Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [260,2,Mod(177,260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(260, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("260.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 260 = 2^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 260.r (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: | \(2.07611045255\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 260.177 |
Dual form | 260.2.r.b.213.1 |
$q$-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 \(\left(\mathbb{Z}/260\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(131\) | \(157\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.618034 | + | 0.618034i | −0.356822 | + | 0.356822i | −0.862640 | − | 0.505818i | \(-0.831191\pi\) |
0.505818 | + | 0.862640i | \(0.331191\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | −1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607i | 0.745356i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.61803 | + | 2.61803i | −0.789367 | + | 0.789367i | −0.981390 | − | 0.192023i | \(-0.938495\pi\) |
0.192023 | + | 0.981390i | \(0.438495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 2.00000i | −0.832050 | + | 0.554700i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.38197 | − | 1.38197i | 0.356822 | − | 0.356822i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.23607 | − | 2.23607i | 0.542326 | − | 0.542326i | −0.381884 | − | 0.924210i | \(-0.624725\pi\) |
0.924210 | + | 0.381884i | \(0.124725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.85410 | + | 5.85410i | −1.34302 | + | 1.34302i | −0.449989 | + | 0.893034i | \(0.648572\pi\) |
−0.893034 | + | 0.449989i | \(0.851428\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.38197 | − | 3.38197i | −0.705189 | − | 0.705189i | 0.260331 | − | 0.965519i | \(-0.416168\pi\) |
−0.965519 | + | 0.260331i | \(0.916168\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.23607 | − | 3.23607i | −0.622782 | − | 0.622782i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.23607i | − | 0.972313i | −0.873872 | − | 0.486157i | \(-0.838398\pi\) | ||
0.873872 | − | 0.486157i | \(-0.161602\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.85410 | + | 5.85410i | 1.05143 | + | 1.05143i | 0.998604 | + | 0.0528239i | \(0.0168222\pi\) |
0.0528239 | + | 0.998604i | \(0.483178\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 3.23607i | − | 0.563327i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.70820 | 1.59602 | 0.798009 | − | 0.602645i | \(-0.205886\pi\) | ||||
0.798009 | + | 0.602645i | \(0.205886\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.618034 | − | 3.09017i | 0.0989646 | − | 0.494823i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.76393 | + | 3.76393i | 0.587827 | + | 0.587827i | 0.937043 | − | 0.349215i | \(-0.113552\pi\) |
−0.349215 | + | 0.937043i | \(0.613552\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.85410 | + | 3.85410i | 0.587745 | + | 0.587745i | 0.937020 | − | 0.349275i | \(-0.113572\pi\) |
−0.349275 | + | 0.937020i | \(0.613572\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 5.00000i | − | 0.745356i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.94427 | −1.30466 | −0.652328 | − | 0.757937i | \(-0.726208\pi\) | ||||
−0.652328 | + | 0.757937i | \(0.726208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.76393i | 0.387028i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.47214 | − | 1.47214i | 0.202213 | − | 0.202213i | −0.598734 | − | 0.800948i | \(-0.704329\pi\) |
0.800948 | + | 0.598734i | \(0.204329\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.85410 | − | 5.85410i | 0.789367 | − | 0.789367i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.23607i | − | 0.958441i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.38197 | + | 3.38197i | 0.440294 | + | 0.440294i | 0.892111 | − | 0.451816i | \(-0.149224\pi\) |
−0.451816 | + | 0.892111i | \(0.649224\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.70820 | 0.730861 | 0.365430 | − | 0.930839i | \(-0.380922\pi\) | ||||
0.365430 | + | 0.930839i | \(0.380922\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.70820 | − | 4.47214i | 0.832050 | − | 0.554700i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 0.291796i | − | 0.0356486i | −0.999841 | − | 0.0178243i | \(-0.994326\pi\) | ||
0.999841 | − | 0.0178243i | \(-0.00567395\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.18034 | 0.503254 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.61803 | + | 2.61803i | 0.310703 | + | 0.310703i | 0.845182 | − | 0.534479i | \(-0.179492\pi\) |
−0.534479 | + | 0.845182i | \(0.679492\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 11.7082i | − | 1.37034i | −0.728382 | − | 0.685171i | \(-0.759728\pi\) | ||
0.728382 | − | 0.685171i | \(-0.240272\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.09017 | + | 3.09017i | −0.356822 | + | 0.356822i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.70820i | − | 0.417206i | −0.978000 | − | 0.208603i | \(-0.933108\pi\) | ||
0.978000 | − | 0.208603i | \(-0.0668916\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.70820 | −0.300912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.4721 | −1.14947 | −0.574733 | − | 0.818341i | \(-0.694894\pi\) | ||||
−0.574733 | + | 0.818341i | \(0.694894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | + | 5.00000i | −0.542326 | + | 0.542326i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.23607 | + | 3.23607i | 0.346943 | + | 0.346943i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.23607 | + | 2.23607i | 0.237023 | + | 0.237023i | 0.815616 | − | 0.578593i | \(-0.196398\pi\) |
−0.578593 | + | 0.815616i | \(0.696398\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.23607 | −0.750345 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.0902 | − | 13.0902i | 1.34302 | − | 1.34302i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.4164i | 1.56530i | 0.622463 | + | 0.782650i | \(0.286132\pi\) | ||||
−0.622463 | + | 0.782650i | \(0.713868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.85410 | − | 5.85410i | −0.588359 | − | 0.588359i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.52786i | 0.152028i | 0.997107 | + | 0.0760141i | \(0.0242194\pi\) | ||||
−0.997107 | + | 0.0760141i | \(0.975781\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.85410 | + | 3.85410i | 0.379756 | + | 0.379756i | 0.871014 | − | 0.491258i | \(-0.163463\pi\) |
−0.491258 | + | 0.871014i | \(0.663463\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.61803 | − | 2.61803i | −0.253095 | − | 0.253095i | 0.569143 | − | 0.822238i | \(-0.307275\pi\) |
−0.822238 | + | 0.569143i | \(0.807275\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.70820 | + | 4.70820i | −0.450964 | + | 0.450964i | −0.895674 | − | 0.444710i | \(-0.853307\pi\) |
0.444710 | + | 0.895674i | \(0.353307\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.00000 | + | 6.00000i | −0.569495 | + | 0.569495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.9443 | + | 11.9443i | −1.12362 | + | 1.12362i | −0.132430 | + | 0.991192i | \(0.542278\pi\) |
−0.991192 | + | 0.132430i | \(0.957722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.56231 | + | 7.56231i | 0.705189 | + | 0.705189i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.47214 | − | 6.70820i | −0.413449 | − | 0.620174i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.70820i | − | 0.246200i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.65248 | −0.419500 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.1803 | −1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.145898 | − | 0.145898i | 0.0129464 | − | 0.0129464i | −0.700604 | − | 0.713550i | \(-0.747086\pi\) |
0.713550 | + | 0.700604i | \(0.247086\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.76393 | −0.419441 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.41641 | −0.647975 | −0.323987 | − | 0.946061i | \(-0.605024\pi\) | ||||
−0.323987 | + | 0.946061i | \(0.605024\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.23607 | + | 7.23607i | 0.622782 | + | 0.622782i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4721 | 1.40731 | 0.703655 | − | 0.710542i | \(-0.251550\pi\) | ||||
0.703655 | + | 0.710542i | \(0.251550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.1246i | 1.96140i | 0.195509 | + | 0.980702i | \(0.437364\pi\) | ||||
−0.195509 | + | 0.980702i | \(0.562636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.52786 | − | 5.52786i | 0.465530 | − | 0.465530i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.61803 | − | 13.0902i | 0.218931 | − | 1.09466i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.7082i | 0.972313i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.32624 | − | 4.32624i | 0.356822 | − | 0.356822i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.94427 | + | 5.94427i | −0.486974 | + | 0.486974i | −0.907350 | − | 0.420376i | \(-0.861898\pi\) |
0.420376 | + | 0.907350i | \(0.361898\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.145898 | + | 0.145898i | −0.0118730 | + | 0.0118730i | −0.713018 | − | 0.701145i | \(-0.752672\pi\) |
0.701145 | + | 0.713018i | \(0.252672\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.00000 | + | 5.00000i | 0.404226 | + | 0.404226i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −13.0902 | − | 13.0902i | −1.05143 | − | 1.05143i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | − | 5.00000i | −0.399043 | − | 0.399043i | 0.478852 | − | 0.877896i | \(-0.341053\pi\) |
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.81966i | 0.144308i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.29180i | − | 0.336159i | −0.985773 | − | 0.168080i | \(-0.946243\pi\) | ||
0.985773 | − | 0.168080i | \(-0.0537566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.23607i | 0.563327i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.5279 | −1.04682 | −0.523409 | − | 0.852082i | \(-0.675340\pi\) | ||||
−0.523409 | + | 0.852082i | \(0.675340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.00000 | − | 12.0000i | 0.384615 | − | 0.923077i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13.0902 | − | 13.0902i | −1.00103 | − | 1.00103i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 17.1803 | + | 17.1803i | 1.30620 | + | 1.30620i | 0.924138 | + | 0.382059i | \(0.124785\pi\) |
0.382059 | + | 0.924138i | \(0.375215\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.18034 | −0.314214 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 8.29180i | − | 0.616324i | −0.951334 | − | 0.308162i | \(-0.900286\pi\) | ||
0.951334 | − | 0.308162i | \(-0.0997139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.52786 | + | 3.52786i | −0.260787 | + | 0.260787i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.7082 | −1.59602 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.7082i | 0.856189i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.41641 | 0.536632 | 0.268316 | − | 0.963331i | \(-0.413533\pi\) | ||||
0.268316 | + | 0.963331i | \(0.413533\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 3.41641i | − | 0.245918i | −0.992412 | − | 0.122959i | \(-0.960762\pi\) | ||
0.992412 | − | 0.122959i | \(-0.0392384\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.38197 | + | 6.90983i | −0.0989646 | + | 0.494823i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4164 | 0.809288 | 0.404644 | − | 0.914474i | \(-0.367395\pi\) | ||||
0.404644 | + | 0.914474i | \(0.367395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.180340 | + | 0.180340i | 0.0127202 | + | 0.0127202i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.41641 | − | 8.41641i | −0.587827 | − | 0.587827i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.56231 | − | 7.56231i | 0.525617 | − | 0.525617i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 30.6525i | − | 2.12028i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.41641 | 0.235195 | 0.117598 | − | 0.993061i | \(-0.462481\pi\) | ||||
0.117598 | + | 0.993061i | \(0.462481\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.23607 | −0.221732 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.61803 | − | 8.61803i | −0.587745 | − | 0.587745i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.23607 | + | 7.23607i | 0.488968 | + | 0.488968i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.23607 | + | 11.1803i | −0.150414 | + | 0.752071i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.41641 | 0.496639 | 0.248320 | − | 0.968678i | \(-0.420122\pi\) | ||||
0.248320 | + | 0.968678i | \(0.420122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 11.1803i | 0.745356i | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.29180i | 0.550346i | 0.961395 | + | 0.275173i | \(0.0887351\pi\) | ||||
−0.961395 | + | 0.275173i | \(0.911265\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.41641 | − | 8.41641i | −0.556172 | − | 0.556172i | 0.372043 | − | 0.928215i | \(-0.378657\pi\) |
−0.928215 | + | 0.372043i | \(0.878657\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.47214 | + | 7.47214i | 0.489516 | + | 0.489516i | 0.908153 | − | 0.418638i | \(-0.137492\pi\) |
−0.418638 | + | 0.908153i | \(0.637492\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 20.0000 | 1.30466 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.29180 | + | 2.29180i | 0.148868 | + | 0.148868i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.61803 | − | 8.61803i | 0.557454 | − | 0.557454i | −0.371128 | − | 0.928582i | \(-0.621029\pi\) |
0.928582 | + | 0.371128i | \(0.121029\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.70820 | + | 2.70820i | −0.174451 | + | 0.174451i | −0.788932 | − | 0.614481i | \(-0.789365\pi\) |
0.614481 | + | 0.788932i | \(0.289365\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.3820 | − | 11.3820i | 0.730153 | − | 0.730153i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.6525 | 1.00000 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.85410 | − | 29.2705i | 0.372488 | − | 1.86244i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.47214 | − | 6.47214i | 0.410155 | − | 0.410155i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.1803i | − | 1.65249i | −0.563312 | − | 0.826244i | \(-0.690473\pi\) | ||
0.563312 | − | 0.826244i | \(-0.309527\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.7082 | 1.11331 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 6.18034i | − | 0.387028i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −17.1803 | + | 17.1803i | −1.07168 | + | 1.07168i | −0.0744558 | + | 0.997224i | \(0.523722\pi\) |
−0.997224 | + | 0.0744558i | \(0.976278\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.7082 | 0.724720 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0344 | − | 22.0344i | 1.35870 | − | 1.35870i | 0.483182 | − | 0.875520i | \(-0.339481\pi\) |
0.875520 | − | 0.483182i | \(-0.160519\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.29180 | + | 3.29180i | −0.202213 | + | 0.202213i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.76393 | −0.169150 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 13.5279i | − | 0.824808i | −0.911001 | − | 0.412404i | \(-0.864689\pi\) | ||
0.911001 | − | 0.412404i | \(-0.135311\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.56231 | + | 7.56231i | −0.459377 | + | 0.459377i | −0.898451 | − | 0.439074i | \(-0.855307\pi\) |
0.439074 | + | 0.898451i | \(0.355307\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.0902 | + | 13.0902i | −0.789367 | + | 0.789367i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.70820 | − | 2.70820i | 0.162720 | − | 0.162720i | −0.621050 | − | 0.783771i | \(-0.713294\pi\) |
0.783771 | + | 0.621050i | \(0.213294\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.0902 | + | 13.0902i | −0.783688 | + | 0.783688i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.23607 | − | 2.23607i | 0.133393 | − | 0.133393i | −0.637258 | − | 0.770651i | \(-0.719931\pi\) |
0.770651 | + | 0.637258i | \(0.219931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.8541 | + | 15.8541i | 0.942429 | + | 0.942429i | 0.998431 | − | 0.0560021i | \(-0.0178354\pi\) |
−0.0560021 | + | 0.998431i | \(0.517835\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.1803i | 0.958441i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000i | 0.411765i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.52786 | − | 9.52786i | −0.558533 | − | 0.558533i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 27.7082i | − | 1.61873i | −0.587306 | − | 0.809365i | \(-0.699811\pi\) | ||
0.587306 | − | 0.809365i | \(-0.300189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.56231 | − | 7.56231i | −0.440294 | − | 0.440294i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.9443 | 0.983206 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.9098 | + | 3.38197i | 0.977921 | + | 0.195584i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.944272 | − | 0.944272i | −0.0542470 | − | 0.0542470i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −12.7639 | −0.730861 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.76393 | −0.271011 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.18034i | − | 0.123636i | −0.998087 | − | 0.0618179i | \(-0.980310\pi\) | ||
0.998087 | − | 0.0618179i | \(-0.0196898\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.7082 | + | 14.7082i | −0.831357 | + | 0.831357i | −0.987702 | − | 0.156346i | \(-0.950029\pi\) |
0.156346 | + | 0.987702i | \(0.450029\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.70820i | − | 0.208273i | −0.994563 | − | 0.104137i | \(-0.966792\pi\) | ||
0.994563 | − | 0.104137i | \(-0.0332080\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.7082 | + | 13.7082i | 0.767512 | + | 0.767512i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.23607 | 0.180620 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 26.1803i | 1.45671i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.0000 | + | 10.0000i | −0.832050 | + | 0.554700i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 5.81966i | − | 0.321828i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.8541 | − | 15.8541i | −0.871420 | − | 0.871420i | 0.121207 | − | 0.992627i | \(-0.461324\pi\) |
−0.992627 | + | 0.121207i | \(0.961324\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.7082i | 1.18960i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.652476i | 0.0356486i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.4164 | + | 14.4164i | −0.785312 | + | 0.785312i | −0.980722 | − | 0.195410i | \(-0.937396\pi\) |
0.195410 | + | 0.980722i | \(0.437396\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 14.7639i | − | 0.801867i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.6525 | −1.65992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.34752 | −0.503254 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.09017 | + | 7.09017i | 0.380620 | + | 0.380620i | 0.871326 | − | 0.490705i | \(-0.163261\pi\) |
−0.490705 | + | 0.871326i | \(0.663261\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.7082 | − | 16.7082i | −0.894370 | − | 0.894370i | 0.100561 | − | 0.994931i | \(-0.467936\pi\) |
−0.994931 | + | 0.100561i | \(0.967936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.1803 | + | 3.23607i | 0.863643 | + | 0.172729i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.7639 | −0.679356 | −0.339678 | − | 0.940542i | \(-0.610318\pi\) | ||||
−0.339678 | + | 0.940542i | \(0.610318\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.85410 | − | 5.85410i | −0.310703 | − | 0.310703i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.0902 | + | 13.0902i | 0.690873 | + | 0.690873i | 0.962424 | − | 0.271551i | \(-0.0875366\pi\) |
−0.271551 | + | 0.962424i | \(0.587537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 49.5410i | − | 2.60742i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.67376 | + | 1.67376i | 0.0878497 | + | 0.0878497i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 26.1803i | 1.37034i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.8541 | + | 11.8541i | 0.618779 | + | 0.618779i | 0.945218 | − | 0.326439i | \(-0.105849\pi\) |
−0.326439 | + | 0.945218i | \(0.605849\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8.41641 | + | 8.41641i | −0.438141 | + | 0.438141i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.416408 | + | 0.416408i | −0.0215608 | + | 0.0215608i | −0.717805 | − | 0.696244i | \(-0.754853\pi\) |
0.696244 | + | 0.717805i | \(0.254853\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.90983 | − | 6.90983i | 0.356822 | − | 0.356822i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.4721 | + | 15.7082i | 0.539342 | + | 0.809014i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.85410 | − | 3.85410i | 0.197972 | − | 0.197972i | −0.601158 | − | 0.799130i | \(-0.705294\pi\) |
0.799130 | + | 0.601158i | \(0.205294\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.180340i | 0.00923909i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.8885 | −0.914062 | −0.457031 | − | 0.889451i | \(-0.651087\pi\) | ||||
−0.457031 | + | 0.889451i | \(0.651087\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.61803 | + | 8.61803i | −0.438079 | + | 0.438079i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.4164 | 1.28866 | 0.644332 | − | 0.764746i | \(-0.277136\pi\) | ||||
0.644332 | + | 0.764746i | \(0.277136\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.1246 | −0.764884 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.58359 | − | 4.58359i | 0.231212 | − | 0.231212i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.29180i | 0.417206i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.12461 | −0.257197 | −0.128598 | − | 0.991697i | \(-0.541048\pi\) | ||||
−0.128598 | + | 0.991697i | \(0.541048\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.23607 | − | 2.23607i | 0.111664 | − | 0.111664i | −0.649067 | − | 0.760731i | \(-0.724841\pi\) |
0.760731 | + | 0.649067i | \(0.224841\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.2705 | − | 5.85410i | −1.45807 | − | 0.291614i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.05573 | 0.300912 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.4164 | + | 25.4164i | −1.25984 | + | 1.25984i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.29180 | + | 3.29180i | −0.162769 | + | 0.162769i | −0.783792 | − | 0.621023i | \(-0.786717\pi\) |
0.621023 | + | 0.783792i | \(0.286717\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.1803 | + | 10.1803i | −0.502159 | + | 0.502159i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.4164 | 1.14947 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.2918 | − | 14.2918i | −0.699872 | − | 0.699872i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.5967i | 1.05507i | 0.849533 | + | 0.527535i | \(0.176884\pi\) | ||||
−0.849533 | + | 0.527535i | \(0.823116\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.29180 | + | 3.29180i | 0.160432 | + | 0.160432i | 0.782758 | − | 0.622326i | \(-0.213812\pi\) |
−0.622326 | + | 0.782758i | \(0.713812\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 20.0000i | − | 0.972433i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.1803 | − | 11.1803i | 0.542326 | − | 0.542326i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.47214 | + | 9.70820i | 0.312478 | + | 0.468717i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.9098 | + | 16.9098i | 0.814518 | + | 0.814518i | 0.985308 | − | 0.170790i | \(-0.0546319\pi\) |
−0.170790 | + | 0.985308i | \(0.554632\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | + | 17.0000i | 0.816968 | + | 0.816968i | 0.985668 | − | 0.168700i | \(-0.0539568\pi\) |
−0.168700 | + | 0.985668i | \(0.553957\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.23607 | − | 7.23607i | −0.346943 | − | 0.346943i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 39.5967 | 1.89417 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.0000 | −0.954548 | −0.477274 | − | 0.878755i | \(-0.658375\pi\) | ||||
−0.477274 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 15.6525i | − | 0.745356i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.326238 | − | 0.326238i | 0.0155000 | − | 0.0155000i | −0.699314 | − | 0.714814i | \(-0.746511\pi\) |
0.714814 | + | 0.699314i | \(0.246511\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.00000 | − | 5.00000i | −0.237023 | − | 0.237023i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 7.34752i | − | 0.347526i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5279 | + | 10.5279i | 0.496841 | + | 0.496841i | 0.910453 | − | 0.413612i | \(-0.135733\pi\) |
−0.413612 | + | 0.910453i | \(0.635733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.7082 | −0.928023 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 0.180340i | − | 0.00847311i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 23.4164i | − | 1.09537i | −0.836684 | − | 0.547687i | \(-0.815509\pi\) | ||
0.836684 | − | 0.547687i | \(-0.184491\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.4721 | −0.675501 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.1803 | + | 17.1803i | 0.800168 | + | 0.800168i | 0.983122 | − | 0.182953i | \(-0.0585657\pi\) |
−0.182953 | + | 0.983122i | \(0.558566\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.29180i | − | 0.199457i | −0.995015 | − | 0.0997283i | \(-0.968203\pi\) | ||
0.995015 | − | 0.0997283i | \(-0.0317974\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.1803 | 0.750345 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.0344 | + | 16.0344i | −0.741985 | + | 0.741985i | −0.972960 | − | 0.230974i | \(-0.925809\pi\) |
0.230974 | + | 0.972960i | \(0.425809\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.18034 | 0.284775 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.1803 | −0.927893 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −29.2705 | + | 29.2705i | −1.34302 | + | 1.34302i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.29180 | + | 3.29180i | 0.150721 | + | 0.150721i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.7426 | − | 25.7426i | −1.17621 | − | 1.17621i | −0.980702 | − | 0.195510i | \(-0.937364\pi\) |
−0.195510 | − | 0.980702i | \(-0.562636\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.1246 | + | 19.4164i | −1.32797 | + | 0.885312i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 34.4721i | − | 1.56530i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.1246i | − | 0.685362i | −0.939452 | − | 0.342681i | \(-0.888665\pi\) | ||
0.939452 | − | 0.342681i | \(-0.111335\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.65248 | + | 2.65248i | 0.119949 | + | 0.119949i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.6525i | 1.11255i | 0.830998 | + | 0.556275i | \(0.187770\pi\) | ||||
−0.830998 | + | 0.556275i | \(0.812230\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.7082 | − | 11.7082i | −0.527311 | − | 0.527311i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 13.0902 | + | 13.0902i | 0.588359 | + | 0.588359i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.9787 | − | 20.9787i | 0.939136 | − | 0.939136i | −0.0591150 | − | 0.998251i | \(-0.518828\pi\) |
0.998251 | + | 0.0591150i | \(0.0188279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.36068 | − | 8.36068i | 0.373528 | − | 0.373528i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −11.6738 | + | 11.6738i | −0.520507 | + | 0.520507i | −0.917725 | − | 0.397217i | \(-0.869976\pi\) |
0.397217 | + | 0.917725i | \(0.369976\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.41641i | − | 0.152028i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.32624 | + | 10.5066i | 0.192135 | + | 0.466614i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.76393 | − | 9.76393i | 0.432779 | − | 0.432779i | −0.456794 | − | 0.889573i | \(-0.651002\pi\) |
0.889573 | + | 0.456794i | \(0.151002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 37.8885 | 1.67282 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.61803 | − | 8.61803i | −0.379756 | − | 0.379756i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.4164 | − | 23.4164i | 1.02985 | − | 1.02985i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −21.2361 | −0.932160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.1246 | 1.80170 | 0.900851 | − | 0.434128i | \(-0.142944\pi\) | ||||
0.900851 | + | 0.434128i | \(0.142944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.2705 | − | 25.2705i | 1.10500 | − | 1.10500i | 0.111205 | − | 0.993798i | \(-0.464529\pi\) |
0.993798 | − | 0.111205i | \(-0.0354709\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.1803 | 1.14043 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 0.124612i | − | 0.00541790i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.56231 | + | 7.56231i | −0.328176 | + | 0.328176i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.8197 | − | 3.76393i | −0.815170 | − | 0.163034i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.85410 | + | 5.85410i | 0.253095 | + | 0.253095i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −7.41641 | + | 7.41641i | −0.320042 | + | 0.320042i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.3262 | − | 18.3262i | 0.789367 | − | 0.789367i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.4164 | − | 14.4164i | 0.619810 | − | 0.619810i | −0.325673 | − | 0.945483i | \(-0.605591\pi\) |
0.945483 | + | 0.325673i | \(0.105591\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.12461 | + | 5.12461i | 0.219918 | + | 0.219918i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.5279 | − | 10.5279i | 0.450964 | − | 0.450964i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.56231 | − | 7.56231i | −0.323341 | − | 0.323341i | 0.526706 | − | 0.850047i | \(-0.323427\pi\) |
−0.850047 | + | 0.526706i | \(0.823427\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.7639i | 0.544751i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.6525 | + | 30.6525i | 1.30584 | + | 1.30584i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.4164 | − | 13.4164i | 0.569495 | − | 0.569495i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −35.2361 | −1.49300 | −0.746500 | − | 0.665385i | \(-0.768267\pi\) | ||||
−0.746500 | + | 0.665385i | \(0.768267\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −19.2705 | − | 3.85410i | −0.815056 | − | 0.163011i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.23607 | − | 7.23607i | −0.305507 | − | 0.305507i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.09017 | − | 1.09017i | −0.0459452 | − | 0.0459452i | 0.683761 | − | 0.729706i | \(-0.260343\pi\) |
−0.729706 | + | 0.683761i | \(0.760343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.7082 | − | 26.7082i | 1.12362 | − | 1.12362i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 17.1246 | 0.717901 | 0.358951 | − | 0.933357i | \(-0.383135\pi\) | ||||
0.358951 | + | 0.933357i | \(0.383135\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.29180i | − | 0.347001i | −0.984834 | − | 0.173500i | \(-0.944492\pi\) | ||
0.984834 | − | 0.173500i | \(-0.0555078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4.58359 | + | 4.58359i | −0.191482 | + | 0.191482i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.9098 | − | 16.9098i | −0.705189 | − | 0.705189i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 27.1246i | − | 1.12921i | −0.825360 | − | 0.564606i | \(-0.809028\pi\) | ||
0.825360 | − | 0.564606i | \(-0.190972\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.11146 | + | 2.11146i | 0.0877491 | + | 0.0877491i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.70820i | 0.319241i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.0000 | + | 15.0000i | 0.413449 | + | 0.620174i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 23.1246i | − | 0.954455i | −0.878780 | − | 0.477227i | \(-0.841642\pi\) | ||
0.878780 | − | 0.477227i | \(-0.158358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −68.5410 | −2.82418 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.41641 | − | 7.41641i | −0.305070 | − | 0.305070i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 16.5836i | − | 0.681007i | −0.940243 | − | 0.340503i | \(-0.889403\pi\) | ||
0.940243 | − | 0.340503i | \(-0.110597\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.05573 | + | 7.05573i | −0.288772 | + | 0.288772i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 41.0132i | 1.67575i | 0.545861 | + | 0.837876i | \(0.316203\pi\) | ||||
−0.545861 | + | 0.837876i | \(0.683797\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0000 | 0.571072 | 0.285536 | − | 0.958368i | \(-0.407828\pi\) | ||||
0.285536 | + | 0.958368i | \(0.407828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.652476 | 0.0265709 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.05573i | 0.246200i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.2705 | − | 29.2705i | −1.18805 | − | 1.18805i | −0.977605 | − | 0.210448i | \(-0.932508\pi\) |
−0.210448 | − | 0.977605i | \(-0.567492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 26.8328 | − | 17.8885i | 1.08554 | − | 0.723693i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4164 | 0.541884 | 0.270942 | − | 0.962596i | \(-0.412665\pi\) | ||||
0.270942 | + | 0.962596i | \(0.412665\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.4033 | 0.419500 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.58359i | 0.184528i | 0.995735 | + | 0.0922642i | \(0.0294104\pi\) | ||||
−0.995735 | + | 0.0922642i | \(0.970590\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.2705 | + | 17.2705i | 0.694160 | + | 0.694160i | 0.963145 | − | 0.268984i | \(-0.0866879\pi\) |
−0.268984 | + | 0.963145i | \(0.586688\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 21.8885i | 0.878357i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.9443 | + | 18.9443i | 0.756561 | + | 0.756561i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.7082 | − | 21.7082i | 0.865563 | − | 0.865563i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.2705 | + | 29.2705i | −1.16524 | + | 1.16524i | −0.181929 | + | 0.983312i | \(0.558234\pi\) |
−0.983312 | + | 0.181929i | \(0.941766\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.11146 | + | 2.11146i | −0.0839228 | + | 0.0839228i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.326238 | + | 0.326238i | −0.0129464 | + | 0.0129464i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.0000 | − | 14.0000i | 0.832050 | − | 0.554700i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.85410 | + | 5.85410i | −0.231585 | + | 0.231585i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.9443i | 1.30122i | 0.759412 | + | 0.650610i | \(0.225487\pi\) | ||||
−0.759412 | + | 0.650610i | \(0.774513\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.4164 | 1.71218 | 0.856088 | − | 0.516830i | \(-0.172888\pi\) | ||||
0.856088 | + | 0.516830i | \(0.172888\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.6525 | 0.419441 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.09017 | − | 1.09017i | 0.0428590 | − | 0.0428590i | −0.685352 | − | 0.728211i | \(-0.740352\pi\) |
0.728211 | + | 0.685352i | \(0.240352\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.7082 | −0.695108 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.0689 | + | 29.0689i | −1.13755 | + | 1.13755i | −0.148666 | + | 0.988887i | \(0.547498\pi\) |
−0.988887 | + | 0.148666i | \(0.952502\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 16.5836 | 0.647975 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 26.1803 | 1.02139 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 32.0689i | − | 1.24923i | −0.780934 | − | 0.624613i | \(-0.785257\pi\) | ||
0.780934 | − | 0.624613i | \(-0.214743\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.7082 | − | 10.7082i | 0.416501 | − | 0.416501i | −0.467495 | − | 0.883996i | \(-0.654843\pi\) |
0.883996 | + | 0.467495i | \(0.154843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.52786 | − | 8.29180i | −0.214684 | − | 0.322027i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.7082 | + | 17.7082i | −0.685664 | + | 0.685664i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.58359 | + | 4.58359i | −0.177212 | + | 0.177212i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.9443 | + | 14.9443i | −0.576917 | + | 0.576917i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.1246 | − | 30.1246i | −1.16122 | − | 1.16122i | −0.984209 | − | 0.177009i | \(-0.943358\pi\) |
−0.177009 | − | 0.984209i | \(-0.556642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.1803 | − | 16.1803i | −0.622782 | − | 0.622782i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.0557281 | − | 0.0557281i | −0.00214180 | − | 0.00214180i | 0.706035 | − | 0.708177i | \(-0.250482\pi\) |
−0.708177 | + | 0.706035i | \(0.750482\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.12461 | − | 5.12461i | −0.196376 | − | 0.196376i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 35.1246i | − | 1.34401i | −0.740548 | − | 0.672003i | \(-0.765434\pi\) | ||
0.740548 | − | 0.672003i | \(-0.234566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.8328 | −1.40731 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.4033 | 0.396909 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.47214 | + | 7.36068i | −0.0560839 | + | 0.280420i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.9787 | + | 34.9787i | 1.33065 | + | 1.33065i | 0.904786 | + | 0.425867i | \(0.140031\pi\) |
0.425867 | + | 0.904786i | \(0.359969\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 51.7082i | − | 1.96140i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.8328 | 0.637588 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.23607 | −0.349340 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.3607i | 1.07117i | 0.844482 | + | 0.535584i | \(0.179908\pi\) | ||||
−0.844482 | + | 0.535584i | \(0.820092\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −56.8328 | + | 56.8328i | −2.14349 | + | 2.14349i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −12.3607 | + | 12.3607i | −0.465530 | + | 0.465530i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.4164 | + | 18.4164i | 0.691643 | + | 0.691643i | 0.962593 | − | 0.270951i | \(-0.0873380\pi\) |
−0.270951 | + | 0.962593i | \(0.587338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.29180 | 0.310967 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 39.5967i | − | 1.48291i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.85410 | + | 29.2705i | −0.218931 | + | 1.09466i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 10.6525i | 0.397824i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.4164 | −1.17163 | −0.585817 | − | 0.810443i | \(-0.699226\pi\) | ||||
−0.585817 | + | 0.810443i | \(0.699226\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 3.34752i | − | 0.124496i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 26.1803i | − | 0.972313i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.8541 | − | 21.8541i | 0.810524 | − | 0.810524i | −0.174189 | − | 0.984712i | \(-0.555730\pi\) |
0.984712 | + | 0.174189i | \(0.0557302\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.94427i | 0.220158i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.2361 | 0.637499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.0000 | −1.10808 | −0.554038 | − | 0.832492i | \(-0.686914\pi\) | ||||
−0.554038 | + | 0.832492i | \(0.686914\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.67376 | + | 9.67376i | −0.356822 | + | 0.356822i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.763932 | + | 0.763932i | 0.0281398 | + | 0.0281398i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.56231 | + | 7.56231i | 0.278184 | + | 0.278184i | 0.832384 | − | 0.554200i | \(-0.186976\pi\) |
−0.554200 | + | 0.832384i | \(0.686976\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14.4721 | + | 21.7082i | 0.531647 | + | 0.797471i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.3050 | −1.36859 | −0.684293 | − | 0.729207i | \(-0.739889\pi\) | ||||
−0.684293 | + | 0.729207i | \(0.739889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.2918 | − | 13.2918i | 0.486974 | − | 0.486974i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 23.4164i | − | 0.856762i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 11.1246i | − | 0.405943i | −0.979185 | − | 0.202971i | \(-0.934940\pi\) | ||
0.979185 | − | 0.202971i | \(-0.0650599\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.1803 | + | 16.1803i | 0.589644 | + | 0.589644i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.326238 | − | 0.326238i | 0.0118730 | − | 0.0118730i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.2918 | − | 13.2918i | −0.483099 | − | 0.483099i | 0.423021 | − | 0.906120i | \(-0.360970\pi\) |
−0.906120 | + | 0.423021i | \(0.860970\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.9443 | + | 10.9443i | −0.397252 | + | 0.397252i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.4721 | + | 25.4721i | −0.923364 | + | 0.923364i | −0.997266 | − | 0.0739013i | \(-0.976455\pi\) |
0.0739013 | + | 0.997266i | \(0.476455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.1803 | − | 11.1803i | −0.404226 | − | 0.404226i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.9098 | − | 3.38197i | −0.610579 | − | 0.122116i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.00000 | − | 5.00000i | 0.180305 | − | 0.180305i | −0.611184 | − | 0.791489i | \(-0.709306\pi\) |
0.791489 | + | 0.611184i | \(0.209306\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 21.2361i | − | 0.764798i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.6525 | 1.10249 | 0.551246 | − | 0.834342i | \(-0.314152\pi\) | ||||
0.551246 | + | 0.834342i | \(0.314152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.2705 | + | 29.2705i | 1.05143 | + | 1.05143i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −44.0689 | −1.57893 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7082 | −0.490518 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −16.9443 | + | 16.9443i | −0.605539 | + | 0.605539i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.1803 | + | 11.1803i | 0.399043 | + | 0.399043i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.5836 | 0.591141 | 0.295571 | − | 0.955321i | \(-0.404490\pi\) | ||||
0.295571 | + | 0.955321i | \(0.404490\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.2361i | 0.969630i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.1246 | + | 11.4164i | −0.608113 | + | 0.405409i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 4.06888i | − | 0.144308i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26.8885 | + | 26.8885i | −0.952441 | + | 0.952441i | −0.998919 | − | 0.0464782i | \(-0.985200\pi\) |
0.0464782 | + | 0.998919i | \(0.485200\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.0000 | + | 20.0000i | −0.707549 | + | 0.707549i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.00000 | + | 5.00000i | −0.176666 | + | 0.176666i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 30.6525 | + | 30.6525i | 1.08170 | + | 1.08170i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.36068 | + | 8.36068i | 0.294310 | + | 0.294310i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.1803i | 0.920452i | 0.887802 | + | 0.460226i | \(0.152232\pi\) | ||||
−0.887802 | + | 0.460226i | \(0.847768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.56231 | + | 3.56231i | 0.125089 | + | 0.125089i | 0.766880 | − | 0.641791i | \(-0.221808\pi\) |
−0.641791 | + | 0.766880i | \(0.721808\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 9.34752i | − | 0.327832i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.59675i | 0.336159i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −45.1246 | −1.57871 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.3607 | − | 37.3607i | −1.30390 | − | 1.30390i | −0.925743 | − | 0.378154i | \(-0.876559\pi\) |
−0.378154 | − | 0.925743i | \(-0.623441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.9787 | − | 22.9787i | −0.800988 | − | 0.800988i | 0.182262 | − | 0.983250i | \(-0.441658\pi\) |
−0.983250 | + | 0.182262i | \(0.941658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 16.1803i | − | 0.563327i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.4721 | 0.781433 | 0.390716 | − | 0.920511i | \(-0.372227\pi\) | ||||
0.390716 | + | 0.920511i | \(0.372227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.7082 | 0.476106 | 0.238053 | − | 0.971252i | \(-0.423491\pi\) | ||||
0.238053 | + | 0.971252i | \(0.423491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.34752i | 0.116124i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.6525 | + | 15.6525i | −0.542326 | + | 0.542326i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.2492 | 1.04682 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 37.8885i | − | 1.30962i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22.7984 | + | 22.7984i | 0.787087 | + | 0.787087i | 0.981016 | − | 0.193928i | \(-0.0621230\pi\) |
−0.193928 | + | 0.981016i | \(0.562123\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.58359 | 0.0546066 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.76393i | 0.0951949i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.1803 | + | 26.8328i | −0.384615 | + | 0.923077i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.5967 | −0.672559 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −32.8328 | − | 32.8328i | −1.12549 | − | 1.12549i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.87539i | 0.166930i | 0.996511 | + | 0.0834651i | \(0.0265987\pi\) | ||||
−0.996511 | + | 0.0834651i | \(0.973401\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.2705 | + | 29.2705i | 1.00103 | + | 1.00103i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.65248 | − | 9.65248i | 0.329722 | − | 0.329722i | −0.522759 | − | 0.852481i | \(-0.675097\pi\) |
0.852481 | + | 0.522759i | \(0.175097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 51.7082i | − | 1.76426i | −0.471005 | − | 0.882131i | \(-0.656109\pi\) | ||
0.471005 | − | 0.882131i | \(-0.343891\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −34.4721 | −1.17345 | −0.586723 | − | 0.809788i | \(-0.699582\pi\) | ||||
−0.586723 | + | 0.809788i | \(0.699582\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −38.4164 | − | 38.4164i | −1.30620 | − | 1.30620i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.32624 | − | 4.32624i | −0.146927 | − | 0.146927i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.70820 | + | 9.70820i | 0.329328 | + | 0.329328i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.583592 | + | 0.875388i | 0.0197743 | + | 0.0296614i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.4721 | −1.16671 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.8328i | 1.58143i | 0.612183 | + | 0.790716i | \(0.290291\pi\) | ||||
−0.612183 | + | 0.790716i | \(0.709709\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 17.1246 | + | 17.1246i | 0.577599 | + | 0.577599i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.0689i | 0.676138i | 0.941121 | + | 0.338069i | \(0.109774\pi\) | ||||
−0.941121 | + | 0.338069i | \(0.890226\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.8541 | + | 27.8541i | 0.937365 | + | 0.937365i | 0.998151 | − | 0.0607857i | \(-0.0193606\pi\) |
−0.0607857 | + | 0.998151i | \(0.519361\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.34752 | 0.314214 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.3820 | + | 21.3820i | 0.717936 | + | 0.717936i | 0.968182 | − | 0.250246i | \(-0.0805115\pi\) |
−0.250246 | + | 0.968182i | \(0.580512\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.09017 | − | 7.09017i | 0.237530 | − | 0.237530i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.3607 | − | 52.3607i | 1.75218 | − | 1.75218i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −26.8328 | −0.896922 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.5410 | + | 8.36068i | −0.418732 | + | 0.279155i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.6525 | − | 30.6525i | 1.02232 | − | 1.02232i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.58359i | − | 0.219331i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.5410i | 0.616324i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.27051 | − | 5.27051i | 0.175004 | − | 0.175004i | −0.614170 | − | 0.789174i | \(-0.710509\pi\) |
0.789174 | + | 0.614170i | \(0.210509\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.41641 | −0.113315 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 50.8328 | 1.68417 | 0.842083 | − | 0.539348i | \(-0.181329\pi\) | ||||
0.842083 | + | 0.539348i | \(0.181329\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.4164 | − | 27.4164i | 0.907351 | − | 0.907351i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.88854 | − | 7.88854i | 0.260787 | − | 0.260787i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 35.1246i | − | 1.15865i | −0.815095 | − | 0.579327i | \(-0.803315\pi\) | ||
0.815095 | − | 0.579327i | \(-0.196685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.41641 | − | 7.41641i | 0.244379 | − | 0.244379i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −13.0902 | − | 2.61803i | −0.430868 | − | 0.0861736i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.5410 | 1.59602 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.61803 | + | 8.61803i | −0.283053 | + | 0.283053i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.88854 | − | 2.88854i | 0.0947700 | − | 0.0947700i | −0.658132 | − | 0.752902i | \(-0.728653\pi\) |
0.752902 | + | 0.658132i | \(0.228653\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.9787 | − | 40.9787i | 1.34302 | − | 1.34302i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.34752 | + | 1.34752i | 0.0441160 | + | 0.0441160i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 26.1803i | − | 0.856189i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.4164 | + | 32.4164i | 1.05900 | + | 1.05900i | 0.998147 | + | 0.0608510i | \(0.0193815\pi\) |
0.0608510 | + | 0.998147i | \(0.480619\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 18.1803i | − | 0.593293i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.3607 | − | 13.3607i | −0.435546 | − | 0.435546i | 0.454964 | − | 0.890510i | \(-0.349652\pi\) |
−0.890510 | + | 0.454964i | \(0.849652\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 25.4590i | − | 0.829058i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.05573 | 0.0992978 | 0.0496489 | − | 0.998767i | \(-0.484190\pi\) | ||||
0.0496489 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.4164 | + | 35.1246i | 0.760129 | + | 1.14019i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.29180 | + | 2.29180i | 0.0743166 | + | 0.0743166i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.7639 | + | 27.7639i | 0.899362 | + | 0.899362i | 0.995380 | − | 0.0960177i | \(-0.0306105\pi\) |
−0.0960177 | + | 0.995380i | \(0.530611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.5836 | −0.536632 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.9443 | −0.547731 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.5410i | 1.21100i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.85410 | − | 5.85410i | 0.188646 | − | 0.188646i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.63932i | 0.245918i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.12461i | 0.229112i | 0.993417 | + | 0.114556i | \(0.0365445\pi\) | ||||
−0.993417 | + | 0.114556i | \(0.963455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.1803 | − | 16.1803i | −0.519787 | − | 0.519787i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.09017 | − | 15.4508i | 0.0989646 | − | 0.494823i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.70820i | 0.118636i | 0.998239 | + | 0.0593180i | \(0.0188926\pi\) | ||||
−0.998239 | + | 0.0593180i | \(0.981107\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.7082 | −0.374196 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.5279 | − | 10.5279i | −0.336129 | − | 0.336129i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.2918i | 1.02995i | 0.857206 | + | 0.514974i | \(0.172198\pi\) | ||||
−0.857206 | + | 0.514974i | \(0.827802\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 26.8328i | − | 0.854965i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 26.0689i | − | 0.828942i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.5836 | −0.653859 | −0.326930 | − | 0.945049i | \(-0.606014\pi\) | ||||
−0.326930 | + | 0.945049i | \(0.606014\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 19.5967 | 0.621884 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.5279 | −0.809288 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29.0000 | − | 29.0000i | −0.918439 | − | 0.918439i | 0.0784767 | − | 0.996916i | \(-0.474994\pi\) |
−0.996916 | + | 0.0784767i | \(0.974994\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −31.4164 | − | 31.4164i | −0.993971 | − | 0.993971i |
(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 | 260.2.r.b.177.1 | yes | 4 | |
3.2 | odd | 2 | 2340.2.bp.e.1477.2 | 4 | |||
4.3 | odd | 2 | 1040.2.cd.j.177.2 | 4 | |||
5.2 | odd | 4 | 1300.2.m.b.593.2 | 4 | |||
5.3 | odd | 4 | 260.2.m.b.73.1 | yes | 4 | ||
5.4 | even | 2 | 1300.2.r.b.957.2 | 4 | |||
13.5 | odd | 4 | 260.2.m.b.57.1 | ✓ | 4 | ||
15.8 | even | 4 | 2340.2.u.f.73.2 | 4 | |||
20.3 | even | 4 | 1040.2.bg.j.593.2 | 4 | |||
39.5 | even | 4 | 2340.2.u.f.577.1 | 4 | |||
52.31 | even | 4 | 1040.2.bg.j.577.2 | 4 | |||
65.18 | even | 4 | inner | 260.2.r.b.213.1 | yes | 4 | |
65.44 | odd | 4 | 1300.2.m.b.57.2 | 4 | |||
65.57 | even | 4 | 1300.2.r.b.993.2 | 4 | |||
195.83 | odd | 4 | 2340.2.bp.e.1513.2 | 4 | |||
260.83 | odd | 4 | 1040.2.cd.j.993.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.m.b.57.1 | ✓ | 4 | 13.5 | odd | 4 | ||
260.2.m.b.73.1 | yes | 4 | 5.3 | odd | 4 | ||
260.2.r.b.177.1 | yes | 4 | 1.1 | even | 1 | trivial | |
260.2.r.b.213.1 | yes | 4 | 65.18 | even | 4 | inner | |
1040.2.bg.j.577.2 | 4 | 52.31 | even | 4 | |||
1040.2.bg.j.593.2 | 4 | 20.3 | even | 4 | |||
1040.2.cd.j.177.2 | 4 | 4.3 | odd | 2 | |||
1040.2.cd.j.993.2 | 4 | 260.83 | odd | 4 | |||
1300.2.m.b.57.2 | 4 | 65.44 | odd | 4 | |||
1300.2.m.b.593.2 | 4 | 5.2 | odd | 4 | |||
1300.2.r.b.957.2 | 4 | 5.4 | even | 2 | |||
1300.2.r.b.993.2 | 4 | 65.57 | even | 4 | |||
2340.2.u.f.73.2 | 4 | 15.8 | even | 4 | |||
2340.2.u.f.577.1 | 4 | 39.5 | even | 4 | |||
2340.2.bp.e.1477.2 | 4 | 3.2 | odd | 2 | |||
2340.2.bp.e.1513.2 | 4 | 195.83 | odd | 4 |