Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,2,Mod(37,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.w (of order \(12\), 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: | \(0.894324502638\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 93.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.93 |
Dual form | 112.2.w.a.53.1 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 0.366025i | −0.965926 | − | 0.258819i | ||||
\(3\) | −0.133975 | + | 0.500000i | −0.0773503 | + | 0.288675i | −0.993756 | − | 0.111576i | \(-0.964410\pi\) |
0.916406 | + | 0.400251i | \(0.131077\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | 0.232051 | + | 0.866025i | 0.103776 | + | 0.387298i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0.366025 | − | 0.633975i | 0.149429 | − | 0.258819i | ||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | 2.36603 | + | 1.36603i | 0.788675 | + | 0.455342i | ||||
\(10\) | − | 1.26795i | − | 0.400961i | ||||||
\(11\) | 2.86603 | + | 0.767949i | 0.864139 | + | 0.231545i | 0.663552 | − | 0.748130i | \(-0.269048\pi\) |
0.200587 | + | 0.979676i | \(0.435715\pi\) | |||||||
\(12\) | −0.732051 | + | 0.732051i | −0.211325 | + | 0.211325i | ||||
\(13\) | 3.73205 | + | 3.73205i | 1.03508 | + | 1.03508i | 0.999362 | + | 0.0357229i | \(0.0113734\pi\) |
0.0357229 | + | 0.999362i | \(0.488627\pi\) | |||||||
\(14\) | 3.09808 | − | 2.09808i | 0.827996 | − | 0.560734i | ||||
\(15\) | −0.464102 | −0.119831 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | −3.23205 | − | 5.59808i | −0.783887 | − | 1.35773i | −0.929661 | − | 0.368415i | \(-0.879901\pi\) |
0.145774 | − | 0.989318i | \(-0.453433\pi\) | |||||||
\(18\) | −2.73205 | − | 2.73205i | −0.643951 | − | 0.643951i | ||||
\(19\) | −2.86603 | + | 0.767949i | −0.657511 | + | 0.176180i | −0.572123 | − | 0.820168i | \(-0.693880\pi\) |
−0.0853887 | + | 0.996348i | \(0.527213\pi\) | |||||||
\(20\) | −0.464102 | + | 1.73205i | −0.103776 | + | 0.387298i | ||||
\(21\) | −0.767949 | − | 1.13397i | −0.167580 | − | 0.247454i | ||||
\(22\) | −3.63397 | − | 2.09808i | −0.774766 | − | 0.447311i | ||||
\(23\) | −3.86603 | − | 2.23205i | −0.806122 | − | 0.465415i | 0.0394853 | − | 0.999220i | \(-0.487428\pi\) |
−0.845607 | + | 0.533805i | \(0.820761\pi\) | |||||||
\(24\) | 1.26795 | − | 0.732051i | 0.258819 | − | 0.149429i | ||||
\(25\) | 3.63397 | − | 2.09808i | 0.726795 | − | 0.419615i | ||||
\(26\) | −3.73205 | − | 6.46410i | −0.731915 | − | 1.26771i | ||||
\(27\) | −2.09808 | + | 2.09808i | −0.403775 | + | 0.403775i | ||||
\(28\) | −5.00000 | + | 1.73205i | −0.944911 | + | 0.327327i | ||||
\(29\) | −0.267949 | − | 0.267949i | −0.0497569 | − | 0.0497569i | 0.681791 | − | 0.731547i | \(-0.261202\pi\) |
−0.731547 | + | 0.681791i | \(0.761202\pi\) | |||||||
\(30\) | 0.633975 | + | 0.169873i | 0.115747 | + | 0.0310144i | ||||
\(31\) | −1.86603 | − | 3.23205i | −0.335148 | − | 0.580493i | 0.648365 | − | 0.761329i | \(-0.275453\pi\) |
−0.983513 | + | 0.180836i | \(0.942120\pi\) | |||||||
\(32\) | −1.46410 | − | 5.46410i | −0.258819 | − | 0.965926i | ||||
\(33\) | −0.767949 | + | 1.33013i | −0.133683 | + | 0.231545i | ||||
\(34\) | 2.36603 | + | 8.83013i | 0.405770 | + | 1.51435i | ||||
\(35\) | −2.13397 | − | 1.03590i | −0.360708 | − | 0.175099i | ||||
\(36\) | 2.73205 | + | 4.73205i | 0.455342 | + | 0.788675i | ||||
\(37\) | 0.303848 | + | 1.13397i | 0.0499522 | + | 0.186424i | 0.986394 | − | 0.164399i | \(-0.0525685\pi\) |
−0.936442 | + | 0.350823i | \(0.885902\pi\) | |||||||
\(38\) | 4.19615 | 0.680706 | ||||||||
\(39\) | −2.36603 | + | 1.36603i | −0.378867 | + | 0.218739i | ||||
\(40\) | 1.26795 | − | 2.19615i | 0.200480 | − | 0.347242i | ||||
\(41\) | − | 4.92820i | − | 0.769656i | −0.922988 | − | 0.384828i | \(-0.874261\pi\) | ||
0.922988 | − | 0.384828i | \(-0.125739\pi\) | |||||||
\(42\) | 0.633975 | + | 1.83013i | 0.0978244 | + | 0.282395i | ||||
\(43\) | 6.46410 | − | 6.46410i | 0.985766 | − | 0.985766i | −0.0141339 | − | 0.999900i | \(-0.504499\pi\) |
0.999900 | + | 0.0141339i | \(0.00449910\pi\) | |||||||
\(44\) | 4.19615 | + | 4.19615i | 0.632594 | + | 0.632594i | ||||
\(45\) | −0.633975 | + | 2.36603i | −0.0945074 | + | 0.352706i | ||||
\(46\) | 4.46410 | + | 4.46410i | 0.658196 | + | 0.658196i | ||||
\(47\) | −2.13397 | + | 3.69615i | −0.311272 | + | 0.539139i | −0.978638 | − | 0.205591i | \(-0.934088\pi\) |
0.667366 | + | 0.744730i | \(0.267422\pi\) | |||||||
\(48\) | −2.00000 | + | 0.535898i | −0.288675 | + | 0.0773503i | ||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | −5.73205 | + | 1.53590i | −0.810634 | + | 0.217209i | ||||
\(51\) | 3.23205 | − | 0.866025i | 0.452578 | − | 0.121268i | ||||
\(52\) | 2.73205 | + | 10.1962i | 0.378867 | + | 1.41395i | ||||
\(53\) | 3.96410 | + | 1.06218i | 0.544511 | + | 0.145901i | 0.520581 | − | 0.853812i | \(-0.325715\pi\) |
0.0239302 | + | 0.999714i | \(0.492382\pi\) | |||||||
\(54\) | 3.63397 | − | 2.09808i | 0.494521 | − | 0.285512i | ||||
\(55\) | 2.66025i | 0.358709i | ||||||||
\(56\) | 7.46410 | − | 0.535898i | 0.997433 | − | 0.0716124i | ||||
\(57\) | − | 1.53590i | − | 0.203435i | ||||||
\(58\) | 0.267949 | + | 0.464102i | 0.0351835 | + | 0.0609395i | ||||
\(59\) | 11.3301 | + | 3.03590i | 1.47506 | + | 0.395240i | 0.904662 | − | 0.426130i | \(-0.140123\pi\) |
0.570395 | + | 0.821370i | \(0.306790\pi\) | |||||||
\(60\) | −0.803848 | − | 0.464102i | −0.103776 | − | 0.0599153i | ||||
\(61\) | −6.96410 | + | 1.86603i | −0.891662 | + | 0.238920i | −0.675432 | − | 0.737422i | \(-0.736043\pi\) |
−0.216230 | + | 0.976342i | \(0.569376\pi\) | |||||||
\(62\) | 1.36603 | + | 5.09808i | 0.173485 | + | 0.647456i | ||||
\(63\) | −6.83013 | + | 2.36603i | −0.860515 | + | 0.298091i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −2.36603 | + | 4.09808i | −0.293469 | + | 0.508304i | ||||
\(66\) | 1.53590 | − | 1.53590i | 0.189056 | − | 0.189056i | ||||
\(67\) | 1.33013 | − | 4.96410i | 0.162501 | − | 0.606462i | −0.835845 | − | 0.548966i | \(-0.815022\pi\) |
0.998346 | − | 0.0574958i | \(-0.0183116\pi\) | |||||||
\(68\) | − | 12.9282i | − | 1.56777i | ||||||
\(69\) | 1.63397 | − | 1.63397i | 0.196707 | − | 0.196707i | ||||
\(70\) | 2.53590 | + | 2.19615i | 0.303098 | + | 0.262490i | ||||
\(71\) | 0.535898i | 0.0635994i | 0.999494 | + | 0.0317997i | \(0.0101239\pi\) | ||||
−0.999494 | + | 0.0317997i | \(0.989876\pi\) | |||||||
\(72\) | −2.00000 | − | 7.46410i | −0.235702 | − | 0.879653i | ||||
\(73\) | −6.23205 | + | 3.59808i | −0.729406 | + | 0.421123i | −0.818205 | − | 0.574927i | \(-0.805031\pi\) |
0.0887986 | + | 0.996050i | \(0.471697\pi\) | |||||||
\(74\) | − | 1.66025i | − | 0.193001i | ||||||
\(75\) | 0.562178 | + | 2.09808i | 0.0649147 | + | 0.242265i | ||||
\(76\) | −5.73205 | − | 1.53590i | −0.657511 | − | 0.176180i | ||||
\(77\) | −6.50000 | + | 4.40192i | −0.740744 | + | 0.501646i | ||||
\(78\) | 3.73205 | − | 1.00000i | 0.422572 | − | 0.113228i | ||||
\(79\) | 8.33013 | − | 14.4282i | 0.937213 | − | 1.62330i | 0.166572 | − | 0.986029i | \(-0.446730\pi\) |
0.770640 | − | 0.637270i | \(-0.219937\pi\) | |||||||
\(80\) | −2.53590 | + | 2.53590i | −0.283522 | + | 0.283522i | ||||
\(81\) | 3.33013 | + | 5.76795i | 0.370014 | + | 0.640883i | ||||
\(82\) | −1.80385 | + | 6.73205i | −0.199202 | + | 0.743431i | ||||
\(83\) | 1.53590 | + | 1.53590i | 0.168587 | + | 0.168587i | 0.786358 | − | 0.617771i | \(-0.211964\pi\) |
−0.617771 | + | 0.786358i | \(0.711964\pi\) | |||||||
\(84\) | −0.196152 | − | 2.73205i | −0.0214020 | − | 0.298091i | ||||
\(85\) | 4.09808 | − | 4.09808i | 0.444499 | − | 0.444499i | ||||
\(86\) | −11.1962 | + | 6.46410i | −1.20731 | + | 0.697042i | ||||
\(87\) | 0.169873 | − | 0.0980762i | 0.0182123 | − | 0.0105149i | ||||
\(88\) | −4.19615 | − | 7.26795i | −0.447311 | − | 0.774766i | ||||
\(89\) | 4.50000 | + | 2.59808i | 0.476999 | + | 0.275396i | 0.719165 | − | 0.694839i | \(-0.244525\pi\) |
−0.242166 | + | 0.970235i | \(0.577858\pi\) | |||||||
\(90\) | 1.73205 | − | 3.00000i | 0.182574 | − | 0.316228i | ||||
\(91\) | −13.9282 | + | 1.00000i | −1.46007 | + | 0.104828i | ||||
\(92\) | −4.46410 | − | 7.73205i | −0.465415 | − | 0.806122i | ||||
\(93\) | 1.86603 | − | 0.500000i | 0.193498 | − | 0.0518476i | ||||
\(94\) | 4.26795 | − | 4.26795i | 0.440205 | − | 0.440205i | ||||
\(95\) | −1.33013 | − | 2.30385i | −0.136468 | − | 0.236370i | ||||
\(96\) | 2.92820 | 0.298858 | ||||||||
\(97\) | −2.92820 | −0.297314 | −0.148657 | − | 0.988889i | \(-0.547495\pi\) | ||||
−0.148657 | + | 0.988889i | \(0.547495\pi\) | |||||||
\(98\) | −1.16987 | + | 9.83013i | −0.118175 | + | 0.992993i | ||||
\(99\) | 5.73205 | + | 5.73205i | 0.576093 | + | 0.576093i | ||||
\(100\) | 8.39230 | 0.839230 | ||||||||
\(101\) | −18.8923 | − | 5.06218i | −1.87985 | − | 0.503706i | −0.999572 | − | 0.0292559i | \(-0.990686\pi\) |
−0.880283 | − | 0.474450i | \(-0.842647\pi\) | |||||||
\(102\) | −4.73205 | −0.468543 | ||||||||
\(103\) | 5.59808 | + | 3.23205i | 0.551595 | + | 0.318463i | 0.749765 | − | 0.661704i | \(-0.230167\pi\) |
−0.198170 | + | 0.980168i | \(0.563500\pi\) | |||||||
\(104\) | − | 14.9282i | − | 1.46383i | ||||||
\(105\) | 0.803848 | − | 0.928203i | 0.0784475 | − | 0.0905834i | ||||
\(106\) | −5.02628 | − | 2.90192i | −0.488195 | − | 0.281860i | ||||
\(107\) | −0.866025 | − | 3.23205i | −0.0837218 | − | 0.312454i | 0.911347 | − | 0.411638i | \(-0.135043\pi\) |
−0.995069 | + | 0.0991843i | \(0.968377\pi\) | |||||||
\(108\) | −5.73205 | + | 1.53590i | −0.551567 | + | 0.147792i | ||||
\(109\) | 0.571797 | − | 2.13397i | 0.0547682 | − | 0.204398i | −0.933120 | − | 0.359565i | \(-0.882925\pi\) |
0.987888 | + | 0.155167i | \(0.0495917\pi\) | |||||||
\(110\) | 0.973721 | − | 3.63397i | 0.0928406 | − | 0.346486i | ||||
\(111\) | −0.607695 | −0.0576799 | ||||||||
\(112\) | −10.3923 | − | 2.00000i | −0.981981 | − | 0.188982i | ||||
\(113\) | −1.46410 | −0.137731 | −0.0688655 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688655 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(114\) | −0.562178 | + | 2.09808i | −0.0526528 | + | 0.196503i | ||||
\(115\) | 1.03590 | − | 3.86603i | 0.0965980 | − | 0.360509i | ||||
\(116\) | −0.196152 | − | 0.732051i | −0.0182123 | − | 0.0679692i | ||||
\(117\) | 3.73205 | + | 13.9282i | 0.345028 | + | 1.28766i | ||||
\(118\) | −14.3660 | − | 8.29423i | −1.32250 | − | 0.763546i | ||||
\(119\) | 16.7942 | + | 3.23205i | 1.53952 | + | 0.296282i | ||||
\(120\) | 0.928203 | + | 0.928203i | 0.0847330 | + | 0.0847330i | ||||
\(121\) | −1.90192 | − | 1.09808i | −0.172902 | − | 0.0998251i | ||||
\(122\) | 10.1962 | 0.923116 | ||||||||
\(123\) | 2.46410 | + | 0.660254i | 0.222181 | + | 0.0595331i | ||||
\(124\) | − | 7.46410i | − | 0.670296i | ||||||
\(125\) | 5.83013 | + | 5.83013i | 0.521462 | + | 0.521462i | ||||
\(126\) | 10.1962 | − | 0.732051i | 0.908345 | − | 0.0652163i | ||||
\(127\) | 9.46410 | 0.839803 | 0.419902 | − | 0.907570i | \(-0.362065\pi\) | ||||
0.419902 | + | 0.907570i | \(0.362065\pi\) | |||||||
\(128\) | 2.92820 | − | 10.9282i | 0.258819 | − | 0.965926i | ||||
\(129\) | 2.36603 | + | 4.09808i | 0.208317 | + | 0.360815i | ||||
\(130\) | 4.73205 | − | 4.73205i | 0.415028 | − | 0.415028i | ||||
\(131\) | 7.59808 | − | 2.03590i | 0.663847 | − | 0.177877i | 0.0888654 | − | 0.996044i | \(-0.471676\pi\) |
0.574982 | + | 0.818166i | \(0.305009\pi\) | |||||||
\(132\) | −2.66025 | + | 1.53590i | −0.231545 | + | 0.133683i | ||||
\(133\) | 3.42820 | − | 7.06218i | 0.297263 | − | 0.612368i | ||||
\(134\) | −3.63397 | + | 6.29423i | −0.313928 | + | 0.543739i | ||||
\(135\) | −2.30385 | − | 1.33013i | −0.198284 | − | 0.114479i | ||||
\(136\) | −4.73205 | + | 17.6603i | −0.405770 | + | 1.51435i | ||||
\(137\) | −15.2321 | + | 8.79423i | −1.30136 | + | 0.751342i | −0.980638 | − | 0.195831i | \(-0.937260\pi\) |
−0.320724 | + | 0.947173i | \(0.603926\pi\) | |||||||
\(138\) | −2.83013 | + | 1.63397i | −0.240916 | + | 0.139093i | ||||
\(139\) | −11.9282 | + | 11.9282i | −1.01174 | + | 1.01174i | −0.0118067 | + | 0.999930i | \(0.503758\pi\) |
−0.999930 | + | 0.0118067i | \(0.996242\pi\) | |||||||
\(140\) | −2.66025 | − | 3.92820i | −0.224833 | − | 0.331994i | ||||
\(141\) | −1.56218 | − | 1.56218i | −0.131559 | − | 0.131559i | ||||
\(142\) | 0.196152 | − | 0.732051i | 0.0164607 | − | 0.0614323i | ||||
\(143\) | 7.83013 | + | 13.5622i | 0.654788 | + | 1.13413i | ||||
\(144\) | 10.9282i | 0.910684i | ||||||||
\(145\) | 0.169873 | − | 0.294229i | 0.0141072 | − | 0.0244344i | ||||
\(146\) | 9.83013 | − | 2.63397i | 0.813547 | − | 0.217989i | ||||
\(147\) | 3.59808 | + | 0.428203i | 0.296764 | + | 0.0353176i | ||||
\(148\) | −0.607695 | + | 2.26795i | −0.0499522 | + | 0.186424i | ||||
\(149\) | 2.03590 | + | 7.59808i | 0.166787 | + | 0.622459i | 0.997805 | + | 0.0662134i | \(0.0210918\pi\) |
−0.831018 | + | 0.556245i | \(0.812242\pi\) | |||||||
\(150\) | − | 3.07180i | − | 0.250811i | ||||||
\(151\) | −9.86603 | + | 5.69615i | −0.802886 | + | 0.463546i | −0.844479 | − | 0.535588i | \(-0.820090\pi\) |
0.0415935 | + | 0.999135i | \(0.486757\pi\) | |||||||
\(152\) | 7.26795 | + | 4.19615i | 0.589509 | + | 0.340353i | ||||
\(153\) | − | 17.6603i | − | 1.42775i | ||||||
\(154\) | 10.4904 | − | 3.63397i | 0.845339 | − | 0.292834i | ||||
\(155\) | 2.36603 | − | 2.36603i | 0.190044 | − | 0.190044i | ||||
\(156\) | −5.46410 | −0.437478 | ||||||||
\(157\) | 4.89230 | − | 18.2583i | 0.390448 | − | 1.45717i | −0.438948 | − | 0.898513i | \(-0.644649\pi\) |
0.829396 | − | 0.558661i | \(-0.188685\pi\) | |||||||
\(158\) | −16.6603 | + | 16.6603i | −1.32542 | + | 1.32542i | ||||
\(159\) | −1.06218 | + | 1.83975i | −0.0842362 | + | 0.145901i | ||||
\(160\) | 4.39230 | − | 2.53590i | 0.347242 | − | 0.200480i | ||||
\(161\) | 11.1603 | − | 3.86603i | 0.879551 | − | 0.304685i | ||||
\(162\) | −2.43782 | − | 9.09808i | −0.191533 | − | 0.714812i | ||||
\(163\) | −12.0622 | + | 3.23205i | −0.944783 | + | 0.253154i | −0.698147 | − | 0.715954i | \(-0.745992\pi\) |
−0.246636 | + | 0.969108i | \(0.579325\pi\) | |||||||
\(164\) | 4.92820 | − | 8.53590i | 0.384828 | − | 0.666542i | ||||
\(165\) | −1.33013 | − | 0.356406i | −0.103550 | − | 0.0277462i | ||||
\(166\) | −1.53590 | − | 2.66025i | −0.119209 | − | 0.206476i | ||||
\(167\) | − | 21.8564i | − | 1.69130i | −0.533738 | − | 0.845650i | \(-0.679213\pi\) | ||
0.533738 | − | 0.845650i | \(-0.320787\pi\) | |||||||
\(168\) | −0.732051 | + | 3.80385i | −0.0564789 | + | 0.293473i | ||||
\(169\) | 14.8564i | 1.14280i | ||||||||
\(170\) | −7.09808 | + | 4.09808i | −0.544398 | + | 0.314308i | ||||
\(171\) | −7.83013 | − | 2.09808i | −0.598785 | − | 0.160444i | ||||
\(172\) | 17.6603 | − | 4.73205i | 1.34658 | − | 0.360815i | ||||
\(173\) | −2.23205 | + | 0.598076i | −0.169700 | + | 0.0454709i | −0.342668 | − | 0.939456i | \(-0.611331\pi\) |
0.172969 | + | 0.984927i | \(0.444664\pi\) | |||||||
\(174\) | −0.267949 | + | 0.0717968i | −0.0203132 | + | 0.00544290i | ||||
\(175\) | −2.09808 | + | 10.9019i | −0.158600 | + | 0.824108i | ||||
\(176\) | 3.07180 | + | 11.4641i | 0.231545 | + | 0.864139i | ||||
\(177\) | −3.03590 | + | 5.25833i | −0.228192 | + | 0.395240i | ||||
\(178\) | −5.19615 | − | 5.19615i | −0.389468 | − | 0.389468i | ||||
\(179\) | −2.40192 | + | 8.96410i | −0.179528 | + | 0.670008i | 0.816208 | + | 0.577759i | \(0.196072\pi\) |
−0.995736 | + | 0.0922498i | \(0.970594\pi\) | |||||||
\(180\) | −3.46410 | + | 3.46410i | −0.258199 | + | 0.258199i | ||||
\(181\) | 13.3923 | − | 13.3923i | 0.995442 | − | 0.995442i | −0.00454748 | − | 0.999990i | \(-0.501448\pi\) |
0.999990 | + | 0.00454748i | \(0.00144751\pi\) | |||||||
\(182\) | 19.3923 | + | 3.73205i | 1.43745 | + | 0.276638i | ||||
\(183\) | − | 3.73205i | − | 0.275881i | ||||||
\(184\) | 3.26795 | + | 12.1962i | 0.240916 | + | 0.899112i | ||||
\(185\) | −0.911543 | + | 0.526279i | −0.0670180 | + | 0.0386928i | ||||
\(186\) | −2.73205 | −0.200324 | ||||||||
\(187\) | −4.96410 | − | 18.5263i | −0.363011 | − | 1.35478i | ||||
\(188\) | −7.39230 | + | 4.26795i | −0.539139 | + | 0.311272i | ||||
\(189\) | −0.562178 | − | 7.83013i | −0.0408924 | − | 0.569558i | ||||
\(190\) | 0.973721 | + | 3.63397i | 0.0706411 | + | 0.263636i | ||||
\(191\) | −4.33013 | + | 7.50000i | −0.313317 | + | 0.542681i | −0.979078 | − | 0.203484i | \(-0.934774\pi\) |
0.665761 | + | 0.746165i | \(0.268107\pi\) | |||||||
\(192\) | −4.00000 | − | 1.07180i | −0.288675 | − | 0.0773503i | ||||
\(193\) | 11.5000 | + | 19.9186i | 0.827788 | + | 1.43377i | 0.899770 | + | 0.436365i | \(0.143734\pi\) |
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 4.00000 | + | 1.07180i | 0.287183 | + | 0.0769505i | ||||
\(195\) | −1.73205 | − | 1.73205i | −0.124035 | − | 0.124035i | ||||
\(196\) | 5.19615 | − | 13.0000i | 0.371154 | − | 0.928571i | ||||
\(197\) | −16.6603 | + | 16.6603i | −1.18699 | + | 1.18699i | −0.209100 | + | 0.977894i | \(0.567053\pi\) |
−0.977894 | + | 0.209100i | \(0.932947\pi\) | |||||||
\(198\) | −5.73205 | − | 9.92820i | −0.407359 | − | 0.705567i | ||||
\(199\) | 10.3301 | − | 5.96410i | 0.732283 | − | 0.422784i | −0.0869736 | − | 0.996211i | \(-0.527720\pi\) |
0.819257 | + | 0.573427i | \(0.194386\pi\) | |||||||
\(200\) | −11.4641 | − | 3.07180i | −0.810634 | − | 0.217209i | ||||
\(201\) | 2.30385 | + | 1.33013i | 0.162501 | + | 0.0938199i | ||||
\(202\) | 23.9545 | + | 13.8301i | 1.68543 | + | 0.973084i | ||||
\(203\) | 1.00000 | − | 0.0717968i | 0.0701862 | − | 0.00503915i | ||||
\(204\) | 6.46410 | + | 1.73205i | 0.452578 | + | 0.121268i | ||||
\(205\) | 4.26795 | − | 1.14359i | 0.298087 | − | 0.0798720i | ||||
\(206\) | −6.46410 | − | 6.46410i | −0.450375 | − | 0.450375i | ||||
\(207\) | −6.09808 | − | 10.5622i | −0.423846 | − | 0.734122i | ||||
\(208\) | −5.46410 | + | 20.3923i | −0.378867 | + | 1.41395i | ||||
\(209\) | −8.80385 | −0.608975 | ||||||||
\(210\) | −1.43782 | + | 0.973721i | −0.0992192 | + | 0.0671931i | ||||
\(211\) | −15.9282 | − | 15.9282i | −1.09654 | − | 1.09654i | −0.994812 | − | 0.101731i | \(-0.967562\pi\) |
−0.101731 | − | 0.994812i | \(-0.532438\pi\) | |||||||
\(212\) | 5.80385 | + | 5.80385i | 0.398610 | + | 0.398610i | ||||
\(213\) | −0.267949 | − | 0.0717968i | −0.0183596 | − | 0.00491943i | ||||
\(214\) | 4.73205i | 0.323476i | ||||||||
\(215\) | 7.09808 | + | 4.09808i | 0.484085 | + | 0.279486i | ||||
\(216\) | 8.39230 | 0.571024 | ||||||||
\(217\) | 9.69615 | + | 1.86603i | 0.658218 | + | 0.126674i | ||||
\(218\) | −1.56218 | + | 2.70577i | −0.105804 | + | 0.183258i | ||||
\(219\) | −0.964102 | − | 3.59808i | −0.0651479 | − | 0.243135i | ||||
\(220\) | −2.66025 | + | 4.60770i | −0.179354 | + | 0.310651i | ||||
\(221\) | 8.83013 | − | 32.9545i | 0.593979 | − | 2.21676i | ||||
\(222\) | 0.830127 | + | 0.222432i | 0.0557145 | + | 0.0149286i | ||||
\(223\) | 9.85641 | 0.660034 | 0.330017 | − | 0.943975i | \(-0.392946\pi\) | ||||
0.330017 | + | 0.943975i | \(0.392946\pi\) | |||||||
\(224\) | 13.4641 | + | 6.53590i | 0.899608 | + | 0.436698i | ||||
\(225\) | 11.4641 | 0.764273 | ||||||||
\(226\) | 2.00000 | + | 0.535898i | 0.133038 | + | 0.0356474i | ||||
\(227\) | −2.99038 | + | 11.1603i | −0.198479 | + | 0.740732i | 0.792860 | + | 0.609403i | \(0.208591\pi\) |
−0.991339 | + | 0.131329i | \(0.958076\pi\) | |||||||
\(228\) | 1.53590 | − | 2.66025i | 0.101717 | − | 0.176180i | ||||
\(229\) | −3.57180 | − | 13.3301i | −0.236031 | − | 0.880880i | −0.977681 | − | 0.210093i | \(-0.932623\pi\) |
0.741650 | − | 0.670787i | \(-0.234043\pi\) | |||||||
\(230\) | −2.83013 | + | 4.90192i | −0.186613 | + | 0.323223i | ||||
\(231\) | −1.33013 | − | 3.83975i | −0.0875159 | − | 0.252637i | ||||
\(232\) | 1.07180i | 0.0703669i | ||||||||
\(233\) | −0.696152 | − | 0.401924i | −0.0456065 | − | 0.0263309i | 0.477023 | − | 0.878891i | \(-0.341716\pi\) |
−0.522630 | + | 0.852560i | \(0.675049\pi\) | |||||||
\(234\) | − | 20.3923i | − | 1.33309i | ||||||
\(235\) | −3.69615 | − | 0.990381i | −0.241110 | − | 0.0646053i | ||||
\(236\) | 16.5885 | + | 16.5885i | 1.07982 | + | 1.07982i | ||||
\(237\) | 6.09808 | + | 6.09808i | 0.396113 | + | 0.396113i | ||||
\(238\) | −21.7583 | − | 10.5622i | −1.41038 | − | 0.684644i | ||||
\(239\) | −8.53590 | −0.552141 | −0.276071 | − | 0.961137i | \(-0.589032\pi\) | ||||
−0.276071 | + | 0.961137i | \(0.589032\pi\) | |||||||
\(240\) | −0.928203 | − | 1.60770i | −0.0599153 | − | 0.103776i | ||||
\(241\) | −6.96410 | − | 12.0622i | −0.448597 | − | 0.776993i | 0.549698 | − | 0.835364i | \(-0.314743\pi\) |
−0.998295 | + | 0.0583704i | \(0.981410\pi\) | |||||||
\(242\) | 2.19615 | + | 2.19615i | 0.141174 | + | 0.141174i | ||||
\(243\) | −11.9282 | + | 3.19615i | −0.765195 | + | 0.205033i | ||||
\(244\) | −13.9282 | − | 3.73205i | −0.891662 | − | 0.238920i | ||||
\(245\) | 5.76795 | − | 2.47372i | 0.368501 | − | 0.158040i | ||||
\(246\) | −3.12436 | − | 1.80385i | −0.199202 | − | 0.115009i | ||||
\(247\) | −13.5622 | − | 7.83013i | −0.862941 | − | 0.498219i | ||||
\(248\) | −2.73205 | + | 10.1962i | −0.173485 | + | 0.647456i | ||||
\(249\) | −0.973721 | + | 0.562178i | −0.0617070 | + | 0.0356266i | ||||
\(250\) | −5.83013 | − | 10.0981i | −0.368730 | − | 0.638658i | ||||
\(251\) | −17.5885 | + | 17.5885i | −1.11017 | + | 1.11017i | −0.117047 | + | 0.993126i | \(0.537343\pi\) |
−0.993126 | + | 0.117047i | \(0.962657\pi\) | |||||||
\(252\) | −14.1962 | − | 2.73205i | −0.894274 | − | 0.172103i | ||||
\(253\) | −9.36603 | − | 9.36603i | −0.588837 | − | 0.588837i | ||||
\(254\) | −12.9282 | − | 3.46410i | −0.811188 | − | 0.217357i | ||||
\(255\) | 1.50000 | + | 2.59808i | 0.0939336 | + | 0.162698i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 9.69615 | − | 16.7942i | 0.604829 | − | 1.04760i | −0.387249 | − | 0.921975i | \(-0.626575\pi\) |
0.992078 | − | 0.125620i | \(-0.0400920\pi\) | |||||||
\(258\) | −1.73205 | − | 6.46410i | −0.107833 | − | 0.402437i | ||||
\(259\) | −2.79423 | − | 1.35641i | −0.173625 | − | 0.0842830i | ||||
\(260\) | −8.19615 | + | 4.73205i | −0.508304 | + | 0.293469i | ||||
\(261\) | −0.267949 | − | 1.00000i | −0.0165856 | − | 0.0618984i | ||||
\(262\) | −11.1244 | −0.687265 | ||||||||
\(263\) | −3.99038 | + | 2.30385i | −0.246057 | + | 0.142061i | −0.617958 | − | 0.786211i | \(-0.712040\pi\) |
0.371900 | + | 0.928273i | \(0.378706\pi\) | |||||||
\(264\) | 4.19615 | − | 1.12436i | 0.258255 | − | 0.0691993i | ||||
\(265\) | 3.67949i | 0.226029i | ||||||||
\(266\) | −7.26795 | + | 8.39230i | −0.445627 | + | 0.514565i | ||||
\(267\) | −1.90192 | + | 1.90192i | −0.116396 | + | 0.116396i | ||||
\(268\) | 7.26795 | − | 7.26795i | 0.443961 | − | 0.443961i | ||||
\(269\) | −2.62436 | + | 9.79423i | −0.160010 | + | 0.597165i | 0.838614 | + | 0.544726i | \(0.183366\pi\) |
−0.998624 | + | 0.0524390i | \(0.983300\pi\) | |||||||
\(270\) | 2.66025 | + | 2.66025i | 0.161898 | + | 0.161898i | ||||
\(271\) | −6.06218 | + | 10.5000i | −0.368251 | + | 0.637830i | −0.989292 | − | 0.145948i | \(-0.953377\pi\) |
0.621041 | + | 0.783778i | \(0.286710\pi\) | |||||||
\(272\) | 12.9282 | − | 22.3923i | 0.783887 | − | 1.35773i | ||||
\(273\) | 1.36603 | − | 7.09808i | 0.0826756 | − | 0.429595i | ||||
\(274\) | 24.0263 | − | 6.43782i | 1.45148 | − | 0.388923i | ||||
\(275\) | 12.0263 | − | 3.22243i | 0.725212 | − | 0.194320i | ||||
\(276\) | 4.46410 | − | 1.19615i | 0.268707 | − | 0.0719999i | ||||
\(277\) | 4.50000 | + | 1.20577i | 0.270379 | + | 0.0724478i | 0.391461 | − | 0.920195i | \(-0.371970\pi\) |
−0.121082 | + | 0.992642i | \(0.538636\pi\) | |||||||
\(278\) | 20.6603 | − | 11.9282i | 1.23912 | − | 0.715406i | ||||
\(279\) | − | 10.1962i | − | 0.610428i | ||||||
\(280\) | 2.19615 | + | 6.33975i | 0.131245 | + | 0.378872i | ||||
\(281\) | − | 0.928203i | − | 0.0553720i | −0.999617 | − | 0.0276860i | \(-0.991186\pi\) | ||
0.999617 | − | 0.0276860i | \(-0.00881385\pi\) | |||||||
\(282\) | 1.56218 | + | 2.70577i | 0.0930263 | + | 0.161126i | ||||
\(283\) | 14.5263 | + | 3.89230i | 0.863498 | + | 0.231374i | 0.663274 | − | 0.748377i | \(-0.269166\pi\) |
0.200224 | + | 0.979750i | \(0.435833\pi\) | |||||||
\(284\) | −0.535898 | + | 0.928203i | −0.0317997 | + | 0.0550787i | ||||
\(285\) | 1.33013 | − | 0.356406i | 0.0787899 | − | 0.0211117i | ||||
\(286\) | −5.73205 | − | 21.3923i | −0.338943 | − | 1.26495i | ||||
\(287\) | 9.85641 | + | 8.53590i | 0.581805 | + | 0.503858i | ||||
\(288\) | 4.00000 | − | 14.9282i | 0.235702 | − | 0.879653i | ||||
\(289\) | −12.3923 | + | 21.4641i | −0.728959 | + | 1.26259i | ||||
\(290\) | −0.339746 | + | 0.339746i | −0.0199506 | + | 0.0199506i | ||||
\(291\) | 0.392305 | − | 1.46410i | 0.0229973 | − | 0.0858272i | ||||
\(292\) | −14.3923 | −0.842246 | ||||||||
\(293\) | −7.92820 | + | 7.92820i | −0.463171 | + | 0.463171i | −0.899693 | − | 0.436523i | \(-0.856210\pi\) |
0.436523 | + | 0.899693i | \(0.356210\pi\) | |||||||
\(294\) | −4.75833 | − | 1.90192i | −0.277511 | − | 0.110922i | ||||
\(295\) | 10.5167i | 0.612304i | ||||||||
\(296\) | 1.66025 | − | 2.87564i | 0.0965003 | − | 0.167143i | ||||
\(297\) | −7.62436 | + | 4.40192i | −0.442410 | + | 0.255426i | ||||
\(298\) | − | 11.1244i | − | 0.644417i | ||||||
\(299\) | −6.09808 | − | 22.7583i | −0.352661 | − | 1.31615i | ||||
\(300\) | −1.12436 | + | 4.19615i | −0.0649147 | + | 0.242265i | ||||
\(301\) | 1.73205 | + | 24.1244i | 0.0998337 | + | 1.39050i | ||||
\(302\) | 15.5622 | − | 4.16987i | 0.895503 | − | 0.239949i | ||||
\(303\) | 5.06218 | − | 8.76795i | 0.290815 | − | 0.503706i | ||||
\(304\) | −8.39230 | − | 8.39230i | −0.481332 | − | 0.481332i | ||||
\(305\) | −3.23205 | − | 5.59808i | −0.185067 | − | 0.320545i | ||||
\(306\) | −6.46410 | + | 24.1244i | −0.369528 | + | 1.37910i | ||||
\(307\) | 9.00000 | + | 9.00000i | 0.513657 | + | 0.513657i | 0.915645 | − | 0.401988i | \(-0.131681\pi\) |
−0.401988 | + | 0.915645i | \(0.631681\pi\) | |||||||
\(308\) | −15.6603 | + | 1.12436i | −0.892326 | + | 0.0640661i | ||||
\(309\) | −2.36603 | + | 2.36603i | −0.134598 | + | 0.134598i | ||||
\(310\) | −4.09808 | + | 2.36603i | −0.232755 | + | 0.134381i | ||||
\(311\) | −5.59808 | + | 3.23205i | −0.317438 | + | 0.183273i | −0.650250 | − | 0.759720i | \(-0.725336\pi\) |
0.332812 | + | 0.942993i | \(0.392002\pi\) | |||||||
\(312\) | 7.46410 | + | 2.00000i | 0.422572 | + | 0.113228i | ||||
\(313\) | 18.6962 | + | 10.7942i | 1.05677 | + | 0.610126i | 0.924537 | − | 0.381093i | \(-0.124452\pi\) |
0.132232 | + | 0.991219i | \(0.457786\pi\) | |||||||
\(314\) | −13.3660 | + | 23.1506i | −0.754288 | + | 1.30647i | ||||
\(315\) | −3.63397 | − | 5.36603i | −0.204751 | − | 0.302341i | ||||
\(316\) | 28.8564 | − | 16.6603i | 1.62330 | − | 0.937213i | ||||
\(317\) | 14.1603 | − | 3.79423i | 0.795319 | − | 0.213105i | 0.161791 | − | 0.986825i | \(-0.448273\pi\) |
0.633528 | + | 0.773720i | \(0.281606\pi\) | |||||||
\(318\) | 2.12436 | − | 2.12436i | 0.119128 | − | 0.119128i | ||||
\(319\) | −0.562178 | − | 0.973721i | −0.0314759 | − | 0.0545179i | ||||
\(320\) | −6.92820 | + | 1.85641i | −0.387298 | + | 0.103776i | ||||
\(321\) | 1.73205 | 0.0966736 | ||||||||
\(322\) | −16.6603 | + | 1.19615i | −0.928440 | + | 0.0666590i | ||||
\(323\) | 13.5622 | + | 13.5622i | 0.754620 | + | 0.754620i | ||||
\(324\) | 13.3205i | 0.740028i | ||||||||
\(325\) | 21.3923 | + | 5.73205i | 1.18663 | + | 0.317957i | ||||
\(326\) | 17.6603 | 0.978111 | ||||||||
\(327\) | 0.990381 | + | 0.571797i | 0.0547682 | + | 0.0316204i | ||||
\(328\) | −9.85641 | + | 9.85641i | −0.544229 | + | 0.544229i | ||||
\(329\) | −3.69615 | − | 10.6699i | −0.203775 | − | 0.588249i | ||||
\(330\) | 1.68653 | + | 0.973721i | 0.0928406 | + | 0.0536016i | ||||
\(331\) | 5.25833 | + | 19.6244i | 0.289024 | + | 1.07865i | 0.945848 | + | 0.324609i | \(0.105233\pi\) |
−0.656824 | + | 0.754044i | \(0.728101\pi\) | |||||||
\(332\) | 1.12436 | + | 4.19615i | 0.0617070 | + | 0.230294i | ||||
\(333\) | −0.830127 | + | 3.09808i | −0.0454907 | + | 0.169774i | ||||
\(334\) | −8.00000 | + | 29.8564i | −0.437741 | + | 1.63367i | ||||
\(335\) | 4.60770 | 0.251745 | ||||||||
\(336\) | 2.39230 | − | 4.92820i | 0.130511 | − | 0.268856i | ||||
\(337\) | −6.14359 | −0.334663 | −0.167331 | − | 0.985901i | \(-0.553515\pi\) | ||||
−0.167331 | + | 0.985901i | \(0.553515\pi\) | |||||||
\(338\) | 5.43782 | − | 20.2942i | 0.295779 | − | 1.10386i | ||||
\(339\) | 0.196152 | − | 0.732051i | 0.0106535 | − | 0.0397595i | ||||
\(340\) | 11.1962 | − | 3.00000i | 0.607197 | − | 0.162698i | ||||
\(341\) | −2.86603 | − | 10.6962i | −0.155204 | − | 0.579229i | ||||
\(342\) | 9.92820 | + | 5.73205i | 0.536856 | + | 0.309954i | ||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | −25.8564 | −1.39408 | ||||||||
\(345\) | 1.79423 | + | 1.03590i | 0.0965980 | + | 0.0557709i | ||||
\(346\) | 3.26795 | 0.175686 | ||||||||
\(347\) | 23.5263 | + | 6.30385i | 1.26296 | + | 0.338408i | 0.827329 | − | 0.561718i | \(-0.189860\pi\) |
0.435628 | + | 0.900127i | \(0.356526\pi\) | |||||||
\(348\) | 0.392305 | 0.0210297 | ||||||||
\(349\) | 6.12436 | + | 6.12436i | 0.327829 | + | 0.327829i | 0.851761 | − | 0.523931i | \(-0.175535\pi\) |
−0.523931 | + | 0.851761i | \(0.675535\pi\) | |||||||
\(350\) | 6.85641 | − | 14.1244i | 0.366490 | − | 0.754979i | ||||
\(351\) | −15.6603 | −0.835883 | ||||||||
\(352\) | − | 16.7846i | − | 0.894623i | ||||||
\(353\) | 13.8923 | + | 24.0622i | 0.739413 | + | 1.28070i | 0.952760 | + | 0.303724i | \(0.0982301\pi\) |
−0.213347 | + | 0.976976i | \(0.568437\pi\) | |||||||
\(354\) | 6.07180 | − | 6.07180i | 0.322712 | − | 0.322712i | ||||
\(355\) | −0.464102 | + | 0.124356i | −0.0246320 | + | 0.00660011i | ||||
\(356\) | 5.19615 | + | 9.00000i | 0.275396 | + | 0.476999i | ||||
\(357\) | −3.86603 | + | 7.96410i | −0.204612 | + | 0.421505i | ||||
\(358\) | 6.56218 | − | 11.3660i | 0.346822 | − | 0.600713i | ||||
\(359\) | 3.86603 | + | 2.23205i | 0.204041 | + | 0.117803i | 0.598539 | − | 0.801094i | \(-0.295748\pi\) |
−0.394498 | + | 0.918897i | \(0.629081\pi\) | |||||||
\(360\) | 6.00000 | − | 3.46410i | 0.316228 | − | 0.182574i | ||||
\(361\) | −8.83013 | + | 5.09808i | −0.464744 | + | 0.268320i | ||||
\(362\) | −23.1962 | + | 13.3923i | −1.21916 | + | 0.703884i | ||||
\(363\) | 0.803848 | − | 0.803848i | 0.0421911 | − | 0.0421911i | ||||
\(364\) | −25.1244 | − | 12.1962i | −1.31687 | − | 0.639252i | ||||
\(365\) | −4.56218 | − | 4.56218i | −0.238795 | − | 0.238795i | ||||
\(366\) | −1.36603 | + | 5.09808i | −0.0714033 | + | 0.266481i | ||||
\(367\) | −3.06218 | − | 5.30385i | −0.159844 | − | 0.276859i | 0.774968 | − | 0.632000i | \(-0.217766\pi\) |
−0.934812 | + | 0.355142i | \(0.884433\pi\) | |||||||
\(368\) | − | 17.8564i | − | 0.930830i | ||||||
\(369\) | 6.73205 | − | 11.6603i | 0.350457 | − | 0.607009i | ||||
\(370\) | 1.43782 | − | 0.385263i | 0.0747488 | − | 0.0200289i | ||||
\(371\) | −8.99038 | + | 6.08846i | −0.466757 | + | 0.316097i | ||||
\(372\) | 3.73205 | + | 1.00000i | 0.193498 | + | 0.0518476i | ||||
\(373\) | −0.232051 | − | 0.866025i | −0.0120151 | − | 0.0448411i | 0.959658 | − | 0.281170i | \(-0.0907224\pi\) |
−0.971673 | + | 0.236329i | \(0.924056\pi\) | |||||||
\(374\) | 27.1244i | 1.40257i | ||||||||
\(375\) | −3.69615 | + | 2.13397i | −0.190868 | + | 0.110198i | ||||
\(376\) | 11.6603 | − | 3.12436i | 0.601332 | − | 0.161126i | ||||
\(377\) | − | 2.00000i | − | 0.103005i | ||||||
\(378\) | −2.09808 | + | 10.9019i | −0.107913 | + | 0.560734i | ||||
\(379\) | 0.124356 | − | 0.124356i | 0.00638772 | − | 0.00638772i | −0.703906 | − | 0.710293i | \(-0.748562\pi\) |
0.710293 | + | 0.703906i | \(0.248562\pi\) | |||||||
\(380\) | − | 5.32051i | − | 0.272936i | ||||||
\(381\) | −1.26795 | + | 4.73205i | −0.0649590 | + | 0.242430i | ||||
\(382\) | 8.66025 | − | 8.66025i | 0.443097 | − | 0.443097i | ||||
\(383\) | 12.5981 | − | 21.8205i | 0.643732 | − | 1.11498i | −0.340861 | − | 0.940114i | \(-0.610719\pi\) |
0.984593 | − | 0.174862i | \(-0.0559480\pi\) | |||||||
\(384\) | 5.07180 | + | 2.92820i | 0.258819 | + | 0.149429i | ||||
\(385\) | −5.32051 | − | 4.60770i | −0.271158 | − | 0.234830i | ||||
\(386\) | −8.41858 | − | 31.4186i | −0.428495 | − | 1.59916i | ||||
\(387\) | 24.1244 | − | 6.46410i | 1.22631 | − | 0.328589i | ||||
\(388\) | −5.07180 | − | 2.92820i | −0.257481 | − | 0.148657i | ||||
\(389\) | −22.3564 | − | 5.99038i | −1.13351 | − | 0.303724i | −0.357174 | − | 0.934038i | \(-0.616260\pi\) |
−0.776341 | + | 0.630313i | \(0.782926\pi\) | |||||||
\(390\) | 1.73205 | + | 3.00000i | 0.0877058 | + | 0.151911i | ||||
\(391\) | 28.8564i | 1.45933i | ||||||||
\(392\) | −11.8564 | + | 15.8564i | −0.598839 | + | 0.800869i | ||||
\(393\) | 4.07180i | 0.205395i | ||||||||
\(394\) | 28.8564 | − | 16.6603i | 1.45376 | − | 0.839331i | ||||
\(395\) | 14.4282 | + | 3.86603i | 0.725962 | + | 0.194521i | ||||
\(396\) | 4.19615 | + | 15.6603i | 0.210865 | + | 0.786957i | ||||
\(397\) | −25.6244 | + | 6.86603i | −1.28605 | + | 0.344596i | −0.836159 | − | 0.548488i | \(-0.815204\pi\) |
−0.449891 | + | 0.893084i | \(0.648537\pi\) | |||||||
\(398\) | −16.2942 | + | 4.36603i | −0.816756 | + | 0.218849i | ||||
\(399\) | 3.07180 | + | 2.66025i | 0.153782 | + | 0.133179i | ||||
\(400\) | 14.5359 | + | 8.39230i | 0.726795 | + | 0.419615i | ||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | −2.66025 | − | 2.66025i | −0.132681 | − | 0.132681i | ||||
\(403\) | 5.09808 | − | 19.0263i | 0.253953 | − | 0.947766i | ||||
\(404\) | −27.6603 | − | 27.6603i | −1.37615 | − | 1.37615i | ||||
\(405\) | −4.22243 | + | 4.22243i | −0.209814 | + | 0.209814i | ||||
\(406\) | −1.39230 | − | 0.267949i | −0.0690989 | − | 0.0132981i | ||||
\(407\) | 3.48334i | 0.172663i | ||||||||
\(408\) | −8.19615 | − | 4.73205i | −0.405770 | − | 0.234271i | ||||
\(409\) | 7.50000 | − | 4.33013i | 0.370851 | − | 0.214111i | −0.302979 | − | 0.952997i | \(-0.597981\pi\) |
0.673830 | + | 0.738886i | \(0.264648\pi\) | |||||||
\(410\) | −6.24871 | −0.308602 | ||||||||
\(411\) | −2.35641 | − | 8.79423i | −0.116233 | − | 0.433787i | ||||
\(412\) | 6.46410 | + | 11.1962i | 0.318463 | + | 0.551595i | ||||
\(413\) | −25.6962 | + | 17.4019i | −1.26442 | + | 0.856293i | ||||
\(414\) | 4.46410 | + | 16.6603i | 0.219399 | + | 0.818807i | ||||
\(415\) | −0.973721 | + | 1.68653i | −0.0477981 | + | 0.0827887i | ||||
\(416\) | 14.9282 | − | 25.8564i | 0.731915 | − | 1.26771i | ||||
\(417\) | −4.36603 | − | 7.56218i | −0.213805 | − | 0.370321i | ||||
\(418\) | 12.0263 | + | 3.22243i | 0.588225 | + | 0.157614i | ||||
\(419\) | −19.0000 | − | 19.0000i | −0.928211 | − | 0.928211i | 0.0693796 | − | 0.997590i | \(-0.477898\pi\) |
−0.997590 | + | 0.0693796i | \(0.977898\pi\) | |||||||
\(420\) | 2.32051 | − | 0.803848i | 0.113229 | − | 0.0392237i | ||||
\(421\) | 8.66025 | − | 8.66025i | 0.422075 | − | 0.422075i | −0.463843 | − | 0.885918i | \(-0.653530\pi\) |
0.885918 | + | 0.463843i | \(0.153530\pi\) | |||||||
\(422\) | 15.9282 | + | 27.5885i | 0.775373 | + | 1.34299i | ||||
\(423\) | −10.0981 | + | 5.83013i | −0.490985 | + | 0.283470i | ||||
\(424\) | −5.80385 | − | 10.0526i | −0.281860 | − | 0.488195i | ||||
\(425\) | −23.4904 | − | 13.5622i | −1.13945 | − | 0.657862i | ||||
\(426\) | 0.339746 | + | 0.196152i | 0.0164607 | + | 0.00950362i | ||||
\(427\) | 8.33013 | − | 17.1603i | 0.403123 | − | 0.830443i | ||||
\(428\) | 1.73205 | − | 6.46410i | 0.0837218 | − | 0.312454i | ||||
\(429\) | −7.83013 | + | 2.09808i | −0.378042 | + | 0.101296i | ||||
\(430\) | −8.19615 | − | 8.19615i | −0.395254 | − | 0.395254i | ||||
\(431\) | −15.3301 | − | 26.5526i | −0.738426 | − | 1.27899i | −0.953204 | − | 0.302329i | \(-0.902236\pi\) |
0.214777 | − | 0.976663i | \(-0.431097\pi\) | |||||||
\(432\) | −11.4641 | − | 3.07180i | −0.551567 | − | 0.147792i | ||||
\(433\) | −33.1769 | −1.59438 | −0.797190 | − | 0.603728i | \(-0.793681\pi\) | ||||
−0.797190 | + | 0.603728i | \(0.793681\pi\) | |||||||
\(434\) | −12.5622 | − | 6.09808i | −0.603004 | − | 0.292717i | ||||
\(435\) | 0.124356 | + | 0.124356i | 0.00596240 | + | 0.00596240i | ||||
\(436\) | 3.12436 | − | 3.12436i | 0.149629 | − | 0.149629i | ||||
\(437\) | 12.7942 | + | 3.42820i | 0.612031 | + | 0.163993i | ||||
\(438\) | 5.26795i | 0.251712i | ||||||||
\(439\) | −6.52628 | − | 3.76795i | −0.311482 | − | 0.179834i | 0.336107 | − | 0.941824i | \(-0.390890\pi\) |
−0.647590 | + | 0.761989i | \(0.724223\pi\) | |||||||
\(440\) | 5.32051 | − | 5.32051i | 0.253645 | − | 0.253645i | ||||
\(441\) | 7.09808 | − | 17.7583i | 0.338004 | − | 0.845635i | ||||
\(442\) | −24.1244 | + | 41.7846i | −1.14748 | + | 1.98749i | ||||
\(443\) | 2.79423 | + | 10.4282i | 0.132758 | + | 0.495459i | 0.999997 | − | 0.00243278i | \(-0.000774379\pi\) |
−0.867239 | + | 0.497892i | \(0.834108\pi\) | |||||||
\(444\) | −1.05256 | − | 0.607695i | −0.0499522 | − | 0.0288399i | ||||
\(445\) | −1.20577 | + | 4.50000i | −0.0571590 | + | 0.213320i | ||||
\(446\) | −13.4641 | − | 3.60770i | −0.637544 | − | 0.170829i | ||||
\(447\) | −4.07180 | −0.192589 | ||||||||
\(448\) | −16.0000 | − | 13.8564i | −0.755929 | − | 0.654654i | ||||
\(449\) | −23.3205 | −1.10056 | −0.550281 | − | 0.834979i | \(-0.685480\pi\) | ||||
−0.550281 | + | 0.834979i | \(0.685480\pi\) | |||||||
\(450\) | −15.6603 | − | 4.19615i | −0.738231 | − | 0.197809i | ||||
\(451\) | 3.78461 | − | 14.1244i | 0.178210 | − | 0.665090i | ||||
\(452\) | −2.53590 | − | 1.46410i | −0.119279 | − | 0.0688655i | ||||
\(453\) | −1.52628 | − | 5.69615i | −0.0717109 | − | 0.267629i | ||||
\(454\) | 8.16987 | − | 14.1506i | 0.383431 | − | 0.664122i | ||||
\(455\) | −4.09808 | − | 11.8301i | −0.192121 | − | 0.554605i | ||||
\(456\) | −3.07180 | + | 3.07180i | −0.143850 | + | 0.143850i | ||||
\(457\) | −16.2846 | − | 9.40192i | −0.761762 | − | 0.439803i | 0.0681661 | − | 0.997674i | \(-0.478285\pi\) |
−0.829928 | + | 0.557871i | \(0.811619\pi\) | |||||||
\(458\) | 19.5167i | 0.911954i | ||||||||
\(459\) | 18.5263 | + | 4.96410i | 0.864733 | + | 0.231704i | ||||
\(460\) | 5.66025 | − | 5.66025i | 0.263911 | − | 0.263911i | ||||
\(461\) | 18.6603 | + | 18.6603i | 0.869095 | + | 0.869095i | 0.992372 | − | 0.123278i | \(-0.0393405\pi\) |
−0.123278 | + | 0.992372i | \(0.539341\pi\) | |||||||
\(462\) | 0.411543 | + | 5.73205i | 0.0191467 | + | 0.266679i | ||||
\(463\) | 2.14359 | 0.0996212 | 0.0498106 | − | 0.998759i | \(-0.484138\pi\) | ||||
0.0498106 | + | 0.998759i | \(0.484138\pi\) | |||||||
\(464\) | 0.392305 | − | 1.46410i | 0.0182123 | − | 0.0679692i | ||||
\(465\) | 0.866025 | + | 1.50000i | 0.0401610 | + | 0.0695608i | ||||
\(466\) | 0.803848 | + | 0.803848i | 0.0372375 | + | 0.0372375i | ||||
\(467\) | 25.9904 | − | 6.96410i | 1.20269 | − | 0.322260i | 0.398801 | − | 0.917038i | \(-0.369426\pi\) |
0.803890 | + | 0.594777i | \(0.202760\pi\) | |||||||
\(468\) | −7.46410 | + | 27.8564i | −0.345028 | + | 1.28766i | ||||
\(469\) | 7.62436 | + | 11.2583i | 0.352060 | + | 0.519861i | ||||
\(470\) | 4.68653 | + | 2.70577i | 0.216174 | + | 0.124808i | ||||
\(471\) | 8.47372 | + | 4.89230i | 0.390448 | + | 0.225426i | ||||
\(472\) | −16.5885 | − | 28.7321i | −0.763546 | − | 1.32250i | ||||
\(473\) | 23.4904 | − | 13.5622i | 1.08009 | − | 0.623590i | ||||
\(474\) | −6.09808 | − | 10.5622i | −0.280094 | − | 0.485137i | ||||
\(475\) | −8.80385 | + | 8.80385i | −0.403948 | + | 0.403948i | ||||
\(476\) | 25.8564 | + | 22.3923i | 1.18513 | + | 1.02635i | ||||
\(477\) | 7.92820 | + | 7.92820i | 0.363007 | + | 0.363007i | ||||
\(478\) | 11.6603 | + | 3.12436i | 0.533328 | + | 0.142905i | ||||
\(479\) | −7.79423 | − | 13.5000i | −0.356127 | − | 0.616831i | 0.631183 | − | 0.775634i | \(-0.282570\pi\) |
−0.987310 | + | 0.158803i | \(0.949236\pi\) | |||||||
\(480\) | 0.679492 | + | 2.53590i | 0.0310144 | + | 0.115747i | ||||
\(481\) | −3.09808 | + | 5.36603i | −0.141260 | + | 0.244670i | ||||
\(482\) | 5.09808 | + | 19.0263i | 0.232211 | + | 0.866623i | ||||
\(483\) | 0.437822 | + | 6.09808i | 0.0199216 | + | 0.277472i | ||||
\(484\) | −2.19615 | − | 3.80385i | −0.0998251 | − | 0.172902i | ||||
\(485\) | −0.679492 | − | 2.53590i | −0.0308541 | − | 0.115149i | ||||
\(486\) | 17.4641 | 0.792188 | ||||||||
\(487\) | −10.6699 | + | 6.16025i | −0.483498 | + | 0.279148i | −0.721873 | − | 0.692025i | \(-0.756719\pi\) |
0.238375 | + | 0.971173i | \(0.423385\pi\) | |||||||
\(488\) | 17.6603 | + | 10.1962i | 0.799442 | + | 0.461558i | ||||
\(489\) | − | 6.46410i | − | 0.292317i | ||||||
\(490\) | −8.78461 | + | 1.26795i | −0.396848 | + | 0.0572801i | ||||
\(491\) | −3.58846 | + | 3.58846i | −0.161945 | + | 0.161945i | −0.783428 | − | 0.621483i | \(-0.786531\pi\) |
0.621483 | + | 0.783428i | \(0.286531\pi\) | |||||||
\(492\) | 3.60770 | + | 3.60770i | 0.162647 | + | 0.162647i | ||||
\(493\) | −0.633975 | + | 2.36603i | −0.0285528 | + | 0.106560i | ||||
\(494\) | 15.6603 | + | 15.6603i | 0.704588 | + | 0.704588i | ||||
\(495\) | −3.63397 | + | 6.29423i | −0.163335 | + | 0.282905i | ||||
\(496\) | 7.46410 | − | 12.9282i | 0.335148 | − | 0.580493i | ||||
\(497\) | −1.07180 | − | 0.928203i | −0.0480767 | − | 0.0416356i | ||||
\(498\) | 1.53590 | − | 0.411543i | 0.0688253 | − | 0.0184417i | ||||
\(499\) | −24.9904 | + | 6.69615i | −1.11872 | + | 0.299761i | −0.770367 | − | 0.637601i | \(-0.779927\pi\) |
−0.348356 | + | 0.937362i | \(0.613260\pi\) | |||||||
\(500\) | 4.26795 | + | 15.9282i | 0.190868 | + | 0.712331i | ||||
\(501\) | 10.9282 | + | 2.92820i | 0.488236 | + | 0.130822i | ||||
\(502\) | 30.4641 | − | 17.5885i | 1.35968 | − | 0.785011i | ||||
\(503\) | − | 31.8564i | − | 1.42041i | −0.703996 | − | 0.710203i | \(-0.748603\pi\) | ||
0.703996 | − | 0.710203i | \(-0.251397\pi\) | |||||||
\(504\) | 18.3923 | + | 8.92820i | 0.819258 | + | 0.397694i | ||||
\(505\) | − | 17.5359i | − | 0.780337i | ||||||
\(506\) | 9.36603 | + | 16.2224i | 0.416371 | + | 0.721175i | ||||
\(507\) | −7.42820 | − | 1.99038i | −0.329898 | − | 0.0883959i | ||||
\(508\) | 16.3923 | + | 9.46410i | 0.727291 | + | 0.419902i | ||||
\(509\) | −9.42820 | + | 2.52628i | −0.417898 | + | 0.111975i | −0.461640 | − | 0.887067i | \(-0.652739\pi\) |
0.0437420 | + | 0.999043i | \(0.486072\pi\) | |||||||
\(510\) | −1.09808 | − | 4.09808i | −0.0486236 | − | 0.181466i | ||||
\(511\) | 3.59808 | − | 18.6962i | 0.159170 | − | 0.827069i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 4.40192 | − | 7.62436i | 0.194350 | − | 0.336624i | ||||
\(514\) | −19.3923 | + | 19.3923i | −0.855358 | + | 0.855358i | ||||
\(515\) | −1.50000 | + | 5.59808i | −0.0660979 | + | 0.246681i | ||||
\(516\) | 9.46410i | 0.416634i | ||||||||
\(517\) | −8.95448 | + | 8.95448i | −0.393818 | + | 0.393818i | ||||
\(518\) | 3.32051 | + | 2.87564i | 0.145895 | + | 0.126349i | ||||
\(519\) | − | 1.19615i | − | 0.0525053i | ||||||
\(520\) | 12.9282 | − | 3.46410i | 0.566939 | − | 0.151911i | ||||
\(521\) | 13.3756 | − | 7.72243i | 0.585998 | − | 0.338326i | −0.177516 | − | 0.984118i | \(-0.556806\pi\) |
0.763513 | + | 0.645792i | \(0.223473\pi\) | |||||||
\(522\) | 1.46410i | 0.0640820i | ||||||||
\(523\) | 8.65064 | + | 32.2846i | 0.378266 | + | 1.41171i | 0.848514 | + | 0.529173i | \(0.177498\pi\) |
−0.470248 | + | 0.882534i | \(0.655836\pi\) | |||||||
\(524\) | 15.1962 | + | 4.07180i | 0.663847 | + | 0.177877i | ||||
\(525\) | −5.16987 | − | 2.50962i | −0.225632 | − | 0.109529i | ||||
\(526\) | 6.29423 | − | 1.68653i | 0.274441 | − | 0.0735364i | ||||
\(527\) | −12.0622 | + | 20.8923i | −0.525437 | + | 0.910083i | ||||
\(528\) | −6.14359 | −0.267366 | ||||||||
\(529\) | −1.53590 | − | 2.66025i | −0.0667782 | − | 0.115663i | ||||
\(530\) | 1.34679 | − | 5.02628i | 0.0585007 | − | 0.218328i | ||||
\(531\) | 22.6603 | + | 22.6603i | 0.983371 | + | 0.983371i | ||||
\(532\) | 13.0000 | − | 8.80385i | 0.563621 | − | 0.381695i | ||||
\(533\) | 18.3923 | − | 18.3923i | 0.796659 | − | 0.796659i | ||||
\(534\) | 3.29423 | − | 1.90192i | 0.142555 | − | 0.0823043i | ||||
\(535\) | 2.59808 | − | 1.50000i | 0.112325 | − | 0.0648507i | ||||
\(536\) | −12.5885 | + | 7.26795i | −0.543739 | + | 0.313928i | ||||
\(537\) | −4.16025 | − | 2.40192i | −0.179528 | − | 0.103651i | ||||
\(538\) | 7.16987 | − | 12.4186i | 0.309115 | − | 0.535403i | ||||
\(539\) | 2.45448 | − | 20.6244i | 0.105722 | − | 0.888354i | ||||
\(540\) | −2.66025 | − | 4.60770i | −0.114479 | − | 0.198284i | ||||
\(541\) | −9.23205 | + | 2.47372i | −0.396917 | + | 0.106354i | −0.451756 | − | 0.892142i | \(-0.649202\pi\) |
0.0548389 | + | 0.998495i | \(0.482535\pi\) | |||||||
\(542\) | 12.1244 | − | 12.1244i | 0.520786 | − | 0.520786i | ||||
\(543\) | 4.90192 | + | 8.49038i | 0.210362 | + | 0.364357i | ||||
\(544\) | −25.8564 | + | 25.8564i | −1.10858 | + | 1.10858i | ||||
\(545\) | 1.98076 | 0.0848465 | ||||||||
\(546\) | −4.46410 | + | 9.19615i | −0.191046 | + | 0.393559i | ||||
\(547\) | −23.0526 | − | 23.0526i | −0.985656 | − | 0.985656i | 0.0142423 | − | 0.999899i | \(-0.495466\pi\) |
−0.999899 | + | 0.0142423i | \(0.995466\pi\) | |||||||
\(548\) | −35.1769 | −1.50268 | ||||||||
\(549\) | −19.0263 | − | 5.09808i | −0.812022 | − | 0.217581i | ||||
\(550\) | −17.6077 | −0.750795 | ||||||||
\(551\) | 0.973721 | + | 0.562178i | 0.0414819 | + | 0.0239496i | ||||
\(552\) | −6.53590 | −0.278186 | ||||||||
\(553\) | 14.4282 | + | 41.6506i | 0.613550 | + | 1.77117i | ||||
\(554\) | −5.70577 | − | 3.29423i | −0.242415 | − | 0.139958i | ||||
\(555\) | −0.141016 | − | 0.526279i | −0.00598580 | − | 0.0223393i | ||||
\(556\) | −32.5885 | + | 8.73205i | −1.38206 | + | 0.370321i | ||||
\(557\) | −1.76795 | + | 6.59808i | −0.0749104 | + | 0.279569i | −0.993213 | − | 0.116310i | \(-0.962893\pi\) |
0.918303 | + | 0.395879i | \(0.129560\pi\) | |||||||
\(558\) | −3.73205 | + | 13.9282i | −0.157990 | + | 0.589628i | ||||
\(559\) | 48.2487 | 2.04070 | ||||||||
\(560\) | −0.679492 | − | 9.46410i | −0.0287138 | − | 0.399931i | ||||
\(561\) | 9.92820 | 0.419169 | ||||||||
\(562\) | −0.339746 | + | 1.26795i | −0.0143313 | + | 0.0534852i | ||||
\(563\) | 0.650635 | − | 2.42820i | 0.0274210 | − | 0.102337i | −0.950859 | − | 0.309624i | \(-0.899797\pi\) |
0.978280 | + | 0.207287i | \(0.0664635\pi\) | |||||||
\(564\) | −1.14359 | − | 4.26795i | −0.0481540 | − | 0.179713i | ||||
\(565\) | −0.339746 | − | 1.26795i | −0.0142932 | − | 0.0533430i | ||||
\(566\) | −18.4186 | − | 10.6340i | −0.774191 | − | 0.446979i | ||||
\(567\) | −17.3038 | − | 3.33013i | −0.726693 | − | 0.139852i | ||||
\(568\) | 1.07180 | − | 1.07180i | 0.0449716 | − | 0.0449716i | ||||
\(569\) | 5.08846 | + | 2.93782i | 0.213319 | + | 0.123160i | 0.602853 | − | 0.797852i | \(-0.294031\pi\) |
−0.389534 | + | 0.921012i | \(0.627364\pi\) | |||||||
\(570\) | −1.94744 | −0.0815693 | ||||||||
\(571\) | 26.7224 | + | 7.16025i | 1.11830 | + | 0.299647i | 0.770195 | − | 0.637809i | \(-0.220159\pi\) |
0.348104 | + | 0.937456i | \(0.386826\pi\) | |||||||
\(572\) | 31.3205i | 1.30958i | ||||||||
\(573\) | −3.16987 | − | 3.16987i | −0.132423 | − | 0.132423i | ||||
\(574\) | −10.3397 | − | 15.2679i | −0.431573 | − | 0.637272i | ||||
\(575\) | −18.7321 | −0.781181 | ||||||||
\(576\) | −10.9282 | + | 18.9282i | −0.455342 | + | 0.788675i | ||||
\(577\) | −6.62436 | − | 11.4737i | −0.275776 | − | 0.477657i | 0.694555 | − | 0.719440i | \(-0.255601\pi\) |
−0.970330 | + | 0.241782i | \(0.922268\pi\) | |||||||
\(578\) | 24.7846 | − | 24.7846i | 1.03090 | − | 1.03090i | ||||
\(579\) | −11.5000 | + | 3.08142i | −0.477924 | + | 0.128059i | ||||
\(580\) | 0.588457 | − | 0.339746i | 0.0244344 | − | 0.0141072i | ||||
\(581\) | −5.73205 | + | 0.411543i | −0.237806 | + | 0.0170737i | ||||
\(582\) | −1.07180 | + | 1.85641i | −0.0444274 | + | 0.0769505i | ||||
\(583\) | 10.5455 | + | 6.08846i | 0.436751 | + | 0.252158i | ||||
\(584\) | 19.6603 | + | 5.26795i | 0.813547 | + | 0.217989i | ||||
\(585\) | −11.1962 | + | 6.46410i | −0.462904 | + | 0.267258i | ||||
\(586\) | 13.7321 | − | 7.92820i | 0.567266 | − | 0.327511i | ||||
\(587\) | 21.9282 | − | 21.9282i | 0.905074 | − | 0.905074i | −0.0907957 | − | 0.995870i | \(-0.528941\pi\) |
0.995870 | + | 0.0907957i | \(0.0289410\pi\) | |||||||
\(588\) | 5.80385 | + | 4.33975i | 0.239347 | + | 0.178968i | ||||
\(589\) | 7.83013 | + | 7.83013i | 0.322635 | + | 0.322635i | ||||
\(590\) | 3.84936 | − | 14.3660i | 0.158476 | − | 0.591440i | ||||
\(591\) | −6.09808 | − | 10.5622i | −0.250841 | − | 0.434470i | ||||
\(592\) | −3.32051 | + | 3.32051i | −0.136472 | + | 0.136472i | ||||
\(593\) | 5.69615 | − | 9.86603i | 0.233913 | − | 0.405149i | −0.725043 | − | 0.688703i | \(-0.758180\pi\) |
0.958956 | + | 0.283554i | \(0.0915136\pi\) | |||||||
\(594\) | 12.0263 | − | 3.22243i | 0.493444 | − | 0.132218i | ||||
\(595\) | 1.09808 | + | 15.2942i | 0.0450167 | + | 0.627002i | ||||
\(596\) | −4.07180 | + | 15.1962i | −0.166787 | + | 0.622459i | ||||
\(597\) | 1.59808 | + | 5.96410i | 0.0654049 | + | 0.244094i | ||||
\(598\) | 33.3205i | 1.36258i | ||||||||
\(599\) | −16.6699 | + | 9.62436i | −0.681113 | + | 0.393241i | −0.800274 | − | 0.599634i | \(-0.795313\pi\) |
0.119162 | + | 0.992875i | \(0.461979\pi\) | |||||||
\(600\) | 3.07180 | − | 5.32051i | 0.125406 | − | 0.217209i | ||||
\(601\) | 10.0000i | 0.407909i | 0.978980 | + | 0.203954i | \(0.0653794\pi\) | ||||
−0.978980 | + | 0.203954i | \(0.934621\pi\) | |||||||
\(602\) | 6.46410 | − | 33.5885i | 0.263457 | − | 1.36896i | ||||
\(603\) | 9.92820 | − | 9.92820i | 0.404308 | − | 0.404308i | ||||
\(604\) | −22.7846 | −0.927093 | ||||||||
\(605\) | 0.509619 | − | 1.90192i | 0.0207190 | − | 0.0773242i | ||||
\(606\) | −10.1244 | + | 10.1244i | −0.411274 | + | 0.411274i | ||||
\(607\) | −8.52628 | + | 14.7679i | −0.346071 | + | 0.599413i | −0.985548 | − | 0.169398i | \(-0.945818\pi\) |
0.639477 | + | 0.768810i | \(0.279151\pi\) | |||||||
\(608\) | 8.39230 | + | 14.5359i | 0.340353 | + | 0.589509i | ||||
\(609\) | −0.0980762 | + | 0.509619i | −0.00397425 | + | 0.0206508i | ||||
\(610\) | 2.36603 | + | 8.83013i | 0.0957976 | + | 0.357521i | ||||
\(611\) | −21.7583 | + | 5.83013i | −0.880248 | + | 0.235862i | ||||
\(612\) | 17.6603 | − | 30.5885i | 0.713873 | − | 1.23647i | ||||
\(613\) | −9.23205 | − | 2.47372i | −0.372879 | − | 0.0999126i | 0.0675126 | − | 0.997718i | \(-0.478494\pi\) |
−0.440392 | + | 0.897806i | \(0.645160\pi\) | |||||||
\(614\) | −9.00000 | − | 15.5885i | −0.363210 | − | 0.629099i | ||||
\(615\) | 2.28719i | 0.0922283i | ||||||||
\(616\) | 21.8038 | + | 4.19615i | 0.878502 | + | 0.169068i | ||||
\(617\) | 0.535898i | 0.0215745i | 0.999942 | + | 0.0107872i | \(0.00343375\pi\) | ||||
−0.999942 | + | 0.0107872i | \(0.996566\pi\) | |||||||
\(618\) | 4.09808 | − | 2.36603i | 0.164849 | − | 0.0951755i | ||||
\(619\) | −19.0622 | − | 5.10770i | −0.766174 | − | 0.205296i | −0.145493 | − | 0.989359i | \(-0.546477\pi\) |
−0.620680 | + | 0.784064i | \(0.713144\pi\) | |||||||
\(620\) | 6.46410 | − | 1.73205i | 0.259605 | − | 0.0695608i | ||||
\(621\) | 12.7942 | − | 3.42820i | 0.513415 | − | 0.137569i | ||||
\(622\) | 8.83013 | − | 2.36603i | 0.354056 | − | 0.0948690i | ||||
\(623\) | −12.9904 | + | 4.50000i | −0.520449 | + | 0.180289i | ||||
\(624\) | −9.46410 | − | 5.46410i | −0.378867 | − | 0.218739i | ||||
\(625\) | 6.79423 | − | 11.7679i | 0.271769 | − | 0.470718i | ||||
\(626\) | −21.5885 | − | 21.5885i | −0.862848 | − | 0.862848i | ||||
\(627\) | 1.17949 | − | 4.40192i | 0.0471044 | − | 0.175796i | ||||
\(628\) | 26.7321 | − | 26.7321i | 1.06672 | − | 1.06672i | ||||
\(629\) | 5.36603 | − | 5.36603i | 0.213957 | − | 0.213957i | ||||
\(630\) | 3.00000 | + | 8.66025i | 0.119523 | + | 0.345033i | ||||
\(631\) | 32.2487i | 1.28380i | 0.766788 | + | 0.641900i | \(0.221854\pi\) | ||||
−0.766788 | + | 0.641900i | \(0.778146\pi\) | |||||||
\(632\) | −45.5167 | + | 12.1962i | −1.81056 | + | 0.485137i | ||||
\(633\) | 10.0981 | − | 5.83013i | 0.401362 | − | 0.231727i | ||||
\(634\) | −20.7321 | −0.823375 | ||||||||
\(635\) | 2.19615 | + | 8.19615i | 0.0871517 | + | 0.325254i | ||||
\(636\) | −3.67949 | + | 2.12436i | −0.145901 | + | 0.0842362i | ||||
\(637\) | 22.1244 | − | 29.5885i | 0.876599 | − | 1.17234i | ||||
\(638\) | 0.411543 | + | 1.53590i | 0.0162931 | + | 0.0608068i | ||||
\(639\) | −0.732051 | + | 1.26795i | −0.0289595 | + | 0.0501593i | ||||
\(640\) | 10.1436 | 0.400961 | ||||||||
\(641\) | 5.57180 | + | 9.65064i | 0.220073 | + | 0.381177i | 0.954830 | − | 0.297153i | \(-0.0960372\pi\) |
−0.734757 | + | 0.678330i | \(0.762704\pi\) | |||||||
\(642\) | −2.36603 | − | 0.633975i | −0.0933796 | − | 0.0250210i | ||||
\(643\) | −5.39230 | − | 5.39230i | −0.212652 | − | 0.212652i | 0.592741 | − | 0.805393i | \(-0.298046\pi\) |
−0.805393 | + | 0.592741i | \(0.798046\pi\) | |||||||
\(644\) | 23.1962 | + | 4.46410i | 0.914056 | + | 0.175910i | ||||
\(645\) | −3.00000 | + | 3.00000i | −0.118125 | + | 0.118125i | ||||
\(646\) | −13.5622 | − | 23.4904i | −0.533597 | − | 0.924217i | ||||
\(647\) | −30.8660 | + | 17.8205i | −1.21347 | + | 0.700596i | −0.963513 | − | 0.267661i | \(-0.913749\pi\) |
−0.249955 | + | 0.968257i | \(0.580416\pi\) | |||||||
\(648\) | 4.87564 | − | 18.1962i | 0.191533 | − | 0.714812i | ||||
\(649\) | 30.1410 | + | 17.4019i | 1.18314 | + | 0.683085i | ||||
\(650\) | −27.1244 | − | 15.6603i | −1.06390 | − | 0.614246i | ||||
\(651\) | −2.23205 | + | 4.59808i | −0.0874810 | + | 0.180213i | ||||
\(652\) | −24.1244 | − | 6.46410i | −0.944783 | − | 0.253154i | ||||
\(653\) | 32.5526 | − | 8.72243i | 1.27388 | − | 0.341335i | 0.442364 | − | 0.896836i | \(-0.354140\pi\) |
0.831516 | + | 0.555501i | \(0.187473\pi\) | |||||||
\(654\) | −1.14359 | − | 1.14359i | −0.0447180 | − | 0.0447180i | ||||
\(655\) | 3.52628 | + | 6.10770i | 0.137783 | + | 0.238647i | ||||
\(656\) | 17.0718 | − | 9.85641i | 0.666542 | − | 0.384828i | ||||
\(657\) | −19.6603 | −0.767020 | ||||||||
\(658\) | 1.14359 | + | 15.9282i | 0.0445819 | + | 0.620946i | ||||
\(659\) | 18.8564 | + | 18.8564i | 0.734541 | + | 0.734541i | 0.971516 | − | 0.236975i | \(-0.0761558\pi\) |
−0.236975 | + | 0.971516i | \(0.576156\pi\) | |||||||
\(660\) | −1.94744 | − | 1.94744i | −0.0758040 | − | 0.0758040i | ||||
\(661\) | 22.1603 | + | 5.93782i | 0.861934 | + | 0.230955i | 0.662597 | − | 0.748976i | \(-0.269454\pi\) |
0.199337 | + | 0.979931i | \(0.436121\pi\) | |||||||
\(662\) | − | 28.7321i | − | 1.11670i | ||||||
\(663\) | 15.2942 | + | 8.83013i | 0.593979 | + | 0.342934i | ||||
\(664\) | − | 6.14359i | − | 0.238418i | ||||||
\(665\) | 6.91154 | + | 1.33013i | 0.268018 | + | 0.0515801i | ||||
\(666\) | 2.26795 | − | 3.92820i | 0.0878812 | − | 0.152215i | ||||
\(667\) | 0.437822 | + | 1.63397i | 0.0169525 | + | 0.0632677i | ||||
\(668\) | 21.8564 | − | 37.8564i | 0.845650 | − | 1.46471i | ||||
\(669\) | −1.32051 | + | 4.92820i | −0.0510538 | + | 0.190535i | ||||
\(670\) | −6.29423 | − | 1.68653i | −0.243167 | − | 0.0651565i | ||||
\(671\) | −21.3923 | −0.825841 | ||||||||
\(672\) | −5.07180 | + | 5.85641i | −0.195649 | + | 0.225916i | ||||
\(673\) | 40.7846 | 1.57213 | 0.786066 | − | 0.618143i | \(-0.212115\pi\) | ||||
0.786066 | + | 0.618143i | \(0.212115\pi\) | |||||||
\(674\) | 8.39230 | + | 2.24871i | 0.323260 | + | 0.0866171i | ||||
\(675\) | −3.22243 | + | 12.0263i | −0.124031 | + | 0.462892i | ||||
\(676\) | −14.8564 | + | 25.7321i | −0.571400 | + | 0.989694i | ||||
\(677\) | 11.4474 | + | 42.7224i | 0.439961 | + | 1.64196i | 0.728908 | + | 0.684611i | \(0.240028\pi\) |
−0.288947 | + | 0.957345i | \(0.593305\pi\) | |||||||
\(678\) | −0.535898 | + | 0.928203i | −0.0205811 | + | 0.0356474i | ||||
\(679\) | 5.07180 | − | 5.85641i | 0.194638 | − | 0.224748i | ||||
\(680\) | −16.3923 | −0.628616 | ||||||||
\(681\) | −5.17949 | − | 2.99038i | −0.198479 | − | 0.114592i | ||||
\(682\) | 15.6603i | 0.599662i | ||||||||
\(683\) | −45.5788 | − | 12.2128i | −1.74403 | − | 0.467310i | −0.760691 | − | 0.649114i | \(-0.775140\pi\) |
−0.983335 | + | 0.181804i | \(0.941806\pi\) | |||||||
\(684\) | −11.4641 | − | 11.4641i | −0.438341 | − | 0.438341i | ||||
\(685\) | −11.1506 | − | 11.1506i | −0.426044 | − | 0.426044i | ||||
\(686\) | −17.6340 | − | 19.3660i | −0.673268 | − | 0.739398i | ||||
\(687\) | 7.14359 | 0.272545 | ||||||||
\(688\) | 35.3205 | + | 9.46410i | 1.34658 | + | 0.360815i | ||||
\(689\) | 10.8301 | + | 18.7583i | 0.412595 | + | 0.714635i | ||||
\(690\) | −2.07180 | − | 2.07180i | −0.0788720 | − | 0.0788720i | ||||
\(691\) | −22.9904 | + | 6.16025i | −0.874595 | + | 0.234347i | −0.668074 | − | 0.744095i | \(-0.732881\pi\) |
−0.206521 | + | 0.978442i | \(0.566214\pi\) | |||||||
\(692\) | −4.46410 | − | 1.19615i | −0.169700 | − | 0.0454709i | ||||
\(693\) | −21.3923 | + | 1.53590i | −0.812626 | + | 0.0583440i | ||||
\(694\) | −29.8301 | − | 17.2224i | −1.13234 | − | 0.653755i | ||||
\(695\) | −13.0981 | − | 7.56218i | −0.496838 | − | 0.286850i | ||||
\(696\) | −0.535898 | − | 0.143594i | −0.0203132 | − | 0.00544290i | ||||
\(697\) | −27.5885 | + | 15.9282i | −1.04499 | + | 0.603324i | ||||
\(698\) | −6.12436 | − | 10.6077i | −0.231810 | − | 0.401507i | ||||
\(699\) | 0.294229 | − | 0.294229i | 0.0111287 | − | 0.0111287i | ||||
\(700\) | −14.5359 | + | 16.7846i | −0.549405 | + | 0.634399i | ||||
\(701\) | −13.3923 | − | 13.3923i | −0.505820 | − | 0.505820i | 0.407420 | − | 0.913241i | \(-0.366428\pi\) |
−0.913241 | + | 0.407420i | \(0.866428\pi\) | |||||||
\(702\) | 21.3923 | + | 5.73205i | 0.807401 | + | 0.216342i | ||||
\(703\) | −1.74167 | − | 3.01666i | −0.0656883 | − | 0.113776i | ||||
\(704\) | −6.14359 | + | 22.9282i | −0.231545 | + | 0.864139i | ||||
\(705\) | 0.990381 | − | 1.71539i | 0.0372999 | − | 0.0646053i | ||||
\(706\) | −10.1699 | − | 37.9545i | −0.382748 | − | 1.42844i | ||||
\(707\) | 42.8468 | − | 29.0167i | 1.61142 | − | 1.09128i | ||||
\(708\) | −10.5167 | + | 6.07180i | −0.395240 | + | 0.228192i | ||||
\(709\) | −12.2321 | − | 45.6506i | −0.459384 | − | 1.71445i | −0.674868 | − | 0.737938i | \(-0.735800\pi\) |
0.215484 | − | 0.976507i | \(-0.430867\pi\) | |||||||
\(710\) | 0.679492 | 0.0255009 | ||||||||
\(711\) | 39.4186 | − | 22.7583i | 1.47831 | − | 0.853504i | ||||
\(712\) | −3.80385 | − | 14.1962i | −0.142555 | − | 0.532023i | ||||
\(713\) | 16.6603i | 0.623931i | ||||||||
\(714\) | 8.19615 | − | 9.46410i | 0.306733 | − | 0.354185i | ||||
\(715\) | −9.92820 | + | 9.92820i | −0.371294 | + | 0.371294i | ||||
\(716\) | −13.1244 | + | 13.1244i | −0.490480 | + | 0.490480i | ||||
\(717\) | 1.14359 | − | 4.26795i | 0.0427083 | − | 0.159389i | ||||
\(718\) | −4.46410 | − | 4.46410i | −0.166599 | − | 0.166599i | ||||
\(719\) | −0.205771 | + | 0.356406i | −0.00767398 | + | 0.0132917i | −0.869837 | − | 0.493339i | \(-0.835776\pi\) |
0.862163 | + | 0.506631i | \(0.169109\pi\) | |||||||
\(720\) | −9.46410 | + | 2.53590i | −0.352706 | + | 0.0945074i | ||||
\(721\) | −16.1603 | + | 5.59808i | −0.601839 | + | 0.208483i | ||||
\(722\) | 13.9282 | − | 3.73205i | 0.518354 | − | 0.138893i | ||||
\(723\) | 6.96410 | − | 1.86603i | 0.258998 | − | 0.0693982i | ||||
\(724\) | 36.5885 | − | 9.80385i | 1.35980 | − | 0.364357i | ||||
\(725\) | −1.53590 | − | 0.411543i | −0.0570418 | − | 0.0152843i | ||||
\(726\) | −1.39230 | + | 0.803848i | −0.0516733 | + | 0.0298336i | ||||
\(727\) | − | 41.3205i | − | 1.53249i | −0.642547 | − | 0.766246i | \(-0.722122\pi\) | ||
0.642547 | − | 0.766246i | \(-0.277878\pi\) | |||||||
\(728\) | 29.8564 | + | 25.8564i | 1.10655 | + | 0.958302i | ||||
\(729\) | 13.5885i | 0.503276i | ||||||||
\(730\) | 4.56218 | + | 7.90192i | 0.168854 | + | 0.292463i | ||||
\(731\) | −57.0788 | − | 15.2942i | −2.11114 | − | 0.565677i | ||||
\(732\) | 3.73205 | − | 6.46410i | 0.137941 | − | 0.238920i | ||||
\(733\) | 32.8923 | − | 8.81347i | 1.21490 | − | 0.325533i | 0.406220 | − | 0.913775i | \(-0.366847\pi\) |
0.808685 | + | 0.588242i | \(0.200180\pi\) | |||||||
\(734\) | 2.24167 | + | 8.36603i | 0.0827415 | + | 0.308796i | ||||
\(735\) | 0.464102 | + | 3.21539i | 0.0171186 | + | 0.118601i | ||||
\(736\) | −6.53590 | + | 24.3923i | −0.240916 | + | 0.899112i | ||||
\(737\) | 7.62436 | − | 13.2058i | 0.280847 | − | 0.486441i | ||||
\(738\) | −13.4641 | + | 13.4641i | −0.495620 | + | 0.495620i | ||||
\(739\) | −10.3109 | + | 38.4808i | −0.379292 | + | 1.41554i | 0.467679 | + | 0.883899i | \(0.345090\pi\) |
−0.846971 | + | 0.531639i | \(0.821576\pi\) | |||||||
\(740\) | −2.10512 | −0.0773857 | ||||||||
\(741\) | 5.73205 | − | 5.73205i | 0.210572 | − | 0.210572i | ||||
\(742\) | 14.5096 | − | 5.02628i | 0.532665 | − | 0.184521i | ||||
\(743\) | − | 11.0718i | − | 0.406185i | −0.979160 | − | 0.203092i | \(-0.934901\pi\) | ||
0.979160 | − | 0.203092i | \(-0.0650992\pi\) | |||||||
\(744\) | −4.73205 | − | 2.73205i | −0.173485 | − | 0.100162i | ||||
\(745\) | −6.10770 | + | 3.52628i | −0.223769 | + | 0.129193i | ||||
\(746\) | 1.26795i | 0.0464229i | ||||||||
\(747\) | 1.53590 | + | 5.73205i | 0.0561956 | + | 0.209725i | ||||
\(748\) | 9.92820 | − | 37.0526i | 0.363011 | − | 1.35478i | ||||
\(749\) | 7.96410 | + | 3.86603i | 0.291002 | + | 0.141261i | ||||
\(750\) | 5.83013 | − | 1.56218i | 0.212886 | − | 0.0570427i | ||||
\(751\) | −6.52628 | + | 11.3038i | −0.238147 | + | 0.412483i | −0.960183 | − | 0.279373i | \(-0.909873\pi\) |
0.722035 | + | 0.691856i | \(0.243207\pi\) | |||||||
\(752\) | −17.0718 | −0.622544 | ||||||||
\(753\) | −6.43782 | − | 11.1506i | −0.234607 | − | 0.406352i | ||||
\(754\) | −0.732051 | + | 2.73205i | −0.0266597 | + | 0.0994954i | ||||
\(755\) | −7.22243 | − | 7.22243i | −0.262851 | − | 0.262851i | ||||
\(756\) | 6.85641 | − | 14.1244i | 0.249365 | − | 0.513698i | ||||
\(757\) | −18.6603 | + | 18.6603i | −0.678218 | + | 0.678218i | −0.959597 | − | 0.281378i | \(-0.909208\pi\) |
0.281378 | + | 0.959597i | \(0.409208\pi\) | |||||||
\(758\) | −0.215390 | + | 0.124356i | −0.00782333 | + | 0.00451680i | ||||
\(759\) | 5.93782 | − | 3.42820i | 0.215529 | − | 0.124436i | ||||
\(760\) | −1.94744 | + | 7.26795i | −0.0706411 | + | 0.263636i | ||||
\(761\) | −11.7679 | − | 6.79423i | −0.426588 | − | 0.246291i | 0.271304 | − | 0.962494i | \(-0.412545\pi\) |
−0.697892 | + | 0.716203i | \(0.745878\pi\) | |||||||
\(762\) | 3.46410 | − | 6.00000i | 0.125491 | − | 0.217357i | ||||
\(763\) | 3.27757 | + | 4.83975i | 0.118656 | + | 0.175211i | ||||
\(764\) | −15.0000 | + | 8.66025i | −0.542681 | + | 0.313317i | ||||
\(765\) | 15.2942 | − | 4.09808i | 0.552964 | − | 0.148166i | ||||
\(766\) | −25.1962 | + | 25.1962i | −0.910374 | + | 0.910374i | ||||
\(767\) | 30.9545 | + | 53.6147i | 1.11770 | + | 1.93592i | ||||
\(768\) | −5.85641 | − | 5.85641i | −0.211325 | − | 0.211325i | ||||
\(769\) | 9.85641 | 0.355431 | 0.177716 | − | 0.984082i | \(-0.443129\pi\) | ||||
0.177716 | + | 0.984082i | \(0.443129\pi\) | |||||||
\(770\) | 5.58142 | + | 8.24167i | 0.201140 | + | 0.297009i | ||||
\(771\) | 7.09808 | + | 7.09808i | 0.255631 | + | 0.255631i | ||||
\(772\) | 46.0000i | 1.65558i | ||||||||
\(773\) | 10.9641 | + | 2.93782i | 0.394351 | + | 0.105666i | 0.450545 | − | 0.892754i | \(-0.351230\pi\) |
−0.0561936 | + | 0.998420i | \(0.517896\pi\) | |||||||
\(774\) | −35.3205 | −1.26957 | ||||||||
\(775\) | −13.5622 | − | 7.83013i | −0.487168 | − | 0.281266i | ||||
\(776\) | 5.85641 | + | 5.85641i | 0.210233 | + | 0.210233i | ||||
\(777\) | 1.05256 | − | 1.21539i | 0.0377603 | − | 0.0436019i | ||||
\(778\) | 28.3468 | + | 16.3660i | 1.01628 | + | 0.586750i | ||||
\(779\) | 3.78461 | + | 14.1244i | 0.135598 | + | 0.506058i | ||||
\(780\) | −1.26795 | − | 4.73205i | −0.0453999 | − | 0.169435i | ||||
\(781\) | −0.411543 | + | 1.53590i | −0.0147262 | + | 0.0549588i | ||||
\(782\) | 10.5622 | − | 39.4186i | 0.377703 | − | 1.40961i | ||||
\(783\) | 1.12436 | 0.0401812 | ||||||||
\(784\) | 22.0000 | − | 17.3205i | 0.785714 | − | 0.618590i | ||||
\(785\) | 16.9474 | 0.604880 | ||||||||
\(786\) | 1.49038 | − | 5.56218i | 0.0531601 | − | 0.198396i | ||||
\(787\) | 3.52628 | − | 13.1603i | 0.125698 | − | 0.469112i | −0.874165 | − | 0.485628i | \(-0.838591\pi\) |
0.999864 | + | 0.0165161i | \(0.00525747\pi\) | |||||||
\(788\) | −45.5167 | + | 12.1962i | −1.62146 | + | 0.434470i | ||||
\(789\) | −0.617314 | − | 2.30385i | −0.0219770 | − | 0.0820191i | ||||
\(790\) | −18.2942 | − | 10.5622i | −0.650879 | − | 0.375785i | ||||
\(791\) | 2.53590 | − | 2.92820i | 0.0901662 | − | 0.104115i | ||||
\(792\) | − | 22.9282i | − | 0.814718i | ||||||
\(793\) | −32.9545 | − | 19.0263i | −1.17025 | − | 0.675643i | ||||
\(794\) | 37.5167 | 1.33142 | ||||||||
\(795\) | −1.83975 | − | 0.492958i | −0.0652491 | − | 0.0174834i | ||||
\(796\) | 23.8564 | 0.845568 | ||||||||
\(797\) | −13.3397 | − | 13.3397i | −0.472518 | − | 0.472518i | 0.430211 | − | 0.902729i | \(-0.358439\pi\) |
−0.902729 | + | 0.430211i | \(0.858439\pi\) | |||||||
\(798\) | −3.22243 | − | 4.75833i | −0.114073 | − | 0.168443i | ||||
\(799\) | 27.5885 | 0.976009 | ||||||||
\(800\) | −16.7846 | − | 16.7846i | −0.593426 | − | 0.593426i | ||||
\(801\) | 7.09808 | + | 12.2942i | 0.250798 | + | 0.434395i | ||||
\(802\) | −15.0000 | + | 15.0000i | −0.529668 | + | 0.529668i | ||||
\(803\) | −20.6244 | + | 5.52628i | −0.727818 | + | 0.195018i | ||||
\(804\) | 2.66025 | + | 4.60770i | 0.0938199 | + | 0.162501i | ||||
\(805\) | 5.93782 | + | 8.76795i | 0.209281 | + | 0.309030i | ||||
\(806\) | −13.9282 | + | 24.1244i | −0.490600 | + | 0.849744i | ||||
\(807\) | −4.54552 | − | 2.62436i | −0.160010 | − | 0.0923817i | ||||
\(808\) | 27.6603 | + | 47.9090i | 0.973084 | + | 1.68543i | ||||
\(809\) | 29.4282 | − | 16.9904i | 1.03464 | − | 0.597350i | 0.116330 | − | 0.993211i | \(-0.462887\pi\) |
0.918311 | + | 0.395861i | \(0.129554\pi\) | |||||||
\(810\) | 7.31347 | − | 4.22243i | 0.256969 | − | 0.148361i | ||||
\(811\) | 24.3205 | − | 24.3205i | 0.854009 | − | 0.854009i | −0.136616 | − | 0.990624i | \(-0.543623\pi\) |
0.990624 | + | 0.136616i | \(0.0436225\pi\) | |||||||
\(812\) | 1.80385 | + | 0.875644i | 0.0633026 | + | 0.0307291i | ||||
\(813\) | −4.43782 | − | 4.43782i | −0.155641 | − | 0.155641i | ||||
\(814\) | 1.27499 | − | 4.75833i | 0.0446884 | − | 0.166779i | ||||
\(815\) | −5.59808 | − | 9.69615i | −0.196092 | − | 0.339641i | ||||
\(816\) | 9.46410 | + | 9.46410i | 0.331310 | + | 0.331310i | ||||
\(817\) | −13.5622 | + | 23.4904i | −0.474481 | + | 0.821824i | ||||
\(818\) | −11.8301 | + | 3.16987i | −0.413631 | + | 0.110832i | ||||
\(819\) | −34.3205 | − | 16.6603i | −1.19926 | − | 0.582156i | ||||
\(820\) | 8.53590 | + | 2.28719i | 0.298087 | + | 0.0798720i | ||||
\(821\) | −0.160254 | − | 0.598076i | −0.00559290 | − | 0.0208730i | 0.963073 | − | 0.269240i | \(-0.0867726\pi\) |
−0.968666 | + | 0.248367i | \(0.920106\pi\) | |||||||
\(822\) | 12.8756i | 0.449090i | ||||||||
\(823\) | 14.9378 | − | 8.62436i | 0.520700 | − | 0.300626i | −0.216521 | − | 0.976278i | \(-0.569471\pi\) |
0.737221 | + | 0.675652i | \(0.236138\pi\) | |||||||
\(824\) | −4.73205 | − | 17.6603i | −0.164849 | − | 0.615224i | ||||
\(825\) | 6.44486i | 0.224381i | ||||||||
\(826\) | 41.4711 | − | 14.3660i | 1.44297 | − | 0.499858i | ||||
\(827\) | −3.78461 | + | 3.78461i | −0.131604 | + | 0.131604i | −0.769840 | − | 0.638237i | \(-0.779664\pi\) |
0.638237 | + | 0.769840i | \(0.279664\pi\) | |||||||
\(828\) | − | 24.3923i | − | 0.847691i | ||||||
\(829\) | 0.820508 | − | 3.06218i | 0.0284974 | − | 0.106354i | −0.950212 | − | 0.311603i | \(-0.899134\pi\) |
0.978710 | + | 0.205250i | \(0.0658006\pi\) | |||||||
\(830\) | 1.94744 | − | 1.94744i | 0.0675967 | − | 0.0675967i | ||||
\(831\) | −1.20577 | + | 2.08846i | −0.0418277 | + | 0.0724478i | ||||
\(832\) | −29.8564 | + | 29.8564i | −1.03508 | + | 1.03508i | ||||
\(833\) | −35.5526 | + | 27.9904i | −1.23182 | + | 0.969809i | ||||
\(834\) | 3.19615 | + | 11.9282i | 0.110674 | + | 0.413040i | ||||
\(835\) | 18.9282 | − | 5.07180i | 0.655037 | − | 0.175517i | ||||
\(836\) | −15.2487 | − | 8.80385i | −0.527388 | − | 0.304487i | ||||
\(837\) | 10.6962 | + | 2.86603i | 0.369713 | + | 0.0990643i | ||||
\(838\) | 19.0000 | + | 32.9090i | 0.656344 | + | 1.13682i | ||||
\(839\) | 17.7128i | 0.611514i | 0.952110 | + | 0.305757i | \(0.0989096\pi\) | ||||
−0.952110 | + | 0.305757i | \(0.901090\pi\) | |||||||
\(840\) | −3.46410 | + | 0.248711i | −0.119523 | + | 0.00858136i | ||||
\(841\) | − | 28.8564i | − | 0.995048i | ||||||
\(842\) | −15.0000 | + | 8.66025i | −0.516934 | + | 0.298452i | ||||
\(843\) | 0.464102 | + | 0.124356i | 0.0159845 | + | 0.00428304i | ||||
\(844\) | −11.6603 | − | 43.5167i | −0.401362 | − | 1.49791i | ||||
\(845\) | −12.8660 | + | 3.44744i | −0.442605 | + | 0.118596i | ||||
\(846\) | 15.9282 | − | 4.26795i | 0.547623 | − | 0.146735i | ||||
\(847\) | 5.49038 | − | 1.90192i | 0.188652 | − | 0.0653509i | ||||
\(848\) | 4.24871 | + | 15.8564i | 0.145901 | + | 0.544511i | ||||
\(849\) | −3.89230 | + | 6.74167i | −0.133584 | + | 0.231374i | ||||
\(850\) | 27.1244 | + | 27.1244i | 0.930358 | + | 0.930358i | ||||
\(851\) | 1.35641 | − | 5.06218i | 0.0464970 | − | 0.173529i | ||||
\(852\) | −0.392305 | − | 0.392305i | −0.0134401 | − | 0.0134401i | ||||
\(853\) | −11.8756 | + | 11.8756i | −0.406614 | + | 0.406614i | −0.880556 | − | 0.473942i | \(-0.842831\pi\) |
0.473942 | + | 0.880556i | \(0.342831\pi\) | |||||||
\(854\) | −17.6603 | + | 20.3923i | −0.604321 | + | 0.697810i | ||||
\(855\) | − | 7.26795i | − | 0.248559i | ||||||
\(856\) | −4.73205 | + | 8.19615i | −0.161738 | + | 0.280139i | ||||
\(857\) | −11.8923 | + | 6.86603i | −0.406233 | + | 0.234539i | −0.689170 | − | 0.724600i | \(-0.742025\pi\) |
0.282937 | + | 0.959139i | \(0.408691\pi\) | |||||||
\(858\) | 11.4641 | 0.391378 | ||||||||
\(859\) | −3.65064 | − | 13.6244i | −0.124558 | − | 0.464857i | 0.875265 | − | 0.483643i | \(-0.160687\pi\) |
−0.999824 | + | 0.0187858i | \(0.994020\pi\) | |||||||
\(860\) | 8.19615 | + | 14.1962i | 0.279486 | + | 0.484085i | ||||
\(861\) | −5.58846 | + | 3.78461i | −0.190454 | + | 0.128979i | ||||
\(862\) | 11.2224 | + | 41.8827i | 0.382238 | + | 1.42653i | ||||
\(863\) | 16.3301 | − | 28.2846i | 0.555884 | − | 0.962819i | −0.441950 | − | 0.897040i | \(-0.645713\pi\) |
0.997834 | − | 0.0657797i | \(-0.0209535\pi\) | |||||||
\(864\) | 14.5359 | + | 8.39230i | 0.494521 | + | 0.285512i | ||||
\(865\) | −1.03590 | − | 1.79423i | −0.0352216 | − | 0.0610056i | ||||
\(866\) | 45.3205 | + | 12.1436i | 1.54005 | + | 0.412656i | ||||
\(867\) | −9.07180 | − | 9.07180i | −0.308094 | − | 0.308094i | ||||
\(868\) | 14.9282 | + | 12.9282i | 0.506696 | + | 0.438812i | ||||
\(869\) | 34.9545 | − | 34.9545i | 1.18575 | − | 1.18575i | ||||
\(870\) | −0.124356 | − | 0.215390i | −0.00421605 | − | 0.00730242i | ||||
\(871\) | 23.4904 | − | 13.5622i | 0.795941 | − | 0.459537i | ||||
\(872\) | −5.41154 | + | 3.12436i | −0.183258 | + | 0.105804i | ||||
\(873\) | −6.92820 | − | 4.00000i | −0.234484 | − | 0.135379i | ||||
\(874\) | −16.2224 | − | 9.36603i | −0.548732 | − | 0.316811i | ||||
\(875\) | −21.7583 | + | 1.56218i | −0.735566 | + | 0.0528112i | ||||
\(876\) | 1.92820 | − | 7.19615i | 0.0651479 | − | 0.243135i | ||||
\(877\) | −30.5526 | + | 8.18653i | −1.03169 | + | 0.276440i | −0.734664 | − | 0.678431i | \(-0.762660\pi\) |
−0.297022 | + | 0.954871i | \(0.595994\pi\) | |||||||
\(878\) | 7.53590 | + | 7.53590i | 0.254324 | + | 0.254324i | ||||
\(879\) | −2.90192 | − | 5.02628i | −0.0978795 | − | 0.169532i | ||||
\(880\) | −9.21539 | + | 5.32051i | −0.310651 | + | 0.179354i | ||||
\(881\) | 50.0000 | 1.68454 | 0.842271 | − | 0.539054i | \(-0.181218\pi\) | ||||
0.842271 | + | 0.539054i | \(0.181218\pi\) | |||||||
\(882\) | −16.1962 | + | 21.6603i | −0.545353 | + | 0.729339i | ||||
\(883\) | −5.00000 | − | 5.00000i | −0.168263 | − | 0.168263i | 0.617952 | − | 0.786216i | \(-0.287963\pi\) |
−0.786216 | + | 0.617952i | \(0.787963\pi\) | |||||||
\(884\) | 48.2487 | − | 48.2487i | 1.62278 | − | 1.62278i | ||||
\(885\) | −5.25833 | − | 1.40897i | −0.176757 | − | 0.0473619i | ||||
\(886\) | − | 15.2679i | − | 0.512937i | ||||||
\(887\) | 39.7750 | + | 22.9641i | 1.33551 | + | 0.771059i | 0.986139 | − | 0.165924i | \(-0.0530606\pi\) |
0.349375 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(888\) | 1.21539 | + | 1.21539i | 0.0407858 | + | 0.0407858i | ||||
\(889\) | −16.3923 | + | 18.9282i | −0.549780 | + | 0.634832i | ||||
\(890\) | 3.29423 | − | 5.70577i | 0.110423 | − | 0.191258i | ||||
\(891\) | 5.11474 | + | 19.0885i | 0.171350 | + | 0.639487i | ||||
\(892\) | 17.0718 | + | 9.85641i | 0.571606 | + | 0.330017i | ||||
\(893\) | 3.27757 | − | 12.2321i | 0.109680 | − | 0.409330i | ||||
\(894\) | 5.56218 | + | 1.49038i | 0.186027 | + | 0.0498458i | ||||
\(895\) | −8.32051 | −0.278124 | ||||||||
\(896\) | 16.7846 | + | 24.7846i | 0.560734 | + | 0.827996i | ||||
\(897\) | 12.1962 | 0.407218 | ||||||||
\(898\) | 31.8564 | + | 8.53590i | 1.06306 | + | 0.284847i | ||||
\(899\) | −0.366025 | + | 1.36603i | −0.0122076 | + | 0.0455595i | ||||
\(900\) | 19.8564 | + | 11.4641i | 0.661880 | + | 0.382137i | ||||
\(901\) | −6.86603 | − | 25.6244i | −0.228740 | − | 0.853671i | ||||
\(902\) | −10.3397 | + | 17.9090i | −0.344276 | + | 0.596303i | ||||
\(903\) | −12.2942 | − | 2.36603i | −0.409126 | − | 0.0787364i | ||||
\(904\) | 2.92820 | + | 2.92820i | 0.0973906 | + | 0.0973906i | ||||
\(905\) | 14.7058 | + | 8.49038i | 0.488836 | + | 0.282230i | ||||
\(906\) | 8.33975i | 0.277070i | ||||||||
\(907\) | −26.7224 | − | 7.16025i | −0.887304 | − | 0.237752i | −0.213748 | − | 0.976889i | \(-0.568567\pi\) |
−0.673556 | + | 0.739136i | \(0.735234\pi\) | |||||||
\(908\) | −16.3397 | + | 16.3397i | −0.542254 | + | 0.542254i | ||||
\(909\) | −37.7846 | − | 37.7846i | −1.25324 | − | 1.25324i | ||||
\(910\) | 1.26795 | + | 17.6603i | 0.0420321 | + | 0.585432i | ||||
\(911\) | 7.32051 | 0.242539 | 0.121270 | − | 0.992620i | \(-0.461303\pi\) | ||||
0.121270 | + | 0.992620i | \(0.461303\pi\) | |||||||
\(912\) | 5.32051 | − | 3.07180i | 0.176180 | − | 0.101717i | ||||
\(913\) | 3.22243 | + | 5.58142i | 0.106647 | + | 0.184718i | ||||
\(914\) | 18.8038 | + | 18.8038i | 0.621976 | + | 0.621976i | ||||
\(915\) | 3.23205 | − | 0.866025i | 0.106848 | − | 0.0286299i | ||||
\(916\) | 7.14359 | − | 26.6603i | 0.236031 | − | 0.880880i | ||||
\(917\) | −9.08846 | + | 18.7224i | −0.300127 | + | 0.618269i | ||||
\(918\) | −23.4904 | − | 13.5622i | −0.775298 | − | 0.447619i | ||||
\(919\) | 15.8660 | + | 9.16025i | 0.523372 | + | 0.302169i | 0.738313 | − | 0.674458i | \(-0.235623\pi\) |
−0.214941 | + | 0.976627i | \(0.568956\pi\) | |||||||
\(920\) | −9.80385 | + | 5.66025i | −0.323223 | + | 0.186613i | ||||
\(921\) | −5.70577 | + | 3.29423i | −0.188012 | + | 0.108549i | ||||
\(922\) | −18.6603 | − | 32.3205i | −0.614543 | − | 1.06442i | ||||
\(923\) | −2.00000 | + | 2.00000i | −0.0658308 | + | 0.0658308i | ||||
\(924\) | 1.53590 | − | 7.98076i | 0.0505273 | − | 0.262548i | ||||
\(925\) | 3.48334 | + | 3.48334i | 0.114531 | + | 0.114531i | ||||
\(926\) | −2.92820 | − | 0.784610i | −0.0962267 | − | 0.0257839i | ||||
\(927\) | 8.83013 | + | 15.2942i | 0.290019 | + | 0.502328i | ||||
\(928\) | −1.07180 | + | 1.85641i | −0.0351835 | + | 0.0609395i | ||||
\(929\) | −25.0167 | + | 43.3301i | −0.820770 | + | 1.42162i | 0.0843396 | + | 0.996437i | \(0.473122\pi\) |
−0.905110 | + | 0.425178i | \(0.860211\pi\) | |||||||
\(930\) | −0.633975 | − | 2.36603i | −0.0207888 | − | 0.0775850i | ||||
\(931\) | 8.18653 | + | 19.0885i | 0.268303 | + | 0.625599i | ||||
\(932\) | −0.803848 | − | 1.39230i | −0.0263309 | − | 0.0456065i | ||||
\(933\) | −0.866025 | − | 3.23205i | −0.0283524 | − | 0.105813i | ||||
\(934\) | −38.0526 | −1.24512 | ||||||||
\(935\) | 14.8923 | − | 8.59808i | 0.487030 | − | 0.281187i | ||||
\(936\) | 20.3923 | − | 35.3205i | 0.666543 | − | 1.15449i | ||||
\(937\) | − | 29.0718i | − | 0.949734i | −0.880058 | − | 0.474867i | \(-0.842496\pi\) | ||
0.880058 | − | 0.474867i | \(-0.157504\pi\) | |||||||
\(938\) | −6.29423 | − | 18.1699i | −0.205514 | − | 0.593267i | ||||
\(939\) | −7.90192 | + | 7.90192i | −0.257870 | + | 0.257870i | ||||
\(940\) | −5.41154 | − | 5.41154i | −0.176505 | − | 0.176505i | ||||
\(941\) | 6.30385 | − | 23.5263i | 0.205500 | − | 0.766935i | −0.783797 | − | 0.621017i | \(-0.786720\pi\) |
0.989297 | − | 0.145918i | \(-0.0466135\pi\) | |||||||
\(942\) | −9.78461 | − | 9.78461i | −0.318800 | − | 0.318800i | ||||
\(943\) | −11.0000 | + | 19.0526i | −0.358209 | + | 0.620437i | ||||
\(944\) | 12.1436 | + | 45.3205i | 0.395240 | + | 1.47506i | ||||
\(945\) | 6.65064 | − | 2.30385i | 0.216345 | − | 0.0749442i | ||||
\(946\) | −37.0526 | + | 9.92820i | −1.20468 | + | 0.322794i | ||||
\(947\) | 5.40192 | − | 1.44744i | 0.175539 | − | 0.0470355i | −0.169979 | − | 0.985448i | \(-0.554370\pi\) |
0.345518 | + | 0.938412i | \(0.387703\pi\) | |||||||
\(948\) | 4.46410 | + | 16.6603i | 0.144987 | + | 0.541100i | ||||
\(949\) | −36.6865 | − | 9.83013i | −1.19090 | − | 0.319099i | ||||
\(950\) | 15.2487 | − | 8.80385i | 0.494734 | − | 0.285635i | ||||
\(951\) | 7.58846i | 0.246073i | ||||||||
\(952\) | −27.1244 | − | 40.0526i | −0.879105 | − | 1.29811i | ||||
\(953\) | 16.5359i | 0.535650i | 0.963468 | + | 0.267825i | \(0.0863050\pi\) | ||||
−0.963468 | + | 0.267825i | \(0.913695\pi\) | |||||||
\(954\) | −7.92820 | − | 13.7321i | −0.256685 | − | 0.444592i | ||||
\(955\) | −7.50000 | − | 2.00962i | −0.242694 | − | 0.0650297i | ||||
\(956\) | −14.7846 | − | 8.53590i | −0.478168 | − | 0.276071i | ||||
\(957\) | 0.562178 | − | 0.150635i | 0.0181726 | − | 0.00486934i | ||||
\(958\) | 5.70577 | + | 21.2942i | 0.184345 | + | 0.687985i | ||||
\(959\) | 8.79423 | − | 45.6962i | 0.283980 | − | 1.47561i | ||||
\(960\) | − | 3.71281i | − | 0.119831i | ||||||
\(961\) | 8.53590 | − | 14.7846i | 0.275352 | − | 0.476923i | ||||
\(962\) | 6.19615 | − | 6.19615i | 0.199772 | − | 0.199772i | ||||
\(963\) | 2.36603 | − | 8.83013i | 0.0762441 | − | 0.284547i | ||||
\(964\) | − | 27.8564i | − | 0.897194i | ||||||
\(965\) | −14.5814 | + | 14.5814i | −0.469392 | + | 0.469392i | ||||
\(966\) | 1.63397 | − | 8.49038i | 0.0525723 | − | 0.273174i | ||||
\(967\) | − | 60.2487i | − | 1.93747i | −0.248102 | − | 0.968734i | \(-0.579807\pi\) | ||
0.248102 | − | 0.968734i | \(-0.420193\pi\) | |||||||
\(968\) | 1.60770 | + | 6.00000i | 0.0516733 | + | 0.192847i | ||||
\(969\) | −8.59808 | + | 4.96410i | −0.276210 | + | 0.159470i | ||||
\(970\) | 3.71281i | 0.119211i | ||||||||
\(971\) | 14.0429 | + | 52.4090i | 0.450659 | + | 1.68188i | 0.700545 | + | 0.713608i | \(0.252940\pi\) |
−0.249885 | + | 0.968275i | \(0.580393\pi\) | |||||||
\(972\) | −23.8564 | − | 6.39230i | −0.765195 | − | 0.205033i | ||||
\(973\) | −3.19615 | − | 44.5167i | −0.102464 | − | 1.42714i | ||||
\(974\) | 16.8301 | − | 4.50962i | 0.539272 | − | 0.144498i | ||||
\(975\) | −5.73205 | + | 9.92820i | −0.183573 | + | 0.317957i | ||||
\(976\) | −20.3923 | − | 20.3923i | −0.652742 | − | 0.652742i | ||||
\(977\) | 8.57180 | + | 14.8468i | 0.274236 | + | 0.474991i | 0.969942 | − | 0.243336i | \(-0.0782417\pi\) |
−0.695706 | + | 0.718327i | \(0.744908\pi\) | |||||||
\(978\) | −2.36603 | + | 8.83013i | −0.0756571 | + | 0.282356i | ||||
\(979\) | 10.9019 | + | 10.9019i | 0.348427 | + | 0.348427i | ||||
\(980\) | 12.4641 | + | 1.48334i | 0.398151 | + | 0.0473835i | ||||
\(981\) | 4.26795 | − | 4.26795i | 0.136265 | − | 0.136265i | ||||
\(982\) | 6.21539 | − | 3.58846i | 0.198341 | − | 0.114512i | ||||
\(983\) | −17.1340 | + | 9.89230i | −0.546489 | + | 0.315516i | −0.747705 | − | 0.664031i | \(-0.768844\pi\) |
0.201216 | + | 0.979547i | \(0.435511\pi\) | |||||||
\(984\) | −3.60770 | − | 6.24871i | −0.115009 | − | 0.199202i | ||||
\(985\) | −18.2942 | − | 10.5622i | −0.582903 | − | 0.336539i | ||||
\(986\) | 1.73205 | − | 3.00000i | 0.0551597 | − | 0.0955395i | ||||
\(987\) | 5.83013 | − | 0.418584i | 0.185575 | − | 0.0133237i | ||||
\(988\) | −15.6603 | − | 27.1244i | −0.498219 | − | 0.862941i | ||||
\(989\) | −39.4186 | + | 10.5622i | −1.25344 | + | 0.335858i | ||||
\(990\) | 7.26795 | − | 7.26795i | 0.230991 | − | 0.230991i | ||||
\(991\) | 4.20577 | + | 7.28461i | 0.133601 | + | 0.231403i | 0.925062 | − | 0.379816i | \(-0.124013\pi\) |
−0.791461 | + | 0.611219i | \(0.790679\pi\) | |||||||
\(992\) | −14.9282 | + | 14.9282i | −0.473971 | + | 0.473971i | ||||
\(993\) | −10.5167 | −0.333736 | ||||||||
\(994\) | 1.12436 | + | 1.66025i | 0.0356624 | + | 0.0526601i | ||||
\(995\) | 7.56218 | + | 7.56218i | 0.239737 | + | 0.239737i | ||||
\(996\) | −2.24871 | −0.0712531 | ||||||||
\(997\) | −1.50000 | − | 0.401924i | −0.0475055 | − | 0.0127291i | 0.234988 | − | 0.971998i | \(-0.424495\pi\) |
−0.282494 | + | 0.959269i | \(0.591162\pi\) | |||||||
\(998\) | 36.5885 | 1.15819 | ||||||||
\(999\) | −3.01666 | − | 1.74167i | −0.0954429 | − | 0.0551040i |
(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 | 112.2.w.a.93.1 | yes | 4 | |
4.3 | odd | 2 | 448.2.ba.b.401.1 | 4 | |||
7.2 | even | 3 | 784.2.m.e.589.2 | 4 | |||
7.3 | odd | 6 | 784.2.x.h.557.1 | 4 | |||
7.4 | even | 3 | 112.2.w.b.109.1 | yes | 4 | ||
7.5 | odd | 6 | 784.2.m.d.589.2 | 4 | |||
7.6 | odd | 2 | 784.2.x.a.765.1 | 4 | |||
8.3 | odd | 2 | 896.2.ba.a.289.1 | 4 | |||
8.5 | even | 2 | 896.2.ba.d.289.1 | 4 | |||
16.3 | odd | 4 | 896.2.ba.c.737.1 | 4 | |||
16.5 | even | 4 | 112.2.w.b.37.1 | yes | 4 | ||
16.11 | odd | 4 | 448.2.ba.a.177.1 | 4 | |||
16.13 | even | 4 | 896.2.ba.b.737.1 | 4 | |||
28.11 | odd | 6 | 448.2.ba.a.81.1 | 4 | |||
56.11 | odd | 6 | 896.2.ba.c.417.1 | 4 | |||
56.53 | even | 6 | 896.2.ba.b.417.1 | 4 | |||
112.5 | odd | 12 | 784.2.m.d.197.2 | 4 | |||
112.11 | odd | 12 | 448.2.ba.b.305.1 | 4 | |||
112.37 | even | 12 | 784.2.m.e.197.2 | 4 | |||
112.53 | even | 12 | inner | 112.2.w.a.53.1 | ✓ | 4 | |
112.67 | odd | 12 | 896.2.ba.a.865.1 | 4 | |||
112.69 | odd | 4 | 784.2.x.h.373.1 | 4 | |||
112.101 | odd | 12 | 784.2.x.a.165.1 | 4 | |||
112.109 | even | 12 | 896.2.ba.d.865.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.w.a.53.1 | ✓ | 4 | 112.53 | even | 12 | inner | |
112.2.w.a.93.1 | yes | 4 | 1.1 | even | 1 | trivial | |
112.2.w.b.37.1 | yes | 4 | 16.5 | even | 4 | ||
112.2.w.b.109.1 | yes | 4 | 7.4 | even | 3 | ||
448.2.ba.a.81.1 | 4 | 28.11 | odd | 6 | |||
448.2.ba.a.177.1 | 4 | 16.11 | odd | 4 | |||
448.2.ba.b.305.1 | 4 | 112.11 | odd | 12 | |||
448.2.ba.b.401.1 | 4 | 4.3 | odd | 2 | |||
784.2.m.d.197.2 | 4 | 112.5 | odd | 12 | |||
784.2.m.d.589.2 | 4 | 7.5 | odd | 6 | |||
784.2.m.e.197.2 | 4 | 112.37 | even | 12 | |||
784.2.m.e.589.2 | 4 | 7.2 | even | 3 | |||
784.2.x.a.165.1 | 4 | 112.101 | odd | 12 | |||
784.2.x.a.765.1 | 4 | 7.6 | odd | 2 | |||
784.2.x.h.373.1 | 4 | 112.69 | odd | 4 | |||
784.2.x.h.557.1 | 4 | 7.3 | odd | 6 | |||
896.2.ba.a.289.1 | 4 | 8.3 | odd | 2 | |||
896.2.ba.a.865.1 | 4 | 112.67 | odd | 12 | |||
896.2.ba.b.417.1 | 4 | 56.53 | even | 6 | |||
896.2.ba.b.737.1 | 4 | 16.13 | even | 4 | |||
896.2.ba.c.417.1 | 4 | 56.11 | odd | 6 | |||
896.2.ba.c.737.1 | 4 | 16.3 | odd | 4 | |||
896.2.ba.d.289.1 | 4 | 8.5 | even | 2 | |||
896.2.ba.d.865.1 | 4 | 112.109 | even | 12 |