Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,3,Mod(7,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.f (of order \(4\), 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: | \(2.04360198270\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} + 9 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.43 |
Dual form | 75.3.f.a.7.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 1.22474i | −0.612372 | + | 0.612372i | −0.943564 | − | 0.331191i | \(-0.892549\pi\) |
0.331191 | + | 0.943564i | \(0.392549\pi\) | |||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.250000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 3.00000 | 0.500000 | ||||||||
\(7\) | −7.34847 | + | 7.34847i | −1.04978 | + | 1.04978i | −0.0510871 | + | 0.998694i | \(0.516269\pi\) |
−0.998694 | + | 0.0510871i | \(0.983731\pi\) | |||||||
\(8\) | −6.12372 | − | 6.12372i | −0.765466 | − | 0.765466i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −18.0000 | −1.63636 | −0.818182 | − | 0.574960i | \(-0.805018\pi\) | ||||
−0.818182 | + | 0.574960i | \(0.805018\pi\) | |||||||
\(12\) | 1.22474 | − | 1.22474i | 0.102062 | − | 0.102062i | ||||
\(13\) | 7.34847 | + | 7.34847i | 0.565267 | + | 0.565267i | 0.930799 | − | 0.365532i | \(-0.119113\pi\) |
−0.365532 | + | 0.930799i | \(0.619113\pi\) | |||||||
\(14\) | − | 18.0000i | − | 1.28571i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 11.0000 | 0.687500 | ||||||||
\(17\) | 4.89898 | − | 4.89898i | 0.288175 | − | 0.288175i | −0.548183 | − | 0.836358i | \(-0.684680\pi\) |
0.836358 | + | 0.548183i | \(0.184680\pi\) | |||||||
\(18\) | −3.67423 | − | 3.67423i | −0.204124 | − | 0.204124i | ||||
\(19\) | 10.0000i | 0.526316i | 0.964753 | + | 0.263158i | \(0.0847640\pi\) | ||||
−0.964753 | + | 0.263158i | \(0.915236\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 18.0000 | 0.857143 | ||||||||
\(22\) | 22.0454 | − | 22.0454i | 1.00206 | − | 1.00206i | ||||
\(23\) | 19.5959 | + | 19.5959i | 0.851996 | + | 0.851996i | 0.990379 | − | 0.138382i | \(-0.0441903\pi\) |
−0.138382 | + | 0.990379i | \(0.544190\pi\) | |||||||
\(24\) | 15.0000i | 0.625000i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −18.0000 | −0.692308 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | −7.34847 | − | 7.34847i | −0.262445 | − | 0.262445i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.0000 | 0.709677 | 0.354839 | − | 0.934928i | \(-0.384536\pi\) | ||||
0.354839 | + | 0.934928i | \(0.384536\pi\) | |||||||
\(32\) | 11.0227 | − | 11.0227i | 0.344459 | − | 0.344459i | ||||
\(33\) | 22.0454 | + | 22.0454i | 0.668043 | + | 0.668043i | ||||
\(34\) | 12.0000i | 0.352941i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.0833333 | ||||||||
\(37\) | −7.34847 | + | 7.34847i | −0.198607 | + | 0.198607i | −0.799403 | − | 0.600795i | \(-0.794851\pi\) |
0.600795 | + | 0.799403i | \(0.294851\pi\) | |||||||
\(38\) | −12.2474 | − | 12.2474i | −0.322301 | − | 0.322301i | ||||
\(39\) | − | 18.0000i | − | 0.461538i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.0000 | −0.439024 | −0.219512 | − | 0.975610i | \(-0.570447\pi\) | ||||
−0.219512 | + | 0.975610i | \(0.570447\pi\) | |||||||
\(42\) | −22.0454 | + | 22.0454i | −0.524891 | + | 0.524891i | ||||
\(43\) | −29.3939 | − | 29.3939i | −0.683579 | − | 0.683579i | 0.277226 | − | 0.960805i | \(-0.410585\pi\) |
−0.960805 | + | 0.277226i | \(0.910585\pi\) | |||||||
\(44\) | − | 18.0000i | − | 0.409091i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.0000 | −1.04348 | ||||||||
\(47\) | −44.0908 | + | 44.0908i | −0.938102 | + | 0.938102i | −0.998193 | − | 0.0600905i | \(-0.980861\pi\) |
0.0600905 | + | 0.998193i | \(0.480861\pi\) | |||||||
\(48\) | −13.4722 | − | 13.4722i | −0.280671 | − | 0.280671i | ||||
\(49\) | − | 59.0000i | − | 1.20408i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.0000 | −0.235294 | ||||||||
\(52\) | −7.34847 | + | 7.34847i | −0.141317 | + | 0.141317i | ||||
\(53\) | −4.89898 | − | 4.89898i | −0.0924336 | − | 0.0924336i | 0.659378 | − | 0.751812i | \(-0.270820\pi\) |
−0.751812 | + | 0.659378i | \(0.770820\pi\) | |||||||
\(54\) | 9.00000i | 0.166667i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 90.0000 | 1.60714 | ||||||||
\(57\) | 12.2474 | − | 12.2474i | 0.214868 | − | 0.214868i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 90.0000i | 1.52542i | 0.646738 | + | 0.762712i | \(0.276133\pi\) | ||||
−0.646738 | + | 0.762712i | \(0.723867\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.0327869 | 0.0163934 | − | 0.999866i | \(-0.494782\pi\) | ||||
0.0163934 | + | 0.999866i | \(0.494782\pi\) | |||||||
\(62\) | −26.9444 | + | 26.9444i | −0.434587 | + | 0.434587i | ||||
\(63\) | −22.0454 | − | 22.0454i | −0.349927 | − | 0.349927i | ||||
\(64\) | 71.0000i | 1.10938i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −54.0000 | −0.818182 | ||||||||
\(67\) | −44.0908 | + | 44.0908i | −0.658072 | + | 0.658072i | −0.954924 | − | 0.296852i | \(-0.904063\pi\) |
0.296852 | + | 0.954924i | \(0.404063\pi\) | |||||||
\(68\) | 4.89898 | + | 4.89898i | 0.0720438 | + | 0.0720438i | ||||
\(69\) | − | 48.0000i | − | 0.695652i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 72.0000 | 1.01408 | 0.507042 | − | 0.861921i | \(-0.330739\pi\) | ||||
0.507042 | + | 0.861921i | \(0.330739\pi\) | |||||||
\(72\) | 18.3712 | − | 18.3712i | 0.255155 | − | 0.255155i | ||||
\(73\) | 44.0908 | + | 44.0908i | 0.603984 | + | 0.603984i | 0.941367 | − | 0.337384i | \(-0.109542\pi\) |
−0.337384 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(74\) | − | 18.0000i | − | 0.243243i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.0000 | −0.131579 | ||||||||
\(77\) | 132.272 | − | 132.272i | 1.71782 | − | 1.71782i | ||||
\(78\) | 22.0454 | + | 22.0454i | 0.282633 | + | 0.282633i | ||||
\(79\) | − | 70.0000i | − | 0.886076i | −0.896503 | − | 0.443038i | \(-0.853901\pi\) | ||
0.896503 | − | 0.443038i | \(-0.146099\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 22.0454 | − | 22.0454i | 0.268846 | − | 0.268846i | ||||
\(83\) | −53.8888 | − | 53.8888i | −0.649262 | − | 0.649262i | 0.303552 | − | 0.952815i | \(-0.401827\pi\) |
−0.952815 | + | 0.303552i | \(0.901827\pi\) | |||||||
\(84\) | 18.0000i | 0.214286i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 72.0000 | 0.837209 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 110.227 | + | 110.227i | 1.25258 | + | 1.25258i | ||||
\(89\) | 90.0000i | 1.01124i | 0.862757 | + | 0.505618i | \(0.168735\pi\) | ||||
−0.862757 | + | 0.505618i | \(0.831265\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −108.000 | −1.18681 | ||||||||
\(92\) | −19.5959 | + | 19.5959i | −0.212999 | + | 0.212999i | ||||
\(93\) | −26.9444 | − | 26.9444i | −0.289725 | − | 0.289725i | ||||
\(94\) | − | 108.000i | − | 1.14894i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −27.0000 | −0.281250 | ||||||||
\(97\) | 102.879 | − | 102.879i | 1.06060 | − | 1.06060i | 0.0625628 | − | 0.998041i | \(-0.480073\pi\) |
0.998041 | − | 0.0625628i | \(-0.0199274\pi\) | |||||||
\(98\) | 72.2599 | + | 72.2599i | 0.737346 | + | 0.737346i | ||||
\(99\) | − | 54.0000i | − | 0.545455i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −108.000 | −1.06931 | −0.534653 | − | 0.845071i | \(-0.679558\pi\) | ||||
−0.534653 | + | 0.845071i | \(0.679558\pi\) | |||||||
\(102\) | 14.6969 | − | 14.6969i | 0.144088 | − | 0.144088i | ||||
\(103\) | −66.1362 | − | 66.1362i | −0.642099 | − | 0.642099i | 0.308972 | − | 0.951071i | \(-0.400015\pi\) |
−0.951071 | + | 0.308972i | \(0.900015\pi\) | |||||||
\(104\) | − | 90.0000i | − | 0.865385i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.0000 | 0.113208 | ||||||||
\(107\) | −44.0908 | + | 44.0908i | −0.412064 | + | 0.412064i | −0.882457 | − | 0.470393i | \(-0.844112\pi\) |
0.470393 | + | 0.882457i | \(0.344112\pi\) | |||||||
\(108\) | 3.67423 | + | 3.67423i | 0.0340207 | + | 0.0340207i | ||||
\(109\) | 170.000i | 1.55963i | 0.626008 | + | 0.779817i | \(0.284688\pi\) | ||||
−0.626008 | + | 0.779817i | \(0.715312\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.0000 | 0.162162 | ||||||||
\(112\) | −80.8332 | + | 80.8332i | −0.721725 | + | 0.721725i | ||||
\(113\) | 44.0908 | + | 44.0908i | 0.390184 | + | 0.390184i | 0.874753 | − | 0.484569i | \(-0.161024\pi\) |
−0.484569 | + | 0.874753i | \(0.661024\pi\) | |||||||
\(114\) | 30.0000i | 0.263158i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −22.0454 | + | 22.0454i | −0.188422 | + | 0.188422i | ||||
\(118\) | −110.227 | − | 110.227i | −0.934127 | − | 0.934127i | ||||
\(119\) | 72.0000i | 0.605042i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 203.000 | 1.67769 | ||||||||
\(122\) | −2.44949 | + | 2.44949i | −0.0200778 | + | 0.0200778i | ||||
\(123\) | 22.0454 | + | 22.0454i | 0.179231 | + | 0.179231i | ||||
\(124\) | 22.0000i | 0.177419i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 54.0000 | 0.428571 | ||||||||
\(127\) | −7.34847 | + | 7.34847i | −0.0578620 | + | 0.0578620i | −0.735446 | − | 0.677584i | \(-0.763027\pi\) |
0.677584 | + | 0.735446i | \(0.263027\pi\) | |||||||
\(128\) | −42.8661 | − | 42.8661i | −0.334891 | − | 0.334891i | ||||
\(129\) | 72.0000i | 0.558140i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −0.137405 | −0.0687023 | − | 0.997637i | \(-0.521886\pi\) | ||||
−0.0687023 | + | 0.997637i | \(0.521886\pi\) | |||||||
\(132\) | −22.0454 | + | 22.0454i | −0.167011 | + | 0.167011i | ||||
\(133\) | −73.4847 | − | 73.4847i | −0.552516 | − | 0.552516i | ||||
\(134\) | − | 108.000i | − | 0.805970i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −60.0000 | −0.441176 | ||||||||
\(137\) | −142.070 | + | 142.070i | −1.03701 | + | 1.03701i | −0.0377220 | + | 0.999288i | \(0.512010\pi\) |
−0.999288 | + | 0.0377220i | \(0.987990\pi\) | |||||||
\(138\) | 58.7878 | + | 58.7878i | 0.425998 | + | 0.425998i | ||||
\(139\) | − | 170.000i | − | 1.22302i | −0.791236 | − | 0.611511i | \(-0.790562\pi\) | ||
0.791236 | − | 0.611511i | \(-0.209438\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 108.000 | 0.765957 | ||||||||
\(142\) | −88.1816 | + | 88.1816i | −0.620997 | + | 0.620997i | ||||
\(143\) | −132.272 | − | 132.272i | −0.924982 | − | 0.924982i | ||||
\(144\) | 33.0000i | 0.229167i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −108.000 | −0.739726 | ||||||||
\(147\) | −72.2599 | + | 72.2599i | −0.491564 | + | 0.491564i | ||||
\(148\) | −7.34847 | − | 7.34847i | −0.0496518 | − | 0.0496518i | ||||
\(149\) | − | 180.000i | − | 1.20805i | −0.796964 | − | 0.604027i | \(-0.793562\pi\) | ||
0.796964 | − | 0.604027i | \(-0.206438\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.0000 | 0.145695 | 0.0728477 | − | 0.997343i | \(-0.476791\pi\) | ||||
0.0728477 | + | 0.997343i | \(0.476791\pi\) | |||||||
\(152\) | 61.2372 | − | 61.2372i | 0.402877 | − | 0.402877i | ||||
\(153\) | 14.6969 | + | 14.6969i | 0.0960584 | + | 0.0960584i | ||||
\(154\) | 324.000i | 2.10390i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 18.0000 | 0.115385 | ||||||||
\(157\) | 139.621 | − | 139.621i | 0.889305 | − | 0.889305i | −0.105151 | − | 0.994456i | \(-0.533533\pi\) |
0.994456 | + | 0.105151i | \(0.0335326\pi\) | |||||||
\(158\) | 85.7321 | + | 85.7321i | 0.542608 | + | 0.542608i | ||||
\(159\) | 12.0000i | 0.0754717i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −288.000 | −1.78882 | ||||||||
\(162\) | 11.0227 | − | 11.0227i | 0.0680414 | − | 0.0680414i | ||||
\(163\) | 117.576 | + | 117.576i | 0.721322 | + | 0.721322i | 0.968875 | − | 0.247552i | \(-0.0796262\pi\) |
−0.247552 | + | 0.968875i | \(0.579626\pi\) | |||||||
\(164\) | − | 18.0000i | − | 0.109756i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 132.000 | 0.795181 | ||||||||
\(167\) | −19.5959 | + | 19.5959i | −0.117341 | + | 0.117341i | −0.763339 | − | 0.645998i | \(-0.776441\pi\) |
0.645998 | + | 0.763339i | \(0.276441\pi\) | |||||||
\(168\) | −110.227 | − | 110.227i | −0.656113 | − | 0.656113i | ||||
\(169\) | − | 61.0000i | − | 0.360947i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −30.0000 | −0.175439 | ||||||||
\(172\) | 29.3939 | − | 29.3939i | 0.170895 | − | 0.170895i | ||||
\(173\) | 142.070 | + | 142.070i | 0.821216 | + | 0.821216i | 0.986282 | − | 0.165066i | \(-0.0527838\pi\) |
−0.165066 | + | 0.986282i | \(0.552784\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −198.000 | −1.12500 | ||||||||
\(177\) | 110.227 | − | 110.227i | 0.622752 | − | 0.622752i | ||||
\(178\) | −110.227 | − | 110.227i | −0.619253 | − | 0.619253i | ||||
\(179\) | − | 90.0000i | − | 0.502793i | −0.967884 | − | 0.251397i | \(-0.919110\pi\) | ||
0.967884 | − | 0.251397i | \(-0.0808899\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −98.0000 | −0.541436 | −0.270718 | − | 0.962659i | \(-0.587261\pi\) | ||||
−0.270718 | + | 0.962659i | \(0.587261\pi\) | |||||||
\(182\) | 132.272 | − | 132.272i | 0.726772 | − | 0.726772i | ||||
\(183\) | −2.44949 | − | 2.44949i | −0.0133852 | − | 0.0133852i | ||||
\(184\) | − | 240.000i | − | 1.30435i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 66.0000 | 0.354839 | ||||||||
\(187\) | −88.1816 | + | 88.1816i | −0.471560 | + | 0.471560i | ||||
\(188\) | −44.0908 | − | 44.0908i | −0.234526 | − | 0.234526i | ||||
\(189\) | 54.0000i | 0.285714i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 252.000 | 1.31937 | 0.659686 | − | 0.751541i | \(-0.270689\pi\) | ||||
0.659686 | + | 0.751541i | \(0.270689\pi\) | |||||||
\(192\) | 86.9569 | − | 86.9569i | 0.452900 | − | 0.452900i | ||||
\(193\) | 264.545 | + | 264.545i | 1.37070 | + | 1.37070i | 0.859407 | + | 0.511292i | \(0.170833\pi\) |
0.511292 | + | 0.859407i | \(0.329167\pi\) | |||||||
\(194\) | 252.000i | 1.29897i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 59.0000 | 0.301020 | ||||||||
\(197\) | 127.373 | − | 127.373i | 0.646566 | − | 0.646566i | −0.305596 | − | 0.952161i | \(-0.598856\pi\) |
0.952161 | + | 0.305596i | \(0.0988556\pi\) | |||||||
\(198\) | 66.1362 | + | 66.1362i | 0.334021 | + | 0.334021i | ||||
\(199\) | 290.000i | 1.45729i | 0.684893 | + | 0.728643i | \(0.259849\pi\) | ||||
−0.684893 | + | 0.728643i | \(0.740151\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 108.000 | 0.537313 | ||||||||
\(202\) | 132.272 | − | 132.272i | 0.654814 | − | 0.654814i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 12.0000i | − | 0.0588235i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 162.000 | 0.786408 | ||||||||
\(207\) | −58.7878 | + | 58.7878i | −0.283999 | + | 0.283999i | ||||
\(208\) | 80.8332 | + | 80.8332i | 0.388621 | + | 0.388621i | ||||
\(209\) | − | 180.000i | − | 0.861244i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 122.000 | 0.578199 | 0.289100 | − | 0.957299i | \(-0.406644\pi\) | ||||
0.289100 | + | 0.957299i | \(0.406644\pi\) | |||||||
\(212\) | 4.89898 | − | 4.89898i | 0.0231084 | − | 0.0231084i | ||||
\(213\) | −88.1816 | − | 88.1816i | −0.413998 | − | 0.413998i | ||||
\(214\) | − | 108.000i | − | 0.504673i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −45.0000 | −0.208333 | ||||||||
\(217\) | −161.666 | + | 161.666i | −0.745006 | + | 0.745006i | ||||
\(218\) | −208.207 | − | 208.207i | −0.955076 | − | 0.955076i | ||||
\(219\) | − | 108.000i | − | 0.493151i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 72.0000 | 0.325792 | ||||||||
\(222\) | −22.0454 | + | 22.0454i | −0.0993036 | + | 0.0993036i | ||||
\(223\) | 80.8332 | + | 80.8332i | 0.362481 | + | 0.362481i | 0.864725 | − | 0.502245i | \(-0.167492\pi\) |
−0.502245 | + | 0.864725i | \(0.667492\pi\) | |||||||
\(224\) | 162.000i | 0.723214i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −108.000 | −0.477876 | ||||||||
\(227\) | 53.8888 | − | 53.8888i | 0.237395 | − | 0.237395i | −0.578375 | − | 0.815771i | \(-0.696313\pi\) |
0.815771 | + | 0.578375i | \(0.196313\pi\) | |||||||
\(228\) | 12.2474 | + | 12.2474i | 0.0537169 | + | 0.0537169i | ||||
\(229\) | − | 50.0000i | − | 0.218341i | −0.994023 | − | 0.109170i | \(-0.965181\pi\) | ||
0.994023 | − | 0.109170i | \(-0.0348194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −324.000 | −1.40260 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 44.0908 | + | 44.0908i | 0.189231 | + | 0.189231i | 0.795364 | − | 0.606133i | \(-0.207280\pi\) |
−0.606133 | + | 0.795364i | \(0.707280\pi\) | |||||||
\(234\) | − | 54.0000i | − | 0.230769i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −90.0000 | −0.381356 | ||||||||
\(237\) | −85.7321 | + | 85.7321i | −0.361739 | + | 0.361739i | ||||
\(238\) | −88.1816 | − | 88.1816i | −0.370511 | − | 0.370511i | ||||
\(239\) | 180.000i | 0.753138i | 0.926389 | + | 0.376569i | \(0.122896\pi\) | ||||
−0.926389 | + | 0.376569i | \(0.877104\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −178.000 | −0.738589 | −0.369295 | − | 0.929312i | \(-0.620401\pi\) | ||||
−0.369295 | + | 0.929312i | \(0.620401\pi\) | |||||||
\(242\) | −248.623 | + | 248.623i | −1.02737 | + | 1.02737i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 2.00000i | 0.00819672i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −54.0000 | −0.219512 | ||||||||
\(247\) | −73.4847 | + | 73.4847i | −0.297509 | + | 0.297509i | ||||
\(248\) | −134.722 | − | 134.722i | −0.543234 | − | 0.543234i | ||||
\(249\) | 132.000i | 0.530120i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 342.000 | 1.36255 | 0.681275 | − | 0.732028i | \(-0.261426\pi\) | ||||
0.681275 | + | 0.732028i | \(0.261426\pi\) | |||||||
\(252\) | 22.0454 | − | 22.0454i | 0.0874818 | − | 0.0874818i | ||||
\(253\) | −352.727 | − | 352.727i | −1.39418 | − | 1.39418i | ||||
\(254\) | − | 18.0000i | − | 0.0708661i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −179.000 | −0.699219 | ||||||||
\(257\) | −289.040 | + | 289.040i | −1.12467 | + | 1.12467i | −0.133638 | + | 0.991030i | \(0.542666\pi\) |
−0.991030 | + | 0.133638i | \(0.957334\pi\) | |||||||
\(258\) | −88.1816 | − | 88.1816i | −0.341789 | − | 0.341789i | ||||
\(259\) | − | 108.000i | − | 0.416988i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.0454 | − | 22.0454i | 0.0841428 | − | 0.0841428i | ||||
\(263\) | 264.545 | + | 264.545i | 1.00587 | + | 1.00587i | 0.999983 | + | 0.00589147i | \(0.00187532\pi\) |
0.00589147 | + | 0.999983i | \(0.498125\pi\) | |||||||
\(264\) | − | 270.000i | − | 1.02273i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 180.000 | 0.676692 | ||||||||
\(267\) | 110.227 | − | 110.227i | 0.412835 | − | 0.412835i | ||||
\(268\) | −44.0908 | − | 44.0908i | −0.164518 | − | 0.164518i | ||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −478.000 | −1.76384 | −0.881919 | − | 0.471401i | \(-0.843748\pi\) | ||||
−0.881919 | + | 0.471401i | \(0.843748\pi\) | |||||||
\(272\) | 53.8888 | − | 53.8888i | 0.198120 | − | 0.198120i | ||||
\(273\) | 132.272 | + | 132.272i | 0.484514 | + | 0.484514i | ||||
\(274\) | − | 348.000i | − | 1.27007i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 48.0000 | 0.173913 | ||||||||
\(277\) | −80.8332 | + | 80.8332i | −0.291816 | + | 0.291816i | −0.837798 | − | 0.545981i | \(-0.816157\pi\) |
0.545981 | + | 0.837798i | \(0.316157\pi\) | |||||||
\(278\) | 208.207 | + | 208.207i | 0.748945 | + | 0.748945i | ||||
\(279\) | 66.0000i | 0.236559i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 162.000 | 0.576512 | 0.288256 | − | 0.957553i | \(-0.406925\pi\) | ||||
0.288256 | + | 0.957553i | \(0.406925\pi\) | |||||||
\(282\) | −132.272 | + | 132.272i | −0.469051 | + | 0.469051i | ||||
\(283\) | −249.848 | − | 249.848i | −0.882855 | − | 0.882855i | 0.110969 | − | 0.993824i | \(-0.464605\pi\) |
−0.993824 | + | 0.110969i | \(0.964605\pi\) | |||||||
\(284\) | 72.0000i | 0.253521i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 324.000 | 1.13287 | ||||||||
\(287\) | 132.272 | − | 132.272i | 0.460880 | − | 0.460880i | ||||
\(288\) | 33.0681 | + | 33.0681i | 0.114820 | + | 0.114820i | ||||
\(289\) | 241.000i | 0.833910i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −252.000 | −0.865979 | ||||||||
\(292\) | −44.0908 | + | 44.0908i | −0.150996 | + | 0.150996i | ||||
\(293\) | −372.322 | − | 372.322i | −1.27073 | − | 1.27073i | −0.945708 | − | 0.325017i | \(-0.894630\pi\) |
−0.325017 | − | 0.945708i | \(-0.605370\pi\) | |||||||
\(294\) | − | 177.000i | − | 0.602041i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 90.0000 | 0.304054 | ||||||||
\(297\) | −66.1362 | + | 66.1362i | −0.222681 | + | 0.222681i | ||||
\(298\) | 220.454 | + | 220.454i | 0.739779 | + | 0.739779i | ||||
\(299\) | 288.000i | 0.963211i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 432.000 | 1.43522 | ||||||||
\(302\) | −26.9444 | + | 26.9444i | −0.0892198 | + | 0.0892198i | ||||
\(303\) | 132.272 | + | 132.272i | 0.436543 | + | 0.436543i | ||||
\(304\) | 110.000i | 0.361842i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −36.0000 | −0.117647 | ||||||||
\(307\) | 396.817 | − | 396.817i | 1.29256 | − | 1.29256i | 0.359369 | − | 0.933195i | \(-0.382992\pi\) |
0.933195 | − | 0.359369i | \(-0.117008\pi\) | |||||||
\(308\) | 132.272 | + | 132.272i | 0.429456 | + | 0.429456i | ||||
\(309\) | 162.000i | 0.524272i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 252.000 | 0.810289 | 0.405145 | − | 0.914253i | \(-0.367221\pi\) | ||||
0.405145 | + | 0.914253i | \(0.367221\pi\) | |||||||
\(312\) | −110.227 | + | 110.227i | −0.353292 | + | 0.353292i | ||||
\(313\) | 117.576 | + | 117.576i | 0.375641 | + | 0.375641i | 0.869527 | − | 0.493886i | \(-0.164424\pi\) |
−0.493886 | + | 0.869527i | \(0.664424\pi\) | |||||||
\(314\) | 342.000i | 1.08917i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 70.0000 | 0.221519 | ||||||||
\(317\) | 274.343 | − | 274.343i | 0.865435 | − | 0.865435i | −0.126528 | − | 0.991963i | \(-0.540383\pi\) |
0.991963 | + | 0.126528i | \(0.0403834\pi\) | |||||||
\(318\) | −14.6969 | − | 14.6969i | −0.0462168 | − | 0.0462168i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 108.000 | 0.336449 | ||||||||
\(322\) | 352.727 | − | 352.727i | 1.09542 | − | 1.09542i | ||||
\(323\) | 48.9898 | + | 48.9898i | 0.151671 | + | 0.151671i | ||||
\(324\) | − | 9.00000i | − | 0.0277778i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −288.000 | −0.883436 | ||||||||
\(327\) | 208.207 | − | 208.207i | 0.636718 | − | 0.636718i | ||||
\(328\) | 110.227 | + | 110.227i | 0.336058 | + | 0.336058i | ||||
\(329\) | − | 648.000i | − | 1.96960i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −418.000 | −1.26284 | −0.631420 | − | 0.775441i | \(-0.717528\pi\) | ||||
−0.631420 | + | 0.775441i | \(0.717528\pi\) | |||||||
\(332\) | 53.8888 | − | 53.8888i | 0.162316 | − | 0.162316i | ||||
\(333\) | −22.0454 | − | 22.0454i | −0.0662024 | − | 0.0662024i | ||||
\(334\) | − | 48.0000i | − | 0.143713i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 198.000 | 0.589286 | ||||||||
\(337\) | −191.060 | + | 191.060i | −0.566944 | + | 0.566944i | −0.931271 | − | 0.364327i | \(-0.881299\pi\) |
0.364327 | + | 0.931271i | \(0.381299\pi\) | |||||||
\(338\) | 74.7094 | + | 74.7094i | 0.221034 | + | 0.221034i | ||||
\(339\) | − | 108.000i | − | 0.318584i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −396.000 | −1.16129 | ||||||||
\(342\) | 36.7423 | − | 36.7423i | 0.107434 | − | 0.107434i | ||||
\(343\) | 73.4847 | + | 73.4847i | 0.214241 | + | 0.214241i | ||||
\(344\) | 360.000i | 1.04651i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −348.000 | −1.00578 | ||||||||
\(347\) | −44.0908 | + | 44.0908i | −0.127063 | + | 0.127063i | −0.767778 | − | 0.640716i | \(-0.778638\pi\) |
0.640716 | + | 0.767778i | \(0.278638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 70.0000i | 0.200573i | 0.994959 | + | 0.100287i | \(0.0319759\pi\) | ||||
−0.994959 | + | 0.100287i | \(0.968024\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 54.0000 | 0.153846 | ||||||||
\(352\) | −198.409 | + | 198.409i | −0.563661 | + | 0.563661i | ||||
\(353\) | 44.0908 | + | 44.0908i | 0.124903 | + | 0.124903i | 0.766795 | − | 0.641892i | \(-0.221850\pi\) |
−0.641892 | + | 0.766795i | \(0.721850\pi\) | |||||||
\(354\) | 270.000i | 0.762712i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −90.0000 | −0.252809 | ||||||||
\(357\) | 88.1816 | − | 88.1816i | 0.247007 | − | 0.247007i | ||||
\(358\) | 110.227 | + | 110.227i | 0.307897 | + | 0.307897i | ||||
\(359\) | − | 540.000i | − | 1.50418i | −0.659061 | − | 0.752089i | \(-0.729046\pi\) | ||
0.659061 | − | 0.752089i | \(-0.270954\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 261.000 | 0.722992 | ||||||||
\(362\) | 120.025 | − | 120.025i | 0.331561 | − | 0.331561i | ||||
\(363\) | −248.623 | − | 248.623i | −0.684912 | − | 0.684912i | ||||
\(364\) | − | 108.000i | − | 0.296703i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.00000 | 0.0163934 | ||||||||
\(367\) | 66.1362 | − | 66.1362i | 0.180208 | − | 0.180208i | −0.611239 | − | 0.791446i | \(-0.709328\pi\) |
0.791446 | + | 0.611239i | \(0.209328\pi\) | |||||||
\(368\) | 215.555 | + | 215.555i | 0.585748 | + | 0.585748i | ||||
\(369\) | − | 54.0000i | − | 0.146341i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 72.0000 | 0.194070 | ||||||||
\(372\) | 26.9444 | − | 26.9444i | 0.0724311 | − | 0.0724311i | ||||
\(373\) | −213.106 | − | 213.106i | −0.571329 | − | 0.571329i | 0.361171 | − | 0.932500i | \(-0.382377\pi\) |
−0.932500 | + | 0.361171i | \(0.882377\pi\) | |||||||
\(374\) | − | 216.000i | − | 0.577540i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 540.000 | 1.43617 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −66.1362 | − | 66.1362i | −0.174964 | − | 0.174964i | ||||
\(379\) | − | 170.000i | − | 0.448549i | −0.974526 | − | 0.224274i | \(-0.927999\pi\) | ||
0.974526 | − | 0.224274i | \(-0.0720012\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | 0.0472441 | ||||||||
\(382\) | −308.636 | + | 308.636i | −0.807947 | + | 0.807947i | ||||
\(383\) | −151.868 | − | 151.868i | −0.396523 | − | 0.396523i | 0.480482 | − | 0.877005i | \(-0.340462\pi\) |
−0.877005 | + | 0.480482i | \(0.840462\pi\) | |||||||
\(384\) | 105.000i | 0.273438i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −648.000 | −1.67876 | ||||||||
\(387\) | 88.1816 | − | 88.1816i | 0.227860 | − | 0.227860i | ||||
\(388\) | 102.879 | + | 102.879i | 0.265151 | + | 0.265151i | ||||
\(389\) | − | 360.000i | − | 0.925450i | −0.886502 | − | 0.462725i | \(-0.846872\pi\) | ||
0.886502 | − | 0.462725i | \(-0.153128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 192.000 | 0.491049 | ||||||||
\(392\) | −361.300 | + | 361.300i | −0.921683 | + | 0.921683i | ||||
\(393\) | 22.0454 | + | 22.0454i | 0.0560952 | + | 0.0560952i | ||||
\(394\) | 312.000i | 0.791878i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 54.0000 | 0.136364 | ||||||||
\(397\) | −301.287 | + | 301.287i | −0.758910 | + | 0.758910i | −0.976124 | − | 0.217214i | \(-0.930303\pi\) |
0.217214 | + | 0.976124i | \(0.430303\pi\) | |||||||
\(398\) | −355.176 | − | 355.176i | −0.892402 | − | 0.892402i | ||||
\(399\) | 180.000i | 0.451128i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −558.000 | −1.39152 | −0.695761 | − | 0.718274i | \(-0.744933\pi\) | ||||
−0.695761 | + | 0.718274i | \(0.744933\pi\) | |||||||
\(402\) | −132.272 | + | 132.272i | −0.329036 | + | 0.329036i | ||||
\(403\) | 161.666 | + | 161.666i | 0.401157 | + | 0.401157i | ||||
\(404\) | − | 108.000i | − | 0.267327i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 132.272 | − | 132.272i | 0.324994 | − | 0.324994i | ||||
\(408\) | 73.4847 | + | 73.4847i | 0.180110 | + | 0.180110i | ||||
\(409\) | 670.000i | 1.63814i | 0.573692 | + | 0.819071i | \(0.305511\pi\) | ||||
−0.573692 | + | 0.819071i | \(0.694489\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 348.000 | 0.846715 | ||||||||
\(412\) | 66.1362 | − | 66.1362i | 0.160525 | − | 0.160525i | ||||
\(413\) | −661.362 | − | 661.362i | −1.60136 | − | 1.60136i | ||||
\(414\) | − | 144.000i | − | 0.347826i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 162.000 | 0.389423 | ||||||||
\(417\) | −208.207 | + | 208.207i | −0.499296 | + | 0.499296i | ||||
\(418\) | 220.454 | + | 220.454i | 0.527402 | + | 0.527402i | ||||
\(419\) | 630.000i | 1.50358i | 0.659403 | + | 0.751790i | \(0.270809\pi\) | ||||
−0.659403 | + | 0.751790i | \(0.729191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 142.000 | 0.337292 | 0.168646 | − | 0.985677i | \(-0.446061\pi\) | ||||
0.168646 | + | 0.985677i | \(0.446061\pi\) | |||||||
\(422\) | −149.419 | + | 149.419i | −0.354073 | + | 0.354073i | ||||
\(423\) | −132.272 | − | 132.272i | −0.312701 | − | 0.312701i | ||||
\(424\) | 60.0000i | 0.141509i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 216.000 | 0.507042 | ||||||||
\(427\) | −14.6969 | + | 14.6969i | −0.0344191 | + | 0.0344191i | ||||
\(428\) | −44.0908 | − | 44.0908i | −0.103016 | − | 0.103016i | ||||
\(429\) | 324.000i | 0.755245i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 612.000 | 1.41995 | 0.709977 | − | 0.704225i | \(-0.248705\pi\) | ||||
0.709977 | + | 0.704225i | \(0.248705\pi\) | |||||||
\(432\) | 40.4166 | − | 40.4166i | 0.0935569 | − | 0.0935569i | ||||
\(433\) | −102.879 | − | 102.879i | −0.237595 | − | 0.237595i | 0.578259 | − | 0.815853i | \(-0.303732\pi\) |
−0.815853 | + | 0.578259i | \(0.803732\pi\) | |||||||
\(434\) | − | 396.000i | − | 0.912442i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −170.000 | −0.389908 | ||||||||
\(437\) | −195.959 | + | 195.959i | −0.448419 | + | 0.448419i | ||||
\(438\) | 132.272 | + | 132.272i | 0.301992 | + | 0.301992i | ||||
\(439\) | − | 430.000i | − | 0.979499i | −0.871863 | − | 0.489749i | \(-0.837088\pi\) | ||
0.871863 | − | 0.489749i | \(-0.162912\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 177.000 | 0.401361 | ||||||||
\(442\) | −88.1816 | + | 88.1816i | −0.199506 | + | 0.199506i | ||||
\(443\) | 582.979 | + | 582.979i | 1.31598 | + | 1.31598i | 0.916930 | + | 0.399049i | \(0.130660\pi\) |
0.399049 | + | 0.916930i | \(0.369340\pi\) | |||||||
\(444\) | 18.0000i | 0.0405405i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −198.000 | −0.443946 | ||||||||
\(447\) | −220.454 | + | 220.454i | −0.493186 | + | 0.493186i | ||||
\(448\) | −521.741 | − | 521.741i | −1.16460 | − | 1.16460i | ||||
\(449\) | 90.0000i | 0.200445i | 0.994965 | + | 0.100223i | \(0.0319555\pi\) | ||||
−0.994965 | + | 0.100223i | \(0.968044\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 324.000 | 0.718404 | ||||||||
\(452\) | −44.0908 | + | 44.0908i | −0.0975461 | + | 0.0975461i | ||||
\(453\) | −26.9444 | − | 26.9444i | −0.0594799 | − | 0.0594799i | ||||
\(454\) | 132.000i | 0.290749i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −150.000 | −0.328947 | ||||||||
\(457\) | −191.060 | + | 191.060i | −0.418075 | + | 0.418075i | −0.884540 | − | 0.466465i | \(-0.845527\pi\) |
0.466465 | + | 0.884540i | \(0.345527\pi\) | |||||||
\(458\) | 61.2372 | + | 61.2372i | 0.133706 | + | 0.133706i | ||||
\(459\) | − | 36.0000i | − | 0.0784314i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −828.000 | −1.79610 | −0.898048 | − | 0.439898i | \(-0.855015\pi\) | ||||
−0.898048 | + | 0.439898i | \(0.855015\pi\) | |||||||
\(462\) | 396.817 | − | 396.817i | 0.858912 | − | 0.858912i | ||||
\(463\) | 7.34847 | + | 7.34847i | 0.0158714 | + | 0.0158714i | 0.714998 | − | 0.699127i | \(-0.246428\pi\) |
−0.699127 | + | 0.714998i | \(0.746428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −108.000 | −0.231760 | ||||||||
\(467\) | 347.828 | − | 347.828i | 0.744813 | − | 0.744813i | −0.228687 | − | 0.973500i | \(-0.573443\pi\) |
0.973500 | + | 0.228687i | \(0.0734433\pi\) | |||||||
\(468\) | −22.0454 | − | 22.0454i | −0.0471056 | − | 0.0471056i | ||||
\(469\) | − | 648.000i | − | 1.38166i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −342.000 | −0.726115 | ||||||||
\(472\) | 551.135 | − | 551.135i | 1.16766 | − | 1.16766i | ||||
\(473\) | 529.090 | + | 529.090i | 1.11858 | + | 1.11858i | ||||
\(474\) | − | 210.000i | − | 0.443038i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −72.0000 | −0.151261 | ||||||||
\(477\) | 14.6969 | − | 14.6969i | 0.0308112 | − | 0.0308112i | ||||
\(478\) | −220.454 | − | 220.454i | −0.461201 | − | 0.461201i | ||||
\(479\) | − | 360.000i | − | 0.751566i | −0.926708 | − | 0.375783i | \(-0.877374\pi\) | ||
0.926708 | − | 0.375783i | \(-0.122626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −108.000 | −0.224532 | ||||||||
\(482\) | 218.005 | − | 218.005i | 0.452292 | − | 0.452292i | ||||
\(483\) | 352.727 | + | 352.727i | 0.730283 | + | 0.730283i | ||||
\(484\) | 203.000i | 0.419421i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −27.0000 | −0.0555556 | ||||||||
\(487\) | 580.529 | − | 580.529i | 1.19205 | − | 1.19205i | 0.215561 | − | 0.976490i | \(-0.430842\pi\) |
0.976490 | − | 0.215561i | \(-0.0691581\pi\) | |||||||
\(488\) | −12.2474 | − | 12.2474i | −0.0250972 | − | 0.0250972i | ||||
\(489\) | − | 288.000i | − | 0.588957i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0000 | −0.0366599 | −0.0183299 | − | 0.999832i | \(-0.505835\pi\) | ||||
−0.0183299 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(492\) | −22.0454 | + | 22.0454i | −0.0448077 | + | 0.0448077i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 180.000i | − | 0.364372i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 242.000 | 0.487903 | ||||||||
\(497\) | −529.090 | + | 529.090i | −1.06457 | + | 1.06457i | ||||
\(498\) | −161.666 | − | 161.666i | −0.324631 | − | 0.324631i | ||||
\(499\) | 590.000i | 1.18236i | 0.806538 | + | 0.591182i | \(0.201339\pi\) | ||||
−0.806538 | + | 0.591182i | \(0.798661\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 48.0000 | 0.0958084 | ||||||||
\(502\) | −418.863 | + | 418.863i | −0.834388 | + | 0.834388i | ||||
\(503\) | 93.0806 | + | 93.0806i | 0.185051 | + | 0.185051i | 0.793553 | − | 0.608502i | \(-0.208229\pi\) |
−0.608502 | + | 0.793553i | \(0.708229\pi\) | |||||||
\(504\) | 270.000i | 0.535714i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 864.000 | 1.70751 | ||||||||
\(507\) | −74.7094 | + | 74.7094i | −0.147356 | + | 0.147356i | ||||
\(508\) | −7.34847 | − | 7.34847i | −0.0144655 | − | 0.0144655i | ||||
\(509\) | 540.000i | 1.06090i | 0.847715 | + | 0.530452i | \(0.177978\pi\) | ||||
−0.847715 | + | 0.530452i | \(0.822022\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −648.000 | −1.26810 | ||||||||
\(512\) | 390.694 | − | 390.694i | 0.763073 | − | 0.763073i | ||||
\(513\) | 36.7423 | + | 36.7423i | 0.0716225 | + | 0.0716225i | ||||
\(514\) | − | 708.000i | − | 1.37743i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −72.0000 | −0.139535 | ||||||||
\(517\) | 793.635 | − | 793.635i | 1.53508 | − | 1.53508i | ||||
\(518\) | 132.272 | + | 132.272i | 0.255352 | + | 0.255352i | ||||
\(519\) | − | 348.000i | − | 0.670520i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 342.000 | 0.656430 | 0.328215 | − | 0.944603i | \(-0.393553\pi\) | ||||
0.328215 | + | 0.944603i | \(0.393553\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 264.545 | + | 264.545i | 0.505822 | + | 0.505822i | 0.913241 | − | 0.407419i | \(-0.133571\pi\) |
−0.407419 | + | 0.913241i | \(0.633571\pi\) | |||||||
\(524\) | − | 18.0000i | − | 0.0343511i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −648.000 | −1.23194 | ||||||||
\(527\) | 107.778 | − | 107.778i | 0.204511 | − | 0.204511i | ||||
\(528\) | 242.499 | + | 242.499i | 0.459279 | + | 0.459279i | ||||
\(529\) | 239.000i | 0.451796i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −270.000 | −0.508475 | ||||||||
\(532\) | 73.4847 | − | 73.4847i | 0.138129 | − | 0.138129i | ||||
\(533\) | −132.272 | − | 132.272i | −0.248166 | − | 0.248166i | ||||
\(534\) | 270.000i | 0.505618i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 540.000 | 1.00746 | ||||||||
\(537\) | −110.227 | + | 110.227i | −0.205265 | + | 0.205265i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1062.00i | 1.97032i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.00369686 | 0.00184843 | − | 0.999998i | \(-0.499412\pi\) | ||||
0.00184843 | + | 0.999998i | \(0.499412\pi\) | |||||||
\(542\) | 585.428 | − | 585.428i | 1.08013 | − | 1.08013i | ||||
\(543\) | 120.025 | + | 120.025i | 0.221041 | + | 0.221041i | ||||
\(544\) | − | 108.000i | − | 0.198529i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −324.000 | −0.593407 | ||||||||
\(547\) | −264.545 | + | 264.545i | −0.483629 | + | 0.483629i | −0.906288 | − | 0.422660i | \(-0.861097\pi\) |
0.422660 | + | 0.906288i | \(0.361097\pi\) | |||||||
\(548\) | −142.070 | − | 142.070i | −0.259253 | − | 0.259253i | ||||
\(549\) | 6.00000i | 0.0109290i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −293.939 | + | 293.939i | −0.532498 | + | 0.532498i | ||||
\(553\) | 514.393 | + | 514.393i | 0.930186 | + | 0.930186i | ||||
\(554\) | − | 198.000i | − | 0.357401i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 170.000 | 0.305755 | ||||||||
\(557\) | −484.999 | + | 484.999i | −0.870734 | + | 0.870734i | −0.992552 | − | 0.121818i | \(-0.961128\pi\) |
0.121818 | + | 0.992552i | \(0.461128\pi\) | |||||||
\(558\) | −80.8332 | − | 80.8332i | −0.144862 | − | 0.144862i | ||||
\(559\) | − | 432.000i | − | 0.772809i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 216.000 | 0.385027 | ||||||||
\(562\) | −198.409 | + | 198.409i | −0.353040 | + | 0.353040i | ||||
\(563\) | −396.817 | − | 396.817i | −0.704827 | − | 0.704827i | 0.260616 | − | 0.965443i | \(-0.416074\pi\) |
−0.965443 | + | 0.260616i | \(0.916074\pi\) | |||||||
\(564\) | 108.000i | 0.191489i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 612.000 | 1.08127 | ||||||||
\(567\) | 66.1362 | − | 66.1362i | 0.116642 | − | 0.116642i | ||||
\(568\) | −440.908 | − | 440.908i | −0.776247 | − | 0.776247i | ||||
\(569\) | 630.000i | 1.10721i | 0.832781 | + | 0.553603i | \(0.186747\pi\) | ||||
−0.832781 | + | 0.553603i | \(0.813253\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 302.000 | 0.528897 | 0.264448 | − | 0.964400i | \(-0.414810\pi\) | ||||
0.264448 | + | 0.964400i | \(0.414810\pi\) | |||||||
\(572\) | 132.272 | − | 132.272i | 0.231246 | − | 0.231246i | ||||
\(573\) | −308.636 | − | 308.636i | −0.538631 | − | 0.538631i | ||||
\(574\) | 324.000i | 0.564460i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −213.000 | −0.369792 | ||||||||
\(577\) | −484.999 | + | 484.999i | −0.840553 | + | 0.840553i | −0.988931 | − | 0.148378i | \(-0.952595\pi\) |
0.148378 | + | 0.988931i | \(0.452595\pi\) | |||||||
\(578\) | −295.164 | − | 295.164i | −0.510664 | − | 0.510664i | ||||
\(579\) | − | 648.000i | − | 1.11917i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 792.000 | 1.36317 | ||||||||
\(582\) | 308.636 | − | 308.636i | 0.530302 | − | 0.530302i | ||||
\(583\) | 88.1816 | + | 88.1816i | 0.151255 | + | 0.151255i | ||||
\(584\) | − | 540.000i | − | 0.924658i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 912.000 | 1.55631 | ||||||||
\(587\) | −582.979 | + | 582.979i | −0.993149 | + | 0.993149i | −0.999977 | − | 0.00682753i | \(-0.997827\pi\) |
0.00682753 | + | 0.999977i | \(0.497827\pi\) | |||||||
\(588\) | −72.2599 | − | 72.2599i | −0.122891 | − | 0.122891i | ||||
\(589\) | 220.000i | 0.373514i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −312.000 | −0.527919 | ||||||||
\(592\) | −80.8332 | + | 80.8332i | −0.136543 | + | 0.136543i | ||||
\(593\) | 533.989 | + | 533.989i | 0.900487 | + | 0.900487i | 0.995478 | − | 0.0949912i | \(-0.0302823\pi\) |
−0.0949912 | + | 0.995478i | \(0.530282\pi\) | |||||||
\(594\) | − | 162.000i | − | 0.272727i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 180.000 | 0.302013 | ||||||||
\(597\) | 355.176 | − | 355.176i | 0.594935 | − | 0.594935i | ||||
\(598\) | −352.727 | − | 352.727i | −0.589844 | − | 0.589844i | ||||
\(599\) | − | 540.000i | − | 0.901503i | −0.892650 | − | 0.450751i | \(-0.851156\pi\) | ||
0.892650 | − | 0.450751i | \(-0.148844\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −758.000 | −1.26123 | −0.630616 | − | 0.776095i | \(-0.717198\pi\) | ||||
−0.630616 | + | 0.776095i | \(0.717198\pi\) | |||||||
\(602\) | −529.090 | + | 529.090i | −0.878887 | + | 0.878887i | ||||
\(603\) | −132.272 | − | 132.272i | −0.219357 | − | 0.219357i | ||||
\(604\) | 22.0000i | 0.0364238i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −324.000 | −0.534653 | ||||||||
\(607\) | −668.711 | + | 668.711i | −1.10167 | + | 1.10167i | −0.107455 | + | 0.994210i | \(0.534270\pi\) |
−0.994210 | + | 0.107455i | \(0.965730\pi\) | |||||||
\(608\) | 110.227 | + | 110.227i | 0.181294 | + | 0.181294i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −648.000 | −1.06056 | ||||||||
\(612\) | −14.6969 | + | 14.6969i | −0.0240146 | + | 0.0240146i | ||||
\(613\) | −66.1362 | − | 66.1362i | −0.107889 | − | 0.107889i | 0.651101 | − | 0.758991i | \(-0.274307\pi\) |
−0.758991 | + | 0.651101i | \(0.774307\pi\) | |||||||
\(614\) | 972.000i | 1.58306i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1620.00 | −2.62987 | ||||||||
\(617\) | 592.777 | − | 592.777i | 0.960740 | − | 0.960740i | −0.0385180 | − | 0.999258i | \(-0.512264\pi\) |
0.999258 | + | 0.0385180i | \(0.0122637\pi\) | |||||||
\(618\) | −198.409 | − | 198.409i | −0.321050 | − | 0.321050i | ||||
\(619\) | − | 1030.00i | − | 1.66397i | −0.554795 | − | 0.831987i | \(-0.687203\pi\) | ||
0.554795 | − | 0.831987i | \(-0.312797\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 144.000 | 0.231884 | ||||||||
\(622\) | −308.636 | + | 308.636i | −0.496199 | + | 0.496199i | ||||
\(623\) | −661.362 | − | 661.362i | −1.06158 | − | 1.06158i | ||||
\(624\) | − | 198.000i | − | 0.317308i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −288.000 | −0.460064 | ||||||||
\(627\) | −220.454 | + | 220.454i | −0.351601 | + | 0.351601i | ||||
\(628\) | 139.621 | + | 139.621i | 0.222326 | + | 0.222326i | ||||
\(629\) | 72.0000i | 0.114467i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 242.000 | 0.383518 | 0.191759 | − | 0.981442i | \(-0.438581\pi\) | ||||
0.191759 | + | 0.981442i | \(0.438581\pi\) | |||||||
\(632\) | −428.661 | + | 428.661i | −0.678261 | + | 0.678261i | ||||
\(633\) | −149.419 | − | 149.419i | −0.236049 | − | 0.236049i | ||||
\(634\) | 672.000i | 1.05994i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.0000 | −0.0188679 | ||||||||
\(637\) | 433.560 | − | 433.560i | 0.680627 | − | 0.680627i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 216.000i | 0.338028i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 162.000 | 0.252730 | 0.126365 | − | 0.991984i | \(-0.459669\pi\) | ||||
0.126365 | + | 0.991984i | \(0.459669\pi\) | |||||||
\(642\) | −132.272 | + | 132.272i | −0.206032 | + | 0.206032i | ||||
\(643\) | 264.545 | + | 264.545i | 0.411423 | + | 0.411423i | 0.882234 | − | 0.470811i | \(-0.156039\pi\) |
−0.470811 | + | 0.882234i | \(0.656039\pi\) | |||||||
\(644\) | − | 288.000i | − | 0.447205i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −120.000 | −0.185759 | ||||||||
\(647\) | −93.0806 | + | 93.0806i | −0.143865 | + | 0.143865i | −0.775371 | − | 0.631506i | \(-0.782437\pi\) |
0.631506 | + | 0.775371i | \(0.282437\pi\) | |||||||
\(648\) | 55.1135 | + | 55.1135i | 0.0850517 | + | 0.0850517i | ||||
\(649\) | − | 1620.00i | − | 2.49615i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 396.000 | 0.608295 | ||||||||
\(652\) | −117.576 | + | 117.576i | −0.180331 | + | 0.180331i | ||||
\(653\) | 68.5857 | + | 68.5857i | 0.105032 | + | 0.105032i | 0.757670 | − | 0.652638i | \(-0.226338\pi\) |
−0.652638 | + | 0.757670i | \(0.726338\pi\) | |||||||
\(654\) | 510.000i | 0.779817i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −198.000 | −0.301829 | ||||||||
\(657\) | −132.272 | + | 132.272i | −0.201328 | + | 0.201328i | ||||
\(658\) | 793.635 | + | 793.635i | 1.20613 | + | 1.20613i | ||||
\(659\) | 630.000i | 0.955994i | 0.878361 | + | 0.477997i | \(0.158637\pi\) | ||||
−0.878361 | + | 0.477997i | \(0.841363\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 622.000 | 0.940998 | 0.470499 | − | 0.882400i | \(-0.344074\pi\) | ||||
0.470499 | + | 0.882400i | \(0.344074\pi\) | |||||||
\(662\) | 511.943 | − | 511.943i | 0.773328 | − | 0.773328i | ||||
\(663\) | −88.1816 | − | 88.1816i | −0.133004 | − | 0.133004i | ||||
\(664\) | 660.000i | 0.993976i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 54.0000 | 0.0810811 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −19.5959 | − | 19.5959i | −0.0293352 | − | 0.0293352i | ||||
\(669\) | − | 198.000i | − | 0.295964i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.0000 | −0.0536513 | ||||||||
\(672\) | 198.409 | − | 198.409i | 0.295251 | − | 0.295251i | ||||
\(673\) | −102.879 | − | 102.879i | −0.152866 | − | 0.152866i | 0.626531 | − | 0.779397i | \(-0.284474\pi\) |
−0.779397 | + | 0.626531i | \(0.784474\pi\) | |||||||
\(674\) | − | 468.000i | − | 0.694362i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 61.0000 | 0.0902367 | ||||||||
\(677\) | 176.363 | − | 176.363i | 0.260507 | − | 0.260507i | −0.564753 | − | 0.825260i | \(-0.691029\pi\) |
0.825260 | + | 0.564753i | \(0.191029\pi\) | |||||||
\(678\) | 132.272 | + | 132.272i | 0.195092 | + | 0.195092i | ||||
\(679\) | 1512.00i | 2.22680i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −132.000 | −0.193833 | ||||||||
\(682\) | 484.999 | − | 484.999i | 0.711142 | − | 0.711142i | ||||
\(683\) | −445.807 | − | 445.807i | −0.652719 | − | 0.652719i | 0.300928 | − | 0.953647i | \(-0.402704\pi\) |
−0.953647 | + | 0.300928i | \(0.902704\pi\) | |||||||
\(684\) | − | 30.0000i | − | 0.0438596i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −180.000 | −0.262391 | ||||||||
\(687\) | −61.2372 | + | 61.2372i | −0.0891372 | + | 0.0891372i | ||||
\(688\) | −323.333 | − | 323.333i | −0.469960 | − | 0.469960i | ||||
\(689\) | − | 72.0000i | − | 0.104499i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 682.000 | 0.986975 | 0.493488 | − | 0.869753i | \(-0.335722\pi\) | ||||
0.493488 | + | 0.869753i | \(0.335722\pi\) | |||||||
\(692\) | −142.070 | + | 142.070i | −0.205304 | + | 0.205304i | ||||
\(693\) | 396.817 | + | 396.817i | 0.572608 | + | 0.572608i | ||||
\(694\) | − | 108.000i | − | 0.155620i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −88.1816 | + | 88.1816i | −0.126516 | + | 0.126516i | ||||
\(698\) | −85.7321 | − | 85.7321i | −0.122825 | − | 0.122825i | ||||
\(699\) | − | 108.000i | − | 0.154506i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −468.000 | −0.667618 | −0.333809 | − | 0.942641i | \(-0.608334\pi\) | ||||
−0.333809 | + | 0.942641i | \(0.608334\pi\) | |||||||
\(702\) | −66.1362 | + | 66.1362i | −0.0942111 | + | 0.0942111i | ||||
\(703\) | −73.4847 | − | 73.4847i | −0.104530 | − | 0.104530i | ||||
\(704\) | − | 1278.00i | − | 1.81534i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −108.000 | −0.152975 | ||||||||
\(707\) | 793.635 | − | 793.635i | 1.12254 | − | 1.12254i | ||||
\(708\) | 110.227 | + | 110.227i | 0.155688 | + | 0.155688i | ||||
\(709\) | 310.000i | 0.437236i | 0.975811 | + | 0.218618i | \(0.0701548\pi\) | ||||
−0.975811 | + | 0.218618i | \(0.929845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 210.000 | 0.295359 | ||||||||
\(712\) | 551.135 | − | 551.135i | 0.774066 | − | 0.774066i | ||||
\(713\) | 431.110 | + | 431.110i | 0.604643 | + | 0.604643i | ||||
\(714\) | 216.000i | 0.302521i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 90.0000 | 0.125698 | ||||||||
\(717\) | 220.454 | − | 220.454i | 0.307467 | − | 0.307467i | ||||
\(718\) | 661.362 | + | 661.362i | 0.921117 | + | 0.921117i | ||||
\(719\) | 180.000i | 0.250348i | 0.992135 | + | 0.125174i | \(0.0399489\pi\) | ||||
−0.992135 | + | 0.125174i | \(0.960051\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 972.000 | 1.34813 | ||||||||
\(722\) | −319.658 | + | 319.658i | −0.442740 | + | 0.442740i | ||||
\(723\) | 218.005 | + | 218.005i | 0.301528 | + | 0.301528i | ||||
\(724\) | − | 98.0000i | − | 0.135359i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 609.000 | 0.838843 | ||||||||
\(727\) | 507.044 | − | 507.044i | 0.697448 | − | 0.697448i | −0.266412 | − | 0.963859i | \(-0.585838\pi\) |
0.963859 | + | 0.266412i | \(0.0858381\pi\) | |||||||
\(728\) | 661.362 | + | 661.362i | 0.908465 | + | 0.908465i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −288.000 | −0.393981 | ||||||||
\(732\) | 2.44949 | − | 2.44949i | 0.00334630 | − | 0.00334630i | ||||
\(733\) | −800.983 | − | 800.983i | −1.09275 | − | 1.09275i | −0.995234 | − | 0.0975121i | \(-0.968912\pi\) |
−0.0975121 | − | 0.995234i | \(-0.531088\pi\) | |||||||
\(734\) | 162.000i | 0.220708i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 432.000 | 0.586957 | ||||||||
\(737\) | 793.635 | − | 793.635i | 1.07684 | − | 1.07684i | ||||
\(738\) | 66.1362 | + | 66.1362i | 0.0896155 | + | 0.0896155i | ||||
\(739\) | − | 350.000i | − | 0.473613i | −0.971557 | − | 0.236806i | \(-0.923899\pi\) | ||
0.971557 | − | 0.236806i | \(-0.0761007\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 180.000 | 0.242915 | ||||||||
\(742\) | −88.1816 | + | 88.1816i | −0.118843 | + | 0.118843i | ||||
\(743\) | 925.907 | + | 925.907i | 1.24617 | + | 1.24617i | 0.957396 | + | 0.288778i | \(0.0932488\pi\) |
0.288778 | + | 0.957396i | \(0.406751\pi\) | |||||||
\(744\) | 330.000i | 0.443548i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 522.000 | 0.699732 | ||||||||
\(747\) | 161.666 | − | 161.666i | 0.216421 | − | 0.216421i | ||||
\(748\) | −88.1816 | − | 88.1816i | −0.117890 | − | 0.117890i | ||||
\(749\) | − | 648.000i | − | 0.865154i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −338.000 | −0.450067 | −0.225033 | − | 0.974351i | \(-0.572249\pi\) | ||||
−0.225033 | + | 0.974351i | \(0.572249\pi\) | |||||||
\(752\) | −484.999 | + | 484.999i | −0.644945 | + | 0.644945i | ||||
\(753\) | −418.863 | − | 418.863i | −0.556259 | − | 0.556259i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −54.0000 | −0.0714286 | ||||||||
\(757\) | 286.590 | − | 286.590i | 0.378587 | − | 0.378587i | −0.492005 | − | 0.870592i | \(-0.663736\pi\) |
0.870592 | + | 0.492005i | \(0.163736\pi\) | |||||||
\(758\) | 208.207 | + | 208.207i | 0.274679 | + | 0.274679i | ||||
\(759\) | 864.000i | 1.13834i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1278.00 | −1.67937 | −0.839685 | − | 0.543074i | \(-0.817260\pi\) | ||||
−0.839685 | + | 0.543074i | \(0.817260\pi\) | |||||||
\(762\) | −22.0454 | + | 22.0454i | −0.0289310 | + | 0.0289310i | ||||
\(763\) | −1249.24 | − | 1249.24i | −1.63727 | − | 1.63727i | ||||
\(764\) | 252.000i | 0.329843i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 372.000 | 0.485640 | ||||||||
\(767\) | −661.362 | + | 661.362i | −0.862271 | + | 0.862271i | ||||
\(768\) | 219.229 | + | 219.229i | 0.285455 | + | 0.285455i | ||||
\(769\) | 590.000i | 0.767230i | 0.923493 | + | 0.383615i | \(0.125321\pi\) | ||||
−0.923493 | + | 0.383615i | \(0.874679\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 708.000 | 0.918288 | ||||||||
\(772\) | −264.545 | + | 264.545i | −0.342675 | + | 0.342675i | ||||
\(773\) | −127.373 | − | 127.373i | −0.164778 | − | 0.164778i | 0.619902 | − | 0.784680i | \(-0.287173\pi\) |
−0.784680 | + | 0.619902i | \(0.787173\pi\) | |||||||
\(774\) | 216.000i | 0.279070i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1260.00 | −1.62371 | ||||||||
\(777\) | −132.272 | + | 132.272i | −0.170235 | + | 0.170235i | ||||
\(778\) | 440.908 | + | 440.908i | 0.566720 | + | 0.566720i | ||||
\(779\) | − | 180.000i | − | 0.231065i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1296.00 | −1.65941 | ||||||||
\(782\) | −235.151 | + | 235.151i | −0.300705 | + | 0.300705i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 649.000i | − | 0.827806i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −54.0000 | −0.0687023 | ||||||||
\(787\) | −264.545 | + | 264.545i | −0.336143 | + | 0.336143i | −0.854914 | − | 0.518770i | \(-0.826390\pi\) |
0.518770 | + | 0.854914i | \(0.326390\pi\) | |||||||
\(788\) | 127.373 | + | 127.373i | 0.161641 | + | 0.161641i | ||||
\(789\) | − | 648.000i | − | 0.821293i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −648.000 | −0.819216 | ||||||||
\(792\) | −330.681 | + | 330.681i | −0.417527 | + | 0.417527i | ||||
\(793\) | 14.6969 | + | 14.6969i | 0.0185333 | + | 0.0185333i | ||||
\(794\) | − | 738.000i | − | 0.929471i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −290.000 | −0.364322 | ||||||||
\(797\) | 200.858 | − | 200.858i | 0.252018 | − | 0.252018i | −0.569780 | − | 0.821797i | \(-0.692971\pi\) |
0.821797 | + | 0.569780i | \(0.192971\pi\) | |||||||
\(798\) | −220.454 | − | 220.454i | −0.276258 | − | 0.276258i | ||||
\(799\) | 432.000i | 0.540676i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −270.000 | −0.337079 | ||||||||
\(802\) | 683.408 | − | 683.408i | 0.852129 | − | 0.852129i | ||||
\(803\) | −793.635 | − | 793.635i | −0.988337 | − | 0.988337i | ||||
\(804\) | 108.000i | 0.134328i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −396.000 | −0.491315 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 661.362 | + | 661.362i | 0.818518 | + | 0.818518i | ||||
\(809\) | − | 630.000i | − | 0.778739i | −0.921082 | − | 0.389370i | \(-0.872693\pi\) | ||
0.921082 | − | 0.389370i | \(-0.127307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −218.000 | −0.268804 | −0.134402 | − | 0.990927i | \(-0.542911\pi\) | ||||
−0.134402 | + | 0.990927i | \(0.542911\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 585.428 | + | 585.428i | 0.720084 | + | 0.720084i | ||||
\(814\) | 324.000i | 0.398034i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −132.000 | −0.161765 | ||||||||
\(817\) | 293.939 | − | 293.939i | 0.359778 | − | 0.359778i | ||||
\(818\) | −820.579 | − | 820.579i | −1.00315 | − | 1.00315i | ||||
\(819\) | − | 324.000i | − | 0.395604i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 432.000 | 0.526188 | 0.263094 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263094 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(822\) | −426.211 | + | 426.211i | −0.518505 | + | 0.518505i | ||||
\(823\) | −360.075 | − | 360.075i | −0.437515 | − | 0.437515i | 0.453660 | − | 0.891175i | \(-0.350118\pi\) |
−0.891175 | + | 0.453660i | \(0.850118\pi\) | |||||||
\(824\) | 810.000i | 0.983010i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1620.00 | 1.96126 | ||||||||
\(827\) | −876.917 | + | 876.917i | −1.06036 | + | 1.06036i | −0.0623022 | + | 0.998057i | \(0.519844\pi\) |
−0.998057 | + | 0.0623022i | \(0.980156\pi\) | |||||||
\(828\) | −58.7878 | − | 58.7878i | −0.0709997 | − | 0.0709997i | ||||
\(829\) | 70.0000i | 0.0844391i | 0.999108 | + | 0.0422195i | \(0.0134429\pi\) | ||||
−0.999108 | + | 0.0422195i | \(0.986557\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 198.000 | 0.238267 | ||||||||
\(832\) | −521.741 | + | 521.741i | −0.627093 | + | 0.627093i | ||||
\(833\) | −289.040 | − | 289.040i | −0.346987 | − | 0.346987i | ||||
\(834\) | − | 510.000i | − | 0.611511i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 180.000 | 0.215311 | ||||||||
\(837\) | 80.8332 | − | 80.8332i | 0.0965749 | − | 0.0965749i | ||||
\(838\) | −771.589 | − | 771.589i | −0.920751 | − | 0.920751i | ||||
\(839\) | − | 540.000i | − | 0.643623i | −0.946804 | − | 0.321812i | \(-0.895708\pi\) | ||
0.946804 | − | 0.321812i | \(-0.104292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 1.00000 | ||||||||
\(842\) | −173.914 | + | 173.914i | −0.206548 | + | 0.206548i | ||||
\(843\) | −198.409 | − | 198.409i | −0.235360 | − | 0.235360i | ||||
\(844\) | 122.000i | 0.144550i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 324.000 | 0.382979 | ||||||||
\(847\) | −1491.74 | + | 1491.74i | −1.76120 | + | 1.76120i | ||||
\(848\) | −53.8888 | − | 53.8888i | −0.0635481 | − | 0.0635481i | ||||
\(849\) | 612.000i | 0.720848i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −288.000 | −0.338425 | ||||||||
\(852\) | 88.1816 | − | 88.1816i | 0.103500 | − | 0.103500i | ||||
\(853\) | 815.680 | + | 815.680i | 0.956249 | + | 0.956249i | 0.999082 | − | 0.0428336i | \(-0.0136385\pi\) |
−0.0428336 | + | 0.999082i | \(0.513639\pi\) | |||||||
\(854\) | − | 36.0000i | − | 0.0421546i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 540.000 | 0.630841 | ||||||||
\(857\) | 298.838 | − | 298.838i | 0.348702 | − | 0.348702i | −0.510924 | − | 0.859626i | \(-0.670697\pi\) |
0.859626 | + | 0.510924i | \(0.170697\pi\) | |||||||
\(858\) | −396.817 | − | 396.817i | −0.462491 | − | 0.462491i | ||||
\(859\) | − | 310.000i | − | 0.360885i | −0.983586 | − | 0.180442i | \(-0.942247\pi\) | ||
0.983586 | − | 0.180442i | \(-0.0577529\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −324.000 | −0.376307 | ||||||||
\(862\) | −749.544 | + | 749.544i | −0.869540 | + | 0.869540i | ||||
\(863\) | −225.353 | − | 225.353i | −0.261128 | − | 0.261128i | 0.564385 | − | 0.825512i | \(-0.309114\pi\) |
−0.825512 | + | 0.564385i | \(0.809114\pi\) | |||||||
\(864\) | − | 81.0000i | − | 0.0937500i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 252.000 | 0.290993 | ||||||||
\(867\) | 295.164 | − | 295.164i | 0.340442 | − | 0.340442i | ||||
\(868\) | −161.666 | − | 161.666i | −0.186252 | − | 0.186252i | ||||
\(869\) | 1260.00i | 1.44994i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −648.000 | −0.743972 | ||||||||
\(872\) | 1041.03 | − | 1041.03i | 1.19385 | − | 1.19385i | ||||
\(873\) | 308.636 | + | 308.636i | 0.353535 | + | 0.353535i | ||||
\(874\) | − | 480.000i | − | 0.549199i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 108.000 | 0.123288 | ||||||||
\(877\) | 213.106 | − | 213.106i | 0.242994 | − | 0.242994i | −0.575094 | − | 0.818088i | \(-0.695034\pi\) |
0.818088 | + | 0.575094i | \(0.195034\pi\) | |||||||
\(878\) | 526.640 | + | 526.640i | 0.599818 | + | 0.599818i | ||||
\(879\) | 912.000i | 1.03754i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1062.00 | 1.20545 | 0.602724 | − | 0.797950i | \(-0.294082\pi\) | ||||
0.602724 | + | 0.797950i | \(0.294082\pi\) | |||||||
\(882\) | −216.780 | + | 216.780i | −0.245782 | + | 0.245782i | ||||
\(883\) | 117.576 | + | 117.576i | 0.133155 | + | 0.133155i | 0.770543 | − | 0.637388i | \(-0.219985\pi\) |
−0.637388 | + | 0.770543i | \(0.719985\pi\) | |||||||
\(884\) | 72.0000i | 0.0814480i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1428.00 | −1.61174 | ||||||||
\(887\) | −509.494 | + | 509.494i | −0.574401 | + | 0.574401i | −0.933355 | − | 0.358954i | \(-0.883133\pi\) |
0.358954 | + | 0.933355i | \(0.383133\pi\) | |||||||
\(888\) | −110.227 | − | 110.227i | −0.124130 | − | 0.124130i | ||||
\(889\) | − | 108.000i | − | 0.121485i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 162.000 | 0.181818 | ||||||||
\(892\) | −80.8332 | + | 80.8332i | −0.0906201 | + | 0.0906201i | ||||
\(893\) | −440.908 | − | 440.908i | −0.493738 | − | 0.493738i | ||||
\(894\) | − | 540.000i | − | 0.604027i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 630.000 | 0.703125 | ||||||||
\(897\) | 352.727 | − | 352.727i | 0.393229 | − | 0.393229i | ||||
\(898\) | −110.227 | − | 110.227i | −0.122747 | − | 0.122747i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −48.0000 | −0.0532741 | ||||||||
\(902\) | −396.817 | + | 396.817i | −0.439931 | + | 0.439931i | ||||
\(903\) | −529.090 | − | 529.090i | −0.585924 | − | 0.585924i | ||||
\(904\) | − | 540.000i | − | 0.597345i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 66.0000 | 0.0728477 | ||||||||
\(907\) | −411.514 | + | 411.514i | −0.453709 | + | 0.453709i | −0.896584 | − | 0.442874i | \(-0.853959\pi\) |
0.442874 | + | 0.896584i | \(0.353959\pi\) | |||||||
\(908\) | 53.8888 | + | 53.8888i | 0.0593489 | + | 0.0593489i | ||||
\(909\) | − | 324.000i | − | 0.356436i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 792.000 | 0.869374 | 0.434687 | − | 0.900582i | \(-0.356859\pi\) | ||||
0.434687 | + | 0.900582i | \(0.356859\pi\) | |||||||
\(912\) | 134.722 | − | 134.722i | 0.147721 | − | 0.147721i | ||||
\(913\) | 969.998 | + | 969.998i | 1.06243 | + | 1.06243i | ||||
\(914\) | − | 468.000i | − | 0.512035i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 50.0000 | 0.0545852 | ||||||||
\(917\) | 132.272 | − | 132.272i | 0.144245 | − | 0.144245i | ||||
\(918\) | 44.0908 | + | 44.0908i | 0.0480292 | + | 0.0480292i | ||||
\(919\) | 430.000i | 0.467900i | 0.972249 | + | 0.233950i | \(0.0751652\pi\) | ||||
−0.972249 | + | 0.233950i | \(0.924835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −972.000 | −1.05537 | ||||||||
\(922\) | 1014.09 | − | 1014.09i | 1.09988 | − | 1.09988i | ||||
\(923\) | 529.090 | + | 529.090i | 0.573228 | + | 0.573228i | ||||
\(924\) | − | 324.000i | − | 0.350649i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.0000 | −0.0194384 | ||||||||
\(927\) | 198.409 | − | 198.409i | 0.214033 | − | 0.214033i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1530.00i | 1.64693i | 0.567365 | + | 0.823466i | \(0.307963\pi\) | ||||
−0.567365 | + | 0.823466i | \(0.692037\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 590.000 | 0.633727 | ||||||||
\(932\) | −44.0908 | + | 44.0908i | −0.0473077 | + | 0.0473077i | ||||
\(933\) | −308.636 | − | 308.636i | −0.330799 | − | 0.330799i | ||||
\(934\) | 852.000i | 0.912206i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 270.000 | 0.288462 | ||||||||
\(937\) | 323.333 | − | 323.333i | 0.345072 | − | 0.345072i | −0.513198 | − | 0.858270i | \(-0.671539\pi\) |
0.858270 | + | 0.513198i | \(0.171539\pi\) | |||||||
\(938\) | 793.635 | + | 793.635i | 0.846092 | + | 0.846092i | ||||
\(939\) | − | 288.000i | − | 0.306709i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1152.00 | 1.22423 | 0.612115 | − | 0.790769i | \(-0.290319\pi\) | ||||
0.612115 | + | 0.790769i | \(0.290319\pi\) | |||||||
\(942\) | 418.863 | − | 418.863i | 0.444653 | − | 0.444653i | ||||
\(943\) | −352.727 | − | 352.727i | −0.374047 | − | 0.374047i | ||||
\(944\) | 990.000i | 1.04873i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1296.00 | −1.36998 | ||||||||
\(947\) | 739.746 | − | 739.746i | 0.781147 | − | 0.781147i | −0.198878 | − | 0.980024i | \(-0.563730\pi\) |
0.980024 | + | 0.198878i | \(0.0637296\pi\) | |||||||
\(948\) | −85.7321 | − | 85.7321i | −0.0904347 | − | 0.0904347i | ||||
\(949\) | 648.000i | 0.682824i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −672.000 | −0.706625 | ||||||||
\(952\) | 440.908 | − | 440.908i | 0.463139 | − | 0.463139i | ||||
\(953\) | 44.0908 | + | 44.0908i | 0.0462653 | + | 0.0462653i | 0.729861 | − | 0.683596i | \(-0.239585\pi\) |
−0.683596 | + | 0.729861i | \(0.739585\pi\) | |||||||
\(954\) | 36.0000i | 0.0377358i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −180.000 | −0.188285 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 440.908 | + | 440.908i | 0.460238 | + | 0.460238i | ||||
\(959\) | − | 2088.00i | − | 2.17727i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −477.000 | −0.496358 | ||||||||
\(962\) | 132.272 | − | 132.272i | 0.137497 | − | 0.137497i | ||||
\(963\) | −132.272 | − | 132.272i | −0.137355 | − | 0.137355i | ||||
\(964\) | − | 178.000i | − | 0.184647i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −864.000 | −0.894410 | ||||||||
\(967\) | 727.498 | − | 727.498i | 0.752325 | − | 0.752325i | −0.222588 | − | 0.974913i | \(-0.571450\pi\) |
0.974913 | + | 0.222588i | \(0.0714503\pi\) | |||||||
\(968\) | −1243.12 | − | 1243.12i | −1.28421 | − | 1.28421i | ||||
\(969\) | − | 120.000i | − | 0.123839i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1278.00 | −1.31617 | −0.658084 | − | 0.752944i | \(-0.728633\pi\) | ||||
−0.658084 | + | 0.752944i | \(0.728633\pi\) | |||||||
\(972\) | −11.0227 | + | 11.0227i | −0.0113402 | + | 0.0113402i | ||||
\(973\) | 1249.24 | + | 1249.24i | 1.28391 | + | 1.28391i | ||||
\(974\) | 1422.00i | 1.45996i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.0000 | 0.0225410 | ||||||||
\(977\) | 396.817 | − | 396.817i | 0.406159 | − | 0.406159i | −0.474238 | − | 0.880397i | \(-0.657276\pi\) |
0.880397 | + | 0.474238i | \(0.157276\pi\) | |||||||
\(978\) | 352.727 | + | 352.727i | 0.360661 | + | 0.360661i | ||||
\(979\) | − | 1620.00i | − | 1.65475i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −510.000 | −0.519878 | ||||||||
\(982\) | 22.0454 | − | 22.0454i | 0.0224495 | − | 0.0224495i | ||||
\(983\) | 827.928 | + | 827.928i | 0.842246 | + | 0.842246i | 0.989151 | − | 0.146905i | \(-0.0469311\pi\) |
−0.146905 | + | 0.989151i | \(0.546931\pi\) | |||||||
\(984\) | − | 270.000i | − | 0.274390i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −793.635 | + | 793.635i | −0.804088 | + | 0.804088i | ||||
\(988\) | −73.4847 | − | 73.4847i | −0.0743772 | − | 0.0743772i | ||||
\(989\) | − | 1152.00i | − | 1.16481i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −118.000 | −0.119072 | −0.0595358 | − | 0.998226i | \(-0.518962\pi\) | ||||
−0.0595358 | + | 0.998226i | \(0.518962\pi\) | |||||||
\(992\) | 242.499 | − | 242.499i | 0.244455 | − | 0.244455i | ||||
\(993\) | 511.943 | + | 511.943i | 0.515552 | + | 0.515552i | ||||
\(994\) | − | 1296.00i | − | 1.30382i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −132.000 | −0.132530 | ||||||||
\(997\) | −815.680 | + | 815.680i | −0.818134 | + | 0.818134i | −0.985838 | − | 0.167703i | \(-0.946365\pi\) |
0.167703 | + | 0.985838i | \(0.446365\pi\) | |||||||
\(998\) | −722.599 | − | 722.599i | −0.724048 | − | 0.724048i | ||||
\(999\) | 54.0000i | 0.0540541i |
(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 | 75.3.f.a.43.1 | yes | 4 | |
3.2 | odd | 2 | 225.3.g.f.118.2 | 4 | |||
4.3 | odd | 2 | 1200.3.bg.j.193.2 | 4 | |||
5.2 | odd | 4 | inner | 75.3.f.a.7.1 | ✓ | 4 | |
5.3 | odd | 4 | inner | 75.3.f.a.7.2 | yes | 4 | |
5.4 | even | 2 | inner | 75.3.f.a.43.2 | yes | 4 | |
15.2 | even | 4 | 225.3.g.f.82.2 | 4 | |||
15.8 | even | 4 | 225.3.g.f.82.1 | 4 | |||
15.14 | odd | 2 | 225.3.g.f.118.1 | 4 | |||
20.3 | even | 4 | 1200.3.bg.j.1057.1 | 4 | |||
20.7 | even | 4 | 1200.3.bg.j.1057.2 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.j.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.f.a.7.1 | ✓ | 4 | 5.2 | odd | 4 | inner | |
75.3.f.a.7.2 | yes | 4 | 5.3 | odd | 4 | inner | |
75.3.f.a.43.1 | yes | 4 | 1.1 | even | 1 | trivial | |
75.3.f.a.43.2 | yes | 4 | 5.4 | even | 2 | inner | |
225.3.g.f.82.1 | 4 | 15.8 | even | 4 | |||
225.3.g.f.82.2 | 4 | 15.2 | even | 4 | |||
225.3.g.f.118.1 | 4 | 15.14 | odd | 2 | |||
225.3.g.f.118.2 | 4 | 3.2 | odd | 2 | |||
1200.3.bg.j.193.1 | 4 | 20.19 | odd | 2 | |||
1200.3.bg.j.193.2 | 4 | 4.3 | odd | 2 | |||
1200.3.bg.j.1057.1 | 4 | 20.3 | even | 4 | |||
1200.3.bg.j.1057.2 | 4 | 20.7 | even | 4 |