Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7569,2,Mod(1,7569)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7569, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7569.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7569 = 3^{2} \cdot 29^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7569.a (trivial) |
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: | yes |
Analytic conductor: | \(60.4387692899\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 261) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7569.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.61803 | 1.14412 | 0.572061 | − | 0.820211i | \(-0.306144\pi\) | ||||
0.572061 | + | 0.820211i | \(0.306144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.618034 | 0.309017 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.23607 | 0.845154 | 0.422577 | − | 0.906327i | \(-0.361126\pi\) | ||||
0.422577 | + | 0.906327i | \(0.361126\pi\) | |||||||
\(8\) | −2.23607 | −0.790569 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.23607 | −1.02333 | ||||||||
\(11\) | 1.76393 | 0.531846 | 0.265923 | − | 0.963994i | \(-0.414323\pi\) | ||||
0.265923 | + | 0.963994i | \(0.414323\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.47214 | −1.51770 | −0.758849 | − | 0.651267i | \(-0.774238\pi\) | ||||
−0.758849 | + | 0.651267i | \(0.774238\pi\) | |||||||
\(14\) | 3.61803 | 0.966960 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.85410 | −1.21353 | ||||||||
\(17\) | 5.47214 | 1.32719 | 0.663594 | − | 0.748093i | \(-0.269030\pi\) | ||||
0.663594 | + | 0.748093i | \(0.269030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −1.23607 | −0.276393 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.85410 | 0.608497 | ||||||||
\(23\) | 0.472136 | 0.0984472 | 0.0492236 | − | 0.998788i | \(-0.484325\pi\) | ||||
0.0492236 | + | 0.998788i | \(0.484325\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −8.85410 | −1.73643 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.38197 | 0.261167 | ||||||||
\(29\) | 0 | 0 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.94427 | 1.60644 | 0.803219 | − | 0.595683i | \(-0.203119\pi\) | ||||
0.803219 | + | 0.595683i | \(0.203119\pi\) | |||||||
\(32\) | −3.38197 | −0.597853 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.85410 | 1.51847 | ||||||||
\(35\) | −4.47214 | −0.755929 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.47214 | 0.707107 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.472136 | −0.0720001 | −0.0360000 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360000 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(44\) | 1.09017 | 0.164349 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.763932 | 0.112636 | ||||||||
\(47\) | −8.70820 | −1.27022 | −0.635111 | − | 0.772421i | \(-0.719046\pi\) | ||||
−0.635111 | + | 0.772421i | \(0.719046\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.00000 | −0.285714 | ||||||||
\(50\) | −1.61803 | −0.228825 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.38197 | −0.468994 | ||||||||
\(53\) | 8.00000 | 1.09888 | 0.549442 | − | 0.835532i | \(-0.314840\pi\) | ||||
0.549442 | + | 0.835532i | \(0.314840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.52786 | −0.475697 | ||||||||
\(56\) | −5.00000 | −0.668153 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.4721 | −1.62373 | −0.811867 | − | 0.583843i | \(-0.801549\pi\) | ||||
−0.811867 | + | 0.583843i | \(0.801549\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.94427 | −0.889123 | −0.444561 | − | 0.895748i | \(-0.646640\pi\) | ||||
−0.444561 | + | 0.895748i | \(0.646640\pi\) | |||||||
\(62\) | 14.4721 | 1.83796 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.23607 | 0.529508 | ||||||||
\(65\) | 10.9443 | 1.35747 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.23607 | 1.00620 | 0.503098 | − | 0.864229i | \(-0.332194\pi\) | ||||
0.503098 | + | 0.864229i | \(0.332194\pi\) | |||||||
\(68\) | 3.38197 | 0.410124 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.23607 | −0.864876 | ||||||||
\(71\) | −8.94427 | −1.06149 | −0.530745 | − | 0.847532i | \(-0.678088\pi\) | ||||
−0.530745 | + | 0.847532i | \(0.678088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 6.47214 | 0.752371 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.94427 | 0.449492 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.4721 | −1.40322 | −0.701612 | − | 0.712559i | \(-0.747536\pi\) | ||||
−0.701612 | + | 0.712559i | \(0.747536\pi\) | |||||||
\(80\) | 9.70820 | 1.08541 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.23607 | −0.357364 | ||||||||
\(83\) | −16.9443 | −1.85988 | −0.929938 | − | 0.367717i | \(-0.880140\pi\) | ||||
−0.929938 | + | 0.367717i | \(0.880140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.9443 | −1.18707 | ||||||||
\(86\) | −0.763932 | −0.0823769 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.94427 | −0.420461 | ||||||||
\(89\) | −14.4164 | −1.52814 | −0.764068 | − | 0.645136i | \(-0.776801\pi\) | ||||
−0.764068 | + | 0.645136i | \(0.776801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.2361 | −1.28269 | ||||||||
\(92\) | 0.291796 | 0.0304218 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.0902 | −1.45329 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | −3.23607 | −0.326892 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.618034 | −0.0618034 | ||||||||
\(101\) | 15.9443 | 1.58651 | 0.793257 | − | 0.608887i | \(-0.208384\pi\) | ||||
0.793257 | + | 0.608887i | \(0.208384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.944272 | 0.0930419 | 0.0465209 | − | 0.998917i | \(-0.485187\pi\) | ||||
0.0465209 | + | 0.998917i | \(0.485187\pi\) | |||||||
\(104\) | 12.2361 | 1.19985 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.9443 | 1.25726 | ||||||||
\(107\) | 4.47214 | 0.432338 | 0.216169 | − | 0.976356i | \(-0.430644\pi\) | ||||
0.216169 | + | 0.976356i | \(0.430644\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.4721 | −1.48196 | −0.740981 | − | 0.671526i | \(-0.765639\pi\) | ||||
−0.740981 | + | 0.671526i | \(0.765639\pi\) | |||||||
\(110\) | −5.70820 | −0.544256 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.8541 | −1.02562 | ||||||||
\(113\) | −3.47214 | −0.326631 | −0.163316 | − | 0.986574i | \(-0.552219\pi\) | ||||
−0.163316 | + | 0.986574i | \(0.552219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.944272 | −0.0880538 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −20.1803 | −1.85775 | ||||||||
\(119\) | 12.2361 | 1.12168 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.88854 | −0.717140 | ||||||||
\(122\) | −11.2361 | −1.01727 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.52786 | 0.496417 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.9443 | −1.50356 | −0.751780 | − | 0.659413i | \(-0.770805\pi\) | ||||
−0.751780 | + | 0.659413i | \(0.770805\pi\) | |||||||
\(128\) | 13.6180 | 1.20368 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 17.7082 | 1.55311 | ||||||||
\(131\) | 13.7639 | 1.20256 | 0.601280 | − | 0.799038i | \(-0.294658\pi\) | ||||
0.601280 | + | 0.799038i | \(0.294658\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 13.3262 | 1.15121 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.2361 | −1.04923 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.29180 | −0.279206 | −0.139603 | − | 0.990208i | \(-0.544583\pi\) | ||||
−0.139603 | + | 0.990208i | \(0.544583\pi\) | |||||||
\(140\) | −2.76393 | −0.233595 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.4721 | −1.21447 | ||||||||
\(143\) | −9.65248 | −0.807181 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.23607 | 0.267819 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.47214 | 0.203208 | ||||||||
\(149\) | 13.8885 | 1.13779 | 0.568897 | − | 0.822409i | \(-0.307370\pi\) | ||||
0.568897 | + | 0.822409i | \(0.307370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94427 | −0.727875 | −0.363937 | − | 0.931423i | \(-0.618568\pi\) | ||||
−0.363937 | + | 0.931423i | \(0.618568\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.38197 | 0.514273 | ||||||||
\(155\) | −17.8885 | −1.43684 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.0000 | −0.957704 | −0.478852 | − | 0.877896i | \(-0.658947\pi\) | ||||
−0.478852 | + | 0.877896i | \(0.658947\pi\) | |||||||
\(158\) | −20.1803 | −1.60546 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.76393 | 0.534736 | ||||||||
\(161\) | 1.05573 | 0.0832030 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.47214 | 0.663589 | 0.331794 | − | 0.943352i | \(-0.392346\pi\) | ||||
0.331794 | + | 0.943352i | \(0.392346\pi\) | |||||||
\(164\) | −1.23607 | −0.0965207 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −27.4164 | −2.12793 | ||||||||
\(167\) | 7.52786 | 0.582524 | 0.291262 | − | 0.956643i | \(-0.405925\pi\) | ||||
0.291262 | + | 0.956643i | \(0.405925\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.9443 | 1.30341 | ||||||||
\(170\) | −17.7082 | −1.35816 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.291796 | −0.0222492 | ||||||||
\(173\) | −23.8885 | −1.81621 | −0.908106 | − | 0.418740i | \(-0.862472\pi\) | ||||
−0.908106 | + | 0.418740i | \(0.862472\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.23607 | −0.169031 | ||||||||
\(176\) | −8.56231 | −0.645408 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −23.3262 | −1.74838 | ||||||||
\(179\) | −21.4164 | −1.60074 | −0.800369 | − | 0.599508i | \(-0.795363\pi\) | ||||
−0.800369 | + | 0.599508i | \(0.795363\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.52786 | −0.336553 | −0.168277 | − | 0.985740i | \(-0.553820\pi\) | ||||
−0.168277 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(182\) | −19.7984 | −1.46755 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.05573 | −0.0778293 | ||||||||
\(185\) | −8.00000 | −0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.65248 | 0.705859 | ||||||||
\(188\) | −5.38197 | −0.392520 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8885 | 1.00494 | 0.502470 | − | 0.864595i | \(-0.332425\pi\) | ||||
0.502470 | + | 0.864595i | \(0.332425\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.8885 | −1.57557 | −0.787786 | − | 0.615949i | \(-0.788773\pi\) | ||||
−0.787786 | + | 0.615949i | \(0.788773\pi\) | |||||||
\(194\) | −12.9443 | −0.929345 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.23607 | −0.0882906 | ||||||||
\(197\) | 16.0000 | 1.13995 | 0.569976 | − | 0.821661i | \(-0.306952\pi\) | ||||
0.569976 | + | 0.821661i | \(0.306952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.70820 | 0.191979 | 0.0959897 | − | 0.995382i | \(-0.469398\pi\) | ||||
0.0959897 | + | 0.995382i | \(0.469398\pi\) | |||||||
\(200\) | 2.23607 | 0.158114 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 25.7984 | 1.81517 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | 0.279372 | ||||||||
\(206\) | 1.52786 | 0.106451 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 26.5623 | 1.84176 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.9443 | 1.71723 | 0.858617 | − | 0.512617i | \(-0.171324\pi\) | ||||
0.858617 | + | 0.512617i | \(0.171324\pi\) | |||||||
\(212\) | 4.94427 | 0.339574 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.23607 | 0.494647 | ||||||||
\(215\) | 0.944272 | 0.0643988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.0000 | 1.35769 | ||||||||
\(218\) | −25.0344 | −1.69555 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.18034 | −0.146998 | ||||||||
\(221\) | −29.9443 | −2.01427 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.2361 | −0.953318 | −0.476659 | − | 0.879088i | \(-0.658152\pi\) | ||||
−0.476659 | + | 0.879088i | \(0.658152\pi\) | |||||||
\(224\) | −7.56231 | −0.505278 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.61803 | −0.373706 | ||||||||
\(227\) | 8.94427 | 0.593652 | 0.296826 | − | 0.954932i | \(-0.404072\pi\) | ||||
0.296826 | + | 0.954932i | \(0.404072\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.0000 | −1.58596 | −0.792982 | − | 0.609245i | \(-0.791473\pi\) | ||||
−0.792982 | + | 0.609245i | \(0.791473\pi\) | |||||||
\(230\) | −1.52786 | −0.100744 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.9443 | 1.50313 | 0.751565 | − | 0.659659i | \(-0.229299\pi\) | ||||
0.751565 | + | 0.659659i | \(0.229299\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.4164 | 1.13612 | ||||||||
\(236\) | −7.70820 | −0.501761 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 19.7984 | 1.28334 | ||||||||
\(239\) | 16.9443 | 1.09603 | 0.548017 | − | 0.836467i | \(-0.315383\pi\) | ||||
0.548017 | + | 0.836467i | \(0.315383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.88854 | −0.443730 | −0.221865 | − | 0.975077i | \(-0.571214\pi\) | ||||
−0.221865 | + | 0.975077i | \(0.571214\pi\) | |||||||
\(242\) | −12.7639 | −0.820497 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.29180 | −0.274754 | ||||||||
\(245\) | 4.00000 | 0.255551 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −20.0000 | −1.27000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.4164 | 1.22800 | ||||||||
\(251\) | 13.7639 | 0.868772 | 0.434386 | − | 0.900727i | \(-0.356965\pi\) | ||||
0.434386 | + | 0.900727i | \(0.356965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.832816 | 0.0523587 | ||||||||
\(254\) | −27.4164 | −1.72026 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.5623 | 0.847644 | ||||||||
\(257\) | −5.88854 | −0.367317 | −0.183659 | − | 0.982990i | \(-0.558794\pi\) | ||||
−0.183659 | + | 0.982990i | \(0.558794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.94427 | 0.555770 | ||||||||
\(260\) | 6.76393 | 0.419481 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 22.2705 | 1.37588 | ||||||||
\(263\) | −20.0000 | −1.23325 | −0.616626 | − | 0.787256i | \(-0.711501\pi\) | ||||
−0.616626 | + | 0.787256i | \(0.711501\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.0000 | −0.982872 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.09017 | 0.310932 | ||||||||
\(269\) | 3.00000 | 0.182913 | 0.0914566 | − | 0.995809i | \(-0.470848\pi\) | ||||
0.0914566 | + | 0.995809i | \(0.470848\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.4721 | −1.24359 | −0.621797 | − | 0.783179i | \(-0.713597\pi\) | ||||
−0.621797 | + | 0.783179i | \(0.713597\pi\) | |||||||
\(272\) | −26.5623 | −1.61058 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.70820 | −0.586494 | ||||||||
\(275\) | −1.76393 | −0.106369 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −31.4721 | −1.89098 | −0.945489 | − | 0.325655i | \(-0.894415\pi\) | ||||
−0.945489 | + | 0.325655i | \(0.894415\pi\) | |||||||
\(278\) | −5.32624 | −0.319447 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.0000 | 0.597614 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.05573 | −0.181644 | −0.0908221 | − | 0.995867i | \(-0.528949\pi\) | ||||
−0.0908221 | + | 0.995867i | \(0.528949\pi\) | |||||||
\(284\) | −5.52786 | −0.328018 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.6180 | −0.923514 | ||||||||
\(287\) | −4.47214 | −0.263982 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.9443 | 0.761428 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.23607 | 0.0723354 | ||||||||
\(293\) | −10.0557 | −0.587462 | −0.293731 | − | 0.955888i | \(-0.594897\pi\) | ||||
−0.293731 | + | 0.955888i | \(0.594897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.9443 | 1.45231 | ||||||||
\(296\) | −8.94427 | −0.519875 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.4721 | 1.30178 | ||||||||
\(299\) | −2.58359 | −0.149413 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.05573 | −0.0608512 | ||||||||
\(302\) | −14.4721 | −0.832778 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.8885 | 0.795256 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.88854 | 0.564369 | 0.282185 | − | 0.959360i | \(-0.408941\pi\) | ||||
0.282185 | + | 0.959360i | \(0.408941\pi\) | |||||||
\(308\) | 2.43769 | 0.138901 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.9443 | −1.64392 | ||||||||
\(311\) | 4.23607 | 0.240205 | 0.120103 | − | 0.992761i | \(-0.461678\pi\) | ||||
0.120103 | + | 0.992761i | \(0.461678\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.9443 | −1.12732 | −0.563658 | − | 0.826008i | \(-0.690607\pi\) | ||||
−0.563658 | + | 0.826008i | \(0.690607\pi\) | |||||||
\(314\) | −19.4164 | −1.09573 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.70820 | −0.433620 | ||||||||
\(317\) | −3.00000 | −0.168497 | −0.0842484 | − | 0.996445i | \(-0.526849\pi\) | ||||
−0.0842484 | + | 0.996445i | \(0.526849\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −8.47214 | −0.473607 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.70820 | 0.0951945 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.47214 | 0.303539 | ||||||||
\(326\) | 13.7082 | 0.759227 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.47214 | 0.246932 | ||||||||
\(329\) | −19.4721 | −1.07353 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.944272 | 0.0519019 | 0.0259509 | − | 0.999663i | \(-0.491739\pi\) | ||||
0.0259509 | + | 0.999663i | \(0.491739\pi\) | |||||||
\(332\) | −10.4721 | −0.574733 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1803 | 0.666479 | ||||||||
\(335\) | −16.4721 | −0.899969 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.88854 | −0.429716 | −0.214858 | − | 0.976645i | \(-0.568929\pi\) | ||||
−0.214858 | + | 0.976645i | \(0.568929\pi\) | |||||||
\(338\) | 27.4164 | 1.49126 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.76393 | −0.366826 | ||||||||
\(341\) | 15.7771 | 0.854377 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1246 | −1.08663 | ||||||||
\(344\) | 1.05573 | 0.0569210 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.6525 | −2.07797 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.8885 | 1.27872 | 0.639362 | − | 0.768906i | \(-0.279198\pi\) | ||||
0.639362 | + | 0.768906i | \(0.279198\pi\) | |||||||
\(350\) | −3.61803 | −0.193392 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.96556 | −0.317965 | ||||||||
\(353\) | −28.0000 | −1.49029 | −0.745145 | − | 0.666903i | \(-0.767620\pi\) | ||||
−0.745145 | + | 0.666903i | \(0.767620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.8885 | 0.949425 | ||||||||
\(356\) | −8.90983 | −0.472220 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −34.6525 | −1.83144 | ||||||||
\(359\) | 28.9443 | 1.52762 | 0.763810 | − | 0.645441i | \(-0.223326\pi\) | ||||
0.763810 | + | 0.645441i | \(0.223326\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | −7.32624 | −0.385059 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.56231 | −0.396373 | ||||||||
\(365\) | −4.00000 | −0.209370 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.4164 | 0.700331 | 0.350165 | − | 0.936688i | \(-0.386125\pi\) | ||||
0.350165 | + | 0.936688i | \(0.386125\pi\) | |||||||
\(368\) | −2.29180 | −0.119468 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −12.9443 | −0.672941 | ||||||||
\(371\) | 17.8885 | 0.928727 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.8885 | −1.23690 | −0.618451 | − | 0.785823i | \(-0.712239\pi\) | ||||
−0.618451 | + | 0.785823i | \(0.712239\pi\) | |||||||
\(374\) | 15.6180 | 0.807589 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.4721 | 1.00420 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.4164 | −0.894621 | −0.447310 | − | 0.894379i | \(-0.647618\pi\) | ||||
−0.447310 | + | 0.894379i | \(0.647618\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 22.4721 | 1.14977 | ||||||||
\(383\) | −1.41641 | −0.0723751 | −0.0361875 | − | 0.999345i | \(-0.511521\pi\) | ||||
−0.0361875 | + | 0.999345i | \(0.511521\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.88854 | −0.402037 | ||||||||
\(386\) | −35.4164 | −1.80265 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.94427 | −0.251007 | ||||||||
\(389\) | 5.00000 | 0.253510 | 0.126755 | − | 0.991934i | \(-0.459544\pi\) | ||||
0.126755 | + | 0.991934i | \(0.459544\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.58359 | 0.130658 | ||||||||
\(392\) | 4.47214 | 0.225877 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.8885 | 1.30425 | ||||||||
\(395\) | 24.9443 | 1.25508 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.8885 | 1.39969 | 0.699843 | − | 0.714297i | \(-0.253253\pi\) | ||||
0.699843 | + | 0.714297i | \(0.253253\pi\) | |||||||
\(398\) | 4.38197 | 0.219648 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.85410 | 0.242705 | ||||||||
\(401\) | −17.0557 | −0.851722 | −0.425861 | − | 0.904789i | \(-0.640029\pi\) | ||||
−0.425861 | + | 0.904789i | \(0.640029\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.9443 | −2.43809 | ||||||||
\(404\) | 9.85410 | 0.490260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.05573 | 0.349739 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.00000 | 0.395575 | 0.197787 | − | 0.980245i | \(-0.436624\pi\) | ||||
0.197787 | + | 0.980245i | \(0.436624\pi\) | |||||||
\(410\) | 6.47214 | 0.319636 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.583592 | 0.0287515 | ||||||||
\(413\) | −27.8885 | −1.37231 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.8885 | 1.66352 | ||||||||
\(416\) | 18.5066 | 0.907360 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5836 | −0.517042 | −0.258521 | − | 0.966006i | \(-0.583235\pi\) | ||||
−0.258521 | + | 0.966006i | \(0.583235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.05573 | 0.441349 | 0.220675 | − | 0.975347i | \(-0.429174\pi\) | ||||
0.220675 | + | 0.975347i | \(0.429174\pi\) | |||||||
\(422\) | 40.3607 | 1.96473 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.8885 | −0.868744 | ||||||||
\(425\) | −5.47214 | −0.265438 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.5279 | −0.751446 | ||||||||
\(428\) | 2.76393 | 0.133600 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.52786 | 0.0736801 | ||||||||
\(431\) | 35.3050 | 1.70058 | 0.850290 | − | 0.526315i | \(-0.176427\pi\) | ||||
0.850290 | + | 0.526315i | \(0.176427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.8885 | 0.763555 | 0.381777 | − | 0.924254i | \(-0.375312\pi\) | ||||
0.381777 | + | 0.924254i | \(0.375312\pi\) | |||||||
\(434\) | 32.3607 | 1.55336 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.56231 | −0.457951 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.65248 | 0.174323 | 0.0871616 | − | 0.996194i | \(-0.472220\pi\) | ||||
0.0871616 | + | 0.996194i | \(0.472220\pi\) | |||||||
\(440\) | 7.88854 | 0.376072 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −48.4508 | −2.30457 | ||||||||
\(443\) | 26.2361 | 1.24651 | 0.623257 | − | 0.782017i | \(-0.285809\pi\) | ||||
0.623257 | + | 0.782017i | \(0.285809\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.8328 | 1.36681 | ||||||||
\(446\) | −23.0344 | −1.09071 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.47214 | 0.447516 | ||||||||
\(449\) | 22.4164 | 1.05790 | 0.528948 | − | 0.848654i | \(-0.322587\pi\) | ||||
0.528948 | + | 0.848654i | \(0.322587\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.52786 | −0.166121 | ||||||||
\(452\) | −2.14590 | −0.100935 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 14.4721 | 0.679211 | ||||||||
\(455\) | 24.4721 | 1.14727 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.0000 | −0.701670 | −0.350835 | − | 0.936437i | \(-0.614102\pi\) | ||||
−0.350835 | + | 0.936437i | \(0.614102\pi\) | |||||||
\(458\) | −38.8328 | −1.81454 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.583592 | −0.0272101 | ||||||||
\(461\) | −10.0000 | −0.465746 | −0.232873 | − | 0.972507i | \(-0.574813\pi\) | ||||
−0.232873 | + | 0.972507i | \(0.574813\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.1246 | −0.749374 | −0.374687 | − | 0.927151i | \(-0.622250\pi\) | ||||
−0.374687 | + | 0.927151i | \(0.622250\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 37.1246 | 1.71976 | ||||||||
\(467\) | 41.8885 | 1.93837 | 0.969185 | − | 0.246333i | \(-0.0792256\pi\) | ||||
0.969185 | + | 0.246333i | \(0.0792256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.4164 | 0.850391 | ||||||||
\(470\) | 28.1803 | 1.29986 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 27.8885 | 1.28367 | ||||||||
\(473\) | −0.832816 | −0.0382929 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.56231 | 0.346618 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.4164 | 1.25400 | ||||||||
\(479\) | 20.9443 | 0.956968 | 0.478484 | − | 0.878096i | \(-0.341186\pi\) | ||||
0.478484 | + | 0.878096i | \(0.341186\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.8885 | −0.998032 | ||||||||
\(482\) | −11.1459 | −0.507682 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.87539 | −0.221609 | ||||||||
\(485\) | 16.0000 | 0.726523 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.8328 | −1.57843 | −0.789213 | − | 0.614120i | \(-0.789511\pi\) | ||||
−0.789213 | + | 0.614120i | \(0.789511\pi\) | |||||||
\(488\) | 15.5279 | 0.702913 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.47214 | 0.292381 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −43.4164 | −1.94945 | ||||||||
\(497\) | −20.0000 | −0.897123 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.29180 | −0.147361 | −0.0736805 | − | 0.997282i | \(-0.523475\pi\) | ||||
−0.0736805 | + | 0.997282i | \(0.523475\pi\) | |||||||
\(500\) | 7.41641 | 0.331672 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 22.2705 | 0.993981 | ||||||||
\(503\) | −8.70820 | −0.388280 | −0.194140 | − | 0.980974i | \(-0.562192\pi\) | ||||
−0.194140 | + | 0.980974i | \(0.562192\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.8885 | −1.41902 | ||||||||
\(506\) | 1.34752 | 0.0599048 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.4721 | −0.464626 | ||||||||
\(509\) | −2.00000 | −0.0886484 | −0.0443242 | − | 0.999017i | \(-0.514113\pi\) | ||||
−0.0443242 | + | 0.999017i | \(0.514113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.47214 | 0.197836 | ||||||||
\(512\) | −5.29180 | −0.233867 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.52786 | −0.420256 | ||||||||
\(515\) | −1.88854 | −0.0832192 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.3607 | −0.675562 | ||||||||
\(518\) | 14.4721 | 0.635869 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.4721 | −1.07317 | ||||||||
\(521\) | −9.05573 | −0.396739 | −0.198369 | − | 0.980127i | \(-0.563565\pi\) | ||||
−0.198369 | + | 0.980127i | \(0.563565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.1803 | −1.10106 | −0.550530 | − | 0.834816i | \(-0.685574\pi\) | ||||
−0.550530 | + | 0.834816i | \(0.685574\pi\) | |||||||
\(524\) | 8.50658 | 0.371612 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −32.3607 | −1.41099 | ||||||||
\(527\) | 48.9443 | 2.13205 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7771 | −0.990308 | ||||||||
\(530\) | −25.8885 | −1.12453 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.9443 | 0.474049 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.94427 | −0.386695 | ||||||||
\(536\) | −18.4164 | −0.795468 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.85410 | 0.209275 | ||||||||
\(539\) | −3.52786 | −0.151956 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.9443 | −0.470531 | −0.235266 | − | 0.971931i | \(-0.575596\pi\) | ||||
−0.235266 | + | 0.971931i | \(0.575596\pi\) | |||||||
\(542\) | −33.1246 | −1.42282 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −18.5066 | −0.793463 | ||||||||
\(545\) | 30.9443 | 1.32551 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.5967 | 0.966167 | 0.483084 | − | 0.875574i | \(-0.339517\pi\) | ||||
0.483084 | + | 0.875574i | \(0.339517\pi\) | |||||||
\(548\) | −3.70820 | −0.158407 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.85410 | −0.121699 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.8885 | −1.18594 | ||||||||
\(554\) | −50.9230 | −2.16351 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.03444 | −0.0862796 | ||||||||
\(557\) | 5.88854 | 0.249506 | 0.124753 | − | 0.992188i | \(-0.460186\pi\) | ||||
0.124753 | + | 0.992188i | \(0.460186\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.58359 | 0.109274 | ||||||||
\(560\) | 21.7082 | 0.917339 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.5410 | −1.24501 | −0.622503 | − | 0.782618i | \(-0.713884\pi\) | ||||
−0.622503 | + | 0.782618i | \(0.713884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.94427 | 0.292148 | ||||||||
\(566\) | −4.94427 | −0.207823 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.0000 | 0.839181 | ||||||||
\(569\) | 3.47214 | 0.145560 | 0.0727798 | − | 0.997348i | \(-0.476813\pi\) | ||||
0.0727798 | + | 0.997348i | \(0.476813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.9443 | 0.541701 | 0.270850 | − | 0.962621i | \(-0.412695\pi\) | ||||
0.270850 | + | 0.962621i | \(0.412695\pi\) | |||||||
\(572\) | −5.96556 | −0.249433 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.23607 | −0.302028 | ||||||||
\(575\) | −0.472136 | −0.0196894 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.88854 | 0.161882 | 0.0809411 | − | 0.996719i | \(-0.474207\pi\) | ||||
0.0809411 | + | 0.996719i | \(0.474207\pi\) | |||||||
\(578\) | 20.9443 | 0.871167 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −37.8885 | −1.57188 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.1115 | 0.584437 | ||||||||
\(584\) | −4.47214 | −0.185058 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.2705 | −0.672129 | ||||||||
\(587\) | −6.36068 | −0.262533 | −0.131267 | − | 0.991347i | \(-0.541904\pi\) | ||||
−0.131267 | + | 0.991347i | \(0.541904\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 40.3607 | 1.66162 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.4164 | −0.798009 | ||||||||
\(593\) | 40.8328 | 1.67680 | 0.838401 | − | 0.545053i | \(-0.183491\pi\) | ||||
0.838401 | + | 0.545053i | \(0.183491\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.4721 | −1.00326 | ||||||||
\(596\) | 8.58359 | 0.351598 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.18034 | −0.170947 | ||||||||
\(599\) | −38.5967 | −1.57702 | −0.788510 | − | 0.615022i | \(-0.789147\pi\) | ||||
−0.788510 | + | 0.615022i | \(0.789147\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.8885 | −1.38234 | −0.691171 | − | 0.722691i | \(-0.742905\pi\) | ||||
−0.691171 | + | 0.722691i | \(0.742905\pi\) | |||||||
\(602\) | −1.70820 | −0.0696212 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.52786 | −0.224926 | ||||||||
\(605\) | 15.7771 | 0.641430 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 42.8328 | 1.73853 | 0.869265 | − | 0.494346i | \(-0.164592\pi\) | ||||
0.869265 | + | 0.494346i | \(0.164592\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.4721 | 0.909870 | ||||||||
\(611\) | 47.6525 | 1.92781 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.41641 | 0.178377 | 0.0891885 | − | 0.996015i | \(-0.471573\pi\) | ||||
0.0891885 | + | 0.996015i | \(0.471573\pi\) | |||||||
\(614\) | 16.0000 | 0.645707 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.81966 | −0.355354 | ||||||||
\(617\) | 41.7771 | 1.68188 | 0.840941 | − | 0.541127i | \(-0.182002\pi\) | ||||
0.840941 | + | 0.541127i | \(0.182002\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.4721 | −0.983618 | −0.491809 | − | 0.870703i | \(-0.663664\pi\) | ||||
−0.491809 | + | 0.870703i | \(0.663664\pi\) | |||||||
\(620\) | −11.0557 | −0.444009 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.85410 | 0.274824 | ||||||||
\(623\) | −32.2361 | −1.29151 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −32.2705 | −1.28979 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.41641 | −0.295947 | ||||||||
\(629\) | 21.8885 | 0.872753 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.6525 | 0.463878 | 0.231939 | − | 0.972730i | \(-0.425493\pi\) | ||||
0.231939 | + | 0.972730i | \(0.425493\pi\) | |||||||
\(632\) | 27.8885 | 1.10935 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.85410 | −0.192781 | ||||||||
\(635\) | 33.8885 | 1.34483 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.9443 | 0.433628 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −27.2361 | −1.07660 | ||||||||
\(641\) | −15.3607 | −0.606710 | −0.303355 | − | 0.952878i | \(-0.598107\pi\) | ||||
−0.303355 | + | 0.952878i | \(0.598107\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.7082 | −0.501163 | −0.250581 | − | 0.968096i | \(-0.580622\pi\) | ||||
−0.250581 | + | 0.968096i | \(0.580622\pi\) | |||||||
\(644\) | 0.652476 | 0.0257112 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.472136 | 0.0185616 | 0.00928079 | − | 0.999957i | \(-0.497046\pi\) | ||||
0.00928079 | + | 0.999957i | \(0.497046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.0000 | −0.863576 | ||||||||
\(650\) | 8.85410 | 0.347286 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.23607 | 0.205060 | ||||||||
\(653\) | −27.9443 | −1.09354 | −0.546772 | − | 0.837282i | \(-0.684144\pi\) | ||||
−0.546772 | + | 0.837282i | \(0.684144\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.5279 | −1.07560 | ||||||||
\(656\) | 9.70820 | 0.379042 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −31.5066 | −1.22825 | ||||||||
\(659\) | 33.0689 | 1.28818 | 0.644090 | − | 0.764949i | \(-0.277236\pi\) | ||||
0.644090 | + | 0.764949i | \(0.277236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.3050 | 1.02314 | 0.511572 | − | 0.859240i | \(-0.329063\pi\) | ||||
0.511572 | + | 0.859240i | \(0.329063\pi\) | |||||||
\(662\) | 1.52786 | 0.0593821 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 37.8885 | 1.47036 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 4.65248 | 0.180010 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.6525 | −1.02967 | ||||||||
\(671\) | −12.2492 | −0.472876 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.05573 | 0.156337 | 0.0781684 | − | 0.996940i | \(-0.475093\pi\) | ||||
0.0781684 | + | 0.996940i | \(0.475093\pi\) | |||||||
\(674\) | −12.7639 | −0.491648 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.4721 | 0.402774 | ||||||||
\(677\) | 35.0000 | 1.34516 | 0.672580 | − | 0.740025i | \(-0.265186\pi\) | ||||
0.672580 | + | 0.740025i | \(0.265186\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.8885 | −0.686499 | ||||||||
\(680\) | 24.4721 | 0.938464 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 25.5279 | 0.977512 | ||||||||
\(683\) | −16.0000 | −0.612223 | −0.306111 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306111 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | −32.5623 | −1.24323 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.29180 | 0.0873739 | ||||||||
\(689\) | −43.7771 | −1.66777 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.1246 | 0.993827 | 0.496914 | − | 0.867800i | \(-0.334467\pi\) | ||||
0.496914 | + | 0.867800i | \(0.334467\pi\) | |||||||
\(692\) | −14.7639 | −0.561240 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.58359 | 0.249730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.9443 | −0.414544 | ||||||||
\(698\) | 38.6525 | 1.46302 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.38197 | −0.0522334 | ||||||||
\(701\) | 6.11146 | 0.230827 | 0.115413 | − | 0.993318i | \(-0.463181\pi\) | ||||
0.115413 | + | 0.993318i | \(0.463181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 7.47214 | 0.281617 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.3050 | −1.70507 | ||||||||
\(707\) | 35.6525 | 1.34085 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.8885 | −1.34782 | −0.673911 | − | 0.738812i | \(-0.735387\pi\) | ||||
−0.673911 | + | 0.738812i | \(0.735387\pi\) | |||||||
\(710\) | 28.9443 | 1.08626 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32.2361 | 1.20810 | ||||||||
\(713\) | 4.22291 | 0.158149 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.3050 | 0.721964 | ||||||||
\(716\) | −13.2361 | −0.494655 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 46.8328 | 1.74779 | ||||||||
\(719\) | −16.4721 | −0.614307 | −0.307154 | − | 0.951660i | \(-0.599377\pi\) | ||||
−0.307154 | + | 0.951660i | \(0.599377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.11146 | 0.0786347 | ||||||||
\(722\) | −30.7426 | −1.14412 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.79837 | −0.104001 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.5279 | 0.427545 | 0.213772 | − | 0.976883i | \(-0.431425\pi\) | ||||
0.213772 | + | 0.976883i | \(0.431425\pi\) | |||||||
\(728\) | 27.3607 | 1.01405 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.47214 | −0.239544 | ||||||||
\(731\) | −2.58359 | −0.0955576 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.9443 | −0.699723 | −0.349861 | − | 0.936802i | \(-0.613771\pi\) | ||||
−0.349861 | + | 0.936802i | \(0.613771\pi\) | |||||||
\(734\) | 21.7082 | 0.801264 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.59675 | −0.0588569 | ||||||||
\(737\) | 14.5279 | 0.535141 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.9443 | 1.21187 | 0.605937 | − | 0.795512i | \(-0.292798\pi\) | ||||
0.605937 | + | 0.795512i | \(0.292798\pi\) | |||||||
\(740\) | −4.94427 | −0.181755 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.9443 | 1.06258 | ||||||||
\(743\) | −30.5967 | −1.12249 | −0.561243 | − | 0.827651i | \(-0.689677\pi\) | ||||
−0.561243 | + | 0.827651i | \(0.689677\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.7771 | −1.01767 | ||||||||
\(746\) | −38.6525 | −1.41517 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.96556 | 0.218122 | ||||||||
\(749\) | 10.0000 | 0.365392 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.944272 | 0.0344570 | 0.0172285 | − | 0.999852i | \(-0.494516\pi\) | ||||
0.0172285 | + | 0.999852i | \(0.494516\pi\) | |||||||
\(752\) | 42.2705 | 1.54145 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.8885 | 0.651031 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.8328 | 1.04795 | 0.523973 | − | 0.851735i | \(-0.324449\pi\) | ||||
0.523973 | + | 0.851735i | \(0.324449\pi\) | |||||||
\(758\) | −28.1803 | −1.02356 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.9443 | −1.41173 | −0.705864 | − | 0.708347i | \(-0.749441\pi\) | ||||
−0.705864 | + | 0.708347i | \(0.749441\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.5967 | −1.25249 | ||||||||
\(764\) | 8.58359 | 0.310543 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.29180 | −0.0828060 | ||||||||
\(767\) | 68.2492 | 2.46434 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.7771 | 1.29015 | 0.645077 | − | 0.764117i | \(-0.276825\pi\) | ||||
0.645077 | + | 0.764117i | \(0.276825\pi\) | |||||||
\(770\) | −12.7639 | −0.459980 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.5279 | −0.486878 | ||||||||
\(773\) | −10.0000 | −0.359675 | −0.179838 | − | 0.983696i | \(-0.557557\pi\) | ||||
−0.179838 | + | 0.983696i | \(0.557557\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.94427 | −0.321288 | ||||||||
\(776\) | 17.8885 | 0.642161 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.09017 | 0.290047 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.7771 | −0.564549 | ||||||||
\(782\) | 4.18034 | 0.149489 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.70820 | 0.346722 | ||||||||
\(785\) | 24.0000 | 0.856597 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.05573 | 0.108925 | 0.0544625 | − | 0.998516i | \(-0.482655\pi\) | ||||
0.0544625 | + | 0.998516i | \(0.482655\pi\) | |||||||
\(788\) | 9.88854 | 0.352265 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 40.3607 | 1.43597 | ||||||||
\(791\) | −7.76393 | −0.276054 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.0000 | 1.34942 | ||||||||
\(794\) | 45.1246 | 1.60141 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.67376 | 0.0593249 | ||||||||
\(797\) | −25.7771 | −0.913071 | −0.456536 | − | 0.889705i | \(-0.650910\pi\) | ||||
−0.456536 | + | 0.889705i | \(0.650910\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.6525 | −1.68582 | ||||||||
\(800\) | 3.38197 | 0.119571 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −27.5967 | −0.974475 | ||||||||
\(803\) | 3.52786 | 0.124496 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.11146 | −0.0744191 | ||||||||
\(806\) | −79.1935 | −2.78947 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −35.6525 | −1.25425 | ||||||||
\(809\) | 12.3050 | 0.432619 | 0.216310 | − | 0.976325i | \(-0.430598\pi\) | ||||
0.216310 | + | 0.976325i | \(0.430598\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.18034 | 0.0414473 | 0.0207237 | − | 0.999785i | \(-0.493403\pi\) | ||||
0.0207237 | + | 0.999785i | \(0.493403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.4164 | 0.400145 | ||||||||
\(815\) | −16.9443 | −0.593532 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 12.9443 | 0.452586 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.47214 | 0.0863307 | ||||||||
\(821\) | −28.0000 | −0.977207 | −0.488603 | − | 0.872506i | \(-0.662493\pi\) | ||||
−0.488603 | + | 0.872506i | \(0.662493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.3050 | 0.533497 | 0.266749 | − | 0.963766i | \(-0.414051\pi\) | ||||
0.266749 | + | 0.963766i | \(0.414051\pi\) | |||||||
\(824\) | −2.11146 | −0.0735561 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −45.1246 | −1.57009 | ||||||||
\(827\) | −9.88854 | −0.343858 | −0.171929 | − | 0.985109i | \(-0.555000\pi\) | ||||
−0.171929 | + | 0.985109i | \(0.555000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.9443 | −0.380110 | −0.190055 | − | 0.981773i | \(-0.560867\pi\) | ||||
−0.190055 | + | 0.981773i | \(0.560867\pi\) | |||||||
\(830\) | 54.8328 | 1.90327 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −23.1803 | −0.803634 | ||||||||
\(833\) | −10.9443 | −0.379197 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −15.0557 | −0.521025 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −17.1246 | −0.591560 | ||||||||
\(839\) | −6.81966 | −0.235441 | −0.117720 | − | 0.993047i | \(-0.537559\pi\) | ||||
−0.117720 | + | 0.993047i | \(0.537559\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0 | 0 | ||||||||
\(842\) | 14.6525 | 0.504958 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.4164 | 0.530655 | ||||||||
\(845\) | −33.8885 | −1.16580 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.6393 | −0.606094 | ||||||||
\(848\) | −38.8328 | −1.33352 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8.85410 | −0.303693 | ||||||||
\(851\) | 1.88854 | 0.0647384 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8328 | 1.12417 | 0.562087 | − | 0.827078i | \(-0.309999\pi\) | ||||
0.562087 | + | 0.827078i | \(0.309999\pi\) | |||||||
\(854\) | −25.1246 | −0.859747 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.0000 | −0.341793 | ||||||||
\(857\) | −5.88854 | −0.201149 | −0.100574 | − | 0.994930i | \(-0.532068\pi\) | ||||
−0.100574 | + | 0.994930i | \(0.532068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.2492 | 1.23681 | 0.618404 | − | 0.785861i | \(-0.287780\pi\) | ||||
0.618404 | + | 0.785861i | \(0.287780\pi\) | |||||||
\(860\) | 0.583592 | 0.0199003 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 57.1246 | 1.94567 | ||||||||
\(863\) | 49.8885 | 1.69823 | 0.849113 | − | 0.528211i | \(-0.177137\pi\) | ||||
0.849113 | + | 0.528211i | \(0.177137\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 47.7771 | 1.62447 | ||||||||
\(866\) | 25.7082 | 0.873600 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 12.3607 | 0.419549 | ||||||||
\(869\) | −22.0000 | −0.746299 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −45.0689 | −1.52710 | ||||||||
\(872\) | 34.5967 | 1.17159 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 26.8328 | 0.907115 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.8885 | 0.536518 | 0.268259 | − | 0.963347i | \(-0.413552\pi\) | ||||
0.268259 | + | 0.963347i | \(0.413552\pi\) | |||||||
\(878\) | 5.90983 | 0.199447 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 17.1246 | 0.577271 | ||||||||
\(881\) | 36.4164 | 1.22690 | 0.613450 | − | 0.789734i | \(-0.289781\pi\) | ||||
0.613450 | + | 0.789734i | \(0.289781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 46.8328 | 1.57605 | 0.788025 | − | 0.615643i | \(-0.211104\pi\) | ||||
0.788025 | + | 0.615643i | \(0.211104\pi\) | |||||||
\(884\) | −18.5066 | −0.622444 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 42.4508 | 1.42616 | ||||||||
\(887\) | −47.0689 | −1.58042 | −0.790209 | − | 0.612837i | \(-0.790028\pi\) | ||||
−0.790209 | + | 0.612837i | \(0.790028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.8885 | −1.27074 | ||||||||
\(890\) | 46.6525 | 1.56379 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.79837 | −0.294591 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 42.8328 | 1.43174 | ||||||||
\(896\) | 30.4508 | 1.01729 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 36.2705 | 1.21036 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.7771 | 1.45843 | ||||||||
\(902\) | −5.70820 | −0.190062 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.76393 | 0.258225 | ||||||||
\(905\) | 9.05573 | 0.301023 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.3607 | 0.344021 | 0.172010 | − | 0.985095i | \(-0.444974\pi\) | ||||
0.172010 | + | 0.985095i | \(0.444974\pi\) | |||||||
\(908\) | 5.52786 | 0.183449 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 39.5967 | 1.31262 | ||||||||
\(911\) | 1.18034 | 0.0391064 | 0.0195532 | − | 0.999809i | \(-0.493776\pi\) | ||||
0.0195532 | + | 0.999809i | \(0.493776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −29.8885 | −0.989166 | ||||||||
\(914\) | −24.2705 | −0.802797 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.8328 | −0.490090 | ||||||||
\(917\) | 30.7771 | 1.01635 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.6525 | 1.70386 | 0.851929 | − | 0.523657i | \(-0.175433\pi\) | ||||
0.851929 | + | 0.523657i | \(0.175433\pi\) | |||||||
\(920\) | 2.11146 | 0.0696126 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.1803 | −0.532871 | ||||||||
\(923\) | 48.9443 | 1.61102 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | −26.0902 | −0.857376 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.9443 | −0.490306 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 14.1803 | 0.464492 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 67.7771 | 2.21773 | ||||||||
\(935\) | −19.3050 | −0.631339 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.94427 | −0.194191 | −0.0970954 | − | 0.995275i | \(-0.530955\pi\) | ||||
−0.0970954 | + | 0.995275i | \(0.530955\pi\) | |||||||
\(938\) | 29.7984 | 0.972951 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.7639 | 0.351081 | ||||||||
\(941\) | 37.7771 | 1.23150 | 0.615749 | − | 0.787942i | \(-0.288854\pi\) | ||||
0.615749 | + | 0.787942i | \(0.288854\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.944272 | −0.0307497 | ||||||||
\(944\) | 60.5410 | 1.97044 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.34752 | −0.0438118 | ||||||||
\(947\) | −2.23607 | −0.0726624 | −0.0363312 | − | 0.999340i | \(-0.511567\pi\) | ||||
−0.0363312 | + | 0.999340i | \(0.511567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.9443 | −0.355266 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −27.3607 | −0.886765 | ||||||||
\(953\) | 54.9443 | 1.77982 | 0.889910 | − | 0.456137i | \(-0.150767\pi\) | ||||
0.889910 | + | 0.456137i | \(0.150767\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.7771 | −0.898845 | ||||||||
\(956\) | 10.4721 | 0.338693 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.8885 | 1.09489 | ||||||||
\(959\) | −13.4164 | −0.433238 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.0000 | 1.58065 | ||||||||
\(962\) | −35.4164 | −1.14187 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.25735 | −0.137120 | ||||||||
\(965\) | 43.7771 | 1.40923 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.8328 | −1.12015 | −0.560074 | − | 0.828443i | \(-0.689227\pi\) | ||||
−0.560074 | + | 0.828443i | \(0.689227\pi\) | |||||||
\(968\) | 17.6393 | 0.566949 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 25.8885 | 0.831231 | ||||||||
\(971\) | −0.944272 | −0.0303031 | −0.0151516 | − | 0.999885i | \(-0.504823\pi\) | ||||
−0.0151516 | + | 0.999885i | \(0.504823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.36068 | −0.235973 | ||||||||
\(974\) | −56.3607 | −1.80591 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33.7082 | 1.07897 | ||||||||
\(977\) | 17.8885 | 0.572305 | 0.286153 | − | 0.958184i | \(-0.407624\pi\) | ||||
0.286153 | + | 0.958184i | \(0.407624\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.4296 | −0.812732 | ||||||||
\(980\) | 2.47214 | 0.0789695 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −12.9443 | −0.413068 | ||||||||
\(983\) | −10.1115 | −0.322505 | −0.161253 | − | 0.986913i | \(-0.551553\pi\) | ||||
−0.161253 | + | 0.986913i | \(0.551553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −32.0000 | −1.01960 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.222912 | −0.00708820 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.7639 | −1.19961 | −0.599805 | − | 0.800146i | \(-0.704755\pi\) | ||||
−0.599805 | + | 0.800146i | \(0.704755\pi\) | |||||||
\(992\) | −30.2492 | −0.960414 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −32.3607 | −1.02642 | ||||||||
\(995\) | −5.41641 | −0.171712 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.8885 | −0.566536 | −0.283268 | − | 0.959041i | \(-0.591419\pi\) | ||||
−0.283268 | + | 0.959041i | \(0.591419\pi\) | |||||||
\(998\) | −5.32624 | −0.168599 | ||||||||
\(999\) | 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 | 7569.2.a.j.1.2 | 2 | ||
3.2 | odd | 2 | 7569.2.a.h.1.1 | 2 | |||
29.28 | even | 2 | 261.2.a.a.1.1 | ✓ | 2 | ||
87.86 | odd | 2 | 261.2.a.c.1.2 | yes | 2 | ||
116.115 | odd | 2 | 4176.2.a.bm.1.1 | 2 | |||
145.144 | even | 2 | 6525.2.a.z.1.2 | 2 | |||
348.347 | even | 2 | 4176.2.a.bt.1.1 | 2 | |||
435.434 | odd | 2 | 6525.2.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
261.2.a.a.1.1 | ✓ | 2 | 29.28 | even | 2 | ||
261.2.a.c.1.2 | yes | 2 | 87.86 | odd | 2 | ||
4176.2.a.bm.1.1 | 2 | 116.115 | odd | 2 | |||
4176.2.a.bt.1.1 | 2 | 348.347 | even | 2 | |||
6525.2.a.q.1.1 | 2 | 435.434 | odd | 2 | |||
6525.2.a.z.1.2 | 2 | 145.144 | even | 2 | |||
7569.2.a.h.1.1 | 2 | 3.2 | odd | 2 | |||
7569.2.a.j.1.2 | 2 | 1.1 | even | 1 | trivial |