Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.m (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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.1 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1457 |
Dual form | 3150.2.m.b.2843.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.41421i | − | 1.02942i | −0.857363 | − | 0.514712i | \(-0.827899\pi\) | ||
0.857363 | − | 0.514712i | \(-0.172101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.00000 | + | 4.00000i | −1.10940 | + | 1.10940i | −0.116171 | + | 0.993229i | \(0.537062\pi\) |
−0.993229 | + | 0.116171i | \(0.962938\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −3.41421 | + | 3.41421i | −0.828068 | + | 0.828068i | −0.987249 | − | 0.159181i | \(-0.949115\pi\) |
0.159181 | + | 0.987249i | \(0.449115\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.41421 | + | 2.41421i | 0.514712 | + | 0.514712i | ||||
\(23\) | 0.828427 | + | 0.828427i | 0.172739 | + | 0.172739i | 0.788182 | − | 0.615443i | \(-0.211023\pi\) |
−0.615443 | + | 0.788182i | \(0.711023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 5.65685i | − | 1.10940i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2426 | 1.83963 | 0.919816 | − | 0.392349i | \(-0.128338\pi\) | ||||
0.919816 | + | 0.392349i | \(0.128338\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.82843i | − | 0.828068i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.24264 | + | 2.24264i | 0.368688 | + | 0.368688i | 0.866999 | − | 0.498311i | \(-0.166046\pi\) |
−0.498311 | + | 0.866999i | \(0.666046\pi\) | |||||||
\(38\) | 2.00000 | + | 2.00000i | 0.324443 | + | 0.324443i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.82843i | 1.37877i | 0.724396 | + | 0.689384i | \(0.242119\pi\) | ||||
−0.724396 | + | 0.689384i | \(0.757881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.07107 | − | 8.07107i | 1.23083 | − | 1.23083i | 0.267180 | − | 0.963647i | \(-0.413908\pi\) |
0.963647 | − | 0.267180i | \(-0.0860917\pi\) | |||||||
\(44\) | −3.41421 | −0.514712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.17157 | −0.172739 | ||||||||
\(47\) | −0.757359 | + | 0.757359i | −0.110472 | + | 0.110472i | −0.760182 | − | 0.649710i | \(-0.774890\pi\) |
0.649710 | + | 0.760182i | \(0.274890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.00000 | + | 4.00000i | 0.554700 | + | 0.554700i | ||||
\(53\) | 5.41421 | + | 5.41421i | 0.743699 | + | 0.743699i | 0.973288 | − | 0.229588i | \(-0.0737380\pi\) |
−0.229588 | + | 0.973288i | \(0.573738\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.41421 | − | 3.41421i | 0.448308 | − | 0.448308i | ||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.89949 | 1.26750 | 0.633750 | − | 0.773538i | \(-0.281515\pi\) | ||||
0.633750 | + | 0.773538i | \(0.281515\pi\) | |||||||
\(62\) | −7.24264 | + | 7.24264i | −0.919816 | + | 0.919816i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.58579 | − | 5.58579i | −0.682412 | − | 0.682412i | 0.278131 | − | 0.960543i | \(-0.410285\pi\) |
−0.960543 | + | 0.278131i | \(0.910285\pi\) | |||||||
\(68\) | 3.41421 | + | 3.41421i | 0.414034 | + | 0.414034i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.82843i | − | 0.810385i | −0.914231 | − | 0.405193i | \(-0.867204\pi\) | ||
0.914231 | − | 0.405193i | \(-0.132796\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.07107 | − | 7.07107i | 0.827606 | − | 0.827606i | −0.159579 | − | 0.987185i | \(-0.551014\pi\) |
0.987185 | + | 0.159579i | \(0.0510137\pi\) | |||||||
\(74\) | −3.17157 | −0.368688 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.82843 | −0.324443 | ||||||||
\(77\) | −2.41421 | + | 2.41421i | −0.275125 | + | 0.275125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 5.65685i | − | 0.636446i | −0.948016 | − | 0.318223i | \(-0.896914\pi\) | ||
0.948016 | − | 0.318223i | \(-0.103086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.24264 | − | 6.24264i | −0.689384 | − | 0.689384i | ||||
\(83\) | −4.82843 | − | 4.82843i | −0.529989 | − | 0.529989i | 0.390580 | − | 0.920569i | \(-0.372274\pi\) |
−0.920569 | + | 0.390580i | \(0.872274\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 11.4142i | 1.23083i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.41421 | − | 2.41421i | 0.257356 | − | 0.257356i | ||||
\(89\) | 8.82843 | 0.935811 | 0.467906 | − | 0.883778i | \(-0.345009\pi\) | ||||
0.467906 | + | 0.883778i | \(0.345009\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65685 | 0.592999 | ||||||||
\(92\) | 0.828427 | − | 0.828427i | 0.0863695 | − | 0.0863695i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 1.07107i | − | 0.110472i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.41421 | + | 7.41421i | 0.752799 | + | 0.752799i | 0.975001 | − | 0.222201i | \(-0.0713243\pi\) |
−0.222201 | + | 0.975001i | \(0.571324\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.34315i | − | 0.631167i | −0.948898 | − | 0.315583i | \(-0.897800\pi\) | ||
0.948898 | − | 0.315583i | \(-0.102200\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.58579 | − | 4.58579i | 0.451851 | − | 0.451851i | −0.444118 | − | 0.895969i | \(-0.646483\pi\) |
0.895969 | + | 0.444118i | \(0.146483\pi\) | |||||||
\(104\) | −5.65685 | −0.554700 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.65685 | −0.743699 | ||||||||
\(107\) | 10.8284 | − | 10.8284i | 1.04682 | − | 1.04682i | 0.0479750 | − | 0.998849i | \(-0.484723\pi\) |
0.998849 | − | 0.0479750i | \(-0.0152768\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.3137i | − | 1.27522i | −0.770358 | − | 0.637611i | \(-0.779923\pi\) | ||
0.770358 | − | 0.637611i | \(-0.220077\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.707107 | + | 0.707107i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | −11.3137 | − | 11.3137i | −1.06430 | − | 1.06430i | −0.997785 | − | 0.0665190i | \(-0.978811\pi\) |
−0.0665190 | − | 0.997785i | \(-0.521189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.82843i | 0.448308i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | − | 2.00000i | 0.184115 | − | 0.184115i | ||||
\(119\) | 4.82843 | 0.442621 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.656854 | −0.0597140 | ||||||||
\(122\) | −7.00000 | + | 7.00000i | −0.633750 | + | 0.633750i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 10.2426i | − | 0.919816i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.65685 | + | 3.65685i | 0.324493 | + | 0.324493i | 0.850488 | − | 0.525995i | \(-0.176307\pi\) |
−0.525995 | + | 0.850488i | \(0.676307\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.485281i | 0.0423992i | 0.999775 | + | 0.0211996i | \(0.00674855\pi\) | ||||
−0.999775 | + | 0.0211996i | \(0.993251\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | + | 2.00000i | −0.173422 | + | 0.173422i | ||||
\(134\) | 7.89949 | 0.682412 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.82843 | −0.414034 | ||||||||
\(137\) | −12.0000 | + | 12.0000i | −1.02523 | + | 1.02523i | −0.0255558 | + | 0.999673i | \(0.508136\pi\) |
−0.999673 | + | 0.0255558i | \(0.991864\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.34315i | 0.538019i | 0.963138 | + | 0.269009i | \(0.0866962\pi\) | ||||
−0.963138 | + | 0.269009i | \(0.913304\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.82843 | + | 4.82843i | 0.405193 | + | 0.405193i | ||||
\(143\) | 13.6569 | + | 13.6569i | 1.14204 | + | 1.14204i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000i | 0.827606i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.24264 | − | 2.24264i | 0.184344 | − | 0.184344i | ||||
\(149\) | 20.1421 | 1.65011 | 0.825054 | − | 0.565054i | \(-0.191145\pi\) | ||||
0.825054 | + | 0.565054i | \(0.191145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.1716 | −1.07189 | −0.535944 | − | 0.844254i | \(-0.680044\pi\) | ||||
−0.535944 | + | 0.844254i | \(0.680044\pi\) | |||||||
\(152\) | 2.00000 | − | 2.00000i | 0.162221 | − | 0.162221i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 3.41421i | − | 0.275125i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.65685 | − | 1.65685i | −0.132231 | − | 0.132231i | 0.637893 | − | 0.770125i | \(-0.279806\pi\) |
−0.770125 | + | 0.637893i | \(0.779806\pi\) | |||||||
\(158\) | 4.00000 | + | 4.00000i | 0.318223 | + | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.17157i | − | 0.0923329i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.7279 | − | 13.7279i | 1.07525 | − | 1.07525i | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) |
0.996928 | − | 0.0783260i | \(-0.0249575\pi\) | |||||||
\(164\) | 8.82843 | 0.689384 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.82843 | 0.529989 | ||||||||
\(167\) | 10.4142 | − | 10.4142i | 0.805876 | − | 0.805876i | −0.178131 | − | 0.984007i | \(-0.557005\pi\) |
0.984007 | + | 0.178131i | \(0.0570050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 19.0000i | − | 1.46154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.07107 | − | 8.07107i | −0.615413 | − | 0.615413i | ||||
\(173\) | −5.48528 | − | 5.48528i | −0.417038 | − | 0.417038i | 0.467143 | − | 0.884182i | \(-0.345283\pi\) |
−0.884182 | + | 0.467143i | \(0.845283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41421i | 0.257356i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.24264 | + | 6.24264i | −0.467906 | + | 0.467906i | ||||
\(179\) | 19.4142 | 1.45109 | 0.725543 | − | 0.688177i | \(-0.241589\pi\) | ||||
0.725543 | + | 0.688177i | \(0.241589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.92893 | −0.366365 | −0.183182 | − | 0.983079i | \(-0.558640\pi\) | ||||
−0.183182 | + | 0.983079i | \(0.558640\pi\) | |||||||
\(182\) | −4.00000 | + | 4.00000i | −0.296500 | + | 0.296500i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.17157i | 0.0863695i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.6569 | + | 11.6569i | 0.852434 | + | 0.852434i | ||||
\(188\) | 0.757359 | + | 0.757359i | 0.0552361 | + | 0.0552361i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.6569i | 1.85646i | 0.372001 | + | 0.928232i | \(0.378672\pi\) | ||||
−0.372001 | + | 0.928232i | \(0.621328\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.48528 | − | 3.48528i | 0.250876 | − | 0.250876i | −0.570454 | − | 0.821330i | \(-0.693233\pi\) |
0.821330 | + | 0.570454i | \(0.193233\pi\) | |||||||
\(194\) | −10.4853 | −0.752799 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 1.75736 | − | 1.75736i | 0.125207 | − | 0.125207i | −0.641727 | − | 0.766933i | \(-0.721782\pi\) |
0.766933 | + | 0.641727i | \(0.221782\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.8995i | 1.69419i | 0.531441 | + | 0.847095i | \(0.321651\pi\) | ||||
−0.531441 | + | 0.847095i | \(0.678349\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.48528 | + | 4.48528i | 0.315583 | + | 0.315583i | ||||
\(203\) | 3.41421 | + | 3.41421i | 0.239631 | + | 0.239631i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.48528i | 0.451851i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000 | − | 4.00000i | 0.277350 | − | 0.277350i | ||||
\(209\) | −9.65685 | −0.667979 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 5.41421 | − | 5.41421i | 0.371850 | − | 0.371850i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.3137i | 1.04682i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.24264 | − | 7.24264i | −0.491662 | − | 0.491662i | ||||
\(218\) | 9.41421 | + | 9.41421i | 0.637611 | + | 0.637611i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 27.3137i | − | 1.83732i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.3137 | − | 15.3137i | 1.02548 | − | 1.02548i | 0.0258150 | − | 0.999667i | \(-0.491782\pi\) |
0.999667 | − | 0.0258150i | \(-0.00821809\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.0000 | 1.06430 | ||||||||
\(227\) | −6.82843 | + | 6.82843i | −0.453219 | + | 0.453219i | −0.896421 | − | 0.443203i | \(-0.853842\pi\) |
0.443203 | + | 0.896421i | \(0.353842\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.242641i | 0.0160341i | 0.999968 | + | 0.00801707i | \(0.00255194\pi\) | ||||
−0.999968 | + | 0.00801707i | \(0.997448\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.41421 | − | 3.41421i | −0.224154 | − | 0.224154i | ||||
\(233\) | −9.17157 | − | 9.17157i | −0.600850 | − | 0.600850i | 0.339688 | − | 0.940538i | \(-0.389678\pi\) |
−0.940538 | + | 0.339688i | \(0.889678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.82843i | 0.184115i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.41421 | + | 3.41421i | −0.221311 | + | 0.221311i | ||||
\(239\) | 2.34315 | 0.151565 | 0.0757827 | − | 0.997124i | \(-0.475854\pi\) | ||||
0.0757827 | + | 0.997124i | \(0.475854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.1421 | 1.55513 | 0.777566 | − | 0.628802i | \(-0.216454\pi\) | ||||
0.777566 | + | 0.628802i | \(0.216454\pi\) | |||||||
\(242\) | 0.464466 | − | 0.464466i | 0.0298570 | − | 0.0298570i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 9.89949i | − | 0.633750i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.3137 | + | 11.3137i | 0.719874 | + | 0.719874i | ||||
\(248\) | 7.24264 | + | 7.24264i | 0.459908 | + | 0.459908i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 18.6274i | − | 1.17575i | −0.808951 | − | 0.587876i | \(-0.799964\pi\) | ||
0.808951 | − | 0.587876i | \(-0.200036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.82843 | − | 2.82843i | 0.177822 | − | 0.177822i | ||||
\(254\) | −5.17157 | −0.324493 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.4142 | + | 11.4142i | −0.711999 | + | 0.711999i | −0.966953 | − | 0.254954i | \(-0.917940\pi\) |
0.254954 | + | 0.966953i | \(0.417940\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 3.17157i | − | 0.197072i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.343146 | − | 0.343146i | −0.0211996 | − | 0.0211996i | ||||
\(263\) | 3.65685 | + | 3.65685i | 0.225491 | + | 0.225491i | 0.810806 | − | 0.585315i | \(-0.199029\pi\) |
−0.585315 | + | 0.810806i | \(0.699029\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 2.82843i | − | 0.173422i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.58579 | + | 5.58579i | −0.341206 | + | 0.341206i | ||||
\(269\) | −5.65685 | −0.344904 | −0.172452 | − | 0.985018i | \(-0.555169\pi\) | ||||
−0.172452 | + | 0.985018i | \(0.555169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.8995 | 1.45179 | 0.725895 | − | 0.687805i | \(-0.241426\pi\) | ||||
0.725895 | + | 0.687805i | \(0.241426\pi\) | |||||||
\(272\) | 3.41421 | − | 3.41421i | 0.207017 | − | 0.207017i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 16.9706i | − | 1.02523i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.8995 | + | 21.8995i | 1.31581 | + | 1.31581i | 0.917057 | + | 0.398756i | \(0.130558\pi\) |
0.398756 | + | 0.917057i | \(0.369442\pi\) | |||||||
\(278\) | −4.48528 | − | 4.48528i | −0.269009 | − | 0.269009i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.92893i | 0.294035i | 0.989134 | + | 0.147018i | \(0.0469674\pi\) | ||||
−0.989134 | + | 0.147018i | \(0.953033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.31371 | + | 1.31371i | −0.0780919 | + | 0.0780919i | −0.745074 | − | 0.666982i | \(-0.767586\pi\) |
0.666982 | + | 0.745074i | \(0.267586\pi\) | |||||||
\(284\) | −6.82843 | −0.405193 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −19.3137 | −1.14204 | ||||||||
\(287\) | 6.24264 | − | 6.24264i | 0.368491 | − | 0.368491i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 6.31371i | − | 0.371395i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.07107 | − | 7.07107i | −0.413803 | − | 0.413803i | ||||
\(293\) | 2.65685 | + | 2.65685i | 0.155215 | + | 0.155215i | 0.780443 | − | 0.625227i | \(-0.214994\pi\) |
−0.625227 | + | 0.780443i | \(0.714994\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.17157i | 0.184344i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.2426 | + | 14.2426i | −0.825054 | + | 0.825054i | ||||
\(299\) | −6.62742 | −0.383273 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.4142 | −0.657904 | ||||||||
\(302\) | 9.31371 | − | 9.31371i | 0.535944 | − | 0.535944i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.82843i | 0.162221i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(308\) | 2.41421 | + | 2.41421i | 0.137563 | + | 0.137563i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 0.828427i | − | 0.0469758i | −0.999724 | − | 0.0234879i | \(-0.992523\pi\) | ||
0.999724 | − | 0.0234879i | \(-0.00747712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.24264 | − | 6.24264i | 0.352855 | − | 0.352855i | −0.508316 | − | 0.861171i | \(-0.669732\pi\) |
0.861171 | + | 0.508316i | \(0.169732\pi\) | |||||||
\(314\) | 2.34315 | 0.132231 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.65685 | −0.318223 | ||||||||
\(317\) | −0.727922 | + | 0.727922i | −0.0408842 | + | 0.0408842i | −0.727253 | − | 0.686369i | \(-0.759203\pi\) |
0.686369 | + | 0.727253i | \(0.259203\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.4853i | 0.922999i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.828427 | + | 0.828427i | 0.0461664 | + | 0.0461664i | ||||
\(323\) | 9.65685 | + | 9.65685i | 0.537322 | + | 0.537322i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19.4142i | 1.07525i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.24264 | + | 6.24264i | −0.344692 | + | 0.344692i | ||||
\(329\) | 1.07107 | 0.0590499 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −26.6274 | −1.46358 | −0.731788 | − | 0.681533i | \(-0.761314\pi\) | ||||
−0.731788 | + | 0.681533i | \(0.761314\pi\) | |||||||
\(332\) | −4.82843 | + | 4.82843i | −0.264994 | + | 0.264994i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 14.7279i | 0.805876i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.8284 | − | 15.8284i | −0.862229 | − | 0.862229i | 0.129367 | − | 0.991597i | \(-0.458705\pi\) |
−0.991597 | + | 0.129367i | \(0.958705\pi\) | |||||||
\(338\) | 13.4350 | + | 13.4350i | 0.730769 | + | 0.730769i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 34.9706i | − | 1.89376i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | 11.4142 | 0.615413 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.75736 | 0.417038 | ||||||||
\(347\) | −8.48528 | + | 8.48528i | −0.455514 | + | 0.455514i | −0.897180 | − | 0.441666i | \(-0.854388\pi\) |
0.441666 | + | 0.897180i | \(0.354388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 7.27208i | − | 0.389265i | −0.980876 | − | 0.194633i | \(-0.937649\pi\) | ||
0.980876 | − | 0.194633i | \(-0.0623515\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.41421 | − | 2.41421i | −0.128678 | − | 0.128678i | ||||
\(353\) | 18.3848 | + | 18.3848i | 0.978523 | + | 0.978523i | 0.999774 | − | 0.0212513i | \(-0.00676499\pi\) |
−0.0212513 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 8.82843i | − | 0.467906i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.7279 | + | 13.7279i | −0.725543 | + | 0.725543i | ||||
\(359\) | −15.7990 | −0.833839 | −0.416919 | − | 0.908943i | \(-0.636890\pi\) | ||||
−0.416919 | + | 0.908943i | \(0.636890\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 3.48528 | − | 3.48528i | 0.183182 | − | 0.183182i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 5.65685i | − | 0.296500i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.75736 | + | 1.75736i | 0.0917334 | + | 0.0917334i | 0.751484 | − | 0.659751i | \(-0.229338\pi\) |
−0.659751 | + | 0.751484i | \(0.729338\pi\) | |||||||
\(368\) | −0.828427 | − | 0.828427i | −0.0431847 | − | 0.0431847i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.65685i | − | 0.397524i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.07107 | + | 3.07107i | −0.159014 | + | 0.159014i | −0.782130 | − | 0.623116i | \(-0.785867\pi\) |
0.623116 | + | 0.782130i | \(0.285867\pi\) | |||||||
\(374\) | −16.4853 | −0.852434 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.07107 | −0.0552361 | ||||||||
\(377\) | 19.3137 | − | 19.3137i | 0.994707 | − | 0.994707i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.7990i | 0.708806i | 0.935093 | + | 0.354403i | \(0.115316\pi\) | ||||
−0.935093 | + | 0.354403i | \(0.884684\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.1421 | − | 18.1421i | −0.928232 | − | 0.928232i | ||||
\(383\) | −1.58579 | − | 1.58579i | −0.0810299 | − | 0.0810299i | 0.665430 | − | 0.746460i | \(-0.268248\pi\) |
−0.746460 | + | 0.665430i | \(0.768248\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.92893i | 0.250876i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.41421 | − | 7.41421i | 0.376400 | − | 0.376400i | ||||
\(389\) | 29.7990 | 1.51087 | 0.755434 | − | 0.655224i | \(-0.227426\pi\) | ||||
0.755434 | + | 0.655224i | \(0.227426\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.65685 | −0.286079 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.48528i | 0.125207i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.0711 | + | 15.0711i | 0.756395 | + | 0.756395i | 0.975664 | − | 0.219269i | \(-0.0703673\pi\) |
−0.219269 | + | 0.975664i | \(0.570367\pi\) | |||||||
\(398\) | −16.8995 | − | 16.8995i | −0.847095 | − | 0.847095i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.8701i | 1.34183i | 0.741536 | + | 0.670913i | \(0.234098\pi\) | ||||
−0.741536 | + | 0.670913i | \(0.765902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −40.9706 | + | 40.9706i | −2.04089 | + | 2.04089i | ||||
\(404\) | −6.34315 | −0.315583 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.82843 | −0.239631 | ||||||||
\(407\) | 7.65685 | − | 7.65685i | 0.379536 | − | 0.379536i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0000i | 0.494468i | 0.968956 | + | 0.247234i | \(0.0795217\pi\) | ||||
−0.968956 | + | 0.247234i | \(0.920478\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.58579 | − | 4.58579i | −0.225925 | − | 0.225925i | ||||
\(413\) | 2.00000 | + | 2.00000i | 0.0984136 | + | 0.0984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.65685i | 0.277350i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.82843 | − | 6.82843i | 0.333989 | − | 0.333989i | ||||
\(419\) | 26.6274 | 1.30083 | 0.650417 | − | 0.759577i | \(-0.274594\pi\) | ||||
0.650417 | + | 0.759577i | \(0.274594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.62742 | 0.225527 | 0.112763 | − | 0.993622i | \(-0.464030\pi\) | ||||
0.112763 | + | 0.993622i | \(0.464030\pi\) | |||||||
\(422\) | 2.82843 | − | 2.82843i | 0.137686 | − | 0.137686i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.65685i | 0.371850i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | − | 7.00000i | −0.338754 | − | 0.338754i | ||||
\(428\) | −10.8284 | − | 10.8284i | −0.523412 | − | 0.523412i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.14214i | 0.103183i | 0.998668 | + | 0.0515915i | \(0.0164294\pi\) | ||||
−0.998668 | + | 0.0515915i | \(0.983571\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.75736 | + | 9.75736i | −0.468909 | + | 0.468909i | −0.901561 | − | 0.432652i | \(-0.857578\pi\) |
0.432652 | + | 0.901561i | \(0.357578\pi\) | |||||||
\(434\) | 10.2426 | 0.491662 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.3137 | −0.637611 | ||||||||
\(437\) | 2.34315 | − | 2.34315i | 0.112088 | − | 0.112088i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 15.8995i | − | 0.758841i | −0.925224 | − | 0.379421i | \(-0.876123\pi\) | ||
0.925224 | − | 0.379421i | \(-0.123877\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.3137 | + | 19.3137i | 0.918659 | + | 0.918659i | ||||
\(443\) | 20.4853 | + | 20.4853i | 0.973285 | + | 0.973285i | 0.999652 | − | 0.0263672i | \(-0.00839392\pi\) |
−0.0263672 | + | 0.999652i | \(0.508394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.6569i | 1.02548i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 8.72792 | 0.411896 | 0.205948 | − | 0.978563i | \(-0.433972\pi\) | ||||
0.205948 | + | 0.978563i | \(0.433972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.1421 | 1.41934 | ||||||||
\(452\) | −11.3137 | + | 11.3137i | −0.532152 | + | 0.532152i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 9.65685i | − | 0.453219i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.82843 | − | 7.82843i | −0.366198 | − | 0.366198i | 0.499890 | − | 0.866089i | \(-0.333374\pi\) |
−0.866089 | + | 0.499890i | \(0.833374\pi\) | |||||||
\(458\) | −0.171573 | − | 0.171573i | −0.00801707 | − | 0.00801707i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.3137i | − | 0.806380i | −0.915116 | − | 0.403190i | \(-0.867901\pi\) | ||
0.915116 | − | 0.403190i | \(-0.132099\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.7990 | + | 19.7990i | −0.920137 | + | 0.920137i | −0.997039 | − | 0.0769016i | \(-0.975497\pi\) |
0.0769016 | + | 0.997039i | \(0.475497\pi\) | |||||||
\(464\) | 4.82843 | 0.224154 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.9706 | 0.600850 | ||||||||
\(467\) | 14.0000 | − | 14.0000i | 0.647843 | − | 0.647843i | −0.304629 | − | 0.952471i | \(-0.598532\pi\) |
0.952471 | + | 0.304629i | \(0.0985323\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.89949i | 0.364765i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.00000 | − | 2.00000i | −0.0920575 | − | 0.0920575i | ||||
\(473\) | −27.5563 | − | 27.5563i | −1.26704 | − | 1.26704i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.82843i | − | 0.221311i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.65685 | + | 1.65685i | −0.0757827 | + | 0.0757827i | ||||
\(479\) | 24.8284 | 1.13444 | 0.567220 | − | 0.823566i | \(-0.308019\pi\) | ||||
0.567220 | + | 0.823566i | \(0.308019\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.9411 | −0.818045 | ||||||||
\(482\) | −17.0711 | + | 17.0711i | −0.777566 | + | 0.777566i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.656854i | 0.0298570i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.9706 | + | 14.9706i | 0.678381 | + | 0.678381i | 0.959634 | − | 0.281253i | \(-0.0907499\pi\) |
−0.281253 | + | 0.959634i | \(0.590750\pi\) | |||||||
\(488\) | 7.00000 | + | 7.00000i | 0.316875 | + | 0.316875i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.27208i | 0.0574081i | 0.999588 | + | 0.0287040i | \(0.00913803\pi\) | ||||
−0.999588 | + | 0.0287040i | \(0.990862\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.4853 | − | 16.4853i | 0.742460 | − | 0.742460i | ||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.2426 | −0.459908 | ||||||||
\(497\) | −4.82843 | + | 4.82843i | −0.216585 | + | 0.216585i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 27.4558i | 1.22909i | 0.788881 | + | 0.614546i | \(0.210661\pi\) | ||||
−0.788881 | + | 0.614546i | \(0.789339\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.1716 | + | 13.1716i | 0.587876 | + | 0.587876i | ||||
\(503\) | −14.5563 | − | 14.5563i | −0.649036 | − | 0.649036i | 0.303724 | − | 0.952760i | \(-0.401770\pi\) |
−0.952760 | + | 0.303724i | \(0.901770\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.00000i | 0.177822i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.65685 | − | 3.65685i | 0.162247 | − | 0.162247i | ||||
\(509\) | −29.6569 | −1.31452 | −0.657258 | − | 0.753665i | \(-0.728284\pi\) | ||||
−0.657258 | + | 0.753665i | \(0.728284\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 16.1421i | − | 0.711999i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.58579 | + | 2.58579i | 0.113723 | + | 0.113723i | ||||
\(518\) | 2.24264 | + | 2.24264i | 0.0985360 | + | 0.0985360i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 30.7696i | 1.34804i | 0.738714 | + | 0.674019i | \(0.235434\pi\) | ||||
−0.738714 | + | 0.674019i | \(0.764566\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.68629 | − | 2.68629i | 0.117463 | − | 0.117463i | −0.645932 | − | 0.763395i | \(-0.723531\pi\) |
0.763395 | + | 0.645932i | \(0.223531\pi\) | |||||||
\(524\) | 0.485281 | 0.0211996 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.17157 | −0.225491 | ||||||||
\(527\) | −34.9706 | + | 34.9706i | −1.52334 | + | 1.52334i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 21.6274i | − | 0.940322i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | + | 2.00000i | 0.0867110 | + | 0.0867110i | ||||
\(533\) | −35.3137 | − | 35.3137i | −1.52961 | − | 1.52961i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 7.89949i | − | 0.341206i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.00000 | − | 4.00000i | 0.172452 | − | 0.172452i | ||||
\(539\) | 3.41421 | 0.147061 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.1127 | 1.42363 | 0.711813 | − | 0.702369i | \(-0.247874\pi\) | ||||
0.711813 | + | 0.702369i | \(0.247874\pi\) | |||||||
\(542\) | −16.8995 | + | 16.8995i | −0.725895 | + | 0.725895i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.82843i | 0.207017i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.5563 | − | 18.5563i | −0.793412 | − | 0.793412i | 0.188635 | − | 0.982047i | \(-0.439594\pi\) |
−0.982047 | + | 0.188635i | \(0.939594\pi\) | |||||||
\(548\) | 12.0000 | + | 12.0000i | 0.512615 | + | 0.512615i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.6569i | 0.581802i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | + | 4.00000i | −0.170097 | + | 0.170097i | ||||
\(554\) | −30.9706 | −1.31581 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.34315 | 0.269009 | ||||||||
\(557\) | 23.5563 | − | 23.5563i | 0.998115 | − | 0.998115i | −0.00188368 | − | 0.999998i | \(-0.500600\pi\) |
0.999998 | + | 0.00188368i | \(0.000599594\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 64.5685i | 2.73096i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.48528 | − | 3.48528i | −0.147018 | − | 0.147018i | ||||
\(563\) | −29.3137 | − | 29.3137i | −1.23543 | − | 1.23543i | −0.961851 | − | 0.273575i | \(-0.911794\pi\) |
−0.273575 | − | 0.961851i | \(-0.588206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 1.85786i | − | 0.0780919i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.82843 | − | 4.82843i | 0.202596 | − | 0.202596i | ||||
\(569\) | −33.8995 | −1.42114 | −0.710570 | − | 0.703626i | \(-0.751563\pi\) | ||||
−0.710570 | + | 0.703626i | \(0.751563\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.9706 | −1.88196 | −0.940980 | − | 0.338463i | \(-0.890093\pi\) | ||||
−0.940980 | + | 0.338463i | \(0.890093\pi\) | |||||||
\(572\) | 13.6569 | − | 13.6569i | 0.571022 | − | 0.571022i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.82843i | 0.368491i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.7279 | − | 14.7279i | −0.613131 | − | 0.613131i | 0.330629 | − | 0.943761i | \(-0.392739\pi\) |
−0.943761 | + | 0.330629i | \(0.892739\pi\) | |||||||
\(578\) | 4.46447 | + | 4.46447i | 0.185697 | + | 0.185697i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.82843i | 0.283291i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.4853 | − | 18.4853i | 0.765582 | − | 0.765582i | ||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.75736 | −0.155215 | ||||||||
\(587\) | 21.7990 | − | 21.7990i | 0.899741 | − | 0.899741i | −0.0956723 | − | 0.995413i | \(-0.530500\pi\) |
0.995413 | + | 0.0956723i | \(0.0305001\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 28.9706i | − | 1.19371i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.24264 | − | 2.24264i | −0.0921720 | − | 0.0921720i | ||||
\(593\) | −20.3848 | − | 20.3848i | −0.837102 | − | 0.837102i | 0.151374 | − | 0.988477i | \(-0.451630\pi\) |
−0.988477 | + | 0.151374i | \(0.951630\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 20.1421i | − | 0.825054i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.68629 | − | 4.68629i | 0.191637 | − | 0.191637i | ||||
\(599\) | 7.31371 | 0.298830 | 0.149415 | − | 0.988775i | \(-0.452261\pi\) | ||||
0.149415 | + | 0.988775i | \(0.452261\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.1421 | 0.984778 | 0.492389 | − | 0.870375i | \(-0.336124\pi\) | ||||
0.492389 | + | 0.870375i | \(0.336124\pi\) | |||||||
\(602\) | 8.07107 | − | 8.07107i | 0.328952 | − | 0.328952i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 13.1716i | 0.535944i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.3137 | − | 15.3137i | −0.621564 | − | 0.621564i | 0.324367 | − | 0.945931i | \(-0.394849\pi\) |
−0.945931 | + | 0.324367i | \(0.894849\pi\) | |||||||
\(608\) | −2.00000 | − | 2.00000i | −0.0811107 | − | 0.0811107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6.05887i | − | 0.245116i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.07107 | + | 5.07107i | −0.204818 | + | 0.204818i | −0.802061 | − | 0.597242i | \(-0.796263\pi\) |
0.597242 | + | 0.802061i | \(0.296263\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.41421 | −0.137563 | ||||||||
\(617\) | 24.0416 | − | 24.0416i | 0.967880 | − | 0.967880i | −0.0316203 | − | 0.999500i | \(-0.510067\pi\) |
0.999500 | + | 0.0316203i | \(0.0100667\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 46.1421i | 1.85461i | 0.374308 | + | 0.927305i | \(0.377880\pi\) | ||||
−0.374308 | + | 0.927305i | \(0.622120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.585786 | + | 0.585786i | 0.0234879 | + | 0.0234879i | ||||
\(623\) | −6.24264 | − | 6.24264i | −0.250106 | − | 0.250106i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.82843i | 0.352855i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.65685 | + | 1.65685i | −0.0661157 | + | 0.0661157i | ||||
\(629\) | −15.3137 | −0.610598 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.7990 | −1.58437 | −0.792186 | − | 0.610279i | \(-0.791057\pi\) | ||||
−0.792186 | + | 0.610279i | \(0.791057\pi\) | |||||||
\(632\) | 4.00000 | − | 4.00000i | 0.159111 | − | 0.159111i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 1.02944i | − | 0.0408842i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00000 | − | 4.00000i | −0.158486 | − | 0.158486i | ||||
\(638\) | −11.6569 | − | 11.6569i | −0.461499 | − | 0.461499i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 21.2132i | − | 0.837871i | −0.908016 | − | 0.418936i | \(-0.862403\pi\) | ||
0.908016 | − | 0.418936i | \(-0.137597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.9706 | + | 22.9706i | −0.905871 | + | 0.905871i | −0.995936 | − | 0.0900653i | \(-0.971292\pi\) |
0.0900653 | + | 0.995936i | \(0.471292\pi\) | |||||||
\(644\) | −1.17157 | −0.0461664 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −13.6569 | −0.537322 | ||||||||
\(647\) | 24.7574 | − | 24.7574i | 0.973312 | − | 0.973312i | −0.0263408 | − | 0.999653i | \(-0.508386\pi\) |
0.999653 | + | 0.0263408i | \(0.00838550\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.65685i | 0.379065i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.7279 | − | 13.7279i | −0.537627 | − | 0.537627i | ||||
\(653\) | −5.75736 | − | 5.75736i | −0.225303 | − | 0.225303i | 0.585424 | − | 0.810727i | \(-0.300928\pi\) |
−0.810727 | + | 0.585424i | \(0.800928\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 8.82843i | − | 0.344692i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.757359 | + | 0.757359i | −0.0295249 | + | 0.0295249i | ||||
\(659\) | −1.27208 | −0.0495531 | −0.0247766 | − | 0.999693i | \(-0.507887\pi\) | ||||
−0.0247766 | + | 0.999693i | \(0.507887\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.04163 | −0.312783 | −0.156392 | − | 0.987695i | \(-0.549986\pi\) | ||||
−0.156392 | + | 0.987695i | \(0.549986\pi\) | |||||||
\(662\) | 18.8284 | − | 18.8284i | 0.731788 | − | 0.731788i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.82843i | − | 0.264994i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.00000 | − | 4.00000i | −0.154881 | − | 0.154881i | ||||
\(668\) | −10.4142 | − | 10.4142i | −0.402938 | − | 0.402938i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 33.7990i | − | 1.30480i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.6569 | + | 14.6569i | −0.564980 | + | 0.564980i | −0.930718 | − | 0.365738i | \(-0.880817\pi\) |
0.365738 | + | 0.930718i | \(0.380817\pi\) | |||||||
\(674\) | 22.3848 | 0.862229 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −19.0000 | −0.730769 | ||||||||
\(677\) | −10.1716 | + | 10.1716i | −0.390925 | + | 0.390925i | −0.875017 | − | 0.484092i | \(-0.839150\pi\) |
0.484092 | + | 0.875017i | \(0.339150\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 10.4853i | − | 0.402388i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 24.7279 | + | 24.7279i | 0.946881 | + | 0.946881i | ||||
\(683\) | 12.3848 | + | 12.3848i | 0.473890 | + | 0.473890i | 0.903171 | − | 0.429281i | \(-0.141233\pi\) |
−0.429281 | + | 0.903171i | \(0.641233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.07107 | + | 8.07107i | −0.307707 | + | 0.307707i | ||||
\(689\) | −43.3137 | −1.65012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(692\) | −5.48528 | + | 5.48528i | −0.208519 | + | 0.208519i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 12.0000i | − | 0.455514i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.1421 | − | 30.1421i | −1.14171 | − | 1.14171i | ||||
\(698\) | 5.14214 | + | 5.14214i | 0.194633 | + | 0.194633i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.1716i | − | 1.32841i | −0.747550 | − | 0.664206i | \(-0.768770\pi\) | ||
0.747550 | − | 0.664206i | \(-0.231230\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.34315 | − | 6.34315i | 0.239236 | − | 0.239236i | ||||
\(704\) | 3.41421 | 0.128678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.0000 | −0.978523 | ||||||||
\(707\) | −4.48528 | + | 4.48528i | −0.168686 | + | 0.168686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.1716i | 1.32090i | 0.750872 | + | 0.660448i | \(0.229634\pi\) | ||||
−0.750872 | + | 0.660448i | \(0.770366\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.24264 | + | 6.24264i | 0.233953 | + | 0.233953i | ||||
\(713\) | 8.48528 | + | 8.48528i | 0.317776 | + | 0.317776i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 19.4142i | − | 0.725543i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.1716 | − | 11.1716i | 0.416919 | − | 0.416919i | ||||
\(719\) | −6.62742 | −0.247161 | −0.123580 | − | 0.992335i | \(-0.539438\pi\) | ||||
−0.123580 | + | 0.992335i | \(0.539438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.48528 | −0.241524 | ||||||||
\(722\) | −7.77817 | + | 7.77817i | −0.289474 | + | 0.289474i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.92893i | 0.183182i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.6274 | − | 22.6274i | −0.839204 | − | 0.839204i | 0.149550 | − | 0.988754i | \(-0.452218\pi\) |
−0.988754 | + | 0.149550i | \(0.952218\pi\) | |||||||
\(728\) | 4.00000 | + | 4.00000i | 0.148250 | + | 0.148250i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 55.1127i | 2.03842i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.5563 | − | 31.5563i | 1.16556 | − | 1.16556i | 0.182321 | − | 0.983239i | \(-0.441639\pi\) |
0.983239 | − | 0.182321i | \(-0.0583611\pi\) | |||||||
\(734\) | −2.48528 | −0.0917334 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.17157 | 0.0431847 | ||||||||
\(737\) | −19.0711 | + | 19.0711i | −0.702492 | + | 0.702492i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 43.4558i | − | 1.59855i | −0.600966 | − | 0.799275i | \(-0.705217\pi\) | ||
0.600966 | − | 0.799275i | \(-0.294783\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.41421 | + | 5.41421i | 0.198762 | + | 0.198762i | ||||
\(743\) | −31.1127 | − | 31.1127i | −1.14141 | − | 1.14141i | −0.988192 | − | 0.153222i | \(-0.951035\pi\) |
−0.153222 | − | 0.988192i | \(-0.548965\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 4.34315i | − | 0.159014i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 11.6569 | − | 11.6569i | 0.426217 | − | 0.426217i | ||||
\(749\) | −15.3137 | −0.559551 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.5147 | 1.14999 | 0.574994 | − | 0.818157i | \(-0.305004\pi\) | ||||
0.574994 | + | 0.818157i | \(0.305004\pi\) | |||||||
\(752\) | 0.757359 | − | 0.757359i | 0.0276181 | − | 0.0276181i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 27.3137i | 0.994707i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.55635 | − | 7.55635i | −0.274640 | − | 0.274640i | 0.556325 | − | 0.830965i | \(-0.312211\pi\) |
−0.830965 | + | 0.556325i | \(0.812211\pi\) | |||||||
\(758\) | −9.75736 | − | 9.75736i | −0.354403 | − | 0.354403i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.9706i | 0.542682i | 0.962483 | + | 0.271341i | \(0.0874672\pi\) | ||||
−0.962483 | + | 0.271341i | \(0.912533\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.41421 | + | 9.41421i | −0.340817 | + | 0.340817i | ||||
\(764\) | 25.6569 | 0.928232 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.24264 | 0.0810299 | ||||||||
\(767\) | 11.3137 | − | 11.3137i | 0.408514 | − | 0.408514i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37.5980i | − | 1.35582i | −0.735146 | − | 0.677909i | \(-0.762886\pi\) | ||
0.735146 | − | 0.677909i | \(-0.237114\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.48528 | − | 3.48528i | −0.125438 | − | 0.125438i | ||||
\(773\) | 32.9411 | + | 32.9411i | 1.18481 | + | 1.18481i | 0.978483 | + | 0.206327i | \(0.0661510\pi\) |
0.206327 | + | 0.978483i | \(0.433849\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 10.4853i | 0.376400i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −21.0711 | + | 21.0711i | −0.755434 | + | 0.755434i | ||||
\(779\) | 24.9706 | 0.894663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.3137 | −0.834230 | ||||||||
\(782\) | 4.00000 | − | 4.00000i | 0.143040 | − | 0.143040i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.4853 | + | 32.4853i | 1.15798 | + | 1.15798i | 0.984910 | + | 0.173065i | \(0.0553670\pi\) |
0.173065 | + | 0.984910i | \(0.444633\pi\) | |||||||
\(788\) | −1.75736 | − | 1.75736i | −0.0626033 | − | 0.0626033i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.0000i | 0.568895i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −39.5980 | + | 39.5980i | −1.40617 | + | 1.40617i | ||||
\(794\) | −21.3137 | −0.756395 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.8995 | 0.847095 | ||||||||
\(797\) | −25.8284 | + | 25.8284i | −0.914890 | + | 0.914890i | −0.996652 | − | 0.0817621i | \(-0.973945\pi\) |
0.0817621 | + | 0.996652i | \(0.473945\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.17157i | − | 0.182957i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.0000 | − | 19.0000i | −0.670913 | − | 0.670913i | ||||
\(803\) | −24.1421 | − | 24.1421i | −0.851957 | − | 0.851957i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 57.9411i | − | 2.04089i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.48528 | − | 4.48528i | 0.157792 | − | 0.157792i | ||||
\(809\) | −9.61522 | −0.338053 | −0.169027 | − | 0.985611i | \(-0.554062\pi\) | ||||
−0.169027 | + | 0.985611i | \(0.554062\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.97056 | −0.174540 | −0.0872700 | − | 0.996185i | \(-0.527814\pi\) | ||||
−0.0872700 | + | 0.996185i | \(0.527814\pi\) | |||||||
\(812\) | 3.41421 | − | 3.41421i | 0.119815 | − | 0.119815i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.8284i | 0.379536i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.8284 | − | 22.8284i | −0.798666 | − | 0.798666i | ||||
\(818\) | −7.07107 | − | 7.07107i | −0.247234 | − | 0.247234i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 29.7990i | − | 1.03999i | −0.854169 | − | 0.519996i | \(-0.825933\pi\) | ||
0.854169 | − | 0.519996i | \(-0.174067\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5147 | + | 11.5147i | −0.401378 | + | 0.401378i | −0.878718 | − | 0.477341i | \(-0.841601\pi\) |
0.477341 | + | 0.878718i | \(0.341601\pi\) | |||||||
\(824\) | 6.48528 | 0.225925 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.82843 | −0.0984136 | ||||||||
\(827\) | 5.75736 | − | 5.75736i | 0.200203 | − | 0.200203i | −0.599884 | − | 0.800087i | \(-0.704787\pi\) |
0.800087 | + | 0.599884i | \(0.204787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.2426i | 0.703056i | 0.936177 | + | 0.351528i | \(0.114338\pi\) | ||||
−0.936177 | + | 0.351528i | \(0.885662\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | − | 4.00000i | −0.138675 | − | 0.138675i | ||||
\(833\) | −3.41421 | − | 3.41421i | −0.118295 | − | 0.118295i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.65685i | 0.333989i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.8284 | + | 18.8284i | −0.650417 | + | 0.650417i | ||||
\(839\) | −13.5147 | −0.466580 | −0.233290 | − | 0.972407i | \(-0.574949\pi\) | ||||
−0.233290 | + | 0.972407i | \(0.574949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | −3.27208 | + | 3.27208i | −0.112763 | + | 0.112763i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.00000i | 0.137686i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.464466 | + | 0.464466i | 0.0159592 | + | 0.0159592i | ||||
\(848\) | −5.41421 | − | 5.41421i | −0.185925 | − | 0.185925i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.71573i | 0.127374i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.928932 | − | 0.928932i | 0.0318060 | − | 0.0318060i | −0.691025 | − | 0.722831i | \(-0.742841\pi\) |
0.722831 | + | 0.691025i | \(0.242841\pi\) | |||||||
\(854\) | 9.89949 | 0.338754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.3137 | 0.523412 | ||||||||
\(857\) | −37.5563 | + | 37.5563i | −1.28290 | + | 1.28290i | −0.343891 | + | 0.939010i | \(0.611745\pi\) |
−0.939010 | + | 0.343891i | \(0.888255\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.0000i | − | 1.36478i | −0.730987 | − | 0.682391i | \(-0.760940\pi\) | ||
0.730987 | − | 0.682391i | \(-0.239060\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.51472 | − | 1.51472i | −0.0515915 | − | 0.0515915i | ||||
\(863\) | 26.8284 | + | 26.8284i | 0.913250 | + | 0.913250i | 0.996527 | − | 0.0832762i | \(-0.0265384\pi\) |
−0.0832762 | + | 0.996527i | \(0.526538\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 13.7990i | − | 0.468909i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.24264 | + | 7.24264i | −0.245831 | + | 0.245831i | ||||
\(869\) | −19.3137 | −0.655173 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.6863 | 1.51414 | ||||||||
\(872\) | 9.41421 | − | 9.41421i | 0.318805 | − | 0.318805i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.31371i | 0.112088i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.6985 | − | 21.6985i | −0.732706 | − | 0.732706i | 0.238449 | − | 0.971155i | \(-0.423361\pi\) |
−0.971155 | + | 0.238449i | \(0.923361\pi\) | |||||||
\(878\) | 11.2426 | + | 11.2426i | 0.379421 | + | 0.379421i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 36.6274i | − | 1.23401i | −0.786960 | − | 0.617005i | \(-0.788346\pi\) | ||
0.786960 | − | 0.617005i | \(-0.211654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.615224 | + | 0.615224i | −0.0207039 | + | 0.0207039i | −0.717383 | − | 0.696679i | \(-0.754660\pi\) |
0.696679 | + | 0.717383i | \(0.254660\pi\) | |||||||
\(884\) | −27.3137 | −0.918659 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −28.9706 | −0.973285 | ||||||||
\(887\) | 14.2721 | − | 14.2721i | 0.479209 | − | 0.479209i | −0.425669 | − | 0.904879i | \(-0.639961\pi\) |
0.904879 | + | 0.425669i | \(0.139961\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.17157i | − | 0.173449i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.3137 | − | 15.3137i | −0.512741 | − | 0.512741i | ||||
\(893\) | 2.14214 | + | 2.14214i | 0.0716838 | + | 0.0716838i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.17157 | + | 6.17157i | −0.205948 | + | 0.205948i | ||||
\(899\) | −49.4558 | −1.64944 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36.9706 | −1.23167 | ||||||||
\(902\) | −21.3137 | + | 21.3137i | −0.709669 | + | 0.709669i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.0000i | − | 0.532152i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.4142 | − | 22.4142i | −0.744252 | − | 0.744252i | 0.229141 | − | 0.973393i | \(-0.426408\pi\) |
−0.973393 | + | 0.229141i | \(0.926408\pi\) | |||||||
\(908\) | 6.82843 | + | 6.82843i | 0.226609 | + | 0.226609i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 4.00000i | − | 0.132526i | −0.997802 | − | 0.0662630i | \(-0.978892\pi\) | ||
0.997802 | − | 0.0662630i | \(-0.0211076\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.4853 | + | 16.4853i | −0.545583 | + | 0.545583i | ||||
\(914\) | 11.0711 | 0.366198 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.242641 | 0.00801707 | ||||||||
\(917\) | 0.343146 | − | 0.343146i | 0.0113317 | − | 0.0113317i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 16.2010i | − | 0.534422i | −0.963638 | − | 0.267211i | \(-0.913898\pi\) | ||
0.963638 | − | 0.267211i | \(-0.0861021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.2426 | + | 12.2426i | 0.403190 | + | 0.403190i | ||||
\(923\) | 27.3137 | + | 27.3137i | 0.899042 | + | 0.899042i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 28.0000i | − | 0.920137i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.41421 | + | 3.41421i | −0.112077 | + | 0.112077i | ||||
\(929\) | −46.9706 | −1.54105 | −0.770527 | − | 0.637407i | \(-0.780007\pi\) | ||||
−0.770527 | + | 0.637407i | \(0.780007\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.82843 | 0.0926980 | ||||||||
\(932\) | −9.17157 | + | 9.17157i | −0.300425 | + | 0.300425i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.7990i | 0.647843i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.2132 | − | 13.2132i | −0.431657 | − | 0.431657i | 0.457535 | − | 0.889192i | \(-0.348732\pi\) |
−0.889192 | + | 0.457535i | \(0.848732\pi\) | |||||||
\(938\) | −5.58579 | − | 5.58579i | −0.182382 | − | 0.182382i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.2843i | 1.50882i | 0.656401 | + | 0.754412i | \(0.272078\pi\) | ||||
−0.656401 | + | 0.754412i | \(0.727922\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.31371 | + | 7.31371i | −0.238167 | + | 0.238167i | ||||
\(944\) | 2.82843 | 0.0920575 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.9706 | 1.26704 | ||||||||
\(947\) | −18.2426 | + | 18.2426i | −0.592806 | + | 0.592806i | −0.938388 | − | 0.345582i | \(-0.887681\pi\) |
0.345582 | + | 0.938388i | \(0.387681\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 56.5685i | 1.83629i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.41421 | + | 3.41421i | 0.110655 | + | 0.110655i | ||||
\(953\) | 36.2426 | + | 36.2426i | 1.17401 | + | 1.17401i | 0.981244 | + | 0.192770i | \(0.0617473\pi\) |
0.192770 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 2.34315i | − | 0.0757827i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.5563 | + | 17.5563i | −0.567220 | + | 0.567220i | ||||
\(959\) | 16.9706 | 0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9117 | 2.38425 | ||||||||
\(962\) | 12.6863 | − | 12.6863i | 0.409022 | − | 0.409022i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 24.1421i | − | 0.777566i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2843 | + | 36.2843i | 1.16682 | + | 1.16682i | 0.982950 | + | 0.183874i | \(0.0588637\pi\) |
0.183874 | + | 0.982950i | \(0.441136\pi\) | |||||||
\(968\) | −0.464466 | − | 0.464466i | −0.0149285 | − | 0.0149285i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.0000i | 1.15529i | 0.816286 | + | 0.577647i | \(0.196029\pi\) | ||||
−0.816286 | + | 0.577647i | \(0.803971\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.48528 | − | 4.48528i | 0.143792 | − | 0.143792i | ||||
\(974\) | −21.1716 | −0.678381 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.89949 | −0.316875 | ||||||||
\(977\) | 0.970563 | − | 0.970563i | 0.0310511 | − | 0.0310511i | −0.691411 | − | 0.722462i | \(-0.743010\pi\) |
0.722462 | + | 0.691411i | \(0.243010\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 30.1421i | − | 0.963347i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.899495 | − | 0.899495i | −0.0287040 | − | 0.0287040i | ||||
\(983\) | −9.44365 | − | 9.44365i | −0.301206 | − | 0.301206i | 0.540280 | − | 0.841485i | \(-0.318318\pi\) |
−0.841485 | + | 0.540280i | \(0.818318\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 23.3137i | 0.742460i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 11.3137 | − | 11.3137i | 0.359937 | − | 0.359937i | ||||
\(989\) | 13.3726 | 0.425223 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.85786 | −0.0590170 | −0.0295085 | − | 0.999565i | \(-0.509394\pi\) | ||||
−0.0295085 | + | 0.999565i | \(0.509394\pi\) | |||||||
\(992\) | 7.24264 | − | 7.24264i | 0.229954 | − | 0.229954i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 6.82843i | − | 0.216585i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.8995 | + | 17.8995i | 0.566883 | + | 0.566883i | 0.931254 | − | 0.364371i | \(-0.118716\pi\) |
−0.364371 | + | 0.931254i | \(0.618716\pi\) | |||||||
\(998\) | −19.4142 | − | 19.4142i | −0.614546 | − | 0.614546i | ||||
\(999\) | 0 | 0 |
(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 | 3150.2.m.b.1457.1 | 4 | ||
3.2 | odd | 2 | 3150.2.m.a.1457.2 | 4 | |||
5.2 | odd | 4 | 630.2.m.b.323.1 | yes | 4 | ||
5.3 | odd | 4 | 3150.2.m.a.2843.2 | 4 | |||
5.4 | even | 2 | 630.2.m.a.197.2 | ✓ | 4 | ||
15.2 | even | 4 | 630.2.m.a.323.2 | yes | 4 | ||
15.8 | even | 4 | inner | 3150.2.m.b.2843.1 | 4 | ||
15.14 | odd | 2 | 630.2.m.b.197.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.m.a.197.2 | ✓ | 4 | 5.4 | even | 2 | ||
630.2.m.a.323.2 | yes | 4 | 15.2 | even | 4 | ||
630.2.m.b.197.1 | yes | 4 | 15.14 | odd | 2 | ||
630.2.m.b.323.1 | yes | 4 | 5.2 | odd | 4 | ||
3150.2.m.a.1457.2 | 4 | 3.2 | odd | 2 | |||
3150.2.m.a.2843.2 | 4 | 5.3 | odd | 4 | |||
3150.2.m.b.1457.1 | 4 | 1.1 | even | 1 | trivial | ||
3150.2.m.b.2843.1 | 4 | 15.8 | even | 4 | inner |