Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(13,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(0.838429221223\) |
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: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(-1.40927 + 0.118126i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.97 |
Dual form | 105.2.m.a.13.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | 0.645573 | − | 0.763699i | \(-0.276619\pi\) |
−0.763699 | + | 0.645573i | \(0.776619\pi\) | |||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.94418i | − | 0.972092i | ||||||
\(5\) | 2.23450 | + | 0.0836010i | 0.999301 | + | 0.0373875i | ||||
\(6\) | − | 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 | ||||||||
\(10\) | −0.359321 | − | 0.387253i | −0.113627 | − | 0.122460i | ||||
\(11\) | 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 | 0.773091 | − | 0.634295i | \(-0.218709\pi\) |
−0.634295 | + | 0.773091i | \(0.718709\pi\) | |||||||
\(14\) | 0.431387 | + | 0.452341i | 0.115293 | + | 0.120893i | ||||
\(15\) | 1.52092 | + | 1.63915i | 0.392699 | + | 0.423226i | ||||
\(16\) | −3.66822 | −0.917056 | ||||||||
\(17\) | −1.67840 | + | 1.67840i | −0.407071 | + | 0.407071i | −0.880716 | − | 0.473645i | \(-0.842938\pi\) |
0.473645 | + | 0.880716i | \(0.342938\pi\) | |||||||
\(18\) | 0.167056 | − | 0.167056i | 0.0393754 | − | 0.0393754i | ||||
\(19\) | −7.21850 | −1.65604 | −0.828019 | − | 0.560700i | \(-0.810532\pi\) | ||||
−0.828019 | + | 0.560700i | \(0.810532\pi\) | |||||||
\(20\) | 0.162536 | − | 4.34429i | 0.0363441 | − | 0.971413i | ||||
\(21\) | −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 | \(0.525198\pi\) |
−0.996868 | + | 0.0790800i | \(0.974802\pi\) | |||||||
\(24\) | −0.931824 | −0.190208 | ||||||||
\(25\) | 4.98602 | + | 0.373614i | 0.997204 | + | 0.0747227i | ||||
\(26\) | − | 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 | \(-0.110113\pi\) | |||||||
\(30\) | 0.0197510 | − | 0.527908i | 0.00360602 | − | 0.0963823i | ||||
\(31\) | − | 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 | ||||||||
\(35\) | −5.90504 | − | 0.361268i | −0.998134 | − | 0.0610654i | ||||
\(36\) | 1.94418 | 0.324031 | ||||||||
\(37\) | 0.292275 | + | 0.292275i | 0.0480497 | + | 0.0480497i | 0.730723 | − | 0.682674i | \(-0.239183\pi\) |
−0.682674 | + | 0.730723i | \(0.739183\pi\) | |||||||
\(38\) | 1.20589 | + | 1.20589i | 0.195622 | + | 0.195622i | ||||
\(39\) | 0.707725i | 0.113327i | ||||||||
\(40\) | −1.52740 | + | 1.41723i | −0.241503 | + | 0.224084i | ||||
\(41\) | 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 | −0.371516 | − | 0.928427i | \(-0.621162\pi\) |
0.928427 | + | 0.371516i | \(0.121162\pi\) | |||||||
\(44\) | − | 7.74956i | − | 1.16829i | ||||||
\(45\) | −0.0836010 | + | 2.23450i | −0.0124625 | + | 0.333100i | ||||
\(46\) | 1.72404 | 0.254196 | ||||||||
\(47\) | −0.305303 | + | 0.305303i | −0.0445331 | + | 0.0445331i | −0.729023 | − | 0.684490i | \(-0.760025\pi\) |
0.684490 | + | 0.729023i | \(0.260025\pi\) | |||||||
\(48\) | −2.59383 | − | 2.59383i | −0.374386 | − | 0.374386i | ||||
\(49\) | 6.99213 | + | 0.331777i | 0.998876 | + | 0.0473967i | ||||
\(50\) | −0.770530 | − | 0.895358i | −0.108969 | − | 0.126623i | ||||
\(51\) | −2.37361 | −0.332372 | ||||||||
\(52\) | 0.972943 | − | 0.972943i | 0.134923 | − | 0.134923i | ||||
\(53\) | 5.39653 | − | 5.39653i | 0.741270 | − | 0.741270i | −0.231553 | − | 0.972822i | \(-0.574381\pi\) |
0.972822 | + | 0.231553i | \(0.0743805\pi\) | |||||||
\(54\) | 0.236253 | 0.0321499 | ||||||||
\(55\) | 8.90678 | + | 0.333235i | 1.20099 | + | 0.0449335i | ||||
\(56\) | 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 | \(0.369808\pi\) | |||||||
\(60\) | 3.18681 | − | 2.95695i | 0.411415 | − | 0.381740i | ||||
\(61\) | − | 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 | ||||||||
\(65\) | 1.07639 | + | 1.16007i | 0.133510 | + | 0.143889i | ||||
\(66\) | − | 0.941708i | − | 0.115916i | ||||||
\(67\) | 0.944185 | + | 0.944185i | 0.115351 | + | 0.115351i | 0.762426 | − | 0.647075i | \(-0.224008\pi\) |
−0.647075 | + | 0.762426i | \(0.724008\pi\) | |||||||
\(68\) | 3.26312 | + | 3.26312i | 0.395711 | + | 0.395711i | ||||
\(69\) | −7.29744 | −0.878508 | ||||||||
\(70\) | 0.926119 | + | 1.04682i | 0.110692 | + | 0.125119i | ||||
\(71\) | 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 | 0.783393 | − | 0.621527i | \(-0.213487\pi\) |
−0.621527 | + | 0.783393i | \(0.713487\pi\) | |||||||
\(74\) | − | 0.0976524i | − | 0.0113519i | ||||||
\(75\) | 3.26147 | + | 3.78983i | 0.376602 | + | 0.437612i | ||||
\(76\) | 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 | \(0.838436\pi\) | |||||||
\(80\) | −8.19666 | − | 0.306667i | −0.916415 | − | 0.0342864i | ||||
\(81\) | −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 | \(-0.869315\pi\) |
−0.399122 | − | 0.916898i | \(-0.630685\pi\) | |||||||
\(84\) | −3.72244 | + | 3.54999i | −0.406151 | + | 0.387336i | ||||
\(85\) | −3.89070 | + | 3.61007i | −0.422006 | + | 0.391567i | ||||
\(86\) | −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 | \(0.363863\pi\) | |||||||
\(90\) | 0.387253 | − | 0.359321i | 0.0408201 | − | 0.0378758i | ||||
\(91\) | −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 | ||||||||
\(95\) | −16.1298 | − | 0.603474i | −1.65488 | − | 0.0619151i | ||||
\(96\) | 2.73028i | 0.278658i | ||||||||
\(97\) | 7.43671 | − | 7.43671i | 0.755083 | − | 0.755083i | −0.220340 | − | 0.975423i | \(-0.570717\pi\) |
0.975423 | + | 0.220340i | \(0.0707167\pi\) | |||||||
\(98\) | −1.11265 | − | 1.22350i | −0.112395 | − | 0.123592i | ||||
\(99\) | 3.98602i | 0.400610i | ||||||||
\(100\) | 0.726374 | − | 9.69375i | 0.0726374 | − | 0.969375i | ||||
\(101\) | − | 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 | \(-0.911668\pi\) |
−0.273954 | − | 0.961743i | \(-0.588332\pi\) | |||||||
\(104\) | −0.659476 | −0.0646669 | ||||||||
\(105\) | −3.92004 | − | 4.43095i | −0.382557 | − | 0.432416i | ||||
\(106\) | −1.80304 | −0.175127 | ||||||||
\(107\) | 7.48020 | + | 7.48020i | 0.723138 | + | 0.723138i | 0.969243 | − | 0.246105i | \(-0.0791508\pi\) |
−0.246105 | + | 0.969243i | \(0.579151\pi\) | |||||||
\(108\) | 1.37475 | + | 1.37475i | 0.132285 | + | 0.132285i | ||||
\(109\) | 0.668223i | 0.0640042i | 0.999488 | + | 0.0320021i | \(0.0101883\pi\) | ||||
−0.999488 | + | 0.0320021i | \(0.989812\pi\) | |||||||
\(110\) | −1.43226 | − | 1.54360i | −0.136561 | − | 0.147176i | ||||
\(111\) | 0.413339i | 0.0392324i | ||||||||
\(112\) | 9.70248 | + | 0.230062i | 0.916798 | + | 0.0217388i | ||||
\(113\) | −3.39653 | + | 3.39653i | −0.319518 | + | 0.319518i | −0.848582 | − | 0.529064i | \(-0.822543\pi\) |
0.529064 | + | 0.848582i | \(0.322543\pi\) | |||||||
\(114\) | 1.70539i | 0.159724i | ||||||||
\(115\) | −11.9616 | + | 11.0988i | −1.11542 | + | 1.03497i | ||||
\(116\) | −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 | ||||
\(120\) | −2.08217 | − | 0.0779014i | −0.190075 | − | 0.00711139i | ||||
\(121\) | 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 | ||||||||
\(125\) | 11.1101 | + | 1.25168i | 0.993713 | + | 0.111953i | ||||
\(126\) | −0.452341 | + | 0.431387i | −0.0402978 | + | 0.0384310i | ||||
\(127\) | −5.88837 | − | 5.88837i | −0.522508 | − | 0.522508i | 0.395820 | − | 0.918328i | \(-0.370460\pi\) |
−0.918328 | + | 0.395820i | \(0.870460\pi\) | |||||||
\(128\) | 4.97903 | − | 4.97903i | 0.440088 | − | 0.440088i | ||||
\(129\) | 5.16458 | 0.454716 | ||||||||
\(130\) | 0.0139783 | − | 0.373614i | 0.00122597 | − | 0.0327681i | ||||
\(131\) | 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 | ||||||
\(135\) | −1.63915 | + | 1.52092i | −0.141075 | + | 0.130900i | ||||
\(136\) | − | 2.21179i | − | 0.189659i | ||||||
\(137\) | −0.811977 | − | 0.811977i | −0.0693719 | − | 0.0693719i | 0.671570 | − | 0.740941i | \(-0.265620\pi\) |
−0.740941 | + | 0.671570i | \(0.765620\pi\) | |||||||
\(138\) | 1.21908 | + | 1.21908i | 0.103775 | + | 0.103775i | ||||
\(139\) | −0.442439 | −0.0375272 | −0.0187636 | − | 0.999824i | \(-0.505973\pi\) | ||||
−0.0187636 | + | 0.999824i | \(0.505973\pi\) | |||||||
\(140\) | −0.702371 | + | 11.4805i | −0.0593612 | + | 0.970278i | ||||
\(141\) | −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 | ||||||
\(145\) | 0.305303 | − | 8.16021i | 0.0253541 | − | 0.677669i | ||||
\(146\) | − | 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 | \(-0.0410696\pi\) | |||||||
\(150\) | 0.0882672 | − | 1.17796i | 0.00720699 | − | 0.0961801i | ||||
\(151\) | −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 | ||||
\(155\) | 0.412839 | − | 11.0345i | 0.0331601 | − | 0.886309i | ||||
\(156\) | 1.37595 | 0.110164 | ||||||||
\(157\) | −7.96508 | + | 7.96508i | −0.635682 | + | 0.635682i | −0.949487 | − | 0.313805i | \(-0.898396\pi\) |
0.313805 | + | 0.949487i | \(0.398396\pi\) | |||||||
\(158\) | 1.44341 | − | 1.44341i | 0.114831 | − | 0.114831i | ||||
\(159\) | 7.63184 | 0.605244 | ||||||||
\(160\) | 4.15253 | + | 4.47533i | 0.328286 | + | 0.353806i | ||||
\(161\) | 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 | −0.167722 | − | 0.985834i | \(-0.553641\pi\) |
0.985834 | + | 0.167722i | \(0.0536410\pi\) | |||||||
\(164\) | 14.8377 | 1.15863 | ||||||||
\(165\) | 6.06241 | + | 6.53368i | 0.471958 | + | 0.508646i | ||||
\(166\) | 4.00584i | 0.310913i | ||||||||
\(167\) | 4.63621 | − | 4.63621i | 0.358761 | − | 0.358761i | −0.504595 | − | 0.863356i | \(-0.668358\pi\) |
0.863356 | + | 0.504595i | \(0.168358\pi\) | |||||||
\(168\) | 2.46468 | + | 0.0584417i | 0.190154 | + | 0.00450887i | ||||
\(169\) | − | 12.4991i | − | 0.961471i | ||||||
\(170\) | 1.25305 | + | 0.0468811i | 0.0961045 | + | 0.00359562i | ||||
\(171\) | − | 7.21850i | − | 0.552013i | ||||||
\(172\) | −7.09999 | − | 7.09999i | −0.541369 | − | 0.541369i | ||||
\(173\) | −2.48531 | − | 2.48531i | −0.188954 | − | 0.188954i | 0.606290 | − | 0.795244i | \(-0.292657\pi\) |
−0.795244 | + | 0.606290i | \(0.792657\pi\) | |||||||
\(174\) | −0.862773 | −0.0654067 | ||||||||
\(175\) | −13.1646 | − | 1.30092i | −0.995153 | − | 0.0983404i | ||||
\(176\) | −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 | \(0.690430\pi\) | |||||||
\(180\) | 4.34429 | + | 0.162536i | 0.323804 | + | 0.0121147i | ||||
\(181\) | 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 | ||||||
\(185\) | 0.628655 | + | 0.677524i | 0.0462196 | + | 0.0498125i | ||||
\(186\) | −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 | ||||
\(190\) | 2.59376 | + | 2.79539i | 0.188171 | + | 0.202799i | ||||
\(191\) | 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 | −0.951204 | − | 0.308562i | \(-0.900152\pi\) |
0.308562 | + | 0.951204i | \(0.400152\pi\) | |||||||
\(194\) | −2.48469 | −0.178390 | ||||||||
\(195\) | −0.0591665 | + | 1.58142i | −0.00423700 | + | 0.113248i | ||||
\(196\) | 0.645035 | − | 13.5940i | 0.0460739 | − | 0.971000i | ||||
\(197\) | −2.68715 | − | 2.68715i | −0.191451 | − | 0.191451i | 0.604872 | − | 0.796323i | \(-0.293224\pi\) |
−0.796323 | + | 0.604872i | \(0.793224\pi\) | |||||||
\(198\) | 0.665888 | − | 0.665888i | 0.0473226 | − | 0.0473226i | ||||
\(199\) | 0.616637 | 0.0437122 | 0.0218561 | − | 0.999761i | \(-0.493042\pi\) | ||||
0.0218561 | + | 0.999761i | \(0.493042\pi\) | |||||||
\(200\) | −3.53146 | + | 3.03911i | −0.249712 | + | 0.214898i | ||||
\(201\) | 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 | ||||||||
\(205\) | −0.638029 | + | 17.0534i | −0.0445619 | + | 1.19106i | ||||
\(206\) | 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 | ||||||||
\(210\) | −0.0853505 | + | 1.39508i | −0.00588974 | + | 0.0962697i | ||||
\(211\) | 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 | ||||||
\(215\) | 8.46551 | − | 7.85491i | 0.577343 | − | 0.535700i | ||||
\(216\) | − | 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 | ||||||||
\(220\) | 0.647871 | − | 17.3164i | 0.0436795 | − | 1.16747i | ||||
\(221\) | −1.67987 | −0.113000 | ||||||||
\(222\) | 0.0690507 | − | 0.0690507i | 0.00463438 | − | 0.00463438i | ||||
\(223\) | −1.35505 | − | 1.35505i | −0.0907407 | − | 0.0907407i | 0.660279 | − | 0.751020i | \(-0.270438\pi\) |
−0.751020 | + | 0.660279i | \(0.770438\pi\) | |||||||
\(224\) | −4.98536 | − | 5.22753i | −0.333098 | − | 0.349279i | ||||
\(225\) | −0.373614 | + | 4.98602i | −0.0249076 | + | 0.332401i | ||||
\(226\) | 1.13482 | 0.0754870 | ||||||||
\(227\) | 4.15437 | − | 4.15437i | 0.275735 | − | 0.275735i | −0.555668 | − | 0.831404i | \(-0.687538\pi\) |
0.831404 | + | 0.555668i | \(0.187538\pi\) | |||||||
\(228\) | −9.92361 | + | 9.92361i | −0.657207 | + | 0.657207i | ||||
\(229\) | 12.9900 | 0.858403 | 0.429202 | − | 0.903209i | \(-0.358795\pi\) | ||||
0.429202 | + | 0.903209i | \(0.358795\pi\) | |||||||
\(230\) | 3.85237 | + | 0.144131i | 0.254018 | + | 0.00950374i | ||||
\(231\) | −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 | \(0.526114\pi\) |
−0.996637 | + | 0.0819485i | \(0.973886\pi\) | |||||||
\(234\) | 0.167202 | 0.0109303 | ||||||||
\(235\) | −0.707725 | + | 0.656678i | −0.0461669 | + | 0.0428370i | ||||
\(236\) | − | 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 | \(0.943279\pi\) | |||||||
\(240\) | −5.57907 | − | 6.01276i | −0.360127 | − | 0.388122i | ||||
\(241\) | − | 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 | ||||||||
\(245\) | 15.5962 | + | 1.32591i | 0.996406 | + | 0.0847090i | ||||
\(246\) | 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 | ||||||
\(250\) | −1.64690 | − | 2.06510i | −0.104159 | − | 0.130608i | ||||
\(251\) | 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 | ||||||||
\(255\) | −5.30385 | − | 0.198436i | −0.332140 | − | 0.0124266i | ||||
\(256\) | 11.7193 | 0.732454 | ||||||||
\(257\) | −9.39248 | + | 9.39248i | −0.585887 | + | 0.585887i | −0.936515 | − | 0.350628i | \(-0.885968\pi\) |
0.350628 | + | 0.936515i | \(0.385968\pi\) | |||||||
\(258\) | −0.862773 | − | 0.862773i | −0.0537139 | − | 0.0537139i | ||||
\(259\) | −0.754738 | − | 0.791399i | −0.0468971 | − | 0.0491752i | ||||
\(260\) | 2.25538 | − | 2.09271i | 0.139873 | − | 0.129784i | ||||
\(261\) | 3.65191 | 0.226048 | ||||||||
\(262\) | 3.14306 | − | 3.14306i | 0.194179 | − | 0.194179i | ||||
\(263\) | 15.3779 | − | 15.3779i | 0.948241 | − | 0.948241i | −0.0504843 | − | 0.998725i | \(-0.516076\pi\) |
0.998725 | + | 0.0504843i | \(0.0160765\pi\) | |||||||
\(264\) | −3.71427 | −0.228598 | ||||||||
\(265\) | 12.5097 | − | 11.6074i | 0.768466 | − | 0.713037i | ||||
\(266\) | −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 | \(0.747135\pi\) | |||||||
\(270\) | 0.527908 | + | 0.0197510i | 0.0321274 | + | 0.00120201i | ||||
\(271\) | 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 | ||||||||
\(275\) | 19.8744 | + | 1.48923i | 1.19847 | + | 0.0898041i | ||||
\(276\) | 14.1876i | 0.853991i | ||||||||
\(277\) | 4.80771 | + | 4.80771i | 0.288867 | + | 0.288867i | 0.836632 | − | 0.547765i | \(-0.184521\pi\) |
−0.547765 | + | 0.836632i | \(0.684521\pi\) | |||||||
\(278\) | 0.0739121 | + | 0.0739121i | 0.00443295 | + | 0.00443295i | ||||
\(279\) | 4.93821 | 0.295643 | ||||||||
\(280\) | 4.12886 | − | 3.65279i | 0.246747 | − | 0.218296i | ||||
\(281\) | −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 | 0.994163 | − | 0.107885i | \(-0.0344079\pi\) |
−0.107885 | + | 0.994163i | \(0.534408\pi\) | |||||||
\(284\) | − | 2.31935i | − | 0.137628i | ||||||
\(285\) | −10.9788 | − | 11.8322i | −0.650325 | − | 0.700879i | ||||
\(286\) | − | 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 | ||||||||
\(290\) | −1.41421 | + | 1.31221i | −0.0830455 | + | 0.0770555i | ||||
\(291\) | 10.5171 | 0.616523 | ||||||||
\(292\) | 2.68877 | − | 2.68877i | 0.157348 | − | 0.157348i | ||||
\(293\) | 4.79236 | + | 4.79236i | 0.279973 | + | 0.279973i | 0.833098 | − | 0.553125i | \(-0.186565\pi\) |
−0.553125 | + | 0.833098i | \(0.686565\pi\) | |||||||
\(294\) | 0.0783831 | − | 1.65191i | 0.00457140 | − | 0.0963413i | ||||
\(295\) | 13.6519 | + | 0.510768i | 0.794845 | + | 0.0297381i | ||||
\(296\) | −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 | ||||||||
\(300\) | 7.36814 | − | 6.34089i | 0.425400 | − | 0.366091i | ||||
\(301\) | −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 | ||||||||
\(305\) | 0.594442 | − | 15.8884i | 0.0340377 | − | 0.909765i | ||||
\(306\) | 0.560773i | 0.0320572i | ||||||||
\(307\) | 9.85063 | − | 9.85063i | 0.562205 | − | 0.562205i | −0.367728 | − | 0.929933i | \(-0.619864\pi\) |
0.929933 | + | 0.367728i | \(0.119864\pi\) | |||||||
\(308\) | −0.486033 | + | 20.4977i | −0.0276943 | + | 1.16796i | ||||
\(309\) | − | 17.7356i | − | 1.00894i | ||||||
\(310\) | −1.91234 | + | 1.77440i | −0.108614 | + | 0.100779i | ||||
\(311\) | − | 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 | \(0.0150455\pi\) |
0.0472492 | + | 0.998883i | \(0.484955\pi\) | |||||||
\(314\) | 2.66123 | 0.150182 | ||||||||
\(315\) | 0.361268 | − | 5.90504i | 0.0203551 | − | 0.332711i | ||||
\(316\) | 16.7983 | 0.944977 | ||||||||
\(317\) | −21.8793 | − | 21.8793i | −1.22887 | − | 1.22887i | −0.964393 | − | 0.264473i | \(-0.914802\pi\) |
−0.264473 | − | 0.964393i | \(-0.585198\pi\) | |||||||
\(318\) | −1.27494 | − | 1.27494i | −0.0714953 | − | 0.0714953i | ||||
\(319\) | − | 14.5566i | − | 0.815013i | ||||||
\(320\) | −0.559409 | + | 14.9520i | −0.0312719 | + | 0.835842i | ||||
\(321\) | 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 | ||||||||
\(325\) | 2.30822 | + | 2.68216i | 0.128037 | + | 0.148780i | ||||
\(326\) | −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 | ||||
\(330\) | 0.0787277 | − | 2.10425i | 0.00433382 | − | 0.115835i | ||||
\(331\) | −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 | ||||||||
\(335\) | 2.03085 | + | 2.18872i | 0.110957 | + | 0.119583i | ||||
\(336\) | 6.69801 | + | 7.02337i | 0.365406 | + | 0.383156i | ||||
\(337\) | 2.54028 | + | 2.54028i | 0.138378 | + | 0.138378i | 0.772903 | − | 0.634525i | \(-0.218804\pi\) |
−0.634525 | + | 0.772903i | \(0.718804\pi\) | |||||||
\(338\) | −2.08805 | + | 2.08805i | −0.113575 | + | 0.113575i | ||||
\(339\) | −4.80341 | −0.260886 | ||||||||
\(340\) | 7.01865 | + | 7.56425i | 0.380640 | + | 0.410229i | ||||
\(341\) | − | 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 | ||||||||
\(345\) | −16.3062 | − | 0.610073i | −0.877894 | − | 0.0328452i | ||||
\(346\) | 0.830370i | 0.0446410i | ||||||||
\(347\) | 13.6980 | + | 13.6980i | 0.735348 | + | 0.735348i | 0.971674 | − | 0.236326i | \(-0.0759433\pi\) |
−0.236326 | + | 0.971674i | \(0.575943\pi\) | |||||||
\(348\) | −5.02045 | − | 5.02045i | −0.269124 | − | 0.269124i | ||||
\(349\) | 0.508601 | 0.0272248 | 0.0136124 | − | 0.999907i | \(-0.495667\pi\) | ||||
0.0136124 | + | 0.999907i | \(0.495667\pi\) | |||||||
\(350\) | 1.98190 | + | 2.41656i | 0.105937 | + | 0.129170i | ||||
\(351\) | −0.707725 | −0.0377756 | ||||||||
\(352\) | 7.69540 | + | 7.69540i | 0.410166 | + | 0.410166i | ||||
\(353\) | 10.9217 | + | 10.9217i | 0.581305 | + | 0.581305i | 0.935262 | − | 0.353957i | \(-0.115164\pi\) |
−0.353957 | + | 0.935262i | \(0.615164\pi\) | |||||||
\(354\) | − | 1.44341i | − | 0.0767162i | ||||||
\(355\) | 2.66570 | + | 0.0997335i | 0.141480 | + | 0.00529330i | ||||
\(356\) | − | 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 | \(-0.138621\pi\) | |||||||
\(360\) | −1.41723 | − | 1.52740i | −0.0746945 | − | 0.0805009i | ||||
\(361\) | 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 | ||||
\(365\) | 2.97465 | + | 3.20589i | 0.155701 | + | 0.167804i | ||||
\(366\) | −1.67987 | −0.0878080 | ||||||||
\(367\) | 0.410036 | − | 0.410036i | 0.0214037 | − | 0.0214037i | −0.696324 | − | 0.717728i | \(-0.745182\pi\) |
0.717728 | + | 0.696324i | \(0.245182\pi\) | |||||||
\(368\) | 18.9283 | − | 18.9283i | 0.986705 | − | 0.986705i | ||||
\(369\) | −7.63184 | −0.397298 | ||||||||
\(370\) | 0.00816384 | − | 0.218205i | 0.000424418 | − | 0.0113439i | ||||
\(371\) | −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 | −0.790646 | − | 0.612273i | \(-0.790255\pi\) |
0.612273 | + | 0.790646i | \(0.290255\pi\) | |||||||
\(374\) | 2.23525 | 0.115582 | ||||||||
\(375\) | 6.97092 | + | 8.74106i | 0.359977 | + | 0.451387i | ||||
\(376\) | − | 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 | \(-0.107647\pi\) | |||||||
\(380\) | −1.17326 | + | 31.3593i | −0.0601872 | + | 1.60870i | ||||
\(381\) | − | 8.32741i | − | 0.426626i | ||||||
\(382\) | −2.55426 | − | 2.55426i | −0.130687 | − | 0.130687i | ||||
\(383\) | −10.0770 | − | 10.0770i | −0.514910 | − | 0.514910i | 0.401117 | − | 0.916027i | \(-0.368622\pi\) |
−0.916027 | + | 0.401117i | \(0.868622\pi\) | |||||||
\(384\) | 7.04142 | 0.359331 | ||||||||
\(385\) | −23.5376 | − | 1.44002i | −1.19959 | − | 0.0733903i | ||||
\(386\) | 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 | \(0.788433\pi\) | |||||||
\(390\) | 0.274069 | − | 0.254301i | 0.0138780 | − | 0.0128770i | ||||
\(391\) | − | 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 | ||||||||
\(395\) | −0.722335 | + | 19.3067i | −0.0363446 | + | 0.971426i | ||||
\(396\) | 7.74956 | 0.389430 | ||||||||
\(397\) | 6.80633 | − | 6.80633i | 0.341600 | − | 0.341600i | −0.515369 | − | 0.856969i | \(-0.672345\pi\) |
0.856969 | + | 0.515369i | \(0.172345\pi\) | |||||||
\(398\) | −0.103013 | − | 0.103013i | −0.00516356 | − | 0.00516356i | ||||
\(399\) | 13.1807 | + | 13.8209i | 0.659858 | + | 0.691911i | ||||
\(400\) | −18.2898 | − | 1.37050i | −0.914492 | − | 0.0685249i | ||||
\(401\) | −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 | ||||||||
\(405\) | −2.23450 | − | 0.0836010i | −0.111033 | − | 0.00415417i | ||||
\(406\) | 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 | \(0.694432\pi\) | |||||||
\(410\) | 2.95545 | − | 2.74228i | 0.145959 | − | 0.135432i | ||||
\(411\) | − | 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 | ||||||||
\(415\) | −25.7883 | − | 27.7930i | −1.26590 | − | 1.36430i | ||||
\(416\) | 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 | \(0.396819\pi\) | |||||||
\(420\) | −8.61458 | + | 7.62128i | −0.420349 | + | 0.371880i | ||||
\(421\) | −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 | ||||||||
\(425\) | −8.99560 | + | 7.74146i | −0.436351 | + | 0.375516i | ||||
\(426\) | − | 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 | ||||||||
\(430\) | −2.72642 | − | 0.102005i | −0.131480 | − | 0.00491914i | ||||
\(431\) | −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 | 0.0398028 | − | 0.999208i | \(-0.487327\pi\) |
−0.999208 | + | 0.0398028i | \(0.987327\pi\) | |||||||
\(434\) | 2.23376 | − | 2.13028i | 0.107224 | − | 0.102257i | ||||
\(435\) | 5.98602 | − | 5.55426i | 0.287008 | − | 0.266306i | ||||
\(436\) | 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 | \(0.243890\pi\) | |||||||
\(440\) | −6.08824 | + | 5.64910i | −0.290246 | + | 0.269310i | ||||
\(441\) | −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 | −0.941742 | − | 0.336337i | \(-0.890812\pi\) |
0.336337 | + | 0.941742i | \(0.390812\pi\) | |||||||
\(444\) | 0.803607 | 0.0381375 | ||||||||
\(445\) | 17.4868 | + | 0.654245i | 0.828954 | + | 0.0310142i | ||||
\(446\) | 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 | \(0.745180\pi\) | |||||||
\(450\) | 0.895358 | − | 0.770530i | 0.0422076 | − | 0.0363231i | ||||
\(451\) | 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 | ||||||||
\(455\) | −2.77431 | − | 3.13589i | −0.130062 | − | 0.147013i | ||||
\(456\) | 6.72637 | 0.314991 | ||||||||
\(457\) | 1.31546 | + | 1.31546i | 0.0615348 | + | 0.0615348i | 0.737204 | − | 0.675670i | \(-0.236145\pi\) |
−0.675670 | + | 0.737204i | \(0.736145\pi\) | |||||||
\(458\) | −2.17005 | − | 2.17005i | −0.101400 | − | 0.101400i | ||||
\(459\) | − | 2.37361i | − | 0.110791i | ||||||
\(460\) | 21.5781 | + | 23.2555i | 1.00609 | + | 1.08429i | ||||
\(461\) | − | 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 | −0.209809 | − | 0.977742i | \(-0.567284\pi\) |
0.977742 | + | 0.209809i | \(0.0672841\pi\) | |||||||
\(464\) | 13.3960i | 0.621895i | ||||||||
\(465\) | 8.09446 | − | 7.51062i | 0.375372 | − | 0.348297i | ||||
\(466\) | 5.50078 | 0.254819 | ||||||||
\(467\) | 20.1009 | − | 20.1009i | 0.930157 | − | 0.930157i | −0.0675588 | − | 0.997715i | \(-0.521521\pi\) |
0.997715 | + | 0.0675588i | \(0.0215210\pi\) | |||||||
\(468\) | 0.972943 | + | 0.972943i | 0.0449743 | + | 0.0449743i | ||||
\(469\) | −2.43816 | − | 2.55659i | −0.112584 | − | 0.118052i | ||||
\(470\) | 0.227932 | + | 0.00852775i | 0.0105137 | + | 0.000393356i | ||||
\(471\) | −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 | ||||||||
\(475\) | −35.9916 | − | 2.69693i | −1.65141 | − | 0.123744i | ||||
\(476\) | −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 | \(0.581487\pi\) | |||||||
\(480\) | −0.228254 | + | 6.10081i | −0.0104183 | + | 0.278463i | ||||
\(481\) | 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 | ||||||
\(485\) | 17.2391 | − | 15.9956i | 0.782786 | − | 0.726325i | ||||
\(486\) | 0.236253i | 0.0107166i | ||||||||
\(487\) | −13.6519 | − | 13.6519i | −0.618627 | − | 0.618627i | 0.326552 | − | 0.945179i | \(-0.394113\pi\) |
−0.945179 | + | 0.326552i | \(0.894113\pi\) | |||||||
\(488\) | 4.68508 | + | 4.68508i | 0.212084 | + | 0.212084i | ||||
\(489\) | 14.7714 | 0.667986 | ||||||||
\(490\) | −2.38394 | − | 2.82694i | −0.107695 | − | 0.127708i | ||||
\(491\) | 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 | ||||||||
\(495\) | −0.333235 | + | 8.90678i | −0.0149778 | + | 0.400330i | ||||
\(496\) | 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 | \(0.969500\pi\) | |||||||
\(500\) | 2.43349 | − | 21.6000i | 0.108829 | − | 0.965981i | ||||
\(501\) | 6.55659 | 0.292927 | ||||||||
\(502\) | 3.53333 | − | 3.53333i | 0.157700 | − | 0.157700i | ||||
\(503\) | 17.5637 | + | 17.5637i | 0.783128 | + | 0.783128i | 0.980357 | − | 0.197229i | \(-0.0631943\pi\) |
−0.197229 | + | 0.980357i | \(0.563194\pi\) | |||||||
\(504\) | 1.70147 | + | 1.78412i | 0.0757894 | + | 0.0794709i | ||||
\(505\) | 0.528051 | − | 14.1139i | 0.0234980 | − | 0.628059i | ||||
\(506\) | 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 | \(0.712333\pi\) | |||||||
\(510\) | 0.852889 | + | 0.919189i | 0.0377666 | + | 0.0407024i | ||||
\(511\) | −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 | ||||||||
\(515\) | −26.9744 | − | 29.0713i | −1.18863 | − | 1.28103i | ||||
\(516\) | − | 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 | ||||||
\(520\) | −1.47360 | − | 0.0551328i | −0.0646217 | − | 0.00241773i | ||||
\(521\) | 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 | 0.625290 | − | 0.780392i | \(-0.284981\pi\) |
−0.780392 | + | 0.625290i | \(0.784981\pi\) | |||||||
\(524\) | 36.5788 | 1.59795 | ||||||||
\(525\) | −8.38891 | − | 10.2287i | −0.366122 | − | 0.446417i | ||||
\(526\) | −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 | ||||||
\(530\) | −4.02891 | − | 0.150736i | −0.175005 | − | 0.00654756i | ||||
\(531\) | 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 | ||||||
\(535\) | 16.0892 | + | 17.3399i | 0.695596 | + | 0.749669i | ||||
\(536\) | −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 | ||||
\(540\) | 2.95695 | + | 3.18681i | 0.127247 | + | 0.137138i | ||||
\(541\) | −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 | ||||||||
\(545\) | −0.0558641 | + | 1.49315i | −0.00239296 | + | 0.0639594i | ||||
\(546\) | −0.320133 | + | 0.305303i | −0.0137004 | + | 0.0130658i | ||||
\(547\) | 28.2200 | + | 28.2200i | 1.20660 | + | 1.20660i | 0.972121 | + | 0.234482i | \(0.0753392\pi\) |
0.234482 | + | 0.972121i | \(0.424661\pi\) | |||||||
\(548\) | −1.57863 | + | 1.57863i | −0.0674359 | + | 0.0674359i | ||||
\(549\) | 7.11047 | 0.303467 | ||||||||
\(550\) | −3.07135 | − | 3.56892i | −0.130963 | − | 0.152179i | ||||
\(551\) | 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 | ||||||
\(555\) | −0.0345555 | + | 0.923607i | −0.00146680 | + | 0.0392050i | ||||
\(556\) | 0.860184i | 0.0364799i | ||||||||
\(557\) | 28.1616 | + | 28.1616i | 1.19325 | + | 1.19325i | 0.976150 | + | 0.217096i | \(0.0696584\pi\) |
0.217096 | + | 0.976150i | \(0.430342\pi\) | |||||||
\(558\) | −0.824957 | − | 0.824957i | −0.0349232 | − | 0.0349232i | ||||
\(559\) | 3.65510 | 0.154594 | ||||||||
\(560\) | 21.6610 | + | 1.32521i | 0.915344 | + | 0.0560004i | ||||
\(561\) | −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 | \(-0.946467\pi\) |
−0.167386 | − | 0.985891i | \(-0.553533\pi\) | |||||||
\(564\) | 0.839429i | 0.0353463i | ||||||||
\(565\) | −7.87351 | + | 7.30560i | −0.331241 | + | 0.307349i | ||||
\(566\) | − | 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 | \(-0.121540\pi\) | |||||||
\(570\) | −0.142572 | + | 3.81070i | −0.00597170 | + | 0.159613i | ||||
\(571\) | −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 | ||||
\(575\) | −27.6561 | + | 23.8003i | −1.15334 | + | 0.992543i | ||||
\(576\) | −6.69141 | −0.278809 | ||||||||
\(577\) | 3.89677 | − | 3.89677i | 0.162225 | − | 0.162225i | −0.621327 | − | 0.783552i | \(-0.713406\pi\) |
0.783552 | + | 0.621327i | \(0.213406\pi\) | |||||||
\(578\) | 1.89875 | − | 1.89875i | 0.0789776 | − | 0.0789776i | ||||
\(579\) | −12.6259 | −0.524715 | ||||||||
\(580\) | −15.8650 | − | 0.593566i | −0.658756 | − | 0.0246465i | ||||
\(581\) | 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 | ||||||||
\(585\) | −1.16007 | + | 1.07639i | −0.0479629 | + | 0.0445034i | ||||
\(586\) | − | 1.60118i | − | 0.0661443i | ||||||
\(587\) | −15.1058 | + | 15.1058i | −0.623484 | + | 0.623484i | −0.946420 | − | 0.322937i | \(-0.895330\pi\) |
0.322937 | + | 0.946420i | \(0.395330\pi\) | |||||||
\(588\) | 10.0685 | − | 9.15630i | 0.415219 | − | 0.377599i | ||||
\(589\) | 35.6465i | 1.46879i | ||||||||
\(590\) | −2.19530 | − | 2.36596i | −0.0903793 | − | 0.0974050i | ||||
\(591\) | − | 3.80020i | − | 0.156319i | ||||||
\(592\) | −1.07213 | − | 1.07213i | −0.0440642 | − | 0.0440642i | ||||
\(593\) | −3.43032 | − | 3.43032i | −0.140866 | − | 0.140866i | 0.633157 | − | 0.774023i | \(-0.281759\pi\) |
−0.774023 | + | 0.633157i | \(0.781759\pi\) | |||||||
\(594\) | 0.941708 | 0.0386388 | ||||||||
\(595\) | 10.5174 | − | 9.30466i | 0.431170 | − | 0.381454i | ||||
\(596\) | −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 | \(0.933839\pi\) | |||||||
\(600\) | −4.64610 | − | 0.348142i | −0.189676 | − | 0.0142128i | ||||
\(601\) | − | 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 | ||||||||
\(605\) | 10.9231 | + | 0.408673i | 0.444087 | + | 0.0166149i | ||||
\(606\) | −1.49225 | −0.0606185 | ||||||||
\(607\) | 10.2931 | − | 10.2931i | 0.417783 | − | 0.417783i | −0.466656 | − | 0.884439i | \(-0.654541\pi\) |
0.884439 | + | 0.466656i | \(0.154541\pi\) | |||||||
\(608\) | −13.9360 | − | 13.9360i | −0.565180 | − | 0.565180i | ||||
\(609\) | −6.99213 | + | 6.66822i | −0.283336 | + | 0.270210i | ||||
\(610\) | −2.75355 | + | 2.55494i | −0.111488 | + | 0.103447i | ||||
\(611\) | −0.305570 | −0.0123621 | ||||||||
\(612\) | −3.26312 | + | 3.26312i | −0.131904 | + | 0.131904i | ||||
\(613\) | −14.4155 | + | 14.4155i | −0.582235 | + | 0.582235i | −0.935517 | − | 0.353282i | \(-0.885066\pi\) |
0.353282 | + | 0.935517i | \(0.385066\pi\) | |||||||
\(614\) | −3.29121 | −0.132822 | ||||||||
\(615\) | −12.5097 | + | 11.6074i | −0.504440 | + | 0.468056i | ||||
\(616\) | 7.11153 | − | 6.78209i | 0.286532 | − | 0.273258i | ||||
\(617\) | −25.4196 | − | 25.4196i | −1.02336 | − | 1.02336i | −0.999721 | − | 0.0236346i | \(-0.992476\pi\) |
−0.0236346 | − | 0.999721i | \(-0.507524\pi\) | |||||||
\(618\) | −2.96283 | + | 2.96283i | −0.119183 | + | 0.119183i | ||||
\(619\) | −11.1991 | −0.450129 | −0.225064 | − | 0.974344i | \(-0.572259\pi\) | ||||
−0.225064 | + | 0.974344i | \(0.572259\pi\) | |||||||
\(620\) | −21.4530 | − | 0.802636i | −0.861574 | − | 0.0322346i | ||||
\(621\) | − | 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 | ||||||
\(625\) | 24.7208 | + | 3.72569i | 0.988833 | + | 0.149028i | ||||
\(626\) | − | 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 | ||||||||
\(630\) | −1.04682 | + | 0.926119i | −0.0417064 | + | 0.0368975i | ||||
\(631\) | 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 | ||||||||
\(635\) | −12.6653 | − | 13.6499i | −0.502608 | − | 0.541678i | ||||
\(636\) | − | 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 | ||||||||
\(640\) | 11.5419 | − | 10.7094i | 0.456235 | − | 0.423327i | ||||
\(641\) | −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 | 0.893652 | − | 0.448761i | \(-0.148134\pi\) |
−0.448761 | + | 0.893652i | \(0.648134\pi\) | |||||||
\(644\) | −25.9059 | − | 27.1642i | −1.02083 | − | 1.07042i | ||||
\(645\) | 11.5403 | + | 0.431764i | 0.454398 | + | 0.0170007i | ||||
\(646\) | −4.04794 | −0.159264 | ||||||||
\(647\) | −26.2395 | + | 26.2395i | −1.03158 | + | 1.03158i | −0.0320982 | + | 0.999485i | \(0.510219\pi\) |
−0.999485 | + | 0.0320982i | \(0.989781\pi\) | |||||||
\(648\) | 0.658899 | − | 0.658899i | 0.0258840 | − | 0.0258840i | ||||
\(649\) | 24.3530 | 0.955937 | ||||||||
\(650\) | 0.0624689 | − | 0.833673i | 0.00245023 | − | 0.0326993i | ||||
\(651\) | −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 | −0.744720 | − | 0.667377i | \(-0.767417\pi\) |
0.667377 | + | 0.744720i | \(0.267417\pi\) | |||||||
\(654\) | 0.157870 | 0.00617319 | ||||||||
\(655\) | −1.57291 | + | 42.0410i | −0.0614585 | + | 1.64268i | ||||
\(656\) | − | 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 | \(-0.0950507\pi\) | |||||||
\(660\) | 12.7027 | − | 11.7865i | 0.494451 | − | 0.458787i | ||||
\(661\) | − | 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 | ||||||||
\(665\) | 42.6255 | + | 2.60781i | 1.65295 | + | 0.101127i | ||||
\(666\) | 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 | ||||||
\(670\) | 0.0263730 | − | 0.704904i | 0.00101888 | − | 0.0272328i | ||||
\(671\) | − | 28.3425i | − | 1.09415i | ||||||
\(672\) | 0.171236 | − | 7.22160i | 0.00660558 | − | 0.278579i | ||||
\(673\) | −11.4381 | + | 11.4381i | −0.440906 | + | 0.440906i | −0.892316 | − | 0.451411i | \(-0.850921\pi\) |
0.451411 | + | 0.892316i | \(0.350921\pi\) | |||||||
\(674\) | − | 0.848737i | − | 0.0326921i | ||||||
\(675\) | −3.78983 | + | 3.26147i | −0.145871 | + | 0.125534i | ||||
\(676\) | −24.3006 | −0.934639 | ||||||||
\(677\) | −24.6007 | + | 24.6007i | −0.945481 | + | 0.945481i | −0.998589 | − | 0.0531077i | \(-0.983087\pi\) |
0.0531077 | + | 0.998589i | \(0.483087\pi\) | |||||||
\(678\) | 0.802438 | + | 0.802438i | 0.0308175 | + | 0.0308175i | ||||
\(679\) | −20.1366 | + | 19.2037i | −0.772770 | + | 0.736972i | ||||
\(680\) | 0.184908 | − | 4.94226i | 0.00709089 | − | 0.189527i | ||||
\(681\) | 5.87517 | 0.225137 | ||||||||
\(682\) | −3.28830 | + | 3.28830i | −0.125915 | + | 0.125915i | ||||
\(683\) | −13.8654 | + | 13.8654i | −0.530543 | + | 0.530543i | −0.920734 | − | 0.390191i | \(-0.872409\pi\) |
0.390191 | + | 0.920734i | \(0.372409\pi\) | |||||||
\(684\) | −14.0341 | −0.536607 | ||||||||
\(685\) | −1.74648 | − | 1.88225i | −0.0667297 | − | 0.0719170i | ||||
\(686\) | 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 | ||||||||
\(690\) | 2.62212 | + | 2.82596i | 0.0998225 | + | 0.107582i | ||||
\(691\) | − | 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 | ||||||
\(695\) | −0.988633 | − | 0.0369884i | −0.0375010 | − | 0.00140305i | ||||
\(696\) | 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 | ||||||||
\(700\) | −2.52923 | + | 25.5945i | −0.0955960 | + | 0.967380i | ||||
\(701\) | 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 | ||||||||
\(705\) | −0.964779 | − | 0.0360959i | −0.0363357 | − | 0.00135945i | ||||
\(706\) | − | 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 | \(-0.364891\pi\) | |||||||
\(710\) | −0.428659 | − | 0.461981i | −0.0160873 | − | 0.0173378i | ||||
\(711\) | −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 | ||||
\(715\) | 4.29052 | + | 4.62405i | 0.160457 | + | 0.172930i | ||||
\(716\) | 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 | \(0.197962\pi\) | |||||||
\(720\) | 0.306667 | − | 8.19666i | 0.0114288 | − | 0.305472i | ||||
\(721\) | 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 | ||||||||
\(725\) | 1.36440 | − | 18.2085i | 0.0506727 | − | 0.676247i | ||||
\(726\) | − | 1.15489i | − | 0.0428620i | ||||||
\(727\) | 10.4498 | − | 10.4498i | 0.387563 | − | 0.387563i | −0.486254 | − | 0.873817i | \(-0.661637\pi\) |
0.873817 | + | 0.486254i | \(0.161637\pi\) | |||||||
\(728\) | 1.74432 | + | 0.0413607i | 0.0646487 | + | 0.00153293i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0.0386295 | − | 1.03250i | 0.00142974 | − | 0.0382144i | ||||
\(731\) | 12.2587i | 0.453405i | ||||||||
\(732\) | −9.77509 | − | 9.77509i | −0.361298 | − | 0.361298i | ||||
\(733\) | 18.8687 | + | 18.8687i | 0.696933 | + | 0.696933i | 0.963748 | − | 0.266815i | \(-0.0859712\pi\) |
−0.266815 | + | 0.963748i | \(0.585971\pi\) | |||||||
\(734\) | −0.136998 | −0.00505669 | ||||||||
\(735\) | 10.0906 | + | 11.9657i | 0.372199 | + | 0.441363i | ||||
\(736\) | −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 | \(0.873968\pi\) | |||||||
\(740\) | 1.31723 | − | 1.22222i | 0.0484224 | − | 0.0449297i | ||||
\(741\) | − | 5.10872i | − | 0.187673i | ||||||
\(742\) | 4.76906 | + | 0.113082i | 0.175078 | + | 0.00415138i | ||||
\(743\) | 9.18724 | − | 9.18724i | 0.337047 | − | 0.337047i | −0.518208 | − | 0.855255i | \(-0.673401\pi\) |
0.855255 | + | 0.518208i | \(0.173401\pi\) | |||||||
\(744\) | 4.60155i | 0.168701i | ||||||||
\(745\) | 0.262603 | − | 7.01890i | 0.00962102 | − | 0.257152i | ||||
\(746\) | 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 | ||||
\(750\) | 0.295712 | − | 2.62478i | 0.0107979 | − | 0.0958434i | ||||
\(751\) | 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 | ||||||||
\(755\) | −32.9007 | − | 1.23094i | −1.19738 | − | 0.0447984i | ||||
\(756\) | −3.54999 | − | 3.72244i | −0.129112 | − | 0.135384i | ||||
\(757\) | −13.9324 | − | 13.9324i | −0.506383 | − | 0.506383i | 0.407031 | − | 0.913414i | \(-0.366564\pi\) |
−0.913414 | + | 0.407031i | \(0.866564\pi\) | |||||||
\(758\) | −2.15801 | + | 2.15801i | −0.0783824 | + | 0.0783824i | ||||
\(759\) | −29.0877 | −1.05582 | ||||||||
\(760\) | 11.0255 | − | 10.2303i | 0.399938 | − | 0.371091i | ||||
\(761\) | − | 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 | ||||||
\(765\) | −3.61007 | − | 3.89070i | −0.130522 | − | 0.140669i | ||||
\(766\) | 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 | \(0.564832\pi\) | |||||||
\(770\) | 3.69153 | + | 4.17266i | 0.133034 | + | 0.150372i | ||||
\(771\) | −13.2830 | −0.478374 | ||||||||
\(772\) | 17.3574 | + | 17.3574i | 0.624708 | + | 0.624708i | ||||
\(773\) | 21.5065 | + | 21.5065i | 0.773535 | + | 0.773535i | 0.978723 | − | 0.205188i | \(-0.0657806\pi\) |
−0.205188 | + | 0.978723i | \(0.565781\pi\) | |||||||
\(774\) | − | 1.22015i | − | 0.0438572i | ||||||
\(775\) | 1.84498 | − | 24.6220i | 0.0662738 | − | 0.884450i | ||||
\(776\) | 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 | ||||||
\(780\) | 3.07456 | + | 0.115031i | 0.110087 | + | 0.00411876i | ||||
\(781\) | 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 | ||||
\(785\) | −18.4639 | + | 17.1321i | −0.659004 | + | 0.611471i | ||||
\(786\) | 4.44496 | 0.158547 | ||||||||
\(787\) | 37.4673 | − | 37.4673i | 1.33557 | − | 1.33557i | 0.435262 | − | 0.900304i | \(-0.356656\pi\) |
0.900304 | − | 0.435262i | \(-0.143344\pi\) | |||||||
\(788\) | −5.22431 | + | 5.22431i | −0.186108 | + | 0.186108i | ||||
\(789\) | 21.7476 | 0.774235 | ||||||||
\(790\) | 3.34597 | − | 3.10463i | 0.119044 | − | 0.110458i | ||||
\(791\) | 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 | ||||||||
\(795\) | 17.0534 | + | 0.638029i | 0.604821 | + | 0.0226286i | ||||
\(796\) | − | 1.19886i | − | 0.0424923i | ||||||
\(797\) | 6.96365 | − | 6.96365i | 0.246665 | − | 0.246665i | −0.572935 | − | 0.819601i | \(-0.694195\pi\) |
0.819601 | + | 0.572935i | \(0.194195\pi\) | |||||||
\(798\) | 0.106958 | − | 4.51077i | 0.00378627 | − | 0.159680i | ||||
\(799\) | − | 1.02484i | − | 0.0362563i | ||||||
\(800\) | 8.90470 | + | 10.3473i | 0.314829 | + | 0.365832i | ||||
\(801\) | 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 | ||||||||
\(805\) | 32.3346 | − | 28.6062i | 1.13964 | − | 1.00824i | ||||
\(806\) | −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 | \(-0.266387\pi\) | |||||||
\(810\) | 0.359321 | + | 0.387253i | 0.0126253 | + | 0.0136067i | ||||
\(811\) | − | 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 | ||||||
\(815\) | 24.2125 | − | 22.4661i | 0.848128 | − | 0.786953i | ||||
\(816\) | 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 | ||||
\(820\) | 33.1549 | + | 1.24045i | 1.15782 | + | 0.0433183i | ||||
\(821\) | −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 | −0.799752 | − | 0.600330i | \(-0.795036\pi\) |
0.600330 | + | 0.799752i | \(0.295036\pi\) | |||||||
\(824\) | 16.5264 | 0.575726 | ||||||||
\(825\) | 13.0003 | + | 15.1064i | 0.452611 | + | 0.525936i | ||||
\(826\) | 2.63560 | + | 2.76362i | 0.0917041 | + | 0.0961587i | ||||
\(827\) | 17.0630 | + | 17.0630i | 0.593339 | + | 0.593339i | 0.938532 | − | 0.345193i | \(-0.112187\pi\) |
−0.345193 | + | 0.938532i | \(0.612187\pi\) | |||||||
\(828\) | −10.0321 | + | 10.0321i | −0.348640 | + | 0.348640i | ||||
\(829\) | −37.7146 | −1.30988 | −0.654940 | − | 0.755680i | \(-0.727306\pi\) | ||||
−0.654940 | + | 0.755680i | \(0.727306\pi\) | |||||||
\(830\) | −0.334892 | + | 8.95106i | −0.0116243 | + | 0.310696i | ||||
\(831\) | 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 | ||||||||
\(835\) | 10.7472 | − | 9.97204i | 0.371923 | − | 0.345097i | ||||
\(836\) | 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 | \(0.373834\pi\) | |||||||
\(840\) | 5.50246 | + | 0.336638i | 0.189853 | + | 0.0116151i | ||||
\(841\) | 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 | ||||||
\(845\) | 1.04494 | − | 27.9294i | 0.0359470 | − | 0.960799i | ||||
\(846\) | 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 | ||||||||
\(850\) | 2.79602 | + | 0.209512i | 0.0959028 | + | 0.00718621i | ||||
\(851\) | −3.01631 | −0.103398 | ||||||||
\(852\) | 1.64003 | − | 1.64003i | 0.0561865 | − | 0.0561865i | ||||
\(853\) | 24.1276 | + | 24.1276i | 0.826114 | + | 0.826114i | 0.986977 | − | 0.160863i | \(-0.0514276\pi\) |
−0.160863 | + | 0.986977i | \(0.551428\pi\) | |||||||
\(854\) | 3.21636 | − | 3.06736i | 0.110062 | − | 0.104963i | ||||
\(855\) | 0.603474 | − | 16.1298i | 0.0206384 | − | 0.551627i | ||||
\(856\) | −9.85740 | −0.336919 | ||||||||
\(857\) | −1.53096 | + | 1.53096i | −0.0522968 | + | 0.0522968i | −0.732772 | − | 0.680475i | \(-0.761774\pi\) |
0.680475 | + | 0.732772i | \(0.261774\pi\) | |||||||
\(858\) | 0.471266 | − | 0.471266i | 0.0160888 | − | 0.0160888i | ||||
\(859\) | −41.8095 | −1.42652 | −0.713261 | − | 0.700899i | \(-0.752782\pi\) | ||||
−0.713261 | + | 0.700899i | \(0.752782\pi\) | |||||||
\(860\) | −15.2714 | − | 16.4585i | −0.520750 | − | 0.561231i | ||||
\(861\) | 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 | −0.904738 | − | 0.425968i | \(-0.859933\pi\) |
0.425968 | + | 0.904738i | \(0.359933\pi\) | |||||||
\(864\) | −2.73028 | −0.0928859 | ||||||||
\(865\) | −5.34566 | − | 5.76121i | −0.181758 | − | 0.195887i | ||||
\(866\) | 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 | ||||||||
\(870\) | −1.92787 | − | 0.0721287i | −0.0653610 | − | 0.00244539i | ||||
\(871\) | 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 | ||||||||
\(875\) | −29.3077 | − | 4.00749i | −0.990780 | − | 0.135478i | ||||
\(876\) | 3.80249 | 0.128474 | ||||||||
\(877\) | −39.3844 | − | 39.3844i | −1.32992 | − | 1.32992i | −0.905438 | − | 0.424477i | \(-0.860458\pi\) |
−0.424477 | − | 0.905438i | \(-0.639542\pi\) | |||||||
\(878\) | −5.04414 | − | 5.04414i | −0.170231 | − | 0.170231i | ||||
\(879\) | 6.77742i | 0.228597i | ||||||||
\(880\) | −32.6721 | − | 1.22238i | −1.10138 | − | 0.0412065i | ||||
\(881\) | − | 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 | −0.989450 | − | 0.144876i | \(-0.953722\pi\) |
0.144876 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(884\) | 3.26597i | 0.109846i | ||||||||
\(885\) | 9.29219 | + | 10.0145i | 0.312354 | + | 0.336635i | ||||
\(886\) | 4.25735 | 0.143028 | ||||||||
\(887\) | −37.8947 | + | 37.8947i | −1.27238 | + | 1.27238i | −0.327541 | + | 0.944837i | \(0.606220\pi\) |
−0.944837 | + | 0.327541i | \(0.893780\pi\) | |||||||
\(888\) | −0.272349 | − | 0.272349i | −0.00913942 | − | 0.00913942i | ||||
\(889\) | 15.2055 | + | 15.9441i | 0.509975 | + | 0.534748i | ||||
\(890\) | −2.81198 | − | 3.03057i | −0.0942577 | − | 0.101585i | ||||
\(891\) | −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 | ||||||||
\(895\) | −1.84849 | + | 49.4068i | −0.0617882 | + | 1.65149i | ||||
\(896\) | −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 | ||||||||
\(900\) | 9.69375 | + | 0.726374i | 0.323125 | + | 0.0242125i | ||||
\(901\) | 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 | ||||||
\(905\) | −0.709378 | + | 18.9604i | −0.0235805 | + | 0.630265i | ||||
\(906\) | 3.47857i | 0.115568i | ||||||||
\(907\) | −30.5961 | − | 30.5961i | −1.01593 | − | 1.01593i | −0.999871 | − | 0.0160555i | \(-0.994889\pi\) |
−0.0160555 | − | 0.999871i | \(-0.505111\pi\) | |||||||
\(908\) | −8.07687 | − | 8.07687i | −0.268040 | − | 0.268040i | ||||
\(909\) | 6.31633 | 0.209499 | ||||||||
\(910\) | −0.0604047 | + | 0.987334i | −0.00200240 | + | 0.0327298i | ||||
\(911\) | 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 | ||||||
\(915\) | 11.6551 | − | 10.8144i | 0.385306 | − | 0.357514i | ||||
\(916\) | − | 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 | \(0.712579\pi\) | |||||||
\(920\) | 0.568481 | − | 15.1945i | 0.0187423 | − | 0.500947i | ||||
\(921\) | 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 | ||||
\(925\) | 1.34809 | + | 1.56649i | 0.0443249 | + | 0.0515057i | ||||
\(926\) | −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 | \(0.267623\pi\) | |||||||
\(930\) | −2.60692 | − | 0.0975344i | −0.0854843 | − | 0.00319828i | ||||
\(931\) | −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 | ||||||||
\(935\) | −15.5084 | + | 14.3898i | −0.507180 | + | 0.470598i | ||||
\(936\) | − | 0.659476i | − | 0.0215556i | ||||||
\(937\) | −8.25994 | + | 8.25994i | −0.269841 | + | 0.269841i | −0.829036 | − | 0.559195i | \(-0.811110\pi\) |
0.559195 | + | 0.829036i | \(0.311110\pi\) | |||||||
\(938\) | −0.0197851 | + | 0.834403i | −0.000646005 | + | 0.0272442i | ||||
\(939\) | 26.1742i | 0.854163i | ||||||||
\(940\) | 1.27670 | + | 1.37595i | 0.0416415 | + | 0.0448785i | ||||
\(941\) | − | 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 | ||||||||
\(945\) | 4.43095 | − | 3.92004i | 0.144139 | − | 0.127519i | ||||
\(946\) | −4.86353 | −0.158127 | ||||||||
\(947\) | 4.26936 | + | 4.26936i | 0.138736 | + | 0.138736i | 0.773064 | − | 0.634328i | \(-0.218723\pi\) |
−0.634328 | + | 0.773064i | \(0.718723\pi\) | |||||||
\(948\) | 11.8782 | + | 11.8782i | 0.385785 | + | 0.385785i | ||||
\(949\) | 1.38419i | 0.0449327i | ||||||||
\(950\) | 5.56207 | + | 6.46315i | 0.180457 | + | 0.209692i | ||||
\(951\) | − | 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 | \(-0.489861\pi\) |
0.999493 | − | 0.0318472i | \(-0.0101390\pi\) | |||||||
\(954\) | − | 1.80304i | − | 0.0583757i | ||||||
\(955\) | 34.1652 | + | 1.27825i | 1.10556 | + | 0.0413631i | ||||
\(956\) | 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 | ||||
\(960\) | −10.9682 | + | 10.1771i | −0.353998 | + | 0.328464i | ||||
\(961\) | 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 | ||||||||
\(965\) | −20.6957 | + | 19.2030i | −0.666220 | + | 0.618166i | ||||
\(966\) | −3.14802 | − | 3.30093i | −0.101286 | − | 0.106206i | ||||
\(967\) | −17.5518 | − | 17.5518i | −0.564429 | − | 0.564429i | 0.366134 | − | 0.930562i | \(-0.380681\pi\) |
−0.930562 | + | 0.366134i | \(0.880681\pi\) | |||||||
\(968\) | −3.22094 | + | 3.22094i | −0.103525 | + | 0.103525i | ||||
\(969\) | 17.1339 | 0.550421 | ||||||||
\(970\) | −5.55205 | − | 0.207723i | −0.178266 | − | 0.00666957i | ||||
\(971\) | 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 | ||||||||
\(975\) | −0.264416 | + | 3.52873i | −0.00846808 | + | 0.113010i | ||||
\(976\) | 26.0828i | 0.834889i | ||||||||
\(977\) | 5.19792 | + | 5.19792i | 0.166296 | + | 0.166296i | 0.785349 | − | 0.619053i | \(-0.212483\pi\) |
−0.619053 | + | 0.785349i | \(0.712483\pi\) | |||||||
\(978\) | −2.46765 | − | 2.46765i | −0.0789067 | − | 0.0789067i | ||||
\(979\) | 31.1938 | 0.996959 | ||||||||
\(980\) | 2.57781 | − | 30.3219i | 0.0823450 | − | 0.968598i | ||||
\(981\) | −0.668223 | −0.0213347 | ||||||||
\(982\) | −5.36509 | − | 5.36509i | −0.171207 | − | 0.171207i | ||||
\(983\) | −30.3939 | − | 30.3939i | −0.969415 | − | 0.969415i | 0.0301305 | − | 0.999546i | \(-0.490408\pi\) |
−0.999546 | + | 0.0301305i | \(0.990408\pi\) | |||||||
\(984\) | − | 7.11153i | − | 0.226707i | ||||||
\(985\) | −5.77980 | − | 6.22909i | −0.184160 | − | 0.198475i | ||||
\(986\) | − | 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 | ||||||||
\(990\) | 1.54360 | − | 1.43226i | 0.0490588 | − | 0.0455203i | ||||
\(991\) | 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 | ||||
\(995\) | 1.37788 | + | 0.0515514i | 0.0436817 | + | 0.00163429i | ||||
\(996\) | −32.9651 | −1.04454 | ||||||||
\(997\) | −21.1809 | + | 21.1809i | −0.670805 | + | 0.670805i | −0.957902 | − | 0.287097i | \(-0.907310\pi\) |
0.287097 | + | 0.957902i | \(0.407310\pi\) | |||||||
\(998\) | 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 | 105.2.m.a.97.4 | yes | 16 | |
3.2 | odd | 2 | 315.2.p.e.307.5 | 16 | |||
4.3 | odd | 2 | 1680.2.cz.d.97.4 | 16 | |||
5.2 | odd | 4 | 525.2.m.b.118.6 | 16 | |||
5.3 | odd | 4 | inner | 105.2.m.a.13.3 | ✓ | 16 | |
5.4 | even | 2 | 525.2.m.b.307.5 | 16 | |||
7.2 | even | 3 | 735.2.v.a.472.3 | 32 | |||
7.3 | odd | 6 | 735.2.v.a.607.5 | 32 | |||
7.4 | even | 3 | 735.2.v.a.607.6 | 32 | |||
7.5 | odd | 6 | 735.2.v.a.472.4 | 32 | |||
7.6 | odd | 2 | inner | 105.2.m.a.97.3 | yes | 16 | |
15.8 | even | 4 | 315.2.p.e.118.6 | 16 | |||
20.3 | even | 4 | 1680.2.cz.d.433.5 | 16 | |||
21.20 | even | 2 | 315.2.p.e.307.6 | 16 | |||
28.27 | even | 2 | 1680.2.cz.d.97.5 | 16 | |||
35.3 | even | 12 | 735.2.v.a.313.3 | 32 | |||
35.13 | even | 4 | inner | 105.2.m.a.13.4 | yes | 16 | |
35.18 | odd | 12 | 735.2.v.a.313.4 | 32 | |||
35.23 | odd | 12 | 735.2.v.a.178.5 | 32 | |||
35.27 | even | 4 | 525.2.m.b.118.5 | 16 | |||
35.33 | even | 12 | 735.2.v.a.178.6 | 32 | |||
35.34 | odd | 2 | 525.2.m.b.307.6 | 16 | |||
105.83 | odd | 4 | 315.2.p.e.118.5 | 16 | |||
140.83 | odd | 4 | 1680.2.cz.d.433.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.3 | ✓ | 16 | 5.3 | odd | 4 | inner | |
105.2.m.a.13.4 | yes | 16 | 35.13 | even | 4 | inner | |
105.2.m.a.97.3 | yes | 16 | 7.6 | odd | 2 | inner | |
105.2.m.a.97.4 | yes | 16 | 1.1 | even | 1 | trivial | |
315.2.p.e.118.5 | 16 | 105.83 | odd | 4 | |||
315.2.p.e.118.6 | 16 | 15.8 | even | 4 | |||
315.2.p.e.307.5 | 16 | 3.2 | odd | 2 | |||
315.2.p.e.307.6 | 16 | 21.20 | even | 2 | |||
525.2.m.b.118.5 | 16 | 35.27 | even | 4 | |||
525.2.m.b.118.6 | 16 | 5.2 | odd | 4 | |||
525.2.m.b.307.5 | 16 | 5.4 | even | 2 | |||
525.2.m.b.307.6 | 16 | 35.34 | odd | 2 | |||
735.2.v.a.178.5 | 32 | 35.23 | odd | 12 | |||
735.2.v.a.178.6 | 32 | 35.33 | even | 12 | |||
735.2.v.a.313.3 | 32 | 35.3 | even | 12 | |||
735.2.v.a.313.4 | 32 | 35.18 | odd | 12 | |||
735.2.v.a.472.3 | 32 | 7.2 | even | 3 | |||
735.2.v.a.472.4 | 32 | 7.5 | odd | 6 | |||
735.2.v.a.607.5 | 32 | 7.3 | odd | 6 | |||
735.2.v.a.607.6 | 32 | 7.4 | even | 3 | |||
1680.2.cz.d.97.4 | 16 | 4.3 | odd | 2 | |||
1680.2.cz.d.97.5 | 16 | 28.27 | even | 2 | |||
1680.2.cz.d.433.4 | 16 | 140.83 | odd | 4 | |||
1680.2.cz.d.433.5 | 16 | 20.3 | even | 4 |