Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1755,2,Mod(586,1755)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1755, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1755.586");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1755 = 3^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1755.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0137455547\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 5 x^{15} + 20 x^{14} - 44 x^{13} + 96 x^{12} - 107 x^{11} + 178 x^{10} - 19 x^{9} + 231 x^{8} + \cdots + 268 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | no (minimal twist has level 585) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1171.6 | ||
Root | \(-0.317019 + 1.12493i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1755.1171 |
Dual form | 1755.2.i.f.586.6 |
$q$-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 \(\left(\mathbb{Z}/1755\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.817019 | + | 1.41512i | 0.577719 | + | 1.00064i | 0.995740 | + | 0.0922020i | \(0.0293905\pi\) |
−0.418021 | + | 0.908437i | \(0.637276\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.335039 | + | 0.580304i | −0.167519 | + | 0.290152i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.06506 | − | 1.84473i | −0.402554 | − | 0.697244i | 0.591479 | − | 0.806320i | \(-0.298544\pi\) |
−0.994033 | + | 0.109076i | \(0.965211\pi\) | |||||||
\(8\) | 2.17314 | 0.768322 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.63404 | −0.516728 | ||||||||
\(11\) | −0.0263229 | − | 0.0455925i | −0.00793664 | − | 0.0137467i | 0.862030 | − | 0.506858i | \(-0.169193\pi\) |
−0.869966 | + | 0.493111i | \(0.835860\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | ||||
\(14\) | 1.74034 | − | 3.01437i | 0.465127 | − | 0.805623i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.44558 | + | 4.23586i | 0.611394 | + | 1.05897i | ||||
\(17\) | 2.48047 | 0.601603 | 0.300801 | − | 0.953687i | \(-0.402746\pi\) | ||||
0.300801 | + | 0.953687i | \(0.402746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.13105 | 0.488895 | 0.244448 | − | 0.969662i | \(-0.421393\pi\) | ||||
0.244448 | + | 0.969662i | \(0.421393\pi\) | |||||||
\(20\) | −0.335039 | − | 0.580304i | −0.0749170 | − | 0.129760i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0430125 | − | 0.0744999i | 0.00917030 | − | 0.0158834i | ||||
\(23\) | 2.46542 | − | 4.27023i | 0.514075 | − | 0.890404i | −0.485792 | − | 0.874074i | \(-0.661469\pi\) |
0.999867 | − | 0.0163291i | \(-0.00519795\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.63404 | 0.320461 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.42734 | 0.269743 | ||||||||
\(29\) | −1.24347 | − | 2.15375i | −0.230906 | − | 0.399941i | 0.727169 | − | 0.686459i | \(-0.240836\pi\) |
−0.958075 | + | 0.286517i | \(0.907502\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.08030 | − | 7.06728i | 0.732843 | − | 1.26932i | −0.222820 | − | 0.974860i | \(-0.571526\pi\) |
0.955663 | − | 0.294462i | \(-0.0951404\pi\) | |||||||
\(32\) | −1.82302 | + | 3.15756i | −0.322267 | + | 0.558183i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.02659 | + | 3.51016i | 0.347558 | + | 0.601987i | ||||
\(35\) | 2.13012 | 0.360055 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.11963 | −0.184066 | −0.0920331 | − | 0.995756i | \(-0.529337\pi\) | ||||
−0.0920331 | + | 0.995756i | \(0.529337\pi\) | |||||||
\(38\) | 1.74110 | + | 3.01568i | 0.282444 | + | 0.489208i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.08657 | + | 1.88200i | −0.171802 | + | 0.297570i | ||||
\(41\) | −2.73708 | + | 4.74077i | −0.427461 | + | 0.740384i | −0.996647 | − | 0.0818250i | \(-0.973925\pi\) |
0.569186 | + | 0.822209i | \(0.307258\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.73861 | + | 8.20752i | 0.722632 | + | 1.25163i | 0.959941 | + | 0.280201i | \(0.0904010\pi\) |
−0.237310 | + | 0.971434i | \(0.576266\pi\) | |||||||
\(44\) | 0.0352767 | 0.00531816 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.05716 | 1.18796 | ||||||||
\(47\) | 4.88280 | + | 8.45726i | 0.712230 | + | 1.23362i | 0.964018 | + | 0.265836i | \(0.0856479\pi\) |
−0.251789 | + | 0.967782i | \(0.581019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.23130 | − | 2.13268i | 0.175900 | − | 0.304668i | ||||
\(50\) | 0.817019 | − | 1.41512i | 0.115544 | − | 0.200128i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.335039 | + | 0.580304i | 0.0464615 | + | 0.0804737i | ||||
\(53\) | 3.64091 | 0.500118 | 0.250059 | − | 0.968231i | \(-0.419550\pi\) | ||||
0.250059 | + | 0.968231i | \(0.419550\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0526457 | 0.00709875 | ||||||||
\(56\) | −2.31452 | − | 4.00887i | −0.309291 | − | 0.535708i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.03187 | − | 3.51931i | 0.266798 | − | 0.462108i | ||||
\(59\) | 3.74544 | − | 6.48728i | 0.487614 | − | 0.844572i | −0.512284 | − | 0.858816i | \(-0.671201\pi\) |
0.999899 | + | 0.0142434i | \(0.00453397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.89202 | + | 5.00912i | 0.370285 | + | 0.641352i | 0.989609 | − | 0.143783i | \(-0.0459267\pi\) |
−0.619324 | + | 0.785135i | \(0.712593\pi\) | |||||||
\(62\) | 13.3347 | 1.69351 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.82454 | 0.478067 | ||||||||
\(65\) | 0.500000 | + | 0.866025i | 0.0620174 | + | 0.107417i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.11795 | − | 5.40045i | 0.380919 | − | 0.659770i | −0.610275 | − | 0.792189i | \(-0.708941\pi\) |
0.991194 | + | 0.132419i | \(0.0422745\pi\) | |||||||
\(68\) | −0.831054 | + | 1.43943i | −0.100780 | + | 0.174556i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.74034 | + | 3.01437i | 0.208011 | + | 0.360286i | ||||
\(71\) | −2.50050 | −0.296755 | −0.148377 | − | 0.988931i | \(-0.547405\pi\) | ||||
−0.148377 | + | 0.988931i | \(0.547405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.10245 | −0.129032 | −0.0645159 | − | 0.997917i | \(-0.520550\pi\) | ||||
−0.0645159 | + | 0.997917i | \(0.520550\pi\) | |||||||
\(74\) | −0.914759 | − | 1.58441i | −0.106339 | − | 0.184184i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.713983 | + | 1.23666i | −0.0818995 | + | 0.141854i | ||||
\(77\) | −0.0560707 | + | 0.0971174i | −0.00638985 | + | 0.0110676i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.80779 | + | 13.5235i | 0.878445 | + | 1.52151i | 0.853048 | + | 0.521833i | \(0.174752\pi\) |
0.0253969 | + | 0.999677i | \(0.491915\pi\) | |||||||
\(80\) | −4.89115 | −0.546847 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −8.94500 | −0.987810 | ||||||||
\(83\) | 0.244576 | + | 0.423618i | 0.0268457 | + | 0.0464981i | 0.879136 | − | 0.476571i | \(-0.158120\pi\) |
−0.852290 | + | 0.523069i | \(0.824787\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.24024 | + | 2.14815i | −0.134522 | + | 0.233000i | ||||
\(86\) | −7.74307 | + | 13.4114i | −0.834957 | + | 1.44619i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0572033 | − | 0.0990790i | −0.00609789 | − | 0.0105619i | ||||
\(89\) | 4.64901 | 0.492794 | 0.246397 | − | 0.969169i | \(-0.420753\pi\) | ||||
0.246397 | + | 0.969169i | \(0.420753\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.13012 | −0.223297 | ||||||||
\(92\) | 1.65202 | + | 2.86138i | 0.172235 | + | 0.298320i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.97868 | + | 13.8195i | −0.822938 | + | 1.42537i | ||||
\(95\) | −1.06552 | + | 1.84554i | −0.109320 | + | 0.189348i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.67049 | − | 6.35747i | −0.372682 | − | 0.645503i | 0.617296 | − | 0.786731i | \(-0.288228\pi\) |
−0.989977 | + | 0.141228i | \(0.954895\pi\) | |||||||
\(98\) | 4.02399 | 0.406484 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.670078 | 0.0670078 | ||||||||
\(101\) | 0.276429 | + | 0.478790i | 0.0275058 | + | 0.0476414i | 0.879451 | − | 0.475990i | \(-0.157910\pi\) |
−0.851945 | + | 0.523632i | \(0.824577\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.91898 | − | 6.78787i | 0.386148 | − | 0.668828i | −0.605780 | − | 0.795633i | \(-0.707139\pi\) |
0.991928 | + | 0.126804i | \(0.0404720\pi\) | |||||||
\(104\) | 1.08657 | − | 1.88200i | 0.106547 | − | 0.184545i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.97469 | + | 5.15232i | 0.288928 | + | 0.500437i | ||||
\(107\) | −19.4173 | −1.87714 | −0.938572 | − | 0.345084i | \(-0.887851\pi\) | ||||
−0.938572 | + | 0.345084i | \(0.887851\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.13502 | −0.204498 | −0.102249 | − | 0.994759i | \(-0.532604\pi\) | ||||
−0.102249 | + | 0.994759i | \(0.532604\pi\) | |||||||
\(110\) | 0.0430125 | + | 0.0744999i | 0.00410108 | + | 0.00710328i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.20936 | − | 9.02288i | 0.492238 | − | 0.852582i | ||||
\(113\) | −3.11765 | + | 5.39992i | −0.293283 | + | 0.507982i | −0.974584 | − | 0.224022i | \(-0.928081\pi\) |
0.681301 | + | 0.732004i | \(0.261415\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.46542 | + | 4.27023i | 0.229901 | + | 0.398201i | ||||
\(116\) | 1.66644 | 0.154725 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.2404 | 1.12682 | ||||||||
\(119\) | −2.64185 | − | 4.57581i | −0.242178 | − | 0.419464i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.49861 | − | 9.52388i | 0.499874 | − | 0.865807i | ||||
\(122\) | −4.72567 | + | 8.18509i | −0.427842 | + | 0.741043i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.73412 | + | 4.73563i | 0.245531 | + | 0.425272i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.6036 | −0.940918 | −0.470459 | − | 0.882422i | \(-0.655912\pi\) | ||||
−0.470459 | + | 0.882422i | \(0.655912\pi\) | |||||||
\(128\) | 6.77076 | + | 11.7273i | 0.598456 | + | 1.03656i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.817019 | + | 1.41512i | −0.0716573 | + | 0.124114i | ||||
\(131\) | −8.09616 | + | 14.0230i | −0.707365 | + | 1.22519i | 0.258467 | + | 0.966020i | \(0.416783\pi\) |
−0.965831 | + | 0.259171i | \(0.916551\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.26969 | − | 3.93121i | −0.196807 | − | 0.340880i | ||||
\(134\) | 10.1897 | 0.880256 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.39042 | 0.462224 | ||||||||
\(137\) | −10.3843 | − | 17.9861i | −0.887189 | − | 1.53666i | −0.843184 | − | 0.537626i | \(-0.819321\pi\) |
−0.0440058 | − | 0.999031i | \(-0.514012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.25038 | − | 2.16571i | 0.106055 | − | 0.183693i | −0.808113 | − | 0.589027i | \(-0.799511\pi\) |
0.914169 | + | 0.405333i | \(0.132845\pi\) | |||||||
\(140\) | −0.713672 | + | 1.23612i | −0.0603163 | + | 0.104471i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.04295 | − | 3.53850i | −0.171441 | − | 0.296944i | ||||
\(143\) | −0.0526457 | −0.00440245 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.48694 | 0.206529 | ||||||||
\(146\) | −0.900721 | − | 1.56009i | −0.0745442 | − | 0.129114i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.375120 | − | 0.649727i | 0.0308347 | − | 0.0534072i | ||||
\(149\) | −0.945127 | + | 1.63701i | −0.0774279 | + | 0.134109i | −0.902139 | − | 0.431444i | \(-0.858004\pi\) |
0.824712 | + | 0.565553i | \(0.191337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.44343 | + | 4.23214i | 0.198843 | + | 0.344406i | 0.948154 | − | 0.317812i | \(-0.102948\pi\) |
−0.749310 | + | 0.662219i | \(0.769615\pi\) | |||||||
\(152\) | 4.63107 | 0.375629 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.183243 | −0.0147662 | ||||||||
\(155\) | 4.08030 | + | 7.06728i | 0.327737 | + | 0.567658i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.99989 | − | 15.5883i | 0.718269 | − | 1.24408i | −0.243416 | − | 0.969922i | \(-0.578268\pi\) |
0.961685 | − | 0.274157i | \(-0.0883987\pi\) | |||||||
\(158\) | −12.7582 | + | 22.0979i | −1.01499 | + | 1.75801i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.82302 | − | 3.15756i | −0.144122 | − | 0.249627i | ||||
\(161\) | −10.5032 | −0.827772 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.41748 | 0.737634 | 0.368817 | − | 0.929502i | \(-0.379763\pi\) | ||||
0.368817 | + | 0.929502i | \(0.379763\pi\) | |||||||
\(164\) | −1.83406 | − | 3.17668i | −0.143216 | − | 0.248057i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.399646 | + | 0.692207i | −0.0310185 | + | 0.0537257i | ||||
\(167\) | −7.74523 | + | 13.4151i | −0.599344 | + | 1.03809i | 0.393574 | + | 0.919293i | \(0.371238\pi\) |
−0.992918 | + | 0.118801i | \(0.962095\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | −4.05318 | −0.310865 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.35048 | −0.484219 | ||||||||
\(173\) | −4.83831 | − | 8.38021i | −0.367850 | − | 0.637135i | 0.621379 | − | 0.783510i | \(-0.286573\pi\) |
−0.989229 | + | 0.146375i | \(0.953239\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.06506 | + | 1.84473i | −0.0805108 | + | 0.139449i | ||||
\(176\) | 0.128749 | − | 0.223000i | 0.00970482 | − | 0.0168092i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.79832 | + | 6.57889i | 0.284696 | + | 0.493109i | ||||
\(179\) | 3.31630 | 0.247872 | 0.123936 | − | 0.992290i | \(-0.460448\pi\) | ||||
0.123936 | + | 0.992290i | \(0.460448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.6189 | −1.68125 | −0.840623 | − | 0.541621i | \(-0.817811\pi\) | ||||
−0.840623 | + | 0.541621i | \(0.817811\pi\) | |||||||
\(182\) | −1.74034 | − | 3.01437i | −0.129003 | − | 0.223440i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.35770 | − | 9.27981i | 0.394975 | − | 0.684117i | ||||
\(185\) | 0.559815 | − | 0.969629i | 0.0411585 | − | 0.0712885i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0652931 | − | 0.113091i | −0.00477470 | − | 0.00827003i | ||||
\(188\) | −6.54371 | −0.477249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.48221 | −0.252626 | ||||||||
\(191\) | 2.94105 | + | 5.09405i | 0.212807 | + | 0.368593i | 0.952592 | − | 0.304251i | \(-0.0984061\pi\) |
−0.739785 | + | 0.672843i | \(0.765073\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.229769 | − | 0.397972i | 0.0165392 | − | 0.0286467i | −0.857637 | − | 0.514255i | \(-0.828069\pi\) |
0.874177 | + | 0.485608i | \(0.161402\pi\) | |||||||
\(194\) | 5.99771 | − | 10.3883i | 0.430611 | − | 0.745840i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.825068 | + | 1.42906i | 0.0589335 | + | 0.102076i | ||||
\(197\) | 2.31119 | 0.164665 | 0.0823326 | − | 0.996605i | \(-0.473763\pi\) | ||||
0.0823326 | + | 0.996605i | \(0.473763\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.3734 | 1.72779 | 0.863893 | − | 0.503675i | \(-0.168019\pi\) | ||||
0.863893 | + | 0.503675i | \(0.168019\pi\) | |||||||
\(200\) | −1.08657 | − | 1.88200i | −0.0768322 | − | 0.133077i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.451696 | + | 0.782360i | −0.0317812 | + | 0.0550467i | ||||
\(203\) | −2.64873 | + | 4.58774i | −0.185904 | + | 0.321996i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.73708 | − | 4.74077i | −0.191166 | − | 0.331110i | ||||
\(206\) | 12.8075 | 0.892341 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.89115 | 0.339140 | ||||||||
\(209\) | −0.0560952 | − | 0.0971597i | −0.00388019 | − | 0.00672068i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.6969 | + | 23.7237i | −0.942934 | + | 1.63321i | −0.183097 | + | 0.983095i | \(0.558612\pi\) |
−0.759836 | + | 0.650114i | \(0.774721\pi\) | |||||||
\(212\) | −1.21985 | + | 2.11284i | −0.0837794 | + | 0.145110i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −15.8643 | − | 27.4778i | −1.08446 | − | 1.87834i | ||||
\(215\) | −9.47722 | −0.646341 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.3830 | −1.18004 | ||||||||
\(218\) | −1.74435 | − | 3.02131i | −0.118142 | − | 0.204629i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.0176384 | + | 0.0305505i | −0.00118918 | + | 0.00205972i | ||||
\(221\) | 1.24024 | − | 2.14815i | 0.0834273 | − | 0.144500i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.6679 | − | 21.9415i | −0.848307 | − | 1.46931i | −0.882718 | − | 0.469904i | \(-0.844289\pi\) |
0.0344101 | − | 0.999408i | \(-0.489045\pi\) | |||||||
\(224\) | 7.76649 | 0.518920 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.1887 | −0.677742 | ||||||||
\(227\) | −10.6209 | − | 18.3959i | −0.704931 | − | 1.22098i | −0.966716 | − | 0.255850i | \(-0.917645\pi\) |
0.261785 | − | 0.965126i | \(-0.415689\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.11686 | + | 10.5947i | −0.404214 | + | 0.700119i | −0.994230 | − | 0.107273i | \(-0.965788\pi\) |
0.590016 | + | 0.807392i | \(0.299121\pi\) | |||||||
\(230\) | −4.02858 | + | 6.97771i | −0.265637 | + | 0.460096i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.70223 | − | 4.68040i | −0.177410 | − | 0.307284i | ||||
\(233\) | −11.4048 | −0.747154 | −0.373577 | − | 0.927599i | \(-0.621869\pi\) | ||||
−0.373577 | + | 0.927599i | \(0.621869\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.76560 | −0.637038 | ||||||||
\(236\) | 2.50973 | + | 4.34698i | 0.163370 | + | 0.282965i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.31687 | − | 7.47705i | 0.279821 | − | 0.484665i | ||||
\(239\) | 7.42854 | − | 12.8666i | 0.480512 | − | 0.832272i | −0.519238 | − | 0.854630i | \(-0.673784\pi\) |
0.999750 | + | 0.0223581i | \(0.00711739\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.29538 | + | 16.1001i | 0.598768 | + | 1.03710i | 0.993003 | + | 0.118087i | \(0.0376763\pi\) |
−0.394235 | + | 0.919010i | \(0.628990\pi\) | |||||||
\(242\) | 17.9699 | 1.15515 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.87575 | −0.248120 | ||||||||
\(245\) | 1.23130 | + | 2.13268i | 0.0786650 | + | 0.136252i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.06552 | − | 1.84554i | 0.0677976 | − | 0.117429i | ||||
\(248\) | 8.86707 | − | 15.3582i | 0.563059 | − | 0.975247i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.817019 | + | 1.41512i | 0.0516728 | + | 0.0894999i | ||||
\(251\) | −30.0723 | −1.89815 | −0.949073 | − | 0.315058i | \(-0.897976\pi\) | ||||
−0.949073 | + | 0.315058i | \(0.897976\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.259587 | −0.0163201 | ||||||||
\(254\) | −8.66334 | − | 15.0054i | −0.543587 | − | 0.941520i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −7.23913 | + | 12.5385i | −0.452446 | + | 0.783659i | ||||
\(257\) | 1.52032 | − | 2.63327i | 0.0948348 | − | 0.164259i | −0.814705 | − | 0.579876i | \(-0.803101\pi\) |
0.909540 | + | 0.415617i | \(0.136434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.19247 | + | 2.06542i | 0.0740966 | + | 0.128339i | ||||
\(260\) | −0.670078 | −0.0415565 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −26.4588 | −1.63463 | ||||||||
\(263\) | −2.40051 | − | 4.15780i | −0.148022 | − | 0.256381i | 0.782474 | − | 0.622683i | \(-0.213957\pi\) |
−0.930496 | + | 0.366301i | \(0.880624\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.82046 | + | 3.15312i | −0.111830 | + | 0.193695i | ||||
\(266\) | 3.70875 | − | 6.42375i | 0.227398 | − | 0.393865i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.08927 | + | 3.61872i | 0.127623 | + | 0.221049i | ||||
\(269\) | 16.8723 | 1.02873 | 0.514363 | − | 0.857573i | \(-0.328029\pi\) | ||||
0.514363 | + | 0.857573i | \(0.328029\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.34099 | −0.142205 | −0.0711026 | − | 0.997469i | \(-0.522652\pi\) | ||||
−0.0711026 | + | 0.997469i | \(0.522652\pi\) | |||||||
\(272\) | 6.06618 | + | 10.5069i | 0.367816 | + | 0.637076i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.9683 | − | 29.3900i | 1.02509 | − | 1.77551i | ||||
\(275\) | −0.0263229 | + | 0.0455925i | −0.00158733 | + | 0.00274933i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.88617 | + | 3.26693i | 0.113329 | + | 0.196291i | 0.917110 | − | 0.398633i | \(-0.130515\pi\) |
−0.803782 | + | 0.594924i | \(0.797182\pi\) | |||||||
\(278\) | 4.08632 | 0.245081 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.62905 | 0.276638 | ||||||||
\(281\) | 5.47798 | + | 9.48813i | 0.326789 | + | 0.566015i | 0.981873 | − | 0.189541i | \(-0.0607001\pi\) |
−0.655084 | + | 0.755556i | \(0.727367\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.78483 | + | 15.2158i | −0.522204 | + | 0.904484i | 0.477462 | + | 0.878652i | \(0.341557\pi\) |
−0.999666 | + | 0.0258318i | \(0.991777\pi\) | |||||||
\(284\) | 0.837764 | − | 1.45105i | 0.0497122 | − | 0.0861040i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0430125 | − | 0.0744999i | −0.00254338 | − | 0.00440527i | ||||
\(287\) | 11.6606 | 0.688305 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.8473 | −0.638074 | ||||||||
\(290\) | 2.03187 | + | 3.51931i | 0.119316 | + | 0.206661i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.369363 | − | 0.639756i | 0.0216153 | − | 0.0374389i | ||||
\(293\) | 12.2723 | − | 21.2562i | 0.716953 | − | 1.24180i | −0.245249 | − | 0.969460i | \(-0.578870\pi\) |
0.962202 | − | 0.272338i | \(-0.0877969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.74544 | + | 6.48728i | 0.218068 | + | 0.377704i | ||||
\(296\) | −2.43312 | −0.141422 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.08875 | −0.178926 | ||||||||
\(299\) | −2.46542 | − | 4.27023i | −0.142579 | − | 0.246954i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0938 | − | 17.4830i | 0.581797 | − | 1.00770i | ||||
\(302\) | −3.99265 | + | 6.91547i | −0.229751 | + | 0.397941i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.21163 | + | 9.02681i | 0.298908 | + | 0.517723i | ||||
\(305\) | −5.78404 | −0.331193 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0689 | −0.631735 | −0.315868 | − | 0.948803i | \(-0.602296\pi\) | ||||
−0.315868 | + | 0.948803i | \(0.602296\pi\) | |||||||
\(308\) | −0.0375718 | − | 0.0650762i | −0.00214085 | − | 0.00370806i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.66736 | + | 11.5482i | −0.378680 | + | 0.655894i | ||||
\(311\) | 7.39666 | − | 12.8114i | 0.419426 | − | 0.726468i | −0.576456 | − | 0.817129i | \(-0.695565\pi\) |
0.995882 | + | 0.0906608i | \(0.0288979\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.5262 | − | 23.4281i | −0.764548 | − | 1.32424i | −0.940485 | − | 0.339834i | \(-0.889629\pi\) |
0.175937 | − | 0.984401i | \(-0.443704\pi\) | |||||||
\(314\) | 29.4123 | 1.65983 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.4636 | −0.588626 | ||||||||
\(317\) | 0.288999 | + | 0.500561i | 0.0162318 | + | 0.0281143i | 0.874027 | − | 0.485877i | \(-0.161500\pi\) |
−0.857795 | + | 0.513991i | \(0.828166\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0654632 | + | 0.113386i | −0.00366524 | + | 0.00634838i | ||||
\(320\) | −1.91227 | + | 3.31215i | −0.106899 | + | 0.185155i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.58135 | − | 14.8633i | −0.478220 | − | 0.828301i | ||||
\(323\) | 5.28600 | 0.294121 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | 7.69425 | + | 13.3268i | 0.426145 | + | 0.738105i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.94808 | + | 10.3024i | −0.328428 | + | 0.568853i | ||||
\(329\) | 10.4009 | − | 18.0149i | 0.573422 | − | 0.993196i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0570 | + | 20.8833i | 0.662712 | + | 1.14785i | 0.979900 | + | 0.199489i | \(0.0639281\pi\) |
−0.317188 | + | 0.948363i | \(0.602739\pi\) | |||||||
\(332\) | −0.327770 | −0.0179887 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.3120 | −1.38501 | ||||||||
\(335\) | 3.11795 | + | 5.40045i | 0.170352 | + | 0.295058i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.06746 | + | 5.31299i | −0.167095 | + | 0.289417i | −0.937397 | − | 0.348262i | \(-0.886772\pi\) |
0.770302 | + | 0.637679i | \(0.220105\pi\) | |||||||
\(338\) | 0.817019 | − | 1.41512i | 0.0444400 | − | 0.0769723i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.831054 | − | 1.43943i | −0.0450702 | − | 0.0780640i | ||||
\(341\) | −0.429620 | −0.0232652 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1564 | −1.08835 | ||||||||
\(344\) | 10.2977 | + | 17.8361i | 0.555214 | + | 0.961658i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.90599 | − | 13.6936i | 0.425028 | − | 0.736171i | ||||
\(347\) | −1.86200 | + | 3.22507i | −0.0999572 | + | 0.173131i | −0.911667 | − | 0.410930i | \(-0.865204\pi\) |
0.811710 | + | 0.584061i | \(0.198537\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.67433 | + | 2.90002i | 0.0896246 | + | 0.155234i | 0.907352 | − | 0.420371i | \(-0.138100\pi\) |
−0.817728 | + | 0.575605i | \(0.804767\pi\) | |||||||
\(350\) | −3.48069 | −0.186051 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.191948 | 0.0102309 | ||||||||
\(353\) | −17.7813 | − | 30.7981i | −0.946403 | − | 1.63922i | −0.752917 | − | 0.658115i | \(-0.771354\pi\) |
−0.193486 | − | 0.981103i | \(-0.561979\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.25025 | − | 2.16550i | 0.0663563 | − | 0.114933i | ||||
\(356\) | −1.55760 | + | 2.69784i | −0.0825525 | + | 0.142985i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.70948 | + | 4.69296i | 0.143200 | + | 0.248030i | ||||
\(359\) | −9.06902 | −0.478645 | −0.239322 | − | 0.970940i | \(-0.576925\pi\) | ||||
−0.239322 | + | 0.970940i | \(0.576925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4586 | −0.760981 | ||||||||
\(362\) | −18.4800 | − | 32.0083i | −0.971289 | − | 1.68232i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.713672 | − | 1.23612i | 0.0374066 | − | 0.0647901i | ||||
\(365\) | 0.551224 | − | 0.954749i | 0.0288524 | − | 0.0499738i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3093 | + | 21.3203i | 0.642541 | + | 1.11291i | 0.984864 | + | 0.173331i | \(0.0554529\pi\) |
−0.342323 | + | 0.939582i | \(0.611214\pi\) | |||||||
\(368\) | 24.1174 | 1.25721 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.82952 | 0.0951121 | ||||||||
\(371\) | −3.87778 | − | 6.71652i | −0.201324 | − | 0.348704i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.4879 | + | 23.3617i | −0.698376 | + | 1.20962i | 0.270653 | + | 0.962677i | \(0.412760\pi\) |
−0.969029 | + | 0.246946i | \(0.920573\pi\) | |||||||
\(374\) | 0.106691 | − | 0.184795i | 0.00551688 | − | 0.00955551i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.6110 | + | 18.3788i | 0.547222 | + | 0.947816i | ||||
\(377\) | −2.48694 | −0.128084 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2429 | 0.731611 | 0.365805 | − | 0.930691i | \(-0.380794\pi\) | ||||
0.365805 | + | 0.930691i | \(0.380794\pi\) | |||||||
\(380\) | −0.713983 | − | 1.23666i | −0.0366266 | − | 0.0634391i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.80579 | + | 8.32387i | −0.245886 | + | 0.425886i | ||||
\(383\) | 12.9868 | − | 22.4938i | 0.663595 | − | 1.14938i | −0.316070 | − | 0.948736i | \(-0.602363\pi\) |
0.979664 | − | 0.200644i | \(-0.0643033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.0560707 | − | 0.0971174i | −0.00285763 | − | 0.00494956i | ||||
\(386\) | 0.750903 | 0.0382200 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.91902 | 0.249726 | ||||||||
\(389\) | 12.8953 | + | 22.3354i | 0.653819 | + | 1.13245i | 0.982189 | + | 0.187898i | \(0.0601675\pi\) |
−0.328370 | + | 0.944549i | \(0.606499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.11539 | − | 10.5922i | 0.309269 | − | 0.535669i | ||||
\(392\) | 2.67580 | − | 4.63461i | 0.135148 | − | 0.234083i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.88828 | + | 3.27060i | 0.0951303 | + | 0.164771i | ||||
\(395\) | −15.6156 | −0.785705 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.2890 | −0.968086 | −0.484043 | − | 0.875044i | \(-0.660832\pi\) | ||||
−0.484043 | + | 0.875044i | \(0.660832\pi\) | |||||||
\(398\) | 19.9135 | + | 34.4913i | 0.998176 | + | 1.72889i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.44558 | − | 4.23586i | 0.122279 | − | 0.211793i | ||||
\(401\) | −8.23155 | + | 14.2575i | −0.411064 | + | 0.711983i | −0.995006 | − | 0.0998116i | \(-0.968176\pi\) |
0.583943 | + | 0.811795i | \(0.301509\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.08030 | − | 7.06728i | −0.203254 | − | 0.352046i | ||||
\(404\) | −0.370458 | −0.0184310 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.65625 | −0.429602 | ||||||||
\(407\) | 0.0294719 | + | 0.0510468i | 0.00146087 | + | 0.00253030i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.87631 | − | 17.1063i | 0.488352 | − | 0.845850i | −0.511558 | − | 0.859249i | \(-0.670932\pi\) |
0.999910 | + | 0.0133982i | \(0.00426491\pi\) | |||||||
\(410\) | 4.47250 | − | 7.74660i | 0.220881 | − | 0.382577i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.62602 | + | 4.54840i | 0.129375 | + | 0.224084i | ||||
\(413\) | −15.9564 | −0.785164 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.489152 | −0.0240115 | ||||||||
\(416\) | 1.82302 | + | 3.15756i | 0.0893809 | + | 0.154812i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.0916617 | − | 0.158763i | 0.00448332 | − | 0.00776533i | ||||
\(419\) | −8.72915 | + | 15.1193i | −0.426447 | + | 0.738628i | −0.996554 | − | 0.0829423i | \(-0.973568\pi\) |
0.570107 | + | 0.821570i | \(0.306902\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.70798 | + | 6.42241i | 0.180716 | + | 0.313009i | 0.942125 | − | 0.335263i | \(-0.108825\pi\) |
−0.761409 | + | 0.648272i | \(0.775492\pi\) | |||||||
\(422\) | −44.7625 | −2.17900 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.91222 | 0.384251 | ||||||||
\(425\) | −1.24024 | − | 2.14815i | −0.0601603 | − | 0.104201i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.16034 | − | 10.6700i | 0.298120 | − | 0.516358i | ||||
\(428\) | 6.50556 | − | 11.2680i | 0.314458 | − | 0.544657i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.74307 | − | 13.4114i | −0.373404 | − | 0.646755i | ||||
\(431\) | −33.6097 | −1.61892 | −0.809461 | − | 0.587174i | \(-0.800240\pi\) | ||||
−0.809461 | + | 0.587174i | \(0.800240\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.2826 | 1.45529 | 0.727644 | − | 0.685955i | \(-0.240615\pi\) | ||||
0.727644 | + | 0.685955i | \(0.240615\pi\) | |||||||
\(434\) | −14.2022 | − | 24.5990i | −0.681730 | − | 1.18079i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.715315 | − | 1.23896i | 0.0342574 | − | 0.0593355i | ||||
\(437\) | 5.25391 | − | 9.10005i | 0.251329 | − | 0.435314i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.3685 | + | 24.8870i | 0.685772 | + | 1.18779i | 0.973194 | + | 0.229987i | \(0.0738685\pi\) |
−0.287422 | + | 0.957804i | \(0.592798\pi\) | |||||||
\(440\) | 0.114407 | 0.00545412 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.05318 | 0.192790 | ||||||||
\(443\) | −11.2109 | − | 19.4179i | −0.532646 | − | 0.922570i | −0.999273 | − | 0.0381159i | \(-0.987864\pi\) |
0.466627 | − | 0.884454i | \(-0.345469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.32450 | + | 4.02616i | −0.110192 | + | 0.190858i | ||||
\(446\) | 20.6999 | − | 35.8532i | 0.980167 | − | 1.69770i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.07336 | − | 7.05526i | −0.192448 | − | 0.333330i | ||||
\(449\) | −16.0149 | −0.755791 | −0.377895 | − | 0.925848i | \(-0.623352\pi\) | ||||
−0.377895 | + | 0.925848i | \(0.623352\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.288192 | 0.0135704 | ||||||||
\(452\) | −2.08907 | − | 3.61837i | −0.0982614 | − | 0.170194i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.3549 | − | 30.0595i | 0.814505 | − | 1.41076i | ||||
\(455\) | 1.06506 | − | 1.84473i | 0.0499307 | − | 0.0864825i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.532780 | − | 0.922803i | −0.0249224 | − | 0.0431669i | 0.853295 | − | 0.521428i | \(-0.174601\pi\) |
−0.878218 | + | 0.478261i | \(0.841267\pi\) | |||||||
\(458\) | −19.9904 | −0.934089 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.30404 | −0.154052 | ||||||||
\(461\) | 12.3193 | + | 21.3377i | 0.573769 | + | 0.993798i | 0.996174 | + | 0.0873903i | \(0.0278527\pi\) |
−0.422405 | + | 0.906407i | \(0.638814\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.56164 | + | 6.16895i | −0.165524 | + | 0.286695i | −0.936841 | − | 0.349755i | \(-0.886265\pi\) |
0.771318 | + | 0.636451i | \(0.219598\pi\) | |||||||
\(464\) | 6.08199 | − | 10.5343i | 0.282349 | − | 0.489043i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.31794 | − | 16.1391i | −0.431645 | − | 0.747631i | ||||
\(467\) | −20.4662 | −0.947063 | −0.473531 | − | 0.880777i | \(-0.657021\pi\) | ||||
−0.473531 | + | 0.880777i | \(0.657021\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −13.2832 | −0.613361 | ||||||||
\(470\) | −7.97868 | − | 13.8195i | −0.368029 | − | 0.637445i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.13936 | − | 14.0978i | 0.374645 | − | 0.648903i | ||||
\(473\) | 0.249468 | − | 0.432090i | 0.0114705 | − | 0.0198675i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.06552 | − | 1.84554i | −0.0488895 | − | 0.0846792i | ||||
\(476\) | 3.54048 | 0.162278 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 24.2770 | 1.11041 | ||||||||
\(479\) | −7.23493 | − | 12.5313i | −0.330573 | − | 0.572568i | 0.652052 | − | 0.758175i | \(-0.273908\pi\) |
−0.982624 | + | 0.185606i | \(0.940575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.559815 | + | 0.969629i | −0.0255254 | + | 0.0442113i | ||||
\(482\) | −15.1890 | + | 26.3081i | −0.691840 | + | 1.19830i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.68450 | + | 6.38174i | 0.167477 | + | 0.290079i | ||||
\(485\) | 7.34097 | 0.333336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.8595 | 1.35306 | 0.676531 | − | 0.736414i | \(-0.263483\pi\) | ||||
0.676531 | + | 0.736414i | \(0.263483\pi\) | |||||||
\(488\) | 6.28477 | + | 10.8855i | 0.284498 | + | 0.492765i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.01199 | + | 3.48488i | −0.0908926 | + | 0.157431i | ||||
\(491\) | 11.0235 | − | 19.0932i | 0.497483 | − | 0.861665i | −0.502513 | − | 0.864570i | \(-0.667591\pi\) |
0.999996 | + | 0.00290444i | \(0.000924514\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.08439 | − | 5.34231i | −0.138914 | − | 0.240606i | ||||
\(494\) | 3.48221 | 0.156672 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 39.9147 | 1.79222 | ||||||||
\(497\) | 2.66318 | + | 4.61276i | 0.119460 | + | 0.206910i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.5861 | + | 18.3357i | −0.473901 | + | 0.820820i | −0.999554 | − | 0.0298789i | \(-0.990488\pi\) |
0.525653 | + | 0.850699i | \(0.323821\pi\) | |||||||
\(500\) | −0.335039 | + | 0.580304i | −0.0149834 | + | 0.0259520i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −24.5696 | − | 42.5558i | −1.09660 | − | 1.89936i | ||||
\(503\) | 40.3143 | 1.79752 | 0.898762 | − | 0.438436i | \(-0.144467\pi\) | ||||
0.898762 | + | 0.438436i | \(0.144467\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.552859 | −0.0246019 | ||||||||
\(506\) | −0.212088 | − | 0.367346i | −0.00942844 | − | 0.0163305i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.55262 | − | 6.15332i | 0.157622 | − | 0.273009i | ||||
\(509\) | 9.50834 | − | 16.4689i | 0.421450 | − | 0.729973i | −0.574632 | − | 0.818412i | \(-0.694855\pi\) |
0.996082 | + | 0.0884396i | \(0.0281880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.17417 | + | 2.03373i | 0.0519423 | + | 0.0899667i | ||||
\(512\) | 3.42501 | 0.151366 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.96851 | 0.219152 | ||||||||
\(515\) | 3.91898 | + | 6.78787i | 0.172691 | + | 0.299109i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.257059 | − | 0.445238i | 0.0113054 | − | 0.0195816i | ||||
\(518\) | −1.94854 | + | 3.37498i | −0.0856141 | + | 0.148288i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.08657 | + | 1.88200i | 0.0476493 | + | 0.0825310i | ||||
\(521\) | 33.4407 | 1.46507 | 0.732533 | − | 0.680732i | \(-0.238338\pi\) | ||||
0.732533 | + | 0.680732i | \(0.238338\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.40250 | −0.279962 | −0.139981 | − | 0.990154i | \(-0.544704\pi\) | ||||
−0.139981 | + | 0.990154i | \(0.544704\pi\) | |||||||
\(524\) | −5.42505 | − | 9.39647i | −0.236995 | − | 0.410487i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.92252 | − | 6.79401i | 0.171030 | − | 0.296233i | ||||
\(527\) | 10.1211 | − | 17.5302i | 0.440880 | − | 0.763627i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.656552 | − | 1.13718i | −0.0285457 | − | 0.0494426i | ||||
\(530\) | −5.94939 | −0.258425 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.04173 | 0.131876 | ||||||||
\(533\) | 2.73708 | + | 4.74077i | 0.118556 | + | 0.205346i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.70866 | − | 16.8159i | 0.419742 | − | 0.727015i | ||||
\(536\) | 6.77576 | − | 11.7360i | 0.292668 | − | 0.506916i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.7850 | + | 23.8764i | 0.594315 | + | 1.02938i | ||||
\(539\) | −0.129646 | −0.00558423 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.4745 | −0.751286 | −0.375643 | − | 0.926764i | \(-0.622578\pi\) | ||||
−0.375643 | + | 0.926764i | \(0.622578\pi\) | |||||||
\(542\) | −1.91264 | − | 3.31278i | −0.0821547 | − | 0.142296i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.52195 | + | 7.83224i | −0.193877 | + | 0.335805i | ||||
\(545\) | 1.06751 | − | 1.84898i | 0.0457271 | − | 0.0792017i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.03733 | + | 8.72491i | 0.215381 | + | 0.373050i | 0.953390 | − | 0.301740i | \(-0.0975675\pi\) |
−0.738010 | + | 0.674790i | \(0.764234\pi\) | |||||||
\(548\) | 13.9166 | 0.594486 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0860250 | −0.00366812 | ||||||||
\(551\) | −2.64989 | − | 4.58974i | −0.112889 | − | 0.195529i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.6315 | − | 28.8066i | 0.707243 | − | 1.22498i | ||||
\(554\) | −3.08206 | + | 5.33829i | −0.130944 | + | 0.226802i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.837849 | + | 1.45120i | 0.0355327 | + | 0.0615444i | ||||
\(557\) | −21.2315 | −0.899607 | −0.449804 | − | 0.893127i | \(-0.648506\pi\) | ||||
−0.449804 | + | 0.893127i | \(0.648506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.47722 | 0.400844 | ||||||||
\(560\) | 5.20936 | + | 9.02288i | 0.220136 | + | 0.381286i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.95122 | + | 15.5040i | −0.377584 | + | 0.653995i | ||||
\(563\) | 6.17245 | − | 10.6910i | 0.260138 | − | 0.450572i | −0.706140 | − | 0.708072i | \(-0.749565\pi\) |
0.966278 | + | 0.257500i | \(0.0828986\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.11765 | − | 5.39992i | −0.131160 | − | 0.227176i | ||||
\(566\) | −28.7095 | −1.20675 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.43394 | −0.228003 | ||||||||
\(569\) | 3.87874 | + | 6.71817i | 0.162605 | + | 0.281640i | 0.935802 | − | 0.352526i | \(-0.114677\pi\) |
−0.773197 | + | 0.634166i | \(0.781344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.10696 | − | 8.84552i | 0.213720 | − | 0.370173i | −0.739156 | − | 0.673534i | \(-0.764775\pi\) |
0.952876 | + | 0.303361i | \(0.0981087\pi\) | |||||||
\(572\) | 0.0176384 | − | 0.0305505i | 0.000737497 | − | 0.00127738i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.52694 | + | 16.5011i | 0.397647 | + | 0.688745i | ||||
\(575\) | −4.93083 | −0.205630 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.5539 | −1.85480 | −0.927402 | − | 0.374065i | \(-0.877964\pi\) | ||||
−0.927402 | + | 0.374065i | \(0.877964\pi\) | |||||||
\(578\) | −8.86242 | − | 15.3502i | −0.368628 | − | 0.638482i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.833220 | + | 1.44318i | −0.0345976 | + | 0.0599248i | ||||
\(581\) | 0.520975 | − | 0.902355i | 0.0216137 | − | 0.0374360i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.0958392 | − | 0.165998i | −0.00396925 | − | 0.00687495i | ||||
\(584\) | −2.39578 | −0.0991380 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 40.1066 | 1.65679 | ||||||||
\(587\) | 10.4535 | + | 18.1059i | 0.431461 | + | 0.747312i | 0.996999 | − | 0.0774099i | \(-0.0246650\pi\) |
−0.565539 | + | 0.824722i | \(0.691332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.69530 | − | 15.0607i | 0.358284 | − | 0.620565i | ||||
\(590\) | −6.12018 | + | 10.6005i | −0.251964 | + | 0.436414i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.73814 | − | 4.74260i | −0.112537 | − | 0.194920i | ||||
\(593\) | 7.48843 | 0.307513 | 0.153756 | − | 0.988109i | \(-0.450863\pi\) | ||||
0.153756 | + | 0.988109i | \(0.450863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28369 | 0.216610 | ||||||||
\(596\) | −0.633309 | − | 1.09692i | −0.0259413 | − | 0.0449317i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.02858 | − | 6.97771i | 0.164741 | − | 0.285340i | ||||
\(599\) | −13.9657 | + | 24.1893i | −0.570623 | + | 0.988349i | 0.425879 | + | 0.904780i | \(0.359965\pi\) |
−0.996502 | + | 0.0835684i | \(0.973368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.3890 | − | 28.3866i | −0.668521 | − | 1.15791i | −0.978318 | − | 0.207110i | \(-0.933594\pi\) |
0.309796 | − | 0.950803i | \(-0.399739\pi\) | |||||||
\(602\) | 32.9873 | 1.34446 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.27457 | −0.133240 | ||||||||
\(605\) | 5.49861 | + | 9.52388i | 0.223550 | + | 0.387201i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.5852 | + | 33.9226i | −0.794940 | + | 1.37688i | 0.127938 | + | 0.991782i | \(0.459164\pi\) |
−0.922878 | + | 0.385093i | \(0.874169\pi\) | |||||||
\(608\) | −3.88494 | + | 6.72891i | −0.157555 | + | 0.272893i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.72567 | − | 8.18509i | −0.191337 | − | 0.331405i | ||||
\(611\) | 9.76560 | 0.395074 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.2019 | −0.412051 | −0.206026 | − | 0.978547i | \(-0.566053\pi\) | ||||
−0.206026 | + | 0.978547i | \(0.566053\pi\) | |||||||
\(614\) | −9.04350 | − | 15.6638i | −0.364966 | − | 0.632139i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.121850 | + | 0.211050i | −0.00490946 | + | 0.00850344i | ||||
\(617\) | −4.84474 | + | 8.39133i | −0.195042 | + | 0.337822i | −0.946914 | − | 0.321486i | \(-0.895818\pi\) |
0.751872 | + | 0.659309i | \(0.229151\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.93748 | + | 17.2122i | 0.399421 | + | 0.691818i | 0.993655 | − | 0.112475i | \(-0.0358778\pi\) |
−0.594233 | + | 0.804293i | \(0.702544\pi\) | |||||||
\(620\) | −5.46823 | −0.219610 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.1728 | 0.969243 | ||||||||
\(623\) | −4.95146 | − | 8.57618i | −0.198376 | − | 0.343598i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 22.1024 | − | 38.2824i | 0.883388 | − | 1.53007i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.03062 | + | 10.4453i | 0.240648 | + | 0.416815i | ||||
\(629\) | −2.77721 | −0.110735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −38.9270 | −1.54966 | −0.774830 | − | 0.632170i | \(-0.782165\pi\) | ||||
−0.774830 | + | 0.632170i | \(0.782165\pi\) | |||||||
\(632\) | 16.9674 | + | 29.3885i | 0.674928 | + | 1.16901i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.472235 | + | 0.817935i | −0.0187548 | + | 0.0324843i | ||||
\(635\) | 5.30180 | − | 9.18299i | 0.210396 | − | 0.364416i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.23130 | − | 2.13268i | −0.0487860 | − | 0.0844998i | ||||
\(638\) | −0.213939 | −0.00846991 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.5415 | −0.535275 | ||||||||
\(641\) | −3.94706 | − | 6.83651i | −0.155899 | − | 0.270026i | 0.777487 | − | 0.628899i | \(-0.216494\pi\) |
−0.933386 | + | 0.358874i | \(0.883161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.8875 | + | 30.9821i | −0.705415 | + | 1.22182i | 0.261126 | + | 0.965305i | \(0.415906\pi\) |
−0.966541 | + | 0.256511i | \(0.917427\pi\) | |||||||
\(644\) | 3.51900 | − | 6.09508i | 0.138668 | − | 0.240180i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.31876 | + | 7.48031i | 0.169919 | + | 0.294309i | ||||
\(647\) | 1.47889 | 0.0581412 | 0.0290706 | − | 0.999577i | \(-0.490745\pi\) | ||||
0.0290706 | + | 0.999577i | \(0.490745\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.394362 | −0.0154801 | ||||||||
\(650\) | −0.817019 | − | 1.41512i | −0.0320461 | − | 0.0555055i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.15522 | + | 5.46500i | −0.123568 | + | 0.214026i | ||||
\(653\) | −3.47523 | + | 6.01927i | −0.135996 | + | 0.235552i | −0.925978 | − | 0.377579i | \(-0.876757\pi\) |
0.789981 | + | 0.613131i | \(0.210090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.09616 | − | 14.0230i | −0.316343 | − | 0.547922i | ||||
\(656\) | −26.7750 | −1.04539 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 33.9910 | 1.32511 | ||||||||
\(659\) | 15.4773 | + | 26.8075i | 0.602910 | + | 1.04427i | 0.992378 | + | 0.123230i | \(0.0393254\pi\) |
−0.389469 | + | 0.921040i | \(0.627341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.78839 | + | 3.09758i | −0.0695603 | + | 0.120482i | −0.898708 | − | 0.438548i | \(-0.855493\pi\) |
0.829147 | + | 0.559030i | \(0.188826\pi\) | |||||||
\(662\) | −19.7016 | + | 34.1241i | −0.765724 | + | 1.32627i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.531498 | + | 0.920582i | 0.0206261 | + | 0.0357255i | ||||
\(665\) | 4.53938 | 0.176029 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12.2627 | −0.474812 | ||||||||
\(668\) | −5.18991 | − | 8.98918i | −0.200804 | − | 0.347802i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.09485 | + | 8.82454i | −0.196831 | + | 0.340922i | ||||
\(671\) | 0.152252 | − | 0.263709i | 0.00587764 | − | 0.0101804i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0497 | + | 24.3347i | 0.541575 | + | 0.938035i | 0.998814 | + | 0.0486913i | \(0.0155051\pi\) |
−0.457239 | + | 0.889344i | \(0.651162\pi\) | |||||||
\(674\) | −10.0247 | −0.386136 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.670078 | 0.0257722 | ||||||||
\(677\) | 22.1467 | + | 38.3592i | 0.851167 | + | 1.47426i | 0.880156 | + | 0.474685i | \(0.157438\pi\) |
−0.0289890 | + | 0.999580i | \(0.509229\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.81856 | + | 13.5422i | −0.300049 | + | 0.519700i | ||||
\(680\) | −2.69521 | + | 4.66824i | −0.103357 | + | 0.179019i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.351008 | − | 0.607963i | −0.0134408 | − | 0.0232801i | ||||
\(683\) | 1.69041 | 0.0646816 | 0.0323408 | − | 0.999477i | \(-0.489704\pi\) | ||||
0.0323408 | + | 0.999477i | \(0.489704\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.7686 | 0.793526 | ||||||||
\(686\) | −16.4682 | − | 28.5237i | −0.628759 | − | 1.08904i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −23.1773 | + | 40.1442i | −0.883625 | + | 1.53048i | ||||
\(689\) | 1.82046 | − | 3.15312i | 0.0693538 | − | 0.120124i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.40719 | + | 9.36552i | 0.205699 | + | 0.356281i | 0.950355 | − | 0.311167i | \(-0.100720\pi\) |
−0.744656 | + | 0.667448i | \(0.767387\pi\) | |||||||
\(692\) | 6.48409 | 0.246488 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.08514 | −0.230989 | ||||||||
\(695\) | 1.25038 | + | 2.16571i | 0.0474294 | + | 0.0821502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.78926 | + | 11.7593i | −0.257162 | + | 0.445417i | ||||
\(698\) | −2.73591 | + | 4.73874i | −0.103556 | + | 0.179364i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.713672 | − | 1.23612i | −0.0269743 | − | 0.0467208i | ||||
\(701\) | 32.1755 | 1.21525 | 0.607626 | − | 0.794224i | \(-0.292122\pi\) | ||||
0.607626 | + | 0.794224i | \(0.292122\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.38598 | −0.0899891 | ||||||||
\(704\) | −0.100673 | − | 0.174370i | −0.00379425 | − | 0.00657183i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 29.0553 | − | 50.3253i | 1.09351 | − | 1.89402i | ||||
\(707\) | 0.588827 | − | 1.01988i | 0.0221451 | − | 0.0383565i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.9560 | − | 27.6366i | −0.599240 | − | 1.03791i | −0.992934 | − | 0.118672i | \(-0.962136\pi\) |
0.393694 | − | 0.919242i | \(-0.371197\pi\) | |||||||
\(710\) | 4.08591 | 0.153341 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.1030 | 0.378624 | ||||||||
\(713\) | −20.1193 | − | 34.8476i | −0.753472 | − | 1.30505i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0263229 | − | 0.0455925i | 0.000984419 | − | 0.00170506i | ||||
\(716\) | −1.11109 | + | 1.92446i | −0.0415234 | + | 0.0719206i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.40956 | − | 12.8337i | −0.276522 | − | 0.478951i | ||||
\(719\) | −20.6891 | −0.771572 | −0.385786 | − | 0.922588i | \(-0.626070\pi\) | ||||
−0.385786 | + | 0.922588i | \(0.626070\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.6958 | −0.621782 | ||||||||
\(722\) | −11.8130 | − | 20.4607i | −0.439634 | − | 0.761468i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.57820 | − | 13.1258i | 0.281641 | − | 0.487817i | ||||
\(725\) | −1.24347 | + | 2.15375i | −0.0461812 | + | 0.0799882i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.3396 | + | 21.3728i | 0.457649 | + | 0.792672i | 0.998836 | − | 0.0482305i | \(-0.0153582\pi\) |
−0.541187 | + | 0.840902i | \(0.682025\pi\) | |||||||
\(728\) | −4.62905 | −0.171564 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.80144 | 0.0666744 | ||||||||
\(731\) | 11.7540 | + | 20.3585i | 0.434737 | + | 0.752987i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.8729 | − | 18.8325i | 0.401602 | − | 0.695594i | −0.592318 | − | 0.805704i | \(-0.701787\pi\) |
0.993919 | + | 0.110110i | \(0.0351203\pi\) | |||||||
\(734\) | −20.1139 | + | 34.8382i | −0.742416 | + | 1.28590i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.98900 | + | 15.5694i | 0.331339 | + | 0.573896i | ||||
\(737\) | −0.328294 | −0.0120929 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.0460 | 1.58347 | 0.791736 | − | 0.610864i | \(-0.209178\pi\) | ||||
0.791736 | + | 0.610864i | \(0.209178\pi\) | |||||||
\(740\) | 0.375120 | + | 0.649727i | 0.0137897 | + | 0.0238844i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.33644 | − | 10.9750i | 0.232618 | − | 0.402906i | ||||
\(743\) | 3.94908 | − | 6.84001i | 0.144878 | − | 0.250936i | −0.784450 | − | 0.620193i | \(-0.787054\pi\) |
0.929327 | + | 0.369257i | \(0.120388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.945127 | − | 1.63701i | −0.0346268 | − | 0.0599754i | ||||
\(746\) | −44.0794 | −1.61386 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.0875029 | 0.00319942 | ||||||||
\(749\) | 20.6806 | + | 35.8198i | 0.755652 | + | 1.30883i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.3225 | + | 33.4676i | −0.705089 | + | 1.22125i | 0.261571 | + | 0.965184i | \(0.415759\pi\) |
−0.966660 | + | 0.256065i | \(0.917574\pi\) | |||||||
\(752\) | −23.8825 | + | 41.3657i | −0.870906 | + | 1.50845i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.03187 | − | 3.51931i | −0.0739964 | − | 0.128166i | ||||
\(755\) | −4.88685 | −0.177851 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.3437 | −0.557678 | −0.278839 | − | 0.960338i | \(-0.589950\pi\) | ||||
−0.278839 | + | 0.960338i | \(0.589950\pi\) | |||||||
\(758\) | 11.6367 | + | 20.1554i | 0.422666 | + | 0.732078i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.31553 | + | 4.01062i | −0.0839932 | + | 0.145481i | ||||
\(761\) | 24.3585 | − | 42.1902i | 0.882995 | − | 1.52939i | 0.0350009 | − | 0.999387i | \(-0.488857\pi\) |
0.847994 | − | 0.530005i | \(-0.177810\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.27392 | + | 3.93855i | 0.0823215 | + | 0.142585i | ||||
\(764\) | −3.94147 | −0.142597 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 42.4418 | 1.53349 | ||||||||
\(767\) | −3.74544 | − | 6.48728i | −0.135240 | − | 0.234242i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.18555 | + | 5.51753i | −0.114874 | + | 0.198967i | −0.917729 | − | 0.397206i | \(-0.869980\pi\) |
0.802856 | + | 0.596174i | \(0.203313\pi\) | |||||||
\(770\) | 0.0916217 | − | 0.158693i | 0.00330182 | − | 0.00571891i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.153963 | + | 0.266672i | 0.00554126 | + | 0.00959775i | ||||
\(773\) | −29.8732 | −1.07446 | −0.537232 | − | 0.843435i | \(-0.680530\pi\) | ||||
−0.537232 | + | 0.843435i | \(0.680530\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.16059 | −0.293137 | ||||||||
\(776\) | −7.97649 | − | 13.8157i | −0.286339 | − | 0.495954i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.0714 | + | 36.4968i | −0.755448 | + | 1.30847i | ||||
\(779\) | −5.83285 | + | 10.1028i | −0.208984 | + | 0.361970i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0658203 | + | 0.114004i | 0.00235523 | + | 0.00407938i | ||||
\(782\) | 19.9856 | 0.714682 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0450 | 0.430178 | ||||||||
\(785\) | 8.99989 | + | 15.5883i | 0.321220 | + | 0.556369i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.8278 | − | 20.4864i | 0.421616 | − | 0.730261i | −0.574482 | − | 0.818518i | \(-0.694796\pi\) |
0.996098 | + | 0.0882568i | \(0.0281296\pi\) | |||||||
\(788\) | −0.774338 | + | 1.34119i | −0.0275846 | + | 0.0477780i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.7582 | − | 22.0979i | −0.453917 | − | 0.786207i | ||||
\(791\) | 13.2819 | 0.472250 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.78404 | 0.205397 | ||||||||
\(794\) | −15.7594 | − | 27.2962i | −0.559282 | − | 0.968705i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.16605 | + | 14.1440i | −0.289438 | + | 0.501321i | ||||
\(797\) | −15.0003 | + | 25.9813i | −0.531339 | + | 0.920305i | 0.467992 | + | 0.883732i | \(0.344977\pi\) |
−0.999331 | + | 0.0365729i | \(0.988356\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.1116 | + | 20.9780i | 0.428479 | + | 0.742148i | ||||
\(800\) | 3.64604 | 0.128907 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.9013 | −0.949918 | ||||||||
\(803\) | 0.0290196 | + | 0.0502634i | 0.00102408 | + | 0.00177376i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.25162 | − | 9.09608i | 0.185095 | − | 0.320595i | ||||
\(806\) | 6.66736 | − | 11.5482i | 0.234848 | − | 0.406768i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.600720 | + | 1.04048i | 0.0211333 | + | 0.0366039i | ||||
\(809\) | −37.0787 | −1.30362 | −0.651808 | − | 0.758384i | \(-0.725989\pi\) | ||||
−0.651808 | + | 0.758384i | \(0.725989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.7582 | −1.50144 | −0.750722 | − | 0.660618i | \(-0.770294\pi\) | ||||
−0.750722 | + | 0.660618i | \(0.770294\pi\) | |||||||
\(812\) | −1.77486 | − | 3.07414i | −0.0622852 | − | 0.107881i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.0481581 | + | 0.0834124i | −0.00168794 | + | 0.00292360i | ||||
\(815\) | −4.70874 | + | 8.15577i | −0.164940 | + | 0.285684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0982 | + | 17.4906i | 0.353291 | + | 0.611918i | ||||
\(818\) | 32.2765 | 1.12852 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.66812 | 0.128096 | ||||||||
\(821\) | 14.2835 | + | 24.7397i | 0.498496 | + | 0.863421i | 0.999998 | − | 0.00173559i | \(-0.000552457\pi\) |
−0.501502 | + | 0.865156i | \(0.667219\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −16.0021 | + | 27.7164i | −0.557797 | + | 0.966133i | 0.439883 | + | 0.898055i | \(0.355020\pi\) |
−0.997680 | + | 0.0680777i | \(0.978313\pi\) | |||||||
\(824\) | 8.51649 | − | 14.7510i | 0.296686 | − | 0.513875i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.0367 | − | 22.5802i | −0.453605 | − | 0.785666i | ||||
\(827\) | −31.4986 | −1.09531 | −0.547657 | − | 0.836703i | \(-0.684480\pi\) | ||||
−0.547657 | + | 0.836703i | \(0.684480\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.3851 | 1.12478 | 0.562390 | − | 0.826872i | \(-0.309882\pi\) | ||||
0.562390 | + | 0.826872i | \(0.309882\pi\) | |||||||
\(830\) | −0.399646 | − | 0.692207i | −0.0138719 | − | 0.0240269i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.91227 | − | 3.31215i | 0.0662960 | − | 0.114828i | ||||
\(833\) | 3.05421 | − | 5.29005i | 0.105822 | − | 0.183289i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.74523 | − | 13.4151i | −0.268035 | − | 0.464250i | ||||
\(836\) | 0.0751763 | 0.00260003 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −28.5275 | −0.985467 | ||||||||
\(839\) | 23.0381 | + | 39.9032i | 0.795365 | + | 1.37761i | 0.922607 | + | 0.385741i | \(0.126054\pi\) |
−0.127242 | + | 0.991872i | \(0.540612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.4076 | − | 19.7585i | 0.393365 | − | 0.681328i | ||||
\(842\) | −6.05898 | + | 10.4945i | −0.208806 | + | 0.361663i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.17799 | − | 15.8967i | −0.315919 | − | 0.547189i | ||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.4254 | −0.804905 | ||||||||
\(848\) | 8.90413 | + | 15.4224i | 0.305769 | + | 0.529607i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.02659 | − | 3.51016i | 0.0695115 | − | 0.120397i | ||||
\(851\) | −2.76036 | + | 4.78108i | −0.0946238 | + | 0.163893i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.3786 | − | 42.2250i | −0.834709 | − | 1.44576i | −0.894267 | − | 0.447533i | \(-0.852303\pi\) |
0.0595585 | − | 0.998225i | \(-0.481031\pi\) | |||||||
\(854\) | 20.1324 | 0.688918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −42.1966 | −1.44225 | ||||||||
\(857\) | 15.9740 | + | 27.6677i | 0.545660 | + | 0.945111i | 0.998565 | + | 0.0535519i | \(0.0170542\pi\) |
−0.452905 | + | 0.891559i | \(0.649612\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.66749 | − | 6.35229i | 0.125133 | − | 0.216737i | −0.796652 | − | 0.604439i | \(-0.793397\pi\) |
0.921785 | + | 0.387701i | \(0.126731\pi\) | |||||||
\(860\) | 3.17524 | − | 5.49967i | 0.108275 | − | 0.187537i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −27.4597 | − | 47.5617i | −0.935282 | − | 1.61996i | ||||
\(863\) | −28.4742 | −0.969273 | −0.484637 | − | 0.874716i | \(-0.661048\pi\) | ||||
−0.484637 | + | 0.874716i | \(0.661048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.67663 | 0.329015 | ||||||||
\(866\) | 24.7414 | + | 42.8534i | 0.840748 | + | 1.45622i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.82399 | − | 10.0874i | 0.197679 | − | 0.342390i | ||||
\(869\) | 0.411046 | − | 0.711953i | 0.0139438 | − | 0.0241514i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.11795 | − | 5.40045i | −0.105648 | − | 0.182987i | ||||
\(872\) | −4.63970 | −0.157120 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 17.1702 | 0.580790 | ||||||||
\(875\) | −1.06506 | − | 1.84473i | −0.0360055 | − | 0.0623634i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.9264 | + | 39.7098i | −0.774171 | + | 1.34090i | 0.161089 | + | 0.986940i | \(0.448499\pi\) |
−0.935259 | + | 0.353963i | \(0.884834\pi\) | |||||||
\(878\) | −23.4787 | + | 40.6663i | −0.792367 | + | 1.37242i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.128749 | + | 0.223000i | 0.00434013 | + | 0.00751732i | ||||
\(881\) | 37.4454 | 1.26157 | 0.630784 | − | 0.775959i | \(-0.282733\pi\) | ||||
0.630784 | + | 0.775959i | \(0.282733\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.8068 | 1.70978 | 0.854892 | − | 0.518805i | \(-0.173623\pi\) | ||||
0.854892 | + | 0.518805i | \(0.173623\pi\) | |||||||
\(884\) | 0.831054 | + | 1.43943i | 0.0279514 | + | 0.0484132i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.3190 | − | 31.7295i | 0.615440 | − | 1.06597i | ||||
\(887\) | −22.6484 | + | 39.2282i | −0.760459 | + | 1.31715i | 0.182155 | + | 0.983270i | \(0.441693\pi\) |
−0.942614 | + | 0.333884i | \(0.891641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.2935 | + | 19.5608i | 0.378770 | + | 0.656050i | ||||
\(890\) | −7.59665 | −0.254640 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.9770 | 0.568432 | ||||||||
\(893\) | 10.4055 | + | 18.0228i | 0.348206 | + | 0.603110i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.65815 | + | 2.87200i | −0.0554258 | + | 0.0960004i | ||||
\(896\) | 14.4225 | − | 24.9805i | 0.481822 | − | 0.834540i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −13.0845 | − | 22.6630i | −0.436635 | − | 0.756274i | ||||
\(899\) | −20.2949 | −0.676872 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.03118 | 0.300872 | ||||||||
\(902\) | 0.235458 | + | 0.407825i | 0.00783989 | + | 0.0135791i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.77509 | + | 11.7348i | −0.225336 | + | 0.390294i | ||||
\(905\) | 11.3094 | − | 19.5885i | 0.375938 | − | 0.651144i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.18452 | − | 12.4439i | −0.238558 | − | 0.413195i | 0.721743 | − | 0.692161i | \(-0.243341\pi\) |
−0.960301 | + | 0.278967i | \(0.910008\pi\) | |||||||
\(908\) | 14.2336 | 0.472359 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.48069 | 0.115384 | ||||||||
\(911\) | 26.9532 | + | 46.6843i | 0.892998 | + | 1.54672i | 0.836262 | + | 0.548329i | \(0.184736\pi\) |
0.0567359 | + | 0.998389i | \(0.481931\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.0128759 | − | 0.0223017i | 0.000426129 | − | 0.000738077i | ||||
\(914\) | 0.870583 | − | 1.50789i | 0.0287963 | − | 0.0498767i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.09877 | − | 7.09929i | −0.135427 | − | 0.234567i | ||||
\(917\) | 34.4915 | 1.13901 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.6573 | −0.516487 | −0.258244 | − | 0.966080i | \(-0.583144\pi\) | ||||
−0.258244 | + | 0.966080i | \(0.583144\pi\) | |||||||
\(920\) | 5.35770 | + | 9.27981i | 0.176638 | + | 0.305946i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.1303 | + | 34.8667i | −0.662955 | + | 1.14827i | ||||
\(923\) | −1.25025 | + | 2.16550i | −0.0411525 | + | 0.0712781i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.559815 | + | 0.969629i | 0.0184066 | + | 0.0318812i | ||||
\(926\) | −11.6397 | −0.382505 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.06746 | 0.297654 | ||||||||
\(929\) | −11.5720 | − | 20.0432i | −0.379664 | − | 0.657597i | 0.611350 | − | 0.791361i | \(-0.290627\pi\) |
−0.991013 | + | 0.133764i | \(0.957294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.62396 | − | 4.54483i | 0.0859969 | − | 0.148951i | ||||
\(932\) | 3.82105 | − | 6.61826i | 0.125163 | − | 0.216788i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.7213 | − | 28.9621i | −0.547137 | − | 0.947668i | ||||
\(935\) | 0.130586 | 0.00427062 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.6354 | 0.478118 | 0.239059 | − | 0.971005i | \(-0.423161\pi\) | ||||
0.239059 | + | 0.971005i | \(0.423161\pi\) | |||||||
\(938\) | −10.8526 | − | 18.7973i | −0.354351 | − | 0.613754i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.27186 | − | 5.66702i | 0.106716 | − | 0.184838i | ||||
\(941\) | −11.0197 | + | 19.0866i | −0.359231 | + | 0.622206i | −0.987833 | − | 0.155521i | \(-0.950294\pi\) |
0.628602 | + | 0.777727i | \(0.283628\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.4961 | + | 23.3759i | 0.439494 | + | 0.761225i | ||||
\(944\) | 36.6390 | 1.19250 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.815279 | 0.0265070 | ||||||||
\(947\) | −25.1953 | − | 43.6396i | −0.818737 | − | 1.41809i | −0.906613 | − | 0.421963i | \(-0.861341\pi\) |
0.0878754 | − | 0.996131i | \(-0.471992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.551224 | + | 0.954749i | −0.0178935 | + | 0.0309925i | ||||
\(950\) | 1.74110 | − | 3.01568i | 0.0564889 | − | 0.0978416i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.74111 | − | 9.94389i | −0.186070 | − | 0.322283i | ||||
\(953\) | 7.28058 | 0.235841 | 0.117921 | − | 0.993023i | \(-0.462377\pi\) | ||||
0.117921 | + | 0.993023i | \(0.462377\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.88211 | −0.190340 | ||||||||
\(956\) | 4.97770 | + | 8.62163i | 0.160990 | + | 0.278843i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.8222 | − | 20.4766i | 0.381956 | − | 0.661568i | ||||
\(959\) | −22.1197 | + | 38.3125i | −0.714283 | + | 1.23718i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.7977 | − | 30.8264i | −0.574118 | − | 0.994401i | ||||
\(962\) | −1.82952 | −0.0589861 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.4573 | −0.401221 | ||||||||
\(965\) | 0.229769 | + | 0.397972i | 0.00739654 | + | 0.0128112i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.821636 | + | 1.42312i | −0.0264220 | + | 0.0457643i | −0.878934 | − | 0.476943i | \(-0.841745\pi\) |
0.852512 | + | 0.522708i | \(0.175078\pi\) | |||||||
\(968\) | 11.9493 | − | 20.6967i | 0.384064 | − | 0.665219i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.99771 | + | 10.3883i | 0.192575 | + | 0.333550i | ||||
\(971\) | −59.5135 | −1.90988 | −0.954939 | − | 0.296803i | \(-0.904080\pi\) | ||||
−0.954939 | + | 0.296803i | \(0.904080\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.32689 | −0.170772 | ||||||||
\(974\) | 24.3957 | + | 42.2547i | 0.781690 | + | 1.35393i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.1453 | + | 24.5004i | −0.452780 | + | 0.784238i | ||||
\(977\) | −7.66363 | + | 13.2738i | −0.245181 | + | 0.424666i | −0.962183 | − | 0.272405i | \(-0.912181\pi\) |
0.717001 | + | 0.697072i | \(0.245514\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.122375 | − | 0.211960i | −0.00391112 | − | 0.00677427i | ||||
\(980\) | −1.65014 | −0.0527117 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 36.0255 | 1.14962 | ||||||||
\(983\) | −1.63477 | − | 2.83150i | −0.0521411 | − | 0.0903110i | 0.838777 | − | 0.544475i | \(-0.183271\pi\) |
−0.890918 | + | 0.454164i | \(0.849938\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.15559 | + | 2.00155i | −0.0368203 | + | 0.0637746i | ||||
\(986\) | 5.04000 | − | 8.72954i | 0.160506 | − | 0.278005i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.713983 | + | 1.23666i | 0.0227148 | + | 0.0393432i | ||||
\(989\) | 46.7306 | 1.48595 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.2309 | −1.24621 | −0.623106 | − | 0.782138i | \(-0.714129\pi\) | ||||
−0.623106 | + | 0.782138i | \(0.714129\pi\) | |||||||
\(992\) | 14.8769 | + | 25.7676i | 0.472343 | + | 0.818122i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.35173 | + | 7.53742i | −0.138028 | + | 0.239072i | ||||
\(995\) | −12.1867 | + | 21.1080i | −0.386345 | + | 0.669169i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.4127 | + | 28.4276i | 0.519795 | + | 0.900312i | 0.999735 | + | 0.0230105i | \(0.00732513\pi\) |
−0.479940 | + | 0.877301i | \(0.659342\pi\) | |||||||
\(998\) | −34.5963 | −1.09513 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1755.2.i.f.1171.6 | 16 | ||
3.2 | odd | 2 | 585.2.i.e.391.3 | yes | 16 | ||
9.2 | odd | 6 | 585.2.i.e.196.3 | ✓ | 16 | ||
9.4 | even | 3 | 5265.2.a.ba.1.3 | 8 | |||
9.5 | odd | 6 | 5265.2.a.bf.1.6 | 8 | |||
9.7 | even | 3 | inner | 1755.2.i.f.586.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.e.196.3 | ✓ | 16 | 9.2 | odd | 6 | ||
585.2.i.e.391.3 | yes | 16 | 3.2 | odd | 2 | ||
1755.2.i.f.586.6 | 16 | 9.7 | even | 3 | inner | ||
1755.2.i.f.1171.6 | 16 | 1.1 | even | 1 | trivial | ||
5265.2.a.ba.1.3 | 8 | 9.4 | even | 3 | |||
5265.2.a.bf.1.6 | 8 | 9.5 | odd | 6 |