Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(19,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.y (of order \(30\), degree \(8\), 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: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{30})\) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{30}]$ |
Embedding invariants
Embedding label | 604.9 | ||
Character | \(\chi\) | \(=\) | 675.604 |
Dual form | 675.2.y.a.19.9 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.250369 | − | 1.17789i | −0.177038 | − | 0.832897i | −0.973586 | − | 0.228322i | \(-0.926676\pi\) |
0.796548 | − | 0.604575i | \(-0.206657\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.502342 | − | 0.223657i | 0.251171 | − | 0.111828i | ||||
\(5\) | 1.04324 | + | 1.97779i | 0.466553 | + | 0.884493i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.32094 | − | 1.33999i | 0.877233 | − | 0.506470i | 0.00748764 | − | 0.999972i | \(-0.497617\pi\) |
0.869745 | + | 0.493501i | \(0.164283\pi\) | |||||||
\(8\) | −1.80485 | − | 2.48416i | −0.638110 | − | 0.878283i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.06843 | − | 1.72401i | 0.654094 | − | 0.545179i | ||||
\(11\) | −1.37561 | + | 0.292396i | −0.414763 | + | 0.0881606i | −0.410567 | − | 0.911831i | \(-0.634669\pi\) |
−0.00419636 | + | 0.999991i | \(0.501336\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.0338103 | + | 0.159065i | −0.00937729 | + | 0.0441167i | −0.982587 | − | 0.185800i | \(-0.940512\pi\) |
0.973210 | + | 0.229917i | \(0.0738455\pi\) | |||||||
\(14\) | −2.15946 | − | 2.39833i | −0.577141 | − | 0.640980i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.73831 | + | 1.93059i | −0.434578 | + | 0.482648i | ||||
\(17\) | −0.113531 | − | 0.156262i | −0.0275354 | − | 0.0378992i | 0.795027 | − | 0.606574i | \(-0.207456\pi\) |
−0.822563 | + | 0.568674i | \(0.807456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.07397 | − | 4.41300i | 1.39346 | − | 1.01241i | 0.397989 | − | 0.917390i | \(-0.369708\pi\) |
0.995475 | − | 0.0950213i | \(-0.0302919\pi\) | |||||||
\(20\) | 0.966411 | + | 0.760196i | 0.216096 | + | 0.169985i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.688822 | + | 1.54712i | 0.146857 | + | 0.329847i | ||||
\(23\) | 4.38392 | − | 3.94730i | 0.914110 | − | 0.823069i | −0.0705575 | − | 0.997508i | \(-0.522478\pi\) |
0.984668 | + | 0.174439i | \(0.0558112\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.82328 | + | 4.12663i | −0.564656 | + | 0.825326i | ||||
\(26\) | 0.195827 | 0.0384048 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.866205 | − | 1.19223i | 0.163697 | − | 0.225310i | ||||
\(29\) | −0.636956 | + | 6.06023i | −0.118280 | + | 1.12536i | 0.760901 | + | 0.648868i | \(0.224757\pi\) |
−0.879180 | + | 0.476489i | \(0.841909\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.0629147 | + | 0.598594i | 0.0112998 | + | 0.107511i | 0.998718 | − | 0.0506203i | \(-0.0161198\pi\) |
−0.987418 | + | 0.158131i | \(0.949453\pi\) | |||||||
\(32\) | −2.60917 | − | 1.50640i | −0.461240 | − | 0.266297i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.155636 | + | 0.172851i | −0.0266913 | + | 0.0296437i | ||||
\(35\) | 5.07153 | + | 3.19238i | 0.857245 | + | 0.539611i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.888903 | − | 0.288822i | 0.146135 | − | 0.0474821i | −0.235036 | − | 0.971987i | \(-0.575521\pi\) |
0.381171 | + | 0.924505i | \(0.375521\pi\) | |||||||
\(38\) | −6.71878 | − | 6.04962i | −1.08993 | − | 0.981377i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.03024 | − | 6.16119i | 0.479123 | − | 0.974169i | ||||
\(41\) | 5.53191 | + | 1.17584i | 0.863940 | + | 0.183636i | 0.618509 | − | 0.785778i | \(-0.287737\pi\) |
0.245431 | + | 0.969414i | \(0.421071\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.91893 | − | 3.41730i | 0.902629 | − | 0.521133i | 0.0245768 | − | 0.999698i | \(-0.492176\pi\) |
0.878052 | + | 0.478565i | \(0.158843\pi\) | |||||||
\(44\) | −0.625632 | + | 0.454548i | −0.0943175 | + | 0.0685257i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.74710 | − | 4.17551i | −0.847363 | − | 0.615645i | ||||
\(47\) | 0.217685 | + | 0.0228796i | 0.0317525 | + | 0.00333733i | 0.120391 | − | 0.992727i | \(-0.461585\pi\) |
−0.0886389 | + | 0.996064i | \(0.528252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0911727 | − | 0.157916i | 0.0130247 | − | 0.0225594i | ||||
\(50\) | 5.56760 | + | 2.29234i | 0.787377 | + | 0.324186i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.0185917 | + | 0.0874669i | 0.00257820 | + | 0.0121295i | ||||
\(53\) | 7.64631 | − | 10.5242i | 1.05030 | − | 1.44562i | 0.161754 | − | 0.986831i | \(-0.448285\pi\) |
0.888547 | − | 0.458785i | \(-0.151715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.01340 | − | 2.41563i | −0.271486 | − | 0.325723i | ||||
\(56\) | −7.51770 | − | 3.34710i | −1.00460 | − | 0.447275i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.29779 | − | 0.767028i | 0.958246 | − | 0.100716i | ||||
\(59\) | −5.81390 | − | 1.23578i | −0.756905 | − | 0.160885i | −0.186733 | − | 0.982411i | \(-0.559790\pi\) |
−0.570172 | + | 0.821525i | \(0.693123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.7973 | + | 2.93271i | −1.76656 | + | 0.375495i | −0.972602 | − | 0.232475i | \(-0.925318\pi\) |
−0.793961 | + | 0.607969i | \(0.791984\pi\) | |||||||
\(62\) | 0.689328 | − | 0.223976i | 0.0875447 | − | 0.0284450i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.72670 | + | 8.39191i | −0.340837 | + | 1.04899i | ||||
\(65\) | −0.349869 | + | 0.0990742i | −0.0433959 | + | 0.0122886i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.42391 | + | 0.675180i | −0.784805 | + | 0.0824863i | −0.488450 | − | 0.872592i | \(-0.662438\pi\) |
−0.296355 | + | 0.955078i | \(0.595771\pi\) | |||||||
\(68\) | −0.0919806 | − | 0.0531050i | −0.0111543 | − | 0.00643993i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.49053 | − | 6.77300i | 0.297675 | − | 0.809528i | ||||
\(71\) | −2.90460 | − | 2.11032i | −0.344713 | − | 0.250449i | 0.401935 | − | 0.915668i | \(-0.368338\pi\) |
−0.746648 | + | 0.665220i | \(0.768338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.0652 | − | 3.59530i | −1.29508 | − | 0.420798i | −0.421215 | − | 0.906961i | \(-0.638396\pi\) |
−0.873868 | + | 0.486163i | \(0.838396\pi\) | |||||||
\(74\) | −0.562756 | − | 0.974721i | −0.0654190 | − | 0.113309i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.06421 | − | 3.57532i | 0.236781 | − | 0.410117i | ||||
\(77\) | −2.80091 | + | 2.52195i | −0.319193 | + | 0.287403i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.42166 | + | 13.5262i | −0.159950 | + | 1.52182i | 0.560407 | + | 0.828217i | \(0.310645\pi\) |
−0.720357 | + | 0.693603i | \(0.756022\pi\) | |||||||
\(80\) | −5.63178 | − | 1.42393i | −0.629653 | − | 0.159200i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 6.81040i | − | 0.752083i | ||||||
\(83\) | −5.96001 | + | 13.3864i | −0.654196 | + | 1.46935i | 0.215875 | + | 0.976421i | \(0.430740\pi\) |
−0.870071 | + | 0.492927i | \(0.835927\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.190613 | − | 0.387560i | 0.0206748 | − | 0.0420368i | ||||
\(86\) | −5.50713 | − | 6.11629i | −0.593849 | − | 0.659537i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.20913 | + | 2.88951i | 0.342094 | + | 0.308023i | ||||
\(89\) | 3.38521 | − | 10.4186i | 0.358831 | − | 1.10437i | −0.594923 | − | 0.803783i | \(-0.702817\pi\) |
0.953754 | − | 0.300587i | \(-0.0971825\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.134675 | + | 0.414486i | 0.0141177 | + | 0.0434499i | ||||
\(92\) | 1.31938 | − | 2.96339i | 0.137555 | − | 0.308954i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.0275518 | − | 0.262138i | −0.00284175 | − | 0.0270374i | ||||
\(95\) | 15.0646 | + | 7.40918i | 1.54560 | + | 0.760166i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.08167 | + | 0.323896i | 0.312896 | + | 0.0328867i | 0.259675 | − | 0.965696i | \(-0.416385\pi\) |
0.0532209 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(98\) | −0.208835 | − | 0.0678546i | −0.0210955 | − | 0.00685435i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.495302 | + | 2.70443i | −0.0495302 | + | 0.270443i | ||||
\(101\) | −4.01857 | − | 6.96037i | −0.399863 | − | 0.692583i | 0.593846 | − | 0.804579i | \(-0.297609\pi\) |
−0.993709 | + | 0.111996i | \(0.964276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.219557 | + | 0.493132i | 0.0216336 | + | 0.0485898i | 0.924039 | − | 0.382298i | \(-0.124867\pi\) |
−0.902406 | + | 0.430888i | \(0.858201\pi\) | |||||||
\(104\) | 0.456165 | − | 0.203098i | 0.0447307 | − | 0.0199154i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.3108 | − | 6.37160i | −1.38999 | − | 0.618864i | ||||
\(107\) | − | 0.671621i | − | 0.0649281i | −0.999473 | − | 0.0324640i | \(-0.989665\pi\) | ||
0.999473 | − | 0.0324640i | \(-0.0103354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.32136 | + | 13.2998i | 0.413911 | + | 1.27389i | 0.913221 | + | 0.407464i | \(0.133587\pi\) |
−0.499310 | + | 0.866423i | \(0.666413\pi\) | |||||||
\(110\) | −2.34126 | + | 2.97637i | −0.223231 | + | 0.283785i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.44753 | + | 6.81012i | −0.136779 | + | 0.643495i | ||||
\(113\) | 0.769916 | − | 3.62217i | 0.0724276 | − | 0.340745i | −0.926982 | − | 0.375106i | \(-0.877606\pi\) |
0.999409 | + | 0.0343611i | \(0.0109396\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.3804 | + | 4.55246i | 1.15448 | + | 0.424519i | ||||
\(116\) | 1.03544 | + | 3.18677i | 0.0961386 | + | 0.295884i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.15756i | 0.658907i | ||||||||
\(119\) | −0.472890 | − | 0.210544i | −0.0433497 | − | 0.0193005i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.24218 | + | 3.66966i | −0.749289 | + | 0.333605i | ||||
\(122\) | 6.90883 | + | 15.5175i | 0.625496 | + | 1.40489i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.165484 | + | 0.286627i | 0.0148609 | + | 0.0257399i | ||||
\(125\) | −11.1070 | − | 1.27876i | −0.993438 | − | 0.114376i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.6104 | + | 4.42230i | 1.20773 | + | 0.392416i | 0.842600 | − | 0.538540i | \(-0.181024\pi\) |
0.365132 | + | 0.930956i | \(0.381024\pi\) | |||||||
\(128\) | 4.57486 | + | 0.480838i | 0.404365 | + | 0.0425004i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.204295 | + | 0.387304i | 0.0179179 | + | 0.0339688i | ||||
\(131\) | 1.22397 | + | 11.6453i | 0.106938 | + | 1.01745i | 0.908029 | + | 0.418908i | \(0.137587\pi\) |
−0.801090 | + | 0.598543i | \(0.795746\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.18392 | − | 18.3814i | 0.709636 | − | 1.59387i | ||||
\(134\) | 2.40364 | + | 7.39763i | 0.207643 | + | 0.639058i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.183274 | + | 0.564059i | −0.0157156 | + | 0.0483677i | ||||
\(137\) | 15.2933 | + | 13.7702i | 1.30660 | + | 1.17647i | 0.972231 | + | 0.234022i | \(0.0751888\pi\) |
0.334366 | + | 0.942443i | \(0.391478\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.609700 | − | 0.677140i | −0.0517141 | − | 0.0574343i | 0.716733 | − | 0.697348i | \(-0.245637\pi\) |
−0.768447 | + | 0.639914i | \(0.778970\pi\) | |||||||
\(140\) | 3.26164 | + | 0.469382i | 0.275659 | + | 0.0396701i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.75851 | + | 3.94967i | −0.147571 | + | 0.331449i | ||||
\(143\) | − | 0.228698i | − | 0.0191247i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.6504 | + | 5.06254i | −1.05055 | + | 0.420421i | ||||
\(146\) | −1.46450 | + | 13.9338i | −0.121203 | + | 1.15317i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.381936 | − | 0.343897i | 0.0313949 | − | 0.0282681i | ||||
\(149\) | −10.6085 | + | 18.3745i | −0.869083 | + | 1.50530i | −0.00614869 | + | 0.999981i | \(0.501957\pi\) |
−0.862935 | + | 0.505315i | \(0.831376\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.66528 | − | 4.61641i | −0.216898 | − | 0.375678i | 0.736960 | − | 0.675936i | \(-0.236260\pi\) |
−0.953858 | + | 0.300258i | \(0.902927\pi\) | |||||||
\(152\) | −21.9252 | − | 7.12392i | −1.77837 | − | 0.577826i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.67185 | + | 2.66775i | 0.295886 | + | 0.214974i | ||||
\(155\) | −1.11826 | + | 0.748912i | −0.0898204 | + | 0.0601540i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4979 | + | 6.06096i | 0.837823 | + | 0.483717i | 0.856524 | − | 0.516108i | \(-0.172620\pi\) |
−0.0187007 | + | 0.999825i | \(0.505953\pi\) | |||||||
\(158\) | 16.2884 | − | 1.71198i | 1.29584 | − | 0.136198i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.257344 | − | 6.73192i | 0.0203448 | − | 0.532205i | ||||
\(161\) | 4.88545 | − | 15.0359i | 0.385027 | − | 1.18499i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.508454 | + | 0.165207i | −0.0398252 | + | 0.0129400i | −0.328862 | − | 0.944378i | \(-0.606665\pi\) |
0.289037 | + | 0.957318i | \(0.406665\pi\) | |||||||
\(164\) | 3.04190 | − | 0.646575i | 0.237532 | − | 0.0504890i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.2600 | + | 3.66872i | 1.33963 | + | 0.284748i | ||||
\(167\) | −10.8420 | + | 1.13954i | −0.838979 | + | 0.0881803i | −0.514264 | − | 0.857632i | \(-0.671935\pi\) |
−0.324715 | + | 0.945812i | \(0.605268\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8519 | + | 5.27682i | 0.911687 | + | 0.405909i | ||||
\(170\) | −0.504228 | − | 0.127488i | −0.0386726 | − | 0.00977791i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.20903 | − | 3.04046i | 0.168437 | − | 0.231833i | ||||
\(173\) | −2.18261 | − | 10.2684i | −0.165941 | − | 0.780689i | −0.979856 | − | 0.199706i | \(-0.936001\pi\) |
0.813915 | − | 0.580983i | \(-0.197332\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.02300 | + | 13.3608i | −0.0773313 | + | 1.00998i | ||||
\(176\) | 1.82675 | − | 3.16402i | 0.137696 | − | 0.238497i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.1196 | − | 1.37892i | −0.983352 | − | 0.103355i | ||||
\(179\) | 11.1491 | + | 8.10027i | 0.833321 | + | 0.605443i | 0.920497 | − | 0.390750i | \(-0.127784\pi\) |
−0.0871761 | + | 0.996193i | \(0.527784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.95243 | + | 4.32469i | −0.442441 | + | 0.321452i | −0.786604 | − | 0.617458i | \(-0.788163\pi\) |
0.344163 | + | 0.938910i | \(0.388163\pi\) | |||||||
\(182\) | 0.454502 | − | 0.262407i | 0.0336899 | − | 0.0194509i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.7180 | − | 3.76608i | −1.30619 | − | 0.277639i | ||||
\(185\) | 1.49857 | + | 1.45675i | 0.110177 | + | 0.107102i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.201865 | + | 0.181760i | 0.0147619 | + | 0.0132916i | ||||
\(188\) | 0.114469 | − | 0.0371933i | 0.00834852 | − | 0.00271260i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.95552 | − | 19.5995i | 0.359511 | − | 1.42190i | ||||
\(191\) | −0.746068 | + | 0.828592i | −0.0539836 | + | 0.0599548i | −0.769532 | − | 0.638609i | \(-0.779510\pi\) |
0.715548 | + | 0.698563i | \(0.246177\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.9469 | − | 12.6711i | −1.57977 | − | 0.912083i | −0.994890 | − | 0.100966i | \(-0.967807\pi\) |
−0.584884 | − | 0.811117i | \(-0.698860\pi\) | |||||||
\(194\) | −0.390039 | − | 3.71097i | −0.0280031 | − | 0.266432i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.0104809 | − | 0.0997191i | 0.000748636 | − | 0.00712279i | ||||
\(197\) | −9.37839 | + | 12.9082i | −0.668182 | + | 0.919674i | −0.999717 | − | 0.0237688i | \(-0.992433\pi\) |
0.331535 | + | 0.943443i | \(0.392433\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.2943 | −1.36774 | −0.683868 | − | 0.729606i | \(-0.739704\pi\) | ||||
−0.683868 | + | 0.729606i | \(0.739704\pi\) | |||||||
\(200\) | 15.3468 | − | 0.434461i | 1.08518 | − | 0.0307210i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.19245 | + | 6.47611i | −0.506059 | + | 0.455658i | ||||
\(203\) | 6.64235 | + | 14.9190i | 0.466201 | + | 1.04711i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.44557 | + | 12.1676i | 0.240649 | + | 0.849825i | ||||
\(206\) | 0.525887 | − | 0.382080i | 0.0366403 | − | 0.0266207i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.248317 | − | 0.341779i | −0.0172177 | − | 0.0236981i | ||||
\(209\) | −7.06509 | + | 7.84658i | −0.488703 | + | 0.542759i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.02834 | + | 2.25270i | 0.139637 | + | 0.155082i | 0.808907 | − | 0.587937i | \(-0.200060\pi\) |
−0.669270 | + | 0.743019i | \(0.733393\pi\) | |||||||
\(212\) | 1.48724 | − | 6.99692i | 0.102144 | − | 0.480550i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.791098 | + | 0.168153i | −0.0540784 | + | 0.0114947i | ||||
\(215\) | 12.9336 | + | 8.14131i | 0.882063 | + | 0.555233i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.948134 | + | 1.30499i | 0.0643635 | + | 0.0885888i | ||||
\(218\) | 14.5838 | − | 8.41995i | 0.987738 | − | 0.570271i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.55169 | − | 0.763161i | −0.104615 | − | 0.0514523i | ||||
\(221\) | 0.0286944 | − | 0.0127756i | 0.00193019 | − | 0.000859378i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.78775 | − | 17.8200i | −0.253647 | − | 1.19331i | −0.901919 | − | 0.431905i | \(-0.857842\pi\) |
0.648273 | − | 0.761408i | \(-0.275492\pi\) | |||||||
\(224\) | −8.07429 | −0.539486 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.45929 | −0.296628 | ||||||||
\(227\) | 1.75915 | + | 8.27617i | 0.116759 | + | 0.549309i | 0.997175 | + | 0.0751071i | \(0.0239299\pi\) |
−0.880416 | + | 0.474202i | \(0.842737\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.93614 | + | 3.97862i | −0.590517 | + | 0.262915i | −0.680166 | − | 0.733059i | \(-0.738092\pi\) |
0.0896491 | + | 0.995973i | \(0.471425\pi\) | |||||||
\(230\) | 2.26264 | − | 15.7226i | 0.149194 | − | 1.03672i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.2042 | − | 9.35550i | 1.06386 | − | 0.614218i | ||||
\(233\) | 1.49631 | + | 2.05949i | 0.0980263 | + | 0.134922i | 0.855213 | − | 0.518277i | \(-0.173427\pi\) |
−0.757186 | + | 0.653199i | \(0.773427\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.181847 | + | 0.454403i | 0.0118624 | + | 0.0296420i | ||||
\(236\) | −3.19696 | + | 0.679534i | −0.208104 | + | 0.0442339i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.129602 | + | 0.609728i | −0.00840082 | + | 0.0395228i | ||||
\(239\) | −7.06013 | − | 7.84107i | −0.456682 | − | 0.507197i | 0.470195 | − | 0.882563i | \(-0.344184\pi\) |
−0.926877 | + | 0.375366i | \(0.877517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.05683 | + | 2.28434i | −0.132492 | + | 0.147147i | −0.805740 | − | 0.592270i | \(-0.798232\pi\) |
0.673248 | + | 0.739417i | \(0.264899\pi\) | |||||||
\(242\) | 6.38605 | + | 8.78965i | 0.410511 | + | 0.565020i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.27504 | + | 4.55908i | −0.401718 | + | 0.291865i | ||||
\(245\) | 0.407439 | + | 0.0155754i | 0.0260303 | + | 0.000995074i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.496591 | + | 1.11536i | 0.0315973 | + | 0.0709687i | ||||
\(248\) | 1.37345 | − | 1.23666i | 0.0872142 | − | 0.0785280i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.27460 | + | 13.4030i | 0.0806127 | + | 0.847680i | ||||
\(251\) | 23.8819 | 1.50741 | 0.753707 | − | 0.657211i | \(-0.228264\pi\) | ||||
0.753707 | + | 0.657211i | \(0.228264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.87640 | + | 6.71180i | −0.306577 | + | 0.421967i | ||||
\(254\) | 1.80137 | − | 17.1389i | 0.113028 | − | 1.07539i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.26564 | + | 12.0418i | 0.0791027 | + | 0.752612i | ||||
\(257\) | 4.15137 | + | 2.39680i | 0.258955 | + | 0.149508i | 0.623858 | − | 0.781538i | \(-0.285564\pi\) |
−0.364903 | + | 0.931046i | \(0.618898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.67607 | − | 1.86146i | 0.104146 | − | 0.115666i | ||||
\(260\) | −0.153595 | + | 0.128020i | −0.00952557 | + | 0.00793945i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.4104 | − | 4.35732i | 0.828500 | − | 0.269196i | ||||
\(263\) | −17.2869 | − | 15.5652i | −1.06595 | − | 0.959790i | −0.0666763 | − | 0.997775i | \(-0.521239\pi\) |
−0.999278 | + | 0.0379848i | \(0.987906\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.7917 | + | 4.14341i | 1.76866 | + | 0.254528i | ||||
\(266\) | −23.7003 | − | 5.03766i | −1.45316 | − | 0.308879i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.07599 | + | 1.77592i | −0.187896 | + | 0.108482i | ||||
\(269\) | −6.79619 | + | 4.93772i | −0.414371 | + | 0.301058i | −0.775369 | − | 0.631508i | \(-0.782436\pi\) |
0.360998 | + | 0.932567i | \(0.382436\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4715 | + | 11.9673i | 1.00058 | + | 0.726960i | 0.962211 | − | 0.272304i | \(-0.0877855\pi\) |
0.0383636 | + | 0.999264i | \(0.487785\pi\) | |||||||
\(272\) | 0.499031 | + | 0.0524503i | 0.0302582 | + | 0.00318027i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.3908 | − | 21.4615i | 0.748557 | − | 1.29654i | ||||
\(275\) | 2.67713 | − | 6.50216i | 0.161437 | − | 0.392095i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.12195 | − | 9.98301i | −0.127496 | − | 0.599821i | −0.994783 | − | 0.102013i | \(-0.967472\pi\) |
0.867287 | − | 0.497808i | \(-0.165862\pi\) | |||||||
\(278\) | −0.644950 | + | 0.887697i | −0.0386815 | + | 0.0532405i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.22296 | − | 18.3602i | −0.0730859 | − | 1.09723i | ||||
\(281\) | −21.4178 | − | 9.53583i | −1.27768 | − | 0.568860i | −0.348093 | − | 0.937460i | \(-0.613171\pi\) |
−0.929588 | + | 0.368600i | \(0.879837\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.1357 | + | 1.69593i | −0.959166 | + | 0.100812i | −0.571155 | − | 0.820842i | \(-0.693505\pi\) |
−0.388011 | + | 0.921655i | \(0.626838\pi\) | |||||||
\(284\) | −1.93109 | − | 0.410466i | −0.114589 | − | 0.0243567i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.269382 | + | 0.0572589i | −0.0159289 | + | 0.00338579i | ||||
\(287\) | 14.4149 | − | 4.68367i | 0.850882 | − | 0.276468i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.24176 | − | 16.1325i | 0.308339 | − | 0.948969i | ||||
\(290\) | 9.13040 | + | 13.6333i | 0.536155 | + | 0.800573i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.36263 | + | 0.668739i | −0.372344 | + | 0.0391350i | ||||
\(293\) | 2.77885 | + | 1.60437i | 0.162342 | + | 0.0937283i | 0.578970 | − | 0.815349i | \(-0.303455\pi\) |
−0.416628 | + | 0.909077i | \(0.636788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.62121 | − | 12.7879i | −0.210835 | − | 0.744539i | ||||
\(296\) | −2.32181 | − | 1.68690i | −0.134953 | − | 0.0980489i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 24.2992 | + | 7.89530i | 1.40762 | + | 0.457363i | ||||
\(299\) | 0.479656 | + | 0.830788i | 0.0277392 | + | 0.0480457i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.15833 | − | 15.8627i | 0.527877 | − | 0.914310i | ||||
\(302\) | −4.77033 | + | 4.29523i | −0.274502 | + | 0.247162i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.03876 | + | 19.3975i | −0.116931 | + | 1.11252i | ||||
\(305\) | −20.1942 | − | 24.2286i | −1.15632 | − | 1.38732i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5271i | 0.943250i | 0.881799 | + | 0.471625i | \(0.156332\pi\) | ||||
−0.881799 | + | 0.471625i | \(0.843668\pi\) | |||||||
\(308\) | −0.842961 | + | 1.89332i | −0.0480322 | + | 0.107882i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.16212 | + | 1.12968i | 0.0660037 | + | 0.0641616i | ||||
\(311\) | −12.5827 | − | 13.9745i | −0.713499 | − | 0.792421i | 0.271965 | − | 0.962307i | \(-0.412327\pi\) |
−0.985464 | + | 0.169886i | \(0.945660\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.34979 | + | 2.11576i | 0.132818 | + | 0.119590i | 0.732862 | − | 0.680377i | \(-0.238184\pi\) |
−0.600045 | + | 0.799967i | \(0.704851\pi\) | |||||||
\(314\) | 4.51082 | − | 13.8829i | 0.254560 | − | 0.783456i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.31108 | + | 7.11276i | 0.130008 | + | 0.400124i | ||||
\(317\) | 0.163144 | − | 0.366428i | 0.00916309 | − | 0.0205806i | −0.908906 | − | 0.417001i | \(-0.863081\pi\) |
0.918069 | + | 0.396421i | \(0.129748\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.895781 | − | 8.52278i | −0.0501541 | − | 0.477184i | ||||
\(320\) | −19.4420 | + | 3.36199i | −1.08684 | + | 0.187941i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −18.9338 | − | 1.99003i | −1.05514 | − | 0.110900i | ||||
\(323\) | −1.37917 | − | 0.448120i | −0.0767391 | − | 0.0249340i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.560947 | − | 0.588608i | −0.0311157 | − | 0.0326501i | ||||
\(326\) | 0.321897 | + | 0.557543i | 0.0178282 | + | 0.0308794i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.06327 | − | 15.8644i | −0.390004 | − | 0.875963i | ||||
\(329\) | 0.535891 | − | 0.238594i | 0.0295446 | − | 0.0131541i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0829 | + | 9.83194i | 1.21379 | + | 0.540412i | 0.910905 | − | 0.412616i | \(-0.135385\pi\) |
0.302881 | + | 0.953028i | \(0.402052\pi\) | |||||||
\(332\) | 8.05754i | 0.442215i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.05676 | + | 12.4854i | 0.221976 | + | 0.683172i | ||||
\(335\) | −8.03707 | − | 12.0007i | −0.439112 | − | 0.655670i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.94302 | − | 32.6643i | 0.378210 | − | 1.77934i | −0.217418 | − | 0.976079i | \(-0.569763\pi\) |
0.595628 | − | 0.803260i | \(-0.296903\pi\) | |||||||
\(338\) | 3.24818 | − | 15.2815i | 0.176678 | − | 0.831202i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.00907213 | − | 0.237320i | 0.000492005 | − | 0.0128705i | ||||
\(341\) | −0.261573 | − | 0.805038i | −0.0141649 | − | 0.0435952i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2712i | 0.986554i | ||||||||
\(344\) | −19.1719 | − | 8.53587i | −1.03368 | − | 0.460223i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.5486 | + | 5.14176i | −0.620856 | + | 0.276423i | ||||
\(347\) | −1.52284 | − | 3.42036i | −0.0817505 | − | 0.183615i | 0.868045 | − | 0.496485i | \(-0.165376\pi\) |
−0.949796 | + | 0.312870i | \(0.898710\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.67752 | − | 15.0299i | −0.464497 | − | 0.804532i | 0.534682 | − | 0.845053i | \(-0.320431\pi\) |
−0.999179 | + | 0.0405213i | \(0.987098\pi\) | |||||||
\(350\) | 15.9938 | − | 2.14016i | 0.854904 | − | 0.114396i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.02967 | + | 1.30932i | 0.214782 | + | 0.0697869i | ||||
\(353\) | −5.49417 | − | 0.577460i | −0.292425 | − | 0.0307351i | −0.0428198 | − | 0.999083i | \(-0.513634\pi\) |
−0.249605 | + | 0.968348i | \(0.580301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.14355 | − | 7.94627i | 0.0606932 | − | 0.421744i | ||||
\(356\) | −0.629661 | − | 5.99082i | −0.0333720 | − | 0.317513i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.74988 | − | 15.1605i | 0.356742 | − | 0.801256i | ||||
\(359\) | 4.30244 | + | 13.2416i | 0.227074 | + | 0.698863i | 0.998074 | + | 0.0620276i | \(0.0197567\pi\) |
−0.771000 | + | 0.636835i | \(0.780243\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.5473 | − | 35.5388i | 0.607750 | − | 1.87046i | ||||
\(362\) | 6.58434 | + | 5.92856i | 0.346065 | + | 0.311598i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.160355 | + | 0.178093i | 0.00840490 | + | 0.00933459i | ||||
\(365\) | −4.43297 | − | 25.6354i | −0.232032 | − | 1.34182i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.9221 | + | 33.5157i | −0.778930 | + | 1.74950i | −0.126077 | + | 0.992021i | \(0.540239\pi\) |
−0.652853 | + | 0.757484i | \(0.726428\pi\) | |||||||
\(368\) | 15.3252i | 0.798881i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.34070 | − | 2.12988i | 0.0696996 | − | 0.110727i | ||||
\(371\) | 3.64419 | − | 34.6721i | 0.189197 | − | 1.80009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.9005 | + | 12.5161i | −0.719740 | + | 0.648057i | −0.945311 | − | 0.326170i | \(-0.894242\pi\) |
0.225571 | + | 0.974227i | \(0.427575\pi\) | |||||||
\(374\) | 0.163554 | − | 0.283283i | 0.00845716 | − | 0.0146482i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.336051 | − | 0.582057i | −0.0173305 | − | 0.0300173i | ||||
\(377\) | −0.942436 | − | 0.306216i | −0.0485379 | − | 0.0157709i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.54812 | + | 1.12477i | 0.0795216 | + | 0.0577758i | 0.626836 | − | 0.779151i | \(-0.284350\pi\) |
−0.547314 | + | 0.836927i | \(0.684350\pi\) | |||||||
\(380\) | 9.22470 | + | 0.352637i | 0.473217 | + | 0.0180899i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.16279 | + | 0.671335i | 0.0594933 | + | 0.0343485i | ||||
\(383\) | −9.60659 | + | 1.00969i | −0.490874 | + | 0.0515929i | −0.346732 | − | 0.937964i | \(-0.612709\pi\) |
−0.144142 | + | 0.989557i | \(0.546042\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.90990 | − | 2.90859i | −0.403126 | − | 0.148235i | ||||
\(386\) | −9.43034 | + | 29.0236i | −0.479991 | + | 1.47726i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.62049 | − | 0.526529i | 0.0822680 | − | 0.0267305i | ||||
\(389\) | 22.3540 | − | 4.75150i | 1.13339 | − | 0.240910i | 0.397234 | − | 0.917717i | \(-0.369970\pi\) |
0.736161 | + | 0.676807i | \(0.236637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.11453 | − | 0.236900i | −0.0563640 | − | 0.0119805i | ||||
\(392\) | −0.556841 | + | 0.0585263i | −0.0281247 | + | 0.00295603i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 17.5526 | + | 7.81492i | 0.884287 | + | 0.393710i | ||||
\(395\) | −28.2352 | + | 11.2994i | −1.42066 | + | 0.568536i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.64077 | − | 7.76385i | 0.283102 | − | 0.389657i | −0.643656 | − | 0.765315i | \(-0.722583\pi\) |
0.926758 | + | 0.375658i | \(0.122583\pi\) | |||||||
\(398\) | 4.83069 | + | 22.7266i | 0.242141 | + | 1.13918i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.05910 | − | 12.6240i | −0.152955 | − | 0.631199i | ||||
\(401\) | 3.09035 | − | 5.35264i | 0.154325 | − | 0.267298i | −0.778488 | − | 0.627659i | \(-0.784013\pi\) |
0.932813 | + | 0.360361i | \(0.117347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0973425 | − | 0.0102311i | −0.00484898 | − | 0.000509648i | ||||
\(404\) | −3.57543 | − | 2.59770i | −0.177884 | − | 0.129241i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.9099 | − | 11.5592i | 0.789595 | − | 0.573675i | ||||
\(407\) | −1.13834 | + | 0.657219i | −0.0564252 | + | 0.0325771i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.87866 | + | 0.611877i | 0.142340 | + | 0.0302554i | 0.278531 | − | 0.960427i | \(-0.410153\pi\) |
−0.136190 | + | 0.990683i | \(0.543486\pi\) | |||||||
\(410\) | 13.4695 | − | 7.10492i | 0.665212 | − | 0.350887i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.220585 | + | 0.198616i | 0.0108674 | + | 0.00978509i | ||||
\(413\) | −15.1497 | + | 4.92242i | −0.745466 | + | 0.242216i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.6932 | + | 2.17766i | −1.60484 | + | 0.106897i | ||||
\(416\) | 0.327833 | − | 0.364095i | 0.0160733 | − | 0.0178512i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.0113 | + | 6.35739i | 0.538581 | + | 0.310950i | ||||
\(419\) | 0.638257 | + | 6.07261i | 0.0311809 | + | 0.296666i | 0.998988 | + | 0.0449739i | \(0.0143205\pi\) |
−0.967807 | + | 0.251692i | \(0.919013\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.139754 | + | 1.32967i | −0.00681119 | + | 0.0648041i | −0.997400 | − | 0.0720709i | \(-0.977039\pi\) |
0.990588 | + | 0.136875i | \(0.0437059\pi\) | |||||||
\(422\) | 2.14561 | − | 2.95318i | 0.104447 | − | 0.143759i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −39.9443 | −1.93987 | ||||||||
\(425\) | 0.965367 | − | 0.0273291i | 0.0468272 | − | 0.00132566i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.0929 | + | 25.2949i | −1.35951 | + | 1.22411i | ||||
\(428\) | −0.150213 | − | 0.337383i | −0.00726081 | − | 0.0163080i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.35143 | − | 17.2727i | 0.306293 | − | 0.832965i | ||||
\(431\) | 26.8953 | − | 19.5406i | 1.29550 | − | 0.941237i | 0.295600 | − | 0.955312i | \(-0.404480\pi\) |
0.999901 | + | 0.0140751i | \(0.00448038\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.84957 | − | 9.42763i | −0.329169 | − | 0.453063i | 0.612070 | − | 0.790804i | \(-0.290337\pi\) |
−0.941239 | + | 0.337741i | \(0.890337\pi\) | |||||||
\(434\) | 1.29976 | − | 1.44353i | 0.0623905 | − | 0.0692917i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.14538 | + | 5.71453i | 0.246419 | + | 0.273676i | ||||
\(437\) | 9.20838 | − | 43.3220i | 0.440496 | − | 2.07237i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7048 | − | 4.61349i | 1.03591 | − | 0.220190i | 0.341586 | − | 0.939851i | \(-0.389036\pi\) |
0.694326 | + | 0.719661i | \(0.255703\pi\) | |||||||
\(440\) | −2.36693 | + | 9.36144i | −0.112839 | + | 0.446289i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0222324 | − | 0.0306003i | −0.00105749 | − | 0.00145551i | ||||
\(443\) | −6.90522 | + | 3.98673i | −0.328077 | + | 0.189415i | −0.654987 | − | 0.755640i | \(-0.727326\pi\) |
0.326910 | + | 0.945055i | \(0.393993\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.1374 | − | 4.17393i | 1.14422 | − | 0.197863i | ||||
\(446\) | −20.0417 | + | 8.92314i | −0.949002 | + | 0.422523i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.91662 | + | 23.1309i | 0.232289 | + | 1.09283i | ||||
\(449\) | −19.4821 | −0.919419 | −0.459710 | − | 0.888069i | \(-0.652047\pi\) | ||||
−0.459710 | + | 0.888069i | \(0.652047\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.95358 | −0.374520 | ||||||||
\(452\) | −0.423362 | − | 1.99176i | −0.0199133 | − | 0.0936847i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.30801 | − | 4.14419i | 0.436847 | − | 0.194497i | ||||
\(455\) | −0.679266 | + | 0.698768i | −0.0318445 | + | 0.0327587i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0307 | − | 8.67800i | 0.703108 | − | 0.405940i | −0.105396 | − | 0.994430i | \(-0.533611\pi\) |
0.808504 | + | 0.588491i | \(0.200278\pi\) | |||||||
\(458\) | 6.92373 | + | 9.52970i | 0.323525 | + | 0.445293i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7.23739 | − | 0.482076i | 0.337445 | − | 0.0224769i | ||||
\(461\) | 29.1923 | − | 6.20502i | 1.35962 | − | 0.288997i | 0.530320 | − | 0.847798i | \(-0.322072\pi\) |
0.829302 | + | 0.558801i | \(0.188738\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.42807 | − | 11.4232i | 0.112842 | − | 0.530879i | −0.885022 | − | 0.465549i | \(-0.845857\pi\) |
0.997864 | − | 0.0653297i | \(-0.0208099\pi\) | |||||||
\(464\) | −10.5926 | − | 11.7643i | −0.491750 | − | 0.546143i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.05123 | − | 2.27812i | 0.0950214 | − | 0.105532i | ||||
\(467\) | 8.44207 | + | 11.6195i | 0.390652 | + | 0.537687i | 0.958367 | − | 0.285538i | \(-0.0921724\pi\) |
−0.567715 | + | 0.823225i | \(0.692172\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0048 | + | 10.1751i | −0.646680 | + | 0.469840i | ||||
\(470\) | 0.489709 | − | 0.327965i | 0.0225886 | − | 0.0151279i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.42332 | + | 16.6731i | 0.341686 | + | 0.767439i | ||||
\(473\) | −7.14296 | + | 6.43155i | −0.328434 | + | 0.295723i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.06229 | + | 37.5242i | 0.0487414 | + | 1.72173i | ||||
\(476\) | −0.284642 | −0.0130465 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.46831 | + | 10.2792i | −0.341592 | + | 0.470162i | ||||
\(479\) | 0.537542 | − | 5.11437i | 0.0245609 | − | 0.233682i | −0.975354 | − | 0.220645i | \(-0.929184\pi\) |
0.999915 | − | 0.0130363i | \(-0.00414970\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0158874 | + | 0.151159i | 0.000724403 | + | 0.00689224i | ||||
\(482\) | 3.20568 | + | 1.85080i | 0.146015 | + | 0.0843016i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.31965 | + | 3.68684i | −0.150893 | + | 0.167584i | ||||
\(485\) | 2.57433 | + | 6.43278i | 0.116895 | + | 0.292098i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.7356 | − | 12.5860i | 1.75528 | − | 0.570324i | 0.758584 | − | 0.651575i | \(-0.225892\pi\) |
0.996694 | + | 0.0812511i | \(0.0258916\pi\) | |||||||
\(488\) | 32.1873 | + | 28.9816i | 1.45705 | + | 1.31194i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0836640 | − | 0.483820i | −0.00377956 | − | 0.0218568i | ||||
\(491\) | 39.2083 | + | 8.33398i | 1.76945 | + | 0.376107i | 0.973397 | − | 0.229125i | \(-0.0735864\pi\) |
0.796049 | + | 0.605232i | \(0.206920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.01930 | − | 0.588493i | 0.0459070 | − | 0.0265044i | ||||
\(494\) | 1.18945 | − | 0.864183i | 0.0535157 | − | 0.0388814i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.26501 | − | 0.919080i | −0.0568004 | − | 0.0412679i | ||||
\(497\) | −9.56923 | − | 1.00577i | −0.429239 | − | 0.0451148i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6136 | − | 25.3114i | 0.654193 | − | 1.13310i | −0.327903 | − | 0.944712i | \(-0.606342\pi\) |
0.982096 | − | 0.188384i | \(-0.0603249\pi\) | |||||||
\(500\) | −5.86550 | + | 1.84178i | −0.262313 | + | 0.0823667i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.97930 | − | 28.1304i | −0.266869 | − | 1.25552i | ||||
\(503\) | −4.96862 | + | 6.83872i | −0.221540 | + | 0.304923i | −0.905291 | − | 0.424792i | \(-0.860347\pi\) |
0.683751 | + | 0.729715i | \(0.260347\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.57377 | − | 15.2092i | 0.426027 | − | 0.676803i | ||||
\(506\) | 9.12668 | + | 4.06346i | 0.405731 | + | 0.180643i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.82617 | − | 0.822564i | 0.347230 | − | 0.0364954i | ||||
\(509\) | 12.2912 | + | 2.61257i | 0.544797 | + | 0.115800i | 0.472085 | − | 0.881553i | \(-0.343501\pi\) |
0.0727116 | + | 0.997353i | \(0.476835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.4993 | + | 6.48283i | −1.34921 | + | 0.286784i | ||||
\(512\) | 22.6169 | − | 7.34868i | 0.999536 | − | 0.324769i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.78380 | − | 5.48996i | 0.0786799 | − | 0.242152i | ||||
\(515\) | −0.746259 | + | 0.948694i | −0.0328841 | + | 0.0418045i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.306140 | + | 0.0321766i | −0.0134640 | + | 0.00141512i | ||||
\(518\) | −2.61224 | − | 1.50818i | −0.114775 | − | 0.0662656i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.877576 | + | 0.690317i | 0.0384843 | + | 0.0302724i | ||||
\(521\) | −15.5846 | − | 11.3229i | −0.682773 | − | 0.496063i | 0.191504 | − | 0.981492i | \(-0.438664\pi\) |
−0.874276 | + | 0.485429i | \(0.838664\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3250 | + | 7.90367i | 1.06366 | + | 0.345604i | 0.788015 | − | 0.615656i | \(-0.211109\pi\) |
0.275644 | + | 0.961260i | \(0.411109\pi\) | |||||||
\(524\) | 3.21939 | + | 5.57615i | 0.140640 | + | 0.243595i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.0060 | + | 24.2591i | −0.610692 | + | 1.05775i | ||||
\(527\) | 0.0863949 | − | 0.0777903i | 0.00376342 | − | 0.00338860i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.23343 | − | 11.7353i | 0.0536273 | − | 0.510230i | ||||
\(530\) | −2.32805 | − | 34.9509i | −0.101124 | − | 1.51817i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 11.0641i | − | 0.479691i | ||||||
\(533\) | −0.374071 | + | 0.840178i | −0.0162028 | + | 0.0363922i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.32832 | − | 0.700665i | 0.0574284 | − | 0.0302924i | ||||
\(536\) | 13.2714 | + | 14.7394i | 0.573238 | + | 0.636645i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.51767 | + | 6.76894i | 0.324110 | + | 0.291830i | ||||
\(539\) | −0.0792445 | + | 0.243890i | −0.00341330 | + | 0.0105051i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.8581 | − | 36.4956i | −0.509821 | − | 1.56907i | −0.792511 | − | 0.609858i | \(-0.791227\pi\) |
0.282690 | − | 0.959211i | \(-0.408773\pi\) | |||||||
\(542\) | 9.97222 | − | 22.3980i | 0.428343 | − | 0.962075i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.0608278 | + | 0.578738i | 0.00260797 | + | 0.0248132i | ||||
\(545\) | −21.7959 | + | 22.4216i | −0.933633 | + | 0.960437i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.0946 | − | 3.26818i | −1.32951 | − | 0.139737i | −0.587008 | − | 0.809581i | \(-0.699694\pi\) |
−0.742502 | + | 0.669844i | \(0.766361\pi\) | |||||||
\(548\) | 10.7623 | + | 3.49687i | 0.459741 | + | 0.149379i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.32913 | − | 1.52544i | −0.355155 | − | 0.0650449i | ||||
\(551\) | 22.8750 | + | 39.6206i | 0.974506 | + | 1.68789i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.8255 | + | 33.2986i | 0.630444 | + | 1.41600i | ||||
\(554\) | −11.2277 | + | 4.99887i | −0.477017 | + | 0.212382i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.457725 | − | 0.203792i | −0.0194119 | − | 0.00864272i | ||||
\(557\) | 24.3166i | 1.03033i | 0.857091 | + | 0.515165i | \(0.172269\pi\) | ||||
−0.857091 | + | 0.515165i | \(0.827731\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.343452 | + | 1.05704i | 0.0145265 | + | 0.0447078i | ||||
\(560\) | −14.9791 | + | 4.24170i | −0.632982 | + | 0.179245i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.86984 | + | 27.6154i | −0.247604 | + | 1.16489i | ||||
\(563\) | −3.38628 | + | 15.9312i | −0.142715 | + | 0.671419i | 0.847376 | + | 0.530993i | \(0.178181\pi\) |
−0.990091 | + | 0.140427i | \(0.955153\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.96709 | − | 2.25608i | 0.335178 | − | 0.0949140i | ||||
\(566\) | 6.03750 | + | 18.5815i | 0.253775 | + | 0.781039i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.0243i | 0.462569i | ||||||||
\(569\) | 17.4967 | + | 7.79004i | 0.733500 | + | 0.326575i | 0.739271 | − | 0.673408i | \(-0.235170\pi\) |
−0.00577081 | + | 0.999983i | \(0.501837\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.20374 | − | 1.87163i | 0.175921 | − | 0.0783251i | −0.316886 | − | 0.948464i | \(-0.602637\pi\) |
0.492807 | + | 0.870138i | \(0.335971\pi\) | |||||||
\(572\) | −0.0511499 | − | 0.114885i | −0.00213868 | − | 0.00480356i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.12590 | − | 15.8065i | −0.380908 | − | 0.659752i | ||||
\(575\) | 3.91201 | + | 29.2352i | 0.163142 | + | 1.21919i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.5521 | − | 11.8765i | −1.52168 | − | 0.494425i | −0.575429 | − | 0.817852i | \(-0.695165\pi\) |
−0.946253 | + | 0.323427i | \(0.895165\pi\) | |||||||
\(578\) | −20.3147 | − | 2.13516i | −0.844981 | − | 0.0888111i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.22253 | + | 5.37247i | −0.216854 | + | 0.223080i | ||||
\(581\) | 4.10489 | + | 39.0554i | 0.170299 | + | 1.62029i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.44112 | + | 16.7130i | −0.308180 | + | 0.692183i | ||||
\(584\) | 11.0397 | + | 33.9767i | 0.456826 | + | 1.40597i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.19404 | − | 3.67487i | 0.0493253 | − | 0.151808i | ||||
\(587\) | −19.3123 | − | 17.3889i | −0.797103 | − | 0.717715i | 0.166211 | − | 0.986090i | \(-0.446847\pi\) |
−0.963314 | + | 0.268375i | \(0.913513\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.02374 | + | 3.35820i | 0.124591 | + | 0.138372i | ||||
\(590\) | −14.1561 | + | 7.46709i | −0.582798 | + | 0.307415i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.987594 | + | 2.21817i | −0.0405898 | + | 0.0911663i | ||||
\(593\) | − | 32.5216i | − | 1.33550i | −0.744385 | − | 0.667750i | \(-0.767257\pi\) | ||
0.744385 | − | 0.667750i | \(-0.232743\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0769285 | − | 1.15492i | −0.00315376 | − | 0.0473473i | ||||
\(596\) | −1.21952 | + | 11.6029i | −0.0499534 | + | 0.475275i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.858489 | − | 0.772987i | 0.0351062 | − | 0.0316098i | ||||
\(599\) | −5.00962 | + | 8.67692i | −0.204688 | + | 0.354529i | −0.950033 | − | 0.312149i | \(-0.898951\pi\) |
0.745346 | + | 0.666678i | \(0.232285\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.09862 | + | 10.5631i | 0.248768 | + | 0.430878i | 0.963184 | − | 0.268842i | \(-0.0866411\pi\) |
−0.714416 | + | 0.699721i | \(0.753308\pi\) | |||||||
\(602\) | −20.9775 | − | 6.81601i | −0.854980 | − | 0.277800i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.37137 | − | 1.72290i | −0.0964899 | − | 0.0701040i | ||||
\(605\) | −15.8564 | − | 12.4729i | −0.644655 | − | 0.507097i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.1063 | + | 10.4537i | 0.734910 | + | 0.424301i | 0.820216 | − | 0.572054i | \(-0.193853\pi\) |
−0.0853054 | + | 0.996355i | \(0.527187\pi\) | |||||||
\(608\) | −22.4957 | + | 2.36440i | −0.912323 | + | 0.0958890i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −23.4827 | + | 29.8527i | −0.950786 | + | 1.20870i | ||||
\(611\) | −0.0109993 | + | 0.0338524i | −0.000444985 | + | 0.00136952i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.43863 | + | 1.11728i | −0.138885 | + | 0.0451265i | −0.377635 | − | 0.925955i | \(-0.623262\pi\) |
0.238750 | + | 0.971081i | \(0.423262\pi\) | |||||||
\(614\) | 19.4671 | − | 4.13787i | 0.785630 | − | 0.166991i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.3201 | + | 2.40617i | 0.456101 | + | 0.0969472i | ||||
\(617\) | −5.85144 | + | 0.615011i | −0.235570 | + | 0.0247594i | −0.221578 | − | 0.975143i | \(-0.571121\pi\) |
−0.0139922 | + | 0.999902i | \(0.504454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −25.2160 | − | 11.2269i | −1.01352 | − | 0.451247i | −0.168338 | − | 0.985729i | \(-0.553840\pi\) |
−0.845180 | + | 0.534482i | \(0.820507\pi\) | |||||||
\(620\) | −0.394247 | + | 0.626315i | −0.0158333 | + | 0.0251534i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −13.3102 | + | 18.3199i | −0.533689 | + | 0.734559i | ||||
\(623\) | −6.10401 | − | 28.7171i | −0.244552 | − | 1.15053i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.05817 | − | 23.3013i | −0.362327 | − | 0.932051i | ||||
\(626\) | 1.90382 | − | 3.29752i | 0.0760921 | − | 0.131795i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.62910 | + | 0.696747i | 0.264530 | + | 0.0278032i | ||||
\(629\) | −0.146050 | − | 0.106112i | −0.00582340 | − | 0.00423095i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.50355 | + | 3.99857i | −0.219093 | + | 0.159180i | −0.691918 | − | 0.721976i | \(-0.743234\pi\) |
0.472825 | + | 0.881156i | \(0.343234\pi\) | |||||||
\(632\) | 36.1672 | − | 20.8811i | 1.43865 | − | 0.830607i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.472460 | − | 0.100424i | −0.0187638 | − | 0.00398836i | ||||
\(635\) | 5.45266 | + | 31.5321i | 0.216382 | + | 1.25131i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0220363 | + | 0.0198416i | 0.000873110 | + | 0.000786152i | ||||
\(638\) | −9.81466 | + | 3.18898i | −0.388566 | + | 0.126253i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.82171 | + | 9.54974i | 0.151066 | + | 0.377486i | ||||
\(641\) | −1.26962 | + | 1.41006i | −0.0501471 | + | 0.0556940i | −0.767696 | − | 0.640814i | \(-0.778597\pi\) |
0.717549 | + | 0.696508i | \(0.245264\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.7142 | − | 7.91791i | −0.540836 | − | 0.312252i | 0.204581 | − | 0.978850i | \(-0.434417\pi\) |
−0.745418 | + | 0.666598i | \(0.767750\pi\) | |||||||
\(644\) | −0.908711 | − | 8.64581i | −0.0358082 | − | 0.340693i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.182536 | + | 1.73671i | −0.00718177 | + | 0.0683300i | ||||
\(647\) | 1.30998 | − | 1.80303i | 0.0515007 | − | 0.0708846i | −0.782490 | − | 0.622663i | \(-0.786051\pi\) |
0.833991 | + | 0.551779i | \(0.186051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.35902 | 0.328120 | ||||||||
\(650\) | −0.552874 | + | 0.808105i | −0.0216855 | + | 0.0316965i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.218468 | + | 0.196710i | −0.00855588 | + | 0.00770375i | ||||
\(653\) | −0.410721 | − | 0.922493i | −0.0160727 | − | 0.0361000i | 0.905331 | − | 0.424707i | \(-0.139623\pi\) |
−0.921403 | + | 0.388607i | \(0.872956\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.7549 | + | 14.5696i | −0.850036 | + | 0.569282i | ||||
\(656\) | −11.8863 | + | 8.63588i | −0.464081 | + | 0.337174i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.415209 | − | 0.571486i | −0.0161865 | − | 0.0222788i | ||||
\(659\) | −9.81851 | + | 10.9046i | −0.382475 | + | 0.424782i | −0.903385 | − | 0.428830i | \(-0.858926\pi\) |
0.520910 | + | 0.853611i | \(0.325593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1903 | + | 23.5343i | 0.824209 | + | 0.915377i | 0.997583 | − | 0.0694791i | \(-0.0221337\pi\) |
−0.173374 | + | 0.984856i | \(0.555467\pi\) | |||||||
\(662\) | 6.05211 | − | 28.4729i | 0.235222 | − | 1.10663i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 44.0108 | − | 9.35479i | 1.70795 | − | 0.363036i | ||||
\(665\) | 44.8923 | − | 2.99024i | 1.74085 | − | 0.115956i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.1292 | + | 29.0818i | 0.818126 | + | 1.12605i | ||||
\(668\) | −5.19152 | + | 2.99733i | −0.200866 | + | 0.115970i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.1234 | + | 12.4714i | −0.468366 | + | 0.481813i | ||||
\(671\) | 18.1222 | − | 8.06854i | 0.699601 | − | 0.311483i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.41881 | − | 39.6074i | −0.324521 | − | 1.52675i | −0.773840 | − | 0.633382i | \(-0.781666\pi\) |
0.449318 | − | 0.893372i | \(-0.351667\pi\) | |||||||
\(674\) | −40.2134 | −1.54896 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.13392 | 0.274381 | ||||||||
\(677\) | −0.524831 | − | 2.46914i | −0.0201709 | − | 0.0948967i | 0.966911 | − | 0.255115i | \(-0.0821134\pi\) |
−0.987082 | + | 0.160219i | \(0.948780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.58638 | − | 3.37767i | 0.291138 | − | 0.129623i | ||||
\(680\) | −1.30679 | + | 0.225975i | −0.0501130 | + | 0.00866575i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.882759 | + | 0.509661i | −0.0338026 | + | 0.0195159i | ||||
\(683\) | −12.8169 | − | 17.6409i | −0.490425 | − | 0.675012i | 0.490042 | − | 0.871699i | \(-0.336982\pi\) |
−0.980466 | + | 0.196687i | \(0.936982\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2798 | + | 44.6126i | −0.430978 | + | 1.70456i | ||||
\(686\) | 21.5216 | − | 4.57455i | 0.821698 | − | 0.174657i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.69155 | + | 17.3674i | −0.140739 | + | 0.662125i | ||||
\(689\) | 1.41551 | + | 1.57209i | 0.0539268 | + | 0.0598918i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.57457 | − | 9.52302i | 0.326192 | − | 0.362273i | −0.557635 | − | 0.830086i | \(-0.688291\pi\) |
0.883827 | + | 0.467813i | \(0.154958\pi\) | |||||||
\(692\) | −3.39301 | − | 4.67007i | −0.128983 | − | 0.177529i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.64755 | + | 2.65010i | −0.138459 | + | 0.100596i | ||||
\(695\) | 0.703173 | − | 1.91228i | 0.0266729 | − | 0.0725369i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.444305 | − | 0.997924i | −0.0168292 | − | 0.0377991i | ||||
\(698\) | −15.5310 | + | 13.9842i | −0.587859 | + | 0.529310i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.47435 | + | 6.94051i | 0.0935217 | + | 0.262327i | ||||
\(701\) | −48.5879 | −1.83514 | −0.917569 | − | 0.397577i | \(-0.869851\pi\) | ||||
−0.917569 | + | 0.397577i | \(0.869851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.12460 | − | 5.67702i | 0.155562 | − | 0.214113i | ||||
\(704\) | 1.29712 | − | 12.3413i | 0.0488872 | − | 0.465130i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.695382 | + | 6.61612i | 0.0261711 | + | 0.249001i | ||||
\(707\) | −18.6537 | − | 10.7697i | −0.701545 | − | 0.405037i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.03486 | + | 5.59178i | −0.189088 | + | 0.210004i | −0.830233 | − | 0.557416i | \(-0.811793\pi\) |
0.641145 | + | 0.767420i | \(0.278460\pi\) | |||||||
\(710\) | −9.64617 | + | 0.642523i | −0.362014 | + | 0.0241135i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31.9912 | + | 10.3946i | −1.19892 | + | 0.389554i | ||||
\(713\) | 2.63864 | + | 2.37584i | 0.0988179 | + | 0.0889761i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.452316 | − | 0.238588i | 0.0169157 | − | 0.00892268i | ||||
\(716\) | 7.41233 | + | 1.57554i | 0.277012 | + | 0.0588806i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.5199 | − | 8.38310i | 0.541880 | − | 0.312854i | ||||
\(719\) | 35.5528 | − | 25.8307i | 1.32590 | − | 0.963321i | 0.326059 | − | 0.945349i | \(-0.394279\pi\) |
0.999839 | − | 0.0179714i | \(-0.00572079\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.17037 | + | 0.850325i | 0.0435869 | + | 0.0316678i | ||||
\(722\) | −44.7520 | − | 4.70362i | −1.66550 | − | 0.175051i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.02291 | + | 3.50378i | −0.0751807 | + | 0.130217i | ||||
\(725\) | −23.2100 | − | 19.7382i | −0.862000 | − | 0.733059i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.73183 | − | 36.3754i | −0.286758 | − | 1.34909i | −0.851731 | − | 0.523979i | \(-0.824447\pi\) |
0.564973 | − | 0.825109i | \(-0.308886\pi\) | |||||||
\(728\) | 0.786582 | − | 1.08264i | 0.0291527 | − | 0.0401252i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −29.0859 | + | 11.6399i | −1.07652 | + | 0.430811i | ||||
\(731\) | −1.20598 | − | 0.536936i | −0.0446047 | − | 0.0198593i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.49330 | + | 0.577369i | −0.202900 | + | 0.0213256i | −0.205433 | − | 0.978671i | \(-0.565860\pi\) |
0.00253335 | + | 0.999997i | \(0.499194\pi\) | |||||||
\(734\) | 43.2140 | + | 9.18541i | 1.59506 | + | 0.339040i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −17.3846 | + | 3.69521i | −0.640804 | + | 0.136207i | ||||
\(737\) | 8.63939 | − | 2.80711i | 0.318236 | − | 0.103401i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.0729 | − | 40.2342i | 0.480894 | − | 1.48004i | −0.356946 | − | 0.934125i | \(-0.616182\pi\) |
0.837840 | − | 0.545915i | \(-0.183818\pi\) | |||||||
\(740\) | 1.07861 | + | 0.396619i | 0.0396504 | + | 0.0145800i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −41.7525 | + | 4.38836i | −1.53278 | + | 0.161102i | ||||
\(743\) | −16.0074 | − | 9.24189i | −0.587256 | − | 0.339052i | 0.176756 | − | 0.984255i | \(-0.443440\pi\) |
−0.764012 | + | 0.645203i | \(0.776773\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −47.4081 | − | 1.81229i | −1.73690 | − | 0.0663972i | ||||
\(746\) | 18.2228 | + | 13.2397i | 0.667186 | + | 0.484739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.142057 | + | 0.0461573i | 0.00519413 | + | 0.00168768i | ||||
\(749\) | −0.899969 | − | 1.55879i | −0.0328841 | − | 0.0569570i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.6388 | − | 21.8911i | 0.461197 | − | 0.798816i | −0.537824 | − | 0.843057i | \(-0.680754\pi\) |
0.999021 | + | 0.0442409i | \(0.0140869\pi\) | |||||||
\(752\) | −0.422575 | + | 0.380488i | −0.0154097 | + | 0.0138750i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.124733 | + | 1.18676i | −0.00454251 | + | 0.0432191i | ||||
\(755\) | 6.34972 | − | 10.0874i | 0.231090 | − | 0.367118i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.6646i | 0.532993i | 0.963836 | + | 0.266497i | \(0.0858661\pi\) | ||||
−0.963836 | + | 0.266497i | \(0.914134\pi\) | |||||||
\(758\) | 0.937264 | − | 2.10513i | 0.0340430 | − | 0.0764617i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.78373 | − | 50.7953i | −0.318619 | − | 1.84254i | ||||
\(761\) | −6.68308 | − | 7.42231i | −0.242261 | − | 0.269059i | 0.609736 | − | 0.792605i | \(-0.291275\pi\) |
−0.851997 | + | 0.523546i | \(0.824609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.8512 | + | 25.0774i | 1.00828 | + | 0.907861i | ||||
\(764\) | −0.189461 | + | 0.583100i | −0.00685444 | + | 0.0210958i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.59450 | + | 11.0627i | 0.129875 | + | 0.399713i | ||||
\(767\) | 0.393140 | − | 0.883006i | 0.0141954 | − | 0.0318835i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.93245 | + | 18.3860i | 0.0696860 | + | 0.663018i | 0.972487 | + | 0.232958i | \(0.0748406\pi\) |
−0.902801 | + | 0.430059i | \(0.858493\pi\) | |||||||
\(770\) | −1.44561 | + | 10.0452i | −0.0520962 | + | 0.362006i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.8588 | − | 1.45662i | −0.498790 | − | 0.0524250i | ||||
\(773\) | −3.41227 | − | 1.10871i | −0.122731 | − | 0.0398777i | 0.247008 | − | 0.969014i | \(-0.420553\pi\) |
−0.369739 | + | 0.929136i | \(0.620553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.64780 | − | 1.43037i | −0.0951119 | − | 0.0513805i | ||||
\(776\) | −4.75733 | − | 8.23993i | −0.170778 | − | 0.295796i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −11.1935 | − | 25.1411i | −0.401307 | − | 0.901350i | ||||
\(779\) | 38.7897 | − | 17.2703i | 1.38978 | − | 0.618772i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.61266 | + | 2.05369i | 0.165054 | + | 0.0734868i | ||||
\(782\) | 1.37211i | 0.0490664i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.146384 | + | 0.450524i | 0.00522801 | + | 0.0160902i | ||||
\(785\) | −1.03542 | + | 27.0857i | −0.0369556 | + | 0.966728i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.36327 | − | 15.8229i | 0.119888 | − | 0.564026i | −0.876668 | − | 0.481096i | \(-0.840239\pi\) |
0.996555 | − | 0.0829303i | \(-0.0264279\pi\) | |||||||
\(788\) | −1.82414 | + | 8.58189i | −0.0649822 | + | 0.305717i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.3787 | + | 30.4290i | 0.725043 | + | 1.08261i | ||||
\(791\) | −3.06676 | − | 9.43852i | −0.109041 | − | 0.335595i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.29382i | − | 0.0814561i | ||||||
\(794\) | −10.5573 | − | 4.70040i | −0.374664 | − | 0.166811i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.69232 | + | 4.31530i | −0.343535 | + | 0.152952i | ||||
\(797\) | 7.73579 | + | 17.3749i | 0.274016 | + | 0.615450i | 0.997165 | − | 0.0752419i | \(-0.0239729\pi\) |
−0.723149 | + | 0.690692i | \(0.757306\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.0211388 | − | 0.0366134i | −0.000747836 | − | 0.00129529i | ||||
\(800\) | 13.5828 | − | 6.51407i | 0.480224 | − | 0.230307i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.07857 | − | 2.29997i | −0.249953 | − | 0.0812146i | ||||
\(803\) | 16.2727 | + | 1.71033i | 0.574251 | + | 0.0603562i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 34.8345 | − | 6.02372i | 1.22775 | − | 0.212308i | ||||
\(806\) | 0.0123204 | + | 0.117221i | 0.000433967 | + | 0.00412892i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.0378 | + | 22.5452i | −0.353127 | + | 0.793137i | ||||
\(809\) | −3.06508 | − | 9.43335i | −0.107763 | − | 0.331659i | 0.882606 | − | 0.470113i | \(-0.155787\pi\) |
−0.990369 | + | 0.138454i | \(0.955787\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.46694 | − | 26.0585i | 0.297314 | − | 0.915039i | −0.685120 | − | 0.728430i | \(-0.740250\pi\) |
0.982434 | − | 0.186609i | \(-0.0597498\pi\) | |||||||
\(812\) | 6.67346 | + | 6.00881i | 0.234192 | + | 0.210868i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.05914 | + | 1.17629i | 0.0371228 | + | 0.0412290i | ||||
\(815\) | −0.857186 | − | 0.833263i | −0.0300259 | − | 0.0291879i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.8709 | − | 46.8768i | 0.730181 | − | 1.64001i | ||||
\(818\) | − | 3.54395i | − | 0.123911i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.45223 | + | 5.34169i | 0.155479 | + | 0.186540i | ||||
\(821\) | −1.00345 | + | 9.54718i | −0.0350206 | + | 0.333199i | 0.962958 | + | 0.269651i | \(0.0869083\pi\) |
−0.997979 | + | 0.0635480i | \(0.979758\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.5845 | + | 23.0364i | −0.891819 | + | 0.802998i | −0.981199 | − | 0.193000i | \(-0.938178\pi\) |
0.0893794 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(824\) | 0.828753 | − | 1.43544i | 0.0288710 | − | 0.0500060i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.59109 | + | 16.6123i | 0.333717 | + | 0.578014i | ||||
\(827\) | −25.3249 | − | 8.22855i | −0.880632 | − | 0.286135i | −0.166412 | − | 0.986056i | \(-0.553218\pi\) |
−0.714220 | + | 0.699922i | \(0.753218\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 28.0528 | + | 20.3815i | 0.974314 | + | 0.707880i | 0.956431 | − | 0.291960i | \(-0.0943073\pi\) |
0.0178831 | + | 0.999840i | \(0.494307\pi\) | |||||||
\(830\) | 10.7504 | + | 37.9639i | 0.373152 | + | 1.31775i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.24267 | − | 0.717456i | −0.0430818 | − | 0.0248733i | ||||
\(833\) | −0.0350272 | + | 0.00368151i | −0.00121362 | + | 0.000127557i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.5646 | − | 20.2543i | −0.469423 | − | 0.700931i | ||||
\(836\) | −1.79415 | + | 5.52182i | −0.0620519 | + | 0.190976i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.99309 | − | 2.27219i | 0.241572 | − | 0.0784916i | ||||
\(839\) | 4.59725 | − | 0.977175i | 0.158715 | − | 0.0337358i | −0.127869 | − | 0.991791i | \(-0.540814\pi\) |
0.286584 | + | 0.958055i | \(0.407480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.95445 | − | 1.69077i | −0.274291 | − | 0.0583024i | ||||
\(842\) | 1.60120 | − | 0.168293i | 0.0551810 | − | 0.00579975i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.52275 | + | 0.677974i | 0.0524154 | + | 0.0233368i | ||||
\(845\) | 1.92804 | + | 28.9456i | 0.0663267 | + | 0.995759i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.2123 | + | 19.5615i | −0.488340 | + | 0.672142i | ||||
\(848\) | 7.02634 | + | 33.0563i | 0.241285 | + | 1.13516i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.273889 | − | 1.13026i | −0.00939431 | − | 0.0387675i | ||||
\(851\) | 2.75681 | − | 4.77494i | 0.0945023 | − | 0.163683i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.6763 | + | 1.96296i | 0.639465 | + | 0.0672105i | 0.418712 | − | 0.908119i | \(-0.362482\pi\) |
0.220753 | + | 0.975330i | \(0.429148\pi\) | |||||||
\(854\) | 36.8283 | + | 26.7574i | 1.26024 | + | 0.915618i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.66841 | + | 1.21217i | −0.0570252 | + | 0.0414312i | ||||
\(857\) | −28.3893 | + | 16.3906i | −0.969759 | + | 0.559891i | −0.899163 | − | 0.437614i | \(-0.855824\pi\) |
−0.0705962 | + | 0.997505i | \(0.522490\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.26946 | − | 1.97028i | −0.316270 | − | 0.0672252i | 0.0470417 | − | 0.998893i | \(-0.485021\pi\) |
−0.363312 | + | 0.931668i | \(0.618354\pi\) | |||||||
\(860\) | 8.31794 | + | 1.19703i | 0.283639 | + | 0.0408185i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −29.7505 | − | 26.7875i | −1.01331 | − | 0.912384i | ||||
\(863\) | 32.4083 | − | 10.5301i | 1.10319 | − | 0.358449i | 0.299862 | − | 0.953983i | \(-0.403059\pi\) |
0.803330 | + | 0.595534i | \(0.203059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.0316 | − | 15.0291i | 0.613094 | − | 0.511006i | ||||
\(866\) | −9.38982 | + | 10.4285i | −0.319079 | + | 0.354373i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0.768158 | + | 0.443496i | 0.0260730 | + | 0.0150532i | ||||
\(869\) | −1.99935 | − | 19.0226i | −0.0678233 | − | 0.645296i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.109797 | − | 1.04465i | 0.00372032 | − | 0.0353965i | ||||
\(872\) | 25.2394 | − | 34.7390i | 0.854712 | − | 1.17641i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −53.3342 | −1.80406 | ||||||||
\(875\) | −27.4921 | + | 11.9154i | −0.929404 | + | 0.402813i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.0817 | − | 18.0816i | 0.678109 | − | 0.610572i | −0.256375 | − | 0.966577i | \(-0.582528\pi\) |
0.934484 | + | 0.356005i | \(0.115861\pi\) | |||||||
\(878\) | −10.8684 | − | 24.4108i | −0.366791 | − | 0.823826i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.16351 | + | 0.312070i | 0.275192 | + | 0.0105199i | ||||
\(881\) | −44.5745 | + | 32.3853i | −1.50175 | + | 1.09109i | −0.532078 | + | 0.846695i | \(0.678589\pi\) |
−0.969676 | + | 0.244393i | \(0.921411\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.9914 | + | 33.0214i | 0.807376 | + | 1.11126i | 0.991723 | + | 0.128396i | \(0.0409829\pi\) |
−0.184347 | + | 0.982861i | \(0.559017\pi\) | |||||||
\(884\) | 0.0115570 | − | 0.0128354i | 0.000388706 | − | 0.000431701i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.42480 | + | 7.13546i | 0.215845 | + | 0.239721i | ||||
\(887\) | −6.07787 | + | 28.5941i | −0.204075 | + | 0.960096i | 0.750211 | + | 0.661199i | \(0.229952\pi\) |
−0.954285 | + | 0.298897i | \(0.903381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 37.5149 | − | 7.97403i | 1.25821 | − | 0.267440i | ||||
\(890\) | −10.9597 | − | 27.3862i | −0.367370 | − | 0.917989i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −5.88831 | − | 8.10456i | −0.197155 | − | 0.271361i | ||||
\(893\) | 1.42318 | − | 0.821672i | 0.0476248 | − | 0.0274962i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.38940 | + | 30.5011i | −0.146722 | + | 1.01954i | ||||
\(896\) | 11.2623 | − | 5.01430i | 0.376247 | − | 0.167516i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.87773 | + | 22.9479i | 0.162772 | + | 0.765781i | ||||
\(899\) | −3.66769 | −0.122324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.51264 | −0.0837081 | ||||||||
\(902\) | 1.99133 | + | 9.36848i | 0.0663041 | + | 0.311936i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.3876 | + | 4.62487i | −0.345487 | + | 0.153821i | ||||
\(905\) | −14.7632 | − | 7.26093i | −0.490744 | − | 0.241361i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.5281 | − | 15.3160i | 0.880851 | − | 0.508560i | 0.00991216 | − | 0.999951i | \(-0.496845\pi\) |
0.870939 | + | 0.491391i | \(0.163511\pi\) | |||||||
\(908\) | 2.73472 | + | 3.76402i | 0.0907548 | + | 0.124913i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.993142 | + | 0.625153i | 0.0329223 | + | 0.0207236i | ||||
\(911\) | −9.96400 | + | 2.11791i | −0.330122 | + | 0.0701696i | −0.369991 | − | 0.929035i | \(-0.620639\pi\) |
0.0398691 | + | 0.999205i | \(0.487306\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.28454 | − | 20.1572i | 0.141798 | − | 0.667105i | ||||
\(914\) | −13.9850 | − | 15.5319i | −0.462583 | − | 0.513750i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.59915 | + | 3.99726i | −0.118919 | + | 0.132073i | ||||
\(917\) | 18.4453 | + | 25.3878i | 0.609119 | + | 0.838380i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.8946 | − | 15.9074i | 0.722236 | − | 0.524735i | −0.164862 | − | 0.986317i | \(-0.552718\pi\) |
0.887098 | + | 0.461581i | \(0.152718\pi\) | |||||||
\(920\) | −11.0357 | − | 38.9714i | −0.363837 | − | 1.28485i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −14.6177 | − | 32.8319i | −0.481409 | − | 1.08126i | ||||
\(923\) | 0.433884 | − | 0.390670i | 0.0142814 | − | 0.0128591i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.31776 | + | 4.48360i | −0.0433277 | + | 0.147420i | ||||
\(926\) | −14.0632 | −0.462145 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.7911 | − | 14.8526i | 0.354234 | − | 0.487562i | ||||
\(929\) | −2.13333 | + | 20.2972i | −0.0699922 | + | 0.665931i | 0.902131 | + | 0.431462i | \(0.142002\pi\) |
−0.972123 | + | 0.234470i | \(0.924665\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.143102 | − | 1.36152i | −0.00468997 | − | 0.0446221i | ||||
\(932\) | 1.21228 | + | 0.699908i | 0.0397094 | + | 0.0229262i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.5729 | − | 12.8530i | 0.378677 | − | 0.420564i | ||||
\(935\) | −0.148888 | + | 0.588867i | −0.00486917 | + | 0.0192580i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.4195 | − | 6.30978i | 0.634408 | − | 0.206132i | 0.0258811 | − | 0.999665i | \(-0.491761\pi\) |
0.608527 | + | 0.793533i | \(0.291761\pi\) | |||||||
\(938\) | 15.4915 | + | 13.9486i | 0.505815 | + | 0.455438i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.192980 | + | 0.187594i | 0.00629431 | + | 0.00611864i | ||||
\(941\) | −0.576816 | − | 0.122606i | −0.0188037 | − | 0.00399684i | 0.198500 | − | 0.980101i | \(-0.436393\pi\) |
−0.217304 | + | 0.976104i | \(0.569726\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.8929 | − | 16.6813i | 0.940881 | − | 0.543218i | ||||
\(944\) | 12.4922 | − | 9.07609i | 0.406585 | − | 0.295402i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.36406 | + | 6.80339i | 0.304452 | + | 0.221197i | ||||
\(947\) | −26.8317 | − | 2.82012i | −0.871913 | − | 0.0916417i | −0.342006 | − | 0.939698i | \(-0.611106\pi\) |
−0.529907 | + | 0.848056i | \(0.677773\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.946005 | − | 1.63853i | 0.0307086 | − | 0.0531889i | ||||
\(950\) | 43.9335 | − | 10.6462i | 1.42539 | − | 0.345407i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.330469 | + | 1.55473i | 0.0107106 | + | 0.0503892i | ||||
\(953\) | 10.0812 | − | 13.8756i | 0.326563 | − | 0.449475i | −0.613894 | − | 0.789388i | \(-0.710398\pi\) |
0.940457 | + | 0.339913i | \(0.110398\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.41711 | − | 0.611139i | −0.0782159 | − | 0.0197760i | ||||
\(956\) | −5.30031 | − | 2.35985i | −0.171424 | − | 0.0763230i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −6.15877 | + | 0.647313i | −0.198981 | + | 0.0209137i | ||||
\(959\) | 53.9469 | + | 11.4668i | 1.74203 | + | 0.370281i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.9682 | − | 6.36994i | 0.966717 | − | 0.205482i | ||||
\(962\) | 0.174071 | − | 0.0565591i | 0.00561227 | − | 0.00182354i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.522323 | + | 1.60755i | −0.0168229 | + | 0.0517756i | ||||
\(965\) | 2.16464 | − | 56.6254i | 0.0696824 | − | 1.82283i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.3682 | + | 1.40505i | −0.429892 | + | 0.0451835i | −0.317004 | − | 0.948424i | \(-0.602677\pi\) |
−0.112888 | + | 0.993608i | \(0.536010\pi\) | |||||||
\(968\) | 23.9919 | + | 13.8517i | 0.771129 | + | 0.445211i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.93260 | − | 4.64286i | 0.222592 | − | 0.149073i | ||||
\(971\) | 17.9377 | + | 13.0325i | 0.575648 | + | 0.418232i | 0.837152 | − | 0.546970i | \(-0.184219\pi\) |
−0.261505 | + | 0.965202i | \(0.584219\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.32244 | − | 0.754607i | −0.0744541 | − | 0.0241916i | ||||
\(974\) | −24.5231 | − | 42.4753i | −0.785771 | − | 1.36100i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.3222 | − | 31.7349i | 0.586478 | − | 1.01581i | ||||
\(977\) | 15.5249 | − | 13.9787i | 0.496687 | − | 0.447219i | −0.382318 | − | 0.924031i | \(-0.624874\pi\) |
0.879006 | + | 0.476812i | \(0.158208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.61038 | + | 15.3218i | −0.0514681 | + | 0.489686i | ||||
\(980\) | 0.208157 | − | 0.0833025i | 0.00664934 | − | 0.00266100i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 48.2698i | − | 1.54035i | ||||||
\(983\) | 11.1398 | − | 25.0205i | 0.355306 | − | 0.798030i | −0.644145 | − | 0.764903i | \(-0.722787\pi\) |
0.999451 | − | 0.0331270i | \(-0.0105466\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −35.3137 | − | 5.08199i | −1.12519 | − | 0.161926i | ||||
\(986\) | −0.948384 | − | 1.05329i | −0.0302027 | − | 0.0335435i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.498917 | + | 0.449227i | 0.0158727 | + | 0.0142918i | ||||
\(989\) | 12.4590 | − | 38.3450i | 0.396174 | − | 1.21930i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.58088 | − | 14.0985i | −0.145516 | − | 0.447854i | 0.851561 | − | 0.524256i | \(-0.175657\pi\) |
−0.997077 | + | 0.0764026i | \(0.975657\pi\) | |||||||
\(992\) | 0.737568 | − | 1.65660i | 0.0234178 | − | 0.0525973i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.21115 | + | 11.5233i | 0.0384154 | + | 0.365498i | ||||
\(995\) | −20.1287 | − | 38.1600i | −0.638122 | − | 1.20975i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.06076 | − | 0.216595i | −0.0652651 | − | 0.00685964i | 0.0718396 | − | 0.997416i | \(-0.477113\pi\) |
−0.137105 | + | 0.990557i | \(0.543780\pi\) | |||||||
\(998\) | −33.4730 | − | 10.8760i | −1.05957 | − | 0.344275i | ||||
\(999\) | 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 | 675.2.y.a.604.9 | 224 | ||
3.2 | odd | 2 | 225.2.u.a.4.20 | ✓ | 224 | ||
9.2 | odd | 6 | 225.2.u.a.79.20 | yes | 224 | ||
9.7 | even | 3 | inner | 675.2.y.a.154.9 | 224 | ||
25.19 | even | 10 | inner | 675.2.y.a.469.9 | 224 | ||
75.44 | odd | 10 | 225.2.u.a.94.20 | yes | 224 | ||
225.119 | odd | 30 | 225.2.u.a.169.20 | yes | 224 | ||
225.169 | even | 30 | inner | 675.2.y.a.19.9 | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.u.a.4.20 | ✓ | 224 | 3.2 | odd | 2 | ||
225.2.u.a.79.20 | yes | 224 | 9.2 | odd | 6 | ||
225.2.u.a.94.20 | yes | 224 | 75.44 | odd | 10 | ||
225.2.u.a.169.20 | yes | 224 | 225.119 | odd | 30 | ||
675.2.y.a.19.9 | 224 | 225.169 | even | 30 | inner | ||
675.2.y.a.154.9 | 224 | 9.7 | even | 3 | inner | ||
675.2.y.a.469.9 | 224 | 25.19 | even | 10 | inner | ||
675.2.y.a.604.9 | 224 | 1.1 | even | 1 | trivial |