Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(101,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.n (of order \(6\), 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: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.3 | ||
Root | \(-0.666048i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.101 |
Dual form | 325.2.n.e.251.3 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.576815 | − | 0.333024i | 0.407869 | − | 0.235484i | −0.282004 | − | 0.959413i | \(-0.590999\pi\) |
0.689874 | + | 0.723930i | \(0.257666\pi\) | |||||||
\(3\) | 1.24146 | + | 2.15028i | 0.716759 | + | 1.24146i | 0.962277 | + | 0.272070i | \(0.0877084\pi\) |
−0.245519 | + | 0.969392i | \(0.578958\pi\) | |||||||
\(4\) | −0.778190 | + | 1.34786i | −0.389095 | + | 0.673932i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.43219 | + | 0.826874i | 0.584688 | + | 0.337570i | ||||
\(7\) | 0.509002 | + | 0.293872i | 0.192384 | + | 0.111073i | 0.593098 | − | 0.805130i | \(-0.297905\pi\) |
−0.400714 | + | 0.916203i | \(0.631238\pi\) | |||||||
\(8\) | 2.36872i | 0.837469i | ||||||||
\(9\) | −1.58246 | + | 2.74090i | −0.527486 | + | 0.913632i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.58582 | + | 1.49292i | −0.779653 | + | 0.450133i | −0.836307 | − | 0.548261i | \(-0.815290\pi\) |
0.0566544 | + | 0.998394i | \(0.481957\pi\) | |||||||
\(12\) | −3.86437 | −1.11555 | ||||||||
\(13\) | −1.93746 | − | 3.04076i | −0.537355 | − | 0.843356i | ||||
\(14\) | 0.391466 | 0.104624 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.767539 | − | 1.32942i | −0.191885 | − | 0.332354i | ||||
\(17\) | 3.28719 | − | 5.69358i | 0.797261 | − | 1.38090i | −0.124132 | − | 0.992266i | \(-0.539615\pi\) |
0.921393 | − | 0.388631i | \(-0.127052\pi\) | |||||||
\(18\) | 2.10798i | 0.496857i | ||||||||
\(19\) | 5.19894 | + | 3.00161i | 1.19272 | + | 0.688617i | 0.958922 | − | 0.283668i | \(-0.0915515\pi\) |
0.233797 | + | 0.972285i | \(0.424885\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.45932i | 0.318451i | ||||||||
\(22\) | −0.994358 | + | 1.72228i | −0.211998 | + | 0.367191i | ||||
\(23\) | 0.335352 | + | 0.580847i | 0.0699258 | + | 0.121115i | 0.898868 | − | 0.438219i | \(-0.144390\pi\) |
−0.828943 | + | 0.559334i | \(0.811057\pi\) | |||||||
\(24\) | −5.09340 | + | 2.94068i | −1.03969 | + | 0.600263i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.13020 | − | 1.10874i | −0.417767 | − | 0.217441i | ||||
\(27\) | −0.409469 | −0.0788023 | ||||||||
\(28\) | −0.792200 | + | 0.457377i | −0.149712 | + | 0.0864361i | ||||
\(29\) | 3.94620 | + | 6.83501i | 0.732790 | + | 1.26923i | 0.955686 | + | 0.294388i | \(0.0951157\pi\) |
−0.222896 | + | 0.974842i | \(0.571551\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.53727i | 0.814917i | 0.913224 | + | 0.407459i | \(0.133585\pi\) | ||||
−0.913224 | + | 0.407459i | \(0.866415\pi\) | |||||||
\(32\) | −4.98820 | − | 2.87994i | −0.881797 | − | 0.509106i | ||||
\(33\) | −6.42039 | − | 3.70681i | −1.11765 | − | 0.645273i | ||||
\(34\) | − | 4.37886i | − | 0.750967i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.46290 | − | 4.26588i | −0.410484 | − | 0.710979i | ||||
\(37\) | 6.70933 | − | 3.87363i | 1.10301 | − | 0.636821i | 0.165998 | − | 0.986126i | \(-0.446916\pi\) |
0.937009 | + | 0.349305i | \(0.113582\pi\) | |||||||
\(38\) | 3.99844 | 0.648632 | ||||||||
\(39\) | 4.13319 | − | 7.94107i | 0.661841 | − | 1.27159i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.629569 | + | 0.363482i | −0.0983222 | + | 0.0567663i | −0.548355 | − | 0.836246i | \(-0.684746\pi\) |
0.450033 | + | 0.893012i | \(0.351412\pi\) | |||||||
\(42\) | 0.485990 | + | 0.841760i | 0.0749899 | + | 0.129886i | ||||
\(43\) | −0.503359 | + | 0.871843i | −0.0767615 | + | 0.132955i | −0.901851 | − | 0.432047i | \(-0.857791\pi\) |
0.825089 | + | 0.565002i | \(0.191125\pi\) | |||||||
\(44\) | − | 4.64711i | − | 0.700578i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.386872 | + | 0.223361i | 0.0570412 | + | 0.0329327i | ||||
\(47\) | 3.15624i | 0.460386i | 0.973145 | + | 0.230193i | \(0.0739357\pi\) | ||||
−0.973145 | + | 0.230193i | \(0.926064\pi\) | |||||||
\(48\) | 1.90574 | − | 3.30084i | 0.275070 | − | 0.476436i | ||||
\(49\) | −3.32728 | − | 5.76302i | −0.475325 | − | 0.823288i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 16.3237 | 2.28577 | ||||||||
\(52\) | 5.60625 | − | 0.245144i | 0.777447 | − | 0.0339954i | ||||
\(53\) | 4.94455 | 0.679186 | 0.339593 | − | 0.940573i | \(-0.389711\pi\) | ||||
0.339593 | + | 0.940573i | \(0.389711\pi\) | |||||||
\(54\) | −0.236188 | + | 0.136363i | −0.0321411 | + | 0.0185567i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.696101 | + | 1.20568i | −0.0930204 | + | 0.161116i | ||||
\(57\) | 14.9056i | 1.97429i | ||||||||
\(58\) | 4.55245 | + | 2.62836i | 0.597766 | + | 0.345120i | ||||
\(59\) | −12.3630 | − | 7.13776i | −1.60952 | − | 0.929257i | −0.989477 | − | 0.144689i | \(-0.953782\pi\) |
−0.620043 | − | 0.784568i | \(-0.712885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.03067 | − | 6.98133i | 0.516075 | − | 0.893867i | −0.483751 | − | 0.875205i | \(-0.660726\pi\) |
0.999826 | − | 0.0186618i | \(-0.00594058\pi\) | |||||||
\(62\) | 1.51102 | + | 2.61716i | 0.191900 | + | 0.332380i | ||||
\(63\) | −1.61095 | + | 0.930080i | −0.202960 | + | 0.117179i | ||||
\(64\) | −0.766197 | −0.0957747 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.93783 | −0.607805 | ||||||||
\(67\) | −0.551372 | + | 0.318335i | −0.0673608 | + | 0.0388908i | −0.533302 | − | 0.845925i | \(-0.679049\pi\) |
0.465941 | + | 0.884816i | \(0.345716\pi\) | |||||||
\(68\) | 5.11612 | + | 8.86138i | 0.620421 | + | 1.07460i | ||||
\(69\) | −0.832654 | + | 1.44220i | −0.100240 | + | 0.173620i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.79982 | − | 4.50323i | −0.925668 | − | 0.534435i | −0.0402292 | − | 0.999190i | \(-0.512809\pi\) |
−0.885439 | + | 0.464756i | \(0.846142\pi\) | |||||||
\(72\) | −6.49242 | − | 3.74840i | −0.765138 | − | 0.441753i | ||||
\(73\) | − | 16.8200i | − | 1.96864i | −0.176403 | − | 0.984318i | \(-0.556446\pi\) | ||
0.176403 | − | 0.984318i | \(-0.443554\pi\) | |||||||
\(74\) | 2.58003 | − | 4.46874i | 0.299922 | − | 0.519480i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.09153 | + | 4.67165i | −0.928162 | + | 0.535875i | ||||
\(77\) | −1.75491 | −0.199991 | ||||||||
\(78\) | −0.260480 | − | 5.95698i | −0.0294936 | − | 0.674495i | ||||
\(79\) | 15.0859 | 1.69729 | 0.848646 | − | 0.528961i | \(-0.177418\pi\) | ||||
0.848646 | + | 0.528961i | \(0.177418\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.23903 | + | 7.34222i | 0.471003 | + | 0.815802i | ||||
\(82\) | −0.242096 | + | 0.419323i | −0.0267351 | + | 0.0463065i | ||||
\(83\) | 0.370576i | 0.0406760i | 0.999793 | + | 0.0203380i | \(0.00647423\pi\) | ||||
−0.999793 | + | 0.0203380i | \(0.993526\pi\) | |||||||
\(84\) | −1.96697 | − | 1.13563i | −0.214614 | − | 0.123908i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.670523i | 0.0723043i | ||||||||
\(87\) | −9.79811 | + | 16.9708i | −1.05047 | + | 1.81946i | ||||
\(88\) | −3.53631 | − | 6.12507i | −0.376972 | − | 0.652935i | ||||
\(89\) | −8.00015 | + | 4.61889i | −0.848014 | + | 0.489601i | −0.859980 | − | 0.510327i | \(-0.829524\pi\) |
0.0119665 | + | 0.999928i | \(0.496191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0925751 | − | 2.11712i | −0.00970451 | − | 0.221934i | ||||
\(92\) | −1.04387 | −0.108831 | ||||||||
\(93\) | −9.75637 | + | 5.63284i | −1.01169 | + | 0.584099i | ||||
\(94\) | 1.05111 | + | 1.82057i | 0.108413 | + | 0.187777i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 14.3013i | − | 1.45962i | ||||||
\(97\) | −5.99502 | − | 3.46123i | −0.608702 | − | 0.351434i | 0.163755 | − | 0.986501i | \(-0.447639\pi\) |
−0.772457 | + | 0.635067i | \(0.780973\pi\) | |||||||
\(98\) | −3.83845 | − | 2.21613i | −0.387742 | − | 0.223863i | ||||
\(99\) | − | 9.44994i | − | 0.949754i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.91837 | − | 11.9830i | −0.688403 | − | 1.19235i | −0.972354 | − | 0.233511i | \(-0.924979\pi\) |
0.283951 | − | 0.958839i | \(-0.408355\pi\) | |||||||
\(102\) | 9.41575 | − | 5.43618i | 0.932298 | − | 0.538262i | ||||
\(103\) | −4.42075 | −0.435590 | −0.217795 | − | 0.975995i | \(-0.569886\pi\) | ||||
−0.217795 | + | 0.975995i | \(0.569886\pi\) | |||||||
\(104\) | 7.20272 | − | 4.58930i | 0.706285 | − | 0.450018i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.85209 | − | 1.64665i | 0.277019 | − | 0.159937i | ||||
\(107\) | −1.35336 | − | 2.34408i | −0.130834 | − | 0.226611i | 0.793164 | − | 0.609008i | \(-0.208432\pi\) |
−0.923998 | + | 0.382397i | \(0.875099\pi\) | |||||||
\(108\) | 0.318645 | − | 0.551909i | 0.0306616 | − | 0.0531074i | ||||
\(109\) | 11.3266i | 1.08489i | 0.840091 | + | 0.542446i | \(0.182502\pi\) | ||||
−0.840091 | + | 0.542446i | \(0.817498\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.6588 | + | 9.61794i | 1.58118 | + | 0.912894i | ||||
\(112\) | − | 0.902234i | − | 0.0852531i | ||||||
\(113\) | −1.25454 | + | 2.17293i | −0.118018 | + | 0.204413i | −0.918982 | − | 0.394299i | \(-0.870987\pi\) |
0.800964 | + | 0.598712i | \(0.204321\pi\) | |||||||
\(114\) | 4.96391 | + | 8.59774i | 0.464912 | + | 0.805252i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −12.2836 | −1.14050 | ||||||||
\(117\) | 11.4004 | − | 0.498503i | 1.05396 | − | 0.0460866i | ||||
\(118\) | −9.50818 | −0.875299 | ||||||||
\(119\) | 3.34637 | − | 1.93203i | 0.306761 | − | 0.177109i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.04237 | + | 1.80544i | −0.0947609 | + | 0.164131i | ||||
\(122\) | − | 5.36924i | − | 0.486108i | ||||||
\(123\) | −1.56317 | − | 0.902498i | −0.140947 | − | 0.0813755i | ||||
\(124\) | −6.11562 | − | 3.53085i | −0.549199 | − | 0.317080i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.619478 | + | 1.07297i | −0.0551875 | + | 0.0955875i | ||||
\(127\) | 3.00538 | + | 5.20546i | 0.266684 | + | 0.461910i | 0.968003 | − | 0.250937i | \(-0.0807387\pi\) |
−0.701319 | + | 0.712847i | \(0.747405\pi\) | |||||||
\(128\) | 9.53444 | − | 5.50471i | 0.842734 | − | 0.486553i | ||||
\(129\) | −2.49961 | −0.220078 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.11618 | 0.0975211 | 0.0487605 | − | 0.998810i | \(-0.484473\pi\) | ||||
0.0487605 | + | 0.998810i | \(0.484473\pi\) | |||||||
\(132\) | 9.99256 | − | 5.76921i | 0.869741 | − | 0.502145i | ||||
\(133\) | 1.76418 | + | 3.05565i | 0.152974 | + | 0.264958i | ||||
\(134\) | −0.212026 | + | 0.367240i | −0.0183163 | + | 0.0317247i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.4865 | + | 7.78644i | 1.15646 | + | 0.667681i | ||||
\(137\) | −17.0529 | − | 9.84550i | −1.45693 | − | 0.841158i | −0.458069 | − | 0.888917i | \(-0.651459\pi\) |
−0.998859 | + | 0.0477593i | \(0.984792\pi\) | |||||||
\(138\) | 1.10918i | 0.0944193i | ||||||||
\(139\) | −4.93518 | + | 8.54798i | −0.418596 | + | 0.725030i | −0.995799 | − | 0.0915711i | \(-0.970811\pi\) |
0.577202 | + | 0.816601i | \(0.304144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.78680 | + | 3.91836i | −0.571551 | + | 0.329985i | ||||
\(142\) | −5.99873 | −0.503402 | ||||||||
\(143\) | 9.54954 | + | 4.97038i | 0.798573 | + | 0.415644i | ||||
\(144\) | 4.85839 | 0.404866 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.60148 | − | 9.70204i | −0.463581 | − | 0.802946i | ||||
\(147\) | 8.26138 | − | 14.3091i | 0.681387 | − | 1.18020i | ||||
\(148\) | 12.0577i | 0.991136i | ||||||||
\(149\) | −7.04577 | − | 4.06788i | −0.577212 | − | 0.333254i | 0.182813 | − | 0.983148i | \(-0.441480\pi\) |
−0.760025 | + | 0.649894i | \(0.774813\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0169i | 1.05930i | 0.848216 | + | 0.529650i | \(0.177677\pi\) | ||||
−0.848216 | + | 0.529650i | \(0.822323\pi\) | |||||||
\(152\) | −7.10998 | + | 12.3148i | −0.576695 | + | 0.998866i | ||||
\(153\) | 10.4037 | + | 18.0197i | 0.841088 | + | 1.45681i | ||||
\(154\) | −1.01226 | + | 0.584428i | −0.0815702 | + | 0.0470946i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.48708 | + | 11.7506i | 0.599446 | + | 0.940805i | ||||
\(157\) | 12.3177 | 0.983061 | 0.491530 | − | 0.870860i | \(-0.336438\pi\) | ||||
0.491530 | + | 0.870860i | \(0.336438\pi\) | |||||||
\(158\) | 8.70174 | − | 5.02395i | 0.692274 | − | 0.399684i | ||||
\(159\) | 6.13847 | + | 10.6321i | 0.486812 | + | 0.843184i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.394203i | 0.0310675i | ||||||||
\(162\) | 4.89027 | + | 2.82340i | 0.384216 | + | 0.221827i | ||||
\(163\) | 1.84793 | + | 1.06690i | 0.144741 | + | 0.0835664i | 0.570622 | − | 0.821213i | \(-0.306702\pi\) |
−0.425880 | + | 0.904779i | \(0.640036\pi\) | |||||||
\(164\) | − | 1.13143i | − | 0.0883500i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.123411 | + | 0.213754i | 0.00957852 | + | 0.0165905i | ||||
\(167\) | −0.0948176 | + | 0.0547430i | −0.00733720 | + | 0.00423614i | −0.503664 | − | 0.863900i | \(-0.668015\pi\) |
0.496327 | + | 0.868136i | \(0.334682\pi\) | |||||||
\(168\) | −3.45673 | −0.266693 | ||||||||
\(169\) | −5.49249 | + | 11.7827i | −0.422499 | + | 0.906363i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.4542 | + | 9.49984i | −1.25828 | + | 0.726471i | ||||
\(172\) | −0.783418 | − | 1.35692i | −0.0597351 | − | 0.103464i | ||||
\(173\) | −4.09968 | + | 7.10085i | −0.311693 | + | 0.539868i | −0.978729 | − | 0.205158i | \(-0.934229\pi\) |
0.667036 | + | 0.745025i | \(0.267563\pi\) | |||||||
\(174\) | 13.0520i | 0.989471i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.96943 | + | 2.29175i | 0.299207 | + | 0.172747i | ||||
\(177\) | − | 35.4450i | − | 2.66421i | ||||||
\(178\) | −3.07640 | + | 5.32848i | −0.230586 | + | 0.399387i | ||||
\(179\) | −0.0150584 | − | 0.0260820i | −0.00112552 | − | 0.00194946i | 0.865462 | − | 0.500974i | \(-0.167025\pi\) |
−0.866588 | + | 0.499025i | \(0.833692\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.4087 | 0.848004 | 0.424002 | − | 0.905661i | \(-0.360625\pi\) | ||||
0.424002 | + | 0.905661i | \(0.360625\pi\) | |||||||
\(182\) | −0.758450 | − | 1.19036i | −0.0562201 | − | 0.0882350i | ||||
\(183\) | 20.0157 | 1.47960 | ||||||||
\(184\) | −1.37586 | + | 0.794356i | −0.101430 | + | 0.0585607i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.75175 | + | 6.49821i | −0.275091 | + | 0.476472i | ||||
\(187\) | 19.6301i | 1.43549i | ||||||||
\(188\) | −4.25419 | − | 2.45616i | −0.310269 | − | 0.179134i | ||||
\(189\) | −0.208420 | − | 0.120332i | −0.0151603 | − | 0.00875283i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.66801 | − | 4.62112i | 0.193050 | − | 0.334373i | −0.753209 | − | 0.657781i | \(-0.771495\pi\) |
0.946260 | + | 0.323408i | \(0.104829\pi\) | |||||||
\(192\) | −0.951205 | − | 1.64754i | −0.0686473 | − | 0.118901i | ||||
\(193\) | −9.20113 | + | 5.31227i | −0.662312 | + | 0.382386i | −0.793157 | − | 0.609017i | \(-0.791564\pi\) |
0.130846 | + | 0.991403i | \(0.458231\pi\) | |||||||
\(194\) | −4.61069 | −0.331028 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.3570 | 0.739787 | ||||||||
\(197\) | 4.88920 | − | 2.82278i | 0.348341 | − | 0.201115i | −0.315613 | − | 0.948888i | \(-0.602210\pi\) |
0.663954 | + | 0.747773i | \(0.268877\pi\) | |||||||
\(198\) | −3.14706 | − | 5.45086i | −0.223652 | − | 0.387376i | ||||
\(199\) | 7.79679 | − | 13.5044i | 0.552700 | − | 0.957305i | −0.445378 | − | 0.895342i | \(-0.646931\pi\) |
0.998079 | − | 0.0619621i | \(-0.0197358\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.36901 | − | 0.790401i | −0.0965628 | − | 0.0557506i | ||||
\(202\) | −7.98123 | − | 4.60797i | −0.561558 | − | 0.324215i | ||||
\(203\) | 4.63871i | 0.325574i | ||||||||
\(204\) | −12.7029 | + | 22.0021i | −0.889383 | + | 1.54046i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.54996 | + | 1.47222i | −0.177664 | + | 0.102574i | ||||
\(207\) | −2.12272 | −0.147539 | ||||||||
\(208\) | −2.55536 | + | 4.90960i | −0.177183 | + | 0.340419i | ||||
\(209\) | −17.9247 | −1.23988 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.46675 | − | 14.6648i | −0.582875 | − | 1.00957i | −0.995137 | − | 0.0985037i | \(-0.968594\pi\) |
0.412262 | − | 0.911066i | \(-0.364739\pi\) | |||||||
\(212\) | −3.84780 | + | 6.66458i | −0.264268 | + | 0.457725i | ||||
\(213\) | − | 22.3623i | − | 1.53224i | ||||||
\(214\) | −1.56127 | − | 0.901400i | −0.106726 | − | 0.0616184i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 0.969917i | − | 0.0659945i | ||||||
\(217\) | −1.33338 | + | 2.30948i | −0.0905155 | + | 0.156777i | ||||
\(218\) | 3.77203 | + | 6.53335i | 0.255474 | + | 0.442494i | ||||
\(219\) | 36.1677 | − | 20.8814i | 2.44399 | − | 1.41104i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −23.6816 | + | 1.03553i | −1.59300 | + | 0.0696570i | ||||
\(222\) | 12.8120 | 0.859886 | ||||||||
\(223\) | 14.2283 | − | 8.21470i | 0.952796 | − | 0.550097i | 0.0588475 | − | 0.998267i | \(-0.481257\pi\) |
0.893948 | + | 0.448170i | \(0.147924\pi\) | |||||||
\(224\) | −1.69267 | − | 2.93179i | −0.113096 | − | 0.195888i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.67117i | 0.111165i | ||||||||
\(227\) | −14.9348 | − | 8.62262i | −0.991259 | − | 0.572304i | −0.0856085 | − | 0.996329i | \(-0.527283\pi\) |
−0.905650 | + | 0.424025i | \(0.860617\pi\) | |||||||
\(228\) | −20.0907 | − | 11.5993i | −1.33054 | − | 0.768186i | ||||
\(229\) | 10.0809i | 0.666162i | 0.942898 | + | 0.333081i | \(0.108088\pi\) | ||||
−0.942898 | + | 0.333081i | \(0.891912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.17866 | − | 3.77355i | −0.143345 | − | 0.248281i | ||||
\(232\) | −16.1902 | + | 9.34744i | −1.06294 | + | 0.613689i | ||||
\(233\) | −19.7103 | −1.29126 | −0.645632 | − | 0.763648i | \(-0.723406\pi\) | ||||
−0.645632 | + | 0.763648i | \(0.723406\pi\) | |||||||
\(234\) | 6.40988 | − | 4.08414i | 0.419027 | − | 0.266989i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 19.2415 | − | 11.1091i | 1.25251 | − | 0.723138i | ||||
\(237\) | 18.7285 | + | 32.4388i | 1.21655 | + | 2.10712i | ||||
\(238\) | 1.28682 | − | 2.22884i | 0.0834124 | − | 0.144474i | ||||
\(239\) | 11.2372i | 0.726871i | 0.931619 | + | 0.363435i | \(0.118396\pi\) | ||||
−0.931619 | + | 0.363435i | \(0.881604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.24657 | + | 1.87441i | 0.209130 | + | 0.120741i | 0.600907 | − | 0.799319i | \(-0.294806\pi\) |
−0.391777 | + | 0.920060i | \(0.628140\pi\) | |||||||
\(242\) | 1.38854i | 0.0892586i | ||||||||
\(243\) | −11.1394 | + | 19.2940i | −0.714593 | + | 1.23771i | ||||
\(244\) | 6.27326 | + | 10.8656i | 0.401604 | + | 0.695599i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.20221 | −0.0766504 | ||||||||
\(247\) | −0.945563 | − | 21.6243i | −0.0601647 | − | 1.37592i | ||||
\(248\) | −10.7475 | −0.682468 | ||||||||
\(249\) | −0.796840 | + | 0.460056i | −0.0504977 | + | 0.0291549i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.1871 | − | 17.6446i | 0.643007 | − | 1.11372i | −0.341751 | − | 0.939790i | \(-0.611020\pi\) |
0.984758 | − | 0.173930i | \(-0.0556466\pi\) | |||||||
\(252\) | − | 2.89512i | − | 0.182375i | ||||||
\(253\) | −1.73432 | − | 1.00131i | −0.109036 | − | 0.0629518i | ||||
\(254\) | 3.46709 | + | 2.00172i | 0.217545 | + | 0.125599i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.43260 | − | 7.67749i | 0.277038 | − | 0.479843i | ||||
\(257\) | 7.17856 | + | 12.4336i | 0.447786 | + | 0.775588i | 0.998242 | − | 0.0592763i | \(-0.0188793\pi\) |
−0.550456 | + | 0.834864i | \(0.685546\pi\) | |||||||
\(258\) | −1.44181 | + | 0.832429i | −0.0897631 | + | 0.0518247i | ||||
\(259\) | 4.55341 | 0.282935 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.9787 | −1.54615 | ||||||||
\(262\) | 0.643829 | − | 0.371715i | 0.0397759 | − | 0.0229646i | ||||
\(263\) | −13.3709 | − | 23.1590i | −0.824484 | − | 1.42805i | −0.902313 | − | 0.431081i | \(-0.858132\pi\) |
0.0778291 | − | 0.996967i | \(-0.475201\pi\) | |||||||
\(264\) | 8.78040 | − | 15.2081i | 0.540396 | − | 0.935994i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.03521 | + | 1.17503i | 0.124787 | + | 0.0720456i | ||||
\(267\) | −19.8638 | − | 11.4683i | −1.21564 | − | 0.701851i | ||||
\(268\) | − | 0.990899i | − | 0.0605288i | ||||||
\(269\) | −0.215092 | + | 0.372550i | −0.0131144 | + | 0.0227148i | −0.872508 | − | 0.488600i | \(-0.837508\pi\) |
0.859394 | + | 0.511314i | \(0.170841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1868 | − | 5.88137i | 0.618806 | − | 0.357268i | −0.157598 | − | 0.987503i | \(-0.550375\pi\) |
0.776404 | + | 0.630235i | \(0.217042\pi\) | |||||||
\(272\) | −10.0922 | −0.611929 | ||||||||
\(273\) | 4.43746 | − | 2.82739i | 0.268567 | − | 0.171121i | ||||
\(274\) | −13.1151 | −0.792315 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.29593 | − | 2.24461i | −0.0780056 | − | 0.135110i | ||||
\(277\) | 1.98793 | − | 3.44320i | 0.119443 | − | 0.206882i | −0.800104 | − | 0.599861i | \(-0.795222\pi\) |
0.919547 | + | 0.392980i | \(0.128556\pi\) | |||||||
\(278\) | 6.57413i | 0.394290i | ||||||||
\(279\) | −12.4362 | − | 7.18003i | −0.744534 | − | 0.429857i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.3267i | 1.03363i | 0.856098 | + | 0.516814i | \(0.172882\pi\) | ||||
−0.856098 | + | 0.516814i | \(0.827118\pi\) | |||||||
\(282\) | −2.60982 | + | 4.52033i | −0.155412 | + | 0.269182i | ||||
\(283\) | 4.50729 | + | 7.80686i | 0.267931 | + | 0.464070i | 0.968327 | − | 0.249684i | \(-0.0803268\pi\) |
−0.700397 | + | 0.713754i | \(0.746994\pi\) | |||||||
\(284\) | 12.1395 | − | 7.00873i | 0.720346 | − | 0.415892i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.16357 | − | 0.313241i | 0.423591 | − | 0.0185223i | ||||
\(287\) | −0.427269 | −0.0252209 | ||||||||
\(288\) | 15.7872 | − | 9.11476i | 0.930271 | − | 0.537092i | ||||
\(289\) | −13.1113 | − | 22.7094i | −0.771250 | − | 1.33584i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 17.1879i | − | 1.00757i | ||||||
\(292\) | 22.6711 | + | 13.0892i | 1.32673 | + | 0.765986i | ||||
\(293\) | 23.5400 | + | 13.5908i | 1.37522 | + | 0.793984i | 0.991580 | − | 0.129498i | \(-0.0413366\pi\) |
0.383641 | + | 0.923482i | \(0.374670\pi\) | |||||||
\(294\) | − | 11.0050i | − | 0.641822i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 9.17555 | + | 15.8925i | 0.533318 | + | 0.923734i | ||||
\(297\) | 1.05881 | − | 0.611305i | 0.0614385 | − | 0.0354715i | ||||
\(298\) | −5.41881 | −0.313903 | ||||||||
\(299\) | 1.11649 | − | 2.14510i | 0.0645681 | − | 0.124054i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.512421 | + | 0.295846i | −0.0295355 | + | 0.0170523i | ||||
\(302\) | 4.33494 | + | 7.50833i | 0.249448 | + | 0.432056i | ||||
\(303\) | 17.1778 | − | 29.7528i | 0.986838 | − | 1.70925i | ||||
\(304\) | − | 9.21542i | − | 0.528541i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 12.0020 | + | 6.92935i | 0.686108 | + | 0.396125i | ||||
\(307\) | 15.4630i | 0.882522i | 0.897379 | + | 0.441261i | \(0.145469\pi\) | ||||
−0.897379 | + | 0.441261i | \(0.854531\pi\) | |||||||
\(308\) | 1.36566 | − | 2.36538i | 0.0778154 | − | 0.134780i | ||||
\(309\) | −5.48820 | − | 9.50584i | −0.312213 | − | 0.540768i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.50072 | −0.482032 | −0.241016 | − | 0.970521i | \(-0.577481\pi\) | ||||
−0.241016 | + | 0.970521i | \(0.577481\pi\) | |||||||
\(312\) | 18.8102 | + | 9.79038i | 1.06492 | + | 0.554271i | ||||
\(313\) | 4.81358 | 0.272080 | 0.136040 | − | 0.990703i | \(-0.456562\pi\) | ||||
0.136040 | + | 0.990703i | \(0.456562\pi\) | |||||||
\(314\) | 7.10504 | − | 4.10209i | 0.400960 | − | 0.231495i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11.7397 | + | 20.3337i | −0.660408 | + | 1.14386i | ||||
\(317\) | 3.35387i | 0.188372i | 0.995555 | + | 0.0941860i | \(0.0300248\pi\) | ||||
−0.995555 | + | 0.0941860i | \(0.969975\pi\) | |||||||
\(318\) | 7.08152 | + | 4.08852i | 0.397112 | + | 0.229273i | ||||
\(319\) | −20.4083 | − | 11.7827i | −1.14264 | − | 0.659706i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.36028 | − | 5.82017i | 0.187552 | − | 0.324850i | ||||
\(322\) | 0.131279 | + | 0.227382i | 0.00731589 | + | 0.0126715i | ||||
\(323\) | 34.1798 | − | 19.7337i | 1.90182 | − | 1.09801i | ||||
\(324\) | −13.1951 | −0.733060 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.42122 | 0.0787141 | ||||||||
\(327\) | −24.3553 | + | 14.0616i | −1.34685 | + | 0.777606i | ||||
\(328\) | −0.860987 | − | 1.49127i | −0.0475400 | − | 0.0823418i | ||||
\(329\) | −0.927533 | + | 1.60653i | −0.0511365 | + | 0.0885711i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8085 | − | 10.2817i | −0.978842 | − | 0.565135i | −0.0769218 | − | 0.997037i | \(-0.524509\pi\) |
−0.901920 | + | 0.431902i | \(0.857843\pi\) | |||||||
\(332\) | −0.499486 | − | 0.288378i | −0.0274129 | − | 0.0158268i | ||||
\(333\) | 24.5194i | 1.34366i | ||||||||
\(334\) | −0.0364614 | + | 0.0631531i | −0.00199508 | + | 0.00345558i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.94005 | − | 1.12009i | 0.105838 | − | 0.0611059i | ||||
\(337\) | −15.3344 | −0.835316 | −0.417658 | − | 0.908604i | \(-0.637149\pi\) | ||||
−0.417658 | + | 0.908604i | \(0.637149\pi\) | |||||||
\(338\) | 0.755785 | + | 8.62558i | 0.0411093 | + | 0.469170i | ||||
\(339\) | −6.22988 | −0.338361 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.77378 | − | 11.7325i | −0.366821 | − | 0.635352i | ||||
\(342\) | −6.32735 | + | 10.9593i | −0.342144 | + | 0.592611i | ||||
\(343\) | − | 8.02539i | − | 0.433330i | ||||||
\(344\) | −2.06515 | − | 1.19232i | −0.111346 | − | 0.0642854i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.46116i | 0.293594i | ||||||||
\(347\) | 7.52585 | − | 13.0352i | 0.404009 | − | 0.699764i | −0.590197 | − | 0.807260i | \(-0.700950\pi\) |
0.994206 | + | 0.107495i | \(0.0342831\pi\) | |||||||
\(348\) | −15.2496 | − | 26.4130i | −0.817463 | − | 1.41589i | ||||
\(349\) | 26.8768 | − | 15.5173i | 1.43868 | − | 0.830623i | 0.440923 | − | 0.897545i | \(-0.354651\pi\) |
0.997758 | + | 0.0669222i | \(0.0213179\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.793330 | + | 1.24510i | 0.0423448 | + | 0.0664584i | ||||
\(352\) | 17.1981 | 0.916661 | ||||||||
\(353\) | −24.7048 | + | 14.2633i | −1.31491 | + | 0.759161i | −0.982904 | − | 0.184118i | \(-0.941057\pi\) |
−0.332002 | + | 0.943279i | \(0.607724\pi\) | |||||||
\(354\) | −11.8040 | − | 20.4452i | −0.627378 | − | 1.08665i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 14.3775i | − | 0.762005i | ||||||
\(357\) | 8.30879 | + | 4.79708i | 0.439748 | + | 0.253888i | ||||
\(358\) | −0.0173718 | − | 0.0100296i | −0.000918131 | − | 0.000530083i | ||||
\(359\) | 16.4735i | 0.869437i | 0.900566 | + | 0.434718i | \(0.143152\pi\) | ||||
−0.900566 | + | 0.434718i | \(0.856848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.51935 | + | 14.7559i | 0.448387 | + | 0.776628i | ||||
\(362\) | 6.58072 | − | 3.79938i | 0.345875 | − | 0.199691i | ||||
\(363\) | −5.17625 | −0.271683 | ||||||||
\(364\) | 2.92563 | + | 1.52274i | 0.153345 | + | 0.0798134i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 11.5453 | − | 6.66571i | 0.603485 | − | 0.348422i | ||||
\(367\) | −1.88471 | − | 3.26441i | −0.0983809 | − | 0.170401i | 0.812634 | − | 0.582775i | \(-0.198033\pi\) |
−0.911015 | + | 0.412374i | \(0.864700\pi\) | |||||||
\(368\) | 0.514792 | − | 0.891646i | 0.0268354 | − | 0.0464803i | ||||
\(369\) | − | 2.30078i | − | 0.119774i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.51678 | + | 1.45306i | 0.130665 | + | 0.0754394i | ||||
\(372\) | − | 17.5337i | − | 0.909080i | ||||||
\(373\) | −6.63155 | + | 11.4862i | −0.343368 | + | 0.594732i | −0.985056 | − | 0.172235i | \(-0.944901\pi\) |
0.641688 | + | 0.766966i | \(0.278235\pi\) | |||||||
\(374\) | 6.53729 | + | 11.3229i | 0.338035 | + | 0.585494i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.47626 | −0.385559 | ||||||||
\(377\) | 13.1381 | − | 25.2420i | 0.676644 | − | 1.30003i | ||||
\(378\) | −0.160293 | −0.00824459 | ||||||||
\(379\) | 19.0442 | − | 10.9952i | 0.978235 | − | 0.564784i | 0.0764985 | − | 0.997070i | \(-0.475626\pi\) |
0.901737 | + | 0.432285i | \(0.142293\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.46212 | + | 12.9248i | −0.382296 | + | 0.662156i | ||||
\(382\) | − | 3.55404i | − | 0.181841i | ||||||
\(383\) | −19.6380 | − | 11.3380i | −1.00345 | − | 0.579344i | −0.0941845 | − | 0.995555i | \(-0.530024\pi\) |
−0.909268 | + | 0.416211i | \(0.863358\pi\) | |||||||
\(384\) | 23.6733 | + | 13.6678i | 1.20807 | + | 0.697481i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.53823 | + | 6.12839i | −0.180091 | + | 0.311927i | ||||
\(387\) | −1.59309 | − | 2.75931i | −0.0809812 | − | 0.140264i | ||||
\(388\) | 9.33053 | − | 5.38698i | 0.473686 | − | 0.273483i | ||||
\(389\) | −18.3322 | −0.929480 | −0.464740 | − | 0.885447i | \(-0.653852\pi\) | ||||
−0.464740 | + | 0.885447i | \(0.653852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.40947 | 0.222996 | ||||||||
\(392\) | 13.6510 | − | 7.88139i | 0.689478 | − | 0.398070i | ||||
\(393\) | 1.38569 | + | 2.40009i | 0.0698991 | + | 0.121069i | ||||
\(394\) | 1.88011 | − | 3.25644i | 0.0947184 | − | 0.164057i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 12.7372 | + | 7.35385i | 0.640070 | + | 0.369545i | ||||
\(397\) | −4.63902 | − | 2.67834i | −0.232826 | − | 0.134422i | 0.379049 | − | 0.925377i | \(-0.376251\pi\) |
−0.611875 | + | 0.790954i | \(0.709584\pi\) | |||||||
\(398\) | − | 10.3861i | − | 0.520607i | ||||||
\(399\) | −4.38033 | + | 7.58695i | −0.219291 | + | 0.379822i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.93714 | − | 5.73721i | 0.496237 | − | 0.286503i | −0.230921 | − | 0.972972i | \(-0.574174\pi\) |
0.727158 | + | 0.686470i | \(0.240841\pi\) | |||||||
\(402\) | −1.05289 | −0.0525134 | ||||||||
\(403\) | 13.7968 | − | 8.79078i | 0.687265 | − | 0.437900i | ||||
\(404\) | 21.5352 | 1.07142 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.54480 | + | 2.67568i | 0.0766672 | + | 0.132792i | ||||
\(407\) | −11.5661 | + | 20.0330i | −0.573308 | + | 0.992999i | ||||
\(408\) | 38.6663i | 1.91427i | ||||||||
\(409\) | −15.0683 | − | 8.69969i | −0.745080 | − | 0.430172i | 0.0788336 | − | 0.996888i | \(-0.474880\pi\) |
−0.823913 | + | 0.566716i | \(0.808214\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 48.8912i | − | 2.41163i | ||||||
\(412\) | 3.44019 | − | 5.95858i | 0.169486 | − | 0.293558i | ||||
\(413\) | −4.19518 | − | 7.26626i | −0.206431 | − | 0.357549i | ||||
\(414\) | −1.22442 | + | 0.706918i | −0.0601768 | + | 0.0347431i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.907233 | + | 20.7477i | 0.0444808 | + | 1.01724i | ||||
\(417\) | −24.5073 | −1.20013 | ||||||||
\(418\) | −10.3392 | + | 5.96935i | −0.505708 | + | 0.291970i | ||||
\(419\) | 11.2389 | + | 19.4664i | 0.549058 | + | 0.950996i | 0.998339 | + | 0.0576056i | \(0.0183466\pi\) |
−0.449282 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.16889i | 0.251916i | 0.992036 | + | 0.125958i | \(0.0402005\pi\) | ||||
−0.992036 | + | 0.125958i | \(0.959799\pi\) | |||||||
\(422\) | −9.76749 | − | 5.63926i | −0.475474 | − | 0.274515i | ||||
\(423\) | −8.65094 | − | 4.99462i | −0.420623 | − | 0.242847i | ||||
\(424\) | 11.7122i | 0.568797i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.44720 | − | 12.8989i | −0.360818 | − | 0.624955i | ||||
\(427\) | 4.10324 | − | 2.36900i | 0.198569 | − | 0.114644i | ||||
\(428\) | 4.21267 | 0.203627 | ||||||||
\(429\) | 1.16771 | + | 26.7047i | 0.0563777 | + | 1.28931i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.7964 | + | 13.1615i | −1.09806 | + | 0.633968i | −0.935712 | − | 0.352765i | \(-0.885241\pi\) |
−0.162352 | + | 0.986733i | \(0.551908\pi\) | |||||||
\(432\) | 0.314284 | + | 0.544355i | 0.0151210 | + | 0.0261903i | ||||
\(433\) | −9.45546 | + | 16.3773i | −0.454401 | + | 0.787045i | −0.998654 | − | 0.0518762i | \(-0.983480\pi\) |
0.544253 | + | 0.838921i | \(0.316813\pi\) | |||||||
\(434\) | 1.77619i | 0.0852596i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.2667 | − | 8.81425i | −0.731144 | − | 0.422126i | ||||
\(437\) | 4.02639i | 0.192608i | ||||||||
\(438\) | 13.9080 | − | 24.0894i | 0.664552 | − | 1.15104i | ||||
\(439\) | 13.7455 | + | 23.8079i | 0.656037 | + | 1.13629i | 0.981633 | + | 0.190780i | \(0.0611018\pi\) |
−0.325596 | + | 0.945509i | \(0.605565\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0611 | 1.00291 | ||||||||
\(442\) | −13.3151 | + | 8.48386i | −0.633333 | + | 0.403536i | ||||
\(443\) | −19.2846 | −0.916240 | −0.458120 | − | 0.888890i | \(-0.651477\pi\) | ||||
−0.458120 | + | 0.888890i | \(0.651477\pi\) | |||||||
\(444\) | −25.9274 | + | 14.9692i | −1.23046 | + | 0.710405i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.47138 | − | 9.47672i | 0.259078 | − | 0.448735i | ||||
\(447\) | − | 20.2005i | − | 0.955450i | ||||||
\(448\) | −0.389996 | − | 0.225164i | −0.0184256 | − | 0.0106380i | ||||
\(449\) | 5.66090 | + | 3.26832i | 0.267154 | + | 0.154242i | 0.627594 | − | 0.778541i | \(-0.284040\pi\) |
−0.360439 | + | 0.932783i | \(0.617373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.08530 | − | 1.87979i | 0.0511048 | − | 0.0885161i | ||||
\(452\) | −1.95255 | − | 3.38191i | −0.0918401 | − | 0.159072i | ||||
\(453\) | −27.9899 | + | 16.1600i | −1.31508 | + | 0.759262i | ||||
\(454\) | −11.4862 | −0.539072 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −35.3071 | −1.65341 | ||||||||
\(457\) | −12.4763 | + | 7.20317i | −0.583614 | + | 0.336950i | −0.762569 | − | 0.646907i | \(-0.776062\pi\) |
0.178954 | + | 0.983857i | \(0.442729\pi\) | |||||||
\(458\) | 3.35717 | + | 5.81478i | 0.156870 | + | 0.271707i | ||||
\(459\) | −1.34600 | + | 2.33135i | −0.0628260 | + | 0.108818i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.4829 | + | 6.62968i | 0.534814 | + | 0.308775i | 0.742975 | − | 0.669320i | \(-0.233414\pi\) |
−0.208161 | + | 0.978095i | \(0.566748\pi\) | |||||||
\(462\) | −2.51336 | − | 1.45109i | −0.116932 | − | 0.0675108i | ||||
\(463\) | − | 18.8671i | − | 0.876827i | −0.898773 | − | 0.438413i | \(-0.855541\pi\) | ||
0.898773 | − | 0.438413i | \(-0.144459\pi\) | |||||||
\(464\) | 6.05772 | − | 10.4923i | 0.281223 | − | 0.487092i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.3692 | + | 6.56400i | −0.526667 | + | 0.304072i | ||||
\(467\) | 21.8870 | 1.01281 | 0.506406 | − | 0.862295i | \(-0.330974\pi\) | ||||
0.506406 | + | 0.862295i | \(0.330974\pi\) | |||||||
\(468\) | −8.19974 | + | 15.7541i | −0.379033 | + | 0.728233i | ||||
\(469\) | −0.374199 | −0.0172789 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.2920 | + | 26.4865i | 0.704617 | + | 1.22043i | ||||
\(472\) | 16.9073 | − | 29.2844i | 0.778224 | − | 1.34792i | ||||
\(473\) | − | 3.00590i | − | 0.138212i | ||||||
\(474\) | 21.6058 | + | 12.4741i | 0.992386 | + | 0.572954i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.01394i | 0.275648i | ||||||||
\(477\) | −7.82453 | + | 13.5525i | −0.358261 | + | 0.620526i | ||||
\(478\) | 3.74224 | + | 6.48175i | 0.171166 | + | 0.296468i | ||||
\(479\) | −24.3402 | + | 14.0528i | −1.11213 | + | 0.642089i | −0.939381 | − | 0.342876i | \(-0.888599\pi\) |
−0.172751 | + | 0.984966i | \(0.555266\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.7779 | − | 12.8965i | −1.12977 | − | 0.588028i | ||||
\(482\) | 2.49689 | 0.113730 | ||||||||
\(483\) | −0.847645 | + | 0.489388i | −0.0385692 | + | 0.0222679i | ||||
\(484\) | −1.62232 | − | 2.80995i | −0.0737420 | − | 0.127725i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.8387i | 0.673099i | ||||||||
\(487\) | 15.8678 | + | 9.16127i | 0.719038 | + | 0.415137i | 0.814398 | − | 0.580306i | \(-0.197067\pi\) |
−0.0953608 | + | 0.995443i | \(0.530400\pi\) | |||||||
\(488\) | 16.5368 | + | 9.54753i | 0.748586 | + | 0.432196i | ||||
\(489\) | 5.29809i | 0.239588i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.8603 | + | 18.8106i | 0.490118 | + | 0.848908i | 0.999935 | − | 0.0113739i | \(-0.00362052\pi\) |
−0.509818 | + | 0.860282i | \(0.670287\pi\) | |||||||
\(492\) | 2.43289 | − | 1.40463i | 0.109683 | − | 0.0633256i | ||||
\(493\) | 51.8876 | 2.33690 | ||||||||
\(494\) | −7.74681 | − | 12.1583i | −0.348546 | − | 0.547028i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.03192 | − | 3.48253i | 0.270841 | − | 0.156370i | ||||
\(497\) | −2.64675 | − | 4.58430i | −0.118723 | − | 0.205634i | ||||
\(498\) | −0.306419 | + | 0.530734i | −0.0137310 | + | 0.0237828i | ||||
\(499\) | 14.7418i | 0.659933i | 0.943993 | + | 0.329966i | \(0.107037\pi\) | ||||
−0.943993 | + | 0.329966i | \(0.892963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.235425 | − | 0.135923i | −0.0105180 | − | 0.00607257i | ||||
\(502\) | − | 13.5703i | − | 0.605670i | ||||||
\(503\) | −18.5694 | + | 32.1631i | −0.827969 | + | 1.43408i | 0.0716604 | + | 0.997429i | \(0.477170\pi\) |
−0.899629 | + | 0.436655i | \(0.856163\pi\) | |||||||
\(504\) | −2.20310 | − | 3.81588i | −0.0981338 | − | 0.169973i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.33384 | −0.0592964 | ||||||||
\(507\) | −32.1548 | + | 2.81745i | −1.42805 | + | 0.125127i | ||||
\(508\) | −9.35501 | −0.415062 | ||||||||
\(509\) | −11.0110 | + | 6.35722i | −0.488055 | + | 0.281779i | −0.723767 | − | 0.690044i | \(-0.757591\pi\) |
0.235712 | + | 0.971823i | \(0.424258\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.94294 | − | 8.56142i | 0.218663 | − | 0.378735i | ||||
\(512\) | 16.1142i | 0.712154i | ||||||||
\(513\) | −2.12881 | − | 1.22907i | −0.0939891 | − | 0.0542646i | ||||
\(514\) | 8.28139 | + | 4.78126i | 0.365276 | + | 0.210892i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.94517 | − | 3.36913i | 0.0856312 | − | 0.148318i | ||||
\(517\) | −4.71203 | − | 8.16147i | −0.207235 | − | 0.358941i | ||||
\(518\) | 2.62647 | − | 1.51640i | 0.115401 | − | 0.0666266i | ||||
\(519\) | −20.3584 | −0.893634 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.3347 | 1.50423 | 0.752116 | − | 0.659031i | \(-0.229033\pi\) | ||||
0.752116 | + | 0.659031i | \(0.229033\pi\) | |||||||
\(522\) | −14.4081 | + | 8.31852i | −0.630626 | + | 0.364092i | ||||
\(523\) | 11.9219 | + | 20.6494i | 0.521309 | + | 0.902934i | 0.999693 | + | 0.0247827i | \(0.00788940\pi\) |
−0.478384 | + | 0.878151i | \(0.658777\pi\) | |||||||
\(524\) | −0.868600 | + | 1.50446i | −0.0379450 | + | 0.0657226i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.4250 | − | 8.90565i | −0.672564 | − | 0.388305i | ||||
\(527\) | 25.8333 | + | 14.9149i | 1.12532 | + | 0.649702i | ||||
\(528\) | 11.3805i | 0.495272i | ||||||||
\(529\) | 11.2751 | − | 19.5290i | 0.490221 | − | 0.849087i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.1277 | − | 22.5904i | 1.69800 | − | 0.980339i | ||||
\(532\) | −5.49147 | −0.238085 | ||||||||
\(533\) | 2.32503 | + | 1.21014i | 0.100708 | + | 0.0524169i | ||||
\(534\) | −15.2769 | −0.661098 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.754046 | − | 1.30605i | −0.0325698 | − | 0.0564126i | ||||
\(537\) | 0.0373890 | − | 0.0647596i | 0.00161345 | − | 0.00279458i | ||||
\(538\) | 0.286523i | 0.0123529i | ||||||||
\(539\) | 17.2075 | + | 9.93473i | 0.741178 | + | 0.427919i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.3426i | 0.702624i | 0.936258 | + | 0.351312i | \(0.114264\pi\) | ||||
−0.936258 | + | 0.351312i | \(0.885736\pi\) | |||||||
\(542\) | 3.91728 | − | 6.78492i | 0.168261 | − | 0.291437i | ||||
\(543\) | 14.1635 | + | 24.5319i | 0.607814 | + | 1.05277i | ||||
\(544\) | −32.7943 | + | 18.9338i | −1.40605 | + | 0.811781i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.61801 | − | 3.10866i | 0.0692442 | − | 0.133038i | ||||
\(547\) | −3.13542 | −0.134061 | −0.0670305 | − | 0.997751i | \(-0.521352\pi\) | ||||
−0.0670305 | + | 0.997751i | \(0.521352\pi\) | |||||||
\(548\) | 26.5408 | − | 15.3233i | 1.13377 | − | 0.654580i | ||||
\(549\) | 12.7567 | + | 22.0953i | 0.544444 | + | 0.943004i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 47.3798i | 2.01845i | ||||||||
\(552\) | −3.41617 | − | 1.97233i | −0.145402 | − | 0.0839477i | ||||
\(553\) | 7.67873 | + | 4.43331i | 0.326533 | + | 0.188524i | ||||
\(554\) | − | 2.64812i | − | 0.112508i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.68101 | − | 13.3039i | −0.325747 | − | 0.564211i | ||||
\(557\) | 20.4120 | − | 11.7849i | 0.864883 | − | 0.499341i | −0.000761144 | − | 1.00000i | \(-0.500242\pi\) |
0.865645 | + | 0.500659i | \(0.166909\pi\) | |||||||
\(558\) | −9.56449 | −0.404897 | ||||||||
\(559\) | 3.62631 | − | 0.158567i | 0.153377 | − | 0.00670668i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −42.2101 | + | 24.3700i | −1.78211 | + | 1.02890i | ||||
\(562\) | 5.77022 | + | 9.99432i | 0.243402 | + | 0.421585i | ||||
\(563\) | 7.30716 | − | 12.6564i | 0.307960 | − | 0.533402i | −0.669956 | − | 0.742401i | \(-0.733687\pi\) |
0.977916 | + | 0.208999i | \(0.0670204\pi\) | |||||||
\(564\) | − | 12.1969i | − | 0.513583i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 5.19974 | + | 3.00207i | 0.218561 | + | 0.126187i | ||||
\(567\) | 4.98293i | 0.209263i | ||||||||
\(568\) | 10.6669 | − | 18.4756i | 0.447573 | − | 0.775218i | ||||
\(569\) | −8.80300 | − | 15.2472i | −0.369041 | − | 0.639198i | 0.620375 | − | 0.784305i | \(-0.286980\pi\) |
−0.989416 | + | 0.145108i | \(0.953647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.82424 | −0.160039 | −0.0800197 | − | 0.996793i | \(-0.525498\pi\) | ||||
−0.0800197 | + | 0.996793i | \(0.525498\pi\) | |||||||
\(572\) | −14.1308 | + | 9.00359i | −0.590836 | + | 0.376459i | ||||
\(573\) | 13.2489 | 0.553482 | ||||||||
\(574\) | −0.246455 | + | 0.142291i | −0.0102868 | + | 0.00593910i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.21247 | − | 2.10007i | 0.0505198 | − | 0.0875028i | ||||
\(577\) | − | 6.37523i | − | 0.265405i | −0.991156 | − | 0.132702i | \(-0.957635\pi\) | ||
0.991156 | − | 0.132702i | \(-0.0423654\pi\) | |||||||
\(578\) | −15.1255 | − | 8.73273i | −0.629139 | − | 0.363234i | ||||
\(579\) | −22.8457 | − | 13.1900i | −0.949435 | − | 0.548156i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.108902 | + | 0.188624i | −0.00451801 | + | 0.00782543i | ||||
\(582\) | −5.72399 | − | 9.91424i | −0.237267 | − | 0.410959i | ||||
\(583\) | −12.7857 | + | 7.38182i | −0.529529 | + | 0.305724i | ||||
\(584\) | 39.8419 | 1.64867 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 18.1043 | 0.747881 | ||||||||
\(587\) | 40.9293 | − | 23.6306i | 1.68933 | − | 0.975338i | 0.734308 | − | 0.678816i | \(-0.237507\pi\) |
0.955026 | − | 0.296522i | \(-0.0958267\pi\) | |||||||
\(588\) | 12.8578 | + | 22.2704i | 0.530249 | + | 0.918418i | ||||
\(589\) | −13.6191 | + | 23.5890i | −0.561166 | + | 0.971967i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.1395 | + | 7.00875i | 0.499353 | + | 0.288301i | ||||
\(592\) | −10.2993 | − | 5.94633i | −0.423301 | − | 0.244393i | ||||
\(593\) | 6.35373i | 0.260916i | 0.991454 | + | 0.130458i | \(0.0416448\pi\) | ||||
−0.991454 | + | 0.130458i | \(0.958355\pi\) | |||||||
\(594\) | 0.407159 | − | 0.705219i | 0.0167059 | − | 0.0289355i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.9659 | − | 6.33117i | 0.449181 | − | 0.259335i | ||||
\(597\) | 38.7177 | 1.58461 | ||||||||
\(598\) | −0.0703627 | − | 1.60914i | −0.00287735 | − | 0.0658026i | ||||
\(599\) | 43.2542 | 1.76732 | 0.883658 | − | 0.468132i | \(-0.155073\pi\) | ||||
0.883658 | + | 0.468132i | \(0.155073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.89558 | + | 5.01529i | 0.118113 | + | 0.204578i | 0.919020 | − | 0.394211i | \(-0.128982\pi\) |
−0.800907 | + | 0.598789i | \(0.795649\pi\) | |||||||
\(602\) | −0.197048 | + | 0.341297i | −0.00803107 | + | 0.0139102i | ||||
\(603\) | − | 2.01500i | − | 0.0820573i | ||||||
\(604\) | −17.5450 | − | 10.1296i | −0.713896 | − | 0.412168i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 22.8825i | − | 0.929537i | ||||||
\(607\) | 11.6175 | − | 20.1221i | 0.471540 | − | 0.816731i | −0.527930 | − | 0.849288i | \(-0.677032\pi\) |
0.999470 | + | 0.0325569i | \(0.0103650\pi\) | |||||||
\(608\) | −17.2889 | − | 29.9453i | −0.701158 | − | 1.21444i | ||||
\(609\) | −9.97450 | + | 5.75878i | −0.404187 | + | 0.233358i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.59739 | − | 6.11510i | 0.388269 | − | 0.247391i | ||||
\(612\) | −32.3842 | −1.30905 | ||||||||
\(613\) | −20.1997 | + | 11.6623i | −0.815857 | + | 0.471035i | −0.848986 | − | 0.528416i | \(-0.822786\pi\) |
0.0331286 | + | 0.999451i | \(0.489453\pi\) | |||||||
\(614\) | 5.14956 | + | 8.91930i | 0.207819 | + | 0.359954i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 4.15690i | − | 0.167486i | ||||||
\(617\) | −15.8269 | − | 9.13768i | −0.637168 | − | 0.367869i | 0.146355 | − | 0.989232i | \(-0.453246\pi\) |
−0.783523 | + | 0.621363i | \(0.786579\pi\) | |||||||
\(618\) | −6.33135 | − | 3.65540i | −0.254684 | − | 0.147042i | ||||
\(619\) | − | 45.4589i | − | 1.82715i | −0.406675 | − | 0.913573i | \(-0.633312\pi\) | ||
0.406675 | − | 0.913573i | \(-0.366688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.137316 | − | 0.237839i | −0.00551032 | − | 0.00954415i | ||||
\(622\) | −4.90334 | + | 2.83095i | −0.196606 | + | 0.113511i | ||||
\(623\) | −5.42945 | −0.217526 | ||||||||
\(624\) | −13.7294 | + | 0.600344i | −0.549615 | + | 0.0240330i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.77654 | − | 1.60304i | 0.110973 | − | 0.0640703i | ||||
\(627\) | −22.2528 | − | 38.5430i | −0.888692 | − | 1.53926i | ||||
\(628\) | −9.58552 | + | 16.6026i | −0.382504 | + | 0.662516i | ||||
\(629\) | − | 50.9335i | − | 2.03085i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.5920 | − | 19.3944i | −1.33728 | − | 0.772077i | −0.350874 | − | 0.936423i | \(-0.614115\pi\) |
−0.986403 | + | 0.164346i | \(0.947449\pi\) | |||||||
\(632\) | 35.7342i | 1.42143i | ||||||||
\(633\) | 21.0223 | − | 36.4117i | 0.835561 | − | 1.44723i | ||||
\(634\) | 1.11692 | + | 1.93456i | 0.0443585 | + | 0.0768312i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −19.1076 | −0.757665 | ||||||||
\(637\) | −11.0775 | + | 21.2831i | −0.438906 | + | 0.843267i | ||||
\(638\) | −15.6957 | −0.621400 | ||||||||
\(639\) | 24.6858 | − | 14.2523i | 0.976553 | − | 0.563813i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.4454 | − | 18.0920i | 0.412569 | − | 0.714591i | −0.582601 | − | 0.812758i | \(-0.697965\pi\) |
0.995170 | + | 0.0981679i | \(0.0312982\pi\) | |||||||
\(642\) | − | 4.47621i | − | 0.176662i | ||||||
\(643\) | −1.24581 | − | 0.719272i | −0.0491301 | − | 0.0283653i | 0.475234 | − | 0.879860i | \(-0.342364\pi\) |
−0.524364 | + | 0.851494i | \(0.675697\pi\) | |||||||
\(644\) | −0.531332 | − | 0.306765i | −0.0209374 | − | 0.0120882i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.1436 | − | 22.7654i | 0.517129 | − | 0.895694i | ||||
\(647\) | 24.0711 | + | 41.6923i | 0.946331 | + | 1.63909i | 0.753063 | + | 0.657948i | \(0.228575\pi\) |
0.193268 | + | 0.981146i | \(0.438091\pi\) | |||||||
\(648\) | −17.3917 | + | 10.0411i | −0.683209 | + | 0.394451i | ||||
\(649\) | 42.6244 | 1.67316 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.62134 | −0.259511 | ||||||||
\(652\) | −2.87609 | + | 1.66051i | −0.112636 | + | 0.0650305i | ||||
\(653\) | −18.7787 | − | 32.5257i | −0.734869 | − | 1.27283i | −0.954781 | − | 0.297311i | \(-0.903910\pi\) |
0.219911 | − | 0.975520i | \(-0.429423\pi\) | |||||||
\(654\) | −9.36567 | + | 16.2218i | −0.366227 | + | 0.634323i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.966438 | + | 0.557973i | 0.0377331 | + | 0.0217852i | ||||
\(657\) | 46.1020 | + | 26.6170i | 1.79861 | + | 1.03843i | ||||
\(658\) | 1.23556i | 0.0481672i | ||||||||
\(659\) | 6.65871 | − | 11.5332i | 0.259387 | − | 0.449271i | −0.706691 | − | 0.707522i | \(-0.749813\pi\) |
0.966078 | + | 0.258251i | \(0.0831463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.4052 | + | 18.7091i | −1.26041 | + | 0.727701i | −0.973155 | − | 0.230152i | \(-0.926078\pi\) |
−0.287260 | + | 0.957853i | \(0.592744\pi\) | |||||||
\(662\) | −13.6962 | −0.532320 | ||||||||
\(663\) | −31.6265 | − | 49.6365i | −1.22827 | − | 1.92772i | ||||
\(664\) | −0.877790 | −0.0340649 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.16556 | + | 14.1432i | 0.316409 | + | 0.548036i | ||||
\(667\) | −2.64673 | + | 4.58427i | −0.102482 | + | 0.177504i | ||||
\(668\) | − | 0.170402i | − | 0.00659304i | ||||||
\(669\) | 35.3277 | + | 20.3965i | 1.36585 | + | 0.788573i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0699i | 0.929208i | ||||||||
\(672\) | 4.20276 | − | 7.27940i | 0.162125 | − | 0.280809i | ||||
\(673\) | −23.7113 | − | 41.0691i | −0.914002 | − | 1.58310i | −0.808356 | − | 0.588695i | \(-0.799642\pi\) |
−0.105647 | − | 0.994404i | \(-0.533691\pi\) | |||||||
\(674\) | −8.84509 | + | 5.10671i | −0.340700 | + | 0.196703i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.6073 | − | 16.5723i | −0.446435 | − | 0.637397i | ||||
\(677\) | 5.91735 | 0.227422 | 0.113711 | − | 0.993514i | \(-0.463726\pi\) | ||||
0.113711 | + | 0.993514i | \(0.463726\pi\) | |||||||
\(678\) | −3.59348 | + | 2.07470i | −0.138007 | + | 0.0796783i | ||||
\(679\) | −2.03432 | − | 3.52354i | −0.0780699 | − | 0.135221i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 42.8186i | − | 1.64081i | ||||||
\(682\) | −7.81443 | − | 4.51166i | −0.299230 | − | 0.172761i | ||||
\(683\) | −12.9911 | − | 7.50043i | −0.497092 | − | 0.286996i | 0.230420 | − | 0.973091i | \(-0.425990\pi\) |
−0.727512 | + | 0.686095i | \(0.759323\pi\) | |||||||
\(684\) | − | 29.5707i | − | 1.13067i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.67265 | − | 4.62916i | −0.102042 | − | 0.176742i | ||||
\(687\) | −21.6766 | + | 12.5150i | −0.827014 | + | 0.477477i | ||||
\(688\) | 1.54539 | 0.0589175 | ||||||||
\(689\) | −9.57987 | − | 15.0352i | −0.364964 | − | 0.572795i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.2700 | − | 16.3217i | 1.07544 | − | 0.620907i | 0.145779 | − | 0.989317i | \(-0.453431\pi\) |
0.929663 | + | 0.368410i | \(0.120098\pi\) | |||||||
\(692\) | −6.38066 | − | 11.0516i | −0.242556 | − | 0.420120i | ||||
\(693\) | 2.77707 | − | 4.81003i | 0.105492 | − | 0.182718i | ||||
\(694\) | − | 10.0252i | − | 0.380550i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −40.1991 | − | 23.2090i | −1.52374 | − | 0.879734i | ||||
\(697\) | 4.77934i | 0.181030i | ||||||||
\(698\) | 10.3353 | − | 17.9012i | 0.391196 | − | 0.677571i | ||||
\(699\) | −24.4696 | − | 42.3826i | −0.925525 | − | 1.60306i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.83225 | −0.295820 | −0.147910 | − | 0.989001i | \(-0.547255\pi\) | ||||
−0.147910 | + | 0.989001i | \(0.547255\pi\) | |||||||
\(702\) | 0.872252 | + | 0.453993i | 0.0329210 | + | 0.0171349i | ||||
\(703\) | 46.5086 | 1.75410 | ||||||||
\(704\) | 1.98125 | − | 1.14387i | 0.0746710 | − | 0.0431113i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.50007 | + | 16.4546i | −0.357540 | + | 0.619277i | ||||
\(707\) | − | 8.13246i | − | 0.305853i | ||||||
\(708\) | 47.7751 | + | 27.5830i | 1.79550 | + | 1.03663i | ||||
\(709\) | 27.3294 | + | 15.7786i | 1.02638 | + | 0.592580i | 0.915945 | − | 0.401304i | \(-0.131443\pi\) |
0.110433 | + | 0.993884i | \(0.464776\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −23.8727 | + | 41.3488i | −0.895297 | + | 1.55070i | ||||
\(712\) | −10.9408 | − | 18.9501i | −0.410026 | − | 0.710185i | ||||
\(713\) | −2.63546 | + | 1.52158i | −0.0986987 | + | 0.0569837i | ||||
\(714\) | 6.39017 | 0.239146 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.0468733 | 0.00175174 | ||||||||
\(717\) | −24.1630 | + | 13.9505i | −0.902383 | + | 0.520991i | ||||
\(718\) | 5.48606 | + | 9.50214i | 0.204738 | + | 0.354617i | ||||
\(719\) | −8.91325 | + | 15.4382i | −0.332408 | + | 0.575748i | −0.982984 | − | 0.183694i | \(-0.941195\pi\) |
0.650575 | + | 0.759442i | \(0.274528\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.25017 | − | 1.29914i | −0.0838007 | − | 0.0483824i | ||||
\(722\) | 9.82816 | + | 5.67429i | 0.365766 | + | 0.211175i | ||||
\(723\) | 9.30803i | 0.346169i | ||||||||
\(724\) | −8.87816 | + | 15.3774i | −0.329954 | + | 0.571498i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.98574 | + | 1.72382i | −0.110811 | + | 0.0639768i | ||||
\(727\) | −4.62813 | −0.171648 | −0.0858240 | − | 0.996310i | \(-0.527352\pi\) | ||||
−0.0858240 | + | 0.996310i | \(0.527352\pi\) | |||||||
\(728\) | 5.01486 | − | 0.219285i | 0.185863 | − | 0.00812722i | ||||
\(729\) | −29.8824 | −1.10675 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.30928 | + | 5.73183i | 0.122398 | + | 0.211999i | ||||
\(732\) | −15.5760 | + | 26.9785i | −0.575706 | + | 0.997152i | ||||
\(733\) | − | 9.92820i | − | 0.366706i | −0.983047 | − | 0.183353i | \(-0.941305\pi\) | ||
0.983047 | − | 0.183353i | \(-0.0586952\pi\) | |||||||
\(734\) | −2.17425 | − | 1.25531i | −0.0802531 | − | 0.0463342i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 3.86318i | − | 0.142399i | ||||||
\(737\) | 0.950497 | − | 1.64631i | 0.0350120 | − | 0.0606426i | ||||
\(738\) | −0.766214 | − | 1.32712i | −0.0282047 | − | 0.0488520i | ||||
\(739\) | −24.7225 | + | 14.2735i | −0.909432 | + | 0.525061i | −0.880248 | − | 0.474513i | \(-0.842624\pi\) |
−0.0291834 | + | 0.999574i | \(0.509291\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 45.3243 | − | 28.8789i | 1.66503 | − | 1.06089i | ||||
\(742\) | 1.93562 | 0.0710589 | ||||||||
\(743\) | −20.0170 | + | 11.5568i | −0.734354 | + | 0.423979i | −0.820013 | − | 0.572345i | \(-0.806034\pi\) |
0.0856590 | + | 0.996325i | \(0.472700\pi\) | |||||||
\(744\) | −13.3426 | − | 23.1101i | −0.489165 | − | 0.847258i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.83386i | 0.323430i | ||||||||
\(747\) | −1.01571 | − | 0.586420i | −0.0371629 | − | 0.0214560i | ||||
\(748\) | −26.4587 | − | 15.2759i | −0.967425 | − | 0.558543i | ||||
\(749\) | − | 1.59085i | − | 0.0581285i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.8691 | + | 22.2900i | 0.469601 | + | 0.813372i | 0.999396 | − | 0.0347534i | \(-0.0110646\pi\) |
−0.529795 | + | 0.848126i | \(0.677731\pi\) | |||||||
\(752\) | 4.19597 | − | 2.42254i | 0.153011 | − | 0.0883410i | ||||
\(753\) | 50.5878 | 1.84352 | ||||||||
\(754\) | −0.827980 | − | 18.9353i | −0.0301533 | − | 0.689581i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.324381 | − | 0.187282i | 0.0117976 | − | 0.00681137i | ||||
\(757\) | −7.09047 | − | 12.2811i | −0.257708 | − | 0.446363i | 0.707920 | − | 0.706293i | \(-0.249634\pi\) |
−0.965627 | + | 0.259930i | \(0.916300\pi\) | |||||||
\(758\) | 7.32332 | − | 12.6844i | 0.265995 | − | 0.460717i | ||||
\(759\) | − | 4.97235i | − | 0.180485i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1030 | + | 12.1838i | 0.764983 | + | 0.441663i | 0.831082 | − | 0.556150i | \(-0.187722\pi\) |
−0.0660987 | + | 0.997813i | \(0.521055\pi\) | |||||||
\(762\) | 9.94026i | 0.360098i | ||||||||
\(763\) | −3.32857 | + | 5.76526i | −0.120502 | + | 0.208716i | ||||
\(764\) | 4.15243 | + | 7.19222i | 0.150230 | + | 0.260206i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.1033 | −0.545704 | ||||||||
\(767\) | 2.24852 | + | 51.4220i | 0.0811895 | + | 1.85674i | ||||
\(768\) | 22.0116 | 0.794276 | ||||||||
\(769\) | −10.2768 | + | 5.93333i | −0.370592 | + | 0.213961i | −0.673717 | − | 0.738989i | \(-0.735303\pi\) |
0.303125 | + | 0.952951i | \(0.401970\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.8238 | + | 30.8717i | −0.641909 | + | 1.11182i | ||||
\(772\) | − | 16.5358i | − | 0.595137i | ||||||
\(773\) | 1.52359 | + | 0.879642i | 0.0547995 | + | 0.0316385i | 0.527149 | − | 0.849773i | \(-0.323261\pi\) |
−0.472350 | + | 0.881411i | \(0.656594\pi\) | |||||||
\(774\) | −1.83783 | − | 1.06107i | −0.0660595 | − | 0.0381395i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.19867 | − | 14.2005i | 0.294315 | − | 0.509769i | ||||
\(777\) | 5.65289 | + | 9.79109i | 0.202796 | + | 0.351253i | ||||
\(778\) | −10.5743 | + | 6.10507i | −0.379107 | + | 0.218877i | ||||
\(779\) | −4.36413 | −0.156361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 26.8919 | 0.962266 | ||||||||
\(782\) | 2.54345 | − | 1.46846i | 0.0909534 | − | 0.0525120i | ||||
\(783\) | −1.61585 | − | 2.79873i | −0.0577456 | − | 0.100018i | ||||
\(784\) | −5.10763 | + | 8.84668i | −0.182415 | + | 0.315953i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.59858 | + | 0.922939i | 0.0570194 | + | 0.0329202i | ||||
\(787\) | 27.0347 | + | 15.6085i | 0.963684 | + | 0.556383i | 0.897305 | − | 0.441411i | \(-0.145522\pi\) |
0.0663793 | + | 0.997794i | \(0.478855\pi\) | |||||||
\(788\) | 8.78664i | 0.313011i | ||||||||
\(789\) | 33.1989 | − | 57.5022i | 1.18191 | − | 2.04713i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.27713 | + | 0.737351i | −0.0454095 | + | 0.0262172i | ||||
\(792\) | 22.3843 | 0.795390 | ||||||||
\(793\) | −29.0378 | + | 1.26974i | −1.03116 | + | 0.0450896i | ||||
\(794\) | −3.56781 | −0.126617 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 12.1348 | + | 21.0180i | 0.430106 | + | 0.744965i | ||||
\(797\) | 1.95382 | − | 3.38411i | 0.0692077 | − | 0.119871i | −0.829345 | − | 0.558737i | \(-0.811286\pi\) |
0.898553 | + | 0.438866i | \(0.144620\pi\) | |||||||
\(798\) | 5.83502i | 0.206557i | ||||||||
\(799\) | 17.9703 | + | 10.3752i | 0.635745 | + | 0.367048i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 29.2368i | − | 1.03303i | ||||||
\(802\) | 3.82126 | − | 6.61861i | 0.134933 | − | 0.233711i | ||||
\(803\) | 25.1110 | + | 43.4935i | 0.886148 | + | 1.53485i | ||||
\(804\) | 2.13071 | − | 1.23016i | 0.0751442 | − | 0.0433845i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.03063 | − | 9.66530i | 0.177196 | − | 0.340446i | ||||
\(807\) | −1.06811 | −0.0375994 | ||||||||
\(808\) | 28.3843 | − | 16.3877i | 0.998556 | − | 0.576517i | ||||
\(809\) | 10.0804 | + | 17.4597i | 0.354407 | + | 0.613851i | 0.987016 | − | 0.160620i | \(-0.0513493\pi\) |
−0.632609 | + | 0.774471i | \(0.718016\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 34.1631i | − | 1.19963i | −0.800139 | − | 0.599815i | \(-0.795241\pi\) | ||
0.800139 | − | 0.599815i | \(-0.204759\pi\) | |||||||
\(812\) | −6.25235 | − | 3.60980i | −0.219415 | − | 0.126679i | ||||
\(813\) | 25.2931 | + | 14.6030i | 0.887069 | + | 0.512150i | ||||
\(814\) | 15.4071i | 0.540019i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.5291 | − | 21.7010i | −0.438605 | − | 0.759687i | ||||
\(817\) | −5.23387 | + | 3.02178i | −0.183110 | + | 0.105719i | ||||
\(818\) | −11.5888 | −0.405194 | ||||||||
\(819\) | 5.94930 | + | 3.09651i | 0.207885 | + | 0.108201i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.8414 | − | 25.8892i | 1.56497 | − | 0.903538i | 0.568233 | − | 0.822868i | \(-0.307627\pi\) |
0.996741 | − | 0.0806706i | \(-0.0257062\pi\) | |||||||
\(822\) | −16.2820 | − | 28.2012i | −0.567899 | − | 0.983629i | ||||
\(823\) | −14.0554 | + | 24.3447i | −0.489941 | + | 0.848602i | −0.999933 | − | 0.0115767i | \(-0.996315\pi\) |
0.509992 | + | 0.860179i | \(0.329648\pi\) | |||||||
\(824\) | − | 10.4715i | − | 0.364793i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.83968 | − | 2.79419i | −0.168394 | − | 0.0972223i | ||||
\(827\) | 49.5177i | 1.72190i | 0.508691 | + | 0.860949i | \(0.330130\pi\) | ||||
−0.508691 | + | 0.860949i | \(0.669870\pi\) | |||||||
\(828\) | 1.65188 | − | 2.86114i | 0.0574068 | − | 0.0994316i | ||||
\(829\) | −10.8664 | − | 18.8212i | −0.377406 | − | 0.653687i | 0.613278 | − | 0.789867i | \(-0.289851\pi\) |
−0.990684 | + | 0.136180i | \(0.956517\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.87177 | 0.342448 | ||||||||
\(832\) | 1.48448 | + | 2.32982i | 0.0514650 | + | 0.0807721i | ||||
\(833\) | −43.7496 | −1.51583 | ||||||||
\(834\) | −14.1362 | + | 8.16154i | −0.489496 | + | 0.282611i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 13.9488 | − | 24.1600i | 0.482430 | − | 0.835593i | ||||
\(837\) | − | 1.85787i | − | 0.0642174i | ||||||
\(838\) | 12.9656 | + | 7.48567i | 0.447888 | + | 0.258588i | ||||
\(839\) | −31.2115 | − | 18.0199i | −1.07754 | − | 0.622118i | −0.147308 | − | 0.989091i | \(-0.547061\pi\) |
−0.930232 | + | 0.366973i | \(0.880394\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.6449 | + | 28.8299i | −0.573963 | + | 0.994134i | ||||
\(842\) | 1.72137 | + | 2.98149i | 0.0593222 | + | 0.102749i | ||||
\(843\) | −37.2573 | + | 21.5105i | −1.28321 | + | 0.740861i | ||||
\(844\) | 26.3550 | 0.907175 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.65332 | −0.228746 | ||||||||
\(847\) | −1.06114 | + | 0.612647i | −0.0364611 | + | 0.0210508i | ||||
\(848\) | −3.79513 | − | 6.57337i | −0.130325 | − | 0.225730i | ||||
\(849\) | −11.1913 | + | 19.3838i | −0.384083 | + | 0.665252i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.49998 | + | 2.59806i | 0.154257 | + | 0.0890605i | ||||
\(852\) | 30.1414 | + | 17.4022i | 1.03263 | + | 0.596188i | ||||
\(853\) | − | 38.4465i | − | 1.31638i | −0.752851 | − | 0.658191i | \(-0.771322\pi\) | ||
0.752851 | − | 0.658191i | \(-0.228678\pi\) | |||||||
\(854\) | 1.57787 | − | 2.73295i | 0.0539936 | − | 0.0935197i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.55247 | − | 3.20572i | 0.189780 | − | 0.109569i | ||||
\(857\) | −2.31635 | −0.0791251 | −0.0395625 | − | 0.999217i | \(-0.512596\pi\) | ||||
−0.0395625 | + | 0.999217i | \(0.512596\pi\) | |||||||
\(858\) | 9.56685 | + | 15.0148i | 0.326607 | + | 0.512596i | ||||
\(859\) | −1.38239 | −0.0471667 | −0.0235833 | − | 0.999722i | \(-0.507508\pi\) | ||||
−0.0235833 | + | 0.999722i | \(0.507508\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.530438 | − | 0.918746i | −0.0180773 | − | 0.0313108i | ||||
\(862\) | −8.76620 | + | 15.1835i | −0.298578 | + | 0.517152i | ||||
\(863\) | − | 10.5783i | − | 0.360091i | −0.983658 | − | 0.180046i | \(-0.942375\pi\) | ||
0.983658 | − | 0.180046i | \(-0.0576245\pi\) | |||||||
\(864\) | 2.04251 | + | 1.17925i | 0.0694877 | + | 0.0401187i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 12.5956i | 0.428015i | ||||||||
\(867\) | 32.5543 | − | 56.3856i | 1.10560 | − | 1.91496i | ||||
\(868\) | −2.07524 | − | 3.59442i | −0.0704382 | − | 0.122003i | ||||
\(869\) | −39.0093 | + | 22.5220i | −1.32330 | + | 0.764007i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.03624 | + | 1.05983i | 0.0689954 | + | 0.0359110i | ||||
\(872\) | −26.8296 | −0.908563 | ||||||||
\(873\) | 18.9737 | − | 10.9545i | 0.642163 | − | 0.370753i | ||||
\(874\) | 1.34088 | + | 2.32248i | 0.0453561 | + | 0.0785591i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 64.9989i | 2.19611i | ||||||||
\(877\) | −16.2742 | − | 9.39590i | −0.549540 | − | 0.317277i | 0.199397 | − | 0.979919i | \(-0.436102\pi\) |
−0.748936 | + | 0.662642i | \(0.769435\pi\) | |||||||
\(878\) | 15.8572 | + | 9.15516i | 0.535155 | + | 0.308972i | ||||
\(879\) | 67.4900i | 2.27638i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8767 | + | 34.4275i | 0.669663 | + | 1.15989i | 0.977998 | + | 0.208613i | \(0.0668948\pi\) |
−0.308335 | + | 0.951278i | \(0.599772\pi\) | |||||||
\(882\) | 12.1483 | − | 7.01385i | 0.409056 | − | 0.236169i | ||||
\(883\) | 17.2515 | 0.580560 | 0.290280 | − | 0.956942i | \(-0.406252\pi\) | ||||
0.290280 | + | 0.956942i | \(0.406252\pi\) | |||||||
\(884\) | 17.0331 | − | 32.7255i | 0.572884 | − | 1.10068i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −11.1237 | + | 6.42224i | −0.373706 | + | 0.215760i | ||||
\(887\) | −18.2982 | − | 31.6934i | −0.614394 | − | 1.06416i | −0.990491 | − | 0.137581i | \(-0.956067\pi\) |
0.376097 | − | 0.926580i | \(-0.377266\pi\) | |||||||
\(888\) | −22.7822 | + | 39.4599i | −0.764521 | + | 1.32419i | ||||
\(889\) | 3.53279i | 0.118486i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.9227 | − | 12.6571i | −0.734438 | − | 0.424028i | ||||
\(892\) | 25.5704i | 0.856160i | ||||||||
\(893\) | −9.47382 | + | 16.4091i | −0.317029 | + | 0.549111i | ||||
\(894\) | −6.72724 | − | 11.6519i | −0.224993 | − | 0.389699i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.47073 | 0.216172 | ||||||||
\(897\) | 5.99862 | − | 0.262301i | 0.200288 | − | 0.00875799i | ||||
\(898\) | 4.35372 | 0.145286 | ||||||||
\(899\) | −31.0123 | + | 17.9049i | −1.03432 | + | 0.597163i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16.2537 | − | 28.1522i | 0.541488 | − | 0.937885i | ||||
\(902\) | − | 1.44572i | − | 0.0481373i | ||||||
\(903\) | −1.27230 | − | 0.734564i | −0.0423396 | − | 0.0244448i | ||||
\(904\) | −5.14707 | − | 2.97166i | −0.171189 | − | 0.0988361i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.7633 | + | 18.6426i | −0.357587 | + | 0.619360i | ||||
\(907\) | −19.6178 | − | 33.9791i | −0.651400 | − | 1.12826i | −0.982783 | − | 0.184762i | \(-0.940849\pi\) |
0.331384 | − | 0.943496i | \(-0.392485\pi\) | |||||||
\(908\) | 23.2443 | − | 13.4201i | 0.771388 | − | 0.445361i | ||||
\(909\) | 43.7921 | 1.45249 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.66019 | −0.253793 | −0.126897 | − | 0.991916i | \(-0.540502\pi\) | ||||
−0.126897 | + | 0.991916i | \(0.540502\pi\) | |||||||
\(912\) | 19.8157 | − | 11.4406i | 0.656163 | − | 0.378836i | ||||
\(913\) | −0.553241 | − | 0.958241i | −0.0183096 | − | 0.0317131i | ||||
\(914\) | −4.79766 | + | 8.30978i | −0.158692 | + | 0.274863i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.5876 | − | 7.84482i | −0.448948 | − | 0.259200i | ||||
\(917\) | 0.568137 | + | 0.328014i | 0.0187615 | + | 0.0108320i | ||||
\(918\) | 1.79301i | 0.0591780i | ||||||||
\(919\) | −6.62625 | + | 11.4770i | −0.218580 | + | 0.378592i | −0.954374 | − | 0.298614i | \(-0.903476\pi\) |
0.735794 | + | 0.677205i | \(0.236809\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −33.2498 | + | 19.1968i | −1.09562 | + | 0.632555i | ||||
\(922\) | 8.83137 | 0.290846 | ||||||||
\(923\) | 1.41860 | + | 32.4422i | 0.0466938 | + | 1.06785i | ||||
\(924\) | 6.78164 | 0.223100 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −6.28319 | − | 10.8828i | −0.206478 | − | 0.357631i | ||||
\(927\) | 6.99565 | − | 12.1168i | 0.229767 | − | 0.397969i | ||||
\(928\) | − | 45.4592i | − | 1.49227i | ||||||
\(929\) | 39.4042 | + | 22.7500i | 1.29281 | + | 0.746405i | 0.979152 | − | 0.203131i | \(-0.0651117\pi\) |
0.313659 | + | 0.949536i | \(0.398445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 39.9488i | − | 1.30927i | ||||||
\(932\) | 15.3384 | − | 26.5668i | 0.502425 | − | 0.870225i | ||||
\(933\) | −10.5533 | − | 18.2789i | −0.345500 | − | 0.598424i | ||||
\(934\) | 12.6248 | − | 7.28891i | 0.413095 | − | 0.238500i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.18081 | + | 27.0043i | 0.0385961 | + | 0.882662i | ||||
\(937\) | −16.8095 | −0.549141 | −0.274570 | − | 0.961567i | \(-0.588536\pi\) | ||||
−0.274570 | + | 0.961567i | \(0.588536\pi\) | |||||||
\(938\) | −0.215843 | + | 0.124617i | −0.00704753 | + | 0.00406889i | ||||
\(939\) | 5.97588 | + | 10.3505i | 0.195015 | + | 0.337777i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.88910i | 0.289776i | 0.989448 | + | 0.144888i | \(0.0462822\pi\) | ||||
−0.989448 | + | 0.144888i | \(0.953718\pi\) | |||||||
\(942\) | 17.6413 | + | 10.1852i | 0.574784 | + | 0.331851i | ||||
\(943\) | −0.422255 | − | 0.243789i | −0.0137505 | − | 0.00793886i | ||||
\(944\) | 21.9140i | 0.713241i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.00104 | − | 1.73385i | −0.0325465 | − | 0.0563723i | ||||
\(947\) | −26.3710 | + | 15.2253i | −0.856942 | + | 0.494756i | −0.862987 | − | 0.505226i | \(-0.831409\pi\) |
0.00604474 | + | 0.999982i | \(0.498076\pi\) | |||||||
\(948\) | −58.2974 | −1.89341 | ||||||||
\(949\) | −51.1457 | + | 32.5882i | −1.66026 | + | 1.05786i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.21174 | + | 4.16370i | −0.233857 | + | 0.135017i | ||||
\(952\) | 4.57643 | + | 7.92662i | 0.148323 | + | 0.256903i | ||||
\(953\) | 2.42924 | − | 4.20756i | 0.0786907 | − | 0.136296i | −0.823995 | − | 0.566598i | \(-0.808259\pi\) |
0.902685 | + | 0.430301i | \(0.141593\pi\) | |||||||
\(954\) | 10.4230i | 0.337458i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −15.1462 | − | 8.74464i | −0.489862 | − | 0.282822i | ||||
\(957\) | − | 58.5112i | − | 1.89140i | ||||||
\(958\) | −9.35985 | + | 16.2117i | −0.302403 | + | 0.523777i | ||||
\(959\) | −5.78663 | − | 10.0227i | −0.186860 | − | 0.323651i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.4132 | 0.335910 | ||||||||
\(962\) | −18.5871 | + | 0.812755i | −0.599271 | + | 0.0262043i | ||||
\(963\) | 8.56651 | 0.276052 | ||||||||
\(964\) | −5.05290 | + | 2.91729i | −0.162743 | + | 0.0939597i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.325956 | + | 0.564572i | −0.0104875 | + | 0.0181648i | ||||
\(967\) | − | 26.5631i | − | 0.854211i | −0.904202 | − | 0.427106i | \(-0.859533\pi\) | ||
0.904202 | − | 0.427106i | \(-0.140467\pi\) | |||||||
\(968\) | −4.27658 | − | 2.46908i | −0.137454 | − | 0.0793593i | ||||
\(969\) | 84.8660 | + | 48.9974i | 2.72629 | + | 1.57402i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.6053 | + | 37.4216i | −0.693349 | + | 1.20091i | 0.277386 | + | 0.960759i | \(0.410532\pi\) |
−0.970734 | + | 0.240156i | \(0.922801\pi\) | |||||||
\(972\) | −17.3371 | − | 30.0288i | −0.556089 | − | 0.963174i | ||||
\(973\) | −5.02403 | + | 2.90062i | −0.161063 | + | 0.0929897i | ||||
\(974\) | 12.2037 | 0.391031 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.3748 | −0.396107 | ||||||||
\(977\) | −39.3665 | + | 22.7283i | −1.25945 | + | 0.727141i | −0.972967 | − | 0.230945i | \(-0.925818\pi\) |
−0.286479 | + | 0.958086i | \(0.592485\pi\) | |||||||
\(978\) | 1.76439 | + | 3.05601i | 0.0564190 | + | 0.0977205i | ||||
\(979\) | 13.7913 | − | 23.8872i | 0.440771 | − | 0.763438i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −31.0450 | − | 17.9239i | −0.991192 | − | 0.572265i | ||||
\(982\) | 12.5287 | + | 7.23347i | 0.399808 | + | 0.230829i | ||||
\(983\) | 9.31963i | 0.297250i | 0.988894 | + | 0.148625i | \(0.0474847\pi\) | ||||
−0.988894 | + | 0.148625i | \(0.952515\pi\) | |||||||
\(984\) | 2.13777 | − | 3.70272i | 0.0681495 | − | 0.118038i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 29.9295 | − | 17.2798i | 0.953150 | − | 0.550302i | ||||
\(987\) | −4.60599 | −0.146610 | ||||||||
\(988\) | 29.8824 | + | 15.5533i | 0.950686 | + | 0.494816i | ||||
\(989\) | −0.675210 | −0.0214704 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.01694 | + | 3.49344i | 0.0640702 | + | 0.110973i | 0.896281 | − | 0.443486i | \(-0.146258\pi\) |
−0.832211 | + | 0.554459i | \(0.812925\pi\) | |||||||
\(992\) | 13.0670 | − | 22.6328i | 0.414879 | − | 0.718592i | ||||
\(993\) | − | 51.0575i | − | 1.62026i | ||||||
\(994\) | −3.05336 | − | 1.76286i | −0.0968468 | − | 0.0559145i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 1.43204i | − | 0.0453760i | ||||||
\(997\) | −27.5880 | + | 47.7839i | −0.873722 | + | 1.51333i | −0.0156032 | + | 0.999878i | \(0.504967\pi\) |
−0.858118 | + | 0.513452i | \(0.828366\pi\) | |||||||
\(998\) | 4.90937 | + | 8.50327i | 0.155403 | + | 0.269166i | ||||
\(999\) | −2.74726 | + | 1.58613i | −0.0869195 | + | 0.0501830i |
(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 | 325.2.n.e.101.3 | ✓ | 10 | |
5.2 | odd | 4 | 325.2.m.d.49.6 | 20 | |||
5.3 | odd | 4 | 325.2.m.d.49.5 | 20 | |||
5.4 | even | 2 | 325.2.n.f.101.3 | yes | 10 | ||
13.2 | odd | 12 | 4225.2.a.bv.1.6 | 10 | |||
13.4 | even | 6 | inner | 325.2.n.e.251.3 | yes | 10 | |
13.11 | odd | 12 | 4225.2.a.bv.1.5 | 10 | |||
65.4 | even | 6 | 325.2.n.f.251.3 | yes | 10 | ||
65.17 | odd | 12 | 325.2.m.d.199.5 | 20 | |||
65.24 | odd | 12 | 4225.2.a.bu.1.6 | 10 | |||
65.43 | odd | 12 | 325.2.m.d.199.6 | 20 | |||
65.54 | odd | 12 | 4225.2.a.bu.1.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.m.d.49.5 | 20 | 5.3 | odd | 4 | |||
325.2.m.d.49.6 | 20 | 5.2 | odd | 4 | |||
325.2.m.d.199.5 | 20 | 65.17 | odd | 12 | |||
325.2.m.d.199.6 | 20 | 65.43 | odd | 12 | |||
325.2.n.e.101.3 | ✓ | 10 | 1.1 | even | 1 | trivial | |
325.2.n.e.251.3 | yes | 10 | 13.4 | even | 6 | inner | |
325.2.n.f.101.3 | yes | 10 | 5.4 | even | 2 | ||
325.2.n.f.251.3 | yes | 10 | 65.4 | even | 6 | ||
4225.2.a.bu.1.5 | 10 | 65.54 | odd | 12 | |||
4225.2.a.bu.1.6 | 10 | 65.24 | odd | 12 | |||
4225.2.a.bv.1.5 | 10 | 13.11 | odd | 12 | |||
4225.2.a.bv.1.6 | 10 | 13.2 | odd | 12 |