Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [375,2,Mod(49,375)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(375, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("375.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 375 = 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 375.i (of order \(10\), degree \(4\), 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: | \(2.99439007580\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{14} + 6x^{12} - 20x^{10} - 79x^{8} - 80x^{6} + 96x^{4} + 320x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(0.132563 + 1.40799i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 375.274 |
Dual form | 375.2.i.b.349.4 |
$q$-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 \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.01846 | + | 0.655837i | 1.42727 | + | 0.463747i | 0.917903 | − | 0.396805i | \(-0.129881\pi\) |
0.509363 | + | 0.860552i | \(0.329881\pi\) | |||||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | 2.02602 | + | 1.47199i | 1.01301 | + | 0.735995i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.71700 | + | 1.24748i | −0.700964 | + | 0.509280i | ||||
\(7\) | 4.35840i | 1.64732i | 0.567083 | + | 0.823660i | \(0.308072\pi\) | ||||
−0.567083 | + | 0.823660i | \(0.691928\pi\) | |||||||
\(8\) | 0.629102 | + | 0.865884i | 0.222421 | + | 0.306136i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.488218 | + | 1.50258i | −0.147203 | + | 0.453045i | −0.997288 | − | 0.0736014i | \(-0.976551\pi\) |
0.850085 | + | 0.526646i | \(0.176551\pi\) | |||||||
\(12\) | −2.38173 | + | 0.773871i | −0.687546 | + | 0.223397i | ||||
\(13\) | 1.13931 | − | 0.370184i | 0.315987 | − | 0.102670i | −0.146729 | − | 0.989177i | \(-0.546875\pi\) |
0.462717 | + | 0.886506i | \(0.346875\pi\) | |||||||
\(14\) | −2.85840 | + | 8.79726i | −0.763940 | + | 2.35117i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.845805 | − | 2.60312i | −0.211451 | − | 0.650780i | ||||
\(17\) | 0.659691 | + | 0.907987i | 0.159999 | + | 0.220219i | 0.881488 | − | 0.472206i | \(-0.156542\pi\) |
−0.721490 | + | 0.692425i | \(0.756542\pi\) | |||||||
\(18\) | − | 2.12233i | − | 0.500239i | ||||||
\(19\) | 6.21218 | − | 4.51341i | 1.42517 | − | 1.03545i | 0.434281 | − | 0.900777i | \(-0.357002\pi\) |
0.990890 | − | 0.134670i | \(-0.0429975\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.52602 | − | 2.56180i | −0.769441 | − | 0.559031i | ||||
\(22\) | −1.97090 | + | 2.71270i | −0.420196 | + | 0.578351i | ||||
\(23\) | 2.20671 | + | 0.717004i | 0.460131 | + | 0.149506i | 0.529905 | − | 0.848057i | \(-0.322228\pi\) |
−0.0697736 | + | 0.997563i | \(0.522228\pi\) | |||||||
\(24\) | −1.07029 | −0.218472 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.54243 | 0.498611 | ||||||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | −6.41552 | + | 8.83021i | −1.21242 | + | 1.66875i | ||||
\(29\) | −4.45307 | − | 3.23535i | −0.826915 | − | 0.600789i | 0.0917701 | − | 0.995780i | \(-0.470748\pi\) |
−0.918685 | + | 0.394992i | \(0.870748\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.88495 | + | 2.82258i | −0.697757 | + | 0.506950i | −0.879201 | − | 0.476451i | \(-0.841923\pi\) |
0.181444 | + | 0.983401i | \(0.441923\pi\) | |||||||
\(32\) | − | 7.94959i | − | 1.40530i | ||||||
\(33\) | −0.928645 | − | 1.27817i | −0.161656 | − | 0.222501i | ||||
\(34\) | 0.736068 | + | 2.26538i | 0.126235 | + | 0.388510i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.773871 | − | 2.38173i | 0.128979 | − | 0.396955i | ||||
\(37\) | 6.06043 | − | 1.96915i | 0.996329 | − | 0.323727i | 0.234931 | − | 0.972012i | \(-0.424514\pi\) |
0.761398 | + | 0.648285i | \(0.224514\pi\) | |||||||
\(38\) | 15.4991 | − | 5.03596i | 2.51428 | − | 0.816941i | ||||
\(39\) | −0.370184 | + | 1.13931i | −0.0592768 | + | 0.182435i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.30902 | − | 7.10642i | −0.360608 | − | 1.10984i | −0.952686 | − | 0.303956i | \(-0.901692\pi\) |
0.592078 | − | 0.805881i | \(-0.298308\pi\) | |||||||
\(42\) | −5.43700 | − | 7.48339i | −0.838948 | − | 1.15471i | ||||
\(43\) | 1.24998i | 0.190620i | 0.995448 | + | 0.0953102i | \(0.0303843\pi\) | ||||
−0.995448 | + | 0.0953102i | \(0.969616\pi\) | |||||||
\(44\) | −3.20092 | + | 2.32561i | −0.482557 | + | 0.350598i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.98392 | + | 2.89449i | 0.587397 | + | 0.426769i | ||||
\(47\) | 2.42617 | − | 3.33934i | 0.353893 | − | 0.487092i | −0.594541 | − | 0.804065i | \(-0.702666\pi\) |
0.948435 | + | 0.316973i | \(0.102666\pi\) | |||||||
\(48\) | 2.60312 | + | 0.845805i | 0.375728 | + | 0.122081i | ||||
\(49\) | −11.9957 | −1.71367 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.12233 | −0.157158 | ||||||||
\(52\) | 2.85317 | + | 0.927051i | 0.395663 | + | 0.128559i | ||||
\(53\) | −2.20166 | + | 3.03032i | −0.302421 | + | 0.416247i | −0.932999 | − | 0.359879i | \(-0.882818\pi\) |
0.630578 | + | 0.776126i | \(0.282818\pi\) | |||||||
\(54\) | 1.71700 | + | 1.24748i | 0.233655 | + | 0.169760i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.77387 | + | 2.74188i | −0.504305 | + | 0.366399i | ||||
\(57\) | 7.67867i | 1.01707i | ||||||||
\(58\) | −6.86648 | − | 9.45090i | −0.901613 | − | 1.24096i | ||||
\(59\) | −2.82940 | − | 8.70799i | −0.368356 | − | 1.13368i | −0.947853 | − | 0.318709i | \(-0.896751\pi\) |
0.579496 | − | 0.814975i | \(-0.303249\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.431351 | − | 1.32756i | 0.0552288 | − | 0.169977i | −0.919637 | − | 0.392769i | \(-0.871517\pi\) |
0.974866 | + | 0.222792i | \(0.0715172\pi\) | |||||||
\(62\) | −9.69276 | + | 3.14937i | −1.23098 | + | 0.399970i | ||||
\(63\) | 4.14509 | − | 1.34682i | 0.522232 | − | 0.169683i | ||||
\(64\) | 3.52202 | − | 10.8397i | 0.440253 | − | 1.35496i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.03616 | − | 3.18898i | −0.127543 | − | 0.392536i | ||||
\(67\) | 2.27044 | + | 3.12499i | 0.277378 | + | 0.381778i | 0.924863 | − | 0.380300i | \(-0.124179\pi\) |
−0.647485 | + | 0.762078i | \(0.724179\pi\) | |||||||
\(68\) | 2.81066i | 0.340843i | ||||||||
\(69\) | −1.87714 | + | 1.36382i | −0.225981 | + | 0.164185i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.57970 | + | 6.23352i | 1.01822 | + | 0.739783i | 0.965918 | − | 0.258848i | \(-0.0833430\pi\) |
0.0523057 | + | 0.998631i | \(0.483343\pi\) | |||||||
\(72\) | 0.629102 | − | 0.865884i | 0.0741403 | − | 0.102045i | ||||
\(73\) | −4.75216 | − | 1.54407i | −0.556198 | − | 0.180720i | 0.0174117 | − | 0.999848i | \(-0.494457\pi\) |
−0.573610 | + | 0.819129i | \(0.694457\pi\) | |||||||
\(74\) | 13.5242 | 1.57215 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.2297 | 2.20580 | ||||||||
\(77\) | −6.54885 | − | 2.12785i | −0.746310 | − | 0.242491i | ||||
\(78\) | −1.49440 | + | 2.05687i | −0.169208 | + | 0.232894i | ||||
\(79\) | 11.7737 | + | 8.55407i | 1.32464 | + | 0.962408i | 0.999862 | + | 0.0166185i | \(0.00529009\pi\) |
0.324779 | + | 0.945790i | \(0.394710\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | − | 15.8584i | − | 1.75126i | ||||||
\(83\) | −5.13491 | − | 7.06760i | −0.563630 | − | 0.775770i | 0.428153 | − | 0.903706i | \(-0.359165\pi\) |
−0.991782 | + | 0.127937i | \(0.959165\pi\) | |||||||
\(84\) | −3.37284 | − | 10.3805i | −0.368007 | − | 1.13261i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.819784 | + | 2.52304i | −0.0883996 | + | 0.272066i | ||||
\(87\) | 5.23490 | − | 1.70092i | 0.561240 | − | 0.182358i | ||||
\(88\) | −1.60820 | + | 0.522535i | −0.171435 | + | 0.0557025i | ||||
\(89\) | 3.10195 | − | 9.54683i | 0.328806 | − | 1.01196i | −0.640887 | − | 0.767635i | \(-0.721433\pi\) |
0.969693 | − | 0.244326i | \(-0.0785668\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.61341 | + | 4.96556i | 0.169131 | + | 0.520532i | ||||
\(92\) | 3.41542 | + | 4.70092i | 0.356082 | + | 0.490105i | ||||
\(93\) | − | 4.80206i | − | 0.497950i | ||||||
\(94\) | 7.08719 | − | 5.14914i | 0.730988 | − | 0.531094i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.43135 | + | 4.67265i | 0.656397 | + | 0.476900i | ||||
\(97\) | −4.40837 | + | 6.06760i | −0.447602 | + | 0.616071i | −0.971880 | − | 0.235476i | \(-0.924335\pi\) |
0.524278 | + | 0.851547i | \(0.324335\pi\) | |||||||
\(98\) | −24.2128 | − | 7.86720i | −2.44586 | − | 0.794707i | ||||
\(99\) | 1.57991 | 0.158787 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.51821 | −0.648586 | −0.324293 | − | 0.945957i | \(-0.605126\pi\) | ||||
−0.324293 | + | 0.945957i | \(0.605126\pi\) | |||||||
\(102\) | −2.26538 | − | 0.736068i | −0.224306 | − | 0.0728816i | ||||
\(103\) | −4.73094 | + | 6.51158i | −0.466153 | + | 0.641605i | −0.975771 | − | 0.218796i | \(-0.929787\pi\) |
0.509617 | + | 0.860401i | \(0.329787\pi\) | |||||||
\(104\) | 1.03728 | + | 0.753626i | 0.101713 | + | 0.0738991i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.43135 | + | 4.67265i | −0.624668 | + | 0.453848i | ||||
\(107\) | 9.47745i | 0.916220i | 0.888896 | + | 0.458110i | \(0.151473\pi\) | ||||
−0.888896 | + | 0.458110i | \(0.848527\pi\) | |||||||
\(108\) | 1.47199 | + | 2.02602i | 0.141642 | + | 0.194954i | ||||
\(109\) | 3.60491 | + | 11.0948i | 0.345288 | + | 1.06269i | 0.961429 | + | 0.275052i | \(0.0886949\pi\) |
−0.616142 | + | 0.787635i | \(0.711305\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.96915 | + | 6.06043i | −0.186904 | + | 0.575231i | ||||
\(112\) | 11.3454 | − | 3.68636i | 1.07204 | − | 0.348328i | ||||
\(113\) | −14.1949 | + | 4.61219i | −1.33534 | + | 0.433879i | −0.887736 | − | 0.460353i | \(-0.847723\pi\) |
−0.447605 | + | 0.894231i | \(0.647723\pi\) | |||||||
\(114\) | −5.03596 | + | 15.4991i | −0.471661 | + | 1.45162i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.25962 | − | 13.1098i | −0.395496 | − | 1.21721i | ||||
\(117\) | −0.704131 | − | 0.969154i | −0.0650970 | − | 0.0895983i | ||||
\(118\) | − | 19.4324i | − | 1.78889i | ||||||
\(119\) | −3.95737 | + | 2.87520i | −0.362772 | + | 0.263569i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.87980 | + | 4.99847i | 0.625436 | + | 0.454406i | ||||
\(122\) | 1.74133 | − | 2.39673i | 0.157652 | − | 0.216990i | ||||
\(123\) | 7.10642 | + | 2.30902i | 0.640765 | + | 0.208197i | ||||
\(124\) | −12.0258 | −1.07995 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.24998 | 0.824054 | ||||||||
\(127\) | −16.1638 | − | 5.25195i | −1.43431 | − | 0.466035i | −0.514190 | − | 0.857676i | \(-0.671908\pi\) |
−0.920118 | + | 0.391641i | \(0.871908\pi\) | |||||||
\(128\) | 4.87282 | − | 6.70686i | 0.430701 | − | 0.592809i | ||||
\(129\) | −1.01126 | − | 0.734721i | −0.0890362 | − | 0.0646886i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.266063 | − | 0.193306i | 0.0232461 | − | 0.0168892i | −0.576102 | − | 0.817378i | \(-0.695427\pi\) |
0.599348 | + | 0.800489i | \(0.295427\pi\) | |||||||
\(132\) | − | 3.95656i | − | 0.344374i | ||||||
\(133\) | 19.6713 | + | 27.0752i | 1.70571 | + | 2.34771i | ||||
\(134\) | 2.53330 | + | 7.79670i | 0.218844 | + | 0.673533i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.371199 | + | 1.14243i | −0.0318300 | + | 0.0979628i | ||||
\(137\) | −4.33939 | + | 1.40995i | −0.370739 | + | 0.120461i | −0.488460 | − | 0.872586i | \(-0.662441\pi\) |
0.117721 | + | 0.993047i | \(0.462441\pi\) | |||||||
\(138\) | −4.68338 | + | 1.52172i | −0.398676 | + | 0.129538i | ||||
\(139\) | 1.46289 | − | 4.50230i | 0.124080 | − | 0.381880i | −0.869652 | − | 0.493665i | \(-0.835657\pi\) |
0.993732 | + | 0.111785i | \(0.0356568\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.27551 | + | 3.92563i | 0.107418 | + | 0.330597i | ||||
\(142\) | 13.2296 | + | 18.2090i | 1.11020 | + | 1.52806i | ||||
\(143\) | 1.89263i | 0.158270i | ||||||||
\(144\) | −2.21435 | + | 1.60882i | −0.184529 | + | 0.134068i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.57938 | − | 6.23328i | −0.710035 | − | 0.515870i | ||||
\(147\) | 7.05087 | − | 9.70470i | 0.581546 | − | 0.800430i | ||||
\(148\) | 15.1771 | + | 4.93135i | 1.24755 | + | 0.405355i | ||||
\(149\) | −4.67644 | −0.383109 | −0.191555 | − | 0.981482i | \(-0.561353\pi\) | ||||
−0.191555 | + | 0.981482i | \(0.561353\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.54178 | −0.532362 | −0.266181 | − | 0.963923i | \(-0.585762\pi\) | ||||
−0.266181 | + | 0.963923i | \(0.585762\pi\) | |||||||
\(152\) | 7.81618 | + | 2.53963i | 0.633976 | + | 0.205991i | ||||
\(153\) | 0.659691 | − | 0.907987i | 0.0533329 | − | 0.0734064i | ||||
\(154\) | −11.8231 | − | 8.58995i | −0.952729 | − | 0.692198i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.42705 | + | 1.76336i | −0.194320 | + | 0.141181i | ||||
\(157\) | 3.99404i | 0.318759i | 0.987217 | + | 0.159379i | \(0.0509493\pi\) | ||||
−0.987217 | + | 0.159379i | \(0.949051\pi\) | |||||||
\(158\) | 18.1546 | + | 24.9877i | 1.44430 | + | 1.98791i | ||||
\(159\) | −1.15748 | − | 3.56236i | −0.0917941 | − | 0.282513i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.12499 | + | 9.61773i | −0.246284 | + | 0.757984i | ||||
\(162\) | −2.01846 | + | 0.655837i | −0.158585 | + | 0.0515274i | ||||
\(163\) | 4.56641 | − | 1.48372i | 0.357669 | − | 0.116214i | −0.124670 | − | 0.992198i | \(-0.539787\pi\) |
0.482339 | + | 0.875985i | \(0.339787\pi\) | |||||||
\(164\) | 5.78247 | − | 17.7966i | 0.451535 | − | 1.38968i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.72941 | − | 17.6333i | −0.444689 | − | 1.36861i | ||||
\(167\) | −13.9070 | − | 19.1414i | −1.07616 | − | 1.48120i | −0.863682 | − | 0.504036i | \(-0.831848\pi\) |
−0.212474 | − | 0.977167i | \(-0.568152\pi\) | |||||||
\(168\) | − | 4.66476i | − | 0.359894i | ||||||
\(169\) | −9.35623 | + | 6.79770i | −0.719710 | + | 0.522900i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.21218 | − | 4.51341i | −0.475057 | − | 0.345149i | ||||
\(172\) | −1.83996 | + | 2.53249i | −0.140296 | + | 0.193100i | ||||
\(173\) | −13.7944 | − | 4.48208i | −1.04877 | − | 0.340766i | −0.266584 | − | 0.963812i | \(-0.585895\pi\) |
−0.782185 | + | 0.623046i | \(0.785895\pi\) | |||||||
\(174\) | 11.6820 | 0.885607 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.32433 | 0.325959 | ||||||||
\(177\) | 8.70799 | + | 2.82940i | 0.654533 | + | 0.212671i | ||||
\(178\) | 12.5223 | − | 17.2355i | 0.938588 | − | 1.29186i | ||||
\(179\) | 0.644581 | + | 0.468315i | 0.0481782 | + | 0.0350035i | 0.611614 | − | 0.791157i | \(-0.290521\pi\) |
−0.563436 | + | 0.826160i | \(0.690521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.5030 | − | 8.35741i | 0.855010 | − | 0.621201i | −0.0715129 | − | 0.997440i | \(-0.522783\pi\) |
0.926523 | + | 0.376239i | \(0.122783\pi\) | |||||||
\(182\) | 11.0809i | 0.821372i | ||||||||
\(183\) | 0.820477 | + | 1.12929i | 0.0606514 | + | 0.0834795i | ||||
\(184\) | 0.767403 | + | 2.36182i | 0.0565737 | + | 0.174116i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.14937 | − | 9.69276i | 0.230923 | − | 0.710708i | ||||
\(187\) | −1.68640 | + | 0.547943i | −0.123321 | + | 0.0400696i | ||||
\(188\) | 9.83094 | − | 3.19427i | 0.716995 | − | 0.232966i | ||||
\(189\) | −1.34682 | + | 4.14509i | −0.0979667 | + | 0.301511i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.20441 | − | 9.86215i | −0.231863 | − | 0.713600i | −0.997522 | − | 0.0703540i | \(-0.977587\pi\) |
0.765659 | − | 0.643246i | \(-0.222413\pi\) | |||||||
\(192\) | 6.69929 | + | 9.22078i | 0.483479 | + | 0.665452i | ||||
\(193\) | − | 4.34712i | − | 0.312913i | −0.987685 | − | 0.156456i | \(-0.949993\pi\) | ||
0.987685 | − | 0.156456i | \(-0.0500071\pi\) | |||||||
\(194\) | −12.8775 | + | 9.35603i | −0.924548 | + | 0.671724i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −24.3035 | − | 17.6575i | −1.73596 | − | 1.26125i | ||||
\(197\) | 1.10498 | − | 1.52087i | 0.0787263 | − | 0.108358i | −0.767838 | − | 0.640644i | \(-0.778667\pi\) |
0.846564 | + | 0.532287i | \(0.178667\pi\) | |||||||
\(198\) | 3.18898 | + | 1.03616i | 0.226631 | + | 0.0736367i | ||||
\(199\) | −4.26028 | −0.302003 | −0.151002 | − | 0.988534i | \(-0.548250\pi\) | ||||
−0.151002 | + | 0.988534i | \(0.548250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.86270 | −0.272454 | ||||||||
\(202\) | −13.1567 | − | 4.27489i | −0.925705 | − | 0.300780i | ||||
\(203\) | 14.1009 | − | 19.4083i | 0.989692 | − | 1.36219i | ||||
\(204\) | −2.27387 | − | 1.65206i | −0.159203 | − | 0.115668i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −13.8197 | + | 10.0406i | −0.962867 | + | 0.699564i | ||||
\(207\) | − | 2.32027i | − | 0.161270i | ||||||
\(208\) | −1.92727 | − | 2.65265i | −0.133632 | − | 0.183928i | ||||
\(209\) | 3.74887 | + | 11.5378i | 0.259314 | + | 0.798088i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.87284 | + | 8.84170i | −0.197775 | + | 0.608687i | 0.802158 | + | 0.597111i | \(0.203685\pi\) |
−0.999933 | + | 0.0115762i | \(0.996315\pi\) | |||||||
\(212\) | −8.92120 | + | 2.89868i | −0.612711 | + | 0.199082i | ||||
\(213\) | −10.0860 | + | 3.27716i | −0.691085 | + | 0.224547i | ||||
\(214\) | −6.21566 | + | 19.1298i | −0.424894 | + | 1.30769i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.330738 | + | 1.01791i | 0.0225039 | + | 0.0692599i | ||||
\(217\) | −12.3019 | − | 16.9322i | −0.835110 | − | 1.14943i | ||||
\(218\) | 24.7586i | 1.67686i | ||||||||
\(219\) | 4.04243 | − | 2.93700i | 0.273162 | − | 0.198464i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.08771 | + | 0.790270i | 0.0731675 | + | 0.0531593i | ||||
\(222\) | −7.94931 | + | 10.9413i | −0.533523 | + | 0.734331i | ||||
\(223\) | 3.23129 | + | 1.04991i | 0.216383 | + | 0.0703072i | 0.415203 | − | 0.909729i | \(-0.363711\pi\) |
−0.198819 | + | 0.980036i | \(0.563711\pi\) | |||||||
\(224\) | 34.6475 | 2.31498 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.6766 | −2.10710 | ||||||||
\(227\) | 25.4858 | + | 8.28083i | 1.69155 | + | 0.549618i | 0.987096 | − | 0.160132i | \(-0.0511919\pi\) |
0.704454 | + | 0.709750i | \(0.251192\pi\) | |||||||
\(228\) | −11.3029 | + | 15.5572i | −0.748555 | + | 1.03030i | ||||
\(229\) | −0.956255 | − | 0.694760i | −0.0631911 | − | 0.0459110i | 0.555741 | − | 0.831355i | \(-0.312435\pi\) |
−0.618932 | + | 0.785444i | \(0.712435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.57078 | − | 4.04741i | 0.366530 | − | 0.266300i | ||||
\(232\) | − | 5.89121i | − | 0.386777i | ||||||
\(233\) | 4.17024 | + | 5.73984i | 0.273201 | + | 0.376030i | 0.923467 | − | 0.383677i | \(-0.125342\pi\) |
−0.650266 | + | 0.759707i | \(0.725342\pi\) | |||||||
\(234\) | −0.785653 | − | 2.41799i | −0.0513598 | − | 0.158069i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.08566 | − | 21.8074i | 0.461237 | − | 1.41954i | ||||
\(237\) | −13.8408 | + | 4.49714i | −0.899055 | + | 0.292121i | ||||
\(238\) | −9.87345 | + | 3.20808i | −0.640001 | + | 0.207949i | ||||
\(239\) | −0.0132236 | + | 0.0406981i | −0.000855365 | + | 0.00263254i | −0.951483 | − | 0.307700i | \(-0.900441\pi\) |
0.950628 | + | 0.310333i | \(0.100441\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.63746 | − | 11.1950i | −0.234310 | − | 0.721131i | −0.997212 | − | 0.0746174i | \(-0.976226\pi\) |
0.762903 | − | 0.646513i | \(-0.223774\pi\) | |||||||
\(242\) | 10.6084 | + | 14.6012i | 0.681934 | + | 0.938602i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 2.82808 | − | 2.05472i | 0.181049 | − | 0.131540i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.8297 | + | 9.32131i | 0.817991 | + | 0.594305i | ||||
\(247\) | 5.40680 | − | 7.44182i | 0.344026 | − | 0.473511i | ||||
\(248\) | −4.88806 | − | 1.58823i | −0.310392 | − | 0.100852i | ||||
\(249\) | 8.73603 | 0.553623 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.4764 | 1.10310 | 0.551550 | − | 0.834142i | \(-0.314036\pi\) | ||||
0.551550 | + | 0.834142i | \(0.314036\pi\) | |||||||
\(252\) | 10.3805 | + | 3.37284i | 0.653912 | + | 0.212469i | ||||
\(253\) | −2.15471 | + | 2.96571i | −0.135466 | + | 0.186452i | ||||
\(254\) | −29.1816 | − | 21.2017i | −1.83102 | − | 1.33031i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.20735 | + | 3.05682i | −0.262960 | + | 0.191051i | ||||
\(257\) | 15.4671i | 0.964814i | 0.875947 | + | 0.482407i | \(0.160237\pi\) | ||||
−0.875947 | + | 0.482407i | \(0.839763\pi\) | |||||||
\(258\) | −1.55932 | − | 2.14622i | −0.0970792 | − | 0.133618i | ||||
\(259\) | 8.58236 | + | 26.4138i | 0.533282 | + | 1.64127i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.70092 | + | 5.23490i | −0.105284 | + | 0.324032i | ||||
\(262\) | 0.663815 | − | 0.215687i | 0.0410106 | − | 0.0133252i | ||||
\(263\) | 1.37674 | − | 0.447331i | 0.0848936 | − | 0.0275836i | −0.266262 | − | 0.963901i | \(-0.585789\pi\) |
0.351156 | + | 0.936317i | \(0.385789\pi\) | |||||||
\(264\) | 0.522535 | − | 1.60820i | 0.0321598 | − | 0.0989778i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 21.9487 | + | 67.5513i | 1.34576 | + | 4.14183i | ||||
\(267\) | 5.90026 | + | 8.12102i | 0.361090 | + | 0.496998i | ||||
\(268\) | 9.67336i | 0.590895i | ||||||||
\(269\) | −7.04344 | + | 5.11736i | −0.429446 | + | 0.312011i | −0.781427 | − | 0.623996i | \(-0.785508\pi\) |
0.351981 | + | 0.936007i | \(0.385508\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1652 | + | 16.8305i | 1.40719 | + | 1.02238i | 0.993724 | + | 0.111860i | \(0.0356807\pi\) |
0.413462 | + | 0.910521i | \(0.364319\pi\) | |||||||
\(272\) | 1.80563 | − | 2.48524i | 0.109482 | − | 0.150690i | ||||
\(273\) | −4.96556 | − | 1.61341i | −0.300530 | − | 0.0976480i | ||||
\(274\) | −9.68359 | −0.585007 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.81066 | −0.349761 | ||||||||
\(277\) | 5.04259 | + | 1.63844i | 0.302980 | + | 0.0984442i | 0.456562 | − | 0.889692i | \(-0.349081\pi\) |
−0.153582 | + | 0.988136i | \(0.549081\pi\) | |||||||
\(278\) | 5.90555 | − | 8.12830i | 0.354192 | − | 0.487503i | ||||
\(279\) | 3.88495 | + | 2.82258i | 0.232586 | + | 0.168983i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.4837 | − | 14.1557i | 1.16230 | − | 0.844461i | 0.172234 | − | 0.985056i | \(-0.444902\pi\) |
0.990067 | + | 0.140595i | \(0.0449015\pi\) | |||||||
\(282\) | 8.76025i | 0.521665i | ||||||||
\(283\) | −15.9374 | − | 21.9359i | −0.947380 | − | 1.30396i | −0.952682 | − | 0.303970i | \(-0.901688\pi\) |
0.00530192 | − | 0.999986i | \(-0.498312\pi\) | |||||||
\(284\) | 8.20698 | + | 25.2585i | 0.486995 | + | 1.49882i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.24126 | + | 3.82020i | −0.0733971 | + | 0.225893i | ||||
\(287\) | 30.9726 | − | 10.0636i | 1.82826 | − | 0.594037i | ||||
\(288\) | −7.56051 | + | 2.45656i | −0.445507 | + | 0.144754i | ||||
\(289\) | 4.86404 | − | 14.9700i | 0.286120 | − | 0.880587i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.31762 | − | 7.13289i | −0.135861 | − | 0.418137i | ||||
\(292\) | −7.35512 | − | 10.1234i | −0.430426 | − | 0.592430i | ||||
\(293\) | 20.3016i | 1.18603i | 0.805190 | + | 0.593017i | \(0.202063\pi\) | ||||
−0.805190 | + | 0.593017i | \(0.797937\pi\) | |||||||
\(294\) | 20.5966 | − | 14.9643i | 1.20122 | − | 0.872736i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.51769 | + | 4.00883i | 0.320709 | + | 0.233009i | ||||
\(297\) | −0.928645 | + | 1.27817i | −0.0538855 | + | 0.0741670i | ||||
\(298\) | −9.43921 | − | 3.06698i | −0.546799 | − | 0.177666i | ||||
\(299\) | 2.77955 | 0.160745 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.44792 | −0.314013 | ||||||||
\(302\) | −13.2043 | − | 4.29034i | −0.759823 | − | 0.246881i | ||||
\(303\) | 3.83131 | − | 5.27335i | 0.220103 | − | 0.302946i | ||||
\(304\) | −17.0032 | − | 12.3536i | −0.975203 | − | 0.708527i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.92705 | − | 1.40008i | 0.110162 | − | 0.0800375i | ||||
\(307\) | − | 2.51330i | − | 0.143442i | −0.997425 | − | 0.0717208i | \(-0.977151\pi\) | ||
0.997425 | − | 0.0717208i | \(-0.0228491\pi\) | |||||||
\(308\) | −10.1359 | − | 13.9509i | −0.577548 | − | 0.794927i | ||||
\(309\) | −2.48720 | − | 7.65482i | −0.141492 | − | 0.435468i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.49075 | − | 4.58806i | 0.0845327 | − | 0.260165i | −0.899852 | − | 0.436195i | \(-0.856326\pi\) |
0.984385 | + | 0.176030i | \(0.0563257\pi\) | |||||||
\(312\) | −1.21939 | + | 0.396205i | −0.0690345 | + | 0.0224307i | ||||
\(313\) | −5.69504 | + | 1.85043i | −0.321903 | + | 0.104592i | −0.465511 | − | 0.885042i | \(-0.654129\pi\) |
0.143608 | + | 0.989635i | \(0.454129\pi\) | |||||||
\(314\) | −2.61944 | + | 8.06180i | −0.147823 | + | 0.454954i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2622 | + | 34.6615i | 0.633548 | + | 1.94986i | ||||
\(317\) | −10.1999 | − | 14.0389i | −0.572883 | − | 0.788506i | 0.420010 | − | 0.907520i | \(-0.362027\pi\) |
−0.992893 | + | 0.119014i | \(0.962027\pi\) | |||||||
\(318\) | − | 7.94959i | − | 0.445791i | ||||||
\(319\) | 7.03543 | − | 5.11154i | 0.393909 | − | 0.286191i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.66742 | − | 5.57071i | −0.427954 | − | 0.310926i | ||||
\(322\) | −12.6153 | + | 17.3635i | −0.703025 | + | 0.967631i | ||||
\(323\) | 8.19624 | + | 2.66312i | 0.456051 | + | 0.148180i | ||||
\(324\) | −2.50430 | −0.139128 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 10.1902 | 0.564383 | ||||||||
\(327\) | −11.0948 | − | 3.60491i | −0.613543 | − | 0.199352i | ||||
\(328\) | 4.70073 | − | 6.47000i | 0.259555 | − | 0.357246i | ||||
\(329\) | 14.5542 | + | 10.5742i | 0.802398 | + | 0.582976i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4518 | + | 11.9529i | −0.904270 | + | 0.656991i | −0.939559 | − | 0.342386i | \(-0.888765\pi\) |
0.0352890 | + | 0.999377i | \(0.488765\pi\) | |||||||
\(332\) | − | 21.8776i | − | 1.20069i | ||||||
\(333\) | −3.74555 | − | 5.15531i | −0.205255 | − | 0.282509i | ||||
\(334\) | −15.5171 | − | 47.7568i | −0.849059 | − | 2.61314i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.68636 | + | 11.3454i | −0.201107 | + | 0.618945i | ||||
\(337\) | −32.5805 | + | 10.5860i | −1.77477 | + | 0.576658i | −0.998551 | − | 0.0538048i | \(-0.982865\pi\) |
−0.776219 | + | 0.630463i | \(0.782865\pi\) | |||||||
\(338\) | −23.3434 | + | 7.58472i | −1.26971 | + | 0.412554i | ||||
\(339\) | 4.61219 | − | 14.1949i | 0.250500 | − | 0.770960i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.34445 | − | 7.21548i | −0.126959 | − | 0.390740i | ||||
\(342\) | −9.57897 | − | 13.1843i | −0.517971 | − | 0.712926i | ||||
\(343\) | − | 21.7731i | − | 1.17564i | ||||||
\(344\) | −1.08234 | + | 0.786366i | −0.0583558 | + | 0.0423980i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.9039 | − | 18.0938i | −1.33884 | − | 0.972727i | ||||
\(347\) | −0.0290140 | + | 0.0399344i | −0.00155756 | + | 0.00214379i | −0.809795 | − | 0.586713i | \(-0.800422\pi\) |
0.808238 | + | 0.588857i | \(0.200422\pi\) | |||||||
\(348\) | 13.1098 | + | 4.25962i | 0.702757 | + | 0.228340i | ||||
\(349\) | 7.47437 | 0.400094 | 0.200047 | − | 0.979786i | \(-0.435891\pi\) | ||||
0.200047 | + | 0.979786i | \(0.435891\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.19794 | 0.0639413 | ||||||||
\(352\) | 11.9449 | + | 3.88113i | 0.636665 | + | 0.206865i | ||||
\(353\) | 10.9122 | − | 15.0194i | 0.580799 | − | 0.799401i | −0.412984 | − | 0.910738i | \(-0.635513\pi\) |
0.993783 | + | 0.111337i | \(0.0355133\pi\) | |||||||
\(354\) | 15.7211 | + | 11.4220i | 0.835567 | + | 0.607075i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.3375 | − | 14.7760i | 1.07788 | − | 0.783128i | ||||
\(357\) | − | 4.89158i | − | 0.258890i | ||||||
\(358\) | 0.993921 | + | 1.36802i | 0.0525304 | + | 0.0723019i | ||||
\(359\) | −3.27695 | − | 10.0854i | −0.172951 | − | 0.532289i | 0.826583 | − | 0.562815i | \(-0.190282\pi\) |
−0.999534 | + | 0.0305264i | \(0.990282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3490 | − | 38.0062i | 0.649945 | − | 2.00032i | ||||
\(362\) | 28.6994 | − | 9.32500i | 1.50841 | − | 0.490111i | ||||
\(363\) | −8.08769 | + | 2.62785i | −0.424493 | + | 0.137926i | ||||
\(364\) | −4.04046 | + | 12.4353i | −0.211778 | + | 0.651785i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.915470 | + | 2.81753i | 0.0478524 | + | 0.147274i | ||||
\(367\) | 6.82867 | + | 9.39886i | 0.356454 | + | 0.490617i | 0.949156 | − | 0.314805i | \(-0.101939\pi\) |
−0.592703 | + | 0.805421i | \(0.701939\pi\) | |||||||
\(368\) | − | 6.35078i | − | 0.331057i | ||||||
\(369\) | −6.04508 | + | 4.39201i | −0.314695 | + | 0.228639i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.2074 | − | 9.59570i | −0.685692 | − | 0.498184i | ||||
\(372\) | 7.06859 | − | 9.72907i | 0.366489 | − | 0.504429i | ||||
\(373\) | 21.9953 | + | 7.14671i | 1.13887 | + | 0.370043i | 0.816942 | − | 0.576720i | \(-0.195668\pi\) |
0.321932 | + | 0.946763i | \(0.395668\pi\) | |||||||
\(374\) | −3.76328 | −0.194595 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.41779 | 0.227830 | ||||||||
\(377\) | −6.27109 | − | 2.03760i | −0.322978 | − | 0.104942i | ||||
\(378\) | −5.43700 | + | 7.48339i | −0.279649 | + | 0.384904i | ||||
\(379\) | 20.1374 | + | 14.6307i | 1.03439 | + | 0.751527i | 0.969182 | − | 0.246345i | \(-0.0792296\pi\) |
0.0652058 | + | 0.997872i | \(0.479230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.7498 | − | 9.98980i | 0.704423 | − | 0.511793i | ||||
\(382\) | − | 22.0079i | − | 1.12602i | ||||||
\(383\) | −9.24123 | − | 12.7195i | −0.472205 | − | 0.649934i | 0.504779 | − | 0.863249i | \(-0.331574\pi\) |
−0.976984 | + | 0.213315i | \(0.931574\pi\) | |||||||
\(384\) | 2.56179 | + | 7.88439i | 0.130731 | + | 0.402349i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.85100 | − | 8.77449i | 0.145112 | − | 0.446610i | ||||
\(387\) | 1.18880 | − | 0.386266i | 0.0604303 | − | 0.0196350i | ||||
\(388\) | −17.8629 | + | 5.80400i | −0.906851 | + | 0.294654i | ||||
\(389\) | 2.62860 | − | 8.09000i | 0.133275 | − | 0.410179i | −0.862042 | − | 0.506836i | \(-0.830815\pi\) |
0.995318 | + | 0.0966568i | \(0.0308149\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.804717 | + | 2.47667i | 0.0406963 | + | 0.125250i | ||||
\(392\) | −7.54649 | − | 10.3869i | −0.381155 | − | 0.524615i | ||||
\(393\) | 0.328872i | 0.0165894i | ||||||||
\(394\) | 3.22779 | − | 2.34513i | 0.162614 | − | 0.118146i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.20092 | + | 2.32561i | 0.160852 | + | 0.116866i | ||||
\(397\) | 15.4322 | − | 21.2407i | 0.774522 | − | 1.06604i | −0.221343 | − | 0.975196i | \(-0.571044\pi\) |
0.995865 | − | 0.0908420i | \(-0.0289558\pi\) | |||||||
\(398\) | −8.59921 | − | 2.79405i | −0.431039 | − | 0.140053i | ||||
\(399\) | −33.4667 | −1.67543 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.2815 | −1.26250 | −0.631250 | − | 0.775579i | \(-0.717458\pi\) | ||||
−0.631250 | + | 0.775579i | \(0.717458\pi\) | |||||||
\(402\) | −7.79670 | − | 2.53330i | −0.388864 | − | 0.126350i | ||||
\(403\) | −3.38128 | + | 4.65393i | −0.168434 | + | 0.231829i | ||||
\(404\) | −13.2060 | − | 9.59475i | −0.657025 | − | 0.477356i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 41.1908 | − | 29.9269i | 2.04427 | − | 1.48525i | ||||
\(407\) | 10.0677i | 0.499035i | ||||||||
\(408\) | −0.706062 | − | 0.971811i | −0.0349553 | − | 0.0481118i | ||||
\(409\) | −10.4427 | − | 32.1392i | −0.516357 | − | 1.58918i | −0.780800 | − | 0.624781i | \(-0.785188\pi\) |
0.264443 | − | 0.964401i | \(-0.414812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.40995 | − | 4.33939i | 0.0695479 | − | 0.214046i | ||||
\(412\) | −19.1700 | + | 6.22870i | −0.944437 | + | 0.306866i | ||||
\(413\) | 37.9529 | − | 12.3317i | 1.86754 | − | 0.606801i | ||||
\(414\) | 1.52172 | − | 4.68338i | 0.0747885 | − | 0.230175i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.94281 | − | 9.05703i | −0.144283 | − | 0.444057i | ||||
\(417\) | 2.78258 | + | 3.82989i | 0.136263 | + | 0.187550i | ||||
\(418\) | 25.7473i | 1.25934i | ||||||||
\(419\) | 6.41819 | − | 4.66309i | 0.313549 | − | 0.227807i | −0.419869 | − | 0.907585i | \(-0.637924\pi\) |
0.733418 | + | 0.679778i | \(0.237924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.05788 | − | 4.40131i | −0.295243 | − | 0.214507i | 0.430296 | − | 0.902688i | \(-0.358409\pi\) |
−0.725539 | + | 0.688181i | \(0.758409\pi\) | |||||||
\(422\) | −11.5974 | + | 15.9625i | −0.564554 | + | 0.777042i | ||||
\(423\) | −3.92563 | − | 1.27551i | −0.190870 | − | 0.0620176i | ||||
\(424\) | −4.00897 | −0.194693 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −22.5076 | −1.09049 | ||||||||
\(427\) | 5.78604 | + | 1.88000i | 0.280006 | + | 0.0909795i | ||||
\(428\) | −13.9507 | + | 19.2015i | −0.674333 | + | 0.928140i | ||||
\(429\) | −1.53117 | − | 1.11246i | −0.0739257 | − | 0.0537101i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.8882 | + | 13.7231i | −0.909811 | + | 0.661016i | −0.940967 | − | 0.338498i | \(-0.890081\pi\) |
0.0311564 | + | 0.999515i | \(0.490081\pi\) | |||||||
\(432\) | − | 2.73708i | − | 0.131688i | ||||||
\(433\) | −1.97306 | − | 2.71569i | −0.0948193 | − | 0.130508i | 0.758971 | − | 0.651124i | \(-0.225702\pi\) |
−0.853791 | + | 0.520616i | \(0.825702\pi\) | |||||||
\(434\) | −13.7262 | − | 42.2449i | −0.658879 | − | 2.02782i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.02778 | + | 27.7846i | −0.432352 | + | 1.33064i | ||||
\(437\) | 16.9446 | − | 5.50564i | 0.810571 | − | 0.263370i | ||||
\(438\) | 10.0857 | − | 3.27703i | 0.481912 | − | 0.156583i | ||||
\(439\) | 2.93072 | − | 9.01984i | 0.139876 | − | 0.430493i | −0.856441 | − | 0.516245i | \(-0.827329\pi\) |
0.996317 | + | 0.0857520i | \(0.0273293\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.70686 | + | 11.4086i | 0.176517 | + | 0.543264i | ||||
\(442\) | 1.67722 | + | 2.30849i | 0.0797771 | + | 0.109804i | ||||
\(443\) | − | 9.65446i | − | 0.458697i | −0.973344 | − | 0.229349i | \(-0.926340\pi\) | ||
0.973344 | − | 0.229349i | \(-0.0736596\pi\) | |||||||
\(444\) | −12.9104 | + | 9.37999i | −0.612703 | + | 0.445154i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.83366 | + | 4.23840i | 0.276232 | + | 0.200694i | ||||
\(447\) | 2.74874 | − | 3.78332i | 0.130011 | − | 0.178945i | ||||
\(448\) | 47.2437 | + | 15.3504i | 2.23205 | + | 0.725238i | ||||
\(449\) | −31.5260 | −1.48780 | −0.743902 | − | 0.668289i | \(-0.767027\pi\) | ||||
−0.743902 | + | 0.668289i | \(0.767027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.8053 | 0.555888 | ||||||||
\(452\) | −35.5482 | − | 11.5503i | −1.67205 | − | 0.543281i | ||||
\(453\) | 3.84516 | − | 5.29241i | 0.180661 | − | 0.248659i | ||||
\(454\) | 46.0111 | + | 33.4290i | 2.15941 | + | 1.56890i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.64884 | + | 4.83067i | −0.311361 | + | 0.226217i | ||||
\(457\) | − | 9.94467i | − | 0.465192i | −0.972573 | − | 0.232596i | \(-0.925278\pi\) | ||
0.972573 | − | 0.232596i | \(-0.0747220\pi\) | |||||||
\(458\) | −1.47451 | − | 2.02949i | −0.0688994 | − | 0.0948319i | ||||
\(459\) | 0.346820 | + | 1.06740i | 0.0161882 | + | 0.0498221i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.31863 | + | 22.5244i | −0.340863 | + | 1.04907i | 0.622899 | + | 0.782302i | \(0.285955\pi\) |
−0.963762 | + | 0.266765i | \(0.914045\pi\) | |||||||
\(462\) | 13.8988 | − | 4.51601i | 0.646632 | − | 0.210104i | ||||
\(463\) | 26.2971 | − | 8.54443i | 1.22213 | − | 0.397094i | 0.374272 | − | 0.927319i | \(-0.377893\pi\) |
0.847857 | + | 0.530226i | \(0.177893\pi\) | |||||||
\(464\) | −4.65556 | + | 14.3284i | −0.216129 | + | 0.665177i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.65306 | + | 14.3206i | 0.215549 | + | 0.663391i | ||||
\(467\) | −2.56180 | − | 3.52602i | −0.118546 | − | 0.163165i | 0.745620 | − | 0.666371i | \(-0.232153\pi\) |
−0.864166 | + | 0.503207i | \(0.832153\pi\) | |||||||
\(468\) | − | 3.00000i | − | 0.138675i | ||||||
\(469\) | −13.6200 | + | 9.89548i | −0.628912 | + | 0.456931i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.23124 | − | 2.34764i | −0.148888 | − | 0.108173i | ||||
\(472\) | 5.76013 | − | 7.92814i | 0.265132 | − | 0.364922i | ||||
\(473\) | −1.87820 | − | 0.610263i | −0.0863596 | − | 0.0280599i | ||||
\(474\) | −30.8864 | −1.41866 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −12.2500 | −0.561477 | ||||||||
\(477\) | 3.56236 | + | 1.15748i | 0.163109 | + | 0.0529973i | ||||
\(478\) | −0.0533827 | + | 0.0734750i | −0.00244167 | + | 0.00336067i | ||||
\(479\) | 10.3670 | + | 7.53204i | 0.473679 | + | 0.344148i | 0.798873 | − | 0.601499i | \(-0.205430\pi\) |
−0.325195 | + | 0.945647i | \(0.605430\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.17575 | − | 4.48695i | 0.281590 | − | 0.204587i | ||||
\(482\) | − | 24.9822i | − | 1.13791i | ||||||
\(483\) | −5.94409 | − | 8.18133i | −0.270465 | − | 0.372263i | ||||
\(484\) | 6.58092 | + | 20.2540i | 0.299133 | + | 0.920636i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.655837 | − | 2.01846i | 0.0297494 | − | 0.0915592i | ||||
\(487\) | 6.58330 | − | 2.13904i | 0.298318 | − | 0.0969293i | −0.156034 | − | 0.987752i | \(-0.549871\pi\) |
0.454352 | + | 0.890822i | \(0.349871\pi\) | |||||||
\(488\) | 1.42088 | − | 0.461671i | 0.0643201 | − | 0.0208989i | ||||
\(489\) | −1.48372 | + | 4.56641i | −0.0670960 | + | 0.206500i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.28665 | + | 25.5037i | 0.373971 | + | 1.15096i | 0.944170 | + | 0.329458i | \(0.106866\pi\) |
−0.570199 | + | 0.821507i | \(0.693134\pi\) | |||||||
\(492\) | 10.9989 | + | 15.1387i | 0.495869 | + | 0.682505i | ||||
\(493\) | − | 6.17766i | − | 0.278228i | ||||||
\(494\) | 15.7940 | − | 11.4750i | 0.710606 | − | 0.516286i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.6334 | + | 7.72564i | 0.477455 | + | 0.346891i | ||||
\(497\) | −27.1682 | + | 37.3938i | −1.21866 | + | 1.67734i | ||||
\(498\) | 17.6333 | + | 5.72941i | 0.790168 | + | 0.256741i | ||||
\(499\) | −2.75460 | −0.123313 | −0.0616565 | − | 0.998097i | \(-0.519638\pi\) | ||||
−0.0616565 | + | 0.998097i | \(0.519638\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.6600 | 1.05705 | ||||||||
\(502\) | 35.2754 | + | 11.4617i | 1.57442 | + | 0.511559i | ||||
\(503\) | −9.23422 | + | 12.7098i | −0.411733 | + | 0.566702i | −0.963640 | − | 0.267203i | \(-0.913900\pi\) |
0.551907 | + | 0.833906i | \(0.313900\pi\) | |||||||
\(504\) | 3.77387 | + | 2.74188i | 0.168102 | + | 0.122133i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.29422 | + | 4.57302i | −0.279812 | + | 0.203295i | ||||
\(507\) | − | 11.5649i | − | 0.513617i | ||||||
\(508\) | −25.0175 | − | 34.4336i | −1.10997 | − | 1.52774i | ||||
\(509\) | 12.6970 | + | 39.0774i | 0.562785 | + | 1.73207i | 0.674442 | + | 0.738328i | \(0.264384\pi\) |
−0.111657 | + | 0.993747i | \(0.535616\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.72968 | − | 20.7118i | 0.297703 | − | 0.916237i | ||||
\(512\) | −26.2659 | + | 8.53432i | −1.16080 | + | 0.377167i | ||||
\(513\) | 7.30285 | − | 2.37284i | 0.322429 | − | 0.104763i | ||||
\(514\) | −10.1439 | + | 31.2198i | −0.447430 | + | 1.37705i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.967325 | − | 2.97712i | −0.0425841 | − | 0.131060i | ||||
\(517\) | 3.83312 | + | 5.27584i | 0.168580 | + | 0.232031i | ||||
\(518\) | 58.9438i | 2.58984i | ||||||||
\(519\) | 11.7342 | − | 8.52541i | 0.515075 | − | 0.374224i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.2630 | − | 21.2608i | −1.28203 | − | 0.931452i | −0.282421 | − | 0.959290i | \(-0.591138\pi\) |
−0.999612 | + | 0.0278383i | \(0.991138\pi\) | |||||||
\(522\) | −6.86648 | + | 9.45090i | −0.300538 | + | 0.413655i | ||||
\(523\) | −26.6761 | − | 8.66761i | −1.16647 | − | 0.379008i | −0.339144 | − | 0.940735i | \(-0.610137\pi\) |
−0.827323 | + | 0.561727i | \(0.810137\pi\) | |||||||
\(524\) | 0.823595 | 0.0359789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.07228 | 0.133958 | ||||||||
\(527\) | −5.12573 | − | 1.66545i | −0.223280 | − | 0.0725482i | ||||
\(528\) | −2.54178 | + | 3.49846i | −0.110617 | + | 0.152251i | ||||
\(529\) | −14.2519 | − | 10.3546i | −0.619648 | − | 0.450201i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.40746 | + | 5.38184i | −0.321456 | + | 0.233552i | ||||
\(532\) | 83.8108i | 3.63366i | ||||||||
\(533\) | −5.26137 | − | 7.24165i | −0.227895 | − | 0.313671i | ||||
\(534\) | 6.58338 | + | 20.2616i | 0.284891 | + | 0.876803i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.27754 | + | 3.93187i | −0.0551815 | + | 0.169831i | ||||
\(537\) | −0.757750 | + | 0.246208i | −0.0326993 | + | 0.0106247i | ||||
\(538\) | −17.5731 | + | 5.70983i | −0.757628 | + | 0.246168i | ||||
\(539\) | 5.85650 | − | 18.0244i | 0.252257 | − | 0.776368i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.06865 | + | 3.28896i | 0.0459448 | + | 0.141404i | 0.971397 | − | 0.237460i | \(-0.0763149\pi\) |
−0.925452 | + | 0.378864i | \(0.876315\pi\) | |||||||
\(542\) | 35.7200 | + | 49.1643i | 1.53430 | + | 2.11179i | ||||
\(543\) | 14.2185i | 0.610173i | ||||||||
\(544\) | 7.21812 | − | 5.24427i | 0.309474 | − | 0.224846i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.96465 | − | 6.51320i | −0.383652 | − | 0.278739i | ||||
\(547\) | 8.20751 | − | 11.2967i | 0.350928 | − | 0.483011i | −0.596665 | − | 0.802490i | \(-0.703508\pi\) |
0.947593 | + | 0.319479i | \(0.103508\pi\) | |||||||
\(548\) | −10.8671 | − | 3.53095i | −0.464221 | − | 0.150835i | ||||
\(549\) | −1.39588 | −0.0595747 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −42.2657 | −1.80058 | ||||||||
\(552\) | −2.36182 | − | 0.767403i | −0.100526 | − | 0.0326629i | ||||
\(553\) | −37.2821 | + | 51.3144i | −1.58540 | + | 2.18211i | ||||
\(554\) | 9.10372 | + | 6.61424i | 0.386780 | + | 0.281012i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.59118 | − | 6.96840i | 0.406757 | − | 0.295526i | ||||
\(557\) | − | 6.59585i | − | 0.279475i | −0.990189 | − | 0.139738i | \(-0.955374\pi\) | ||
0.990189 | − | 0.139738i | \(-0.0446259\pi\) | |||||||
\(558\) | 5.99046 | + | 8.24516i | 0.253596 | + | 0.349045i | ||||
\(559\) | 0.462723 | + | 1.42411i | 0.0195711 | + | 0.0602336i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.547943 | − | 1.68640i | 0.0231342 | − | 0.0711997i | ||||
\(562\) | 48.6110 | − | 15.7947i | 2.05053 | − | 0.666257i | ||||
\(563\) | −15.2376 | + | 4.95100i | −0.642189 | + | 0.208660i | −0.611967 | − | 0.790883i | \(-0.709621\pi\) |
−0.0302222 | + | 0.999543i | \(0.509621\pi\) | |||||||
\(564\) | −3.19427 | + | 9.83094i | −0.134503 | + | 0.413957i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.7826 | − | 54.7291i | −0.747457 | − | 2.30044i | ||||
\(567\) | −2.56180 | − | 3.52602i | −0.107586 | − | 0.148079i | ||||
\(568\) | 11.3505i | 0.476258i | ||||||||
\(569\) | 18.6813 | − | 13.5728i | 0.783162 | − | 0.569001i | −0.122764 | − | 0.992436i | \(-0.539176\pi\) |
0.905926 | + | 0.423435i | \(0.139176\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.5148 | + | 19.9907i | 1.15146 | + | 0.836583i | 0.988674 | − | 0.150078i | \(-0.0479526\pi\) |
0.162784 | + | 0.986662i | \(0.447953\pi\) | |||||||
\(572\) | −2.78594 | + | 3.83451i | −0.116486 | + | 0.160329i | ||||
\(573\) | 9.86215 | + | 3.20441i | 0.411997 | + | 0.133866i | ||||
\(574\) | 69.1171 | 2.88489 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.3975 | −0.474896 | ||||||||
\(577\) | −6.15074 | − | 1.99850i | −0.256059 | − | 0.0831985i | 0.178175 | − | 0.983999i | \(-0.442981\pi\) |
−0.434233 | + | 0.900800i | \(0.642981\pi\) | |||||||
\(578\) | 19.6357 | − | 27.0263i | 0.816739 | − | 1.12414i | ||||
\(579\) | 3.51690 | + | 2.55517i | 0.146157 | + | 0.106189i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.8034 | − | 22.3800i | 1.27794 | − | 0.928479i | ||||
\(582\) | − | 15.9174i | − | 0.659798i | ||||||
\(583\) | −3.47841 | − | 4.78762i | −0.144061 | − | 0.198283i | ||||
\(584\) | −1.65261 | − | 5.08620i | −0.0683853 | − | 0.210468i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.3146 | + | 40.9780i | −0.550019 | + | 1.69279i | ||||
\(587\) | −36.6168 | + | 11.8975i | −1.51134 | + | 0.491063i | −0.943301 | − | 0.331940i | \(-0.892297\pi\) |
−0.568037 | + | 0.823003i | \(0.692297\pi\) | |||||||
\(588\) | 28.5704 | − | 9.28310i | 1.17822 | − | 0.382828i | ||||
\(589\) | −11.3945 | + | 35.0687i | −0.469503 | + | 1.44498i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.580921 | + | 1.78789i | 0.0238959 | + | 0.0735440i | ||||
\(592\) | −10.2519 | − | 14.1105i | −0.421350 | − | 0.579939i | ||||
\(593\) | − | 4.93069i | − | 0.202479i | −0.994862 | − | 0.101240i | \(-0.967719\pi\) | ||
0.994862 | − | 0.101240i | \(-0.0322808\pi\) | |||||||
\(594\) | −2.71270 | + | 1.97090i | −0.111304 | + | 0.0808668i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.47457 | − | 6.88368i | −0.388093 | − | 0.281966i | ||||
\(597\) | 2.50413 | − | 3.44664i | 0.102487 | − | 0.141062i | ||||
\(598\) | 5.61040 | + | 1.82293i | 0.229426 | + | 0.0745452i | ||||
\(599\) | 35.0268 | 1.43116 | 0.715578 | − | 0.698533i | \(-0.246164\pi\) | ||||
0.715578 | + | 0.698533i | \(0.246164\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.90570 | −0.200108 | −0.100054 | − | 0.994982i | \(-0.531901\pi\) | ||||
−0.100054 | + | 0.994982i | \(0.531901\pi\) | |||||||
\(602\) | −10.9964 | − | 3.57295i | −0.448180 | − | 0.145623i | ||||
\(603\) | 2.27044 | − | 3.12499i | 0.0924594 | − | 0.127259i | ||||
\(604\) | −13.2538 | − | 9.62943i | −0.539289 | − | 0.391816i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.1918 | − | 8.13132i | 0.454636 | − | 0.330312i | ||||
\(607\) | 48.6955i | 1.97649i | 0.152884 | + | 0.988244i | \(0.451144\pi\) | ||||
−0.152884 | + | 0.988244i | \(0.548856\pi\) | |||||||
\(608\) | −35.8798 | − | 49.3842i | −1.45512 | − | 2.00280i | ||||
\(609\) | 7.41330 | + | 22.8158i | 0.300402 | + | 0.924543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.52799 | − | 4.70266i | 0.0618158 | − | 0.190249i | ||||
\(612\) | 2.67310 | − | 0.868541i | 0.108053 | − | 0.0351087i | ||||
\(613\) | 16.3714 | − | 5.31938i | 0.661234 | − | 0.214848i | 0.0408728 | − | 0.999164i | \(-0.486986\pi\) |
0.620361 | + | 0.784317i | \(0.286986\pi\) | |||||||
\(614\) | 1.64832 | − | 5.07299i | 0.0665206 | − | 0.204729i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.27742 | − | 7.00918i | −0.0917598 | − | 0.282408i | ||||
\(617\) | 18.5794 | + | 25.5723i | 0.747978 | + | 1.02950i | 0.998120 | + | 0.0612947i | \(0.0195229\pi\) |
−0.250141 | + | 0.968209i | \(0.580477\pi\) | |||||||
\(618\) | − | 17.0821i | − | 0.687145i | ||||||
\(619\) | −18.4615 | + | 13.4130i | −0.742029 | + | 0.539116i | −0.893346 | − | 0.449370i | \(-0.851649\pi\) |
0.151317 | + | 0.988485i | \(0.451649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.87714 | + | 1.36382i | 0.0753271 | + | 0.0547283i | ||||
\(622\) | 6.01804 | − | 8.28312i | 0.241301 | − | 0.332123i | ||||
\(623\) | 41.6089 | + | 13.5196i | 1.66703 | + | 0.541649i | ||||
\(624\) | 3.27886 | 0.131259 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −12.7088 | −0.507945 | ||||||||
\(627\) | −11.5378 | − | 3.74887i | −0.460776 | − | 0.149715i | ||||
\(628\) | −5.87918 | + | 8.09200i | −0.234605 | + | 0.322906i | ||||
\(629\) | 5.78598 | + | 4.20376i | 0.230702 | + | 0.167615i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.7830 | + | 22.3652i | −1.22545 | + | 0.890344i | −0.996541 | − | 0.0831027i | \(-0.973517\pi\) |
−0.228913 | + | 0.973447i | \(0.573517\pi\) | |||||||
\(632\) | 15.5760i | 0.619581i | ||||||||
\(633\) | −5.46447 | − | 7.52120i | −0.217193 | − | 0.298941i | ||||
\(634\) | −11.3808 | − | 35.0265i | −0.451989 | − | 1.39108i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.89868 | − | 8.92120i | 0.114940 | − | 0.353749i | ||||
\(637\) | −13.6668 | + | 4.44060i | −0.541497 | + | 0.175943i | ||||
\(638\) | 17.5531 | − | 5.70334i | 0.694933 | − | 0.225797i | ||||
\(639\) | 3.27716 | − | 10.0860i | 0.129642 | − | 0.398998i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.19229 | + | 25.2133i | 0.323576 | + | 0.995864i | 0.972079 | + | 0.234652i | \(0.0753952\pi\) |
−0.648504 | + | 0.761212i | \(0.724605\pi\) | |||||||
\(642\) | −11.8229 | − | 16.2728i | −0.466612 | − | 0.642237i | ||||
\(643\) | 36.0014i | 1.41976i | 0.704324 | + | 0.709879i | \(0.251250\pi\) | ||||
−0.704324 | + | 0.709879i | \(0.748750\pi\) | |||||||
\(644\) | −20.4885 | + | 14.8858i | −0.807360 | + | 0.586582i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.7972 | + | 10.7508i | 0.582188 | + | 0.422984i | ||||
\(647\) | 24.5600 | − | 33.8040i | 0.965554 | − | 1.32897i | 0.0212924 | − | 0.999773i | \(-0.493222\pi\) |
0.944261 | − | 0.329197i | \(-0.106778\pi\) | |||||||
\(648\) | −1.01791 | − | 0.330738i | −0.0399872 | − | 0.0129926i | ||||
\(649\) | 14.4658 | 0.567833 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.9293 | 0.820284 | ||||||||
\(652\) | 11.4357 | + | 3.71567i | 0.447855 | + | 0.145517i | ||||
\(653\) | −12.6023 | + | 17.3456i | −0.493168 | + | 0.678787i | −0.980968 | − | 0.194168i | \(-0.937799\pi\) |
0.487801 | + | 0.872955i | \(0.337799\pi\) | |||||||
\(654\) | −20.0301 | − | 14.5527i | −0.783240 | − | 0.569057i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16.5459 | + | 12.0213i | −0.646009 | + | 0.469353i | ||||
\(657\) | 4.99672i | 0.194940i | ||||||||
\(658\) | 22.4420 | + | 30.8888i | 0.874882 | + | 1.20417i | ||||
\(659\) | 5.20135 | + | 16.0081i | 0.202616 | + | 0.623587i | 0.999803 | + | 0.0198549i | \(0.00632042\pi\) |
−0.797187 | + | 0.603732i | \(0.793680\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.629918 | − | 1.93869i | 0.0245010 | − | 0.0754062i | −0.938058 | − | 0.346477i | \(-0.887378\pi\) |
0.962559 | + | 0.271071i | \(0.0873778\pi\) | |||||||
\(662\) | −41.0463 | + | 13.3368i | −1.59531 | + | 0.518348i | ||||
\(663\) | −1.27868 | + | 0.415470i | −0.0496600 | + | 0.0161355i | ||||
\(664\) | 2.88934 | − | 8.89248i | 0.112128 | − | 0.345095i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.17920 | − | 12.8623i | −0.161941 | − | 0.498402i | ||||
\(667\) | −7.50689 | − | 10.3323i | −0.290668 | − | 0.400070i | ||||
\(668\) | − | 59.2518i | − | 2.29252i | ||||||
\(669\) | −2.74870 | + | 1.99705i | −0.106271 | + | 0.0772104i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.78417 | + | 1.29628i | 0.0688772 | + | 0.0500422i | ||||
\(672\) | −20.3653 | + | 28.0304i | −0.785608 | + | 1.08130i | ||||
\(673\) | −33.6461 | − | 10.9323i | −1.29696 | − | 0.421409i | −0.422439 | − | 0.906391i | \(-0.638826\pi\) |
−0.874524 | + | 0.484983i | \(0.838826\pi\) | |||||||
\(674\) | −72.7050 | −2.80049 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −28.9621 | −1.11393 | ||||||||
\(677\) | 42.2434 | + | 13.7257i | 1.62354 | + | 0.527522i | 0.972775 | − | 0.231753i | \(-0.0744462\pi\) |
0.650770 | + | 0.759275i | \(0.274446\pi\) | |||||||
\(678\) | 18.6190 | − | 25.6269i | 0.715060 | − | 0.984196i | ||||
\(679\) | −26.4450 | − | 19.2134i | −1.01487 | − | 0.737344i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −21.6795 | + | 15.7511i | −0.830760 | + | 0.603582i | ||||
\(682\) | − | 16.1017i | − | 0.616567i | ||||||
\(683\) | 24.9780 | + | 34.3793i | 0.955758 | + | 1.31549i | 0.948922 | + | 0.315512i | \(0.102176\pi\) |
0.00683639 | + | 0.999977i | \(0.497824\pi\) | |||||||
\(684\) | −5.94230 | − | 18.2885i | −0.227210 | − | 0.699280i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14.2796 | − | 43.9481i | 0.545198 | − | 1.67795i | ||||
\(687\) | 1.12415 | − | 0.365257i | 0.0428888 | − | 0.0139354i | ||||
\(688\) | 3.25385 | − | 1.05724i | 0.124052 | − | 0.0403069i | ||||
\(689\) | −1.38659 | + | 4.26749i | −0.0528249 | + | 0.162578i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.67746 | + | 26.7065i | 0.330106 | + | 1.01596i | 0.969083 | + | 0.246736i | \(0.0793580\pi\) |
−0.638977 | + | 0.769226i | \(0.720642\pi\) | |||||||
\(692\) | −21.3502 | − | 29.3860i | −0.811612 | − | 1.11709i | ||||
\(693\) | 6.88586i | 0.261572i | ||||||||
\(694\) | −0.0847541 | + | 0.0615775i | −0.00321722 | + | 0.00233745i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.76609 | + | 3.46276i | 0.180658 | + | 0.131256i | ||||
\(697\) | 4.92930 | − | 6.78460i | 0.186711 | − | 0.256985i | ||||
\(698\) | 15.0867 | + | 4.90197i | 0.571040 | + | 0.185542i | ||||
\(699\) | −7.09483 | −0.268351 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.4314 | 1.75369 | 0.876845 | − | 0.480772i | \(-0.159644\pi\) | ||||
0.876845 | + | 0.480772i | \(0.159644\pi\) | |||||||
\(702\) | 2.41799 | + | 0.785653i | 0.0912612 | + | 0.0296526i | ||||
\(703\) | 28.7609 | − | 39.5860i | 1.08474 | − | 1.49301i | ||||
\(704\) | 14.5680 | + | 10.5842i | 0.549051 | + | 0.398909i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 31.8762 | − | 23.1594i | 1.19967 | − | 0.871615i | ||||
\(707\) | − | 28.4090i | − | 1.06843i | ||||||
\(708\) | 13.4777 | + | 18.5505i | 0.506524 | + | 0.697171i | ||||
\(709\) | −15.0285 | − | 46.2529i | −0.564406 | − | 1.73706i | −0.669710 | − | 0.742622i | \(-0.733582\pi\) |
0.105305 | − | 0.994440i | \(-0.466418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.49714 | − | 13.8408i | 0.168656 | − | 0.519070i | ||||
\(712\) | 10.2179 | − | 3.31999i | 0.382932 | − | 0.124422i | ||||
\(713\) | −10.5968 | + | 3.44310i | −0.396852 | + | 0.128945i | ||||
\(714\) | 3.20808 | − | 9.87345i | 0.120059 | − | 0.369505i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.616579 | + | 1.89763i | 0.0230426 | + | 0.0709179i | ||||
\(717\) | −0.0251528 | − | 0.0346199i | −0.000939350 | − | 0.00129290i | ||||
\(718\) | − | 22.5062i | − | 0.839923i | ||||||
\(719\) | −17.1475 | + | 12.4584i | −0.639493 | + | 0.464619i | −0.859676 | − | 0.510840i | \(-0.829334\pi\) |
0.220183 | + | 0.975459i | \(0.429334\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.3801 | − | 20.6193i | −1.05693 | − | 0.767904i | ||||
\(722\) | 49.8517 | − | 68.6150i | 1.85529 | − | 2.55359i | ||||
\(723\) | 11.1950 | + | 3.63746i | 0.416345 | + | 0.135279i | ||||
\(724\) | 35.6073 | 1.32333 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −18.0481 | −0.669828 | ||||||||
\(727\) | 12.9259 | + | 4.19988i | 0.479396 | + | 0.155765i | 0.538739 | − | 0.842473i | \(-0.318901\pi\) |
−0.0593437 | + | 0.998238i | \(0.518901\pi\) | |||||||
\(728\) | −3.28460 | + | 4.52087i | −0.121736 | + | 0.167555i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.13497 | + | 0.824602i | −0.0419783 | + | 0.0304990i | ||||
\(732\) | 3.49570i | 0.129205i | ||||||||
\(733\) | 10.9640 | + | 15.0907i | 0.404965 | + | 0.557386i | 0.961981 | − | 0.273115i | \(-0.0880540\pi\) |
−0.557017 | + | 0.830501i | \(0.688054\pi\) | |||||||
\(734\) | 7.61927 | + | 23.4497i | 0.281233 | + | 0.865545i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.69988 | − | 17.5424i | 0.210101 | − | 0.646623i | ||||
\(737\) | −5.80402 | + | 1.88584i | −0.213794 | + | 0.0694658i | ||||
\(738\) | −15.0822 | + | 4.90050i | −0.555183 | + | 0.180390i | ||||
\(739\) | −8.17202 | + | 25.1509i | −0.300613 | + | 0.925191i | 0.680665 | + | 0.732594i | \(0.261691\pi\) |
−0.981278 | + | 0.192596i | \(0.938309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.84252 | + | 8.74838i | 0.104423 | + | 0.321380i | ||||
\(742\) | −20.3653 | − | 28.0304i | −0.747633 | − | 1.02903i | ||||
\(743\) | 29.0191i | 1.06461i | 0.846553 | + | 0.532304i | \(0.178674\pi\) | ||||
−0.846553 | + | 0.532304i | \(0.821326\pi\) | |||||||
\(744\) | 4.15803 | − | 3.02098i | 0.152441 | − | 0.110755i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 39.7096 | + | 28.8507i | 1.45387 | + | 1.05630i | ||||
\(747\) | −5.13491 | + | 7.06760i | −0.187877 | + | 0.258590i | ||||
\(748\) | −4.22324 | − | 1.37221i | −0.154417 | − | 0.0501731i | ||||
\(749\) | −41.3065 | −1.50931 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.9489 | 0.581985 | 0.290992 | − | 0.956725i | \(-0.406015\pi\) | ||||
0.290992 | + | 0.956725i | \(0.406015\pi\) | |||||||
\(752\) | −10.7448 | − | 3.49119i | −0.391821 | − | 0.127310i | ||||
\(753\) | −10.2724 | + | 14.1387i | −0.374346 | + | 0.515243i | ||||
\(754\) | −11.3216 | − | 8.22563i | −0.412309 | − | 0.299560i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.83021 | + | 6.41552i | −0.321152 | + | 0.233330i | ||||
\(757\) | − | 16.4183i | − | 0.596734i | −0.954451 | − | 0.298367i | \(-0.903558\pi\) | ||
0.954451 | − | 0.298367i | \(-0.0964419\pi\) | |||||||
\(758\) | 31.0512 | + | 42.7382i | 1.12783 | + | 1.55232i | ||||
\(759\) | −1.13280 | − | 3.48640i | −0.0411180 | − | 0.126548i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.2257 | + | 46.8600i | −0.551932 | + | 1.69867i | 0.151978 | + | 0.988384i | \(0.451436\pi\) |
−0.703910 | + | 0.710289i | \(0.748564\pi\) | |||||||
\(762\) | 34.3051 | − | 11.1464i | 1.24274 | − | 0.403791i | ||||
\(763\) | −48.3555 | + | 15.7117i | −1.75059 | + | 0.568800i | ||||
\(764\) | 8.02480 | − | 24.6978i | 0.290327 | − | 0.893534i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.3111 | − | 31.7345i | −0.372557 | − | 1.14661i | ||||
\(767\) | −6.44711 | − | 8.87369i | −0.232792 | − | 0.320410i | ||||
\(768\) | − | 5.20057i | − | 0.187660i | ||||||
\(769\) | 39.9845 | − | 29.0504i | 1.44188 | − | 1.04759i | 0.454232 | − | 0.890884i | \(-0.349914\pi\) |
0.987646 | − | 0.156702i | \(-0.0500862\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.5132 | − | 9.09136i | −0.450651 | − | 0.327417i | ||||
\(772\) | 6.39892 | − | 8.80736i | 0.230302 | − | 0.316984i | ||||
\(773\) | −24.6403 | − | 8.00613i | −0.886251 | − | 0.287960i | −0.169701 | − | 0.985496i | \(-0.554280\pi\) |
−0.716550 | + | 0.697535i | \(0.754280\pi\) | |||||||
\(774\) | 2.65288 | 0.0953557 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.02715 | −0.288158 | ||||||||
\(777\) | −26.4138 | − | 8.58236i | −0.947590 | − | 0.307891i | ||||
\(778\) | 10.6114 | − | 14.6054i | 0.380439 | − | 0.523629i | ||||
\(779\) | −46.4182 | − | 33.7248i | −1.66311 | − | 1.20832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.5551 | + | 9.84838i | −0.485041 | + | 0.352403i | ||||
\(782\) | 5.52681i | 0.197638i | ||||||||
\(783\) | −3.23535 | − | 4.45307i | −0.115622 | − | 0.159140i | ||||
\(784\) | 10.1460 | + | 31.2262i | 0.362357 | + | 1.11522i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.215687 | + | 0.663815i | −0.00769329 | + | 0.0236775i | ||||
\(787\) | −29.2122 | + | 9.49160i | −1.04130 | + | 0.338339i | −0.779249 | − | 0.626715i | \(-0.784399\pi\) |
−0.262052 | + | 0.965054i | \(0.584399\pi\) | |||||||
\(788\) | 4.47741 | − | 1.45480i | 0.159501 | − | 0.0518251i | ||||
\(789\) | −0.447331 | + | 1.37674i | −0.0159254 | + | 0.0490134i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.1018 | − | 61.8670i | −0.714737 | − | 2.19974i | ||||
\(792\) | 0.993921 | + | 1.36802i | 0.0353175 | + | 0.0486103i | ||||
\(793\) | − | 1.67218i | − | 0.0593808i | ||||||
\(794\) | 45.0798 | − | 32.7524i | 1.59982 | − | 1.16234i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.63142 | − | 6.27109i | −0.305933 | − | 0.222273i | ||||
\(797\) | −19.8166 | + | 27.2753i | −0.701942 | + | 0.966140i | 0.297991 | + | 0.954569i | \(0.403683\pi\) |
−0.999933 | + | 0.0115713i | \(0.996317\pi\) | |||||||
\(798\) | −67.5513 | − | 21.9487i | −2.39129 | − | 0.776977i | ||||
\(799\) | 4.63260 | 0.163890 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.0381 | −0.354680 | ||||||||
\(802\) | −51.0298 | − | 16.5806i | −1.80192 | − | 0.585480i | ||||
\(803\) | 4.64018 | − | 6.38665i | 0.163748 | − | 0.225380i | ||||
\(804\) | −7.82591 | − | 5.68586i | −0.275999 | − | 0.200525i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.87720 | + | 7.17621i | −0.347910 | + | 0.252771i | ||||
\(807\) | − | 8.70617i | − | 0.306472i | ||||||
\(808\) | −4.10062 | − | 5.64402i | −0.144259 | − | 0.198556i | ||||
\(809\) | 0.285227 | + | 0.877838i | 0.0100280 | + | 0.0308632i | 0.955945 | − | 0.293545i | \(-0.0948350\pi\) |
−0.945917 | + | 0.324408i | \(0.894835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.27593 | − | 25.4707i | 0.290607 | − | 0.894397i | −0.694055 | − | 0.719922i | \(-0.744177\pi\) |
0.984662 | − | 0.174474i | \(-0.0558226\pi\) | |||||||
\(812\) | 57.1376 | − | 18.5651i | 2.00514 | − | 0.651508i | ||||
\(813\) | −27.2323 | + | 8.84832i | −0.955080 | + | 0.310324i | ||||
\(814\) | −6.60274 | + | 20.3212i | −0.231426 | + | 0.712256i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.949275 | + | 2.92157i | 0.0332313 | + | 0.102275i | ||||
\(817\) | 5.64168 | + | 7.76511i | 0.197377 | + | 0.271667i | ||||
\(818\) | − | 71.7204i | − | 2.50765i | ||||||
\(819\) | 4.22396 | − | 3.06889i | 0.147597 | − | 0.107236i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.8114 | + | 21.6592i | 1.04042 | + | 0.755912i | 0.970368 | − | 0.241631i | \(-0.0776822\pi\) |
0.0700559 | + | 0.997543i | \(0.477682\pi\) | |||||||
\(822\) | 5.69187 | − | 7.83419i | 0.198527 | − | 0.273249i | ||||
\(823\) | −19.4265 | − | 6.31204i | −0.677164 | − | 0.220024i | −0.0498106 | − | 0.998759i | \(-0.515862\pi\) |
−0.627353 | + | 0.778735i | \(0.715862\pi\) | |||||||
\(824\) | −8.61452 | −0.300101 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 84.6940 | 2.94688 | ||||||||
\(827\) | 4.11824 | + | 1.33810i | 0.143205 | + | 0.0465302i | 0.379743 | − | 0.925092i | \(-0.376013\pi\) |
−0.236537 | + | 0.971622i | \(0.576013\pi\) | |||||||
\(828\) | 3.41542 | − | 4.70092i | 0.118694 | − | 0.163368i | ||||
\(829\) | −0.497018 | − | 0.361104i | −0.0172621 | − | 0.0125417i | 0.579121 | − | 0.815242i | \(-0.303396\pi\) |
−0.596383 | + | 0.802700i | \(0.703396\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.28949 | + | 3.11649i | −0.148801 | + | 0.108110i | ||||
\(832\) | − | 13.6535i | − | 0.473351i | ||||||
\(833\) | −7.91343 | − | 10.8919i | −0.274184 | − | 0.377382i | ||||
\(834\) | 3.10473 | + | 9.55539i | 0.107508 | + | 0.330876i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.38828 | + | 28.8942i | −0.324701 | + | 0.999325i | ||||
\(837\) | −4.56703 | + | 1.48392i | −0.157860 | + | 0.0512917i | ||||
\(838\) | 16.0131 | − | 5.20297i | 0.553163 | − | 0.179733i | ||||
\(839\) | −1.66863 | + | 5.13553i | −0.0576077 | + | 0.177298i | −0.975720 | − | 0.219023i | \(-0.929713\pi\) |
0.918112 | + | 0.396321i | \(0.129713\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.400892 | + | 1.23382i | 0.0138239 | + | 0.0425455i | ||||
\(842\) | −9.34105 | − | 12.8568i | −0.321914 | − | 0.443076i | ||||
\(843\) | 24.0832i | 0.829469i | ||||||||
\(844\) | −18.8353 | + | 13.6847i | −0.648339 | + | 0.471046i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.08719 | − | 5.14914i | −0.243663 | − | 0.177031i | ||||
\(847\) | −21.7853 | + | 29.9849i | −0.748552 | + | 1.03029i | ||||
\(848\) | 9.75046 | + | 3.16812i | 0.334832 | + | 0.108794i | ||||
\(849\) | 27.1143 | 0.930561 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.7855 | 0.506841 | ||||||||
\(852\) | −25.2585 | − | 8.20698i | −0.865341 | − | 0.281166i | ||||
\(853\) | 23.3900 | − | 32.1936i | 0.800860 | − | 1.10229i | −0.191810 | − | 0.981432i | \(-0.561436\pi\) |
0.992670 | − | 0.120857i | \(-0.0385642\pi\) | |||||||
\(854\) | 10.4459 | + | 7.58940i | 0.357452 | + | 0.259704i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.20637 | + | 5.96228i | −0.280488 | + | 0.203787i | ||||
\(857\) | − | 42.8643i | − | 1.46422i | −0.681188 | − | 0.732109i | \(-0.738536\pi\) | ||
0.681188 | − | 0.732109i | \(-0.261464\pi\) | |||||||
\(858\) | −2.36101 | − | 3.24966i | −0.0806037 | − | 0.110941i | ||||
\(859\) | 1.41064 | + | 4.34152i | 0.0481306 | + | 0.148131i | 0.972233 | − | 0.234013i | \(-0.0751859\pi\) |
−0.924103 | + | 0.382144i | \(0.875186\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.0636 | + | 30.9726i | −0.342967 | + | 1.05554i | ||||
\(862\) | −47.1251 | + | 15.3119i | −1.60509 | + | 0.521524i | ||||
\(863\) | −35.7857 | + | 11.6275i | −1.21816 | + | 0.395804i | −0.846411 | − | 0.532530i | \(-0.821241\pi\) |
−0.371747 | + | 0.928334i | \(0.621241\pi\) | |||||||
\(864\) | 2.45656 | − | 7.56051i | 0.0835738 | − | 0.257214i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.20150 | − | 6.77551i | −0.0748099 | − | 0.230241i | ||||
\(867\) | 9.25196 | + | 12.7342i | 0.314213 | + | 0.432477i | ||||
\(868\) | − | 52.4133i | − | 1.77902i | ||||||
\(869\) | −18.6013 | + | 13.5146i | −0.631006 | + | 0.458452i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.74355 | + | 2.71985i | 0.126845 | + | 0.0921586i | ||||
\(872\) | −7.33894 | + | 10.1012i | −0.248528 | + | 0.342069i | ||||
\(873\) | 7.13289 | + | 2.31762i | 0.241412 | + | 0.0784394i | ||||
\(874\) | 37.8128 | 1.27904 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.5133 | 0.422784 | ||||||||
\(877\) | 49.8393 | + | 16.1938i | 1.68295 | + | 0.546825i | 0.985481 | − | 0.169787i | \(-0.0543080\pi\) |
0.697472 | + | 0.716612i | \(0.254308\pi\) | |||||||
\(878\) | 11.8311 | − | 16.2841i | 0.399280 | − | 0.549562i | ||||
\(879\) | −16.4244 | − | 11.9330i | −0.553980 | − | 0.402490i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.42180 | − | 4.66571i | 0.216356 | − | 0.157192i | −0.474329 | − | 0.880348i | \(-0.657309\pi\) |
0.690685 | + | 0.723156i | \(0.257309\pi\) | |||||||
\(882\) | 25.4588i | 0.857242i | ||||||||
\(883\) | 18.6280 | + | 25.6393i | 0.626883 | + | 0.862831i | 0.997831 | − | 0.0658227i | \(-0.0209672\pi\) |
−0.370948 | + | 0.928654i | \(0.620967\pi\) | |||||||
\(884\) | 1.04046 | + | 3.20221i | 0.0349945 | + | 0.107702i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.33175 | − | 19.4871i | 0.212719 | − | 0.654683i | ||||
\(887\) | −2.68297 | + | 0.871749i | −0.0900853 | + | 0.0292705i | −0.353713 | − | 0.935354i | \(-0.615081\pi\) |
0.263628 | + | 0.964625i | \(0.415081\pi\) | |||||||
\(888\) | −6.48643 | + | 2.10757i | −0.217670 | + | 0.0707254i | ||||
\(889\) | 22.8901 | − | 70.4485i | 0.767709 | − | 2.36277i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.488218 | − | 1.50258i | −0.0163559 | − | 0.0503383i | ||||
\(892\) | 5.00121 | + | 6.88357i | 0.167453 | + | 0.230479i | ||||
\(893\) | − | 31.6949i | − | 1.06063i | ||||||
\(894\) | 8.02947 | − | 5.83375i | 0.268546 | − | 0.195110i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 29.2312 | + | 21.2377i | 0.976546 | + | 0.709502i | ||||
\(897\) | −1.63378 | + | 2.24870i | −0.0545502 | + | 0.0750820i | ||||
\(898\) | −63.6340 | − | 20.6759i | −2.12349 | − | 0.689965i | ||||
\(899\) | 26.4320 | 0.881556 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.20390 | −0.140052 | ||||||||
\(902\) | 23.8285 | + | 7.74233i | 0.793401 | + | 0.257792i | ||||
\(903\) | 3.20221 | − | 4.40746i | 0.106563 | − | 0.146671i | ||||
\(904\) | −12.9236 | − | 9.38958i | −0.429834 | − | 0.312293i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.2323 | − | 8.16071i | 0.373167 | − | 0.271122i | ||||
\(907\) | − | 44.1799i | − | 1.46697i | −0.679705 | − | 0.733485i | \(-0.737892\pi\) | ||
0.679705 | − | 0.733485i | \(-0.262108\pi\) | |||||||
\(908\) | 39.4454 | + | 54.2919i | 1.30904 | + | 1.80174i | ||||
\(909\) | 2.01424 | + | 6.19919i | 0.0668081 | + | 0.205614i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.6691 | + | 32.8362i | −0.353484 | + | 1.08791i | 0.603400 | + | 0.797439i | \(0.293812\pi\) |
−0.956883 | + | 0.290472i | \(0.906188\pi\) | |||||||
\(912\) | 19.9885 | − | 6.49466i | 0.661886 | − | 0.215060i | ||||
\(913\) | 13.1266 | − | 4.26509i | 0.434426 | − | 0.141154i | ||||
\(914\) | 6.52209 | − | 20.0729i | 0.215731 | − | 0.663953i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.914713 | − | 2.81520i | −0.0302230 | − | 0.0930167i | ||||
\(917\) | 0.842506 | + | 1.15961i | 0.0278220 | + | 0.0382937i | ||||
\(918\) | 2.38197i | 0.0786166i | ||||||||
\(919\) | −0.429648 | + | 0.312158i | −0.0141728 | + | 0.0102971i | −0.594849 | − | 0.803837i | \(-0.702788\pi\) |
0.580676 | + | 0.814135i | \(0.302788\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.03330 | + | 1.47728i | 0.0669996 | + | 0.0486781i | ||||
\(922\) | −29.5447 | + | 40.6648i | −0.973003 | + | 1.33922i | ||||
\(923\) | 12.0825 | + | 3.92584i | 0.397700 | + | 0.129220i | ||||
\(924\) | 17.2443 | 0.567295 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 58.6833 | 1.92845 | ||||||||
\(927\) | 7.65482 | + | 2.48720i | 0.251417 | + | 0.0816905i | ||||
\(928\) | −25.7197 | + | 35.4001i | −0.844289 | + | 1.16206i | ||||
\(929\) | 37.3735 | + | 27.1534i | 1.22618 | + | 0.890874i | 0.996598 | − | 0.0824143i | \(-0.0262631\pi\) |
0.229585 | + | 0.973289i | \(0.426263\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −74.5192 | + | 54.1414i | −2.44227 | + | 1.77441i | ||||
\(932\) | 17.7676i | 0.581997i | ||||||||
\(933\) | 2.83558 | + | 3.90284i | 0.0928326 | + | 0.127773i | ||||
\(934\) | −2.85840 | − | 8.79726i | −0.0935298 | − | 0.287855i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.396205 | − | 1.21939i | 0.0129504 | − | 0.0398571i | ||||
\(937\) | 28.6477 | − | 9.30820i | 0.935880 | − | 0.304086i | 0.198915 | − | 0.980017i | \(-0.436258\pi\) |
0.736965 | + | 0.675931i | \(0.236258\pi\) | |||||||
\(938\) | −33.9812 | + | 11.0412i | −1.10952 | + | 0.360506i | ||||
\(939\) | 1.85043 | − | 5.69504i | 0.0603865 | − | 0.185851i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6382 | + | 54.2847i | 0.574988 | + | 1.76963i | 0.636220 | + | 0.771508i | \(0.280497\pi\) |
−0.0612315 | + | 0.998124i | \(0.519503\pi\) | |||||||
\(942\) | −4.98246 | − | 6.85777i | −0.162337 | − | 0.223438i | ||||
\(943\) | − | 17.3374i | − | 0.564583i | ||||||
\(944\) | −20.2748 | + | 14.7305i | −0.659890 | + | 0.479438i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.39083 | − | 2.46358i | −0.110245 | − | 0.0800980i | ||||
\(947\) | −24.1727 | + | 33.2708i | −0.785506 | + | 1.08116i | 0.209147 | + | 0.977884i | \(0.432931\pi\) |
−0.994653 | + | 0.103273i | \(0.967069\pi\) | |||||||
\(948\) | −34.6615 | − | 11.2622i | −1.12575 | − | 0.365779i | ||||
\(949\) | −5.98576 | −0.194306 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.3531 | 0.562712 | ||||||||
\(952\) | −4.97918 | − | 1.61783i | −0.161376 | − | 0.0524343i | ||||
\(953\) | −20.4633 | + | 28.1654i | −0.662873 | + | 0.912366i | −0.999572 | − | 0.0292462i | \(-0.990689\pi\) |
0.336700 | + | 0.941612i | \(0.390689\pi\) | |||||||
\(954\) | 6.43135 | + | 4.67265i | 0.208223 | + | 0.151283i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.0866986 | + | 0.0629902i | −0.00280403 | + | 0.00203725i | ||||
\(957\) | 8.69627i | 0.281111i | ||||||||
\(958\) | 15.9855 | + | 22.0022i | 0.516468 | + | 0.710857i | ||||
\(959\) | −6.14515 | − | 18.9128i | −0.198437 | − | 0.610727i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45366 | + | 7.55160i | −0.0791504 | + | 0.243600i | ||||
\(962\) | 15.4082 | − | 5.00643i | 0.496781 | − | 0.161414i | ||||
\(963\) | 9.01359 | − | 2.92869i | 0.290459 | − | 0.0943758i | ||||
\(964\) | 9.10930 | − | 28.0355i | 0.293391 | − | 0.902964i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −6.63227 | − | 20.4120i | −0.213390 | − | 0.656746i | ||||
\(967\) | 21.9066 | + | 30.1519i | 0.704469 | + | 0.969618i | 0.999898 | + | 0.0142537i | \(0.00453725\pi\) |
−0.295430 | + | 0.955365i | \(0.595463\pi\) | |||||||
\(968\) | 9.10165i | 0.292538i | ||||||||
\(969\) | −6.97214 | + | 5.06555i | −0.223977 | + | 0.162729i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0419 | + | 15.2879i | 0.675267 | + | 0.490611i | 0.871784 | − | 0.489890i | \(-0.162963\pi\) |
−0.196517 | + | 0.980500i | \(0.562963\pi\) | |||||||
\(972\) | 1.47199 | − | 2.02602i | 0.0472141 | − | 0.0649846i | ||||
\(973\) | 19.6228 | + | 6.37585i | 0.629079 | + | 0.204400i | ||||
\(974\) | 14.6910 | 0.470729 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.82064 | −0.122296 | ||||||||
\(977\) | 0.436134 | + | 0.141709i | 0.0139532 | + | 0.00453366i | 0.315985 | − | 0.948764i | \(-0.397665\pi\) |
−0.302032 | + | 0.953298i | \(0.597665\pi\) | |||||||
\(978\) | −5.98965 | + | 8.24404i | −0.191528 | + | 0.263615i | ||||
\(979\) | 12.8304 | + | 9.32186i | 0.410063 | + | 0.297928i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.43778 | − | 6.85695i | 0.301325 | − | 0.218926i | ||||
\(982\) | 56.9128i | 1.81616i | ||||||||
\(983\) | 5.25812 | + | 7.23718i | 0.167708 | + | 0.230830i | 0.884596 | − | 0.466358i | \(-0.154434\pi\) |
−0.716888 | + | 0.697188i | \(0.754434\pi\) | |||||||
\(984\) | 2.47132 | + | 7.60595i | 0.0787829 | + | 0.242469i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.05154 | − | 12.4694i | 0.129027 | − | 0.397105i | ||||
\(987\) | −17.1095 | + | 5.55920i | −0.544600 | + | 0.176951i | ||||
\(988\) | 21.9086 | − | 7.11852i | 0.697004 | − | 0.226470i | ||||
\(989\) | −0.896242 | + | 2.75835i | −0.0284988 | + | 0.0877104i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.4699 | − | 53.7667i | −0.554949 | − | 1.70796i | −0.696079 | − | 0.717965i | \(-0.745074\pi\) |
0.141130 | − | 0.989991i | \(-0.454926\pi\) | |||||||
\(992\) | 22.4383 | + | 30.8837i | 0.712418 | + | 0.980559i | ||||
\(993\) | − | 20.3355i | − | 0.645327i | ||||||
\(994\) | −79.3621 | + | 57.6599i | −2.51721 | + | 1.82886i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 17.6994 | + | 12.8594i | 0.560826 | + | 0.407464i | ||||
\(997\) | 23.2830 | − | 32.0463i | 0.737380 | − | 1.01492i | −0.261385 | − | 0.965235i | \(-0.584179\pi\) |
0.998765 | − | 0.0496816i | \(-0.0158207\pi\) | |||||||
\(998\) | −5.56005 | − | 1.80657i | −0.176000 | − | 0.0571860i | ||||
\(999\) | 6.37232 | 0.201611 |
(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 | 375.2.i.b.274.4 | 16 | ||
5.2 | odd | 4 | 375.2.g.b.226.1 | 8 | |||
5.3 | odd | 4 | 75.2.g.b.46.2 | yes | 8 | ||
5.4 | even | 2 | inner | 375.2.i.b.274.1 | 16 | ||
15.8 | even | 4 | 225.2.h.c.46.1 | 8 | |||
25.6 | even | 5 | inner | 375.2.i.b.349.1 | 16 | ||
25.8 | odd | 20 | 75.2.g.b.31.2 | ✓ | 8 | ||
25.9 | even | 10 | 1875.2.b.c.1249.2 | 8 | |||
25.12 | odd | 20 | 1875.2.a.e.1.2 | 4 | |||
25.13 | odd | 20 | 1875.2.a.h.1.3 | 4 | |||
25.16 | even | 5 | 1875.2.b.c.1249.7 | 8 | |||
25.17 | odd | 20 | 375.2.g.b.151.1 | 8 | |||
25.19 | even | 10 | inner | 375.2.i.b.349.4 | 16 | ||
75.8 | even | 20 | 225.2.h.c.181.1 | 8 | |||
75.38 | even | 20 | 5625.2.a.i.1.2 | 4 | |||
75.62 | even | 20 | 5625.2.a.n.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.b.31.2 | ✓ | 8 | 25.8 | odd | 20 | ||
75.2.g.b.46.2 | yes | 8 | 5.3 | odd | 4 | ||
225.2.h.c.46.1 | 8 | 15.8 | even | 4 | |||
225.2.h.c.181.1 | 8 | 75.8 | even | 20 | |||
375.2.g.b.151.1 | 8 | 25.17 | odd | 20 | |||
375.2.g.b.226.1 | 8 | 5.2 | odd | 4 | |||
375.2.i.b.274.1 | 16 | 5.4 | even | 2 | inner | ||
375.2.i.b.274.4 | 16 | 1.1 | even | 1 | trivial | ||
375.2.i.b.349.1 | 16 | 25.6 | even | 5 | inner | ||
375.2.i.b.349.4 | 16 | 25.19 | even | 10 | inner | ||
1875.2.a.e.1.2 | 4 | 25.12 | odd | 20 | |||
1875.2.a.h.1.3 | 4 | 25.13 | odd | 20 | |||
1875.2.b.c.1249.2 | 8 | 25.9 | even | 10 | |||
1875.2.b.c.1249.7 | 8 | 25.16 | even | 5 | |||
5625.2.a.i.1.2 | 4 | 75.38 | even | 20 | |||
5625.2.a.n.1.3 | 4 | 75.62 | even | 20 |