Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,2,Mod(1,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, 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("1143.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.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: | \(9.12690095103\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 127) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.347296\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1143.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34730 | 0.952682 | 0.476341 | − | 0.879261i | \(-0.341963\pi\) | ||||
0.476341 | + | 0.879261i | \(0.341963\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.184793 | −0.0923963 | ||||||||
\(5\) | 3.53209 | 1.57960 | 0.789799 | − | 0.613366i | \(-0.210185\pi\) | ||||
0.789799 | + | 0.613366i | \(0.210185\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.53209 | −0.957040 | −0.478520 | − | 0.878077i | \(-0.658827\pi\) | ||||
−0.478520 | + | 0.878077i | \(0.658827\pi\) | |||||||
\(8\) | −2.94356 | −1.04071 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.75877 | 1.50486 | ||||||||
\(11\) | 2.57398 | 0.776084 | 0.388042 | − | 0.921642i | \(-0.373152\pi\) | ||||
0.388042 | + | 0.921642i | \(0.373152\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.94356 | 1.09375 | 0.546874 | − | 0.837215i | \(-0.315818\pi\) | ||||
0.546874 | + | 0.837215i | \(0.315818\pi\) | |||||||
\(14\) | −3.41147 | −0.911755 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.59627 | −0.899067 | ||||||||
\(17\) | 5.65270 | 1.37098 | 0.685491 | − | 0.728081i | \(-0.259588\pi\) | ||||
0.685491 | + | 0.728081i | \(0.259588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.532089 | −0.122070 | −0.0610348 | − | 0.998136i | \(-0.519440\pi\) | ||||
−0.0610348 | + | 0.998136i | \(0.519440\pi\) | |||||||
\(20\) | −0.652704 | −0.145949 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.46791 | 0.739361 | ||||||||
\(23\) | −0.411474 | −0.0857983 | −0.0428991 | − | 0.999079i | \(-0.513659\pi\) | ||||
−0.0428991 | + | 0.999079i | \(0.513659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.47565 | 1.49513 | ||||||||
\(26\) | 5.31315 | 1.04199 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.467911 | 0.0884269 | ||||||||
\(29\) | −0.162504 | −0.0301762 | −0.0150881 | − | 0.999886i | \(-0.504803\pi\) | ||||
−0.0150881 | + | 0.999886i | \(0.504803\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.29086 | 1.66869 | 0.834344 | − | 0.551244i | \(-0.185847\pi\) | ||||
0.834344 | + | 0.551244i | \(0.185847\pi\) | |||||||
\(32\) | 1.04189 | 0.184182 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.61587 | 1.30611 | ||||||||
\(35\) | −8.94356 | −1.51174 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.43376 | 0.893305 | 0.446653 | − | 0.894707i | \(-0.352616\pi\) | ||||
0.446653 | + | 0.894707i | \(0.352616\pi\) | |||||||
\(38\) | −0.716881 | −0.116294 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.3969 | −1.64390 | ||||||||
\(41\) | −3.51754 | −0.549348 | −0.274674 | − | 0.961537i | \(-0.588570\pi\) | ||||
−0.274674 | + | 0.961537i | \(0.588570\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1925 | −1.85934 | −0.929672 | − | 0.368388i | \(-0.879910\pi\) | ||||
−0.929672 | + | 0.368388i | \(0.879910\pi\) | |||||||
\(44\) | −0.475652 | −0.0717072 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.554378 | −0.0817385 | ||||||||
\(47\) | 6.14796 | 0.896772 | 0.448386 | − | 0.893840i | \(-0.351999\pi\) | ||||
0.448386 | + | 0.893840i | \(0.351999\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.588526 | −0.0840751 | ||||||||
\(50\) | 10.0719 | 1.42438 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.728741 | −0.101058 | ||||||||
\(53\) | 10.0719 | 1.38348 | 0.691742 | − | 0.722145i | \(-0.256843\pi\) | ||||
0.691742 | + | 0.722145i | \(0.256843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.09152 | 1.22590 | ||||||||
\(56\) | 7.45336 | 0.995998 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.218941 | −0.0287483 | ||||||||
\(59\) | −2.57398 | −0.335103 | −0.167552 | − | 0.985863i | \(-0.553586\pi\) | ||||
−0.167552 | + | 0.985863i | \(0.553586\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.9709 | −1.66075 | −0.830377 | − | 0.557202i | \(-0.811875\pi\) | ||||
−0.830377 | + | 0.557202i | \(0.811875\pi\) | |||||||
\(62\) | 12.5175 | 1.58973 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.59627 | 1.07453 | ||||||||
\(65\) | 13.9290 | 1.72768 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.532089 | 0.0650050 | 0.0325025 | − | 0.999472i | \(-0.489652\pi\) | ||||
0.0325025 | + | 0.999472i | \(0.489652\pi\) | |||||||
\(68\) | −1.04458 | −0.126674 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.0496 | −1.44021 | ||||||||
\(71\) | −6.84255 | −0.812061 | −0.406031 | − | 0.913859i | \(-0.633087\pi\) | ||||
−0.406031 | + | 0.913859i | \(0.633087\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.4192 | −1.21948 | −0.609738 | − | 0.792603i | \(-0.708726\pi\) | ||||
−0.609738 | + | 0.792603i | \(0.708726\pi\) | |||||||
\(74\) | 7.32089 | 0.851036 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0983261 | 0.0112788 | ||||||||
\(77\) | −6.51754 | −0.742743 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.568926 | 0.0640091 | 0.0320046 | − | 0.999488i | \(-0.489811\pi\) | ||||
0.0320046 | + | 0.999488i | \(0.489811\pi\) | |||||||
\(80\) | −12.7023 | −1.42016 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.73917 | −0.523354 | ||||||||
\(83\) | −15.4807 | −1.69923 | −0.849614 | − | 0.527405i | \(-0.823165\pi\) | ||||
−0.849614 | + | 0.527405i | \(0.823165\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.9659 | 2.16560 | ||||||||
\(86\) | −16.4270 | −1.77136 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −7.57667 | −0.807675 | ||||||||
\(89\) | 13.0223 | 1.38036 | 0.690180 | − | 0.723638i | \(-0.257531\pi\) | ||||
0.690180 | + | 0.723638i | \(0.257531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.98545 | −1.04676 | ||||||||
\(92\) | 0.0760373 | 0.00792744 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.28312 | 0.854338 | ||||||||
\(95\) | −1.87939 | −0.192821 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.2344 | −1.54682 | −0.773411 | − | 0.633905i | \(-0.781451\pi\) | ||||
−0.773411 | + | 0.633905i | \(0.781451\pi\) | |||||||
\(98\) | −0.792919 | −0.0800969 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.38144 | −0.138144 | ||||||||
\(101\) | 8.43107 | 0.838923 | 0.419462 | − | 0.907773i | \(-0.362219\pi\) | ||||
0.419462 | + | 0.907773i | \(0.362219\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.10607 | −0.306050 | −0.153025 | − | 0.988222i | \(-0.548901\pi\) | ||||
−0.153025 | + | 0.988222i | \(0.548901\pi\) | |||||||
\(104\) | −11.6081 | −1.13827 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.5699 | 1.31802 | ||||||||
\(107\) | −7.50980 | −0.726000 | −0.363000 | − | 0.931789i | \(-0.618247\pi\) | ||||
−0.363000 | + | 0.931789i | \(0.618247\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.4534 | 1.09703 | 0.548517 | − | 0.836140i | \(-0.315193\pi\) | ||||
0.548517 | + | 0.836140i | \(0.315193\pi\) | |||||||
\(110\) | 12.2490 | 1.16789 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 9.10607 | 0.860442 | ||||||||
\(113\) | 9.80066 | 0.921968 | 0.460984 | − | 0.887408i | \(-0.347496\pi\) | ||||
0.460984 | + | 0.887408i | \(0.347496\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.45336 | −0.135527 | ||||||||
\(116\) | 0.0300295 | 0.00278817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.46791 | −0.319247 | ||||||||
\(119\) | −14.3131 | −1.31208 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.37464 | −0.397694 | ||||||||
\(122\) | −17.4757 | −1.58217 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.71688 | −0.154181 | ||||||||
\(125\) | 8.74422 | 0.782107 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | 9.49794 | 0.839507 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 18.7665 | 1.64593 | ||||||||
\(131\) | −6.76146 | −0.590751 | −0.295376 | − | 0.955381i | \(-0.595445\pi\) | ||||
−0.295376 | + | 0.955381i | \(0.595445\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.34730 | 0.116825 | ||||||||
\(134\) | 0.716881 | 0.0619291 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.6391 | −1.42679 | ||||||||
\(137\) | 11.0000 | 0.939793 | 0.469897 | − | 0.882721i | \(-0.344291\pi\) | ||||
0.469897 | + | 0.882721i | \(0.344291\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.25671 | 0.785144 | 0.392572 | − | 0.919721i | \(-0.371585\pi\) | ||||
0.392572 | + | 0.919721i | \(0.371585\pi\) | |||||||
\(140\) | 1.65270 | 0.139679 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.21894 | −0.773636 | ||||||||
\(143\) | 10.1506 | 0.848840 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.573978 | −0.0476663 | ||||||||
\(146\) | −14.0378 | −1.16177 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00412 | −0.0825381 | ||||||||
\(149\) | −18.9632 | −1.55352 | −0.776761 | − | 0.629795i | \(-0.783139\pi\) | ||||
−0.776761 | + | 0.629795i | \(0.783139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0993 | 1.39152 | 0.695759 | − | 0.718275i | \(-0.255068\pi\) | ||||
0.695759 | + | 0.718275i | \(0.255068\pi\) | |||||||
\(152\) | 1.56624 | 0.127039 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.78106 | −0.707598 | ||||||||
\(155\) | 32.8161 | 2.63586 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.41921 | 0.272883 | 0.136442 | − | 0.990648i | \(-0.456433\pi\) | ||||
0.136442 | + | 0.990648i | \(0.456433\pi\) | |||||||
\(158\) | 0.766511 | 0.0609804 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.68004 | 0.290933 | ||||||||
\(161\) | 1.04189 | 0.0821124 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.453363 | 0.0355101 | 0.0177551 | − | 0.999842i | \(-0.494348\pi\) | ||||
0.0177551 | + | 0.999842i | \(0.494348\pi\) | |||||||
\(164\) | 0.650015 | 0.0507577 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.8571 | −1.61882 | ||||||||
\(167\) | 7.82295 | 0.605358 | 0.302679 | − | 0.953093i | \(-0.402119\pi\) | ||||
0.302679 | + | 0.953093i | \(0.402119\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.55169 | 0.196284 | ||||||||
\(170\) | 26.8999 | 2.06313 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.25309 | 0.171796 | ||||||||
\(173\) | −19.8580 | −1.50978 | −0.754889 | − | 0.655853i | \(-0.772309\pi\) | ||||
−0.754889 | + | 0.655853i | \(0.772309\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.9290 | −1.43090 | ||||||||
\(176\) | −9.25671 | −0.697751 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.5449 | 1.31504 | ||||||||
\(179\) | −11.8452 | −0.885355 | −0.442677 | − | 0.896681i | \(-0.645971\pi\) | ||||
−0.442677 | + | 0.896681i | \(0.645971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.47565 | 0.332673 | 0.166336 | − | 0.986069i | \(-0.446806\pi\) | ||||
0.166336 | + | 0.986069i | \(0.446806\pi\) | |||||||
\(182\) | −13.4534 | −0.997230 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.21120 | 0.0892909 | ||||||||
\(185\) | 19.1925 | 1.41106 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.5499 | 1.06400 | ||||||||
\(188\) | −1.13610 | −0.0828583 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.53209 | −0.183697 | ||||||||
\(191\) | −5.74422 | −0.415637 | −0.207819 | − | 0.978167i | \(-0.566636\pi\) | ||||
−0.207819 | + | 0.978167i | \(0.566636\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.91447 | −0.641677 | −0.320839 | − | 0.947134i | \(-0.603965\pi\) | ||||
−0.320839 | + | 0.947134i | \(0.603965\pi\) | |||||||
\(194\) | −20.5253 | −1.47363 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.108755 | 0.00776823 | ||||||||
\(197\) | −17.6236 | −1.25563 | −0.627815 | − | 0.778363i | \(-0.716051\pi\) | ||||
−0.627815 | + | 0.778363i | \(0.716051\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.1925 | −1.00608 | −0.503041 | − | 0.864263i | \(-0.667786\pi\) | ||||
−0.503041 | + | 0.864263i | \(0.667786\pi\) | |||||||
\(200\) | −22.0051 | −1.55599 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 11.3592 | 0.799227 | ||||||||
\(203\) | 0.411474 | 0.0288798 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.4243 | −0.867748 | ||||||||
\(206\) | −4.18479 | −0.291568 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −14.1821 | −0.983352 | ||||||||
\(209\) | −1.36959 | −0.0947362 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.4192 | −1.13035 | −0.565173 | − | 0.824973i | \(-0.691190\pi\) | ||||
−0.565173 | + | 0.824973i | \(0.691190\pi\) | |||||||
\(212\) | −1.86122 | −0.127829 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.1179 | −0.691647 | ||||||||
\(215\) | −43.0651 | −2.93702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −23.5253 | −1.59700 | ||||||||
\(218\) | 15.4311 | 1.04512 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.68004 | −0.113269 | ||||||||
\(221\) | 22.2918 | 1.49951 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −23.0283 | −1.54209 | −0.771044 | − | 0.636782i | \(-0.780265\pi\) | ||||
−0.771044 | + | 0.636782i | \(0.780265\pi\) | |||||||
\(224\) | −2.63816 | −0.176269 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.2044 | 0.878343 | ||||||||
\(227\) | 7.12061 | 0.472612 | 0.236306 | − | 0.971679i | \(-0.424063\pi\) | ||||
0.236306 | + | 0.971679i | \(0.424063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.34730 | −0.617687 | −0.308843 | − | 0.951113i | \(-0.599942\pi\) | ||||
−0.308843 | + | 0.951113i | \(0.599942\pi\) | |||||||
\(230\) | −1.95811 | −0.129114 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.478340 | 0.0314046 | ||||||||
\(233\) | 13.6800 | 0.896210 | 0.448105 | − | 0.893981i | \(-0.352099\pi\) | ||||
0.448105 | + | 0.893981i | \(0.352099\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.7151 | 1.41654 | ||||||||
\(236\) | 0.475652 | 0.0309623 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −19.2841 | −1.25000 | ||||||||
\(239\) | 16.4415 | 1.06351 | 0.531756 | − | 0.846897i | \(-0.321532\pi\) | ||||
0.531756 | + | 0.846897i | \(0.321532\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.52259 | 0.548989 | 0.274494 | − | 0.961589i | \(-0.411490\pi\) | ||||
0.274494 | + | 0.961589i | \(0.411490\pi\) | |||||||
\(242\) | −5.89393 | −0.378876 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.39693 | 0.153447 | ||||||||
\(245\) | −2.07873 | −0.132805 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.09833 | −0.133513 | ||||||||
\(248\) | −27.3482 | −1.73661 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.7811 | 0.745100 | ||||||||
\(251\) | −16.2713 | −1.02703 | −0.513516 | − | 0.858080i | \(-0.671657\pi\) | ||||
−0.513516 | + | 0.858080i | \(0.671657\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.05913 | −0.0665866 | ||||||||
\(254\) | −1.34730 | −0.0845369 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.39599 | −0.274750 | ||||||||
\(257\) | −5.78611 | −0.360928 | −0.180464 | − | 0.983582i | \(-0.557760\pi\) | ||||
−0.180464 | + | 0.983582i | \(0.557760\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.7588 | −0.854928 | ||||||||
\(260\) | −2.57398 | −0.159631 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.10969 | −0.562798 | ||||||||
\(263\) | −28.4270 | −1.75288 | −0.876441 | − | 0.481510i | \(-0.840089\pi\) | ||||
−0.876441 | + | 0.481510i | \(0.840089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.5749 | 2.18535 | ||||||||
\(266\) | 1.81521 | 0.111298 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.0983261 | −0.00600622 | ||||||||
\(269\) | −6.84255 | −0.417198 | −0.208599 | − | 0.978001i | \(-0.566890\pi\) | ||||
−0.208599 | + | 0.978001i | \(0.566890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −26.0523 | −1.58257 | −0.791283 | − | 0.611450i | \(-0.790586\pi\) | ||||
−0.791283 | + | 0.611450i | \(0.790586\pi\) | |||||||
\(272\) | −20.3286 | −1.23260 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.8203 | 0.895325 | ||||||||
\(275\) | 19.2422 | 1.16035 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.98814 | −0.359792 | −0.179896 | − | 0.983686i | \(-0.557576\pi\) | ||||
−0.179896 | + | 0.983686i | \(0.557576\pi\) | |||||||
\(278\) | 12.4715 | 0.747993 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 26.3259 | 1.57328 | ||||||||
\(281\) | −8.22937 | −0.490923 | −0.245462 | − | 0.969406i | \(-0.578940\pi\) | ||||
−0.245462 | + | 0.969406i | \(0.578940\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.92808 | 0.114613 | 0.0573063 | − | 0.998357i | \(-0.481749\pi\) | ||||
0.0573063 | + | 0.998357i | \(0.481749\pi\) | |||||||
\(284\) | 1.26445 | 0.0750314 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.6759 | 0.808674 | ||||||||
\(287\) | 8.90673 | 0.525747 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9531 | 0.879592 | ||||||||
\(290\) | −0.773318 | −0.0454108 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.92539 | 0.112675 | ||||||||
\(293\) | 31.5577 | 1.84362 | 0.921810 | − | 0.387643i | \(-0.126711\pi\) | ||||
0.921810 | + | 0.387643i | \(0.126711\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.09152 | −0.529329 | ||||||||
\(296\) | −15.9946 | −0.929669 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −25.5490 | −1.48001 | ||||||||
\(299\) | −1.62267 | −0.0938417 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.8726 | 1.77947 | ||||||||
\(302\) | 23.0378 | 1.32567 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.91353 | 0.109749 | ||||||||
\(305\) | −45.8144 | −2.62332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.830689 | 0.0474099 | 0.0237050 | − | 0.999719i | \(-0.492454\pi\) | ||||
0.0237050 | + | 0.999719i | \(0.492454\pi\) | |||||||
\(308\) | 1.20439 | 0.0686267 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 44.2131 | 2.51113 | ||||||||
\(311\) | 0.615867 | 0.0349226 | 0.0174613 | − | 0.999848i | \(-0.494442\pi\) | ||||
0.0174613 | + | 0.999848i | \(0.494442\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.85298 | 0.161260 | 0.0806299 | − | 0.996744i | \(-0.474307\pi\) | ||||
0.0806299 | + | 0.996744i | \(0.474307\pi\) | |||||||
\(314\) | 4.60670 | 0.259971 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.105133 | −0.00591420 | ||||||||
\(317\) | 22.7493 | 1.27773 | 0.638863 | − | 0.769320i | \(-0.279405\pi\) | ||||
0.638863 | + | 0.769320i | \(0.279405\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.418281 | −0.0234193 | ||||||||
\(320\) | 30.3628 | 1.69733 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.40373 | 0.0782270 | ||||||||
\(323\) | −3.00774 | −0.167355 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 29.4807 | 1.63530 | ||||||||
\(326\) | 0.610815 | 0.0338299 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.3541 | 0.571710 | ||||||||
\(329\) | −15.5672 | −0.858246 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.4388 | 1.67307 | 0.836534 | − | 0.547915i | \(-0.184578\pi\) | ||||
0.836534 | + | 0.547915i | \(0.184578\pi\) | |||||||
\(332\) | 2.86072 | 0.157002 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.5398 | 0.576714 | ||||||||
\(335\) | 1.87939 | 0.102682 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.9855 | 0.707363 | 0.353681 | − | 0.935366i | \(-0.384930\pi\) | ||||
0.353681 | + | 0.935366i | \(0.384930\pi\) | |||||||
\(338\) | 3.43788 | 0.186996 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.68954 | −0.200093 | ||||||||
\(341\) | 23.9145 | 1.29504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2148 | 1.03750 | ||||||||
\(344\) | 35.8895 | 1.93503 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −26.7547 | −1.43834 | ||||||||
\(347\) | 29.6382 | 1.59106 | 0.795530 | − | 0.605914i | \(-0.207193\pi\) | ||||
0.795530 | + | 0.605914i | \(0.207193\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.6486 | −1.26588 | −0.632940 | − | 0.774201i | \(-0.718152\pi\) | ||||
−0.632940 | + | 0.774201i | \(0.718152\pi\) | |||||||
\(350\) | −25.5030 | −1.36319 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.68180 | 0.142940 | ||||||||
\(353\) | 17.9118 | 0.953348 | 0.476674 | − | 0.879080i | \(-0.341842\pi\) | ||||
0.476674 | + | 0.879080i | \(0.341842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −24.1685 | −1.28273 | ||||||||
\(356\) | −2.40642 | −0.127540 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.9590 | −0.843462 | ||||||||
\(359\) | 6.10607 | 0.322266 | 0.161133 | − | 0.986933i | \(-0.448485\pi\) | ||||
0.161133 | + | 0.986933i | \(0.448485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.7169 | −0.985099 | ||||||||
\(362\) | 6.03003 | 0.316931 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.84524 | 0.0967167 | ||||||||
\(365\) | −36.8016 | −1.92628 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.84793 | 0.409658 | 0.204829 | − | 0.978798i | \(-0.434336\pi\) | ||||
0.204829 | + | 0.978798i | \(0.434336\pi\) | |||||||
\(368\) | 1.47977 | 0.0771384 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 25.8580 | 1.34429 | ||||||||
\(371\) | −25.5030 | −1.32405 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.66456 | 0.345078 | 0.172539 | − | 0.985003i | \(-0.444803\pi\) | ||||
0.172539 | + | 0.985003i | \(0.444803\pi\) | |||||||
\(374\) | 19.6031 | 1.01365 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −18.0969 | −0.933276 | ||||||||
\(377\) | −0.640844 | −0.0330051 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.69728 | 0.138550 | 0.0692750 | − | 0.997598i | \(-0.477931\pi\) | ||||
0.0692750 | + | 0.997598i | \(0.477931\pi\) | |||||||
\(380\) | 0.347296 | 0.0178159 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.73917 | −0.395970 | ||||||||
\(383\) | 28.2686 | 1.44446 | 0.722228 | − | 0.691655i | \(-0.243118\pi\) | ||||
0.722228 | + | 0.691655i | \(0.243118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −23.0205 | −1.17324 | ||||||||
\(386\) | −12.0104 | −0.611315 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.81521 | 0.142921 | ||||||||
\(389\) | 28.0523 | 1.42231 | 0.711154 | − | 0.703036i | \(-0.248173\pi\) | ||||
0.711154 | + | 0.703036i | \(0.248173\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.32594 | −0.117628 | ||||||||
\(392\) | 1.73236 | 0.0874975 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.7442 | −1.19622 | ||||||||
\(395\) | 2.00950 | 0.101109 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.51249 | 0.226475 | 0.113238 | − | 0.993568i | \(-0.463878\pi\) | ||||
0.113238 | + | 0.993568i | \(0.463878\pi\) | |||||||
\(398\) | −19.1215 | −0.958477 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −26.8844 | −1.34422 | ||||||||
\(401\) | −8.57398 | −0.428164 | −0.214082 | − | 0.976816i | \(-0.568676\pi\) | ||||
−0.214082 | + | 0.976816i | \(0.568676\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.6391 | 1.82512 | ||||||||
\(404\) | −1.55800 | −0.0775134 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.554378 | 0.0275133 | ||||||||
\(407\) | 13.9864 | 0.693279 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.10338 | −0.0545586 | −0.0272793 | − | 0.999628i | \(-0.508684\pi\) | ||||
−0.0272793 | + | 0.999628i | \(0.508684\pi\) | |||||||
\(410\) | −16.7392 | −0.826689 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.573978 | 0.0282779 | ||||||||
\(413\) | 6.51754 | 0.320707 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −54.6792 | −2.68410 | ||||||||
\(416\) | 4.10876 | 0.201448 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.84524 | −0.0902535 | ||||||||
\(419\) | 31.7939 | 1.55323 | 0.776616 | − | 0.629975i | \(-0.216935\pi\) | ||||
0.776616 | + | 0.629975i | \(0.216935\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.45067 | 0.168176 | 0.0840878 | − | 0.996458i | \(-0.473202\pi\) | ||||
0.0840878 | + | 0.996458i | \(0.473202\pi\) | |||||||
\(422\) | −22.1215 | −1.07686 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −29.6473 | −1.43980 | ||||||||
\(425\) | 42.2576 | 2.04980 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.8435 | 1.58941 | ||||||||
\(428\) | 1.38775 | 0.0670797 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −58.0215 | −2.79804 | ||||||||
\(431\) | −19.3773 | −0.933373 | −0.466686 | − | 0.884423i | \(-0.654552\pi\) | ||||
−0.466686 | + | 0.884423i | \(0.654552\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.1857 | −1.73898 | −0.869488 | − | 0.493955i | \(-0.835551\pi\) | ||||
−0.869488 | + | 0.493955i | \(0.835551\pi\) | |||||||
\(434\) | −31.6955 | −1.52143 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.11650 | −0.101362 | ||||||||
\(437\) | 0.218941 | 0.0104734 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.5827 | −1.31645 | −0.658224 | − | 0.752822i | \(-0.728692\pi\) | ||||
−0.658224 | + | 0.752822i | \(0.728692\pi\) | |||||||
\(440\) | −26.7615 | −1.27580 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.0337 | 1.42856 | ||||||||
\(443\) | −5.07697 | −0.241214 | −0.120607 | − | 0.992700i | \(-0.538484\pi\) | ||||
−0.120607 | + | 0.992700i | \(0.538484\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 45.9959 | 2.18041 | ||||||||
\(446\) | −31.0259 | −1.46912 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.7665 | −1.02837 | ||||||||
\(449\) | −1.12836 | −0.0532504 | −0.0266252 | − | 0.999645i | \(-0.508476\pi\) | ||||
−0.0266252 | + | 0.999645i | \(0.508476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.05407 | −0.426340 | ||||||||
\(452\) | −1.81109 | −0.0851864 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.59358 | 0.450249 | ||||||||
\(455\) | −35.2695 | −1.65346 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.3678 | 1.65444 | 0.827219 | − | 0.561880i | \(-0.189922\pi\) | ||||
0.827219 | + | 0.561880i | \(0.189922\pi\) | |||||||
\(458\) | −12.5936 | −0.588459 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.268571 | 0.0125222 | ||||||||
\(461\) | 19.1685 | 0.892766 | 0.446383 | − | 0.894842i | \(-0.352712\pi\) | ||||
0.446383 | + | 0.894842i | \(0.352712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.3601 | 0.574422 | 0.287211 | − | 0.957867i | \(-0.407272\pi\) | ||||
0.287211 | + | 0.957867i | \(0.407272\pi\) | |||||||
\(464\) | 0.584407 | 0.0271304 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.4311 | 0.853803 | ||||||||
\(467\) | 19.1566 | 0.886463 | 0.443232 | − | 0.896407i | \(-0.353832\pi\) | ||||
0.443232 | + | 0.896407i | \(0.353832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.34730 | −0.0622124 | ||||||||
\(470\) | 29.2567 | 1.34951 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.57667 | 0.348744 | ||||||||
\(473\) | −31.3833 | −1.44301 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.97771 | −0.182510 | ||||||||
\(476\) | 2.64496 | 0.121232 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.1516 | 1.01319 | ||||||||
\(479\) | −24.0104 | −1.09706 | −0.548532 | − | 0.836129i | \(-0.684813\pi\) | ||||
−0.548532 | + | 0.836129i | \(0.684813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.4284 | 0.977050 | ||||||||
\(482\) | 11.4825 | 0.523012 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.808400 | 0.0367455 | ||||||||
\(485\) | −53.8093 | −2.44336 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.811089 | −0.0367539 | −0.0183770 | − | 0.999831i | \(-0.505850\pi\) | ||||
−0.0183770 | + | 0.999831i | \(0.505850\pi\) | |||||||
\(488\) | 38.1807 | 1.72836 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.80066 | −0.126521 | ||||||||
\(491\) | 5.59358 | 0.252435 | 0.126217 | − | 0.992003i | \(-0.459716\pi\) | ||||
0.126217 | + | 0.992003i | \(0.459716\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.918586 | −0.0413710 | ||||||||
\(494\) | −2.82707 | −0.127196 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −33.4124 | −1.50026 | ||||||||
\(497\) | 17.3259 | 0.777175 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.3928 | 1.31580 | 0.657901 | − | 0.753104i | \(-0.271444\pi\) | ||||
0.657901 | + | 0.753104i | \(0.271444\pi\) | |||||||
\(500\) | −1.61587 | −0.0722638 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.9222 | −0.978436 | ||||||||
\(503\) | −19.6774 | −0.877370 | −0.438685 | − | 0.898641i | \(-0.644556\pi\) | ||||
−0.438685 | + | 0.898641i | \(0.644556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.7793 | 1.32516 | ||||||||
\(506\) | −1.42696 | −0.0634359 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.184793 | 0.00819884 | ||||||||
\(509\) | −11.5149 | −0.510387 | −0.255193 | − | 0.966890i | \(-0.582139\pi\) | ||||
−0.255193 | + | 0.966890i | \(0.582139\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.3824 | 1.16709 | ||||||||
\(512\) | −24.9186 | −1.10126 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.79561 | −0.343849 | ||||||||
\(515\) | −10.9709 | −0.483436 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.8247 | 0.695970 | ||||||||
\(518\) | −18.5371 | −0.814475 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −41.0009 | −1.79801 | ||||||||
\(521\) | 4.21213 | 0.184537 | 0.0922685 | − | 0.995734i | \(-0.470588\pi\) | ||||
0.0922685 | + | 0.995734i | \(0.470588\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.4124 | 1.76711 | 0.883556 | − | 0.468326i | \(-0.155143\pi\) | ||||
0.883556 | + | 0.468326i | \(0.155143\pi\) | |||||||
\(524\) | 1.24947 | 0.0545832 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −38.2995 | −1.66994 | ||||||||
\(527\) | 52.5185 | 2.28774 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8307 | −0.992639 | ||||||||
\(530\) | 47.9299 | 2.08194 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.248970 | −0.0107942 | ||||||||
\(533\) | −13.8716 | −0.600848 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.5253 | −1.14679 | ||||||||
\(536\) | −1.56624 | −0.0676511 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −9.21894 | −0.397457 | ||||||||
\(539\) | −1.51485 | −0.0652493 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.2635 | 0.656230 | 0.328115 | − | 0.944638i | \(-0.393587\pi\) | ||||
0.328115 | + | 0.944638i | \(0.393587\pi\) | |||||||
\(542\) | −35.1002 | −1.50768 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.88949 | 0.252510 | ||||||||
\(545\) | 40.4543 | 1.73287 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.14971 | −0.220186 | −0.110093 | − | 0.993921i | \(-0.535115\pi\) | ||||
−0.110093 | + | 0.993921i | \(0.535115\pi\) | |||||||
\(548\) | −2.03272 | −0.0868334 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.9249 | 1.10544 | ||||||||
\(551\) | 0.0864665 | 0.00368360 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.44057 | −0.0612593 | ||||||||
\(554\) | −8.06780 | −0.342768 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.71057 | −0.0725444 | ||||||||
\(557\) | −5.26176 | −0.222948 | −0.111474 | − | 0.993767i | \(-0.535557\pi\) | ||||
−0.111474 | + | 0.993767i | \(0.535557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.0820 | −2.03365 | ||||||||
\(560\) | 32.1634 | 1.35915 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.0874 | −0.467694 | ||||||||
\(563\) | −4.39961 | −0.185422 | −0.0927108 | − | 0.995693i | \(-0.529553\pi\) | ||||
−0.0927108 | + | 0.995693i | \(0.529553\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 34.6168 | 1.45634 | ||||||||
\(566\) | 2.59770 | 0.109189 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 20.1415 | 0.845117 | ||||||||
\(569\) | −15.1625 | −0.635645 | −0.317823 | − | 0.948150i | \(-0.602952\pi\) | ||||
−0.317823 | + | 0.948150i | \(0.602952\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.9240 | −0.582700 | −0.291350 | − | 0.956617i | \(-0.594104\pi\) | ||||
−0.291350 | + | 0.956617i | \(0.594104\pi\) | |||||||
\(572\) | −1.87576 | −0.0784296 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.0000 | 0.500870 | ||||||||
\(575\) | −3.07604 | −0.128280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.6117 | −1.60743 | −0.803714 | − | 0.595016i | \(-0.797146\pi\) | ||||
−0.803714 | + | 0.595016i | \(0.797146\pi\) | |||||||
\(578\) | 20.1462 | 0.837971 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.106067 | 0.00440419 | ||||||||
\(581\) | 39.1985 | 1.62623 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.9249 | 1.07370 | ||||||||
\(584\) | 30.6696 | 1.26912 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.5175 | 1.75638 | ||||||||
\(587\) | 20.4260 | 0.843072 | 0.421536 | − | 0.906812i | \(-0.361491\pi\) | ||||
0.421536 | + | 0.906812i | \(0.361491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.94356 | −0.203696 | ||||||||
\(590\) | −12.2490 | −0.504282 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −19.5413 | −0.803141 | ||||||||
\(593\) | −8.53209 | −0.350371 | −0.175185 | − | 0.984535i | \(-0.556053\pi\) | ||||
−0.175185 | + | 0.984535i | \(0.556053\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −50.5553 | −2.07257 | ||||||||
\(596\) | 3.50425 | 0.143540 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.18622 | −0.0894013 | ||||||||
\(599\) | 19.2294 | 0.785691 | 0.392845 | − | 0.919605i | \(-0.371491\pi\) | ||||
0.392845 | + | 0.919605i | \(0.371491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.25166 | 0.255010 | 0.127505 | − | 0.991838i | \(-0.459303\pi\) | ||||
0.127505 | + | 0.991838i | \(0.459303\pi\) | |||||||
\(602\) | 41.5945 | 1.69527 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.15982 | −0.128571 | ||||||||
\(605\) | −15.4516 | −0.628197 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.9718 | 1.37887 | 0.689437 | − | 0.724345i | \(-0.257858\pi\) | ||||
0.689437 | + | 0.724345i | \(0.257858\pi\) | |||||||
\(608\) | −0.554378 | −0.0224830 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −61.7256 | −2.49919 | ||||||||
\(611\) | 24.2449 | 0.980842 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.2422 | −0.696404 | −0.348202 | − | 0.937419i | \(-0.613208\pi\) | ||||
−0.348202 | + | 0.937419i | \(0.613208\pi\) | |||||||
\(614\) | 1.11918 | 0.0451666 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.1848 | 0.772977 | ||||||||
\(617\) | 11.5193 | 0.463749 | 0.231875 | − | 0.972746i | \(-0.425514\pi\) | ||||
0.231875 | + | 0.972746i | \(0.425514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.55531 | −0.223287 | −0.111643 | − | 0.993748i | \(-0.535611\pi\) | ||||
−0.111643 | + | 0.993748i | \(0.535611\pi\) | |||||||
\(620\) | −6.06418 | −0.243543 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.829755 | 0.0332702 | ||||||||
\(623\) | −32.9736 | −1.32106 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.49289 | −0.259716 | ||||||||
\(626\) | 3.84381 | 0.153629 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.631845 | −0.0252134 | ||||||||
\(629\) | 30.7155 | 1.22471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.01960 | 0.0405896 | 0.0202948 | − | 0.999794i | \(-0.493540\pi\) | ||||
0.0202948 | + | 0.999794i | \(0.493540\pi\) | |||||||
\(632\) | −1.67467 | −0.0666147 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.6500 | 1.21727 | ||||||||
\(635\) | −3.53209 | −0.140167 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.32089 | −0.0919570 | ||||||||
\(638\) | −0.563549 | −0.0223111 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 33.5476 | 1.32608 | ||||||||
\(641\) | −12.9709 | −0.512320 | −0.256160 | − | 0.966634i | \(-0.582457\pi\) | ||||
−0.256160 | + | 0.966634i | \(0.582457\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.8479 | −0.467237 | −0.233618 | − | 0.972328i | \(-0.575057\pi\) | ||||
−0.233618 | + | 0.972328i | \(0.575057\pi\) | |||||||
\(644\) | −0.192533 | −0.00758688 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.05232 | −0.159436 | ||||||||
\(647\) | 36.1293 | 1.42039 | 0.710194 | − | 0.704006i | \(-0.248607\pi\) | ||||
0.710194 | + | 0.704006i | \(0.248607\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.62536 | −0.260068 | ||||||||
\(650\) | 39.7192 | 1.55792 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0837781 | −0.00328100 | ||||||||
\(653\) | −39.9887 | −1.56488 | −0.782440 | − | 0.622726i | \(-0.786025\pi\) | ||||
−0.782440 | + | 0.622726i | \(0.786025\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.8821 | −0.933150 | ||||||||
\(656\) | 12.6500 | 0.493900 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −20.9736 | −0.817636 | ||||||||
\(659\) | 12.8598 | 0.500946 | 0.250473 | − | 0.968124i | \(-0.419414\pi\) | ||||
0.250473 | + | 0.968124i | \(0.419414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.58946 | 0.139614 | 0.0698069 | − | 0.997561i | \(-0.477762\pi\) | ||||
0.0698069 | + | 0.997561i | \(0.477762\pi\) | |||||||
\(662\) | 41.0101 | 1.59390 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 45.5684 | 1.76840 | ||||||||
\(665\) | 4.75877 | 0.184537 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.0668661 | 0.00258907 | ||||||||
\(668\) | −1.44562 | −0.0559328 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.53209 | 0.0978231 | ||||||||
\(671\) | −33.3868 | −1.28888 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2449 | 1.32004 | 0.660021 | − | 0.751247i | \(-0.270547\pi\) | ||||
0.660021 | + | 0.751247i | \(0.270547\pi\) | |||||||
\(674\) | 17.4953 | 0.673892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.471533 | −0.0181359 | ||||||||
\(677\) | 8.76382 | 0.336821 | 0.168411 | − | 0.985717i | \(-0.446137\pi\) | ||||
0.168411 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.5749 | 1.48037 | ||||||||
\(680\) | −58.7707 | −2.25376 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 32.2199 | 1.23376 | ||||||||
\(683\) | −19.4439 | −0.743999 | −0.371999 | − | 0.928233i | \(-0.621328\pi\) | ||||
−0.371999 | + | 0.928233i | \(0.621328\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 38.8530 | 1.48450 | ||||||||
\(686\) | 25.8881 | 0.988411 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 43.8476 | 1.67167 | ||||||||
\(689\) | 39.7192 | 1.51318 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.58441 | 0.0983155 | 0.0491577 | − | 0.998791i | \(-0.484346\pi\) | ||||
0.0491577 | + | 0.998791i | \(0.484346\pi\) | |||||||
\(692\) | 3.66962 | 0.139498 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 39.9314 | 1.51577 | ||||||||
\(695\) | 32.6955 | 1.24021 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.8836 | −0.753146 | ||||||||
\(698\) | −31.8617 | −1.20598 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.49794 | 0.132210 | ||||||||
\(701\) | −25.5458 | −0.964852 | −0.482426 | − | 0.875937i | \(-0.660244\pi\) | ||||
−0.482426 | + | 0.875937i | \(0.660244\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.89124 | −0.109045 | ||||||||
\(704\) | 22.1266 | 0.833928 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.1325 | 0.908238 | ||||||||
\(707\) | −21.3482 | −0.802883 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.4192 | 0.917083 | 0.458541 | − | 0.888673i | \(-0.348372\pi\) | ||||
0.458541 | + | 0.888673i | \(0.348372\pi\) | |||||||
\(710\) | −32.5621 | −1.22203 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −38.3319 | −1.43655 | ||||||||
\(713\) | −3.82295 | −0.143171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.8530 | 1.34083 | ||||||||
\(716\) | 2.18891 | 0.0818035 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.22668 | 0.307017 | ||||||||
\(719\) | −28.9127 | −1.07826 | −0.539131 | − | 0.842222i | \(-0.681247\pi\) | ||||
−0.539131 | + | 0.842222i | \(0.681247\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.86484 | 0.292902 | ||||||||
\(722\) | −25.2172 | −0.938486 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.827067 | −0.0307377 | ||||||||
\(725\) | −1.21482 | −0.0451174 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.7752 | −1.92024 | −0.960118 | − | 0.279596i | \(-0.909799\pi\) | ||||
−0.960118 | + | 0.279596i | \(0.909799\pi\) | |||||||
\(728\) | 29.3928 | 1.08937 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −49.5827 | −1.83514 | ||||||||
\(731\) | −68.9208 | −2.54913 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.7023 | −1.35563 | −0.677816 | − | 0.735232i | \(-0.737073\pi\) | ||||
−0.677816 | + | 0.735232i | \(0.737073\pi\) | |||||||
\(734\) | 10.5735 | 0.390274 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.428710 | −0.0158025 | ||||||||
\(737\) | 1.36959 | 0.0504493 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.8699 | −1.76092 | −0.880461 | − | 0.474118i | \(-0.842767\pi\) | ||||
−0.880461 | + | 0.474118i | \(0.842767\pi\) | |||||||
\(740\) | −3.54664 | −0.130377 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.3601 | −1.26140 | ||||||||
\(743\) | −24.6631 | −0.904803 | −0.452401 | − | 0.891814i | \(-0.649433\pi\) | ||||
−0.452401 | + | 0.891814i | \(0.649433\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −66.9796 | −2.45394 | ||||||||
\(746\) | 8.97914 | 0.328750 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.68872 | −0.0983093 | ||||||||
\(749\) | 19.0155 | 0.694811 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.86753 | 0.360071 | 0.180036 | − | 0.983660i | \(-0.442379\pi\) | ||||
0.180036 | + | 0.983660i | \(0.442379\pi\) | |||||||
\(752\) | −22.1097 | −0.806257 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.863407 | −0.0314434 | ||||||||
\(755\) | 60.3961 | 2.19804 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.8939 | 0.759403 | 0.379701 | − | 0.925109i | \(-0.376027\pi\) | ||||
0.379701 | + | 0.925109i | \(0.376027\pi\) | |||||||
\(758\) | 3.63404 | 0.131994 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.53209 | 0.200670 | ||||||||
\(761\) | 38.2959 | 1.38823 | 0.694113 | − | 0.719866i | \(-0.255797\pi\) | ||||
0.694113 | + | 0.719866i | \(0.255797\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −29.0009 | −1.04990 | ||||||||
\(764\) | 1.06149 | 0.0384033 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38.0861 | 1.37611 | ||||||||
\(767\) | −10.1506 | −0.366519 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.25402 | 0.333709 | 0.166854 | − | 0.985982i | \(-0.446639\pi\) | ||||
0.166854 | + | 0.985982i | \(0.446639\pi\) | |||||||
\(770\) | −31.0155 | −1.11772 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.64733 | 0.0592886 | ||||||||
\(773\) | 11.6509 | 0.419056 | 0.209528 | − | 0.977803i | \(-0.432807\pi\) | ||||
0.209528 | + | 0.977803i | \(0.432807\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 69.4552 | 2.49491 | ||||||||
\(776\) | 44.8435 | 1.60979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.7948 | 1.35501 | ||||||||
\(779\) | 1.87164 | 0.0670586 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.6126 | −0.630227 | ||||||||
\(782\) | −3.13373 | −0.112062 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.11650 | 0.0755891 | ||||||||
\(785\) | 12.0770 | 0.431046 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.5672 | 1.69559 | 0.847793 | − | 0.530327i | \(-0.177931\pi\) | ||||
0.847793 | + | 0.530327i | \(0.177931\pi\) | |||||||
\(788\) | 3.25671 | 0.116016 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.70739 | 0.0963245 | ||||||||
\(791\) | −24.8161 | −0.882360 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −51.1516 | −1.81645 | ||||||||
\(794\) | 6.07966 | 0.215759 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.62267 | 0.0929582 | ||||||||
\(797\) | −26.1046 | −0.924674 | −0.462337 | − | 0.886704i | \(-0.652989\pi\) | ||||
−0.462337 | + | 0.886704i | \(0.652989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.7526 | 1.22946 | ||||||||
\(800\) | 7.78880 | 0.275376 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.5517 | −0.407904 | ||||||||
\(803\) | −26.8188 | −0.946416 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.68004 | 0.129705 | ||||||||
\(806\) | 49.3637 | 1.73876 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −24.8174 | −0.873073 | ||||||||
\(809\) | −15.1361 | −0.532157 | −0.266078 | − | 0.963951i | \(-0.585728\pi\) | ||||
−0.266078 | + | 0.963951i | \(0.585728\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.696957 | −0.0244735 | −0.0122367 | − | 0.999925i | \(-0.503895\pi\) | ||||
−0.0122367 | + | 0.999925i | \(0.503895\pi\) | |||||||
\(812\) | −0.0760373 | −0.00266839 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.8438 | 0.660475 | ||||||||
\(815\) | 1.60132 | 0.0560918 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.48751 | 0.226969 | ||||||||
\(818\) | −1.48658 | −0.0519770 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.29591 | 0.0801767 | ||||||||
\(821\) | −23.1881 | −0.809270 | −0.404635 | − | 0.914478i | \(-0.632601\pi\) | ||||
−0.404635 | + | 0.914478i | \(0.632601\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.7229 | −0.896643 | −0.448321 | − | 0.893872i | \(-0.647978\pi\) | ||||
−0.448321 | + | 0.893872i | \(0.647978\pi\) | |||||||
\(824\) | 9.14290 | 0.318508 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.78106 | 0.305532 | ||||||||
\(827\) | 29.2481 | 1.01706 | 0.508529 | − | 0.861045i | \(-0.330189\pi\) | ||||
0.508529 | + | 0.861045i | \(0.330189\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.38238 | 0.152206 | 0.0761031 | − | 0.997100i | \(-0.475752\pi\) | ||||
0.0761031 | + | 0.997100i | \(0.475752\pi\) | |||||||
\(830\) | −73.6691 | −2.55709 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.8999 | 1.17527 | ||||||||
\(833\) | −3.32676 | −0.115265 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 27.6313 | 0.956222 | ||||||||
\(836\) | 0.253089 | 0.00875327 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 42.8357 | 1.47974 | ||||||||
\(839\) | −25.8753 | −0.893313 | −0.446657 | − | 0.894705i | \(-0.647385\pi\) | ||||
−0.446657 | + | 0.894705i | \(0.647385\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9736 | −0.999089 | ||||||||
\(842\) | 4.64908 | 0.160218 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.03415 | 0.104440 | ||||||||
\(845\) | 9.01279 | 0.310050 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.0770 | 0.380609 | ||||||||
\(848\) | −36.2213 | −1.24384 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 56.9336 | 1.95281 | ||||||||
\(851\) | −2.23585 | −0.0766440 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.5262 | −1.21639 | −0.608197 | − | 0.793786i | \(-0.708107\pi\) | ||||
−0.608197 | + | 0.793786i | \(0.708107\pi\) | |||||||
\(854\) | 44.2499 | 1.51420 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 22.1056 | 0.755553 | ||||||||
\(857\) | 35.9632 | 1.22848 | 0.614239 | − | 0.789120i | \(-0.289463\pi\) | ||||
0.614239 | + | 0.789120i | \(0.289463\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.0806 | −1.16281 | −0.581407 | − | 0.813613i | \(-0.697498\pi\) | ||||
−0.581407 | + | 0.813613i | \(0.697498\pi\) | |||||||
\(860\) | 7.95811 | 0.271369 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −26.1070 | −0.889208 | ||||||||
\(863\) | 13.6391 | 0.464280 | 0.232140 | − | 0.972682i | \(-0.425427\pi\) | ||||
0.232140 | + | 0.972682i | \(0.425427\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −70.1403 | −2.38484 | ||||||||
\(866\) | −48.7529 | −1.65669 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.34730 | 0.147557 | ||||||||
\(869\) | 1.46440 | 0.0496764 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.09833 | 0.0710991 | ||||||||
\(872\) | −33.7137 | −1.14169 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.294978 | 0.00997778 | ||||||||
\(875\) | −22.1411 | −0.748507 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.7888 | −1.17473 | −0.587367 | − | 0.809321i | \(-0.699836\pi\) | ||||
−0.587367 | + | 0.809321i | \(0.699836\pi\) | |||||||
\(878\) | −37.1620 | −1.25416 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −32.6955 | −1.10217 | ||||||||
\(881\) | −36.1735 | −1.21872 | −0.609359 | − | 0.792895i | \(-0.708573\pi\) | ||||
−0.609359 | + | 0.792895i | \(0.708573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 54.6154 | 1.83795 | 0.918977 | − | 0.394312i | \(-0.129017\pi\) | ||||
0.918977 | + | 0.394312i | \(0.129017\pi\) | |||||||
\(884\) | −4.11936 | −0.138549 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.84018 | −0.229800 | ||||||||
\(887\) | 39.3732 | 1.32202 | 0.661011 | − | 0.750376i | \(-0.270127\pi\) | ||||
0.661011 | + | 0.750376i | \(0.270127\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.53209 | 0.0849235 | ||||||||
\(890\) | 61.9701 | 2.07724 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.25545 | 0.142483 | ||||||||
\(893\) | −3.27126 | −0.109469 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.8384 | −1.39850 | ||||||||
\(896\) | −24.0496 | −0.803442 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.52023 | −0.0507307 | ||||||||
\(899\) | −1.50980 | −0.0503547 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 56.9336 | 1.89673 | ||||||||
\(902\) | −12.1985 | −0.406166 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.8489 | −0.959499 | ||||||||
\(905\) | 15.8084 | 0.525489 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.4356 | −1.30944 | −0.654719 | − | 0.755872i | \(-0.727213\pi\) | ||||
−0.654719 | + | 0.755872i | \(0.727213\pi\) | |||||||
\(908\) | −1.31584 | −0.0436676 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −47.5185 | −1.57522 | ||||||||
\(911\) | 42.8566 | 1.41990 | 0.709951 | − | 0.704251i | \(-0.248717\pi\) | ||||
0.709951 | + | 0.704251i | \(0.248717\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.8470 | −1.31874 | ||||||||
\(914\) | 47.6509 | 1.57615 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.72731 | 0.0570719 | ||||||||
\(917\) | 17.1206 | 0.565373 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.3583 | 1.13338 | 0.566688 | − | 0.823932i | \(-0.308224\pi\) | ||||
0.566688 | + | 0.823932i | \(0.308224\pi\) | |||||||
\(920\) | 4.27807 | 0.141044 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 25.8256 | 0.850522 | ||||||||
\(923\) | −26.9840 | −0.888190 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.6209 | 1.33561 | ||||||||
\(926\) | 16.6527 | 0.547242 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.169311 | −0.00555790 | ||||||||
\(929\) | −5.15476 | −0.169122 | −0.0845611 | − | 0.996418i | \(-0.526949\pi\) | ||||
−0.0845611 | + | 0.996418i | \(0.526949\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.313148 | 0.0102630 | ||||||||
\(932\) | −2.52797 | −0.0828064 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 25.8097 | 0.844518 | ||||||||
\(935\) | 51.3917 | 1.68069 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.8862 | −0.453642 | −0.226821 | − | 0.973936i | \(-0.572833\pi\) | ||||
−0.226821 | + | 0.973936i | \(0.572833\pi\) | |||||||
\(938\) | −1.81521 | −0.0592686 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.01279 | −0.130883 | ||||||||
\(941\) | 2.16519 | 0.0705832 | 0.0352916 | − | 0.999377i | \(-0.488764\pi\) | ||||
0.0352916 | + | 0.999377i | \(0.488764\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.44738 | 0.0471331 | ||||||||
\(944\) | 9.25671 | 0.301280 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −42.2826 | −1.37473 | ||||||||
\(947\) | 8.10019 | 0.263221 | 0.131610 | − | 0.991302i | \(-0.457985\pi\) | ||||
0.131610 | + | 0.991302i | \(0.457985\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −41.0888 | −1.33380 | ||||||||
\(950\) | −5.35916 | −0.173874 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 42.1317 | 1.36549 | ||||||||
\(953\) | 5.63579 | 0.182561 | 0.0912806 | − | 0.995825i | \(-0.470904\pi\) | ||||
0.0912806 | + | 0.995825i | \(0.470904\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.2891 | −0.656540 | ||||||||
\(956\) | −3.03827 | −0.0982646 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.3492 | −1.04515 | ||||||||
\(959\) | −27.8530 | −0.899420 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 55.3201 | 1.78452 | ||||||||
\(962\) | 28.8704 | 0.930819 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.57491 | −0.0507245 | ||||||||
\(965\) | −31.4867 | −1.01359 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27.2540 | 0.876430 | 0.438215 | − | 0.898870i | \(-0.355611\pi\) | ||||
0.438215 | + | 0.898870i | \(0.355611\pi\) | |||||||
\(968\) | 12.8770 | 0.413883 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −72.4971 | −2.32774 | ||||||||
\(971\) | −20.8179 | −0.668078 | −0.334039 | − | 0.942559i | \(-0.608412\pi\) | ||||
−0.334039 | + | 0.942559i | \(0.608412\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.4388 | −0.751414 | ||||||||
\(974\) | −1.09278 | −0.0350148 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 46.6468 | 1.49313 | ||||||||
\(977\) | −33.1448 | −1.06040 | −0.530198 | − | 0.847874i | \(-0.677882\pi\) | ||||
−0.530198 | + | 0.847874i | \(0.677882\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 33.5191 | 1.07127 | ||||||||
\(980\) | 0.384133 | 0.0122707 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.53621 | 0.240490 | ||||||||
\(983\) | −19.8749 | −0.633912 | −0.316956 | − | 0.948440i | \(-0.602661\pi\) | ||||
−0.316956 | + | 0.948440i | \(0.602661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −62.2481 | −1.98339 | ||||||||
\(986\) | −1.23761 | −0.0394135 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.387755 | 0.0123361 | ||||||||
\(989\) | 5.01691 | 0.159529 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.2490 | 0.833826 | 0.416913 | − | 0.908946i | \(-0.363112\pi\) | ||||
0.416913 | + | 0.908946i | \(0.363112\pi\) | |||||||
\(992\) | 9.68004 | 0.307342 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 23.3432 | 0.740401 | ||||||||
\(995\) | −50.1293 | −1.58921 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.38001 | 0.233727 | 0.116864 | − | 0.993148i | \(-0.462716\pi\) | ||||
0.116864 | + | 0.993148i | \(0.462716\pi\) | |||||||
\(998\) | 39.6008 | 1.25354 | ||||||||
\(999\) | 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 | 1143.2.a.e.1.2 | 3 | ||
3.2 | odd | 2 | 127.2.a.a.1.2 | ✓ | 3 | ||
12.11 | even | 2 | 2032.2.a.k.1.1 | 3 | |||
15.14 | odd | 2 | 3175.2.a.h.1.2 | 3 | |||
21.20 | even | 2 | 6223.2.a.e.1.2 | 3 | |||
24.5 | odd | 2 | 8128.2.a.bd.1.1 | 3 | |||
24.11 | even | 2 | 8128.2.a.w.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
127.2.a.a.1.2 | ✓ | 3 | 3.2 | odd | 2 | ||
1143.2.a.e.1.2 | 3 | 1.1 | even | 1 | trivial | ||
2032.2.a.k.1.1 | 3 | 12.11 | even | 2 | |||
3175.2.a.h.1.2 | 3 | 15.14 | odd | 2 | |||
6223.2.a.e.1.2 | 3 | 21.20 | even | 2 | |||
8128.2.a.w.1.3 | 3 | 24.11 | even | 2 | |||
8128.2.a.bd.1.1 | 3 | 24.5 | odd | 2 |