Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(379,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.g (of order \(2\), degree \(1\), 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: | \(5.03057532734\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.379 |
Dual form | 630.2.g.d.379.2 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.00000 | − | 2.00000i | 0.447214 | − | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | − | 1.00000i | −0.632456 | − | 0.316228i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.00000i | − | 0.554700i | −0.960769 | − | 0.277350i | \(-0.910544\pi\) | ||
0.960769 | − | 0.277350i | \(-0.0894562\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 8.00000i | − | 1.94029i | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||
0.242536 | − | 0.970143i | \(-0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −1.00000 | + | 2.00000i | −0.223607 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.00000 | −1.37199 | ||||||||
\(35\) | 2.00000 | + | 1.00000i | 0.338062 | + | 0.169031i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.00000i | 1.31519i | 0.753371 | + | 0.657596i | \(0.228427\pi\) | ||||
−0.753371 | + | 0.657596i | \(0.771573\pi\) | |||||||
\(38\) | − | 2.00000i | − | 0.324443i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.00000 | + | 1.00000i | 0.316228 | + | 0.158114i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.00000i | − | 1.21999i | −0.792406 | − | 0.609994i | \(-0.791172\pi\) | ||
0.792406 | − | 0.609994i | \(-0.208828\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000i | 0.277350i | ||||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.00000 | − | 4.00000i | 0.269680 | − | 0.539360i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000i | 0.787839i | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | − | 6.00000i | − | 0.762001i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.00000 | − | 2.00000i | −0.496139 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | 8.00000i | 0.970143i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | − | 2.00000i | 0.119523 | − | 0.239046i | ||||
\(71\) | 14.0000 | 1.66149 | 0.830747 | − | 0.556650i | \(-0.187914\pi\) | ||||
0.830747 | + | 0.556650i | \(0.187914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0000i | 1.17041i | 0.810885 | + | 0.585206i | \(0.198986\pi\) | ||||
−0.810885 | + | 0.585206i | \(0.801014\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 1.00000 | − | 2.00000i | 0.111803 | − | 0.223607i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.00000i | 0.662589i | ||||||||
\(83\) | 16.0000i | 1.75623i | 0.478451 | + | 0.878114i | \(0.341198\pi\) | ||||
−0.478451 | + | 0.878114i | \(0.658802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.0000 | − | 8.00000i | −1.73544 | − | 0.867722i | ||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000i | 0.213201i | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.00000 | −0.412568 | ||||||||
\(95\) | 2.00000 | − | 4.00000i | 0.205196 | − | 0.410391i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 12.0000i | 1.16008i | 0.814587 | + | 0.580042i | \(0.196964\pi\) | ||||
−0.814587 | + | 0.580042i | \(0.803036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.00000 | 0.574696 | 0.287348 | − | 0.957826i | \(-0.407226\pi\) | ||||
0.287348 | + | 0.957826i | \(0.407226\pi\) | |||||||
\(110\) | −4.00000 | − | 2.00000i | −0.381385 | − | 0.190693i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00000i | 0.736460i | ||||||||
\(119\) | 8.00000 | 0.733359 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | − | 10.0000i | − | 0.905357i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | −11.0000 | + | 2.00000i | −0.983870 | + | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000i | 1.06483i | 0.846484 | + | 0.532414i | \(0.178715\pi\) | ||||
−0.846484 | + | 0.532414i | \(0.821285\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | + | 4.00000i | −0.175412 | + | 0.350823i | ||||
\(131\) | 20.0000 | 1.74741 | 0.873704 | − | 0.486458i | \(-0.161711\pi\) | ||||
0.873704 | + | 0.486458i | \(0.161711\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.00000i | 0.173422i | ||||||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.00000 | 0.685994 | ||||||||
\(137\) | 14.0000i | 1.19610i | 0.801459 | + | 0.598050i | \(0.204058\pi\) | ||||
−0.801459 | + | 0.598050i | \(0.795942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | −2.00000 | − | 1.00000i | −0.169031 | − | 0.0845154i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 14.0000i | − | 1.17485i | ||||||
\(143\) | − | 4.00000i | − | 0.334497i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | + | 12.0000i | −0.498273 | + | 0.996546i | ||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 8.00000i | − | 0.657596i | ||||||
\(149\) | −18.0000 | −1.47462 | −0.737309 | − | 0.675556i | \(-0.763904\pi\) | ||||
−0.737309 | + | 0.675556i | \(0.763904\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 2.00000i | 0.162221i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.00000 | 0.161165 | ||||||||
\(155\) | 6.00000 | − | 12.0000i | 0.481932 | − | 0.963863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.0000i | − | 0.798087i | −0.916932 | − | 0.399043i | \(-0.869342\pi\) | ||
0.916932 | − | 0.399043i | \(-0.130658\pi\) | |||||||
\(158\) | 4.00000i | 0.318223i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.0000 | 1.24184 | ||||||||
\(167\) | 8.00000i | 0.619059i | 0.950890 | + | 0.309529i | \(0.100171\pi\) | ||||
−0.950890 | + | 0.309529i | \(0.899829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | −8.00000 | + | 16.0000i | −0.613572 | + | 1.22714i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000i | 0.609994i | ||||||||
\(173\) | − | 16.0000i | − | 1.21646i | −0.793762 | − | 0.608229i | \(-0.791880\pi\) | ||
0.793762 | − | 0.608229i | \(-0.208120\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | − | 3.00000i | 0.302372 | − | 0.226779i | ||||
\(176\) | 2.00000 | 0.150756 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 10.0000i | − | 0.749532i | ||||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | − | 2.00000i | − | 0.148250i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.0000 | + | 8.00000i | 1.17634 | + | 0.588172i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.0000i | − | 1.17004i | ||||||
\(188\) | 4.00000i | 0.291730i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | − | 2.00000i | −0.290191 | − | 0.145095i | ||||
\(191\) | −14.0000 | −1.01300 | −0.506502 | − | 0.862239i | \(-0.669062\pi\) | ||||
−0.506502 | + | 0.862239i | \(0.669062\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 26.0000 | 1.84309 | 0.921546 | − | 0.388270i | \(-0.126927\pi\) | ||||
0.921546 | + | 0.388270i | \(0.126927\pi\) | |||||||
\(200\) | 4.00000 | − | 3.00000i | 0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 10.0000i | − | 0.703598i | ||||||
\(203\) | − | 6.00000i | − | 0.421117i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | + | 12.0000i | −0.419058 | + | 0.838116i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 2.00000i | − | 0.138675i | ||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 2.00000i | 0.137361i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | −16.0000 | − | 8.00000i | −1.09119 | − | 0.545595i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000i | 0.407307i | ||||||||
\(218\) | − | 6.00000i | − | 0.406371i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.00000 | + | 4.00000i | −0.134840 | + | 0.269680i | ||||
\(221\) | −16.0000 | −1.07628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | 8.00000i | 0.530979i | 0.964114 | + | 0.265489i | \(0.0855335\pi\) | ||||
−0.964114 | + | 0.265489i | \(0.914466\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.0000 | −1.71813 | −0.859064 | − | 0.511868i | \(-0.828954\pi\) | ||||
−0.859064 | + | 0.511868i | \(0.828954\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.00000i | − | 0.393919i | ||||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | − | 4.00000i | −0.521862 | − | 0.260931i | ||||
\(236\) | 8.00000 | 0.520756 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 8.00000i | − | 0.518563i | ||||||
\(239\) | −22.0000 | −1.42306 | −0.711531 | − | 0.702655i | \(-0.751998\pi\) | ||||
−0.711531 | + | 0.702655i | \(0.751998\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 7.00000i | 0.449977i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | −1.00000 | + | 2.00000i | −0.0638877 | + | 0.127775i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.00000i | − | 0.254514i | ||||||
\(248\) | 6.00000i | 0.381000i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.00000 | + | 11.0000i | 0.126491 | + | 0.695701i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 12.0000 | 0.752947 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.0000i | 1.24757i | 0.781598 | + | 0.623783i | \(0.214405\pi\) | ||||
−0.781598 | + | 0.623783i | \(0.785595\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | −0.497096 | ||||||||
\(260\) | 4.00000 | + | 2.00000i | 0.248069 | + | 0.124035i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 20.0000i | − | 1.23560i | ||||||
\(263\) | − | 24.0000i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | − | 2.00000i | −0.245718 | − | 0.122859i | ||||
\(266\) | 2.00000 | 0.122628 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.00000 | 0.121491 | 0.0607457 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607457 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(272\) | − | 8.00000i | − | 0.485071i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0000 | 0.845771 | ||||||||
\(275\) | −6.00000 | − | 8.00000i | −0.361814 | − | 0.482418i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 8.00000i | − | 0.480673i | −0.970690 | − | 0.240337i | \(-0.922742\pi\) | ||
0.970690 | − | 0.240337i | \(-0.0772579\pi\) | |||||||
\(278\) | − | 2.00000i | − | 0.119952i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | + | 2.00000i | −0.0597614 | + | 0.119523i | ||||
\(281\) | −22.0000 | −1.31241 | −0.656205 | − | 0.754583i | \(-0.727839\pi\) | ||||
−0.656205 | + | 0.754583i | \(0.727839\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | −14.0000 | −0.830747 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.00000 | −0.236525 | ||||||||
\(287\) | − | 6.00000i | − | 0.354169i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −47.0000 | −2.76471 | ||||||||
\(290\) | 12.0000 | + | 6.00000i | 0.704664 | + | 0.352332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 10.0000i | − | 0.585206i | ||||||
\(293\) | − | 16.0000i | − | 0.934730i | −0.884064 | − | 0.467365i | \(-0.845203\pi\) | ||
0.884064 | − | 0.467365i | \(-0.154797\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | + | 16.0000i | −0.465778 | + | 0.931556i | ||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.0000i | 1.04271i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000 | 0.461112 | ||||||||
\(302\) | − | 8.00000i | − | 0.460348i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | 0.114708 | ||||||||
\(305\) | 10.0000 | − | 20.0000i | 0.572598 | − | 1.14520i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | − | 2.00000i | − | 0.113961i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.0000 | − | 6.00000i | −0.681554 | − | 0.340777i | ||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.0000i | − | 0.565233i | −0.959233 | − | 0.282617i | \(-0.908798\pi\) | ||
0.959233 | − | 0.282617i | \(-0.0912024\pi\) | |||||||
\(314\) | −10.0000 | −0.564333 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | 2.00000i | 0.112331i | 0.998421 | + | 0.0561656i | \(0.0178875\pi\) | ||||
−0.998421 | + | 0.0561656i | \(0.982113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.0000 | −0.671871 | ||||||||
\(320\) | −1.00000 | + | 2.00000i | −0.0559017 | + | 0.111803i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 16.0000i | − | 0.890264i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.00000 | + | 6.00000i | −0.443760 | + | 0.332820i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 6.00000i | − | 0.331295i | ||||||
\(329\) | 4.00000 | 0.220527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(332\) | − | 16.0000i | − | 0.878114i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.00000 | 0.437741 | ||||||||
\(335\) | −24.0000 | − | 12.0000i | −1.31126 | − | 0.655630i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.0000i | 1.74315i | 0.490261 | + | 0.871576i | \(0.336901\pi\) | ||||
−0.490261 | + | 0.871576i | \(0.663099\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.0000 | + | 8.00000i | 0.867722 | + | 0.433861i | ||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 8.00000 | 0.431331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.0000 | −0.860165 | ||||||||
\(347\) | − | 4.00000i | − | 0.214731i | −0.994220 | − | 0.107366i | \(-0.965758\pi\) | ||
0.994220 | − | 0.107366i | \(-0.0342415\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.0000 | −0.963518 | −0.481759 | − | 0.876304i | \(-0.660002\pi\) | ||||
−0.481759 | + | 0.876304i | \(0.660002\pi\) | |||||||
\(350\) | −3.00000 | − | 4.00000i | −0.160357 | − | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 2.00000i | − | 0.106600i | ||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 14.0000 | − | 28.0000i | 0.743043 | − | 1.48609i | ||||
\(356\) | −10.0000 | −0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.00000i | 0.105703i | ||||||||
\(359\) | 14.0000 | 0.738892 | 0.369446 | − | 0.929252i | \(-0.379548\pi\) | ||||
0.369446 | + | 0.929252i | \(0.379548\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | − | 22.0000i | − | 1.15629i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 20.0000 | + | 10.0000i | 1.04685 | + | 0.523424i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 32.0000i | − | 1.67039i | −0.549957 | − | 0.835193i | \(-0.685356\pi\) | ||
0.549957 | − | 0.835193i | \(-0.314644\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | − | 16.0000i | 0.415900 | − | 0.831800i | ||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 36.0000i | − | 1.86401i | −0.362446 | − | 0.932005i | \(-0.618058\pi\) | ||
0.362446 | − | 0.932005i | \(-0.381942\pi\) | |||||||
\(374\) | −16.0000 | −0.827340 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | −2.00000 | + | 4.00000i | −0.102598 | + | 0.205196i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.0000i | 0.716302i | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | + | 2.00000i | 0.203859 | + | 0.101929i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 10.0000i | − | 0.507673i | ||||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 1.00000i | − | 0.0505076i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | 0.302276 | ||||||||
\(395\) | −4.00000 | + | 8.00000i | −0.201262 | + | 0.402524i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.00000i | 0.100377i | 0.998740 | + | 0.0501886i | \(0.0159822\pi\) | ||||
−0.998740 | + | 0.0501886i | \(0.984018\pi\) | |||||||
\(398\) | − | 26.0000i | − | 1.30326i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 12.0000i | − | 0.597763i | ||||||
\(404\) | −10.0000 | −0.497519 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | 16.0000i | 0.793091i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 12.0000 | + | 6.00000i | 0.592638 | + | 0.296319i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8.00000i | − | 0.393654i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.0000 | + | 16.0000i | 1.57082 | + | 0.785409i | ||||
\(416\) | −2.00000 | −0.0980581 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 4.00000i | − | 0.195646i | ||||||
\(419\) | 12.0000 | 0.586238 | 0.293119 | − | 0.956076i | \(-0.405307\pi\) | ||||
0.293119 | + | 0.956076i | \(0.405307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 8.00000i | 0.389434i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.00000 | 0.0971286 | ||||||||
\(425\) | −32.0000 | + | 24.0000i | −1.55223 | + | 1.16417i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000i | 0.483934i | ||||||||
\(428\) | − | 12.0000i | − | 0.580042i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | + | 16.0000i | −0.385794 | + | 0.771589i | ||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.0000i | − | 1.24948i | −0.780833 | − | 0.624740i | \(-0.785205\pi\) | ||
0.780833 | − | 0.624740i | \(-0.214795\pi\) | |||||||
\(434\) | 6.00000 | 0.288009 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.00000 | −0.287348 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.00000 | −0.286364 | −0.143182 | − | 0.989696i | \(-0.545733\pi\) | ||||
−0.143182 | + | 0.989696i | \(0.545733\pi\) | |||||||
\(440\) | 4.00000 | + | 2.00000i | 0.190693 | + | 0.0953463i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.0000i | 0.761042i | ||||||||
\(443\) | 36.0000i | 1.71041i | 0.518289 | + | 0.855206i | \(0.326569\pi\) | ||||
−0.518289 | + | 0.855206i | \(0.673431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | − | 20.0000i | 0.474045 | − | 0.948091i | ||||
\(446\) | 16.0000 | 0.757622 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.0000 | −0.565058 | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 2.00000 | − | 4.00000i | 0.0937614 | − | 0.187523i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 28.0000i | − | 1.30978i | −0.755722 | − | 0.654892i | \(-0.772714\pi\) | ||
0.755722 | − | 0.654892i | \(-0.227286\pi\) | |||||||
\(458\) | 26.0000i | 1.21490i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.0000i | 0.557687i | 0.960337 | + | 0.278844i | \(0.0899511\pi\) | ||||
−0.960337 | + | 0.278844i | \(0.910049\pi\) | |||||||
\(464\) | −6.00000 | −0.278543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.00000 | 0.277945 | ||||||||
\(467\) | − | 16.0000i | − | 0.740392i | −0.928954 | − | 0.370196i | \(-0.879291\pi\) | ||
0.928954 | − | 0.370196i | \(-0.120709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.0000 | 0.554109 | ||||||||
\(470\) | −4.00000 | + | 8.00000i | −0.184506 | + | 0.369012i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 8.00000i | − | 0.368230i | ||||||
\(473\) | − | 16.0000i | − | 0.735681i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | − | 8.00000i | −0.275299 | − | 0.367065i | ||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.0000i | 1.00626i | ||||||||
\(479\) | 8.00000 | 0.365529 | 0.182765 | − | 0.983157i | \(-0.441495\pi\) | ||||
0.182765 | + | 0.983157i | \(0.441495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | 0.729537 | ||||||||
\(482\) | 10.0000i | 0.455488i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 20.0000 | + | 10.0000i | 0.908153 | + | 0.454077i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.0000i | 1.63132i | 0.578535 | + | 0.815658i | \(0.303625\pi\) | ||||
−0.578535 | + | 0.815658i | \(0.696375\pi\) | |||||||
\(488\) | 10.0000i | 0.452679i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.00000 | + | 1.00000i | 0.0903508 | + | 0.0451754i | ||||
\(491\) | 42.0000 | 1.89543 | 0.947717 | − | 0.319113i | \(-0.103385\pi\) | ||||
0.947717 | + | 0.319113i | \(0.103385\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 48.0000i | 2.16181i | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 14.0000i | 0.627986i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0000 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(500\) | 11.0000 | − | 2.00000i | 0.491935 | − | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.0000i | 1.07011i | 0.844818 | + | 0.535054i | \(0.179709\pi\) | ||||
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | − | 20.0000i | 0.444994 | − | 0.889988i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 12.0000i | − | 0.532414i | ||||||
\(509\) | 2.00000 | 0.0886484 | 0.0443242 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443242 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.0000 | −0.442374 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 20.0000 | 0.882162 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.00000i | − | 0.351840i | ||||||
\(518\) | 8.00000i | 0.351500i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.00000 | − | 4.00000i | 0.0877058 | − | 0.175412i | ||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.0000i | 0.524723i | 0.964970 | + | 0.262362i | \(0.0845013\pi\) | ||||
−0.964970 | + | 0.262362i | \(0.915499\pi\) | |||||||
\(524\) | −20.0000 | −0.873704 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | − | 48.0000i | − | 2.09091i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | −2.00000 | + | 4.00000i | −0.0868744 | + | 0.173749i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 2.00000i | − | 0.0867110i | ||||||
\(533\) | 12.0000i | 0.519778i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000 | + | 12.0000i | 1.03761 | + | 0.518805i | ||||
\(536\) | 12.0000 | 0.518321 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | − | 2.00000i | − | 0.0859074i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.00000 | −0.342997 | ||||||||
\(545\) | 6.00000 | − | 12.0000i | 0.257012 | − | 0.514024i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000i | 0.855138i | 0.903983 | + | 0.427569i | \(0.140630\pi\) | ||||
−0.903983 | + | 0.427569i | \(0.859370\pi\) | |||||||
\(548\) | − | 14.0000i | − | 0.598050i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.00000 | + | 6.00000i | −0.341121 | + | 0.255841i | ||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.00000i | − | 0.170097i | ||||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.00000 | −0.0848189 | ||||||||
\(557\) | − | 6.00000i | − | 0.254228i | −0.991888 | − | 0.127114i | \(-0.959429\pi\) | ||
0.991888 | − | 0.127114i | \(-0.0405714\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.0000 | −0.676728 | ||||||||
\(560\) | 2.00000 | + | 1.00000i | 0.0845154 | + | 0.0422577i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.0000i | 0.928014i | ||||||||
\(563\) | 12.0000i | 0.505740i | 0.967500 | + | 0.252870i | \(0.0813744\pi\) | ||||
−0.967500 | + | 0.252870i | \(0.918626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.0000 | + | 6.00000i | 0.504844 | + | 0.252422i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.0000i | 0.587427i | ||||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.0000 | −1.84134 | −0.920671 | − | 0.390339i | \(-0.872358\pi\) | ||||
−0.920671 | + | 0.390339i | \(0.872358\pi\) | |||||||
\(572\) | 4.00000i | 0.167248i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | 47.0000i | 1.95494i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6.00000 | − | 12.0000i | 0.249136 | − | 0.498273i | ||||
\(581\) | −16.0000 | −0.663792 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.00000i | − | 0.165663i | ||||||
\(584\) | −10.0000 | −0.413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.0000 | −0.660954 | ||||||||
\(587\) | − | 4.00000i | − | 0.165098i | −0.996587 | − | 0.0825488i | \(-0.973694\pi\) | ||
0.996587 | − | 0.0825488i | \(-0.0263060\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 16.0000 | + | 8.00000i | 0.658710 | + | 0.329355i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.00000i | 0.328798i | ||||||||
\(593\) | − | 32.0000i | − | 1.31408i | −0.753855 | − | 0.657041i | \(-0.771808\pi\) | ||
0.753855 | − | 0.657041i | \(-0.228192\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.00000 | − | 16.0000i | 0.327968 | − | 0.655936i | ||||
\(596\) | 18.0000 | 0.737309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0000 | 0.572024 | 0.286012 | − | 0.958226i | \(-0.407670\pi\) | ||||
0.286012 | + | 0.958226i | \(0.407670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −42.0000 | −1.71322 | −0.856608 | − | 0.515968i | \(-0.827432\pi\) | ||||
−0.856608 | + | 0.515968i | \(0.827432\pi\) | |||||||
\(602\) | − | 8.00000i | − | 0.326056i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.00000 | −0.325515 | ||||||||
\(605\) | −7.00000 | + | 14.0000i | −0.284590 | + | 0.569181i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 16.0000i | − | 0.649420i | −0.945814 | − | 0.324710i | \(-0.894733\pi\) | ||
0.945814 | − | 0.324710i | \(-0.105267\pi\) | |||||||
\(608\) | − | 2.00000i | − | 0.0811107i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −20.0000 | − | 10.0000i | −0.809776 | − | 0.404888i | ||||
\(611\) | −8.00000 | −0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 32.0000i | − | 1.29247i | −0.763139 | − | 0.646234i | \(-0.776343\pi\) | ||
0.763139 | − | 0.646234i | \(-0.223657\pi\) | |||||||
\(614\) | 28.0000 | 1.12999 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.00000 | −0.0805823 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.0000 | 0.723481 | 0.361741 | − | 0.932279i | \(-0.382183\pi\) | ||||
0.361741 | + | 0.932279i | \(0.382183\pi\) | |||||||
\(620\) | −6.00000 | + | 12.0000i | −0.240966 | + | 0.481932i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 8.00000i | − | 0.320771i | ||||||
\(623\) | 10.0000i | 0.400642i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.0000i | 0.399043i | ||||||||
\(629\) | 64.0000 | 2.55185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.0000 | 0.477712 | 0.238856 | − | 0.971055i | \(-0.423228\pi\) | ||||
0.238856 | + | 0.971055i | \(0.423228\pi\) | |||||||
\(632\) | − | 4.00000i | − | 0.159111i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.00000 | 0.0794301 | ||||||||
\(635\) | 24.0000 | + | 12.0000i | 0.952411 | + | 0.476205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.00000i | 0.0792429i | ||||||||
\(638\) | 12.0000i | 0.475085i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.00000 | + | 1.00000i | 0.0790569 | + | 0.0395285i | ||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.0000i | 0.788723i | 0.918955 | + | 0.394362i | \(0.129034\pi\) | ||||
−0.918955 | + | 0.394362i | \(0.870966\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −16.0000 | −0.629512 | ||||||||
\(647\) | − | 16.0000i | − | 0.629025i | −0.949253 | − | 0.314512i | \(-0.898159\pi\) | ||
0.949253 | − | 0.314512i | \(-0.101841\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0000 | −0.628055 | ||||||||
\(650\) | 6.00000 | + | 8.00000i | 0.235339 | + | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 14.0000i | − | 0.547862i | −0.961749 | − | 0.273931i | \(-0.911676\pi\) | ||
0.961749 | − | 0.273931i | \(-0.0883240\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 20.0000 | − | 40.0000i | 0.781465 | − | 1.56293i | ||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 4.00000i | − | 0.155936i | ||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0000 | 0.388955 | 0.194477 | − | 0.980907i | \(-0.437699\pi\) | ||||
0.194477 | + | 0.980907i | \(0.437699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.0000 | −0.620920 | ||||||||
\(665\) | 4.00000 | + | 2.00000i | 0.155113 | + | 0.0775567i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 8.00000i | − | 0.309529i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.0000 | + | 24.0000i | −0.463600 | + | 0.927201i | ||||
\(671\) | 20.0000 | 0.772091 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 12.0000i | − | 0.462566i | −0.972887 | − | 0.231283i | \(-0.925708\pi\) | ||
0.972887 | − | 0.231283i | \(-0.0742923\pi\) | |||||||
\(674\) | 32.0000 | 1.23259 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0000 | −0.383765 | ||||||||
\(680\) | 8.00000 | − | 16.0000i | 0.306786 | − | 0.613572i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 12.0000i | − | 0.459504i | ||||||
\(683\) | 28.0000i | 1.07139i | 0.844411 | + | 0.535695i | \(0.179950\pi\) | ||||
−0.844411 | + | 0.535695i | \(0.820050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.0000 | + | 14.0000i | 1.06983 | + | 0.534913i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 8.00000i | − | 0.304997i | ||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.0000 | −0.532585 | −0.266293 | − | 0.963892i | \(-0.585799\pi\) | ||||
−0.266293 | + | 0.963892i | \(0.585799\pi\) | |||||||
\(692\) | 16.0000i | 0.608229i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.00000 | −0.151838 | ||||||||
\(695\) | 2.00000 | − | 4.00000i | 0.0758643 | − | 0.151729i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.0000i | 1.81813i | ||||||||
\(698\) | 18.0000i | 0.681310i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.00000 | + | 3.00000i | −0.151186 | + | 0.113389i | ||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000i | 0.603451i | ||||||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0000i | 0.376089i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | −28.0000 | − | 14.0000i | −1.05082 | − | 0.525411i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.00000 | − | 4.00000i | −0.299183 | − | 0.149592i | ||||
\(716\) | 2.00000 | 0.0747435 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 14.0000i | − | 0.522475i | ||||||
\(719\) | −20.0000 | −0.745874 | −0.372937 | − | 0.927857i | \(-0.621649\pi\) | ||||
−0.372937 | + | 0.927857i | \(0.621649\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.0000i | 0.558242i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.0000 | −0.817624 | ||||||||
\(725\) | 18.0000 | + | 24.0000i | 0.668503 | + | 0.891338i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0000i | 0.593407i | 0.954970 | + | 0.296704i | \(0.0958873\pi\) | ||||
−0.954970 | + | 0.296704i | \(0.904113\pi\) | |||||||
\(728\) | 2.00000i | 0.0741249i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0000 | − | 20.0000i | 0.370117 | − | 0.740233i | ||||
\(731\) | −64.0000 | −2.36713 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.0000i | 1.10808i | 0.832492 | + | 0.554038i | \(0.186914\pi\) | ||||
−0.832492 | + | 0.554038i | \(0.813086\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 24.0000i | − | 0.884051i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | −16.0000 | − | 8.00000i | −0.588172 | − | 0.294086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 2.00000i | − | 0.0734223i | ||||||
\(743\) | 16.0000i | 0.586983i | 0.955962 | + | 0.293492i | \(0.0948173\pi\) | ||||
−0.955962 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | + | 36.0000i | −0.659469 | + | 1.31894i | ||||
\(746\) | −36.0000 | −1.31805 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.0000i | 0.585018i | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.00000 | 0.145962 | 0.0729810 | − | 0.997333i | \(-0.476749\pi\) | ||||
0.0729810 | + | 0.997333i | \(0.476749\pi\) | |||||||
\(752\) | − | 4.00000i | − | 0.145865i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | 0.437014 | ||||||||
\(755\) | 8.00000 | − | 16.0000i | 0.291150 | − | 0.582300i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.00000i | − | 0.145382i | −0.997354 | − | 0.0726912i | \(-0.976841\pi\) | ||
0.997354 | − | 0.0726912i | \(-0.0231588\pi\) | |||||||
\(758\) | − | 28.0000i | − | 1.01701i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.00000 | + | 2.00000i | 0.145095 | + | 0.0725476i | ||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.00000i | 0.217215i | ||||||||
\(764\) | 14.0000 | 0.506502 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.0000i | 0.577727i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.0000 | 1.51456 | 0.757279 | − | 0.653091i | \(-0.226528\pi\) | ||||
0.757279 | + | 0.653091i | \(0.226528\pi\) | |||||||
\(770\) | 2.00000 | − | 4.00000i | 0.0720750 | − | 0.144150i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 32.0000i | − | 1.15096i | −0.817816 | − | 0.575480i | \(-0.804815\pi\) | ||
0.817816 | − | 0.575480i | \(-0.195185\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.0000 | − | 24.0000i | −0.646579 | − | 0.862105i | ||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 6.00000i | − | 0.215110i | ||||||
\(779\) | −12.0000 | −0.429945 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.0000 | 1.00192 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | −20.0000 | − | 10.0000i | −0.713831 | − | 0.356915i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 44.0000i | − | 1.56843i | −0.620489 | − | 0.784215i | \(-0.713066\pi\) | ||
0.620489 | − | 0.784215i | \(-0.286934\pi\) | |||||||
\(788\) | − | 6.00000i | − | 0.213741i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.00000 | + | 4.00000i | 0.284627 | + | 0.142314i | ||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 20.0000i | − | 0.710221i | ||||||
\(794\) | 2.00000 | 0.0709773 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −26.0000 | −0.921546 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.0000 | −1.13208 | ||||||||
\(800\) | −4.00000 | + | 3.00000i | −0.141421 | + | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0000i | 0.635602i | ||||||||
\(803\) | 20.0000i | 0.705785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | −0.422682 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.0000i | 0.351799i | ||||||||
\(809\) | 6.00000 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.0000 | 0.491606 | 0.245803 | − | 0.969320i | \(-0.420948\pi\) | ||||
0.245803 | + | 0.969320i | \(0.420948\pi\) | |||||||
\(812\) | 6.00000i | 0.210559i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 16.0000 | 0.560800 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 16.0000i | − | 0.559769i | ||||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | − | 12.0000i | 0.209529 | − | 0.419058i | ||||
\(821\) | 6.00000 | 0.209401 | 0.104701 | − | 0.994504i | \(-0.466612\pi\) | ||||
0.104701 | + | 0.994504i | \(0.466612\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.00000i | 0.139431i | 0.997567 | + | 0.0697156i | \(0.0222092\pi\) | ||||
−0.997567 | + | 0.0697156i | \(0.977791\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | −0.278356 | ||||||||
\(827\) | 36.0000i | 1.25184i | 0.779886 | + | 0.625921i | \(0.215277\pi\) | ||||
−0.779886 | + | 0.625921i | \(0.784723\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.0000 | 1.18087 | 0.590434 | − | 0.807086i | \(-0.298956\pi\) | ||||
0.590434 | + | 0.807086i | \(0.298956\pi\) | |||||||
\(830\) | 16.0000 | − | 32.0000i | 0.555368 | − | 1.11074i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.00000i | 0.0693375i | ||||||||
\(833\) | 8.00000i | 0.277184i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | + | 8.00000i | 0.553703 | + | 0.276851i | ||||
\(836\) | −4.00000 | −0.138343 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 12.0000i | − | 0.414533i | ||||||
\(839\) | 44.0000 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | − | 10.0000i | − | 0.344623i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | 9.00000 | − | 18.0000i | 0.309609 | − | 0.619219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.00000i | − | 0.240523i | ||||||
\(848\) | − | 2.00000i | − | 0.0686803i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.0000 | + | 32.0000i | 0.823193 | + | 1.09759i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 10.0000i | − | 0.342393i | −0.985237 | − | 0.171197i | \(-0.945237\pi\) | ||
0.985237 | − | 0.171197i | \(-0.0547634\pi\) | |||||||
\(854\) | 10.0000 | 0.342193 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | − | 20.0000i | − | 0.683187i | −0.939848 | − | 0.341593i | \(-0.889033\pi\) | ||
0.939848 | − | 0.341593i | \(-0.110967\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.00000 | 0.204717 | 0.102359 | − | 0.994748i | \(-0.467361\pi\) | ||||
0.102359 | + | 0.994748i | \(0.467361\pi\) | |||||||
\(860\) | 16.0000 | + | 8.00000i | 0.545595 | + | 0.272798i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 6.00000i | − | 0.204361i | ||||||
\(863\) | 48.0000i | 1.63394i | 0.576681 | + | 0.816970i | \(0.304348\pi\) | ||||
−0.576681 | + | 0.816970i | \(0.695652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.0000 | − | 16.0000i | −1.08803 | − | 0.544016i | ||||
\(866\) | −26.0000 | −0.883516 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 6.00000i | − | 0.203653i | ||||||
\(869\) | −8.00000 | −0.271381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.0000 | −0.813209 | ||||||||
\(872\) | 6.00000i | 0.203186i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.00000 | − | 11.0000i | −0.0676123 | − | 0.371868i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 48.0000i | − | 1.62084i | −0.585846 | − | 0.810422i | \(-0.699238\pi\) | ||
0.585846 | − | 0.810422i | \(-0.300762\pi\) | |||||||
\(878\) | 6.00000i | 0.202490i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.00000 | − | 4.00000i | 0.0674200 | − | 0.134840i | ||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 52.0000i | − | 1.74994i | −0.484178 | − | 0.874970i | \(-0.660881\pi\) | ||
0.484178 | − | 0.874970i | \(-0.339119\pi\) | |||||||
\(884\) | 16.0000 | 0.538138 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 36.0000 | 1.20944 | ||||||||
\(887\) | − | 36.0000i | − | 1.20876i | −0.796696 | − | 0.604381i | \(-0.793421\pi\) | ||
0.796696 | − | 0.604381i | \(-0.206579\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | −20.0000 | − | 10.0000i | −0.670402 | − | 0.335201i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 16.0000i | − | 0.535720i | ||||||
\(893\) | − | 8.00000i | − | 0.267710i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.00000 | + | 4.00000i | −0.0668526 | + | 0.133705i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 30.0000i | 1.00111i | ||||||||
\(899\) | −36.0000 | −1.20067 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −16.0000 | −0.533037 | ||||||||
\(902\) | 12.0000i | 0.399556i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 22.0000 | − | 44.0000i | 0.731305 | − | 1.46261i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 44.0000i | − | 1.46100i | −0.682915 | − | 0.730498i | \(-0.739288\pi\) | ||
0.682915 | − | 0.730498i | \(-0.260712\pi\) | |||||||
\(908\) | − | 8.00000i | − | 0.265489i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | − | 2.00000i | −0.132599 | − | 0.0662994i | ||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0000i | 1.05905i | ||||||||
\(914\) | −28.0000 | −0.926158 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.0000 | 0.859064 | ||||||||
\(917\) | 20.0000i | 0.660458i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.0000i | 0.592798i | ||||||||
\(923\) | − | 28.0000i | − | 0.921631i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.0000 | − | 24.0000i | 1.05215 | − | 0.789115i | ||||
\(926\) | 12.0000 | 0.394344 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.00000 | −0.0655474 | ||||||||
\(932\) | − | 6.00000i | − | 0.196537i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −16.0000 | −0.523536 | ||||||||
\(935\) | −32.0000 | − | 16.0000i | −1.04651 | − | 0.523256i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.0000i | − | 0.849383i | −0.905338 | − | 0.424691i | \(-0.860383\pi\) | ||
0.905338 | − | 0.424691i | \(-0.139617\pi\) | |||||||
\(938\) | − | 12.0000i | − | 0.391814i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.00000 | + | 4.00000i | 0.260931 | + | 0.130466i | ||||
\(941\) | 6.00000 | 0.195594 | 0.0977972 | − | 0.995206i | \(-0.468820\pi\) | ||||
0.0977972 | + | 0.995206i | \(0.468820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −8.00000 | −0.260378 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0000 | −0.520205 | ||||||||
\(947\) | − | 12.0000i | − | 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.0000 | 0.649227 | ||||||||
\(950\) | −8.00000 | + | 6.00000i | −0.259554 | + | 0.194666i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.00000i | 0.259281i | ||||||||
\(953\) | − | 18.0000i | − | 0.583077i | −0.956559 | − | 0.291539i | \(-0.905833\pi\) | ||
0.956559 | − | 0.291539i | \(-0.0941672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.0000 | + | 28.0000i | −0.453029 | + | 0.906059i | ||||
\(956\) | 22.0000 | 0.711531 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 8.00000i | − | 0.258468i | ||||||
\(959\) | −14.0000 | −0.452084 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | − | 16.0000i | − | 0.515861i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 24.0000i | − | 0.771788i | −0.922543 | − | 0.385894i | \(-0.873893\pi\) | ||
0.922543 | − | 0.385894i | \(-0.126107\pi\) | |||||||
\(968\) | − | 7.00000i | − | 0.224989i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | − | 20.0000i | 0.321081 | − | 0.642161i | ||||
\(971\) | −24.0000 | −0.770197 | −0.385098 | − | 0.922876i | \(-0.625832\pi\) | ||||
−0.385098 | + | 0.922876i | \(0.625832\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.00000i | 0.0641171i | ||||||||
\(974\) | 36.0000 | 1.15351 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 18.0000i | 0.575871i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) | ||||
−0.957650 | + | 0.287936i | \(0.907031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.0000 | 0.639203 | ||||||||
\(980\) | 1.00000 | − | 2.00000i | 0.0319438 | − | 0.0638877i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 42.0000i | − | 1.34027i | ||||||
\(983\) | 12.0000i | 0.382741i | 0.981518 | + | 0.191370i | \(0.0612931\pi\) | ||||
−0.981518 | + | 0.191370i | \(0.938707\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.0000 | + | 6.00000i | 0.382352 | + | 0.191176i | ||||
\(986\) | 48.0000 | 1.52863 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000i | 0.127257i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −60.0000 | −1.90596 | −0.952981 | − | 0.303029i | \(-0.902002\pi\) | ||||
−0.952981 | + | 0.303029i | \(0.902002\pi\) | |||||||
\(992\) | − | 6.00000i | − | 0.190500i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.0000 | 0.444053 | ||||||||
\(995\) | 26.0000 | − | 52.0000i | 0.824255 | − | 1.64851i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 38.0000i | − | 1.20347i | −0.798695 | − | 0.601736i | \(-0.794476\pi\) | ||
0.798695 | − | 0.601736i | \(-0.205524\pi\) | |||||||
\(998\) | − | 28.0000i | − | 0.886325i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 630.2.g.d.379.1 | 2 | ||
3.2 | odd | 2 | 210.2.g.a.169.2 | yes | 2 | ||
4.3 | odd | 2 | 5040.2.t.k.1009.1 | 2 | |||
5.2 | odd | 4 | 3150.2.a.be.1.1 | 1 | |||
5.3 | odd | 4 | 3150.2.a.q.1.1 | 1 | |||
5.4 | even | 2 | inner | 630.2.g.d.379.2 | 2 | ||
12.11 | even | 2 | 1680.2.t.d.1009.1 | 2 | |||
15.2 | even | 4 | 1050.2.a.g.1.1 | 1 | |||
15.8 | even | 4 | 1050.2.a.m.1.1 | 1 | |||
15.14 | odd | 2 | 210.2.g.a.169.1 | ✓ | 2 | ||
20.19 | odd | 2 | 5040.2.t.k.1009.2 | 2 | |||
21.2 | odd | 6 | 1470.2.n.g.949.2 | 4 | |||
21.5 | even | 6 | 1470.2.n.c.949.2 | 4 | |||
21.11 | odd | 6 | 1470.2.n.g.79.1 | 4 | |||
21.17 | even | 6 | 1470.2.n.c.79.1 | 4 | |||
21.20 | even | 2 | 1470.2.g.e.589.2 | 2 | |||
60.23 | odd | 4 | 8400.2.a.ca.1.1 | 1 | |||
60.47 | odd | 4 | 8400.2.a.bd.1.1 | 1 | |||
60.59 | even | 2 | 1680.2.t.d.1009.2 | 2 | |||
105.44 | odd | 6 | 1470.2.n.g.949.1 | 4 | |||
105.59 | even | 6 | 1470.2.n.c.79.2 | 4 | |||
105.62 | odd | 4 | 7350.2.a.g.1.1 | 1 | |||
105.74 | odd | 6 | 1470.2.n.g.79.2 | 4 | |||
105.83 | odd | 4 | 7350.2.a.co.1.1 | 1 | |||
105.89 | even | 6 | 1470.2.n.c.949.1 | 4 | |||
105.104 | even | 2 | 1470.2.g.e.589.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.g.a.169.1 | ✓ | 2 | 15.14 | odd | 2 | ||
210.2.g.a.169.2 | yes | 2 | 3.2 | odd | 2 | ||
630.2.g.d.379.1 | 2 | 1.1 | even | 1 | trivial | ||
630.2.g.d.379.2 | 2 | 5.4 | even | 2 | inner | ||
1050.2.a.g.1.1 | 1 | 15.2 | even | 4 | |||
1050.2.a.m.1.1 | 1 | 15.8 | even | 4 | |||
1470.2.g.e.589.1 | 2 | 105.104 | even | 2 | |||
1470.2.g.e.589.2 | 2 | 21.20 | even | 2 | |||
1470.2.n.c.79.1 | 4 | 21.17 | even | 6 | |||
1470.2.n.c.79.2 | 4 | 105.59 | even | 6 | |||
1470.2.n.c.949.1 | 4 | 105.89 | even | 6 | |||
1470.2.n.c.949.2 | 4 | 21.5 | even | 6 | |||
1470.2.n.g.79.1 | 4 | 21.11 | odd | 6 | |||
1470.2.n.g.79.2 | 4 | 105.74 | odd | 6 | |||
1470.2.n.g.949.1 | 4 | 105.44 | odd | 6 | |||
1470.2.n.g.949.2 | 4 | 21.2 | odd | 6 | |||
1680.2.t.d.1009.1 | 2 | 12.11 | even | 2 | |||
1680.2.t.d.1009.2 | 2 | 60.59 | even | 2 | |||
3150.2.a.q.1.1 | 1 | 5.3 | odd | 4 | |||
3150.2.a.be.1.1 | 1 | 5.2 | odd | 4 | |||
5040.2.t.k.1009.1 | 2 | 4.3 | odd | 2 | |||
5040.2.t.k.1009.2 | 2 | 20.19 | odd | 2 | |||
7350.2.a.g.1.1 | 1 | 105.62 | odd | 4 | |||
7350.2.a.co.1.1 | 1 | 105.83 | odd | 4 | |||
8400.2.a.bd.1.1 | 1 | 60.47 | odd | 4 | |||
8400.2.a.ca.1.1 | 1 | 60.23 | odd | 4 |