Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3584,1,Mod(13,3584)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3584, base_ring=CyclotomicField(128))
chi = DirichletCharacter(H, H._module([0, 111, 64]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3584.13");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3584 = 2^{9} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3584.cd (of order \(128\), degree \(64\), 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: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Coefficient field: | \(\Q(\zeta_{128})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{64} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{128}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{128} - \cdots)\) |
Embedding invariants
Embedding label | 1469.1 | ||
Root | \(0.0490677 - 0.998795i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3584.1469 |
Dual form | 3584.1.cd.a.405.1 |
$q$-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 \(\left(\mathbb{Z}/3584\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{115}{128}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.242980 | + | 0.970031i | 0.242980 | + | 0.970031i | ||||
\(3\) | 0 | 0 | −0.170962 | − | 0.985278i | \(-0.554688\pi\) | ||||
0.170962 | + | 0.985278i | \(0.445312\pi\) | |||||||
\(4\) | −0.881921 | + | 0.471397i | −0.881921 | + | 0.471397i | ||||
\(5\) | 0 | 0 | 0.949528 | − | 0.313682i | \(-0.101562\pi\) | ||||
−0.949528 | + | 0.313682i | \(0.898438\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0490677 | − | 0.998795i | −0.0490677 | − | 0.998795i | ||||
\(8\) | −0.671559 | − | 0.740951i | −0.671559 | − | 0.740951i | ||||
\(9\) | −0.941544 | + | 0.336890i | −0.941544 | + | 0.336890i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.399485 | + | 0.901225i | 0.399485 | + | 0.901225i | 0.995185 | + | 0.0980171i | \(0.0312500\pi\) |
−0.595699 | + | 0.803208i | \(0.703125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.653173 | − | 0.757209i | \(-0.273438\pi\) | ||||
−0.653173 | + | 0.757209i | \(0.726562\pi\) | |||||||
\(14\) | 0.956940 | − | 0.290285i | 0.956940 | − | 0.290285i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.555570 | − | 0.831470i | 0.555570 | − | 0.831470i | ||||
\(17\) | 0 | 0 | −0.881921 | − | 0.471397i | \(-0.843750\pi\) | ||||
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(18\) | −0.555570 | − | 0.831470i | −0.555570 | − | 0.831470i | ||||
\(19\) | 0 | 0 | 0.492898 | − | 0.870087i | \(-0.335938\pi\) | ||||
−0.492898 | + | 0.870087i | \(0.664062\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.777149 | + | 0.606493i | −0.777149 | + | 0.606493i | ||||
\(23\) | −0.439303 | + | 1.75380i | −0.439303 | + | 1.75380i | 0.195090 | + | 0.980785i | \(0.437500\pi\) |
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.803208 | − | 0.595699i | 0.803208 | − | 0.595699i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.514103 | + | 0.857729i | 0.514103 | + | 0.857729i | ||||
\(29\) | −0.0438416 | + | 1.78591i | −0.0438416 | + | 1.78591i | 0.427555 | + | 0.903989i | \(0.359375\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(32\) | 0.941544 | + | 0.336890i | 0.941544 | + | 0.336890i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.671559 | − | 0.740951i | 0.671559 | − | 0.740951i | ||||
\(37\) | 0.0992117 | + | 0.804387i | 0.0992117 | + | 0.804387i | 0.956940 | + | 0.290285i | \(0.0937500\pi\) |
−0.857729 | + | 0.514103i | \(0.828125\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.803208 | − | 0.595699i | \(-0.796875\pi\) | ||||
0.803208 | + | 0.595699i | \(0.203125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.18427 | + | 0.834055i | −1.18427 | + | 0.834055i | −0.989177 | − | 0.146730i | \(-0.953125\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(44\) | −0.777149 | − | 0.606493i | −0.777149 | − | 0.606493i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.80798 | −1.80798 | ||||||||
\(47\) | 0 | 0 | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) | ||||
−0.0980171 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.995185 | + | 0.0980171i | −0.995185 | + | 0.0980171i | ||||
\(50\) | 0.773010 | + | 0.634393i | 0.773010 | + | 0.634393i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.0262590 | + | 1.06967i | 0.0262590 | + | 1.06967i | 0.857729 | + | 0.514103i | \(0.171875\pi\) |
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.707107 | + | 0.707107i | −0.707107 | + | 0.707107i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.74304 | + | 0.391413i | −1.74304 | + | 0.391413i | ||||
\(59\) | 0 | 0 | 0.757209 | − | 0.653173i | \(-0.226562\pi\) | ||||
−0.757209 | + | 0.653173i | \(0.773438\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.219101 | − | 0.975702i | \(-0.429688\pi\) | ||||
−0.219101 | + | 0.975702i | \(0.570312\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(64\) | −0.0980171 | + | 0.995185i | −0.0980171 | + | 0.995185i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.616112 | − | 0.972947i | −0.616112 | − | 0.972947i | −0.998795 | − | 0.0490677i | \(-0.984375\pi\) |
0.382683 | − | 0.923880i | \(-0.375000\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.39759 | − | 0.661009i | 1.39759 | − | 0.661009i | 0.427555 | − | 0.903989i | \(-0.359375\pi\) |
0.970031 | + | 0.242980i | \(0.0781250\pi\) | |||||||
\(72\) | 0.881921 | + | 0.471397i | 0.881921 | + | 0.471397i | ||||
\(73\) | 0 | 0 | 0.0490677 | − | 0.998795i | \(-0.484375\pi\) | ||||
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(74\) | −0.756174 | + | 0.291689i | −0.756174 | + | 0.291689i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.880537 | − | 0.443225i | 0.880537 | − | 0.443225i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.25505 | + | 1.52929i | −1.25505 | + | 1.52929i | −0.514103 | + | 0.857729i | \(0.671875\pi\) |
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.773010 | − | 0.634393i | 0.773010 | − | 0.634393i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.122411 | − | 0.992480i | \(-0.460938\pi\) | ||||
−0.122411 | + | 0.992480i | \(0.539062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.09681 | − | 0.946117i | −1.09681 | − | 0.946117i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.399485 | − | 0.901225i | 0.399485 | − | 0.901225i | ||||
\(89\) | 0 | 0 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.439303 | − | 1.75380i | −0.439303 | − | 1.75380i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(98\) | −0.336890 | − | 0.941544i | −0.336890 | − | 0.941544i | ||||
\(99\) | −0.679747 | − | 0.713960i | −0.679747 | − | 0.713960i | ||||
\(100\) | −0.427555 | + | 0.903989i | −0.427555 | + | 0.903989i | ||||
\(101\) | 0 | 0 | 0.266713 | − | 0.963776i | \(-0.414062\pi\) | ||||
−0.266713 | + | 0.963776i | \(0.585938\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.03124 | + | 0.285381i | −1.03124 | + | 0.285381i | ||||
\(107\) | −0.234437 | + | 0.370217i | −0.234437 | + | 0.370217i | −0.941544 | − | 0.336890i | \(-0.890625\pi\) |
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.91306 | − | 0.529414i | 1.91306 | − | 0.529414i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.989177 | − | 0.146730i | \(-0.0468750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.857729 | − | 0.514103i | −0.857729 | − | 0.514103i | ||||
\(113\) | −0.579870 | + | 1.91158i | −0.579870 | + | 1.91158i | −0.242980 | + | 0.970031i | \(0.578125\pi\) |
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.803208 | − | 1.59570i | −0.803208 | − | 1.59570i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.0189416 | − | 0.0208989i | 0.0189416 | − | 0.0208989i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.803208 | + | 0.595699i | −0.803208 | + | 0.595699i | ||||
\(127\) | −0.410525 | + | 0.410525i | −0.410525 | + | 0.410525i | −0.881921 | − | 0.471397i | \(-0.843750\pi\) |
0.471397 | + | 0.881921i | \(0.343750\pi\) | |||||||
\(128\) | −0.989177 | + | 0.146730i | −0.989177 | + | 0.146730i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.817585 | − | 0.575808i | \(-0.804688\pi\) | ||||
0.817585 | + | 0.575808i | \(0.195312\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0.794086 | − | 0.834055i | 0.794086 | − | 0.834055i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.45218 | − | 0.686831i | −1.45218 | − | 0.686831i | −0.471397 | − | 0.881921i | \(-0.656250\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.932993 | − | 0.359895i | \(-0.882812\pi\) | ||||
0.932993 | + | 0.359895i | \(0.117188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.980785 | + | 1.19509i | 0.980785 | + | 1.19509i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.242980 | + | 0.970031i | −0.242980 | + | 0.970031i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.466683 | − | 0.662638i | −0.466683 | − | 0.662638i | ||||
\(149\) | 1.66483 | + | 1.05424i | 1.66483 | + | 1.05424i | 0.923880 | + | 0.382683i | \(0.125000\pi\) |
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.249834 | − | 0.416822i | −0.249834 | − | 0.416822i | 0.707107 | − | 0.707107i | \(-0.250000\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.643895 | + | 0.746454i | 0.643895 | + | 0.746454i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.724247 | − | 0.689541i | \(-0.242188\pi\) | ||||
−0.724247 | + | 0.689541i | \(0.757812\pi\) | |||||||
\(158\) | −1.78841 | − | 0.845855i | −1.78841 | − | 0.845855i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.77324 | + | 0.352719i | 1.77324 | + | 0.352719i | ||||
\(162\) | 0.803208 | + | 0.595699i | 0.803208 | + | 0.595699i | ||||
\(163\) | 1.19427 | + | 0.529385i | 1.19427 | + | 0.529385i | 0.903989 | − | 0.427555i | \(-0.140625\pi\) |
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) | ||||
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.146730 | − | 0.989177i | −0.146730 | − | 0.989177i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.651259 | − | 1.29383i | 0.651259 | − | 1.29383i | ||||
\(173\) | 0 | 0 | −0.992480 | − | 0.122411i | \(-0.960938\pi\) | ||||
0.992480 | + | 0.122411i | \(0.0390625\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.634393 | − | 0.773010i | −0.634393 | − | 0.773010i | ||||
\(176\) | 0.971283 | + | 0.168534i | 0.971283 | + | 0.168534i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.838968 | − | 1.66674i | −0.838968 | − | 1.66674i | −0.740951 | − | 0.671559i | \(-0.765625\pi\) |
−0.0980171 | − | 0.995185i | \(-0.531250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 0.689541 | − | 0.724247i | \(-0.257812\pi\) | ||||
−0.689541 | + | 0.724247i | \(0.742188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.59449 | − | 0.852275i | 1.59449 | − | 0.852275i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.58488 | − | 0.656477i | −1.58488 | − | 0.656477i | −0.595699 | − | 0.803208i | \(-0.703125\pi\) |
−0.989177 | + | 0.146730i | \(0.953125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.73975 | − | 0.720627i | 1.73975 | − | 0.720627i | 0.740951 | − | 0.671559i | \(-0.234375\pi\) |
0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.831470 | − | 0.555570i | 0.831470 | − | 0.555570i | ||||
\(197\) | 1.30595 | + | 1.51396i | 1.30595 | + | 1.51396i | 0.671559 | + | 0.740951i | \(0.265625\pi\) |
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(198\) | 0.527399 | − | 0.832854i | 0.527399 | − | 0.832854i | ||||
\(199\) | 0 | 0 | 0.336890 | − | 0.941544i | \(-0.390625\pi\) | ||||
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(200\) | −0.980785 | − | 0.195090i | −0.980785 | − | 0.195090i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.78591 | − | 0.0438416i | 1.78591 | − | 0.0438416i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.177213 | − | 1.79927i | −0.177213 | − | 1.79927i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.16836 | − | 1.49711i | −1.16836 | − | 1.49711i | −0.831470 | − | 0.555570i | \(-0.812500\pi\) |
−0.336890 | − | 0.941544i | \(-0.609375\pi\) | |||||||
\(212\) | −0.527399 | − | 0.930989i | −0.527399 | − | 0.930989i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.416086 | − | 0.137456i | −0.416086 | − | 0.137456i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.978383 | + | 1.72709i | 0.978383 | + | 1.72709i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(224\) | 0.290285 | − | 0.956940i | 0.290285 | − | 0.956940i | ||||
\(225\) | −0.555570 | + | 0.831470i | −0.555570 | + | 0.831470i | ||||
\(226\) | −1.99518 | − | 0.0980171i | −1.99518 | − | 0.0980171i | ||||
\(227\) | 0 | 0 | −0.999699 | − | 0.0245412i | \(-0.992188\pi\) | ||||
0.999699 | + | 0.0245412i | \(0.00781250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.870087 | − | 0.492898i | \(-0.164062\pi\) | ||||
−0.870087 | + | 0.492898i | \(0.835938\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.35271 | − | 1.16686i | 1.35271 | − | 1.16686i | ||||
\(233\) | −0.284666 | − | 0.0713052i | −0.284666 | − | 0.0713052i | 0.0980171 | − | 0.995185i | \(-0.468750\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.831470 | − | 1.55557i | 0.831470 | − | 1.55557i | − | 1.00000i | \(-0.5\pi\) | |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(242\) | 0.0248750 | + | 0.0132960i | 0.0248750 | + | 0.0132960i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.313682 | − | 0.949528i | \(-0.601562\pi\) | ||||
0.313682 | + | 0.949528i | \(0.398438\pi\) | |||||||
\(252\) | −0.773010 | − | 0.634393i | −0.773010 | − | 0.634393i | ||||
\(253\) | −1.75606 | + | 0.304705i | −1.75606 | + | 0.304705i | ||||
\(254\) | −0.497971 | − | 0.298472i | −0.497971 | − | 0.298472i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.382683 | − | 0.923880i | −0.382683 | − | 0.923880i | ||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.798550 | − | 0.138562i | 0.798550 | − | 0.138562i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.560376 | − | 1.69628i | −0.560376 | − | 1.69628i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.389711 | + | 0.0191453i | −0.389711 | + | 0.0191453i | −0.242980 | − | 0.970031i | \(-0.578125\pi\) |
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.00201 | + | 0.567630i | 1.00201 | + | 0.567630i | ||||
\(269\) | 0 | 0 | −0.757209 | − | 0.653173i | \(-0.773438\pi\) | ||||
0.757209 | + | 0.653173i | \(0.226562\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.881921 | − | 0.471397i | \(-0.156250\pi\) | ||||
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.313396 | − | 1.57555i | 0.313396 | − | 1.57555i | ||||
\(275\) | 0.857729 | + | 0.485897i | 0.857729 | + | 0.485897i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.345455 | + | 1.53838i | 0.345455 | + | 1.53838i | 0.773010 | + | 0.634393i | \(0.218750\pi\) |
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.15569 | − | 1.55827i | −1.15569 | − | 1.55827i | −0.773010 | − | 0.634393i | \(-0.781250\pi\) |
−0.382683 | − | 0.923880i | \(-0.625000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.870087 | − | 0.492898i | \(-0.164062\pi\) | ||||
−0.870087 | + | 0.492898i | \(0.835938\pi\) | |||||||
\(284\) | −0.920964 | + | 1.24178i | −0.920964 | + | 1.24178i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.00000 | −1.00000 | ||||||||
\(289\) | 0.555570 | + | 0.831470i | 0.555570 | + | 0.831470i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 0.992480 | − | 0.122411i | \(-0.0390625\pi\) | ||||
−0.992480 | + | 0.122411i | \(0.960938\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.529385 | − | 0.613705i | 0.529385 | − | 0.613705i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.618127 | + | 1.87110i | −0.618127 | + | 1.87110i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.891159 | + | 1.14192i | 0.891159 | + | 1.14192i | ||||
\(302\) | 0.343626 | − | 0.343626i | 0.343626 | − | 0.343626i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | −0.949528 | − | 0.313682i | \(-0.898438\pi\) | ||||
0.949528 | + | 0.313682i | \(0.101562\pi\) | |||||||
\(308\) | −0.567630 | + | 0.805972i | −0.567630 | + | 0.805972i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.740951 | − | 0.671559i | \(-0.234375\pi\) | ||||
−0.740951 | + | 0.671559i | \(0.765625\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.336890 | − | 0.941544i | \(-0.390625\pi\) | ||||
−0.336890 | + | 0.941544i | \(0.609375\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.385958 | − | 1.94034i | 0.385958 | − | 1.94034i | ||||
\(317\) | 1.47762 | + | 0.331811i | 1.47762 | + | 0.331811i | 0.881921 | − | 0.471397i | \(-0.156250\pi\) |
0.595699 | + | 0.803208i | \(0.296875\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.62702 | + | 0.673934i | −1.62702 | + | 0.673934i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0887133 | + | 1.80580i | 0.0887133 | + | 1.80580i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.382683 | + | 0.923880i | −0.382683 | + | 0.923880i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.223335 | + | 1.28711i | −0.223335 | + | 1.28711i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.101451 | + | 0.106558i | −0.101451 | + | 0.106558i | −0.773010 | − | 0.634393i | \(-0.781250\pi\) |
0.671559 | + | 0.740951i | \(0.265625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.364402 | − | 0.723943i | −0.364402 | − | 0.723943i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.852065 | + | 1.03824i | 0.852065 | + | 1.03824i | 0.998795 | + | 0.0490677i | \(0.0156250\pi\) |
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(338\) | 0.923880 | − | 0.382683i | 0.923880 | − | 0.382683i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.146730 | + | 0.989177i | 0.146730 | + | 0.989177i | ||||
\(344\) | 1.41330 | + | 0.317367i | 1.41330 | + | 0.317367i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.22713 | − | 1.57242i | 1.22713 | − | 1.57242i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.671559 | − | 0.740951i | \(-0.265625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.914210 | − | 0.405241i | \(-0.867188\pi\) | ||||
0.914210 | + | 0.405241i | \(0.132812\pi\) | |||||||
\(350\) | 0.595699 | − | 0.803208i | 0.595699 | − | 0.803208i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.0725197 | + | 0.983125i | 0.0725197 | + | 0.983125i | ||||
\(353\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.41294 | − | 1.21881i | 1.41294 | − | 1.21881i | ||||
\(359\) | −1.32858 | − | 0.197076i | −1.32858 | − | 0.197076i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.514103 | − | 0.857729i | −0.514103 | − | 0.857729i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.290285 | − | 0.956940i | \(-0.593750\pi\) | ||||
0.290285 | + | 0.956940i | \(0.406250\pi\) | |||||||
\(368\) | 1.21416 | + | 1.33962i | 1.21416 | + | 1.33962i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.06710 | − | 0.0787137i | 1.06710 | − | 0.0787137i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.79839 | − | 0.693716i | −1.79839 | − | 0.693716i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
−0.803208 | − | 0.595699i | \(-0.796875\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.50929 | + | 0.759711i | 1.50929 | + | 0.759711i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.251710 | − | 1.69689i | 0.251710 | − | 1.69689i | ||||
\(383\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.12175 | + | 1.51251i | 1.12175 | + | 1.51251i | ||||
\(387\) | 0.834055 | − | 1.18427i | 0.834055 | − | 1.18427i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.620050 | + | 1.23183i | −0.620050 | + | 1.23183i | 0.336890 | + | 0.941544i | \(0.390625\pi\) |
−0.956940 | + | 0.290285i | \(0.906250\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.740951 | + | 0.671559i | 0.740951 | + | 0.671559i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.15127 | + | 1.63468i | −1.15127 | + | 1.63468i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.936041 | + | 0.309226i | 0.936041 | + | 0.309226i | ||||
\(397\) | 0 | 0 | −0.0735646 | − | 0.997290i | \(-0.523438\pi\) | ||||
0.0735646 | + | 0.997290i | \(0.476562\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.0490677 | − | 0.998795i | −0.0490677 | − | 0.998795i | ||||
\(401\) | 1.41809 | − | 0.430174i | 1.41809 | − | 0.430174i | 0.514103 | − | 0.857729i | \(-0.328125\pi\) |
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.476469 | + | 1.72174i | 0.476469 | + | 1.72174i | ||||
\(407\) | −0.685300 | + | 0.410753i | −0.685300 | + | 0.410753i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 0.146730 | − | 0.989177i | \(-0.453125\pi\) | ||||
−0.146730 | + | 0.989177i | \(0.546875\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.70229 | − | 0.609090i | 1.70229 | − | 0.609090i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.405241 | − | 0.914210i | \(-0.367188\pi\) | ||||
−0.405241 | + | 0.914210i | \(0.632812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.02985 | + | 0.803705i | 1.02985 | + | 0.803705i | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) |
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(422\) | 1.16836 | − | 1.49711i | 1.16836 | − | 1.49711i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.774941 | − | 0.737805i | 0.774941 | − | 0.737805i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.0322362 | − | 0.437015i | 0.0322362 | − | 0.437015i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.858923 | + | 0.704900i | −0.858923 | + | 0.704900i | −0.956940 | − | 0.290285i | \(-0.906250\pi\) |
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 0.634393 | − | 0.773010i | \(-0.281250\pi\) | ||||
−0.634393 | + | 0.773010i | \(0.718750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.43760 | + | 1.36871i | −1.43760 | + | 1.36871i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.0490677 | − | 0.998795i | \(-0.484375\pi\) | ||||
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.903989 | − | 0.427555i | 0.903989 | − | 0.427555i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.82347 | + | 0.134507i | 1.82347 | + | 0.134507i | 0.941544 | − | 0.336890i | \(-0.109375\pi\) |
0.881921 | + | 0.471397i | \(0.156250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.998795 | + | 0.0490677i | 0.998795 | + | 0.0490677i | ||||
\(449\) | 0.0750191 | + | 0.181112i | 0.0750191 | + | 0.181112i | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) |
−0.881921 | + | 0.471397i | \(0.843750\pi\) | |||||||
\(450\) | −0.941544 | − | 0.336890i | −0.941544 | − | 0.336890i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −0.389711 | − | 1.95921i | −0.389711 | − | 1.95921i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.18452 | + | 1.30692i | 1.18452 | + | 1.30692i | 0.941544 | + | 0.336890i | \(0.109375\pi\) |
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.313682 | − | 0.949528i | \(-0.398438\pi\) | ||||
−0.313682 | + | 0.949528i | \(0.601562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.47477 | + | 0.145252i | −1.47477 | + | 0.145252i | −0.803208 | − | 0.595699i | \(-0.796875\pi\) |
−0.671559 | + | 0.740951i | \(0.734375\pi\) | |||||||
\(464\) | 1.46057 | + | 1.02865i | 1.46057 | + | 1.02865i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 0.293461i | − | 0.293461i | ||||||
\(467\) | 0 | 0 | 0.788346 | − | 0.615232i | \(-0.210938\pi\) | ||||
−0.788346 | + | 0.615232i | \(0.789062\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.941544 | + | 0.663110i | −0.941544 | + | 0.663110i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.22477 | − | 0.734098i | −1.22477 | − | 0.734098i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.385086 | − | 0.998298i | −0.385086 | − | 0.998298i | ||||
\(478\) | 1.71098 | + | 0.428579i | 1.71098 | + | 0.428579i | ||||
\(479\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.00685337 | + | 0.0273602i | −0.00685337 | + | 0.0273602i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.29028 | + | 0.956940i | −1.29028 | + | 0.956940i | −0.290285 | + | 0.956940i | \(0.593750\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.92267 | − | 0.431751i | 1.92267 | − | 0.431751i | 0.923880 | − | 0.382683i | \(-0.125000\pi\) |
0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.728789 | − | 1.36347i | −0.728789 | − | 1.36347i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.223335 | + | 0.258908i | −0.223335 | + | 0.258908i | −0.857729 | − | 0.514103i | \(-0.828125\pi\) |
0.634393 | + | 0.773010i | \(0.281250\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(504\) | 0.427555 | − | 0.903989i | 0.427555 | − | 0.903989i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.722261 | − | 1.62939i | −0.722261 | − | 1.62939i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.168530 | − | 0.555570i | 0.168530 | − | 0.555570i | ||||
\(509\) | 0 | 0 | −0.170962 | − | 0.985278i | \(-0.554688\pi\) | ||||
0.170962 | + | 0.985278i | \(0.445312\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.803208 | − | 0.595699i | 0.803208 | − | 0.595699i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0.328441 | + | 0.740951i | 0.328441 | + | 0.740951i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.941544 | − | 0.336890i | \(-0.109375\pi\) | ||||
−0.941544 | + | 0.336890i | \(0.890625\pi\) | |||||||
\(522\) | 1.50929 | − | 0.955746i | 1.50929 | − | 0.955746i | ||||
\(523\) | 0 | 0 | −0.405241 | − | 0.914210i | \(-0.632812\pi\) | ||||
0.405241 | + | 0.914210i | \(0.367188\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.113263 | − | 0.373380i | −0.113263 | − | 0.373380i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.00089 | − | 1.06950i | −2.00089 | − | 1.06950i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.307151 | + | 1.10990i | −0.307151 | + | 1.10990i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.485897 | − | 0.857729i | −0.485897 | − | 0.857729i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0478899 | − | 1.95082i | 0.0478899 | − | 1.95082i | −0.195090 | − | 0.980785i | \(-0.562500\pi\) |
0.242980 | − | 0.970031i | \(-0.421875\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.225785 | − | 0.585326i | −0.225785 | − | 0.585326i | 0.773010 | − | 0.634393i | \(-0.218750\pi\) |
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(548\) | 1.60448 | − | 0.0788231i | 1.60448 | − | 0.0788231i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.262924 | + | 0.950087i | −0.262924 | + | 0.950087i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.58903 | + | 1.17850i | 1.58903 | + | 1.17850i | ||||
\(554\) | −1.40834 | + | 0.708899i | −1.40834 | + | 0.708899i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.970031 | − | 0.757020i | 0.970031 | − | 0.757020i | − | 1.00000i | \(-0.5\pi\) | |
0.970031 | + | 0.242980i | \(0.0781250\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.23076 | − | 1.49969i | 1.23076 | − | 1.49969i | ||||
\(563\) | 0 | 0 | 0.313682 | − | 0.949528i | \(-0.398438\pi\) | ||||
−0.313682 | + | 0.949528i | \(0.601562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.671559 | − | 0.740951i | −0.671559 | − | 0.740951i | ||||
\(568\) | −1.42834 | − | 0.591637i | −1.42834 | − | 0.591637i | ||||
\(569\) | 0.546632 | + | 0.195588i | 0.546632 | + | 0.195588i | 0.595699 | − | 0.803208i | \(-0.296875\pi\) |
−0.0490677 | + | 0.998795i | \(0.515625\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.680899 | + | 0.587348i | −0.680899 | + | 0.587348i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.691883 | + | 1.67035i | 0.691883 | + | 1.67035i | ||||
\(576\) | −0.242980 | − | 0.970031i | −0.242980 | − | 0.970031i | ||||
\(577\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(578\) | −0.671559 | + | 0.740951i | −0.671559 | + | 0.740951i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.953526 | + | 0.450984i | −0.953526 | + | 0.450984i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.724247 | − | 0.689541i | \(-0.757812\pi\) | ||||
0.724247 | + | 0.689541i | \(0.242188\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.723943 | + | 0.364402i | 0.723943 | + | 0.364402i | ||||
\(593\) | 0 | 0 | 0.773010 | − | 0.634393i | \(-0.218750\pi\) | ||||
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.96522 | − | 0.144963i | −1.96522 | − | 0.144963i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.94034 | − | 0.287822i | 1.94034 | − | 0.287822i | 0.941544 | − | 0.336890i | \(-0.109375\pi\) |
0.998795 | + | 0.0490677i | \(0.0156250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | −0.242980 | − | 0.970031i | \(-0.578125\pi\) | ||||
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(602\) | −0.891159 | + | 1.14192i | −0.891159 | + | 1.14192i | ||||
\(603\) | 0.907873 | + | 0.708511i | 0.907873 | + | 0.708511i | ||||
\(604\) | 0.416822 | + | 0.249834i | 0.416822 | + | 0.249834i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.531980 | − | 1.92233i | 0.531980 | − | 1.92233i | 0.195090 | − | 0.980785i | \(-0.437500\pi\) |
0.336890 | − | 0.941544i | \(-0.390625\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.919741 | − | 0.354783i | −0.919741 | − | 0.354783i | ||||
\(617\) | −0.808661 | + | 0.484693i | −0.808661 | + | 0.484693i | −0.857729 | − | 0.514103i | \(-0.828125\pi\) |
0.0490677 | + | 0.998795i | \(0.484375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.534998 | − | 0.844854i | \(-0.320312\pi\) | ||||
−0.534998 | + | 0.844854i | \(0.679688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.290285 | − | 0.956940i | 0.290285 | − | 0.956940i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0838155 | − | 0.177213i | 0.0838155 | − | 0.177213i | −0.857729 | − | 0.514103i | \(-0.828125\pi\) |
0.941544 | + | 0.336890i | \(0.109375\pi\) | |||||||
\(632\) | 1.97597 | − | 0.0970732i | 1.97597 | − | 0.0970732i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.0371657 | + | 1.51396i | 0.0371657 | + | 1.51396i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.04907 | − | 1.41451i | −1.04907 | − | 1.41451i | ||||
\(639\) | −1.09320 | + | 1.09320i | −1.09320 | + | 1.09320i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.476434 | − | 0.476434i | −0.476434 | − | 0.476434i | 0.427555 | − | 0.903989i | \(-0.359375\pi\) |
−0.903989 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.817585 | − | 0.575808i | \(-0.804688\pi\) | ||||
0.817585 | + | 0.575808i | \(0.195312\pi\) | |||||||
\(644\) | −1.73013 | + | 0.524828i | −1.73013 | + | 0.524828i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.740951 | − | 0.671559i | \(-0.765625\pi\) | ||||
0.740951 | + | 0.671559i | \(0.234375\pi\) | |||||||
\(648\) | −0.989177 | − | 0.146730i | −0.989177 | − | 0.146730i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.30281 | + | 0.0961008i | −1.30281 | + | 0.0961008i | ||||
\(653\) | −0.531980 | + | 0.0392412i | −0.531980 | + | 0.0392412i | −0.336890 | − | 0.941544i | \(-0.609375\pi\) |
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.0652970 | + | 0.235953i | 0.0652970 | + | 0.235953i | 0.989177 | − | 0.146730i | \(-0.0468750\pi\) |
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.844854 | − | 0.534998i | \(-0.820312\pi\) | ||||
0.844854 | + | 0.534998i | \(0.179688\pi\) | |||||||
\(662\) | −0.128015 | − | 0.0725197i | −0.128015 | − | 0.0725197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.613705 | − | 0.529385i | 0.613705 | − | 0.529385i | ||||
\(667\) | −3.11286 | − | 0.861445i | −3.11286 | − | 0.861445i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.95213 | − | 0.388302i | −1.95213 | − | 0.388302i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
−0.956940 | − | 0.290285i | \(-0.906250\pi\) | |||||||
\(674\) | −0.800094 | + | 1.07880i | −0.800094 | + | 1.07880i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.595699 | + | 0.803208i | 0.595699 | + | 0.803208i | ||||
\(677\) | 0 | 0 | 0.615232 | − | 0.788346i | \(-0.289062\pi\) | ||||
−0.615232 | + | 0.788346i | \(0.710938\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.123057 | + | 0.709193i | −0.123057 | + | 0.709193i | 0.857729 | + | 0.514103i | \(0.171875\pi\) |
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.923880 | + | 0.382683i | −0.923880 | + | 0.382683i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.0355478 | + | 1.44806i | 0.0355478 | + | 1.44806i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.449611 | − | 0.893224i | \(-0.648438\pi\) | ||||
0.449611 | + | 0.893224i | \(0.351562\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.679747 | + | 0.713960i | −0.679747 | + | 0.713960i | ||||
\(694\) | 1.82347 | + | 0.808287i | 1.82347 | + | 0.808287i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.923880 | + | 0.382683i | 0.923880 | + | 0.382683i | ||||
\(701\) | −0.0414675 | + | 0.0262590i | −0.0414675 | + | 0.0262590i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) |
0.514103 | + | 0.857729i | \(0.328125\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −0.936041 | + | 0.309226i | −0.936041 | + | 0.309226i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.348419 | − | 0.403915i | −0.348419 | − | 0.403915i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
−0.903989 | + | 0.427555i | \(0.859375\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.666487 | − | 1.86271i | 0.666487 | − | 1.86271i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.52560 | + | 1.07445i | 1.52560 | + | 1.07445i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.131649 | − | 1.33665i | −0.131649 | − | 1.33665i | ||||
\(719\) | 0 | 0 | −0.0980171 | − | 0.995185i | \(-0.531250\pi\) | ||||
0.0980171 | + | 0.995185i | \(0.468750\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.707107 | − | 0.707107i | 0.707107 | − | 0.707107i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.02865 | + | 1.46057i | 1.02865 | + | 1.46057i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | 0.595699 | − | 0.803208i | \(-0.296875\pi\) | ||||
−0.595699 | + | 0.803208i | \(0.703125\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.514103 | + | 0.857729i | −0.514103 | + | 0.857729i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.932993 | − | 0.359895i | \(-0.117188\pi\) | ||||
−0.932993 | + | 0.359895i | \(0.882812\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00446 | + | 1.50328i | −1.00446 | + | 1.50328i | ||||
\(737\) | 0.630716 | − | 0.943934i | 0.630716 | − | 0.943934i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.57622 | + | 0.0386940i | 1.57622 | + | 0.0386940i | 0.803208 | − | 0.595699i | \(-0.203125\pi\) |
0.773010 | + | 0.634393i | \(0.218750\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.335638 | + | 1.01599i | 0.335638 | + | 1.01599i | ||||
\(743\) | 0.612501 | + | 0.825862i | 0.612501 | + | 0.825862i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.235953 | − | 1.91306i | 0.235953 | − | 1.91306i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.381274 | + | 0.215989i | 0.381274 | + | 0.215989i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0924099 | + | 0.172887i | −0.0924099 | + | 0.172887i | −0.923880 | − | 0.382683i | \(-0.875000\pi\) |
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.400609 | + | 0.177578i | −0.400609 | + | 0.177578i | −0.595699 | − | 0.803208i | \(-0.703125\pi\) |
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(758\) | −0.370217 | + | 1.64865i | −0.370217 | + | 1.64865i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.998795 | − | 0.0490677i | \(-0.0156250\pi\) | ||||
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.622645 | − | 1.88477i | −0.622645 | − | 1.88477i | ||||
\(764\) | 1.70720 | − | 0.168144i | 1.70720 | − | 0.168144i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.19462 | + | 1.45565i | −1.19462 | + | 1.45565i | ||||
\(773\) | 0 | 0 | −0.313682 | − | 0.949528i | \(-0.601562\pi\) | ||||
0.313682 | + | 0.949528i | \(0.398438\pi\) | |||||||
\(774\) | 1.35143 | + | 0.521306i | 1.35143 | + | 0.521306i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.34557 | − | 0.302158i | −1.34557 | − | 0.302158i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.15403 | + | 0.995476i | 1.15403 | + | 0.995476i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.471397 | + | 0.881921i | −0.471397 | + | 0.881921i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.870087 | − | 0.492898i | \(-0.835938\pi\) | ||||
0.870087 | + | 0.492898i | \(0.164062\pi\) | |||||||
\(788\) | −1.86542 | − | 0.719573i | −1.86542 | − | 0.719573i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.93773 | + | 0.485375i | 1.93773 | + | 0.485375i | ||||
\(792\) | −0.0725197 | + | 0.983125i | −0.0725197 | + | 0.983125i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | −0.999699 | − | 0.0245412i | \(-0.992188\pi\) | ||||
0.999699 | + | 0.0245412i | \(0.00781250\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0.956940 | − | 0.290285i | 0.956940 | − | 0.290285i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.761850 | + | 1.27107i | 0.761850 | + | 1.27107i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.561621 | − | 0.757259i | 0.561621 | − | 0.757259i | −0.427555 | − | 0.903989i | \(-0.640625\pi\) |
0.989177 | + | 0.146730i | \(0.0468750\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.575808 | − | 0.817585i | \(-0.695312\pi\) | ||||
0.575808 | + | 0.817585i | \(0.304688\pi\) | |||||||
\(812\) | −1.55437 | + | 0.880537i | −1.55437 | + | 0.880537i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.564958 | − | 0.564958i | −0.564958 | − | 0.564958i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.99398 | − | 0.0489495i | 1.99398 | − | 0.0489495i | 0.995185 | − | 0.0980171i | \(-0.0312500\pi\) |
0.998795 | + | 0.0490677i | \(0.0156250\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.45343 | − | 1.31731i | 1.45343 | − | 1.31731i | 0.595699 | − | 0.803208i | \(-0.296875\pi\) |
0.857729 | − | 0.514103i | \(-0.171875\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.0320593 | − | 0.0371657i | −0.0320593 | − | 0.0371657i | 0.740951 | − | 0.671559i | \(-0.234375\pi\) |
−0.773010 | + | 0.634393i | \(0.781250\pi\) | |||||||
\(828\) | 1.00446 | + | 1.50328i | 1.00446 | + | 1.50328i | ||||
\(829\) | 0 | 0 | −0.975702 | − | 0.219101i | \(-0.929688\pi\) | ||||
0.975702 | + | 0.219101i | \(0.0703125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.427555 | − | 0.903989i | \(-0.640625\pi\) | ||||
0.427555 | + | 0.903989i | \(0.359375\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.18876 | − | 0.107527i | −2.18876 | − | 0.107527i | ||||
\(842\) | −0.529385 | + | 1.19427i | −0.529385 | + | 1.19427i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.73614 | + | 0.769576i | 1.73614 | + | 0.769576i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0218031 | − | 0.0178934i | −0.0218031 | − | 0.0178934i | ||||
\(848\) | 0.903989 | + | 0.572445i | 0.903989 | + | 0.572445i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.45432 | − | 0.179373i | −1.45432 | − | 0.179373i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.170962 | − | 0.985278i | \(-0.445312\pi\) | ||||
−0.170962 | + | 0.985278i | \(0.554688\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.431751 | − | 0.0749159i | 0.431751 | − | 0.0749159i | ||||
\(857\) | 0 | 0 | 0.970031 | − | 0.242980i | \(-0.0781250\pi\) | ||||
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.615232 | − | 0.788346i | \(-0.289062\pi\) | ||||
−0.615232 | + | 0.788346i | \(0.710938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.892476 | − | 0.661906i | −0.892476 | − | 0.661906i | ||||
\(863\) | −1.90278 | − | 0.378487i | −1.90278 | − | 0.378487i | −0.903989 | − | 0.427555i | \(-0.859375\pi\) |
−0.998795 | + | 0.0490677i | \(0.984375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.87961 | − | 0.520157i | −1.87961 | − | 0.520157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −1.67700 | − | 1.06195i | −1.67700 | − | 1.06195i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.0130909 | − | 0.0473045i | −0.0130909 | − | 0.0473045i | 0.956940 | − | 0.290285i | \(-0.0937500\pi\) |
−0.970031 | + | 0.242980i | \(0.921875\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.956940 | − | 0.290285i | \(-0.906250\pi\) | ||||
0.956940 | + | 0.290285i | \(0.0937500\pi\) | |||||||
\(882\) | 0.634393 | + | 0.773010i | 0.634393 | + | 0.773010i | ||||
\(883\) | −1.51031 | + | 0.111407i | −1.51031 | + | 0.111407i | −0.803208 | − | 0.595699i | \(-0.796875\pi\) |
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.312590 | + | 1.80150i | 0.312590 | + | 1.80150i | ||||
\(887\) | 0 | 0 | −0.903989 | − | 0.427555i | \(-0.859375\pi\) | ||||
0.903989 | + | 0.427555i | \(0.140625\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.430174 | + | 0.389887i | 0.430174 | + | 0.389887i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.880537 | + | 0.443225i | 0.880537 | + | 0.443225i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.195090 | + | 0.980785i | 0.195090 | + | 0.980785i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −0.157456 | + | 0.116777i | −0.157456 | + | 0.116777i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.0980171 | − | 0.995185i | 0.0980171 | − | 0.995185i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.80580 | − | 0.854080i | 1.80580 | − | 0.854080i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.714377 | + | 1.85195i | −0.714377 | + | 1.85195i | −0.242980 | + | 0.970031i | \(0.578125\pi\) |
−0.471397 | + | 0.881921i | \(0.656250\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.273678 | − | 0.902197i | 0.273678 | − | 0.902197i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.980785 | − | 0.195090i | \(-0.0625000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.979938 | + | 1.46658i | −0.979938 | + | 1.46658i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.64159 | − | 0.983931i | 1.64159 | − | 0.983931i | 0.671559 | − | 0.740951i | \(-0.265625\pi\) |
0.970031 | − | 0.242980i | \(-0.0781250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.558861 | + | 0.586990i | 0.558861 | + | 0.586990i | ||||
\(926\) | −0.499238 | − | 1.39528i | −0.499238 | − | 1.39528i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.642934 | + | 1.66674i | −0.642934 | + | 1.66674i | ||||
\(929\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0.284666 | − | 0.0713052i | 0.284666 | − | 0.0713052i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.989177 | − | 0.146730i | \(-0.0468750\pi\) | ||||
−0.989177 | + | 0.146730i | \(0.953125\pi\) | |||||||
\(938\) | −0.872014 | − | 0.752205i | −0.872014 | − | 0.752205i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.122411 | − | 0.992480i | \(-0.460938\pi\) | ||||
−0.122411 | + | 0.992480i | \(0.539062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.414503 | − | 1.36643i | 0.414503 | − | 1.36643i | ||||
\(947\) | −1.40834 | + | 0.708899i | −1.40834 | + | 0.708899i | −0.980785 | − | 0.195090i | \(-0.937500\pi\) |
−0.427555 | + | 0.903989i | \(0.640625\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.55075 | − | 0.733452i | 1.55075 | − | 0.733452i | 0.555570 | − | 0.831470i | \(-0.312500\pi\) |
0.995185 | + | 0.0980171i | \(0.0312500\pi\) | |||||||
\(954\) | 0.874812 | − | 0.616112i | 0.874812 | − | 0.616112i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.76384i | 1.76384i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.614748 | + | 1.48413i | −0.614748 | + | 1.48413i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.382683 | + | 0.923880i | 0.382683 | + | 0.923880i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.0960107 | − | 0.427555i | 0.0960107 | − | 0.427555i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.82665 | − | 0.653587i | −1.82665 | − | 0.653587i | −0.995185 | − | 0.0980171i | \(-0.968750\pi\) |
−0.831470 | − | 0.555570i | \(-0.812500\pi\) | |||||||
\(968\) | −0.0282055 | −0.0282055 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.0245412 | − | 0.999699i | \(-0.507812\pi\) | ||||
0.0245412 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.24178 | − | 1.01910i | −1.24178 | − | 1.01910i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.124363 | − | 1.26268i | 0.124363 | − | 1.26268i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.831470 | − | 0.555570i | \(-0.187500\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.62287 | + | 1.14296i | −1.62287 | + | 1.14296i | ||||
\(982\) | 0.885984 | + | 1.76015i | 0.885984 | + | 1.76015i | ||||
\(983\) | 0 | 0 | −0.803208 | − | 0.595699i | \(-0.796875\pi\) | ||||
0.803208 | + | 0.595699i | \(0.203125\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.942510 | − | 2.44336i | −0.942510 | − | 2.44336i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.23216 | − | 0.823301i | 1.23216 | − | 0.823301i | 0.242980 | − | 0.970031i | \(-0.421875\pi\) |
0.989177 | + | 0.146730i | \(0.0468750\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.14553 | − | 1.03824i | 1.14553 | − | 1.03824i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.492898 | − | 0.870087i | \(-0.664062\pi\) | ||||
0.492898 | + | 0.870087i | \(0.335938\pi\) | |||||||
\(998\) | −0.305415 | − | 0.153733i | −0.305415 | − | 0.153733i | ||||
\(999\) | 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 | 3584.1.cd.a.1469.1 | yes | 64 | |
7.6 | odd | 2 | CM | 3584.1.cd.a.1469.1 | yes | 64 | |
512.405 | even | 128 | inner | 3584.1.cd.a.405.1 | ✓ | 64 | |
3584.405 | odd | 128 | inner | 3584.1.cd.a.405.1 | ✓ | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3584.1.cd.a.405.1 | ✓ | 64 | 512.405 | even | 128 | inner | |
3584.1.cd.a.405.1 | ✓ | 64 | 3584.405 | odd | 128 | inner | |
3584.1.cd.a.1469.1 | yes | 64 | 1.1 | even | 1 | trivial | |
3584.1.cd.a.1469.1 | yes | 64 | 7.6 | odd | 2 | CM |