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 | 7.2 | ||
Root | \(1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.7 |
Dual form | 75.3.f.a.43.2 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | \(-0.107451\pi\) |
−0.331191 | + | 0.943564i | \(0.607451\pi\) | |||||||
\(3\) | 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 | 0.998694 | + | 0.0510871i | \(0.0162686\pi\) |
0.0510871 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(8\) | 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 | \(-0.880887\pi\) |
0.365532 | + | 0.930799i | \(0.380887\pi\) | |||||||
\(14\) | 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 | \(-0.315320\pi\) |
−0.836358 | + | 0.548183i | \(0.815320\pi\) | |||||||
\(18\) | 3.67423 | − | 3.67423i | 0.204124 | − | 0.204124i | ||||
\(19\) | − | 10.0000i | − | 0.526316i | −0.964753 | − | 0.263158i | \(-0.915236\pi\) | ||
0.964753 | − | 0.263158i | \(-0.0847640\pi\) | |||||||
\(20\) | 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 | \(-0.955810\pi\) |
0.138382 | + | 0.990379i | \(0.455810\pi\) | |||||||
\(24\) | − | 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 | \(-0.205149\pi\) |
−0.600795 | + | 0.799403i | \(0.705149\pi\) | |||||||
\(38\) | 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 | \(-0.589415\pi\) |
0.960805 | + | 0.277226i | \(0.0894151\pi\) | |||||||
\(44\) | 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 | \(-0.0191389\pi\) |
−0.0600905 | + | 0.998193i | \(0.519139\pi\) | |||||||
\(48\) | 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 | \(-0.729180\pi\) |
0.751812 | + | 0.659378i | \(0.229180\pi\) | |||||||
\(54\) | − | 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 | \(-0.723867\pi\) | ||
0.646738 | − | 0.762712i | \(-0.276133\pi\) | |||||||
\(60\) | 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 | \(-0.0959367\pi\) |
−0.296852 | + | 0.954924i | \(0.595937\pi\) | |||||||
\(68\) | −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 | \(-0.890458\pi\) |
0.337384 | + | 0.941367i | \(0.390458\pi\) | |||||||
\(74\) | 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 | \(0.146099\pi\) | ||||
−0.896503 | + | 0.443038i | \(0.853901\pi\) | |||||||
\(80\) | 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 | \(-0.598173\pi\) |
0.952815 | + | 0.303552i | \(0.0981727\pi\) | |||||||
\(84\) | − | 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 | \(-0.831265\pi\) | ||
0.862757 | − | 0.505618i | \(-0.168735\pi\) | |||||||
\(90\) | 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 | −0.998041 | − | 0.0625628i | \(-0.980073\pi\) |
−0.0625628 | − | 0.998041i | \(-0.519927\pi\) | |||||||
\(98\) | −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 | \(-0.599985\pi\) |
0.951071 | + | 0.308972i | \(0.0999849\pi\) | |||||||
\(104\) | 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 | \(-0.155888\pi\) |
−0.470393 | + | 0.882457i | \(0.655888\pi\) | |||||||
\(108\) | −3.67423 | + | 3.67423i | −0.0340207 | + | 0.0340207i | ||||
\(109\) | − | 170.000i | − | 1.55963i | −0.626008 | − | 0.779817i | \(-0.715312\pi\) | ||
0.626008 | − | 0.779817i | \(-0.284688\pi\) | |||||||
\(110\) | 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 | \(-0.838976\pi\) |
0.484569 | + | 0.874753i | \(0.338976\pi\) | |||||||
\(114\) | − | 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 | \(-0.236973\pi\) |
−0.677584 | + | 0.735446i | \(0.736973\pi\) | |||||||
\(128\) | 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 | 0.999288 | + | 0.0377220i | \(0.0120101\pi\) |
0.0377220 | + | 0.999288i | \(0.487990\pi\) | |||||||
\(138\) | −58.7878 | + | 58.7878i | −0.425998 | + | 0.425998i | ||||
\(139\) | 170.000i | 1.22302i | 0.791236 | + | 0.611511i | \(0.209438\pi\) | ||||
−0.791236 | + | 0.611511i | \(0.790562\pi\) | |||||||
\(140\) | 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 | \(0.206438\pi\) | ||||
−0.796964 | + | 0.604027i | \(0.793562\pi\) | |||||||
\(150\) | 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 | \(-0.466467\pi\) |
−0.994456 | + | 0.105151i | \(0.966467\pi\) | |||||||
\(158\) | −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 | \(-0.920374\pi\) |
0.247552 | + | 0.968875i | \(0.420374\pi\) | |||||||
\(164\) | 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 | \(-0.223559\pi\) |
−0.645998 | + | 0.763339i | \(0.723559\pi\) | |||||||
\(168\) | 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 | \(-0.947216\pi\) |
0.165066 | + | 0.986282i | \(0.447216\pi\) | |||||||
\(174\) | 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 | \(0.0808899\pi\) | ||||
−0.967884 | + | 0.251397i | \(0.919110\pi\) | |||||||
\(180\) | 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 | −0.511292 | + | 0.859407i | \(0.670833\pi\) |
−0.859407 | + | 0.511292i | \(0.829167\pi\) | |||||||
\(194\) | − | 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 | \(-0.401144\pi\) |
−0.952161 | + | 0.305596i | \(0.901144\pi\) | |||||||
\(198\) | −66.1362 | + | 66.1362i | −0.334021 | + | 0.334021i | ||||
\(199\) | − | 290.000i | − | 1.45729i | −0.684893 | − | 0.728643i | \(-0.740151\pi\) | ||
0.684893 | − | 0.728643i | \(-0.259849\pi\) | |||||||
\(200\) | 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 | \(-0.832508\pi\) |
0.502245 | + | 0.864725i | \(0.332508\pi\) | |||||||
\(224\) | − | 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 | \(-0.303687\pi\) |
−0.815771 | + | 0.578375i | \(0.803687\pi\) | |||||||
\(228\) | −12.2474 | + | 12.2474i | −0.0537169 | + | 0.0537169i | ||||
\(229\) | 50.0000i | 0.218341i | 0.994023 | + | 0.109170i | \(0.0348194\pi\) | ||||
−0.994023 | + | 0.109170i | \(0.965181\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −324.000 | −1.40260 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −44.0908 | + | 44.0908i | −0.189231 | + | 0.189231i | −0.795364 | − | 0.606133i | \(-0.792720\pi\) |
0.606133 | + | 0.795364i | \(0.292720\pi\) | |||||||
\(234\) | 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 | \(-0.877104\pi\) | ||
0.926389 | − | 0.376569i | \(-0.122896\pi\) | |||||||
\(240\) | 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 | 0.991030 | + | 0.133638i | \(0.0426660\pi\) |
0.133638 | + | 0.991030i | \(0.457334\pi\) | |||||||
\(258\) | 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 | −0.00589147 | + | 0.999983i | \(0.501875\pi\) |
−0.999983 | + | 0.00589147i | \(0.998125\pi\) | |||||||
\(264\) | 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 | \(-0.183843\pi\) |
−0.545981 | + | 0.837798i | \(0.683843\pi\) | |||||||
\(278\) | −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 | \(-0.535395\pi\) |
0.993824 | + | 0.110969i | \(0.0353954\pi\) | |||||||
\(284\) | − | 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 | 0.325017 | − | 0.945708i | \(-0.394630\pi\) |
0.945708 | − | 0.325017i | \(-0.105370\pi\) | |||||||
\(294\) | 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 | −0.933195 | − | 0.359369i | \(-0.882992\pi\) |
−0.359369 | − | 0.933195i | \(-0.617008\pi\) | |||||||
\(308\) | −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 | \(-0.835576\pi\) |
0.493886 | + | 0.869527i | \(0.335576\pi\) | |||||||
\(314\) | − | 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 | \(-0.459617\pi\) |
−0.991963 | + | 0.126528i | \(0.959617\pi\) | |||||||
\(318\) | 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 | \(-0.118701\pi\) |
−0.364327 | + | 0.931271i | \(0.618701\pi\) | |||||||
\(338\) | −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 | \(-0.221362\pi\) |
−0.640716 | + | 0.767778i | \(0.721362\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 70.0000i | − | 0.200573i | −0.994959 | − | 0.100287i | \(-0.968024\pi\) | ||
0.994959 | − | 0.100287i | \(-0.0319759\pi\) | |||||||
\(350\) | 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 | \(-0.778150\pi\) |
0.641892 | + | 0.766795i | \(0.278150\pi\) | |||||||
\(354\) | − | 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 | \(0.270954\pi\) | ||||
−0.659061 | + | 0.752089i | \(0.729046\pi\) | |||||||
\(360\) | 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 | \(-0.290672\pi\) |
−0.791446 | + | 0.611239i | \(0.790672\pi\) | |||||||
\(368\) | −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 | \(-0.617623\pi\) |
0.932500 | + | 0.361171i | \(0.117623\pi\) | |||||||
\(374\) | 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 | \(0.0720012\pi\) | ||||
−0.974526 | + | 0.224274i | \(0.927999\pi\) | |||||||
\(380\) | 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 | \(-0.659538\pi\) |
0.877005 | + | 0.480482i | \(0.159538\pi\) | |||||||
\(384\) | − | 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 | \(0.153128\pi\) | ||||
−0.886502 | + | 0.462725i | \(0.846872\pi\) | |||||||
\(390\) | 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 | \(-0.0696970\pi\) |
−0.217214 | + | 0.976124i | \(0.569697\pi\) | |||||||
\(398\) | 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 | \(-0.694489\pi\) | ||
0.573692 | − | 0.819071i | \(-0.305511\pi\) | |||||||
\(410\) | 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 | \(-0.729191\pi\) | ||
0.659403 | − | 0.751790i | \(-0.270809\pi\) | |||||||
\(420\) | 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 | \(-0.696268\pi\) |
0.815853 | + | 0.578259i | \(0.196268\pi\) | |||||||
\(434\) | 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 | \(0.162912\pi\) | ||||
−0.871863 | + | 0.489749i | \(0.837088\pi\) | |||||||
\(440\) | 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 | −0.399049 | + | 0.916930i | \(0.630660\pi\) |
−0.916930 | + | 0.399049i | \(0.869340\pi\) | |||||||
\(444\) | − | 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 | \(-0.968044\pi\) | ||
0.994965 | − | 0.100223i | \(-0.0319555\pi\) | |||||||
\(450\) | 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 | \(-0.154473\pi\) |
−0.466465 | + | 0.884540i | \(0.654473\pi\) | |||||||
\(458\) | −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 | \(-0.753572\pi\) |
0.699127 | + | 0.714998i | \(0.253572\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −108.000 | −0.231760 | ||||||||
\(467\) | −347.828 | − | 347.828i | −0.744813 | − | 0.744813i | 0.228687 | − | 0.973500i | \(-0.426557\pi\) |
−0.973500 | + | 0.228687i | \(0.926557\pi\) | |||||||
\(468\) | 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 | \(0.122626\pi\) | ||||
−0.926708 | + | 0.375783i | \(0.877374\pi\) | |||||||
\(480\) | 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 | −0.976490 | − | 0.215561i | \(-0.930842\pi\) |
−0.215561 | − | 0.976490i | \(-0.569158\pi\) | |||||||
\(488\) | 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 | \(-0.798661\pi\) | ||
0.806538 | − | 0.591182i | \(-0.201339\pi\) | |||||||
\(500\) | 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 | \(-0.791771\pi\) |
0.608502 | + | 0.793553i | \(0.291771\pi\) | |||||||
\(504\) | − | 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 | \(-0.822022\pi\) | ||
0.847715 | − | 0.530452i | \(-0.177978\pi\) | |||||||
\(510\) | 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 | \(-0.866429\pi\) |
0.407419 | + | 0.913241i | \(0.366429\pi\) | |||||||
\(524\) | 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 | \(-0.138903\pi\) |
−0.422660 | + | 0.906288i | \(0.638903\pi\) | |||||||
\(548\) | 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 | \(-0.0388725\pi\) |
−0.121818 | + | 0.992552i | \(0.538872\pi\) | |||||||
\(558\) | 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 | \(-0.583926\pi\) |
0.965443 | + | 0.260616i | \(0.0839256\pi\) | |||||||
\(564\) | − | 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 | \(-0.813253\pi\) | ||
0.832781 | − | 0.553603i | \(-0.186747\pi\) | |||||||
\(570\) | 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 | \(-0.0474052\pi\) |
−0.148378 | + | 0.988931i | \(0.547405\pi\) | |||||||
\(578\) | 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 | \(-0.00217329\pi\) |
−0.00682753 | + | 0.999977i | \(0.502173\pi\) | |||||||
\(588\) | 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 | \(-0.969718\pi\) |
0.0949912 | + | 0.995478i | \(0.469718\pi\) | |||||||
\(594\) | 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 | \(0.148844\pi\) | ||||
−0.892650 | + | 0.450751i | \(0.851156\pi\) | |||||||
\(600\) | 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 | 0.994210 | + | 0.107455i | \(0.0342702\pi\) |
0.107455 | + | 0.994210i | \(0.465730\pi\) | |||||||
\(608\) | −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 | \(-0.725693\pi\) |
0.758991 | + | 0.651101i | \(0.225693\pi\) | |||||||
\(614\) | − | 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 | \(-0.487736\pi\) |
−0.999258 | + | 0.0385180i | \(0.987736\pi\) | |||||||
\(618\) | 198.409 | − | 198.409i | 0.321050 | − | 0.321050i | ||||
\(619\) | 1030.00i | 1.66397i | 0.554795 | + | 0.831987i | \(0.312797\pi\) | ||||
−0.554795 | + | 0.831987i | \(0.687203\pi\) | |||||||
\(620\) | 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 | \(-0.843961\pi\) |
0.470811 | + | 0.882234i | \(0.343961\pi\) | |||||||
\(644\) | 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 | \(-0.217563\pi\) |
−0.631506 | + | 0.775371i | \(0.717563\pi\) | |||||||
\(648\) | −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 | \(-0.773662\pi\) |
0.652638 | + | 0.757670i | \(0.273662\pi\) | |||||||
\(654\) | − | 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 | \(-0.841363\pi\) | ||
0.878361 | − | 0.477997i | \(-0.158637\pi\) | |||||||
\(660\) | 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 | \(-0.715526\pi\) |
0.779397 | + | 0.626531i | \(0.215526\pi\) | |||||||
\(674\) | 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 | \(-0.308971\pi\) |
−0.825260 | + | 0.564753i | \(0.808971\pi\) | |||||||
\(678\) | −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 | \(-0.597296\pi\) |
0.953647 | + | 0.300928i | \(0.0972963\pi\) | |||||||
\(684\) | 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 | \(-0.929845\pi\) | ||
0.975811 | − | 0.218618i | \(-0.0701548\pi\) | |||||||
\(710\) | 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 | \(-0.960051\pi\) | ||
0.992135 | − | 0.125174i | \(-0.0399489\pi\) | |||||||
\(720\) | 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 | \(-0.414162\pi\) |
−0.963859 | + | 0.266412i | \(0.914162\pi\) | |||||||
\(728\) | −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 | 0.0975121 | − | 0.995234i | \(-0.468912\pi\) |
0.995234 | − | 0.0975121i | \(-0.0310885\pi\) | |||||||
\(734\) | − | 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 | \(0.0761007\pi\) | ||||
−0.971557 | + | 0.236806i | \(0.923899\pi\) | |||||||
\(740\) | 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 | −0.288778 | + | 0.957396i | \(0.593249\pi\) |
−0.957396 | + | 0.288778i | \(0.906751\pi\) | |||||||
\(744\) | − | 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 | \(-0.336264\pi\) |
−0.870592 | + | 0.492005i | \(0.836264\pi\) | |||||||
\(758\) | −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 | \(-0.874679\pi\) | ||
0.923493 | − | 0.383615i | \(-0.125321\pi\) | |||||||
\(770\) | 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 | \(-0.712827\pi\) |
0.784680 | + | 0.619902i | \(0.212827\pi\) | |||||||
\(774\) | − | 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 | \(-0.173610\pi\) |
−0.518770 | + | 0.854914i | \(0.673610\pi\) | |||||||
\(788\) | −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 | \(-0.307029\pi\) |
−0.821797 | + | 0.569780i | \(0.807029\pi\) | |||||||
\(798\) | 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 | \(0.127307\pi\) | ||||
−0.921082 | + | 0.389370i | \(0.872693\pi\) | |||||||
\(810\) | 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 | \(-0.649882\pi\) |
0.891175 | + | 0.453660i | \(0.149882\pi\) | |||||||
\(824\) | − | 810.000i | − | 0.983010i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1620.00 | 1.96126 | ||||||||
\(827\) | 876.917 | + | 876.917i | 1.06036 | + | 1.06036i | 0.998057 | + | 0.0623022i | \(0.0198443\pi\) |
0.0623022 | + | 0.998057i | \(0.480156\pi\) | |||||||
\(828\) | 58.7878 | − | 58.7878i | 0.0709997 | − | 0.0709997i | ||||
\(829\) | − | 70.0000i | − | 0.0844391i | −0.999108 | − | 0.0422195i | \(-0.986557\pi\) | ||
0.999108 | − | 0.0422195i | \(-0.0134429\pi\) | |||||||
\(830\) | 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 | \(0.104292\pi\) | ||||
−0.946804 | + | 0.321812i | \(0.895708\pi\) | |||||||
\(840\) | 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 | \(-0.986361\pi\) |
0.0428336 | + | 0.999082i | \(0.486361\pi\) | |||||||
\(854\) | 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 | \(-0.329303\pi\) |
−0.859626 | + | 0.510924i | \(0.829303\pi\) | |||||||
\(858\) | 396.817 | − | 396.817i | 0.462491 | − | 0.462491i | ||||
\(859\) | 310.000i | 0.360885i | 0.983586 | + | 0.180442i | \(0.0577529\pi\) | ||||
−0.983586 | + | 0.180442i | \(0.942247\pi\) | |||||||
\(860\) | 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 | \(-0.690886\pi\) |
0.825512 | + | 0.564385i | \(0.190886\pi\) | |||||||
\(864\) | 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 | \(-0.304966\pi\) |
−0.818088 | + | 0.575094i | \(0.804966\pi\) | |||||||
\(878\) | −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 | \(-0.780015\pi\) |
0.637388 | + | 0.770543i | \(0.280015\pi\) | |||||||
\(884\) | − | 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 | \(-0.116867\pi\) |
−0.358954 | + | 0.933355i | \(0.616867\pi\) | |||||||
\(888\) | 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 | \(-0.146041\pi\) |
−0.442874 | + | 0.896584i | \(0.646041\pi\) | |||||||
\(908\) | −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 | \(-0.924835\pi\) | ||
0.972249 | − | 0.233950i | \(-0.0751652\pi\) | |||||||
\(920\) | 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 | \(-0.692037\pi\) | ||
0.567365 | − | 0.823466i | \(-0.307963\pi\) | |||||||
\(930\) | 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 | \(-0.328461\pi\) |
−0.858270 | + | 0.513198i | \(0.828461\pi\) | |||||||
\(938\) | −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 | \(-0.436270\pi\) |
−0.980024 | + | 0.198878i | \(0.936270\pi\) | |||||||
\(948\) | 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 | \(-0.760415\pi\) |
0.683596 | + | 0.729861i | \(0.260415\pi\) | |||||||
\(954\) | − | 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 | \(-0.428550\pi\) |
−0.974913 | + | 0.222588i | \(0.928550\pi\) | |||||||
\(968\) | 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 | \(-0.342724\pi\) |
−0.880397 | + | 0.474238i | \(0.842724\pi\) | |||||||
\(978\) | −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 | \(-0.953069\pi\) |
0.146905 | + | 0.989151i | \(0.453069\pi\) | |||||||
\(984\) | 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 | \(-0.0536350\pi\) |
−0.167703 | + | 0.985838i | \(0.553635\pi\) | |||||||
\(998\) | 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.7.2 | yes | 4 | |
3.2 | odd | 2 | 225.3.g.f.82.1 | 4 | |||
4.3 | odd | 2 | 1200.3.bg.j.1057.1 | 4 | |||
5.2 | odd | 4 | inner | 75.3.f.a.43.1 | yes | 4 | |
5.3 | odd | 4 | inner | 75.3.f.a.43.2 | yes | 4 | |
5.4 | even | 2 | inner | 75.3.f.a.7.1 | ✓ | 4 | |
15.2 | even | 4 | 225.3.g.f.118.2 | 4 | |||
15.8 | even | 4 | 225.3.g.f.118.1 | 4 | |||
15.14 | odd | 2 | 225.3.g.f.82.2 | 4 | |||
20.3 | even | 4 | 1200.3.bg.j.193.1 | 4 | |||
20.7 | even | 4 | 1200.3.bg.j.193.2 | 4 | |||
20.19 | odd | 2 | 1200.3.bg.j.1057.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.3.f.a.7.1 | ✓ | 4 | 5.4 | even | 2 | inner | |
75.3.f.a.7.2 | yes | 4 | 1.1 | even | 1 | trivial | |
75.3.f.a.43.1 | yes | 4 | 5.2 | odd | 4 | inner | |
75.3.f.a.43.2 | yes | 4 | 5.3 | odd | 4 | inner | |
225.3.g.f.82.1 | 4 | 3.2 | odd | 2 | |||
225.3.g.f.82.2 | 4 | 15.14 | odd | 2 | |||
225.3.g.f.118.1 | 4 | 15.8 | even | 4 | |||
225.3.g.f.118.2 | 4 | 15.2 | even | 4 | |||
1200.3.bg.j.193.1 | 4 | 20.3 | even | 4 | |||
1200.3.bg.j.193.2 | 4 | 20.7 | even | 4 | |||
1200.3.bg.j.1057.1 | 4 | 4.3 | odd | 2 | |||
1200.3.bg.j.1057.2 | 4 | 20.19 | odd | 2 |