Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [552,2,Mod(91,552)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(552, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("552.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 552 = 2^{3} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 552.n (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.40774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 91.1 | ||
Character | \(\chi\) | \(=\) | 552.91 |
Dual form | 552.2.n.b.91.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/552\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(185\) | \(277\) | \(415\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.38507 | − | 0.285614i | −0.979394 | − | 0.201960i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.83685 | + | 0.791193i | 0.918424 | + | 0.395596i | ||||
\(5\) | −2.03317 | −0.909259 | −0.454630 | − | 0.890681i | \(-0.650228\pi\) | ||||
−0.454630 | + | 0.890681i | \(0.650228\pi\) | |||||||
\(6\) | 1.38507 | + | 0.285614i | 0.565453 | + | 0.116602i | ||||
\(7\) | 1.21988 | 0.461071 | 0.230535 | − | 0.973064i | \(-0.425952\pi\) | ||||
0.230535 | + | 0.973064i | \(0.425952\pi\) | |||||||
\(8\) | −2.31819 | − | 1.62049i | −0.819605 | − | 0.572930i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.81608 | + | 0.580701i | 0.890523 | + | 0.183634i | ||||
\(11\) | 1.88814i | 0.569296i | 0.958632 | + | 0.284648i | \(0.0918768\pi\) | ||||
−0.958632 | + | 0.284648i | \(0.908123\pi\) | |||||||
\(12\) | −1.83685 | − | 0.791193i | −0.530253 | − | 0.228398i | ||||
\(13\) | − | 3.19024i | − | 0.884814i | −0.896814 | − | 0.442407i | \(-0.854125\pi\) | ||
0.896814 | − | 0.442407i | \(-0.145875\pi\) | |||||||
\(14\) | −1.68962 | − | 0.348415i | −0.451570 | − | 0.0931178i | ||||
\(15\) | 2.03317 | 0.524961 | ||||||||
\(16\) | 2.74803 | + | 2.90660i | 0.687007 | + | 0.726651i | ||||
\(17\) | 5.91574i | 1.43478i | 0.696673 | + | 0.717389i | \(0.254663\pi\) | ||||
−0.696673 | + | 0.717389i | \(0.745337\pi\) | |||||||
\(18\) | −1.38507 | − | 0.285614i | −0.326465 | − | 0.0673199i | ||||
\(19\) | − | 6.08344i | − | 1.39564i | −0.716274 | − | 0.697819i | \(-0.754154\pi\) | ||
0.716274 | − | 0.697819i | \(-0.245846\pi\) | |||||||
\(20\) | −3.73462 | − | 1.60863i | −0.835086 | − | 0.359700i | ||||
\(21\) | −1.21988 | −0.266199 | ||||||||
\(22\) | 0.539280 | − | 2.61521i | 0.114975 | − | 0.557565i | ||||
\(23\) | −3.96642 | + | 2.69583i | −0.827056 | + | 0.562120i | ||||
\(24\) | 2.31819 | + | 1.62049i | 0.473199 | + | 0.330781i | ||||
\(25\) | −0.866240 | −0.173248 | ||||||||
\(26\) | −0.911179 | + | 4.41871i | −0.178697 | + | 0.866581i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.24073 | + | 0.965159i | 0.423459 | + | 0.182398i | ||||
\(29\) | − | 9.30575i | − | 1.72804i | −0.503462 | − | 0.864018i | \(-0.667941\pi\) | ||
0.503462 | − | 0.864018i | \(-0.332059\pi\) | |||||||
\(30\) | −2.81608 | − | 0.580701i | −0.514144 | − | 0.106021i | ||||
\(31\) | 3.55669i | 0.638800i | 0.947620 | + | 0.319400i | \(0.103481\pi\) | ||||
−0.947620 | + | 0.319400i | \(0.896519\pi\) | |||||||
\(32\) | −2.97605 | − | 4.81073i | −0.526096 | − | 0.850425i | ||||
\(33\) | − | 1.88814i | − | 0.328683i | ||||||
\(34\) | 1.68962 | − | 8.19372i | 0.289767 | − | 1.40521i | ||||
\(35\) | −2.48021 | −0.419233 | ||||||||
\(36\) | 1.83685 | + | 0.791193i | 0.306141 | + | 0.131865i | ||||
\(37\) | −11.1137 | −1.82709 | −0.913544 | − | 0.406739i | \(-0.866666\pi\) | ||||
−0.913544 | + | 0.406739i | \(0.866666\pi\) | |||||||
\(38\) | −1.73752 | + | 8.42601i | −0.281863 | + | 1.36688i | ||||
\(39\) | 3.19024i | 0.510848i | ||||||||
\(40\) | 4.71327 | + | 3.29472i | 0.745233 | + | 0.520941i | ||||
\(41\) | −2.52410 | −0.394198 | −0.197099 | − | 0.980384i | \(-0.563152\pi\) | ||||
−0.197099 | + | 0.980384i | \(0.563152\pi\) | |||||||
\(42\) | 1.68962 | + | 0.348415i | 0.260714 | + | 0.0537616i | ||||
\(43\) | 11.6630i | 1.77859i | 0.457330 | + | 0.889297i | \(0.348806\pi\) | ||||
−0.457330 | + | 0.889297i | \(0.651194\pi\) | |||||||
\(44\) | −1.49388 | + | 3.46823i | −0.225212 | + | 0.522856i | ||||
\(45\) | −2.03317 | −0.303086 | ||||||||
\(46\) | 6.26374 | − | 2.60106i | 0.923539 | − | 0.383505i | ||||
\(47\) | − | 11.2078i | − | 1.63483i | −0.576052 | − | 0.817413i | \(-0.695408\pi\) | ||
0.576052 | − | 0.817413i | \(-0.304592\pi\) | |||||||
\(48\) | −2.74803 | − | 2.90660i | −0.396644 | − | 0.419532i | ||||
\(49\) | −5.51190 | −0.787414 | ||||||||
\(50\) | 1.19980 | + | 0.247411i | 0.169678 | + | 0.0349891i | ||||
\(51\) | − | 5.91574i | − | 0.828369i | ||||||
\(52\) | 2.52410 | − | 5.85999i | 0.350029 | − | 0.812635i | ||||
\(53\) | −11.0682 | −1.52034 | −0.760169 | − | 0.649725i | \(-0.774884\pi\) | ||||
−0.760169 | + | 0.649725i | \(0.774884\pi\) | |||||||
\(54\) | 1.38507 | + | 0.285614i | 0.188484 | + | 0.0388672i | ||||
\(55\) | − | 3.83890i | − | 0.517638i | ||||||
\(56\) | −2.82791 | − | 1.97680i | −0.377896 | − | 0.264161i | ||||
\(57\) | 6.08344i | 0.805772i | ||||||||
\(58\) | −2.65786 | + | 12.8891i | −0.348994 | + | 1.69243i | ||||
\(59\) | 0.657857 | 0.0856456 | 0.0428228 | − | 0.999083i | \(-0.486365\pi\) | ||||
0.0428228 | + | 0.999083i | \(0.486365\pi\) | |||||||
\(60\) | 3.73462 | + | 1.60863i | 0.482137 | + | 0.207673i | ||||
\(61\) | −10.3789 | −1.32888 | −0.664441 | − | 0.747341i | \(-0.731330\pi\) | ||||
−0.664441 | + | 0.747341i | \(0.731330\pi\) | |||||||
\(62\) | 1.01584 | − | 4.92627i | 0.129012 | − | 0.625637i | ||||
\(63\) | 1.21988 | 0.153690 | ||||||||
\(64\) | 2.74803 | + | 7.51321i | 0.343503 | + | 0.939151i | ||||
\(65\) | 6.48629i | 0.804525i | ||||||||
\(66\) | −0.539280 | + | 2.61521i | −0.0663808 | + | 0.321910i | ||||
\(67\) | 2.45869i | 0.300377i | 0.988657 | + | 0.150189i | \(0.0479881\pi\) | ||||
−0.988657 | + | 0.150189i | \(0.952012\pi\) | |||||||
\(68\) | −4.68049 | + | 10.8663i | −0.567593 | + | 1.31773i | ||||
\(69\) | 3.96642 | − | 2.69583i | 0.477501 | − | 0.324540i | ||||
\(70\) | 3.43528 | + | 0.708385i | 0.410594 | + | 0.0846682i | ||||
\(71\) | − | 4.84611i | − | 0.575127i | −0.957762 | − | 0.287564i | \(-0.907155\pi\) | ||
0.957762 | − | 0.287564i | \(-0.0928453\pi\) | |||||||
\(72\) | −2.31819 | − | 1.62049i | −0.273202 | − | 0.190977i | ||||
\(73\) | −7.87149 | −0.921288 | −0.460644 | − | 0.887585i | \(-0.652382\pi\) | ||||
−0.460644 | + | 0.887585i | \(0.652382\pi\) | |||||||
\(74\) | 15.3933 | + | 3.17425i | 1.78944 | + | 0.368999i | ||||
\(75\) | 0.866240 | 0.100025 | ||||||||
\(76\) | 4.81318 | − | 11.1744i | 0.552109 | − | 1.28179i | ||||
\(77\) | 2.30330i | 0.262486i | ||||||||
\(78\) | 0.911179 | − | 4.41871i | 0.103171 | − | 0.500321i | ||||
\(79\) | 4.23131 | 0.476060 | 0.238030 | − | 0.971258i | \(-0.423498\pi\) | ||||
0.238030 | + | 0.971258i | \(0.423498\pi\) | |||||||
\(80\) | −5.58719 | − | 5.90960i | −0.624667 | − | 0.660714i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.49606 | + | 0.720918i | 0.386075 | + | 0.0796121i | ||||
\(83\) | 7.58314i | 0.832358i | 0.909283 | + | 0.416179i | \(0.136631\pi\) | ||||
−0.909283 | + | 0.416179i | \(0.863369\pi\) | |||||||
\(84\) | −2.24073 | − | 0.965159i | −0.244484 | − | 0.105307i | ||||
\(85\) | − | 12.0277i | − | 1.30458i | ||||||
\(86\) | 3.33113 | − | 16.1541i | 0.359205 | − | 1.74194i | ||||
\(87\) | 9.30575i | 0.997681i | ||||||||
\(88\) | 3.05971 | − | 4.37708i | 0.326167 | − | 0.466598i | ||||
\(89\) | − | 3.85989i | − | 0.409147i | −0.978851 | − | 0.204574i | \(-0.934419\pi\) | ||
0.978851 | − | 0.204574i | \(-0.0655808\pi\) | |||||||
\(90\) | 2.81608 | + | 0.580701i | 0.296841 | + | 0.0612113i | ||||
\(91\) | − | 3.89171i | − | 0.407962i | ||||||
\(92\) | −9.41864 | + | 1.81364i | −0.981961 | + | 0.189085i | ||||
\(93\) | − | 3.55669i | − | 0.368811i | ||||||
\(94\) | −3.20111 | + | 15.5236i | −0.330169 | + | 1.60114i | ||||
\(95\) | 12.3686i | 1.26900i | ||||||||
\(96\) | 2.97605 | + | 4.81073i | 0.303742 | + | 0.490993i | ||||
\(97\) | − | 3.03678i | − | 0.308338i | −0.988044 | − | 0.154169i | \(-0.950730\pi\) | ||
0.988044 | − | 0.154169i | \(-0.0492701\pi\) | |||||||
\(98\) | 7.63437 | + | 1.57428i | 0.771188 | + | 0.159026i | ||||
\(99\) | 1.88814i | 0.189765i | ||||||||
\(100\) | −1.59115 | − | 0.685363i | −0.159115 | − | 0.0685363i | ||||
\(101\) | 7.00245i | 0.696770i | 0.937352 | + | 0.348385i | \(0.113270\pi\) | ||||
−0.937352 | + | 0.348385i | \(0.886730\pi\) | |||||||
\(102\) | −1.68962 | + | 8.19372i | −0.167297 | + | 0.811299i | ||||
\(103\) | 3.05695 | 0.301210 | 0.150605 | − | 0.988594i | \(-0.451878\pi\) | ||||
0.150605 | + | 0.988594i | \(0.451878\pi\) | |||||||
\(104\) | −5.16975 | + | 7.39559i | −0.506936 | + | 0.725198i | ||||
\(105\) | 2.48021 | 0.242044 | ||||||||
\(106\) | 15.3303 | + | 3.16124i | 1.48901 | + | 0.307047i | ||||
\(107\) | − | 4.21095i | − | 0.407088i | −0.979066 | − | 0.203544i | \(-0.934754\pi\) | ||
0.979066 | − | 0.203544i | \(-0.0652459\pi\) | |||||||
\(108\) | −1.83685 | − | 0.791193i | −0.176751 | − | 0.0761326i | ||||
\(109\) | −3.18091 | −0.304676 | −0.152338 | − | 0.988328i | \(-0.548680\pi\) | ||||
−0.152338 | + | 0.988328i | \(0.548680\pi\) | |||||||
\(110\) | −1.09645 | + | 5.31716i | −0.104542 | + | 0.506971i | ||||
\(111\) | 11.1137 | 1.05487 | ||||||||
\(112\) | 3.35226 | + | 3.54570i | 0.316759 | + | 0.335037i | ||||
\(113\) | − | 18.9194i | − | 1.77979i | −0.456169 | − | 0.889893i | \(-0.650779\pi\) | ||
0.456169 | − | 0.889893i | \(-0.349221\pi\) | |||||||
\(114\) | 1.73752 | − | 8.42601i | 0.162734 | − | 0.789168i | ||||
\(115\) | 8.06438 | − | 5.48108i | 0.752008 | − | 0.511113i | ||||
\(116\) | 7.36265 | − | 17.0933i | 0.683604 | − | 1.58707i | ||||
\(117\) | − | 3.19024i | − | 0.294938i | ||||||
\(118\) | −0.911179 | − | 0.187893i | −0.0838808 | − | 0.0172970i | ||||
\(119\) | 7.21648i | 0.661534i | ||||||||
\(120\) | −4.71327 | − | 3.29472i | −0.430260 | − | 0.300766i | ||||
\(121\) | 7.43492 | 0.675902 | ||||||||
\(122\) | 14.3755 | + | 2.96436i | 1.30150 | + | 0.268381i | ||||
\(123\) | 2.52410 | 0.227590 | ||||||||
\(124\) | −2.81403 | + | 6.53310i | −0.252707 | + | 0.586690i | ||||
\(125\) | 11.9270 | 1.06679 | ||||||||
\(126\) | −1.68962 | − | 0.348415i | −0.150523 | − | 0.0310393i | ||||
\(127\) | 7.44653i | 0.660773i | 0.943846 | + | 0.330386i | \(0.107179\pi\) | ||||
−0.943846 | + | 0.330386i | \(0.892821\pi\) | |||||||
\(128\) | −1.66034 | − | 11.1912i | −0.146754 | − | 0.989173i | ||||
\(129\) | − | 11.6630i | − | 1.02687i | ||||||
\(130\) | 1.85258 | − | 8.98398i | 0.162482 | − | 0.787947i | ||||
\(131\) | 1.82236 | 0.159220 | 0.0796101 | − | 0.996826i | \(-0.474632\pi\) | ||||
0.0796101 | + | 0.996826i | \(0.474632\pi\) | |||||||
\(132\) | 1.49388 | − | 3.46823i | 0.130026 | − | 0.301871i | ||||
\(133\) | − | 7.42106i | − | 0.643488i | ||||||
\(134\) | 0.702238 | − | 3.40547i | 0.0606641 | − | 0.294187i | ||||
\(135\) | 2.03317 | 0.174987 | ||||||||
\(136\) | 9.58639 | − | 13.7138i | 0.822026 | − | 1.17595i | ||||
\(137\) | − | 0.220739i | − | 0.0188590i | −0.999956 | − | 0.00942952i | \(-0.996998\pi\) | ||
0.999956 | − | 0.00942952i | \(-0.00300155\pi\) | |||||||
\(138\) | −6.26374 | + | 2.60106i | −0.533205 | + | 0.221417i | ||||
\(139\) | 21.9828 | 1.86456 | 0.932279 | − | 0.361741i | \(-0.117817\pi\) | ||||
0.932279 | + | 0.361741i | \(0.117817\pi\) | |||||||
\(140\) | −4.55578 | − | 1.96233i | −0.385034 | − | 0.165847i | ||||
\(141\) | 11.2078i | 0.943867i | ||||||||
\(142\) | −1.38412 | + | 6.71221i | −0.116153 | + | 0.563276i | ||||
\(143\) | 6.02363 | 0.503721 | ||||||||
\(144\) | 2.74803 | + | 2.90660i | 0.229002 | + | 0.242217i | ||||
\(145\) | 18.9201i | 1.57123i | ||||||||
\(146\) | 10.9026 | + | 2.24821i | 0.902304 | + | 0.186063i | ||||
\(147\) | 5.51190 | 0.454614 | ||||||||
\(148\) | −20.4143 | − | 8.79312i | −1.67804 | − | 0.722790i | ||||
\(149\) | 14.3997 | 1.17967 | 0.589835 | − | 0.807524i | \(-0.299193\pi\) | ||||
0.589835 | + | 0.807524i | \(0.299193\pi\) | |||||||
\(150\) | −1.19980 | − | 0.247411i | −0.0979636 | − | 0.0202010i | ||||
\(151\) | − | 4.90495i | − | 0.399160i | −0.979882 | − | 0.199580i | \(-0.936042\pi\) | ||
0.979882 | − | 0.199580i | \(-0.0639577\pi\) | |||||||
\(152\) | −9.85816 | + | 14.1026i | −0.799602 | + | 1.14387i | ||||
\(153\) | 5.91574i | 0.478259i | ||||||||
\(154\) | 0.657857 | − | 3.19024i | 0.0530116 | − | 0.257077i | ||||
\(155\) | − | 7.23133i | − | 0.580835i | ||||||
\(156\) | −2.52410 | + | 5.85999i | −0.202089 | + | 0.469175i | ||||
\(157\) | 5.78202 | 0.461455 | 0.230728 | − | 0.973018i | \(-0.425889\pi\) | ||||
0.230728 | + | 0.973018i | \(0.425889\pi\) | |||||||
\(158\) | −5.86067 | − | 1.20852i | −0.466250 | − | 0.0961450i | ||||
\(159\) | 11.0682 | 0.877768 | ||||||||
\(160\) | 6.05080 | + | 9.78101i | 0.478358 | + | 0.773257i | ||||
\(161\) | −4.83855 | + | 3.28859i | −0.381331 | + | 0.259177i | ||||
\(162\) | −1.38507 | − | 0.285614i | −0.108822 | − | 0.0224400i | ||||
\(163\) | −11.2880 | −0.884146 | −0.442073 | − | 0.896979i | \(-0.645757\pi\) | ||||
−0.442073 | + | 0.896979i | \(0.645757\pi\) | |||||||
\(164\) | −4.63638 | − | 1.99705i | −0.362041 | − | 0.155943i | ||||
\(165\) | 3.83890i | 0.298858i | ||||||||
\(166\) | 2.16585 | − | 10.5032i | 0.168103 | − | 0.815206i | ||||
\(167\) | − | 0.358139i | − | 0.0277136i | −0.999904 | − | 0.0138568i | \(-0.995589\pi\) | ||
0.999904 | − | 0.0138568i | \(-0.00441090\pi\) | |||||||
\(168\) | 2.82791 | + | 1.97680i | 0.218178 | + | 0.152513i | ||||
\(169\) | 2.82236 | 0.217104 | ||||||||
\(170\) | −3.43528 | + | 16.6592i | −0.263474 | + | 1.27770i | ||||
\(171\) | − | 6.08344i | − | 0.465213i | ||||||
\(172\) | −9.22770 | + | 21.4232i | −0.703605 | + | 1.63350i | ||||
\(173\) | 10.1430i | 0.771157i | 0.922675 | + | 0.385578i | \(0.125998\pi\) | ||||
−0.922675 | + | 0.385578i | \(0.874002\pi\) | |||||||
\(174\) | 2.65786 | − | 12.8891i | 0.201492 | − | 0.977123i | ||||
\(175\) | −1.05671 | −0.0798796 | ||||||||
\(176\) | −5.48808 | + | 5.18867i | −0.413680 | + | 0.391110i | ||||
\(177\) | −0.657857 | −0.0494475 | ||||||||
\(178\) | −1.10244 | + | 5.34622i | −0.0826313 | + | 0.400716i | ||||
\(179\) | −11.8262 | −0.883931 | −0.441966 | − | 0.897032i | \(-0.645719\pi\) | ||||
−0.441966 | + | 0.897032i | \(0.645719\pi\) | |||||||
\(180\) | −3.73462 | − | 1.60863i | −0.278362 | − | 0.119900i | ||||
\(181\) | −20.2209 | −1.50301 | −0.751506 | − | 0.659727i | \(-0.770672\pi\) | ||||
−0.751506 | + | 0.659727i | \(0.770672\pi\) | |||||||
\(182\) | −1.11153 | + | 5.39029i | −0.0823919 | + | 0.399555i | ||||
\(183\) | 10.3789 | 0.767230 | ||||||||
\(184\) | 13.5635 | + | 0.178080i | 0.999914 | + | 0.0131282i | ||||
\(185\) | 22.5961 | 1.66130 | ||||||||
\(186\) | −1.01584 | + | 4.92627i | −0.0744851 | + | 0.361212i | ||||
\(187\) | −11.1698 | −0.816813 | ||||||||
\(188\) | 8.86753 | − | 20.5870i | 0.646731 | − | 1.50146i | ||||
\(189\) | −1.21988 | −0.0887331 | ||||||||
\(190\) | 3.53266 | − | 17.1315i | 0.256286 | − | 1.24285i | ||||
\(191\) | −4.20470 | −0.304241 | −0.152121 | − | 0.988362i | \(-0.548610\pi\) | ||||
−0.152121 | + | 0.988362i | \(0.548610\pi\) | |||||||
\(192\) | −2.74803 | − | 7.51321i | −0.198322 | − | 0.542219i | ||||
\(193\) | −6.30116 | −0.453567 | −0.226784 | − | 0.973945i | \(-0.572821\pi\) | ||||
−0.226784 | + | 0.973945i | \(0.572821\pi\) | |||||||
\(194\) | −0.867348 | + | 4.20616i | −0.0622719 | + | 0.301985i | ||||
\(195\) | − | 6.48629i | − | 0.464493i | ||||||
\(196\) | −10.1245 | − | 4.36097i | −0.723180 | − | 0.311498i | ||||
\(197\) | 11.6091i | 0.827111i | 0.910479 | + | 0.413556i | \(0.135713\pi\) | ||||
−0.910479 | + | 0.413556i | \(0.864287\pi\) | |||||||
\(198\) | 0.539280 | − | 2.61521i | 0.0383250 | − | 0.185855i | ||||
\(199\) | 8.61769 | 0.610892 | 0.305446 | − | 0.952209i | \(-0.401194\pi\) | ||||
0.305446 | + | 0.952209i | \(0.401194\pi\) | |||||||
\(200\) | 2.00811 | + | 1.40373i | 0.141995 | + | 0.0992589i | ||||
\(201\) | − | 2.45869i | − | 0.173423i | ||||||
\(202\) | 2.00000 | − | 9.69890i | 0.140720 | − | 0.682412i | ||||
\(203\) | − | 11.3519i | − | 0.796746i | ||||||
\(204\) | 4.68049 | − | 10.8663i | 0.327700 | − | 0.760794i | ||||
\(205\) | 5.13190 | 0.358428 | ||||||||
\(206\) | −4.23410 | − | 0.873109i | −0.295004 | − | 0.0608324i | ||||
\(207\) | −3.96642 | + | 2.69583i | −0.275685 | + | 0.187373i | ||||
\(208\) | 9.27277 | − | 8.76687i | 0.642951 | − | 0.607873i | ||||
\(209\) | 11.4864 | 0.794531 | ||||||||
\(210\) | −3.43528 | − | 0.708385i | −0.237057 | − | 0.0488832i | ||||
\(211\) | −19.6552 | −1.35312 | −0.676561 | − | 0.736387i | \(-0.736530\pi\) | ||||
−0.676561 | + | 0.736387i | \(0.736530\pi\) | |||||||
\(212\) | −20.3307 | − | 8.75710i | −1.39632 | − | 0.601440i | ||||
\(213\) | 4.84611i | 0.332050i | ||||||||
\(214\) | −1.20271 | + | 5.83246i | −0.0822153 | + | 0.398699i | ||||
\(215\) | − | 23.7128i | − | 1.61720i | ||||||
\(216\) | 2.31819 | + | 1.62049i | 0.157733 | + | 0.110260i | ||||
\(217\) | 4.33873i | 0.294532i | ||||||||
\(218\) | 4.40579 | + | 0.908513i | 0.298398 | + | 0.0615323i | ||||
\(219\) | 7.87149 | 0.531906 | ||||||||
\(220\) | 3.03731 | − | 7.05149i | 0.204776 | − | 0.475411i | ||||
\(221\) | 18.8726 | 1.26951 | ||||||||
\(222\) | −15.3933 | − | 3.17425i | −1.03313 | − | 0.213041i | ||||
\(223\) | 14.8511i | 0.994501i | 0.867607 | + | 0.497250i | \(0.165657\pi\) | ||||
−0.867607 | + | 0.497250i | \(0.834343\pi\) | |||||||
\(224\) | −3.63042 | − | 5.86851i | −0.242567 | − | 0.392106i | ||||
\(225\) | −0.866240 | −0.0577493 | ||||||||
\(226\) | −5.40365 | + | 26.2047i | −0.359445 | + | 1.74311i | ||||
\(227\) | − | 17.2433i | − | 1.14448i | −0.820086 | − | 0.572240i | \(-0.806074\pi\) | ||
0.820086 | − | 0.572240i | \(-0.193926\pi\) | |||||||
\(228\) | −4.81318 | + | 11.1744i | −0.318760 | + | 0.740041i | ||||
\(229\) | −2.59033 | −0.171174 | −0.0855869 | − | 0.996331i | \(-0.527277\pi\) | ||||
−0.0855869 | + | 0.996331i | \(0.527277\pi\) | |||||||
\(230\) | −12.7352 | + | 5.28838i | −0.839736 | + | 0.348705i | ||||
\(231\) | − | 2.30330i | − | 0.151546i | ||||||
\(232\) | −15.0799 | + | 21.5725i | −0.990042 | + | 1.41631i | ||||
\(233\) | −22.1288 | −1.44970 | −0.724852 | − | 0.688905i | \(-0.758092\pi\) | ||||
−0.724852 | + | 0.688905i | \(0.758092\pi\) | |||||||
\(234\) | −0.911179 | + | 4.41871i | −0.0595656 | + | 0.288860i | ||||
\(235\) | 22.7873i | 1.48648i | ||||||||
\(236\) | 1.20838 | + | 0.520491i | 0.0786590 | + | 0.0338811i | ||||
\(237\) | −4.23131 | −0.274853 | ||||||||
\(238\) | 2.06113 | − | 9.99535i | 0.133603 | − | 0.647902i | ||||
\(239\) | 20.5586i | 1.32983i | 0.746920 | + | 0.664914i | \(0.231532\pi\) | ||||
−0.746920 | + | 0.664914i | \(0.768468\pi\) | |||||||
\(240\) | 5.58719 | + | 5.90960i | 0.360652 | + | 0.381463i | ||||
\(241\) | − | 13.5001i | − | 0.869619i | −0.900522 | − | 0.434810i | \(-0.856816\pi\) | ||
0.900522 | − | 0.434810i | \(-0.143184\pi\) | |||||||
\(242\) | −10.2979 | − | 2.12352i | −0.661974 | − | 0.136505i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −19.0645 | − | 8.21171i | −1.22048 | − | 0.525701i | ||||
\(245\) | 11.2066 | 0.715963 | ||||||||
\(246\) | −3.49606 | − | 0.720918i | −0.222900 | − | 0.0459641i | ||||
\(247\) | −19.4077 | −1.23488 | ||||||||
\(248\) | 5.76358 | − | 8.24509i | 0.365987 | − | 0.523563i | ||||
\(249\) | − | 7.58314i | − | 0.480562i | ||||||
\(250\) | −16.5198 | − | 3.40653i | −1.04480 | − | 0.215448i | ||||
\(251\) | 25.0872i | 1.58349i | 0.610853 | + | 0.791744i | \(0.290827\pi\) | ||||
−0.610853 | + | 0.791744i | \(0.709173\pi\) | |||||||
\(252\) | 2.24073 | + | 0.965159i | 0.141153 | + | 0.0607993i | ||||
\(253\) | −5.09012 | − | 7.48916i | −0.320013 | − | 0.470840i | ||||
\(254\) | 2.12684 | − | 10.3140i | 0.133450 | − | 0.647157i | ||||
\(255\) | 12.0277i | 0.753202i | ||||||||
\(256\) | −0.896688 | + | 15.9749i | −0.0560430 | + | 0.998428i | ||||
\(257\) | −12.4382 | −0.775875 | −0.387937 | − | 0.921686i | \(-0.626812\pi\) | ||||
−0.387937 | + | 0.921686i | \(0.626812\pi\) | |||||||
\(258\) | −3.33113 | + | 16.1541i | −0.207387 | + | 1.00571i | ||||
\(259\) | −13.5574 | −0.842417 | ||||||||
\(260\) | −5.13190 | + | 11.9143i | −0.318267 | + | 0.738895i | ||||
\(261\) | − | 9.30575i | − | 0.576012i | ||||||
\(262\) | −2.52410 | − | 0.520491i | −0.155939 | − | 0.0321561i | ||||
\(263\) | −10.3726 | −0.639602 | −0.319801 | − | 0.947485i | \(-0.603616\pi\) | ||||
−0.319801 | + | 0.947485i | \(0.603616\pi\) | |||||||
\(264\) | −3.05971 | + | 4.37708i | −0.188312 | + | 0.269390i | ||||
\(265\) | 22.5035 | 1.38238 | ||||||||
\(266\) | −2.11956 | + | 10.2787i | −0.129959 | + | 0.630228i | ||||
\(267\) | 3.85989i | 0.236221i | ||||||||
\(268\) | −1.94530 | + | 4.51625i | −0.118828 | + | 0.275874i | ||||
\(269\) | 17.9895i | 1.09684i | 0.836202 | + | 0.548421i | \(0.184771\pi\) | ||||
−0.836202 | + | 0.548421i | \(0.815229\pi\) | |||||||
\(270\) | −2.81608 | − | 0.580701i | −0.171381 | − | 0.0353403i | ||||
\(271\) | − | 7.39559i | − | 0.449250i | −0.974445 | − | 0.224625i | \(-0.927884\pi\) | ||
0.974445 | − | 0.224625i | \(-0.0721158\pi\) | |||||||
\(272\) | −17.1947 | + | 16.2566i | −1.04258 | + | 0.985702i | ||||
\(273\) | 3.89171i | 0.235537i | ||||||||
\(274\) | −0.0630463 | + | 0.305740i | −0.00380877 | + | 0.0184704i | ||||
\(275\) | − | 1.63558i | − | 0.0986294i | ||||||
\(276\) | 9.41864 | − | 1.81364i | 0.566935 | − | 0.109168i | ||||
\(277\) | − | 30.0768i | − | 1.80714i | −0.428441 | − | 0.903570i | \(-0.640937\pi\) | ||
0.428441 | − | 0.903570i | \(-0.359063\pi\) | |||||||
\(278\) | −30.4478 | − | 6.27861i | −1.82614 | − | 0.376566i | ||||
\(279\) | 3.55669i | 0.212933i | ||||||||
\(280\) | 5.74961 | + | 4.01916i | 0.343605 | + | 0.240191i | ||||
\(281\) | 6.06727i | 0.361943i | 0.983488 | + | 0.180971i | \(0.0579242\pi\) | ||||
−0.983488 | + | 0.180971i | \(0.942076\pi\) | |||||||
\(282\) | 3.20111 | − | 15.5236i | 0.190623 | − | 0.924418i | ||||
\(283\) | − | 25.5734i | − | 1.52018i | −0.649818 | − | 0.760090i | \(-0.725155\pi\) | ||
0.649818 | − | 0.760090i | \(-0.274845\pi\) | |||||||
\(284\) | 3.83421 | − | 8.90157i | 0.227518 | − | 0.528211i | ||||
\(285\) | − | 12.3686i | − | 0.732655i | ||||||
\(286\) | −8.34316 | − | 1.72044i | −0.493341 | − | 0.101731i | ||||
\(287\) | −3.07909 | −0.181753 | ||||||||
\(288\) | −2.97605 | − | 4.81073i | −0.175365 | − | 0.283475i | ||||
\(289\) | −17.9960 | −1.05859 | ||||||||
\(290\) | 5.40386 | − | 26.2057i | 0.317326 | − | 1.53885i | ||||
\(291\) | 3.03678i | 0.178019i | ||||||||
\(292\) | −14.4587 | − | 6.22787i | −0.846134 | − | 0.364458i | ||||
\(293\) | 19.4122 | 1.13407 | 0.567035 | − | 0.823694i | \(-0.308090\pi\) | ||||
0.567035 | + | 0.823694i | \(0.308090\pi\) | |||||||
\(294\) | −7.63437 | − | 1.57428i | −0.445246 | − | 0.0918137i | ||||
\(295\) | −1.33753 | −0.0778741 | ||||||||
\(296\) | 25.7638 | + | 18.0097i | 1.49749 | + | 1.04679i | ||||
\(297\) | − | 1.88814i | − | 0.109561i | ||||||
\(298\) | −19.9446 | − | 4.11276i | −1.15536 | − | 0.238246i | ||||
\(299\) | 8.60036 | + | 12.6538i | 0.497372 | + | 0.731790i | ||||
\(300\) | 1.59115 | + | 0.685363i | 0.0918652 | + | 0.0395694i | ||||
\(301\) | 14.2275i | 0.820058i | ||||||||
\(302\) | −1.40093 | + | 6.79371i | −0.0806142 | + | 0.390934i | ||||
\(303\) | − | 7.00245i | − | 0.402280i | ||||||
\(304\) | 17.6822 | − | 16.7175i | 1.01414 | − | 0.958813i | ||||
\(305\) | 21.1020 | 1.20830 | ||||||||
\(306\) | 1.68962 | − | 8.19372i | 0.0965891 | − | 0.468404i | ||||
\(307\) | 2.20932 | 0.126093 | 0.0630464 | − | 0.998011i | \(-0.479918\pi\) | ||||
0.0630464 | + | 0.998011i | \(0.479918\pi\) | |||||||
\(308\) | −1.82236 | + | 4.23082i | −0.103838 | + | 0.241073i | ||||
\(309\) | −3.05695 | −0.173904 | ||||||||
\(310\) | −2.06537 | + | 10.0159i | −0.117305 | + | 0.568866i | ||||
\(311\) | − | 18.3744i | − | 1.04192i | −0.853583 | − | 0.520958i | \(-0.825575\pi\) | ||
0.853583 | − | 0.520958i | \(-0.174425\pi\) | |||||||
\(312\) | 5.16975 | − | 7.39559i | 0.292680 | − | 0.418693i | ||||
\(313\) | 14.6786i | 0.829684i | 0.909893 | + | 0.414842i | \(0.136163\pi\) | ||||
−0.909893 | + | 0.414842i | \(0.863837\pi\) | |||||||
\(314\) | −8.00851 | − | 1.65143i | −0.451947 | − | 0.0931955i | ||||
\(315\) | −2.48021 | −0.139744 | ||||||||
\(316\) | 7.77228 | + | 3.34778i | 0.437225 | + | 0.188328i | ||||
\(317\) | 1.06596i | 0.0598705i | 0.999552 | + | 0.0299353i | \(0.00953011\pi\) | ||||
−0.999552 | + | 0.0299353i | \(0.990470\pi\) | |||||||
\(318\) | −15.3303 | − | 3.16124i | −0.859680 | − | 0.177274i | ||||
\(319\) | 17.5706 | 0.983764 | ||||||||
\(320\) | −5.58719 | − | 15.2756i | −0.312334 | − | 0.853932i | ||||
\(321\) | 4.21095i | 0.235032i | ||||||||
\(322\) | 7.64101 | − | 3.17297i | 0.425817 | − | 0.176823i | ||||
\(323\) | 35.9881 | 2.00243 | ||||||||
\(324\) | 1.83685 | + | 0.791193i | 0.102047 | + | 0.0439552i | ||||
\(325\) | 2.76351i | 0.153292i | ||||||||
\(326\) | 15.6347 | + | 3.22402i | 0.865927 | + | 0.178562i | ||||
\(327\) | 3.18091 | 0.175905 | ||||||||
\(328\) | 5.85134 | + | 4.09027i | 0.323086 | + | 0.225847i | ||||
\(329\) | − | 13.6722i | − | 0.753770i | ||||||
\(330\) | 1.09645 | − | 5.31716i | 0.0603574 | − | 0.292700i | ||||
\(331\) | 11.3481 | 0.623748 | 0.311874 | − | 0.950124i | \(-0.399043\pi\) | ||||
0.311874 | + | 0.950124i | \(0.399043\pi\) | |||||||
\(332\) | −5.99973 | + | 13.9291i | −0.329278 | + | 0.764458i | ||||
\(333\) | −11.1137 | −0.609030 | ||||||||
\(334\) | −0.102290 | + | 0.496048i | −0.00559703 | + | 0.0271425i | ||||
\(335\) | − | 4.99893i | − | 0.273121i | ||||||
\(336\) | −3.35226 | − | 3.54570i | −0.182881 | − | 0.193434i | ||||
\(337\) | 9.38843i | 0.511420i | 0.966754 | + | 0.255710i | \(0.0823093\pi\) | ||||
−0.966754 | + | 0.255710i | \(0.917691\pi\) | |||||||
\(338\) | −3.90917 | − | 0.806106i | −0.212631 | − | 0.0438464i | ||||
\(339\) | 18.9194i | 1.02756i | ||||||||
\(340\) | 9.51621 | − | 22.0930i | 0.516089 | − | 1.19816i | ||||
\(341\) | −6.71553 | −0.363666 | ||||||||
\(342\) | −1.73752 | + | 8.42601i | −0.0939543 | + | 0.455626i | ||||
\(343\) | −15.2630 | −0.824124 | ||||||||
\(344\) | 18.8998 | − | 27.0371i | 1.01901 | − | 1.45774i | ||||
\(345\) | −8.06438 | + | 5.48108i | −0.434172 | + | 0.295091i | ||||
\(346\) | 2.89698 | − | 14.0488i | 0.155743 | − | 0.755266i | ||||
\(347\) | 4.53959 | 0.243698 | 0.121849 | − | 0.992549i | \(-0.461118\pi\) | ||||
0.121849 | + | 0.992549i | \(0.461118\pi\) | |||||||
\(348\) | −7.36265 | + | 17.0933i | −0.394679 | + | 0.916295i | ||||
\(349\) | 35.2981i | 1.88946i | 0.327847 | + | 0.944731i | \(0.393677\pi\) | ||||
−0.327847 | + | 0.944731i | \(0.606323\pi\) | |||||||
\(350\) | 1.46362 | + | 0.301811i | 0.0782336 | + | 0.0161325i | ||||
\(351\) | 3.19024i | 0.170283i | ||||||||
\(352\) | 9.08334 | − | 5.61920i | 0.484144 | − | 0.299505i | ||||
\(353\) | 31.1526 | 1.65808 | 0.829042 | − | 0.559187i | \(-0.188886\pi\) | ||||
0.829042 | + | 0.559187i | \(0.188886\pi\) | |||||||
\(354\) | 0.911179 | + | 0.187893i | 0.0484286 | + | 0.00998642i | ||||
\(355\) | 9.85294i | 0.522940i | ||||||||
\(356\) | 3.05392 | − | 7.09003i | 0.161857 | − | 0.375771i | ||||
\(357\) | − | 7.21648i | − | 0.381937i | ||||||
\(358\) | 16.3801 | + | 3.37773i | 0.865717 | + | 0.178519i | ||||
\(359\) | −24.9684 | −1.31778 | −0.658891 | − | 0.752239i | \(-0.728974\pi\) | ||||
−0.658891 | + | 0.752239i | \(0.728974\pi\) | |||||||
\(360\) | 4.71327 | + | 3.29472i | 0.248411 | + | 0.173647i | ||||
\(361\) | −18.0083 | −0.947805 | ||||||||
\(362\) | 28.0075 | + | 5.77539i | 1.47204 | + | 0.303548i | ||||
\(363\) | −7.43492 | −0.390232 | ||||||||
\(364\) | 3.07909 | − | 7.14848i | 0.161388 | − | 0.374682i | ||||
\(365\) | 16.0040 | 0.837690 | ||||||||
\(366\) | −14.3755 | − | 2.96436i | −0.751421 | − | 0.154950i | ||||
\(367\) | 25.0550 | 1.30786 | 0.653931 | − | 0.756554i | \(-0.273119\pi\) | ||||
0.653931 | + | 0.756554i | \(0.273119\pi\) | |||||||
\(368\) | −18.7355 | − | 4.12058i | −0.976658 | − | 0.214800i | ||||
\(369\) | −2.52410 | −0.131399 | ||||||||
\(370\) | −31.2972 | − | 6.45377i | −1.62706 | − | 0.335515i | ||||
\(371\) | −13.5019 | −0.700983 | ||||||||
\(372\) | 2.81403 | − | 6.53310i | 0.145900 | − | 0.338725i | ||||
\(373\) | −17.3417 | −0.897918 | −0.448959 | − | 0.893552i | \(-0.648205\pi\) | ||||
−0.448959 | + | 0.893552i | \(0.648205\pi\) | |||||||
\(374\) | 15.4709 | + | 3.19024i | 0.799982 | + | 0.164963i | ||||
\(375\) | −11.9270 | −0.615909 | ||||||||
\(376\) | −18.1621 | + | 25.9818i | −0.936640 | + | 1.33991i | ||||
\(377\) | −29.6876 | −1.52899 | ||||||||
\(378\) | 1.68962 | + | 0.348415i | 0.0869046 | + | 0.0179205i | ||||
\(379\) | − | 16.9340i | − | 0.869841i | −0.900469 | − | 0.434920i | \(-0.856777\pi\) | ||
0.900469 | − | 0.434920i | \(-0.143223\pi\) | |||||||
\(380\) | −9.78599 | + | 22.7193i | −0.502010 | + | 1.16548i | ||||
\(381\) | − | 7.44653i | − | 0.381497i | ||||||
\(382\) | 5.82381 | + | 1.20092i | 0.297972 | + | 0.0614445i | ||||
\(383\) | 29.5868 | 1.51182 | 0.755908 | − | 0.654677i | \(-0.227196\pi\) | ||||
0.755908 | + | 0.654677i | \(0.227196\pi\) | |||||||
\(384\) | 1.66034 | + | 11.1912i | 0.0847286 | + | 0.571099i | ||||
\(385\) | − | 4.68300i | − | 0.238668i | ||||||
\(386\) | 8.72756 | + | 1.79970i | 0.444221 | + | 0.0916024i | ||||
\(387\) | 11.6630i | 0.592865i | ||||||||
\(388\) | 2.40268 | − | 5.57811i | 0.121978 | − | 0.283185i | ||||
\(389\) | 9.18306 | 0.465600 | 0.232800 | − | 0.972525i | \(-0.425211\pi\) | ||||
0.232800 | + | 0.972525i | \(0.425211\pi\) | |||||||
\(390\) | −1.85258 | + | 8.98398i | −0.0938089 | + | 0.454921i | ||||
\(391\) | −15.9478 | − | 23.4643i | −0.806517 | − | 1.18664i | ||||
\(392\) | 12.7776 | + | 8.93197i | 0.645368 | + | 0.451133i | ||||
\(393\) | −1.82236 | −0.0919258 | ||||||||
\(394\) | 3.31571 | − | 16.0794i | 0.167043 | − | 0.810067i | ||||
\(395\) | −8.60296 | −0.432862 | ||||||||
\(396\) | −1.49388 | + | 3.46823i | −0.0750705 | + | 0.174285i | ||||
\(397\) | − | 12.2452i | − | 0.614568i | −0.951618 | − | 0.307284i | \(-0.900580\pi\) | ||
0.951618 | − | 0.307284i | \(-0.0994202\pi\) | |||||||
\(398\) | −11.9361 | − | 2.46134i | −0.598304 | − | 0.123376i | ||||
\(399\) | 7.42106i | 0.371518i | ||||||||
\(400\) | −2.38045 | − | 2.51782i | −0.119023 | − | 0.125891i | ||||
\(401\) | − | 8.99372i | − | 0.449125i | −0.974460 | − | 0.224563i | \(-0.927905\pi\) | ||
0.974460 | − | 0.224563i | \(-0.0720953\pi\) | |||||||
\(402\) | −0.702238 | + | 3.40547i | −0.0350244 | + | 0.169849i | ||||
\(403\) | 11.3467 | 0.565219 | ||||||||
\(404\) | −5.54029 | + | 12.8624i | −0.275640 | + | 0.639930i | ||||
\(405\) | −2.03317 | −0.101029 | ||||||||
\(406\) | −3.24226 | + | 15.7232i | −0.160911 | + | 0.780328i | ||||
\(407\) | − | 20.9843i | − | 1.04015i | ||||||
\(408\) | −9.58639 | + | 13.7138i | −0.474597 | + | 0.678935i | ||||
\(409\) | 29.6011 | 1.46368 | 0.731840 | − | 0.681477i | \(-0.238662\pi\) | ||||
0.731840 | + | 0.681477i | \(0.238662\pi\) | |||||||
\(410\) | −7.10806 | − | 1.46575i | −0.351042 | − | 0.0723880i | ||||
\(411\) | 0.220739i | 0.0108883i | ||||||||
\(412\) | 5.61516 | + | 2.41864i | 0.276639 | + | 0.119158i | ||||
\(413\) | 0.802505 | 0.0394887 | ||||||||
\(414\) | 6.26374 | − | 2.60106i | 0.307846 | − | 0.127835i | ||||
\(415\) | − | 15.4178i | − | 0.756829i | ||||||
\(416\) | −15.3474 | + | 9.49431i | −0.752468 | + | 0.465497i | ||||
\(417\) | −21.9828 | −1.07650 | ||||||||
\(418\) | −15.9095 | − | 3.28068i | −0.778159 | − | 0.160463i | ||||
\(419\) | − | 13.6353i | − | 0.666126i | −0.942905 | − | 0.333063i | \(-0.891918\pi\) | ||
0.942905 | − | 0.333063i | \(-0.108082\pi\) | |||||||
\(420\) | 4.55578 | + | 1.96233i | 0.222299 | + | 0.0957518i | ||||
\(421\) | −4.56033 | −0.222257 | −0.111128 | − | 0.993806i | \(-0.535447\pi\) | ||||
−0.111128 | + | 0.993806i | \(0.535447\pi\) | |||||||
\(422\) | 27.2239 | + | 5.61381i | 1.32524 | + | 0.273276i | ||||
\(423\) | − | 11.2078i | − | 0.544942i | ||||||
\(424\) | 25.6583 | + | 17.9359i | 1.24608 | + | 0.871047i | ||||
\(425\) | − | 5.12445i | − | 0.248572i | ||||||
\(426\) | 1.38412 | − | 6.71221i | 0.0670608 | − | 0.325208i | ||||
\(427\) | −12.6610 | −0.612709 | ||||||||
\(428\) | 3.33167 | − | 7.73487i | 0.161042 | − | 0.373879i | ||||
\(429\) | −6.02363 | −0.290824 | ||||||||
\(430\) | −6.77273 | + | 32.8440i | −0.326610 | + | 1.58388i | ||||
\(431\) | −30.0775 | −1.44878 | −0.724392 | − | 0.689389i | \(-0.757879\pi\) | ||||
−0.724392 | + | 0.689389i | \(0.757879\pi\) | |||||||
\(432\) | −2.74803 | − | 2.90660i | −0.132215 | − | 0.139844i | ||||
\(433\) | − | 17.0843i | − | 0.821018i | −0.911857 | − | 0.410509i | \(-0.865351\pi\) | ||
0.911857 | − | 0.410509i | \(-0.134649\pi\) | |||||||
\(434\) | 1.23920 | − | 6.00945i | 0.0594836 | − | 0.288463i | ||||
\(435\) | − | 18.9201i | − | 0.907151i | ||||||
\(436\) | −5.84285 | − | 2.51671i | −0.279822 | − | 0.120529i | ||||
\(437\) | 16.4000 | + | 24.1295i | 0.784516 | + | 1.15427i | ||||
\(438\) | −10.9026 | − | 2.24821i | −0.520946 | − | 0.107424i | ||||
\(439\) | 17.2515i | 0.823371i | 0.911326 | + | 0.411685i | \(0.135060\pi\) | ||||
−0.911326 | + | 0.411685i | \(0.864940\pi\) | |||||||
\(440\) | −6.22090 | + | 8.89932i | −0.296570 | + | 0.424258i | ||||
\(441\) | −5.51190 | −0.262471 | ||||||||
\(442\) | −26.1400 | − | 5.39029i | −1.24335 | − | 0.256390i | ||||
\(443\) | −19.0033 | −0.902875 | −0.451437 | − | 0.892303i | \(-0.649089\pi\) | ||||
−0.451437 | + | 0.892303i | \(0.649089\pi\) | |||||||
\(444\) | 20.4143 | + | 8.79312i | 0.968819 | + | 0.417303i | ||||
\(445\) | 7.84779i | 0.372021i | ||||||||
\(446\) | 4.24168 | − | 20.5698i | 0.200849 | − | 0.974008i | ||||
\(447\) | −14.3997 | −0.681083 | ||||||||
\(448\) | 3.35226 | + | 9.16520i | 0.158379 | + | 0.433015i | ||||
\(449\) | 9.95996 | 0.470039 | 0.235020 | − | 0.971991i | \(-0.424485\pi\) | ||||
0.235020 | + | 0.971991i | \(0.424485\pi\) | |||||||
\(450\) | 1.19980 | + | 0.247411i | 0.0565593 | + | 0.0116630i | ||||
\(451\) | − | 4.76585i | − | 0.224415i | ||||||
\(452\) | 14.9689 | − | 34.7520i | 0.704077 | − | 1.63460i | ||||
\(453\) | 4.90495i | 0.230455i | ||||||||
\(454\) | −4.92495 | + | 23.8833i | −0.231139 | + | 1.12090i | ||||
\(455\) | 7.91248i | 0.370943i | ||||||||
\(456\) | 9.85816 | − | 14.1026i | 0.461651 | − | 0.660414i | ||||
\(457\) | − | 11.2976i | − | 0.528478i | −0.964457 | − | 0.264239i | \(-0.914879\pi\) | ||
0.964457 | − | 0.264239i | \(-0.0851207\pi\) | |||||||
\(458\) | 3.58779 | + | 0.739835i | 0.167647 | + | 0.0345702i | ||||
\(459\) | − | 5.91574i | − | 0.276123i | ||||||
\(460\) | 19.1496 | − | 3.68742i | 0.892857 | − | 0.171927i | ||||
\(461\) | − | 7.73780i | − | 0.360385i | −0.983631 | − | 0.180193i | \(-0.942328\pi\) | ||
0.983631 | − | 0.180193i | \(-0.0576721\pi\) | |||||||
\(462\) | −0.657857 | + | 3.19024i | −0.0306063 | + | 0.148423i | ||||
\(463\) | 15.8063i | 0.734581i | 0.930106 | + | 0.367290i | \(0.119714\pi\) | ||||
−0.930106 | + | 0.367290i | \(0.880286\pi\) | |||||||
\(464\) | 27.0481 | − | 25.5725i | 1.25568 | − | 1.18717i | ||||
\(465\) | 7.23133i | 0.335345i | ||||||||
\(466\) | 30.6499 | + | 6.32029i | 1.41983 | + | 0.292782i | ||||
\(467\) | 32.5241i | 1.50504i | 0.658572 | + | 0.752518i | \(0.271161\pi\) | ||||
−0.658572 | + | 0.752518i | \(0.728839\pi\) | |||||||
\(468\) | 2.52410 | − | 5.85999i | 0.116676 | − | 0.270878i | ||||
\(469\) | 2.99931i | 0.138495i | ||||||||
\(470\) | 6.50838 | − | 31.5621i | 0.300209 | − | 1.45585i | ||||
\(471\) | −5.78202 | −0.266421 | ||||||||
\(472\) | −1.52504 | − | 1.06605i | −0.0701956 | − | 0.0490689i | ||||
\(473\) | −22.0214 | −1.01255 | ||||||||
\(474\) | 5.86067 | + | 1.20852i | 0.269190 | + | 0.0555093i | ||||
\(475\) | 5.26972i | 0.241791i | ||||||||
\(476\) | −5.70963 | + | 13.2556i | −0.261700 | + | 0.607569i | ||||
\(477\) | −11.0682 | −0.506779 | ||||||||
\(478\) | 5.87184 | − | 28.4752i | 0.268572 | − | 1.30243i | ||||
\(479\) | 16.2098 | 0.740643 | 0.370322 | − | 0.928904i | \(-0.379247\pi\) | ||||
0.370322 | + | 0.928904i | \(0.379247\pi\) | |||||||
\(480\) | −6.05080 | − | 9.78101i | −0.276180 | − | 0.446440i | ||||
\(481\) | 35.4555i | 1.61663i | ||||||||
\(482\) | −3.85583 | + | 18.6986i | −0.175628 | + | 0.851700i | ||||
\(483\) | 4.83855 | − | 3.28859i | 0.220162 | − | 0.149636i | ||||
\(484\) | 13.6568 | + | 5.88246i | 0.620765 | + | 0.267384i | ||||
\(485\) | 6.17427i | 0.280359i | ||||||||
\(486\) | 1.38507 | + | 0.285614i | 0.0628281 | + | 0.0129557i | ||||
\(487\) | 15.4990i | 0.702327i | 0.936314 | + | 0.351164i | \(0.114214\pi\) | ||||
−0.936314 | + | 0.351164i | \(0.885786\pi\) | |||||||
\(488\) | 24.0603 | + | 16.8189i | 1.08916 | + | 0.761356i | ||||
\(489\) | 11.2880 | 0.510462 | ||||||||
\(490\) | −15.5219 | − | 3.20076i | −0.701210 | − | 0.144596i | ||||
\(491\) | 25.3264 | 1.14296 | 0.571481 | − | 0.820615i | \(-0.306369\pi\) | ||||
0.571481 | + | 0.820615i | \(0.306369\pi\) | |||||||
\(492\) | 4.63638 | + | 1.99705i | 0.209024 | + | 0.0900338i | ||||
\(493\) | 55.0504 | 2.47935 | ||||||||
\(494\) | 26.8810 | + | 5.54311i | 1.20943 | + | 0.249396i | ||||
\(495\) | − | 3.83890i | − | 0.172546i | ||||||
\(496\) | −10.3379 | + | 9.77388i | −0.464185 | + | 0.438860i | ||||
\(497\) | − | 5.91166i | − | 0.265174i | ||||||
\(498\) | −2.16585 | + | 10.5032i | −0.0970542 | + | 0.470659i | ||||
\(499\) | 1.02051 | 0.0456842 | 0.0228421 | − | 0.999739i | \(-0.492729\pi\) | ||||
0.0228421 | + | 0.999739i | \(0.492729\pi\) | |||||||
\(500\) | 21.9082 | + | 9.43658i | 0.979763 | + | 0.422017i | ||||
\(501\) | 0.358139i | 0.0160005i | ||||||||
\(502\) | 7.16526 | − | 34.7476i | 0.319801 | − | 1.55086i | ||||
\(503\) | −14.2820 | −0.636805 | −0.318403 | − | 0.947956i | \(-0.603146\pi\) | ||||
−0.318403 | + | 0.947956i | \(0.603146\pi\) | |||||||
\(504\) | −2.82791 | − | 1.97680i | −0.125965 | − | 0.0880537i | ||||
\(505\) | − | 14.2371i | − | 0.633544i | ||||||
\(506\) | 4.91117 | + | 11.8268i | 0.218328 | + | 0.525767i | ||||
\(507\) | −2.82236 | −0.125345 | ||||||||
\(508\) | −5.89164 | + | 13.6782i | −0.261399 | + | 0.606870i | ||||
\(509\) | 16.0929i | 0.713307i | 0.934237 | + | 0.356654i | \(0.116082\pi\) | ||||
−0.934237 | + | 0.356654i | \(0.883918\pi\) | |||||||
\(510\) | 3.43528 | − | 16.6592i | 0.152117 | − | 0.737681i | ||||
\(511\) | −9.60226 | −0.424779 | ||||||||
\(512\) | 5.80462 | − | 21.8702i | 0.256531 | − | 0.966536i | ||||
\(513\) | 6.08344i | 0.268591i | ||||||||
\(514\) | 17.2278 | + | 3.55253i | 0.759887 | + | 0.156695i | ||||
\(515\) | −6.21529 | −0.273878 | ||||||||
\(516\) | 9.22770 | − | 21.4232i | 0.406227 | − | 0.943104i | ||||
\(517\) | 21.1619 | 0.930700 | ||||||||
\(518\) | 18.7780 | + | 3.87219i | 0.825058 | + | 0.170134i | ||||
\(519\) | − | 10.1430i | − | 0.445227i | ||||||
\(520\) | 10.5110 | − | 15.0365i | 0.460936 | − | 0.659392i | ||||
\(521\) | − | 40.0850i | − | 1.75615i | −0.478519 | − | 0.878077i | \(-0.658826\pi\) | ||
0.478519 | − | 0.878077i | \(-0.341174\pi\) | |||||||
\(522\) | −2.65786 | + | 12.8891i | −0.116331 | + | 0.564142i | ||||
\(523\) | − | 3.67778i | − | 0.160818i | −0.996762 | − | 0.0804091i | \(-0.974377\pi\) | ||
0.996762 | − | 0.0804091i | \(-0.0256227\pi\) | |||||||
\(524\) | 3.34740 | + | 1.44184i | 0.146232 | + | 0.0629869i | ||||
\(525\) | 1.05671 | 0.0461185 | ||||||||
\(526\) | 14.3668 | + | 2.96256i | 0.626422 | + | 0.129174i | ||||
\(527\) | −21.0404 | −0.916536 | ||||||||
\(528\) | 5.48808 | − | 5.18867i | 0.238838 | − | 0.225808i | ||||
\(529\) | 8.46496 | − | 21.3856i | 0.368042 | − | 0.929809i | ||||
\(530\) | −31.1690 | − | 6.42733i | −1.35390 | − | 0.279185i | ||||
\(531\) | 0.657857 | 0.0285485 | ||||||||
\(532\) | 5.87149 | − | 13.6314i | 0.254561 | − | 0.590995i | ||||
\(533\) | 8.05248i | 0.348792i | ||||||||
\(534\) | 1.10244 | − | 5.34622i | 0.0477072 | − | 0.231354i | ||||
\(535\) | 8.56155i | 0.370148i | ||||||||
\(536\) | 3.98429 | − | 5.69972i | 0.172095 | − | 0.246190i | ||||
\(537\) | 11.8262 | 0.510338 | ||||||||
\(538\) | 5.13807 | − | 24.9168i | 0.221518 | − | 1.07424i | ||||
\(539\) | − | 10.4072i | − | 0.448272i | ||||||
\(540\) | 3.73462 | + | 1.60863i | 0.160712 | + | 0.0692242i | ||||
\(541\) | − | 39.3379i | − | 1.69127i | −0.533761 | − | 0.845635i | \(-0.679222\pi\) | ||
0.533761 | − | 0.845635i | \(-0.320778\pi\) | |||||||
\(542\) | −2.11229 | + | 10.2434i | −0.0907305 | + | 0.439993i | ||||
\(543\) | 20.2209 | 0.867764 | ||||||||
\(544\) | 28.4590 | − | 17.6055i | 1.22017 | − | 0.754831i | ||||
\(545\) | 6.46731 | 0.277029 | ||||||||
\(546\) | 1.11153 | − | 5.39029i | 0.0475690 | − | 0.230683i | ||||
\(547\) | 14.0964 | 0.602718 | 0.301359 | − | 0.953511i | \(-0.402560\pi\) | ||||
0.301359 | + | 0.953511i | \(0.402560\pi\) | |||||||
\(548\) | 0.174647 | − | 0.405465i | 0.00746057 | − | 0.0173206i | ||||
\(549\) | −10.3789 | −0.442961 | ||||||||
\(550\) | −0.467146 | + | 2.26540i | −0.0199192 | + | 0.0965970i | ||||
\(551\) | −56.6110 | −2.41171 | ||||||||
\(552\) | −13.5635 | − | 0.178080i | −0.577301 | − | 0.00757959i | ||||
\(553\) | 5.16169 | 0.219497 | ||||||||
\(554\) | −8.59036 | + | 41.6585i | −0.364970 | + | 1.76990i | ||||
\(555\) | −22.5961 | −0.959150 | ||||||||
\(556\) | 40.3791 | + | 17.3926i | 1.71246 | + | 0.737612i | ||||
\(557\) | 10.4485 | 0.442715 | 0.221358 | − | 0.975193i | \(-0.428951\pi\) | ||||
0.221358 | + | 0.975193i | \(0.428951\pi\) | |||||||
\(558\) | 1.01584 | − | 4.92627i | 0.0430040 | − | 0.208546i | ||||
\(559\) | 37.2079 | 1.57372 | ||||||||
\(560\) | −6.81570 | − | 7.20900i | −0.288016 | − | 0.304636i | ||||
\(561\) | 11.1698 | 0.471587 | ||||||||
\(562\) | 1.73290 | − | 8.40361i | 0.0730979 | − | 0.354485i | ||||
\(563\) | 19.6672i | 0.828873i | 0.910078 | + | 0.414436i | \(0.136021\pi\) | ||||
−0.910078 | + | 0.414436i | \(0.863979\pi\) | |||||||
\(564\) | −8.86753 | + | 20.5870i | −0.373390 | + | 0.866871i | ||||
\(565\) | 38.4662i | 1.61829i | ||||||||
\(566\) | −7.30412 | + | 35.4210i | −0.307015 | + | 1.48885i | ||||
\(567\) | 1.21988 | 0.0512301 | ||||||||
\(568\) | −7.85307 | + | 11.2342i | −0.329507 | + | 0.471377i | ||||
\(569\) | − | 1.07567i | − | 0.0450943i | −0.999746 | − | 0.0225471i | \(-0.992822\pi\) | ||
0.999746 | − | 0.0225471i | \(-0.00717759\pi\) | |||||||
\(570\) | −3.53266 | + | 17.1315i | −0.147967 | + | 0.717558i | ||||
\(571\) | 28.5359i | 1.19419i | 0.802170 | + | 0.597096i | \(0.203679\pi\) | ||||
−0.802170 | + | 0.597096i | \(0.796321\pi\) | |||||||
\(572\) | 11.0645 | + | 4.76585i | 0.462630 | + | 0.199270i | ||||
\(573\) | 4.20470 | 0.175654 | ||||||||
\(574\) | 4.26476 | + | 0.879433i | 0.178008 | + | 0.0367068i | ||||
\(575\) | 3.43587 | − | 2.33524i | 0.143286 | − | 0.0973862i | ||||
\(576\) | 2.74803 | + | 7.51321i | 0.114501 | + | 0.313050i | ||||
\(577\) | 4.04788 | 0.168515 | 0.0842577 | − | 0.996444i | \(-0.473148\pi\) | ||||
0.0842577 | + | 0.996444i | \(0.473148\pi\) | |||||||
\(578\) | 24.9257 | + | 5.13990i | 1.03677 | + | 0.213792i | ||||
\(579\) | 6.30116 | 0.261867 | ||||||||
\(580\) | −14.9695 | + | 34.7534i | −0.621574 | + | 1.44306i | ||||
\(581\) | 9.25051i | 0.383776i | ||||||||
\(582\) | 0.867348 | − | 4.20616i | 0.0359527 | − | 0.174351i | ||||
\(583\) | − | 20.8984i | − | 0.865523i | ||||||
\(584\) | 18.2476 | + | 12.7557i | 0.755092 | + | 0.527833i | ||||
\(585\) | 6.48629i | 0.268175i | ||||||||
\(586\) | −26.8872 | − | 5.54439i | −1.11070 | − | 0.229037i | ||||
\(587\) | −15.3197 | −0.632312 | −0.316156 | − | 0.948707i | \(-0.602392\pi\) | ||||
−0.316156 | + | 0.948707i | \(0.602392\pi\) | |||||||
\(588\) | 10.1245 | + | 4.36097i | 0.417528 | + | 0.179844i | ||||
\(589\) | 21.6369 | 0.891534 | ||||||||
\(590\) | 1.85258 | + | 0.382018i | 0.0762694 | + | 0.0157274i | ||||
\(591\) | − | 11.6091i | − | 0.477533i | ||||||
\(592\) | −30.5409 | − | 32.3033i | −1.25522 | − | 1.32766i | ||||
\(593\) | 2.25798 | 0.0927240 | 0.0463620 | − | 0.998925i | \(-0.485237\pi\) | ||||
0.0463620 | + | 0.998925i | \(0.485237\pi\) | |||||||
\(594\) | −0.539280 | + | 2.61521i | −0.0221269 | + | 0.107303i | ||||
\(595\) | − | 14.6723i | − | 0.601506i | ||||||
\(596\) | 26.4501 | + | 11.3929i | 1.08344 | + | 0.466673i | ||||
\(597\) | −8.61769 | −0.352699 | ||||||||
\(598\) | −8.29800 | − | 19.9829i | −0.339331 | − | 0.817160i | ||||
\(599\) | − | 22.8436i | − | 0.933362i | −0.884426 | − | 0.466681i | \(-0.845450\pi\) | ||
0.884426 | − | 0.466681i | \(-0.154550\pi\) | |||||||
\(600\) | −2.00811 | − | 1.40373i | −0.0819808 | − | 0.0573071i | ||||
\(601\) | −9.74798 | −0.397628 | −0.198814 | − | 0.980037i | \(-0.563709\pi\) | ||||
−0.198814 | + | 0.980037i | \(0.563709\pi\) | |||||||
\(602\) | 4.06357 | − | 19.7061i | 0.165619 | − | 0.803159i | ||||
\(603\) | 2.45869i | 0.100126i | ||||||||
\(604\) | 3.88076 | − | 9.00966i | 0.157906 | − | 0.366598i | ||||
\(605\) | −15.1164 | −0.614570 | ||||||||
\(606\) | −2.00000 | + | 9.69890i | −0.0812444 | + | 0.393991i | ||||
\(607\) | − | 27.7790i | − | 1.12752i | −0.825940 | − | 0.563758i | \(-0.809355\pi\) | ||
0.825940 | − | 0.563758i | \(-0.190645\pi\) | |||||||
\(608\) | −29.2658 | + | 18.1046i | −1.18689 | + | 0.734240i | ||||
\(609\) | 11.3519i | 0.460002i | ||||||||
\(610\) | −29.2278 | − | 6.02704i | −1.18340 | − | 0.244028i | ||||
\(611\) | −35.7556 | −1.44652 | ||||||||
\(612\) | −4.68049 | + | 10.8663i | −0.189198 | + | 0.439245i | ||||
\(613\) | −13.1317 | −0.530386 | −0.265193 | − | 0.964195i | \(-0.585436\pi\) | ||||
−0.265193 | + | 0.964195i | \(0.585436\pi\) | |||||||
\(614\) | −3.06007 | − | 0.631015i | −0.123495 | − | 0.0254657i | ||||
\(615\) | −5.13190 | −0.206938 | ||||||||
\(616\) | 3.73248 | − | 5.33950i | 0.150386 | − | 0.215135i | ||||
\(617\) | 26.8543i | 1.08111i | 0.841307 | + | 0.540557i | \(0.181787\pi\) | ||||
−0.841307 | + | 0.540557i | \(0.818213\pi\) | |||||||
\(618\) | 4.23410 | + | 0.873109i | 0.170320 | + | 0.0351216i | ||||
\(619\) | − | 37.7150i | − | 1.51589i | −0.652317 | − | 0.757946i | \(-0.726203\pi\) | ||
0.652317 | − | 0.757946i | \(-0.273797\pi\) | |||||||
\(620\) | 5.72138 | − | 13.2829i | 0.229776 | − | 0.533453i | ||||
\(621\) | 3.96642 | − | 2.69583i | 0.159167 | − | 0.108180i | ||||
\(622\) | −5.24799 | + | 25.4498i | −0.210425 | + | 1.02045i | ||||
\(623\) | − | 4.70859i | − | 0.188646i | ||||||
\(624\) | −9.27277 | + | 8.76687i | −0.371208 | + | 0.350956i | ||||
\(625\) | −19.9184 | −0.796737 | ||||||||
\(626\) | 4.19242 | − | 20.3309i | 0.167563 | − | 0.812588i | ||||
\(627\) | −11.4864 | −0.458723 | ||||||||
\(628\) | 10.6207 | + | 4.57469i | 0.423812 | + | 0.182550i | ||||
\(629\) | − | 65.7460i | − | 2.62147i | ||||||
\(630\) | 3.43528 | + | 0.708385i | 0.136865 | + | 0.0282227i | ||||
\(631\) | −38.4398 | −1.53027 | −0.765133 | − | 0.643872i | \(-0.777327\pi\) | ||||
−0.765133 | + | 0.643872i | \(0.777327\pi\) | |||||||
\(632\) | −9.80899 | − | 6.85680i | −0.390181 | − | 0.272749i | ||||
\(633\) | 19.6552 | 0.781225 | ||||||||
\(634\) | 0.304455 | − | 1.47644i | 0.0120914 | − | 0.0586368i | ||||
\(635\) | − | 15.1400i | − | 0.600814i | ||||||
\(636\) | 20.3307 | + | 8.75710i | 0.806163 | + | 0.347242i | ||||
\(637\) | 17.5843i | 0.696715i | ||||||||
\(638\) | −24.3365 | − | 5.01841i | −0.963492 | − | 0.198681i | ||||
\(639\) | − | 4.84611i | − | 0.191709i | ||||||
\(640\) | 3.37574 | + | 22.7536i | 0.133438 | + | 0.899414i | ||||
\(641\) | 45.0011i | 1.77744i | 0.458455 | + | 0.888718i | \(0.348403\pi\) | ||||
−0.458455 | + | 0.888718i | \(0.651597\pi\) | |||||||
\(642\) | 1.20271 | − | 5.83246i | 0.0474670 | − | 0.230189i | ||||
\(643\) | 25.2162i | 0.994430i | 0.867627 | + | 0.497215i | \(0.165644\pi\) | ||||
−0.867627 | + | 0.497215i | \(0.834356\pi\) | |||||||
\(644\) | −11.4896 | + | 2.21242i | −0.452753 | + | 0.0871814i | ||||
\(645\) | 23.7128i | 0.933692i | ||||||||
\(646\) | −49.8461 | − | 10.2787i | −1.96117 | − | 0.404410i | ||||
\(647\) | − | 18.2382i | − | 0.717017i | −0.933527 | − | 0.358508i | \(-0.883285\pi\) | ||
0.933527 | − | 0.358508i | \(-0.116715\pi\) | |||||||
\(648\) | −2.31819 | − | 1.62049i | −0.0910672 | − | 0.0636588i | ||||
\(649\) | 1.24213i | 0.0487577i | ||||||||
\(650\) | 0.789299 | − | 3.82767i | 0.0309589 | − | 0.150133i | ||||
\(651\) | − | 4.33873i | − | 0.170048i | ||||||
\(652\) | −20.7344 | − | 8.93100i | −0.812021 | − | 0.349765i | ||||
\(653\) | 12.8376i | 0.502373i | 0.967939 | + | 0.251186i | \(0.0808207\pi\) | ||||
−0.967939 | + | 0.251186i | \(0.919179\pi\) | |||||||
\(654\) | −4.40579 | − | 0.908513i | −0.172280 | − | 0.0355257i | ||||
\(655\) | −3.70515 | −0.144772 | ||||||||
\(656\) | −6.93629 | − | 7.33655i | −0.270817 | − | 0.286444i | ||||
\(657\) | −7.87149 | −0.307096 | ||||||||
\(658\) | −3.90496 | + | 18.9369i | −0.152231 | + | 0.738238i | ||||
\(659\) | − | 6.88484i | − | 0.268195i | −0.990968 | − | 0.134098i | \(-0.957186\pi\) | ||
0.990968 | − | 0.134098i | \(-0.0428136\pi\) | |||||||
\(660\) | −3.03731 | + | 7.05149i | −0.118227 | + | 0.274479i | ||||
\(661\) | 11.3609 | 0.441888 | 0.220944 | − | 0.975287i | \(-0.429086\pi\) | ||||
0.220944 | + | 0.975287i | \(0.429086\pi\) | |||||||
\(662\) | −15.7179 | − | 3.24118i | −0.610895 | − | 0.125972i | ||||
\(663\) | −18.8726 | −0.732952 | ||||||||
\(664\) | 12.2884 | − | 17.5792i | 0.476882 | − | 0.682204i | ||||
\(665\) | 15.0882i | 0.585097i | ||||||||
\(666\) | 15.3933 | + | 3.17425i | 0.596480 | + | 0.123000i | ||||
\(667\) | 25.0868 | + | 36.9105i | 0.971363 | + | 1.42918i | ||||
\(668\) | 0.283357 | − | 0.657846i | 0.0109634 | − | 0.0254528i | ||||
\(669\) | − | 14.8511i | − | 0.574175i | ||||||
\(670\) | −1.42777 | + | 6.92388i | −0.0551594 | + | 0.267493i | ||||
\(671\) | − | 19.5968i | − | 0.756527i | ||||||
\(672\) | 3.63042 | + | 5.86851i | 0.140046 | + | 0.226383i | ||||
\(673\) | 1.24484 | 0.0479849 | 0.0239925 | − | 0.999712i | \(-0.492362\pi\) | ||||
0.0239925 | + | 0.999712i | \(0.492362\pi\) | |||||||
\(674\) | 2.68147 | − | 13.0036i | 0.103286 | − | 0.500882i | ||||
\(675\) | 0.866240 | 0.0333416 | ||||||||
\(676\) | 5.18424 | + | 2.23303i | 0.199394 | + | 0.0858857i | ||||
\(677\) | −18.1961 | −0.699333 | −0.349667 | − | 0.936874i | \(-0.613705\pi\) | ||||
−0.349667 | + | 0.936874i | \(0.613705\pi\) | |||||||
\(678\) | 5.40365 | − | 26.2047i | 0.207526 | − | 1.00639i | ||||
\(679\) | − | 3.70450i | − | 0.142166i | ||||||
\(680\) | −19.4907 | + | 27.8824i | −0.747435 | + | 1.06924i | ||||
\(681\) | 17.2433i | 0.660766i | ||||||||
\(682\) | 9.30150 | + | 1.91805i | 0.356173 | + | 0.0734460i | ||||
\(683\) | 22.9048 | 0.876428 | 0.438214 | − | 0.898871i | \(-0.355611\pi\) | ||||
0.438214 | + | 0.898871i | \(0.355611\pi\) | |||||||
\(684\) | 4.81318 | − | 11.1744i | 0.184036 | − | 0.427263i | ||||
\(685\) | 0.448799i | 0.0171477i | ||||||||
\(686\) | 21.1403 | + | 4.35933i | 0.807142 | + | 0.166440i | ||||
\(687\) | 2.59033 | 0.0988272 | ||||||||
\(688\) | −33.8998 | + | 32.0503i | −1.29242 | + | 1.22191i | ||||
\(689\) | 35.3103i | 1.34522i | ||||||||
\(690\) | 12.7352 | − | 5.28838i | 0.484822 | − | 0.201325i | ||||
\(691\) | 39.6585 | 1.50868 | 0.754340 | − | 0.656484i | \(-0.227957\pi\) | ||||
0.754340 | + | 0.656484i | \(0.227957\pi\) | |||||||
\(692\) | −8.02505 | + | 18.6311i | −0.305067 | + | 0.708249i | ||||
\(693\) | 2.30330i | 0.0874953i | ||||||||
\(694\) | −6.28766 | − | 1.29657i | −0.238676 | − | 0.0492172i | ||||
\(695\) | −44.6947 | −1.69537 | ||||||||
\(696\) | 15.0799 | − | 21.5725i | 0.571601 | − | 0.817704i | ||||
\(697\) | − | 14.9319i | − | 0.565586i | ||||||
\(698\) | 10.0816 | − | 48.8904i | 0.381595 | − | 1.85053i | ||||
\(699\) | 22.1288 | 0.836987 | ||||||||
\(700\) | −1.94101 | − | 0.836059i | −0.0733633 | − | 0.0316001i | ||||
\(701\) | −22.9169 | −0.865560 | −0.432780 | − | 0.901499i | \(-0.642467\pi\) | ||||
−0.432780 | + | 0.901499i | \(0.642467\pi\) | |||||||
\(702\) | 0.911179 | − | 4.41871i | 0.0343902 | − | 0.166774i | ||||
\(703\) | 67.6099i | 2.54995i | ||||||||
\(704\) | −14.1860 | + | 5.18867i | −0.534655 | + | 0.195555i | ||||
\(705\) | − | 22.7873i | − | 0.858220i | ||||||
\(706\) | −43.1485 | − | 8.89762i | −1.62392 | − | 0.334866i | ||||
\(707\) | 8.54214i | 0.321260i | ||||||||
\(708\) | −1.20838 | − | 0.520491i | −0.0454138 | − | 0.0195613i | ||||
\(709\) | 5.57334 | 0.209311 | 0.104656 | − | 0.994509i | \(-0.466626\pi\) | ||||
0.104656 | + | 0.994509i | \(0.466626\pi\) | |||||||
\(710\) | 2.81414 | − | 13.6470i | 0.105613 | − | 0.512164i | ||||
\(711\) | 4.23131 | 0.158687 | ||||||||
\(712\) | −6.25491 | + | 8.94796i | −0.234413 | + | 0.335339i | ||||
\(713\) | −9.58824 | − | 14.1073i | −0.359082 | − | 0.528323i | ||||
\(714\) | −2.06113 | + | 9.99535i | −0.0771359 | + | 0.374066i | ||||
\(715\) | −12.2470 | −0.458013 | ||||||||
\(716\) | −21.7229 | − | 9.35680i | −0.811824 | − | 0.349680i | ||||
\(717\) | − | 20.5586i | − | 0.767776i | ||||||
\(718\) | 34.5830 | + | 7.13133i | 1.29063 | + | 0.266139i | ||||
\(719\) | − | 3.83953i | − | 0.143190i | −0.997434 | − | 0.0715952i | \(-0.977191\pi\) | ||
0.997434 | − | 0.0715952i | \(-0.0228090\pi\) | |||||||
\(720\) | −5.58719 | − | 5.90960i | −0.208222 | − | 0.220238i | ||||
\(721\) | 3.72911 | 0.138879 | ||||||||
\(722\) | 24.9428 | + | 5.14343i | 0.928274 | + | 0.191419i | ||||
\(723\) | 13.5001i | 0.502075i | ||||||||
\(724\) | −37.1428 | − | 15.9987i | −1.38040 | − | 0.594586i | ||||
\(725\) | 8.06101i | 0.299379i | ||||||||
\(726\) | 10.2979 | + | 2.12352i | 0.382191 | + | 0.0788112i | ||||
\(727\) | −12.5993 | −0.467281 | −0.233641 | − | 0.972323i | \(-0.575064\pi\) | ||||
−0.233641 | + | 0.972323i | \(0.575064\pi\) | |||||||
\(728\) | −6.30647 | + | 9.02172i | −0.233733 | + | 0.334367i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −22.1668 | − | 4.57098i | −0.820428 | − | 0.169180i | ||||
\(731\) | −68.9954 | −2.55189 | ||||||||
\(732\) | 19.0645 | + | 8.21171i | 0.704643 | + | 0.303514i | ||||
\(733\) | −5.84348 | −0.215834 | −0.107917 | − | 0.994160i | \(-0.534418\pi\) | ||||
−0.107917 | + | 0.994160i | \(0.534418\pi\) | |||||||
\(734\) | −34.7030 | − | 7.15608i | −1.28091 | − | 0.264136i | ||||
\(735\) | −11.2066 | −0.413361 | ||||||||
\(736\) | 24.7732 | + | 11.0584i | 0.913152 | + | 0.407620i | ||||
\(737\) | −4.64236 | −0.171004 | ||||||||
\(738\) | 3.49606 | + | 0.720918i | 0.128692 | + | 0.0265374i | ||||
\(739\) | −22.0429 | −0.810861 | −0.405430 | − | 0.914126i | \(-0.632878\pi\) | ||||
−0.405430 | + | 0.914126i | \(0.632878\pi\) | |||||||
\(740\) | 41.5056 | + | 17.8779i | 1.52578 | + | 0.657203i | ||||
\(741\) | 19.4077 | 0.712958 | ||||||||
\(742\) | 18.7011 | + | 3.85633i | 0.686539 | + | 0.141570i | ||||
\(743\) | 27.7944 | 1.01968 | 0.509839 | − | 0.860270i | \(-0.329705\pi\) | ||||
0.509839 | + | 0.860270i | \(0.329705\pi\) | |||||||
\(744\) | −5.76358 | + | 8.24509i | −0.211303 | + | 0.302280i | ||||
\(745\) | −29.2770 | −1.07263 | ||||||||
\(746\) | 24.0195 | + | 4.95303i | 0.879415 | + | 0.181343i | ||||
\(747\) | 7.58314i | 0.277453i | ||||||||
\(748\) | −20.5171 | − | 8.83743i | −0.750181 | − | 0.323128i | ||||
\(749\) | − | 5.13684i | − | 0.187696i | ||||||
\(750\) | 16.5198 | + | 3.40653i | 0.603218 | + | 0.124389i | ||||
\(751\) | −38.5857 | −1.40801 | −0.704005 | − | 0.710195i | \(-0.748607\pi\) | ||||
−0.704005 | + | 0.710195i | \(0.748607\pi\) | |||||||
\(752\) | 32.5766 | − | 30.7993i | 1.18795 | − | 1.12314i | ||||
\(753\) | − | 25.0872i | − | 0.914228i | ||||||
\(754\) | 41.1195 | + | 8.47921i | 1.49748 | + | 0.308794i | ||||
\(755\) | 9.97258i | 0.362939i | ||||||||
\(756\) | −2.24073 | − | 0.965159i | −0.0814946 | − | 0.0351025i | ||||
\(757\) | −38.4124 | −1.39612 | −0.698060 | − | 0.716039i | \(-0.745953\pi\) | ||||
−0.698060 | + | 0.716039i | \(0.745953\pi\) | |||||||
\(758\) | −4.83659 | + | 23.4548i | −0.175673 | + | 0.851916i | ||||
\(759\) | 5.09012 | + | 7.48916i | 0.184760 | + | 0.271839i | ||||
\(760\) | 20.0433 | − | 28.6729i | 0.727046 | − | 1.04008i | ||||
\(761\) | 26.4292 | 0.958056 | 0.479028 | − | 0.877800i | \(-0.340989\pi\) | ||||
0.479028 | + | 0.877800i | \(0.340989\pi\) | |||||||
\(762\) | −2.12684 | + | 10.3140i | −0.0770472 | + | 0.373636i | ||||
\(763\) | −3.88032 | −0.140477 | ||||||||
\(764\) | −7.72339 | − | 3.32673i | −0.279423 | − | 0.120357i | ||||
\(765\) | − | 12.0277i | − | 0.434861i | ||||||
\(766\) | −40.9799 | − | 8.45043i | −1.48066 | − | 0.305326i | ||||
\(767\) | − | 2.09872i | − | 0.0757804i | ||||||
\(768\) | 0.896688 | − | 15.9749i | 0.0323564 | − | 0.576443i | ||||
\(769\) | − | 31.7255i | − | 1.14405i | −0.820236 | − | 0.572025i | \(-0.806158\pi\) | ||
0.820236 | − | 0.572025i | \(-0.193842\pi\) | |||||||
\(770\) | −1.33753 | + | 6.48629i | −0.0482013 | + | 0.233750i | ||||
\(771\) | 12.4382 | 0.447951 | ||||||||
\(772\) | −11.5743 | − | 4.98543i | −0.416567 | − | 0.179430i | ||||
\(773\) | 21.0369 | 0.756645 | 0.378322 | − | 0.925674i | \(-0.376501\pi\) | ||||
0.378322 | + | 0.925674i | \(0.376501\pi\) | |||||||
\(774\) | 3.33113 | − | 16.1541i | 0.119735 | − | 0.580648i | ||||
\(775\) | − | 3.08095i | − | 0.110671i | ||||||
\(776\) | −4.92107 | + | 7.03984i | −0.176656 | + | 0.252715i | ||||
\(777\) | 13.5574 | 0.486370 | ||||||||
\(778\) | −12.7192 | − | 2.62281i | −0.456006 | − | 0.0940325i | ||||
\(779\) | 15.3552i | 0.550157i | ||||||||
\(780\) | 5.13190 | − | 11.9143i | 0.183752 | − | 0.426601i | ||||
\(781\) | 9.15014 | 0.327418 | ||||||||
\(782\) | 15.3872 | + | 37.0547i | 0.550244 | + | 1.32507i | ||||
\(783\) | 9.30575i | 0.332560i | ||||||||
\(784\) | −15.1468 | − | 16.0209i | −0.540959 | − | 0.572175i | ||||
\(785\) | −11.7558 | −0.419583 | ||||||||
\(786\) | 2.52410 | + | 0.520491i | 0.0900315 | + | 0.0185653i | ||||
\(787\) | − | 26.6770i | − | 0.950934i | −0.879734 | − | 0.475467i | \(-0.842279\pi\) | ||
0.879734 | − | 0.475467i | \(-0.157721\pi\) | |||||||
\(788\) | −9.18500 | + | 21.3241i | −0.327202 | + | 0.759639i | ||||
\(789\) | 10.3726 | 0.369274 | ||||||||
\(790\) | 11.9157 | + | 2.45713i | 0.423942 | + | 0.0874207i | ||||
\(791\) | − | 23.0793i | − | 0.820607i | ||||||
\(792\) | 3.05971 | − | 4.37708i | 0.108722 | − | 0.155533i | ||||
\(793\) | 33.1112i | 1.17581i | ||||||||
\(794\) | −3.49740 | + | 16.9605i | −0.124118 | + | 0.601904i | ||||
\(795\) | −22.5035 | −0.798118 | ||||||||
\(796\) | 15.8294 | + | 6.81826i | 0.561058 | + | 0.241667i | ||||
\(797\) | −25.5900 | −0.906443 | −0.453222 | − | 0.891398i | \(-0.649725\pi\) | ||||
−0.453222 | + | 0.891398i | \(0.649725\pi\) | |||||||
\(798\) | 2.11956 | − | 10.2787i | 0.0750317 | − | 0.363862i | ||||
\(799\) | 66.3024 | 2.34561 | ||||||||
\(800\) | 2.57797 | + | 4.16725i | 0.0911451 | + | 0.147334i | ||||
\(801\) | − | 3.85989i | − | 0.136382i | ||||||
\(802\) | −2.56874 | + | 12.4570i | −0.0907052 | + | 0.439870i | ||||
\(803\) | − | 14.8625i | − | 0.524486i | ||||||
\(804\) | 1.94530 | − | 4.51625i | 0.0686054 | − | 0.159276i | ||||
\(805\) | 9.83757 | − | 6.68625i | 0.346729 | − | 0.235659i | ||||
\(806\) | −15.7160 | − | 3.24078i | −0.553572 | − | 0.114152i | ||||
\(807\) | − | 17.9895i | − | 0.633262i | ||||||
\(808\) | 11.3474 | − | 16.2330i | 0.399200 | − | 0.571076i | ||||
\(809\) | −34.2026 | −1.20250 | −0.601250 | − | 0.799061i | \(-0.705331\pi\) | ||||
−0.601250 | + | 0.799061i | \(0.705331\pi\) | |||||||
\(810\) | 2.81608 | + | 0.580701i | 0.0989470 | + | 0.0204038i | ||||
\(811\) | −52.9847 | −1.86054 | −0.930272 | − | 0.366869i | \(-0.880430\pi\) | ||||
−0.930272 | + | 0.366869i | \(0.880430\pi\) | |||||||
\(812\) | 8.98153 | − | 20.8517i | 0.315190 | − | 0.731751i | ||||
\(813\) | 7.39559i | 0.259375i | ||||||||
\(814\) | −5.99343 | + | 29.0648i | −0.210070 | + | 1.01872i | ||||
\(815\) | 22.9504 | 0.803918 | ||||||||
\(816\) | 17.1947 | − | 16.2566i | 0.601935 | − | 0.569095i | ||||
\(817\) | 70.9513 | 2.48227 | ||||||||
\(818\) | −40.9996 | − | 8.45450i | −1.43352 | − | 0.295605i | ||||
\(819\) | − | 3.89171i | − | 0.135987i | ||||||
\(820\) | 9.42653 | + | 4.06033i | 0.329189 | + | 0.141793i | ||||
\(821\) | − | 31.4859i | − | 1.09886i | −0.835538 | − | 0.549432i | \(-0.814844\pi\) | ||
0.835538 | − | 0.549432i | \(-0.185156\pi\) | |||||||
\(822\) | 0.0630463 | − | 0.305740i | 0.00219899 | − | 0.0106639i | ||||
\(823\) | − | 48.2371i | − | 1.68144i | −0.541469 | − | 0.840720i | \(-0.682132\pi\) | ||
0.541469 | − | 0.840720i | \(-0.317868\pi\) | |||||||
\(824\) | −7.08660 | − | 4.95376i | −0.246873 | − | 0.172572i | ||||
\(825\) | 1.63558i | 0.0569437i | ||||||||
\(826\) | −1.11153 | − | 0.229207i | −0.0386750 | − | 0.00797513i | ||||
\(827\) | 1.17993i | 0.0410300i | 0.999790 | + | 0.0205150i | \(0.00653059\pi\) | ||||
−0.999790 | + | 0.0205150i | \(0.993469\pi\) | |||||||
\(828\) | −9.41864 | + | 1.81364i | −0.327320 | + | 0.0630282i | ||||
\(829\) | 26.1335i | 0.907654i | 0.891090 | + | 0.453827i | \(0.149942\pi\) | ||||
−0.891090 | + | 0.453827i | \(0.850058\pi\) | |||||||
\(830\) | −4.40354 | + | 21.3547i | −0.152849 | + | 0.741233i | ||||
\(831\) | 30.0768i | 1.04335i | ||||||||
\(832\) | 23.9690 | − | 8.76687i | 0.830974 | − | 0.303937i | ||||
\(833\) | − | 32.6069i | − | 1.12976i | ||||||
\(834\) | 30.4478 | + | 6.27861i | 1.05432 | + | 0.217410i | ||||
\(835\) | 0.728155i | 0.0251988i | ||||||||
\(836\) | 21.0988 | + | 9.08796i | 0.729717 | + | 0.314314i | ||||
\(837\) | − | 3.55669i | − | 0.122937i | ||||||
\(838\) | −3.89443 | + | 18.8858i | −0.134531 | + | 0.652400i | ||||
\(839\) | −20.5929 | −0.710946 | −0.355473 | − | 0.934687i | \(-0.615680\pi\) | ||||
−0.355473 | + | 0.934687i | \(0.615680\pi\) | |||||||
\(840\) | −5.74961 | − | 4.01916i | −0.198380 | − | 0.138674i | ||||
\(841\) | −57.5970 | −1.98610 | ||||||||
\(842\) | 6.31639 | + | 1.30250i | 0.217677 | + | 0.0448870i | ||||
\(843\) | − | 6.06727i | − | 0.208968i | ||||||
\(844\) | −36.1037 | − | 15.5511i | −1.24274 | − | 0.535290i | ||||
\(845\) | −5.73832 | −0.197404 | ||||||||
\(846\) | −3.20111 | + | 15.5236i | −0.110056 | + | 0.533713i | ||||
\(847\) | 9.06970 | 0.311639 | ||||||||
\(848\) | −30.4158 | − | 32.1710i | −1.04448 | − | 1.10476i | ||||
\(849\) | 25.5734i | 0.877676i | ||||||||
\(850\) | −1.46362 | + | 7.09773i | −0.0502016 | + | 0.243450i | ||||
\(851\) | 44.0818 | − | 29.9608i | 1.51110 | − | 1.02704i | ||||
\(852\) | −3.83421 | + | 8.90157i | −0.131358 | + | 0.304963i | ||||
\(853\) | 13.1368i | 0.449794i | 0.974383 | + | 0.224897i | \(0.0722045\pi\) | ||||
−0.974383 | + | 0.224897i | \(0.927795\pi\) | |||||||
\(854\) | 17.5364 | + | 3.61616i | 0.600083 | + | 0.123743i | ||||
\(855\) | 12.3686i | 0.422999i | ||||||||
\(856\) | −6.82379 | + | 9.76178i | −0.233232 | + | 0.333651i | ||||
\(857\) | 31.3190 | 1.06984 | 0.534918 | − | 0.844904i | \(-0.320342\pi\) | ||||
0.534918 | + | 0.844904i | \(0.320342\pi\) | |||||||
\(858\) | 8.34316 | + | 1.72044i | 0.284831 | + | 0.0587347i | ||||
\(859\) | 10.4517 | 0.356606 | 0.178303 | − | 0.983976i | \(-0.442939\pi\) | ||||
0.178303 | + | 0.983976i | \(0.442939\pi\) | |||||||
\(860\) | 18.7614 | − | 43.5569i | 0.639760 | − | 1.48528i | ||||
\(861\) | 3.07909 | 0.104935 | ||||||||
\(862\) | 41.6595 | + | 8.59057i | 1.41893 | + | 0.292596i | ||||
\(863\) | 31.2021i | 1.06213i | 0.847331 | + | 0.531066i | \(0.178208\pi\) | ||||
−0.847331 | + | 0.531066i | \(0.821792\pi\) | |||||||
\(864\) | 2.97605 | + | 4.81073i | 0.101247 | + | 0.163664i | ||||
\(865\) | − | 20.6224i | − | 0.701181i | ||||||
\(866\) | −4.87951 | + | 23.6630i | −0.165813 | + | 0.804100i | ||||
\(867\) | 17.9960 | 0.611175 | ||||||||
\(868\) | −3.43277 | + | 7.96959i | −0.116516 | + | 0.270505i | ||||
\(869\) | 7.98932i | 0.271019i | ||||||||
\(870\) | −5.40386 | + | 26.2057i | −0.183208 | + | 0.888458i | ||||
\(871\) | 7.84382 | 0.265778 | ||||||||
\(872\) | 7.37396 | + | 5.15463i | 0.249714 | + | 0.174558i | ||||
\(873\) | − | 3.03678i | − | 0.102779i | ||||||
\(874\) | −15.8234 | − | 38.1051i | −0.535234 | − | 1.28893i | ||||
\(875\) | 14.5495 | 0.491864 | ||||||||
\(876\) | 14.4587 | + | 6.22787i | 0.488516 | + | 0.210420i | ||||
\(877\) | 33.3576i | 1.12641i | 0.826318 | + | 0.563203i | \(0.190431\pi\) | ||||
−0.826318 | + | 0.563203i | \(0.809569\pi\) | |||||||
\(878\) | 4.92728 | − | 23.8946i | 0.166288 | − | 0.806404i | ||||
\(879\) | −19.4122 | −0.654756 | ||||||||
\(880\) | 11.1582 | − | 10.5494i | 0.376142 | − | 0.355621i | ||||
\(881\) | 3.93660i | 0.132627i | 0.997799 | + | 0.0663137i | \(0.0211238\pi\) | ||||
−0.997799 | + | 0.0663137i | \(0.978876\pi\) | |||||||
\(882\) | 7.63437 | + | 1.57428i | 0.257063 | + | 0.0530087i | ||||
\(883\) | 25.8164 | 0.868790 | 0.434395 | − | 0.900722i | \(-0.356962\pi\) | ||||
0.434395 | + | 0.900722i | \(0.356962\pi\) | |||||||
\(884\) | 34.6662 | + | 14.9319i | 1.16595 | + | 0.502214i | ||||
\(885\) | 1.33753 | 0.0449606 | ||||||||
\(886\) | 26.3210 | + | 5.42762i | 0.884270 | + | 0.182344i | ||||
\(887\) | 50.2556i | 1.68742i | 0.536800 | + | 0.843709i | \(0.319633\pi\) | ||||
−0.536800 | + | 0.843709i | \(0.680367\pi\) | |||||||
\(888\) | −25.7638 | − | 18.0097i | −0.864576 | − | 0.604366i | ||||
\(889\) | 9.08387i | 0.304663i | ||||||||
\(890\) | 2.24144 | − | 10.8698i | 0.0751333 | − | 0.364355i | ||||
\(891\) | 1.88814i | 0.0632551i | ||||||||
\(892\) | −11.7501 | + | 27.2792i | −0.393421 | + | 0.913374i | ||||
\(893\) | −68.1820 | −2.28162 | ||||||||
\(894\) | 19.9446 | + | 4.11276i | 0.667048 | + | 0.137551i | ||||
\(895\) | 24.0446 | 0.803723 | ||||||||
\(896\) | −2.02541 | − | 13.6519i | −0.0676641 | − | 0.456079i | ||||
\(897\) | −8.60036 | − | 12.6538i | −0.287158 | − | 0.422499i | ||||
\(898\) | −13.7953 | − | 2.84471i | −0.460354 | − | 0.0949291i | ||||
\(899\) | 33.0977 | 1.10387 | ||||||||
\(900\) | −1.59115 | − | 0.685363i | −0.0530384 | − | 0.0228454i | ||||
\(901\) | − | 65.4767i | − | 2.18135i | ||||||
\(902\) | −1.36120 | + | 6.60105i | −0.0453229 | + | 0.219791i | ||||
\(903\) | − | 14.2275i | − | 0.473460i | ||||||
\(904\) | −30.6587 | + | 43.8588i | −1.01969 | + | 1.45872i | ||||
\(905\) | 41.1125 | 1.36663 | ||||||||
\(906\) | 1.40093 | − | 6.79371i | 0.0465426 | − | 0.225706i | ||||
\(907\) | − | 18.7971i | − | 0.624147i | −0.950058 | − | 0.312074i | \(-0.898976\pi\) | ||
0.950058 | − | 0.312074i | \(-0.101024\pi\) | |||||||
\(908\) | 13.6428 | − | 31.6734i | 0.452753 | − | 1.05112i | ||||
\(909\) | 7.00245i | 0.232257i | ||||||||
\(910\) | 2.25992 | − | 10.9594i | 0.0749156 | − | 0.363299i | ||||
\(911\) | −5.60263 | −0.185623 | −0.0928117 | − | 0.995684i | \(-0.529585\pi\) | ||||
−0.0928117 | + | 0.995684i | \(0.529585\pi\) | |||||||
\(912\) | −17.6822 | + | 16.7175i | −0.585515 | + | 0.553571i | ||||
\(913\) | −14.3180 | −0.473858 | ||||||||
\(914\) | −3.22675 | + | 15.6479i | −0.106731 | + | 0.517588i | ||||
\(915\) | −21.1020 | −0.697611 | ||||||||
\(916\) | −4.75804 | − | 2.04945i | −0.157210 | − | 0.0677157i | ||||
\(917\) | 2.22305 | 0.0734117 | ||||||||
\(918\) | −1.68962 | + | 8.19372i | −0.0557658 | + | 0.270433i | ||||
\(919\) | 29.5139 | 0.973572 | 0.486786 | − | 0.873521i | \(-0.338169\pi\) | ||||
0.486786 | + | 0.873521i | \(0.338169\pi\) | |||||||
\(920\) | −27.5768 | − | 0.362066i | −0.909181 | − | 0.0119370i | ||||
\(921\) | −2.20932 | −0.0727997 | ||||||||
\(922\) | −2.21003 | + | 10.7174i | −0.0727833 | + | 0.352959i | ||||
\(923\) | −15.4603 | −0.508881 | ||||||||
\(924\) | 1.82236 | − | 4.23082i | 0.0599512 | − | 0.139184i | ||||
\(925\) | 9.62717 | 0.316539 | ||||||||
\(926\) | 4.51450 | − | 21.8929i | 0.148356 | − | 0.719444i | ||||
\(927\) | 3.05695 | 0.100403 | ||||||||
\(928\) | −44.7675 | + | 27.6944i | −1.46956 | + | 0.909112i | ||||
\(929\) | −59.0986 | −1.93896 | −0.969481 | − | 0.245165i | \(-0.921158\pi\) | ||||
−0.969481 | + | 0.245165i | \(0.921158\pi\) | |||||||
\(930\) | 2.06537 | − | 10.0159i | 0.0677262 | − | 0.328435i | ||||
\(931\) | 33.5313i | 1.09894i | ||||||||
\(932\) | −40.6472 | − | 17.5081i | −1.33144 | − | 0.573498i | ||||
\(933\) | 18.3744i | 0.601550i | ||||||||
\(934\) | 9.28935 | − | 45.0482i | 0.303957 | − | 1.47402i | ||||
\(935\) | 22.7100 | 0.742695 | ||||||||
\(936\) | −5.16975 | + | 7.39559i | −0.168979 | + | 0.241733i | ||||
\(937\) | 13.5151i | 0.441518i | 0.975328 | + | 0.220759i | \(0.0708535\pi\) | ||||
−0.975328 | + | 0.220759i | \(0.929147\pi\) | |||||||
\(938\) | 0.856645 | − | 4.15426i | 0.0279704 | − | 0.135641i | ||||
\(939\) | − | 14.6786i | − | 0.479018i | ||||||
\(940\) | −18.0292 | + | 41.8568i | −0.588046 | + | 1.36522i | ||||
\(941\) | 13.6282 | 0.444267 | 0.222133 | − | 0.975016i | \(-0.428698\pi\) | ||||
0.222133 | + | 0.975016i | \(0.428698\pi\) | |||||||
\(942\) | 8.00851 | + | 1.65143i | 0.260931 | + | 0.0538064i | ||||
\(943\) | 10.0116 | − | 6.80454i | 0.326023 | − | 0.221586i | ||||
\(944\) | 1.80781 | + | 1.91213i | 0.0588391 | + | 0.0622345i | ||||
\(945\) | 2.48021 | 0.0806814 | ||||||||
\(946\) | 30.5013 | + | 6.28964i | 0.991682 | + | 0.204494i | ||||
\(947\) | 5.13751 | 0.166947 | 0.0834733 | − | 0.996510i | \(-0.473399\pi\) | ||||
0.0834733 | + | 0.996510i | \(0.473399\pi\) | |||||||
\(948\) | −7.77228 | − | 3.34778i | −0.252432 | − | 0.108731i | ||||
\(949\) | 25.1120i | 0.815169i | ||||||||
\(950\) | 1.50511 | − | 7.29894i | 0.0488322 | − | 0.236809i | ||||
\(951\) | − | 1.06596i | − | 0.0345663i | ||||||
\(952\) | 11.6942 | − | 16.7292i | 0.379012 | − | 0.542196i | ||||
\(953\) | 20.0968i | 0.651000i | 0.945542 | + | 0.325500i | \(0.105533\pi\) | ||||
−0.945542 | + | 0.325500i | \(0.894467\pi\) | |||||||
\(954\) | 15.3303 | + | 3.16124i | 0.496337 | + | 0.102349i | ||||
\(955\) | 8.54884 | 0.276634 | ||||||||
\(956\) | −16.2658 | + | 37.7631i | −0.526075 | + | 1.22135i | ||||
\(957\) | −17.5706 | −0.567976 | ||||||||
\(958\) | −22.4517 | − | 4.62974i | −0.725381 | − | 0.149580i | ||||
\(959\) | − | 0.269275i | − | 0.00869535i | ||||||
\(960\) | 5.58719 | + | 15.2756i | 0.180326 | + | 0.493018i | ||||
\(961\) | 18.3500 | 0.591935 | ||||||||
\(962\) | 10.1266 | − | 49.1085i | 0.326495 | − | 1.58332i | ||||
\(963\) | − | 4.21095i | − | 0.135696i | ||||||
\(964\) | 10.6812 | − | 24.7977i | 0.344018 | − | 0.798680i | ||||
\(965\) | 12.8113 | 0.412410 | ||||||||
\(966\) | −7.64101 | + | 3.17297i | −0.245845 | + | 0.102089i | ||||
\(967\) | 4.12341i | 0.132600i | 0.997800 | + | 0.0663000i | \(0.0211194\pi\) | ||||
−0.997800 | + | 0.0663000i | \(0.978881\pi\) | |||||||
\(968\) | −17.2356 | − | 12.0482i | −0.553972 | − | 0.387244i | ||||
\(969\) | −35.9881 | −1.15610 | ||||||||
\(970\) | 1.76346 | − | 8.55181i | 0.0566213 | − | 0.274582i | ||||
\(971\) | 29.8517i | 0.957987i | 0.877818 | + | 0.478993i | \(0.158998\pi\) | ||||
−0.877818 | + | 0.478993i | \(0.841002\pi\) | |||||||
\(972\) | −1.83685 | − | 0.791193i | −0.0589170 | − | 0.0253775i | ||||
\(973\) | 26.8164 | 0.859693 | ||||||||
\(974\) | 4.42674 | − | 21.4672i | 0.141842 | − | 0.687855i | ||||
\(975\) | − | 2.76351i | − | 0.0885033i | ||||||
\(976\) | −28.5215 | − | 30.1673i | −0.912951 | − | 0.965633i | ||||
\(977\) | − | 27.9916i | − | 0.895531i | −0.894151 | − | 0.447766i | \(-0.852220\pi\) | ||
0.894151 | − | 0.447766i | \(-0.147780\pi\) | |||||||
\(978\) | −15.6347 | − | 3.22402i | −0.499943 | − | 0.103093i | ||||
\(979\) | 7.28802 | 0.232926 | ||||||||
\(980\) | 20.5848 | + | 8.86658i | 0.657558 | + | 0.283232i | ||||
\(981\) | −3.18091 | −0.101559 | ||||||||
\(982\) | −35.0788 | − | 7.23357i | −1.11941 | − | 0.230833i | ||||
\(983\) | 23.2880 | 0.742773 | 0.371386 | − | 0.928478i | \(-0.378882\pi\) | ||||
0.371386 | + | 0.928478i | \(0.378882\pi\) | |||||||
\(984\) | −5.85134 | − | 4.09027i | −0.186534 | − | 0.130393i | ||||
\(985\) | − | 23.6031i | − | 0.752058i | ||||||
\(986\) | −76.2488 | − | 15.7232i | −2.42826 | − | 0.500728i | ||||
\(987\) | 13.6722i | 0.435189i | ||||||||
\(988\) | −35.6489 | − | 15.3552i | −1.13414 | − | 0.488514i | ||||
\(989\) | −31.4416 | − | 46.2604i | −0.999784 | − | 1.47100i | ||||
\(990\) | −1.09645 | + | 5.31716i | −0.0348473 | + | 0.168990i | ||||
\(991\) | − | 20.0895i | − | 0.638164i | −0.947727 | − | 0.319082i | \(-0.896626\pi\) | ||
0.947727 | − | 0.319082i | \(-0.103374\pi\) | |||||||
\(992\) | 17.1103 | − | 10.5849i | 0.543252 | − | 0.336070i | ||||
\(993\) | −11.3481 | −0.360121 | ||||||||
\(994\) | −1.68846 | + | 8.18808i | −0.0535546 | + | 0.259710i | ||||
\(995\) | −17.5212 | −0.555459 | ||||||||
\(996\) | 5.99973 | − | 13.9291i | 0.190109 | − | 0.441360i | ||||
\(997\) | 28.4733i | 0.901758i | 0.892585 | + | 0.450879i | \(0.148889\pi\) | ||||
−0.892585 | + | 0.450879i | \(0.851111\pi\) | |||||||
\(998\) | −1.41348 | − | 0.291471i | −0.0447428 | − | 0.00922637i | ||||
\(999\) | 11.1137 | 0.351623 |
(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 | 552.2.n.b.91.1 | ✓ | 24 | |
4.3 | odd | 2 | 2208.2.n.b.367.7 | 24 | |||
8.3 | odd | 2 | inner | 552.2.n.b.91.4 | yes | 24 | |
8.5 | even | 2 | 2208.2.n.b.367.17 | 24 | |||
23.22 | odd | 2 | inner | 552.2.n.b.91.2 | yes | 24 | |
92.91 | even | 2 | 2208.2.n.b.367.18 | 24 | |||
184.45 | odd | 2 | 2208.2.n.b.367.8 | 24 | |||
184.91 | even | 2 | inner | 552.2.n.b.91.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
552.2.n.b.91.1 | ✓ | 24 | 1.1 | even | 1 | trivial | |
552.2.n.b.91.2 | yes | 24 | 23.22 | odd | 2 | inner | |
552.2.n.b.91.3 | yes | 24 | 184.91 | even | 2 | inner | |
552.2.n.b.91.4 | yes | 24 | 8.3 | odd | 2 | inner | |
2208.2.n.b.367.7 | 24 | 4.3 | odd | 2 | |||
2208.2.n.b.367.8 | 24 | 184.45 | odd | 2 | |||
2208.2.n.b.367.17 | 24 | 8.5 | even | 2 | |||
2208.2.n.b.367.18 | 24 | 92.91 | even | 2 |