Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(100,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.n (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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 11 x^{14} - 4 x^{13} + 87 x^{12} - 35 x^{11} + 326 x^{10} - 205 x^{9} + 895 x^{8} - 481 x^{7} + 1005 x^{6} - 544 x^{5} + 811 x^{4} - 312 x^{3} + 195 x^{2} + 13 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 172.5 | ||
Root | \(-0.0340180 + 0.0589209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.172 |
Dual form | 819.2.n.e.100.5 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0340180 | − | 0.0589209i | 0.0240543 | − | 0.0416633i | −0.853748 | − | 0.520687i | \(-0.825676\pi\) |
0.877802 | + | 0.479024i | \(0.159009\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.997686 | + | 1.72804i | 0.498843 | + | 0.864021i | ||||
\(5\) | −1.52954 | − | 2.64923i | −0.684030 | − | 1.18477i | −0.973741 | − | 0.227660i | \(-0.926893\pi\) |
0.289711 | − | 0.957114i | \(-0.406441\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.60654 | + | 0.453835i | −0.985178 | + | 0.171533i | ||||
\(8\) | 0.271829 | 0.0961060 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.208127 | −0.0658155 | ||||||||
\(11\) | 4.35793 | 1.31396 | 0.656982 | − | 0.753906i | \(-0.271833\pi\) | ||||
0.656982 | + | 0.753906i | \(0.271833\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.79952 | − | 3.12437i | −0.499098 | − | 0.866545i | ||||
\(14\) | −0.0619288 | + | 0.169018i | −0.0165512 | + | 0.0451719i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.98612 | + | 3.44007i | −0.496531 | + | 0.860017i | ||||
\(17\) | −1.76434 | − | 3.05592i | −0.427914 | − | 0.741170i | 0.568773 | − | 0.822494i | \(-0.307418\pi\) |
−0.996688 | + | 0.0813248i | \(0.974085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.90224 | 1.58348 | 0.791741 | − | 0.610857i | \(-0.209175\pi\) | ||||
0.791741 | + | 0.610857i | \(0.209175\pi\) | |||||||
\(20\) | 3.05199 | − | 5.28621i | 0.682446 | − | 1.18203i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.148248 | − | 0.256773i | 0.0316066 | − | 0.0547442i | ||||
\(23\) | 1.66762 | − | 2.88840i | 0.347722 | − | 0.602273i | −0.638122 | − | 0.769935i | \(-0.720289\pi\) |
0.985844 | + | 0.167662i | \(0.0536218\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.17896 | + | 3.77408i | −0.435793 | + | 0.754815i | ||||
\(26\) | −0.245307 | 0.000255364i | −0.0481087 | 5.00811e-5i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.38475 | − | 4.05142i | −0.639658 | − | 0.765647i | ||||
\(29\) | −4.95991 | − | 8.59082i | −0.921033 | − | 1.59528i | −0.797820 | − | 0.602896i | \(-0.794013\pi\) |
−0.123213 | − | 0.992380i | \(-0.539320\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.62451 | − | 8.00989i | 0.830587 | − | 1.43862i | −0.0669867 | − | 0.997754i | \(-0.521339\pi\) |
0.897574 | − | 0.440865i | \(-0.145328\pi\) | |||||||
\(32\) | 0.406957 | + | 0.704870i | 0.0719405 | + | 0.124605i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.240077 | −0.0411728 | ||||||||
\(35\) | 5.18911 | + | 6.21117i | 0.877119 | + | 1.04988i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0545230 | − | 0.0944366i | 0.00896352 | − | 0.0155253i | −0.861509 | − | 0.507743i | \(-0.830480\pi\) |
0.870472 | + | 0.492217i | \(0.163813\pi\) | |||||||
\(38\) | 0.234800 | − | 0.406686i | 0.0380896 | − | 0.0659731i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.415772 | − | 0.720139i | −0.0657394 | − | 0.113864i | ||||
\(41\) | −1.76899 | − | 3.06399i | −0.276270 | − | 0.478514i | 0.694185 | − | 0.719797i | \(-0.255765\pi\) |
−0.970455 | + | 0.241283i | \(0.922432\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.844102 | + | 1.46203i | −0.128724 | + | 0.222957i | −0.923183 | − | 0.384362i | \(-0.874422\pi\) |
0.794458 | + | 0.607319i | \(0.207755\pi\) | |||||||
\(44\) | 4.34784 | + | 7.53068i | 0.655462 | + | 1.13529i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.113458 | − | 0.196515i | −0.0167285 | − | 0.0289746i | ||||
\(47\) | −1.28133 | − | 2.21933i | −0.186902 | − | 0.323723i | 0.757314 | − | 0.653051i | \(-0.226511\pi\) |
−0.944216 | + | 0.329328i | \(0.893178\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.58807 | − | 2.36587i | 0.941153 | − | 0.337982i | ||||
\(50\) | 0.148248 | + | 0.256773i | 0.0209654 | + | 0.0363132i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.60369 | − | 6.22680i | 0.499742 | − | 0.863501i | ||||
\(53\) | −2.65681 | + | 4.60173i | −0.364941 | + | 0.632097i | −0.988767 | − | 0.149467i | \(-0.952244\pi\) |
0.623825 | + | 0.781564i | \(0.285578\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.66561 | − | 11.5452i | −0.898791 | − | 1.55675i | ||||
\(56\) | −0.708532 | + | 0.123365i | −0.0946816 | + | 0.0164854i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.674905 | −0.0886194 | ||||||||
\(59\) | 3.77852 | + | 6.54459i | 0.491921 | + | 0.852033i | 0.999957 | − | 0.00930353i | \(-0.00296145\pi\) |
−0.508035 | + | 0.861336i | \(0.669628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.87317 | 0.623945 | 0.311973 | − | 0.950091i | \(-0.399010\pi\) | ||||
0.311973 | + | 0.950091i | \(0.399010\pi\) | |||||||
\(62\) | −0.314633 | − | 0.544960i | −0.0399584 | − | 0.0692101i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88912 | −0.986140 | ||||||||
\(65\) | −5.52476 | + | 9.54621i | −0.685263 | + | 1.18406i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.680435 | 0.0831284 | 0.0415642 | − | 0.999136i | \(-0.486766\pi\) | ||||
0.0415642 | + | 0.999136i | \(0.486766\pi\) | |||||||
\(68\) | 3.52051 | − | 6.09770i | 0.426924 | − | 0.739454i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.542491 | − | 0.0944552i | 0.0648400 | − | 0.0112896i | ||||
\(71\) | 2.61572 | − | 4.53055i | 0.310428 | − | 0.537678i | −0.668027 | − | 0.744137i | \(-0.732861\pi\) |
0.978455 | + | 0.206460i | \(0.0661942\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.75956 | − | 3.04764i | 0.205941 | − | 0.356699i | −0.744491 | − | 0.667632i | \(-0.767308\pi\) |
0.950432 | + | 0.310933i | \(0.100641\pi\) | |||||||
\(74\) | −0.00370952 | − | 0.00642508i | −0.000431223 | − | 0.000746901i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.88626 | + | 11.9274i | 0.789908 | + | 1.36816i | ||||
\(77\) | −11.3591 | + | 1.97778i | −1.29449 | + | 0.225389i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.85408 | + | 8.40751i | 0.546126 | + | 0.945919i | 0.998535 | + | 0.0541080i | \(0.0172315\pi\) |
−0.452409 | + | 0.891811i | \(0.649435\pi\) | |||||||
\(80\) | 12.1514 | 1.35857 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.240710 | −0.0265820 | ||||||||
\(83\) | −5.41662 | −0.594551 | −0.297275 | − | 0.954792i | \(-0.596078\pi\) | ||||
−0.297275 | + | 0.954792i | \(0.596078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.39723 | + | 9.34828i | −0.585412 | + | 1.01396i | ||||
\(86\) | 0.0574293 | + | 0.0994705i | 0.00619276 | + | 0.0107262i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.18461 | 0.126280 | ||||||||
\(89\) | −3.85207 | + | 6.67198i | −0.408319 | + | 0.707229i | −0.994702 | − | 0.102805i | \(-0.967218\pi\) |
0.586383 | + | 0.810034i | \(0.300551\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.10848 | + | 7.32711i | 0.640342 | + | 0.768090i | ||||
\(92\) | 6.65503 | 0.693835 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.174354 | −0.0179832 | ||||||||
\(95\) | −10.5572 | − | 18.2856i | −1.08315 | − | 1.87607i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.86359 | + | 6.69194i | −0.392288 | + | 0.679463i | −0.992751 | − | 0.120189i | \(-0.961650\pi\) |
0.600463 | + | 0.799653i | \(0.294983\pi\) | |||||||
\(98\) | 0.0847135 | − | 0.468657i | 0.00855735 | − | 0.0473415i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.69568 | −0.869568 | ||||||||
\(101\) | 3.88031 | 0.386105 | 0.193053 | − | 0.981188i | \(-0.438161\pi\) | ||||
0.193053 | + | 0.981188i | \(0.438161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.29088 | − | 7.43202i | −0.422793 | − | 0.732299i | 0.573419 | − | 0.819263i | \(-0.305617\pi\) |
−0.996211 | + | 0.0869638i | \(0.972284\pi\) | |||||||
\(104\) | −0.489163 | − | 0.849295i | −0.0479663 | − | 0.0832802i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.180759 | + | 0.313083i | 0.0175568 | + | 0.0304093i | ||||
\(107\) | −5.60158 | + | 9.70222i | −0.541525 | + | 0.937949i | 0.457291 | + | 0.889317i | \(0.348820\pi\) |
−0.998817 | + | 0.0486324i | \(0.984514\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.98282 | − | 12.0946i | 0.668833 | − | 1.15845i | −0.309398 | − | 0.950933i | \(-0.600128\pi\) |
0.978231 | − | 0.207520i | \(-0.0665391\pi\) | |||||||
\(110\) | −0.907002 | −0.0864793 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.61568 | − | 9.86804i | 0.341650 | − | 0.932442i | ||||
\(113\) | 3.38888 | − | 5.86972i | 0.318799 | − | 0.552176i | −0.661439 | − | 0.749999i | \(-0.730054\pi\) |
0.980238 | + | 0.197823i | \(0.0633871\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.2027 | −0.951410 | ||||||||
\(116\) | 9.89687 | − | 17.1419i | 0.918901 | − | 1.59158i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.514150 | 0.0473314 | ||||||||
\(119\) | 5.98569 | + | 7.16465i | 0.548707 | + | 0.656783i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.99154 | 0.726503 | ||||||||
\(122\) | 0.165775 | − | 0.287131i | 0.0150086 | − | 0.0259956i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.4552 | 1.65733 | ||||||||
\(125\) | −1.96415 | −0.175679 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.68899 | − | 11.5857i | −0.593552 | − | 1.02806i | −0.993750 | − | 0.111633i | \(-0.964392\pi\) |
0.400198 | − | 0.916429i | \(-0.368941\pi\) | |||||||
\(128\) | −1.08229 | + | 1.87457i | −0.0956614 | + | 0.165690i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.374529 | + | 0.650266i | 0.0328484 | + | 0.0570321i | ||||
\(131\) | −9.06148 | − | 15.6949i | −0.791705 | − | 1.37127i | −0.924910 | − | 0.380185i | \(-0.875860\pi\) |
0.133205 | − | 0.991089i | \(-0.457473\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.9909 | + | 3.13247i | −1.56001 | + | 0.271620i | ||||
\(134\) | 0.0231470 | − | 0.0400918i | 0.00199960 | − | 0.00346341i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.479598 | − | 0.830688i | −0.0411252 | − | 0.0712309i | ||||
\(137\) | 10.6703 | + | 18.4814i | 0.911622 | + | 1.57898i | 0.811773 | + | 0.583973i | \(0.198503\pi\) |
0.0998490 | + | 0.995003i | \(0.468164\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0705287 | + | 0.122159i | −0.00598217 | + | 0.0103614i | −0.869001 | − | 0.494810i | \(-0.835238\pi\) |
0.863019 | + | 0.505172i | \(0.168571\pi\) | |||||||
\(140\) | −5.55607 | + | 15.1638i | −0.469573 | + | 1.28157i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.177963 | − | 0.308240i | −0.0149343 | − | 0.0258670i | ||||
\(143\) | −7.84220 | − | 13.6158i | −0.655797 | − | 1.13861i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.1727 | + | 26.2800i | −1.26003 | + | 2.18243i | ||||
\(146\) | −0.119713 | − | 0.207349i | −0.00990753 | − | 0.0171603i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.217587 | 0.0178856 | ||||||||
\(149\) | 14.3559 | 1.17609 | 0.588043 | − | 0.808830i | \(-0.299899\pi\) | ||||
0.588043 | + | 0.808830i | \(0.299899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.83172 | + | 13.5649i | −0.637336 | + | 1.10390i | 0.348679 | + | 0.937242i | \(0.386631\pi\) |
−0.986015 | + | 0.166657i | \(0.946703\pi\) | |||||||
\(152\) | 1.87623 | 0.152182 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.269881 | + | 0.736568i | −0.0217476 | + | 0.0593543i | ||||
\(155\) | −28.2934 | −2.27258 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.75022 | + | 11.6917i | −0.538726 | + | 0.933101i | 0.460247 | + | 0.887791i | \(0.347761\pi\) |
−0.998973 | + | 0.0453098i | \(0.985572\pi\) | |||||||
\(158\) | 0.660504 | 0.0525469 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.24491 | − | 2.15625i | 0.0984188 | − | 0.170466i | ||||
\(161\) | −3.03585 | + | 8.28554i | −0.239259 | + | 0.652992i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.65724 | −0.208131 | −0.104066 | − | 0.994570i | \(-0.533185\pi\) | ||||
−0.104066 | + | 0.994570i | \(0.533185\pi\) | |||||||
\(164\) | 3.52980 | − | 6.11379i | 0.275631 | − | 0.477407i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.184262 | + | 0.319152i | −0.0143015 | + | 0.0247710i | ||||
\(167\) | 10.9142 | + | 18.9040i | 0.844567 | + | 1.46283i | 0.885997 | + | 0.463692i | \(0.153475\pi\) |
−0.0414294 | + | 0.999141i | \(0.513191\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.52343 | + | 11.2448i | −0.501802 | + | 0.864983i | ||||
\(170\) | 0.367206 | + | 0.636019i | 0.0281634 | + | 0.0487805i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.36860 | −0.256853 | ||||||||
\(173\) | −17.6824 | −1.34437 | −0.672184 | − | 0.740384i | \(-0.734644\pi\) | ||||
−0.672184 | + | 0.740384i | \(0.734644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.96674 | − | 10.8262i | 0.299858 | − | 0.818381i | ||||
\(176\) | −8.65539 | + | 14.9916i | −0.652424 | + | 1.13003i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.262079 | + | 0.453935i | 0.0196437 | + | 0.0340239i | ||||
\(179\) | −9.72998 | −0.727253 | −0.363626 | − | 0.931545i | \(-0.618462\pi\) | ||||
−0.363626 | + | 0.931545i | \(0.618462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.01332 | 0.298308 | 0.149154 | − | 0.988814i | \(-0.452345\pi\) | ||||
0.149154 | + | 0.988814i | \(0.452345\pi\) | |||||||
\(182\) | 0.639518 | − | 0.110663i | 0.0474042 | − | 0.00820290i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.453307 | − | 0.785150i | 0.0334182 | − | 0.0578820i | ||||
\(185\) | −0.333580 | −0.0245253 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.68885 | − | 13.3175i | −0.562265 | − | 0.973871i | ||||
\(188\) | 2.55674 | − | 4.42840i | 0.186469 | − | 0.322974i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.43654 | −0.104218 | ||||||||
\(191\) | 14.7904 | 1.07019 | 0.535097 | − | 0.844790i | \(-0.320275\pi\) | ||||
0.535097 | + | 0.844790i | \(0.320275\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.3431 | 1.60829 | 0.804146 | − | 0.594432i | \(-0.202623\pi\) | ||||
0.804146 | + | 0.594432i | \(0.202623\pi\) | |||||||
\(194\) | 0.262863 | + | 0.455292i | 0.0188725 | + | 0.0326881i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.6611 | + | 9.02406i | 0.761511 | + | 0.644576i | ||||
\(197\) | 3.16282 | + | 5.47816i | 0.225342 | + | 0.390303i | 0.956422 | − | 0.291988i | \(-0.0943169\pi\) |
−0.731080 | + | 0.682291i | \(0.760984\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.01808 | + | 5.22748i | 0.213946 | + | 0.370566i | 0.952946 | − | 0.303140i | \(-0.0980349\pi\) |
−0.739000 | + | 0.673706i | \(0.764702\pi\) | |||||||
\(200\) | −0.592305 | + | 1.02590i | −0.0418823 | + | 0.0725423i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.132000 | − | 0.228631i | 0.00928751 | − | 0.0160864i | ||||
\(203\) | 16.8270 | + | 20.1413i | 1.18102 | + | 1.41364i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.41148 | + | 9.37295i | −0.377954 | + | 0.654636i | ||||
\(206\) | −0.583868 | −0.0406800 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 14.3221 | + | 0.0149093i | 0.993061 | + | 0.00103378i | ||||
\(209\) | 30.0795 | 2.08064 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.646092 | + | 1.11906i | 0.0444788 | + | 0.0770395i | 0.887408 | − | 0.460985i | \(-0.152504\pi\) |
−0.842929 | + | 0.538025i | \(0.819171\pi\) | |||||||
\(212\) | −10.6027 | −0.728193 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.381109 | + | 0.660100i | 0.0260521 | + | 0.0451235i | ||||
\(215\) | 5.16434 | 0.352205 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.41880 | + | 22.9768i | −0.571505 | + | 1.55977i | ||||
\(218\) | −0.475083 | − | 0.822868i | −0.0321767 | − | 0.0557316i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.3004 | − | 23.0369i | 0.896710 | − | 1.55315i | ||||
\(221\) | −6.37287 | + | 11.0117i | −0.428686 | + | 0.740724i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.79892 | + | 10.0440i | 0.388324 | + | 0.672597i | 0.992224 | − | 0.124463i | \(-0.0397207\pi\) |
−0.603900 | + | 0.797060i | \(0.706387\pi\) | |||||||
\(224\) | −1.38064 | − | 1.65258i | −0.0922480 | − | 0.110418i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.230566 | − | 0.399352i | −0.0153370 | − | 0.0265645i | ||||
\(227\) | −0.399249 | − | 0.691520i | −0.0264991 | − | 0.0458978i | 0.852472 | − | 0.522773i | \(-0.175103\pi\) |
−0.878971 | + | 0.476876i | \(0.841769\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6073 | − | 20.1044i | −0.767030 | − | 1.32854i | −0.939166 | − | 0.343463i | \(-0.888400\pi\) |
0.172136 | − | 0.985073i | \(-0.444933\pi\) | |||||||
\(230\) | −0.347076 | + | 0.601154i | −0.0228855 | + | 0.0396389i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.34825 | − | 2.33523i | −0.0885168 | − | 0.153316i | ||||
\(233\) | −6.09388 | − | 10.5549i | −0.399223 | − | 0.691475i | 0.594407 | − | 0.804164i | \(-0.297387\pi\) |
−0.993630 | + | 0.112689i | \(0.964054\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.91969 | + | 6.78911i | −0.255693 | + | 0.442873i | ||||
\(236\) | −7.53955 | + | 13.0589i | −0.490783 | + | 0.850061i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.625769 | − | 0.108955i | 0.0405626 | − | 0.00706251i | ||||
\(239\) | 0.484332 | 0.0313289 | 0.0156644 | − | 0.999877i | \(-0.495014\pi\) | ||||
0.0156644 | + | 0.999877i | \(0.495014\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.16006 | + | 2.00929i | 0.0747261 | + | 0.129429i | 0.900967 | − | 0.433887i | \(-0.142858\pi\) |
−0.826241 | + | 0.563317i | \(0.809525\pi\) | |||||||
\(242\) | 0.271856 | − | 0.470868i | 0.0174756 | − | 0.0302686i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.86189 | + | 8.42104i | 0.311251 | + | 0.539102i | ||||
\(245\) | −16.3444 | − | 13.8347i | −1.04421 | − | 0.883863i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −12.4207 | − | 21.5652i | −0.790313 | − | 1.37216i | ||||
\(248\) | 1.25708 | − | 2.17732i | 0.0798244 | − | 0.138260i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.0668163 | + | 0.115729i | −0.00422583 | + | 0.00731935i | ||||
\(251\) | −13.7950 | + | 23.8936i | −0.870732 | + | 1.50815i | −0.00949135 | + | 0.999955i | \(0.503021\pi\) |
−0.861241 | + | 0.508197i | \(0.830312\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.26736 | − | 12.5874i | 0.456895 | − | 0.791365i | ||||
\(254\) | −0.910183 | −0.0571100 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.81549 | − | 13.5368i | −0.488468 | − | 0.846051i | ||||
\(257\) | 4.56503 | − | 7.90686i | 0.284758 | − | 0.493216i | −0.687792 | − | 0.725908i | \(-0.741420\pi\) |
0.972551 | + | 0.232692i | \(0.0747533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0992576 | + | 0.270897i | −0.00616757 | + | 0.0168327i | ||||
\(260\) | −22.0082 | − | 0.0229105i | −1.36489 | − | 0.00142085i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.23301 | −0.0761758 | ||||||||
\(263\) | 5.58969 | 0.344675 | 0.172338 | − | 0.985038i | \(-0.444868\pi\) | ||||
0.172338 | + | 0.985038i | \(0.444868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.2548 | 0.998522 | ||||||||
\(266\) | −0.427447 | + | 1.16660i | −0.0262085 | + | 0.0715290i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.678860 | + | 1.17582i | 0.0414680 | + | 0.0718247i | ||||
\(269\) | 10.6461 | + | 18.4395i | 0.649102 | + | 1.12428i | 0.983338 | + | 0.181789i | \(0.0581886\pi\) |
−0.334235 | + | 0.942490i | \(0.608478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.66348 | + | 9.80944i | −0.344032 | + | 0.595881i | −0.985177 | − | 0.171539i | \(-0.945126\pi\) |
0.641145 | + | 0.767419i | \(0.278460\pi\) | |||||||
\(272\) | 14.0168 | 0.849891 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.45192 | 0.0877139 | ||||||||
\(275\) | −9.49577 | + | 16.4472i | −0.572616 | + | 0.991801i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.68116 | + | 9.84006i | 0.341348 | + | 0.591232i | 0.984683 | − | 0.174353i | \(-0.0557832\pi\) |
−0.643335 | + | 0.765584i | \(0.722450\pi\) | |||||||
\(278\) | 0.00479849 | + | 0.00831123i | 0.000287794 | + | 0.000498474i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.41055 | + | 1.68838i | 0.0842965 | + | 0.100900i | ||||
\(281\) | −7.98667 | −0.476445 | −0.238222 | − | 0.971211i | \(-0.576565\pi\) | ||||
−0.238222 | + | 0.971211i | \(0.576565\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.13874 | 0.246022 | 0.123011 | − | 0.992405i | \(-0.460745\pi\) | ||||
0.123011 | + | 0.992405i | \(0.460745\pi\) | |||||||
\(284\) | 10.4386 | 0.619420 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.06903 | − | 0.00111286i | −0.0632131 | − | 6.58048e-5i | ||||
\(287\) | 6.00149 | + | 7.18356i | 0.354257 | + | 0.424032i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.27423 | − | 3.93909i | 0.133778 | − | 0.231711i | ||||
\(290\) | 1.03229 | + | 1.78798i | 0.0606183 | + | 0.104994i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.02194 | 0.410928 | ||||||||
\(293\) | 14.1626 | − | 24.5303i | 0.827385 | − | 1.43307i | −0.0726976 | − | 0.997354i | \(-0.523161\pi\) |
0.900083 | − | 0.435719i | \(-0.143506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.5588 | − | 20.0204i | 0.672977 | − | 1.16563i | ||||
\(296\) | 0.0148209 | − | 0.0256706i | 0.000861449 | − | 0.00149207i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.488360 | − | 0.845865i | 0.0282900 | − | 0.0489996i | ||||
\(299\) | −12.0254 | − | 0.0125184i | −0.695444 | − | 0.000723957i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.53666 | − | 4.19391i | 0.0885719 | − | 0.241733i | ||||
\(302\) | 0.532839 | + | 0.922904i | 0.0306614 | + | 0.0531071i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.7087 | + | 23.7442i | −0.786248 | + | 1.36182i | ||||
\(305\) | −7.45369 | − | 12.9102i | −0.426797 | − | 0.739234i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 18.0617 | 1.03083 | 0.515417 | − | 0.856939i | \(-0.327637\pi\) | ||||
0.515417 | + | 0.856939i | \(0.327637\pi\) | |||||||
\(308\) | −14.7505 | − | 17.6558i | −0.840487 | − | 1.00603i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.962486 | + | 1.66707i | −0.0546655 | + | 0.0946834i | ||||
\(311\) | 6.03959 | − | 10.4609i | 0.342474 | − | 0.593182i | −0.642418 | − | 0.766355i | \(-0.722069\pi\) |
0.984891 | + | 0.173173i | \(0.0554019\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.3790 | − | 17.9769i | −0.586654 | − | 1.01611i | −0.994667 | − | 0.103138i | \(-0.967112\pi\) |
0.408013 | − | 0.912976i | \(-0.366222\pi\) | |||||||
\(314\) | 0.459257 | + | 0.795457i | 0.0259174 | + | 0.0448902i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.68569 | + | 16.7761i | −0.544862 | + | 0.943729i | ||||
\(317\) | 8.73476 | + | 15.1290i | 0.490593 | + | 0.849732i | 0.999941 | − | 0.0108284i | \(-0.00344685\pi\) |
−0.509348 | + | 0.860560i | \(0.670114\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.6150 | − | 37.4382i | −1.21020 | − | 2.09614i | ||||
\(320\) | 12.0667 | + | 20.9001i | 0.674549 | + | 1.16835i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.384918 | + | 0.460732i | 0.0214506 | + | 0.0256756i | ||||
\(323\) | −12.1779 | − | 21.0927i | −0.677595 | − | 1.17363i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.7127 | + | 0.0163569i | 0.871585 | + | 0.000907319i | ||||
\(326\) | −0.0903939 | + | 0.156567i | −0.00500646 | + | 0.00867144i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.480863 | − | 0.832880i | −0.0265512 | − | 0.0459881i | ||||
\(329\) | 4.34705 | + | 5.20326i | 0.239661 | + | 0.286865i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.12617 | 0.391690 | 0.195845 | − | 0.980635i | \(-0.437255\pi\) | ||||
0.195845 | + | 0.980635i | \(0.437255\pi\) | |||||||
\(332\) | −5.40408 | − | 9.36014i | −0.296587 | − | 0.513705i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.48512 | 0.0812620 | ||||||||
\(335\) | −1.04075 | − | 1.80263i | −0.0568623 | − | 0.0984883i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.8396 | −1.24415 | −0.622077 | − | 0.782956i | \(-0.713711\pi\) | ||||
−0.622077 | + | 0.782956i | \(0.713711\pi\) | |||||||
\(338\) | 0.440638 | + | 0.766890i | 0.0239675 | + | 0.0417133i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −21.5390 | −1.16811 | ||||||||
\(341\) | 20.1533 | − | 34.9065i | 1.09136 | − | 1.89029i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0983 | + | 9.15663i | −0.869228 | + | 0.494412i | ||||
\(344\) | −0.229451 | + | 0.397422i | −0.0123712 | + | 0.0214275i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.601520 | + | 1.04186i | −0.0323379 | + | 0.0560109i | ||||
\(347\) | −8.62904 | − | 14.9459i | −0.463231 | − | 0.802340i | 0.535889 | − | 0.844289i | \(-0.319977\pi\) |
−0.999120 | + | 0.0419489i | \(0.986643\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −15.3687 | − | 26.6193i | −0.822665 | − | 1.42490i | −0.903691 | − | 0.428186i | \(-0.859153\pi\) |
0.0810257 | − | 0.996712i | \(-0.474180\pi\) | |||||||
\(350\) | −0.502946 | − | 0.602008i | −0.0268836 | − | 0.0321787i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.77349 | + | 3.07177i | 0.0945272 | + | 0.163726i | ||||
\(353\) | 0.960641 | 0.0511298 | 0.0255649 | − | 0.999673i | \(-0.491862\pi\) | ||||
0.0255649 | + | 0.999673i | \(0.491862\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0033 | −0.849369 | ||||||||
\(356\) | −15.3726 | −0.814748 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.330994 | + | 0.573299i | −0.0174936 | + | 0.0302998i | ||||
\(359\) | −16.4526 | − | 28.4967i | −0.868334 | − | 1.50400i | −0.863698 | − | 0.504009i | \(-0.831858\pi\) |
−0.00463555 | − | 0.999989i | \(-0.501476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 28.6409 | 1.50741 | ||||||||
\(362\) | 0.136525 | − | 0.236468i | 0.00717559 | − | 0.0124285i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.56722 | + | 17.8659i | −0.344216 | + | 0.936425i | ||||
\(365\) | −10.7652 | −0.563478 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0554 | 1.15129 | 0.575643 | − | 0.817701i | \(-0.304752\pi\) | ||||
0.575643 | + | 0.817701i | \(0.304752\pi\) | |||||||
\(368\) | 6.62419 | + | 11.4734i | 0.345310 | + | 0.598094i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.0113477 | + | 0.0196548i | −0.000589939 | + | 0.00102180i | ||||
\(371\) | 4.83665 | − | 13.2003i | 0.251107 | − | 0.685328i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.9119 | 1.34167 | 0.670835 | − | 0.741607i | \(-0.265936\pi\) | ||||
0.670835 | + | 0.741607i | \(0.265936\pi\) | |||||||
\(374\) | −1.04624 | −0.0540996 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.348303 | − | 0.603279i | −0.0179624 | − | 0.0311118i | ||||
\(377\) | −17.9155 | + | 30.9560i | −0.922693 | + | 1.59432i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.77121 | − | 3.06783i | −0.0909811 | − | 0.157584i | 0.816943 | − | 0.576718i | \(-0.195667\pi\) |
−0.907924 | + | 0.419134i | \(0.862334\pi\) | |||||||
\(380\) | 21.0656 | − | 36.4867i | 1.08064 | − | 1.87173i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.503139 | − | 0.871462i | 0.0257428 | − | 0.0445879i | ||||
\(383\) | 29.3950 | 1.50202 | 0.751008 | − | 0.660293i | \(-0.229568\pi\) | ||||
0.751008 | + | 0.660293i | \(0.229568\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 22.6138 | + | 27.0678i | 1.15250 | + | 1.37950i | ||||
\(386\) | 0.760067 | − | 1.31648i | 0.0386864 | − | 0.0670068i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.4186 | −0.782761 | ||||||||
\(389\) | −1.32057 | + | 2.28730i | −0.0669556 | + | 0.115971i | −0.897560 | − | 0.440893i | \(-0.854662\pi\) |
0.830604 | + | 0.556863i | \(0.187995\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.7690 | −0.595182 | ||||||||
\(392\) | 1.79083 | − | 0.643113i | 0.0904504 | − | 0.0324821i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.430371 | 0.0216818 | ||||||||
\(395\) | 14.8490 | − | 25.7192i | 0.747133 | − | 1.29407i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.575977 | 0.0289075 | 0.0144537 | − | 0.999896i | \(-0.495399\pi\) | ||||
0.0144537 | + | 0.999896i | \(0.495399\pi\) | |||||||
\(398\) | 0.410677 | 0.0205854 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.65539 | − | 14.9916i | −0.432769 | − | 0.749578i | ||||
\(401\) | −4.75598 | + | 8.23761i | −0.237503 | + | 0.411366i | −0.959997 | − | 0.280010i | \(-0.909662\pi\) |
0.722494 | + | 0.691377i | \(0.242995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −33.3478 | − | 0.0347150i | −1.66117 | − | 0.00172928i | ||||
\(404\) | 3.87133 | + | 6.70534i | 0.192606 | + | 0.333603i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.75916 | − | 0.306295i | 0.0873059 | − | 0.0152012i | ||||
\(407\) | 0.237607 | − | 0.411548i | 0.0117778 | − | 0.0203997i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0931606 | + | 0.161359i | 0.00460649 | + | 0.00797868i | 0.868319 | − | 0.496005i | \(-0.165200\pi\) |
−0.863713 | + | 0.503984i | \(0.831867\pi\) | |||||||
\(410\) | 0.368175 | + | 0.637698i | 0.0181829 | + | 0.0314937i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.56190 | − | 14.8296i | 0.421814 | − | 0.730604i | ||||
\(413\) | −12.8190 | − | 15.3439i | −0.630782 | − | 0.755023i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.28491 | + | 14.3499i | 0.406690 | + | 0.704408i | ||||
\(416\) | 1.46995 | − | 2.53992i | 0.0720701 | − | 0.124530i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.02324 | − | 1.77231i | 0.0500484 | − | 0.0866864i | ||||
\(419\) | 0.448814 | + | 0.777369i | 0.0219260 | + | 0.0379769i | 0.876780 | − | 0.480891i | \(-0.159687\pi\) |
−0.854854 | + | 0.518868i | \(0.826354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.34862 | −0.211939 | −0.105969 | − | 0.994369i | \(-0.533795\pi\) | ||||
−0.105969 | + | 0.994369i | \(0.533795\pi\) | |||||||
\(422\) | 0.0879150 | 0.00427963 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.722198 | + | 1.25088i | −0.0350731 | + | 0.0607483i | ||||
\(425\) | 15.3777 | 0.745928 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.7021 | + | 2.21161i | −0.614697 | + | 0.107027i | ||||
\(428\) | −22.3545 | −1.08054 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.175680 | − | 0.304287i | 0.00847206 | − | 0.0146740i | ||||
\(431\) | 10.7267 | 0.516685 | 0.258342 | − | 0.966053i | \(-0.416824\pi\) | ||||
0.258342 | + | 0.966053i | \(0.416824\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.46111 | − | 5.99482i | 0.166330 | − | 0.288093i | −0.770797 | − | 0.637081i | \(-0.780142\pi\) |
0.937127 | + | 0.348989i | \(0.113475\pi\) | |||||||
\(434\) | 1.06742 | + | 1.27767i | 0.0512380 | + | 0.0613300i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.8666 | 1.33457 | ||||||||
\(437\) | 11.5103 | − | 19.9364i | 0.550612 | − | 0.953688i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.6090 | + | 21.8394i | −0.601794 | + | 1.04234i | 0.390756 | + | 0.920494i | \(0.372214\pi\) |
−0.992549 | + | 0.121843i | \(0.961120\pi\) | |||||||
\(440\) | −1.81191 | − | 3.13831i | −0.0863792 | − | 0.149613i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.432024 | + | 0.750089i | 0.0205493 | + | 0.0356781i | ||||
\(443\) | 8.71266 | + | 15.0908i | 0.413951 | + | 0.716984i | 0.995318 | − | 0.0966574i | \(-0.0308151\pi\) |
−0.581367 | + | 0.813642i | \(0.697482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.5675 | 1.11721 | ||||||||
\(446\) | 0.789070 | 0.0373635 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.5633 | − | 3.58036i | 0.971524 | − | 0.169156i | ||||
\(449\) | 5.91239 | − | 10.2406i | 0.279023 | − | 0.483282i | −0.692119 | − | 0.721783i | \(-0.743323\pi\) |
0.971142 | + | 0.238501i | \(0.0766561\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.70914 | − | 13.3526i | −0.363009 | − | 0.628751i | ||||
\(452\) | 13.5242 | 0.636123 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.0543266 | −0.00254967 | ||||||||
\(455\) | 10.0681 | − | 27.3899i | 0.472000 | − | 1.28406i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.16626 | − | 7.21617i | 0.194889 | − | 0.337558i | −0.751975 | − | 0.659192i | \(-0.770899\pi\) |
0.946864 | + | 0.321634i | \(0.104232\pi\) | |||||||
\(458\) | −1.57942 | −0.0738017 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.1791 | − | 17.6307i | −0.474604 | − | 0.822038i | ||||
\(461\) | −2.20305 | + | 3.81579i | −0.102606 | + | 0.177719i | −0.912758 | − | 0.408502i | \(-0.866051\pi\) |
0.810152 | + | 0.586221i | \(0.199385\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.2243 | 0.939904 | 0.469952 | − | 0.882692i | \(-0.344271\pi\) | ||||
0.469952 | + | 0.882692i | \(0.344271\pi\) | |||||||
\(464\) | 39.4040 | 1.82929 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.829206 | −0.0384122 | ||||||||
\(467\) | 3.27010 | + | 5.66398i | 0.151322 | + | 0.262098i | 0.931714 | − | 0.363193i | \(-0.118314\pi\) |
−0.780392 | + | 0.625291i | \(0.784980\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.77358 | + | 0.308805i | −0.0818963 | + | 0.0142593i | ||||
\(470\) | 0.266680 | + | 0.461903i | 0.0123010 | + | 0.0213060i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.02711 | + | 1.77901i | 0.0472766 | + | 0.0818855i | ||||
\(473\) | −3.67854 | + | 6.37141i | −0.169139 | + | 0.292958i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0397 | + | 26.0496i | −0.690070 | + | 1.19524i | ||||
\(476\) | −6.40898 | + | 17.4916i | −0.293755 | + | 0.801726i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.0164760 | − | 0.0285373i | 0.000753595 | − | 0.00130527i | ||||
\(479\) | 7.81335 | 0.357001 | 0.178500 | − | 0.983940i | \(-0.442875\pi\) | ||||
0.178500 | + | 0.983940i | \(0.442875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.393171 | 0.000409290i | −0.0179270 | 1.86620e-5i | ||||||
\(482\) | 0.157852 | 0.00718995 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.97304 | + | 13.8097i | 0.362411 | + | 0.627714i | ||||
\(485\) | 23.6380 | 1.07335 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.5370 | + | 18.2507i | 0.477479 | + | 0.827018i | 0.999667 | − | 0.0258123i | \(-0.00821724\pi\) |
−0.522188 | + | 0.852831i | \(0.674884\pi\) | |||||||
\(488\) | 1.32467 | 0.0599649 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.37115 | + | 0.492402i | −0.0619425 | + | 0.0222445i | ||||
\(491\) | 4.36913 | + | 7.56755i | 0.197176 | + | 0.341519i | 0.947612 | − | 0.319425i | \(-0.103490\pi\) |
−0.750436 | + | 0.660943i | \(0.770156\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17.5019 | + | 30.3142i | −0.788247 | + | 1.36528i | ||||
\(494\) | −1.69317 | − | 0.00176259i | −0.0761792 | − | 7.93025e-5i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.3697 | + | 31.8173i | 0.824824 | + | 1.42864i | ||||
\(497\) | −4.76184 | + | 12.9962i | −0.213598 | + | 0.582957i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.6426 | − | 18.4336i | −0.476430 | − | 0.825200i | 0.523206 | − | 0.852206i | \(-0.324736\pi\) |
−0.999635 | + | 0.0270062i | \(0.991403\pi\) | |||||||
\(500\) | −1.95960 | − | 3.39413i | −0.0876360 | − | 0.151790i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.938555 | + | 1.62563i | 0.0418898 | + | 0.0725552i | ||||
\(503\) | 2.29846 | − | 3.98105i | 0.102483 | − | 0.177506i | −0.810224 | − | 0.586120i | \(-0.800655\pi\) |
0.912707 | + | 0.408614i | \(0.133988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.93508 | − | 10.2799i | −0.264107 | − | 0.457448i | ||||
\(506\) | −0.494442 | − | 0.856398i | −0.0219806 | − | 0.0380715i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3470 | − | 23.1177i | 0.592178 | − | 1.02568i | ||||
\(509\) | −6.85316 | + | 11.8700i | −0.303761 | + | 0.526129i | −0.976985 | − | 0.213309i | \(-0.931576\pi\) |
0.673224 | + | 0.739439i | \(0.264909\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.20322 | + | 8.74234i | −0.141702 | + | 0.386738i | ||||
\(512\) | −5.39261 | −0.238322 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.310586 | − | 0.537950i | −0.0136994 | − | 0.0237280i | ||||
\(515\) | −13.1261 | + | 22.7351i | −0.578406 | + | 1.00183i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.58396 | − | 9.67170i | −0.245582 | − | 0.425361i | ||||
\(518\) | 0.0125849 | + | 0.0150637i | 0.000552950 | + | 0.000661861i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.50179 | + | 2.59493i | −0.0658579 | + | 0.113795i | ||||
\(521\) | 2.13457 | − | 3.69718i | 0.0935172 | − | 0.161977i | −0.815472 | − | 0.578797i | \(-0.803522\pi\) |
0.908989 | + | 0.416821i | \(0.136856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.0853 | − | 24.3964i | 0.615907 | − | 1.06678i | −0.374318 | − | 0.927300i | \(-0.622123\pi\) |
0.990225 | − | 0.139481i | \(-0.0445436\pi\) | |||||||
\(524\) | 18.0810 | − | 31.3172i | 0.789873 | − | 1.36810i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.190150 | − | 0.329350i | 0.00829094 | − | 0.0143603i | ||||
\(527\) | −32.6368 | −1.42168 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.93810 | + | 10.2851i | 0.258178 | + | 0.447178i | ||||
\(530\) | 0.552954 | − | 0.957745i | 0.0240188 | − | 0.0416018i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −23.3623 | − | 27.9639i | −1.01289 | − | 1.21239i | ||||
\(533\) | −6.38969 | + | 11.0407i | −0.276768 | + | 0.478226i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 34.2713 | 1.48168 | ||||||||
\(536\) | 0.184962 | 0.00798914 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.44863 | 0.0624549 | ||||||||
\(539\) | 28.7103 | − | 10.3103i | 1.23664 | − | 0.444096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.24717 | + | 16.0166i | 0.397567 | + | 0.688606i | 0.993425 | − | 0.114484i | \(-0.0365214\pi\) |
−0.595858 | + | 0.803089i | \(0.703188\pi\) | |||||||
\(542\) | 0.385320 | + | 0.667394i | 0.0165509 | + | 0.0286670i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.43602 | − | 2.48726i | 0.0615687 | − | 0.106640i | ||||
\(545\) | −42.7219 | −1.83001 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.6951 | 1.05589 | 0.527943 | − | 0.849280i | \(-0.322963\pi\) | ||||
0.527943 | + | 0.849280i | \(0.322963\pi\) | |||||||
\(548\) | −21.2911 | + | 36.8773i | −0.909512 | + | 1.57532i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.646054 | + | 1.11900i | 0.0275478 | + | 0.0477142i | ||||
\(551\) | −34.2345 | − | 59.2959i | −1.45844 | − | 2.52609i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.4680 | − | 19.7115i | −0.700289 | − | 0.838220i | ||||
\(554\) | 0.773046 | 0.0328436 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.281462 | −0.0119366 | ||||||||
\(557\) | 2.97174 | 0.125917 | 0.0629584 | − | 0.998016i | \(-0.479946\pi\) | ||||
0.0629584 | + | 0.998016i | \(0.479946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.08691 | + | 0.00633646i | 0.257449 | + | 0.000268004i | ||||
\(560\) | −31.6731 | + | 5.51472i | −1.33843 | + | 0.233040i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.271690 | + | 0.470581i | −0.0114606 | + | 0.0198503i | ||||
\(563\) | −1.60029 | − | 2.77179i | −0.0674443 | − | 0.116817i | 0.830331 | − | 0.557270i | \(-0.188151\pi\) |
−0.897776 | + | 0.440453i | \(0.854818\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.7337 | −0.872272 | ||||||||
\(566\) | 0.140791 | − | 0.243858i | 0.00591791 | − | 0.0102501i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.711027 | − | 1.23154i | 0.0298340 | − | 0.0516741i | ||||
\(569\) | −6.29189 | + | 10.8979i | −0.263770 | + | 0.456862i | −0.967241 | − | 0.253862i | \(-0.918299\pi\) |
0.703471 | + | 0.710724i | \(0.251633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.8472 | − | 20.5200i | 0.495792 | − | 0.858736i | −0.504197 | − | 0.863589i | \(-0.668211\pi\) |
0.999988 | + | 0.00485262i | \(0.00154464\pi\) | |||||||
\(572\) | 15.7046 | − | 27.1359i | 0.656643 | − | 1.13461i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.627420 | − | 0.109243i | 0.0261880 | − | 0.00455970i | ||||
\(575\) | 7.26736 | + | 12.5874i | 0.303070 | + | 0.524932i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.67873 | + | 2.90764i | −0.0698863 | + | 0.121047i | −0.898851 | − | 0.438254i | \(-0.855597\pi\) |
0.828965 | + | 0.559301i | \(0.188930\pi\) | |||||||
\(578\) | −0.154730 | − | 0.267999i | −0.00643590 | − | 0.0111473i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −60.5505 | −2.51422 | ||||||||
\(581\) | 14.1186 | − | 2.45825i | 0.585739 | − | 0.101985i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.5782 | + | 20.0540i | −0.479520 | + | 0.830553i | ||||
\(584\) | 0.478298 | − | 0.828437i | 0.0197921 | − | 0.0342810i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.963563 | − | 1.66894i | −0.0398044 | − | 0.0689433i | ||||
\(587\) | 4.99547 | + | 8.65242i | 0.206185 | + | 0.357123i | 0.950510 | − | 0.310695i | \(-0.100562\pi\) |
−0.744324 | + | 0.667818i | \(0.767228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.9195 | − | 55.2862i | 1.31522 | − | 2.27803i | ||||
\(590\) | −0.786412 | − | 1.36210i | −0.0323761 | − | 0.0560770i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.216579 | + | 0.375126i | 0.00890133 | + | 0.0154176i | ||||
\(593\) | 16.4331 | + | 28.4629i | 0.674825 | + | 1.16883i | 0.976520 | + | 0.215426i | \(0.0691141\pi\) |
−0.301695 | + | 0.953404i | \(0.597553\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.82552 | − | 26.8161i | 0.402807 | − | 1.09935i | ||||
\(596\) | 14.3227 | + | 24.8077i | 0.586682 | + | 1.01616i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.409816 | + | 0.708119i | −0.0167586 | + | 0.0289571i | ||||
\(599\) | −10.6138 | + | 18.3836i | −0.433667 | + | 0.751133i | −0.997186 | − | 0.0749700i | \(-0.976114\pi\) |
0.563519 | + | 0.826103i | \(0.309447\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.776508 | + | 1.34495i | 0.0316744 | + | 0.0548617i | 0.881428 | − | 0.472318i | \(-0.156583\pi\) |
−0.849754 | + | 0.527180i | \(0.823249\pi\) | |||||||
\(602\) | −0.194835 | − | 0.233210i | −0.00794087 | − | 0.00950493i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −31.2544 | −1.27172 | ||||||||
\(605\) | −12.2233 | − | 21.1715i | −0.496950 | − | 0.860742i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.61104 | 0.268334 | 0.134167 | − | 0.990959i | \(-0.457164\pi\) | ||||
0.134167 | + | 0.990959i | \(0.457164\pi\) | |||||||
\(608\) | 2.80891 | + | 4.86518i | 0.113916 | + | 0.197309i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.01424 | −0.0410653 | ||||||||
\(611\) | −4.62824 | + | 7.99711i | −0.187239 | + | 0.323529i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0584 | −0.487034 | −0.243517 | − | 0.969897i | \(-0.578301\pi\) | ||||
−0.243517 | + | 0.969897i | \(0.578301\pi\) | |||||||
\(614\) | 0.614422 | − | 1.06421i | 0.0247960 | − | 0.0429480i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.08773 | + | 0.537617i | −0.124408 | + | 0.0216612i | ||||
\(617\) | 16.5723 | − | 28.7040i | 0.667175 | − | 1.15558i | −0.311515 | − | 0.950241i | \(-0.600837\pi\) |
0.978691 | − | 0.205340i | \(-0.0658301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.8269 | − | 41.2695i | 0.957686 | − | 1.65876i | 0.229587 | − | 0.973288i | \(-0.426263\pi\) |
0.728099 | − | 0.685472i | \(-0.240404\pi\) | |||||||
\(620\) | −28.2280 | − | 48.8923i | −1.13366 | − | 1.96356i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.410909 | − | 0.711716i | −0.0164760 | − | 0.0285372i | ||||
\(623\) | 7.01259 | − | 19.1390i | 0.280953 | − | 0.766787i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.8991 | + | 24.0739i | 0.555962 | + | 0.962955i | ||||
\(626\) | −1.41229 | −0.0564463 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.9384 | −1.07496 | ||||||||
\(629\) | −0.384788 | −0.0153425 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.28825 | − | 2.23132i | 0.0512846 | − | 0.0888276i | −0.839243 | − | 0.543756i | \(-0.817002\pi\) |
0.890528 | + | 0.454928i | \(0.150335\pi\) | |||||||
\(632\) | 1.31948 | + | 2.28540i | 0.0524860 | + | 0.0909085i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.18856 | 0.0472036 | ||||||||
\(635\) | −20.4621 | + | 35.4414i | −0.812014 | + | 1.40645i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.2473 | − | 16.3261i | −0.762604 | − | 0.646865i | ||||
\(638\) | −2.94119 | −0.116443 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.62158 | 0.261741 | ||||||||
\(641\) | 20.3763 | + | 35.2928i | 0.804815 | + | 1.39398i | 0.916416 | + | 0.400227i | \(0.131069\pi\) |
−0.111601 | + | 0.993753i | \(0.535598\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.68006 | + | 8.10610i | −0.184564 | + | 0.319674i | −0.943429 | − | 0.331574i | \(-0.892420\pi\) |
0.758866 | + | 0.651247i | \(0.225754\pi\) | |||||||
\(644\) | −17.3466 | + | 3.02028i | −0.683551 | + | 0.119016i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.65707 | −0.0651964 | ||||||||
\(647\) | −25.0197 | −0.983625 | −0.491812 | − | 0.870701i | \(-0.663665\pi\) | ||||
−0.491812 | + | 0.870701i | \(0.663665\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.4665 | + | 28.5208i | 0.646367 | + | 1.11954i | ||||
\(650\) | 0.535479 | − | 0.925251i | 0.0210032 | − | 0.0362913i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.65109 | − | 4.59182i | −0.103825 | − | 0.179830i | ||||
\(653\) | −9.28070 | + | 16.0746i | −0.363182 | + | 0.629049i | −0.988483 | − | 0.151334i | \(-0.951643\pi\) |
0.625301 | + | 0.780384i | \(0.284976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.7197 | + | 48.0120i | −1.08310 | + | 1.87598i | ||||
\(656\) | 14.0538 | 0.548707 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.454459 | − | 0.0791277i | 0.0177167 | − | 0.00308472i | ||||
\(659\) | −18.4907 | + | 32.0268i | −0.720295 | + | 1.24759i | 0.240587 | + | 0.970628i | \(0.422660\pi\) |
−0.960882 | + | 0.276960i | \(0.910673\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.9233 | 0.619344 | 0.309672 | − | 0.950843i | \(-0.399781\pi\) | ||||
0.309672 | + | 0.950843i | \(0.399781\pi\) | |||||||
\(662\) | 0.242418 | − | 0.419880i | 0.00942184 | − | 0.0163191i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.47239 | −0.0571399 | ||||||||
\(665\) | 35.8165 | + | 42.8710i | 1.38890 | + | 1.66247i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −33.0850 | −1.28106 | ||||||||
\(668\) | −21.7779 | + | 37.7204i | −0.842612 | + | 1.45945i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.141617 | −0.00547114 | ||||||||
\(671\) | 21.2369 | 0.819842 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9624 | + | 18.9874i | 0.422569 | + | 0.731910i | 0.996190 | − | 0.0872103i | \(-0.0277952\pi\) |
−0.573621 | + | 0.819121i | \(0.694462\pi\) | |||||||
\(674\) | −0.776958 | + | 1.34573i | −0.0299273 | + | 0.0518356i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.9398 | − | 0.0540066i | −0.997683 | − | 0.00207718i | ||||
\(677\) | 16.0122 | + | 27.7339i | 0.615398 | + | 1.06590i | 0.990315 | + | 0.138842i | \(0.0443380\pi\) |
−0.374917 | + | 0.927059i | \(0.622329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.03356 | − | 19.1962i | 0.269923 | − | 0.736683i | ||||
\(680\) | −1.46712 | + | 2.54113i | −0.0562617 | + | 0.0974480i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.37115 | − | 2.37490i | −0.0525040 | − | 0.0909396i | ||||
\(683\) | −1.51134 | − | 2.61772i | −0.0578300 | − | 0.100164i | 0.835661 | − | 0.549245i | \(-0.185085\pi\) |
−0.893491 | + | 0.449081i | \(0.851751\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.6411 | − | 56.5361i | 1.24715 | − | 2.16013i | ||||
\(686\) | −0.00811601 | + | 1.26002i | −0.000309871 | + | 0.0481077i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.35298 | − | 5.80754i | −0.127831 | − | 0.221410i | ||||
\(689\) | 19.1585 | + | 0.0199440i | 0.729882 | + | 0.000759807i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.94954 | − | 10.3049i | 0.226331 | − | 0.392017i | −0.730387 | − | 0.683034i | \(-0.760660\pi\) |
0.956718 | + | 0.291017i | \(0.0939936\pi\) | |||||||
\(692\) | −17.6415 | − | 30.5559i | −0.670628 | − | 1.16156i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.17417 | −0.0445709 | ||||||||
\(695\) | 0.431505 | 0.0163679 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.24220 | + | 10.8118i | −0.236440 | + | 0.409526i | ||||
\(698\) | −2.09124 | −0.0791547 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 22.6656 | − | 3.94640i | 0.856680 | − | 0.149160i | ||||
\(701\) | −2.07215 | −0.0782642 | −0.0391321 | − | 0.999234i | \(-0.512459\pi\) | ||||
−0.0391321 | + | 0.999234i | \(0.512459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.376331 | − | 0.651824i | 0.0141936 | − | 0.0245840i | ||||
\(704\) | −34.3802 | −1.29575 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.0326791 | − | 0.0566018i | 0.00122989 | − | 0.00213024i | ||||
\(707\) | −10.1142 | + | 1.76102i | −0.380383 | + | 0.0662300i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.23998 | 0.271903 | 0.135952 | − | 0.990715i | \(-0.456591\pi\) | ||||
0.135952 | + | 0.990715i | \(0.456591\pi\) | |||||||
\(710\) | −0.544401 | + | 0.942930i | −0.0204310 | + | 0.0353875i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.04710 | + | 1.81364i | −0.0392419 | + | 0.0679690i | ||||
\(713\) | −15.4238 | − | 26.7149i | −0.577627 | − | 1.00048i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.0765 | + | 41.6017i | −0.900411 | + | 1.55581i | ||||
\(716\) | −9.70746 | − | 16.8138i | −0.362785 | − | 0.628362i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.23873 | −0.0835488 | ||||||||
\(719\) | −50.9305 | −1.89939 | −0.949694 | − | 0.313179i | \(-0.898606\pi\) | ||||
−0.949694 | + | 0.313179i | \(0.898606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5572 | + | 17.4245i | 0.542140 | + | 0.648922i | ||||
\(722\) | 0.974305 | − | 1.68755i | 0.0362599 | − | 0.0628039i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.00403 | + | 6.93518i | 0.148809 | + | 0.257744i | ||||
\(725\) | 43.2299 | 1.60552 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.6848 | −0.804244 | −0.402122 | − | 0.915586i | \(-0.631727\pi\) | ||||
−0.402122 | + | 0.915586i | \(0.631727\pi\) | |||||||
\(728\) | 1.66046 | + | 1.99172i | 0.0615407 | + | 0.0738181i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.366211 | + | 0.634296i | −0.0135541 | + | 0.0234764i | ||||
\(731\) | 5.95712 | 0.220332 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.8930 | + | 18.8673i | 0.402343 | + | 0.696879i | 0.994008 | − | 0.109305i | \(-0.0348625\pi\) |
−0.591665 | + | 0.806184i | \(0.701529\pi\) | |||||||
\(734\) | 0.750282 | − | 1.29953i | 0.0276934 | − | 0.0479664i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.71459 | 0.100061 | ||||||||
\(737\) | 2.96529 | 0.109228 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.9065 | 1.32084 | 0.660421 | − | 0.750895i | \(-0.270378\pi\) | ||||
0.660421 | + | 0.750895i | \(0.270378\pi\) | |||||||
\(740\) | −0.332808 | − | 0.576440i | −0.0122342 | − | 0.0211903i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.613242 | − | 0.734029i | −0.0225128 | − | 0.0269470i | ||||
\(743\) | −25.6310 | − | 44.3942i | −0.940310 | − | 1.62867i | −0.764879 | − | 0.644174i | \(-0.777201\pi\) |
−0.175431 | − | 0.984492i | \(-0.556132\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.9579 | − | 38.0323i | −0.804477 | − | 1.39339i | ||||
\(746\) | 0.881472 | − | 1.52675i | 0.0322730 | − | 0.0558984i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.3421 | − | 26.5733i | 0.560963 | − | 0.971617i | ||||
\(749\) | 10.1975 | − | 27.8314i | 0.372609 | − | 1.01694i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.3770 | + | 42.2222i | −0.889530 | + | 1.54071i | −0.0490976 | + | 0.998794i | \(0.515635\pi\) |
−0.840432 | + | 0.541917i | \(0.817699\pi\) | |||||||
\(752\) | 10.1795 | 0.371210 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.21451 | + | 2.10866i | 0.0442298 | + | 0.0767927i | ||||
\(755\) | 47.9156 | 1.74383 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.41023 | + | 12.8349i | 0.269329 | + | 0.466492i | 0.968689 | − | 0.248278i | \(-0.0798647\pi\) |
−0.699360 | + | 0.714770i | \(0.746531\pi\) | |||||||
\(758\) | −0.241012 | −0.00875396 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.86976 | − | 4.97057i | −0.104097 | − | 0.180301i | ||||
\(761\) | −11.3103 | −0.409998 | −0.204999 | − | 0.978762i | \(-0.565719\pi\) | ||||
−0.204999 | + | 0.978762i | \(0.565719\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.7120 | + | 34.6941i | −0.460206 | + | 1.25601i | ||||
\(764\) | 14.7562 | + | 25.5584i | 0.533859 | + | 0.924671i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.999960 | − | 1.73198i | 0.0361300 | − | 0.0625790i | ||||
\(767\) | 13.6482 | − | 23.5826i | 0.492808 | − | 0.851520i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.92963 | + | 15.4666i | 0.322011 | + | 0.557739i | 0.980903 | − | 0.194498i | \(-0.0623079\pi\) |
−0.658892 | + | 0.752238i | \(0.728975\pi\) | |||||||
\(770\) | 2.36413 | − | 0.411629i | 0.0851975 | − | 0.0148341i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.2914 | + | 38.6098i | 0.802285 | + | 1.38960i | ||||
\(773\) | 1.43276 | + | 2.48162i | 0.0515329 | + | 0.0892575i | 0.890641 | − | 0.454707i | \(-0.150256\pi\) |
−0.839108 | + | 0.543964i | \(0.816923\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.1533 | + | 34.9065i | 0.723928 | + | 1.25388i | ||||
\(776\) | −1.05024 | + | 1.81906i | −0.0377013 | + | 0.0653005i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.0898463 | + | 0.155618i | 0.00322115 | + | 0.00557919i | ||||
\(779\) | −12.2100 | − | 21.1484i | −0.437469 | − | 0.757718i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.3991 | − | 19.7438i | 0.407892 | − | 0.706489i | ||||
\(782\) | −0.400356 | + | 0.693437i | −0.0143167 | + | 0.0247973i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.94596 | + | 27.3623i | −0.176641 | + | 0.977226i | ||||
\(785\) | 41.2988 | 1.47402 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.58257 | − | 2.74109i | −0.0564125 | − | 0.0977094i | 0.836440 | − | 0.548058i | \(-0.184633\pi\) |
−0.892853 | + | 0.450349i | \(0.851300\pi\) | |||||||
\(788\) | −6.31100 | + | 10.9310i | −0.224820 | + | 0.389400i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.01026 | − | 1.74983i | −0.0359436 | − | 0.0622561i | ||||
\(791\) | −6.16936 | + | 16.8376i | −0.219357 | + | 0.598677i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.76938 | − | 15.2256i | −0.311410 | − | 0.540677i | ||||
\(794\) | 0.0195936 | − | 0.0339371i | 0.000695350 | − | 0.00120438i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.02220 | + | 10.4308i | −0.213451 | + | 0.369708i | ||||
\(797\) | −12.0425 | + | 20.8583i | −0.426568 | + | 0.738838i | −0.996565 | − | 0.0828085i | \(-0.973611\pi\) |
0.569997 | + | 0.821647i | \(0.306944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.52141 | + | 7.83131i | −0.159956 | + | 0.277052i | ||||
\(800\) | −3.54698 | −0.125405 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.323578 | + | 0.560453i | 0.0114259 | + | 0.0197903i | ||||
\(803\) | 7.66802 | − | 13.2814i | 0.270599 | − | 0.468690i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.5938 | − | 4.63035i | 0.937308 | − | 0.163198i | ||||
\(806\) | −1.13647 | + | 1.96370i | −0.0400305 | + | 0.0691684i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.05478 | 0.0371071 | ||||||||
\(809\) | 38.3111 | 1.34695 | 0.673474 | − | 0.739211i | \(-0.264801\pi\) | ||||
0.673474 | + | 0.739211i | \(0.264801\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.79091 | 0.0980022 | 0.0490011 | − | 0.998799i | \(-0.484396\pi\) | ||||
0.0490011 | + | 0.998799i | \(0.484396\pi\) | |||||||
\(812\) | −18.0170 | + | 49.1725i | −0.632272 | + | 1.72562i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0161658 | − | 0.0280000i | −0.000566612 | − | 0.000981401i | ||||
\(815\) | 4.06434 | + | 7.03965i | 0.142368 | + | 0.246588i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.82620 | + | 10.0913i | −0.203833 | + | 0.353049i | ||||
\(818\) | 0.0126765 | 0.000443225 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −21.5958 | −0.754158 | ||||||||
\(821\) | −22.1855 | + | 38.4264i | −0.774279 | + | 1.34109i | 0.160919 | + | 0.986968i | \(0.448554\pi\) |
−0.935199 | + | 0.354124i | \(0.884779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.10746 | + | 7.11433i | 0.143177 | + | 0.247990i | 0.928691 | − | 0.370853i | \(-0.120935\pi\) |
−0.785514 | + | 0.618844i | \(0.787601\pi\) | |||||||
\(824\) | −1.16639 | − | 2.02024i | −0.0406329 | − | 0.0703783i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.34015 | + | 0.233339i | −0.0466298 | + | 0.00811891i | ||||
\(827\) | 37.0687 | 1.28900 | 0.644502 | − | 0.764603i | \(-0.277065\pi\) | ||||
0.644502 | + | 0.764603i | \(0.277065\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.4586 | −1.47465 | −0.737323 | − | 0.675540i | \(-0.763911\pi\) | ||||
−0.737323 | + | 0.675540i | \(0.763911\pi\) | |||||||
\(830\) | 1.12734 | 0.0391307 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 14.1967 | + | 24.6486i | 0.492181 | + | 0.854535i | ||||
\(833\) | −18.8535 | − | 15.9584i | −0.653235 | − | 0.552926i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.3874 | − | 57.8286i | 1.15542 | − | 2.00124i | ||||
\(836\) | 30.0098 | + | 51.9786i | 1.03791 | + | 1.79772i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.0610710 | 0.00210966 | ||||||||
\(839\) | −0.873903 | + | 1.51365i | −0.0301705 | + | 0.0522568i | −0.880716 | − | 0.473644i | \(-0.842938\pi\) |
0.850546 | + | 0.525901i | \(0.176272\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34.7015 | + | 60.1048i | −1.19660 | + | 2.07258i | ||||
\(842\) | −0.147931 | + | 0.256225i | −0.00509805 | + | 0.00883008i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.28919 | + | 2.23295i | −0.0443759 | + | 0.0768612i | ||||
\(845\) | 39.7679 | + | 0.0827967i | 1.36806 | + | 0.00284829i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.8302 | + | 3.62684i | −0.715735 | + | 0.124620i | ||||
\(848\) | −10.5535 | − | 18.2792i | −0.362409 | − | 0.627711i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.523118 | − | 0.906068i | 0.0179428 | − | 0.0310779i | ||||
\(851\) | −0.181847 | − | 0.314968i | −0.00623364 | − | 0.0107970i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −55.5244 | −1.90112 | −0.950560 | − | 0.310540i | \(-0.899490\pi\) | ||||
−0.950560 | + | 0.310540i | \(0.899490\pi\) | |||||||
\(854\) | −0.301789 | + | 0.823653i | −0.0103270 | + | 0.0281848i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.52267 | + | 2.63734i | −0.0520438 | + | 0.0901426i | ||||
\(857\) | −14.8303 | + | 25.6869i | −0.506595 | + | 0.877448i | 0.493376 | + | 0.869816i | \(0.335763\pi\) |
−0.999971 | + | 0.00763209i | \(0.997571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.6791 | − | 18.4967i | −0.364365 | − | 0.631098i | 0.624309 | − | 0.781177i | \(-0.285381\pi\) |
−0.988674 | + | 0.150079i | \(0.952047\pi\) | |||||||
\(860\) | 5.15239 | + | 8.92420i | 0.175695 | + | 0.304313i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.364899 | − | 0.632024i | 0.0124285 | − | 0.0215268i | ||||
\(863\) | −17.5615 | − | 30.4174i | −0.597800 | − | 1.03542i | −0.993145 | − | 0.116887i | \(-0.962708\pi\) |
0.395345 | − | 0.918533i | \(-0.370625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 27.0459 | + | 46.8448i | 0.919587 | + | 1.59277i | ||||
\(866\) | −0.235480 | − | 0.407863i | −0.00800194 | − | 0.0138598i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −48.1042 | + | 8.37562i | −1.63276 | + | 0.284287i | ||||
\(869\) | 21.1537 | + | 36.6393i | 0.717591 | + | 1.24290i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.22446 | − | 2.12593i | −0.0414892 | − | 0.0720345i | ||||
\(872\) | 1.89813 | − | 3.28766i | 0.0642789 | − | 0.111334i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.783114 | − | 1.35639i | −0.0264892 | − | 0.0458807i | ||||
\(875\) | 5.11962 | − | 0.891397i | 0.173075 | − | 0.0301347i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.8056 | 0.635019 | 0.317509 | − | 0.948255i | \(-0.397153\pi\) | ||||
0.317509 | + | 0.948255i | \(0.397153\pi\) | |||||||
\(878\) | 0.857864 | + | 1.48586i | 0.0289515 | + | 0.0501455i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 52.9549 | 1.78511 | ||||||||
\(881\) | 22.3970 | + | 38.7927i | 0.754573 | + | 1.30696i | 0.945586 | + | 0.325371i | \(0.105489\pi\) |
−0.191013 | + | 0.981587i | \(0.561177\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.57264 | −0.0865764 | −0.0432882 | − | 0.999063i | \(-0.513783\pi\) | ||||
−0.0432882 | + | 0.999063i | \(0.513783\pi\) | |||||||
\(884\) | −25.3867 | − | 0.0264275i | −0.853848 | − | 0.000888855i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.18555 | 0.0398293 | ||||||||
\(887\) | −18.4051 | + | 31.8786i | −0.617983 | + | 1.07038i | 0.371870 | + | 0.928285i | \(0.378717\pi\) |
−0.989853 | + | 0.142093i | \(0.954617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 22.6931 | + | 27.1628i | 0.761101 | + | 0.911010i | ||||
\(890\) | 0.801720 | − | 1.38862i | 0.0268737 | − | 0.0465466i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11.5710 | + | 20.0415i | −0.387425 | + | 0.671041i | ||||
\(893\) | −8.84407 | − | 15.3184i | −0.295955 | − | 0.512610i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.8824 | + | 25.7770i | 0.497462 | + | 0.861630i | ||||
\(896\) | 1.97027 | − | 5.37732i | 0.0658221 | − | 0.179644i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.402255 | − | 0.696726i | −0.0134234 | − | 0.0232501i | ||||
\(899\) | −91.7487 | −3.05999 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.7500 | 0.624655 | ||||||||
\(902\) | −1.04900 | −0.0349278 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.921196 | − | 1.59556i | 0.0306385 | − | 0.0530675i | ||||
\(905\) | −6.13852 | − | 10.6322i | −0.204051 | − | 0.353427i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.84939 | 0.127817 | 0.0639084 | − | 0.997956i | \(-0.479643\pi\) | ||||
0.0639084 | + | 0.997956i | \(0.479643\pi\) | |||||||
\(908\) | 0.796650 | − | 1.37984i | 0.0264378 | − | 0.0457915i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.27134 | − | 1.52497i | −0.0421445 | − | 0.0505522i | ||||
\(911\) | 47.0839 | 1.55996 | 0.779980 | − | 0.625804i | \(-0.215229\pi\) | ||||
0.779980 | + | 0.625804i | \(0.215229\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −23.6052 | −0.781219 | ||||||||
\(914\) | −0.283455 | − | 0.490959i | −0.00937587 | − | 0.0162395i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.1608 | − | 40.1157i | 0.765255 | − | 1.32546i | ||||
\(917\) | 30.7420 | + | 36.7970i | 1.01519 | + | 1.21515i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.7761 | −1.83989 | −0.919943 | − | 0.392053i | \(-0.871765\pi\) | ||||
−0.919943 | + | 0.392053i | \(0.871765\pi\) | |||||||
\(920\) | −2.77340 | −0.0914362 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.149886 | + | 0.259611i | 0.00493625 | + | 0.00854983i | ||||
\(923\) | −18.8622 | − | 0.0196355i | −0.620856 | − | 0.000646311i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.237607 | + | 0.411548i | 0.00781248 | + | 0.0135316i | ||||
\(926\) | 0.687990 | − | 1.19163i | 0.0226088 | − | 0.0391595i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.03694 | − | 6.99219i | 0.132519 | − | 0.229530i | ||||
\(929\) | −38.9439 | −1.27771 | −0.638855 | − | 0.769327i | \(-0.720591\pi\) | ||||
−0.638855 | + | 0.769327i | \(0.720591\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.4724 | − | 16.3298i | 1.49030 | − | 0.535188i | ||||
\(932\) | 12.1596 | − | 21.0610i | 0.398299 | − | 0.689875i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.444969 | 0.0145598 | ||||||||
\(935\) | −23.5208 | + | 40.7392i | −0.769211 | + | 1.33231i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.5763 | 0.639531 | 0.319765 | − | 0.947497i | \(-0.396396\pi\) | ||||
0.319765 | + | 0.947497i | \(0.396396\pi\) | |||||||
\(938\) | −0.0421385 | + | 0.115006i | −0.00137587 | + | 0.00375507i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.6425 | −0.510202 | ||||||||
\(941\) | −3.84200 | + | 6.65455i | −0.125246 | + | 0.216932i | −0.921829 | − | 0.387597i | \(-0.873305\pi\) |
0.796583 | + | 0.604529i | \(0.206639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.8000 | −0.384261 | ||||||||
\(944\) | −30.0184 | −0.977017 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.250273 | + | 0.433485i | 0.00813707 | + | 0.0140938i | ||||
\(947\) | 17.1984 | − | 29.7886i | 0.558874 | − | 0.967998i | −0.438717 | − | 0.898625i | \(-0.644567\pi\) |
0.997591 | − | 0.0693727i | \(-0.0220998\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.6883 | − | 0.0132085i | −0.411881 | − | 0.000428767i | ||||
\(950\) | 1.02324 | + | 1.77231i | 0.0331984 | + | 0.0575012i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.62708 | + | 1.94756i | 0.0527341 | + | 0.0631208i | ||||
\(953\) | 23.8888 | − | 41.3766i | 0.773834 | − | 1.34032i | −0.161613 | − | 0.986854i | \(-0.551670\pi\) |
0.935447 | − | 0.353466i | \(-0.114997\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −22.6224 | − | 39.1832i | −0.732045 | − | 1.26794i | ||||
\(956\) | 0.483211 | + | 0.836947i | 0.0156282 | + | 0.0270688i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.265794 | − | 0.460369i | 0.00858742 | − | 0.0148739i | ||||
\(959\) | −36.1999 | − | 43.3300i | −1.16896 | − | 1.39920i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.2722 | − | 47.2369i | −0.879749 | − | 1.52377i | ||||
\(962\) | −0.0133990 | + | 0.0231520i | −0.000432001 | + | 0.000746451i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.31475 | + | 4.00927i | −0.0745532 | + | 0.129130i | ||||
\(965\) | −34.1746 | − | 59.1921i | −1.10012 | − | 1.90546i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.1099 | 1.67574 | 0.837871 | − | 0.545869i | \(-0.183800\pi\) | ||||
0.837871 | + | 0.545869i | \(0.183800\pi\) | |||||||
\(968\) | 2.17233 | 0.0698213 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.804118 | − | 1.39277i | 0.0258187 | − | 0.0447192i | ||||
\(971\) | −20.6294 | −0.662028 | −0.331014 | − | 0.943626i | \(-0.607391\pi\) | ||||
−0.331014 | + | 0.943626i | \(0.607391\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.128396 | − | 0.350421i | 0.00411617 | − | 0.0112340i | ||||
\(974\) | 1.43380 | 0.0459418 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.67871 | + | 16.7640i | −0.309808 | + | 0.536603i | ||||
\(977\) | 25.9590 | 0.830501 | 0.415251 | − | 0.909707i | \(-0.363694\pi\) | ||||
0.415251 | + | 0.909707i | \(0.363694\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.7871 | + | 29.0760i | −0.536516 | + | 0.929274i | ||||
\(980\) | 7.60024 | − | 42.0465i | 0.242781 | − | 1.34313i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.594516 | 0.0189718 | ||||||||
\(983\) | 19.0424 | − | 32.9825i | 0.607359 | − | 1.05198i | −0.384315 | − | 0.923202i | \(-0.625562\pi\) |
0.991674 | − | 0.128775i | \(-0.0411045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.67529 | − | 16.7581i | 0.308281 | − | 0.533958i | ||||
\(986\) | 1.19076 | + | 2.06246i | 0.0379215 | + | 0.0656820i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 24.8735 | − | 42.9788i | 0.791332 | − | 1.36734i | ||||
\(989\) | 2.81528 | + | 4.87621i | 0.0895207 | + | 0.155054i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.3614 | −1.94921 | −0.974605 | − | 0.223930i | \(-0.928111\pi\) | ||||
−0.974605 | + | 0.223930i | \(0.928111\pi\) | |||||||
\(992\) | 7.52791 | 0.239011 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.603757 | + | 0.722675i | 0.0191500 | + | 0.0229218i | ||||
\(995\) | 9.23254 | − | 15.9912i | 0.292691 | − | 0.506956i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.66583 | + | 16.7417i | 0.306120 | + | 0.530215i | 0.977510 | − | 0.210889i | \(-0.0676358\pi\) |
−0.671390 | + | 0.741104i | \(0.734302\pi\) | |||||||
\(998\) | −1.44816 | −0.0458408 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.n.e.172.5 | 16 | ||
3.2 | odd | 2 | 273.2.j.b.172.4 | yes | 16 | ||
7.2 | even | 3 | 819.2.s.e.289.4 | 16 | |||
13.9 | even | 3 | 819.2.s.e.802.4 | 16 | |||
21.2 | odd | 6 | 273.2.l.b.16.5 | yes | 16 | ||
39.35 | odd | 6 | 273.2.l.b.256.5 | yes | 16 | ||
91.9 | even | 3 | inner | 819.2.n.e.100.5 | 16 | ||
273.191 | odd | 6 | 273.2.j.b.100.4 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.j.b.100.4 | ✓ | 16 | 273.191 | odd | 6 | ||
273.2.j.b.172.4 | yes | 16 | 3.2 | odd | 2 | ||
273.2.l.b.16.5 | yes | 16 | 21.2 | odd | 6 | ||
273.2.l.b.256.5 | yes | 16 | 39.35 | odd | 6 | ||
819.2.n.e.100.5 | 16 | 91.9 | even | 3 | inner | ||
819.2.n.e.172.5 | 16 | 1.1 | even | 1 | trivial | ||
819.2.s.e.289.4 | 16 | 7.2 | even | 3 | |||
819.2.s.e.802.4 | 16 | 13.9 | even | 3 |