Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [231,2,Mod(89,231)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(231, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("231.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 231.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.84454428669\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 89.17 | ||
Character | \(\chi\) | \(=\) | 231.89 |
Dual form | 231.2.n.a.122.17 |
$q$-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 \(\left(\mathbb{Z}/231\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.872412 | + | 0.503687i | 0.616888 | + | 0.356161i | 0.775657 | − | 0.631155i | \(-0.217419\pi\) |
−0.158768 | + | 0.987316i | \(0.550752\pi\) | |||||||
\(3\) | −0.195057 | − | 1.72103i | −0.112616 | − | 0.993639i | ||||
\(4\) | −0.492598 | − | 0.853205i | −0.246299 | − | 0.426603i | ||||
\(5\) | −0.168910 | + | 0.292561i | −0.0755389 | + | 0.130837i | −0.901321 | − | 0.433153i | \(-0.857401\pi\) |
0.825782 | + | 0.563990i | \(0.190734\pi\) | |||||||
\(6\) | 0.696692 | − | 1.59970i | 0.284423 | − | 0.653074i | ||||
\(7\) | 2.63835 | + | 0.197774i | 0.997202 | + | 0.0747515i | ||||
\(8\) | − | 3.00721i | − | 1.06321i | ||||||
\(9\) | −2.92391 | + | 0.671400i | −0.974635 | + | 0.223800i | ||||
\(10\) | −0.294718 | + | 0.170156i | −0.0931982 | + | 0.0538080i | ||||
\(11\) | −0.866025 | + | 0.500000i | −0.261116 | + | 0.150756i | ||||
\(12\) | −1.37231 | + | 1.01420i | −0.396151 | + | 0.292775i | ||||
\(13\) | − | 6.18751i | − | 1.71611i | −0.513560 | − | 0.858054i | \(-0.671674\pi\) | ||
0.513560 | − | 0.858054i | \(-0.328326\pi\) | |||||||
\(14\) | 2.20211 | + | 1.50144i | 0.588539 | + | 0.401278i | ||||
\(15\) | 0.536454 | + | 0.233634i | 0.138512 | + | 0.0603240i | ||||
\(16\) | 0.529497 | − | 0.917116i | 0.132374 | − | 0.229279i | ||||
\(17\) | −0.517054 | − | 0.895564i | −0.125404 | − | 0.217206i | 0.796487 | − | 0.604656i | \(-0.206689\pi\) |
−0.921891 | + | 0.387450i | \(0.873356\pi\) | |||||||
\(18\) | −2.88903 | − | 0.886996i | −0.680950 | − | 0.209067i | ||||
\(19\) | 4.76552 | + | 2.75137i | 1.09329 | + | 0.631209i | 0.934449 | − | 0.356096i | \(-0.115893\pi\) |
0.158836 | + | 0.987305i | \(0.449226\pi\) | |||||||
\(20\) | 0.332819 | 0.0744207 | ||||||||
\(21\) | −0.174254 | − | 4.57926i | −0.0380254 | − | 0.999277i | ||||
\(22\) | −1.00737 | −0.214773 | ||||||||
\(23\) | 0.780699 | + | 0.450737i | 0.162787 | + | 0.0939851i | 0.579180 | − | 0.815199i | \(-0.303373\pi\) |
−0.416393 | + | 0.909185i | \(0.636706\pi\) | |||||||
\(24\) | −5.17551 | + | 0.586579i | −1.05645 | + | 0.119735i | ||||
\(25\) | 2.44294 | + | 4.23129i | 0.488588 | + | 0.846259i | ||||
\(26\) | 3.11657 | − | 5.39806i | 0.611210 | − | 1.05865i | ||||
\(27\) | 1.72583 | + | 4.90117i | 0.332136 | + | 0.943231i | ||||
\(28\) | −1.13090 | − | 2.34848i | −0.213721 | − | 0.443820i | ||||
\(29\) | 10.4471i | 1.93997i | 0.243163 | + | 0.969985i | \(0.421815\pi\) | ||||
−0.243163 | + | 0.969985i | \(0.578185\pi\) | |||||||
\(30\) | 0.350331 | + | 0.474030i | 0.0639613 | + | 0.0865456i | ||||
\(31\) | −2.82520 | + | 1.63113i | −0.507421 | + | 0.292959i | −0.731773 | − | 0.681549i | \(-0.761307\pi\) |
0.224352 | + | 0.974508i | \(0.427973\pi\) | |||||||
\(32\) | −4.28476 | + | 2.47381i | −0.757446 | + | 0.437312i | ||||
\(33\) | 1.02944 | + | 1.39293i | 0.179203 | + | 0.242478i | ||||
\(34\) | − | 1.04173i | − | 0.178656i | ||||||
\(35\) | −0.503505 | + | 0.738472i | −0.0851079 | + | 0.124825i | ||||
\(36\) | 2.01315 | + | 2.16396i | 0.335525 | + | 0.360660i | ||||
\(37\) | −1.95816 | + | 3.39162i | −0.321919 | + | 0.557580i | −0.980884 | − | 0.194594i | \(-0.937661\pi\) |
0.658965 | + | 0.752173i | \(0.270994\pi\) | |||||||
\(38\) | 2.77166 | + | 4.80066i | 0.449623 | + | 0.778770i | ||||
\(39\) | −10.6489 | + | 1.20692i | −1.70519 | + | 0.193262i | ||||
\(40\) | 0.879793 | + | 0.507948i | 0.139107 | + | 0.0803137i | ||||
\(41\) | 11.2247 | 1.75301 | 0.876504 | − | 0.481394i | \(-0.159869\pi\) | ||||
0.876504 | + | 0.481394i | \(0.159869\pi\) | |||||||
\(42\) | 2.15449 | − | 4.08277i | 0.332446 | − | 0.629985i | ||||
\(43\) | −6.76228 | −1.03124 | −0.515619 | − | 0.856818i | \(-0.672438\pi\) | ||||
−0.515619 | + | 0.856818i | \(0.672438\pi\) | |||||||
\(44\) | 0.853205 | + | 0.492598i | 0.128626 | + | 0.0742620i | ||||
\(45\) | 0.297452 | − | 0.968827i | 0.0443415 | − | 0.144424i | ||||
\(46\) | 0.454061 | + | 0.786456i | 0.0669476 | + | 0.115957i | ||||
\(47\) | 3.61562 | − | 6.26243i | 0.527392 | − | 0.913469i | −0.472098 | − | 0.881546i | \(-0.656503\pi\) |
0.999490 | − | 0.0319237i | \(-0.0101633\pi\) | |||||||
\(48\) | −1.68167 | − | 0.732392i | −0.242728 | − | 0.105712i | ||||
\(49\) | 6.92177 | + | 1.04359i | 0.988824 | + | 0.149085i | ||||
\(50\) | 4.92191i | 0.696063i | ||||||||
\(51\) | −1.44044 | + | 1.06455i | −0.201702 | + | 0.149067i | ||||
\(52\) | −5.27922 | + | 3.04796i | −0.732096 | + | 0.422676i | ||||
\(53\) | 7.55149 | − | 4.35985i | 1.03728 | − | 0.598872i | 0.118216 | − | 0.992988i | \(-0.462282\pi\) |
0.919061 | + | 0.394116i | \(0.128949\pi\) | |||||||
\(54\) | −0.963024 | + | 5.14512i | −0.131051 | + | 0.700162i | ||||
\(55\) | − | 0.337820i | − | 0.0455517i | ||||||
\(56\) | 0.594748 | − | 7.93407i | 0.0794765 | − | 1.06023i | ||||
\(57\) | 3.80565 | − | 8.73829i | 0.504071 | − | 1.15741i | ||||
\(58\) | −5.26205 | + | 9.11414i | −0.690941 | + | 1.19675i | ||||
\(59\) | −2.65866 | − | 4.60494i | −0.346128 | − | 0.599512i | 0.639430 | − | 0.768849i | \(-0.279170\pi\) |
−0.985558 | + | 0.169338i | \(0.945837\pi\) | |||||||
\(60\) | −0.0649189 | − | 0.572793i | −0.00838099 | − | 0.0739473i | ||||
\(61\) | −2.79724 | − | 1.61499i | −0.358150 | − | 0.206778i | 0.310119 | − | 0.950698i | \(-0.399631\pi\) |
−0.668269 | + | 0.743920i | \(0.732964\pi\) | |||||||
\(62\) | −3.28632 | −0.417362 | ||||||||
\(63\) | −7.84707 | + | 1.19312i | −0.988638 | + | 0.150318i | ||||
\(64\) | −7.10209 | −0.887762 | ||||||||
\(65\) | 1.81023 | + | 1.04513i | 0.224531 | + | 0.129633i | ||||
\(66\) | 0.196496 | + | 1.73372i | 0.0241870 | + | 0.213407i | ||||
\(67\) | −5.29852 | − | 9.17731i | −0.647318 | − | 1.12119i | −0.983761 | − | 0.179484i | \(-0.942557\pi\) |
0.336443 | − | 0.941704i | \(-0.390776\pi\) | |||||||
\(68\) | −0.509400 | + | 0.882306i | −0.0617738 | + | 0.106995i | ||||
\(69\) | 0.623452 | − | 1.43153i | 0.0750547 | − | 0.172336i | ||||
\(70\) | −0.811223 | + | 0.390643i | −0.0969596 | + | 0.0466907i | ||||
\(71\) | 9.05873i | 1.07507i | 0.843240 | + | 0.537537i | \(0.180645\pi\) | ||||
−0.843240 | + | 0.537537i | \(0.819355\pi\) | |||||||
\(72\) | 2.01904 | + | 8.79280i | 0.237946 | + | 1.03624i | ||||
\(73\) | −3.38869 | + | 1.95646i | −0.396616 | + | 0.228987i | −0.685023 | − | 0.728522i | \(-0.740208\pi\) |
0.288407 | + | 0.957508i | \(0.406875\pi\) | |||||||
\(74\) | −3.41664 | + | 1.97260i | −0.397176 | + | 0.229310i | ||||
\(75\) | 6.80568 | − | 5.02972i | 0.785852 | − | 0.580782i | ||||
\(76\) | − | 5.42129i | − | 0.621864i | ||||||
\(77\) | −2.38376 | + | 1.14790i | −0.271655 | + | 0.130815i | ||||
\(78\) | −9.89815 | − | 4.31079i | −1.12074 | − | 0.488101i | ||||
\(79\) | −2.94659 | + | 5.10365i | −0.331518 | + | 0.574205i | −0.982810 | − | 0.184622i | \(-0.940894\pi\) |
0.651292 | + | 0.758827i | \(0.274227\pi\) | |||||||
\(80\) | 0.178875 | + | 0.309821i | 0.0199988 | + | 0.0346390i | ||||
\(81\) | 8.09844 | − | 3.92622i | 0.899827 | − | 0.436247i | ||||
\(82\) | 9.79259 | + | 5.65376i | 1.08141 | + | 0.624353i | ||||
\(83\) | −6.94128 | −0.761904 | −0.380952 | − | 0.924595i | \(-0.624404\pi\) | ||||
−0.380952 | + | 0.924595i | \(0.624404\pi\) | |||||||
\(84\) | −3.82121 | + | 2.40441i | −0.416928 | + | 0.262343i | ||||
\(85\) | 0.349343 | 0.0378915 | ||||||||
\(86\) | −5.89950 | − | 3.40608i | −0.636159 | − | 0.367287i | ||||
\(87\) | 17.9797 | − | 2.03778i | 1.92763 | − | 0.218473i | ||||
\(88\) | 1.50361 | + | 2.60432i | 0.160285 | + | 0.277622i | ||||
\(89\) | 1.82637 | − | 3.16337i | 0.193595 | − | 0.335317i | −0.752844 | − | 0.658199i | \(-0.771319\pi\) |
0.946439 | + | 0.322882i | \(0.104652\pi\) | |||||||
\(90\) | 0.747486 | − | 0.695393i | 0.0787920 | − | 0.0733009i | ||||
\(91\) | 1.22373 | − | 16.3248i | 0.128282 | − | 1.71131i | ||||
\(92\) | − | 0.888129i | − | 0.0925938i | ||||||
\(93\) | 3.35830 | + | 4.54409i | 0.348240 | + | 0.471201i | ||||
\(94\) | 6.30861 | − | 3.64228i | 0.650684 | − | 0.375672i | ||||
\(95\) | −1.60989 | + | 0.929470i | −0.165171 | + | 0.0953616i | ||||
\(96\) | 5.09328 | + | 6.89168i | 0.519831 | + | 0.703379i | ||||
\(97\) | 9.23676i | 0.937851i | 0.883238 | + | 0.468925i | \(0.155359\pi\) | ||||
−0.883238 | + | 0.468925i | \(0.844641\pi\) | |||||||
\(98\) | 5.51299 | + | 4.39685i | 0.556896 | + | 0.444149i | ||||
\(99\) | 2.19648 | − | 2.04340i | 0.220754 | − | 0.205370i | ||||
\(100\) | 2.40677 | − | 4.16866i | 0.240677 | − | 0.416866i | ||||
\(101\) | −0.464343 | − | 0.804266i | −0.0462039 | − | 0.0800275i | 0.841999 | − | 0.539480i | \(-0.181379\pi\) |
−0.888202 | + | 0.459452i | \(0.848046\pi\) | |||||||
\(102\) | −1.79286 | + | 0.203198i | −0.177519 | + | 0.0201196i | ||||
\(103\) | −2.16678 | − | 1.25099i | −0.213499 | − | 0.123264i | 0.389438 | − | 0.921053i | \(-0.372669\pi\) |
−0.602936 | + | 0.797789i | \(0.706003\pi\) | |||||||
\(104\) | −18.6072 | −1.82458 | ||||||||
\(105\) | 1.36915 | + | 0.722504i | 0.133615 | + | 0.0705091i | ||||
\(106\) | 8.78401 | 0.853179 | ||||||||
\(107\) | −7.12304 | − | 4.11249i | −0.688611 | − | 0.397570i | 0.114481 | − | 0.993425i | \(-0.463480\pi\) |
−0.803091 | + | 0.595856i | \(0.796813\pi\) | |||||||
\(108\) | 3.33157 | − | 3.88680i | 0.320580 | − | 0.374007i | ||||
\(109\) | −2.32520 | − | 4.02736i | −0.222714 | − | 0.385751i | 0.732917 | − | 0.680318i | \(-0.238158\pi\) |
−0.955631 | + | 0.294566i | \(0.904825\pi\) | |||||||
\(110\) | 0.170156 | − | 0.294718i | 0.0162237 | − | 0.0281003i | ||||
\(111\) | 6.21905 | + | 2.70849i | 0.590286 | + | 0.257078i | ||||
\(112\) | 1.57838 | − | 2.31495i | 0.149143 | − | 0.218742i | ||||
\(113\) | 4.52821i | 0.425978i | 0.977055 | + | 0.212989i | \(0.0683198\pi\) | ||||
−0.977055 | + | 0.212989i | \(0.931680\pi\) | |||||||
\(114\) | 7.72146 | − | 5.70653i | 0.723181 | − | 0.534465i | ||||
\(115\) | −0.263736 | + | 0.152268i | −0.0245935 | + | 0.0141991i | ||||
\(116\) | 8.91349 | − | 5.14620i | 0.827597 | − | 0.477813i | ||||
\(117\) | 4.15430 | + | 18.0917i | 0.384065 | + | 1.67258i | ||||
\(118\) | − | 5.35654i | − | 0.493109i | ||||||
\(119\) | −1.18705 | − | 2.46507i | −0.108817 | − | 0.225973i | ||||
\(120\) | 0.702586 | − | 1.61323i | 0.0641370 | − | 0.147267i | ||||
\(121\) | 0.500000 | − | 0.866025i | 0.0454545 | − | 0.0787296i | ||||
\(122\) | −1.62690 | − | 2.81787i | −0.147292 | − | 0.255118i | ||||
\(123\) | −2.18947 | − | 19.3181i | −0.197418 | − | 1.74186i | ||||
\(124\) | 2.78338 | + | 1.60698i | 0.249954 | + | 0.144311i | ||||
\(125\) | −3.33965 | −0.298707 | ||||||||
\(126\) | −7.44683 | − | 2.91158i | −0.663417 | − | 0.259384i | ||||
\(127\) | 10.9941 | 0.975572 | 0.487786 | − | 0.872963i | \(-0.337805\pi\) | ||||
0.487786 | + | 0.872963i | \(0.337805\pi\) | |||||||
\(128\) | 2.37357 | + | 1.37038i | 0.209796 | + | 0.121126i | ||||
\(129\) | 1.31903 | + | 11.6381i | 0.116134 | + | 1.02468i | ||||
\(130\) | 1.05284 | + | 1.82357i | 0.0923403 | + | 0.159938i | ||||
\(131\) | −7.13990 | + | 12.3667i | −0.623816 | + | 1.08048i | 0.364952 | + | 0.931026i | \(0.381085\pi\) |
−0.988768 | + | 0.149455i | \(0.952248\pi\) | |||||||
\(132\) | 0.681354 | − | 1.56448i | 0.0593042 | − | 0.136170i | ||||
\(133\) | 12.0290 | + | 8.20158i | 1.04304 | + | 0.711167i | ||||
\(134\) | − | 10.6752i | − | 0.922197i | ||||||
\(135\) | −1.72540 | − | 0.322947i | −0.148499 | − | 0.0277949i | ||||
\(136\) | −2.69315 | + | 1.55489i | −0.230936 | + | 0.133331i | ||||
\(137\) | −4.49906 | + | 2.59753i | −0.384381 | + | 0.221922i | −0.679722 | − | 0.733469i | \(-0.737900\pi\) |
0.295342 | + | 0.955392i | \(0.404566\pi\) | |||||||
\(138\) | 1.26495 | − | 0.934857i | 0.107680 | − | 0.0795803i | ||||
\(139\) | 0.823165i | 0.0698199i | 0.999390 | + | 0.0349100i | \(0.0111144\pi\) | ||||
−0.999390 | + | 0.0349100i | \(0.988886\pi\) | |||||||
\(140\) | 0.878094 | + | 0.0658230i | 0.0742125 | + | 0.00556306i | ||||
\(141\) | −11.4831 | − | 5.00106i | −0.967051 | − | 0.421165i | ||||
\(142\) | −4.56277 | + | 7.90295i | −0.382899 | + | 0.663201i | ||||
\(143\) | 3.09376 | + | 5.35854i | 0.258713 | + | 0.448104i | ||||
\(144\) | −0.932448 | + | 3.03707i | −0.0777040 | + | 0.253089i | ||||
\(145\) | −3.05640 | − | 1.76461i | −0.253820 | − | 0.146543i | ||||
\(146\) | −3.94178 | −0.326224 | ||||||||
\(147\) | 0.445914 | − | 12.1162i | 0.0367784 | − | 0.999323i | ||||
\(148\) | 3.85834 | 0.317153 | ||||||||
\(149\) | −0.992777 | − | 0.573180i | −0.0813314 | − | 0.0469567i | 0.458783 | − | 0.888548i | \(-0.348286\pi\) |
−0.540114 | + | 0.841592i | \(0.681619\pi\) | |||||||
\(150\) | 8.47076 | − | 0.960054i | 0.691635 | − | 0.0783881i | ||||
\(151\) | −7.29020 | − | 12.6270i | −0.593268 | − | 1.02757i | −0.993789 | − | 0.111282i | \(-0.964504\pi\) |
0.400521 | − | 0.916288i | \(-0.368829\pi\) | |||||||
\(152\) | 8.27396 | − | 14.3309i | 0.671107 | − | 1.16239i | ||||
\(153\) | 2.11310 | + | 2.27139i | 0.170834 | + | 0.183631i | ||||
\(154\) | −2.65781 | − | 0.199232i | −0.214172 | − | 0.0160546i | ||||
\(155\) | − | 1.10206i | − | 0.0885193i | ||||||
\(156\) | 6.27539 | + | 8.49118i | 0.502433 | + | 0.679839i | ||||
\(157\) | 10.2799 | − | 5.93507i | 0.820421 | − | 0.473671i | −0.0301404 | − | 0.999546i | \(-0.509595\pi\) |
0.850562 | + | 0.525875i | \(0.176262\pi\) | |||||||
\(158\) | −5.14129 | + | 2.96832i | −0.409019 | + | 0.236147i | ||||
\(159\) | −8.97642 | − | 12.1459i | −0.711877 | − | 0.963235i | ||||
\(160\) | − | 1.67141i | − | 0.132136i | ||||||
\(161\) | 1.97061 | + | 1.34360i | 0.155306 | + | 0.105891i | ||||
\(162\) | 9.04277 | + | 0.653802i | 0.710467 | + | 0.0513675i | ||||
\(163\) | 7.27542 | − | 12.6014i | 0.569855 | − | 0.987017i | −0.426725 | − | 0.904381i | \(-0.640333\pi\) |
0.996580 | − | 0.0826359i | \(-0.0263339\pi\) | |||||||
\(164\) | −5.52928 | − | 9.57700i | −0.431765 | − | 0.747838i | ||||
\(165\) | −0.581400 | + | 0.0658943i | −0.0452619 | + | 0.00512987i | ||||
\(166\) | −6.05565 | − | 3.49623i | −0.470010 | − | 0.271360i | ||||
\(167\) | −19.1863 | −1.48468 | −0.742342 | − | 0.670021i | \(-0.766285\pi\) | ||||
−0.742342 | + | 0.670021i | \(0.766285\pi\) | |||||||
\(168\) | −13.7708 | + | 0.524019i | −1.06244 | + | 0.0404290i | ||||
\(169\) | −25.2853 | −1.94503 | ||||||||
\(170\) | 0.304771 | + | 0.175959i | 0.0233748 | + | 0.0134955i | ||||
\(171\) | −15.7812 | − | 4.84519i | −1.20682 | − | 0.370521i | ||||
\(172\) | 3.33109 | + | 5.76962i | 0.253993 | + | 0.439929i | ||||
\(173\) | 10.3037 | − | 17.8464i | 0.783372 | − | 1.35684i | −0.146595 | − | 0.989197i | \(-0.546831\pi\) |
0.929967 | − | 0.367644i | \(-0.119835\pi\) | |||||||
\(174\) | 16.7121 | + | 7.27838i | 1.26694 | + | 0.551773i | ||||
\(175\) | 5.60849 | + | 11.6468i | 0.423962 | + | 0.880414i | ||||
\(176\) | 1.05899i | 0.0798247i | ||||||||
\(177\) | −7.40665 | + | 5.47387i | −0.556718 | + | 0.411441i | ||||
\(178\) | 3.18670 | − | 1.83984i | 0.238853 | − | 0.137902i | ||||
\(179\) | 0.717382 | − | 0.414181i | 0.0536197 | − | 0.0309573i | −0.472951 | − | 0.881089i | \(-0.656811\pi\) |
0.526570 | + | 0.850132i | \(0.323478\pi\) | |||||||
\(180\) | −0.973132 | + | 0.223455i | −0.0725330 | + | 0.0166554i | ||||
\(181\) | 8.14952i | 0.605749i | 0.953030 | + | 0.302875i | \(0.0979463\pi\) | ||||
−0.953030 | + | 0.302875i | \(0.902054\pi\) | |||||||
\(182\) | 9.29020 | − | 13.6256i | 0.688635 | − | 1.01000i | ||||
\(183\) | −2.23383 | + | 5.12916i | −0.165129 | + | 0.379158i | ||||
\(184\) | 1.35546 | − | 2.34773i | 0.0999259 | − | 0.173077i | ||||
\(185\) | −0.661505 | − | 1.14576i | −0.0486348 | − | 0.0842379i | ||||
\(186\) | 0.641020 | + | 5.65586i | 0.0470019 | + | 0.414707i | ||||
\(187\) | 0.895564 | + | 0.517054i | 0.0654901 | + | 0.0378107i | ||||
\(188\) | −7.12419 | −0.519585 | ||||||||
\(189\) | 3.58402 | + | 13.2723i | 0.260699 | + | 0.965420i | ||||
\(190\) | −1.87265 | −0.135856 | ||||||||
\(191\) | 16.8944 | + | 9.75398i | 1.22244 | + | 0.705773i | 0.965437 | − | 0.260638i | \(-0.0839330\pi\) |
0.256999 | + | 0.966412i | \(0.417266\pi\) | |||||||
\(192\) | 1.38532 | + | 12.2229i | 0.0999765 | + | 0.882114i | ||||
\(193\) | 8.67207 | + | 15.0205i | 0.624230 | + | 1.08120i | 0.988689 | + | 0.149978i | \(0.0479204\pi\) |
−0.364460 | + | 0.931219i | \(0.618746\pi\) | |||||||
\(194\) | −4.65244 | + | 8.05826i | −0.334026 | + | 0.578549i | ||||
\(195\) | 1.44561 | − | 3.31932i | 0.103522 | − | 0.237701i | ||||
\(196\) | −2.51925 | − | 6.41976i | −0.179947 | − | 0.458555i | ||||
\(197\) | − | 5.76409i | − | 0.410675i | −0.978691 | − | 0.205337i | \(-0.934171\pi\) | ||
0.978691 | − | 0.205337i | \(-0.0658292\pi\) | |||||||
\(198\) | 2.94547 | − | 0.676351i | 0.209325 | − | 0.0480662i | ||||
\(199\) | −11.2355 | + | 6.48682i | −0.796464 | + | 0.459839i | −0.842233 | − | 0.539113i | \(-0.818759\pi\) |
0.0457694 | + | 0.998952i | \(0.485426\pi\) | |||||||
\(200\) | 12.7244 | − | 7.34643i | 0.899751 | − | 0.519471i | ||||
\(201\) | −14.7609 | + | 10.9090i | −1.04116 | + | 0.769464i | ||||
\(202\) | − | 0.935535i | − | 0.0658240i | ||||||
\(203\) | −2.06616 | + | 27.5630i | −0.145016 | + | 1.93454i | ||||
\(204\) | 1.61784 | + | 0.704593i | 0.113271 | + | 0.0493314i | ||||
\(205\) | −1.89597 | + | 3.28392i | −0.132420 | + | 0.229359i | ||||
\(206\) | −1.26021 | − | 2.18275i | −0.0878033 | − | 0.152080i | ||||
\(207\) | −2.58531 | − | 0.793750i | −0.179692 | − | 0.0551695i | ||||
\(208\) | −5.67467 | − | 3.27627i | −0.393468 | − | 0.227169i | ||||
\(209\) | −5.50275 | −0.380633 | ||||||||
\(210\) | 0.830544 | + | 1.31994i | 0.0573130 | + | 0.0910847i | ||||
\(211\) | −5.58202 | −0.384282 | −0.192141 | − | 0.981367i | \(-0.561543\pi\) | ||||
−0.192141 | + | 0.981367i | \(0.561543\pi\) | |||||||
\(212\) | −7.43970 | − | 4.29531i | −0.510961 | − | 0.295003i | ||||
\(213\) | 15.5904 | − | 1.76697i | 1.06823 | − | 0.121071i | ||||
\(214\) | −4.14282 | − | 7.17557i | −0.283197 | − | 0.490512i | ||||
\(215\) | 1.14222 | − | 1.97838i | 0.0778987 | − | 0.134924i | ||||
\(216\) | 14.7389 | − | 5.18994i | 1.00285 | − | 0.353130i | ||||
\(217\) | −7.77645 | + | 3.74474i | −0.527900 | + | 0.254209i | ||||
\(218\) | − | 4.68469i | − | 0.317287i | ||||||
\(219\) | 4.02812 | + | 5.45042i | 0.272195 | + | 0.368306i | ||||
\(220\) | −0.288230 | + | 0.166410i | −0.0194325 | + | 0.0112193i | ||||
\(221\) | −5.54131 | + | 3.19928i | −0.372749 | + | 0.215207i | ||||
\(222\) | 4.06134 | + | 5.49537i | 0.272579 | + | 0.368825i | ||||
\(223\) | − | 2.32096i | − | 0.155423i | −0.996976 | − | 0.0777116i | \(-0.975239\pi\) | ||
0.996976 | − | 0.0777116i | \(-0.0247613\pi\) | |||||||
\(224\) | −11.7940 | + | 5.67936i | −0.788017 | + | 0.379468i | ||||
\(225\) | −9.98381 | − | 10.7317i | −0.665587 | − | 0.715448i | ||||
\(226\) | −2.28080 | + | 3.95046i | −0.151717 | + | 0.262781i | ||||
\(227\) | −0.207712 | − | 0.359767i | −0.0137863 | − | 0.0238786i | 0.859050 | − | 0.511892i | \(-0.171055\pi\) |
−0.872836 | + | 0.488013i | \(0.837722\pi\) | |||||||
\(228\) | −9.33021 | + | 1.05746i | −0.617908 | + | 0.0700321i | ||||
\(229\) | 5.54470 | + | 3.20124i | 0.366404 | + | 0.211544i | 0.671886 | − | 0.740654i | \(-0.265484\pi\) |
−0.305482 | + | 0.952198i | \(0.598818\pi\) | |||||||
\(230\) | −0.306782 | −0.0202286 | ||||||||
\(231\) | 2.44054 | + | 3.87863i | 0.160576 | + | 0.255195i | ||||
\(232\) | 31.4165 | 2.06260 | ||||||||
\(233\) | −0.676221 | − | 0.390416i | −0.0443007 | − | 0.0255770i | 0.477686 | − | 0.878531i | \(-0.341476\pi\) |
−0.521987 | + | 0.852954i | \(0.674809\pi\) | |||||||
\(234\) | −5.48830 | + | 17.8759i | −0.358782 | + | 1.16858i | ||||
\(235\) | 1.22143 | + | 2.11558i | 0.0796772 | + | 0.138005i | ||||
\(236\) | −2.61930 | + | 4.53677i | −0.170502 | + | 0.295318i | ||||
\(237\) | 9.35830 | + | 4.07568i | 0.607887 | + | 0.264744i | ||||
\(238\) | 0.206028 | − | 2.74846i | 0.0133548 | − | 0.178156i | ||||
\(239\) | 27.1066i | 1.75338i | 0.481056 | + | 0.876690i | \(0.340253\pi\) | ||||
−0.481056 | + | 0.876690i | \(0.659747\pi\) | |||||||
\(240\) | 0.498320 | − | 0.368282i | 0.0321664 | − | 0.0237725i | ||||
\(241\) | −10.7835 | + | 6.22588i | −0.694629 | + | 0.401044i | −0.805344 | − | 0.592808i | \(-0.798019\pi\) |
0.110715 | + | 0.993852i | \(0.464686\pi\) | |||||||
\(242\) | 0.872412 | − | 0.503687i | 0.0560808 | − | 0.0323782i | ||||
\(243\) | −8.33681 | − | 13.1718i | −0.534807 | − | 0.844974i | ||||
\(244\) | 3.18216i | 0.203717i | ||||||||
\(245\) | −1.47447 | + | 1.84877i | −0.0942006 | + | 0.118113i | ||||
\(246\) | 7.82018 | − | 17.9562i | 0.498596 | − | 1.14484i | ||||
\(247\) | 17.0242 | − | 29.4867i | 1.08322 | − | 1.87620i | ||||
\(248\) | 4.90515 | + | 8.49597i | 0.311477 | + | 0.539494i | ||||
\(249\) | 1.35395 | + | 11.9462i | 0.0858029 | + | 0.757057i | ||||
\(250\) | −2.91355 | − | 1.68214i | −0.184269 | − | 0.106388i | ||||
\(251\) | −6.22012 | −0.392610 | −0.196305 | − | 0.980543i | \(-0.562894\pi\) | ||||
−0.196305 | + | 0.980543i | \(0.562894\pi\) | |||||||
\(252\) | 4.88342 | + | 6.10743i | 0.307627 | + | 0.384732i | ||||
\(253\) | −0.901474 | −0.0566752 | ||||||||
\(254\) | 9.59142 | + | 5.53761i | 0.601819 | + | 0.347460i | ||||
\(255\) | −0.0681419 | − | 0.601230i | −0.00426721 | − | 0.0376505i | ||||
\(256\) | 8.48258 | + | 14.6923i | 0.530161 | + | 0.918267i | ||||
\(257\) | −0.261862 | + | 0.453557i | −0.0163345 | + | 0.0282921i | −0.874077 | − | 0.485787i | \(-0.838533\pi\) |
0.857743 | + | 0.514079i | \(0.171866\pi\) | |||||||
\(258\) | −4.71123 | + | 10.8176i | −0.293308 | + | 0.673475i | ||||
\(259\) | −5.83707 | + | 8.56102i | −0.362698 | + | 0.531956i | ||||
\(260\) | − | 2.05932i | − | 0.127714i | ||||||
\(261\) | −7.01416 | − | 30.5462i | −0.434166 | − | 1.89076i | ||||
\(262\) | −12.4579 | + | 7.19256i | −0.769650 | + | 0.444358i | ||||
\(263\) | 0.672889 | − | 0.388493i | 0.0414921 | − | 0.0239555i | −0.479110 | − | 0.877755i | \(-0.659041\pi\) |
0.520603 | + | 0.853799i | \(0.325707\pi\) | |||||||
\(264\) | 4.18883 | − | 3.09575i | 0.257805 | − | 0.190530i | ||||
\(265\) | 2.94569i | 0.180953i | ||||||||
\(266\) | 6.36317 | + | 13.2140i | 0.390151 | + | 0.810202i | ||||
\(267\) | −5.80051 | − | 2.52621i | −0.354986 | − | 0.154601i | ||||
\(268\) | −5.22009 | + | 9.04146i | −0.318868 | + | 0.552295i | ||||
\(269\) | −5.98065 | − | 10.3588i | −0.364646 | − | 0.631586i | 0.624073 | − | 0.781366i | \(-0.285477\pi\) |
−0.988719 | + | 0.149780i | \(0.952143\pi\) | |||||||
\(270\) | −1.34260 | − | 1.15081i | −0.0817079 | − | 0.0700359i | ||||
\(271\) | −9.58028 | − | 5.53117i | −0.581960 | − | 0.335995i | 0.179952 | − | 0.983675i | \(-0.442406\pi\) |
−0.761912 | + | 0.647681i | \(0.775739\pi\) | |||||||
\(272\) | −1.09511 | −0.0664011 | ||||||||
\(273\) | −28.3342 | + | 1.07820i | −1.71487 | + | 0.0652557i | ||||
\(274\) | −5.23338 | −0.316160 | ||||||||
\(275\) | −4.23129 | − | 2.44294i | −0.255157 | − | 0.147315i | ||||
\(276\) | −1.52850 | + | 0.173236i | −0.0920048 | + | 0.0104276i | ||||
\(277\) | 5.92603 | + | 10.2642i | 0.356061 | + | 0.616716i | 0.987299 | − | 0.158874i | \(-0.0507862\pi\) |
−0.631238 | + | 0.775589i | \(0.717453\pi\) | |||||||
\(278\) | −0.414618 | + | 0.718139i | −0.0248671 | + | 0.0430711i | ||||
\(279\) | 7.16547 | − | 6.66610i | 0.428986 | − | 0.399089i | ||||
\(280\) | 2.22074 | + | 1.51415i | 0.132715 | + | 0.0904875i | ||||
\(281\) | 11.8914i | 0.709379i | 0.934984 | + | 0.354689i | \(0.115413\pi\) | ||||
−0.934984 | + | 0.354689i | \(0.884587\pi\) | |||||||
\(282\) | −7.49902 | − | 10.1469i | −0.446560 | − | 0.604238i | ||||
\(283\) | −23.9902 | + | 13.8507i | −1.42607 | + | 0.823341i | −0.996808 | − | 0.0798405i | \(-0.974559\pi\) |
−0.429260 | + | 0.903181i | \(0.641226\pi\) | |||||||
\(284\) | 7.72896 | − | 4.46232i | 0.458629 | − | 0.264790i | ||||
\(285\) | 1.91367 | + | 2.58937i | 0.113356 | + | 0.153381i | ||||
\(286\) | 6.23314i | 0.368574i | ||||||||
\(287\) | 29.6148 | + | 2.21996i | 1.74810 | + | 0.131040i | ||||
\(288\) | 10.8673 | − | 10.1100i | 0.640363 | − | 0.595736i | ||||
\(289\) | 7.96531 | − | 13.7963i | 0.468548 | − | 0.811548i | ||||
\(290\) | −1.77763 | − | 3.07894i | −0.104386 | − | 0.180802i | ||||
\(291\) | 15.8968 | − | 1.80170i | 0.931885 | − | 0.105617i | ||||
\(292\) | 3.33853 | + | 1.92750i | 0.195372 | + | 0.112798i | ||||
\(293\) | 10.5335 | 0.615376 | 0.307688 | − | 0.951487i | \(-0.400445\pi\) | ||||
0.307688 | + | 0.951487i | \(0.400445\pi\) | |||||||
\(294\) | 6.49177 | − | 10.3457i | 0.378608 | − | 0.603372i | ||||
\(295\) | 1.79630 | 0.104585 | ||||||||
\(296\) | 10.1993 | + | 5.88859i | 0.592824 | + | 0.342267i | ||||
\(297\) | −3.94520 | − | 3.38163i | −0.228924 | − | 0.196222i | ||||
\(298\) | −0.577407 | − | 1.00010i | −0.0334483 | − | 0.0579341i | ||||
\(299\) | 2.78894 | − | 4.83059i | 0.161289 | − | 0.279360i | ||||
\(300\) | −7.64385 | − | 3.32901i | −0.441318 | − | 0.192201i | ||||
\(301\) | −17.8413 | − | 1.33740i | −1.02835 | − | 0.0770866i | ||||
\(302\) | − | 14.6879i | − | 0.845195i | ||||||
\(303\) | −1.29359 | + | 0.956028i | −0.0743151 | + | 0.0549224i | ||||
\(304\) | 5.04666 | − | 2.91369i | 0.289446 | − | 0.167112i | ||||
\(305\) | 0.944965 | − | 0.545576i | 0.0541086 | − | 0.0312396i | ||||
\(306\) | 0.699420 | + | 3.04593i | 0.0399832 | + | 0.174124i | ||||
\(307\) | 1.47636i | 0.0842604i | 0.999112 | + | 0.0421302i | \(0.0134144\pi\) | ||||
−0.999112 | + | 0.0421302i | \(0.986586\pi\) | |||||||
\(308\) | 2.15363 | + | 1.46839i | 0.122714 | + | 0.0836692i | ||||
\(309\) | −1.73035 | + | 3.97311i | −0.0984360 | + | 0.226022i | ||||
\(310\) | 0.555092 | − | 0.961448i | 0.0315271 | − | 0.0546066i | ||||
\(311\) | −11.1828 | − | 19.3692i | −0.634118 | − | 1.09832i | −0.986701 | − | 0.162544i | \(-0.948030\pi\) |
0.352584 | − | 0.935780i | \(-0.385303\pi\) | |||||||
\(312\) | 3.62946 | + | 32.0235i | 0.205478 | + | 1.81298i | ||||
\(313\) | 1.53205 | + | 0.884531i | 0.0865967 | + | 0.0499967i | 0.542673 | − | 0.839944i | \(-0.317412\pi\) |
−0.456076 | + | 0.889941i | \(0.650746\pi\) | |||||||
\(314\) | 11.9577 | 0.674811 | ||||||||
\(315\) | 0.976390 | − | 2.49728i | 0.0550134 | − | 0.140706i | ||||
\(316\) | 5.80595 | 0.326610 | ||||||||
\(317\) | −9.92682 | − | 5.73125i | −0.557546 | − | 0.321899i | 0.194614 | − | 0.980880i | \(-0.437655\pi\) |
−0.752160 | + | 0.658981i | \(0.770988\pi\) | |||||||
\(318\) | −1.71339 | − | 15.1176i | −0.0960819 | − | 0.847751i | ||||
\(319\) | −5.22353 | − | 9.04742i | −0.292462 | − | 0.506558i | ||||
\(320\) | 1.19962 | − | 2.07780i | 0.0670606 | − | 0.116152i | ||||
\(321\) | −5.68833 | + | 13.0612i | −0.317492 | + | 0.729003i | ||||
\(322\) | 1.04243 | + | 2.16475i | 0.0580924 | + | 0.120637i | ||||
\(323\) | − | 5.69044i | − | 0.316624i | ||||||
\(324\) | −7.33915 | − | 4.97559i | −0.407731 | − | 0.276421i | ||||
\(325\) | 26.1812 | − | 15.1157i | 1.45227 | − | 0.838469i | ||||
\(326\) | 12.6943 | − | 7.32907i | 0.703074 | − | 0.405920i | ||||
\(327\) | −6.47768 | + | 4.78731i | −0.358216 | + | 0.264739i | ||||
\(328\) | − | 33.7551i | − | 1.86382i | ||||||
\(329\) | 10.7778 | − | 15.8074i | 0.594199 | − | 0.871490i | ||||
\(330\) | −0.540410 | − | 0.235357i | −0.0297486 | − | 0.0129560i | ||||
\(331\) | 2.04107 | − | 3.53524i | 0.112187 | − | 0.194314i | −0.804465 | − | 0.594001i | \(-0.797548\pi\) |
0.916652 | + | 0.399686i | \(0.130881\pi\) | |||||||
\(332\) | 3.41926 | + | 5.92233i | 0.187656 | + | 0.325030i | ||||
\(333\) | 3.44832 | − | 11.2315i | 0.188967 | − | 0.615482i | ||||
\(334\) | −16.7384 | − | 9.66391i | −0.915884 | − | 0.528786i | ||||
\(335\) | 3.57990 | 0.195591 | ||||||||
\(336\) | −4.29198 | − | 2.26490i | −0.234147 | − | 0.123560i | ||||
\(337\) | −28.2782 | −1.54041 | −0.770207 | − | 0.637795i | \(-0.779847\pi\) | ||||
−0.770207 | + | 0.637795i | \(0.779847\pi\) | |||||||
\(338\) | −22.0592 | − | 12.7359i | −1.19986 | − | 0.692742i | ||||
\(339\) | 7.79319 | − | 0.883260i | 0.423268 | − | 0.0479721i | ||||
\(340\) | −0.172086 | − | 0.298061i | −0.00933265 | − | 0.0161646i | ||||
\(341\) | 1.63113 | − | 2.82520i | 0.0883306 | − | 0.152993i | ||||
\(342\) | −11.3272 | − | 12.1758i | −0.612508 | − | 0.658391i | ||||
\(343\) | 18.0557 | + | 4.12231i | 0.974914 | + | 0.222584i | ||||
\(344\) | 20.3356i | 1.09642i | ||||||||
\(345\) | 0.313502 | + | 0.424197i | 0.0168784 | + | 0.0228380i | ||||
\(346\) | 17.9781 | − | 10.3796i | 0.966506 | − | 0.558013i | ||||
\(347\) | −16.7024 | + | 9.64311i | −0.896629 | + | 0.517669i | −0.876105 | − | 0.482120i | \(-0.839867\pi\) |
−0.0205242 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(348\) | −10.5954 | − | 14.3366i | −0.567974 | − | 0.768522i | ||||
\(349\) | − | 5.54773i | − | 0.296963i | −0.988915 | − | 0.148482i | \(-0.952561\pi\) | ||
0.988915 | − | 0.148482i | \(-0.0474386\pi\) | |||||||
\(350\) | −0.973425 | + | 12.9857i | −0.0520317 | + | 0.694116i | ||||
\(351\) | 30.3261 | − | 10.6786i | 1.61869 | − | 0.569982i | ||||
\(352\) | 2.47381 | − | 4.28476i | 0.131854 | − | 0.228379i | ||||
\(353\) | −7.60042 | − | 13.1643i | −0.404529 | − | 0.700665i | 0.589737 | − | 0.807595i | \(-0.299231\pi\) |
−0.994267 | + | 0.106930i | \(0.965898\pi\) | |||||||
\(354\) | −9.21877 | + | 1.04483i | −0.489972 | + | 0.0555322i | ||||
\(355\) | −2.65023 | − | 1.53011i | −0.140660 | − | 0.0812099i | ||||
\(356\) | −3.59867 | −0.190729 | ||||||||
\(357\) | −4.01092 | + | 2.52378i | −0.212280 | + | 0.133573i | ||||
\(358\) | 0.834471 | 0.0441031 | ||||||||
\(359\) | −21.0219 | − | 12.1370i | −1.10949 | − | 0.640567i | −0.170796 | − | 0.985306i | \(-0.554634\pi\) |
−0.938698 | + | 0.344740i | \(0.887967\pi\) | |||||||
\(360\) | −2.91347 | − | 0.894500i | −0.153553 | − | 0.0471443i | ||||
\(361\) | 5.64012 | + | 9.76897i | 0.296848 | + | 0.514157i | ||||
\(362\) | −4.10481 | + | 7.10974i | −0.215744 | + | 0.373680i | ||||
\(363\) | −1.58799 | − | 0.691592i | −0.0833477 | − | 0.0362991i | ||||
\(364\) | −14.5312 | + | 6.99749i | −0.761643 | + | 0.366768i | ||||
\(365\) | − | 1.32186i | − | 0.0691896i | ||||||
\(366\) | −4.53231 | + | 3.34959i | −0.236908 | + | 0.175086i | ||||
\(367\) | 28.6358 | − | 16.5329i | 1.49478 | − | 0.863010i | 0.494794 | − | 0.869010i | \(-0.335243\pi\) |
0.999982 | + | 0.00600056i | \(0.00191005\pi\) | |||||||
\(368\) | 0.826756 | − | 0.477328i | 0.0430976 | − | 0.0248824i | ||||
\(369\) | −32.8201 | + | 7.53629i | −1.70854 | + | 0.392323i | ||||
\(370\) | − | 1.33277i | − | 0.0692872i | ||||||
\(371\) | 20.7857 | − | 10.0093i | 1.07914 | − | 0.519659i | ||||
\(372\) | 2.22275 | − | 5.10373i | 0.115244 | − | 0.264616i | ||||
\(373\) | −3.11212 | + | 5.39035i | −0.161140 | + | 0.279102i | −0.935278 | − | 0.353915i | \(-0.884850\pi\) |
0.774138 | + | 0.633017i | \(0.218184\pi\) | |||||||
\(374\) | 0.520867 | + | 0.902168i | 0.0269334 | + | 0.0466500i | ||||
\(375\) | 0.651423 | + | 5.74765i | 0.0336394 | + | 0.296807i | ||||
\(376\) | −18.8325 | − | 10.8729i | −0.971210 | − | 0.560728i | ||||
\(377\) | 64.6413 | 3.32920 | ||||||||
\(378\) | −3.55836 | + | 13.3842i | −0.183022 | + | 0.688407i | ||||
\(379\) | 4.68995 | 0.240907 | 0.120453 | − | 0.992719i | \(-0.461565\pi\) | ||||
0.120453 | + | 0.992719i | \(0.461565\pi\) | |||||||
\(380\) | 1.58606 | + | 0.915711i | 0.0813630 | + | 0.0469750i | ||||
\(381\) | −2.14449 | − | 18.9213i | −0.109865 | − | 0.969366i | ||||
\(382\) | 9.82591 | + | 17.0190i | 0.502737 | + | 0.870767i | ||||
\(383\) | −15.1879 | + | 26.3062i | −0.776066 | + | 1.34419i | 0.158127 | + | 0.987419i | \(0.449455\pi\) |
−0.934193 | + | 0.356768i | \(0.883879\pi\) | |||||||
\(384\) | 1.89549 | − | 4.35230i | 0.0967289 | − | 0.222102i | ||||
\(385\) | 0.0668120 | − | 0.891288i | 0.00340506 | − | 0.0454242i | ||||
\(386\) | 17.4721i | 0.889304i | ||||||||
\(387\) | 19.7723 | − | 4.54020i | 1.00508 | − | 0.230791i | ||||
\(388\) | 7.88085 | − | 4.55001i | 0.400090 | − | 0.230992i | ||||
\(389\) | 13.3267 | − | 7.69415i | 0.675688 | − | 0.390109i | −0.122540 | − | 0.992464i | \(-0.539104\pi\) |
0.798228 | + | 0.602355i | \(0.205771\pi\) | |||||||
\(390\) | 2.93307 | − | 2.16768i | 0.148522 | − | 0.109765i | ||||
\(391\) | − | 0.932221i | − | 0.0471444i | ||||||
\(392\) | 3.13830 | − | 20.8152i | 0.158508 | − | 1.05133i | ||||
\(393\) | 22.6761 | + | 9.87580i | 1.14386 | + | 0.498168i | ||||
\(394\) | 2.90330 | − | 5.02867i | 0.146266 | − | 0.253340i | ||||
\(395\) | −0.995419 | − | 1.72412i | −0.0500850 | − | 0.0867497i | ||||
\(396\) | −2.82542 | − | 0.867469i | −0.141983 | − | 0.0435919i | ||||
\(397\) | 17.0604 | + | 9.84982i | 0.856236 | + | 0.494348i | 0.862750 | − | 0.505631i | \(-0.168740\pi\) |
−0.00651405 | + | 0.999979i | \(0.502074\pi\) | |||||||
\(398\) | −13.0693 | −0.655106 | ||||||||
\(399\) | 11.7688 | − | 22.3020i | 0.589179 | − | 1.11650i | ||||
\(400\) | 5.17412 | 0.258706 | ||||||||
\(401\) | 30.2790 | + | 17.4816i | 1.51206 | + | 0.872990i | 0.999901 | + | 0.0141006i | \(0.00448851\pi\) |
0.512162 | + | 0.858889i | \(0.328845\pi\) | |||||||
\(402\) | −18.3724 | + | 2.08228i | −0.916330 | + | 0.103854i | ||||
\(403\) | 10.0926 | + | 17.4810i | 0.502750 | + | 0.870788i | ||||
\(404\) | −0.457469 | + | 0.792360i | −0.0227600 | + | 0.0394214i | ||||
\(405\) | −0.219251 | + | 3.03247i | −0.0108946 | + | 0.150685i | ||||
\(406\) | −15.6857 | + | 23.0056i | −0.778467 | + | 1.14175i | ||||
\(407\) | − | 3.91631i | − | 0.194124i | ||||||
\(408\) | 3.20134 | + | 4.33170i | 0.158490 | + | 0.214451i | ||||
\(409\) | 2.18524 | − | 1.26165i | 0.108053 | − | 0.0623844i | −0.445000 | − | 0.895531i | \(-0.646796\pi\) |
0.553053 | + | 0.833146i | \(0.313463\pi\) | |||||||
\(410\) | −3.30814 | + | 1.90995i | −0.163377 | + | 0.0943259i | ||||
\(411\) | 5.34801 | + | 7.23636i | 0.263798 | + | 0.356943i | ||||
\(412\) | 2.46494i | 0.121439i | ||||||||
\(413\) | −6.10374 | − | 12.6752i | −0.300345 | − | 0.623708i | ||||
\(414\) | −1.85566 | − | 1.99467i | −0.0912006 | − | 0.0980325i | ||||
\(415\) | 1.17245 | − | 2.03075i | 0.0575534 | − | 0.0996854i | ||||
\(416\) | 15.3067 | + | 26.5120i | 0.750474 | + | 1.29986i | ||||
\(417\) | 1.41669 | − | 0.160564i | 0.0693758 | − | 0.00786287i | ||||
\(418\) | −4.80066 | − | 2.77166i | −0.234808 | − | 0.135567i | ||||
\(419\) | −15.0762 | −0.736521 | −0.368260 | − | 0.929723i | \(-0.620046\pi\) | ||||
−0.368260 | + | 0.929723i | \(0.620046\pi\) | |||||||
\(420\) | −0.0579952 | − | 1.52407i | −0.00282988 | − | 0.0743669i | ||||
\(421\) | 16.4642 | 0.802416 | 0.401208 | − | 0.915987i | \(-0.368590\pi\) | ||||
0.401208 | + | 0.915987i | \(0.368590\pi\) | |||||||
\(422\) | −4.86982 | − | 2.81159i | −0.237059 | − | 0.136866i | ||||
\(423\) | −6.36712 | + | 20.7383i | −0.309580 | + | 1.00833i | ||||
\(424\) | −13.1110 | − | 22.7089i | −0.636726 | − | 1.10284i | ||||
\(425\) | 2.52626 | − | 4.37561i | 0.122542 | − | 0.212248i | ||||
\(426\) | 14.4912 | + | 6.31114i | 0.702102 | + | 0.305776i | ||||
\(427\) | −7.06070 | − | 4.81413i | −0.341691 | − | 0.232972i | ||||
\(428\) | 8.10323i | 0.391684i | ||||||||
\(429\) | 8.61877 | − | 6.36968i | 0.416118 | − | 0.307531i | ||||
\(430\) | 1.99297 | − | 1.15064i | 0.0961096 | − | 0.0554889i | ||||
\(431\) | −15.1701 | + | 8.75845i | −0.730717 | + | 0.421880i | −0.818685 | − | 0.574243i | \(-0.805296\pi\) |
0.0879672 | + | 0.996123i | \(0.471963\pi\) | |||||||
\(432\) | 5.40877 | + | 1.01237i | 0.260230 | + | 0.0487077i | ||||
\(433\) | 37.2422i | 1.78974i | 0.446322 | + | 0.894872i | \(0.352733\pi\) | ||||
−0.446322 | + | 0.894872i | \(0.647267\pi\) | |||||||
\(434\) | −8.67045 | − | 0.649947i | −0.416195 | − | 0.0311985i | ||||
\(435\) | −2.44079 | + | 5.60437i | −0.117027 | + | 0.268709i | ||||
\(436\) | −2.29078 | + | 3.96774i | −0.109708 | + | 0.190020i | ||||
\(437\) | 2.48029 | + | 4.29599i | 0.118648 | + | 0.205505i | ||||
\(438\) | 0.768873 | + | 6.78393i | 0.0367382 | + | 0.324149i | ||||
\(439\) | −23.4810 | − | 13.5567i | −1.12069 | − | 0.647028i | −0.179110 | − | 0.983829i | \(-0.557322\pi\) |
−0.941576 | + | 0.336801i | \(0.890655\pi\) | |||||||
\(440\) | −1.01590 | −0.0484310 | ||||||||
\(441\) | −20.9393 | + | 1.59591i | −0.997108 | + | 0.0759958i | ||||
\(442\) | −6.44574 | −0.306593 | ||||||||
\(443\) | −15.4316 | − | 8.90943i | −0.733177 | − | 0.423300i | 0.0864065 | − | 0.996260i | \(-0.472462\pi\) |
−0.819583 | + | 0.572960i | \(0.805795\pi\) | |||||||
\(444\) | −0.752597 | − | 6.64032i | −0.0357167 | − | 0.315136i | ||||
\(445\) | 0.616986 | + | 1.06865i | 0.0292479 | + | 0.0506589i | ||||
\(446\) | 1.16904 | − | 2.02484i | 0.0553557 | − | 0.0958788i | ||||
\(447\) | −0.792813 | + | 1.82040i | −0.0374988 | + | 0.0861022i | ||||
\(448\) | −18.7378 | − | 1.40461i | −0.885278 | − | 0.0663615i | ||||
\(449\) | 27.7358i | 1.30893i | 0.756092 | + | 0.654466i | \(0.227106\pi\) | ||||
−0.756092 | + | 0.654466i | \(0.772894\pi\) | |||||||
\(450\) | −3.30457 | − | 14.3912i | −0.155779 | − | 0.678407i | ||||
\(451\) | −9.72090 | + | 5.61237i | −0.457740 | + | 0.264276i | ||||
\(452\) | 3.86349 | − | 2.23059i | 0.181723 | − | 0.104918i | ||||
\(453\) | −20.3095 | + | 15.0097i | −0.954221 | + | 0.705215i | ||||
\(454\) | − | 0.418487i | − | 0.0196406i | ||||||
\(455\) | 4.56931 | + | 3.11544i | 0.214212 | + | 0.146054i | ||||
\(456\) | −26.2779 | − | 11.4444i | −1.23057 | − | 0.535933i | ||||
\(457\) | 1.13233 | − | 1.96125i | 0.0529682 | − | 0.0917436i | −0.838326 | − | 0.545170i | \(-0.816465\pi\) |
0.891294 | + | 0.453426i | \(0.149798\pi\) | |||||||
\(458\) | 3.22484 | + | 5.58559i | 0.150687 | + | 0.260998i | ||||
\(459\) | 3.49697 | − | 4.07976i | 0.163224 | − | 0.190427i | ||||
\(460\) | 0.259832 | + | 0.150014i | 0.0121147 | + | 0.00699444i | ||||
\(461\) | −20.6585 | −0.962161 | −0.481081 | − | 0.876676i | \(-0.659756\pi\) | ||||
−0.481081 | + | 0.876676i | \(0.659756\pi\) | |||||||
\(462\) | 0.175539 | + | 4.61303i | 0.00816683 | + | 0.214618i | ||||
\(463\) | 29.3828 | 1.36554 | 0.682768 | − | 0.730635i | \(-0.260776\pi\) | ||||
0.682768 | + | 0.730635i | \(0.260776\pi\) | |||||||
\(464\) | 9.58117 | + | 5.53169i | 0.444795 | + | 0.256802i | ||||
\(465\) | −1.89668 | + | 0.214964i | −0.0879562 | + | 0.00996873i | ||||
\(466\) | −0.393295 | − | 0.681208i | −0.0182191 | − | 0.0315563i | ||||
\(467\) | 20.3668 | − | 35.2764i | 0.942464 | − | 1.63240i | 0.181714 | − | 0.983351i | \(-0.441836\pi\) |
0.760750 | − | 0.649045i | \(-0.224831\pi\) | |||||||
\(468\) | 13.3895 | − | 12.4564i | 0.618932 | − | 0.575798i | ||||
\(469\) | −12.1643 | − | 25.2609i | −0.561696 | − | 1.16644i | ||||
\(470\) | 2.46087i | 0.113512i | ||||||||
\(471\) | −12.2196 | − | 16.5343i | −0.563050 | − | 0.761859i | ||||
\(472\) | −13.8480 | + | 7.99516i | −0.637407 | + | 0.368007i | ||||
\(473\) | 5.85631 | − | 3.38114i | 0.269273 | − | 0.155465i | ||||
\(474\) | 6.11142 | + | 8.26933i | 0.280707 | + | 0.379823i | ||||
\(475\) | 26.8858i | 1.23360i | ||||||||
\(476\) | −1.51847 | + | 2.22709i | −0.0695990 | + | 0.102078i | ||||
\(477\) | −19.1526 | + | 17.8179i | −0.876939 | + | 0.815824i | ||||
\(478\) | −13.6532 | + | 23.6481i | −0.624485 | + | 1.08164i | ||||
\(479\) | −8.33913 | − | 14.4438i | −0.381025 | − | 0.659954i | 0.610184 | − | 0.792259i | \(-0.291095\pi\) |
−0.991209 | + | 0.132306i | \(0.957762\pi\) | |||||||
\(480\) | −2.87654 | + | 0.326020i | −0.131296 | + | 0.0148807i | ||||
\(481\) | 20.9857 | + | 12.1161i | 0.956867 | + | 0.552447i | ||||
\(482\) | −12.5436 | −0.571345 | ||||||||
\(483\) | 1.92800 | − | 3.65357i | 0.0877271 | − | 0.166243i | ||||
\(484\) | −0.985197 | −0.0447817 | ||||||||
\(485\) | −2.70232 | − | 1.56018i | −0.122706 | − | 0.0708442i | ||||
\(486\) | −0.638644 | − | 15.6904i | −0.0289695 | − | 0.711732i | ||||
\(487\) | 0.404579 | + | 0.700752i | 0.0183332 | + | 0.0317541i | 0.875046 | − | 0.484039i | \(-0.160831\pi\) |
−0.856713 | + | 0.515793i | \(0.827497\pi\) | |||||||
\(488\) | −4.85661 | + | 8.41190i | −0.219848 | + | 0.380789i | ||||
\(489\) | −23.1065 | − | 10.0632i | −1.04491 | − | 0.455075i | ||||
\(490\) | −2.21755 | + | 0.870213i | −0.100179 | + | 0.0393122i | ||||
\(491\) | 2.13467i | 0.0963365i | 0.998839 | + | 0.0481682i | \(0.0153384\pi\) | ||||
−0.998839 | + | 0.0481682i | \(0.984662\pi\) | |||||||
\(492\) | −15.4038 | + | 11.3841i | −0.694457 | + | 0.513237i | ||||
\(493\) | 9.35601 | − | 5.40169i | 0.421374 | − | 0.243280i | ||||
\(494\) | 29.7042 | − | 17.1497i | 1.33645 | − | 0.771602i | ||||
\(495\) | 0.226813 | + | 0.987755i | 0.0101945 | + | 0.0443963i | ||||
\(496\) | 3.45471i | 0.155121i | ||||||||
\(497\) | −1.79158 | + | 23.9001i | −0.0803633 | + | 1.07207i | ||||
\(498\) | −4.83593 | + | 11.1039i | −0.216703 | + | 0.497579i | ||||
\(499\) | −0.305648 | + | 0.529398i | −0.0136827 | + | 0.0236991i | −0.872786 | − | 0.488104i | \(-0.837689\pi\) |
0.859103 | + | 0.511803i | \(0.171022\pi\) | |||||||
\(500\) | 1.64511 | + | 2.84941i | 0.0735714 | + | 0.127429i | ||||
\(501\) | 3.74244 | + | 33.0203i | 0.167200 | + | 1.47524i | ||||
\(502\) | −5.42651 | − | 3.13299i | −0.242197 | − | 0.139832i | ||||
\(503\) | 29.3406 | 1.30823 | 0.654116 | − | 0.756394i | \(-0.273041\pi\) | ||||
0.654116 | + | 0.756394i | \(0.273041\pi\) | |||||||
\(504\) | 3.58795 | + | 23.5978i | 0.159820 | + | 1.05113i | ||||
\(505\) | 0.313729 | 0.0139608 | ||||||||
\(506\) | −0.786456 | − | 0.454061i | −0.0349622 | − | 0.0201855i | ||||
\(507\) | 4.93209 | + | 43.5169i | 0.219042 | + | 1.93265i | ||||
\(508\) | −5.41569 | − | 9.38025i | −0.240283 | − | 0.416182i | ||||
\(509\) | 2.26128 | − | 3.91665i | 0.100229 | − | 0.173602i | −0.811550 | − | 0.584283i | \(-0.801376\pi\) |
0.911779 | + | 0.410681i | \(0.134709\pi\) | |||||||
\(510\) | 0.243384 | − | 0.558842i | 0.0107772 | − | 0.0247460i | ||||
\(511\) | −9.32749 | + | 4.49163i | −0.412624 | + | 0.198698i | ||||
\(512\) | 11.6087i | 0.513039i | ||||||||
\(513\) | −5.26048 | + | 28.1050i | −0.232256 | + | 1.24087i | ||||
\(514\) | −0.456902 | + | 0.263793i | −0.0201531 | + | 0.0116354i | ||||
\(515\) | 0.731981 | − | 0.422609i | 0.0322549 | − | 0.0186224i | ||||
\(516\) | 9.27994 | − | 6.85832i | 0.408527 | − | 0.301921i | ||||
\(517\) | 7.23123i | 0.318029i | ||||||||
\(518\) | −9.40441 | + | 4.52868i | −0.413206 | + | 0.198979i | ||||
\(519\) | −32.7241 | − | 14.2518i | −1.43643 | − | 0.625586i | ||||
\(520\) | 3.14294 | − | 5.44373i | 0.137827 | − | 0.238723i | ||||
\(521\) | 5.56886 | + | 9.64555i | 0.243976 | + | 0.422579i | 0.961843 | − | 0.273601i | \(-0.0882148\pi\) |
−0.717867 | + | 0.696180i | \(0.754881\pi\) | |||||||
\(522\) | 9.26651 | − | 30.1818i | 0.405584 | − | 1.32102i | ||||
\(523\) | 5.05795 | + | 2.92021i | 0.221169 | + | 0.127692i | 0.606491 | − | 0.795090i | \(-0.292577\pi\) |
−0.385323 | + | 0.922782i | \(0.625910\pi\) | |||||||
\(524\) | 14.0684 | 0.614582 | ||||||||
\(525\) | 18.9505 | − | 11.9242i | 0.827068 | − | 0.520414i | ||||
\(526\) | 0.782716 | 0.0341280 | ||||||||
\(527\) | 2.92156 | + | 1.68676i | 0.127265 | + | 0.0734766i | ||||
\(528\) | 1.82256 | − | 0.206565i | 0.0793169 | − | 0.00898958i | ||||
\(529\) | −11.0937 | − | 19.2148i | −0.482334 | − | 0.835426i | ||||
\(530\) | −1.48371 | + | 2.56986i | −0.0644482 | + | 0.111628i | ||||
\(531\) | 10.8654 | + | 11.6794i | 0.471519 | + | 0.506842i | ||||
\(532\) | 1.07219 | − | 14.3033i | 0.0464853 | − | 0.620125i | ||||
\(533\) | − | 69.4532i | − | 3.00835i | ||||||
\(534\) | −3.78802 | − | 5.12554i | −0.163923 | − | 0.221804i | ||||
\(535\) | 2.40631 | − | 1.38928i | 0.104034 | − | 0.0600640i | ||||
\(536\) | −27.5981 | + | 15.9338i | −1.19206 | + | 0.688235i | ||||
\(537\) | −0.852750 | − | 1.15385i | −0.0367989 | − | 0.0497923i | ||||
\(538\) | − | 12.0495i | − | 0.519491i | ||||||
\(539\) | −6.51623 | + | 2.55711i | −0.280674 | + | 0.110142i | ||||
\(540\) | 0.574390 | + | 1.63121i | 0.0247178 | + | 0.0701959i | ||||
\(541\) | 15.8159 | − | 27.3939i | 0.679978 | − | 1.17776i | −0.295009 | − | 0.955494i | \(-0.595323\pi\) |
0.974987 | − | 0.222262i | \(-0.0713439\pi\) | |||||||
\(542\) | −5.57196 | − | 9.65093i | −0.239336 | − | 0.414543i | ||||
\(543\) | 14.0256 | − | 1.58962i | 0.601896 | − | 0.0682173i | ||||
\(544\) | 4.43091 | + | 2.55819i | 0.189974 | + | 0.109681i | ||||
\(545\) | 1.57100 | 0.0672942 | ||||||||
\(546\) | −25.2622 | − | 13.3310i | −1.08112 | − | 0.570513i | ||||
\(547\) | 6.31442 | 0.269985 | 0.134993 | − | 0.990847i | \(-0.456899\pi\) | ||||
0.134993 | + | 0.990847i | \(0.456899\pi\) | |||||||
\(548\) | 4.43246 | + | 2.55908i | 0.189345 | + | 0.109319i | ||||
\(549\) | 9.26318 | + | 2.84401i | 0.395343 | + | 0.121379i | ||||
\(550\) | −2.46095 | − | 4.26250i | −0.104935 | − | 0.181754i | ||||
\(551\) | −28.7438 | + | 49.7857i | −1.22453 | + | 2.12094i | ||||
\(552\) | −4.30491 | − | 1.87485i | −0.183229 | − | 0.0797989i | ||||
\(553\) | −8.78351 | + | 12.8824i | −0.373513 | + | 0.547817i | ||||
\(554\) | 11.9395i | 0.507260i | ||||||||
\(555\) | −1.84286 | + | 1.36196i | −0.0782250 | + | 0.0578120i | ||||
\(556\) | 0.702329 | − | 0.405490i | 0.0297854 | − | 0.0171966i | ||||
\(557\) | 1.41798 | − | 0.818668i | 0.0600815 | − | 0.0346881i | −0.469658 | − | 0.882848i | \(-0.655623\pi\) |
0.529740 | + | 0.848160i | \(0.322290\pi\) | |||||||
\(558\) | 9.60887 | − | 2.20643i | 0.406776 | − | 0.0934057i | ||||
\(559\) | 41.8417i | 1.76972i | ||||||||
\(560\) | 0.410660 | + | 0.852791i | 0.0173536 | + | 0.0360370i | ||||
\(561\) | 0.715180 | − | 1.64215i | 0.0301949 | − | 0.0693316i | ||||
\(562\) | −5.98952 | + | 10.3742i | −0.252653 | + | 0.437608i | ||||
\(563\) | 10.6341 | + | 18.4189i | 0.448175 | + | 0.776263i | 0.998267 | − | 0.0588414i | \(-0.0187406\pi\) |
−0.550092 | + | 0.835104i | \(0.685407\pi\) | |||||||
\(564\) | 1.38962 | + | 12.2610i | 0.0585138 | + | 0.516279i | ||||
\(565\) | −1.32478 | − | 0.764860i | −0.0557338 | − | 0.0321779i | ||||
\(566\) | −27.9057 | −1.17297 | ||||||||
\(567\) | 22.1430 | − | 8.75708i | 0.929920 | − | 0.367763i | ||||
\(568\) | 27.2415 | 1.14303 | ||||||||
\(569\) | −5.93181 | − | 3.42473i | −0.248674 | − | 0.143572i | 0.370483 | − | 0.928839i | \(-0.379192\pi\) |
−0.619157 | + | 0.785267i | \(0.712526\pi\) | |||||||
\(570\) | 0.365274 | + | 3.22289i | 0.0152996 | + | 0.134992i | ||||
\(571\) | −10.7464 | − | 18.6134i | −0.449725 | − | 0.778946i | 0.548643 | − | 0.836057i | \(-0.315145\pi\) |
−0.998368 | + | 0.0571108i | \(0.981811\pi\) | |||||||
\(572\) | 3.04796 | − | 5.27922i | 0.127442 | − | 0.220735i | ||||
\(573\) | 13.4915 | − | 30.9784i | 0.563617 | − | 1.29414i | ||||
\(574\) | 24.7181 | + | 16.8533i | 1.03171 | + | 0.703443i | ||||
\(575\) | 4.40449i | 0.183680i | ||||||||
\(576\) | 20.7658 | − | 4.76835i | 0.865244 | − | 0.198681i | ||||
\(577\) | 2.43897 | − | 1.40814i | 0.101536 | − | 0.0586216i | −0.448372 | − | 0.893847i | \(-0.647996\pi\) |
0.549908 | + | 0.835225i | \(0.314663\pi\) | |||||||
\(578\) | 13.8981 | − | 8.02405i | 0.578083 | − | 0.333757i | ||||
\(579\) | 24.1592 | − | 17.8548i | 1.00402 | − | 0.742019i | ||||
\(580\) | 3.47699i | 0.144374i | ||||||||
\(581\) | −18.3135 | − | 1.37280i | −0.759772 | − | 0.0569534i | ||||
\(582\) | 14.7760 | + | 6.43517i | 0.612486 | + | 0.266747i | ||||
\(583\) | −4.35985 | + | 7.55149i | −0.180567 | + | 0.312751i | ||||
\(584\) | 5.88349 | + | 10.1905i | 0.243461 | + | 0.421686i | ||||
\(585\) | −5.99463 | − | 1.84049i | −0.247847 | − | 0.0760948i | ||||
\(586\) | 9.18959 | + | 5.30561i | 0.379619 | + | 0.219173i | ||||
\(587\) | −35.6049 | −1.46957 | −0.734785 | − | 0.678300i | \(-0.762717\pi\) | ||||
−0.734785 | + | 0.678300i | \(0.762717\pi\) | |||||||
\(588\) | −10.5572 | + | 5.58794i | −0.435372 | + | 0.230443i | ||||
\(589\) | −17.9514 | −0.739674 | ||||||||
\(590\) | 1.56711 | + | 0.904773i | 0.0645170 | + | 0.0372489i | ||||
\(591\) | −9.92019 | + | 1.12433i | −0.408062 | + | 0.0462487i | ||||
\(592\) | 2.07368 | + | 3.59171i | 0.0852276 | + | 0.147618i | ||||
\(593\) | 11.0826 | − | 19.1956i | 0.455107 | − | 0.788269i | −0.543587 | − | 0.839353i | \(-0.682934\pi\) |
0.998694 | + | 0.0510837i | \(0.0162675\pi\) | |||||||
\(594\) | −1.73856 | − | 4.93732i | −0.0713339 | − | 0.202581i | ||||
\(595\) | 0.921688 | + | 0.0690908i | 0.0377855 | + | 0.00283245i | ||||
\(596\) | 1.12939i | 0.0462616i | ||||||||
\(597\) | 13.3556 | + | 18.0714i | 0.546608 | + | 0.739612i | ||||
\(598\) | 4.86621 | − | 2.80951i | 0.198994 | − | 0.114889i | ||||
\(599\) | 24.1121 | − | 13.9211i | 0.985193 | − | 0.568802i | 0.0813594 | − | 0.996685i | \(-0.474074\pi\) |
0.903834 | + | 0.427883i | \(0.140741\pi\) | |||||||
\(600\) | −15.1254 | − | 20.4661i | −0.617493 | − | 0.835526i | ||||
\(601\) | − | 28.3202i | − | 1.15521i | −0.816318 | − | 0.577603i | \(-0.803988\pi\) | ||
0.816318 | − | 0.577603i | \(-0.196012\pi\) | |||||||
\(602\) | −14.8913 | − | 10.1532i | −0.606924 | − | 0.413813i | ||||
\(603\) | 21.6540 | + | 23.2762i | 0.881820 | + | 0.947879i | ||||
\(604\) | −7.18228 | + | 12.4401i | −0.292243 | + | 0.506179i | ||||
\(605\) | 0.168910 | + | 0.292561i | 0.00686717 | + | 0.0118943i | ||||
\(606\) | −1.61009 | + | 0.182483i | −0.0654053 | + | 0.00741287i | ||||
\(607\) | 22.3848 | + | 12.9239i | 0.908573 | + | 0.524565i | 0.879972 | − | 0.475026i | \(-0.157561\pi\) |
0.0286011 | + | 0.999591i | \(0.490895\pi\) | |||||||
\(608\) | −27.2255 | −1.10414 | ||||||||
\(609\) | 47.8398 | − | 1.82045i | 1.93857 | − | 0.0737682i | ||||
\(610\) | 1.09920 | 0.0445053 | ||||||||
\(611\) | −38.7489 | − | 22.3717i | −1.56761 | − | 0.905061i | ||||
\(612\) | 0.897056 | − | 2.92179i | 0.0362613 | − | 0.118106i | ||||
\(613\) | −9.15558 | − | 15.8579i | −0.369790 | − | 0.640496i | 0.619742 | − | 0.784805i | \(-0.287237\pi\) |
−0.989533 | + | 0.144310i | \(0.953904\pi\) | |||||||
\(614\) | −0.743624 | + | 1.28799i | −0.0300102 | + | 0.0519792i | ||||
\(615\) | 6.02155 | + | 2.62248i | 0.242813 | + | 0.105748i | ||||
\(616\) | 3.45197 | + | 7.16848i | 0.139084 | + | 0.288826i | ||||
\(617\) | − | 41.3739i | − | 1.66565i | −0.553537 | − | 0.832825i | \(-0.686722\pi\) | ||
0.553537 | − | 0.832825i | \(-0.313278\pi\) | |||||||
\(618\) | −3.51078 | + | 2.59463i | −0.141224 | + | 0.104371i | ||||
\(619\) | −14.6907 | + | 8.48170i | −0.590470 | + | 0.340908i | −0.765284 | − | 0.643693i | \(-0.777401\pi\) |
0.174813 | + | 0.984602i | \(0.444068\pi\) | |||||||
\(620\) | −0.940281 | + | 0.542871i | −0.0377626 | + | 0.0218022i | ||||
\(621\) | −0.861785 | + | 4.60424i | −0.0345823 | + | 0.184762i | ||||
\(622\) | − | 22.5305i | − | 0.903391i | ||||||
\(623\) | 5.44424 | − | 7.98487i | 0.218119 | − | 0.319907i | ||||
\(624\) | −4.53168 | + | 10.4054i | −0.181413 | + | 0.416547i | ||||
\(625\) | −11.6506 | + | 20.1794i | −0.466024 | + | 0.807177i | ||||
\(626\) | 0.891054 | + | 1.54335i | 0.0356137 | + | 0.0616847i | ||||
\(627\) | 1.07335 | + | 9.47041i | 0.0428655 | + | 0.378212i | ||||
\(628\) | −10.1277 | − | 5.84721i | −0.404138 | − | 0.233329i | ||||
\(629\) | 4.04989 | 0.161480 | ||||||||
\(630\) | 2.10966 | − | 1.68686i | 0.0840509 | − | 0.0672060i | ||||
\(631\) | 0.630437 | 0.0250973 | 0.0125487 | − | 0.999921i | \(-0.496006\pi\) | ||||
0.0125487 | + | 0.999921i | \(0.496006\pi\) | |||||||
\(632\) | 15.3477 | + | 8.86103i | 0.610501 | + | 0.352473i | ||||
\(633\) | 1.08881 | + | 9.60683i | 0.0432765 | + | 0.381837i | ||||
\(634\) | −5.77352 | − | 10.0000i | −0.229296 | − | 0.397152i | ||||
\(635\) | −1.85702 | + | 3.21646i | −0.0736936 | + | 0.127641i | ||||
\(636\) | −5.94120 | + | 13.6418i | −0.235584 | + | 0.540932i | ||||
\(637\) | 6.45724 | − | 42.8286i | 0.255845 | − | 1.69693i | ||||
\(638\) | − | 10.5241i | − | 0.416653i | ||||||
\(639\) | −6.08203 | − | 26.4869i | −0.240602 | − | 1.04780i | ||||
\(640\) | −0.801841 | + | 0.462943i | −0.0316956 | + | 0.0182994i | ||||
\(641\) | −11.7256 | + | 6.76979i | −0.463134 | + | 0.267391i | −0.713361 | − | 0.700797i | \(-0.752828\pi\) |
0.250227 | + | 0.968187i | \(0.419495\pi\) | |||||||
\(642\) | −11.5413 | + | 8.52958i | −0.455499 | + | 0.336635i | ||||
\(643\) | 1.36678i | 0.0539005i | 0.999637 | + | 0.0269503i | \(0.00857958\pi\) | ||||
−0.999637 | + | 0.0269503i | \(0.991420\pi\) | |||||||
\(644\) | 0.175649 | − | 2.34319i | 0.00692152 | − | 0.0923347i | ||||
\(645\) | −3.62766 | − | 1.57990i | −0.142839 | − | 0.0622084i | ||||
\(646\) | 2.86620 | − | 4.96440i | 0.112769 | − | 0.195322i | ||||
\(647\) | −7.64192 | − | 13.2362i | −0.300435 | − | 0.520368i | 0.675800 | − | 0.737085i | \(-0.263798\pi\) |
−0.976234 | + | 0.216717i | \(0.930465\pi\) | |||||||
\(648\) | −11.8070 | − | 24.3537i | −0.463822 | − | 0.956705i | ||||
\(649\) | 4.60494 | + | 2.65866i | 0.180760 | + | 0.104362i | ||||
\(650\) | 30.4544 | 1.19452 | ||||||||
\(651\) | 7.96167 | + | 12.6531i | 0.312042 | + | 0.495914i | ||||
\(652\) | −14.3354 | −0.561419 | ||||||||
\(653\) | 7.60587 | + | 4.39125i | 0.297641 | + | 0.171843i | 0.641382 | − | 0.767221i | \(-0.278361\pi\) |
−0.343742 | + | 0.939064i | \(0.611695\pi\) | |||||||
\(654\) | −8.06251 | + | 0.913784i | −0.315269 | + | 0.0357318i | ||||
\(655\) | −2.41200 | − | 4.17771i | −0.0942448 | − | 0.163237i | ||||
\(656\) | 5.94347 | − | 10.2944i | 0.232053 | − | 0.401928i | ||||
\(657\) | 8.59464 | − | 7.99568i | 0.335309 | − | 0.311941i | ||||
\(658\) | 17.3647 | − | 8.36193i | 0.676945 | − | 0.325982i | ||||
\(659\) | − | 16.6074i | − | 0.646932i | −0.946240 | − | 0.323466i | \(-0.895152\pi\) | ||
0.946240 | − | 0.323466i | \(-0.104848\pi\) | |||||||
\(660\) | 0.342618 | + | 0.463594i | 0.0133364 | + | 0.0180454i | ||||
\(661\) | 30.8566 | − | 17.8151i | 1.20018 | − | 0.692927i | 0.239588 | − | 0.970875i | \(-0.422988\pi\) |
0.960596 | + | 0.277948i | \(0.0896542\pi\) | |||||||
\(662\) | 3.56131 | − | 2.05612i | 0.138414 | − | 0.0799135i | ||||
\(663\) | 6.58694 | + | 8.91274i | 0.255815 | + | 0.346142i | ||||
\(664\) | 20.8739i | 0.810064i | ||||||||
\(665\) | −4.43128 | + | 2.13387i | −0.171837 | + | 0.0827480i | ||||
\(666\) | 8.66552 | − | 8.06161i | 0.335782 | − | 0.312381i | ||||
\(667\) | −4.70888 | + | 8.15601i | −0.182328 | + | 0.315802i | ||||
\(668\) | 9.45116 | + | 16.3699i | 0.365676 | + | 0.633370i | ||||
\(669\) | −3.99446 | + | 0.452721i | −0.154435 | + | 0.0175032i | ||||
\(670\) | 3.12315 | + | 1.80315i | 0.120658 | + | 0.0696617i | ||||
\(671\) | 3.22998 | 0.124692 | ||||||||
\(672\) | 12.0749 | + | 19.1900i | 0.465798 | + | 0.740269i | ||||
\(673\) | −3.23910 | −0.124858 | −0.0624290 | − | 0.998049i | \(-0.519885\pi\) | ||||
−0.0624290 | + | 0.998049i | \(0.519885\pi\) | |||||||
\(674\) | −24.6703 | − | 14.2434i | −0.950263 | − | 0.548635i | ||||
\(675\) | −16.5222 | + | 19.2758i | −0.635940 | + | 0.741925i | ||||
\(676\) | 12.4555 | + | 21.5736i | 0.479058 | + | 0.829753i | ||||
\(677\) | −9.42272 | + | 16.3206i | −0.362145 | + | 0.627253i | −0.988314 | − | 0.152435i | \(-0.951289\pi\) |
0.626169 | + | 0.779687i | \(0.284622\pi\) | |||||||
\(678\) | 7.24376 | + | 3.15476i | 0.278195 | + | 0.121158i | ||||
\(679\) | −1.82679 | + | 24.3698i | −0.0701057 | + | 0.935227i | ||||
\(680\) | − | 1.05055i | − | 0.0402866i | ||||||
\(681\) | −0.578655 | + | 0.427654i | −0.0221741 | + | 0.0163877i | ||||
\(682\) | 2.84603 | − | 1.64316i | 0.108980 | − | 0.0629198i | ||||
\(683\) | −25.0963 | + | 14.4894i | −0.960284 | + | 0.554420i | −0.896260 | − | 0.443528i | \(-0.853727\pi\) |
−0.0640233 | + | 0.997948i | \(0.520393\pi\) | |||||||
\(684\) | 3.63985 | + | 15.8513i | 0.139173 | + | 0.606091i | ||||
\(685\) | − | 1.75500i | − | 0.0670551i | ||||||
\(686\) | 13.6756 | + | 12.6908i | 0.522137 | + | 0.484535i | ||||
\(687\) | 4.42790 | − | 10.1670i | 0.168935 | − | 0.387897i | ||||
\(688\) | −3.58061 | + | 6.20180i | −0.136510 | + | 0.236441i | ||||
\(689\) | −26.9767 | − | 46.7249i | −1.02773 | − | 1.78008i | ||||
\(690\) | 0.0598401 | + | 0.527982i | 0.00227807 | + | 0.0200999i | ||||
\(691\) | 17.6136 | + | 10.1692i | 0.670052 | + | 0.386855i | 0.796096 | − | 0.605170i | \(-0.206895\pi\) |
−0.126044 | + | 0.992025i | \(0.540228\pi\) | |||||||
\(692\) | −20.3022 | −0.771775 | ||||||||
\(693\) | 6.19920 | − | 4.95680i | 0.235488 | − | 0.188293i | ||||
\(694\) | −19.4284 | −0.737494 | ||||||||
\(695\) | −0.240826 | − | 0.139041i | −0.00913505 | − | 0.00527412i | ||||
\(696\) | −6.12802 | − | 54.0689i | −0.232282 | − | 2.04947i | ||||
\(697\) | −5.80379 | − | 10.0525i | −0.219834 | − | 0.380764i | ||||
\(698\) | 2.79432 | − | 4.83991i | 0.105767 | − | 0.183193i | ||||
\(699\) | −0.540017 | + | 1.23995i | −0.0204253 | + | 0.0468993i | ||||
\(700\) | 7.17436 | − | 10.5224i | 0.271165 | − | 0.397708i | ||||
\(701\) | 16.8832i | 0.637670i | 0.947810 | + | 0.318835i | \(0.103292\pi\) | ||||
−0.947810 | + | 0.318835i | \(0.896708\pi\) | |||||||
\(702\) | 31.8355 | + | 5.95872i | 1.20155 | + | 0.224898i | ||||
\(703\) | −18.6633 | + | 10.7752i | −0.703898 | + | 0.406396i | ||||
\(704\) | 6.15059 | − | 3.55105i | 0.231809 | − | 0.133835i | ||||
\(705\) | 3.40273 | − | 2.51478i | 0.128154 | − | 0.0947120i | ||||
\(706\) | − | 15.3129i | − | 0.576310i | ||||||
\(707\) | −1.06604 | − | 2.21377i | −0.0400924 | − | 0.0832574i | ||||
\(708\) | 8.31884 | + | 3.62298i | 0.312641 | + | 0.136160i | ||||
\(709\) | 20.7229 | − | 35.8931i | 0.778264 | − | 1.34799i | −0.154677 | − | 0.987965i | \(-0.549434\pi\) |
0.932941 | − | 0.360028i | \(-0.117233\pi\) | |||||||
\(710\) | −1.54140 | − | 2.66978i | −0.0578476 | − | 0.100195i | ||||
\(711\) | 5.18897 | − | 16.9009i | 0.194602 | − | 0.633834i | ||||
\(712\) | −9.51292 | − | 5.49229i | −0.356512 | − | 0.205832i | ||||
\(713\) | −2.94084 | −0.110135 | ||||||||
\(714\) | −4.77037 | + | 0.181527i | −0.178527 | + | 0.00679346i | ||||
\(715\) | −2.09027 | −0.0781716 | ||||||||
\(716\) | −0.706763 | − | 0.408050i | −0.0264130 | − | 0.0152495i | ||||
\(717\) | 46.6513 | − | 5.28734i | 1.74223 | − | 0.197459i | ||||
\(718\) | −12.2265 | − | 21.1769i | −0.456289 | − | 0.790316i | ||||
\(719\) | 11.4358 | − | 19.8073i | 0.426482 | − | 0.738689i | −0.570075 | − | 0.821592i | \(-0.693086\pi\) |
0.996558 | + | 0.0829037i | \(0.0264194\pi\) | |||||||
\(720\) | −0.731027 | − | 0.785789i | −0.0272438 | − | 0.0292846i | ||||
\(721\) | −5.46930 | − | 3.72908i | −0.203687 | − | 0.138878i | ||||
\(722\) | 11.3634i | 0.422903i | ||||||||
\(723\) | 12.8183 | + | 17.3444i | 0.476720 | + | 0.645046i | ||||
\(724\) | 6.95321 | − | 4.01444i | 0.258414 | − | 0.149196i | ||||
\(725\) | −44.2046 | + | 25.5215i | −1.64172 | + | 0.947846i | ||||
\(726\) | −1.03703 | − | 1.40320i | −0.0384879 | − | 0.0520777i | ||||
\(727\) | − | 6.85223i | − | 0.254135i | −0.991894 | − | 0.127067i | \(-0.959444\pi\) | ||
0.991894 | − | 0.127067i | \(-0.0405565\pi\) | |||||||
\(728\) | −49.0922 | − | 3.68001i | −1.81948 | − | 0.136390i | ||||
\(729\) | −21.0430 | + | 16.9172i | −0.779371 | + | 0.626563i | ||||
\(730\) | 0.665807 | − | 1.15321i | 0.0246426 | − | 0.0426822i | ||||
\(731\) | 3.49647 | + | 6.05606i | 0.129321 | + | 0.223991i | ||||
\(732\) | 5.47660 | − | 0.620704i | 0.202421 | − | 0.0229419i | ||||
\(733\) | −8.40368 | − | 4.85187i | −0.310397 | − | 0.179208i | 0.336707 | − | 0.941609i | \(-0.390687\pi\) |
−0.647104 | + | 0.762402i | \(0.724020\pi\) | |||||||
\(734\) | 33.3096 | 1.22948 | ||||||||
\(735\) | 3.46939 | + | 2.17700i | 0.127971 | + | 0.0802998i | ||||
\(736\) | −4.46015 | −0.164403 | ||||||||
\(737\) | 9.17731 | + | 5.29852i | 0.338051 | + | 0.195174i | ||||
\(738\) | −32.4285 | − | 9.95630i | −1.19371 | − | 0.366496i | ||||
\(739\) | −7.19141 | − | 12.4559i | −0.264540 | − | 0.458197i | 0.702903 | − | 0.711286i | \(-0.251887\pi\) |
−0.967443 | + | 0.253089i | \(0.918554\pi\) | |||||||
\(740\) | −0.651712 | + | 1.12880i | −0.0239574 | + | 0.0414955i | ||||
\(741\) | −54.0683 | − | 23.5475i | −1.98625 | − | 0.865041i | ||||
\(742\) | 23.1753 | + | 1.73725i | 0.850792 | + | 0.0637764i | ||||
\(743\) | 13.4799i | 0.494531i | 0.968948 | + | 0.247265i | \(0.0795319\pi\) | ||||
−0.968948 | + | 0.247265i | \(0.920468\pi\) | |||||||
\(744\) | 13.6650 | − | 10.0991i | 0.500985 | − | 0.370252i | ||||
\(745\) | 0.335380 | − | 0.193632i | 0.0122874 | − | 0.00709412i | ||||
\(746\) | −5.43010 | + | 3.13507i | −0.198810 | + | 0.114783i | ||||
\(747\) | 20.2956 | − | 4.66037i | 0.742578 | − | 0.170514i | ||||
\(748\) | − | 1.01880i | − | 0.0372510i | ||||||
\(749\) | −17.9797 | − | 12.2589i | −0.656965 | − | 0.447932i | ||||
\(750\) | −2.32671 | + | 5.34243i | −0.0849593 | + | 0.195078i | ||||
\(751\) | −8.97435 | + | 15.5440i | −0.327479 | + | 0.567209i | −0.982011 | − | 0.188825i | \(-0.939532\pi\) |
0.654532 | + | 0.756034i | \(0.272866\pi\) | |||||||
\(752\) | −3.82892 | − | 6.63188i | −0.139626 | − | 0.241840i | ||||
\(753\) | 1.21328 | + | 10.7050i | 0.0442144 | + | 0.390113i | ||||
\(754\) | 56.3939 | + | 32.5590i | 2.05374 | + | 1.18573i | ||||
\(755\) | 4.92555 | 0.179259 | ||||||||
\(756\) | 9.55854 | − | 9.59583i | 0.347641 | − | 0.348997i | ||||
\(757\) | −6.03729 | −0.219429 | −0.109714 | − | 0.993963i | \(-0.534994\pi\) | ||||
−0.109714 | + | 0.993963i | \(0.534994\pi\) | |||||||
\(758\) | 4.09157 | + | 2.36227i | 0.148612 | + | 0.0858015i | ||||
\(759\) | 0.175839 | + | 1.55147i | 0.00638255 | + | 0.0563146i | ||||
\(760\) | 2.79511 | + | 4.84128i | 0.101389 | + | 0.175612i | ||||
\(761\) | 18.9559 | − | 32.8326i | 0.687151 | − | 1.19018i | −0.285605 | − | 0.958348i | \(-0.592194\pi\) |
0.972756 | − | 0.231833i | \(-0.0744723\pi\) | |||||||
\(762\) | 7.65952 | − | 17.5873i | 0.277475 | − | 0.637120i | ||||
\(763\) | −5.33818 | − | 11.0855i | −0.193255 | − | 0.401320i | ||||
\(764\) | − | 19.2192i | − | 0.695326i | ||||||
\(765\) | −1.02144 | + | 0.234549i | −0.0369304 | + | 0.00848013i | ||||
\(766\) | −26.5002 | + | 15.2999i | −0.957493 | + | 0.552809i | ||||
\(767\) | −28.4931 | + | 16.4505i | −1.02883 | + | 0.593993i | ||||
\(768\) | 23.6313 | − | 17.4646i | 0.852720 | − | 0.630201i | ||||
\(769\) | − | 9.07800i | − | 0.327361i | −0.986513 | − | 0.163681i | \(-0.947663\pi\) | ||
0.986513 | − | 0.163681i | \(-0.0523366\pi\) | |||||||
\(770\) | 0.507218 | − | 0.743918i | 0.0182789 | − | 0.0268089i | ||||
\(771\) | 0.831665 | + | 0.362202i | 0.0299517 | + | 0.0130444i | ||||
\(772\) | 8.54370 | − | 14.7981i | 0.307494 | − | 0.532596i | ||||
\(773\) | 24.1552 | + | 41.8380i | 0.868802 | + | 1.50481i | 0.863222 | + | 0.504824i | \(0.168443\pi\) |
0.00557968 | + | 0.999984i | \(0.498224\pi\) | |||||||
\(774\) | 19.5364 | + | 5.99812i | 0.702222 | + | 0.215598i | ||||
\(775\) | −13.8036 | − | 7.96950i | −0.495839 | − | 0.286273i | ||||
\(776\) | 27.7769 | 0.997132 | ||||||||
\(777\) | 15.8724 | + | 8.37590i | 0.569417 | + | 0.300484i | ||||
\(778\) | 15.5018 | 0.555766 | ||||||||
\(779\) | 53.4917 | + | 30.8834i | 1.91654 | + | 1.10651i | ||||
\(780\) | −3.54416 | + | 0.401686i | −0.126901 | + | 0.0143827i | ||||
\(781\) | −4.52937 | − | 7.84509i | −0.162073 | − | 0.280720i | ||||
\(782\) | 0.469548 | − | 0.813281i | 0.0167910 | − | 0.0290829i | ||||
\(783\) | −51.2029 | + | 18.0299i | −1.82984 | + | 0.644335i | ||||
\(784\) | 4.62216 | − | 5.79549i | 0.165077 | − | 0.206982i | ||||
\(785\) | 4.00998i | 0.143122i | ||||||||
\(786\) | 14.8086 | + | 20.0374i | 0.528206 | + | 0.714712i | ||||
\(787\) | −1.67827 | + | 0.968947i | −0.0598237 | + | 0.0345392i | −0.529614 | − | 0.848239i | \(-0.677663\pi\) |
0.469790 | + | 0.882778i | \(0.344330\pi\) | |||||||
\(788\) | −4.91796 | + | 2.83938i | −0.175195 | + | 0.101149i | ||||
\(789\) | −0.799861 | − | 1.08229i | −0.0284758 | − | 0.0385304i | ||||
\(790\) | − | 2.00552i | − | 0.0713532i | ||||||
\(791\) | −0.895560 | + | 11.9470i | −0.0318425 | + | 0.424786i | ||||
\(792\) | −6.14494 | − | 6.60527i | −0.218351 | − | 0.234708i | ||||
\(793\) | −9.99277 | + | 17.3080i | −0.354854 | + | 0.614624i | ||||
\(794\) | 9.92245 | + | 17.1862i | 0.352135 | + | 0.609915i | ||||
\(795\) | 5.06964 | − | 0.574579i | 0.179801 | − | 0.0203782i | ||||
\(796\) | 11.0692 | + | 6.39079i | 0.392337 | + | 0.226516i | ||||
\(797\) | −21.5831 | −0.764512 | −0.382256 | − | 0.924057i | \(-0.624853\pi\) | ||||
−0.382256 | + | 0.924057i | \(0.624853\pi\) | |||||||
\(798\) | 21.5005 | − | 13.5287i | 0.761110 | − | 0.478911i | ||||
\(799\) | −7.47788 | −0.264548 | ||||||||
\(800\) | −20.9348 | − | 12.0867i | −0.740158 | − | 0.427330i | ||||
\(801\) | −3.21625 | + | 10.4756i | −0.113641 | + | 0.370138i | ||||
\(802\) | 17.6105 | + | 30.5023i | 0.621849 | + | 1.07707i | ||||
\(803\) | 1.95646 | − | 3.38869i | 0.0690420 | − | 0.119584i | ||||
\(804\) | 16.5789 | + | 7.22034i | 0.584691 | + | 0.254642i | ||||
\(805\) | −0.725942 | + | 0.349576i | −0.0255861 | + | 0.0123209i | ||||
\(806\) | 20.3341i | 0.716239i | ||||||||
\(807\) | −16.6612 | + | 12.3134i | −0.586503 | + | 0.433454i | ||||
\(808\) | −2.41860 | + | 1.39638i | −0.0850860 | + | 0.0491244i | ||||
\(809\) | −8.50377 | + | 4.90965i | −0.298977 | + | 0.172614i | −0.641983 | − | 0.766719i | \(-0.721888\pi\) |
0.343006 | + | 0.939333i | \(0.388555\pi\) | |||||||
\(810\) | −1.71869 | + | 2.53513i | −0.0603887 | + | 0.0890753i | ||||
\(811\) | − | 32.6254i | − | 1.14563i | −0.819684 | − | 0.572817i | \(-0.805851\pi\) | ||
0.819684 | − | 0.572817i | \(-0.194149\pi\) | |||||||
\(812\) | 24.5347 | − | 11.8146i | 0.860998 | − | 0.414612i | ||||
\(813\) | −7.65063 | + | 17.5669i | −0.268319 | + | 0.616097i | ||||
\(814\) | 1.97260 | − | 3.41664i | 0.0691394 | − | 0.119753i | ||||
\(815\) | 2.45778 | + | 4.25701i | 0.0860924 | + | 0.149116i | ||||
\(816\) | 0.213610 | + | 1.88473i | 0.00747785 | + | 0.0659787i | ||||
\(817\) | −32.2258 | − | 18.6056i | −1.12744 | − | 0.650927i | ||||
\(818\) | 2.54190 | 0.0888755 | ||||||||
\(819\) | 7.38242 | + | 48.5538i | 0.257963 | + | 1.69661i | ||||
\(820\) | 3.73581 | 0.130460 | ||||||||
\(821\) | −0.270687 | − | 0.156281i | −0.00944703 | − | 0.00545425i | 0.495269 | − | 0.868740i | \(-0.335069\pi\) |
−0.504716 | + | 0.863285i | \(0.668403\pi\) | |||||||
\(822\) | 1.02081 | + | 9.00681i | 0.0356048 | + | 0.314149i | ||||
\(823\) | 14.3081 | + | 24.7823i | 0.498749 | + | 0.863858i | 0.999999 | − | 0.00144440i | \(-0.000459768\pi\) |
−0.501250 | + | 0.865302i | \(0.667126\pi\) | |||||||
\(824\) | −3.76199 | + | 6.51595i | −0.131055 | + | 0.226994i | ||||
\(825\) | −3.37903 | + | 7.75871i | −0.117643 | + | 0.270124i | ||||
\(826\) | 1.05938 | − | 14.1324i | 0.0368606 | − | 0.491729i | ||||
\(827\) | − | 50.6285i | − | 1.76052i | −0.474487 | − | 0.880262i | \(-0.657366\pi\) | ||
0.474487 | − | 0.880262i | \(-0.342634\pi\) | |||||||
\(828\) | 0.596290 | + | 2.59680i | 0.0207225 | + | 0.0902452i | ||||
\(829\) | 8.10428 | − | 4.67901i | 0.281473 | − | 0.162509i | −0.352617 | − | 0.935768i | \(-0.614708\pi\) |
0.634090 | + | 0.773259i | \(0.281375\pi\) | |||||||
\(830\) | 2.04572 | − | 1.18110i | 0.0710081 | − | 0.0409965i | ||||
\(831\) | 16.5091 | − | 12.2010i | 0.572694 | − | 0.423248i | ||||
\(832\) | 43.9443i | 1.52349i | ||||||||
\(833\) | −2.64433 | − | 6.73848i | −0.0916204 | − | 0.233475i | ||||
\(834\) | 1.31681 | + | 0.573492i | 0.0455976 | + | 0.0198584i | ||||
\(835\) | 3.24077 | − | 5.61317i | 0.112151 | − | 0.194252i | ||||
\(836\) | 2.71064 | + | 4.69497i | 0.0937496 | + | 0.162379i | ||||
\(837\) | −12.8703 | − | 11.0317i | −0.444861 | − | 0.381313i | ||||
\(838\) | −13.1527 | − | 7.59369i | −0.454351 | − | 0.262320i | ||||
\(839\) | 14.1563 | 0.488730 | 0.244365 | − | 0.969683i | \(-0.421421\pi\) | ||||
0.244365 | + | 0.969683i | \(0.421421\pi\) | |||||||
\(840\) | 2.17272 | − | 4.11731i | 0.0749660 | − | 0.142061i | ||||
\(841\) | −80.1411 | −2.76349 | ||||||||
\(842\) | 14.3636 | + | 8.29281i | 0.495001 | + | 0.285789i | ||||
\(843\) | 20.4654 | − | 2.31950i | 0.704866 | − | 0.0798877i | ||||
\(844\) | 2.74969 | + | 4.76261i | 0.0946483 | + | 0.163936i | ||||
\(845\) | 4.27095 | − | 7.39750i | 0.146925 | − | 0.254482i | ||||
\(846\) | −16.0004 | + | 14.8853i | −0.550104 | + | 0.511767i | ||||
\(847\) | 1.49045 | − | 2.18599i | 0.0512125 | − | 0.0751115i | ||||
\(848\) | − | 9.23412i | − | 0.317101i | ||||||
\(849\) | 28.5170 | + | 38.5862i | 0.978701 | + | 1.32427i | ||||
\(850\) | 4.40788 | − | 2.54489i | 0.151189 | − | 0.0872891i | ||||
\(851\) | −3.05746 | + | 1.76523i | −0.104808 | + | 0.0605111i | ||||
\(852\) | −9.18738 | − | 12.4314i | −0.314755 | − | 0.425892i | ||||
\(853\) | 8.47986i | 0.290345i | 0.989406 | + | 0.145172i | \(0.0463737\pi\) | ||||
−0.989406 | + | 0.145172i | \(0.953626\pi\) | |||||||
\(854\) | −3.73503 | − | 7.75628i | −0.127810 | − | 0.265415i | ||||
\(855\) | 4.08312 | − | 3.79856i | 0.139640 | − | 0.129908i | ||||
\(856\) | −12.3671 | + | 21.4205i | −0.422700 | + | 0.732138i | ||||
\(857\) | −12.7652 | − | 22.1100i | −0.436050 | − | 0.755262i | 0.561330 | − | 0.827592i | \(-0.310290\pi\) |
−0.997381 | + | 0.0723303i | \(0.976956\pi\) | |||||||
\(858\) | 10.7274 | − | 1.21582i | 0.366229 | − | 0.0415074i | ||||
\(859\) | 21.5846 | + | 12.4619i | 0.736458 | + | 0.425195i | 0.820780 | − | 0.571244i | \(-0.193539\pi\) |
−0.0843218 | + | 0.996439i | \(0.526872\pi\) | |||||||
\(860\) | −2.25062 | −0.0767455 | ||||||||
\(861\) | −1.95596 | − | 51.4010i | −0.0666589 | − | 1.75174i | ||||
\(862\) | −17.6461 | −0.601028 | ||||||||
\(863\) | 18.7071 | + | 10.8006i | 0.636799 | + | 0.367656i | 0.783380 | − | 0.621543i | \(-0.213494\pi\) |
−0.146582 | + | 0.989199i | \(0.546827\pi\) | |||||||
\(864\) | −19.5193 | − | 16.7310i | −0.664062 | − | 0.569200i | ||||
\(865\) | 3.48078 | + | 6.02889i | 0.118350 | + | 0.204988i | ||||
\(866\) | −18.7584 | + | 32.4905i | −0.637437 | + | 1.10407i | ||||
\(867\) | −25.2976 | − | 11.0175i | −0.859152 | − | 0.374173i | ||||
\(868\) | 7.02570 | + | 4.79026i | 0.238468 | + | 0.162592i | ||||
\(869\) | − | 5.89319i | − | 0.199913i | ||||||
\(870\) | −4.95222 | + | 3.65993i | −0.167896 | + | 0.124083i | ||||
\(871\) | −56.7848 | + | 32.7847i | −1.92408 | + | 1.11087i | ||||
\(872\) | −12.1111 | + | 6.99237i | −0.410135 | + | 0.236791i | ||||
\(873\) | −6.20156 | − | 27.0074i | −0.209891 | − | 0.914062i | ||||
\(874\) | 4.99716i | 0.169032i | ||||||||
\(875\) | −8.81116 | − | 0.660495i | −0.297872 | − | 0.0223288i | ||||
\(876\) | 2.66608 | − | 6.12169i | 0.0900786 | − | 0.206833i | ||||
\(877\) | −19.1285 | + | 33.1315i | −0.645924 | + | 1.11877i | 0.338164 | + | 0.941087i | \(0.390194\pi\) |
−0.984087 | + | 0.177685i | \(0.943139\pi\) | |||||||
\(878\) | −13.6567 | − | 23.6541i | −0.460892 | − | 0.798288i | ||||
\(879\) | −2.05465 | − | 18.1286i | −0.0693015 | − | 0.611462i | ||||
\(880\) | −0.309821 | − | 0.178875i | −0.0104440 | − | 0.00602987i | ||||
\(881\) | −5.41544 | −0.182451 | −0.0912255 | − | 0.995830i | \(-0.529078\pi\) | ||||
−0.0912255 | + | 0.995830i | \(0.529078\pi\) | |||||||
\(882\) | −19.0715 | − | 9.15455i | −0.642171 | − | 0.308250i | ||||
\(883\) | 39.9085 | 1.34303 | 0.671514 | − | 0.740992i | \(-0.265645\pi\) | ||||
0.671514 | + | 0.740992i | \(0.265645\pi\) | |||||||
\(884\) | 5.45928 | + | 3.15192i | 0.183616 | + | 0.106010i | ||||
\(885\) | −0.350381 | − | 3.09149i | −0.0117779 | − | 0.103919i | ||||
\(886\) | −8.97513 | − | 15.5454i | −0.301525 | − | 0.522257i | ||||
\(887\) | 9.36502 | − | 16.2207i | 0.314447 | − | 0.544638i | −0.664873 | − | 0.746956i | \(-0.731514\pi\) |
0.979320 | + | 0.202319i | \(0.0648477\pi\) | |||||||
\(888\) | 8.14499 | − | 18.7020i | 0.273328 | − | 0.627598i | ||||
\(889\) | 29.0064 | + | 2.17435i | 0.972842 | + | 0.0729254i | ||||
\(890\) | 1.24307i | 0.0416679i | ||||||||
\(891\) | −5.05035 | + | 7.44943i | −0.169193 | + | 0.249565i | ||||
\(892\) | −1.98026 | + | 1.14330i | −0.0663040 | + | 0.0382806i | ||||
\(893\) | 34.4606 | − | 19.8958i | 1.15318 | − | 0.665788i | ||||
\(894\) | −1.60857 | + | 1.18881i | −0.0537988 | + | 0.0397598i | ||||
\(895\) | 0.279837i | 0.00935394i | ||||||||
\(896\) | 5.99129 | + | 4.08498i | 0.200155 | + | 0.136470i | ||||
\(897\) | −8.85760 | − | 3.85762i | −0.295747 | − | 0.128802i | ||||
\(898\) | −13.9702 | + | 24.1970i | −0.466190 | + | 0.807465i | ||||
\(899\) | −17.0405 | − | 29.5150i | −0.568333 | − | 0.984381i | ||||
\(900\) | −4.23835 | + | 13.8047i | −0.141278 | + | 0.460155i | ||||
\(901\) | −7.80905 | − | 4.50856i | −0.260157 | − | 0.150202i | ||||
\(902\) | −11.3075 | −0.376499 | ||||||||
\(903\) | 1.17836 | + | 30.9663i | 0.0392133 | + | 1.03049i | ||||
\(904\) | 13.6173 | 0.452904 | ||||||||
\(905\) | −2.38423 | − | 1.37654i | −0.0792546 | − | 0.0457576i | ||||
\(906\) | −25.2784 | + | 2.86499i | −0.839818 | + | 0.0951828i | ||||
\(907\) | −17.1561 | − | 29.7152i | −0.569658 | − | 0.986677i | −0.996600 | − | 0.0823976i | \(-0.973742\pi\) |
0.426941 | − | 0.904279i | \(-0.359591\pi\) | |||||||
\(908\) | −0.204637 | + | 0.354441i | −0.00679111 | + | 0.0117625i | ||||
\(909\) | 1.89768 | + | 2.03984i | 0.0629421 | + | 0.0676572i | ||||
\(910\) | 2.41711 | + | 5.01945i | 0.0801263 | + | 0.166393i | ||||
\(911\) | − | 40.7756i | − | 1.35095i | −0.737381 | − | 0.675477i | \(-0.763938\pi\) | ||
0.737381 | − | 0.675477i | \(-0.236062\pi\) | |||||||
\(912\) | −5.99894 | − | 8.11713i | −0.198645 | − | 0.268785i | ||||
\(913\) | 6.01132 | − | 3.47064i | 0.198946 | − | 0.114861i | ||||
\(914\) | 1.97572 | − | 1.14068i | 0.0653509 | − | 0.0377304i | ||||
\(915\) | −1.12328 | − | 1.51990i | −0.0371344 | − | 0.0502463i | ||||
\(916\) | − | 6.30769i | − | 0.208412i | ||||||
\(917\) | −21.2834 | + | 31.2155i | −0.702839 | + | 1.03083i | ||||
\(918\) | 5.10572 | − | 1.79786i | 0.168514 | − | 0.0593381i | ||||
\(919\) | −16.9993 | + | 29.4436i | −0.560754 | + | 0.971254i | 0.436677 | + | 0.899618i | \(0.356155\pi\) |
−0.997431 | + | 0.0716354i | \(0.977178\pi\) | |||||||
\(920\) | 0.457902 | + | 0.793110i | 0.0150966 | + | 0.0261481i | ||||
\(921\) | 2.54086 | − | 0.287975i | 0.0837243 | − | 0.00948910i | ||||
\(922\) | −18.0227 | − | 10.4054i | −0.593546 | − | 0.342684i | ||||
\(923\) | 56.0510 | 1.84494 | ||||||||
\(924\) | 2.10706 | − | 3.99289i | 0.0693172 | − | 0.131356i | ||||
\(925\) | −19.1346 | −0.629142 | ||||||||
\(926\) | 25.6339 | + | 14.7998i | 0.842383 | + | 0.486350i | ||||
\(927\) | 7.17536 | + | 2.20300i | 0.235670 | + | 0.0723560i | ||||
\(928\) | −25.8440 | − | 44.7632i | −0.848372 | − | 1.46942i | ||||
\(929\) | −26.6421 | + | 46.1454i | −0.874098 | + | 1.51398i | −0.0163773 | + | 0.999866i | \(0.505213\pi\) |
−0.857721 | + | 0.514116i | \(0.828120\pi\) | |||||||
\(930\) | −1.76296 | − | 0.767794i | −0.0578096 | − | 0.0251770i | ||||
\(931\) | 30.1145 | + | 24.0176i | 0.986964 | + | 0.787146i | ||||
\(932\) | 0.769273i | 0.0251984i | ||||||||
\(933\) | −31.1537 | + | 23.0240i | −1.01992 | + | 0.753773i | ||||
\(934\) | 35.5365 | − | 20.5170i | 1.16279 | − | 0.671337i | ||||
\(935\) | −0.302540 | + | 0.174671i | −0.00989410 | + | 0.00571236i | ||||
\(936\) | 54.4056 | − | 12.4928i | 1.77830 | − | 0.408342i | ||||
\(937\) | − | 45.4029i | − | 1.48325i | −0.670816 | − | 0.741623i | \(-0.734056\pi\) | ||
0.670816 | − | 0.741623i | \(-0.265944\pi\) | |||||||
\(938\) | 2.11127 | − | 28.1649i | 0.0689356 | − | 0.919617i | ||||
\(939\) | 1.22347 | − | 2.80925i | 0.0399264 | − | 0.0916763i | ||||
\(940\) | 1.20335 | − | 2.08426i | 0.0392489 | − | 0.0679810i | ||||
\(941\) | 18.0339 | + | 31.2356i | 0.587888 | + | 1.01825i | 0.994509 | + | 0.104655i | \(0.0333740\pi\) |
−0.406620 | + | 0.913597i | \(0.633293\pi\) | |||||||
\(942\) | −2.33243 | − | 20.5796i | −0.0759948 | − | 0.670518i | ||||
\(943\) | 8.76314 | + | 5.05940i | 0.285367 | + | 0.164757i | ||||
\(944\) | −5.63102 | −0.183274 | ||||||||
\(945\) | −4.48834 | − | 1.19329i | −0.146006 | − | 0.0388176i | ||||
\(946\) | 6.81215 | 0.221482 | ||||||||
\(947\) | 32.9502 | + | 19.0238i | 1.07074 | + | 0.618191i | 0.928383 | − | 0.371625i | \(-0.121199\pi\) |
0.142355 | + | 0.989816i | \(0.454533\pi\) | |||||||
\(948\) | −1.13249 | − | 9.99222i | −0.0367816 | − | 0.324532i | ||||
\(949\) | 12.1056 | + | 20.9676i | 0.392965 | + | 0.680636i | ||||
\(950\) | −13.5420 | + | 23.4555i | −0.439361 | + | 0.760995i | ||||
\(951\) | −7.92738 | + | 18.2023i | −0.257063 | + | 0.590250i | ||||
\(952\) | −7.41298 | + | 3.56971i | −0.240256 | + | 0.115695i | ||||
\(953\) | 48.8499i | 1.58241i | 0.611554 | + | 0.791203i | \(0.290545\pi\) | ||||
−0.611554 | + | 0.791203i | \(0.709455\pi\) | |||||||
\(954\) | −25.6836 | + | 5.89759i | −0.831538 | + | 0.190941i | ||||
\(955\) | −5.70727 | + | 3.29509i | −0.184683 | + | 0.106627i | ||||
\(956\) | 23.1275 | − | 13.3527i | 0.747996 | − | 0.431856i | ||||
\(957\) | −14.5520 | + | 10.7546i | −0.470400 | + | 0.347648i | ||||
\(958\) | − | 16.8013i | − | 0.542824i | ||||||
\(959\) | −12.3838 | + | 5.96340i | −0.399894 | + | 0.192568i | ||||
\(960\) | −3.80995 | − | 1.65929i | −0.122966 | − | 0.0535533i | ||||
\(961\) | −10.1788 | + | 17.6303i | −0.328350 | + | 0.568718i | ||||
\(962\) | 12.2055 | + | 21.1405i | 0.393520 | + | 0.681597i | ||||
\(963\) | 23.5882 | + | 7.24212i | 0.760120 | + | 0.233374i | ||||
\(964\) | 10.6239 | + | 6.13371i | 0.342173 | + | 0.197554i | ||||
\(965\) | −5.85921 | −0.188615 | ||||||||
\(966\) | 3.52227 | − | 2.21631i | 0.113327 | − | 0.0713085i | ||||
\(967\) | −39.0059 | −1.25435 | −0.627173 | − | 0.778880i | \(-0.715788\pi\) | ||||
−0.627173 | + | 0.778880i | \(0.715788\pi\) | |||||||
\(968\) | −2.60432 | − | 1.50361i | −0.0837061 | − | 0.0483277i | ||||
\(969\) | −9.79342 | + | 1.10996i | −0.314610 | + | 0.0356571i | ||||
\(970\) | −1.57169 | − | 2.72224i | −0.0504639 | − | 0.0874060i | ||||
\(971\) | −6.71773 | + | 11.6354i | −0.215582 | + | 0.373399i | −0.953453 | − | 0.301543i | \(-0.902498\pi\) |
0.737870 | + | 0.674943i | \(0.235832\pi\) | |||||||
\(972\) | −7.13159 | + | 13.6014i | −0.228746 | + | 0.436266i | ||||
\(973\) | −0.162800 | + | 2.17180i | −0.00521914 | + | 0.0696246i | ||||
\(974\) | 0.815126i | 0.0261183i | ||||||||
\(975\) | −31.1215 | − | 42.1102i | −0.996685 | − | 1.34861i | ||||
\(976\) | −2.96227 | + | 1.71026i | −0.0948198 | + | 0.0547442i | ||||
\(977\) | −6.62790 | + | 3.82662i | −0.212045 | + | 0.122424i | −0.602262 | − | 0.798299i | \(-0.705734\pi\) |
0.390216 | + | 0.920723i | \(0.372400\pi\) | |||||||
\(978\) | −15.0897 | − | 20.4178i | −0.482515 | − | 0.652888i | ||||
\(979\) | 3.65275i | 0.116742i | ||||||||
\(980\) | 2.30370 | + | 0.347328i | 0.0735890 | + | 0.0110950i | ||||
\(981\) | 9.50263 | + | 10.2145i | 0.303396 | + | 0.326124i | ||||
\(982\) | −1.07521 | + | 1.86231i | −0.0343113 | + | 0.0594289i | ||||
\(983\) | −4.30533 | − | 7.45706i | −0.137319 | − | 0.237843i | 0.789162 | − | 0.614185i | \(-0.210515\pi\) |
−0.926481 | + | 0.376342i | \(0.877182\pi\) | |||||||
\(984\) | −58.0937 | + | 6.58419i | −1.85196 | + | 0.209896i | ||||
\(985\) | 1.68635 | + | 0.973614i | 0.0537316 | + | 0.0310219i | ||||
\(986\) | 10.8831 | 0.346587 | ||||||||
\(987\) | −29.3073 | − | 15.4656i | −0.932863 | − | 0.492275i | ||||
\(988\) | −33.5443 | −1.06719 | ||||||||
\(989\) | −5.27931 | − | 3.04801i | −0.167872 | − | 0.0969211i | ||||
\(990\) | −0.299645 | + | 0.975972i | −0.00952336 | + | 0.0310184i | ||||
\(991\) | 9.55178 | + | 16.5442i | 0.303422 | + | 0.525543i | 0.976909 | − | 0.213657i | \(-0.0685374\pi\) |
−0.673486 | + | 0.739200i | \(0.735204\pi\) | |||||||
\(992\) | 8.07020 | − | 13.9780i | 0.256229 | − | 0.443802i | ||||
\(993\) | −6.48239 | − | 2.82317i | −0.205712 | − | 0.0895907i | ||||
\(994\) | −13.6012 | + | 19.9483i | −0.431403 | + | 0.632723i | ||||
\(995\) | − | 4.38276i | − | 0.138943i | ||||||
\(996\) | 9.52558 | − | 7.03985i | 0.301829 | − | 0.223066i | ||||
\(997\) | −14.5101 | + | 8.37740i | −0.459539 | + | 0.265315i | −0.711850 | − | 0.702331i | \(-0.752143\pi\) |
0.252311 | + | 0.967646i | \(0.418809\pi\) | |||||||
\(998\) | −0.533302 | + | 0.307902i | −0.0168814 | + | 0.00974648i | ||||
\(999\) | −20.0024 | − | 3.74389i | −0.632848 | − | 0.118451i |
(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 | 231.2.n.a.89.17 | yes | 52 | |
3.2 | odd | 2 | inner | 231.2.n.a.89.10 | ✓ | 52 | |
7.3 | odd | 6 | inner | 231.2.n.a.122.10 | yes | 52 | |
21.17 | even | 6 | inner | 231.2.n.a.122.17 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.n.a.89.10 | ✓ | 52 | 3.2 | odd | 2 | inner | |
231.2.n.a.89.17 | yes | 52 | 1.1 | even | 1 | trivial | |
231.2.n.a.122.10 | yes | 52 | 7.3 | odd | 6 | inner | |
231.2.n.a.122.17 | yes | 52 | 21.17 | even | 6 | inner |