Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [561,2,Mod(103,561)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(561, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("561.103");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 561 = 3 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 561.m (of order \(5\), degree \(4\), 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: | \(4.47960755339\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 256.4 | ||
Character | \(\chi\) | \(=\) | 561.256 |
Dual form | 561.2.m.d.103.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/561\mathbb{Z}\right)^\times\).
\(n\) | \(188\) | \(409\) | \(496\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.357186 | − | 0.259511i | 0.252569 | − | 0.183502i | −0.454296 | − | 0.890851i | \(-0.650109\pi\) |
0.706865 | + | 0.707349i | \(0.250109\pi\) | |||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | −0.557798 | + | 1.71673i | −0.278899 | + | 0.858363i | ||||
\(5\) | 3.46967 | + | 2.52087i | 1.55169 | + | 1.12737i | 0.942436 | + | 0.334388i | \(0.108529\pi\) |
0.609250 | + | 0.792978i | \(0.291471\pi\) | |||||||
\(6\) | 0.357186 | + | 0.259511i | 0.145821 | + | 0.105945i | ||||
\(7\) | 0.982692 | − | 3.02442i | 0.371423 | − | 1.14312i | −0.574438 | − | 0.818548i | \(-0.694779\pi\) |
0.945860 | − | 0.324574i | \(-0.105221\pi\) | |||||||
\(8\) | 0.519138 | + | 1.59774i | 0.183543 | + | 0.564887i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 1.89351 | 0.598781 | ||||||||
\(11\) | 3.28652 | + | 0.445822i | 0.990924 | + | 0.134420i | ||||
\(12\) | −1.80507 | −0.521079 | ||||||||
\(13\) | 1.67324 | − | 1.21568i | 0.464074 | − | 0.337169i | −0.331053 | − | 0.943612i | \(-0.607404\pi\) |
0.795127 | + | 0.606443i | \(0.207404\pi\) | |||||||
\(14\) | −0.433865 | − | 1.33530i | −0.115955 | − | 0.356874i | ||||
\(15\) | −1.32530 | + | 4.07885i | −0.342190 | + | 1.05315i | ||||
\(16\) | −2.32061 | − | 1.68602i | −0.580152 | − | 0.421505i | ||||
\(17\) | −0.809017 | − | 0.587785i | −0.196215 | − | 0.142559i | ||||
\(18\) | −0.136433 | + | 0.419898i | −0.0321576 | + | 0.0989708i | ||||
\(19\) | −2.03036 | − | 6.24882i | −0.465797 | − | 1.43358i | −0.857977 | − | 0.513688i | \(-0.828279\pi\) |
0.392179 | − | 0.919889i | \(-0.371721\pi\) | |||||||
\(20\) | −6.26301 | + | 4.55035i | −1.40045 | + | 1.01749i | ||||
\(21\) | 3.18006 | 0.693946 | ||||||||
\(22\) | 1.28960 | − | 0.693648i | 0.274943 | − | 0.147886i | ||||
\(23\) | −4.53626 | −0.945875 | −0.472937 | − | 0.881096i | \(-0.656806\pi\) | ||||
−0.472937 | + | 0.881096i | \(0.656806\pi\) | |||||||
\(24\) | −1.35912 | + | 0.987458i | −0.277429 | + | 0.201564i | ||||
\(25\) | 4.13879 | + | 12.7379i | 0.827758 | + | 2.54758i | ||||
\(26\) | 0.282176 | − | 0.868450i | 0.0553393 | − | 0.170317i | ||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | 4.64395 | + | 3.37403i | 0.877624 | + | 0.637631i | ||||
\(29\) | 0.837857 | − | 2.57866i | 0.155586 | − | 0.478845i | −0.842634 | − | 0.538487i | \(-0.818996\pi\) |
0.998220 | + | 0.0596423i | \(0.0189960\pi\) | |||||||
\(30\) | 0.585128 | + | 1.80084i | 0.106829 | + | 0.328787i | ||||
\(31\) | −6.01941 | + | 4.37335i | −1.08112 | + | 0.785478i | −0.977877 | − | 0.209179i | \(-0.932921\pi\) |
−0.103240 | + | 0.994656i | \(0.532921\pi\) | |||||||
\(32\) | −4.62636 | −0.817832 | ||||||||
\(33\) | 0.591590 | + | 3.26344i | 0.102983 | + | 0.568091i | ||||
\(34\) | −0.441507 | −0.0757178 | ||||||||
\(35\) | 11.0338 | − | 8.01650i | 1.86505 | − | 1.35504i | ||||
\(36\) | −0.557798 | − | 1.71673i | −0.0929663 | − | 0.286121i | ||||
\(37\) | 0.750404 | − | 2.30951i | 0.123366 | − | 0.379681i | −0.870234 | − | 0.492639i | \(-0.836032\pi\) |
0.993600 | + | 0.112958i | \(0.0360325\pi\) | |||||||
\(38\) | −2.34686 | − | 1.70509i | −0.380710 | − | 0.276602i | ||||
\(39\) | 1.67324 | + | 1.21568i | 0.267933 | + | 0.194665i | ||||
\(40\) | −2.22645 | + | 6.85232i | −0.352033 | + | 1.08345i | ||||
\(41\) | 1.58166 | + | 4.86784i | 0.247013 | + | 0.760229i | 0.995299 | + | 0.0968522i | \(0.0308774\pi\) |
−0.748285 | + | 0.663377i | \(0.769123\pi\) | |||||||
\(42\) | 1.13587 | − | 0.825261i | 0.175269 | − | 0.127340i | ||||
\(43\) | −8.01474 | −1.22224 | −0.611118 | − | 0.791540i | \(-0.709280\pi\) | ||||
−0.611118 | + | 0.791540i | \(0.709280\pi\) | |||||||
\(44\) | −2.59857 | + | 5.39338i | −0.391749 | + | 0.813083i | ||||
\(45\) | −4.28875 | −0.639330 | ||||||||
\(46\) | −1.62029 | + | 1.17721i | −0.238899 | + | 0.173570i | ||||
\(47\) | −2.61064 | − | 8.03474i | −0.380802 | − | 1.17199i | −0.939480 | − | 0.342603i | \(-0.888692\pi\) |
0.558679 | − | 0.829384i | \(-0.311308\pi\) | |||||||
\(48\) | 0.886393 | − | 2.72804i | 0.127940 | − | 0.393758i | ||||
\(49\) | −2.51829 | − | 1.82964i | −0.359756 | − | 0.261378i | ||||
\(50\) | 4.78394 | + | 3.47574i | 0.676552 | + | 0.491544i | ||||
\(51\) | 0.309017 | − | 0.951057i | 0.0432710 | − | 0.133175i | ||||
\(52\) | 1.15366 | + | 3.55060i | 0.159984 | + | 0.492380i | ||||
\(53\) | −1.62369 | + | 1.17968i | −0.223031 | + | 0.162042i | −0.693690 | − | 0.720274i | \(-0.744016\pi\) |
0.470659 | + | 0.882315i | \(0.344016\pi\) | |||||||
\(54\) | −0.441507 | −0.0600814 | ||||||||
\(55\) | 10.2793 | + | 9.83175i | 1.38606 | + | 1.32571i | ||||
\(56\) | 5.34239 | 0.713906 | ||||||||
\(57\) | 5.31556 | − | 3.86198i | 0.704063 | − | 0.511532i | ||||
\(58\) | −0.369919 | − | 1.13849i | −0.0485728 | − | 0.149492i | ||||
\(59\) | 3.21633 | − | 9.89884i | 0.418730 | − | 1.28872i | −0.490141 | − | 0.871643i | \(-0.663055\pi\) |
0.908871 | − | 0.417076i | \(-0.136945\pi\) | |||||||
\(60\) | −6.26301 | − | 4.55035i | −0.808551 | − | 0.587447i | ||||
\(61\) | −6.80158 | − | 4.94164i | −0.870853 | − | 0.632712i | 0.0599624 | − | 0.998201i | \(-0.480902\pi\) |
−0.930816 | + | 0.365489i | \(0.880902\pi\) | |||||||
\(62\) | −1.01512 | + | 3.12421i | −0.128920 | + | 0.396774i | ||||
\(63\) | 0.982692 | + | 3.02442i | 0.123808 | + | 0.381041i | ||||
\(64\) | 2.98874 | − | 2.17145i | 0.373593 | − | 0.271431i | ||||
\(65\) | 8.87018 | 1.10021 | ||||||||
\(66\) | 1.05821 | + | 1.01213i | 0.130256 | + | 0.124585i | ||||
\(67\) | 10.6245 | 1.29799 | 0.648995 | − | 0.760792i | \(-0.275189\pi\) | ||||
0.648995 | + | 0.760792i | \(0.275189\pi\) | |||||||
\(68\) | 1.46033 | − | 1.06099i | 0.177091 | − | 0.128665i | ||||
\(69\) | −1.40178 | − | 4.31424i | −0.168755 | − | 0.519373i | ||||
\(70\) | 1.86074 | − | 5.72677i | 0.222401 | − | 0.684480i | ||||
\(71\) | 9.60251 | + | 6.97663i | 1.13961 | + | 0.827974i | 0.987065 | − | 0.160323i | \(-0.0512536\pi\) |
0.152543 | + | 0.988297i | \(0.451254\pi\) | |||||||
\(72\) | −1.35912 | − | 0.987458i | −0.160174 | − | 0.116373i | ||||
\(73\) | −1.62234 | + | 4.99305i | −0.189881 | + | 0.584392i | −0.999998 | − | 0.00187507i | \(-0.999403\pi\) |
0.810118 | + | 0.586267i | \(0.199403\pi\) | |||||||
\(74\) | −0.331309 | − | 1.01966i | −0.0385138 | − | 0.118533i | ||||
\(75\) | −10.8355 | + | 7.87245i | −1.25118 | + | 0.909032i | ||||
\(76\) | 11.8600 | 1.36044 | ||||||||
\(77\) | 4.57799 | − | 9.50171i | 0.521711 | − | 1.08282i | ||||
\(78\) | 0.913142 | 0.103393 | ||||||||
\(79\) | −5.92238 | + | 4.30286i | −0.666320 | + | 0.484110i | −0.868791 | − | 0.495178i | \(-0.835103\pi\) |
0.202471 | + | 0.979288i | \(0.435103\pi\) | |||||||
\(80\) | −3.80152 | − | 11.6999i | −0.425023 | − | 1.30809i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 1.82821 | + | 1.32827i | 0.201892 | + | 0.146683i | ||||
\(83\) | −6.16278 | − | 4.47752i | −0.676453 | − | 0.491472i | 0.195726 | − | 0.980659i | \(-0.437294\pi\) |
−0.872179 | + | 0.489187i | \(0.837294\pi\) | |||||||
\(84\) | −1.77383 | + | 5.45929i | −0.193541 | + | 0.595657i | ||||
\(85\) | −1.32530 | − | 4.07885i | −0.143749 | − | 0.442413i | ||||
\(86\) | −2.86275 | + | 2.07991i | −0.308699 | + | 0.224283i | ||||
\(87\) | 2.71136 | 0.290689 | ||||||||
\(88\) | 0.993851 | + | 5.48246i | 0.105945 | + | 0.584432i | ||||
\(89\) | −8.06013 | −0.854373 | −0.427186 | − | 0.904164i | \(-0.640495\pi\) | ||||
−0.427186 | + | 0.904164i | \(0.640495\pi\) | |||||||
\(90\) | −1.53188 | + | 1.11298i | −0.161475 | + | 0.117318i | ||||
\(91\) | −2.03244 | − | 6.25522i | −0.213058 | − | 0.655725i | ||||
\(92\) | 2.53031 | − | 7.78751i | 0.263804 | − | 0.811904i | ||||
\(93\) | −6.01941 | − | 4.37335i | −0.624183 | − | 0.453496i | ||||
\(94\) | −3.01759 | − | 2.19241i | −0.311241 | − | 0.226129i | ||||
\(95\) | 8.70773 | − | 26.7996i | 0.893394 | − | 2.74959i | ||||
\(96\) | −1.42962 | − | 4.39993i | −0.145910 | − | 0.449066i | ||||
\(97\) | 0.748010 | − | 0.543461i | 0.0759489 | − | 0.0551801i | −0.549163 | − | 0.835715i | \(-0.685053\pi\) |
0.625112 | + | 0.780535i | \(0.285053\pi\) | |||||||
\(98\) | −1.37431 | −0.138826 | ||||||||
\(99\) | −2.92090 | + | 1.57109i | −0.293562 | + | 0.157901i | ||||
\(100\) | −24.1761 | −2.41761 | ||||||||
\(101\) | 8.67601 | − | 6.30349i | 0.863295 | − | 0.627221i | −0.0654844 | − | 0.997854i | \(-0.520859\pi\) |
0.928779 | + | 0.370633i | \(0.120859\pi\) | |||||||
\(102\) | −0.136433 | − | 0.419898i | −0.0135089 | − | 0.0415761i | ||||
\(103\) | −1.50042 | + | 4.61783i | −0.147841 | + | 0.455008i | −0.997365 | − | 0.0725414i | \(-0.976889\pi\) |
0.849524 | + | 0.527549i | \(0.176889\pi\) | |||||||
\(104\) | 2.81099 | + | 2.04230i | 0.275640 | + | 0.200264i | ||||
\(105\) | 11.0338 | + | 8.01650i | 1.07679 | + | 0.782331i | ||||
\(106\) | −0.273820 | + | 0.842732i | −0.0265958 | + | 0.0818534i | ||||
\(107\) | 1.42380 | + | 4.38200i | 0.137644 | + | 0.423624i | 0.995992 | − | 0.0894438i | \(-0.0285090\pi\) |
−0.858348 | + | 0.513068i | \(0.828509\pi\) | |||||||
\(108\) | 1.46033 | − | 1.06099i | 0.140521 | − | 0.102094i | ||||
\(109\) | −1.29614 | −0.124148 | −0.0620740 | − | 0.998072i | \(-0.519771\pi\) | ||||
−0.0620740 | + | 0.998072i | \(0.519771\pi\) | |||||||
\(110\) | 6.22308 | + | 0.844169i | 0.593347 | + | 0.0804884i | ||||
\(111\) | 2.42836 | 0.230490 | ||||||||
\(112\) | −7.37967 | + | 5.36164i | −0.697313 | + | 0.506628i | ||||
\(113\) | −0.776316 | − | 2.38926i | −0.0730297 | − | 0.224762i | 0.907879 | − | 0.419233i | \(-0.137701\pi\) |
−0.980908 | + | 0.194471i | \(0.937701\pi\) | |||||||
\(114\) | 0.896419 | − | 2.75889i | 0.0839573 | − | 0.258394i | ||||
\(115\) | −15.7393 | − | 11.4353i | −1.46770 | − | 1.06635i | ||||
\(116\) | 3.95949 | + | 2.87674i | 0.367630 | + | 0.267099i | ||||
\(117\) | −0.639122 | + | 1.96701i | −0.0590868 | + | 0.181850i | ||||
\(118\) | −1.42003 | − | 4.37040i | −0.130724 | − | 0.402328i | ||||
\(119\) | −2.57272 | + | 1.86919i | −0.235841 | + | 0.171349i | ||||
\(120\) | −7.20495 | −0.657719 | ||||||||
\(121\) | 10.6025 | + | 2.93041i | 0.963862 | + | 0.266401i | ||||
\(122\) | −3.71184 | −0.336054 | ||||||||
\(123\) | −4.14083 | + | 3.00849i | −0.373366 | + | 0.271267i | ||||
\(124\) | −4.15024 | − | 12.7731i | −0.372702 | − | 1.14706i | ||||
\(125\) | −11.1238 | + | 34.2354i | −0.994940 | + | 3.06211i | ||||
\(126\) | 1.13587 | + | 0.825261i | 0.101192 | + | 0.0735201i | ||||
\(127\) | −16.2750 | − | 11.8245i | −1.44418 | − | 1.04926i | −0.987149 | − | 0.159802i | \(-0.948914\pi\) |
−0.457027 | − | 0.889453i | \(-0.651086\pi\) | |||||||
\(128\) | 3.36327 | − | 10.3511i | 0.297274 | − | 0.914915i | ||||
\(129\) | −2.47669 | − | 7.62247i | −0.218060 | − | 0.671121i | ||||
\(130\) | 3.16831 | − | 2.30191i | 0.277879 | − | 0.201891i | ||||
\(131\) | −0.456557 | −0.0398896 | −0.0199448 | − | 0.999801i | \(-0.506349\pi\) | ||||
−0.0199448 | + | 0.999801i | \(0.506349\pi\) | |||||||
\(132\) | −5.93241 | − | 0.804740i | −0.516350 | − | 0.0700437i | ||||
\(133\) | −20.8942 | −1.81176 | ||||||||
\(134\) | 3.79493 | − | 2.75718i | 0.327832 | − | 0.238184i | ||||
\(135\) | −1.32530 | − | 4.07885i | −0.114063 | − | 0.351051i | ||||
\(136\) | 0.519138 | − | 1.59774i | 0.0445157 | − | 0.137005i | ||||
\(137\) | −6.77399 | − | 4.92159i | −0.578741 | − | 0.420480i | 0.259529 | − | 0.965735i | \(-0.416433\pi\) |
−0.838270 | + | 0.545255i | \(0.816433\pi\) | |||||||
\(138\) | −1.62029 | − | 1.17721i | −0.137928 | − | 0.100211i | ||||
\(139\) | −3.48548 | + | 10.7272i | −0.295635 | + | 0.909871i | 0.687372 | + | 0.726305i | \(0.258764\pi\) |
−0.983007 | + | 0.183566i | \(0.941236\pi\) | |||||||
\(140\) | 7.60752 | + | 23.4135i | 0.642953 | + | 1.97881i | ||||
\(141\) | 6.83475 | − | 4.96574i | 0.575590 | − | 0.418191i | ||||
\(142\) | 5.24040 | 0.439764 | ||||||||
\(143\) | 6.04113 | − | 3.24940i | 0.505184 | − | 0.271728i | ||||
\(144\) | 2.86843 | 0.239036 | ||||||||
\(145\) | 9.40755 | − | 6.83498i | 0.781254 | − | 0.567614i | ||||
\(146\) | 0.716274 | + | 2.20446i | 0.0592792 | + | 0.182443i | ||||
\(147\) | 0.961901 | − | 2.96043i | 0.0793363 | − | 0.244172i | ||||
\(148\) | 3.54622 | + | 2.57648i | 0.291497 | + | 0.211785i | ||||
\(149\) | 18.2779 | + | 13.2797i | 1.49738 | + | 1.08791i | 0.971409 | + | 0.237413i | \(0.0762996\pi\) |
0.525975 | + | 0.850500i | \(0.323700\pi\) | |||||||
\(150\) | −1.82730 | + | 5.62386i | −0.149199 | + | 0.459186i | ||||
\(151\) | 4.16581 | + | 12.8210i | 0.339009 | + | 1.04336i | 0.964714 | + | 0.263302i | \(0.0848115\pi\) |
−0.625705 | + | 0.780060i | \(0.715189\pi\) | |||||||
\(152\) | 8.92995 | − | 6.48799i | 0.724315 | − | 0.526246i | ||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | −0.830603 | − | 4.58192i | −0.0669319 | − | 0.369222i | ||||
\(155\) | −31.9100 | −2.56307 | ||||||||
\(156\) | −3.02032 | + | 2.19439i | −0.241819 | + | 0.175692i | ||||
\(157\) | 5.53752 | + | 17.0427i | 0.441942 | + | 1.36016i | 0.885803 | + | 0.464062i | \(0.153609\pi\) |
−0.443861 | + | 0.896096i | \(0.646391\pi\) | |||||||
\(158\) | −0.998753 | + | 3.07385i | −0.0794566 | + | 0.244542i | ||||
\(159\) | −1.62369 | − | 1.17968i | −0.128767 | − | 0.0935548i | ||||
\(160\) | −16.0520 | − | 11.6624i | −1.26902 | − | 0.921996i | ||||
\(161\) | −4.45775 | + | 13.7195i | −0.351320 | + | 1.08125i | ||||
\(162\) | −0.136433 | − | 0.419898i | −0.0107192 | − | 0.0329903i | ||||
\(163\) | 17.7597 | − | 12.9031i | 1.39104 | − | 1.01065i | 0.395294 | − | 0.918555i | \(-0.370643\pi\) |
0.995750 | − | 0.0920976i | \(-0.0293572\pi\) | |||||||
\(164\) | −9.23899 | −0.721444 | ||||||||
\(165\) | −6.17406 | + | 12.8144i | −0.480650 | + | 0.997599i | ||||
\(166\) | −3.36323 | −0.261037 | ||||||||
\(167\) | 11.1854 | − | 8.12669i | 0.865555 | − | 0.628862i | −0.0638358 | − | 0.997960i | \(-0.520333\pi\) |
0.929390 | + | 0.369098i | \(0.120333\pi\) | |||||||
\(168\) | 1.65089 | + | 5.08091i | 0.127369 | + | 0.392001i | ||||
\(169\) | −2.69536 | + | 8.29548i | −0.207336 | + | 0.638114i | ||||
\(170\) | −1.53188 | − | 1.11298i | −0.117490 | − | 0.0853616i | ||||
\(171\) | 5.31556 | + | 3.86198i | 0.406491 | + | 0.295333i | ||||
\(172\) | 4.47060 | − | 13.7591i | 0.340880 | − | 1.04912i | ||||
\(173\) | −3.50485 | − | 10.7868i | −0.266469 | − | 0.820106i | −0.991351 | − | 0.131234i | \(-0.958106\pi\) |
0.724883 | − | 0.688872i | \(-0.241894\pi\) | |||||||
\(174\) | 0.968462 | − | 0.703629i | 0.0734189 | − | 0.0533419i | ||||
\(175\) | 42.5918 | 3.21964 | ||||||||
\(176\) | −6.87507 | − | 6.57572i | −0.518228 | − | 0.495664i | ||||
\(177\) | 10.4083 | 0.782333 | ||||||||
\(178\) | −2.87897 | + | 2.09169i | −0.215788 | + | 0.156779i | ||||
\(179\) | −0.501496 | − | 1.54344i | −0.0374835 | − | 0.115362i | 0.930564 | − | 0.366129i | \(-0.119317\pi\) |
−0.968048 | + | 0.250767i | \(0.919317\pi\) | |||||||
\(180\) | 2.39226 | − | 7.36261i | 0.178308 | − | 0.548777i | ||||
\(181\) | 10.0847 | + | 7.32698i | 0.749592 | + | 0.544610i | 0.895700 | − | 0.444658i | \(-0.146675\pi\) |
−0.146109 | + | 0.989269i | \(0.546675\pi\) | |||||||
\(182\) | −2.34926 | − | 1.70684i | −0.174139 | − | 0.126519i | ||||
\(183\) | 2.59797 | − | 7.99574i | 0.192048 | − | 0.591062i | ||||
\(184\) | −2.35494 | − | 7.24776i | −0.173609 | − | 0.534312i | ||||
\(185\) | 8.42562 | − | 6.12157i | 0.619464 | − | 0.450067i | ||||
\(186\) | −3.28498 | −0.240867 | ||||||||
\(187\) | −2.39681 | − | 2.29245i | −0.175272 | − | 0.167640i | ||||
\(188\) | 15.2496 | 1.11219 | ||||||||
\(189\) | −2.57272 | + | 1.86919i | −0.187138 | + | 0.135964i | ||||
\(190\) | −3.84452 | − | 11.8322i | −0.278911 | − | 0.858399i | ||||
\(191\) | 2.04842 | − | 6.30438i | 0.148218 | − | 0.456169i | −0.849192 | − | 0.528083i | \(-0.822911\pi\) |
0.997411 | + | 0.0719143i | \(0.0229108\pi\) | |||||||
\(192\) | 2.98874 | + | 2.17145i | 0.215694 | + | 0.156711i | ||||
\(193\) | −13.6843 | − | 9.94224i | −0.985019 | − | 0.715658i | −0.0261946 | − | 0.999657i | \(-0.508339\pi\) |
−0.958825 | + | 0.283998i | \(0.908339\pi\) | |||||||
\(194\) | 0.126145 | − | 0.388234i | 0.00905666 | − | 0.0278735i | ||||
\(195\) | 2.74103 | + | 8.43604i | 0.196290 | + | 0.604117i | ||||
\(196\) | 4.54569 | − | 3.30264i | 0.324692 | − | 0.235903i | ||||
\(197\) | −2.01403 | −0.143493 | −0.0717467 | − | 0.997423i | \(-0.522857\pi\) | ||||
−0.0717467 | + | 0.997423i | \(0.522857\pi\) | |||||||
\(198\) | −0.635590 | + | 1.31918i | −0.0451694 | + | 0.0937500i | ||||
\(199\) | 5.50328 | 0.390117 | 0.195059 | − | 0.980792i | \(-0.437510\pi\) | ||||
0.195059 | + | 0.980792i | \(0.437510\pi\) | |||||||
\(200\) | −18.2032 | + | 13.2254i | −1.28716 | + | 0.935179i | ||||
\(201\) | 3.28316 | + | 10.1045i | 0.231576 | + | 0.712717i | ||||
\(202\) | 1.46313 | − | 4.50304i | 0.102945 | − | 0.316833i | ||||
\(203\) | −6.97558 | − | 5.06806i | −0.489590 | − | 0.355708i | ||||
\(204\) | 1.46033 | + | 1.06099i | 0.102244 | + | 0.0742845i | ||||
\(205\) | −6.78334 | + | 20.8770i | −0.473769 | + | 1.45811i | ||||
\(206\) | 0.662447 | + | 2.03880i | 0.0461548 | + | 0.142050i | ||||
\(207\) | 3.66991 | − | 2.66634i | 0.255076 | − | 0.185324i | ||||
\(208\) | −5.93260 | −0.411352 | ||||||||
\(209\) | −3.88698 | − | 21.4421i | −0.268868 | − | 1.48318i | ||||
\(210\) | 6.02148 | 0.415522 | ||||||||
\(211\) | 15.3598 | − | 11.1595i | 1.05741 | − | 0.768255i | 0.0838039 | − | 0.996482i | \(-0.473293\pi\) |
0.973608 | + | 0.228228i | \(0.0732931\pi\) | |||||||
\(212\) | −1.11950 | − | 3.44546i | −0.0768874 | − | 0.236635i | ||||
\(213\) | −3.66783 | + | 11.2884i | −0.251316 | + | 0.773470i | ||||
\(214\) | 1.64574 | + | 1.19570i | 0.112500 | + | 0.0817363i | ||||
\(215\) | −27.8085 | − | 20.2041i | −1.89653 | − | 1.37791i | ||||
\(216\) | 0.519138 | − | 1.59774i | 0.0353228 | − | 0.108713i | ||||
\(217\) | 7.31162 | + | 22.5029i | 0.496345 | + | 1.52759i | ||||
\(218\) | −0.462965 | + | 0.336364i | −0.0313559 | + | 0.0227814i | ||||
\(219\) | −5.25000 | −0.354762 | ||||||||
\(220\) | −22.6122 | + | 12.1626i | −1.52451 | + | 0.820005i | ||||
\(221\) | −2.06824 | −0.139125 | ||||||||
\(222\) | 0.867377 | − | 0.630186i | 0.0582145 | − | 0.0422953i | ||||
\(223\) | 3.50491 | + | 10.7870i | 0.234706 | + | 0.722351i | 0.997160 | + | 0.0753089i | \(0.0239943\pi\) |
−0.762454 | + | 0.647042i | \(0.776006\pi\) | |||||||
\(224\) | −4.54629 | + | 13.9920i | −0.303762 | + | 0.934882i | ||||
\(225\) | −10.8355 | − | 7.87245i | −0.722366 | − | 0.524830i | ||||
\(226\) | −0.897328 | − | 0.651947i | −0.0596894 | − | 0.0433669i | ||||
\(227\) | −6.17006 | + | 18.9895i | −0.409521 | + | 1.26038i | 0.507540 | + | 0.861628i | \(0.330555\pi\) |
−0.917061 | + | 0.398748i | \(0.869445\pi\) | |||||||
\(228\) | 3.66495 | + | 11.2796i | 0.242717 | + | 0.747007i | ||||
\(229\) | 0.899451 | − | 0.653490i | 0.0594374 | − | 0.0431838i | −0.557670 | − | 0.830063i | \(-0.688304\pi\) |
0.617107 | + | 0.786879i | \(0.288304\pi\) | |||||||
\(230\) | −8.58946 | −0.566372 | ||||||||
\(231\) | 10.4513 | + | 1.41774i | 0.687648 | + | 0.0932804i | ||||
\(232\) | 4.55499 | 0.299050 | ||||||||
\(233\) | 10.6592 | − | 7.74436i | 0.698307 | − | 0.507350i | −0.181073 | − | 0.983470i | \(-0.557957\pi\) |
0.879381 | + | 0.476120i | \(0.157957\pi\) | |||||||
\(234\) | 0.282176 | + | 0.868450i | 0.0184464 | + | 0.0567723i | ||||
\(235\) | 11.1964 | − | 34.4590i | 0.730373 | − | 2.24786i | ||||
\(236\) | 15.1995 | + | 11.0431i | 0.989405 | + | 0.718845i | ||||
\(237\) | −5.92238 | − | 4.30286i | −0.384700 | − | 0.279501i | ||||
\(238\) | −0.433865 | + | 1.33530i | −0.0281233 | + | 0.0865546i | ||||
\(239\) | 3.59552 | + | 11.0659i | 0.232575 | + | 0.715791i | 0.997434 | + | 0.0715937i | \(0.0228085\pi\) |
−0.764859 | + | 0.644197i | \(0.777192\pi\) | |||||||
\(240\) | 9.95251 | − | 7.23092i | 0.642432 | − | 0.466754i | ||||
\(241\) | −0.254029 | −0.0163635 | −0.00818174 | − | 0.999967i | \(-0.502604\pi\) | ||||
−0.00818174 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(242\) | 4.54754 | − | 1.70476i | 0.292327 | − | 0.109586i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 12.2773 | − | 8.92001i | 0.785976 | − | 0.571045i | ||||
\(245\) | −4.12536 | − | 12.6965i | −0.263559 | − | 0.811153i | ||||
\(246\) | −0.698312 | + | 2.14918i | −0.0445228 | + | 0.137027i | ||||
\(247\) | −10.9939 | − | 7.98751i | −0.699523 | − | 0.508233i | ||||
\(248\) | −10.1124 | − | 7.34708i | −0.642137 | − | 0.466540i | ||||
\(249\) | 2.35397 | − | 7.24478i | 0.149177 | − | 0.459119i | ||||
\(250\) | 4.91122 | + | 15.1152i | 0.310613 | + | 0.955967i | ||||
\(251\) | 12.2809 | − | 8.92257i | 0.775161 | − | 0.563188i | −0.128362 | − | 0.991727i | \(-0.540972\pi\) |
0.903523 | + | 0.428540i | \(0.140972\pi\) | |||||||
\(252\) | −5.74024 | −0.361601 | ||||||||
\(253\) | −14.9085 | − | 2.02236i | −0.937291 | − | 0.127145i | ||||
\(254\) | −8.88181 | −0.557294 | ||||||||
\(255\) | 3.46967 | − | 2.52087i | 0.217279 | − | 0.157863i | ||||
\(256\) | 0.798290 | + | 2.45689i | 0.0498932 | + | 0.153555i | ||||
\(257\) | −4.14977 | + | 12.7717i | −0.258856 | + | 0.796675i | 0.734190 | + | 0.678944i | \(0.237562\pi\) |
−0.993045 | + | 0.117731i | \(0.962438\pi\) | |||||||
\(258\) | −2.86275 | − | 2.07991i | −0.178227 | − | 0.129490i | ||||
\(259\) | −6.24750 | − | 4.53907i | −0.388200 | − | 0.282044i | ||||
\(260\) | −4.94777 | + | 15.2277i | −0.306847 | + | 0.944379i | ||||
\(261\) | 0.837857 | + | 2.57866i | 0.0518621 | + | 0.159615i | ||||
\(262\) | −0.163076 | + | 0.118482i | −0.0100749 | + | 0.00731982i | ||||
\(263\) | −0.182236 | −0.0112371 | −0.00561857 | − | 0.999984i | \(-0.501788\pi\) | ||||
−0.00561857 | + | 0.999984i | \(0.501788\pi\) | |||||||
\(264\) | −4.90701 | + | 2.63938i | −0.302006 | + | 0.162443i | ||||
\(265\) | −8.60751 | −0.528755 | ||||||||
\(266\) | −7.46314 | + | 5.42229i | −0.457594 | + | 0.332462i | ||||
\(267\) | −2.49072 | − | 7.66564i | −0.152430 | − | 0.469130i | ||||
\(268\) | −5.92633 | + | 18.2394i | −0.362008 | + | 1.11415i | ||||
\(269\) | 16.0300 | + | 11.6465i | 0.977368 | + | 0.710099i | 0.957119 | − | 0.289696i | \(-0.0935542\pi\) |
0.0202488 | + | 0.999795i | \(0.493554\pi\) | |||||||
\(270\) | −1.53188 | − | 1.11298i | −0.0932275 | − | 0.0677337i | ||||
\(271\) | −3.97955 | + | 12.2478i | −0.241740 | + | 0.744000i | 0.754415 | + | 0.656398i | \(0.227921\pi\) |
−0.996155 | + | 0.0876027i | \(0.972079\pi\) | |||||||
\(272\) | 0.886393 | + | 2.72804i | 0.0537455 | + | 0.165412i | ||||
\(273\) | 5.32101 | − | 3.86594i | 0.322042 | − | 0.233977i | ||||
\(274\) | −3.69679 | −0.223331 | ||||||||
\(275\) | 7.92341 | + | 43.7086i | 0.477800 | + | 2.63572i | ||||
\(276\) | 8.18827 | 0.492876 | ||||||||
\(277\) | 0.564572 | − | 0.410185i | 0.0339218 | − | 0.0246457i | −0.570695 | − | 0.821162i | \(-0.693326\pi\) |
0.604617 | + | 0.796516i | \(0.293326\pi\) | |||||||
\(278\) | 1.53886 | + | 4.73614i | 0.0922950 | + | 0.284055i | ||||
\(279\) | 2.29921 | − | 7.07624i | 0.137650 | − | 0.423643i | ||||
\(280\) | 18.5363 | + | 13.4674i | 1.10776 | + | 0.804834i | ||||
\(281\) | −11.1029 | − | 8.06676i | −0.662346 | − | 0.481223i | 0.205108 | − | 0.978739i | \(-0.434245\pi\) |
−0.867454 | + | 0.497517i | \(0.834245\pi\) | |||||||
\(282\) | 1.15262 | − | 3.54739i | 0.0686373 | − | 0.211244i | ||||
\(283\) | 0.814868 | + | 2.50790i | 0.0484389 | + | 0.149079i | 0.972350 | − | 0.233527i | \(-0.0750266\pi\) |
−0.923912 | + | 0.382606i | \(0.875027\pi\) | |||||||
\(284\) | −17.3332 | + | 12.5933i | −1.02854 | + | 0.747276i | ||||
\(285\) | 28.1788 | 1.66917 | ||||||||
\(286\) | 1.31455 | − | 2.72838i | 0.0777312 | − | 0.161333i | ||||
\(287\) | 16.2767 | 0.960781 | ||||||||
\(288\) | 3.74280 | − | 2.71931i | 0.220547 | − | 0.160237i | ||||
\(289\) | 0.309017 | + | 0.951057i | 0.0181775 | + | 0.0559445i | ||||
\(290\) | 1.58649 | − | 4.88272i | 0.0931621 | − | 0.286723i | ||||
\(291\) | 0.748010 | + | 0.543461i | 0.0438491 | + | 0.0318582i | ||||
\(292\) | −7.66676 | − | 5.57022i | −0.448663 | − | 0.325973i | ||||
\(293\) | 0.162890 | − | 0.501325i | 0.00951616 | − | 0.0292877i | −0.946186 | − | 0.323624i | \(-0.895099\pi\) |
0.955702 | + | 0.294336i | \(0.0950986\pi\) | |||||||
\(294\) | −0.424686 | − | 1.30705i | −0.0247682 | − | 0.0762286i | ||||
\(295\) | 36.1133 | − | 26.2378i | 2.10260 | − | 1.52763i | ||||
\(296\) | 4.07956 | 0.237119 | ||||||||
\(297\) | −2.39681 | − | 2.29245i | −0.139077 | − | 0.133021i | ||||
\(298\) | 9.97484 | 0.577827 | ||||||||
\(299\) | −7.59026 | + | 5.51464i | −0.438956 | + | 0.318920i | ||||
\(300\) | −7.47082 | − | 22.9928i | −0.431328 | − | 1.32749i | ||||
\(301\) | −7.87602 | + | 24.2399i | −0.453966 | + | 1.39716i | ||||
\(302\) | 4.81517 | + | 3.49843i | 0.277082 | + | 0.201312i | ||||
\(303\) | 8.67601 | + | 6.30349i | 0.498424 | + | 0.362126i | ||||
\(304\) | −5.82395 | + | 17.9243i | −0.334027 | + | 1.02803i | ||||
\(305\) | −11.1421 | − | 34.2918i | −0.637993 | − | 1.96354i | ||||
\(306\) | 0.357186 | − | 0.259511i | 0.0204190 | − | 0.0148353i | ||||
\(307\) | 14.5402 | 0.829853 | 0.414926 | − | 0.909855i | \(-0.363807\pi\) | ||||
0.414926 | + | 0.909855i | \(0.363807\pi\) | |||||||
\(308\) | 13.7582 | + | 13.1592i | 0.783948 | + | 0.749815i | ||||
\(309\) | −4.85547 | −0.276218 | ||||||||
\(310\) | −11.3978 | + | 8.28100i | −0.647353 | + | 0.470329i | ||||
\(311\) | −10.5522 | − | 32.4764i | −0.598362 | − | 1.84157i | −0.537225 | − | 0.843439i | \(-0.680527\pi\) |
−0.0611369 | − | 0.998129i | \(-0.519473\pi\) | |||||||
\(312\) | −1.07370 | + | 3.30451i | −0.0607864 | + | 0.187081i | ||||
\(313\) | 19.3542 | + | 14.0616i | 1.09396 | + | 0.794809i | 0.980064 | − | 0.198683i | \(-0.0636665\pi\) |
0.113897 | + | 0.993493i | \(0.463666\pi\) | |||||||
\(314\) | 6.40070 | + | 4.65038i | 0.361213 | + | 0.262436i | ||||
\(315\) | −4.21453 | + | 12.9710i | −0.237462 | + | 0.730832i | ||||
\(316\) | −4.08334 | − | 12.5672i | −0.229706 | − | 0.706962i | ||||
\(317\) | −3.07535 | + | 2.23437i | −0.172729 | + | 0.125495i | −0.670791 | − | 0.741647i | \(-0.734045\pi\) |
0.498062 | + | 0.867141i | \(0.334045\pi\) | |||||||
\(318\) | −0.886101 | −0.0496901 | ||||||||
\(319\) | 3.90326 | − | 8.10129i | 0.218541 | − | 0.453585i | ||||
\(320\) | 15.8439 | 0.885701 | ||||||||
\(321\) | −3.72755 | + | 2.70822i | −0.208052 | + | 0.151158i | ||||
\(322\) | 1.96812 | + | 6.05726i | 0.109679 | + | 0.337558i | ||||
\(323\) | −2.03036 | + | 6.24882i | −0.112972 | + | 0.347694i | ||||
\(324\) | 1.46033 | + | 1.06099i | 0.0811297 | + | 0.0589441i | ||||
\(325\) | 22.4104 | + | 16.2821i | 1.24311 | + | 0.903169i | ||||
\(326\) | 2.99500 | − | 9.21765i | 0.165878 | − | 0.510519i | ||||
\(327\) | −0.400531 | − | 1.23271i | −0.0221494 | − | 0.0681688i | ||||
\(328\) | −6.95645 | + | 5.05416i | −0.384106 | + | 0.279069i | ||||
\(329\) | −26.8658 | −1.48116 | ||||||||
\(330\) | 1.12018 | + | 6.17936i | 0.0616641 | + | 0.340163i | ||||
\(331\) | −19.1942 | −1.05501 | −0.527504 | − | 0.849552i | \(-0.676872\pi\) | ||||
−0.527504 | + | 0.849552i | \(0.676872\pi\) | |||||||
\(332\) | 11.1243 | − | 8.08225i | 0.610523 | − | 0.443571i | ||||
\(333\) | 0.750404 | + | 2.30951i | 0.0411219 | + | 0.126560i | ||||
\(334\) | 1.88632 | − | 5.80549i | 0.103215 | − | 0.317662i | ||||
\(335\) | 36.8636 | + | 26.7830i | 2.01407 | + | 1.46331i | ||||
\(336\) | −7.37967 | − | 5.36164i | −0.402594 | − | 0.292502i | ||||
\(337\) | 0.954844 | − | 2.93871i | 0.0520137 | − | 0.160082i | −0.921676 | − | 0.387961i | \(-0.873179\pi\) |
0.973689 | + | 0.227880i | \(0.0731794\pi\) | |||||||
\(338\) | 1.19002 | + | 3.66251i | 0.0647286 | + | 0.199214i | ||||
\(339\) | 2.03242 | − | 1.47664i | 0.110386 | − | 0.0802001i | ||||
\(340\) | 7.74151 | 0.419842 | ||||||||
\(341\) | −21.7327 | + | 11.6896i | −1.17689 | + | 0.633025i | ||||
\(342\) | 2.90087 | 0.156861 | ||||||||
\(343\) | 10.0007 | − | 7.26596i | 0.539989 | − | 0.392325i | ||||
\(344\) | −4.16075 | − | 12.8055i | −0.224333 | − | 0.690425i | ||||
\(345\) | 6.01189 | − | 18.5027i | 0.323669 | − | 0.996152i | ||||
\(346\) | −4.05118 | − | 2.94335i | −0.217793 | − | 0.158236i | ||||
\(347\) | 19.1325 | + | 13.9006i | 1.02708 | + | 0.746221i | 0.967723 | − | 0.252016i | \(-0.0810934\pi\) |
0.0593618 | + | 0.998237i | \(0.481093\pi\) | |||||||
\(348\) | −1.51239 | + | 4.65466i | −0.0810727 | + | 0.249516i | ||||
\(349\) | −0.0927683 | − | 0.285511i | −0.00496577 | − | 0.0152831i | 0.948543 | − | 0.316649i | \(-0.102558\pi\) |
−0.953509 | + | 0.301365i | \(0.902558\pi\) | |||||||
\(350\) | 15.2132 | − | 11.0531i | 0.813181 | − | 0.590811i | ||||
\(351\) | −2.06824 | −0.110395 | ||||||||
\(352\) | −15.2046 | − | 2.06253i | −0.810410 | − | 0.109933i | ||||
\(353\) | −24.7245 | −1.31595 | −0.657975 | − | 0.753040i | \(-0.728587\pi\) | ||||
−0.657975 | + | 0.753040i | \(0.728587\pi\) | |||||||
\(354\) | 3.71769 | − | 2.70106i | 0.197593 | − | 0.143560i | ||||
\(355\) | 15.7304 | + | 48.4133i | 0.834884 | + | 2.56951i | ||||
\(356\) | 4.49593 | − | 13.8370i | 0.238284 | − | 0.733362i | ||||
\(357\) | −2.57272 | − | 1.86919i | −0.136163 | − | 0.0989281i | ||||
\(358\) | −0.579668 | − | 0.421154i | −0.0306364 | − | 0.0222587i | ||||
\(359\) | −10.0376 | + | 30.8926i | −0.529765 | + | 1.63045i | 0.224932 | + | 0.974375i | \(0.427784\pi\) |
−0.754697 | + | 0.656074i | \(0.772216\pi\) | |||||||
\(360\) | −2.22645 | − | 6.85232i | −0.117344 | − | 0.361149i | ||||
\(361\) | −19.5540 | + | 14.2068i | −1.02916 | + | 0.747728i | ||||
\(362\) | 5.50356 | 0.289261 | ||||||||
\(363\) | 0.489365 | + | 10.9891i | 0.0256850 | + | 0.576779i | ||||
\(364\) | 11.8722 | 0.622272 | ||||||||
\(365\) | −18.2158 | + | 13.2346i | −0.953459 | + | 0.692728i | ||||
\(366\) | −1.14702 | − | 3.53017i | −0.0599558 | − | 0.184525i | ||||
\(367\) | −3.03841 | + | 9.35126i | −0.158604 | + | 0.488132i | −0.998508 | − | 0.0546023i | \(-0.982611\pi\) |
0.839905 | + | 0.542734i | \(0.182611\pi\) | |||||||
\(368\) | 10.5269 | + | 7.64822i | 0.548751 | + | 0.398691i | ||||
\(369\) | −4.14083 | − | 3.00849i | −0.215563 | − | 0.156616i | ||||
\(370\) | 1.42090 | − | 4.37308i | 0.0738691 | − | 0.227346i | ||||
\(371\) | 1.97226 | + | 6.06999i | 0.102395 | + | 0.315138i | ||||
\(372\) | 10.8655 | − | 7.89422i | 0.563348 | − | 0.409296i | ||||
\(373\) | −25.3181 | −1.31092 | −0.655460 | − | 0.755230i | \(-0.727525\pi\) | ||||
−0.655460 | + | 0.755230i | \(0.727525\pi\) | |||||||
\(374\) | −1.45102 | − | 0.196833i | −0.0750306 | − | 0.0101780i | ||||
\(375\) | −35.9973 | −1.85889 | ||||||||
\(376\) | 11.4821 | − | 8.34227i | 0.592146 | − | 0.430219i | ||||
\(377\) | −1.73289 | − | 5.33329i | −0.0892484 | − | 0.274678i | ||||
\(378\) | −0.433865 | + | 1.33530i | −0.0223156 | + | 0.0686804i | ||||
\(379\) | −8.79305 | − | 6.38852i | −0.451669 | − | 0.328156i | 0.338586 | − | 0.940936i | \(-0.390052\pi\) |
−0.790254 | + | 0.612779i | \(0.790052\pi\) | |||||||
\(380\) | 41.1505 | + | 29.8976i | 2.11097 | + | 1.53371i | ||||
\(381\) | 6.21651 | − | 19.1325i | 0.318481 | − | 0.980185i | ||||
\(382\) | −0.904390 | − | 2.78343i | −0.0462726 | − | 0.142412i | ||||
\(383\) | 23.5669 | − | 17.1224i | 1.20421 | − | 0.874913i | 0.209522 | − | 0.977804i | \(-0.432809\pi\) |
0.994693 | + | 0.102891i | \(0.0328093\pi\) | |||||||
\(384\) | 10.8838 | 0.555410 | ||||||||
\(385\) | 39.8367 | − | 21.4273i | 2.03027 | − | 1.09204i | ||||
\(386\) | −7.46798 | −0.380110 | ||||||||
\(387\) | 6.48406 | − | 4.71094i | 0.329603 | − | 0.239471i | ||||
\(388\) | 0.515735 | + | 1.58727i | 0.0261825 | + | 0.0805814i | ||||
\(389\) | −8.98695 | + | 27.6590i | −0.455656 | + | 1.40237i | 0.414707 | + | 0.909955i | \(0.363884\pi\) |
−0.870363 | + | 0.492411i | \(0.836116\pi\) | |||||||
\(390\) | 3.16831 | + | 2.30191i | 0.160433 | + | 0.116562i | ||||
\(391\) | 3.66991 | + | 2.66634i | 0.185595 | + | 0.134843i | ||||
\(392\) | 1.61596 | − | 4.97341i | 0.0816183 | − | 0.251195i | ||||
\(393\) | −0.141084 | − | 0.434212i | −0.00711674 | − | 0.0219031i | ||||
\(394\) | −0.719383 | + | 0.522662i | −0.0362420 | + | 0.0263313i | ||||
\(395\) | −31.3957 | −1.57969 | ||||||||
\(396\) | −1.06786 | − | 5.89074i | −0.0536621 | − | 0.296021i | ||||
\(397\) | −10.1358 | −0.508699 | −0.254350 | − | 0.967112i | \(-0.581861\pi\) | ||||
−0.254350 | + | 0.967112i | \(0.581861\pi\) | |||||||
\(398\) | 1.96570 | − | 1.42816i | 0.0985315 | − | 0.0715873i | ||||
\(399\) | −6.45668 | − | 19.8716i | −0.323238 | − | 0.994825i | ||||
\(400\) | 11.8718 | − | 36.5377i | 0.593591 | − | 1.82689i | ||||
\(401\) | −9.56730 | − | 6.95105i | −0.477768 | − | 0.347119i | 0.322693 | − | 0.946504i | \(-0.395412\pi\) |
−0.800461 | + | 0.599385i | \(0.795412\pi\) | |||||||
\(402\) | 3.79493 | + | 2.75718i | 0.189274 | + | 0.137516i | ||||
\(403\) | −4.75532 | + | 14.6354i | −0.236879 | + | 0.729039i | ||||
\(404\) | 5.98190 | + | 18.4104i | 0.297611 | + | 0.915951i | ||||
\(405\) | 3.46967 | − | 2.52087i | 0.172410 | − | 0.125263i | ||||
\(406\) | −3.80680 | −0.188928 | ||||||||
\(407\) | 3.49585 | − | 7.25571i | 0.173283 | − | 0.359652i | ||||
\(408\) | 1.67996 | 0.0831706 | ||||||||
\(409\) | −16.4445 | + | 11.9477i | −0.813130 | + | 0.590773i | −0.914736 | − | 0.404051i | \(-0.867602\pi\) |
0.101606 | + | 0.994825i | \(0.467602\pi\) | |||||||
\(410\) | 2.99489 | + | 9.21732i | 0.147907 | + | 0.455211i | ||||
\(411\) | 2.58744 | − | 7.96331i | 0.127629 | − | 0.392801i | ||||
\(412\) | −7.09061 | − | 5.15163i | −0.349329 | − | 0.253803i | ||||
\(413\) | −26.7776 | − | 19.4550i | −1.31764 | − | 0.957320i | ||||
\(414\) | 0.618895 | − | 1.90476i | 0.0304170 | − | 0.0936140i | ||||
\(415\) | −10.0956 | − | 31.0711i | −0.495574 | − | 1.52522i | ||||
\(416\) | −7.74102 | + | 5.62418i | −0.379535 | + | 0.275748i | ||||
\(417\) | −11.2793 | −0.552348 | ||||||||
\(418\) | −6.95283 | − | 6.65010i | −0.340074 | − | 0.325267i | ||||
\(419\) | −8.25294 | −0.403183 | −0.201591 | − | 0.979470i | \(-0.564611\pi\) | ||||
−0.201591 | + | 0.979470i | \(0.564611\pi\) | |||||||
\(420\) | −19.9168 | + | 14.4704i | −0.971838 | + | 0.706082i | ||||
\(421\) | −10.0678 | − | 30.9856i | −0.490675 | − | 1.51014i | −0.823589 | − | 0.567187i | \(-0.808032\pi\) |
0.332914 | − | 0.942957i | \(-0.391968\pi\) | |||||||
\(422\) | 2.59028 | − | 7.97207i | 0.126093 | − | 0.388074i | ||||
\(423\) | 6.83475 | + | 4.96574i | 0.332317 | + | 0.241443i | ||||
\(424\) | −2.72775 | − | 1.98182i | −0.132471 | − | 0.0962458i | ||||
\(425\) | 4.13879 | − | 12.7379i | 0.200761 | − | 0.617878i | ||||
\(426\) | 1.61937 | + | 4.98391i | 0.0784588 | + | 0.241471i | ||||
\(427\) | −21.6294 | + | 15.7147i | −1.04672 | + | 0.760488i | ||||
\(428\) | −8.31688 | −0.402012 | ||||||||
\(429\) | 4.95717 | + | 4.74133i | 0.239335 | + | 0.228914i | ||||
\(430\) | −15.1760 | −0.731852 | ||||||||
\(431\) | −13.0928 | + | 9.51245i | −0.630656 | + | 0.458199i | −0.856628 | − | 0.515935i | \(-0.827444\pi\) |
0.225971 | + | 0.974134i | \(0.427444\pi\) | |||||||
\(432\) | 0.886393 | + | 2.72804i | 0.0426466 | + | 0.131253i | ||||
\(433\) | −1.65572 | + | 5.09578i | −0.0795687 | + | 0.244887i | −0.982926 | − | 0.184002i | \(-0.941095\pi\) |
0.903357 | + | 0.428889i | \(0.141095\pi\) | |||||||
\(434\) | 8.45135 | + | 6.14027i | 0.405678 | + | 0.294742i | ||||
\(435\) | 9.40755 | + | 6.83498i | 0.451057 | + | 0.327712i | ||||
\(436\) | 0.722987 | − | 2.22512i | 0.0346248 | − | 0.106564i | ||||
\(437\) | 9.21025 | + | 28.3462i | 0.440586 | + | 1.35598i | ||||
\(438\) | −1.87523 | + | 1.36243i | −0.0896019 | + | 0.0650996i | ||||
\(439\) | −14.8465 | −0.708583 | −0.354291 | − | 0.935135i | \(-0.615278\pi\) | ||||
−0.354291 | + | 0.935135i | \(0.615278\pi\) | |||||||
\(440\) | −10.3722 | + | 21.5277i | −0.494475 | + | 1.02629i | ||||
\(441\) | 3.11278 | 0.148228 | ||||||||
\(442\) | −0.738747 | + | 0.536731i | −0.0351386 | + | 0.0255297i | ||||
\(443\) | 2.85099 | + | 8.77446i | 0.135455 | + | 0.416887i | 0.995660 | − | 0.0930602i | \(-0.0296649\pi\) |
−0.860206 | + | 0.509947i | \(0.829665\pi\) | |||||||
\(444\) | −1.35453 | + | 4.16883i | −0.0642833 | + | 0.197844i | ||||
\(445\) | −27.9660 | − | 20.3185i | −1.32572 | − | 0.963190i | ||||
\(446\) | 4.05125 | + | 2.94341i | 0.191832 | + | 0.139374i | ||||
\(447\) | −6.98154 | + | 21.4870i | −0.330215 | + | 1.01630i | ||||
\(448\) | −3.63035 | − | 11.1731i | −0.171518 | − | 0.527878i | ||||
\(449\) | 0.765345 | − | 0.556056i | 0.0361189 | − | 0.0262419i | −0.569579 | − | 0.821936i | \(-0.692894\pi\) |
0.605698 | + | 0.795694i | \(0.292894\pi\) | |||||||
\(450\) | −5.91328 | −0.278755 | ||||||||
\(451\) | 3.02797 | + | 16.7034i | 0.142581 | + | 0.786533i | ||||
\(452\) | 4.53472 | 0.213295 | ||||||||
\(453\) | −10.9062 | + | 7.92384i | −0.512419 | + | 0.372294i | ||||
\(454\) | 2.72412 | + | 8.38398i | 0.127849 | + | 0.393480i | ||||
\(455\) | 8.71665 | − | 26.8271i | 0.408643 | − | 1.25767i | ||||
\(456\) | 8.92995 | + | 6.48799i | 0.418183 | + | 0.303828i | ||||
\(457\) | 11.0718 | + | 8.04410i | 0.517915 | + | 0.376287i | 0.815818 | − | 0.578309i | \(-0.196287\pi\) |
−0.297903 | + | 0.954596i | \(0.596287\pi\) | |||||||
\(458\) | 0.151684 | − | 0.466835i | 0.00708772 | − | 0.0218138i | ||||
\(459\) | 0.309017 | + | 0.951057i | 0.0144237 | + | 0.0443915i | ||||
\(460\) | 28.4106 | − | 20.6415i | 1.32465 | − | 0.962417i | ||||
\(461\) | −21.6426 | −1.00800 | −0.503999 | − | 0.863704i | \(-0.668138\pi\) | ||||
−0.503999 | + | 0.863704i | \(0.668138\pi\) | |||||||
\(462\) | 4.10100 | − | 2.20584i | 0.190796 | − | 0.102625i | ||||
\(463\) | −7.87106 | −0.365799 | −0.182900 | − | 0.983132i | \(-0.558548\pi\) | ||||
−0.182900 | + | 0.983132i | \(0.558548\pi\) | |||||||
\(464\) | −6.29201 | + | 4.57141i | −0.292099 | + | 0.212222i | ||||
\(465\) | −9.86074 | − | 30.3482i | −0.457281 | − | 1.40737i | ||||
\(466\) | 1.79757 | − | 5.53236i | 0.0832710 | − | 0.256282i | ||||
\(467\) | −6.41762 | − | 4.66268i | −0.296972 | − | 0.215763i | 0.429314 | − | 0.903155i | \(-0.358755\pi\) |
−0.726286 | + | 0.687392i | \(0.758755\pi\) | |||||||
\(468\) | −3.02032 | − | 2.19439i | −0.139614 | − | 0.101436i | ||||
\(469\) | 10.4406 | − | 32.1329i | 0.482103 | − | 1.48376i | ||||
\(470\) | −4.94329 | − | 15.2139i | −0.228017 | − | 0.701764i | ||||
\(471\) | −14.4974 | + | 10.5330i | −0.668005 | + | 0.485334i | ||||
\(472\) | 17.4855 | 0.804836 | ||||||||
\(473\) | −26.3406 | − | 3.57314i | −1.21114 | − | 0.164293i | ||||
\(474\) | −3.23203 | −0.148452 | ||||||||
\(475\) | 71.1935 | − | 51.7251i | 3.26658 | − | 2.37331i | ||||
\(476\) | −1.77383 | − | 5.45929i | −0.0813034 | − | 0.250226i | ||||
\(477\) | 0.620195 | − | 1.90877i | 0.0283968 | − | 0.0873964i | ||||
\(478\) | 4.15598 | + | 3.01950i | 0.190090 | + | 0.138109i | ||||
\(479\) | −21.9903 | − | 15.9769i | −1.00476 | − | 0.730004i | −0.0416601 | − | 0.999132i | \(-0.513265\pi\) |
−0.963105 | + | 0.269128i | \(0.913265\pi\) | |||||||
\(480\) | 6.13130 | − | 18.8702i | 0.279854 | − | 0.861303i | ||||
\(481\) | −1.55202 | − | 4.77662i | −0.0707659 | − | 0.217795i | ||||
\(482\) | −0.0907359 | + | 0.0659235i | −0.00413290 | + | 0.00300273i | ||||
\(483\) | −14.4256 | −0.656386 | ||||||||
\(484\) | −10.9448 | + | 16.5670i | −0.497489 | + | 0.753045i | ||||
\(485\) | 3.96534 | 0.180057 | ||||||||
\(486\) | 0.357186 | − | 0.259511i | 0.0162023 | − | 0.0117717i | ||||
\(487\) | −10.0456 | − | 30.9172i | −0.455209 | − | 1.40099i | −0.870889 | − | 0.491479i | \(-0.836456\pi\) |
0.415680 | − | 0.909511i | \(-0.363544\pi\) | |||||||
\(488\) | 4.36450 | − | 13.4326i | 0.197572 | − | 0.608063i | ||||
\(489\) | 17.7597 | + | 12.9031i | 0.803119 | + | 0.583500i | ||||
\(490\) | −4.76842 | − | 3.46446i | −0.215415 | − | 0.156508i | ||||
\(491\) | 3.88876 | − | 11.9684i | 0.175497 | − | 0.540125i | −0.824159 | − | 0.566359i | \(-0.808351\pi\) |
0.999656 | + | 0.0262340i | \(0.00835149\pi\) | |||||||
\(492\) | −2.85501 | − | 8.78681i | −0.128714 | − | 0.396140i | ||||
\(493\) | −2.19354 | + | 1.59370i | −0.0987920 | + | 0.0717766i | ||||
\(494\) | −5.99970 | −0.269939 | ||||||||
\(495\) | −14.0951 | − | 1.91202i | −0.633527 | − | 0.0859389i | ||||
\(496\) | 21.3422 | 0.958295 | ||||||||
\(497\) | 30.5365 | − | 22.1861i | 1.36975 | − | 0.995183i | ||||
\(498\) | −1.03929 | − | 3.19862i | −0.0465719 | − | 0.143334i | ||||
\(499\) | −10.3581 | + | 31.8788i | −0.463690 | + | 1.42709i | 0.396932 | + | 0.917848i | \(0.370075\pi\) |
−0.860622 | + | 0.509244i | \(0.829925\pi\) | |||||||
\(500\) | −52.5680 | − | 38.1929i | −2.35091 | − | 1.70804i | ||||
\(501\) | 11.1854 | + | 8.12669i | 0.499728 | + | 0.363074i | ||||
\(502\) | 2.07105 | − | 6.37404i | 0.0924355 | − | 0.284487i | ||||
\(503\) | 4.96156 | + | 15.2701i | 0.221225 | + | 0.680861i | 0.998653 | + | 0.0518887i | \(0.0165241\pi\) |
−0.777428 | + | 0.628972i | \(0.783476\pi\) | |||||||
\(504\) | −4.32208 | + | 3.14018i | −0.192521 | + | 0.139875i | ||||
\(505\) | 45.9932 | 2.04667 | ||||||||
\(506\) | −5.84994 | + | 3.14657i | −0.260062 | + | 0.139882i | ||||
\(507\) | −8.72238 | −0.387375 | ||||||||
\(508\) | 29.3776 | − | 21.3441i | 1.30342 | − | 0.946991i | ||||
\(509\) | 5.26089 | + | 16.1914i | 0.233185 | + | 0.717670i | 0.997357 | + | 0.0726571i | \(0.0231479\pi\) |
−0.764172 | + | 0.645013i | \(0.776852\pi\) | |||||||
\(510\) | 0.585128 | − | 1.80084i | 0.0259099 | − | 0.0797424i | ||||
\(511\) | 13.5068 | + | 9.81326i | 0.597506 | + | 0.434113i | ||||
\(512\) | 18.5330 | + | 13.4650i | 0.819052 | + | 0.595076i | ||||
\(513\) | −2.03036 | + | 6.24882i | −0.0896428 | + | 0.275892i | ||||
\(514\) | 1.83215 | + | 5.63878i | 0.0808127 | + | 0.248716i | ||||
\(515\) | −16.8469 | + | 12.2400i | −0.742363 | + | 0.539359i | ||||
\(516\) | 14.4672 | 0.636882 | ||||||||
\(517\) | −4.99788 | − | 27.5702i | −0.219807 | − | 1.21254i | ||||
\(518\) | −3.40946 | −0.149803 | ||||||||
\(519\) | 9.17581 | − | 6.66661i | 0.402773 | − | 0.292632i | ||||
\(520\) | 4.60484 | + | 14.1722i | 0.201936 | + | 0.621494i | ||||
\(521\) | 5.31526 | − | 16.3587i | 0.232866 | − | 0.716687i | −0.764532 | − | 0.644586i | \(-0.777030\pi\) |
0.997397 | − | 0.0721005i | \(-0.0229702\pi\) | |||||||
\(522\) | 0.968462 | + | 0.703629i | 0.0423884 | + | 0.0307970i | ||||
\(523\) | −25.7585 | − | 18.7146i | −1.12634 | − | 0.818333i | −0.141181 | − | 0.989984i | \(-0.545090\pi\) |
−0.985158 | + | 0.171651i | \(0.945090\pi\) | |||||||
\(524\) | 0.254667 | − | 0.783783i | 0.0111252 | − | 0.0342397i | ||||
\(525\) | 13.1616 | + | 40.5072i | 0.574419 | + | 1.76788i | ||||
\(526\) | −0.0650922 | + | 0.0472922i | −0.00283815 | + | 0.00206204i | ||||
\(527\) | 7.44040 | 0.324109 | ||||||||
\(528\) | 4.12937 | − | 8.57059i | 0.179708 | − | 0.372987i | ||||
\(529\) | −2.42237 | −0.105321 | ||||||||
\(530\) | −3.07448 | + | 2.23374i | −0.133547 | + | 0.0970276i | ||||
\(531\) | 3.21633 | + | 9.89884i | 0.139577 | + | 0.429573i | ||||
\(532\) | 11.6548 | − | 35.8697i | 0.505298 | − | 1.55515i | ||||
\(533\) | 8.56424 | + | 6.22229i | 0.370958 | + | 0.269517i | ||||
\(534\) | −2.87897 | − | 2.09169i | −0.124585 | − | 0.0905165i | ||||
\(535\) | −6.10632 | + | 18.7933i | −0.263999 | + | 0.812506i | ||||
\(536\) | 5.51558 | + | 16.9752i | 0.238237 | + | 0.733218i | ||||
\(537\) | 1.31293 | − | 0.953901i | 0.0566572 | − | 0.0411639i | ||||
\(538\) | 8.74810 | 0.377157 | ||||||||
\(539\) | −7.46073 | − | 7.13588i | −0.321356 | − | 0.307364i | ||||
\(540\) | 7.74151 | 0.333142 | ||||||||
\(541\) | −28.8389 | + | 20.9527i | −1.23988 | + | 0.900827i | −0.997591 | − | 0.0693759i | \(-0.977899\pi\) |
−0.242292 | + | 0.970203i | \(0.577899\pi\) | |||||||
\(542\) | 1.75700 | + | 5.40748i | 0.0754695 | + | 0.232271i | ||||
\(543\) | −3.85202 | + | 11.8553i | −0.165306 | + | 0.508760i | ||||
\(544\) | 3.74280 | + | 2.71931i | 0.160471 | + | 0.116589i | ||||
\(545\) | −4.49720 | − | 3.26741i | −0.192639 | − | 0.139960i | ||||
\(546\) | 0.897338 | − | 2.76172i | 0.0384025 | − | 0.118191i | ||||
\(547\) | −0.841658 | − | 2.59036i | −0.0359867 | − | 0.110756i | 0.931450 | − | 0.363870i | \(-0.118545\pi\) |
−0.967436 | + | 0.253115i | \(0.918545\pi\) | |||||||
\(548\) | 12.2275 | − | 8.88383i | 0.522335 | − | 0.379499i | ||||
\(549\) | 8.40722 | 0.358811 | ||||||||
\(550\) | 14.1730 | + | 13.5559i | 0.604338 | + | 0.578025i | ||||
\(551\) | −17.8147 | −0.758933 | ||||||||
\(552\) | 6.16532 | − | 4.47936i | 0.262413 | − | 0.190654i | ||||
\(553\) | 7.19377 | + | 22.1401i | 0.305910 | + | 0.941494i | ||||
\(554\) | 0.0952097 | − | 0.293025i | 0.00404507 | − | 0.0124495i | ||||
\(555\) | 8.42562 | + | 6.12157i | 0.357648 | + | 0.259846i | ||||
\(556\) | −16.4715 | − | 11.9672i | −0.698547 | − | 0.507524i | ||||
\(557\) | −4.53567 | + | 13.9594i | −0.192183 | + | 0.591478i | 0.807815 | + | 0.589436i | \(0.200650\pi\) |
−0.999998 | + | 0.00204172i | \(0.999350\pi\) | |||||||
\(558\) | −1.01512 | − | 3.12421i | −0.0429733 | − | 0.132258i | ||||
\(559\) | −13.4106 | + | 9.74337i | −0.567208 | + | 0.412100i | ||||
\(560\) | −39.1210 | −1.65317 | ||||||||
\(561\) | 1.43959 | − | 2.98790i | 0.0607797 | − | 0.126149i | ||||
\(562\) | −6.05923 | −0.255593 | ||||||||
\(563\) | 13.9872 | − | 10.1623i | 0.589489 | − | 0.428289i | −0.252643 | − | 0.967559i | \(-0.581300\pi\) |
0.842133 | + | 0.539270i | \(0.181300\pi\) | |||||||
\(564\) | 4.71240 | + | 14.5033i | 0.198428 | + | 0.610698i | ||||
\(565\) | 3.32943 | − | 10.2469i | 0.140070 | − | 0.431092i | ||||
\(566\) | 0.941889 | + | 0.684322i | 0.0395905 | + | 0.0287642i | ||||
\(567\) | −2.57272 | − | 1.86919i | −0.108044 | − | 0.0784987i | ||||
\(568\) | −6.16183 | + | 18.9642i | −0.258544 | + | 0.795718i | ||||
\(569\) | 10.8888 | + | 33.5121i | 0.456480 | + | 1.40490i | 0.869388 | + | 0.494129i | \(0.164513\pi\) |
−0.412908 | + | 0.910773i | \(0.635487\pi\) | |||||||
\(570\) | 10.0651 | − | 7.31271i | 0.421580 | − | 0.306296i | ||||
\(571\) | −15.1074 | −0.632226 | −0.316113 | − | 0.948722i | \(-0.602378\pi\) | ||||
−0.316113 | + | 0.948722i | \(0.602378\pi\) | |||||||
\(572\) | 2.20860 | + | 12.1835i | 0.0923461 | + | 0.509416i | ||||
\(573\) | 6.62882 | 0.276923 | ||||||||
\(574\) | 5.81380 | − | 4.22397i | 0.242663 | − | 0.176305i | ||||
\(575\) | −18.7746 | − | 57.7823i | −0.782956 | − | 2.40969i | ||||
\(576\) | −1.14160 | + | 3.51348i | −0.0475666 | + | 0.146395i | ||||
\(577\) | −6.90594 | − | 5.01746i | −0.287498 | − | 0.208880i | 0.434683 | − | 0.900583i | \(-0.356860\pi\) |
−0.722181 | + | 0.691704i | \(0.756860\pi\) | |||||||
\(578\) | 0.357186 | + | 0.259511i | 0.0148570 | + | 0.0107942i | ||||
\(579\) | 5.22695 | − | 16.0869i | 0.217225 | − | 0.668548i | ||||
\(580\) | 6.48628 | + | 19.9627i | 0.269328 | + | 0.828906i | ||||
\(581\) | −19.5980 | + | 14.2388i | −0.813062 | + | 0.590724i | ||||
\(582\) | 0.408213 | 0.0169210 | ||||||||
\(583\) | −5.86223 | + | 3.15318i | −0.242789 | + | 0.130591i | ||||
\(584\) | −8.81982 | −0.364967 | ||||||||
\(585\) | −7.17612 | + | 5.21376i | −0.296696 | + | 0.215562i | ||||
\(586\) | −0.0719172 | − | 0.221338i | −0.00297087 | − | 0.00914340i | ||||
\(587\) | 13.2935 | − | 40.9131i | 0.548680 | − | 1.68866i | −0.163395 | − | 0.986561i | \(-0.552244\pi\) |
0.712075 | − | 0.702104i | \(-0.247756\pi\) | |||||||
\(588\) | 4.54569 | + | 3.30264i | 0.187461 | + | 0.136199i | ||||
\(589\) | 39.5499 | + | 28.7347i | 1.62962 | + | 1.18399i | ||||
\(590\) | 6.09016 | − | 18.7436i | 0.250728 | − | 0.771661i | ||||
\(591\) | −0.622368 | − | 1.91545i | −0.0256008 | − | 0.0787912i | ||||
\(592\) | −5.63527 | + | 4.09426i | −0.231608 | + | 0.168273i | ||||
\(593\) | 21.3278 | 0.875830 | 0.437915 | − | 0.899016i | \(-0.355717\pi\) | ||||
0.437915 | + | 0.899016i | \(0.355717\pi\) | |||||||
\(594\) | −1.45102 | − | 0.196833i | −0.0595362 | − | 0.00807617i | ||||
\(595\) | −13.6385 | −0.559124 | ||||||||
\(596\) | −32.9929 | + | 23.9708i | −1.35144 | + | 0.981881i | ||||
\(597\) | 1.70061 | + | 5.23393i | 0.0696012 | + | 0.214211i | ||||
\(598\) | −1.28002 | + | 3.93951i | −0.0523441 | + | 0.161099i | ||||
\(599\) | 29.8852 | + | 21.7129i | 1.22108 | + | 0.887165i | 0.996189 | − | 0.0872198i | \(-0.0277983\pi\) |
0.224888 | + | 0.974385i | \(0.427798\pi\) | |||||||
\(600\) | −18.2032 | − | 13.2254i | −0.743144 | − | 0.539926i | ||||
\(601\) | 10.7085 | − | 32.9572i | 0.436807 | − | 1.34435i | −0.454416 | − | 0.890789i | \(-0.650152\pi\) |
0.891223 | − | 0.453565i | \(-0.149848\pi\) | |||||||
\(602\) | 3.47731 | + | 10.7021i | 0.141725 | + | 0.436184i | ||||
\(603\) | −8.59541 | + | 6.24493i | −0.350032 | + | 0.254313i | ||||
\(604\) | −24.3339 | −0.990132 | ||||||||
\(605\) | 29.4000 | + | 36.8950i | 1.19528 | + | 1.50000i | ||||
\(606\) | 4.73478 | 0.192337 | ||||||||
\(607\) | 15.6038 | − | 11.3368i | 0.633340 | − | 0.460148i | −0.224216 | − | 0.974540i | \(-0.571982\pi\) |
0.857556 | + | 0.514391i | \(0.171982\pi\) | |||||||
\(608\) | 9.39319 | + | 28.9093i | 0.380944 | + | 1.17243i | ||||
\(609\) | 2.66444 | − | 8.20029i | 0.107968 | − | 0.332292i | ||||
\(610\) | −12.8789 | − | 9.35706i | −0.521451 | − | 0.378856i | ||||
\(611\) | −14.1359 | − | 10.2703i | −0.571878 | − | 0.415494i | ||||
\(612\) | −0.557798 | + | 1.71673i | −0.0225476 | + | 0.0693945i | ||||
\(613\) | 0.551225 | + | 1.69650i | 0.0222638 | + | 0.0685208i | 0.961571 | − | 0.274556i | \(-0.0885309\pi\) |
−0.939307 | + | 0.343077i | \(0.888531\pi\) | |||||||
\(614\) | 5.19356 | − | 3.77334i | 0.209595 | − | 0.152280i | ||||
\(615\) | −21.9514 | −0.885164 | ||||||||
\(616\) | 17.5579 | + | 2.38175i | 0.707427 | + | 0.0959635i | ||||
\(617\) | 25.0626 | 1.00898 | 0.504492 | − | 0.863417i | \(-0.331680\pi\) | ||||
0.504492 | + | 0.863417i | \(0.331680\pi\) | |||||||
\(618\) | −1.73431 | + | 1.26005i | −0.0697641 | + | 0.0506866i | ||||
\(619\) | −10.2664 | − | 31.5968i | −0.412642 | − | 1.26998i | −0.914343 | − | 0.404941i | \(-0.867292\pi\) |
0.501701 | − | 0.865041i | \(-0.332708\pi\) | |||||||
\(620\) | 17.7993 | − | 54.7808i | 0.714839 | − | 2.20005i | ||||
\(621\) | 3.66991 | + | 2.66634i | 0.147268 | + | 0.106997i | ||||
\(622\) | −12.1971 | − | 8.86171i | −0.489059 | − | 0.355322i | ||||
\(623\) | −7.92063 | + | 24.3772i | −0.317333 | + | 0.976652i | ||||
\(624\) | −1.83327 | − | 5.64224i | −0.0733897 | − | 0.225870i | ||||
\(625\) | −70.7213 | + | 51.3821i | −2.82885 | + | 2.05528i | ||||
\(626\) | 10.5622 | 0.422150 | ||||||||
\(627\) | 19.1915 | − | 10.3227i | 0.766434 | − | 0.412249i | ||||
\(628\) | −32.3465 | −1.29077 | ||||||||
\(629\) | −1.96458 | + | 1.42735i | −0.0783331 | + | 0.0569123i | ||||
\(630\) | 1.86074 | + | 5.72677i | 0.0741337 | + | 0.228160i | ||||
\(631\) | −2.44085 | + | 7.51217i | −0.0971688 | + | 0.299055i | −0.987813 | − | 0.155646i | \(-0.950254\pi\) |
0.890644 | + | 0.454701i | \(0.150254\pi\) | |||||||
\(632\) | −9.94939 | − | 7.22865i | −0.395765 | − | 0.287540i | ||||
\(633\) | 15.3598 | + | 11.1595i | 0.610497 | + | 0.443552i | ||||
\(634\) | −0.518629 | + | 1.59617i | −0.0205974 | + | 0.0633922i | ||||
\(635\) | −26.6611 | − | 82.0544i | −1.05801 | − | 3.25623i | ||||
\(636\) | 2.93088 | − | 2.12941i | 0.116217 | − | 0.0844366i | ||||
\(637\) | −6.43797 | −0.255082 | ||||||||
\(638\) | −0.708183 | − | 3.90661i | −0.0280373 | − | 0.154664i | ||||
\(639\) | −11.8694 | −0.469544 | ||||||||
\(640\) | 37.7631 | − | 27.4365i | 1.49272 | − | 1.08452i | ||||
\(641\) | 9.92905 | + | 30.5585i | 0.392174 | + | 1.20699i | 0.931141 | + | 0.364660i | \(0.118815\pi\) |
−0.538967 | + | 0.842327i | \(0.681185\pi\) | |||||||
\(642\) | −0.628616 | + | 1.93468i | −0.0248095 | + | 0.0763558i | ||||
\(643\) | −21.8208 | − | 15.8537i | −0.860528 | − | 0.625210i | 0.0675003 | − | 0.997719i | \(-0.478498\pi\) |
−0.928029 | + | 0.372509i | \(0.878498\pi\) | |||||||
\(644\) | −21.0661 | − | 15.3054i | −0.830122 | − | 0.603119i | ||||
\(645\) | 10.6219 | − | 32.6909i | 0.418237 | − | 1.28720i | ||||
\(646\) | 0.896419 | + | 2.75889i | 0.0352691 | + | 0.108547i | ||||
\(647\) | −6.38659 | + | 4.64013i | −0.251083 | + | 0.182422i | −0.706207 | − | 0.708006i | \(-0.749595\pi\) |
0.455124 | + | 0.890428i | \(0.349595\pi\) | |||||||
\(648\) | 1.67996 | 0.0659952 | ||||||||
\(649\) | 14.9837 | − | 31.0989i | 0.588160 | − | 1.22074i | ||||
\(650\) | 12.2301 | 0.479703 | ||||||||
\(651\) | −19.1421 | + | 13.9075i | −0.750237 | + | 0.545079i | ||||
\(652\) | 12.2449 | + | 37.6858i | 0.479546 | + | 1.47589i | ||||
\(653\) | 6.14662 | − | 18.9173i | 0.240536 | − | 0.740293i | −0.755803 | − | 0.654799i | \(-0.772753\pi\) |
0.996339 | − | 0.0854938i | \(-0.0272468\pi\) | |||||||
\(654\) | −0.462965 | − | 0.336364i | −0.0181034 | − | 0.0131529i | ||||
\(655\) | −1.58410 | − | 1.15092i | −0.0618961 | − | 0.0449701i | ||||
\(656\) | 4.53687 | − | 13.9631i | 0.177135 | − | 0.545166i | ||||
\(657\) | −1.62234 | − | 4.99305i | −0.0632935 | − | 0.194797i | ||||
\(658\) | −9.59611 | + | 6.97198i | −0.374095 | + | 0.271796i | ||||
\(659\) | 49.0773 | 1.91178 | 0.955889 | − | 0.293727i | \(-0.0948956\pi\) | ||||
0.955889 | + | 0.293727i | \(0.0948956\pi\) | |||||||
\(660\) | −18.5549 | − | 17.7470i | −0.722249 | − | 0.690801i | ||||
\(661\) | −3.13401 | −0.121899 | −0.0609495 | − | 0.998141i | \(-0.519413\pi\) | ||||
−0.0609495 | + | 0.998141i | \(0.519413\pi\) | |||||||
\(662\) | −6.85591 | + | 4.98111i | −0.266462 | + | 0.193596i | ||||
\(663\) | −0.639122 | − | 1.96701i | −0.0248214 | − | 0.0763925i | ||||
\(664\) | 3.95459 | − | 12.1710i | 0.153468 | − | 0.472325i | ||||
\(665\) | −72.4962 | − | 52.6716i | −2.81128 | − | 2.04252i | ||||
\(666\) | 0.867377 | + | 0.630186i | 0.0336102 | + | 0.0244192i | ||||
\(667\) | −3.80073 | + | 11.6975i | −0.147165 | + | 0.452927i | ||||
\(668\) | 7.71209 | + | 23.7354i | 0.298390 | + | 0.918349i | ||||
\(669\) | −9.17597 | + | 6.66673i | −0.354764 | + | 0.257751i | ||||
\(670\) | 20.1177 | 0.777213 | ||||||||
\(671\) | −20.1505 | − | 19.2731i | −0.777901 | − | 0.744030i | ||||
\(672\) | −14.7121 | −0.567531 | ||||||||
\(673\) | 24.2610 | − | 17.6266i | 0.935191 | − | 0.679456i | −0.0120670 | − | 0.999927i | \(-0.503841\pi\) |
0.947258 | + | 0.320471i | \(0.103841\pi\) | |||||||
\(674\) | −0.421570 | − | 1.29746i | −0.0162383 | − | 0.0499762i | ||||
\(675\) | 4.13879 | − | 12.7379i | 0.159302 | − | 0.490282i | ||||
\(676\) | −12.7376 | − | 9.25440i | −0.489907 | − | 0.355938i | ||||
\(677\) | 20.6970 | + | 15.0372i | 0.795450 | + | 0.577928i | 0.909576 | − | 0.415538i | \(-0.136407\pi\) |
−0.114126 | + | 0.993466i | \(0.536407\pi\) | |||||||
\(678\) | 0.342749 | − | 1.05487i | 0.0131632 | − | 0.0405121i | ||||
\(679\) | −0.908588 | − | 2.79635i | −0.0348684 | − | 0.107314i | ||||
\(680\) | 5.82893 | − | 4.23497i | 0.223529 | − | 0.162404i | ||||
\(681\) | −19.9667 | −0.765126 | ||||||||
\(682\) | −4.72904 | + | 9.81522i | −0.181084 | + | 0.375844i | ||||
\(683\) | 15.9574 | 0.610591 | 0.305296 | − | 0.952258i | \(-0.401245\pi\) | ||||
0.305296 | + | 0.952258i | \(0.401245\pi\) | |||||||
\(684\) | −9.59497 | + | 6.97115i | −0.366873 | + | 0.266549i | ||||
\(685\) | −11.0969 | − | 34.1527i | −0.423990 | − | 1.30491i | ||||
\(686\) | 1.68653 | − | 5.19061i | 0.0643920 | − | 0.198178i | ||||
\(687\) | 0.899451 | + | 0.653490i | 0.0343162 | + | 0.0249322i | ||||
\(688\) | 18.5991 | + | 13.5130i | 0.709082 | + | 0.515179i | ||||
\(689\) | −1.28271 | + | 3.94779i | −0.0488675 | + | 0.150399i | ||||
\(690\) | −2.65429 | − | 8.16906i | −0.101047 | − | 0.310991i | ||||
\(691\) | −6.18079 | + | 4.49061i | −0.235128 | + | 0.170831i | −0.699110 | − | 0.715014i | \(-0.746420\pi\) |
0.463982 | + | 0.885845i | \(0.346420\pi\) | |||||||
\(692\) | 20.4730 | 0.778266 | ||||||||
\(693\) | 1.88129 | + | 10.3779i | 0.0714644 | + | 0.394225i | ||||
\(694\) | 10.4412 | 0.396343 | ||||||||
\(695\) | −39.1354 | + | 28.4335i | −1.48449 | + | 1.07854i | ||||
\(696\) | 1.40757 | + | 4.33205i | 0.0533538 | + | 0.164206i | ||||
\(697\) | 1.58166 | − | 4.86784i | 0.0599096 | − | 0.184383i | ||||
\(698\) | −0.107229 | − | 0.0779064i | −0.00405867 | − | 0.00294880i | ||||
\(699\) | 10.6592 | + | 7.74436i | 0.403168 | + | 0.292919i | ||||
\(700\) | −23.7576 | + | 73.1185i | −0.897954 | + | 2.76362i | ||||
\(701\) | −12.9051 | − | 39.7177i | −0.487417 | − | 1.50012i | −0.828449 | − | 0.560064i | \(-0.810777\pi\) |
0.341032 | − | 0.940052i | \(-0.389223\pi\) | |||||||
\(702\) | −0.738747 | + | 0.536731i | −0.0278822 | + | 0.0202576i | ||||
\(703\) | −15.9553 | −0.601765 | ||||||||
\(704\) | 10.7907 | − | 5.80407i | 0.406688 | − | 0.218749i | ||||
\(705\) | 36.2323 | 1.36459 | ||||||||
\(706\) | −8.83124 | + | 6.41627i | −0.332368 | + | 0.241480i | ||||
\(707\) | −10.5385 | − | 32.4342i | −0.396342 | − | 1.21982i | ||||
\(708\) | −5.80570 | + | 17.8681i | −0.218192 | + | 0.671525i | ||||
\(709\) | −21.7361 | − | 15.7922i | −0.816315 | − | 0.593087i | 0.0993398 | − | 0.995054i | \(-0.468327\pi\) |
−0.915654 | + | 0.401966i | \(0.868327\pi\) | |||||||
\(710\) | 18.1825 | + | 13.2103i | 0.682376 | + | 0.495775i | ||||
\(711\) | 2.26215 | − | 6.96218i | 0.0848372 | − | 0.261102i | ||||
\(712\) | −4.18432 | − | 12.8780i | −0.156814 | − | 0.482624i | ||||
\(713\) | 27.3056 | − | 19.8387i | 1.02260 | − | 0.742964i | ||||
\(714\) | −1.40402 | −0.0525440 | ||||||||
\(715\) | 29.1520 | + | 3.95452i | 1.09022 | + | 0.147891i | ||||
\(716\) | 2.92940 | 0.109477 | ||||||||
\(717\) | −9.41318 | + | 6.83908i | −0.351542 | + | 0.255410i | ||||
\(718\) | 4.43167 | + | 13.6393i | 0.165389 | + | 0.509013i | ||||
\(719\) | −0.0678450 | + | 0.208805i | −0.00253019 | + | 0.00778712i | −0.952314 | − | 0.305121i | \(-0.901303\pi\) |
0.949783 | + | 0.312908i | \(0.101303\pi\) | |||||||
\(720\) | 9.95251 | + | 7.23092i | 0.370908 | + | 0.269481i | ||||
\(721\) | 12.4918 | + | 9.07581i | 0.465218 | + | 0.338001i | ||||
\(722\) | −3.29760 | + | 10.1490i | −0.122724 | + | 0.377706i | ||||
\(723\) | −0.0784994 | − | 0.241596i | −0.00291942 | − | 0.00898507i | ||||
\(724\) | −18.2037 | + | 13.2257i | −0.676533 | + | 0.491530i | ||||
\(725\) | 36.3144 | 1.34868 | ||||||||
\(726\) | 3.02659 | + | 3.79816i | 0.112327 | + | 0.140963i | ||||
\(727\) | −24.0985 | −0.893763 | −0.446881 | − | 0.894593i | \(-0.647465\pi\) | ||||
−0.446881 | + | 0.894593i | \(0.647465\pi\) | |||||||
\(728\) | 8.93910 | − | 6.49464i | 0.331305 | − | 0.240707i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −3.07192 | + | 9.45440i | −0.113697 | + | 0.349923i | ||||
\(731\) | 6.48406 | + | 4.71094i | 0.239822 | + | 0.174241i | ||||
\(732\) | 12.2773 | + | 8.92001i | 0.453784 | + | 0.329693i | ||||
\(733\) | 10.9067 | − | 33.5675i | 0.402850 | − | 1.23984i | −0.519827 | − | 0.854271i | \(-0.674004\pi\) |
0.922677 | − | 0.385573i | \(-0.125996\pi\) | |||||||
\(734\) | 1.34148 | + | 4.12864i | 0.0495148 | + | 0.152391i | ||||
\(735\) | 10.8003 | − | 7.84690i | 0.398376 | − | 0.289437i | ||||
\(736\) | 20.9864 | 0.773567 | ||||||||
\(737\) | 34.9177 | + | 4.73664i | 1.28621 | + | 0.174476i | ||||
\(738\) | −2.25979 | −0.0831839 | ||||||||
\(739\) | −29.4310 | + | 21.3829i | −1.08264 | + | 0.786581i | −0.978141 | − | 0.207944i | \(-0.933323\pi\) |
−0.104495 | + | 0.994525i | \(0.533323\pi\) | |||||||
\(740\) | 5.80926 | + | 17.8791i | 0.213553 | + | 0.657248i | ||||
\(741\) | 4.19928 | − | 12.9241i | 0.154264 | − | 0.474777i | ||||
\(742\) | 2.27969 | + | 1.65629i | 0.0836901 | + | 0.0608044i | ||||
\(743\) | −7.64496 | − | 5.55439i | −0.280466 | − | 0.203771i | 0.438654 | − | 0.898656i | \(-0.355455\pi\) |
−0.719121 | + | 0.694885i | \(0.755455\pi\) | |||||||
\(744\) | 3.86259 | − | 11.8878i | 0.141609 | − | 0.435829i | ||||
\(745\) | 29.9421 | + | 92.1523i | 1.09699 | + | 3.37620i | ||||
\(746\) | −9.04326 | + | 6.57032i | −0.331097 | + | 0.240556i | ||||
\(747\) | 7.61761 | 0.278714 | ||||||||
\(748\) | 5.27244 | − | 2.83594i | 0.192779 | − | 0.103692i | ||||
\(749\) | 14.6521 | 0.535378 | ||||||||
\(750\) | −12.8577 | + | 9.34169i | −0.469498 | + | 0.341110i | ||||
\(751\) | 11.9227 | + | 36.6943i | 0.435066 | + | 1.33899i | 0.893019 | + | 0.450019i | \(0.148583\pi\) |
−0.457953 | + | 0.888976i | \(0.651417\pi\) | |||||||
\(752\) | −7.48844 | + | 23.0471i | −0.273075 | + | 0.840440i | ||||
\(753\) | 12.2809 | + | 8.92257i | 0.447539 | + | 0.325156i | ||||
\(754\) | −2.00301 | − | 1.45527i | −0.0729454 | − | 0.0529979i | ||||
\(755\) | −17.8661 | + | 54.9863i | −0.650215 | + | 2.00116i | ||||
\(756\) | −1.77383 | − | 5.45929i | −0.0645136 | − | 0.198552i | ||||
\(757\) | 33.4612 | − | 24.3110i | 1.21617 | − | 0.883598i | 0.220392 | − | 0.975411i | \(-0.429266\pi\) |
0.995776 | + | 0.0918136i | \(0.0292664\pi\) | |||||||
\(758\) | −4.79865 | −0.174295 | ||||||||
\(759\) | −2.68361 | − | 14.8038i | −0.0974087 | − | 0.537343i | ||||
\(760\) | 47.3394 | 1.71718 | ||||||||
\(761\) | −11.1758 | + | 8.11972i | −0.405124 | + | 0.294340i | −0.771625 | − | 0.636078i | \(-0.780556\pi\) |
0.366501 | + | 0.930418i | \(0.380556\pi\) | |||||||
\(762\) | −2.74463 | − | 8.44710i | −0.0994275 | − | 0.306006i | ||||
\(763\) | −1.27371 | + | 3.92008i | −0.0461114 | + | 0.141916i | ||||
\(764\) | 9.68029 | + | 7.03314i | 0.350221 | + | 0.254450i | ||||
\(765\) | 3.46967 | + | 2.52087i | 0.125446 | + | 0.0911421i | ||||
\(766\) | 3.97434 | − | 12.2318i | 0.143599 | − | 0.441952i | ||||
\(767\) | −6.65214 | − | 20.4732i | −0.240195 | − | 0.739244i | ||||
\(768\) | −2.08995 | + | 1.51844i | −0.0754146 | + | 0.0547919i | ||||
\(769\) | −43.8890 | −1.58268 | −0.791338 | − | 0.611379i | \(-0.790615\pi\) | ||||
−0.791338 | + | 0.611379i | \(0.790615\pi\) | |||||||
\(770\) | 8.66849 | − | 17.9916i | 0.312391 | − | 0.648373i | ||||
\(771\) | −13.4289 | −0.483631 | ||||||||
\(772\) | 24.7012 | − | 17.9465i | 0.889015 | − | 0.645907i | ||||
\(773\) | −8.06867 | − | 24.8328i | −0.290210 | − | 0.893174i | −0.984788 | − | 0.173758i | \(-0.944409\pi\) |
0.694578 | − | 0.719417i | \(-0.255591\pi\) | |||||||
\(774\) | 1.09347 | − | 3.36537i | 0.0393041 | − | 0.120966i | ||||
\(775\) | −80.6204 | − | 58.5741i | −2.89597 | − | 2.10405i | ||||
\(776\) | 1.25663 | + | 0.912995i | 0.0451104 | + | 0.0327746i | ||||
\(777\) | 2.38633 | − | 7.34437i | 0.0856091 | − | 0.263478i | ||||
\(778\) | 3.96780 | + | 12.2116i | 0.142252 | + | 0.437808i | ||||
\(779\) | 27.2069 | − | 19.7670i | 0.974789 | − | 0.708226i | ||||
\(780\) | −16.0113 | −0.573297 | ||||||||
\(781\) | 28.4485 | + | 27.2099i | 1.01797 | + | 0.973646i | ||||
\(782\) | 2.00279 | 0.0716195 | ||||||||
\(783\) | −2.19354 | + | 1.59370i | −0.0783907 | + | 0.0569542i | ||||
\(784\) | 2.75914 | + | 8.49178i | 0.0985409 | + | 0.303278i | ||||
\(785\) | −23.7491 | + | 73.0921i | −0.847640 | + | 2.60877i | ||||
\(786\) | −0.163076 | − | 0.118482i | −0.00581673 | − | 0.00422610i | ||||
\(787\) | −4.55737 | − | 3.31112i | −0.162453 | − | 0.118029i | 0.503589 | − | 0.863943i | \(-0.332013\pi\) |
−0.666042 | + | 0.745915i | \(0.732013\pi\) | |||||||
\(788\) | 1.12342 | − | 3.45753i | 0.0400202 | − | 0.123169i | ||||
\(789\) | −0.0563140 | − | 0.173317i | −0.00200483 | − | 0.00617023i | ||||
\(790\) | −11.2141 | + | 8.14753i | −0.398980 | + | 0.289876i | ||||
\(791\) | −7.98898 | −0.284056 | ||||||||
\(792\) | −4.02655 | − | 3.85123i | −0.143077 | − | 0.136848i | ||||
\(793\) | −17.3882 | −0.617471 | ||||||||
\(794\) | −3.62036 | + | 2.63034i | −0.128482 | + | 0.0933474i | ||||
\(795\) | −2.65987 | − | 8.18622i | −0.0943357 | − | 0.290335i | ||||
\(796\) | −3.06972 | + | 9.44762i | −0.108803 | + | 0.334862i | ||||
\(797\) | −11.8900 | − | 8.63858i | −0.421165 | − | 0.305994i | 0.356942 | − | 0.934127i | \(-0.383820\pi\) |
−0.778106 | + | 0.628133i | \(0.783820\pi\) | |||||||
\(798\) | −7.46314 | − | 5.42229i | −0.264192 | − | 0.191947i | ||||
\(799\) | −2.61064 | + | 8.03474i | −0.0923579 | + | 0.284248i | ||||
\(800\) | −19.1475 | − | 58.9300i | −0.676968 | − | 2.08349i | ||||
\(801\) | 6.52079 | − | 4.73763i | 0.230401 | − | 0.167396i | ||||
\(802\) | −5.22119 | −0.184366 | ||||||||
\(803\) | −7.55787 | + | 15.6865i | −0.266711 | + | 0.553565i | ||||
\(804\) | −19.1780 | −0.676356 | ||||||||
\(805\) | −50.0520 | + | 36.3649i | −1.76410 | + | 1.28170i | ||||
\(806\) | 2.09950 | + | 6.46161i | 0.0739519 | + | 0.227600i | ||||
\(807\) | −6.12292 | + | 18.8444i | −0.215537 | + | 0.663355i | ||||
\(808\) | 14.5754 | + | 10.5896i | 0.512760 | + | 0.372542i | ||||
\(809\) | 16.5239 | + | 12.0053i | 0.580950 | + | 0.422085i | 0.839066 | − | 0.544029i | \(-0.183102\pi\) |
−0.258117 | + | 0.966114i | \(0.583102\pi\) | |||||||
\(810\) | 0.585128 | − | 1.80084i | 0.0205593 | − | 0.0632750i | ||||
\(811\) | 12.1713 | + | 37.4596i | 0.427394 | + | 1.31538i | 0.900683 | + | 0.434476i | \(0.143066\pi\) |
−0.473290 | + | 0.880907i | \(0.656934\pi\) | |||||||
\(812\) | 12.5914 | − | 9.14821i | 0.441872 | − | 0.321039i | ||||
\(813\) | −12.8781 | −0.451654 | ||||||||
\(814\) | −0.634266 | − | 3.49885i | −0.0222310 | − | 0.122635i | ||||
\(815\) | 94.1473 | 3.29784 | ||||||||
\(816\) | −2.32061 | + | 1.68602i | −0.0812375 | + | 0.0590225i | ||||
\(817\) | 16.2728 | + | 50.0826i | 0.569314 | + | 1.75217i | ||||
\(818\) | −2.77321 | + | 8.53508i | −0.0969632 | + | 0.298422i | ||||
\(819\) | 5.32101 | + | 3.86594i | 0.185931 | + | 0.135087i | ||||
\(820\) | −32.0563 | − | 23.2903i | −1.11945 | − | 0.813331i | ||||
\(821\) | 7.42083 | − | 22.8390i | 0.258989 | − | 0.797085i | −0.734029 | − | 0.679118i | \(-0.762362\pi\) |
0.993018 | − | 0.117967i | \(-0.0376377\pi\) | |||||||
\(822\) | −1.14237 | − | 3.51585i | −0.0398447 | − | 0.122629i | ||||
\(823\) | −39.4087 | + | 28.6321i | −1.37370 | + | 0.998051i | −0.376262 | + | 0.926513i | \(0.622791\pi\) |
−0.997438 | + | 0.0715377i | \(0.977209\pi\) | |||||||
\(824\) | −8.15702 | −0.284163 | ||||||||
\(825\) | −39.1208 | + | 21.0423i | −1.36201 | + | 0.732599i | ||||
\(826\) | −14.6134 | −0.508464 | ||||||||
\(827\) | 5.52723 | − | 4.01577i | 0.192201 | − | 0.139642i | −0.487523 | − | 0.873110i | \(-0.662100\pi\) |
0.679724 | + | 0.733468i | \(0.262100\pi\) | |||||||
\(828\) | 2.53031 | + | 7.78751i | 0.0879345 | + | 0.270635i | ||||
\(829\) | −13.3104 | + | 40.9651i | −0.462289 | + | 1.42278i | 0.400072 | + | 0.916484i | \(0.368985\pi\) |
−0.862361 | + | 0.506294i | \(0.831015\pi\) | |||||||
\(830\) | −11.6693 | − | 8.47824i | −0.405047 | − | 0.294284i | ||||
\(831\) | 0.564572 | + | 0.410185i | 0.0195848 | + | 0.0142292i | ||||
\(832\) | 2.36110 | − | 7.26672i | 0.0818564 | − | 0.251928i | ||||
\(833\) | 0.961901 | + | 2.96043i | 0.0333279 | + | 0.102573i | ||||
\(834\) | −4.02880 | + | 2.92709i | −0.139506 | + | 0.101357i | ||||
\(835\) | 59.2961 | 2.05203 | ||||||||
\(836\) | 38.9783 | + | 5.28746i | 1.34809 | + | 0.182871i | ||||
\(837\) | 7.44040 | 0.257178 | ||||||||
\(838\) | −2.94784 | + | 2.14173i | −0.101831 | + | 0.0739848i | ||||
\(839\) | 3.16552 | + | 9.74246i | 0.109286 | + | 0.336347i | 0.990712 | − | 0.135974i | \(-0.0434163\pi\) |
−0.881427 | + | 0.472321i | \(0.843416\pi\) | |||||||
\(840\) | −7.08025 | + | 21.7908i | −0.244292 | + | 0.751853i | ||||
\(841\) | 17.5140 | + | 12.7247i | 0.603932 | + | 0.438782i | ||||
\(842\) | −11.6372 | − | 8.45491i | −0.401044 | − | 0.291375i | ||||
\(843\) | 4.24095 | − | 13.0523i | 0.146066 | − | 0.449545i | ||||
\(844\) | 10.5902 | + | 32.5933i | 0.364530 | + | 1.12191i | ||||
\(845\) | −30.2638 | + | 21.9880i | −1.04111 | + | 0.756409i | ||||
\(846\) | 3.72995 | 0.128238 | ||||||||
\(847\) | 19.2818 | − | 29.1866i | 0.662529 | − | 1.00286i | ||||
\(848\) | 5.75692 | 0.197693 | ||||||||
\(849\) | −2.13335 | + | 1.54997i | −0.0732164 | + | 0.0531948i | ||||
\(850\) | −1.82730 | − | 5.62386i | −0.0626760 | − | 0.192897i | ||||
\(851\) | −3.40403 | + | 10.4765i | −0.116689 | + | 0.359130i | ||||
\(852\) | −17.3332 | − | 12.5933i | −0.593826 | − | 0.431440i | ||||
\(853\) | 34.8342 | + | 25.3085i | 1.19270 | + | 0.866548i | 0.993547 | − | 0.113421i | \(-0.0361807\pi\) |
0.199154 | + | 0.979968i | \(0.436181\pi\) | |||||||
\(854\) | −3.64760 | + | 11.2262i | −0.124818 | + | 0.384151i | ||||
\(855\) | 8.70773 | + | 26.7996i | 0.297798 | + | 0.916528i | ||||
\(856\) | −6.26215 | + | 4.54972i | −0.214036 | + | 0.155506i | ||||
\(857\) | 22.1856 | 0.757845 | 0.378923 | − | 0.925428i | \(-0.376295\pi\) | ||||
0.378923 | + | 0.925428i | \(0.376295\pi\) | |||||||
\(858\) | 3.00106 | + | 0.407098i | 0.102455 | + | 0.0138981i | ||||
\(859\) | 25.7259 | 0.877755 | 0.438878 | − | 0.898547i | \(-0.355376\pi\) | ||||
0.438878 | + | 0.898547i | \(0.355376\pi\) | |||||||
\(860\) | 50.1964 | − | 36.4698i | 1.71168 | − | 1.24361i | ||||
\(861\) | 5.02977 | + | 15.4800i | 0.171414 | + | 0.527558i | ||||
\(862\) | −2.20797 | + | 6.79544i | −0.0752038 | + | 0.231453i | ||||
\(863\) | 24.8273 | + | 18.0381i | 0.845132 | + | 0.614025i | 0.923800 | − | 0.382876i | \(-0.125066\pi\) |
−0.0786673 | + | 0.996901i | \(0.525066\pi\) | |||||||
\(864\) | 3.74280 | + | 2.71931i | 0.127333 | + | 0.0925127i | ||||
\(865\) | 15.0314 | − | 46.2620i | 0.511084 | − | 1.57295i | ||||
\(866\) | 0.731011 | + | 2.24982i | 0.0248407 | + | 0.0764520i | ||||
\(867\) | −0.809017 | + | 0.587785i | −0.0274757 | + | 0.0199622i | ||||
\(868\) | −42.7096 | −1.44966 | ||||||||
\(869\) | −21.3824 | + | 11.5011i | −0.725347 | + | 0.390149i | ||||
\(870\) | 5.13400 | 0.174059 | ||||||||
\(871\) | 17.7774 | − | 12.9160i | 0.602364 | − | 0.437643i | ||||
\(872\) | −0.672877 | − | 2.07090i | −0.0227865 | − | 0.0701296i | ||||
\(873\) | −0.285714 | + | 0.879338i | −0.00966996 | + | 0.0297611i | ||||
\(874\) | 10.6459 | + | 7.73473i | 0.360104 | + | 0.261631i | ||||
\(875\) | 92.6110 | + | 67.2858i | 3.13082 | + | 2.27468i | ||||
\(876\) | 2.92844 | − | 9.01281i | 0.0989428 | − | 0.304515i | ||||
\(877\) | −6.90913 | − | 21.2641i | −0.233305 | − | 0.718038i | −0.997342 | − | 0.0728657i | \(-0.976786\pi\) |
0.764037 | − | 0.645172i | \(-0.223214\pi\) | |||||||
\(878\) | −5.30295 | + | 3.85282i | −0.178966 | + | 0.130026i | ||||
\(879\) | 0.527124 | 0.0177795 | ||||||||
\(880\) | −7.27773 | − | 40.1468i | −0.245332 | − | 1.35335i | ||||
\(881\) | −4.38917 | −0.147875 | −0.0739374 | − | 0.997263i | \(-0.523557\pi\) | ||||
−0.0739374 | + | 0.997263i | \(0.523557\pi\) | |||||||
\(882\) | 1.11184 | − | 0.807800i | 0.0374377 | − | 0.0272000i | ||||
\(883\) | 8.46668 | + | 26.0578i | 0.284926 | + | 0.876914i | 0.986421 | + | 0.164238i | \(0.0525166\pi\) |
−0.701494 | + | 0.712675i | \(0.747483\pi\) | |||||||
\(884\) | 1.15366 | − | 3.55060i | 0.0388018 | − | 0.119420i | ||||
\(885\) | 36.1133 | + | 26.2378i | 1.21393 | + | 0.881975i | ||||
\(886\) | 3.29540 | + | 2.39425i | 0.110711 | + | 0.0804364i | ||||
\(887\) | 13.3794 | − | 41.1775i | 0.449236 | − | 1.38261i | −0.428535 | − | 0.903525i | \(-0.640970\pi\) |
0.877771 | − | 0.479080i | \(-0.159030\pi\) | |||||||
\(888\) | 1.26065 | + | 3.87989i | 0.0423047 | + | 0.130201i | ||||
\(889\) | −51.7556 | + | 37.6026i | −1.73583 | + | 1.26115i | ||||
\(890\) | −15.2620 | −0.511582 | ||||||||
\(891\) | 1.43959 | − | 2.98790i | 0.0482282 | − | 0.100099i | ||||
\(892\) | −20.4734 | −0.685499 | ||||||||
\(893\) | −44.9070 | + | 32.6269i | −1.50276 | + | 1.09182i | ||||
\(894\) | 3.08239 | + | 9.48664i | 0.103091 | + | 0.317281i | ||||
\(895\) | 2.15079 | − | 6.61946i | 0.0718930 | − | 0.221264i | ||||
\(896\) | −28.0009 | − | 20.3439i | −0.935445 | − | 0.679641i | ||||
\(897\) | −7.59026 | − | 5.51464i | −0.253431 | − | 0.184129i | ||||
\(898\) | 0.129068 | − | 0.397231i | 0.00430706 | − | 0.0132558i | ||||
\(899\) | 6.23399 | + | 19.1862i | 0.207915 | + | 0.639897i | ||||
\(900\) | 19.5589 | − | 14.2103i | 0.651962 | − | 0.473678i | ||||
\(901\) | 2.00699 | 0.0668627 | ||||||||
\(902\) | 5.41627 | + | 5.18044i | 0.180342 | + | 0.172490i | ||||
\(903\) | −25.4873 | −0.848165 | ||||||||
\(904\) | 3.41440 | − | 2.48070i | 0.113561 | − | 0.0825070i | ||||
\(905\) | 16.5204 | + | 50.8445i | 0.549156 | + | 1.69013i | ||||
\(906\) | −1.83923 | + | 5.66057i | −0.0611044 | + | 0.188060i | ||||
\(907\) | 0.409591 | + | 0.297585i | 0.0136002 | + | 0.00988116i | 0.594565 | − | 0.804048i | \(-0.297324\pi\) |
−0.580964 | + | 0.813929i | \(0.697324\pi\) | |||||||
\(908\) | −29.1581 | − | 21.1846i | −0.967645 | − | 0.703035i | ||||
\(909\) | −3.31394 | + | 10.1993i | −0.109916 | + | 0.338288i | ||||
\(910\) | −3.84846 | − | 11.8443i | −0.127575 | − | 0.392636i | ||||
\(911\) | 42.0227 | − | 30.5313i | 1.39227 | − | 1.01155i | 0.396662 | − | 0.917965i | \(-0.370169\pi\) |
0.995612 | − | 0.0935812i | \(-0.0298315\pi\) | |||||||
\(912\) | −18.8467 | −0.624077 | ||||||||
\(913\) | −18.2579 | − | 17.4630i | −0.604250 | − | 0.577940i | ||||
\(914\) | 6.04221 | 0.199859 | ||||||||
\(915\) | 29.1703 | − | 21.1935i | 0.964341 | − | 0.700635i | ||||
\(916\) | 0.620150 | + | 1.90863i | 0.0204903 | + | 0.0630628i | ||||
\(917\) | −0.448655 | + | 1.38082i | −0.0148159 | + | 0.0455986i | ||||
\(918\) | 0.357186 | + | 0.259511i | 0.0117889 | + | 0.00856514i | ||||
\(919\) | −48.0239 | − | 34.8914i | −1.58416 | − | 1.15096i | −0.911720 | − | 0.410813i | \(-0.865245\pi\) |
−0.672443 | − | 0.740149i | \(-0.734755\pi\) | |||||||
\(920\) | 10.0998 | − | 31.0839i | 0.332979 | − | 1.02481i | ||||
\(921\) | 4.49317 | + | 13.8286i | 0.148055 | + | 0.455666i | ||||
\(922\) | −7.73045 | + | 5.61650i | −0.254589 | + | 0.184970i | ||||
\(923\) | 24.5487 | 0.808030 | ||||||||
\(924\) | −8.26361 | + | 17.1513i | −0.271853 | + | 0.564235i | ||||
\(925\) | 32.5240 | 1.06938 | ||||||||
\(926\) | −2.81143 | + | 2.04263i | −0.0923895 | + | 0.0671249i | ||||
\(927\) | −1.50042 | − | 4.61783i | −0.0492804 | − | 0.151669i | ||||
\(928\) | −3.87623 | + | 11.9298i | −0.127243 | + | 0.391615i | ||||
\(929\) | −7.80111 | − | 5.66784i | −0.255946 | − | 0.185956i | 0.452412 | − | 0.891809i | \(-0.350564\pi\) |
−0.708358 | + | 0.705853i | \(0.750564\pi\) | |||||||
\(930\) | −11.3978 | − | 8.28100i | −0.373749 | − | 0.271545i | ||||
\(931\) | −6.32007 | + | 19.4512i | −0.207132 | + | 0.637487i | ||||
\(932\) | 7.34926 | + | 22.6187i | 0.240733 | + | 0.740901i | ||||
\(933\) | 27.6261 | − | 20.0715i | 0.904437 | − | 0.657112i | ||||
\(934\) | −3.50230 | −0.114599 | ||||||||
\(935\) | −2.53719 | − | 13.9961i | −0.0829748 | − | 0.457721i | ||||
\(936\) | −3.47457 | −0.113570 | ||||||||
\(937\) | 17.1025 | − | 12.4257i | 0.558715 | − | 0.405930i | −0.272274 | − | 0.962220i | \(-0.587776\pi\) |
0.830988 | + | 0.556290i | \(0.187776\pi\) | |||||||
\(938\) | −4.60961 | − | 14.1869i | −0.150509 | − | 0.463219i | ||||
\(939\) | −7.39263 | + | 22.7522i | −0.241249 | + | 0.742489i | ||||
\(940\) | 52.9113 | + | 38.4423i | 1.72578 | + | 1.25385i | ||||
\(941\) | 16.0729 | + | 11.6776i | 0.523961 | + | 0.380680i | 0.818094 | − | 0.575085i | \(-0.195031\pi\) |
−0.294133 | + | 0.955765i | \(0.595031\pi\) | |||||||
\(942\) | −2.44485 | + | 7.52448i | −0.0796575 | + | 0.245161i | ||||
\(943\) | −7.17481 | − | 22.0818i | −0.233644 | − | 0.719082i | ||||
\(944\) | −24.1535 | + | 17.5485i | −0.786129 | + | 0.571156i | ||||
\(945\) | −13.6385 | −0.443660 | ||||||||
\(946\) | −10.3358 | + | 5.55941i | −0.336045 | + | 0.180752i | ||||
\(947\) | −41.3595 | −1.34400 | −0.672001 | − | 0.740550i | \(-0.734565\pi\) | ||||
−0.672001 | + | 0.740550i | \(0.734565\pi\) | |||||||
\(948\) | 10.6903 | − | 7.76698i | 0.347206 | − | 0.252260i | ||||
\(949\) | 3.35539 | + | 10.3268i | 0.108921 | + | 0.335223i | ||||
\(950\) | 12.0061 | − | 36.9510i | 0.389530 | − | 1.19885i | ||||
\(951\) | −3.07535 | − | 2.23437i | −0.0997251 | − | 0.0724545i | ||||
\(952\) | −4.32208 | − | 3.14018i | −0.140079 | − | 0.101774i | ||||
\(953\) | 4.37100 | − | 13.4526i | 0.141591 | − | 0.435771i | −0.854966 | − | 0.518684i | \(-0.826422\pi\) |
0.996557 | + | 0.0829126i | \(0.0264222\pi\) | |||||||
\(954\) | −0.273820 | − | 0.842732i | −0.00886526 | − | 0.0272845i | ||||
\(955\) | 22.9999 | − | 16.7104i | 0.744258 | − | 0.540735i | ||||
\(956\) | −21.0026 | −0.679273 | ||||||||
\(957\) | 8.91096 | + | 1.20878i | 0.288050 | + | 0.0390744i | ||||
\(958\) | −12.0008 | −0.387730 | ||||||||
\(959\) | −21.5417 | + | 15.6510i | −0.695618 | + | 0.505396i | ||||
\(960\) | 4.89603 | + | 15.0684i | 0.158019 | + | 0.486332i | ||||
\(961\) | 7.52750 | − | 23.1672i | 0.242822 | − | 0.747331i | ||||
\(962\) | −1.79394 | − | 1.30338i | −0.0578391 | − | 0.0420226i | ||||
\(963\) | −3.72755 | − | 2.70822i | −0.120119 | − | 0.0872713i | ||||
\(964\) | 0.141697 | − | 0.436099i | 0.00456376 | − | 0.0140458i | ||||
\(965\) | −22.4171 | − | 68.9927i | −0.721632 | − | 2.22095i | ||||
\(966\) | −5.15262 | + | 3.74359i | −0.165783 | + | 0.120448i | ||||
\(967\) | −34.2641 | −1.10186 | −0.550929 | − | 0.834552i | \(-0.685726\pi\) | ||||
−0.550929 | + | 0.834552i | \(0.685726\pi\) | |||||||
\(968\) | 0.822115 | + | 18.4613i | 0.0264238 | + | 0.593369i | ||||
\(969\) | −6.57040 | −0.211072 | ||||||||
\(970\) | 1.41637 | − | 1.02905i | 0.0454768 | − | 0.0330408i | ||||
\(971\) | −6.49895 | − | 20.0017i | −0.208561 | − | 0.641886i | −0.999548 | − | 0.0300529i | \(-0.990432\pi\) |
0.790987 | − | 0.611833i | \(-0.209568\pi\) | |||||||
\(972\) | −0.557798 | + | 1.71673i | −0.0178914 | + | 0.0550640i | ||||
\(973\) | 29.0184 | + | 21.0831i | 0.930288 | + | 0.675894i | ||||
\(974\) | −11.6115 | − | 8.43624i | −0.372056 | − | 0.270315i | ||||
\(975\) | −8.56002 | + | 26.3450i | −0.274140 | + | 0.843716i | ||||
\(976\) | 7.45210 | + | 22.9352i | 0.238536 | + | 0.734138i | ||||
\(977\) | 5.07954 | − | 3.69050i | 0.162509 | − | 0.118070i | −0.503559 | − | 0.863961i | \(-0.667976\pi\) |
0.666068 | + | 0.745891i | \(0.267976\pi\) | |||||||
\(978\) | 9.69202 | 0.309916 | ||||||||
\(979\) | −26.4898 | − | 3.59338i | −0.846619 | − | 0.114845i | ||||
\(980\) | 24.0976 | 0.769770 | ||||||||
\(981\) | 1.04860 | − | 0.761854i | 0.0334793 | − | 0.0243241i | ||||
\(982\) | −1.71691 | − | 5.28412i | −0.0547889 | − | 0.168623i | ||||
\(983\) | −5.88533 | + | 18.1132i | −0.187713 | + | 0.577721i | −0.999985 | − | 0.00555852i | \(-0.998231\pi\) |
0.812272 | + | 0.583279i | \(0.198231\pi\) | |||||||
\(984\) | −6.95645 | − | 5.05416i | −0.221764 | − | 0.161121i | ||||
\(985\) | −6.98802 | − | 5.07709i | −0.222657 | − | 0.161770i | ||||
\(986\) | −0.369919 | + | 1.13849i | −0.0117806 | + | 0.0362571i | ||||
\(987\) | −8.30200 | − | 25.5509i | −0.264256 | − | 0.813295i | ||||
\(988\) | 19.8447 | − | 14.4180i | 0.631344 | − | 0.458699i | ||||
\(989\) | 36.3569 | 1.15608 | ||||||||
\(990\) | −5.53077 | + | 2.97489i | −0.175779 | + | 0.0945481i | ||||
\(991\) | −12.5386 | −0.398301 | −0.199151 | − | 0.979969i | \(-0.563818\pi\) | ||||
−0.199151 | + | 0.979969i | \(0.563818\pi\) | |||||||
\(992\) | 27.8479 | − | 20.2327i | 0.884173 | − | 0.642389i | ||||
\(993\) | −5.93133 | − | 18.2548i | −0.188225 | − | 0.579298i | ||||
\(994\) | 5.14970 | − | 15.8491i | 0.163339 | − | 0.502704i | ||||
\(995\) | 19.0946 | + | 13.8730i | 0.605339 | + | 0.439805i | ||||
\(996\) | 11.1243 | + | 8.08225i | 0.352486 | + | 0.256096i | ||||
\(997\) | 7.33756 | − | 22.5827i | 0.232383 | − | 0.715201i | −0.765075 | − | 0.643941i | \(-0.777298\pi\) |
0.997458 | − | 0.0712596i | \(-0.0227019\pi\) | |||||||
\(998\) | 4.57315 | + | 14.0747i | 0.144760 | + | 0.445527i | ||||
\(999\) | −1.96458 | + | 1.42735i | −0.0621567 | + | 0.0451595i |
(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 | 561.2.m.d.256.4 | yes | 24 | |
11.2 | odd | 10 | 6171.2.a.bl.1.8 | 12 | |||
11.4 | even | 5 | inner | 561.2.m.d.103.4 | ✓ | 24 | |
11.9 | even | 5 | 6171.2.a.bk.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
561.2.m.d.103.4 | ✓ | 24 | 11.4 | even | 5 | inner | |
561.2.m.d.256.4 | yes | 24 | 1.1 | even | 1 | trivial | |
6171.2.a.bk.1.5 | 12 | 11.9 | even | 5 | |||
6171.2.a.bl.1.8 | 12 | 11.2 | odd | 10 |