Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(118,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.m (of order \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.5 | ||
Root | \(1.40927 - 0.118126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.307 |
Dual form | 525.2.m.b.118.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.167056 | + | 0.167056i | 0.118126 | + | 0.118126i | 0.763699 | − | 0.645573i | \(-0.223381\pi\) |
−0.645573 | + | 0.763699i | \(0.723381\pi\) | |||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 1.94418i | − | 0.972092i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 0.236253i | − | 0.0964497i | ||||||
\(7\) | 2.64501 | + | 0.0627175i | 0.999719 | + | 0.0237050i | ||||
\(8\) | 0.658899 | − | 0.658899i | 0.232956 | − | 0.232956i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.98602 | 1.20183 | 0.600915 | − | 0.799313i | \(-0.294803\pi\) | ||||
0.600915 | + | 0.799313i | \(0.294803\pi\) | |||||||
\(12\) | −1.37475 | + | 1.37475i | −0.396855 | + | 0.396855i | ||||
\(13\) | −0.500437 | − | 0.500437i | −0.138796 | − | 0.138796i | 0.634295 | − | 0.773091i | \(-0.281291\pi\) |
−0.773091 | + | 0.634295i | \(0.781291\pi\) | |||||||
\(14\) | 0.431387 | + | 0.452341i | 0.115293 | + | 0.120893i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.66822 | −0.917056 | ||||||||
\(17\) | 1.67840 | − | 1.67840i | 0.407071 | − | 0.407071i | −0.473645 | − | 0.880716i | \(-0.657062\pi\) |
0.880716 | + | 0.473645i | \(0.157062\pi\) | |||||||
\(18\) | −0.167056 | + | 0.167056i | −0.0393754 | + | 0.0393754i | ||||
\(19\) | −7.21850 | −1.65604 | −0.828019 | − | 0.560700i | \(-0.810532\pi\) | ||||
−0.828019 | + | 0.560700i | \(0.810532\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.82596 | − | 1.91465i | −0.398456 | − | 0.417811i | ||||
\(22\) | 0.665888 | + | 0.665888i | 0.141968 | + | 0.141968i | ||||
\(23\) | 5.16007 | − | 5.16007i | 1.07595 | − | 1.07595i | 0.0790800 | − | 0.996868i | \(-0.474802\pi\) |
0.996868 | − | 0.0790800i | \(-0.0251983\pi\) | |||||||
\(24\) | −0.931824 | −0.190208 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.167202i | − | 0.0327910i | ||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0.121934 | − | 5.14238i | 0.0230434 | − | 0.971819i | ||||
\(29\) | − | 3.65191i | − | 0.678143i | −0.940761 | − | 0.339071i | \(-0.889887\pi\) | ||
0.940761 | − | 0.339071i | \(-0.110113\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.93821i | − | 0.886929i | −0.896292 | − | 0.443465i | \(-0.853749\pi\) | ||
0.896292 | − | 0.443465i | \(-0.146251\pi\) | |||||||
\(32\) | −1.93060 | − | 1.93060i | −0.341284 | − | 0.341284i | ||||
\(33\) | −2.81854 | − | 2.81854i | −0.490645 | − | 0.490645i | ||||
\(34\) | 0.560773 | 0.0961717 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.94418 | 0.324031 | ||||||||
\(37\) | −0.292275 | − | 0.292275i | −0.0480497 | − | 0.0480497i | 0.682674 | − | 0.730723i | \(-0.260817\pi\) |
−0.730723 | + | 0.682674i | \(0.760817\pi\) | |||||||
\(38\) | −1.20589 | − | 1.20589i | −0.195622 | − | 0.195622i | ||||
\(39\) | 0.707725i | 0.113327i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.63184i | 1.19189i | 0.803024 | + | 0.595947i | \(0.203223\pi\) | ||||
−0.803024 | + | 0.595947i | \(0.796777\pi\) | |||||||
\(42\) | 0.0148172 | − | 0.624890i | 0.00228634 | − | 0.0964226i | ||||
\(43\) | −3.65191 | + | 3.65191i | −0.556911 | + | 0.556911i | −0.928427 | − | 0.371516i | \(-0.878838\pi\) |
0.371516 | + | 0.928427i | \(0.378838\pi\) | |||||||
\(44\) | − | 7.74956i | − | 1.16829i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.72404 | 0.254196 | ||||||||
\(47\) | 0.305303 | − | 0.305303i | 0.0445331 | − | 0.0445331i | −0.684490 | − | 0.729023i | \(-0.739975\pi\) |
0.729023 | + | 0.684490i | \(0.239975\pi\) | |||||||
\(48\) | 2.59383 | + | 2.59383i | 0.374386 | + | 0.374386i | ||||
\(49\) | 6.99213 | + | 0.331777i | 0.998876 | + | 0.0473967i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.37361 | −0.332372 | ||||||||
\(52\) | −0.972943 | + | 0.972943i | −0.134923 | + | 0.134923i | ||||
\(53\) | −5.39653 | + | 5.39653i | −0.741270 | + | 0.741270i | −0.972822 | − | 0.231553i | \(-0.925619\pi\) |
0.231553 | + | 0.972822i | \(0.425619\pi\) | |||||||
\(54\) | 0.236253 | 0.0321499 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.78412 | − | 1.70147i | 0.238413 | − | 0.227368i | ||||
\(57\) | 5.10425 | + | 5.10425i | 0.676075 | + | 0.676075i | ||||
\(58\) | 0.610073 | − | 0.610073i | 0.0801065 | − | 0.0801065i | ||||
\(59\) | 6.10959 | 0.795401 | 0.397701 | − | 0.917515i | \(-0.369808\pi\) | ||||
0.397701 | + | 0.917515i | \(0.369808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.11047i | − | 0.910402i | −0.890389 | − | 0.455201i | \(-0.849567\pi\) | ||
0.890389 | − | 0.455201i | \(-0.150433\pi\) | |||||||
\(62\) | 0.824957 | − | 0.824957i | 0.104770 | − | 0.104770i | ||||
\(63\) | −0.0627175 | + | 2.64501i | −0.00790166 | + | 0.333240i | ||||
\(64\) | 6.69141i | 0.836426i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 0.941708i | − | 0.115916i | ||||||
\(67\) | −0.944185 | − | 0.944185i | −0.115351 | − | 0.115351i | 0.647075 | − | 0.762426i | \(-0.275992\pi\) |
−0.762426 | + | 0.647075i | \(0.775992\pi\) | |||||||
\(68\) | −3.26312 | − | 3.26312i | −0.395711 | − | 0.395711i | ||||
\(69\) | −7.29744 | −0.878508 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.19297 | 0.141579 | 0.0707897 | − | 0.997491i | \(-0.477448\pi\) | ||||
0.0707897 | + | 0.997491i | \(0.477448\pi\) | |||||||
\(72\) | 0.658899 | + | 0.658899i | 0.0776520 | + | 0.0776520i | ||||
\(73\) | −1.38298 | − | 1.38298i | −0.161865 | − | 0.161865i | 0.621527 | − | 0.783393i | \(-0.286513\pi\) |
−0.783393 | + | 0.621527i | \(0.786513\pi\) | |||||||
\(74\) | − | 0.0976524i | − | 0.0113519i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.0341i | 1.60982i | ||||||||
\(77\) | 10.5431 | + | 0.249993i | 1.20149 | + | 0.0284894i | ||||
\(78\) | −0.118230 | + | 0.118230i | −0.0133869 | + | 0.0133869i | ||||
\(79\) | 8.64027i | 0.972106i | 0.873929 | + | 0.486053i | \(0.161564\pi\) | ||||
−0.873929 | + | 0.486053i | \(0.838436\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −1.27494 | + | 1.27494i | −0.140794 | + | 0.140794i | ||||
\(83\) | 11.9895 | + | 11.9895i | 1.31602 | + | 1.31602i | 0.916898 | + | 0.399122i | \(0.130685\pi\) |
0.399122 | + | 0.916898i | \(0.369315\pi\) | |||||||
\(84\) | −3.72244 | + | 3.54999i | −0.406151 | + | 0.387336i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.22015 | −0.131572 | ||||||||
\(87\) | −2.58229 | + | 2.58229i | −0.276851 | + | 0.276851i | ||||
\(88\) | 2.62639 | − | 2.62639i | 0.279974 | − | 0.279974i | ||||
\(89\) | 7.82581 | 0.829534 | 0.414767 | − | 0.909928i | \(-0.363863\pi\) | ||||
0.414767 | + | 0.909928i | \(0.363863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.29227 | − | 1.35505i | −0.135467 | − | 0.142048i | ||||
\(92\) | −10.0321 | − | 10.0321i | −1.04592 | − | 1.04592i | ||||
\(93\) | −3.49184 | + | 3.49184i | −0.362087 | + | 0.362087i | ||||
\(94\) | 0.102005 | 0.0105211 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.73028i | 0.278658i | ||||||||
\(97\) | −7.43671 | + | 7.43671i | −0.755083 | + | 0.755083i | −0.975423 | − | 0.220340i | \(-0.929283\pi\) |
0.220340 | + | 0.975423i | \(0.429283\pi\) | |||||||
\(98\) | 1.11265 | + | 1.22350i | 0.112395 | + | 0.123592i | ||||
\(99\) | 3.98602i | 0.400610i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.31633i | − | 0.628498i | −0.949341 | − | 0.314249i | \(-0.898247\pi\) | ||
0.949341 | − | 0.314249i | \(-0.101753\pi\) | |||||||
\(102\) | −0.396526 | − | 0.396526i | −0.0392619 | − | 0.0392619i | ||||
\(103\) | 12.5410 | + | 12.5410i | 1.23570 | + | 1.23570i | 0.961743 | + | 0.273954i | \(0.0883316\pi\) |
0.273954 | + | 0.961743i | \(0.411668\pi\) | |||||||
\(104\) | −0.659476 | −0.0646669 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.80304 | −0.175127 | ||||||||
\(107\) | −7.48020 | − | 7.48020i | −0.723138 | − | 0.723138i | 0.246105 | − | 0.969243i | \(-0.420849\pi\) |
−0.969243 | + | 0.246105i | \(0.920849\pi\) | |||||||
\(108\) | −1.37475 | − | 1.37475i | −0.132285 | − | 0.132285i | ||||
\(109\) | 0.668223i | 0.0640042i | 0.999488 | + | 0.0320021i | \(0.0101883\pi\) | ||||
−0.999488 | + | 0.0320021i | \(0.989812\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.413339i | 0.0392324i | ||||||||
\(112\) | −9.70248 | − | 0.230062i | −0.916798 | − | 0.0217388i | ||||
\(113\) | 3.39653 | − | 3.39653i | 0.319518 | − | 0.319518i | −0.529064 | − | 0.848582i | \(-0.677457\pi\) |
0.848582 | + | 0.529064i | \(0.177457\pi\) | |||||||
\(114\) | 1.70539i | 0.159724i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.09999 | −0.659217 | ||||||||
\(117\) | 0.500437 | − | 0.500437i | 0.0462655 | − | 0.0462655i | ||||
\(118\) | 1.02064 | + | 1.02064i | 0.0939578 | + | 0.0939578i | ||||
\(119\) | 4.54464 | − | 4.33411i | 0.416607 | − | 0.397307i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.88837 | 0.444397 | ||||||||
\(122\) | 1.18785 | − | 1.18785i | 0.107542 | − | 0.107542i | ||||
\(123\) | 5.39653 | − | 5.39653i | 0.486588 | − | 0.486588i | ||||
\(124\) | −9.60080 | −0.862177 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.452341 | + | 0.431387i | −0.0402978 | + | 0.0384310i | ||||
\(127\) | 5.88837 | + | 5.88837i | 0.522508 | + | 0.522508i | 0.918328 | − | 0.395820i | \(-0.129540\pi\) |
−0.395820 | + | 0.918328i | \(0.629540\pi\) | |||||||
\(128\) | −4.97903 | + | 4.97903i | −0.440088 | + | 0.440088i | ||||
\(129\) | 5.16458 | 0.454716 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.8144i | 1.64383i | 0.569613 | + | 0.821913i | \(0.307093\pi\) | ||||
−0.569613 | + | 0.821913i | \(0.692907\pi\) | |||||||
\(132\) | −5.47977 | + | 5.47977i | −0.476953 | + | 0.476953i | ||||
\(133\) | −19.0930 | − | 0.452726i | −1.65557 | − | 0.0392564i | ||||
\(134\) | − | 0.315463i | − | 0.0272519i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 2.21179i | − | 0.189659i | ||||||
\(137\) | 0.811977 | + | 0.811977i | 0.0693719 | + | 0.0693719i | 0.740941 | − | 0.671570i | \(-0.234380\pi\) |
−0.671570 | + | 0.740941i | \(0.734380\pi\) | |||||||
\(138\) | −1.21908 | − | 1.21908i | −0.103775 | − | 0.103775i | ||||
\(139\) | −0.442439 | −0.0375272 | −0.0187636 | − | 0.999824i | \(-0.505973\pi\) | ||||
−0.0187636 | + | 0.999824i | \(0.505973\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.431764 | −0.0363611 | ||||||||
\(142\) | 0.199293 | + | 0.199293i | 0.0167243 | + | 0.0167243i | ||||
\(143\) | −1.99475 | − | 1.99475i | −0.166810 | − | 0.166810i | ||||
\(144\) | − | 3.66822i | − | 0.305685i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 0.462070i | − | 0.0382411i | ||||||
\(147\) | −4.70958 | − | 5.17879i | −0.388440 | − | 0.427139i | ||||
\(148\) | −0.568236 | + | 0.568236i | −0.0467087 | + | 0.0467087i | ||||
\(149\) | − | 3.14114i | − | 0.257332i | −0.991688 | − | 0.128666i | \(-0.958930\pi\) | ||
0.991688 | − | 0.128666i | \(-0.0410696\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.7239 | −1.19822 | −0.599109 | − | 0.800668i | \(-0.704478\pi\) | ||||
−0.599109 | + | 0.800668i | \(0.704478\pi\) | |||||||
\(152\) | −4.75626 | + | 4.75626i | −0.385784 | + | 0.385784i | ||||
\(153\) | 1.67840 | + | 1.67840i | 0.135690 | + | 0.135690i | ||||
\(154\) | 1.71952 | + | 1.80304i | 0.138563 | + | 0.145293i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.37595 | 0.110164 | ||||||||
\(157\) | 7.96508 | − | 7.96508i | 0.635682 | − | 0.635682i | −0.313805 | − | 0.949487i | \(-0.601604\pi\) |
0.949487 | + | 0.313805i | \(0.101604\pi\) | |||||||
\(158\) | −1.44341 | + | 1.44341i | −0.114831 | + | 0.114831i | ||||
\(159\) | 7.63184 | 0.605244 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.9720 | − | 13.3248i | 1.10115 | − | 1.05014i | ||||
\(162\) | −0.167056 | − | 0.167056i | −0.0131251 | − | 0.0131251i | ||||
\(163\) | −10.4450 | + | 10.4450i | −0.818113 | + | 0.818113i | −0.985834 | − | 0.167722i | \(-0.946359\pi\) |
0.167722 | + | 0.985834i | \(0.446359\pi\) | |||||||
\(164\) | 14.8377 | 1.15863 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00584i | 0.310913i | ||||||||
\(167\) | −4.63621 | + | 4.63621i | −0.358761 | + | 0.358761i | −0.863356 | − | 0.504595i | \(-0.831642\pi\) |
0.504595 | + | 0.863356i | \(0.331642\pi\) | |||||||
\(168\) | −2.46468 | − | 0.0584417i | −0.190154 | − | 0.00450887i | ||||
\(169\) | − | 12.4991i | − | 0.961471i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.21850i | − | 0.552013i | ||||||
\(172\) | 7.09999 | + | 7.09999i | 0.541369 | + | 0.541369i | ||||
\(173\) | 2.48531 | + | 2.48531i | 0.188954 | + | 0.188954i | 0.795244 | − | 0.606290i | \(-0.207343\pi\) |
−0.606290 | + | 0.795244i | \(0.707343\pi\) | |||||||
\(174\) | −0.862773 | −0.0654067 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.6216 | −1.10215 | ||||||||
\(177\) | −4.32013 | − | 4.32013i | −0.324721 | − | 0.324721i | ||||
\(178\) | 1.30735 | + | 1.30735i | 0.0979898 | + | 0.0979898i | ||||
\(179\) | 22.1109i | 1.65264i | 0.563199 | + | 0.826321i | \(0.309570\pi\) | ||||
−0.563199 | + | 0.826321i | \(0.690430\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | 0.0104865 | − | 0.442251i | 0.000777310 | − | 0.0327818i | ||||
\(183\) | −5.02786 | + | 5.02786i | −0.371670 | + | 0.371670i | ||||
\(184\) | − | 6.79993i | − | 0.501297i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.16667 | −0.0855441 | ||||||||
\(187\) | 6.69013 | − | 6.69013i | 0.489231 | − | 0.489231i | ||||
\(188\) | −0.593566 | − | 0.593566i | −0.0432903 | − | 0.0432903i | ||||
\(189\) | 1.91465 | − | 1.82596i | 0.139270 | − | 0.132819i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.2898 | 1.10633 | 0.553167 | − | 0.833070i | \(-0.313419\pi\) | ||||
0.553167 | + | 0.833070i | \(0.313419\pi\) | |||||||
\(192\) | 4.73154 | − | 4.73154i | 0.341470 | − | 0.341470i | ||||
\(193\) | 8.92787 | − | 8.92787i | 0.642642 | − | 0.642642i | −0.308562 | − | 0.951204i | \(-0.599848\pi\) |
0.951204 | + | 0.308562i | \(0.0998477\pi\) | |||||||
\(194\) | −2.48469 | −0.178390 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.645035 | − | 13.5940i | 0.0460739 | − | 0.971000i | ||||
\(197\) | 2.68715 | + | 2.68715i | 0.191451 | + | 0.191451i | 0.796323 | − | 0.604872i | \(-0.206776\pi\) |
−0.604872 | + | 0.796323i | \(0.706776\pi\) | |||||||
\(198\) | −0.665888 | + | 0.665888i | −0.0473226 | + | 0.0473226i | ||||
\(199\) | 0.616637 | 0.0437122 | 0.0218561 | − | 0.999761i | \(-0.493042\pi\) | ||||
0.0218561 | + | 0.999761i | \(0.493042\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.33528i | 0.0941833i | ||||||||
\(202\) | 1.05518 | − | 1.05518i | 0.0742422 | − | 0.0742422i | ||||
\(203\) | 0.229039 | − | 9.65933i | 0.0160754 | − | 0.677952i | ||||
\(204\) | 4.61474i | 0.323097i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.19008i | 0.291937i | ||||||||
\(207\) | 5.16007 | + | 5.16007i | 0.358649 | + | 0.358649i | ||||
\(208\) | 1.83572 | + | 1.83572i | 0.127284 | + | 0.127284i | ||||
\(209\) | −28.7731 | −1.99028 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.30849 | 0.640823 | 0.320411 | − | 0.947278i | \(-0.396179\pi\) | ||||
0.320411 | + | 0.947278i | \(0.396179\pi\) | |||||||
\(212\) | 10.4918 | + | 10.4918i | 0.720583 | + | 0.720583i | ||||
\(213\) | −0.843557 | − | 0.843557i | −0.0577996 | − | 0.0577996i | ||||
\(214\) | − | 2.49922i | − | 0.170843i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 0.931824i | − | 0.0634026i | ||||||
\(217\) | 0.309712 | − | 13.0616i | 0.0210246 | − | 0.886680i | ||||
\(218\) | −0.111631 | + | 0.111631i | −0.00756058 | + | 0.00756058i | ||||
\(219\) | 1.95583i | 0.132163i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.67987 | −0.113000 | ||||||||
\(222\) | −0.0690507 | + | 0.0690507i | −0.00463438 | + | 0.00463438i | ||||
\(223\) | 1.35505 | + | 1.35505i | 0.0907407 | + | 0.0907407i | 0.751020 | − | 0.660279i | \(-0.229562\pi\) |
−0.660279 | + | 0.751020i | \(0.729562\pi\) | |||||||
\(224\) | −4.98536 | − | 5.22753i | −0.333098 | − | 0.349279i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.13482 | 0.0754870 | ||||||||
\(227\) | −4.15437 | + | 4.15437i | −0.275735 | + | 0.275735i | −0.831404 | − | 0.555668i | \(-0.812462\pi\) |
0.555668 | + | 0.831404i | \(0.312462\pi\) | |||||||
\(228\) | 9.92361 | − | 9.92361i | 0.657207 | − | 0.657207i | ||||
\(229\) | 12.9900 | 0.858403 | 0.429202 | − | 0.903209i | \(-0.358795\pi\) | ||||
0.429202 | + | 0.903209i | \(0.358795\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.27830 | − | 7.63184i | −0.478877 | − | 0.502138i | ||||
\(232\) | −2.40624 | − | 2.40624i | −0.157977 | − | 0.157977i | ||||
\(233\) | 16.4639 | − | 16.4639i | 1.07859 | − | 1.07859i | 0.0819485 | − | 0.996637i | \(-0.473886\pi\) |
0.996637 | − | 0.0819485i | \(-0.0261143\pi\) | |||||||
\(234\) | 0.167202 | 0.0109303 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 11.8782i | − | 0.773203i | ||||||
\(237\) | 6.10959 | − | 6.10959i | 0.396861 | − | 0.396861i | ||||
\(238\) | 1.48325 | + | 0.0351703i | 0.0961447 | + | 0.00227975i | ||||
\(239\) | 5.48048i | 0.354503i | 0.984166 | + | 0.177251i | \(0.0567205\pi\) | ||||
−0.984166 | + | 0.177251i | \(0.943279\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.6507i | − | 0.943737i | −0.881669 | − | 0.471868i | \(-0.843580\pi\) | ||
0.881669 | − | 0.471868i | \(-0.156420\pi\) | |||||||
\(242\) | 0.816631 | + | 0.816631i | 0.0524950 | + | 0.0524950i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | −13.8241 | −0.884995 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.80304 | 0.114958 | ||||||||
\(247\) | 3.61241 | + | 3.61241i | 0.229852 | + | 0.229852i | ||||
\(248\) | −3.25378 | − | 3.25378i | −0.206615 | − | 0.206615i | ||||
\(249\) | − | 16.9557i | − | 1.07453i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.1506i | 1.33501i | 0.744604 | + | 0.667507i | \(0.232639\pi\) | ||||
−0.744604 | + | 0.667507i | \(0.767361\pi\) | |||||||
\(252\) | 5.14238 | + | 0.121934i | 0.323940 | + | 0.00768115i | ||||
\(253\) | 20.5681 | − | 20.5681i | 1.29311 | − | 1.29311i | ||||
\(254\) | 1.96737i | 0.123444i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.7193 | 0.732454 | ||||||||
\(257\) | 9.39248 | − | 9.39248i | 0.585887 | − | 0.585887i | −0.350628 | − | 0.936515i | \(-0.614032\pi\) |
0.936515 | + | 0.350628i | \(0.114032\pi\) | |||||||
\(258\) | 0.862773 | + | 0.862773i | 0.0537139 | + | 0.0537139i | ||||
\(259\) | −0.754738 | − | 0.791399i | −0.0468971 | − | 0.0491752i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.65191 | 0.226048 | ||||||||
\(262\) | −3.14306 | + | 3.14306i | −0.194179 | + | 0.194179i | ||||
\(263\) | −15.3779 | + | 15.3779i | −0.948241 | + | 0.948241i | −0.998725 | − | 0.0504843i | \(-0.983924\pi\) |
0.0504843 | + | 0.998725i | \(0.483924\pi\) | |||||||
\(264\) | −3.71427 | −0.228598 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.11397 | − | 3.26523i | −0.190929 | − | 0.200204i | ||||
\(267\) | −5.53368 | − | 5.53368i | −0.338656 | − | 0.338656i | ||||
\(268\) | −1.83567 | + | 1.83567i | −0.112131 | + | 0.112131i | ||||
\(269\) | −22.9851 | −1.40143 | −0.700714 | − | 0.713442i | \(-0.747135\pi\) | ||||
−0.700714 | + | 0.713442i | \(0.747135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.7596i | 0.957330i | 0.877998 | + | 0.478665i | \(0.158879\pi\) | ||||
−0.877998 | + | 0.478665i | \(0.841121\pi\) | |||||||
\(272\) | −6.15674 | + | 6.15674i | −0.373307 | + | 0.373307i | ||||
\(273\) | −0.0443868 | + | 1.87194i | −0.00268641 | + | 0.113295i | ||||
\(274\) | 0.271291i | 0.0163893i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 14.1876i | 0.853991i | ||||||||
\(277\) | −4.80771 | − | 4.80771i | −0.288867 | − | 0.288867i | 0.547765 | − | 0.836632i | \(-0.315479\pi\) |
−0.836632 | + | 0.547765i | \(0.815479\pi\) | |||||||
\(278\) | −0.0739121 | − | 0.0739121i | −0.00443295 | − | 0.00443295i | ||||
\(279\) | 4.93821 | 0.295643 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.65658 | −0.576063 | −0.288032 | − | 0.957621i | \(-0.593001\pi\) | ||||
−0.288032 | + | 0.957621i | \(0.593001\pi\) | |||||||
\(282\) | −0.0721287 | − | 0.0721287i | −0.00429520 | − | 0.00429520i | ||||
\(283\) | −14.9095 | − | 14.9095i | −0.886278 | − | 0.886278i | 0.107885 | − | 0.994163i | \(-0.465592\pi\) |
−0.994163 | + | 0.107885i | \(0.965592\pi\) | |||||||
\(284\) | − | 2.31935i | − | 0.137628i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.666471i | − | 0.0394092i | ||||||
\(287\) | −0.478650 | + | 20.1863i | −0.0282538 | + | 1.19156i | ||||
\(288\) | 1.93060 | − | 1.93060i | 0.113761 | − | 0.113761i | ||||
\(289\) | 11.3660i | 0.668586i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.5171 | 0.616523 | ||||||||
\(292\) | −2.68877 | + | 2.68877i | −0.157348 | + | 0.157348i | ||||
\(293\) | −4.79236 | − | 4.79236i | −0.279973 | − | 0.279973i | 0.553125 | − | 0.833098i | \(-0.313435\pi\) |
−0.833098 | + | 0.553125i | \(0.813435\pi\) | |||||||
\(294\) | 0.0783831 | − | 1.65191i | 0.00457140 | − | 0.0963413i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.385159 | −0.0223869 | ||||||||
\(297\) | 2.81854 | − | 2.81854i | 0.163548 | − | 0.163548i | ||||
\(298\) | 0.524746 | − | 0.524746i | 0.0303977 | − | 0.0303977i | ||||
\(299\) | −5.16458 | −0.298675 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.88837 | + | 9.43029i | −0.569956 | + | 0.543553i | ||||
\(302\) | −2.45972 | − | 2.45972i | −0.141541 | − | 0.141541i | ||||
\(303\) | −4.46632 | + | 4.46632i | −0.256583 | + | 0.256583i | ||||
\(304\) | 26.4791 | 1.51868 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.560773i | 0.0320572i | ||||||||
\(307\) | −9.85063 | + | 9.85063i | −0.562205 | + | 0.562205i | −0.929933 | − | 0.367728i | \(-0.880136\pi\) |
0.367728 | + | 0.929933i | \(0.380136\pi\) | |||||||
\(308\) | 0.486033 | − | 20.4977i | 0.0276943 | − | 1.16796i | ||||
\(309\) | − | 17.7356i | − | 1.00894i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 27.3063i | − | 1.54840i | −0.632941 | − | 0.774200i | \(-0.718152\pi\) | ||
0.632941 | − | 0.774200i | \(-0.281848\pi\) | |||||||
\(312\) | 0.466320 | + | 0.466320i | 0.0264002 | + | 0.0264002i | ||||
\(313\) | −18.5080 | − | 18.5080i | −1.04613 | − | 1.04613i | −0.998883 | − | 0.0472492i | \(-0.984955\pi\) |
−0.0472492 | − | 0.998883i | \(-0.515045\pi\) | |||||||
\(314\) | 2.66123 | 0.150182 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.7983 | 0.944977 | ||||||||
\(317\) | 21.8793 | + | 21.8793i | 1.22887 | + | 1.22887i | 0.964393 | + | 0.264473i | \(0.0851980\pi\) |
0.264473 | + | 0.964393i | \(0.414802\pi\) | |||||||
\(318\) | 1.27494 | + | 1.27494i | 0.0714953 | + | 0.0714953i | ||||
\(319\) | − | 14.5566i | − | 0.815013i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.5786i | 0.590440i | ||||||||
\(322\) | 4.56010 | + | 0.108127i | 0.254124 | + | 0.00602570i | ||||
\(323\) | −12.1155 | + | 12.1155i | −0.674126 | + | 0.674126i | ||||
\(324\) | 1.94418i | 0.108010i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.48978 | −0.193281 | ||||||||
\(327\) | 0.472505 | − | 0.472505i | 0.0261296 | − | 0.0261296i | ||||
\(328\) | 5.02861 | + | 5.02861i | 0.277659 | + | 0.277659i | ||||
\(329\) | 0.826678 | − | 0.788382i | 0.0455762 | − | 0.0434649i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.6913 | −0.917438 | −0.458719 | − | 0.888581i | \(-0.651691\pi\) | ||||
−0.458719 | + | 0.888581i | \(0.651691\pi\) | |||||||
\(332\) | 23.3098 | − | 23.3098i | 1.27929 | − | 1.27929i | ||||
\(333\) | 0.292275 | − | 0.292275i | 0.0160166 | − | 0.0160166i | ||||
\(334\) | −1.54901 | −0.0847582 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.69801 | + | 7.02337i | 0.365406 | + | 0.383156i | ||||
\(337\) | −2.54028 | − | 2.54028i | −0.138378 | − | 0.138378i | 0.634525 | − | 0.772903i | \(-0.281196\pi\) |
−0.772903 | + | 0.634525i | \(0.781196\pi\) | |||||||
\(338\) | 2.08805 | − | 2.08805i | 0.113575 | − | 0.113575i | ||||
\(339\) | −4.80341 | −0.260886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 19.6838i | − | 1.06594i | ||||||
\(342\) | 1.20589 | − | 1.20589i | 0.0652072 | − | 0.0652072i | ||||
\(343\) | 18.4734 | + | 1.31608i | 0.997472 | + | 0.0710617i | ||||
\(344\) | 4.81248i | 0.259472i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.830370i | 0.0446410i | ||||||||
\(347\) | −13.6980 | − | 13.6980i | −0.735348 | − | 0.735348i | 0.236326 | − | 0.971674i | \(-0.424057\pi\) |
−0.971674 | + | 0.236326i | \(0.924057\pi\) | |||||||
\(348\) | 5.02045 | + | 5.02045i | 0.269124 | + | 0.269124i | ||||
\(349\) | 0.508601 | 0.0272248 | 0.0136124 | − | 0.999907i | \(-0.495667\pi\) | ||||
0.0136124 | + | 0.999907i | \(0.495667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.707725 | −0.0377756 | ||||||||
\(352\) | −7.69540 | − | 7.69540i | −0.410166 | − | 0.410166i | ||||
\(353\) | −10.9217 | − | 10.9217i | −0.581305 | − | 0.581305i | 0.353957 | − | 0.935262i | \(-0.384836\pi\) |
−0.935262 | + | 0.353957i | \(0.884836\pi\) | |||||||
\(354\) | − | 1.44341i | − | 0.0767162i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 15.2148i | − | 0.806383i | ||||||
\(357\) | −6.27823 | − | 0.148867i | −0.332279 | − | 0.00787888i | ||||
\(358\) | −3.69375 | + | 3.69375i | −0.195221 | + | 0.195221i | ||||
\(359\) | − | 15.9860i | − | 0.843710i | −0.906663 | − | 0.421855i | \(-0.861379\pi\) | ||
0.906663 | − | 0.421855i | \(-0.138621\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.1068 | 1.74246 | ||||||||
\(362\) | −1.41752 | + | 1.41752i | −0.0745030 | + | 0.0745030i | ||||
\(363\) | −3.45660 | − | 3.45660i | −0.181424 | − | 0.181424i | ||||
\(364\) | −2.63446 | + | 2.51242i | −0.138083 | + | 0.131687i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.67987 | −0.0878080 | ||||||||
\(367\) | −0.410036 | + | 0.410036i | −0.0214037 | + | 0.0214037i | −0.717728 | − | 0.696324i | \(-0.754818\pi\) |
0.696324 | + | 0.717728i | \(0.254818\pi\) | |||||||
\(368\) | −18.9283 | + | 18.9283i | −0.986705 | + | 0.986705i | ||||
\(369\) | −7.63184 | −0.397298 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.6123 | + | 13.9354i | −0.758633 | + | 0.723490i | ||||
\(372\) | 6.78879 | + | 6.78879i | 0.351982 | + | 0.351982i | ||||
\(373\) | 3.44496 | − | 3.44496i | 0.178373 | − | 0.178373i | −0.612273 | − | 0.790646i | \(-0.709745\pi\) |
0.790646 | + | 0.612273i | \(0.209745\pi\) | |||||||
\(374\) | 2.23525 | 0.115582 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 0.402328i | − | 0.0207485i | ||||||
\(377\) | −1.82755 | + | 1.82755i | −0.0941237 | + | 0.0941237i | ||||
\(378\) | 0.624890 | + | 0.0148172i | 0.0321409 | + | 0.000762113i | ||||
\(379\) | − | 12.9179i | − | 0.663547i | −0.943359 | − | 0.331773i | \(-0.892353\pi\) | ||
0.943359 | − | 0.331773i | \(-0.107647\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 8.32741i | − | 0.426626i | ||||||
\(382\) | 2.55426 | + | 2.55426i | 0.130687 | + | 0.130687i | ||||
\(383\) | 10.0770 | + | 10.0770i | 0.514910 | + | 0.514910i | 0.916027 | − | 0.401117i | \(-0.131378\pi\) |
−0.401117 | + | 0.916027i | \(0.631378\pi\) | |||||||
\(384\) | 7.04142 | 0.359331 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.98291 | 0.151826 | ||||||||
\(387\) | −3.65191 | − | 3.65191i | −0.185637 | − | 0.185637i | ||||
\(388\) | 14.4583 | + | 14.4583i | 0.734011 | + | 0.734011i | ||||
\(389\) | 24.3300i | 1.23358i | 0.787127 | + | 0.616791i | \(0.211567\pi\) | ||||
−0.787127 | + | 0.616791i | \(0.788433\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.3213i | − | 0.875976i | ||||||
\(392\) | 4.82572 | − | 4.38850i | 0.243736 | − | 0.221653i | ||||
\(393\) | 13.3038 | − | 13.3038i | 0.671089 | − | 0.671089i | ||||
\(394\) | 0.897808i | 0.0452309i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.74956 | 0.389430 | ||||||||
\(397\) | −6.80633 | + | 6.80633i | −0.341600 | + | 0.341600i | −0.856969 | − | 0.515369i | \(-0.827655\pi\) |
0.515369 | + | 0.856969i | \(0.327655\pi\) | |||||||
\(398\) | 0.103013 | + | 0.103013i | 0.00516356 | + | 0.00516356i | ||||
\(399\) | 13.1807 | + | 13.8209i | 0.659858 | + | 0.691911i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.83090 | −0.440994 | −0.220497 | − | 0.975388i | \(-0.570768\pi\) | ||||
−0.220497 | + | 0.975388i | \(0.570768\pi\) | |||||||
\(402\) | −0.223066 | + | 0.223066i | −0.0111255 | + | 0.0111255i | ||||
\(403\) | −2.47127 | + | 2.47127i | −0.123103 | + | 0.123103i | ||||
\(404\) | −12.2801 | −0.610958 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.65191 | − | 1.57539i | 0.0819829 | − | 0.0781851i | ||||
\(407\) | −1.16501 | − | 1.16501i | −0.0577476 | − | 0.0577476i | ||||
\(408\) | −1.56397 | + | 1.56397i | −0.0774282 | + | 0.0774282i | ||||
\(409\) | −23.1985 | −1.14709 | −0.573546 | − | 0.819174i | \(-0.694432\pi\) | ||||
−0.573546 | + | 0.819174i | \(0.694432\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.14831i | − | 0.0566419i | ||||||
\(412\) | 24.3819 | − | 24.3819i | 1.20121 | − | 1.20121i | ||||
\(413\) | 16.1599 | + | 0.383178i | 0.795178 | + | 0.0188550i | ||||
\(414\) | 1.72404i | 0.0847319i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.93229i | 0.0947381i | ||||||||
\(417\) | 0.312852 | + | 0.312852i | 0.0153204 | + | 0.0153204i | ||||
\(418\) | −4.80672 | − | 4.80672i | −0.235104 | − | 0.235104i | ||||
\(419\) | 13.0393 | 0.637009 | 0.318505 | − | 0.947921i | \(-0.396819\pi\) | ||||
0.318505 | + | 0.947921i | \(0.396819\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.3549 | −1.52814 | −0.764071 | − | 0.645132i | \(-0.776802\pi\) | ||||
−0.764071 | + | 0.645132i | \(0.776802\pi\) | |||||||
\(422\) | 1.55504 | + | 1.55504i | 0.0756981 | + | 0.0756981i | ||||
\(423\) | 0.305303 | + | 0.305303i | 0.0148444 | + | 0.0148444i | ||||
\(424\) | 7.11153i | 0.345367i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 0.281842i | − | 0.0136553i | ||||||
\(427\) | 0.445951 | − | 18.8072i | 0.0215811 | − | 0.910146i | ||||
\(428\) | −14.5429 | + | 14.5429i | −0.702957 | + | 0.702957i | ||||
\(429\) | 2.82101i | 0.136200i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −22.5558 | −1.08648 | −0.543238 | − | 0.839579i | \(-0.682802\pi\) | ||||
−0.543238 | + | 0.839579i | \(0.682802\pi\) | |||||||
\(432\) | −2.59383 | + | 2.59383i | −0.124795 | + | 0.124795i | ||||
\(433\) | 19.9639 | + | 19.9639i | 0.959405 | + | 0.959405i | 0.999208 | − | 0.0398028i | \(-0.0126730\pi\) |
−0.0398028 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(434\) | 2.23376 | − | 2.13028i | 0.107224 | − | 0.102257i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.29915 | 0.0622180 | ||||||||
\(437\) | −37.2479 | + | 37.2479i | −1.78181 | + | 1.78181i | ||||
\(438\) | −0.326732 | + | 0.326732i | −0.0156119 | + | 0.0156119i | ||||
\(439\) | 30.1943 | 1.44110 | 0.720548 | − | 0.693405i | \(-0.243890\pi\) | ||||
0.720548 | + | 0.693405i | \(0.243890\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.331777 | + | 6.99213i | −0.0157989 | + | 0.332959i | ||||
\(442\) | −0.280632 | − | 0.280632i | −0.0133483 | − | 0.0133483i | ||||
\(443\) | 12.7423 | − | 12.7423i | 0.605404 | − | 0.605404i | −0.336337 | − | 0.941742i | \(-0.609188\pi\) |
0.941742 | + | 0.336337i | \(0.109188\pi\) | |||||||
\(444\) | 0.803607 | 0.0381375 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.452737i | 0.0214377i | ||||||||
\(447\) | −2.22112 | + | 2.22112i | −0.105056 | + | 0.105056i | ||||
\(448\) | −0.419669 | + | 17.6988i | −0.0198275 | + | 0.836191i | ||||
\(449\) | 30.4170i | 1.43547i | 0.696318 | + | 0.717734i | \(0.254820\pi\) | ||||
−0.696318 | + | 0.717734i | \(0.745180\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.4207i | 1.43245i | ||||||||
\(452\) | −6.60347 | − | 6.60347i | −0.310601 | − | 0.310601i | ||||
\(453\) | 10.4114 | + | 10.4114i | 0.489170 | + | 0.489170i | ||||
\(454\) | −1.38802 | −0.0651432 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.72637 | 0.314991 | ||||||||
\(457\) | −1.31546 | − | 1.31546i | −0.0615348 | − | 0.0615348i | 0.675670 | − | 0.737204i | \(-0.263855\pi\) |
−0.737204 | + | 0.675670i | \(0.763855\pi\) | |||||||
\(458\) | 2.17005 | + | 2.17005i | 0.101400 | + | 0.101400i | ||||
\(459\) | − | 2.37361i | − | 0.110791i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.29957i | − | 0.0605272i | −0.999542 | − | 0.0302636i | \(-0.990365\pi\) | ||
0.999542 | − | 0.0302636i | \(-0.00963467\pi\) | |||||||
\(462\) | 0.0590616 | − | 2.49083i | 0.00274779 | − | 0.115884i | ||||
\(463\) | −16.5240 | + | 16.5240i | −0.767934 | + | 0.767934i | −0.977742 | − | 0.209809i | \(-0.932716\pi\) |
0.209809 | + | 0.977742i | \(0.432716\pi\) | |||||||
\(464\) | 13.3960i | 0.621895i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.50078 | 0.254819 | ||||||||
\(467\) | −20.1009 | + | 20.1009i | −0.930157 | + | 0.930157i | −0.997715 | − | 0.0675588i | \(-0.978479\pi\) |
0.0675588 | + | 0.997715i | \(0.478479\pi\) | |||||||
\(468\) | −0.972943 | − | 0.972943i | −0.0449743 | − | 0.0449743i | ||||
\(469\) | −2.43816 | − | 2.55659i | −0.112584 | − | 0.118052i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.2643 | −0.519032 | ||||||||
\(472\) | 4.02560 | − | 4.02560i | 0.185293 | − | 0.185293i | ||||
\(473\) | −14.5566 | + | 14.5566i | −0.669313 | + | 0.669313i | ||||
\(474\) | 2.04129 | 0.0937594 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.42631 | − | 8.83562i | −0.386219 | − | 0.404980i | ||||
\(477\) | −5.39653 | − | 5.39653i | −0.247090 | − | 0.247090i | ||||
\(478\) | −0.915546 | + | 0.915546i | −0.0418761 | + | 0.0418761i | ||||
\(479\) | −11.0836 | −0.506425 | −0.253212 | − | 0.967411i | \(-0.581487\pi\) | ||||
−0.253212 | + | 0.967411i | \(0.581487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.292530i | 0.0133382i | ||||||||
\(482\) | 2.44749 | − | 2.44749i | 0.111480 | − | 0.111480i | ||||
\(483\) | −19.3018 | − | 0.457677i | −0.878261 | − | 0.0208250i | ||||
\(484\) | − | 9.50389i | − | 0.431995i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.236253i | 0.0107166i | ||||||||
\(487\) | 13.6519 | + | 13.6519i | 0.618627 | + | 0.618627i | 0.945179 | − | 0.326552i | \(-0.105887\pi\) |
−0.326552 | + | 0.945179i | \(0.605887\pi\) | |||||||
\(488\) | −4.68508 | − | 4.68508i | −0.212084 | − | 0.212084i | ||||
\(489\) | 14.7714 | 0.667986 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1155 | 1.44935 | 0.724677 | − | 0.689089i | \(-0.241989\pi\) | ||||
0.724677 | + | 0.689089i | \(0.241989\pi\) | |||||||
\(492\) | −10.4918 | − | 10.4918i | −0.473009 | − | 0.473009i | ||||
\(493\) | −6.12936 | − | 6.12936i | −0.276052 | − | 0.276052i | ||||
\(494\) | 1.20695i | 0.0543032i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.1145i | 0.813364i | ||||||||
\(497\) | 3.15541 | + | 0.0748201i | 0.141540 | + | 0.00335614i | ||||
\(498\) | 2.83255 | − | 2.83255i | 0.126930 | − | 0.126930i | ||||
\(499\) | 4.27431i | 0.191344i | 0.995413 | + | 0.0956722i | \(0.0305000\pi\) | ||||
−0.995413 | + | 0.0956722i | \(0.969500\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.55659 | 0.292927 | ||||||||
\(502\) | −3.53333 | + | 3.53333i | −0.157700 | + | 0.157700i | ||||
\(503\) | −17.5637 | − | 17.5637i | −0.783128 | − | 0.783128i | 0.197229 | − | 0.980357i | \(-0.436806\pi\) |
−0.980357 | + | 0.197229i | \(0.936806\pi\) | |||||||
\(504\) | 1.70147 | + | 1.78412i | 0.0757894 | + | 0.0794709i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.87206 | 0.305500 | ||||||||
\(507\) | −8.83822 | + | 8.83822i | −0.392519 | + | 0.392519i | ||||
\(508\) | 11.4481 | − | 11.4481i | 0.507926 | − | 0.507926i | ||||
\(509\) | −27.9162 | −1.23736 | −0.618682 | − | 0.785641i | \(-0.712333\pi\) | ||||
−0.618682 | + | 0.785641i | \(0.712333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.57125 | − | 3.74473i | −0.157983 | − | 0.165657i | ||||
\(512\) | 11.9158 | + | 11.9158i | 0.526611 | + | 0.526611i | ||||
\(513\) | −5.10425 | + | 5.10425i | −0.225358 | + | 0.225358i | ||||
\(514\) | 3.13814 | 0.138417 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 10.0409i | − | 0.442026i | ||||||
\(517\) | 1.21695 | − | 1.21695i | 0.0535212 | − | 0.0535212i | ||||
\(518\) | 0.00612451 | − | 0.258291i | 0.000269096 | − | 0.0113487i | ||||
\(519\) | − | 3.51476i | − | 0.154281i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.8647i | 1.26458i | 0.774730 | + | 0.632292i | \(0.217886\pi\) | ||||
−0.774730 | + | 0.632292i | \(0.782114\pi\) | |||||||
\(522\) | 0.610073 | + | 0.610073i | 0.0267022 | + | 0.0267022i | ||||
\(523\) | 3.54707 | + | 3.54707i | 0.155103 | + | 0.155103i | 0.780392 | − | 0.625290i | \(-0.215019\pi\) |
−0.625290 | + | 0.780392i | \(0.715019\pi\) | |||||||
\(524\) | 36.5788 | 1.59795 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.13793 | −0.224024 | ||||||||
\(527\) | −8.28829 | − | 8.28829i | −0.361043 | − | 0.361043i | ||||
\(528\) | 10.3390 | + | 10.3390i | 0.449949 | + | 0.449949i | ||||
\(529\) | − | 30.2526i | − | 1.31533i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.10959i | 0.265134i | ||||||||
\(532\) | −0.880184 | + | 37.1203i | −0.0381608 | + | 1.60937i | ||||
\(533\) | 3.81926 | − | 3.81926i | 0.165430 | − | 0.165430i | ||||
\(534\) | − | 1.84887i | − | 0.0800083i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.24424 | −0.0537432 | ||||||||
\(537\) | 15.6347 | − | 15.6347i | 0.674688 | − | 0.674688i | ||||
\(538\) | −3.83980 | − | 3.83980i | −0.165546 | − | 0.165546i | ||||
\(539\) | 27.8708 | + | 1.32247i | 1.20048 | + | 0.0569628i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.08698 | −0.175713 | −0.0878565 | − | 0.996133i | \(-0.528002\pi\) | ||||
−0.0878565 | + | 0.996133i | \(0.528002\pi\) | |||||||
\(542\) | −2.63274 | + | 2.63274i | −0.113086 | + | 0.113086i | ||||
\(543\) | 6.00000 | − | 6.00000i | 0.257485 | − | 0.257485i | ||||
\(544\) | −6.48062 | −0.277854 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.320133 | + | 0.305303i | −0.0137004 | + | 0.0130658i | ||||
\(547\) | −28.2200 | − | 28.2200i | −1.20660 | − | 1.20660i | −0.972121 | − | 0.234482i | \(-0.924661\pi\) |
−0.234482 | − | 0.972121i | \(-0.575339\pi\) | |||||||
\(548\) | 1.57863 | − | 1.57863i | 0.0674359 | − | 0.0674359i | ||||
\(549\) | 7.11047 | 0.303467 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.3613i | 1.12303i | ||||||||
\(552\) | −4.80827 | + | 4.80827i | −0.204654 | + | 0.204654i | ||||
\(553\) | −0.541896 | + | 22.8536i | −0.0230438 | + | 0.971833i | ||||
\(554\) | − | 1.60631i | − | 0.0682457i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.860184i | 0.0364799i | ||||||||
\(557\) | −28.1616 | − | 28.1616i | −1.19325 | − | 1.19325i | −0.976150 | − | 0.217096i | \(-0.930342\pi\) |
−0.217096 | − | 0.976150i | \(-0.569658\pi\) | |||||||
\(558\) | 0.824957 | + | 0.824957i | 0.0349232 | + | 0.0349232i | ||||
\(559\) | 3.65510 | 0.154594 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.46128 | −0.399455 | ||||||||
\(562\) | −1.61319 | − | 1.61319i | −0.0680482 | − | 0.0680482i | ||||
\(563\) | 27.3645 | + | 27.3645i | 1.15328 | + | 1.15328i | 0.985891 | + | 0.167386i | \(0.0535326\pi\) |
0.167386 | + | 0.985891i | \(0.446467\pi\) | |||||||
\(564\) | 0.839429i | 0.0353463i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 4.98144i | − | 0.209386i | ||||||
\(567\) | −2.64501 | − | 0.0627175i | −0.111080 | − | 0.00263389i | ||||
\(568\) | 0.786047 | − | 0.786047i | 0.0329818 | − | 0.0329818i | ||||
\(569\) | − | 17.7767i | − | 0.745240i | −0.927984 | − | 0.372620i | \(-0.878460\pi\) | ||
0.927984 | − | 0.372620i | \(-0.121540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8866 | −0.706683 | −0.353342 | − | 0.935494i | \(-0.614955\pi\) | ||||
−0.353342 | + | 0.935494i | \(0.614955\pi\) | |||||||
\(572\) | −3.87817 | + | 3.87817i | −0.162154 | + | 0.162154i | ||||
\(573\) | −10.8116 | − | 10.8116i | −0.451659 | − | 0.451659i | ||||
\(574\) | −3.45220 | + | 3.29227i | −0.144092 | + | 0.137417i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.69141 | −0.278809 | ||||||||
\(577\) | −3.89677 | + | 3.89677i | −0.162225 | + | 0.162225i | −0.783552 | − | 0.621327i | \(-0.786594\pi\) |
0.621327 | + | 0.783552i | \(0.286594\pi\) | |||||||
\(578\) | −1.89875 | + | 1.89875i | −0.0789776 | + | 0.0789776i | ||||
\(579\) | −12.6259 | −0.524715 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.9604 | + | 32.4643i | 1.28445 | + | 1.34685i | ||||
\(582\) | 1.75694 | + | 1.75694i | 0.0728276 | + | 0.0728276i | ||||
\(583\) | −21.5107 | + | 21.5107i | −0.890881 | + | 0.890881i | ||||
\(584\) | −1.82249 | −0.0754151 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 1.60118i | − | 0.0661443i | ||||||
\(587\) | 15.1058 | − | 15.1058i | 0.623484 | − | 0.623484i | −0.322937 | − | 0.946420i | \(-0.604670\pi\) |
0.946420 | + | 0.322937i | \(0.104670\pi\) | |||||||
\(588\) | −10.0685 | + | 9.15630i | −0.415219 | + | 0.377599i | ||||
\(589\) | 35.6465i | 1.46879i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 3.80020i | − | 0.156319i | ||||||
\(592\) | 1.07213 | + | 1.07213i | 0.0440642 | + | 0.0440642i | ||||
\(593\) | 3.43032 | + | 3.43032i | 0.140866 | + | 0.140866i | 0.774023 | − | 0.633157i | \(-0.218241\pi\) |
−0.633157 | + | 0.774023i | \(0.718241\pi\) | |||||||
\(594\) | 0.941708 | 0.0386388 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.10696 | −0.250151 | ||||||||
\(597\) | −0.436028 | − | 0.436028i | −0.0178454 | − | 0.0178454i | ||||
\(598\) | −0.862773 | − | 0.862773i | −0.0352814 | − | 0.0352814i | ||||
\(599\) | 10.1010i | 0.412714i | 0.978477 | + | 0.206357i | \(0.0661608\pi\) | ||||
−0.978477 | + | 0.206357i | \(0.933839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 38.4063i | − | 1.56663i | −0.621628 | − | 0.783313i | \(-0.713528\pi\) | ||
0.621628 | − | 0.783313i | \(-0.286472\pi\) | |||||||
\(602\) | −3.22730 | − | 0.0765245i | −0.131535 | − | 0.00311891i | ||||
\(603\) | 0.944185 | − | 0.944185i | 0.0384502 | − | 0.0384502i | ||||
\(604\) | 28.6261i | 1.16478i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.49225 | −0.0606185 | ||||||||
\(607\) | −10.2931 | + | 10.2931i | −0.417783 | + | 0.417783i | −0.884439 | − | 0.466656i | \(-0.845459\pi\) |
0.466656 | + | 0.884439i | \(0.345459\pi\) | |||||||
\(608\) | 13.9360 | + | 13.9360i | 0.565180 | + | 0.565180i | ||||
\(609\) | −6.99213 | + | 6.66822i | −0.283336 | + | 0.270210i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.305570 | −0.0123621 | ||||||||
\(612\) | 3.26312 | − | 3.26312i | 0.131904 | − | 0.131904i | ||||
\(613\) | 14.4155 | − | 14.4155i | 0.582235 | − | 0.582235i | −0.353282 | − | 0.935517i | \(-0.614934\pi\) |
0.935517 | + | 0.353282i | \(0.114934\pi\) | |||||||
\(614\) | −3.29121 | −0.132822 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.11153 | − | 6.78209i | 0.286532 | − | 0.273258i | ||||
\(617\) | 25.4196 | + | 25.4196i | 1.02336 | + | 1.02336i | 0.999721 | + | 0.0236346i | \(0.00752382\pi\) |
0.0236346 | + | 0.999721i | \(0.492476\pi\) | |||||||
\(618\) | 2.96283 | − | 2.96283i | 0.119183 | − | 0.119183i | ||||
\(619\) | −11.1991 | −0.450129 | −0.225064 | − | 0.974344i | \(-0.572259\pi\) | ||||
−0.225064 | + | 0.974344i | \(0.572259\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 7.29744i | − | 0.292836i | ||||||
\(622\) | 4.56168 | − | 4.56168i | 0.182907 | − | 0.182907i | ||||
\(623\) | 20.6993 | + | 0.490815i | 0.829301 | + | 0.0196641i | ||||
\(624\) | − | 2.59609i | − | 0.103927i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 6.18373i | − | 0.247152i | ||||||
\(627\) | 20.3457 | + | 20.3457i | 0.812527 | + | 0.812527i | ||||
\(628\) | −15.4856 | − | 15.4856i | −0.617942 | − | 0.617942i | ||||
\(629\) | −0.981107 | −0.0391193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.2015 | 0.844020 | 0.422010 | − | 0.906591i | \(-0.361325\pi\) | ||||
0.422010 | + | 0.906591i | \(0.361325\pi\) | |||||||
\(632\) | 5.69306 | + | 5.69306i | 0.226458 | + | 0.226458i | ||||
\(633\) | −6.58210 | − | 6.58210i | −0.261615 | − | 0.261615i | ||||
\(634\) | 7.31014i | 0.290323i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 14.8377i | − | 0.588353i | ||||||
\(637\) | −3.33309 | − | 3.66516i | −0.132062 | − | 0.145219i | ||||
\(638\) | 2.43176 | − | 2.43176i | 0.0962745 | − | 0.0962745i | ||||
\(639\) | 1.19297i | 0.0471931i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.8969 | −1.18086 | −0.590428 | − | 0.807090i | \(-0.701041\pi\) | ||||
−0.590428 | + | 0.807090i | \(0.701041\pi\) | |||||||
\(642\) | −1.76722 | + | 1.76722i | −0.0697465 | + | 0.0697465i | ||||
\(643\) | −11.2813 | − | 11.2813i | −0.444891 | − | 0.444891i | 0.448761 | − | 0.893652i | \(-0.351866\pi\) |
−0.893652 | + | 0.448761i | \(0.851866\pi\) | |||||||
\(644\) | −25.9059 | − | 27.1642i | −1.02083 | − | 1.07042i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.04794 | −0.159264 | ||||||||
\(647\) | 26.2395 | − | 26.2395i | 1.03158 | − | 1.03158i | 0.0320982 | − | 0.999485i | \(-0.489781\pi\) |
0.999485 | − | 0.0320982i | \(-0.0102189\pi\) | |||||||
\(648\) | −0.658899 | + | 0.658899i | −0.0258840 | + | 0.0258840i | ||||
\(649\) | 24.3530 | 0.955937 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.45495 | + | 9.01695i | −0.370569 | + | 0.353402i | ||||
\(652\) | 20.3069 | + | 20.3069i | 0.795281 | + | 0.795281i | ||||
\(653\) | 1.97641 | − | 1.97641i | 0.0773427 | − | 0.0773427i | −0.667377 | − | 0.744720i | \(-0.732583\pi\) |
0.744720 | + | 0.667377i | \(0.232583\pi\) | |||||||
\(654\) | 0.157870 | 0.00617319 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 27.9953i | − | 1.09303i | ||||||
\(657\) | 1.38298 | − | 1.38298i | 0.0539552 | − | 0.0539552i | ||||
\(658\) | 0.269805 | + | 0.00639752i | 0.0105181 | + | 0.000249401i | ||||
\(659\) | − | 15.1044i | − | 0.588385i | −0.955746 | − | 0.294193i | \(-0.904949\pi\) | ||
0.955746 | − | 0.294193i | \(-0.0950507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1.10054i | − | 0.0428062i | −0.999771 | − | 0.0214031i | \(-0.993187\pi\) | ||
0.999771 | − | 0.0214031i | \(-0.00681333\pi\) | |||||||
\(662\) | −2.78838 | − | 2.78838i | −0.108374 | − | 0.108374i | ||||
\(663\) | 1.18785 | + | 1.18785i | 0.0461321 | + | 0.0461321i | ||||
\(664\) | 15.7998 | 0.613150 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.0976524 | 0.00378395 | ||||||||
\(667\) | −18.8441 | − | 18.8441i | −0.729646 | − | 0.729646i | ||||
\(668\) | 9.01365 | + | 9.01365i | 0.348749 | + | 0.348749i | ||||
\(669\) | − | 1.91633i | − | 0.0740894i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 28.3425i | − | 1.09415i | ||||||
\(672\) | −0.171236 | + | 7.22160i | −0.00660558 | + | 0.278579i | ||||
\(673\) | 11.4381 | − | 11.4381i | 0.440906 | − | 0.440906i | −0.451411 | − | 0.892316i | \(-0.649079\pi\) |
0.892316 | + | 0.451411i | \(0.149079\pi\) | |||||||
\(674\) | − | 0.848737i | − | 0.0326921i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −24.3006 | −0.934639 | ||||||||
\(677\) | 24.6007 | − | 24.6007i | 0.945481 | − | 0.945481i | −0.0531077 | − | 0.998589i | \(-0.516913\pi\) |
0.998589 | + | 0.0531077i | \(0.0169127\pi\) | |||||||
\(678\) | −0.802438 | − | 0.802438i | −0.0308175 | − | 0.0308175i | ||||
\(679\) | −20.1366 | + | 19.2037i | −0.772770 | + | 0.736972i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.87517 | 0.225137 | ||||||||
\(682\) | 3.28830 | − | 3.28830i | 0.125915 | − | 0.125915i | ||||
\(683\) | 13.8654 | − | 13.8654i | 0.530543 | − | 0.530543i | −0.390191 | − | 0.920734i | \(-0.627591\pi\) |
0.920734 | + | 0.390191i | \(0.127591\pi\) | |||||||
\(684\) | −14.0341 | −0.536607 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.86624 | + | 3.30596i | 0.109433 | + | 0.126222i | ||||
\(687\) | −9.18531 | − | 9.18531i | −0.350442 | − | 0.350442i | ||||
\(688\) | 13.3960 | − | 13.3960i | 0.510719 | − | 0.510719i | ||||
\(689\) | 5.40125 | 0.205771 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.4060i | − | 0.471947i | −0.971759 | − | 0.235974i | \(-0.924172\pi\) | ||
0.971759 | − | 0.235974i | \(-0.0758279\pi\) | |||||||
\(692\) | 4.83190 | − | 4.83190i | 0.183681 | − | 0.183681i | ||||
\(693\) | −0.249993 | + | 10.5431i | −0.00949646 | + | 0.400498i | ||||
\(694\) | − | 4.57667i | − | 0.173728i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.40294i | 0.128988i | ||||||||
\(697\) | 12.8093 | + | 12.8093i | 0.485186 | + | 0.485186i | ||||
\(698\) | 0.0849648 | + | 0.0849648i | 0.00321597 | + | 0.00321597i | ||||
\(699\) | −23.2835 | −0.880661 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.45193 | 0.0548388 | 0.0274194 | − | 0.999624i | \(-0.491271\pi\) | ||||
0.0274194 | + | 0.999624i | \(0.491271\pi\) | |||||||
\(702\) | −0.118230 | − | 0.118230i | −0.00446229 | − | 0.00446229i | ||||
\(703\) | 2.10979 | + | 2.10979i | 0.0795720 | + | 0.0795720i | ||||
\(704\) | 26.6721i | 1.00524i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 3.64907i | − | 0.137335i | ||||||
\(707\) | 0.396144 | − | 16.7067i | 0.0148985 | − | 0.628322i | ||||
\(708\) | −8.39914 | + | 8.39914i | −0.315659 | + | 0.315659i | ||||
\(709\) | − | 48.5284i | − | 1.82252i | −0.411827 | − | 0.911262i | \(-0.635109\pi\) | ||
0.411827 | − | 0.911262i | \(-0.364891\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.64027 | −0.324035 | ||||||||
\(712\) | 5.15642 | − | 5.15642i | 0.193245 | − | 0.193245i | ||||
\(713\) | −25.4815 | − | 25.4815i | −0.954290 | − | 0.954290i | ||||
\(714\) | −1.02395 | − | 1.07368i | −0.0383202 | − | 0.0401816i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.9876 | 1.60652 | ||||||||
\(717\) | 3.87528 | − | 3.87528i | 0.144725 | − | 0.144725i | ||||
\(718\) | 2.67056 | − | 2.67056i | 0.0996644 | − | 0.0996644i | ||||
\(719\) | 43.5872 | 1.62553 | 0.812764 | − | 0.582593i | \(-0.197962\pi\) | ||||
0.812764 | + | 0.582593i | \(0.197962\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 32.3844 | + | 33.9575i | 1.20606 | + | 1.26464i | ||||
\(722\) | 5.53068 | + | 5.53068i | 0.205831 | + | 0.205831i | ||||
\(723\) | −10.3596 | + | 10.3596i | −0.385279 | + | 0.385279i | ||||
\(724\) | 16.4970 | 0.613104 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 1.15489i | − | 0.0428620i | ||||||
\(727\) | −10.4498 | + | 10.4498i | −0.387563 | + | 0.387563i | −0.873817 | − | 0.486254i | \(-0.838363\pi\) |
0.486254 | + | 0.873817i | \(0.338363\pi\) | |||||||
\(728\) | −1.74432 | − | 0.0413607i | −0.0646487 | − | 0.00153293i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.2587i | 0.453405i | ||||||||
\(732\) | 9.77509 | + | 9.77509i | 0.361298 | + | 0.361298i | ||||
\(733\) | −18.8687 | − | 18.8687i | −0.696933 | − | 0.696933i | 0.266815 | − | 0.963748i | \(-0.414029\pi\) |
−0.963748 | + | 0.266815i | \(0.914029\pi\) | |||||||
\(734\) | −0.136998 | −0.00505669 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −19.9240 | −0.734409 | ||||||||
\(737\) | −3.76354 | − | 3.76354i | −0.138632 | − | 0.138632i | ||||
\(738\) | −1.27494 | − | 1.27494i | −0.0469313 | − | 0.0469313i | ||||
\(739\) | 20.9689i | 0.771354i | 0.922634 | + | 0.385677i | \(0.126032\pi\) | ||||
−0.922634 | + | 0.385677i | \(0.873968\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 5.10872i | − | 0.187673i | ||||||
\(742\) | −4.76906 | − | 0.113082i | −0.175078 | − | 0.00415138i | ||||
\(743\) | −9.18724 | + | 9.18724i | −0.337047 | + | 0.337047i | −0.855255 | − | 0.518208i | \(-0.826599\pi\) |
0.518208 | + | 0.855255i | \(0.326599\pi\) | |||||||
\(744\) | 4.60155i | 0.168701i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.15100 | 0.0421412 | ||||||||
\(747\) | −11.9895 | + | 11.9895i | −0.438673 | + | 0.438673i | ||||
\(748\) | −13.0069 | − | 13.0069i | −0.475578 | − | 0.475578i | ||||
\(749\) | −19.3160 | − | 20.2543i | −0.705793 | − | 0.740077i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1969 | 0.408579 | 0.204290 | − | 0.978910i | \(-0.434512\pi\) | ||||
0.204290 | + | 0.978910i | \(0.434512\pi\) | |||||||
\(752\) | −1.11992 | + | 1.11992i | −0.0408393 | + | 0.0408393i | ||||
\(753\) | 14.9557 | − | 14.9557i | 0.545017 | − | 0.545017i | ||||
\(754\) | −0.610607 | −0.0222370 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.54999 | − | 3.72244i | −0.129112 | − | 0.135384i | ||||
\(757\) | 13.9324 | + | 13.9324i | 0.506383 | + | 0.506383i | 0.913414 | − | 0.407031i | \(-0.133436\pi\) |
−0.407031 | + | 0.913414i | \(0.633436\pi\) | |||||||
\(758\) | 2.15801 | − | 2.15801i | 0.0783824 | − | 0.0783824i | ||||
\(759\) | −29.0877 | −1.05582 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 8.78825i | − | 0.318574i | −0.987232 | − | 0.159287i | \(-0.949081\pi\) | ||
0.987232 | − | 0.159287i | \(-0.0509195\pi\) | |||||||
\(762\) | 1.39114 | − | 1.39114i | 0.0503958 | − | 0.0503958i | ||||
\(763\) | −0.0419093 | + | 1.76746i | −0.00151722 | + | 0.0639862i | ||||
\(764\) | − | 29.7263i | − | 1.07546i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.36684i | 0.121649i | ||||||||
\(767\) | −3.05747 | − | 3.05747i | −0.110399 | − | 0.110399i | ||||
\(768\) | −8.28678 | − | 8.28678i | −0.299023 | − | 0.299023i | ||||
\(769\) | −11.2183 | −0.404543 | −0.202271 | − | 0.979330i | \(-0.564832\pi\) | ||||
−0.202271 | + | 0.979330i | \(0.564832\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.2830 | −0.478374 | ||||||||
\(772\) | −17.3574 | − | 17.3574i | −0.624708 | − | 0.624708i | ||||
\(773\) | −21.5065 | − | 21.5065i | −0.773535 | − | 0.773535i | 0.205188 | − | 0.978723i | \(-0.434219\pi\) |
−0.978723 | + | 0.205188i | \(0.934219\pi\) | |||||||
\(774\) | − | 1.22015i | − | 0.0438572i | ||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.80008i | 0.351802i | ||||||||
\(777\) | −0.0259236 | + | 1.09328i | −0.000930003 | + | 0.0392214i | ||||
\(778\) | −4.06447 | + | 4.06447i | −0.145718 | + | 0.145718i | ||||
\(779\) | − | 55.0905i | − | 1.97382i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.75520 | 0.170155 | ||||||||
\(782\) | 2.89362 | − | 2.89362i | 0.103476 | − | 0.103476i | ||||
\(783\) | −2.58229 | − | 2.58229i | −0.0922835 | − | 0.0922835i | ||||
\(784\) | −25.6487 | − | 1.21703i | −0.916025 | − | 0.0434654i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.44496 | 0.158547 | ||||||||
\(787\) | −37.4673 | + | 37.4673i | −1.33557 | + | 1.33557i | −0.435262 | + | 0.900304i | \(0.643344\pi\) |
−0.900304 | + | 0.435262i | \(0.856656\pi\) | |||||||
\(788\) | 5.22431 | − | 5.22431i | 0.186108 | − | 0.186108i | ||||
\(789\) | 21.7476 | 0.774235 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.19686 | − | 8.77082i | 0.327003 | − | 0.311854i | ||||
\(792\) | 2.62639 | + | 2.62639i | 0.0933246 | + | 0.0933246i | ||||
\(793\) | −3.55834 | + | 3.55834i | −0.126360 | + | 0.126360i | ||||
\(794\) | −2.27408 | −0.0807039 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 1.19886i | − | 0.0424923i | ||||||
\(797\) | −6.96365 | + | 6.96365i | −0.246665 | + | 0.246665i | −0.819601 | − | 0.572935i | \(-0.805805\pi\) |
0.572935 | + | 0.819601i | \(0.305805\pi\) | |||||||
\(798\) | −0.106958 | + | 4.51077i | −0.00378627 | + | 0.159680i | ||||
\(799\) | − | 1.02484i | − | 0.0362563i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.82581i | 0.276511i | ||||||||
\(802\) | −1.47525 | − | 1.47525i | −0.0520930 | − | 0.0520930i | ||||
\(803\) | −5.51258 | − | 5.51258i | −0.194535 | − | 0.194535i | ||||
\(804\) | 2.59603 | 0.0915549 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.825679 | −0.0290833 | ||||||||
\(807\) | 16.2530 | + | 16.2530i | 0.572131 | + | 0.572131i | ||||
\(808\) | −4.16182 | − | 4.16182i | −0.146412 | − | 0.146412i | ||||
\(809\) | − | 42.2409i | − | 1.48511i | −0.669784 | − | 0.742556i | \(-0.733613\pi\) | ||
0.669784 | − | 0.742556i | \(-0.266387\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 34.9480i | − | 1.22719i | −0.789620 | − | 0.613596i | \(-0.789723\pi\) | ||
0.789620 | − | 0.613596i | \(-0.210277\pi\) | |||||||
\(812\) | −18.7795 | − | 0.445293i | −0.659032 | − | 0.0156267i | ||||
\(813\) | 11.1438 | − | 11.1438i | 0.390828 | − | 0.390828i | ||||
\(814\) | − | 0.389245i | − | 0.0136430i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.70695 | 0.304804 | ||||||||
\(817\) | 26.3613 | − | 26.3613i | 0.922266 | − | 0.922266i | ||||
\(818\) | −3.87544 | − | 3.87544i | −0.135502 | − | 0.135502i | ||||
\(819\) | 1.35505 | − | 1.29227i | 0.0473492 | − | 0.0451557i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.13417 | −0.144284 | −0.0721418 | − | 0.997394i | \(-0.522983\pi\) | ||||
−0.0721418 | + | 0.997394i | \(0.522983\pi\) | |||||||
\(822\) | 0.191832 | − | 0.191832i | 0.00669090 | − | 0.00669090i | ||||
\(823\) | 5.72102 | − | 5.72102i | 0.199422 | − | 0.199422i | −0.600330 | − | 0.799752i | \(-0.704964\pi\) |
0.799752 | + | 0.600330i | \(0.204964\pi\) | |||||||
\(824\) | 16.5264 | 0.575726 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.63560 | + | 2.76362i | 0.0917041 | + | 0.0961587i | ||||
\(827\) | −17.0630 | − | 17.0630i | −0.593339 | − | 0.593339i | 0.345193 | − | 0.938532i | \(-0.387813\pi\) |
−0.938532 | + | 0.345193i | \(0.887813\pi\) | |||||||
\(828\) | 10.0321 | − | 10.0321i | 0.348640 | − | 0.348640i | ||||
\(829\) | −37.7146 | −1.30988 | −0.654940 | − | 0.755680i | \(-0.727306\pi\) | ||||
−0.654940 | + | 0.755680i | \(0.727306\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.79913i | 0.235859i | ||||||||
\(832\) | 3.34863 | − | 3.34863i | 0.116093 | − | 0.116093i | ||||
\(833\) | 12.2924 | − | 11.1787i | 0.425908 | − | 0.387320i | ||||
\(834\) | 0.104527i | 0.00361949i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 55.9402i | 1.93473i | ||||||||
\(837\) | −3.49184 | − | 3.49184i | −0.120696 | − | 0.120696i | ||||
\(838\) | 2.17828 | + | 2.17828i | 0.0752476 | + | 0.0752476i | ||||
\(839\) | 22.3652 | 0.772133 | 0.386066 | − | 0.922471i | \(-0.373834\pi\) | ||||
0.386066 | + | 0.922471i | \(0.373834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6636 | 0.540123 | ||||||||
\(842\) | −5.23801 | − | 5.23801i | −0.180514 | − | 0.180514i | ||||
\(843\) | 6.82823 | + | 6.82823i | 0.235177 | + | 0.235177i | ||||
\(844\) | − | 18.0974i | − | 0.622939i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.102005i | 0.00350702i | ||||||||
\(847\) | 12.9298 | + | 0.306586i | 0.444272 | + | 0.0105344i | ||||
\(848\) | 19.7957 | − | 19.7957i | 0.679786 | − | 0.679786i | ||||
\(849\) | 21.0852i | 0.723643i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.01631 | −0.103398 | ||||||||
\(852\) | −1.64003 | + | 1.64003i | −0.0561865 | + | 0.0561865i | ||||
\(853\) | −24.1276 | − | 24.1276i | −0.826114 | − | 0.826114i | 0.160863 | − | 0.986977i | \(-0.448572\pi\) |
−0.986977 | + | 0.160863i | \(0.948572\pi\) | |||||||
\(854\) | 3.21636 | − | 3.06736i | 0.110062 | − | 0.104963i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.85740 | −0.336919 | ||||||||
\(857\) | 1.53096 | − | 1.53096i | 0.0522968 | − | 0.0522968i | −0.680475 | − | 0.732772i | \(-0.738226\pi\) |
0.732772 | + | 0.680475i | \(0.238226\pi\) | |||||||
\(858\) | −0.471266 | + | 0.471266i | −0.0160888 | + | 0.0160888i | ||||
\(859\) | −41.8095 | −1.42652 | −0.713261 | − | 0.700899i | \(-0.752782\pi\) | ||||
−0.713261 | + | 0.700899i | \(0.752782\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.6123 | − | 13.9354i | 0.497986 | − | 0.474917i | ||||
\(862\) | −3.76808 | − | 3.76808i | −0.128341 | − | 0.128341i | ||||
\(863\) | 14.0647 | − | 14.0647i | 0.478770 | − | 0.478770i | −0.425968 | − | 0.904738i | \(-0.640067\pi\) |
0.904738 | + | 0.425968i | \(0.140067\pi\) | |||||||
\(864\) | −2.73028 | −0.0928859 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.67018i | 0.226662i | ||||||||
\(867\) | 8.03695 | − | 8.03695i | 0.272949 | − | 0.272949i | ||||
\(868\) | −25.3942 | − | 0.602138i | −0.861935 | − | 0.0204379i | ||||
\(869\) | 34.4403i | 1.16831i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.945011i | 0.0320205i | ||||||||
\(872\) | 0.440292 | + | 0.440292i | 0.0149102 | + | 0.0149102i | ||||
\(873\) | −7.43671 | − | 7.43671i | −0.251694 | − | 0.251694i | ||||
\(874\) | −12.4450 | −0.420958 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.80249 | 0.128474 | ||||||||
\(877\) | 39.3844 | + | 39.3844i | 1.32992 | + | 1.32992i | 0.905438 | + | 0.424477i | \(0.139542\pi\) |
0.424477 | + | 0.905438i | \(0.360458\pi\) | |||||||
\(878\) | 5.04414 | + | 5.04414i | 0.170231 | + | 0.170231i | ||||
\(879\) | 6.77742i | 0.228597i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 25.7205i | − | 0.866546i | −0.901263 | − | 0.433273i | \(-0.857359\pi\) | ||
0.901263 | − | 0.433273i | \(-0.142641\pi\) | |||||||
\(882\) | −1.22350 | + | 1.11265i | −0.0411975 | + | 0.0374649i | ||||
\(883\) | 25.0968 | − | 25.0968i | 0.844574 | − | 0.844574i | −0.144876 | − | 0.989450i | \(-0.546278\pi\) |
0.989450 | + | 0.144876i | \(0.0462784\pi\) | |||||||
\(884\) | 3.26597i | 0.109846i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.25735 | 0.143028 | ||||||||
\(887\) | 37.8947 | − | 37.8947i | 1.27238 | − | 1.27238i | 0.327541 | − | 0.944837i | \(-0.393780\pi\) |
0.944837 | − | 0.327541i | \(-0.106220\pi\) | |||||||
\(888\) | 0.272349 | + | 0.272349i | 0.00913942 | + | 0.00913942i | ||||
\(889\) | 15.2055 | + | 15.9441i | 0.509975 | + | 0.534748i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.98602 | −0.133537 | ||||||||
\(892\) | 2.63446 | − | 2.63446i | 0.0882083 | − | 0.0882083i | ||||
\(893\) | −2.20383 | + | 2.20383i | −0.0737484 | + | 0.0737484i | ||||
\(894\) | −0.742103 | −0.0248196 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.4819 | + | 12.8573i | −0.450397 | + | 0.429533i | ||||
\(897\) | 3.65191 | + | 3.65191i | 0.121934 | + | 0.121934i | ||||
\(898\) | −5.08134 | + | 5.08134i | −0.169566 | + | 0.169566i | ||||
\(899\) | −18.0339 | −0.601464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.1150i | 0.603499i | ||||||||
\(902\) | −5.08195 | + | 5.08195i | −0.169211 | + | 0.169211i | ||||
\(903\) | 13.6604 | + | 0.323910i | 0.454588 | + | 0.0107790i | ||||
\(904\) | − | 4.47594i | − | 0.148867i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.47857i | 0.115568i | ||||||||
\(907\) | 30.5961 | + | 30.5961i | 1.01593 | + | 1.01593i | 0.999871 | + | 0.0160555i | \(0.00511086\pi\) |
0.0160555 | + | 0.999871i | \(0.494889\pi\) | |||||||
\(908\) | 8.07687 | + | 8.07687i | 0.268040 | + | 0.268040i | ||||
\(909\) | 6.31633 | 0.209499 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.7843 | 0.688614 | 0.344307 | − | 0.938857i | \(-0.388114\pi\) | ||||
0.344307 | + | 0.938857i | \(0.388114\pi\) | |||||||
\(912\) | −18.7235 | − | 18.7235i | −0.619998 | − | 0.619998i | ||||
\(913\) | 47.7905 | + | 47.7905i | 1.58163 | + | 1.58163i | ||||
\(914\) | − | 0.439512i | − | 0.0145378i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 25.2550i | − | 0.834447i | ||||||
\(917\) | −1.17999 | + | 49.7643i | −0.0389669 | + | 1.64336i | ||||
\(918\) | 0.396526 | − | 0.396526i | 0.0130873 | − | 0.0130873i | ||||
\(919\) | 47.6045i | 1.57033i | 0.619288 | + | 0.785164i | \(0.287421\pi\) | ||||
−0.619288 | + | 0.785164i | \(0.712579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.9309 | 0.459038 | ||||||||
\(922\) | 0.217101 | − | 0.217101i | 0.00714985 | − | 0.00714985i | ||||
\(923\) | −0.597007 | − | 0.597007i | −0.0196507 | − | 0.0196507i | ||||
\(924\) | −14.8377 | + | 14.1504i | −0.488125 | + | 0.465512i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.52085 | −0.181426 | ||||||||
\(927\) | −12.5410 | + | 12.5410i | −0.411899 | + | 0.411899i | ||||
\(928\) | −7.05036 | + | 7.05036i | −0.231440 | + | 0.231440i | ||||
\(929\) | 40.6532 | 1.33379 | 0.666895 | − | 0.745152i | \(-0.267623\pi\) | ||||
0.666895 | + | 0.745152i | \(0.267623\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −50.4727 | − | 2.39493i | −1.65418 | − | 0.0784906i | ||||
\(932\) | −32.0088 | − | 32.0088i | −1.04848 | − | 1.04848i | ||||
\(933\) | −19.3085 | + | 19.3085i | −0.632132 | + | 0.632132i | ||||
\(934\) | −6.71593 | −0.219752 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 0.659476i | − | 0.0215556i | ||||||
\(937\) | 8.25994 | − | 8.25994i | 0.269841 | − | 0.269841i | −0.559195 | − | 0.829036i | \(-0.688890\pi\) |
0.829036 | + | 0.559195i | \(0.188890\pi\) | |||||||
\(938\) | 0.0197851 | − | 0.834403i | 0.000646005 | − | 0.0272442i | ||||
\(939\) | 26.1742i | 0.854163i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28.7824i | − | 0.938281i | −0.883124 | − | 0.469140i | \(-0.844564\pi\) | ||
0.883124 | − | 0.469140i | \(-0.155436\pi\) | |||||||
\(942\) | −1.88177 | − | 1.88177i | −0.0613114 | − | 0.0613114i | ||||
\(943\) | 39.3808 | + | 39.3808i | 1.28242 | + | 1.28242i | ||||
\(944\) | −22.4113 | −0.729427 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.86353 | −0.158127 | ||||||||
\(947\) | −4.26936 | − | 4.26936i | −0.138736 | − | 0.138736i | 0.634328 | − | 0.773064i | \(-0.281277\pi\) |
−0.773064 | + | 0.634328i | \(0.781277\pi\) | |||||||
\(948\) | −11.8782 | − | 11.8782i | −0.385785 | − | 0.385785i | ||||
\(949\) | 1.38419i | 0.0449327i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 30.9421i | − | 1.00336i | ||||||
\(952\) | 0.138718 | − | 5.85020i | 0.00449588 | − | 0.189606i | ||||
\(953\) | −31.8382 | + | 31.8382i | −1.03134 | + | 1.03134i | −0.0318472 | + | 0.999493i | \(0.510139\pi\) |
−0.999493 | + | 0.0318472i | \(0.989861\pi\) | |||||||
\(954\) | − | 1.80304i | − | 0.0583757i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.6551 | 0.344609 | ||||||||
\(957\) | −10.2931 | + | 10.2931i | −0.332728 | + | 0.332728i | ||||
\(958\) | −1.85159 | − | 1.85159i | −0.0598221 | − | 0.0598221i | ||||
\(959\) | 2.09676 | + | 2.19861i | 0.0677079 | + | 0.0709968i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.61406 | 0.213357 | ||||||||
\(962\) | −0.0488689 | + | 0.0488689i | −0.00157560 | + | 0.00157560i | ||||
\(963\) | 7.48020 | − | 7.48020i | 0.241046 | − | 0.241046i | ||||
\(964\) | −28.4837 | −0.917399 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.14802 | − | 3.30093i | −0.101286 | − | 0.106206i | ||||
\(967\) | 17.5518 | + | 17.5518i | 0.564429 | + | 0.564429i | 0.930562 | − | 0.366134i | \(-0.119319\pi\) |
−0.366134 | + | 0.930562i | \(0.619319\pi\) | |||||||
\(968\) | 3.22094 | − | 3.22094i | 0.103525 | − | 0.103525i | ||||
\(969\) | 17.1339 | 0.550421 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0930634i | 0.00298655i | 0.999999 | + | 0.00149327i | \(0.000475324\pi\) | ||||
−0.999999 | + | 0.00149327i | \(0.999525\pi\) | |||||||
\(972\) | 1.37475 | − | 1.37475i | 0.0440950 | − | 0.0440950i | ||||
\(973\) | −1.17026 | − | 0.0277487i | −0.0375167 | − | 0.000889582i | ||||
\(974\) | 4.56126i | 0.146152i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 26.0828i | 0.834889i | ||||||||
\(977\) | −5.19792 | − | 5.19792i | −0.166296 | − | 0.166296i | 0.619053 | − | 0.785349i | \(-0.287517\pi\) |
−0.785349 | + | 0.619053i | \(0.787517\pi\) | |||||||
\(978\) | 2.46765 | + | 2.46765i | 0.0789067 | + | 0.0789067i | ||||
\(979\) | 31.1938 | 0.996959 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.668223 | −0.0213347 | ||||||||
\(982\) | 5.36509 | + | 5.36509i | 0.171207 | + | 0.171207i | ||||
\(983\) | 30.3939 | + | 30.3939i | 0.969415 | + | 0.969415i | 0.999546 | − | 0.0301305i | \(-0.00959230\pi\) |
−0.0301305 | + | 0.999546i | \(0.509592\pi\) | |||||||
\(984\) | − | 7.11153i | − | 0.226707i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 2.04789i | − | 0.0652181i | ||||||
\(987\) | −1.14202 | − | 0.0270792i | −0.0363509 | − | 0.000861939i | ||||
\(988\) | 7.02319 | − | 7.02319i | 0.223437 | − | 0.223437i | ||||
\(989\) | 37.6882i | 1.19842i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.2648 | 1.08846 | 0.544228 | − | 0.838937i | \(-0.316823\pi\) | ||||
0.544228 | + | 0.838937i | \(0.316823\pi\) | |||||||
\(992\) | −9.53370 | + | 9.53370i | −0.302695 | + | 0.302695i | ||||
\(993\) | 11.8025 | + | 11.8025i | 0.374542 | + | 0.374542i | ||||
\(994\) | 0.514631 | + | 0.539630i | 0.0163231 | + | 0.0171160i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −32.9651 | −1.04454 | ||||||||
\(997\) | 21.1809 | − | 21.1809i | 0.670805 | − | 0.670805i | −0.287097 | − | 0.957902i | \(-0.592690\pi\) |
0.957902 | + | 0.287097i | \(0.0926901\pi\) | |||||||
\(998\) | −0.714048 | + | 0.714048i | −0.0226028 | + | 0.0226028i | ||||
\(999\) | −0.413339 | −0.0130775 |
(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 | 525.2.m.b.307.5 | 16 | ||
5.2 | odd | 4 | 105.2.m.a.13.3 | ✓ | 16 | ||
5.3 | odd | 4 | inner | 525.2.m.b.118.6 | 16 | ||
5.4 | even | 2 | 105.2.m.a.97.4 | yes | 16 | ||
7.6 | odd | 2 | inner | 525.2.m.b.307.6 | 16 | ||
15.2 | even | 4 | 315.2.p.e.118.6 | 16 | |||
15.14 | odd | 2 | 315.2.p.e.307.5 | 16 | |||
20.7 | even | 4 | 1680.2.cz.d.433.5 | 16 | |||
20.19 | odd | 2 | 1680.2.cz.d.97.4 | 16 | |||
35.2 | odd | 12 | 735.2.v.a.178.5 | 32 | |||
35.4 | even | 6 | 735.2.v.a.607.6 | 32 | |||
35.9 | even | 6 | 735.2.v.a.472.3 | 32 | |||
35.12 | even | 12 | 735.2.v.a.178.6 | 32 | |||
35.13 | even | 4 | inner | 525.2.m.b.118.5 | 16 | ||
35.17 | even | 12 | 735.2.v.a.313.3 | 32 | |||
35.19 | odd | 6 | 735.2.v.a.472.4 | 32 | |||
35.24 | odd | 6 | 735.2.v.a.607.5 | 32 | |||
35.27 | even | 4 | 105.2.m.a.13.4 | yes | 16 | ||
35.32 | odd | 12 | 735.2.v.a.313.4 | 32 | |||
35.34 | odd | 2 | 105.2.m.a.97.3 | yes | 16 | ||
105.62 | odd | 4 | 315.2.p.e.118.5 | 16 | |||
105.104 | even | 2 | 315.2.p.e.307.6 | 16 | |||
140.27 | odd | 4 | 1680.2.cz.d.433.4 | 16 | |||
140.139 | even | 2 | 1680.2.cz.d.97.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.3 | ✓ | 16 | 5.2 | odd | 4 | ||
105.2.m.a.13.4 | yes | 16 | 35.27 | even | 4 | ||
105.2.m.a.97.3 | yes | 16 | 35.34 | odd | 2 | ||
105.2.m.a.97.4 | yes | 16 | 5.4 | even | 2 | ||
315.2.p.e.118.5 | 16 | 105.62 | odd | 4 | |||
315.2.p.e.118.6 | 16 | 15.2 | even | 4 | |||
315.2.p.e.307.5 | 16 | 15.14 | odd | 2 | |||
315.2.p.e.307.6 | 16 | 105.104 | even | 2 | |||
525.2.m.b.118.5 | 16 | 35.13 | even | 4 | inner | ||
525.2.m.b.118.6 | 16 | 5.3 | odd | 4 | inner | ||
525.2.m.b.307.5 | 16 | 1.1 | even | 1 | trivial | ||
525.2.m.b.307.6 | 16 | 7.6 | odd | 2 | inner | ||
735.2.v.a.178.5 | 32 | 35.2 | odd | 12 | |||
735.2.v.a.178.6 | 32 | 35.12 | even | 12 | |||
735.2.v.a.313.3 | 32 | 35.17 | even | 12 | |||
735.2.v.a.313.4 | 32 | 35.32 | odd | 12 | |||
735.2.v.a.472.3 | 32 | 35.9 | even | 6 | |||
735.2.v.a.472.4 | 32 | 35.19 | odd | 6 | |||
735.2.v.a.607.5 | 32 | 35.24 | odd | 6 | |||
735.2.v.a.607.6 | 32 | 35.4 | even | 6 | |||
1680.2.cz.d.97.4 | 16 | 20.19 | odd | 2 | |||
1680.2.cz.d.97.5 | 16 | 140.139 | even | 2 | |||
1680.2.cz.d.433.4 | 16 | 140.27 | odd | 4 | |||
1680.2.cz.d.433.5 | 16 | 20.7 | even | 4 |