Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [170,2,Mod(89,170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(170, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("170.89");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 170 = 2 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 170.g (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: | \(1.35745683436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
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 | 89.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 170.89 |
Dual form | 170.2.g.b.149.1 |
$q$-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 \(\left(\mathbb{Z}/170\mathbb{Z}\right)^\times\).
\(n\) | \(71\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | −0.707107 | ||||||||
\(3\) | 1.00000 | + | 1.00000i | 0.577350 | + | 0.577350i | 0.934172 | − | 0.356822i | \(-0.116140\pi\) |
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | −1.00000 | − | 1.00000i | −0.408248 | − | 0.408248i | ||||
\(7\) | 1.00000 | − | 1.00000i | 0.377964 | − | 0.377964i | −0.492403 | − | 0.870367i | \(-0.663881\pi\) |
0.870367 | + | 0.492403i | \(0.163881\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.00000 | + | 2.00000i | −0.316228 | + | 0.632456i | ||||
\(11\) | 1.00000 | + | 1.00000i | 0.301511 | + | 0.301511i | 0.841605 | − | 0.540094i | \(-0.181611\pi\) |
−0.540094 | + | 0.841605i | \(0.681611\pi\) | |||||||
\(12\) | 1.00000 | + | 1.00000i | 0.288675 | + | 0.288675i | ||||
\(13\) | 4.00000i | 1.10940i | 0.832050 | + | 0.554700i | \(0.187167\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | −1.00000 | + | 1.00000i | −0.267261 | + | 0.267261i | ||||
\(15\) | 3.00000 | − | 1.00000i | 0.774597 | − | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | − | 4.00000i | 0.242536 | − | 0.970143i | ||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 1.00000 | − | 2.00000i | 0.223607 | − | 0.447214i | ||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | −1.00000 | − | 1.00000i | −0.213201 | − | 0.213201i | ||||
\(23\) | 1.00000 | − | 1.00000i | 0.208514 | − | 0.208514i | −0.595121 | − | 0.803636i | \(-0.702896\pi\) |
0.803636 | + | 0.595121i | \(0.202896\pi\) | |||||||
\(24\) | −1.00000 | − | 1.00000i | −0.204124 | − | 0.204124i | ||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | − | 4.00000i | − | 0.784465i | ||||||
\(27\) | 4.00000 | − | 4.00000i | 0.769800 | − | 0.769800i | ||||
\(28\) | 1.00000 | − | 1.00000i | 0.188982 | − | 0.188982i | ||||
\(29\) | −5.00000 | + | 5.00000i | −0.928477 | + | 0.928477i | −0.997608 | − | 0.0691309i | \(-0.977977\pi\) |
0.0691309 | + | 0.997608i | \(0.477977\pi\) | |||||||
\(30\) | −3.00000 | + | 1.00000i | −0.547723 | + | 0.182574i | ||||
\(31\) | −3.00000 | + | 3.00000i | −0.538816 | + | 0.538816i | −0.923181 | − | 0.384365i | \(-0.874420\pi\) |
0.384365 | + | 0.923181i | \(0.374420\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | −1.00000 | + | 4.00000i | −0.171499 | + | 0.685994i | ||||
\(35\) | −1.00000 | − | 3.00000i | −0.169031 | − | 0.507093i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −1.00000 | − | 1.00000i | −0.164399 | − | 0.164399i | 0.620113 | − | 0.784512i | \(-0.287087\pi\) |
−0.784512 | + | 0.620113i | \(0.787087\pi\) | |||||||
\(38\) | − | 6.00000i | − | 0.973329i | ||||||
\(39\) | −4.00000 | + | 4.00000i | −0.640513 | + | 0.640513i | ||||
\(40\) | −1.00000 | + | 2.00000i | −0.158114 | + | 0.316228i | ||||
\(41\) | −7.00000 | − | 7.00000i | −1.09322 | − | 1.09322i | −0.995183 | − | 0.0980332i | \(-0.968745\pi\) |
−0.0980332 | − | 0.995183i | \(-0.531255\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 1.00000 | + | 1.00000i | 0.150756 | + | 0.150756i | ||||
\(45\) | −2.00000 | − | 1.00000i | −0.298142 | − | 0.149071i | ||||
\(46\) | −1.00000 | + | 1.00000i | −0.147442 | + | 0.147442i | ||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 1.00000 | + | 1.00000i | 0.144338 | + | 0.144338i | ||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 3.00000 | + | 4.00000i | 0.424264 | + | 0.565685i | ||||
\(51\) | 5.00000 | − | 3.00000i | 0.700140 | − | 0.420084i | ||||
\(52\) | 4.00000i | 0.554700i | ||||||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | −4.00000 | + | 4.00000i | −0.544331 | + | 0.544331i | ||||
\(55\) | 3.00000 | − | 1.00000i | 0.404520 | − | 0.134840i | ||||
\(56\) | −1.00000 | + | 1.00000i | −0.133631 | + | 0.133631i | ||||
\(57\) | −6.00000 | + | 6.00000i | −0.794719 | + | 0.794719i | ||||
\(58\) | 5.00000 | − | 5.00000i | 0.656532 | − | 0.656532i | ||||
\(59\) | − | 10.0000i | − | 1.30189i | −0.759125 | − | 0.650945i | \(-0.774373\pi\) | ||
0.759125 | − | 0.650945i | \(-0.225627\pi\) | |||||||
\(60\) | 3.00000 | − | 1.00000i | 0.387298 | − | 0.129099i | ||||
\(61\) | 3.00000 | + | 3.00000i | 0.384111 | + | 0.384111i | 0.872581 | − | 0.488470i | \(-0.162445\pi\) |
−0.488470 | + | 0.872581i | \(0.662445\pi\) | |||||||
\(62\) | 3.00000 | − | 3.00000i | 0.381000 | − | 0.381000i | ||||
\(63\) | −1.00000 | − | 1.00000i | −0.125988 | − | 0.125988i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 8.00000 | + | 4.00000i | 0.992278 | + | 0.496139i | ||||
\(66\) | − | 2.00000i | − | 0.246183i | ||||||
\(67\) | − | 2.00000i | − | 0.244339i | −0.992509 | − | 0.122169i | \(-0.961015\pi\) | ||
0.992509 | − | 0.122169i | \(-0.0389851\pi\) | |||||||
\(68\) | 1.00000 | − | 4.00000i | 0.121268 | − | 0.485071i | ||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 1.00000 | + | 3.00000i | 0.119523 | + | 0.358569i | ||||
\(71\) | 5.00000 | − | 5.00000i | 0.593391 | − | 0.593391i | −0.345155 | − | 0.938546i | \(-0.612174\pi\) |
0.938546 | + | 0.345155i | \(0.112174\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 1.00000 | + | 1.00000i | 0.117041 | + | 0.117041i | 0.763202 | − | 0.646160i | \(-0.223626\pi\) |
−0.646160 | + | 0.763202i | \(0.723626\pi\) | |||||||
\(74\) | 1.00000 | + | 1.00000i | 0.116248 | + | 0.116248i | ||||
\(75\) | 1.00000 | − | 7.00000i | 0.115470 | − | 0.808290i | ||||
\(76\) | 6.00000i | 0.688247i | ||||||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 4.00000 | − | 4.00000i | 0.452911 | − | 0.452911i | ||||
\(79\) | −1.00000 | − | 1.00000i | −0.112509 | − | 0.112509i | 0.648611 | − | 0.761120i | \(-0.275350\pi\) |
−0.761120 | + | 0.648611i | \(0.775350\pi\) | |||||||
\(80\) | 1.00000 | − | 2.00000i | 0.111803 | − | 0.223607i | ||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 7.00000 | + | 7.00000i | 0.773021 | + | 0.773021i | ||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 2.00000 | 0.218218 | ||||||||
\(85\) | −7.00000 | − | 6.00000i | −0.759257 | − | 0.650791i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | −10.0000 | −1.07211 | ||||||||
\(88\) | −1.00000 | − | 1.00000i | −0.106600 | − | 0.106600i | ||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 2.00000 | + | 1.00000i | 0.210819 | + | 0.105409i | ||||
\(91\) | 4.00000 | + | 4.00000i | 0.419314 | + | 0.419314i | ||||
\(92\) | 1.00000 | − | 1.00000i | 0.104257 | − | 0.104257i | ||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | − | 6.00000i | − | 0.618853i | ||||||
\(95\) | 12.0000 | + | 6.00000i | 1.23117 | + | 0.615587i | ||||
\(96\) | −1.00000 | − | 1.00000i | −0.102062 | − | 0.102062i | ||||
\(97\) | −3.00000 | − | 3.00000i | −0.304604 | − | 0.304604i | 0.538208 | − | 0.842812i | \(-0.319101\pi\) |
−0.842812 | + | 0.538208i | \(0.819101\pi\) | |||||||
\(98\) | − | 5.00000i | − | 0.505076i | ||||||
\(99\) | 1.00000 | − | 1.00000i | 0.100504 | − | 0.100504i | ||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | −14.0000 | −1.39305 | −0.696526 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696526 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(102\) | −5.00000 | + | 3.00000i | −0.495074 | + | 0.297044i | ||||
\(103\) | 14.0000i | 1.37946i | 0.724066 | + | 0.689730i | \(0.242271\pi\) | ||||
−0.724066 | + | 0.689730i | \(0.757729\pi\) | |||||||
\(104\) | − | 4.00000i | − | 0.392232i | ||||||
\(105\) | 2.00000 | − | 4.00000i | 0.195180 | − | 0.390360i | ||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | 13.0000 | + | 13.0000i | 1.25676 | + | 1.25676i | 0.952632 | + | 0.304125i | \(0.0983642\pi\) |
0.304125 | + | 0.952632i | \(0.401636\pi\) | |||||||
\(108\) | 4.00000 | − | 4.00000i | 0.384900 | − | 0.384900i | ||||
\(109\) | 7.00000 | + | 7.00000i | 0.670478 | + | 0.670478i | 0.957826 | − | 0.287348i | \(-0.0927736\pi\) |
−0.287348 | + | 0.957826i | \(0.592774\pi\) | |||||||
\(110\) | −3.00000 | + | 1.00000i | −0.286039 | + | 0.0953463i | ||||
\(111\) | − | 2.00000i | − | 0.189832i | ||||||
\(112\) | 1.00000 | − | 1.00000i | 0.0944911 | − | 0.0944911i | ||||
\(113\) | −11.0000 | + | 11.0000i | −1.03479 | + | 1.03479i | −0.0354205 | + | 0.999372i | \(0.511277\pi\) |
−0.999372 | + | 0.0354205i | \(0.988723\pi\) | |||||||
\(114\) | 6.00000 | − | 6.00000i | 0.561951 | − | 0.561951i | ||||
\(115\) | −1.00000 | − | 3.00000i | −0.0932505 | − | 0.279751i | ||||
\(116\) | −5.00000 | + | 5.00000i | −0.464238 | + | 0.464238i | ||||
\(117\) | 4.00000 | 0.369800 | ||||||||
\(118\) | 10.0000i | 0.920575i | ||||||||
\(119\) | −3.00000 | − | 5.00000i | −0.275010 | − | 0.458349i | ||||
\(120\) | −3.00000 | + | 1.00000i | −0.273861 | + | 0.0912871i | ||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | −3.00000 | − | 3.00000i | −0.271607 | − | 0.271607i | ||||
\(123\) | − | 14.0000i | − | 1.26234i | ||||||
\(124\) | −3.00000 | + | 3.00000i | −0.269408 | + | 0.269408i | ||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 1.00000 | + | 1.00000i | 0.0890871 | + | 0.0890871i | ||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.00000 | − | 4.00000i | −0.352180 | − | 0.352180i | ||||
\(130\) | −8.00000 | − | 4.00000i | −0.701646 | − | 0.350823i | ||||
\(131\) | −9.00000 | + | 9.00000i | −0.786334 | + | 0.786334i | −0.980891 | − | 0.194557i | \(-0.937673\pi\) |
0.194557 | + | 0.980891i | \(0.437673\pi\) | |||||||
\(132\) | 2.00000i | 0.174078i | ||||||||
\(133\) | 6.00000 | + | 6.00000i | 0.520266 | + | 0.520266i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | −4.00000 | − | 12.0000i | −0.344265 | − | 1.03280i | ||||
\(136\) | −1.00000 | + | 4.00000i | −0.0857493 | + | 0.342997i | ||||
\(137\) | − | 12.0000i | − | 1.02523i | −0.858619 | − | 0.512615i | \(-0.828677\pi\) | ||
0.858619 | − | 0.512615i | \(-0.171323\pi\) | |||||||
\(138\) | −2.00000 | −0.170251 | ||||||||
\(139\) | 3.00000 | − | 3.00000i | 0.254457 | − | 0.254457i | −0.568338 | − | 0.822795i | \(-0.692414\pi\) |
0.822795 | + | 0.568338i | \(0.192414\pi\) | |||||||
\(140\) | −1.00000 | − | 3.00000i | −0.0845154 | − | 0.253546i | ||||
\(141\) | −6.00000 | + | 6.00000i | −0.505291 | + | 0.505291i | ||||
\(142\) | −5.00000 | + | 5.00000i | −0.419591 | + | 0.419591i | ||||
\(143\) | −4.00000 | + | 4.00000i | −0.334497 | + | 0.334497i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 5.00000 | + | 15.0000i | 0.415227 | + | 1.24568i | ||||
\(146\) | −1.00000 | − | 1.00000i | −0.0827606 | − | 0.0827606i | ||||
\(147\) | −5.00000 | + | 5.00000i | −0.412393 | + | 0.412393i | ||||
\(148\) | −1.00000 | − | 1.00000i | −0.0821995 | − | 0.0821995i | ||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | −1.00000 | + | 7.00000i | −0.0816497 | + | 0.571548i | ||||
\(151\) | − | 2.00000i | − | 0.162758i | −0.996683 | − | 0.0813788i | \(-0.974068\pi\) | ||
0.996683 | − | 0.0813788i | \(-0.0259324\pi\) | |||||||
\(152\) | − | 6.00000i | − | 0.486664i | ||||||
\(153\) | −4.00000 | − | 1.00000i | −0.323381 | − | 0.0808452i | ||||
\(154\) | −2.00000 | −0.161165 | ||||||||
\(155\) | 3.00000 | + | 9.00000i | 0.240966 | + | 0.722897i | ||||
\(156\) | −4.00000 | + | 4.00000i | −0.320256 | + | 0.320256i | ||||
\(157\) | − | 16.0000i | − | 1.27694i | −0.769647 | − | 0.638470i | \(-0.779568\pi\) | ||
0.769647 | − | 0.638470i | \(-0.220432\pi\) | |||||||
\(158\) | 1.00000 | + | 1.00000i | 0.0795557 | + | 0.0795557i | ||||
\(159\) | −10.0000 | − | 10.0000i | −0.793052 | − | 0.793052i | ||||
\(160\) | −1.00000 | + | 2.00000i | −0.0790569 | + | 0.158114i | ||||
\(161\) | − | 2.00000i | − | 0.157622i | ||||||
\(162\) | −5.00000 | −0.392837 | ||||||||
\(163\) | 15.0000 | − | 15.0000i | 1.17489 | − | 1.17489i | 0.193862 | − | 0.981029i | \(-0.437899\pi\) |
0.981029 | − | 0.193862i | \(-0.0621013\pi\) | |||||||
\(164\) | −7.00000 | − | 7.00000i | −0.546608 | − | 0.546608i | ||||
\(165\) | 4.00000 | + | 2.00000i | 0.311400 | + | 0.155700i | ||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | 7.00000 | + | 7.00000i | 0.541676 | + | 0.541676i | 0.924020 | − | 0.382344i | \(-0.124883\pi\) |
−0.382344 | + | 0.924020i | \(0.624883\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 7.00000 | + | 6.00000i | 0.536875 | + | 0.460179i | ||||
\(171\) | 6.00000 | 0.458831 | ||||||||
\(172\) | −4.00000 | −0.304997 | ||||||||
\(173\) | 7.00000 | + | 7.00000i | 0.532200 | + | 0.532200i | 0.921227 | − | 0.389026i | \(-0.127189\pi\) |
−0.389026 | + | 0.921227i | \(0.627189\pi\) | |||||||
\(174\) | 10.0000 | 0.758098 | ||||||||
\(175\) | −7.00000 | − | 1.00000i | −0.529150 | − | 0.0755929i | ||||
\(176\) | 1.00000 | + | 1.00000i | 0.0753778 | + | 0.0753778i | ||||
\(177\) | 10.0000 | − | 10.0000i | 0.751646 | − | 0.751646i | ||||
\(178\) | −6.00000 | −0.449719 | ||||||||
\(179\) | 6.00000i | 0.448461i | 0.974536 | + | 0.224231i | \(0.0719869\pi\) | ||||
−0.974536 | + | 0.224231i | \(0.928013\pi\) | |||||||
\(180\) | −2.00000 | − | 1.00000i | −0.149071 | − | 0.0745356i | ||||
\(181\) | 7.00000 | + | 7.00000i | 0.520306 | + | 0.520306i | 0.917664 | − | 0.397358i | \(-0.130073\pi\) |
−0.397358 | + | 0.917664i | \(0.630073\pi\) | |||||||
\(182\) | −4.00000 | − | 4.00000i | −0.296500 | − | 0.296500i | ||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | −1.00000 | + | 1.00000i | −0.0737210 | + | 0.0737210i | ||||
\(185\) | −3.00000 | + | 1.00000i | −0.220564 | + | 0.0735215i | ||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | 5.00000 | − | 3.00000i | 0.365636 | − | 0.219382i | ||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | − | 8.00000i | − | 0.581914i | ||||||
\(190\) | −12.0000 | − | 6.00000i | −0.870572 | − | 0.435286i | ||||
\(191\) | −24.0000 | −1.73658 | −0.868290 | − | 0.496058i | \(-0.834780\pi\) | ||||
−0.868290 | + | 0.496058i | \(0.834780\pi\) | |||||||
\(192\) | 1.00000 | + | 1.00000i | 0.0721688 | + | 0.0721688i | ||||
\(193\) | 13.0000 | − | 13.0000i | 0.935760 | − | 0.935760i | −0.0622972 | − | 0.998058i | \(-0.519843\pi\) |
0.998058 | + | 0.0622972i | \(0.0198427\pi\) | |||||||
\(194\) | 3.00000 | + | 3.00000i | 0.215387 | + | 0.215387i | ||||
\(195\) | 4.00000 | + | 12.0000i | 0.286446 | + | 0.859338i | ||||
\(196\) | 5.00000i | 0.357143i | ||||||||
\(197\) | 7.00000 | − | 7.00000i | 0.498729 | − | 0.498729i | −0.412313 | − | 0.911042i | \(-0.635279\pi\) |
0.911042 | + | 0.412313i | \(0.135279\pi\) | |||||||
\(198\) | −1.00000 | + | 1.00000i | −0.0710669 | + | 0.0710669i | ||||
\(199\) | 17.0000 | − | 17.0000i | 1.20510 | − | 1.20510i | 0.232502 | − | 0.972596i | \(-0.425309\pi\) |
0.972596 | − | 0.232502i | \(-0.0746913\pi\) | |||||||
\(200\) | 3.00000 | + | 4.00000i | 0.212132 | + | 0.282843i | ||||
\(201\) | 2.00000 | − | 2.00000i | 0.141069 | − | 0.141069i | ||||
\(202\) | 14.0000 | 0.985037 | ||||||||
\(203\) | 10.0000i | 0.701862i | ||||||||
\(204\) | 5.00000 | − | 3.00000i | 0.350070 | − | 0.210042i | ||||
\(205\) | −21.0000 | + | 7.00000i | −1.46670 | + | 0.488901i | ||||
\(206\) | − | 14.0000i | − | 0.975426i | ||||||
\(207\) | −1.00000 | − | 1.00000i | −0.0695048 | − | 0.0695048i | ||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | −6.00000 | + | 6.00000i | −0.415029 | + | 0.415029i | ||||
\(210\) | −2.00000 | + | 4.00000i | −0.138013 | + | 0.276026i | ||||
\(211\) | 13.0000 | + | 13.0000i | 0.894957 | + | 0.894957i | 0.994985 | − | 0.100028i | \(-0.0318932\pi\) |
−0.100028 | + | 0.994985i | \(0.531893\pi\) | |||||||
\(212\) | −10.0000 | −0.686803 | ||||||||
\(213\) | 10.0000 | 0.685189 | ||||||||
\(214\) | −13.0000 | − | 13.0000i | −0.888662 | − | 0.888662i | ||||
\(215\) | −4.00000 | + | 8.00000i | −0.272798 | + | 0.545595i | ||||
\(216\) | −4.00000 | + | 4.00000i | −0.272166 | + | 0.272166i | ||||
\(217\) | 6.00000i | 0.407307i | ||||||||
\(218\) | −7.00000 | − | 7.00000i | −0.474100 | − | 0.474100i | ||||
\(219\) | 2.00000i | 0.135147i | ||||||||
\(220\) | 3.00000 | − | 1.00000i | 0.202260 | − | 0.0674200i | ||||
\(221\) | 16.0000 | + | 4.00000i | 1.07628 | + | 0.269069i | ||||
\(222\) | 2.00000i | 0.134231i | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | −1.00000 | + | 1.00000i | −0.0668153 | + | 0.0668153i | ||||
\(225\) | −4.00000 | + | 3.00000i | −0.266667 | + | 0.200000i | ||||
\(226\) | 11.0000 | − | 11.0000i | 0.731709 | − | 0.731709i | ||||
\(227\) | −9.00000 | + | 9.00000i | −0.597351 | + | 0.597351i | −0.939607 | − | 0.342256i | \(-0.888809\pi\) |
0.342256 | + | 0.939607i | \(0.388809\pi\) | |||||||
\(228\) | −6.00000 | + | 6.00000i | −0.397360 | + | 0.397360i | ||||
\(229\) | − | 28.0000i | − | 1.85029i | −0.379611 | − | 0.925146i | \(-0.623942\pi\) | ||
0.379611 | − | 0.925146i | \(-0.376058\pi\) | |||||||
\(230\) | 1.00000 | + | 3.00000i | 0.0659380 | + | 0.197814i | ||||
\(231\) | 2.00000 | + | 2.00000i | 0.131590 | + | 0.131590i | ||||
\(232\) | 5.00000 | − | 5.00000i | 0.328266 | − | 0.328266i | ||||
\(233\) | 1.00000 | + | 1.00000i | 0.0655122 | + | 0.0655122i | 0.739104 | − | 0.673592i | \(-0.235249\pi\) |
−0.673592 | + | 0.739104i | \(0.735249\pi\) | |||||||
\(234\) | −4.00000 | −0.261488 | ||||||||
\(235\) | 12.0000 | + | 6.00000i | 0.782794 | + | 0.391397i | ||||
\(236\) | − | 10.0000i | − | 0.650945i | ||||||
\(237\) | − | 2.00000i | − | 0.129914i | ||||||
\(238\) | 3.00000 | + | 5.00000i | 0.194461 | + | 0.324102i | ||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 3.00000 | − | 1.00000i | 0.193649 | − | 0.0645497i | ||||
\(241\) | 9.00000 | − | 9.00000i | 0.579741 | − | 0.579741i | −0.355091 | − | 0.934832i | \(-0.615550\pi\) |
0.934832 | + | 0.355091i | \(0.115550\pi\) | |||||||
\(242\) | 9.00000i | 0.578542i | ||||||||
\(243\) | −7.00000 | − | 7.00000i | −0.449050 | − | 0.449050i | ||||
\(244\) | 3.00000 | + | 3.00000i | 0.192055 | + | 0.192055i | ||||
\(245\) | 10.0000 | + | 5.00000i | 0.638877 | + | 0.319438i | ||||
\(246\) | 14.0000i | 0.892607i | ||||||||
\(247\) | −24.0000 | −1.52708 | ||||||||
\(248\) | 3.00000 | − | 3.00000i | 0.190500 | − | 0.190500i | ||||
\(249\) | 12.0000 | + | 12.0000i | 0.760469 | + | 0.760469i | ||||
\(250\) | 11.0000 | − | 2.00000i | 0.695701 | − | 0.126491i | ||||
\(251\) | −20.0000 | −1.26239 | −0.631194 | − | 0.775625i | \(-0.717435\pi\) | ||||
−0.631194 | + | 0.775625i | \(0.717435\pi\) | |||||||
\(252\) | −1.00000 | − | 1.00000i | −0.0629941 | − | 0.0629941i | ||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 8.00000 | 0.501965 | ||||||||
\(255\) | −1.00000 | − | 13.0000i | −0.0626224 | − | 0.814092i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 30.0000 | 1.87135 | 0.935674 | − | 0.352865i | \(-0.114792\pi\) | ||||
0.935674 | + | 0.352865i | \(0.114792\pi\) | |||||||
\(258\) | 4.00000 | + | 4.00000i | 0.249029 | + | 0.249029i | ||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 8.00000 | + | 4.00000i | 0.496139 | + | 0.248069i | ||||
\(261\) | 5.00000 | + | 5.00000i | 0.309492 | + | 0.309492i | ||||
\(262\) | 9.00000 | − | 9.00000i | 0.556022 | − | 0.556022i | ||||
\(263\) | −24.0000 | −1.47990 | −0.739952 | − | 0.672660i | \(-0.765152\pi\) | ||||
−0.739952 | + | 0.672660i | \(0.765152\pi\) | |||||||
\(264\) | − | 2.00000i | − | 0.123091i | ||||||
\(265\) | −10.0000 | + | 20.0000i | −0.614295 | + | 1.22859i | ||||
\(266\) | −6.00000 | − | 6.00000i | −0.367884 | − | 0.367884i | ||||
\(267\) | 6.00000 | + | 6.00000i | 0.367194 | + | 0.367194i | ||||
\(268\) | − | 2.00000i | − | 0.122169i | ||||||
\(269\) | 11.0000 | − | 11.0000i | 0.670682 | − | 0.670682i | −0.287191 | − | 0.957873i | \(-0.592722\pi\) |
0.957873 | + | 0.287191i | \(0.0927216\pi\) | |||||||
\(270\) | 4.00000 | + | 12.0000i | 0.243432 | + | 0.730297i | ||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | 1.00000 | − | 4.00000i | 0.0606339 | − | 0.242536i | ||||
\(273\) | 8.00000i | 0.484182i | ||||||||
\(274\) | 12.0000i | 0.724947i | ||||||||
\(275\) | 1.00000 | − | 7.00000i | 0.0603023 | − | 0.422116i | ||||
\(276\) | 2.00000 | 0.120386 | ||||||||
\(277\) | −5.00000 | − | 5.00000i | −0.300421 | − | 0.300421i | 0.540758 | − | 0.841178i | \(-0.318138\pi\) |
−0.841178 | + | 0.540758i | \(0.818138\pi\) | |||||||
\(278\) | −3.00000 | + | 3.00000i | −0.179928 | + | 0.179928i | ||||
\(279\) | 3.00000 | + | 3.00000i | 0.179605 | + | 0.179605i | ||||
\(280\) | 1.00000 | + | 3.00000i | 0.0597614 | + | 0.179284i | ||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 6.00000 | − | 6.00000i | 0.357295 | − | 0.357295i | ||||
\(283\) | 19.0000 | − | 19.0000i | 1.12943 | − | 1.12943i | 0.139163 | − | 0.990269i | \(-0.455559\pi\) |
0.990269 | − | 0.139163i | \(-0.0444413\pi\) | |||||||
\(284\) | 5.00000 | − | 5.00000i | 0.296695 | − | 0.296695i | ||||
\(285\) | 6.00000 | + | 18.0000i | 0.355409 | + | 1.06623i | ||||
\(286\) | 4.00000 | − | 4.00000i | 0.236525 | − | 0.236525i | ||||
\(287\) | −14.0000 | −0.826394 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −15.0000 | − | 8.00000i | −0.882353 | − | 0.470588i | ||||
\(290\) | −5.00000 | − | 15.0000i | −0.293610 | − | 0.880830i | ||||
\(291\) | − | 6.00000i | − | 0.351726i | ||||||
\(292\) | 1.00000 | + | 1.00000i | 0.0585206 | + | 0.0585206i | ||||
\(293\) | − | 24.0000i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(294\) | 5.00000 | − | 5.00000i | 0.291606 | − | 0.291606i | ||||
\(295\) | −20.0000 | − | 10.0000i | −1.16445 | − | 0.582223i | ||||
\(296\) | 1.00000 | + | 1.00000i | 0.0581238 | + | 0.0581238i | ||||
\(297\) | 8.00000 | 0.464207 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 4.00000 | + | 4.00000i | 0.231326 | + | 0.231326i | ||||
\(300\) | 1.00000 | − | 7.00000i | 0.0577350 | − | 0.404145i | ||||
\(301\) | −4.00000 | + | 4.00000i | −0.230556 | + | 0.230556i | ||||
\(302\) | 2.00000i | 0.115087i | ||||||||
\(303\) | −14.0000 | − | 14.0000i | −0.804279 | − | 0.804279i | ||||
\(304\) | 6.00000i | 0.344124i | ||||||||
\(305\) | 9.00000 | − | 3.00000i | 0.515339 | − | 0.171780i | ||||
\(306\) | 4.00000 | + | 1.00000i | 0.228665 | + | 0.0571662i | ||||
\(307\) | − | 2.00000i | − | 0.114146i | −0.998370 | − | 0.0570730i | \(-0.981823\pi\) | ||
0.998370 | − | 0.0570730i | \(-0.0181768\pi\) | |||||||
\(308\) | 2.00000 | 0.113961 | ||||||||
\(309\) | −14.0000 | + | 14.0000i | −0.796432 | + | 0.796432i | ||||
\(310\) | −3.00000 | − | 9.00000i | −0.170389 | − | 0.511166i | ||||
\(311\) | 17.0000 | − | 17.0000i | 0.963982 | − | 0.963982i | −0.0353919 | − | 0.999374i | \(-0.511268\pi\) |
0.999374 | + | 0.0353919i | \(0.0112680\pi\) | |||||||
\(312\) | 4.00000 | − | 4.00000i | 0.226455 | − | 0.226455i | ||||
\(313\) | −3.00000 | + | 3.00000i | −0.169570 | + | 0.169570i | −0.786790 | − | 0.617220i | \(-0.788259\pi\) |
0.617220 | + | 0.786790i | \(0.288259\pi\) | |||||||
\(314\) | 16.0000i | 0.902932i | ||||||||
\(315\) | −3.00000 | + | 1.00000i | −0.169031 | + | 0.0563436i | ||||
\(316\) | −1.00000 | − | 1.00000i | −0.0562544 | − | 0.0562544i | ||||
\(317\) | −5.00000 | + | 5.00000i | −0.280828 | + | 0.280828i | −0.833439 | − | 0.552611i | \(-0.813631\pi\) |
0.552611 | + | 0.833439i | \(0.313631\pi\) | |||||||
\(318\) | 10.0000 | + | 10.0000i | 0.560772 | + | 0.560772i | ||||
\(319\) | −10.0000 | −0.559893 | ||||||||
\(320\) | 1.00000 | − | 2.00000i | 0.0559017 | − | 0.111803i | ||||
\(321\) | 26.0000i | 1.45118i | ||||||||
\(322\) | 2.00000i | 0.111456i | ||||||||
\(323\) | 24.0000 | + | 6.00000i | 1.33540 | + | 0.333849i | ||||
\(324\) | 5.00000 | 0.277778 | ||||||||
\(325\) | 16.0000 | − | 12.0000i | 0.887520 | − | 0.665640i | ||||
\(326\) | −15.0000 | + | 15.0000i | −0.830773 | + | 0.830773i | ||||
\(327\) | 14.0000i | 0.774202i | ||||||||
\(328\) | 7.00000 | + | 7.00000i | 0.386510 | + | 0.386510i | ||||
\(329\) | 6.00000 | + | 6.00000i | 0.330791 | + | 0.330791i | ||||
\(330\) | −4.00000 | − | 2.00000i | −0.220193 | − | 0.110096i | ||||
\(331\) | − | 10.0000i | − | 0.549650i | −0.961494 | − | 0.274825i | \(-0.911380\pi\) | ||
0.961494 | − | 0.274825i | \(-0.0886199\pi\) | |||||||
\(332\) | 12.0000 | 0.658586 | ||||||||
\(333\) | −1.00000 | + | 1.00000i | −0.0547997 | + | 0.0547997i | ||||
\(334\) | −7.00000 | − | 7.00000i | −0.383023 | − | 0.383023i | ||||
\(335\) | −4.00000 | − | 2.00000i | −0.218543 | − | 0.109272i | ||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | 5.00000 | + | 5.00000i | 0.272367 | + | 0.272367i | 0.830053 | − | 0.557685i | \(-0.188310\pi\) |
−0.557685 | + | 0.830053i | \(0.688310\pi\) | |||||||
\(338\) | 3.00000 | 0.163178 | ||||||||
\(339\) | −22.0000 | −1.19488 | ||||||||
\(340\) | −7.00000 | − | 6.00000i | −0.379628 | − | 0.325396i | ||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 2.00000 | − | 4.00000i | 0.107676 | − | 0.215353i | ||||
\(346\) | −7.00000 | − | 7.00000i | −0.376322 | − | 0.376322i | ||||
\(347\) | −25.0000 | + | 25.0000i | −1.34207 | + | 1.34207i | −0.448074 | + | 0.893997i | \(0.647890\pi\) |
−0.893997 | + | 0.448074i | \(0.852110\pi\) | |||||||
\(348\) | −10.0000 | −0.536056 | ||||||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 7.00000 | + | 1.00000i | 0.374166 | + | 0.0534522i | ||||
\(351\) | 16.0000 | + | 16.0000i | 0.854017 | + | 0.854017i | ||||
\(352\) | −1.00000 | − | 1.00000i | −0.0533002 | − | 0.0533002i | ||||
\(353\) | − | 24.0000i | − | 1.27739i | −0.769460 | − | 0.638696i | \(-0.779474\pi\) | ||
0.769460 | − | 0.638696i | \(-0.220526\pi\) | |||||||
\(354\) | −10.0000 | + | 10.0000i | −0.531494 | + | 0.531494i | ||||
\(355\) | −5.00000 | − | 15.0000i | −0.265372 | − | 0.796117i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | 2.00000 | − | 8.00000i | 0.105851 | − | 0.423405i | ||||
\(358\) | − | 6.00000i | − | 0.317110i | ||||||
\(359\) | 6.00000i | 0.316668i | 0.987386 | + | 0.158334i | \(0.0506123\pi\) | ||||
−0.987386 | + | 0.158334i | \(0.949388\pi\) | |||||||
\(360\) | 2.00000 | + | 1.00000i | 0.105409 | + | 0.0527046i | ||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | −7.00000 | − | 7.00000i | −0.367912 | − | 0.367912i | ||||
\(363\) | 9.00000 | − | 9.00000i | 0.472377 | − | 0.472377i | ||||
\(364\) | 4.00000 | + | 4.00000i | 0.209657 | + | 0.209657i | ||||
\(365\) | 3.00000 | − | 1.00000i | 0.157027 | − | 0.0523424i | ||||
\(366\) | − | 6.00000i | − | 0.313625i | ||||||
\(367\) | −19.0000 | + | 19.0000i | −0.991792 | + | 0.991792i | −0.999967 | − | 0.00817466i | \(-0.997398\pi\) |
0.00817466 | + | 0.999967i | \(0.497398\pi\) | |||||||
\(368\) | 1.00000 | − | 1.00000i | 0.0521286 | − | 0.0521286i | ||||
\(369\) | −7.00000 | + | 7.00000i | −0.364405 | + | 0.364405i | ||||
\(370\) | 3.00000 | − | 1.00000i | 0.155963 | − | 0.0519875i | ||||
\(371\) | −10.0000 | + | 10.0000i | −0.519174 | + | 0.519174i | ||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | 20.0000i | 1.03556i | 0.855514 | + | 0.517780i | \(0.173242\pi\) | ||||
−0.855514 | + | 0.517780i | \(0.826758\pi\) | |||||||
\(374\) | −5.00000 | + | 3.00000i | −0.258544 | + | 0.155126i | ||||
\(375\) | −13.0000 | − | 9.00000i | −0.671317 | − | 0.464758i | ||||
\(376\) | − | 6.00000i | − | 0.309426i | ||||||
\(377\) | −20.0000 | − | 20.0000i | −1.03005 | − | 1.03005i | ||||
\(378\) | 8.00000i | 0.411476i | ||||||||
\(379\) | −5.00000 | + | 5.00000i | −0.256833 | + | 0.256833i | −0.823765 | − | 0.566932i | \(-0.808130\pi\) |
0.566932 | + | 0.823765i | \(0.308130\pi\) | |||||||
\(380\) | 12.0000 | + | 6.00000i | 0.615587 | + | 0.307794i | ||||
\(381\) | −8.00000 | − | 8.00000i | −0.409852 | − | 0.409852i | ||||
\(382\) | 24.0000 | 1.22795 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −1.00000 | − | 1.00000i | −0.0510310 | − | 0.0510310i | ||||
\(385\) | 2.00000 | − | 4.00000i | 0.101929 | − | 0.203859i | ||||
\(386\) | −13.0000 | + | 13.0000i | −0.661683 | + | 0.661683i | ||||
\(387\) | 4.00000i | 0.203331i | ||||||||
\(388\) | −3.00000 | − | 3.00000i | −0.152302 | − | 0.152302i | ||||
\(389\) | 12.0000i | 0.608424i | 0.952604 | + | 0.304212i | \(0.0983931\pi\) | ||||
−0.952604 | + | 0.304212i | \(0.901607\pi\) | |||||||
\(390\) | −4.00000 | − | 12.0000i | −0.202548 | − | 0.607644i | ||||
\(391\) | −3.00000 | − | 5.00000i | −0.151717 | − | 0.252861i | ||||
\(392\) | − | 5.00000i | − | 0.252538i | ||||||
\(393\) | −18.0000 | −0.907980 | ||||||||
\(394\) | −7.00000 | + | 7.00000i | −0.352655 | + | 0.352655i | ||||
\(395\) | −3.00000 | + | 1.00000i | −0.150946 | + | 0.0503155i | ||||
\(396\) | 1.00000 | − | 1.00000i | 0.0502519 | − | 0.0502519i | ||||
\(397\) | 7.00000 | − | 7.00000i | 0.351320 | − | 0.351320i | −0.509281 | − | 0.860601i | \(-0.670088\pi\) |
0.860601 | + | 0.509281i | \(0.170088\pi\) | |||||||
\(398\) | −17.0000 | + | 17.0000i | −0.852133 | + | 0.852133i | ||||
\(399\) | 12.0000i | 0.600751i | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | −19.0000 | − | 19.0000i | −0.948815 | − | 0.948815i | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) |
−0.998752 | + | 0.0499376i | \(0.984098\pi\) | |||||||
\(402\) | −2.00000 | + | 2.00000i | −0.0997509 | + | 0.0997509i | ||||
\(403\) | −12.0000 | − | 12.0000i | −0.597763 | − | 0.597763i | ||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 5.00000 | − | 10.0000i | 0.248452 | − | 0.496904i | ||||
\(406\) | − | 10.0000i | − | 0.496292i | ||||||
\(407\) | − | 2.00000i | − | 0.0991363i | ||||||
\(408\) | −5.00000 | + | 3.00000i | −0.247537 | + | 0.148522i | ||||
\(409\) | −22.0000 | −1.08783 | −0.543915 | − | 0.839140i | \(-0.683059\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 21.0000 | − | 7.00000i | 1.03712 | − | 0.345705i | ||||
\(411\) | 12.0000 | − | 12.0000i | 0.591916 | − | 0.591916i | ||||
\(412\) | 14.0000i | 0.689730i | ||||||||
\(413\) | −10.0000 | − | 10.0000i | −0.492068 | − | 0.492068i | ||||
\(414\) | 1.00000 | + | 1.00000i | 0.0491473 | + | 0.0491473i | ||||
\(415\) | 12.0000 | − | 24.0000i | 0.589057 | − | 1.17811i | ||||
\(416\) | − | 4.00000i | − | 0.196116i | ||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 6.00000 | − | 6.00000i | 0.293470 | − | 0.293470i | ||||
\(419\) | 17.0000 | + | 17.0000i | 0.830504 | + | 0.830504i | 0.987586 | − | 0.157081i | \(-0.0502085\pi\) |
−0.157081 | + | 0.987586i | \(0.550208\pi\) | |||||||
\(420\) | 2.00000 | − | 4.00000i | 0.0975900 | − | 0.195180i | ||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | −13.0000 | − | 13.0000i | −0.632830 | − | 0.632830i | ||||
\(423\) | 6.00000 | 0.291730 | ||||||||
\(424\) | 10.0000 | 0.485643 | ||||||||
\(425\) | −19.0000 | + | 8.00000i | −0.921635 | + | 0.388057i | ||||
\(426\) | −10.0000 | −0.484502 | ||||||||
\(427\) | 6.00000 | 0.290360 | ||||||||
\(428\) | 13.0000 | + | 13.0000i | 0.628379 | + | 0.628379i | ||||
\(429\) | −8.00000 | −0.386244 | ||||||||
\(430\) | 4.00000 | − | 8.00000i | 0.192897 | − | 0.385794i | ||||
\(431\) | 7.00000 | + | 7.00000i | 0.337178 | + | 0.337178i | 0.855304 | − | 0.518126i | \(-0.173370\pi\) |
−0.518126 | + | 0.855304i | \(0.673370\pi\) | |||||||
\(432\) | 4.00000 | − | 4.00000i | 0.192450 | − | 0.192450i | ||||
\(433\) | 30.0000 | 1.44171 | 0.720854 | − | 0.693087i | \(-0.243750\pi\) | ||||
0.720854 | + | 0.693087i | \(0.243750\pi\) | |||||||
\(434\) | − | 6.00000i | − | 0.288009i | ||||||
\(435\) | −10.0000 | + | 20.0000i | −0.479463 | + | 0.958927i | ||||
\(436\) | 7.00000 | + | 7.00000i | 0.335239 | + | 0.335239i | ||||
\(437\) | 6.00000 | + | 6.00000i | 0.287019 | + | 0.287019i | ||||
\(438\) | − | 2.00000i | − | 0.0955637i | ||||||
\(439\) | −11.0000 | + | 11.0000i | −0.525001 | + | 0.525001i | −0.919078 | − | 0.394076i | \(-0.871065\pi\) |
0.394076 | + | 0.919078i | \(0.371065\pi\) | |||||||
\(440\) | −3.00000 | + | 1.00000i | −0.143019 | + | 0.0476731i | ||||
\(441\) | 5.00000 | 0.238095 | ||||||||
\(442\) | −16.0000 | − | 4.00000i | −0.761042 | − | 0.190261i | ||||
\(443\) | − | 10.0000i | − | 0.475114i | −0.971374 | − | 0.237557i | \(-0.923653\pi\) | ||
0.971374 | − | 0.237557i | \(-0.0763467\pi\) | |||||||
\(444\) | − | 2.00000i | − | 0.0949158i | ||||||
\(445\) | 6.00000 | − | 12.0000i | 0.284427 | − | 0.568855i | ||||
\(446\) | 24.0000 | 1.13643 | ||||||||
\(447\) | 6.00000 | + | 6.00000i | 0.283790 | + | 0.283790i | ||||
\(448\) | 1.00000 | − | 1.00000i | 0.0472456 | − | 0.0472456i | ||||
\(449\) | 5.00000 | + | 5.00000i | 0.235965 | + | 0.235965i | 0.815177 | − | 0.579212i | \(-0.196640\pi\) |
−0.579212 | + | 0.815177i | \(0.696640\pi\) | |||||||
\(450\) | 4.00000 | − | 3.00000i | 0.188562 | − | 0.141421i | ||||
\(451\) | − | 14.0000i | − | 0.659234i | ||||||
\(452\) | −11.0000 | + | 11.0000i | −0.517396 | + | 0.517396i | ||||
\(453\) | 2.00000 | − | 2.00000i | 0.0939682 | − | 0.0939682i | ||||
\(454\) | 9.00000 | − | 9.00000i | 0.422391 | − | 0.422391i | ||||
\(455\) | 12.0000 | − | 4.00000i | 0.562569 | − | 0.187523i | ||||
\(456\) | 6.00000 | − | 6.00000i | 0.280976 | − | 0.280976i | ||||
\(457\) | −10.0000 | −0.467780 | −0.233890 | − | 0.972263i | \(-0.575146\pi\) | ||||
−0.233890 | + | 0.972263i | \(0.575146\pi\) | |||||||
\(458\) | 28.0000i | 1.30835i | ||||||||
\(459\) | −12.0000 | − | 20.0000i | −0.560112 | − | 0.933520i | ||||
\(460\) | −1.00000 | − | 3.00000i | −0.0466252 | − | 0.139876i | ||||
\(461\) | 8.00000i | 0.372597i | 0.982493 | + | 0.186299i | \(0.0596492\pi\) | ||||
−0.982493 | + | 0.186299i | \(0.940351\pi\) | |||||||
\(462\) | −2.00000 | − | 2.00000i | −0.0930484 | − | 0.0930484i | ||||
\(463\) | 30.0000i | 1.39422i | 0.716965 | + | 0.697109i | \(0.245531\pi\) | ||||
−0.716965 | + | 0.697109i | \(0.754469\pi\) | |||||||
\(464\) | −5.00000 | + | 5.00000i | −0.232119 | + | 0.232119i | ||||
\(465\) | −6.00000 | + | 12.0000i | −0.278243 | + | 0.556487i | ||||
\(466\) | −1.00000 | − | 1.00000i | −0.0463241 | − | 0.0463241i | ||||
\(467\) | 28.0000 | 1.29569 | 0.647843 | − | 0.761774i | \(-0.275671\pi\) | ||||
0.647843 | + | 0.761774i | \(0.275671\pi\) | |||||||
\(468\) | 4.00000 | 0.184900 | ||||||||
\(469\) | −2.00000 | − | 2.00000i | −0.0923514 | − | 0.0923514i | ||||
\(470\) | −12.0000 | − | 6.00000i | −0.553519 | − | 0.276759i | ||||
\(471\) | 16.0000 | − | 16.0000i | 0.737241 | − | 0.737241i | ||||
\(472\) | 10.0000i | 0.460287i | ||||||||
\(473\) | −4.00000 | − | 4.00000i | −0.183920 | − | 0.183920i | ||||
\(474\) | 2.00000i | 0.0918630i | ||||||||
\(475\) | 24.0000 | − | 18.0000i | 1.10120 | − | 0.825897i | ||||
\(476\) | −3.00000 | − | 5.00000i | −0.137505 | − | 0.229175i | ||||
\(477\) | 10.0000i | 0.457869i | ||||||||
\(478\) | −16.0000 | −0.731823 | ||||||||
\(479\) | −15.0000 | + | 15.0000i | −0.685367 | + | 0.685367i | −0.961204 | − | 0.275837i | \(-0.911045\pi\) |
0.275837 | + | 0.961204i | \(0.411045\pi\) | |||||||
\(480\) | −3.00000 | + | 1.00000i | −0.136931 | + | 0.0456435i | ||||
\(481\) | 4.00000 | − | 4.00000i | 0.182384 | − | 0.182384i | ||||
\(482\) | −9.00000 | + | 9.00000i | −0.409939 | + | 0.409939i | ||||
\(483\) | 2.00000 | − | 2.00000i | 0.0910032 | − | 0.0910032i | ||||
\(484\) | − | 9.00000i | − | 0.409091i | ||||||
\(485\) | −9.00000 | + | 3.00000i | −0.408669 | + | 0.136223i | ||||
\(486\) | 7.00000 | + | 7.00000i | 0.317526 | + | 0.317526i | ||||
\(487\) | 5.00000 | − | 5.00000i | 0.226572 | − | 0.226572i | −0.584687 | − | 0.811259i | \(-0.698783\pi\) |
0.811259 | + | 0.584687i | \(0.198783\pi\) | |||||||
\(488\) | −3.00000 | − | 3.00000i | −0.135804 | − | 0.135804i | ||||
\(489\) | 30.0000 | 1.35665 | ||||||||
\(490\) | −10.0000 | − | 5.00000i | −0.451754 | − | 0.225877i | ||||
\(491\) | − | 18.0000i | − | 0.812329i | −0.913800 | − | 0.406164i | \(-0.866866\pi\) | ||
0.913800 | − | 0.406164i | \(-0.133134\pi\) | |||||||
\(492\) | − | 14.0000i | − | 0.631169i | ||||||
\(493\) | 15.0000 | + | 25.0000i | 0.675566 | + | 1.12594i | ||||
\(494\) | 24.0000 | 1.07981 | ||||||||
\(495\) | −1.00000 | − | 3.00000i | −0.0449467 | − | 0.134840i | ||||
\(496\) | −3.00000 | + | 3.00000i | −0.134704 | + | 0.134704i | ||||
\(497\) | − | 10.0000i | − | 0.448561i | ||||||
\(498\) | −12.0000 | − | 12.0000i | −0.537733 | − | 0.537733i | ||||
\(499\) | 21.0000 | + | 21.0000i | 0.940089 | + | 0.940089i | 0.998304 | − | 0.0582150i | \(-0.0185409\pi\) |
−0.0582150 | + | 0.998304i | \(0.518541\pi\) | |||||||
\(500\) | −11.0000 | + | 2.00000i | −0.491935 | + | 0.0894427i | ||||
\(501\) | 14.0000i | 0.625474i | ||||||||
\(502\) | 20.0000 | 0.892644 | ||||||||
\(503\) | 5.00000 | − | 5.00000i | 0.222939 | − | 0.222939i | −0.586796 | − | 0.809735i | \(-0.699611\pi\) |
0.809735 | + | 0.586796i | \(0.199611\pi\) | |||||||
\(504\) | 1.00000 | + | 1.00000i | 0.0445435 | + | 0.0445435i | ||||
\(505\) | −14.0000 | + | 28.0000i | −0.622992 | + | 1.24598i | ||||
\(506\) | −2.00000 | −0.0889108 | ||||||||
\(507\) | −3.00000 | − | 3.00000i | −0.133235 | − | 0.133235i | ||||
\(508\) | −8.00000 | −0.354943 | ||||||||
\(509\) | 14.0000 | 0.620539 | 0.310270 | − | 0.950649i | \(-0.399581\pi\) | ||||
0.310270 | + | 0.950649i | \(0.399581\pi\) | |||||||
\(510\) | 1.00000 | + | 13.0000i | 0.0442807 | + | 0.575650i | ||||
\(511\) | 2.00000 | 0.0884748 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 24.0000 | + | 24.0000i | 1.05963 | + | 1.05963i | ||||
\(514\) | −30.0000 | −1.32324 | ||||||||
\(515\) | 28.0000 | + | 14.0000i | 1.23383 | + | 0.616914i | ||||
\(516\) | −4.00000 | − | 4.00000i | −0.176090 | − | 0.176090i | ||||
\(517\) | −6.00000 | + | 6.00000i | −0.263880 | + | 0.263880i | ||||
\(518\) | 2.00000 | 0.0878750 | ||||||||
\(519\) | 14.0000i | 0.614532i | ||||||||
\(520\) | −8.00000 | − | 4.00000i | −0.350823 | − | 0.175412i | ||||
\(521\) | −11.0000 | − | 11.0000i | −0.481919 | − | 0.481919i | 0.423825 | − | 0.905744i | \(-0.360687\pi\) |
−0.905744 | + | 0.423825i | \(0.860687\pi\) | |||||||
\(522\) | −5.00000 | − | 5.00000i | −0.218844 | − | 0.218844i | ||||
\(523\) | − | 42.0000i | − | 1.83653i | −0.395964 | − | 0.918266i | \(-0.629590\pi\) | ||
0.395964 | − | 0.918266i | \(-0.370410\pi\) | |||||||
\(524\) | −9.00000 | + | 9.00000i | −0.393167 | + | 0.393167i | ||||
\(525\) | −6.00000 | − | 8.00000i | −0.261861 | − | 0.349149i | ||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 9.00000 | + | 15.0000i | 0.392046 | + | 0.653410i | ||||
\(528\) | 2.00000i | 0.0870388i | ||||||||
\(529\) | 21.0000i | 0.913043i | ||||||||
\(530\) | 10.0000 | − | 20.0000i | 0.434372 | − | 0.868744i | ||||
\(531\) | −10.0000 | −0.433963 | ||||||||
\(532\) | 6.00000 | + | 6.00000i | 0.260133 | + | 0.260133i | ||||
\(533\) | 28.0000 | − | 28.0000i | 1.21281 | − | 1.21281i | ||||
\(534\) | −6.00000 | − | 6.00000i | −0.259645 | − | 0.259645i | ||||
\(535\) | 39.0000 | − | 13.0000i | 1.68612 | − | 0.562039i | ||||
\(536\) | 2.00000i | 0.0863868i | ||||||||
\(537\) | −6.00000 | + | 6.00000i | −0.258919 | + | 0.258919i | ||||
\(538\) | −11.0000 | + | 11.0000i | −0.474244 | + | 0.474244i | ||||
\(539\) | −5.00000 | + | 5.00000i | −0.215365 | + | 0.215365i | ||||
\(540\) | −4.00000 | − | 12.0000i | −0.172133 | − | 0.516398i | ||||
\(541\) | 3.00000 | − | 3.00000i | 0.128980 | − | 0.128980i | −0.639670 | − | 0.768650i | \(-0.720929\pi\) |
0.768650 | + | 0.639670i | \(0.220929\pi\) | |||||||
\(542\) | 8.00000 | 0.343629 | ||||||||
\(543\) | 14.0000i | 0.600798i | ||||||||
\(544\) | −1.00000 | + | 4.00000i | −0.0428746 | + | 0.171499i | ||||
\(545\) | 21.0000 | − | 7.00000i | 0.899541 | − | 0.299847i | ||||
\(546\) | − | 8.00000i | − | 0.342368i | ||||||
\(547\) | −3.00000 | − | 3.00000i | −0.128271 | − | 0.128271i | 0.640057 | − | 0.768328i | \(-0.278911\pi\) |
−0.768328 | + | 0.640057i | \(0.778911\pi\) | |||||||
\(548\) | − | 12.0000i | − | 0.512615i | ||||||
\(549\) | 3.00000 | − | 3.00000i | 0.128037 | − | 0.128037i | ||||
\(550\) | −1.00000 | + | 7.00000i | −0.0426401 | + | 0.298481i | ||||
\(551\) | −30.0000 | − | 30.0000i | −1.27804 | − | 1.27804i | ||||
\(552\) | −2.00000 | −0.0851257 | ||||||||
\(553\) | −2.00000 | −0.0850487 | ||||||||
\(554\) | 5.00000 | + | 5.00000i | 0.212430 | + | 0.212430i | ||||
\(555\) | −4.00000 | − | 2.00000i | −0.169791 | − | 0.0848953i | ||||
\(556\) | 3.00000 | − | 3.00000i | 0.127228 | − | 0.127228i | ||||
\(557\) | − | 20.0000i | − | 0.847427i | −0.905796 | − | 0.423714i | \(-0.860726\pi\) | ||
0.905796 | − | 0.423714i | \(-0.139274\pi\) | |||||||
\(558\) | −3.00000 | − | 3.00000i | −0.127000 | − | 0.127000i | ||||
\(559\) | − | 16.0000i | − | 0.676728i | ||||||
\(560\) | −1.00000 | − | 3.00000i | −0.0422577 | − | 0.126773i | ||||
\(561\) | 8.00000 | + | 2.00000i | 0.337760 | + | 0.0844401i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.00000 | 0.168580 | 0.0842900 | − | 0.996441i | \(-0.473138\pi\) | ||||
0.0842900 | + | 0.996441i | \(0.473138\pi\) | |||||||
\(564\) | −6.00000 | + | 6.00000i | −0.252646 | + | 0.252646i | ||||
\(565\) | 11.0000 | + | 33.0000i | 0.462773 | + | 1.38832i | ||||
\(566\) | −19.0000 | + | 19.0000i | −0.798630 | + | 0.798630i | ||||
\(567\) | 5.00000 | − | 5.00000i | 0.209980 | − | 0.209980i | ||||
\(568\) | −5.00000 | + | 5.00000i | −0.209795 | + | 0.209795i | ||||
\(569\) | − | 8.00000i | − | 0.335377i | −0.985840 | − | 0.167689i | \(-0.946370\pi\) | ||
0.985840 | − | 0.167689i | \(-0.0536304\pi\) | |||||||
\(570\) | −6.00000 | − | 18.0000i | −0.251312 | − | 0.753937i | ||||
\(571\) | 25.0000 | + | 25.0000i | 1.04622 | + | 1.04622i | 0.998879 | + | 0.0473385i | \(0.0150740\pi\) |
0.0473385 | + | 0.998879i | \(0.484926\pi\) | |||||||
\(572\) | −4.00000 | + | 4.00000i | −0.167248 | + | 0.167248i | ||||
\(573\) | −24.0000 | − | 24.0000i | −1.00261 | − | 1.00261i | ||||
\(574\) | 14.0000 | 0.584349 | ||||||||
\(575\) | −7.00000 | − | 1.00000i | −0.291920 | − | 0.0417029i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 20.0000i | − | 0.832611i | −0.909225 | − | 0.416305i | \(-0.863325\pi\) | ||
0.909225 | − | 0.416305i | \(-0.136675\pi\) | |||||||
\(578\) | 15.0000 | + | 8.00000i | 0.623918 | + | 0.332756i | ||||
\(579\) | 26.0000 | 1.08052 | ||||||||
\(580\) | 5.00000 | + | 15.0000i | 0.207614 | + | 0.622841i | ||||
\(581\) | 12.0000 | − | 12.0000i | 0.497844 | − | 0.497844i | ||||
\(582\) | 6.00000i | 0.248708i | ||||||||
\(583\) | −10.0000 | − | 10.0000i | −0.414158 | − | 0.414158i | ||||
\(584\) | −1.00000 | − | 1.00000i | −0.0413803 | − | 0.0413803i | ||||
\(585\) | 4.00000 | − | 8.00000i | 0.165380 | − | 0.330759i | ||||
\(586\) | 24.0000i | 0.991431i | ||||||||
\(587\) | −4.00000 | −0.165098 | −0.0825488 | − | 0.996587i | \(-0.526306\pi\) | ||||
−0.0825488 | + | 0.996587i | \(0.526306\pi\) | |||||||
\(588\) | −5.00000 | + | 5.00000i | −0.206197 | + | 0.206197i | ||||
\(589\) | −18.0000 | − | 18.0000i | −0.741677 | − | 0.741677i | ||||
\(590\) | 20.0000 | + | 10.0000i | 0.823387 | + | 0.411693i | ||||
\(591\) | 14.0000 | 0.575883 | ||||||||
\(592\) | −1.00000 | − | 1.00000i | −0.0410997 | − | 0.0410997i | ||||
\(593\) | −38.0000 | −1.56047 | −0.780236 | − | 0.625485i | \(-0.784901\pi\) | ||||
−0.780236 | + | 0.625485i | \(0.784901\pi\) | |||||||
\(594\) | −8.00000 | −0.328244 | ||||||||
\(595\) | −13.0000 | + | 1.00000i | −0.532948 | + | 0.0409960i | ||||
\(596\) | 6.00000 | 0.245770 | ||||||||
\(597\) | 34.0000 | 1.39153 | ||||||||
\(598\) | −4.00000 | − | 4.00000i | −0.163572 | − | 0.163572i | ||||
\(599\) | 16.0000 | 0.653742 | 0.326871 | − | 0.945069i | \(-0.394006\pi\) | ||||
0.326871 | + | 0.945069i | \(0.394006\pi\) | |||||||
\(600\) | −1.00000 | + | 7.00000i | −0.0408248 | + | 0.285774i | ||||
\(601\) | −11.0000 | − | 11.0000i | −0.448699 | − | 0.448699i | 0.446223 | − | 0.894922i | \(-0.352769\pi\) |
−0.894922 | + | 0.446223i | \(0.852769\pi\) | |||||||
\(602\) | 4.00000 | − | 4.00000i | 0.163028 | − | 0.163028i | ||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | − | 2.00000i | − | 0.0813788i | ||||||
\(605\) | −18.0000 | − | 9.00000i | −0.731804 | − | 0.365902i | ||||
\(606\) | 14.0000 | + | 14.0000i | 0.568711 | + | 0.568711i | ||||
\(607\) | 3.00000 | + | 3.00000i | 0.121766 | + | 0.121766i | 0.765364 | − | 0.643598i | \(-0.222559\pi\) |
−0.643598 | + | 0.765364i | \(0.722559\pi\) | |||||||
\(608\) | − | 6.00000i | − | 0.243332i | ||||||
\(609\) | −10.0000 | + | 10.0000i | −0.405220 | + | 0.405220i | ||||
\(610\) | −9.00000 | + | 3.00000i | −0.364399 | + | 0.121466i | ||||
\(611\) | −24.0000 | −0.970936 | ||||||||
\(612\) | −4.00000 | − | 1.00000i | −0.161690 | − | 0.0404226i | ||||
\(613\) | 8.00000i | 0.323117i | 0.986863 | + | 0.161558i | \(0.0516520\pi\) | ||||
−0.986863 | + | 0.161558i | \(0.948348\pi\) | |||||||
\(614\) | 2.00000i | 0.0807134i | ||||||||
\(615\) | −28.0000 | − | 14.0000i | −1.12907 | − | 0.564534i | ||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | 5.00000 | + | 5.00000i | 0.201292 | + | 0.201292i | 0.800554 | − | 0.599261i | \(-0.204539\pi\) |
−0.599261 | + | 0.800554i | \(0.704539\pi\) | |||||||
\(618\) | 14.0000 | − | 14.0000i | 0.563163 | − | 0.563163i | ||||
\(619\) | 5.00000 | + | 5.00000i | 0.200967 | + | 0.200967i | 0.800414 | − | 0.599447i | \(-0.204613\pi\) |
−0.599447 | + | 0.800414i | \(0.704613\pi\) | |||||||
\(620\) | 3.00000 | + | 9.00000i | 0.120483 | + | 0.361449i | ||||
\(621\) | − | 8.00000i | − | 0.321029i | ||||||
\(622\) | −17.0000 | + | 17.0000i | −0.681638 | + | 0.681638i | ||||
\(623\) | 6.00000 | − | 6.00000i | 0.240385 | − | 0.240385i | ||||
\(624\) | −4.00000 | + | 4.00000i | −0.160128 | + | 0.160128i | ||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 3.00000 | − | 3.00000i | 0.119904 | − | 0.119904i | ||||
\(627\) | −12.0000 | −0.479234 | ||||||||
\(628\) | − | 16.0000i | − | 0.638470i | ||||||
\(629\) | −5.00000 | + | 3.00000i | −0.199363 | + | 0.119618i | ||||
\(630\) | 3.00000 | − | 1.00000i | 0.119523 | − | 0.0398410i | ||||
\(631\) | 46.0000i | 1.83123i | 0.402055 | + | 0.915616i | \(0.368296\pi\) | ||||
−0.402055 | + | 0.915616i | \(0.631704\pi\) | |||||||
\(632\) | 1.00000 | + | 1.00000i | 0.0397779 | + | 0.0397779i | ||||
\(633\) | 26.0000i | 1.03341i | ||||||||
\(634\) | 5.00000 | − | 5.00000i | 0.198575 | − | 0.198575i | ||||
\(635\) | −8.00000 | + | 16.0000i | −0.317470 | + | 0.634941i | ||||
\(636\) | −10.0000 | − | 10.0000i | −0.396526 | − | 0.396526i | ||||
\(637\) | −20.0000 | −0.792429 | ||||||||
\(638\) | 10.0000 | 0.395904 | ||||||||
\(639\) | −5.00000 | − | 5.00000i | −0.197797 | − | 0.197797i | ||||
\(640\) | −1.00000 | + | 2.00000i | −0.0395285 | + | 0.0790569i | ||||
\(641\) | −3.00000 | + | 3.00000i | −0.118493 | + | 0.118493i | −0.763867 | − | 0.645374i | \(-0.776702\pi\) |
0.645374 | + | 0.763867i | \(0.276702\pi\) | |||||||
\(642\) | − | 26.0000i | − | 1.02614i | ||||||
\(643\) | −31.0000 | − | 31.0000i | −1.22252 | − | 1.22252i | −0.966733 | − | 0.255788i | \(-0.917665\pi\) |
−0.255788 | − | 0.966733i | \(-0.582335\pi\) | |||||||
\(644\) | − | 2.00000i | − | 0.0788110i | ||||||
\(645\) | −12.0000 | + | 4.00000i | −0.472500 | + | 0.157500i | ||||
\(646\) | −24.0000 | − | 6.00000i | −0.944267 | − | 0.236067i | ||||
\(647\) | − | 26.0000i | − | 1.02217i | −0.859532 | − | 0.511083i | \(-0.829245\pi\) | ||
0.859532 | − | 0.511083i | \(-0.170755\pi\) | |||||||
\(648\) | −5.00000 | −0.196419 | ||||||||
\(649\) | 10.0000 | − | 10.0000i | 0.392534 | − | 0.392534i | ||||
\(650\) | −16.0000 | + | 12.0000i | −0.627572 | + | 0.470679i | ||||
\(651\) | −6.00000 | + | 6.00000i | −0.235159 | + | 0.235159i | ||||
\(652\) | 15.0000 | − | 15.0000i | 0.587445 | − | 0.587445i | ||||
\(653\) | −29.0000 | + | 29.0000i | −1.13486 | + | 1.13486i | −0.145499 | + | 0.989358i | \(0.546479\pi\) |
−0.989358 | + | 0.145499i | \(0.953521\pi\) | |||||||
\(654\) | − | 14.0000i | − | 0.547443i | ||||||
\(655\) | 9.00000 | + | 27.0000i | 0.351659 | + | 1.05498i | ||||
\(656\) | −7.00000 | − | 7.00000i | −0.273304 | − | 0.273304i | ||||
\(657\) | 1.00000 | − | 1.00000i | 0.0390137 | − | 0.0390137i | ||||
\(658\) | −6.00000 | − | 6.00000i | −0.233904 | − | 0.233904i | ||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 4.00000 | + | 2.00000i | 0.155700 | + | 0.0778499i | ||||
\(661\) | 40.0000i | 1.55582i | 0.628376 | + | 0.777910i | \(0.283720\pi\) | ||||
−0.628376 | + | 0.777910i | \(0.716280\pi\) | |||||||
\(662\) | 10.0000i | 0.388661i | ||||||||
\(663\) | 12.0000 | + | 20.0000i | 0.466041 | + | 0.776736i | ||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 18.0000 | − | 6.00000i | 0.698010 | − | 0.232670i | ||||
\(666\) | 1.00000 | − | 1.00000i | 0.0387492 | − | 0.0387492i | ||||
\(667\) | 10.0000i | 0.387202i | ||||||||
\(668\) | 7.00000 | + | 7.00000i | 0.270838 | + | 0.270838i | ||||
\(669\) | −24.0000 | − | 24.0000i | −0.927894 | − | 0.927894i | ||||
\(670\) | 4.00000 | + | 2.00000i | 0.154533 | + | 0.0772667i | ||||
\(671\) | 6.00000i | 0.231627i | ||||||||
\(672\) | −2.00000 | −0.0771517 | ||||||||
\(673\) | 1.00000 | − | 1.00000i | 0.0385472 | − | 0.0385472i | −0.687570 | − | 0.726118i | \(-0.741323\pi\) |
0.726118 | + | 0.687570i | \(0.241323\pi\) | |||||||
\(674\) | −5.00000 | − | 5.00000i | −0.192593 | − | 0.192593i | ||||
\(675\) | −28.0000 | − | 4.00000i | −1.07772 | − | 0.153960i | ||||
\(676\) | −3.00000 | −0.115385 | ||||||||
\(677\) | −17.0000 | − | 17.0000i | −0.653363 | − | 0.653363i | 0.300438 | − | 0.953801i | \(-0.402867\pi\) |
−0.953801 | + | 0.300438i | \(0.902867\pi\) | |||||||
\(678\) | 22.0000 | 0.844905 | ||||||||
\(679\) | −6.00000 | −0.230259 | ||||||||
\(680\) | 7.00000 | + | 6.00000i | 0.268438 | + | 0.230089i | ||||
\(681\) | −18.0000 | −0.689761 | ||||||||
\(682\) | 6.00000 | 0.229752 | ||||||||
\(683\) | 17.0000 | + | 17.0000i | 0.650487 | + | 0.650487i | 0.953110 | − | 0.302623i | \(-0.0978624\pi\) |
−0.302623 | + | 0.953110i | \(0.597862\pi\) | |||||||
\(684\) | 6.00000 | 0.229416 | ||||||||
\(685\) | −24.0000 | − | 12.0000i | −0.916993 | − | 0.458496i | ||||
\(686\) | −12.0000 | − | 12.0000i | −0.458162 | − | 0.458162i | ||||
\(687\) | 28.0000 | − | 28.0000i | 1.06827 | − | 1.06827i | ||||
\(688\) | −4.00000 | −0.152499 | ||||||||
\(689\) | − | 40.0000i | − | 1.52388i | ||||||
\(690\) | −2.00000 | + | 4.00000i | −0.0761387 | + | 0.152277i | ||||
\(691\) | −31.0000 | − | 31.0000i | −1.17930 | − | 1.17930i | −0.979924 | − | 0.199372i | \(-0.936110\pi\) |
−0.199372 | − | 0.979924i | \(-0.563890\pi\) | |||||||
\(692\) | 7.00000 | + | 7.00000i | 0.266100 | + | 0.266100i | ||||
\(693\) | − | 2.00000i | − | 0.0759737i | ||||||
\(694\) | 25.0000 | − | 25.0000i | 0.948987 | − | 0.948987i | ||||
\(695\) | −3.00000 | − | 9.00000i | −0.113796 | − | 0.341389i | ||||
\(696\) | 10.0000 | 0.379049 | ||||||||
\(697\) | −35.0000 | + | 21.0000i | −1.32572 | + | 0.795432i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.00000i | 0.0756469i | ||||||||
\(700\) | −7.00000 | − | 1.00000i | −0.264575 | − | 0.0377964i | ||||
\(701\) | 2.00000 | 0.0755390 | 0.0377695 | − | 0.999286i | \(-0.487975\pi\) | ||||
0.0377695 | + | 0.999286i | \(0.487975\pi\) | |||||||
\(702\) | −16.0000 | − | 16.0000i | −0.603881 | − | 0.603881i | ||||
\(703\) | 6.00000 | − | 6.00000i | 0.226294 | − | 0.226294i | ||||
\(704\) | 1.00000 | + | 1.00000i | 0.0376889 | + | 0.0376889i | ||||
\(705\) | 6.00000 | + | 18.0000i | 0.225973 | + | 0.677919i | ||||
\(706\) | 24.0000i | 0.903252i | ||||||||
\(707\) | −14.0000 | + | 14.0000i | −0.526524 | + | 0.526524i | ||||
\(708\) | 10.0000 | − | 10.0000i | 0.375823 | − | 0.375823i | ||||
\(709\) | −13.0000 | + | 13.0000i | −0.488225 | + | 0.488225i | −0.907746 | − | 0.419521i | \(-0.862198\pi\) |
0.419521 | + | 0.907746i | \(0.362198\pi\) | |||||||
\(710\) | 5.00000 | + | 15.0000i | 0.187647 | + | 0.562940i | ||||
\(711\) | −1.00000 | + | 1.00000i | −0.0375029 | + | 0.0375029i | ||||
\(712\) | −6.00000 | −0.224860 | ||||||||
\(713\) | 6.00000i | 0.224702i | ||||||||
\(714\) | −2.00000 | + | 8.00000i | −0.0748481 | + | 0.299392i | ||||
\(715\) | 4.00000 | + | 12.0000i | 0.149592 | + | 0.448775i | ||||
\(716\) | 6.00000i | 0.224231i | ||||||||
\(717\) | 16.0000 | + | 16.0000i | 0.597531 | + | 0.597531i | ||||
\(718\) | − | 6.00000i | − | 0.223918i | ||||||
\(719\) | −3.00000 | + | 3.00000i | −0.111881 | + | 0.111881i | −0.760831 | − | 0.648950i | \(-0.775208\pi\) |
0.648950 | + | 0.760831i | \(0.275208\pi\) | |||||||
\(720\) | −2.00000 | − | 1.00000i | −0.0745356 | − | 0.0372678i | ||||
\(721\) | 14.0000 | + | 14.0000i | 0.521387 | + | 0.521387i | ||||
\(722\) | 17.0000 | 0.632674 | ||||||||
\(723\) | 18.0000 | 0.669427 | ||||||||
\(724\) | 7.00000 | + | 7.00000i | 0.260153 | + | 0.260153i | ||||
\(725\) | 35.0000 | + | 5.00000i | 1.29987 | + | 0.185695i | ||||
\(726\) | −9.00000 | + | 9.00000i | −0.334021 | + | 0.334021i | ||||
\(727\) | − | 2.00000i | − | 0.0741759i | −0.999312 | − | 0.0370879i | \(-0.988192\pi\) | ||
0.999312 | − | 0.0370879i | \(-0.0118082\pi\) | |||||||
\(728\) | −4.00000 | − | 4.00000i | −0.148250 | − | 0.148250i | ||||
\(729\) | − | 29.0000i | − | 1.07407i | ||||||
\(730\) | −3.00000 | + | 1.00000i | −0.111035 | + | 0.0370117i | ||||
\(731\) | −4.00000 | + | 16.0000i | −0.147945 | + | 0.591781i | ||||
\(732\) | 6.00000i | 0.221766i | ||||||||
\(733\) | −50.0000 | −1.84679 | −0.923396 | − | 0.383849i | \(-0.874598\pi\) | ||||
−0.923396 | + | 0.383849i | \(0.874598\pi\) | |||||||
\(734\) | 19.0000 | − | 19.0000i | 0.701303 | − | 0.701303i | ||||
\(735\) | 5.00000 | + | 15.0000i | 0.184428 | + | 0.553283i | ||||
\(736\) | −1.00000 | + | 1.00000i | −0.0368605 | + | 0.0368605i | ||||
\(737\) | 2.00000 | − | 2.00000i | 0.0736709 | − | 0.0736709i | ||||
\(738\) | 7.00000 | − | 7.00000i | 0.257674 | − | 0.257674i | ||||
\(739\) | 14.0000i | 0.514998i | 0.966279 | + | 0.257499i | \(0.0828985\pi\) | ||||
−0.966279 | + | 0.257499i | \(0.917102\pi\) | |||||||
\(740\) | −3.00000 | + | 1.00000i | −0.110282 | + | 0.0367607i | ||||
\(741\) | −24.0000 | − | 24.0000i | −0.881662 | − | 0.881662i | ||||
\(742\) | 10.0000 | − | 10.0000i | 0.367112 | − | 0.367112i | ||||
\(743\) | 19.0000 | + | 19.0000i | 0.697042 | + | 0.697042i | 0.963772 | − | 0.266729i | \(-0.0859429\pi\) |
−0.266729 | + | 0.963772i | \(0.585943\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 6.00000 | − | 12.0000i | 0.219823 | − | 0.439646i | ||||
\(746\) | − | 20.0000i | − | 0.732252i | ||||||
\(747\) | − | 12.0000i | − | 0.439057i | ||||||
\(748\) | 5.00000 | − | 3.00000i | 0.182818 | − | 0.109691i | ||||
\(749\) | 26.0000 | 0.950019 | ||||||||
\(750\) | 13.0000 | + | 9.00000i | 0.474693 | + | 0.328634i | ||||
\(751\) | −11.0000 | + | 11.0000i | −0.401396 | + | 0.401396i | −0.878725 | − | 0.477329i | \(-0.841605\pi\) |
0.477329 | + | 0.878725i | \(0.341605\pi\) | |||||||
\(752\) | 6.00000i | 0.218797i | ||||||||
\(753\) | −20.0000 | − | 20.0000i | −0.728841 | − | 0.728841i | ||||
\(754\) | 20.0000 | + | 20.0000i | 0.728357 | + | 0.728357i | ||||
\(755\) | −4.00000 | − | 2.00000i | −0.145575 | − | 0.0727875i | ||||
\(756\) | − | 8.00000i | − | 0.290957i | ||||||
\(757\) | 18.0000 | 0.654221 | 0.327111 | − | 0.944986i | \(-0.393925\pi\) | ||||
0.327111 | + | 0.944986i | \(0.393925\pi\) | |||||||
\(758\) | 5.00000 | − | 5.00000i | 0.181608 | − | 0.181608i | ||||
\(759\) | 2.00000 | + | 2.00000i | 0.0725954 | + | 0.0725954i | ||||
\(760\) | −12.0000 | − | 6.00000i | −0.435286 | − | 0.217643i | ||||
\(761\) | 22.0000 | 0.797499 | 0.398750 | − | 0.917060i | \(-0.369444\pi\) | ||||
0.398750 | + | 0.917060i | \(0.369444\pi\) | |||||||
\(762\) | 8.00000 | + | 8.00000i | 0.289809 | + | 0.289809i | ||||
\(763\) | 14.0000 | 0.506834 | ||||||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | −6.00000 | + | 7.00000i | −0.216930 | + | 0.253086i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 40.0000 | 1.44432 | ||||||||
\(768\) | 1.00000 | + | 1.00000i | 0.0360844 | + | 0.0360844i | ||||
\(769\) | 30.0000 | 1.08183 | 0.540914 | − | 0.841078i | \(-0.318079\pi\) | ||||
0.540914 | + | 0.841078i | \(0.318079\pi\) | |||||||
\(770\) | −2.00000 | + | 4.00000i | −0.0720750 | + | 0.144150i | ||||
\(771\) | 30.0000 | + | 30.0000i | 1.08042 | + | 1.08042i | ||||
\(772\) | 13.0000 | − | 13.0000i | 0.467880 | − | 0.467880i | ||||
\(773\) | −6.00000 | −0.215805 | −0.107903 | − | 0.994161i | \(-0.534413\pi\) | ||||
−0.107903 | + | 0.994161i | \(0.534413\pi\) | |||||||
\(774\) | − | 4.00000i | − | 0.143777i | ||||||
\(775\) | 21.0000 | + | 3.00000i | 0.754342 | + | 0.107763i | ||||
\(776\) | 3.00000 | + | 3.00000i | 0.107694 | + | 0.107694i | ||||
\(777\) | −2.00000 | − | 2.00000i | −0.0717496 | − | 0.0717496i | ||||
\(778\) | − | 12.0000i | − | 0.430221i | ||||||
\(779\) | 42.0000 | − | 42.0000i | 1.50481 | − | 1.50481i | ||||
\(780\) | 4.00000 | + | 12.0000i | 0.143223 | + | 0.429669i | ||||
\(781\) | 10.0000 | 0.357828 | ||||||||
\(782\) | 3.00000 | + | 5.00000i | 0.107280 | + | 0.178800i | ||||
\(783\) | 40.0000i | 1.42948i | ||||||||
\(784\) | 5.00000i | 0.178571i | ||||||||
\(785\) | −32.0000 | − | 16.0000i | −1.14213 | − | 0.571064i | ||||
\(786\) | 18.0000 | 0.642039 | ||||||||
\(787\) | −15.0000 | − | 15.0000i | −0.534692 | − | 0.534692i | 0.387273 | − | 0.921965i | \(-0.373417\pi\) |
−0.921965 | + | 0.387273i | \(0.873417\pi\) | |||||||
\(788\) | 7.00000 | − | 7.00000i | 0.249365 | − | 0.249365i | ||||
\(789\) | −24.0000 | − | 24.0000i | −0.854423 | − | 0.854423i | ||||
\(790\) | 3.00000 | − | 1.00000i | 0.106735 | − | 0.0355784i | ||||
\(791\) | 22.0000i | 0.782230i | ||||||||
\(792\) | −1.00000 | + | 1.00000i | −0.0355335 | + | 0.0355335i | ||||
\(793\) | −12.0000 | + | 12.0000i | −0.426132 | + | 0.426132i | ||||
\(794\) | −7.00000 | + | 7.00000i | −0.248421 | + | 0.248421i | ||||
\(795\) | −30.0000 | + | 10.0000i | −1.06399 | + | 0.354663i | ||||
\(796\) | 17.0000 | − | 17.0000i | 0.602549 | − | 0.602549i | ||||
\(797\) | −18.0000 | −0.637593 | −0.318796 | − | 0.947823i | \(-0.603279\pi\) | ||||
−0.318796 | + | 0.947823i | \(0.603279\pi\) | |||||||
\(798\) | − | 12.0000i | − | 0.424795i | ||||||
\(799\) | 24.0000 | + | 6.00000i | 0.849059 | + | 0.212265i | ||||
\(800\) | 3.00000 | + | 4.00000i | 0.106066 | + | 0.141421i | ||||
\(801\) | − | 6.00000i | − | 0.212000i | ||||||
\(802\) | 19.0000 | + | 19.0000i | 0.670913 | + | 0.670913i | ||||
\(803\) | 2.00000i | 0.0705785i | ||||||||
\(804\) | 2.00000 | − | 2.00000i | 0.0705346 | − | 0.0705346i | ||||
\(805\) | −4.00000 | − | 2.00000i | −0.140981 | − | 0.0704907i | ||||
\(806\) | 12.0000 | + | 12.0000i | 0.422682 | + | 0.422682i | ||||
\(807\) | 22.0000 | 0.774437 | ||||||||
\(808\) | 14.0000 | 0.492518 | ||||||||
\(809\) | −23.0000 | − | 23.0000i | −0.808637 | − | 0.808637i | 0.175791 | − | 0.984428i | \(-0.443752\pi\) |
−0.984428 | + | 0.175791i | \(0.943752\pi\) | |||||||
\(810\) | −5.00000 | + | 10.0000i | −0.175682 | + | 0.351364i | ||||
\(811\) | 39.0000 | − | 39.0000i | 1.36948 | − | 1.36948i | 0.508288 | − | 0.861187i | \(-0.330278\pi\) |
0.861187 | − | 0.508288i | \(-0.169722\pi\) | |||||||
\(812\) | 10.0000i | 0.350931i | ||||||||
\(813\) | −8.00000 | − | 8.00000i | −0.280572 | − | 0.280572i | ||||
\(814\) | 2.00000i | 0.0701000i | ||||||||
\(815\) | −15.0000 | − | 45.0000i | −0.525427 | − | 1.57628i | ||||
\(816\) | 5.00000 | − | 3.00000i | 0.175035 | − | 0.105021i | ||||
\(817\) | − | 24.0000i | − | 0.839654i | ||||||
\(818\) | 22.0000 | 0.769212 | ||||||||
\(819\) | 4.00000 | − | 4.00000i | 0.139771 | − | 0.139771i | ||||
\(820\) | −21.0000 | + | 7.00000i | −0.733352 | + | 0.244451i | ||||
\(821\) | −5.00000 | + | 5.00000i | −0.174501 | + | 0.174501i | −0.788954 | − | 0.614453i | \(-0.789377\pi\) |
0.614453 | + | 0.788954i | \(0.289377\pi\) | |||||||
\(822\) | −12.0000 | + | 12.0000i | −0.418548 | + | 0.418548i | ||||
\(823\) | −15.0000 | + | 15.0000i | −0.522867 | + | 0.522867i | −0.918436 | − | 0.395569i | \(-0.870547\pi\) |
0.395569 | + | 0.918436i | \(0.370547\pi\) | |||||||
\(824\) | − | 14.0000i | − | 0.487713i | ||||||
\(825\) | 8.00000 | − | 6.00000i | 0.278524 | − | 0.208893i | ||||
\(826\) | 10.0000 | + | 10.0000i | 0.347945 | + | 0.347945i | ||||
\(827\) | −9.00000 | + | 9.00000i | −0.312961 | + | 0.312961i | −0.846055 | − | 0.533095i | \(-0.821029\pi\) |
0.533095 | + | 0.846055i | \(0.321029\pi\) | |||||||
\(828\) | −1.00000 | − | 1.00000i | −0.0347524 | − | 0.0347524i | ||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | −12.0000 | + | 24.0000i | −0.416526 | + | 0.833052i | ||||
\(831\) | − | 10.0000i | − | 0.346896i | ||||||
\(832\) | 4.00000i | 0.138675i | ||||||||
\(833\) | 20.0000 | + | 5.00000i | 0.692959 | + | 0.173240i | ||||
\(834\) | −6.00000 | −0.207763 | ||||||||
\(835\) | 21.0000 | − | 7.00000i | 0.726735 | − | 0.242245i | ||||
\(836\) | −6.00000 | + | 6.00000i | −0.207514 | + | 0.207514i | ||||
\(837\) | 24.0000i | 0.829561i | ||||||||
\(838\) | −17.0000 | − | 17.0000i | −0.587255 | − | 0.587255i | ||||
\(839\) | −9.00000 | − | 9.00000i | −0.310715 | − | 0.310715i | 0.534472 | − | 0.845186i | \(-0.320511\pi\) |
−0.845186 | + | 0.534472i | \(0.820511\pi\) | |||||||
\(840\) | −2.00000 | + | 4.00000i | −0.0690066 | + | 0.138013i | ||||
\(841\) | − | 21.0000i | − | 0.724138i | ||||||
\(842\) | −26.0000 | −0.896019 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.0000 | + | 13.0000i | 0.447478 | + | 0.447478i | ||||
\(845\) | −3.00000 | + | 6.00000i | −0.103203 | + | 0.206406i | ||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | −9.00000 | − | 9.00000i | −0.309244 | − | 0.309244i | ||||
\(848\) | −10.0000 | −0.343401 | ||||||||
\(849\) | 38.0000 | 1.30416 | ||||||||
\(850\) | 19.0000 | − | 8.00000i | 0.651695 | − | 0.274398i | ||||
\(851\) | −2.00000 | −0.0685591 | ||||||||
\(852\) | 10.0000 | 0.342594 | ||||||||
\(853\) | 35.0000 | + | 35.0000i | 1.19838 | + | 1.19838i | 0.974652 | + | 0.223725i | \(0.0718217\pi\) |
0.223725 | + | 0.974652i | \(0.428178\pi\) | |||||||
\(854\) | −6.00000 | −0.205316 | ||||||||
\(855\) | 6.00000 | − | 12.0000i | 0.205196 | − | 0.410391i | ||||
\(856\) | −13.0000 | − | 13.0000i | −0.444331 | − | 0.444331i | ||||
\(857\) | −27.0000 | + | 27.0000i | −0.922302 | + | 0.922302i | −0.997192 | − | 0.0748894i | \(-0.976140\pi\) |
0.0748894 | + | 0.997192i | \(0.476140\pi\) | |||||||
\(858\) | 8.00000 | 0.273115 | ||||||||
\(859\) | 6.00000i | 0.204717i | 0.994748 | + | 0.102359i | \(0.0326389\pi\) | ||||
−0.994748 | + | 0.102359i | \(0.967361\pi\) | |||||||
\(860\) | −4.00000 | + | 8.00000i | −0.136399 | + | 0.272798i | ||||
\(861\) | −14.0000 | − | 14.0000i | −0.477119 | − | 0.477119i | ||||
\(862\) | −7.00000 | − | 7.00000i | −0.238421 | − | 0.238421i | ||||
\(863\) | 14.0000i | 0.476566i | 0.971196 | + | 0.238283i | \(0.0765845\pi\) | ||||
−0.971196 | + | 0.238283i | \(0.923415\pi\) | |||||||
\(864\) | −4.00000 | + | 4.00000i | −0.136083 | + | 0.136083i | ||||
\(865\) | 21.0000 | − | 7.00000i | 0.714021 | − | 0.238007i | ||||
\(866\) | −30.0000 | −1.01944 | ||||||||
\(867\) | −7.00000 | − | 23.0000i | −0.237732 | − | 0.781121i | ||||
\(868\) | 6.00000i | 0.203653i | ||||||||
\(869\) | − | 2.00000i | − | 0.0678454i | ||||||
\(870\) | 10.0000 | − | 20.0000i | 0.339032 | − | 0.678064i | ||||
\(871\) | 8.00000 | 0.271070 | ||||||||
\(872\) | −7.00000 | − | 7.00000i | −0.237050 | − | 0.237050i | ||||
\(873\) | −3.00000 | + | 3.00000i | −0.101535 | + | 0.101535i | ||||
\(874\) | −6.00000 | − | 6.00000i | −0.202953 | − | 0.202953i | ||||
\(875\) | −9.00000 | + | 13.0000i | −0.304256 | + | 0.439480i | ||||
\(876\) | 2.00000i | 0.0675737i | ||||||||
\(877\) | −21.0000 | + | 21.0000i | −0.709120 | + | 0.709120i | −0.966350 | − | 0.257230i | \(-0.917190\pi\) |
0.257230 | + | 0.966350i | \(0.417190\pi\) | |||||||
\(878\) | 11.0000 | − | 11.0000i | 0.371232 | − | 0.371232i | ||||
\(879\) | 24.0000 | − | 24.0000i | 0.809500 | − | 0.809500i | ||||
\(880\) | 3.00000 | − | 1.00000i | 0.101130 | − | 0.0337100i | ||||
\(881\) | 13.0000 | − | 13.0000i | 0.437981 | − | 0.437981i | −0.453351 | − | 0.891332i | \(-0.649772\pi\) |
0.891332 | + | 0.453351i | \(0.149772\pi\) | |||||||
\(882\) | −5.00000 | −0.168359 | ||||||||
\(883\) | 14.0000i | 0.471138i | 0.971858 | + | 0.235569i | \(0.0756953\pi\) | ||||
−0.971858 | + | 0.235569i | \(0.924305\pi\) | |||||||
\(884\) | 16.0000 | + | 4.00000i | 0.538138 | + | 0.134535i | ||||
\(885\) | −10.0000 | − | 30.0000i | −0.336146 | − | 1.00844i | ||||
\(886\) | 10.0000i | 0.335957i | ||||||||
\(887\) | −17.0000 | − | 17.0000i | −0.570804 | − | 0.570804i | 0.361549 | − | 0.932353i | \(-0.382248\pi\) |
−0.932353 | + | 0.361549i | \(0.882248\pi\) | |||||||
\(888\) | 2.00000i | 0.0671156i | ||||||||
\(889\) | −8.00000 | + | 8.00000i | −0.268311 | + | 0.268311i | ||||
\(890\) | −6.00000 | + | 12.0000i | −0.201120 | + | 0.402241i | ||||
\(891\) | 5.00000 | + | 5.00000i | 0.167506 | + | 0.167506i | ||||
\(892\) | −24.0000 | −0.803579 | ||||||||
\(893\) | −36.0000 | −1.20469 | ||||||||
\(894\) | −6.00000 | − | 6.00000i | −0.200670 | − | 0.200670i | ||||
\(895\) | 12.0000 | + | 6.00000i | 0.401116 | + | 0.200558i | ||||
\(896\) | −1.00000 | + | 1.00000i | −0.0334077 | + | 0.0334077i | ||||
\(897\) | 8.00000i | 0.267112i | ||||||||
\(898\) | −5.00000 | − | 5.00000i | −0.166852 | − | 0.166852i | ||||
\(899\) | − | 30.0000i | − | 1.00056i | ||||||
\(900\) | −4.00000 | + | 3.00000i | −0.133333 | + | 0.100000i | ||||
\(901\) | −10.0000 | + | 40.0000i | −0.333148 | + | 1.33259i | ||||
\(902\) | 14.0000i | 0.466149i | ||||||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | 11.0000 | − | 11.0000i | 0.365855 | − | 0.365855i | ||||
\(905\) | 21.0000 | − | 7.00000i | 0.698064 | − | 0.232688i | ||||
\(906\) | −2.00000 | + | 2.00000i | −0.0664455 | + | 0.0664455i | ||||
\(907\) | −21.0000 | + | 21.0000i | −0.697294 | + | 0.697294i | −0.963826 | − | 0.266532i | \(-0.914122\pi\) |
0.266532 | + | 0.963826i | \(0.414122\pi\) | |||||||
\(908\) | −9.00000 | + | 9.00000i | −0.298675 | + | 0.298675i | ||||
\(909\) | 14.0000i | 0.464351i | ||||||||
\(910\) | −12.0000 | + | 4.00000i | −0.397796 | + | 0.132599i | ||||
\(911\) | 7.00000 | + | 7.00000i | 0.231920 | + | 0.231920i | 0.813494 | − | 0.581574i | \(-0.197563\pi\) |
−0.581574 | + | 0.813494i | \(0.697563\pi\) | |||||||
\(912\) | −6.00000 | + | 6.00000i | −0.198680 | + | 0.198680i | ||||
\(913\) | 12.0000 | + | 12.0000i | 0.397142 | + | 0.397142i | ||||
\(914\) | 10.0000 | 0.330771 | ||||||||
\(915\) | 12.0000 | + | 6.00000i | 0.396708 | + | 0.198354i | ||||
\(916\) | − | 28.0000i | − | 0.925146i | ||||||
\(917\) | 18.0000i | 0.594412i | ||||||||
\(918\) | 12.0000 | + | 20.0000i | 0.396059 | + | 0.660098i | ||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 1.00000 | + | 3.00000i | 0.0329690 | + | 0.0989071i | ||||
\(921\) | 2.00000 | − | 2.00000i | 0.0659022 | − | 0.0659022i | ||||
\(922\) | − | 8.00000i | − | 0.263466i | ||||||
\(923\) | 20.0000 | + | 20.0000i | 0.658308 | + | 0.658308i | ||||
\(924\) | 2.00000 | + | 2.00000i | 0.0657952 | + | 0.0657952i | ||||
\(925\) | −1.00000 | + | 7.00000i | −0.0328798 | + | 0.230159i | ||||
\(926\) | − | 30.0000i | − | 0.985861i | ||||||
\(927\) | 14.0000 | 0.459820 | ||||||||
\(928\) | 5.00000 | − | 5.00000i | 0.164133 | − | 0.164133i | ||||
\(929\) | 9.00000 | + | 9.00000i | 0.295280 | + | 0.295280i | 0.839162 | − | 0.543882i | \(-0.183046\pi\) |
−0.543882 | + | 0.839162i | \(0.683046\pi\) | |||||||
\(930\) | 6.00000 | − | 12.0000i | 0.196748 | − | 0.393496i | ||||
\(931\) | −30.0000 | −0.983210 | ||||||||
\(932\) | 1.00000 | + | 1.00000i | 0.0327561 | + | 0.0327561i | ||||
\(933\) | 34.0000 | 1.11311 | ||||||||
\(934\) | −28.0000 | −0.916188 | ||||||||
\(935\) | −1.00000 | − | 13.0000i | −0.0327035 | − | 0.425145i | ||||
\(936\) | −4.00000 | −0.130744 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 2.00000 | + | 2.00000i | 0.0653023 | + | 0.0653023i | ||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | 12.0000 | + | 6.00000i | 0.391397 | + | 0.195698i | ||||
\(941\) | 19.0000 | + | 19.0000i | 0.619382 | + | 0.619382i | 0.945373 | − | 0.325991i | \(-0.105698\pi\) |
−0.325991 | + | 0.945373i | \(0.605698\pi\) | |||||||
\(942\) | −16.0000 | + | 16.0000i | −0.521308 | + | 0.521308i | ||||
\(943\) | −14.0000 | −0.455903 | ||||||||
\(944\) | − | 10.0000i | − | 0.325472i | ||||||
\(945\) | −16.0000 | − | 8.00000i | −0.520480 | − | 0.260240i | ||||
\(946\) | 4.00000 | + | 4.00000i | 0.130051 | + | 0.130051i | ||||
\(947\) | 25.0000 | + | 25.0000i | 0.812391 | + | 0.812391i | 0.984992 | − | 0.172601i | \(-0.0552171\pi\) |
−0.172601 | + | 0.984992i | \(0.555217\pi\) | |||||||
\(948\) | − | 2.00000i | − | 0.0649570i | ||||||
\(949\) | −4.00000 | + | 4.00000i | −0.129845 | + | 0.129845i | ||||
\(950\) | −24.0000 | + | 18.0000i | −0.778663 | + | 0.583997i | ||||
\(951\) | −10.0000 | −0.324272 | ||||||||
\(952\) | 3.00000 | + | 5.00000i | 0.0972306 | + | 0.162051i | ||||
\(953\) | − | 12.0000i | − | 0.388718i | −0.980930 | − | 0.194359i | \(-0.937737\pi\) | ||
0.980930 | − | 0.194359i | \(-0.0622627\pi\) | |||||||
\(954\) | − | 10.0000i | − | 0.323762i | ||||||
\(955\) | −24.0000 | + | 48.0000i | −0.776622 | + | 1.55324i | ||||
\(956\) | 16.0000 | 0.517477 | ||||||||
\(957\) | −10.0000 | − | 10.0000i | −0.323254 | − | 0.323254i | ||||
\(958\) | 15.0000 | − | 15.0000i | 0.484628 | − | 0.484628i | ||||
\(959\) | −12.0000 | − | 12.0000i | −0.387500 | − | 0.387500i | ||||
\(960\) | 3.00000 | − | 1.00000i | 0.0968246 | − | 0.0322749i | ||||
\(961\) | 13.0000i | 0.419355i | ||||||||
\(962\) | −4.00000 | + | 4.00000i | −0.128965 | + | 0.128965i | ||||
\(963\) | 13.0000 | − | 13.0000i | 0.418919 | − | 0.418919i | ||||
\(964\) | 9.00000 | − | 9.00000i | 0.289870 | − | 0.289870i | ||||
\(965\) | −13.0000 | − | 39.0000i | −0.418485 | − | 1.25545i | ||||
\(966\) | −2.00000 | + | 2.00000i | −0.0643489 | + | 0.0643489i | ||||
\(967\) | 48.0000 | 1.54358 | 0.771788 | − | 0.635880i | \(-0.219363\pi\) | ||||
0.771788 | + | 0.635880i | \(0.219363\pi\) | |||||||
\(968\) | 9.00000i | 0.289271i | ||||||||
\(969\) | 18.0000 | + | 30.0000i | 0.578243 | + | 0.963739i | ||||
\(970\) | 9.00000 | − | 3.00000i | 0.288973 | − | 0.0963242i | ||||
\(971\) | 38.0000i | 1.21948i | 0.792602 | + | 0.609739i | \(0.208726\pi\) | ||||
−0.792602 | + | 0.609739i | \(0.791274\pi\) | |||||||
\(972\) | −7.00000 | − | 7.00000i | −0.224525 | − | 0.224525i | ||||
\(973\) | − | 6.00000i | − | 0.192351i | ||||||
\(974\) | −5.00000 | + | 5.00000i | −0.160210 | + | 0.160210i | ||||
\(975\) | 28.0000 | + | 4.00000i | 0.896718 | + | 0.128103i | ||||
\(976\) | 3.00000 | + | 3.00000i | 0.0960277 | + | 0.0960277i | ||||
\(977\) | 10.0000 | 0.319928 | 0.159964 | − | 0.987123i | \(-0.448862\pi\) | ||||
0.159964 | + | 0.987123i | \(0.448862\pi\) | |||||||
\(978\) | −30.0000 | −0.959294 | ||||||||
\(979\) | 6.00000 | + | 6.00000i | 0.191761 | + | 0.191761i | ||||
\(980\) | 10.0000 | + | 5.00000i | 0.319438 | + | 0.159719i | ||||
\(981\) | 7.00000 | − | 7.00000i | 0.223493 | − | 0.223493i | ||||
\(982\) | 18.0000i | 0.574403i | ||||||||
\(983\) | −21.0000 | − | 21.0000i | −0.669796 | − | 0.669796i | 0.287873 | − | 0.957669i | \(-0.407052\pi\) |
−0.957669 | + | 0.287873i | \(0.907052\pi\) | |||||||
\(984\) | 14.0000i | 0.446304i | ||||||||
\(985\) | −7.00000 | − | 21.0000i | −0.223039 | − | 0.669116i | ||||
\(986\) | −15.0000 | − | 25.0000i | −0.477697 | − | 0.796162i | ||||
\(987\) | 12.0000i | 0.381964i | ||||||||
\(988\) | −24.0000 | −0.763542 | ||||||||
\(989\) | −4.00000 | + | 4.00000i | −0.127193 | + | 0.127193i | ||||
\(990\) | 1.00000 | + | 3.00000i | 0.0317821 | + | 0.0953463i | ||||
\(991\) | −3.00000 | + | 3.00000i | −0.0952981 | + | 0.0952981i | −0.753149 | − | 0.657850i | \(-0.771466\pi\) |
0.657850 | + | 0.753149i | \(0.271466\pi\) | |||||||
\(992\) | 3.00000 | − | 3.00000i | 0.0952501 | − | 0.0952501i | ||||
\(993\) | 10.0000 | − | 10.0000i | 0.317340 | − | 0.317340i | ||||
\(994\) | 10.0000i | 0.317181i | ||||||||
\(995\) | −17.0000 | − | 51.0000i | −0.538936 | − | 1.61681i | ||||
\(996\) | 12.0000 | + | 12.0000i | 0.380235 | + | 0.380235i | ||||
\(997\) | 15.0000 | − | 15.0000i | 0.475055 | − | 0.475055i | −0.428491 | − | 0.903546i | \(-0.640955\pi\) |
0.903546 | + | 0.428491i | \(0.140955\pi\) | |||||||
\(998\) | −21.0000 | − | 21.0000i | −0.664743 | − | 0.664743i | ||||
\(999\) | −8.00000 | −0.253109 |
(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 | 170.2.g.b.89.1 | ✓ | 2 | |
3.2 | odd | 2 | 1530.2.n.g.1279.1 | 2 | |||
5.2 | odd | 4 | 850.2.h.e.701.1 | 2 | |||
5.3 | odd | 4 | 850.2.h.a.701.1 | 2 | |||
5.4 | even | 2 | 170.2.g.d.89.1 | yes | 2 | ||
15.14 | odd | 2 | 1530.2.n.a.1279.1 | 2 | |||
17.13 | even | 4 | 170.2.g.d.149.1 | yes | 2 | ||
51.47 | odd | 4 | 1530.2.n.a.829.1 | 2 | |||
85.13 | odd | 4 | 850.2.h.a.251.1 | 2 | |||
85.47 | odd | 4 | 850.2.h.e.251.1 | 2 | |||
85.64 | even | 4 | inner | 170.2.g.b.149.1 | yes | 2 | |
255.149 | odd | 4 | 1530.2.n.g.829.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.g.b.89.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
170.2.g.b.149.1 | yes | 2 | 85.64 | even | 4 | inner | |
170.2.g.d.89.1 | yes | 2 | 5.4 | even | 2 | ||
170.2.g.d.149.1 | yes | 2 | 17.13 | even | 4 | ||
850.2.h.a.251.1 | 2 | 85.13 | odd | 4 | |||
850.2.h.a.701.1 | 2 | 5.3 | odd | 4 | |||
850.2.h.e.251.1 | 2 | 85.47 | odd | 4 | |||
850.2.h.e.701.1 | 2 | 5.2 | odd | 4 | |||
1530.2.n.a.829.1 | 2 | 51.47 | odd | 4 | |||
1530.2.n.a.1279.1 | 2 | 15.14 | odd | 2 | |||
1530.2.n.g.829.1 | 2 | 255.149 | odd | 4 | |||
1530.2.n.g.1279.1 | 2 | 3.2 | odd | 2 |