + | 0.993067i | \(0.462496\pi\) |
−0.918796 | + | 0.394732i | \(0.870837\pi\) | |||||||
\(594\) | −791.960 | −0.0547045 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8200.00 | 0.563566 | ||||||||
\(597\) | 8790.00 | − | 15224.7i | 0.602598 | − | 1.04373i | ||||
\(598\) | −7127.64 | − | 12345.4i | −0.487409 | − | 0.844218i | ||||
\(599\) | 5648.00 | + | 9782.62i | 0.385260 | + | 0.667291i | 0.991805 | − | 0.127759i | \(-0.0407783\pi\) |
−0.606545 | + | 0.795049i | \(0.707445\pi\) | |||||||
\(600\) | 7551.90 | − | 13080.3i | 0.513842 | − | 0.890000i | ||||
\(601\) | −8727.11 | −0.592323 | −0.296162 | − | 0.955138i | \(-0.595707\pi\) | ||||
−0.296162 | + | 0.955138i | \(0.595707\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15732.0 | 1.06245 | ||||||||
\(604\) | 944.000 | − | 1635.06i | 0.0635941 | − | 0.110148i | ||||
\(605\) | 11235.9 | + | 19461.2i | 0.755050 | + | 1.30779i | ||||
\(606\) | −7980.00 | − | 13821.8i | −0.534926 | − | 0.926520i | ||||
\(607\) | 9868.38 | − | 17092.5i | 0.659877 | − | 1.14294i | −0.320770 | − | 0.947157i | \(-0.603942\pi\) |
0.980647 | − | 0.195783i | \(-0.0627249\pi\) | |||||||
\(608\) | −45.2548 | −0.00301863 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 560.000 | 0.0371701 | ||||||||
\(611\) | −13320.0 | + | 23070.9i | −0.881947 | + | 1.52758i | ||||
\(612\) | 65.0538 | + | 112.677i | 0.00429681 | + | 0.00744229i | ||||
\(613\) | −8481.00 | − | 14689.5i | −0.558800 | − | 0.967870i | −0.997597 | − | 0.0692837i | \(-0.977929\pi\) |
0.438797 | − | 0.898586i | \(-0.355405\pi\) | |||||||
\(614\) | 4767.31 | − | 8257.23i | 0.313344 | − | 0.542727i | ||||
\(615\) | 17621.1 | 1.15537 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19034.0 | −1.24194 | −0.620972 | − | 0.783832i | \(-0.713262\pi\) | ||||
−0.620972 | + | 0.783832i | \(0.713262\pi\) | |||||||
\(618\) | 6140.00 | − | 10634.8i | 0.399655 | − | 0.692223i | ||||
\(619\) | −9338.76 | − | 16175.2i | −0.606392 | − | 1.05030i | −0.991830 | − | 0.127568i | \(-0.959283\pi\) |
0.385438 | − | 0.922734i | \(-0.374050\pi\) | |||||||
\(620\) | −3696.00 | − | 6401.66i | −0.239411 | − | 0.414672i | ||||
\(621\) | 1979.90 | − | 3429.29i | 0.127940 | − | 0.221598i | ||||
\(622\) | −13553.8 | −0.873728 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5760.00 | −0.369527 | ||||||||
\(625\) | −11144.5 | + | 19302.8i | −0.713248 | + | 1.23538i | ||||
\(626\) | 6190.01 | + | 10721.4i | 0.395212 | + | 0.684527i | ||||
\(627\) | 70.0000 | + | 121.244i | 0.00445858 | + | 0.00772249i | ||||
\(628\) | −4423.66 | + | 7662.00i | −0.281088 | + | 0.486859i | ||||
\(629\) | 53.7401 | 0.00340661 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14716.0 | −0.928423 | −0.464211 | − | 0.885724i | \(-0.653662\pi\) | ||||
−0.464211 | + | 0.885724i | \(0.653662\pi\) | |||||||
\(632\) | 4880.00 | − | 8452.41i | 0.307146 | − | 0.531992i | ||||
\(633\) | 9715.65 | + | 16828.0i | 0.610051 | + | 1.05664i | ||||
\(634\) | 9826.00 | + | 17019.1i | 0.615521 | + | 1.06611i | ||||
\(635\) | −17027.1 | + | 29491.9i | −1.06410 | + | 1.84307i | ||||
\(636\) | −2093.04 | −0.130494 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −8008.00 | −0.496928 | ||||||||
\(639\) | −6762.00 | + | 11712.1i | −0.418624 | + | 0.725078i | ||||
\(640\) | 1267.14 | + | 2194.74i | 0.0782624 | + | 0.135554i | ||||
\(641\) | −2365.00 | − | 4096.30i | −0.145728 | − | 0.252409i | 0.783916 | − | 0.620867i | \(-0.213219\pi\) |
−0.929644 | + | 0.368458i | \(0.879886\pi\) | |||||||
\(642\) | −11907.7 | + | 20624.7i | −0.732023 | + | 1.26790i | ||||
\(643\) | −19056.5 | −1.16877 | −0.584383 | − | 0.811478i | \(-0.698663\pi\) | ||||
−0.584383 | + | 0.811478i | \(0.698663\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4760.00 | −0.290581 | ||||||||
\(646\) | −2.00000 | + | 3.46410i | −0.000121810 | + | 0.000210980i | ||||
\(647\) | 4671.15 | + | 8090.66i | 0.283836 | + | 0.491618i | 0.972326 | − | 0.233627i | \(-0.0750596\pi\) |
−0.688490 | + | 0.725245i | \(0.741726\pi\) | |||||||
\(648\) | −3284.00 | − | 5688.05i | −0.199086 | − | 0.344827i | ||||
\(649\) | −3039.14 | + | 5263.95i | −0.183816 | + | 0.318379i | ||||
\(650\) | 27186.8 | 1.64055 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13144.0 | 0.789507 | ||||||||
\(653\) | −1887.00 | + | 3268.38i | −0.113084 | + | 0.195868i | −0.917012 | − | 0.398859i | \(-0.869406\pi\) |
0.803928 | + | 0.594727i | \(0.202740\pi\) | |||||||
\(654\) | −5784.13 | − | 10018.4i | −0.345837 | − | 0.599008i | ||||
\(655\) | −17178.0 | − | 29753.2i | −1.02473 | − | 1.77489i | ||||
\(656\) | −1006.92 | + | 1744.04i | −0.0599293 | + | 0.103801i | ||||
\(657\) | 6212.64 | 0.368917 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21150.0 | −1.25021 | −0.625104 | − | 0.780541i | \(-0.714943\pi\) | ||||
−0.625104 | + | 0.780541i | \(0.714943\pi\) | |||||||
\(660\) | 3920.00 | − | 6789.64i | 0.231191 | − | 0.400434i | ||||
\(661\) | −5188.75 | − | 8987.18i | −0.305324 | − | 0.528836i | 0.672010 | − | 0.740542i | \(-0.265431\pi\) |
−0.977333 | + | 0.211706i | \(0.932098\pi\) | |||||||
\(662\) | −5738.00 | − | 9938.51i | −0.336879 | − | 0.583491i | ||||
\(663\) | −254.558 | + | 440.908i | −0.0149114 | + | 0.0258272i | ||||
\(664\) | 3382.80 | 0.197708 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1748.00 | 0.101702 | ||||||||
\(667\) | 20020.0 | − | 34675.7i | 1.16219 | − | 2.01296i | ||||
\(668\) | −2981.16 | − | 5163.52i | −0.172672 | − | 0.299076i | ||||
\(669\) | −12120.0 | − | 20992.5i | −0.700428 | − | 1.21318i | ||||
\(670\) | 13542.5 | − | 23456.3i | 0.780885 | − | 1.35253i | ||||
\(671\) | 197.990 | 0.0113909 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1164.00 | −0.0666700 | −0.0333350 | − | 0.999444i | \(-0.510613\pi\) | ||||
−0.0333350 | + | 0.999444i | \(0.510613\pi\) | |||||||
\(674\) | −2254.00 | + | 3904.04i | −0.128814 | + | 0.223113i | ||||
\(675\) | 3775.95 | + | 6540.14i | 0.215313 | + | 0.372933i | ||||
\(676\) | −790.000 | − | 1368.32i | −0.0449477 | − | 0.0778516i | ||||
\(677\) | 13576.5 | − | 23515.1i | 0.770732 | − | 1.33495i | −0.166431 | − | 0.986053i | \(-0.553224\pi\) |
0.937162 | − | 0.348893i | \(-0.113442\pi\) | |||||||
\(678\) | 7636.75 | 0.432578 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 224.000 | 0.0126324 | ||||||||
\(681\) | 18705.0 | − | 32398.0i | 1.05254 | − | 1.82305i | ||||
\(682\) | −1306.73 | − | 2263.33i | −0.0733686 | − | 0.127078i | ||||
\(683\) | 8298.00 | + | 14372.6i | 0.464882 | + | 0.805199i | 0.999196 | − | 0.0400871i | \(-0.0127636\pi\) |
−0.534315 | + | 0.845286i | \(0.679430\pi\) | |||||||
\(684\) | −65.0538 | + | 112.677i | −0.00363654 | + | 0.00629868i | ||||
\(685\) | 16393.6 | 0.914403 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 19440.0 | 1.07960 | ||||||||
\(688\) | 272.000 | − | 471.118i | 0.0150725 | − | 0.0261064i | ||||
\(689\) | −1883.73 | − | 3262.72i | −0.104157 | − | 0.180406i | ||||
\(690\) | 19600.0 | + | 33948.2i | 1.08139 | + | 1.87302i | ||||
\(691\) | 5649.08 | − | 9784.49i | 0.311000 | − | 0.538668i | −0.667579 | − | 0.744539i | \(-0.732669\pi\) |
0.978579 | + | 0.205871i | \(0.0660028\pi\) | |||||||
\(692\) | 8281.63 | 0.454943 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3972.00 | 0.217255 | ||||||||
\(695\) | −4214.00 | + | 7298.86i | −0.229994 | + | 0.398362i | ||||
\(696\) | −8089.30 | − | 14011.1i | −0.440552 | − | 0.763058i | ||||
\(697\) | 89.0000 | + | 154.153i | 0.00483661 | + | 0.00837725i | ||||
\(698\) | −6771.25 | + | 11728.2i | −0.367186 | + | 0.635985i | ||||
\(699\) | 509.117 | 0.0275487 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2754.00 | −0.148384 | −0.0741920 | − | 0.997244i | \(-0.523638\pi\) | ||||
−0.0741920 | + | 0.997244i | \(0.523638\pi\) | |||||||
\(702\) | 1440.00 | − | 2494.15i | 0.0774207 | − | 0.134097i | ||||
\(703\) | 26.8701 | + | 46.5403i | 0.00144157 | + | 0.00249687i | ||||
\(704\) | 448.000 | + | 775.959i | 0.0239839 | + | 0.0415413i | ||||
\(705\) | 36628.1 | − | 63441.8i | 1.95673 | − | 3.38916i | ||||
\(706\) | 13986.6 | 0.745597 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −12280.0 | −0.651851 | ||||||||
\(709\) | −14717.0 | + | 25490.6i | −0.779561 | + | 1.35024i | 0.152634 | + | 0.988283i | \(0.451224\pi\) |
−0.932195 | + | 0.361956i | \(0.882109\pi\) | |||||||
\(710\) | 11641.8 | + | 20164.2i | 0.615365 | + | 1.06584i | ||||
\(711\) | −14030.0 | − | 24300.7i | −0.740037 | − | 1.28178i | ||||
\(712\) | −2472.05 | + | 4281.71i | −0.130118 | + | 0.225370i | ||||
\(713\) | 13067.3 | 0.686361 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14112.0 | 0.738124 | ||||||||
\(716\) | −1080.00 | + | 1870.61i | −0.0563708 | + | 0.0976371i | ||||
\(717\) | −15231.1 | − | 26381.0i | −0.793327 | − | 1.37408i | ||||
\(718\) | 5944.00 | + | 10295.3i | 0.308953 | + | 0.535122i | ||||
\(719\) | −8834.59 | + | 15302.0i | −0.458240 | + | 0.793695i | −0.998868 | − | 0.0475666i | \(-0.984853\pi\) |
0.540628 | + | 0.841262i | \(0.318187\pi\) | |||||||
\(720\) | 7286.03 | 0.377131 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13714.0 | 0.706901 | ||||||||
\(723\) | −5445.00 | + | 9431.02i | −0.280085 | + | 0.485122i | ||||
\(724\) | 7568.87 | + | 13109.7i | 0.388529 | + | 0.672952i | ||||
\(725\) | 38181.0 | + | 66131.4i | 1.95587 | + | 3.38767i | ||||
\(726\) | −8025.66 | + | 13900.9i | −0.410276 | + | 0.710619i | ||||
\(727\) | −28445.5 | −1.45115 | −0.725574 | − | 0.688144i | \(-0.758426\pi\) | ||||
−0.725574 | + | 0.688144i | \(0.758426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13483.0 | −0.685007 | ||||||||
\(730\) | 5348.00 | − | 9263.01i | 0.271148 | − | 0.469643i | ||||
\(731\) | −24.0416 | − | 41.6413i | −0.00121643 | − | 0.00210692i | ||||
\(732\) | 200.000 | + | 346.410i | 0.0100987 | + | 0.0174914i | ||||
\(733\) | 11170.9 | − | 19348.5i | 0.562900 | − | 0.974971i | −0.434342 | − | 0.900748i | \(-0.643019\pi\) |
0.997242 | − | 0.0742230i | \(-0.0236477\pi\) | |||||||
\(734\) | −1685.74 | −0.0847710 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4480.00 | −0.224368 | ||||||||
\(737\) | 4788.00 | − | 8293.06i | 0.239306 | − | 0.414490i | ||||
\(738\) | 2894.90 | + | 5014.11i | 0.144394 | + | 0.250097i | ||||
\(739\) | −10335.0 | − | 17900.7i | −0.514451 | − | 0.891055i | −0.999859 | − | 0.0167675i | \(-0.994662\pi\) |
0.485409 | − | 0.874287i | \(-0.338671\pi\) | |||||||
\(740\) | 1504.72 | − | 2606.26i | 0.0747496 | − | 0.129470i | ||||
\(741\) | −509.117 | −0.0252400 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25400.0 | −1.25415 | −0.627076 | − | 0.778958i | \(-0.715749\pi\) | ||||
−0.627076 | + | 0.778958i | \(0.715749\pi\) | |||||||
\(744\) | 2640.00 | − | 4572.61i | 0.130090 | − | 0.225323i | ||||
\(745\) | −20294.0 | − | 35150.2i | −0.998004 | − | 1.72859i | ||||
\(746\) | −5726.00 | − | 9917.72i | −0.281024 | − | 0.486748i | ||||
\(747\) | 4862.77 | − | 8422.57i | 0.238179 | − | 0.412538i | ||||
\(748\) | 79.1960 | 0.00387124 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −39760.0 | −1.93577 | ||||||||
\(751\) | −14590.0 | + | 25270.6i | −0.708917 | + | 1.22788i | 0.256342 | + | 0.966586i | \(0.417483\pi\) |
−0.965259 | + | 0.261294i | \(0.915851\pi\) | |||||||
\(752\) | 4186.07 | + | 7250.49i | 0.202992 | + | 0.351593i | ||||
\(753\) | 3295.00 | + | 5707.11i | 0.159464 | + | 0.276200i | ||||
\(754\) | 14560.7 | − | 25219.9i | 0.703277 | − | 1.21811i | ||||
\(755\) | −9345.12 | −0.450469 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26206.0 | −1.25822 | −0.629110 | − | 0.777316i | \(-0.716581\pi\) | ||||
−0.629110 | + | 0.777316i | \(0.716581\pi\) | |||||||
\(758\) | 10330.0 | − | 17892.1i | 0.494990 | − | 0.857348i | ||||
\(759\) | 6929.65 | + | 12002.5i | 0.331397 | + | 0.573996i | ||||
\(760\) | 112.000 | + | 193.990i | 0.00534561 | + | 0.00925888i | ||||
\(761\) | 3431.59 | − | 5943.69i | 0.163463 | − | 0.283125i | −0.772646 | − | 0.634838i | \(-0.781067\pi\) |
0.936108 | + | 0.351712i | \(0.114400\pi\) | |||||||
\(762\) | −24324.5 | −1.15641 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4112.00 | 0.194721 | ||||||||
\(765\) | 322.000 | − | 557.720i | 0.0152182 | − | 0.0263587i | ||||
\(766\) | −1004.09 | − | 1739.14i | −0.0473620 | − | 0.0820334i | ||||
\(767\) | −11052.0 | − | 19142.6i | −0.520293 | − | 0.901174i | ||||
\(768\) | −905.097 | + | 1567.67i | −0.0425259 | + | 0.0736570i | ||||
\(769\) | 9058.04 | 0.424761 | 0.212380 | − | 0.977187i | \(-0.431878\pi\) | ||||
0.212380 | + | 0.977187i | \(0.431878\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6630.00 | −0.309693 | ||||||||
\(772\) | −9184.00 | + | 15907.2i | −0.428160 | + | 0.741595i | ||||
\(773\) | −66.4680 | − | 115.126i | −0.00309274 | − | 0.00535679i | 0.864475 | − | 0.502676i | \(-0.167651\pi\) |
−0.867568 | + | 0.497319i | \(0.834318\pi\) | |||||||
\(774\) | −782.000 | − | 1354.46i | −0.0363158 | − | 0.0629008i | ||||
\(775\) | −12460.6 | + | 21582.5i | −0.577547 | + | 1.00034i | ||||
\(776\) | 11868.1 | 0.549020 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10420.0 | −0.480174 | ||||||||
\(779\) | −89.0000 | + | 154.153i | −0.00409340 | + | 0.00708997i | ||||
\(780\) | 14255.3 | + | 24690.9i | 0.654385 | + | 1.13343i | ||||
\(781\) | 4116.00 | + | 7129.12i | 0.188581 | + | 0.326633i | ||||
\(782\) | −197.990 | + | 342.929i | −0.00905384 | + | 0.0156817i | ||||
\(783\) | 8089.30 | 0.369206 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 43792.0 | 1.99109 | ||||||||
\(786\) | 12270.0 | − | 21252.3i | 0.556815 | − | 0.964431i | ||||
\(787\) | −4364.97 | − | 7560.35i | −0.197706 | − | 0.342436i | 0.750078 | − | 0.661349i | \(-0.230016\pi\) |
−0.947784 | + | 0.318913i | \(0.896682\pi\) | |||||||
\(788\) | −1588.00 | − | 2750.50i | −0.0717895 | − | 0.124343i | ||||
\(789\) | −25243.7 | + | 43723.4i | −1.13904 | + | 1.97287i | ||||
\(790\) | −48309.5 | −2.17567 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 2576.00 | 0.115573 | ||||||||
\(793\) | −360.000 | + | 623.538i | −0.0161210 | + | 0.0279224i | ||||
\(794\) | 73.5391 | + | 127.373i | 0.00328691 | + | 0.00569309i | ||||
\(795\) | 5180.00 | + | 8972.02i | 0.231089 | + | 0.400258i | ||||
\(796\) | 4972.37 | − | 8612.41i | 0.221408 | − | 0.383491i | ||||
\(797\) | −7517.96 | −0.334128 | −0.167064 | − | 0.985946i | \(-0.553429\pi\) | ||||
−0.167064 | + | 0.985946i | \(0.553429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 740.000 | 0.0327651 | ||||||||
\(800\) | 4272.00 | − | 7399.32i | 0.188798 | − | 0.327007i | ||||
\(801\) | 7107.13 | + | 12309.9i | 0.313506 | + | 0.543008i | ||||
\(802\) | −498.000 | − | 862.561i | −0.0219264 | − | 0.0379777i | ||||
\(803\) | 1890.80 | − | 3274.97i | 0.0830947 | − | 0.143924i | ||||
\(804\) | 19346.4 | 0.848627 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 9504.00 | 0.415340 | ||||||||
\(807\) | 16300.0 | − | 28232.4i | 0.711013 | − | 1.23151i | ||||
\(808\) | −4514.17 | − | 7818.77i | −0.196544 | − | 0.340425i | ||||
\(809\) | −1888.00 | − | 3270.11i | −0.0820501 | − | 0.142115i | 0.822080 | − | 0.569372i | \(-0.192813\pi\) |
−0.904130 | + | 0.427257i | \(0.859480\pi\) | |||||||
\(810\) | −16255.0 | + | 28154.4i | −0.705113 | + | 1.22129i | ||||
\(811\) | 36227.9 | 1.56860 | 0.784300 | − | 0.620382i | \(-0.213023\pi\) | ||||
0.784300 | + | 0.620382i | \(0.213023\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16720.0 | 0.721274 | ||||||||
\(814\) | 532.000 | − | 921.451i | 0.0229074 | − | 0.0396767i | ||||
\(815\) | −32529.7 | − | 56343.2i | −1.39812 | − | 2.42161i | ||||
\(816\) | 80.0000 | + | 138.564i | 0.00343206 | + | 0.00594450i | ||||
\(817\) | 24.0416 | − | 41.6413i | 0.00102951 | − | 0.00178316i | ||||
\(818\) | 6711.86 | 0.286888 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9968.00 | 0.424509 | ||||||||
\(821\) | 8205.00 | − | 14211.5i | 0.348790 | − | 0.604122i | −0.637245 | − | 0.770661i | \(-0.719926\pi\) |
0.986035 | + | 0.166540i | \(0.0532594\pi\) | |||||||
\(822\) | 5854.84 | + | 10140.9i | 0.248432 | + | 0.430297i | ||||
\(823\) | −11036.0 | − | 19114.9i | −0.467425 | − | 0.809604i | 0.531882 | − | 0.846818i | \(-0.321485\pi\) |
−0.999307 | + | 0.0372144i | \(0.988152\pi\) | |||||||
\(824\) | 3473.31 | − | 6015.95i | 0.146843 | − | 0.254339i | ||||
\(825\) | −26431.7 | −1.11543 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11628.0 | −0.488930 | −0.244465 | − | 0.969658i | \(-0.578612\pi\) | ||||
−0.244465 | + | 0.969658i | \(0.578612\pi\) | |||||||
\(828\) | −6440.00 | + | 11154.4i | −0.270296 | + | 0.468167i | ||||
\(829\) | −15453.1 | − | 26765.6i | −0.647417 | − | 1.12136i | −0.983738 | − | 0.179612i | \(-0.942516\pi\) |
0.336321 | − | 0.941748i | \(-0.390817\pi\) | |||||||
\(830\) | −8372.00 | − | 14500.7i | −0.350116 | − | 0.606419i | ||||
\(831\) | −14163.3 | + | 24531.6i | −0.591241 | + | 1.02406i | ||||
\(832\) | −3258.35 | −0.135773 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −6020.00 | −0.249947 | ||||||||
\(835\) | −14756.0 | + | 25558.1i | −0.611560 | + | 1.05925i | ||||
\(836\) | 39.5980 | + | 68.5857i | 0.00163819 | + | 0.00283742i | ||||
\(837\) | 1320.00 | + | 2286.31i | 0.0545112 | + | 0.0944162i | ||||
\(838\) | −14545.2 | + | 25193.0i | −0.599588 | + | 1.03852i | ||||
\(839\) | −17884.1 | −0.735911 | −0.367955 | − | 0.929843i | \(-0.619942\pi\) | ||||
−0.367955 | + | 0.929843i | \(0.619942\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 57407.0 | 2.35381 | ||||||||
\(842\) | 10854.0 | − | 18799.7i | 0.444244 | − | 0.769453i | ||||
\(843\) | 21156.6 | + | 36644.4i | 0.864381 | + | 1.49715i | ||||
\(844\) | 5496.00 | + | 9519.35i | 0.224147 | + | 0.388234i | ||||
\(845\) | −3910.30 | + | 6772.84i | −0.159193 | + | 0.275731i | ||||
\(846\) | 24069.9 | 0.978181 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1184.00 | −0.0479466 | ||||||||
\(849\) | −17425.0 | + | 30181.0i | −0.704387 | + | 1.22003i | ||||
\(850\) | −377.595 | − | 654.014i | −0.0152369 | − | 0.0263912i | ||||
\(851\) | 2660.00 | + | 4607.26i | 0.107149 | + | 0.185587i | ||||
\(852\) | −8315.58 | + | 14403.0i | −0.334374 | + | 0.579153i | ||||
\(853\) | 20755.0 | 0.833104 | 0.416552 | − | 0.909112i | \(-0.363238\pi\) | ||||
0.416552 | + | 0.909112i | \(0.363238\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 644.000 | 0.0257595 | ||||||||
\(856\) | −6736.00 | + | 11667.1i | −0.268962 | + | 0.465856i | ||||
\(857\) | 22459.8 | + | 38901.6i | 0.895231 | + | 1.55059i | 0.833518 | + | 0.552492i | \(0.186323\pi\) |
0.0617133 | + | 0.998094i | \(0.480344\pi\) | |||||||
\(858\) | 5040.00 | + | 8729.54i | 0.200539 | + | 0.347344i | ||||
\(859\) | 34.6482 | − | 60.0125i | 0.00137623 | − | 0.00238370i | −0.865336 | − | 0.501191i | \(-0.832895\pi\) |
0.866713 | + | 0.498808i | \(0.166229\pi\) | |||||||
\(860\) | −2692.66 | −0.106766 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10728.0 | 0.423895 | ||||||||
\(863\) | 2726.00 | − | 4721.57i | 0.107525 | − | 0.186239i | −0.807242 | − | 0.590221i | \(-0.799041\pi\) |
0.914767 | + | 0.403982i | \(0.132374\pi\) | |||||||
\(864\) | −452.548 | − | 783.837i | −0.0178195 | − | 0.0308642i | ||||
\(865\) | −20496.0 | − | 35500.1i | −0.805647 | − | 1.39542i | ||||
\(866\) | 6487.00 | − | 11235.8i | 0.254546 | − | 0.440887i | ||||
\(867\) | −34726.0 | −1.36027 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17080.0 | −0.666743 | ||||||||
\(870\) | −40040.0 | + | 69351.3i | −1.56033 | + | 2.70256i | ||||
\(871\) | 17411.8 | + | 30158.1i | 0.677355 | + | 1.17321i | ||||
\(872\) | −3272.00 | − | 5667.27i | −0.127069 | − | 0.220089i | ||||
\(873\) | 17060.4 | − | 29549.4i | 0.661404 | − | 1.14559i | ||||
\(874\) | −395.980 | −0.0153252 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7640.00 | 0.294671 | ||||||||
\(877\) | −15553.0 | + | 26938.6i | −0.598845 | + | 1.03723i | 0.394146 | + | 0.919048i | \(0.371040\pi\) |
−0.992992 | + | 0.118183i | \(0.962293\pi\) | |||||||
\(878\) | −13932.8 | − | 24132.4i | −0.535547 | − | 0.927595i | ||||
\(879\) | 6970.00 | + | 12072.4i | 0.267454 | + | 0.463244i | ||||
\(880\) | 2217.49 | − | 3840.80i | 0.0849448 | − | 0.147129i | ||||
\(881\) | −5943.94 | −0.227306 | −0.113653 | − | 0.993521i | \(-0.536255\pi\) | ||||
−0.113653 | + | 0.993521i | \(0.536255\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34796.0 | 1.32614 | 0.663068 | − | 0.748559i | \(-0.269254\pi\) | ||||
0.663068 | + | 0.748559i | \(0.269254\pi\) | |||||||
\(884\) | −144.000 | + | 249.415i | −0.00547878 | + | 0.00948953i | ||||
\(885\) | 30391.4 | + | 52639.5i | 1.15435 | + | 1.99939i | ||||
\(886\) | 5996.00 | + | 10385.4i | 0.227358 | + | 0.393796i | ||||
\(887\) | 4982.27 | − | 8629.55i | 0.188600 | − | 0.326665i | −0.756184 | − | 0.654360i | \(-0.772938\pi\) |
0.944784 | + | 0.327694i | \(0.106272\pi\) | |||||||
\(888\) | 2149.60 | 0.0812342 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24472.0 | 0.921689 | ||||||||
\(891\) | −5747.00 | + | 9954.10i | −0.216085 | + | 0.374270i | ||||
\(892\) | −6856.11 | − | 11875.1i | −0.257354 | − | 0.445750i | ||||
\(893\) | 370.000 | + | 640.859i | 0.0138651 | + | 0.0240151i | ||||
\(894\) | 14495.7 | − | 25107.3i | 0.542291 | − | 0.939276i | ||||
\(895\) | 10691.5 | 0.399303 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −50400.0 | −1.87604 | ||||||||
\(898\) | 2622.00 | − | 4541.44i | 0.0974357 | − | 0.168764i | ||||
\(899\) | 13347.3 | + | 23118.3i | 0.495171 | + | 0.857662i | ||||
\(900\) | −12282.0 | − | 21273.0i | −0.454889 | − | 0.787891i | ||||
\(901\) | −52.3259 | + | 90.6311i | −0.00193477 | + | 0.00335112i | ||||
\(902\) | 3524.22 | 0.130093 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4320.00 | 0.158939 | ||||||||
\(905\) | 37464.0 | − | 64889.6i | 1.37607 | − | 2.38343i | ||||
\(906\) | −3337.54 | − | 5780.80i | −0.122387 | − | 0.211980i | ||||
\(907\) | 14878.0 | + | 25769.5i | 0.544670 | + | 0.943396i | 0.998628 | + | 0.0523731i | \(0.0166785\pi\) |
−0.453957 | + | 0.891023i | \(0.649988\pi\) | |||||||
\(908\) | 10581.1 | − | 18327.1i | 0.386726 | − | 0.669830i | ||||
\(909\) | −25956.5 | −0.947109 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21440.0 | 0.779735 | 0.389868 | − | 0.920871i | \(-0.372521\pi\) | ||||
0.389868 | + | 0.920871i | \(0.372521\pi\) | |||||||
\(912\) | −80.0000 | + | 138.564i | −0.00290468 | + | 0.00503105i | ||||
\(913\) | −2959.95 | − | 5126.78i | −0.107295 | − | 0.185840i | ||||
\(914\) | 11208.0 | + | 19412.8i | 0.405610 | + | 0.702537i | ||||
\(915\) | 989.949 | − | 1714.64i | 0.0357669 | − | 0.0619501i | ||||
\(916\) | 10996.9 | 0.396669 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −80.0000 | −0.00287625 | ||||||||
\(919\) | 4144.00 | − | 7177.62i | 0.148746 | − | 0.257636i | −0.782018 | − | 0.623256i | \(-0.785810\pi\) |
0.930764 | + | 0.365620i | \(0.119143\pi\) | |||||||
\(920\) | 11087.4 | + | 19204.0i | 0.397328 | + | 0.688193i | ||||
\(921\) | −16855.0 | − | 29193.7i | −0.603031 | − | 1.04448i | ||||
\(922\) | −9786.36 | + | 16950.5i | −0.349562 | + | 0.605460i | ||||
\(923\) | −29936.1 | −1.06756 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10146.0 | −0.360647 | ||||||||
\(926\) | 3952.00 | − | 6845.06i | 0.140249 | − | 0.242919i | ||||
\(927\) | −9985.76 | − | 17295.8i | −0.353803 | − | 0.612805i | ||||
\(928\) | −4576.00 | − | 7925.86i | −0.161869 | − | 0.280366i | ||||
\(929\) | −22790.8 | + | 39474.8i | −0.804888 | + | 1.39411i | 0.111479 | + | 0.993767i | \(0.464441\pi\) |
−0.916367 | + | 0.400339i | \(0.868892\pi\) | |||||||
\(930\) | −26134.7 | −0.921494 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 288.000 | 0.0101221 | ||||||||
\(933\) | −23960.0 | + | 41499.9i | −0.840745 | + | 1.45621i | ||||
\(934\) | −17506.5 | − | 30322.2i | −0.613310 | − | 1.06228i | ||||
\(935\) | −196.000 | − | 339.482i | −0.00685549 | − | 0.0118741i | ||||
\(936\) | −4683.88 | + | 8112.71i | −0.163565 | + | 0.283304i | ||||
\(937\) | −11665.8 | −0.406731 | −0.203365 | − | 0.979103i | \(-0.565188\pi\) | ||||
−0.203365 | + | 0.979103i | \(0.565188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43770.0 | 1.52117 | ||||||||
\(940\) | 20720.0 | − | 35888.1i | 0.718949 | − | 1.24526i | ||||
\(941\) | 7.07107 | + | 12.2474i | 0.000244963 | + | 0.000424288i | 0.866148 | − | 0.499788i | \(-0.166589\pi\) |
−0.865903 | + | 0.500212i | \(0.833255\pi\) | |||||||
\(942\) | 15640.0 | + | 27089.3i | 0.540954 | + | 0.936960i | ||||
\(943\) | −8810.55 | + | 15260.3i | −0.304253 | + | 0.526982i | ||||
\(944\) | −6946.62 | −0.239505 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −952.000 | −0.0327190 | ||||||||
\(947\) | −7017.00 | + | 12153.8i | −0.240783 | + | 0.417049i | −0.960938 | − | 0.276765i | \(-0.910738\pi\) |
0.720154 | + | 0.693814i | \(0.244071\pi\) | |||||||
\(948\) | −17253.4 | − | 29883.8i | −0.591102 | − | 1.02382i | ||||
\(949\) | 6876.00 | + | 11909.6i | 0.235200 | + | 0.407378i | ||||
\(950\) | 377.595 | − | 654.014i | 0.0128956 | − | 0.0223358i | ||||
\(951\) | 69480.3 | 2.36914 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −42698.0 | −1.45134 | −0.725668 | − | 0.688045i | \(-0.758469\pi\) | ||||
−0.725668 | + | 0.688045i | \(0.758469\pi\) | |||||||
\(954\) | −1702.00 | + | 2947.95i | −0.0577613 | + | 0.100046i | ||||
\(955\) | −10176.7 | − | 17626.5i | −0.344827 | − | 0.597258i | ||||
\(956\) | −8616.00 | − | 14923.3i | −0.291487 | − | 0.504870i | ||||
\(957\) | −14156.3 | + | 24519.4i | −0.478169 | + | 0.828213i | ||||
\(958\) | 4576.40 | 0.154339 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 8960.00 | 0.301232 | ||||||||
\(961\) | 10539.5 | − | 18254.9i | 0.353781 | − | 0.612767i | ||||
\(962\) | 1934.64 | + | 3350.90i | 0.0648393 | + | 0.112305i | ||||
\(963\) | 19366.0 | + | 33542.9i | 0.648038 | + | 1.12243i | ||||
\(964\) | −3080.16 | + | 5334.99i | −0.102910 | + | 0.178245i | ||||
\(965\) | 90917.0 | 3.03287 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48492.0 | −1.61261 | −0.806307 | − | 0.591497i | \(-0.798537\pi\) | ||||
−0.806307 | + | 0.591497i | \(0.798537\pi\) | |||||||
\(968\) | −4540.00 | + | 7863.51i | −0.150745 | + | 0.261098i | ||||
\(969\) | 7.07107 | + | 12.2474i | 0.000234423 | + | 0.000406032i | ||||
\(970\) | −29372.0 | − | 50873.8i | −0.972245 | − | 1.68398i | ||||
\(971\) | 26334.8 | − | 45613.2i | 0.870364 | − | 1.50751i | 0.00874297 | − | 0.999962i | \(-0.497217\pi\) |
0.861621 | − | 0.507553i | \(-0.169450\pi\) | |||||||
\(972\) | −20166.7 | −0.665480 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1944.00 | −0.0639525 | ||||||||
\(975\) | 48060.0 | − | 83242.4i | 1.57862 | − | 2.73425i | ||||
\(976\) | 113.137 | + | 195.959i | 0.00371048 | + | 0.00642674i | ||||
\(977\) | 27690.0 | + | 47960.5i | 0.906737 | + | 1.57051i | 0.818569 | + | 0.574408i | \(0.194768\pi\) |
0.0881674 | + | 0.996106i | \(0.471899\pi\) | |||||||
\(978\) | 23235.5 | − | 40245.1i | 0.759704 | − | 1.31585i | ||||
\(979\) | 8652.16 | 0.282456 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18814.0 | −0.612319 | ||||||||
\(982\) | −7404.00 | + | 12824.1i | −0.240602 | + | 0.416735i | ||||
\(983\) | −25267.8 | − | 43765.0i | −0.819854 | − | 1.42003i | −0.905790 | − | 0.423728i | \(-0.860721\pi\) |
0.0859360 | − | 0.996301i | \(-0.472612\pi\) | |||||||
\(984\) | 3560.00 | + | 6166.10i | 0.115334 | + | 0.199764i | ||||
\(985\) | −7860.20 | + | 13614.3i | −0.254261 | + | 0.440392i | ||||
\(986\) | −808.930 | −0.0261274 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −288.000 | −0.00927379 | ||||||||
\(989\) | 2380.00 | − | 4122.28i | 0.0765213 | − | 0.132539i | ||||
\(990\) | −6375.27 | − | 11042.3i | −0.204666 | − | 0.354492i | ||||
\(991\) | 19856.0 | + | 34391.6i | 0.636475 | + | 1.10241i | 0.986201 | + | 0.165555i | \(0.0529415\pi\) |
−0.349726 | + | 0.936852i | \(0.613725\pi\) | |||||||
\(992\) | 1493.41 | − | 2586.66i | 0.0477982 | − | 0.0827889i | ||||
\(993\) | −40573.8 | −1.29665 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −49224.0 | −1.56835 | ||||||||
\(996\) | 5980.00 | − | 10357.7i | 0.190245 | − | 0.329513i | ||||
\(997\) | 1093.19 | + | 1893.46i | 0.0347258 | + | 0.0601468i | 0.882866 | − | 0.469625i | \(-0.155611\pi\) |
−0.848140 | + | 0.529772i | \(0.822278\pi\) | |||||||
\(998\) | −12244.0 | − | 21207.2i | −0.388354 | − | 0.672648i | ||||
\(999\) | −537.401 | + | 930.806i | −0.0170196 | + | 0.0294789i |
(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 | 98.4.c.h.79.1 | 4 | ||
3.2 | odd | 2 | 882.4.g.ba.667.2 | 4 | |||
7.2 | even | 3 | 98.4.a.g.1.2 | yes | 2 | ||
7.3 | odd | 6 | inner | 98.4.c.h.67.2 | 4 | ||
7.4 | even | 3 | inner | 98.4.c.h.67.1 | 4 | ||
7.5 | odd | 6 | 98.4.a.g.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | inner | 98.4.c.h.79.2 | 4 | ||
21.2 | odd | 6 | 882.4.a.bg.1.1 | 2 | |||
21.5 | even | 6 | 882.4.a.bg.1.2 | 2 | |||
21.11 | odd | 6 | 882.4.g.ba.361.2 | 4 | |||
21.17 | even | 6 | 882.4.g.ba.361.1 | 4 | |||
21.20 | even | 2 | 882.4.g.ba.667.1 | 4 | |||
28.19 | even | 6 | 784.4.a.y.1.2 | 2 | |||
28.23 | odd | 6 | 784.4.a.y.1.1 | 2 | |||
35.9 | even | 6 | 2450.4.a.bx.1.1 | 2 | |||
35.19 | odd | 6 | 2450.4.a.bx.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
98.4.a.g.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
98.4.a.g.1.2 | yes | 2 | 7.2 | even | 3 | ||
98.4.c.h.67.1 | 4 | 7.4 | even | 3 | inner | ||
98.4.c.h.67.2 | 4 | 7.3 | odd | 6 | inner | ||
98.4.c.h.79.1 | 4 | 1.1 | even | 1 | trivial | ||
98.4.c.h.79.2 | 4 | 7.6 | odd | 2 | inner | ||
784.4.a.y.1.1 | 2 | 28.23 | odd | 6 | |||
784.4.a.y.1.2 | 2 | 28.19 | even | 6 | |||
882.4.a.bg.1.1 | 2 | 21.2 | odd | 6 | |||
882.4.a.bg.1.2 | 2 | 21.5 | even | 6 | |||
882.4.g.ba.361.1 | 4 | 21.17 | even | 6 | |||
882.4.g.ba.361.2 | 4 | 21.11 | odd | 6 | |||
882.4.g.ba.667.1 | 4 | 21.20 | even | 2 | |||
882.4.g.ba.667.2 | 4 | 3.2 | odd | 2 | |||
2450.4.a.bx.1.1 | 2 | 35.9 | even | 6 | |||
2450.4.a.bx.1.2 | 2 | 35.19 | odd | 6 |