Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(118,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.p (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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
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 | 118.1 | ||
Root | \(-1.58114 + 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.118 |
Dual form | 315.2.p.a.307.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58114 | + | 1.58114i | −1.11803 | + | 1.11803i | −0.126004 | + | 0.992030i | \(0.540215\pi\) |
−0.992030 | + | 0.126004i | \(0.959785\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 3.00000i | − | 1.50000i | ||||||
\(5\) | −2.00000 | − | 1.00000i | −0.894427 | − | 0.447214i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.58114 | + | 0.581139i | 0.975579 | + | 0.219650i | ||||
\(8\) | 1.58114 | + | 1.58114i | 0.559017 | + | 0.559017i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.74342 | − | 1.58114i | 1.50000 | − | 0.500000i | ||||
\(11\) | 3.16228 | 0.953463 | 0.476731 | − | 0.879049i | \(-0.341821\pi\) | ||||
0.476731 | + | 0.879049i | \(0.341821\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.16228 | + | 3.16228i | −0.877058 | + | 0.877058i | −0.993229 | − | 0.116171i | \(-0.962938\pi\) |
0.116171 | + | 0.993229i | \(0.462938\pi\) | |||||||
\(14\) | −5.00000 | + | 3.16228i | −1.33631 | + | 0.845154i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.00000 | + | 5.00000i | 1.21268 | + | 1.21268i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) |
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16228 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(20\) | −3.00000 | + | 6.00000i | −0.670820 | + | 1.34164i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.00000 | + | 5.00000i | −1.06600 | + | 1.06600i | ||||
\(23\) | 3.16228 | + | 3.16228i | 0.659380 | + | 0.659380i | 0.955233 | − | 0.295853i | \(-0.0956039\pi\) |
−0.295853 | + | 0.955233i | \(0.595604\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | − | 10.0000i | − | 1.96116i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.74342 | − | 7.74342i | 0.329475 | − | 1.46337i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.16228i | − | 0.567962i | −0.958830 | − | 0.283981i | \(-0.908345\pi\) | ||
0.958830 | − | 0.283981i | \(-0.0916552\pi\) | |||||||
\(32\) | −4.74342 | + | 4.74342i | −0.838525 | + | 0.838525i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −15.8114 | −2.71163 | ||||||||
\(35\) | −4.58114 | − | 3.74342i | −0.774354 | − | 0.632753i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 3.00000i | −0.493197 | + | 0.493197i | −0.909312 | − | 0.416115i | \(-0.863391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(38\) | 5.00000 | − | 5.00000i | 0.811107 | − | 0.811107i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.58114 | − | 4.74342i | −0.250000 | − | 0.750000i | ||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.00000 | + | 6.00000i | 0.914991 | + | 0.914991i | 0.996660 | − | 0.0816682i | \(-0.0260248\pi\) |
−0.0816682 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(44\) | − | 9.48683i | − | 1.43019i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.0000 | −1.47442 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.32456 | + | 3.00000i | 0.903508 | + | 0.428571i | ||||
\(50\) | −11.0680 | − | 1.58114i | −1.56525 | − | 0.223607i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.48683 | + | 9.48683i | 1.31559 | + | 1.31559i | ||||
\(53\) | −3.16228 | − | 3.16228i | −0.434372 | − | 0.434372i | 0.455740 | − | 0.890113i | \(-0.349375\pi\) |
−0.890113 | + | 0.455740i | \(0.849375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.32456 | − | 3.16228i | −0.852803 | − | 0.426401i | ||||
\(56\) | 3.16228 | + | 5.00000i | 0.422577 | + | 0.668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.6491i | 1.61955i | 0.586739 | + | 0.809776i | \(0.300412\pi\) | ||||
−0.586739 | + | 0.809776i | \(0.699588\pi\) | |||||||
\(62\) | 5.00000 | + | 5.00000i | 0.635001 | + | 0.635001i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 13.0000i | − | 1.62500i | ||||||
\(65\) | 9.48683 | − | 3.16228i | 1.17670 | − | 0.392232i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.00000 | − | 8.00000i | 0.977356 | − | 0.977356i | −0.0223937 | − | 0.999749i | \(-0.507129\pi\) |
0.999749 | + | 0.0223937i | \(0.00712872\pi\) | |||||||
\(68\) | 15.0000 | − | 15.0000i | 1.81902 | − | 1.81902i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.1623 | − | 1.32456i | 1.57319 | − | 0.158315i | ||||
\(71\) | 9.48683 | 1.12588 | 0.562940 | − | 0.826498i | \(-0.309670\pi\) | ||||
0.562940 | + | 0.826498i | \(0.309670\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.48683 | − | 9.48683i | 1.11035 | − | 1.11035i | 0.117247 | − | 0.993103i | \(-0.462593\pi\) |
0.993103 | − | 0.117247i | \(-0.0374069\pi\) | |||||||
\(74\) | − | 9.48683i | − | 1.10282i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.48683i | 1.08821i | ||||||||
\(77\) | 8.16228 | + | 1.83772i | 0.930178 | + | 0.209428i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.00000i | − | 0.450035i | −0.974355 | − | 0.225018i | \(-0.927756\pi\) | ||
0.974355 | − | 0.225018i | \(-0.0722440\pi\) | |||||||
\(80\) | −2.00000 | − | 1.00000i | −0.223607 | − | 0.111803i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.0000 | + | 10.0000i | −1.09764 | + | 1.09764i | −0.102957 | + | 0.994686i | \(0.532830\pi\) |
−0.994686 | + | 0.102957i | \(0.967170\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | − | 15.0000i | −0.542326 | − | 1.62698i | ||||
\(86\) | −18.9737 | −2.04598 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.00000 | + | 5.00000i | 0.533002 | + | 0.533002i | ||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | + | 6.32456i | −1.04828 | + | 0.662994i | ||||
\(92\) | 9.48683 | − | 9.48683i | 0.989071 | − | 0.989071i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.32456 | + | 3.16228i | 0.648886 | + | 0.324443i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.16228 | − | 3.16228i | −0.321081 | − | 0.321081i | 0.528101 | − | 0.849182i | \(-0.322904\pi\) |
−0.849182 | + | 0.528101i | \(0.822904\pi\) | |||||||
\(98\) | −14.7434 | + | 5.25658i | −1.48931 | + | 0.530995i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.0000 | − | 9.00000i | 1.20000 | − | 0.900000i | ||||
\(101\) | − | 10.0000i | − | 0.995037i | −0.867453 | − | 0.497519i | \(-0.834245\pi\) | ||
0.867453 | − | 0.497519i | \(-0.165755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.16228 | − | 3.16228i | 0.311588 | − | 0.311588i | −0.533936 | − | 0.845525i | \(-0.679288\pi\) |
0.845525 | + | 0.533936i | \(0.179288\pi\) | |||||||
\(104\) | −10.0000 | −0.980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | −9.48683 | + | 9.48683i | −0.917127 | + | 0.917127i | −0.996819 | − | 0.0796927i | \(-0.974606\pi\) |
0.0796927 | + | 0.996819i | \(0.474606\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 15.0000 | − | 5.00000i | 1.43019 | − | 0.476731i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.58114 | + | 0.581139i | 0.243895 | + | 0.0549125i | ||||
\(113\) | −9.48683 | − | 9.48683i | −0.892446 | − | 0.892446i | 0.102307 | − | 0.994753i | \(-0.467378\pi\) |
−0.994753 | + | 0.102307i | \(0.967378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.16228 | − | 9.48683i | −0.294884 | − | 0.884652i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0000 | + | 15.8114i | 0.916698 | + | 1.44943i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | −20.0000 | − | 20.0000i | −1.81071 | − | 1.81071i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.48683 | −0.851943 | ||||||||
\(125\) | −2.00000 | − | 11.0000i | −0.178885 | − | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.0000 | + | 12.0000i | −1.06483 | + | 1.06483i | −0.0670802 | + | 0.997748i | \(0.521368\pi\) |
−0.997748 | + | 0.0670802i | \(0.978632\pi\) | |||||||
\(128\) | 11.0680 | + | 11.0680i | 0.978280 | + | 0.978280i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.0000 | + | 20.0000i | −0.877058 | + | 1.75412i | ||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.16228 | − | 1.83772i | −0.707759 | − | 0.159351i | ||||
\(134\) | 25.2982i | 2.18543i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 15.8114i | 1.35582i | ||||||||
\(137\) | 3.16228 | − | 3.16228i | 0.270172 | − | 0.270172i | −0.558998 | − | 0.829169i | \(-0.688814\pi\) |
0.829169 | + | 0.558998i | \(0.188814\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.48683 | 0.804663 | 0.402331 | − | 0.915494i | \(-0.368200\pi\) | ||||
0.402331 | + | 0.915494i | \(0.368200\pi\) | |||||||
\(140\) | −11.2302 | + | 13.7434i | −0.949129 | + | 1.16153i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.0000 | + | 15.0000i | −1.25877 | + | 1.25877i | ||||
\(143\) | −10.0000 | + | 10.0000i | −0.836242 | + | 0.836242i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 30.0000i | 2.48282i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.00000 | + | 9.00000i | 0.739795 | + | 0.739795i | ||||
\(149\) | − | 18.9737i | − | 1.55438i | −0.629264 | − | 0.777192i | \(-0.716644\pi\) | ||
0.629264 | − | 0.777192i | \(-0.283356\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | −5.00000 | − | 5.00000i | −0.405554 | − | 0.405554i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15.8114 | + | 10.0000i | −1.27412 | + | 0.805823i | ||||
\(155\) | −3.16228 | + | 6.32456i | −0.254000 | + | 0.508001i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.8114 | − | 15.8114i | −1.26189 | − | 1.26189i | −0.950178 | − | 0.311708i | \(-0.899099\pi\) |
−0.311708 | − | 0.950178i | \(-0.600901\pi\) | |||||||
\(158\) | 6.32456 | + | 6.32456i | 0.503155 | + | 0.503155i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 14.2302 | − | 4.74342i | 1.12500 | − | 0.375000i | ||||
\(161\) | 6.32456 | + | 10.0000i | 0.498445 | + | 0.788110i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.00000 | − | 6.00000i | −0.469956 | − | 0.469956i | 0.431944 | − | 0.901900i | \(-0.357828\pi\) |
−0.901900 | + | 0.431944i | \(0.857828\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 31.6228i | − | 2.45440i | ||||||
\(167\) | −10.0000 | − | 10.0000i | −0.773823 | − | 0.773823i | 0.204949 | − | 0.978773i | \(-0.434297\pi\) |
−0.978773 | + | 0.204949i | \(0.934297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 7.00000i | − | 0.538462i | ||||||
\(170\) | 31.6228 | + | 15.8114i | 2.42536 | + | 1.21268i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 18.0000 | − | 18.0000i | 1.37249 | − | 1.37249i | ||||
\(173\) | −5.00000 | + | 5.00000i | −0.380143 | + | 0.380143i | −0.871154 | − | 0.491011i | \(-0.836628\pi\) |
0.491011 | + | 0.871154i | \(0.336628\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.41886 | + | 12.0680i | 0.409627 | + | 0.912253i | ||||
\(176\) | 3.16228 | 0.238366 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.8114 | + | 15.8114i | −1.18511 | + | 1.18511i | ||||
\(179\) | 9.48683i | 0.709079i | 0.935041 | + | 0.354540i | \(0.115362\pi\) | ||||
−0.935041 | + | 0.354540i | \(0.884638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.32456i | − | 0.470100i | −0.971983 | − | 0.235050i | \(-0.924475\pi\) | ||
0.971983 | − | 0.235050i | \(-0.0755255\pi\) | |||||||
\(182\) | 5.81139 | − | 25.8114i | 0.430769 | − | 1.91327i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 10.0000i | 0.737210i | ||||||||
\(185\) | 9.00000 | − | 3.00000i | 0.661693 | − | 0.220564i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8114 | + | 15.8114i | 1.15624 | + | 1.15624i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.0000 | + | 5.00000i | −1.08821 | + | 0.362738i | ||||
\(191\) | −9.48683 | −0.686443 | −0.343222 | − | 0.939254i | \(-0.611518\pi\) | ||||
−0.343222 | + | 0.939254i | \(0.611518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.00000 | + | 1.00000i | 0.0719816 | + | 0.0719816i | 0.742181 | − | 0.670199i | \(-0.233791\pi\) |
−0.670199 | + | 0.742181i | \(0.733791\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.00000 | − | 18.9737i | 0.642857 | − | 1.35526i | ||||
\(197\) | 3.16228 | − | 3.16228i | 0.225303 | − | 0.225303i | −0.585424 | − | 0.810727i | \(-0.699072\pi\) |
0.810727 | + | 0.585424i | \(0.199072\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.48683 | −0.672504 | −0.336252 | − | 0.941772i | \(-0.609159\pi\) | ||||
−0.336252 | + | 0.941772i | \(0.609159\pi\) | |||||||
\(200\) | −1.58114 | + | 11.0680i | −0.111803 | + | 0.782624i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 15.8114 | + | 15.8114i | 1.11249 | + | 1.11249i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.0000i | 0.696733i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.16228 | + | 3.16228i | −0.219265 | + | 0.219265i | ||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.00000 | 0.550743 | 0.275371 | − | 0.961338i | \(-0.411199\pi\) | ||||
0.275371 | + | 0.961338i | \(0.411199\pi\) | |||||||
\(212\) | −9.48683 | + | 9.48683i | −0.651558 | + | 0.651558i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 30.0000i | − | 2.05076i | ||||||
\(215\) | −6.00000 | − | 18.0000i | −0.409197 | − | 1.22759i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.83772 | − | 8.16228i | 0.124753 | − | 0.554092i | ||||
\(218\) | −6.32456 | − | 6.32456i | −0.428353 | − | 0.428353i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.48683 | + | 18.9737i | −0.639602 | + | 1.27920i | ||||
\(221\) | −31.6228 | −2.12718 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.9737 | − | 18.9737i | 1.27057 | − | 1.27057i | 0.324782 | − | 0.945789i | \(-0.394709\pi\) |
0.945789 | − | 0.324782i | \(-0.105291\pi\) | |||||||
\(224\) | −15.0000 | + | 9.48683i | −1.00223 | + | 0.633866i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 30.0000 | 1.99557 | ||||||||
\(227\) | 10.0000 | + | 10.0000i | 0.663723 | + | 0.663723i | 0.956256 | − | 0.292532i | \(-0.0944979\pi\) |
−0.292532 | + | 0.956256i | \(0.594498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6491 | 0.835877 | 0.417938 | − | 0.908475i | \(-0.362753\pi\) | ||||
0.417938 | + | 0.908475i | \(0.362753\pi\) | |||||||
\(230\) | 20.0000 | + | 10.0000i | 1.31876 | + | 0.659380i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.48683 | − | 9.48683i | −0.621503 | − | 0.621503i | 0.324413 | − | 0.945916i | \(-0.394833\pi\) |
−0.945916 | + | 0.324413i | \(0.894833\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −40.8114 | − | 9.18861i | −2.64541 | − | 0.595609i | ||||
\(239\) | 22.1359i | 1.43186i | 0.698175 | + | 0.715928i | \(0.253996\pi\) | ||||
−0.698175 | + | 0.715928i | \(0.746004\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 6.32456i | − | 0.407400i | −0.979033 | − | 0.203700i | \(-0.934703\pi\) | ||
0.979033 | − | 0.203700i | \(-0.0652968\pi\) | |||||||
\(242\) | 1.58114 | − | 1.58114i | 0.101639 | − | 0.101639i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 37.9473 | 2.42933 | ||||||||
\(245\) | −9.64911 | − | 12.3246i | −0.616459 | − | 0.787387i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.0000 | − | 10.0000i | 0.636285 | − | 0.636285i | ||||
\(248\) | 5.00000 | − | 5.00000i | 0.317500 | − | 0.317500i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 20.5548 | + | 14.2302i | 1.30000 | + | 0.900000i | ||||
\(251\) | − | 20.0000i | − | 1.26239i | −0.775625 | − | 0.631194i | \(-0.782565\pi\) | ||
0.775625 | − | 0.631194i | \(-0.217435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.0000 | + | 10.0000i | 0.628695 | + | 0.628695i | ||||
\(254\) | − | 37.9473i | − | 2.38103i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.00000 | −0.562500 | ||||||||
\(257\) | −5.00000 | − | 5.00000i | −0.311891 | − | 0.311891i | 0.533751 | − | 0.845642i | \(-0.320782\pi\) |
−0.845642 | + | 0.533751i | \(0.820782\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.48683 | + | 6.00000i | −0.589483 | + | 0.372822i | ||||
\(260\) | −9.48683 | − | 28.4605i | −0.588348 | − | 1.76505i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.32456 | + | 6.32456i | 0.389989 | + | 0.389989i | 0.874683 | − | 0.484695i | \(-0.161069\pi\) |
−0.484695 | + | 0.874683i | \(0.661069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.16228 | + | 9.48683i | 0.194257 | + | 0.582772i | ||||
\(266\) | 15.8114 | − | 10.0000i | 0.969458 | − | 0.613139i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −24.0000 | − | 24.0000i | −1.46603 | − | 1.46603i | ||||
\(269\) | 30.0000 | 1.82913 | 0.914566 | − | 0.404436i | \(-0.132532\pi\) | ||||
0.914566 | + | 0.404436i | \(0.132532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.1359i | 1.34466i | 0.740250 | + | 0.672331i | \(0.234707\pi\) | ||||
−0.740250 | + | 0.672331i | \(0.765293\pi\) | |||||||
\(272\) | 5.00000 | + | 5.00000i | 0.303170 | + | 0.303170i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000i | 0.604122i | ||||||||
\(275\) | 9.48683 | + | 12.6491i | 0.572078 | + | 0.762770i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00000 | − | 3.00000i | 0.180253 | − | 0.180253i | −0.611213 | − | 0.791466i | \(-0.709318\pi\) |
0.791466 | + | 0.611213i | \(0.209318\pi\) | |||||||
\(278\) | −15.0000 | + | 15.0000i | −0.899640 | + | 0.899640i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.32456 | − | 13.1623i | −0.0791573 | − | 0.786597i | ||||
\(281\) | 18.9737 | 1.13187 | 0.565937 | − | 0.824448i | \(-0.308515\pi\) | ||||
0.565937 | + | 0.824448i | \(0.308515\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(284\) | − | 28.4605i | − | 1.68882i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 31.6228i | − | 1.86989i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 33.0000i | 1.94118i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −28.4605 | − | 28.4605i | −1.66552 | − | 1.66552i | ||||
\(293\) | 5.00000 | − | 5.00000i | 0.292103 | − | 0.292103i | −0.545807 | − | 0.837911i | \(-0.683777\pi\) |
0.837911 | + | 0.545807i | \(0.183777\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.48683 | −0.551411 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 30.0000 | + | 30.0000i | 1.73785 | + | 1.73785i | ||||
\(299\) | −20.0000 | −1.15663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0000 | + | 18.9737i | 0.691669 | + | 1.09362i | ||||
\(302\) | 18.9737 | − | 18.9737i | 1.09181 | − | 1.09181i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.16228 | −0.181369 | ||||||||
\(305\) | 12.6491 | − | 25.2982i | 0.724286 | − | 1.44857i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.48683 | − | 9.48683i | −0.541442 | − | 0.541442i | 0.382509 | − | 0.923952i | \(-0.375060\pi\) |
−0.923952 | + | 0.382509i | \(0.875060\pi\) | |||||||
\(308\) | 5.51317 | − | 24.4868i | 0.314142 | − | 1.39527i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.00000 | − | 15.0000i | −0.283981 | − | 0.851943i | ||||
\(311\) | 20.0000i | 1.13410i | 0.823685 | + | 0.567048i | \(0.191915\pi\) | ||||
−0.823685 | + | 0.567048i | \(0.808085\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.48683 | + | 9.48683i | −0.536228 | + | 0.536228i | −0.922419 | − | 0.386191i | \(-0.873790\pi\) |
0.386191 | + | 0.922419i | \(0.373790\pi\) | |||||||
\(314\) | 50.0000 | 2.82166 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0000 | −0.675053 | ||||||||
\(317\) | −22.1359 | + | 22.1359i | −1.24328 | + | 1.24328i | −0.284646 | + | 0.958633i | \(0.591876\pi\) |
−0.958633 | + | 0.284646i | \(0.908124\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −13.0000 | + | 26.0000i | −0.726722 | + | 1.45344i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −25.8114 | − | 5.81139i | −1.43841 | − | 0.323856i | ||||
\(323\) | −15.8114 | − | 15.8114i | −0.879769 | − | 0.879769i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.1359 | − | 3.16228i | −1.22788 | − | 0.175412i | ||||
\(326\) | 18.9737 | 1.05085 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.0000 | −0.659580 | −0.329790 | − | 0.944054i | \(-0.606978\pi\) | ||||
−0.329790 | + | 0.944054i | \(0.606978\pi\) | |||||||
\(332\) | 30.0000 | + | 30.0000i | 1.64646 | + | 1.64646i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 31.6228 | 1.73032 | ||||||||
\(335\) | −24.0000 | + | 8.00000i | −1.31126 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.00000 | − | 7.00000i | 0.381314 | − | 0.381314i | −0.490261 | − | 0.871576i | \(-0.663099\pi\) |
0.871576 | + | 0.490261i | \(0.163099\pi\) | |||||||
\(338\) | 11.0680 | + | 11.0680i | 0.602018 | + | 0.602018i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −45.0000 | + | 15.0000i | −2.44047 | + | 0.813489i | ||||
\(341\) | − | 10.0000i | − | 0.541530i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.5811 | + | 11.4189i | 0.787307 | + | 0.616561i | ||||
\(344\) | 18.9737i | 1.02299i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 15.8114i | − | 0.850026i | ||||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.6491 | 0.677091 | 0.338546 | − | 0.940950i | \(-0.390065\pi\) | ||||
0.338546 | + | 0.940950i | \(0.390065\pi\) | |||||||
\(350\) | −27.6491 | − | 10.5132i | −1.47791 | − | 0.561952i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −15.0000 | + | 15.0000i | −0.799503 | + | 0.799503i | ||||
\(353\) | 15.0000 | − | 15.0000i | 0.798369 | − | 0.798369i | −0.184469 | − | 0.982838i | \(-0.559057\pi\) |
0.982838 | + | 0.184469i | \(0.0590565\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.9737 | − | 9.48683i | −1.00702 | − | 0.503509i | ||||
\(356\) | − | 30.0000i | − | 1.59000i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.0000 | − | 15.0000i | −0.792775 | − | 0.792775i | ||||
\(359\) | − | 22.1359i | − | 1.16829i | −0.811649 | − | 0.584145i | \(-0.801430\pi\) | ||
0.811649 | − | 0.584145i | \(-0.198570\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 10.0000 | + | 10.0000i | 0.525588 | + | 0.525588i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.9737 | + | 30.0000i | 0.994490 | + | 1.57243i | ||||
\(365\) | −28.4605 | + | 9.48683i | −1.48969 | + | 0.496564i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.32456 | − | 6.32456i | −0.330139 | − | 0.330139i | 0.522500 | − | 0.852639i | \(-0.324999\pi\) |
−0.852639 | + | 0.522500i | \(0.824999\pi\) | |||||||
\(368\) | 3.16228 | + | 3.16228i | 0.164845 | + | 0.164845i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.48683 | + | 18.9737i | −0.493197 | + | 0.986394i | ||||
\(371\) | −6.32456 | − | 10.0000i | −0.328355 | − | 0.519174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.00000 | + | 9.00000i | 0.466002 | + | 0.466002i | 0.900617 | − | 0.434614i | \(-0.143115\pi\) |
−0.434614 | + | 0.900617i | \(0.643115\pi\) | |||||||
\(374\) | −50.0000 | −2.58544 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.00000i | 0.205466i | 0.994709 | + | 0.102733i | \(0.0327588\pi\) | ||||
−0.994709 | + | 0.102733i | \(0.967241\pi\) | |||||||
\(380\) | 9.48683 | − | 18.9737i | 0.486664 | − | 0.973329i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 15.0000 | − | 15.0000i | 0.767467 | − | 0.767467i | ||||
\(383\) | 10.0000 | − | 10.0000i | 0.510976 | − | 0.510976i | −0.403849 | − | 0.914825i | \(-0.632328\pi\) |
0.914825 | + | 0.403849i | \(0.132328\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.4868 | − | 11.8377i | −0.738317 | − | 0.603306i | ||||
\(386\) | −3.16228 | −0.160956 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.48683 | + | 9.48683i | −0.481621 | + | 0.481621i | ||||
\(389\) | 6.32456i | 0.320668i | 0.987063 | + | 0.160334i | \(0.0512571\pi\) | ||||
−0.987063 | + | 0.160334i | \(0.948743\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.6228i | 1.59923i | ||||||||
\(392\) | 5.25658 | + | 14.7434i | 0.265498 | + | 0.744655i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0000i | 0.503793i | ||||||||
\(395\) | −4.00000 | + | 8.00000i | −0.201262 | + | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.48683 | − | 9.48683i | −0.476130 | − | 0.476130i | 0.427761 | − | 0.903892i | \(-0.359302\pi\) |
−0.903892 | + | 0.427761i | \(0.859302\pi\) | |||||||
\(398\) | 15.0000 | − | 15.0000i | 0.751882 | − | 0.751882i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 12.6491 | 0.631666 | 0.315833 | − | 0.948815i | \(-0.397716\pi\) | ||||
0.315833 | + | 0.948815i | \(0.397716\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.0000 | + | 10.0000i | 0.498135 | + | 0.498135i | ||||
\(404\) | −30.0000 | −1.49256 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.48683 | + | 9.48683i | −0.470245 | + | 0.470245i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.2982 | 1.25092 | 0.625458 | − | 0.780258i | \(-0.284912\pi\) | ||||
0.625458 | + | 0.780258i | \(0.284912\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.48683 | − | 9.48683i | −0.467383 | − | 0.467383i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.0000 | − | 10.0000i | 1.47264 | − | 0.490881i | ||||
\(416\) | − | 30.0000i | − | 1.47087i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.8114 | − | 15.8114i | 0.773360 | − | 0.773360i | ||||
\(419\) | −20.0000 | −0.977064 | −0.488532 | − | 0.872546i | \(-0.662467\pi\) | ||||
−0.488532 | + | 0.872546i | \(0.662467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.00000 | −0.389896 | −0.194948 | − | 0.980814i | \(-0.562454\pi\) | ||||
−0.194948 | + | 0.980814i | \(0.562454\pi\) | |||||||
\(422\) | −12.6491 | + | 12.6491i | −0.615749 | + | 0.615749i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 10.0000i | − | 0.485643i | ||||||
\(425\) | −5.00000 | + | 35.0000i | −0.242536 | + | 1.69775i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.35089 | + | 32.6491i | −0.355734 | + | 1.58000i | ||||
\(428\) | 28.4605 | + | 28.4605i | 1.37569 | + | 1.37569i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 37.9473 | + | 18.9737i | 1.82998 | + | 0.914991i | ||||
\(431\) | −22.1359 | −1.06625 | −0.533125 | − | 0.846036i | \(-0.678983\pi\) | ||||
−0.533125 | + | 0.846036i | \(0.678983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.48683 | + | 9.48683i | −0.455908 | + | 0.455908i | −0.897310 | − | 0.441402i | \(-0.854481\pi\) |
0.441402 | + | 0.897310i | \(0.354481\pi\) | |||||||
\(434\) | 10.0000 | + | 15.8114i | 0.480015 | + | 0.758971i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.0000 | 0.574696 | ||||||||
\(437\) | −10.0000 | − | 10.0000i | −0.478365 | − | 0.478365i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.16228 | 0.150927 | 0.0754636 | − | 0.997149i | \(-0.475956\pi\) | ||||
0.0754636 | + | 0.997149i | \(0.475956\pi\) | |||||||
\(440\) | −5.00000 | − | 15.0000i | −0.238366 | − | 0.715097i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 50.0000 | − | 50.0000i | 2.37826 | − | 2.37826i | ||||
\(443\) | 25.2982 | + | 25.2982i | 1.20195 | + | 1.20195i | 0.973571 | + | 0.228384i | \(0.0733440\pi\) |
0.228384 | + | 0.973571i | \(0.426656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.0000 | − | 10.0000i | −0.948091 | − | 0.474045i | ||||
\(446\) | 60.0000i | 2.84108i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 7.55480 | − | 33.5548i | 0.356931 | − | 1.58532i | ||||
\(449\) | − | 25.2982i | − | 1.19390i | −0.802280 | − | 0.596948i | \(-0.796380\pi\) | ||
0.802280 | − | 0.596948i | \(-0.203620\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −28.4605 | + | 28.4605i | −1.33867 | + | 1.33867i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −31.6228 | −1.48413 | ||||||||
\(455\) | 26.3246 | − | 2.64911i | 1.23411 | − | 0.124192i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.0000 | − | 17.0000i | 0.795226 | − | 0.795226i | −0.187112 | − | 0.982339i | \(-0.559913\pi\) |
0.982339 | + | 0.187112i | \(0.0599128\pi\) | |||||||
\(458\) | −20.0000 | + | 20.0000i | −0.934539 | + | 0.934539i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −28.4605 | + | 9.48683i | −1.32698 | + | 0.442326i | ||||
\(461\) | − | 20.0000i | − | 0.931493i | −0.884918 | − | 0.465746i | \(-0.845786\pi\) | ||
0.884918 | − | 0.465746i | \(-0.154214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | − | 16.0000i | −0.743583 | − | 0.743583i | 0.229683 | − | 0.973266i | \(-0.426231\pi\) |
−0.973266 | + | 0.229683i | \(0.926231\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.0000 | 1.38972 | ||||||||
\(467\) | 10.0000 | + | 10.0000i | 0.462745 | + | 0.462745i | 0.899554 | − | 0.436809i | \(-0.143892\pi\) |
−0.436809 | + | 0.899554i | \(0.643892\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.2982 | − | 16.0000i | 1.16816 | − | 0.738811i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.9737 | + | 18.9737i | 0.872410 | + | 0.872410i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.48683 | − | 12.6491i | −0.435286 | − | 0.580381i | ||||
\(476\) | 47.4342 | − | 30.0000i | 2.17414 | − | 1.37505i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −35.0000 | − | 35.0000i | −1.60086 | − | 1.60086i | ||||
\(479\) | −20.0000 | −0.913823 | −0.456912 | − | 0.889512i | \(-0.651044\pi\) | ||||
−0.456912 | + | 0.889512i | \(0.651044\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 18.9737i | − | 0.865125i | ||||||
\(482\) | 10.0000 | + | 10.0000i | 0.455488 | + | 0.455488i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000i | 0.136364i | ||||||||
\(485\) | 3.16228 | + | 9.48683i | 0.143592 | + | 0.430775i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | + | 8.00000i | −0.362515 | + | 0.362515i | −0.864738 | − | 0.502223i | \(-0.832516\pi\) |
0.502223 | + | 0.864738i | \(0.332516\pi\) | |||||||
\(488\) | −20.0000 | + | 20.0000i | −0.905357 | + | 0.905357i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 34.7434 | + | 4.23025i | 1.56955 | + | 0.191103i | ||||
\(491\) | 34.7851 | 1.56983 | 0.784914 | − | 0.619605i | \(-0.212707\pi\) | ||||
0.784914 | + | 0.619605i | \(0.212707\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 31.6228i | 1.42278i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.16228i | − | 0.141990i | ||||||
\(497\) | 24.4868 | + | 5.51317i | 1.09838 | + | 0.247299i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.0000i | − | 0.716258i | −0.933672 | − | 0.358129i | \(-0.883415\pi\) | ||
0.933672 | − | 0.358129i | \(-0.116585\pi\) | |||||||
\(500\) | −33.0000 | + | 6.00000i | −1.47580 | + | 0.268328i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 31.6228 | + | 31.6228i | 1.41139 | + | 1.41139i | ||||
\(503\) | 10.0000 | − | 10.0000i | 0.445878 | − | 0.445878i | −0.448104 | − | 0.893982i | \(-0.647900\pi\) |
0.893982 | + | 0.448104i | \(0.147900\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0000 | + | 20.0000i | −0.444994 | + | 0.889988i | ||||
\(506\) | −31.6228 | −1.40580 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 36.0000 | + | 36.0000i | 1.59724 | + | 1.59724i | ||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.0000 | − | 18.9737i | 1.32712 | − | 0.839346i | ||||
\(512\) | −7.90569 | + | 7.90569i | −0.349386 | + | 0.349386i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15.8114 | 0.697410 | ||||||||
\(515\) | −9.48683 | + | 3.16228i | −0.418040 | + | 0.139347i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.51317 | − | 24.4868i | 0.242235 | − | 1.07589i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 20.0000 | + | 10.0000i | 0.877058 | + | 0.438529i | ||||
\(521\) | 10.0000i | 0.438108i | 0.975713 | + | 0.219054i | \(0.0702971\pi\) | ||||
−0.975713 | + | 0.219054i | \(0.929703\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.48683 | − | 9.48683i | 0.414830 | − | 0.414830i | −0.468587 | − | 0.883417i | \(-0.655237\pi\) |
0.883417 | + | 0.468587i | \(0.155237\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.0000 | −0.872041 | ||||||||
\(527\) | 15.8114 | − | 15.8114i | 0.688755 | − | 0.688755i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 3.00000i | − | 0.130435i | ||||||
\(530\) | −20.0000 | − | 10.0000i | −0.868744 | − | 0.434372i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.51317 | + | 24.4868i | −0.239026 | + | 1.06164i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 28.4605 | − | 9.48683i | 1.23045 | − | 0.410152i | ||||
\(536\) | 25.2982 | 1.09272 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −47.4342 | + | 47.4342i | −2.04503 | + | 2.04503i | ||||
\(539\) | 20.0000 | + | 9.48683i | 0.861461 | + | 0.408627i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.0000 | −0.773880 | −0.386940 | − | 0.922105i | \(-0.626468\pi\) | ||||
−0.386940 | + | 0.922105i | \(0.626468\pi\) | |||||||
\(542\) | −35.0000 | − | 35.0000i | −1.50338 | − | 1.50338i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −47.4342 | −2.03372 | ||||||||
\(545\) | 4.00000 | − | 8.00000i | 0.171341 | − | 0.342682i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | − | 8.00000i | 0.342055 | − | 0.342055i | −0.515084 | − | 0.857140i | \(-0.672239\pi\) |
0.857140 | + | 0.515084i | \(0.172239\pi\) | |||||||
\(548\) | −9.48683 | − | 9.48683i | −0.405257 | − | 0.405257i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −35.0000 | − | 5.00000i | −1.49241 | − | 0.213201i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.32456 | − | 10.3246i | 0.0988501 | − | 0.439045i | ||||
\(554\) | 9.48683i | 0.403057i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 28.4605i | − | 1.20699i | ||||||
\(557\) | 9.48683 | − | 9.48683i | 0.401970 | − | 0.401970i | −0.476957 | − | 0.878927i | \(-0.658260\pi\) |
0.878927 | + | 0.476957i | \(0.158260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.9473 | −1.60500 | ||||||||
\(560\) | −4.58114 | − | 3.74342i | −0.193588 | − | 0.158188i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −30.0000 | + | 30.0000i | −1.26547 | + | 1.26547i | ||||
\(563\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.48683 | + | 28.4605i | 0.399114 | + | 1.19734i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.0000 | + | 15.0000i | 0.629386 | + | 0.629386i | ||||
\(569\) | 12.6491i | 0.530278i | 0.964210 | + | 0.265139i | \(0.0854179\pi\) | ||||
−0.964210 | + | 0.265139i | \(0.914582\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.00000 | −0.334790 | −0.167395 | − | 0.985890i | \(-0.553535\pi\) | ||||
−0.167395 | + | 0.985890i | \(0.553535\pi\) | |||||||
\(572\) | 30.0000 | + | 30.0000i | 1.25436 | + | 1.25436i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.16228 | + | 22.1359i | −0.131876 | + | 0.923133i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.1359 | + | 22.1359i | 0.921531 | + | 0.921531i | 0.997138 | − | 0.0756064i | \(-0.0240892\pi\) |
−0.0756064 | + | 0.997138i | \(0.524089\pi\) | |||||||
\(578\) | −52.1776 | − | 52.1776i | −2.17030 | − | 2.17030i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.6228 | + | 20.0000i | −1.31193 | + | 0.829740i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0000 | − | 10.0000i | −0.414158 | − | 0.414158i | ||||
\(584\) | 30.0000 | 1.24141 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.8114i | 0.653162i | ||||||||
\(587\) | −20.0000 | − | 20.0000i | −0.825488 | − | 0.825488i | 0.161401 | − | 0.986889i | \(-0.448399\pi\) |
−0.986889 | + | 0.161401i | \(0.948399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0000i | 0.412043i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.00000 | + | 3.00000i | −0.123299 | + | 0.123299i | ||||
\(593\) | −25.0000 | + | 25.0000i | −1.02663 | + | 1.02663i | −0.0269913 | + | 0.999636i | \(0.508593\pi\) |
−0.999636 | + | 0.0269913i | \(0.991407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.18861 | − | 41.6228i | −0.171716 | − | 1.70637i | ||||
\(596\) | −56.9210 | −2.33157 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 31.6228 | − | 31.6228i | 1.29315 | − | 1.29315i | ||||
\(599\) | − | 15.8114i | − | 0.646036i | −0.946393 | − | 0.323018i | \(-0.895303\pi\) | ||
0.946393 | − | 0.323018i | \(-0.104697\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 31.6228i | − | 1.28992i | −0.764216 | − | 0.644960i | \(-0.776874\pi\) | ||
0.764216 | − | 0.644960i | \(-0.223126\pi\) | |||||||
\(602\) | −48.9737 | − | 11.0263i | −1.99602 | − | 0.449400i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.0000i | 1.46482i | ||||||||
\(605\) | 2.00000 | + | 1.00000i | 0.0813116 | + | 0.0406558i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.9737 | − | 18.9737i | −0.770117 | − | 0.770117i | 0.208009 | − | 0.978127i | \(-0.433302\pi\) |
−0.978127 | + | 0.208009i | \(0.933302\pi\) | |||||||
\(608\) | 15.0000 | − | 15.0000i | 0.608330 | − | 0.608330i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 20.0000 | + | 60.0000i | 0.809776 | + | 2.42933i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00000 | − | 1.00000i | −0.0403896 | − | 0.0403896i | 0.686624 | − | 0.727013i | \(-0.259092\pi\) |
−0.727013 | + | 0.686624i | \(0.759092\pi\) | |||||||
\(614\) | 30.0000 | 1.21070 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.0000 | + | 15.8114i | 0.402911 | + | 0.637059i | ||||
\(617\) | 15.8114 | − | 15.8114i | 0.636543 | − | 0.636543i | −0.313158 | − | 0.949701i | \(-0.601387\pi\) |
0.949701 | + | 0.313158i | \(0.101387\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.16228 | −0.127103 | −0.0635513 | − | 0.997979i | \(-0.520243\pi\) | ||||
−0.0635513 | + | 0.997979i | \(0.520243\pi\) | |||||||
\(620\) | 18.9737 | + | 9.48683i | 0.762001 | + | 0.381000i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −31.6228 | − | 31.6228i | −1.26796 | − | 1.26796i | ||||
\(623\) | 25.8114 | + | 5.81139i | 1.03411 | + | 0.232828i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | − | 30.0000i | − | 1.19904i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −47.4342 | + | 47.4342i | −1.89283 | + | 1.89283i | ||||
\(629\) | −30.0000 | −1.19618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.0000 | −1.11466 | −0.557331 | − | 0.830290i | \(-0.688175\pi\) | ||||
−0.557331 | + | 0.830290i | \(0.688175\pi\) | |||||||
\(632\) | 6.32456 | − | 6.32456i | 0.251577 | − | 0.251577i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 70.0000i | − | 2.78006i | ||||||
\(635\) | 36.0000 | − | 12.0000i | 1.42862 | − | 0.476205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.4868 | + | 10.5132i | −1.16831 | + | 0.416547i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.0680 | − | 33.2039i | −0.437500 | − | 1.31250i | ||||
\(641\) | 31.6228 | 1.24902 | 0.624512 | − | 0.781015i | \(-0.285298\pi\) | ||||
0.624512 | + | 0.781015i | \(0.285298\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.48683 | + | 9.48683i | −0.374124 | + | 0.374124i | −0.868977 | − | 0.494853i | \(-0.835222\pi\) |
0.494853 | + | 0.868977i | \(0.335222\pi\) | |||||||
\(644\) | 30.0000 | − | 18.9737i | 1.18217 | − | 0.747667i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 50.0000 | 1.96722 | ||||||||
\(647\) | 10.0000 | + | 10.0000i | 0.393141 | + | 0.393141i | 0.875805 | − | 0.482665i | \(-0.160331\pi\) |
−0.482665 | + | 0.875805i | \(0.660331\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 40.0000 | − | 30.0000i | 1.56893 | − | 1.17670i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.0000 | + | 18.0000i | −0.704934 | + | 0.704934i | ||||
\(653\) | −15.8114 | − | 15.8114i | −0.618747 | − | 0.618747i | 0.326463 | − | 0.945210i | \(-0.394143\pi\) |
−0.945210 | + | 0.326463i | \(0.894143\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 41.1096i | − | 1.60140i | −0.599064 | − | 0.800702i | \(-0.704460\pi\) | ||
0.599064 | − | 0.800702i | \(-0.295540\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.6491i | 0.491993i | 0.969271 | + | 0.245997i | \(0.0791152\pi\) | ||||
−0.969271 | + | 0.245997i | \(0.920885\pi\) | |||||||
\(662\) | 18.9737 | − | 18.9737i | 0.737432 | − | 0.737432i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31.6228 | −1.22720 | ||||||||
\(665\) | 14.4868 | + | 11.8377i | 0.561775 | + | 0.459047i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −30.0000 | + | 30.0000i | −1.16073 | + | 1.16073i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 25.2982 | − | 50.5964i | 0.977356 | − | 1.95471i | ||||
\(671\) | 40.0000i | 1.54418i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.00000 | − | 9.00000i | −0.346925 | − | 0.346925i | 0.512038 | − | 0.858963i | \(-0.328891\pi\) |
−0.858963 | + | 0.512038i | \(0.828891\pi\) | |||||||
\(674\) | 22.1359i | 0.852645i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −21.0000 | −0.807692 | ||||||||
\(677\) | −15.0000 | − | 15.0000i | −0.576497 | − | 0.576497i | 0.357439 | − | 0.933936i | \(-0.383650\pi\) |
−0.933936 | + | 0.357439i | \(0.883650\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.32456 | − | 10.0000i | −0.242714 | − | 0.383765i | ||||
\(680\) | 15.8114 | − | 31.6228i | 0.606339 | − | 1.21268i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.8114 | + | 15.8114i | 0.605449 | + | 0.605449i | ||||
\(683\) | 12.6491 | + | 12.6491i | 0.484005 | + | 0.484005i | 0.906408 | − | 0.422403i | \(-0.138813\pi\) |
−0.422403 | + | 0.906408i | \(0.638813\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.48683 | + | 3.16228i | −0.362473 | + | 0.120824i | ||||
\(686\) | −41.1096 | + | 5.00000i | −1.56957 | + | 0.190901i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.00000 | + | 6.00000i | 0.228748 | + | 0.228748i | ||||
\(689\) | 20.0000 | 0.761939 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.16228i | − | 0.120299i | −0.998189 | − | 0.0601494i | \(-0.980842\pi\) | ||
0.998189 | − | 0.0601494i | \(-0.0191577\pi\) | |||||||
\(692\) | 15.0000 | + | 15.0000i | 0.570214 | + | 0.570214i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.9737 | − | 9.48683i | −0.719712 | − | 0.359856i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −20.0000 | + | 20.0000i | −0.757011 | + | 0.757011i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 36.2039 | − | 16.2566i | 1.36838 | − | 0.614441i | ||||
\(701\) | 12.6491 | 0.477750 | 0.238875 | − | 0.971050i | \(-0.423221\pi\) | ||||
0.238875 | + | 0.971050i | \(0.423221\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.48683 | − | 9.48683i | 0.357803 | − | 0.357803i | ||||
\(704\) | − | 41.1096i | − | 1.54938i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.4342i | 1.78521i | ||||||||
\(707\) | 5.81139 | − | 25.8114i | 0.218560 | − | 0.970737i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.0000i | 0.901339i | 0.892691 | + | 0.450669i | \(0.148815\pi\) | ||||
−0.892691 | + | 0.450669i | \(0.851185\pi\) | |||||||
\(710\) | 45.0000 | − | 15.0000i | 1.68882 | − | 0.562940i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.8114 | + | 15.8114i | 0.592557 | + | 0.592557i | ||||
\(713\) | 10.0000 | − | 10.0000i | 0.374503 | − | 0.374503i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.0000 | − | 10.0000i | 1.12194 | − | 0.373979i | ||||
\(716\) | 28.4605 | 1.06362 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.0000 | + | 35.0000i | 1.30619 | + | 1.30619i | ||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0000 | − | 6.32456i | 0.372419 | − | 0.235539i | ||||
\(722\) | 14.2302 | − | 14.2302i | 0.529595 | − | 0.529595i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.9737 | −0.705151 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.9737 | + | 18.9737i | 0.703694 | + | 0.703694i | 0.965202 | − | 0.261507i | \(-0.0842195\pi\) |
−0.261507 | + | 0.965202i | \(0.584220\pi\) | |||||||
\(728\) | −25.8114 | − | 5.81139i | −0.956634 | − | 0.215384i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 30.0000 | − | 60.0000i | 1.11035 | − | 2.22070i | ||||
\(731\) | 60.0000i | 2.21918i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.8114 | − | 15.8114i | 0.584007 | − | 0.584007i | −0.351995 | − | 0.936002i | \(-0.614497\pi\) |
0.936002 | + | 0.351995i | \(0.114497\pi\) | |||||||
\(734\) | 20.0000 | 0.738213 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30.0000 | −1.10581 | ||||||||
\(737\) | 25.2982 | − | 25.2982i | 0.931872 | − | 0.931872i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 44.0000i | − | 1.61857i | −0.587419 | − | 0.809283i | \(-0.699856\pi\) | ||
0.587419 | − | 0.809283i | \(-0.300144\pi\) | |||||||
\(740\) | −9.00000 | − | 27.0000i | −0.330847 | − | 0.992540i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 25.8114 | + | 5.81139i | 0.947566 | + | 0.213343i | ||||
\(743\) | −18.9737 | − | 18.9737i | −0.696076 | − | 0.696076i | 0.267486 | − | 0.963562i | \(-0.413807\pi\) |
−0.963562 | + | 0.267486i | \(0.913807\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.9737 | + | 37.9473i | −0.695141 | + | 1.39028i | ||||
\(746\) | −28.4605 | −1.04201 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 47.4342 | − | 47.4342i | 1.73436 | − | 1.73436i | ||||
\(749\) | −30.0000 | + | 18.9737i | −1.09618 | + | 0.693283i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.0000 | + | 12.0000i | 0.873449 | + | 0.436725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0000 | − | 17.0000i | 0.617876 | − | 0.617876i | −0.327111 | − | 0.944986i | \(-0.606075\pi\) |
0.944986 | + | 0.327111i | \(0.106075\pi\) | |||||||
\(758\) | −6.32456 | − | 6.32456i | −0.229718 | − | 0.229718i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.00000 | + | 15.0000i | 0.181369 | + | 0.544107i | ||||
\(761\) | 20.0000i | 0.724999i | 0.931984 | + | 0.362500i | \(0.118077\pi\) | ||||
−0.931984 | + | 0.362500i | \(0.881923\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.32456 | + | 10.3246i | −0.0841546 | + | 0.373774i | ||||
\(764\) | 28.4605i | 1.02966i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.6228i | 1.14258i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.32456 | −0.228069 | −0.114035 | − | 0.993477i | \(-0.536377\pi\) | ||||
−0.114035 | + | 0.993477i | \(0.536377\pi\) | |||||||
\(770\) | 41.6228 | − | 4.18861i | 1.49998 | − | 0.150947i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.00000 | − | 3.00000i | 0.107972 | − | 0.107972i | ||||
\(773\) | 35.0000 | − | 35.0000i | 1.25886 | − | 1.25886i | 0.307226 | − | 0.951637i | \(-0.400599\pi\) |
0.951637 | − | 0.307226i | \(-0.0994007\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.6491 | − | 9.48683i | 0.454369 | − | 0.340777i | ||||
\(776\) | − | 10.0000i | − | 0.358979i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0000 | − | 10.0000i | −0.358517 | − | 0.358517i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0000 | 1.07348 | ||||||||
\(782\) | −50.0000 | − | 50.0000i | −1.78800 | − | 1.78800i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.32456 | + | 3.00000i | 0.225877 | + | 0.107143i | ||||
\(785\) | 15.8114 | + | 47.4342i | 0.564333 | + | 1.69300i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8114 | + | 15.8114i | 0.563615 | + | 0.563615i | 0.930332 | − | 0.366717i | \(-0.119518\pi\) |
−0.366717 | + | 0.930332i | \(0.619518\pi\) | |||||||
\(788\) | −9.48683 | − | 9.48683i | −0.337954 | − | 0.337954i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.32456 | − | 18.9737i | −0.225018 | − | 0.675053i | ||||
\(791\) | −18.9737 | − | 30.0000i | −0.674626 | − | 1.06668i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.0000 | − | 40.0000i | −1.42044 | − | 1.42044i | ||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.4605i | 1.00876i | ||||||||
\(797\) | −25.0000 | − | 25.0000i | −0.885545 | − | 0.885545i | 0.108546 | − | 0.994091i | \(-0.465381\pi\) |
−0.994091 | + | 0.108546i | \(0.965381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −33.2039 | − | 4.74342i | −1.17394 | − | 0.167705i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −20.0000 | + | 20.0000i | −0.706225 | + | 0.706225i | ||||
\(803\) | 30.0000 | − | 30.0000i | 1.05868 | − | 1.05868i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.64911 | − | 26.3246i | −0.0933689 | − | 0.927819i | ||||
\(806\) | −31.6228 | −1.11386 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.8114 | − | 15.8114i | 0.556243 | − | 0.556243i | ||||
\(809\) | 18.9737i | 0.667079i | 0.942736 | + | 0.333539i | \(0.108243\pi\) | ||||
−0.942736 | + | 0.333539i | \(0.891757\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 47.4342i | 1.66564i | 0.553545 | + | 0.832819i | \(0.313275\pi\) | ||||
−0.553545 | + | 0.832819i | \(0.686725\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 30.0000i | − | 1.05150i | ||||||
\(815\) | 6.00000 | + | 18.0000i | 0.210171 | + | 0.630512i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.9737 | − | 18.9737i | −0.663805 | − | 0.663805i | ||||
\(818\) | −40.0000 | + | 40.0000i | −1.39857 | + | 1.39857i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.6491 | −0.441457 | −0.220729 | − | 0.975335i | \(-0.570843\pi\) | ||||
−0.220729 | + | 0.975335i | \(0.570843\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000 | + | 24.0000i | 0.836587 | + | 0.836587i | 0.988408 | − | 0.151821i | \(-0.0485136\pi\) |
−0.151821 | + | 0.988408i | \(0.548514\pi\) | |||||||
\(824\) | 10.0000 | 0.348367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −22.1359 | + | 22.1359i | −0.769742 | + | 0.769742i | −0.978061 | − | 0.208319i | \(-0.933201\pi\) |
0.208319 | + | 0.978061i | \(0.433201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.9737 | 0.658983 | 0.329491 | − | 0.944159i | \(-0.393123\pi\) | ||||
0.329491 | + | 0.944159i | \(0.393123\pi\) | |||||||
\(830\) | −31.6228 | + | 63.2456i | −1.09764 | + | 2.19529i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 41.1096 | + | 41.1096i | 1.42522 | + | 1.42522i | ||||
\(833\) | 16.6228 | + | 46.6228i | 0.575945 | + | 1.61538i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.0000 | + | 30.0000i | 0.346064 | + | 1.03819i | ||||
\(836\) | 30.0000i | 1.03757i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 31.6228 | − | 31.6228i | 1.09239 | − | 1.09239i | ||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 12.6491 | − | 12.6491i | 0.435917 | − | 0.435917i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 24.0000i | − | 0.826114i | ||||||
\(845\) | −7.00000 | + | 14.0000i | −0.240807 | + | 0.481615i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.58114 | − | 0.581139i | −0.0886890 | − | 0.0199682i | ||||
\(848\) | −3.16228 | − | 3.16228i | −0.108593 | − | 0.108593i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −47.4342 | − | 63.2456i | −1.62698 | − | 2.16930i | ||||
\(851\) | −18.9737 | −0.650409 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.48683 | − | 9.48683i | 0.324823 | − | 0.324823i | −0.525791 | − | 0.850614i | \(-0.676231\pi\) |
0.850614 | + | 0.525791i | \(0.176231\pi\) | |||||||
\(854\) | −40.0000 | − | 63.2456i | −1.36877 | − | 2.16422i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.0000 | −1.02538 | ||||||||
\(857\) | 5.00000 | + | 5.00000i | 0.170797 | + | 0.170797i | 0.787329 | − | 0.616533i | \(-0.211463\pi\) |
−0.616533 | + | 0.787329i | \(0.711463\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.1359 | −0.755269 | −0.377634 | − | 0.925955i | \(-0.623262\pi\) | ||||
−0.377634 | + | 0.925955i | \(0.623262\pi\) | |||||||
\(860\) | −54.0000 | + | 18.0000i | −1.84138 | + | 0.613795i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 35.0000 | − | 35.0000i | 1.19210 | − | 1.19210i | ||||
\(863\) | −15.8114 | − | 15.8114i | −0.538226 | − | 0.538226i | 0.384782 | − | 0.923008i | \(-0.374277\pi\) |
−0.923008 | + | 0.384782i | \(0.874277\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15.0000 | − | 5.00000i | 0.510015 | − | 0.170005i | ||||
\(866\) | − | 30.0000i | − | 1.01944i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −24.4868 | − | 5.51317i | −0.831137 | − | 0.187129i | ||||
\(869\) | − | 12.6491i | − | 0.429092i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.5964i | 1.71440i | ||||||||
\(872\) | −6.32456 | + | 6.32456i | −0.214176 | + | 0.214176i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 31.6228 | 1.06966 | ||||||||
\(875\) | 1.23025 | − | 29.5548i | 0.0415900 | − | 0.999135i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0000 | − | 23.0000i | 0.776655 | − | 0.776655i | −0.202606 | − | 0.979260i | \(-0.564941\pi\) |
0.979260 | + | 0.202606i | \(0.0649409\pi\) | |||||||
\(878\) | −5.00000 | + | 5.00000i | −0.168742 | + | 0.168742i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.32456 | − | 3.16228i | −0.213201 | − | 0.106600i | ||||
\(881\) | 30.0000i | 1.01073i | 0.862907 | + | 0.505363i | \(0.168641\pi\) | ||||
−0.862907 | + | 0.505363i | \(0.831359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0000 | + | 36.0000i | 1.21150 | + | 1.21150i | 0.970535 | + | 0.240962i | \(0.0774629\pi\) |
0.240962 | + | 0.970535i | \(0.422537\pi\) | |||||||
\(884\) | 94.8683i | 3.19077i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −80.0000 | −2.68765 | ||||||||
\(887\) | −20.0000 | − | 20.0000i | −0.671534 | − | 0.671534i | 0.286535 | − | 0.958070i | \(-0.407496\pi\) |
−0.958070 | + | 0.286535i | \(0.907496\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.9473 | + | 24.0000i | −1.27271 | + | 0.804934i | ||||
\(890\) | 47.4342 | − | 15.8114i | 1.59000 | − | 0.529999i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −56.9210 | − | 56.9210i | −1.90586 | − | 1.90586i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.48683 | − | 18.9737i | 0.317110 | − | 0.634220i | ||||
\(896\) | 22.1359 | + | 35.0000i | 0.739510 | + | 1.16927i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.0000 | + | 40.0000i | 1.33482 | + | 1.33482i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 31.6228i | − | 1.05351i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 30.0000i | − | 0.997785i | ||||||
\(905\) | −6.32456 | + | 12.6491i | −0.210235 | + | 0.420471i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.00000 | + | 8.00000i | −0.265636 | + | 0.265636i | −0.827339 | − | 0.561703i | \(-0.810146\pi\) |
0.561703 | + | 0.827339i | \(0.310146\pi\) | |||||||
\(908\) | 30.0000 | − | 30.0000i | 0.995585 | − | 0.995585i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −37.4342 | + | 45.8114i | −1.24093 | + | 1.51863i | ||||
\(911\) | 28.4605 | 0.942938 | 0.471469 | − | 0.881883i | \(-0.343724\pi\) | ||||
0.471469 | + | 0.881883i | \(0.343724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −31.6228 | + | 31.6228i | −1.04656 | + | 1.04656i | ||||
\(914\) | 53.7587i | 1.77818i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 37.9473i | − | 1.25382i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.0000i | 0.791687i | 0.918318 | + | 0.395843i | \(0.129548\pi\) | ||||
−0.918318 | + | 0.395843i | \(0.870452\pi\) | |||||||
\(920\) | 10.0000 | − | 20.0000i | 0.329690 | − | 0.659380i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 31.6228 | + | 31.6228i | 1.04144 | + | 1.04144i | ||||
\(923\) | −30.0000 | + | 30.0000i | −0.987462 | + | 0.987462i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.0000 | − | 3.00000i | −0.690476 | − | 0.0986394i | ||||
\(926\) | 50.5964 | 1.66270 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.0000 | −0.656179 | −0.328089 | − | 0.944647i | \(-0.606405\pi\) | ||||
−0.328089 | + | 0.944647i | \(0.606405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.0000 | − | 9.48683i | −0.655474 | − | 0.310918i | ||||
\(932\) | −28.4605 | + | 28.4605i | −0.932255 | + | 0.932255i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −31.6228 | −1.03473 | ||||||||
\(935\) | −15.8114 | − | 47.4342i | −0.517088 | − | 1.55126i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.48683 | + | 9.48683i | 0.309921 | + | 0.309921i | 0.844879 | − | 0.534958i | \(-0.179672\pi\) |
−0.534958 | + | 0.844879i | \(0.679672\pi\) | |||||||
\(938\) | −14.7018 | + | 65.2982i | −0.480030 | + | 2.13206i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 60.0000i | − | 1.95594i | −0.208736 | − | 0.977972i | \(-0.566935\pi\) | ||
0.208736 | − | 0.977972i | \(-0.433065\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −60.0000 | −1.95077 | ||||||||
\(947\) | 25.2982 | − | 25.2982i | 0.822082 | − | 0.822082i | −0.164325 | − | 0.986406i | \(-0.552544\pi\) |
0.986406 | + | 0.164325i | \(0.0525444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.0000i | 1.94768i | ||||||||
\(950\) | 35.0000 | + | 5.00000i | 1.13555 | + | 0.162221i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9.18861 | + | 40.8114i | −0.297805 | + | 1.32270i | ||||
\(953\) | 28.4605 | + | 28.4605i | 0.921926 | + | 0.921926i | 0.997165 | − | 0.0752395i | \(-0.0239721\pi\) |
−0.0752395 | + | 0.997165i | \(0.523972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.9737 | + | 9.48683i | 0.613973 | + | 0.306987i | ||||
\(956\) | 66.4078 | 2.14778 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 31.6228 | − | 31.6228i | 1.02169 | − | 1.02169i | ||||
\(959\) | 10.0000 | − | 6.32456i | 0.322917 | − | 0.204231i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | 30.0000 | + | 30.0000i | 0.967239 | + | 0.967239i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.9737 | −0.611101 | ||||||||
\(965\) | −1.00000 | − | 3.00000i | −0.0321911 | − | 0.0965734i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.0000 | + | 42.0000i | −1.35063 | + | 1.35063i | −0.465671 | + | 0.884958i | \(0.654187\pi\) |
−0.884958 | + | 0.465671i | \(0.845813\pi\) | |||||||
\(968\) | −1.58114 | − | 1.58114i | −0.0508197 | − | 0.0508197i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20.0000 | − | 10.0000i | −0.642161 | − | 0.321081i | ||||
\(971\) | − | 20.0000i | − | 0.641831i | −0.947108 | − | 0.320915i | \(-0.896010\pi\) | ||
0.947108 | − | 0.320915i | \(-0.103990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.4868 | + | 5.51317i | 0.785012 | + | 0.176744i | ||||
\(974\) | − | 25.2982i | − | 0.810607i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.6491i | 0.404888i | ||||||||
\(977\) | 3.16228 | − | 3.16228i | 0.101170 | − | 0.101170i | −0.654710 | − | 0.755880i | \(-0.727209\pi\) |
0.755880 | + | 0.654710i | \(0.227209\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.6228 | 1.01067 | ||||||||
\(980\) | −36.9737 | + | 28.9473i | −1.18108 | + | 0.924689i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −55.0000 | + | 55.0000i | −1.75512 | + | 1.75512i | ||||
\(983\) | −20.0000 | + | 20.0000i | −0.637901 | + | 0.637901i | −0.950037 | − | 0.312136i | \(-0.898955\pi\) |
0.312136 | + | 0.950037i | \(0.398955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.48683 | + | 3.16228i | −0.302276 | + | 0.100759i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −30.0000 | − | 30.0000i | −0.954427 | − | 0.954427i | ||||
\(989\) | 37.9473i | 1.20665i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.0000 | 0.889449 | 0.444725 | − | 0.895667i | \(-0.353302\pi\) | ||||
0.444725 | + | 0.895667i | \(0.353302\pi\) | |||||||
\(992\) | 15.0000 | + | 15.0000i | 0.476250 | + | 0.476250i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −47.4342 | + | 30.0000i | −1.50452 | + | 0.951542i | ||||
\(995\) | 18.9737 | + | 9.48683i | 0.601506 | + | 0.300753i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.48683 | − | 9.48683i | −0.300451 | − | 0.300451i | 0.540739 | − | 0.841190i | \(-0.318145\pi\) |
−0.841190 | + | 0.540739i | \(0.818145\pi\) | |||||||
\(998\) | 25.2982 | + | 25.2982i | 0.800801 | + | 0.800801i | ||||
\(999\) | 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 | 315.2.p.a.118.1 | ✓ | 4 | |
3.2 | odd | 2 | 315.2.p.b.118.2 | yes | 4 | ||
5.2 | odd | 4 | 315.2.p.b.307.1 | yes | 4 | ||
7.6 | odd | 2 | 315.2.p.b.118.1 | yes | 4 | ||
15.2 | even | 4 | inner | 315.2.p.a.307.2 | yes | 4 | |
21.20 | even | 2 | inner | 315.2.p.a.118.2 | yes | 4 | |
35.27 | even | 4 | inner | 315.2.p.a.307.1 | yes | 4 | |
105.62 | odd | 4 | 315.2.p.b.307.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.p.a.118.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
315.2.p.a.118.2 | yes | 4 | 21.20 | even | 2 | inner | |
315.2.p.a.307.1 | yes | 4 | 35.27 | even | 4 | inner | |
315.2.p.a.307.2 | yes | 4 | 15.2 | even | 4 | inner | |
315.2.p.b.118.1 | yes | 4 | 7.6 | odd | 2 | ||
315.2.p.b.118.2 | yes | 4 | 3.2 | odd | 2 | ||
315.2.p.b.307.1 | yes | 4 | 5.2 | odd | 4 | ||
315.2.p.b.307.2 | yes | 4 | 105.62 | odd | 4 |