Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [35,2,Mod(13,35)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(35, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("35.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 35 = 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 35.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.279476407074\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 27.1 | ||
Root | \(-1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 35.27 |
Dual form | 35.2.f.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.707107 | − | 0.707107i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(3\) | −1.58114 | − | 1.58114i | −0.912871 | − | 0.912871i | 0.0836263 | − | 0.996497i | \(-0.473350\pi\) |
−0.996497 | + | 0.0836263i | \(0.973350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.58114 | + | 1.58114i | 0.707107 | + | 0.707107i | ||||
\(6\) | 3.16228i | 1.29099i | ||||||||
\(7\) | 2.58114 | − | 0.581139i | 0.975579 | − | 0.219650i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 2.00000i | 0.666667i | ||||||||
\(10\) | − | 3.16228i | − | 1.00000i | ||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58114 | + | 1.58114i | 0.438529 | + | 0.438529i | 0.891517 | − | 0.452988i | \(-0.149642\pi\) |
−0.452988 | + | 0.891517i | \(0.649642\pi\) | |||||||
\(14\) | −3.16228 | − | 2.00000i | −0.845154 | − | 0.534522i | ||||
\(15\) | − | 5.00000i | − | 1.29099i | ||||||
\(16\) | 4.00000 | 1.00000 | ||||||||
\(17\) | −1.58114 | + | 1.58114i | −0.383482 | + | 0.383482i | −0.872355 | − | 0.488873i | \(-0.837408\pi\) |
0.488873 | + | 0.872355i | \(0.337408\pi\) | |||||||
\(18\) | 2.00000 | − | 2.00000i | 0.471405 | − | 0.471405i | ||||
\(19\) | −3.16228 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.00000 | − | 3.16228i | −1.09109 | − | 0.690066i | ||||
\(22\) | 1.00000 | + | 1.00000i | 0.213201 | + | 0.213201i | ||||
\(23\) | 2.00000 | − | 2.00000i | 0.417029 | − | 0.417029i | −0.467150 | − | 0.884178i | \(-0.654719\pi\) |
0.884178 | + | 0.467150i | \(0.154719\pi\) | |||||||
\(24\) | 6.32456 | 1.29099 | ||||||||
\(25\) | 5.00000i | 1.00000i | ||||||||
\(26\) | − | 3.16228i | − | 0.620174i | ||||||
\(27\) | −1.58114 | + | 1.58114i | −0.304290 | + | 0.304290i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.00000i | 0.557086i | 0.960424 | + | 0.278543i | \(0.0898515\pi\) | ||||
−0.960424 | + | 0.278543i | \(0.910149\pi\) | |||||||
\(30\) | −5.00000 | + | 5.00000i | −0.912871 | + | 0.912871i | ||||
\(31\) | 3.16228i | 0.567962i | 0.958830 | + | 0.283981i | \(0.0916552\pi\) | ||||
−0.958830 | + | 0.283981i | \(0.908345\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.58114 | + | 1.58114i | 0.275241 | + | 0.275241i | ||||
\(34\) | 3.16228 | 0.542326 | ||||||||
\(35\) | 5.00000 | + | 3.16228i | 0.845154 | + | 0.534522i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | − | 6.00000i | −0.986394 | − | 0.986394i | 0.0135147 | − | 0.999909i | \(-0.495698\pi\) |
−0.999909 | + | 0.0135147i | \(0.995698\pi\) | |||||||
\(38\) | 3.16228 | + | 3.16228i | 0.512989 | + | 0.512989i | ||||
\(39\) | − | 5.00000i | − | 0.800641i | ||||||
\(40\) | −6.32456 | −1.00000 | ||||||||
\(41\) | − | 9.48683i | − | 1.48159i | −0.671729 | − | 0.740797i | \(-0.734448\pi\) | ||
0.671729 | − | 0.740797i | \(-0.265552\pi\) | |||||||
\(42\) | 1.83772 | + | 8.16228i | 0.283567 | + | 1.25947i | ||||
\(43\) | −3.00000 | + | 3.00000i | −0.457496 | + | 0.457496i | −0.897833 | − | 0.440337i | \(-0.854859\pi\) |
0.440337 | + | 0.897833i | \(0.354859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.16228 | + | 3.16228i | −0.471405 | + | 0.471405i | ||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 4.74342 | − | 4.74342i | 0.691898 | − | 0.691898i | −0.270751 | − | 0.962649i | \(-0.587272\pi\) |
0.962649 | + | 0.270751i | \(0.0872720\pi\) | |||||||
\(48\) | −6.32456 | − | 6.32456i | −0.912871 | − | 0.912871i | ||||
\(49\) | 6.32456 | − | 3.00000i | 0.903508 | − | 0.428571i | ||||
\(50\) | 5.00000 | − | 5.00000i | 0.707107 | − | 0.707107i | ||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | − | 1.00000i | 0.137361 | − | 0.137361i | −0.635083 | − | 0.772444i | \(-0.719034\pi\) |
0.772444 | + | 0.635083i | \(0.219034\pi\) | |||||||
\(54\) | 3.16228 | 0.430331 | ||||||||
\(55\) | −1.58114 | − | 1.58114i | −0.213201 | − | 0.213201i | ||||
\(56\) | −4.00000 | + | 6.32456i | −0.534522 | + | 0.845154i | ||||
\(57\) | 5.00000 | + | 5.00000i | 0.662266 | + | 0.662266i | ||||
\(58\) | 3.00000 | − | 3.00000i | 0.393919 | − | 0.393919i | ||||
\(59\) | −9.48683 | −1.23508 | −0.617540 | − | 0.786539i | \(-0.711871\pi\) | ||||
−0.617540 | + | 0.786539i | \(0.711871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.32456i | 0.809776i | 0.914366 | + | 0.404888i | \(0.132690\pi\) | ||||
−0.914366 | + | 0.404888i | \(0.867310\pi\) | |||||||
\(62\) | 3.16228 | − | 3.16228i | 0.401610 | − | 0.401610i | ||||
\(63\) | 1.16228 | + | 5.16228i | 0.146433 | + | 0.650386i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 5.00000i | 0.620174i | ||||||||
\(66\) | − | 3.16228i | − | 0.389249i | ||||||
\(67\) | −1.00000 | − | 1.00000i | −0.122169 | − | 0.122169i | 0.643379 | − | 0.765548i | \(-0.277532\pi\) |
−0.765548 | + | 0.643379i | \(0.777532\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.32456 | −0.761387 | ||||||||
\(70\) | −1.83772 | − | 8.16228i | −0.219650 | − | 0.975579i | ||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | −4.00000 | − | 4.00000i | −0.471405 | − | 0.471405i | ||||
\(73\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(74\) | 12.0000i | 1.39497i | ||||||||
\(75\) | 7.90569 | − | 7.90569i | 0.912871 | − | 0.912871i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.58114 | + | 0.581139i | −0.294148 | + | 0.0662269i | ||||
\(78\) | −5.00000 | + | 5.00000i | −0.566139 | + | 0.566139i | ||||
\(79\) | 13.0000i | 1.46261i | 0.682048 | + | 0.731307i | \(0.261089\pi\) | ||||
−0.682048 | + | 0.731307i | \(0.738911\pi\) | |||||||
\(80\) | 6.32456 | + | 6.32456i | 0.707107 | + | 0.707107i | ||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | −9.48683 | + | 9.48683i | −1.04765 | + | 1.04765i | ||||
\(83\) | 3.16228 | + | 3.16228i | 0.347105 | + | 0.347105i | 0.859030 | − | 0.511925i | \(-0.171067\pi\) |
−0.511925 | + | 0.859030i | \(0.671067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | −0.542326 | ||||||||
\(86\) | 6.00000 | 0.646997 | ||||||||
\(87\) | 4.74342 | − | 4.74342i | 0.508548 | − | 0.508548i | ||||
\(88\) | 2.00000 | − | 2.00000i | 0.213201 | − | 0.213201i | ||||
\(89\) | 6.32456 | 0.670402 | 0.335201 | − | 0.942147i | \(-0.391196\pi\) | ||||
0.335201 | + | 0.942147i | \(0.391196\pi\) | |||||||
\(90\) | 6.32456 | 0.666667 | ||||||||
\(91\) | 5.00000 | + | 3.16228i | 0.524142 | + | 0.331497i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.00000 | − | 5.00000i | 0.518476 | − | 0.518476i | ||||
\(94\) | −9.48683 | −0.978492 | ||||||||
\(95\) | −5.00000 | − | 5.00000i | −0.512989 | − | 0.512989i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.58114 | − | 1.58114i | 0.160540 | − | 0.160540i | −0.622266 | − | 0.782806i | \(-0.713788\pi\) |
0.782806 | + | 0.622266i | \(0.213788\pi\) | |||||||
\(98\) | −9.32456 | − | 3.32456i | −0.941922 | − | 0.335831i | ||||
\(99\) | − | 2.00000i | − | 0.201008i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.16228i | − | 0.314658i | −0.987546 | − | 0.157329i | \(-0.949712\pi\) | ||
0.987546 | − | 0.157329i | \(-0.0502884\pi\) | |||||||
\(102\) | −5.00000 | − | 5.00000i | −0.495074 | − | 0.495074i | ||||
\(103\) | −11.0680 | − | 11.0680i | −1.09056 | − | 1.09056i | −0.995469 | − | 0.0950911i | \(-0.969686\pi\) |
−0.0950911 | − | 0.995469i | \(-0.530314\pi\) | |||||||
\(104\) | −6.32456 | −0.620174 | ||||||||
\(105\) | −2.90569 | − | 12.9057i | −0.283567 | − | 1.25947i | ||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | −3.00000 | − | 3.00000i | −0.290021 | − | 0.290021i | 0.547068 | − | 0.837088i | \(-0.315744\pi\) |
−0.837088 | + | 0.547068i | \(0.815744\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.00000i | − | 0.670478i | −0.942133 | − | 0.335239i | \(-0.891183\pi\) | ||
0.942133 | − | 0.335239i | \(-0.108817\pi\) | |||||||
\(110\) | 3.16228i | 0.301511i | ||||||||
\(111\) | 18.9737i | 1.80090i | ||||||||
\(112\) | 10.3246 | − | 2.32456i | 0.975579 | − | 0.219650i | ||||
\(113\) | 12.0000 | − | 12.0000i | 1.12887 | − | 1.12887i | 0.138503 | − | 0.990362i | \(-0.455771\pi\) |
0.990362 | − | 0.138503i | \(-0.0442291\pi\) | |||||||
\(114\) | − | 10.0000i | − | 0.936586i | ||||||
\(115\) | 6.32456 | 0.589768 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.16228 | + | 3.16228i | −0.292353 | + | 0.292353i | ||||
\(118\) | 9.48683 | + | 9.48683i | 0.873334 | + | 0.873334i | ||||
\(119\) | −3.16228 | + | 5.00000i | −0.289886 | + | 0.458349i | ||||
\(120\) | 10.0000 | + | 10.0000i | 0.912871 | + | 0.912871i | ||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 6.32456 | − | 6.32456i | 0.572598 | − | 0.572598i | ||||
\(123\) | −15.0000 | + | 15.0000i | −1.35250 | + | 1.35250i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.90569 | + | 7.90569i | −0.707107 | + | 0.707107i | ||||
\(126\) | 4.00000 | − | 6.32456i | 0.356348 | − | 0.563436i | ||||
\(127\) | 9.00000 | + | 9.00000i | 0.798621 | + | 0.798621i | 0.982878 | − | 0.184257i | \(-0.0589879\pi\) |
−0.184257 | + | 0.982878i | \(0.558988\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.707107 | + | 0.707107i | ||||
\(129\) | 9.48683 | 0.835269 | ||||||||
\(130\) | 5.00000 | − | 5.00000i | 0.438529 | − | 0.438529i | ||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.16228 | + | 1.83772i | −0.707759 | + | 0.159351i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | −5.00000 | −0.430331 | ||||||||
\(136\) | − | 6.32456i | − | 0.542326i | ||||||
\(137\) | 2.00000 | + | 2.00000i | 0.170872 | + | 0.170872i | 0.787362 | − | 0.616491i | \(-0.211446\pi\) |
−0.616491 | + | 0.787362i | \(0.711446\pi\) | |||||||
\(138\) | 6.32456 | + | 6.32456i | 0.538382 | + | 0.538382i | ||||
\(139\) | 18.9737 | 1.60933 | 0.804663 | − | 0.593732i | \(-0.202346\pi\) | ||||
0.804663 | + | 0.593732i | \(0.202346\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0000 | −1.26323 | ||||||||
\(142\) | 6.00000 | + | 6.00000i | 0.503509 | + | 0.503509i | ||||
\(143\) | −1.58114 | − | 1.58114i | −0.132221 | − | 0.132221i | ||||
\(144\) | 8.00000i | 0.666667i | ||||||||
\(145\) | −4.74342 | + | 4.74342i | −0.393919 | + | 0.393919i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −14.7434 | − | 5.25658i | −1.21602 | − | 0.433556i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 12.0000i | − | 0.983078i | −0.870855 | − | 0.491539i | \(-0.836434\pi\) | ||
0.870855 | − | 0.491539i | \(-0.163566\pi\) | |||||||
\(150\) | −15.8114 | −1.29099 | ||||||||
\(151\) | 9.00000 | 0.732410 | 0.366205 | − | 0.930534i | \(-0.380657\pi\) | ||||
0.366205 | + | 0.930534i | \(0.380657\pi\) | |||||||
\(152\) | 6.32456 | − | 6.32456i | 0.512989 | − | 0.512989i | ||||
\(153\) | −3.16228 | − | 3.16228i | −0.255655 | − | 0.255655i | ||||
\(154\) | 3.16228 | + | 2.00000i | 0.254824 | + | 0.161165i | ||||
\(155\) | −5.00000 | + | 5.00000i | −0.401610 | + | 0.401610i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.32456 | + | 6.32456i | −0.504754 | + | 0.504754i | −0.912912 | − | 0.408157i | \(-0.866172\pi\) |
0.408157 | + | 0.912912i | \(0.366172\pi\) | |||||||
\(158\) | 13.0000 | − | 13.0000i | 1.03422 | − | 1.03422i | ||||
\(159\) | −3.16228 | −0.250785 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000 | − | 6.32456i | 0.315244 | − | 0.498445i | ||||
\(162\) | −11.0000 | − | 11.0000i | −0.864242 | − | 0.864242i | ||||
\(163\) | 6.00000 | − | 6.00000i | 0.469956 | − | 0.469956i | −0.431944 | − | 0.901900i | \(-0.642172\pi\) |
0.901900 | + | 0.431944i | \(0.142172\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.00000i | 0.389249i | ||||||||
\(166\) | − | 6.32456i | − | 0.490881i | ||||||
\(167\) | −11.0680 | + | 11.0680i | −0.856465 | + | 0.856465i | −0.990920 | − | 0.134454i | \(-0.957072\pi\) |
0.134454 | + | 0.990920i | \(0.457072\pi\) | |||||||
\(168\) | 16.3246 | − | 3.67544i | 1.25947 | − | 0.283567i | ||||
\(169\) | − | 8.00000i | − | 0.615385i | ||||||
\(170\) | 5.00000 | + | 5.00000i | 0.383482 | + | 0.383482i | ||||
\(171\) | − | 6.32456i | − | 0.483651i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.0680 | + | 11.0680i | 0.841482 | + | 0.841482i | 0.989052 | − | 0.147569i | \(-0.0471450\pi\) |
−0.147569 | + | 0.989052i | \(0.547145\pi\) | |||||||
\(174\) | −9.48683 | −0.719195 | ||||||||
\(175\) | 2.90569 | + | 12.9057i | 0.219650 | + | 0.975579i | ||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 15.0000 | + | 15.0000i | 1.12747 | + | 1.12747i | ||||
\(178\) | −6.32456 | − | 6.32456i | −0.474045 | − | 0.474045i | ||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.1359i | − | 1.64535i | −0.568511 | − | 0.822676i | \(-0.692480\pi\) | ||
0.568511 | − | 0.822676i | \(-0.307520\pi\) | |||||||
\(182\) | −1.83772 | − | 8.16228i | −0.136221 | − | 0.605028i | ||||
\(183\) | 10.0000 | − | 10.0000i | 0.739221 | − | 0.739221i | ||||
\(184\) | 8.00000i | 0.589768i | ||||||||
\(185\) | − | 18.9737i | − | 1.39497i | ||||||
\(186\) | −10.0000 | −0.733236 | ||||||||
\(187\) | 1.58114 | − | 1.58114i | 0.115624 | − | 0.115624i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.16228 | + | 5.00000i | −0.230022 | + | 0.363696i | ||||
\(190\) | 10.0000i | 0.725476i | ||||||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | −12.6491 | + | 12.6491i | −0.912871 | + | 0.912871i | ||||
\(193\) | −8.00000 | + | 8.00000i | −0.575853 | + | 0.575853i | −0.933758 | − | 0.357905i | \(-0.883491\pi\) |
0.357905 | + | 0.933758i | \(0.383491\pi\) | |||||||
\(194\) | −3.16228 | −0.227038 | ||||||||
\(195\) | 7.90569 | − | 7.90569i | 0.566139 | − | 0.566139i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.00000 | − | 1.00000i | −0.0712470 | − | 0.0712470i | 0.670585 | − | 0.741832i | \(-0.266043\pi\) |
−0.741832 | + | 0.670585i | \(0.766043\pi\) | |||||||
\(198\) | −2.00000 | + | 2.00000i | −0.142134 | + | 0.142134i | ||||
\(199\) | 9.48683 | 0.672504 | 0.336252 | − | 0.941772i | \(-0.390841\pi\) | ||||
0.336252 | + | 0.941772i | \(0.390841\pi\) | |||||||
\(200\) | −10.0000 | − | 10.0000i | −0.707107 | − | 0.707107i | ||||
\(201\) | 3.16228i | 0.223050i | ||||||||
\(202\) | −3.16228 | + | 3.16228i | −0.222497 | + | 0.222497i | ||||
\(203\) | 1.74342 | + | 7.74342i | 0.122364 | + | 0.543481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.0000 | − | 15.0000i | 1.04765 | − | 1.04765i | ||||
\(206\) | 22.1359i | 1.54228i | ||||||||
\(207\) | 4.00000 | + | 4.00000i | 0.278019 | + | 0.278019i | ||||
\(208\) | 6.32456 | + | 6.32456i | 0.438529 | + | 0.438529i | ||||
\(209\) | 3.16228 | 0.218739 | ||||||||
\(210\) | −10.0000 | + | 15.8114i | −0.690066 | + | 1.09109i | ||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.48683 | + | 9.48683i | 0.650027 | + | 0.650027i | ||||
\(214\) | 6.00000i | 0.410152i | ||||||||
\(215\) | −9.48683 | −0.646997 | ||||||||
\(216\) | − | 6.32456i | − | 0.430331i | ||||||
\(217\) | 1.83772 | + | 8.16228i | 0.124753 | + | 0.554092i | ||||
\(218\) | −7.00000 | + | 7.00000i | −0.474100 | + | 0.474100i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | −0.336336 | ||||||||
\(222\) | 18.9737 | − | 18.9737i | 1.27343 | − | 1.27343i | ||||
\(223\) | −14.2302 | − | 14.2302i | −0.952928 | − | 0.952928i | 0.0460129 | − | 0.998941i | \(-0.485348\pi\) |
−0.998941 | + | 0.0460129i | \(0.985348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.0000 | −0.666667 | ||||||||
\(226\) | −24.0000 | −1.59646 | ||||||||
\(227\) | 1.58114 | − | 1.58114i | 0.104944 | − | 0.104944i | −0.652685 | − | 0.757629i | \(-0.726358\pi\) |
0.757629 | + | 0.652685i | \(0.226358\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −15.8114 | −1.04485 | −0.522423 | − | 0.852686i | \(-0.674972\pi\) | ||||
−0.522423 | + | 0.852686i | \(0.674972\pi\) | |||||||
\(230\) | −6.32456 | − | 6.32456i | −0.417029 | − | 0.417029i | ||||
\(231\) | 5.00000 | + | 3.16228i | 0.328976 | + | 0.208063i | ||||
\(232\) | −6.00000 | − | 6.00000i | −0.393919 | − | 0.393919i | ||||
\(233\) | −18.0000 | + | 18.0000i | −1.17922 | + | 1.17922i | −0.199276 | + | 0.979943i | \(0.563859\pi\) |
−0.979943 | + | 0.199276i | \(0.936141\pi\) | |||||||
\(234\) | 6.32456 | 0.413449 | ||||||||
\(235\) | 15.0000 | 0.978492 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.5548 | − | 20.5548i | 1.33518 | − | 1.33518i | ||||
\(238\) | 8.16228 | − | 1.83772i | 0.529082 | − | 0.119122i | ||||
\(239\) | 19.0000i | 1.22901i | 0.788914 | + | 0.614504i | \(0.210644\pi\) | ||||
−0.788914 | + | 0.614504i | \(0.789356\pi\) | |||||||
\(240\) | − | 20.0000i | − | 1.29099i | ||||||
\(241\) | 25.2982i | 1.62960i | 0.579741 | + | 0.814801i | \(0.303154\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | 10.0000 | + | 10.0000i | 0.642824 | + | 0.642824i | ||||
\(243\) | −12.6491 | − | 12.6491i | −0.811441 | − | 0.811441i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.7434 | + | 5.25658i | 0.941922 | + | 0.335831i | ||||
\(246\) | 30.0000 | 1.91273 | ||||||||
\(247\) | −5.00000 | − | 5.00000i | −0.318142 | − | 0.318142i | ||||
\(248\) | −6.32456 | − | 6.32456i | −0.401610 | − | 0.401610i | ||||
\(249\) | − | 10.0000i | − | 0.633724i | ||||||
\(250\) | 15.8114 | 1.00000 | ||||||||
\(251\) | 12.6491i | 0.798405i | 0.916863 | + | 0.399202i | \(0.130713\pi\) | ||||
−0.916863 | + | 0.399202i | \(0.869287\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | + | 2.00000i | −0.125739 | + | 0.125739i | ||||
\(254\) | − | 18.0000i | − | 1.12942i | ||||||
\(255\) | 7.90569 | + | 7.90569i | 0.495074 | + | 0.495074i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.6491 | + | 12.6491i | −0.789030 | + | 0.789030i | −0.981335 | − | 0.192305i | \(-0.938404\pi\) |
0.192305 | + | 0.981335i | \(0.438404\pi\) | |||||||
\(258\) | −9.48683 | − | 9.48683i | −0.590624 | − | 0.590624i | ||||
\(259\) | −18.9737 | − | 12.0000i | −1.17897 | − | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.00000 | − | 7.00000i | 0.431638 | − | 0.431638i | −0.457547 | − | 0.889185i | \(-0.651272\pi\) |
0.889185 | + | 0.457547i | \(0.151272\pi\) | |||||||
\(264\) | −6.32456 | −0.389249 | ||||||||
\(265\) | 3.16228 | 0.194257 | ||||||||
\(266\) | 10.0000 | + | 6.32456i | 0.613139 | + | 0.387783i | ||||
\(267\) | −10.0000 | − | 10.0000i | −0.611990 | − | 0.611990i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.9737 | 1.15684 | 0.578422 | − | 0.815737i | \(-0.303669\pi\) | ||||
0.578422 | + | 0.815737i | \(0.303669\pi\) | |||||||
\(270\) | 5.00000 | + | 5.00000i | 0.304290 | + | 0.304290i | ||||
\(271\) | − | 12.6491i | − | 0.768379i | −0.923254 | − | 0.384189i | \(-0.874481\pi\) | ||
0.923254 | − | 0.384189i | \(-0.125519\pi\) | |||||||
\(272\) | −6.32456 | + | 6.32456i | −0.383482 | + | 0.383482i | ||||
\(273\) | −2.90569 | − | 12.9057i | −0.175861 | − | 0.781088i | ||||
\(274\) | − | 4.00000i | − | 0.241649i | ||||||
\(275\) | − | 5.00000i | − | 0.301511i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.0000 | − | 18.0000i | −1.08152 | − | 1.08152i | −0.996368 | − | 0.0851468i | \(-0.972864\pi\) |
−0.0851468 | − | 0.996368i | \(-0.527136\pi\) | |||||||
\(278\) | −18.9737 | − | 18.9737i | −1.13796 | − | 1.13796i | ||||
\(279\) | −6.32456 | −0.378641 | ||||||||
\(280\) | −16.3246 | + | 3.67544i | −0.975579 | + | 0.219650i | ||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 15.0000 | + | 15.0000i | 0.893237 | + | 0.893237i | ||||
\(283\) | 4.74342 | + | 4.74342i | 0.281967 | + | 0.281967i | 0.833893 | − | 0.551926i | \(-0.186107\pi\) |
−0.551926 | + | 0.833893i | \(0.686107\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.8114i | 0.936586i | ||||||||
\(286\) | 3.16228i | 0.186989i | ||||||||
\(287\) | −5.51317 | − | 24.4868i | −0.325432 | − | 1.44541i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.0000i | 0.705882i | ||||||||
\(290\) | 9.48683 | 0.557086 | ||||||||
\(291\) | −5.00000 | −0.293105 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.90569 | + | 7.90569i | 0.461856 | + | 0.461856i | 0.899263 | − | 0.437408i | \(-0.144103\pi\) |
−0.437408 | + | 0.899263i | \(0.644103\pi\) | |||||||
\(294\) | 9.48683 | + | 20.0000i | 0.553283 | + | 1.16642i | ||||
\(295\) | −15.0000 | − | 15.0000i | −0.873334 | − | 0.873334i | ||||
\(296\) | 24.0000 | 1.39497 | ||||||||
\(297\) | 1.58114 | − | 1.58114i | 0.0917470 | − | 0.0917470i | ||||
\(298\) | −12.0000 | + | 12.0000i | −0.695141 | + | 0.695141i | ||||
\(299\) | 6.32456 | 0.365758 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | + | 9.48683i | −0.345834 | + | 0.546812i | ||||
\(302\) | −9.00000 | − | 9.00000i | −0.517892 | − | 0.517892i | ||||
\(303\) | −5.00000 | + | 5.00000i | −0.287242 | + | 0.287242i | ||||
\(304\) | −12.6491 | −0.725476 | ||||||||
\(305\) | −10.0000 | + | 10.0000i | −0.572598 | + | 0.572598i | ||||
\(306\) | 6.32456i | 0.361551i | ||||||||
\(307\) | 4.74342 | − | 4.74342i | 0.270721 | − | 0.270721i | −0.558669 | − | 0.829390i | \(-0.688688\pi\) |
0.829390 | + | 0.558669i | \(0.188688\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 35.0000i | 1.99108i | ||||||||
\(310\) | 10.0000 | 0.567962 | ||||||||
\(311\) | − | 22.1359i | − | 1.25521i | −0.778530 | − | 0.627607i | \(-0.784034\pi\) | ||
0.778530 | − | 0.627607i | \(-0.215966\pi\) | |||||||
\(312\) | 10.0000 | + | 10.0000i | 0.566139 | + | 0.566139i | ||||
\(313\) | 14.2302 | + | 14.2302i | 0.804341 | + | 0.804341i | 0.983771 | − | 0.179430i | \(-0.0574252\pi\) |
−0.179430 | + | 0.983771i | \(0.557425\pi\) | |||||||
\(314\) | 12.6491 | 0.713831 | ||||||||
\(315\) | −6.32456 | + | 10.0000i | −0.356348 | + | 0.563436i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.0000 | + | 19.0000i | 1.06715 | + | 1.06715i | 0.997577 | + | 0.0695692i | \(0.0221625\pi\) |
0.0695692 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(318\) | 3.16228 | + | 3.16228i | 0.177332 | + | 0.177332i | ||||
\(319\) | − | 3.00000i | − | 0.167968i | ||||||
\(320\) | 12.6491 | − | 12.6491i | 0.707107 | − | 0.707107i | ||||
\(321\) | 9.48683i | 0.529503i | ||||||||
\(322\) | −10.3246 | + | 2.32456i | −0.575365 | + | 0.129542i | ||||
\(323\) | 5.00000 | − | 5.00000i | 0.278207 | − | 0.278207i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.90569 | + | 7.90569i | −0.438529 | + | 0.438529i | ||||
\(326\) | −12.0000 | −0.664619 | ||||||||
\(327\) | −11.0680 | + | 11.0680i | −0.612060 | + | 0.612060i | ||||
\(328\) | 18.9737 | + | 18.9737i | 1.04765 | + | 1.04765i | ||||
\(329\) | 9.48683 | − | 15.0000i | 0.523026 | − | 0.826977i | ||||
\(330\) | 5.00000 | − | 5.00000i | 0.275241 | − | 0.275241i | ||||
\(331\) | −6.00000 | −0.329790 | −0.164895 | − | 0.986311i | \(-0.552728\pi\) | ||||
−0.164895 | + | 0.986311i | \(0.552728\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.0000 | − | 12.0000i | 0.657596 | − | 0.657596i | ||||
\(334\) | 22.1359 | 1.21122 | ||||||||
\(335\) | − | 3.16228i | − | 0.172774i | ||||||
\(336\) | −20.0000 | − | 12.6491i | −1.09109 | − | 0.690066i | ||||
\(337\) | −8.00000 | − | 8.00000i | −0.435788 | − | 0.435788i | 0.454804 | − | 0.890592i | \(-0.349709\pi\) |
−0.890592 | + | 0.454804i | \(0.849709\pi\) | |||||||
\(338\) | −8.00000 | + | 8.00000i | −0.435143 | + | 0.435143i | ||||
\(339\) | −37.9473 | −2.06102 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.16228i | − | 0.171247i | ||||||
\(342\) | −6.32456 | + | 6.32456i | −0.341993 | + | 0.341993i | ||||
\(343\) | 14.5811 | − | 11.4189i | 0.787307 | − | 0.616561i | ||||
\(344\) | − | 12.0000i | − | 0.646997i | ||||||
\(345\) | −10.0000 | − | 10.0000i | −0.538382 | − | 0.538382i | ||||
\(346\) | − | 22.1359i | − | 1.19004i | ||||||
\(347\) | 24.0000 | + | 24.0000i | 1.28839 | + | 1.28839i | 0.935766 | + | 0.352621i | \(0.114710\pi\) |
0.352621 | + | 0.935766i | \(0.385290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −34.7851 | −1.86200 | −0.931001 | − | 0.365018i | \(-0.881063\pi\) | ||||
−0.931001 | + | 0.365018i | \(0.881063\pi\) | |||||||
\(350\) | 10.0000 | − | 15.8114i | 0.534522 | − | 0.845154i | ||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.2302 | − | 14.2302i | −0.757400 | − | 0.757400i | 0.218449 | − | 0.975848i | \(-0.429900\pi\) |
−0.975848 | + | 0.218449i | \(0.929900\pi\) | |||||||
\(354\) | − | 30.0000i | − | 1.59448i | ||||||
\(355\) | −9.48683 | − | 9.48683i | −0.503509 | − | 0.503509i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 12.9057 | − | 2.90569i | 0.683042 | − | 0.153786i | ||||
\(358\) | −6.00000 | + | 6.00000i | −0.317110 | + | 0.317110i | ||||
\(359\) | − | 22.0000i | − | 1.16112i | −0.814219 | − | 0.580558i | \(-0.802835\pi\) | ||
0.814219 | − | 0.580558i | \(-0.197165\pi\) | |||||||
\(360\) | − | 12.6491i | − | 0.666667i | ||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | −22.1359 | + | 22.1359i | −1.16344 | + | 1.16344i | ||||
\(363\) | 15.8114 | + | 15.8114i | 0.829883 | + | 0.829883i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −20.0000 | −1.04542 | ||||||||
\(367\) | 17.3925 | − | 17.3925i | 0.907883 | − | 0.907883i | −0.0882186 | − | 0.996101i | \(-0.528117\pi\) |
0.996101 | + | 0.0882186i | \(0.0281174\pi\) | |||||||
\(368\) | 8.00000 | − | 8.00000i | 0.417029 | − | 0.417029i | ||||
\(369\) | 18.9737 | 0.987730 | ||||||||
\(370\) | −18.9737 | + | 18.9737i | −0.986394 | + | 0.986394i | ||||
\(371\) | 2.00000 | − | 3.16228i | 0.103835 | − | 0.164177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.0000 | − | 12.0000i | 0.621336 | − | 0.621336i | −0.324537 | − | 0.945873i | \(-0.605208\pi\) |
0.945873 | + | 0.324537i | \(0.105208\pi\) | |||||||
\(374\) | −3.16228 | −0.163517 | ||||||||
\(375\) | 25.0000 | 1.29099 | ||||||||
\(376\) | 18.9737i | 0.978492i | ||||||||
\(377\) | −4.74342 | + | 4.74342i | −0.244298 | + | 0.244298i | ||||
\(378\) | 8.16228 | − | 1.83772i | 0.419822 | − | 0.0945222i | ||||
\(379\) | 8.00000i | 0.410932i | 0.978664 | + | 0.205466i | \(0.0658711\pi\) | ||||
−0.978664 | + | 0.205466i | \(0.934129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 28.4605i | − | 1.45808i | ||||||
\(382\) | 3.00000 | + | 3.00000i | 0.153493 | + | 0.153493i | ||||
\(383\) | 15.8114 | + | 15.8114i | 0.807924 | + | 0.807924i | 0.984319 | − | 0.176395i | \(-0.0564437\pi\) |
−0.176395 | + | 0.984319i | \(0.556444\pi\) | |||||||
\(384\) | 25.2982 | 1.29099 | ||||||||
\(385\) | −5.00000 | − | 3.16228i | −0.254824 | − | 0.161165i | ||||
\(386\) | 16.0000 | 0.814379 | ||||||||
\(387\) | −6.00000 | − | 6.00000i | −0.304997 | − | 0.304997i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.0000i | 1.16615i | 0.812420 | + | 0.583073i | \(0.198150\pi\) | ||||
−0.812420 | + | 0.583073i | \(0.801850\pi\) | |||||||
\(390\) | −15.8114 | −0.800641 | ||||||||
\(391\) | 6.32456i | 0.319847i | ||||||||
\(392\) | −6.64911 | + | 18.6491i | −0.335831 | + | 0.941922i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.00000i | 0.100759i | ||||||||
\(395\) | −20.5548 | + | 20.5548i | −1.03422 | + | 1.03422i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.7171 | − | 23.7171i | 1.19033 | − | 1.19033i | 0.213351 | − | 0.976976i | \(-0.431562\pi\) |
0.976976 | − | 0.213351i | \(-0.0684376\pi\) | |||||||
\(398\) | −9.48683 | − | 9.48683i | −0.475532 | − | 0.475532i | ||||
\(399\) | 15.8114 | + | 10.0000i | 0.791559 | + | 0.500626i | ||||
\(400\) | 20.0000i | 1.00000i | ||||||||
\(401\) | −1.00000 | −0.0499376 | −0.0249688 | − | 0.999688i | \(-0.507949\pi\) | ||||
−0.0249688 | + | 0.999688i | \(0.507949\pi\) | |||||||
\(402\) | 3.16228 | − | 3.16228i | 0.157720 | − | 0.157720i | ||||
\(403\) | −5.00000 | + | 5.00000i | −0.249068 | + | 0.249068i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.3925 | + | 17.3925i | 0.864242 | + | 0.864242i | ||||
\(406\) | 6.00000 | − | 9.48683i | 0.297775 | − | 0.470824i | ||||
\(407\) | 6.00000 | + | 6.00000i | 0.297409 | + | 0.297409i | ||||
\(408\) | −10.0000 | + | 10.0000i | −0.495074 | + | 0.495074i | ||||
\(409\) | −3.16228 | −0.156365 | −0.0781823 | − | 0.996939i | \(-0.524912\pi\) | ||||
−0.0781823 | + | 0.996939i | \(0.524912\pi\) | |||||||
\(410\) | −30.0000 | −1.48159 | ||||||||
\(411\) | − | 6.32456i | − | 0.311967i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −24.4868 | + | 5.51317i | −1.20492 | + | 0.271285i | ||||
\(414\) | − | 8.00000i | − | 0.393179i | ||||||
\(415\) | 10.0000i | 0.490881i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −30.0000 | − | 30.0000i | −1.46911 | − | 1.46911i | ||||
\(418\) | −3.16228 | − | 3.16228i | −0.154672 | − | 0.154672i | ||||
\(419\) | 15.8114 | 0.772437 | 0.386218 | − | 0.922407i | \(-0.373781\pi\) | ||||
0.386218 | + | 0.922407i | \(0.373781\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.0000 | 0.926003 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(422\) | −17.0000 | − | 17.0000i | −0.827547 | − | 0.827547i | ||||
\(423\) | 9.48683 | + | 9.48683i | 0.461266 | + | 0.461266i | ||||
\(424\) | 4.00000i | 0.194257i | ||||||||
\(425\) | −7.90569 | − | 7.90569i | −0.383482 | − | 0.383482i | ||||
\(426\) | − | 18.9737i | − | 0.919277i | ||||||
\(427\) | 3.67544 | + | 16.3246i | 0.177867 | + | 0.790001i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.00000i | 0.241402i | ||||||||
\(430\) | 9.48683 | + | 9.48683i | 0.457496 | + | 0.457496i | ||||
\(431\) | −23.0000 | −1.10787 | −0.553936 | − | 0.832560i | \(-0.686875\pi\) | ||||
−0.553936 | + | 0.832560i | \(0.686875\pi\) | |||||||
\(432\) | −6.32456 | + | 6.32456i | −0.304290 | + | 0.304290i | ||||
\(433\) | −9.48683 | − | 9.48683i | −0.455908 | − | 0.455908i | 0.441402 | − | 0.897310i | \(-0.354481\pi\) |
−0.897310 | + | 0.441402i | \(0.854481\pi\) | |||||||
\(434\) | 6.32456 | − | 10.0000i | 0.303588 | − | 0.480015i | ||||
\(435\) | 15.0000 | 0.719195 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.32456 | + | 6.32456i | −0.302545 | + | 0.302545i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.6491 | 0.603709 | 0.301855 | − | 0.953354i | \(-0.402394\pi\) | ||||
0.301855 | + | 0.953354i | \(0.402394\pi\) | |||||||
\(440\) | 6.32456 | 0.301511 | ||||||||
\(441\) | 6.00000 | + | 12.6491i | 0.285714 | + | 0.602339i | ||||
\(442\) | 5.00000 | + | 5.00000i | 0.237826 | + | 0.237826i | ||||
\(443\) | 1.00000 | − | 1.00000i | 0.0475114 | − | 0.0475114i | −0.682952 | − | 0.730463i | \(-0.739304\pi\) |
0.730463 | + | 0.682952i | \(0.239304\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | + | 10.0000i | 0.474045 | + | 0.474045i | ||||
\(446\) | 28.4605i | 1.34764i | ||||||||
\(447\) | −18.9737 | + | 18.9737i | −0.897424 | + | 0.897424i | ||||
\(448\) | −4.64911 | − | 20.6491i | −0.219650 | − | 0.975579i | ||||
\(449\) | − | 17.0000i | − | 0.802280i | −0.916017 | − | 0.401140i | \(-0.868614\pi\) | ||
0.916017 | − | 0.401140i | \(-0.131386\pi\) | |||||||
\(450\) | 10.0000 | + | 10.0000i | 0.471405 | + | 0.471405i | ||||
\(451\) | 9.48683i | 0.446718i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.2302 | − | 14.2302i | −0.668595 | − | 0.668595i | ||||
\(454\) | −3.16228 | −0.148413 | ||||||||
\(455\) | 2.90569 | + | 12.9057i | 0.136221 | + | 0.605028i | ||||
\(456\) | −20.0000 | −0.936586 | ||||||||
\(457\) | −1.00000 | − | 1.00000i | −0.0467780 | − | 0.0467780i | 0.683331 | − | 0.730109i | \(-0.260531\pi\) |
−0.730109 | + | 0.683331i | \(0.760531\pi\) | |||||||
\(458\) | 15.8114 | + | 15.8114i | 0.738818 | + | 0.738818i | ||||
\(459\) | − | 5.00000i | − | 0.233380i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 6.32456i | − | 0.294564i | −0.989095 | − | 0.147282i | \(-0.952948\pi\) | ||
0.989095 | − | 0.147282i | \(-0.0470525\pi\) | |||||||
\(462\) | −1.83772 | − | 8.16228i | −0.0854986 | − | 0.379744i | ||||
\(463\) | −4.00000 | + | 4.00000i | −0.185896 | + | 0.185896i | −0.793919 | − | 0.608023i | \(-0.791963\pi\) |
0.608023 | + | 0.793919i | \(0.291963\pi\) | |||||||
\(464\) | 12.0000i | 0.557086i | ||||||||
\(465\) | 15.8114 | 0.733236 | ||||||||
\(466\) | 36.0000 | 1.66767 | ||||||||
\(467\) | 11.0680 | − | 11.0680i | 0.512165 | − | 0.512165i | −0.403025 | − | 0.915189i | \(-0.632041\pi\) |
0.915189 | + | 0.403025i | \(0.132041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.16228 | − | 2.00000i | −0.146020 | − | 0.0923514i | ||||
\(470\) | −15.0000 | − | 15.0000i | −0.691898 | − | 0.691898i | ||||
\(471\) | 20.0000 | 0.921551 | ||||||||
\(472\) | 18.9737 | − | 18.9737i | 0.873334 | − | 0.873334i | ||||
\(473\) | 3.00000 | − | 3.00000i | 0.137940 | − | 0.137940i | ||||
\(474\) | −41.1096 | −1.88823 | ||||||||
\(475\) | − | 15.8114i | − | 0.725476i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | + | 2.00000i | 0.0915737 | + | 0.0915737i | ||||
\(478\) | 19.0000 | − | 19.0000i | 0.869040 | − | 0.869040i | ||||
\(479\) | 6.32456 | 0.288976 | 0.144488 | − | 0.989507i | \(-0.453846\pi\) | ||||
0.144488 | + | 0.989507i | \(0.453846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 18.9737i | − | 0.865125i | ||||||
\(482\) | 25.2982 | − | 25.2982i | 1.15230 | − | 1.15230i | ||||
\(483\) | −16.3246 | + | 3.67544i | −0.742793 | + | 0.167239i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.00000 | 0.227038 | ||||||||
\(486\) | 25.2982i | 1.14755i | ||||||||
\(487\) | 4.00000 | + | 4.00000i | 0.181257 | + | 0.181257i | 0.791904 | − | 0.610646i | \(-0.209090\pi\) |
−0.610646 | + | 0.791904i | \(0.709090\pi\) | |||||||
\(488\) | −12.6491 | − | 12.6491i | −0.572598 | − | 0.572598i | ||||
\(489\) | −18.9737 | −0.858019 | ||||||||
\(490\) | −9.48683 | − | 20.0000i | −0.428571 | − | 0.903508i | ||||
\(491\) | −41.0000 | −1.85030 | −0.925152 | − | 0.379597i | \(-0.876063\pi\) | ||||
−0.925152 | + | 0.379597i | \(0.876063\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.74342 | − | 4.74342i | −0.213633 | − | 0.213633i | ||||
\(494\) | 10.0000i | 0.449921i | ||||||||
\(495\) | 3.16228 | − | 3.16228i | 0.142134 | − | 0.142134i | ||||
\(496\) | 12.6491i | 0.567962i | ||||||||
\(497\) | −15.4868 | + | 3.48683i | −0.694679 | + | 0.156406i | ||||
\(498\) | −10.0000 | + | 10.0000i | −0.448111 | + | 0.448111i | ||||
\(499\) | 19.0000i | 0.850557i | 0.905063 | + | 0.425278i | \(0.139824\pi\) | ||||
−0.905063 | + | 0.425278i | \(0.860176\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 35.0000 | 1.56368 | ||||||||
\(502\) | 12.6491 | − | 12.6491i | 0.564557 | − | 0.564557i | ||||
\(503\) | −7.90569 | − | 7.90569i | −0.352497 | − | 0.352497i | 0.508541 | − | 0.861038i | \(-0.330185\pi\) |
−0.861038 | + | 0.508541i | \(0.830185\pi\) | |||||||
\(504\) | −12.6491 | − | 8.00000i | −0.563436 | − | 0.356348i | ||||
\(505\) | 5.00000 | − | 5.00000i | 0.222497 | − | 0.222497i | ||||
\(506\) | 4.00000 | 0.177822 | ||||||||
\(507\) | −12.6491 | + | 12.6491i | −0.561767 | + | 0.561767i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.9737 | −0.840993 | −0.420496 | − | 0.907294i | \(-0.638144\pi\) | ||||
−0.420496 | + | 0.907294i | \(0.638144\pi\) | |||||||
\(510\) | − | 15.8114i | − | 0.700140i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 5.00000 | − | 5.00000i | 0.220755 | − | 0.220755i | ||||
\(514\) | 25.2982 | 1.11586 | ||||||||
\(515\) | − | 35.0000i | − | 1.54228i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.74342 | + | 4.74342i | −0.208615 | + | 0.208615i | ||||
\(518\) | 6.97367 | + | 30.9737i | 0.306405 | + | 1.36090i | ||||
\(519\) | − | 35.0000i | − | 1.53633i | ||||||
\(520\) | −10.0000 | − | 10.0000i | −0.438529 | − | 0.438529i | ||||
\(521\) | 41.1096i | 1.80104i | 0.434810 | + | 0.900522i | \(0.356816\pi\) | ||||
−0.434810 | + | 0.900522i | \(0.643184\pi\) | |||||||
\(522\) | 6.00000 | + | 6.00000i | 0.262613 | + | 0.262613i | ||||
\(523\) | 18.9737 | + | 18.9737i | 0.829660 | + | 0.829660i | 0.987470 | − | 0.157809i | \(-0.0504431\pi\) |
−0.157809 | + | 0.987470i | \(0.550443\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.8114 | − | 25.0000i | 0.690066 | − | 1.09109i | ||||
\(526\) | −14.0000 | −0.610429 | ||||||||
\(527\) | −5.00000 | − | 5.00000i | −0.217803 | − | 0.217803i | ||||
\(528\) | 6.32456 | + | 6.32456i | 0.275241 | + | 0.275241i | ||||
\(529\) | 15.0000i | 0.652174i | ||||||||
\(530\) | −3.16228 | − | 3.16228i | −0.137361 | − | 0.137361i | ||||
\(531\) | − | 18.9737i | − | 0.823387i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15.0000 | − | 15.0000i | 0.649722 | − | 0.649722i | ||||
\(534\) | 20.0000i | 0.865485i | ||||||||
\(535\) | − | 9.48683i | − | 0.410152i | ||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | −9.48683 | + | 9.48683i | −0.409387 | + | 0.409387i | ||||
\(538\) | −18.9737 | − | 18.9737i | −0.818013 | − | 0.818013i | ||||
\(539\) | −6.32456 | + | 3.00000i | −0.272418 | + | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00000 | 0.386940 | 0.193470 | − | 0.981106i | \(-0.438026\pi\) | ||||
0.193470 | + | 0.981106i | \(0.438026\pi\) | |||||||
\(542\) | −12.6491 | + | 12.6491i | −0.543326 | + | 0.543326i | ||||
\(543\) | −35.0000 | + | 35.0000i | −1.50199 | + | 1.50199i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 11.0680 | − | 11.0680i | 0.474100 | − | 0.474100i | ||||
\(546\) | −10.0000 | + | 15.8114i | −0.427960 | + | 0.676665i | ||||
\(547\) | 14.0000 | + | 14.0000i | 0.598597 | + | 0.598597i | 0.939939 | − | 0.341342i | \(-0.110882\pi\) |
−0.341342 | + | 0.939939i | \(0.610882\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.6491 | −0.539851 | ||||||||
\(550\) | −5.00000 | + | 5.00000i | −0.213201 | + | 0.213201i | ||||
\(551\) | − | 9.48683i | − | 0.404153i | ||||||
\(552\) | 12.6491 | − | 12.6491i | 0.538382 | − | 0.538382i | ||||
\(553\) | 7.55480 | + | 33.5548i | 0.321263 | + | 1.42690i | ||||
\(554\) | 36.0000i | 1.52949i | ||||||||
\(555\) | −30.0000 | + | 30.0000i | −1.27343 | + | 1.27343i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00000 | − | 6.00000i | −0.254228 | − | 0.254228i | 0.568473 | − | 0.822702i | \(-0.307534\pi\) |
−0.822702 | + | 0.568473i | \(0.807534\pi\) | |||||||
\(558\) | 6.32456 | + | 6.32456i | 0.267740 | + | 0.267740i | ||||
\(559\) | −9.48683 | −0.401250 | ||||||||
\(560\) | 20.0000 | + | 12.6491i | 0.845154 | + | 0.534522i | ||||
\(561\) | −5.00000 | −0.211100 | ||||||||
\(562\) | −9.00000 | − | 9.00000i | −0.379642 | − | 0.379642i | ||||
\(563\) | −9.48683 | − | 9.48683i | −0.399822 | − | 0.399822i | 0.478348 | − | 0.878170i | \(-0.341236\pi\) |
−0.878170 | + | 0.478348i | \(0.841236\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.9473 | 1.59646 | ||||||||
\(566\) | − | 9.48683i | − | 0.398761i | ||||||
\(567\) | 28.3925 | − | 6.39253i | 1.19237 | − | 0.268461i | ||||
\(568\) | 12.0000 | − | 12.0000i | 0.503509 | − | 0.503509i | ||||
\(569\) | − | 32.0000i | − | 1.34151i | −0.741679 | − | 0.670755i | \(-0.765970\pi\) | ||
0.741679 | − | 0.670755i | \(-0.234030\pi\) | |||||||
\(570\) | 15.8114 | − | 15.8114i | 0.662266 | − | 0.662266i | ||||
\(571\) | −26.0000 | −1.08807 | −0.544033 | − | 0.839064i | \(-0.683103\pi\) | ||||
−0.544033 | + | 0.839064i | \(0.683103\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.74342 | + | 4.74342i | 0.198159 | + | 0.198159i | ||||
\(574\) | −18.9737 | + | 30.0000i | −0.791946 | + | 1.25218i | ||||
\(575\) | 10.0000 | + | 10.0000i | 0.417029 | + | 0.417029i | ||||
\(576\) | 16.0000 | 0.666667 | ||||||||
\(577\) | −20.5548 | + | 20.5548i | −0.855708 | + | 0.855708i | −0.990829 | − | 0.135121i | \(-0.956858\pi\) |
0.135121 | + | 0.990829i | \(0.456858\pi\) | |||||||
\(578\) | 12.0000 | − | 12.0000i | 0.499134 | − | 0.499134i | ||||
\(579\) | 25.2982 | 1.05136 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.0000 | + | 6.32456i | 0.414870 | + | 0.262387i | ||||
\(582\) | 5.00000 | + | 5.00000i | 0.207257 | + | 0.207257i | ||||
\(583\) | −1.00000 | + | 1.00000i | −0.0414158 | + | 0.0414158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.0000 | −0.413449 | ||||||||
\(586\) | − | 15.8114i | − | 0.653162i | ||||||
\(587\) | 15.8114 | − | 15.8114i | 0.652606 | − | 0.652606i | −0.301014 | − | 0.953620i | \(-0.597325\pi\) |
0.953620 | + | 0.301014i | \(0.0973251\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 10.0000i | − | 0.412043i | ||||||
\(590\) | 30.0000i | 1.23508i | ||||||||
\(591\) | 3.16228i | 0.130079i | ||||||||
\(592\) | −24.0000 | − | 24.0000i | −0.986394 | − | 0.986394i | ||||
\(593\) | −20.5548 | − | 20.5548i | −0.844085 | − | 0.844085i | 0.145303 | − | 0.989387i | \(-0.453584\pi\) |
−0.989387 | + | 0.145303i | \(0.953584\pi\) | |||||||
\(594\) | −3.16228 | −0.129750 | ||||||||
\(595\) | −12.9057 | + | 2.90569i | −0.529082 | + | 0.119122i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15.0000 | − | 15.0000i | −0.613909 | − | 0.613909i | ||||
\(598\) | −6.32456 | − | 6.32456i | −0.258630 | − | 0.258630i | ||||
\(599\) | 13.0000i | 0.531166i | 0.964088 | + | 0.265583i | \(0.0855644\pi\) | ||||
−0.964088 | + | 0.265583i | \(0.914436\pi\) | |||||||
\(600\) | 31.6228i | 1.29099i | ||||||||
\(601\) | 22.1359i | 0.902944i | 0.892285 | + | 0.451472i | \(0.149101\pi\) | ||||
−0.892285 | + | 0.451472i | \(0.850899\pi\) | |||||||
\(602\) | 15.4868 | − | 3.48683i | 0.631196 | − | 0.142113i | ||||
\(603\) | 2.00000 | − | 2.00000i | 0.0814463 | − | 0.0814463i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.8114 | − | 15.8114i | −0.642824 | − | 0.642824i | ||||
\(606\) | 10.0000 | 0.406222 | ||||||||
\(607\) | −14.2302 | + | 14.2302i | −0.577588 | + | 0.577588i | −0.934238 | − | 0.356650i | \(-0.883919\pi\) |
0.356650 | + | 0.934238i | \(0.383919\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.48683 | − | 15.0000i | 0.384426 | − | 0.607831i | ||||
\(610\) | 20.0000 | 0.809776 | ||||||||
\(611\) | 15.0000 | 0.606835 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0000 | − | 17.0000i | 0.686624 | − | 0.686624i | −0.274861 | − | 0.961484i | \(-0.588632\pi\) |
0.961484 | + | 0.274861i | \(0.0886317\pi\) | |||||||
\(614\) | −9.48683 | −0.382857 | ||||||||
\(615\) | −47.4342 | −1.91273 | ||||||||
\(616\) | 4.00000 | − | 6.32456i | 0.161165 | − | 0.254824i | ||||
\(617\) | 4.00000 | + | 4.00000i | 0.161034 | + | 0.161034i | 0.783025 | − | 0.621991i | \(-0.213676\pi\) |
−0.621991 | + | 0.783025i | \(0.713676\pi\) | |||||||
\(618\) | 35.0000 | − | 35.0000i | 1.40791 | − | 1.40791i | ||||
\(619\) | 25.2982 | 1.01682 | 0.508411 | − | 0.861115i | \(-0.330233\pi\) | ||||
0.508411 | + | 0.861115i | \(0.330233\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.32456i | 0.253796i | ||||||||
\(622\) | −22.1359 | + | 22.1359i | −0.887570 | + | 0.887570i | ||||
\(623\) | 16.3246 | − | 3.67544i | 0.654029 | − | 0.147254i | ||||
\(624\) | − | 20.0000i | − | 0.800641i | ||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | − | 28.4605i | − | 1.13751i | ||||||
\(627\) | −5.00000 | − | 5.00000i | −0.199681 | − | 0.199681i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.9737 | 0.756530 | ||||||||
\(630\) | 16.3246 | − | 3.67544i | 0.650386 | − | 0.146433i | ||||
\(631\) | −31.0000 | −1.23409 | −0.617045 | − | 0.786928i | \(-0.711670\pi\) | ||||
−0.617045 | + | 0.786928i | \(0.711670\pi\) | |||||||
\(632\) | −26.0000 | − | 26.0000i | −1.03422 | − | 1.03422i | ||||
\(633\) | −26.8794 | − | 26.8794i | −1.06836 | − | 1.06836i | ||||
\(634\) | − | 38.0000i | − | 1.50917i | ||||||
\(635\) | 28.4605i | 1.12942i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.7434 | + | 5.25658i | 0.584155 | + | 0.208273i | ||||
\(638\) | −3.00000 | + | 3.00000i | −0.118771 | + | 0.118771i | ||||
\(639\) | − | 12.0000i | − | 0.474713i | ||||||
\(640\) | −25.2982 | −1.00000 | ||||||||
\(641\) | 44.0000 | 1.73790 | 0.868948 | − | 0.494904i | \(-0.164797\pi\) | ||||
0.868948 | + | 0.494904i | \(0.164797\pi\) | |||||||
\(642\) | 9.48683 | − | 9.48683i | 0.374415 | − | 0.374415i | ||||
\(643\) | −4.74342 | − | 4.74342i | −0.187062 | − | 0.187062i | 0.607363 | − | 0.794425i | \(-0.292228\pi\) |
−0.794425 | + | 0.607363i | \(0.792228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.0000 | + | 15.0000i | 0.590624 | + | 0.590624i | ||||
\(646\) | −10.0000 | −0.393445 | ||||||||
\(647\) | −12.6491 | + | 12.6491i | −0.497288 | + | 0.497288i | −0.910593 | − | 0.413305i | \(-0.864374\pi\) |
0.413305 | + | 0.910593i | \(0.364374\pi\) | |||||||
\(648\) | −22.0000 | + | 22.0000i | −0.864242 | + | 0.864242i | ||||
\(649\) | 9.48683 | 0.372391 | ||||||||
\(650\) | 15.8114 | 0.620174 | ||||||||
\(651\) | 10.0000 | − | 15.8114i | 0.391931 | − | 0.619697i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −19.0000 | + | 19.0000i | −0.743527 | + | 0.743527i | −0.973255 | − | 0.229728i | \(-0.926216\pi\) |
0.229728 | + | 0.973255i | \(0.426216\pi\) | |||||||
\(654\) | 22.1359 | 0.865584 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 37.9473i | − | 1.48159i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.4868 | + | 5.51317i | −0.954596 | + | 0.214926i | ||||
\(659\) | − | 1.00000i | − | 0.0389545i | −0.999810 | − | 0.0194772i | \(-0.993800\pi\) | ||
0.999810 | − | 0.0194772i | \(-0.00620019\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.6491i | − | 0.491993i | −0.969271 | − | 0.245997i | \(-0.920885\pi\) | ||
0.969271 | − | 0.245997i | \(-0.0791152\pi\) | |||||||
\(662\) | 6.00000 | + | 6.00000i | 0.233197 | + | 0.233197i | ||||
\(663\) | 7.90569 | + | 7.90569i | 0.307032 | + | 0.307032i | ||||
\(664\) | −12.6491 | −0.490881 | ||||||||
\(665\) | −15.8114 | − | 10.0000i | −0.613139 | − | 0.387783i | ||||
\(666\) | −24.0000 | −0.929981 | ||||||||
\(667\) | 6.00000 | + | 6.00000i | 0.232321 | + | 0.232321i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 45.0000i | 1.73980i | ||||||||
\(670\) | −3.16228 | + | 3.16228i | −0.122169 | + | 0.122169i | ||||
\(671\) | − | 6.32456i | − | 0.244157i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.0000 | + | 24.0000i | −0.925132 | + | 0.925132i | −0.997386 | − | 0.0722542i | \(-0.976981\pi\) |
0.0722542 | + | 0.997386i | \(0.476981\pi\) | |||||||
\(674\) | 16.0000i | 0.616297i | ||||||||
\(675\) | −7.90569 | − | 7.90569i | −0.304290 | − | 0.304290i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2302 | − | 14.2302i | 0.546913 | − | 0.546913i | −0.378634 | − | 0.925547i | \(-0.623606\pi\) |
0.925547 | + | 0.378634i | \(0.123606\pi\) | |||||||
\(678\) | 37.9473 | + | 37.9473i | 1.45736 | + | 1.45736i | ||||
\(679\) | 3.16228 | − | 5.00000i | 0.121357 | − | 0.191882i | ||||
\(680\) | 10.0000 | − | 10.0000i | 0.383482 | − | 0.383482i | ||||
\(681\) | −5.00000 | −0.191600 | ||||||||
\(682\) | −3.16228 | + | 3.16228i | −0.121090 | + | 0.121090i | ||||
\(683\) | 32.0000 | − | 32.0000i | 1.22445 | − | 1.22445i | 0.258411 | − | 0.966035i | \(-0.416801\pi\) |
0.966035 | − | 0.258411i | \(-0.0831988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.32456i | 0.241649i | ||||||||
\(686\) | −26.0000 | − | 3.16228i | −0.992685 | − | 0.120736i | ||||
\(687\) | 25.0000 | + | 25.0000i | 0.953809 | + | 0.953809i | ||||
\(688\) | −12.0000 | + | 12.0000i | −0.457496 | + | 0.457496i | ||||
\(689\) | 3.16228 | 0.120473 | ||||||||
\(690\) | 20.0000i | 0.761387i | ||||||||
\(691\) | 31.6228i | 1.20299i | 0.798878 | + | 0.601494i | \(0.205427\pi\) | ||||
−0.798878 | + | 0.601494i | \(0.794573\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.16228 | − | 5.16228i | −0.0441513 | − | 0.196099i | ||||
\(694\) | − | 48.0000i | − | 1.82206i | ||||||
\(695\) | 30.0000 | + | 30.0000i | 1.13796 | + | 1.13796i | ||||
\(696\) | 18.9737i | 0.719195i | ||||||||
\(697\) | 15.0000 | + | 15.0000i | 0.568166 | + | 0.568166i | ||||
\(698\) | 34.7851 | + | 34.7851i | 1.31663 | + | 1.31663i | ||||
\(699\) | 56.9210 | 2.15295 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 5.00000 | + | 5.00000i | 0.188713 | + | 0.188713i | ||||
\(703\) | 18.9737 | + | 18.9737i | 0.715605 | + | 0.715605i | ||||
\(704\) | 8.00000i | 0.301511i | ||||||||
\(705\) | −23.7171 | − | 23.7171i | −0.893237 | − | 0.893237i | ||||
\(706\) | 28.4605i | 1.07113i | ||||||||
\(707\) | −1.83772 | − | 8.16228i | −0.0691147 | − | 0.306974i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.00000i | 0.338002i | 0.985616 | + | 0.169001i | \(0.0540541\pi\) | ||||
−0.985616 | + | 0.169001i | \(0.945946\pi\) | |||||||
\(710\) | 18.9737i | 0.712069i | ||||||||
\(711\) | −26.0000 | −0.975076 | ||||||||
\(712\) | −12.6491 | + | 12.6491i | −0.474045 | + | 0.474045i | ||||
\(713\) | 6.32456 | + | 6.32456i | 0.236856 | + | 0.236856i | ||||
\(714\) | −15.8114 | − | 10.0000i | −0.591726 | − | 0.374241i | ||||
\(715\) | − | 5.00000i | − | 0.186989i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 30.0416 | − | 30.0416i | 1.12193 | − | 1.12193i | ||||
\(718\) | −22.0000 | + | 22.0000i | −0.821033 | + | 0.821033i | ||||
\(719\) | −31.6228 | −1.17933 | −0.589665 | − | 0.807648i | \(-0.700740\pi\) | ||||
−0.589665 | + | 0.807648i | \(0.700740\pi\) | |||||||
\(720\) | −12.6491 | + | 12.6491i | −0.471405 | + | 0.471405i | ||||
\(721\) | −35.0000 | − | 22.1359i | −1.30347 | − | 0.824386i | ||||
\(722\) | 9.00000 | + | 9.00000i | 0.334945 | + | 0.334945i | ||||
\(723\) | 40.0000 | − | 40.0000i | 1.48762 | − | 1.48762i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −15.0000 | −0.557086 | ||||||||
\(726\) | − | 31.6228i | − | 1.17363i | ||||||
\(727\) | −9.48683 | + | 9.48683i | −0.351847 | + | 0.351847i | −0.860796 | − | 0.508949i | \(-0.830034\pi\) |
0.508949 | + | 0.860796i | \(0.330034\pi\) | |||||||
\(728\) | −16.3246 | + | 3.67544i | −0.605028 | + | 0.136221i | ||||
\(729\) | 7.00000i | 0.259259i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.48683i | − | 0.350883i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.3925 | − | 17.3925i | −0.642408 | − | 0.642408i | 0.308739 | − | 0.951147i | \(-0.400093\pi\) |
−0.951147 | + | 0.308739i | \(0.900093\pi\) | |||||||
\(734\) | −34.7851 | −1.28394 | ||||||||
\(735\) | −15.0000 | − | 31.6228i | −0.553283 | − | 1.16642i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.00000 | + | 1.00000i | 0.0368355 | + | 0.0368355i | ||||
\(738\) | −18.9737 | − | 18.9737i | −0.698430 | − | 0.698430i | ||||
\(739\) | − | 37.0000i | − | 1.36107i | −0.732717 | − | 0.680534i | \(-0.761748\pi\) | ||
0.732717 | − | 0.680534i | \(-0.238252\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.8114i | 0.580846i | ||||||||
\(742\) | −5.16228 | + | 1.16228i | −0.189513 | + | 0.0426686i | ||||
\(743\) | −9.00000 | + | 9.00000i | −0.330178 | + | 0.330178i | −0.852654 | − | 0.522476i | \(-0.825008\pi\) |
0.522476 | + | 0.852654i | \(0.325008\pi\) | |||||||
\(744\) | 20.0000i | 0.733236i | ||||||||
\(745\) | 18.9737 | − | 18.9737i | 0.695141 | − | 0.695141i | ||||
\(746\) | −24.0000 | −0.878702 | ||||||||
\(747\) | −6.32456 | + | 6.32456i | −0.231403 | + | 0.231403i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.48683 | − | 6.00000i | −0.346641 | − | 0.219235i | ||||
\(750\) | −25.0000 | − | 25.0000i | −0.912871 | − | 0.912871i | ||||
\(751\) | 37.0000 | 1.35015 | 0.675075 | − | 0.737749i | \(-0.264111\pi\) | ||||
0.675075 | + | 0.737749i | \(0.264111\pi\) | |||||||
\(752\) | 18.9737 | − | 18.9737i | 0.691898 | − | 0.691898i | ||||
\(753\) | 20.0000 | − | 20.0000i | 0.728841 | − | 0.728841i | ||||
\(754\) | 9.48683 | 0.345490 | ||||||||
\(755\) | 14.2302 | + | 14.2302i | 0.517892 | + | 0.517892i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.0000 | − | 16.0000i | −0.581530 | − | 0.581530i | 0.353794 | − | 0.935324i | \(-0.384892\pi\) |
−0.935324 | + | 0.353794i | \(0.884892\pi\) | |||||||
\(758\) | 8.00000 | − | 8.00000i | 0.290573 | − | 0.290573i | ||||
\(759\) | 6.32456 | 0.229567 | ||||||||
\(760\) | 20.0000 | 0.725476 | ||||||||
\(761\) | 25.2982i | 0.917060i | 0.888679 | + | 0.458530i | \(0.151624\pi\) | ||||
−0.888679 | + | 0.458530i | \(0.848376\pi\) | |||||||
\(762\) | −28.4605 | + | 28.4605i | −1.03102 | + | 1.03102i | ||||
\(763\) | −4.06797 | − | 18.0680i | −0.147270 | − | 0.654104i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 10.0000i | − | 0.361551i | ||||||
\(766\) | − | 31.6228i | − | 1.14258i | ||||||
\(767\) | −15.0000 | − | 15.0000i | −0.541619 | − | 0.541619i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.1359 | 0.798243 | 0.399121 | − | 0.916898i | \(-0.369315\pi\) | ||||
0.399121 | + | 0.916898i | \(0.369315\pi\) | |||||||
\(770\) | 1.83772 | + | 8.16228i | 0.0662269 | + | 0.294148i | ||||
\(771\) | 40.0000 | 1.44056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.3662 | + | 36.3662i | 1.30800 | + | 1.30800i | 0.922856 | + | 0.385145i | \(0.125849\pi\) |
0.385145 | + | 0.922856i | \(0.374151\pi\) | |||||||
\(774\) | 12.0000i | 0.431331i | ||||||||
\(775\) | −15.8114 | −0.567962 | ||||||||
\(776\) | 6.32456i | 0.227038i | ||||||||
\(777\) | 11.0263 | + | 48.9737i | 0.395568 | + | 1.75692i | ||||
\(778\) | 23.0000 | − | 23.0000i | 0.824590 | − | 0.824590i | ||||
\(779\) | 30.0000i | 1.07486i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.00000 | 0.214697 | ||||||||
\(782\) | 6.32456 | − | 6.32456i | 0.226166 | − | 0.226166i | ||||
\(783\) | −4.74342 | − | 4.74342i | −0.169516 | − | 0.169516i | ||||
\(784\) | 25.2982 | − | 12.0000i | 0.903508 | − | 0.428571i | ||||
\(785\) | −20.0000 | −0.713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.3925 | + | 17.3925i | −0.619977 | + | 0.619977i | −0.945525 | − | 0.325549i | \(-0.894451\pi\) |
0.325549 | + | 0.945525i | \(0.394451\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −22.1359 | −0.788060 | ||||||||
\(790\) | 41.1096 | 1.46261 | ||||||||
\(791\) | 24.0000 | − | 37.9473i | 0.853342 | − | 1.34925i | ||||
\(792\) | 4.00000 | + | 4.00000i | 0.142134 | + | 0.142134i | ||||
\(793\) | −10.0000 | + | 10.0000i | −0.355110 | + | 0.355110i | ||||
\(794\) | −47.4342 | −1.68338 | ||||||||
\(795\) | −5.00000 | − | 5.00000i | −0.177332 | − | 0.177332i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.58114 | + | 1.58114i | −0.0560068 | + | 0.0560068i | −0.734555 | − | 0.678549i | \(-0.762609\pi\) |
0.678549 | + | 0.734555i | \(0.262609\pi\) | |||||||
\(798\) | −5.81139 | − | 25.8114i | −0.205721 | − | 0.913713i | ||||
\(799\) | 15.0000i | 0.530662i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.6491i | 0.446934i | ||||||||
\(802\) | 1.00000 | + | 1.00000i | 0.0353112 | + | 0.0353112i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.3246 | − | 3.67544i | 0.575365 | − | 0.129542i | ||||
\(806\) | 10.0000 | 0.352235 | ||||||||
\(807\) | −30.0000 | − | 30.0000i | −1.05605 | − | 1.05605i | ||||
\(808\) | 6.32456 | + | 6.32456i | 0.222497 | + | 0.222497i | ||||
\(809\) | 3.00000i | 0.105474i | 0.998608 | + | 0.0527372i | \(0.0167946\pi\) | ||||
−0.998608 | + | 0.0527372i | \(0.983205\pi\) | |||||||
\(810\) | − | 34.7851i | − | 1.22222i | ||||||
\(811\) | − | 37.9473i | − | 1.33251i | −0.745724 | − | 0.666256i | \(-0.767896\pi\) | ||
0.745724 | − | 0.666256i | \(-0.232104\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.0000 | + | 20.0000i | −0.701431 | + | 0.701431i | ||||
\(814\) | − | 12.0000i | − | 0.420600i | ||||||
\(815\) | 18.9737 | 0.664619 | ||||||||
\(816\) | 20.0000 | 0.700140 | ||||||||
\(817\) | 9.48683 | − | 9.48683i | 0.331902 | − | 0.331902i | ||||
\(818\) | 3.16228 | + | 3.16228i | 0.110566 | + | 0.110566i | ||||
\(819\) | −6.32456 | + | 10.0000i | −0.220998 | + | 0.349428i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0000 | −0.802706 | −0.401353 | − | 0.915924i | \(-0.631460\pi\) | ||||
−0.401353 | + | 0.915924i | \(0.631460\pi\) | |||||||
\(822\) | −6.32456 | + | 6.32456i | −0.220594 | + | 0.220594i | ||||
\(823\) | −3.00000 | + | 3.00000i | −0.104573 | + | 0.104573i | −0.757458 | − | 0.652884i | \(-0.773559\pi\) |
0.652884 | + | 0.757458i | \(0.273559\pi\) | |||||||
\(824\) | 44.2719 | 1.54228 | ||||||||
\(825\) | −7.90569 | + | 7.90569i | −0.275241 | + | 0.275241i | ||||
\(826\) | 30.0000 | + | 18.9737i | 1.04383 | + | 0.660178i | ||||
\(827\) | −26.0000 | − | 26.0000i | −0.904109 | − | 0.904109i | 0.0916799 | − | 0.995789i | \(-0.470776\pi\) |
−0.995789 | + | 0.0916799i | \(0.970776\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.4605 | −0.988474 | −0.494237 | − | 0.869327i | \(-0.664552\pi\) | ||||
−0.494237 | + | 0.869327i | \(0.664552\pi\) | |||||||
\(830\) | 10.0000 | − | 10.0000i | 0.347105 | − | 0.347105i | ||||
\(831\) | 56.9210i | 1.97457i | ||||||||
\(832\) | 12.6491 | − | 12.6491i | 0.438529 | − | 0.438529i | ||||
\(833\) | −5.25658 | + | 14.7434i | −0.182130 | + | 0.510829i | ||||
\(834\) | 60.0000i | 2.07763i | ||||||||
\(835\) | −35.0000 | −1.21122 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.00000 | − | 5.00000i | −0.172825 | − | 0.172825i | ||||
\(838\) | −15.8114 | − | 15.8114i | −0.546195 | − | 0.546195i | ||||
\(839\) | −50.5964 | −1.74678 | −0.873392 | − | 0.487019i | \(-0.838084\pi\) | ||||
−0.873392 | + | 0.487019i | \(0.838084\pi\) | |||||||
\(840\) | 31.6228 | + | 20.0000i | 1.09109 | + | 0.690066i | ||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −19.0000 | − | 19.0000i | −0.654783 | − | 0.654783i | ||||
\(843\) | −14.2302 | − | 14.2302i | −0.490116 | − | 0.490116i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6491 | − | 12.6491i | 0.435143 | − | 0.435143i | ||||
\(846\) | − | 18.9737i | − | 0.652328i | ||||||
\(847\) | −25.8114 | + | 5.81139i | −0.886890 | + | 0.199682i | ||||
\(848\) | 4.00000 | − | 4.00000i | 0.137361 | − | 0.137361i | ||||
\(849\) | − | 15.0000i | − | 0.514799i | ||||||
\(850\) | 15.8114i | 0.542326i | ||||||||
\(851\) | −24.0000 | −0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(854\) | 12.6491 | − | 20.0000i | 0.432844 | − | 0.684386i | ||||
\(855\) | 10.0000 | − | 10.0000i | 0.341993 | − | 0.341993i | ||||
\(856\) | 12.0000 | 0.410152 | ||||||||
\(857\) | 31.6228 | − | 31.6228i | 1.08021 | − | 1.08021i | 0.0837245 | − | 0.996489i | \(-0.473318\pi\) |
0.996489 | − | 0.0837245i | \(-0.0266816\pi\) | |||||||
\(858\) | 5.00000 | − | 5.00000i | 0.170697 | − | 0.170697i | ||||
\(859\) | −12.6491 | −0.431582 | −0.215791 | − | 0.976440i | \(-0.569233\pi\) | ||||
−0.215791 | + | 0.976440i | \(0.569233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −30.0000 | + | 47.4342i | −1.02240 | + | 1.61655i | ||||
\(862\) | 23.0000 | + | 23.0000i | 0.783383 | + | 0.783383i | ||||
\(863\) | −13.0000 | + | 13.0000i | −0.442525 | + | 0.442525i | −0.892860 | − | 0.450335i | \(-0.851305\pi\) |
0.450335 | + | 0.892860i | \(0.351305\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.0000i | 1.19004i | ||||||||
\(866\) | 18.9737i | 0.644751i | ||||||||
\(867\) | 18.9737 | − | 18.9737i | 0.644379 | − | 0.644379i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13.0000i | − | 0.440995i | ||||||
\(870\) | −15.0000 | − | 15.0000i | −0.508548 | − | 0.508548i | ||||
\(871\) | − | 3.16228i | − | 0.107150i | ||||||
\(872\) | 14.0000 | + | 14.0000i | 0.474100 | + | 0.474100i | ||||
\(873\) | 3.16228 | + | 3.16228i | 0.107027 | + | 0.107027i | ||||
\(874\) | 12.6491 | 0.427863 | ||||||||
\(875\) | −15.8114 | + | 25.0000i | −0.534522 | + | 0.845154i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.0000 | + | 17.0000i | 0.574049 | + | 0.574049i | 0.933257 | − | 0.359208i | \(-0.116953\pi\) |
−0.359208 | + | 0.933257i | \(0.616953\pi\) | |||||||
\(878\) | −12.6491 | − | 12.6491i | −0.426887 | − | 0.426887i | ||||
\(879\) | − | 25.0000i | − | 0.843229i | ||||||
\(880\) | −6.32456 | − | 6.32456i | −0.213201 | − | 0.213201i | ||||
\(881\) | 37.9473i | 1.27848i | 0.769008 | + | 0.639239i | \(0.220751\pi\) | ||||
−0.769008 | + | 0.639239i | \(0.779249\pi\) | |||||||
\(882\) | 6.64911 | − | 18.6491i | 0.223887 | − | 0.627948i | ||||
\(883\) | −18.0000 | + | 18.0000i | −0.605748 | + | 0.605748i | −0.941832 | − | 0.336084i | \(-0.890897\pi\) |
0.336084 | + | 0.941832i | \(0.390897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 47.4342i | 1.59448i | ||||||||
\(886\) | −2.00000 | −0.0671913 | ||||||||
\(887\) | −3.16228 | + | 3.16228i | −0.106179 | + | 0.106179i | −0.758200 | − | 0.652022i | \(-0.773921\pi\) |
0.652022 | + | 0.758200i | \(0.273921\pi\) | |||||||
\(888\) | −37.9473 | − | 37.9473i | −1.27343 | − | 1.27343i | ||||
\(889\) | 28.4605 | + | 18.0000i | 0.954534 | + | 0.603701i | ||||
\(890\) | − | 20.0000i | − | 0.670402i | ||||||
\(891\) | −11.0000 | −0.368514 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −15.0000 | + | 15.0000i | −0.501956 | + | 0.501956i | ||||
\(894\) | 37.9473 | 1.26915 | ||||||||
\(895\) | 9.48683 | − | 9.48683i | 0.317110 | − | 0.317110i | ||||
\(896\) | −16.0000 | + | 25.2982i | −0.534522 | + | 0.845154i | ||||
\(897\) | −10.0000 | − | 10.0000i | −0.333890 | − | 0.333890i | ||||
\(898\) | −17.0000 | + | 17.0000i | −0.567297 | + | 0.567297i | ||||
\(899\) | −9.48683 | −0.316404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.16228i | 0.105351i | ||||||||
\(902\) | 9.48683 | − | 9.48683i | 0.315877 | − | 0.315877i | ||||
\(903\) | 24.4868 | − | 5.51317i | 0.814871 | − | 0.183467i | ||||
\(904\) | 48.0000i | 1.59646i | ||||||||
\(905\) | 35.0000 | − | 35.0000i | 1.16344 | − | 1.16344i | ||||
\(906\) | 28.4605i | 0.945537i | ||||||||
\(907\) | 22.0000 | + | 22.0000i | 0.730498 | + | 0.730498i | 0.970718 | − | 0.240220i | \(-0.0772197\pi\) |
−0.240220 | + | 0.970718i | \(0.577220\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.32456 | 0.209772 | ||||||||
\(910\) | 10.0000 | − | 15.8114i | 0.331497 | − | 0.524142i | ||||
\(911\) | 54.0000 | 1.78910 | 0.894550 | − | 0.446968i | \(-0.147496\pi\) | ||||
0.894550 | + | 0.446968i | \(0.147496\pi\) | |||||||
\(912\) | 20.0000 | + | 20.0000i | 0.662266 | + | 0.662266i | ||||
\(913\) | −3.16228 | − | 3.16228i | −0.104656 | − | 0.104656i | ||||
\(914\) | 2.00000i | 0.0661541i | ||||||||
\(915\) | 31.6228 | 1.04542 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.00000 | + | 5.00000i | −0.165025 | + | 0.165025i | ||||
\(919\) | − | 27.0000i | − | 0.890648i | −0.895370 | − | 0.445324i | \(-0.853089\pi\) | ||
0.895370 | − | 0.445324i | \(-0.146911\pi\) | |||||||
\(920\) | −12.6491 | + | 12.6491i | −0.417029 | + | 0.417029i | ||||
\(921\) | −15.0000 | −0.494267 | ||||||||
\(922\) | −6.32456 | + | 6.32456i | −0.208288 | + | 0.208288i | ||||
\(923\) | −9.48683 | − | 9.48683i | −0.312263 | − | 0.312263i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0000 | − | 30.0000i | 0.986394 | − | 0.986394i | ||||
\(926\) | 8.00000 | 0.262896 | ||||||||
\(927\) | 22.1359 | − | 22.1359i | 0.727040 | − | 0.727040i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.16228 | −0.103751 | −0.0518755 | − | 0.998654i | \(-0.516520\pi\) | ||||
−0.0518755 | + | 0.998654i | \(0.516520\pi\) | |||||||
\(930\) | −15.8114 | − | 15.8114i | −0.518476 | − | 0.518476i | ||||
\(931\) | −20.0000 | + | 9.48683i | −0.655474 | + | 0.310918i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −35.0000 | + | 35.0000i | −1.14585 | + | 1.14585i | ||||
\(934\) | −22.1359 | −0.724310 | ||||||||
\(935\) | 5.00000 | 0.163517 | ||||||||
\(936\) | − | 12.6491i | − | 0.413449i | ||||||
\(937\) | 14.2302 | − | 14.2302i | 0.464882 | − | 0.464882i | −0.435370 | − | 0.900252i | \(-0.643382\pi\) |
0.900252 | + | 0.435370i | \(0.143382\pi\) | |||||||
\(938\) | 1.16228 | + | 5.16228i | 0.0379497 | + | 0.168554i | ||||
\(939\) | − | 45.0000i | − | 1.46852i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 37.9473i | − | 1.23705i | −0.785766 | − | 0.618524i | \(-0.787731\pi\) | ||
0.785766 | − | 0.618524i | \(-0.212269\pi\) | |||||||
\(942\) | −20.0000 | − | 20.0000i | −0.651635 | − | 0.651635i | ||||
\(943\) | −18.9737 | − | 18.9737i | −0.617868 | − | 0.617868i | ||||
\(944\) | −37.9473 | −1.23508 | ||||||||
\(945\) | −12.9057 | + | 2.90569i | −0.419822 | + | 0.0945222i | ||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | 7.00000 | + | 7.00000i | 0.227469 | + | 0.227469i | 0.811635 | − | 0.584165i | \(-0.198578\pi\) |
−0.584165 | + | 0.811635i | \(0.698578\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −15.8114 | + | 15.8114i | −0.512989 | + | 0.512989i | ||||
\(951\) | − | 60.0833i | − | 1.94833i | ||||||
\(952\) | −3.67544 | − | 16.3246i | −0.119122 | − | 0.529082i | ||||
\(953\) | −3.00000 | + | 3.00000i | −0.0971795 | + | 0.0971795i | −0.754025 | − | 0.656846i | \(-0.771890\pi\) |
0.656846 | + | 0.754025i | \(0.271890\pi\) | |||||||
\(954\) | − | 4.00000i | − | 0.129505i | ||||||
\(955\) | −4.74342 | − | 4.74342i | −0.153493 | − | 0.153493i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.74342 | + | 4.74342i | −0.153333 | + | 0.153333i | ||||
\(958\) | −6.32456 | − | 6.32456i | −0.204337 | − | 0.204337i | ||||
\(959\) | 6.32456 | + | 4.00000i | 0.204231 | + | 0.129167i | ||||
\(960\) | −40.0000 | −1.29099 | ||||||||
\(961\) | 21.0000 | 0.677419 | ||||||||
\(962\) | −18.9737 | + | 18.9737i | −0.611736 | + | 0.611736i | ||||
\(963\) | 6.00000 | − | 6.00000i | 0.193347 | − | 0.193347i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25.2982 | −0.814379 | ||||||||
\(966\) | 20.0000 | + | 12.6491i | 0.643489 | + | 0.406978i | ||||
\(967\) | −33.0000 | − | 33.0000i | −1.06121 | − | 1.06121i | −0.998000 | − | 0.0632081i | \(-0.979867\pi\) |
−0.0632081 | − | 0.998000i | \(-0.520133\pi\) | |||||||
\(968\) | 20.0000 | − | 20.0000i | 0.642824 | − | 0.642824i | ||||
\(969\) | −15.8114 | −0.507935 | ||||||||
\(970\) | −5.00000 | − | 5.00000i | −0.160540 | − | 0.160540i | ||||
\(971\) | − | 34.7851i | − | 1.11631i | −0.829738 | − | 0.558153i | \(-0.811510\pi\) | ||
0.829738 | − | 0.558153i | \(-0.188490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 48.9737 | − | 11.0263i | 1.57002 | − | 0.353488i | ||||
\(974\) | − | 8.00000i | − | 0.256337i | ||||||
\(975\) | 25.0000 | 0.800641 | ||||||||
\(976\) | 25.2982i | 0.809776i | ||||||||
\(977\) | −1.00000 | − | 1.00000i | −0.0319928 | − | 0.0319928i | 0.690929 | − | 0.722922i | \(-0.257202\pi\) |
−0.722922 | + | 0.690929i | \(0.757202\pi\) | |||||||
\(978\) | 18.9737 | + | 18.9737i | 0.606711 | + | 0.606711i | ||||
\(979\) | −6.32456 | −0.202134 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 41.0000 | + | 41.0000i | 1.30836 | + | 1.30836i | ||||
\(983\) | 20.5548 | + | 20.5548i | 0.655596 | + | 0.655596i | 0.954335 | − | 0.298739i | \(-0.0965658\pi\) |
−0.298739 | + | 0.954335i | \(0.596566\pi\) | |||||||
\(984\) | − | 60.0000i | − | 1.91273i | ||||||
\(985\) | − | 3.16228i | − | 0.100759i | ||||||
\(986\) | 9.48683i | 0.302122i | ||||||||
\(987\) | −38.7171 | + | 8.71708i | −1.23238 | + | 0.277468i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.0000i | 0.381578i | ||||||||
\(990\) | −6.32456 | −0.201008 | ||||||||
\(991\) | 4.00000 | 0.127064 | 0.0635321 | − | 0.997980i | \(-0.479763\pi\) | ||||
0.0635321 | + | 0.997980i | \(0.479763\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.48683 | + | 9.48683i | 0.301056 | + | 0.301056i | ||||
\(994\) | 18.9737 | + | 12.0000i | 0.601808 | + | 0.380617i | ||||
\(995\) | 15.0000 | + | 15.0000i | 0.475532 | + | 0.475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.2302 | + | 14.2302i | −0.450677 | + | 0.450677i | −0.895579 | − | 0.444902i | \(-0.853238\pi\) |
0.444902 | + | 0.895579i | \(0.353238\pi\) | |||||||
\(998\) | 19.0000 | − | 19.0000i | 0.601434 | − | 0.601434i | ||||
\(999\) | 18.9737 | 0.600300 |
(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 | 35.2.f.a.27.1 | yes | 4 | |
3.2 | odd | 2 | 315.2.p.c.307.1 | 4 | |||
4.3 | odd | 2 | 560.2.bj.a.97.2 | 4 | |||
5.2 | odd | 4 | 175.2.f.c.118.1 | 4 | |||
5.3 | odd | 4 | inner | 35.2.f.a.13.2 | yes | 4 | |
5.4 | even | 2 | 175.2.f.c.132.2 | 4 | |||
7.2 | even | 3 | 245.2.l.c.227.2 | 8 | |||
7.3 | odd | 6 | 245.2.l.c.117.2 | 8 | |||
7.4 | even | 3 | 245.2.l.c.117.1 | 8 | |||
7.5 | odd | 6 | 245.2.l.c.227.1 | 8 | |||
7.6 | odd | 2 | inner | 35.2.f.a.27.2 | yes | 4 | |
15.8 | even | 4 | 315.2.p.c.118.2 | 4 | |||
20.3 | even | 4 | 560.2.bj.a.433.1 | 4 | |||
21.20 | even | 2 | 315.2.p.c.307.2 | 4 | |||
28.27 | even | 2 | 560.2.bj.a.97.1 | 4 | |||
35.3 | even | 12 | 245.2.l.c.68.2 | 8 | |||
35.13 | even | 4 | inner | 35.2.f.a.13.1 | ✓ | 4 | |
35.18 | odd | 12 | 245.2.l.c.68.1 | 8 | |||
35.23 | odd | 12 | 245.2.l.c.178.2 | 8 | |||
35.27 | even | 4 | 175.2.f.c.118.2 | 4 | |||
35.33 | even | 12 | 245.2.l.c.178.1 | 8 | |||
35.34 | odd | 2 | 175.2.f.c.132.1 | 4 | |||
105.83 | odd | 4 | 315.2.p.c.118.1 | 4 | |||
140.83 | odd | 4 | 560.2.bj.a.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.2.f.a.13.1 | ✓ | 4 | 35.13 | even | 4 | inner | |
35.2.f.a.13.2 | yes | 4 | 5.3 | odd | 4 | inner | |
35.2.f.a.27.1 | yes | 4 | 1.1 | even | 1 | trivial | |
35.2.f.a.27.2 | yes | 4 | 7.6 | odd | 2 | inner | |
175.2.f.c.118.1 | 4 | 5.2 | odd | 4 | |||
175.2.f.c.118.2 | 4 | 35.27 | even | 4 | |||
175.2.f.c.132.1 | 4 | 35.34 | odd | 2 | |||
175.2.f.c.132.2 | 4 | 5.4 | even | 2 | |||
245.2.l.c.68.1 | 8 | 35.18 | odd | 12 | |||
245.2.l.c.68.2 | 8 | 35.3 | even | 12 | |||
245.2.l.c.117.1 | 8 | 7.4 | even | 3 | |||
245.2.l.c.117.2 | 8 | 7.3 | odd | 6 | |||
245.2.l.c.178.1 | 8 | 35.33 | even | 12 | |||
245.2.l.c.178.2 | 8 | 35.23 | odd | 12 | |||
245.2.l.c.227.1 | 8 | 7.5 | odd | 6 | |||
245.2.l.c.227.2 | 8 | 7.2 | even | 3 | |||
315.2.p.c.118.1 | 4 | 105.83 | odd | 4 | |||
315.2.p.c.118.2 | 4 | 15.8 | even | 4 | |||
315.2.p.c.307.1 | 4 | 3.2 | odd | 2 | |||
315.2.p.c.307.2 | 4 | 21.20 | even | 2 | |||
560.2.bj.a.97.1 | 4 | 28.27 | even | 2 | |||
560.2.bj.a.97.2 | 4 | 4.3 | odd | 2 | |||
560.2.bj.a.433.1 | 4 | 20.3 | even | 4 | |||
560.2.bj.a.433.2 | 4 | 140.83 | odd | 4 |