Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, 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("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{20})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.90211\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.90211 | −1.34500 | −0.672499 | − | 0.740098i | \(-0.734779\pi\) | ||||
−0.672499 | + | 0.740098i | \(0.734779\pi\) | |||||||
\(3\) | −1.90211 | −1.09819 | −0.549093 | − | 0.835761i | \(-0.685027\pi\) | ||||
−0.549093 | + | 0.835761i | \(0.685027\pi\) | |||||||
\(4\) | 1.61803 | 0.809017 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 3.61803 | 1.47706 | ||||||||
\(7\) | −4.23607 | −1.60108 | −0.800542 | − | 0.599277i | \(-0.795455\pi\) | ||||
−0.800542 | + | 0.599277i | \(0.795455\pi\) | |||||||
\(8\) | 0.726543 | 0.256872 | ||||||||
\(9\) | 0.618034 | 0.206011 | ||||||||
\(10\) | 1.90211 | 0.601501 | ||||||||
\(11\) | −5.85410 | −1.76508 | −0.882539 | − | 0.470239i | \(-0.844168\pi\) | ||||
−0.882539 | + | 0.470239i | \(0.844168\pi\) | |||||||
\(12\) | −3.07768 | −0.888451 | ||||||||
\(13\) | 3.07768 | 0.853596 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(14\) | 8.05748 | 2.15345 | ||||||||
\(15\) | 1.90211 | 0.491123 | ||||||||
\(16\) | −4.61803 | −1.15451 | ||||||||
\(17\) | 5.23607 | 1.26993 | 0.634967 | − | 0.772540i | \(-0.281014\pi\) | ||||
0.634967 | + | 0.772540i | \(0.281014\pi\) | |||||||
\(18\) | −1.17557 | −0.277085 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −1.61803 | −0.361803 | ||||||||
\(21\) | 8.05748 | 1.75829 | ||||||||
\(22\) | 11.1352 | 2.37402 | ||||||||
\(23\) | 4.09017 | 0.852859 | 0.426430 | − | 0.904521i | \(-0.359771\pi\) | ||||
0.426430 | + | 0.904521i | \(0.359771\pi\) | |||||||
\(24\) | −1.38197 | −0.282093 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.85410 | −1.14808 | ||||||||
\(27\) | 4.53077 | 0.871947 | ||||||||
\(28\) | −6.85410 | −1.29530 | ||||||||
\(29\) | −2.80017 | −0.519978 | −0.259989 | − | 0.965612i | \(-0.583719\pi\) | ||||
−0.259989 | + | 0.965612i | \(0.583719\pi\) | |||||||
\(30\) | −3.61803 | −0.660560 | ||||||||
\(31\) | 1.90211 | 0.341630 | 0.170815 | − | 0.985303i | \(-0.445360\pi\) | ||||
0.170815 | + | 0.985303i | \(0.445360\pi\) | |||||||
\(32\) | 7.33094 | 1.29594 | ||||||||
\(33\) | 11.1352 | 1.93838 | ||||||||
\(34\) | −9.95959 | −1.70806 | ||||||||
\(35\) | 4.23607 | 0.716026 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.80017 | −0.460345 | −0.230172 | − | 0.973150i | \(-0.573929\pi\) | ||||
−0.230172 | + | 0.973150i | \(0.573929\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.85410 | −0.937407 | ||||||||
\(40\) | −0.726543 | −0.114876 | ||||||||
\(41\) | −6.88191 | −1.07477 | −0.537387 | − | 0.843336i | \(-0.680588\pi\) | ||||
−0.537387 | + | 0.843336i | \(0.680588\pi\) | |||||||
\(42\) | −15.3262 | −2.36489 | ||||||||
\(43\) | 0.381966 | 0.0582493 | 0.0291246 | − | 0.999576i | \(-0.490728\pi\) | ||||
0.0291246 | + | 0.999576i | \(0.490728\pi\) | |||||||
\(44\) | −9.47214 | −1.42798 | ||||||||
\(45\) | −0.618034 | −0.0921311 | ||||||||
\(46\) | −7.77997 | −1.14709 | ||||||||
\(47\) | −1.47214 | −0.214733 | −0.107367 | − | 0.994220i | \(-0.534242\pi\) | ||||
−0.107367 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(48\) | 8.78402 | 1.26786 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | −1.90211 | −0.268999 | ||||||||
\(51\) | −9.95959 | −1.39462 | ||||||||
\(52\) | 4.97980 | 0.690574 | ||||||||
\(53\) | 11.1352 | 1.52953 | 0.764766 | − | 0.644308i | \(-0.222854\pi\) | ||||
0.764766 | + | 0.644308i | \(0.222854\pi\) | |||||||
\(54\) | −8.61803 | −1.17277 | ||||||||
\(55\) | 5.85410 | 0.789367 | ||||||||
\(56\) | −3.07768 | −0.411273 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.32624 | 0.699369 | ||||||||
\(59\) | 14.0413 | 1.82803 | 0.914013 | − | 0.405685i | \(-0.132967\pi\) | ||||
0.914013 | + | 0.405685i | \(0.132967\pi\) | |||||||
\(60\) | 3.07768 | 0.397327 | ||||||||
\(61\) | 3.94427 | 0.505012 | 0.252506 | − | 0.967595i | \(-0.418745\pi\) | ||||
0.252506 | + | 0.967595i | \(0.418745\pi\) | |||||||
\(62\) | −3.61803 | −0.459491 | ||||||||
\(63\) | −2.61803 | −0.329841 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | −3.07768 | −0.381740 | ||||||||
\(66\) | −21.1803 | −2.60712 | ||||||||
\(67\) | 5.98385 | 0.731044 | 0.365522 | − | 0.930803i | \(-0.380890\pi\) | ||||
0.365522 | + | 0.930803i | \(0.380890\pi\) | |||||||
\(68\) | 8.47214 | 1.02740 | ||||||||
\(69\) | −7.77997 | −0.936598 | ||||||||
\(70\) | −8.05748 | −0.963053 | ||||||||
\(71\) | 0.171513 | 0.0203549 | 0.0101774 | − | 0.999948i | \(-0.496760\pi\) | ||||
0.0101774 | + | 0.999948i | \(0.496760\pi\) | |||||||
\(72\) | 0.449028 | 0.0529185 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | 5.32624 | 0.619163 | ||||||||
\(75\) | −1.90211 | −0.219637 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.7984 | 2.82604 | ||||||||
\(78\) | 11.1352 | 1.26081 | ||||||||
\(79\) | −5.25731 | −0.591494 | −0.295747 | − | 0.955266i | \(-0.595568\pi\) | ||||
−0.295747 | + | 0.955266i | \(0.595568\pi\) | |||||||
\(80\) | 4.61803 | 0.516312 | ||||||||
\(81\) | −10.4721 | −1.16357 | ||||||||
\(82\) | 13.0902 | 1.44557 | ||||||||
\(83\) | −8.76393 | −0.961967 | −0.480983 | − | 0.876730i | \(-0.659720\pi\) | ||||
−0.480983 | + | 0.876730i | \(0.659720\pi\) | |||||||
\(84\) | 13.0373 | 1.42248 | ||||||||
\(85\) | −5.23607 | −0.567931 | ||||||||
\(86\) | −0.726543 | −0.0783451 | ||||||||
\(87\) | 5.32624 | 0.571033 | ||||||||
\(88\) | −4.25325 | −0.453398 | ||||||||
\(89\) | 7.77997 | 0.824675 | 0.412337 | − | 0.911031i | \(-0.364713\pi\) | ||||
0.412337 | + | 0.911031i | \(0.364713\pi\) | |||||||
\(90\) | 1.17557 | 0.123916 | ||||||||
\(91\) | −13.0373 | −1.36668 | ||||||||
\(92\) | 6.61803 | 0.689978 | ||||||||
\(93\) | −3.61803 | −0.375173 | ||||||||
\(94\) | 2.80017 | 0.288815 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −13.9443 | −1.42318 | ||||||||
\(97\) | −2.62866 | −0.266900 | −0.133450 | − | 0.991056i | \(-0.542605\pi\) | ||||
−0.133450 | + | 0.991056i | \(0.542605\pi\) | |||||||
\(98\) | −20.8172 | −2.10286 | ||||||||
\(99\) | −3.61803 | −0.363626 | ||||||||
\(100\) | 1.61803 | 0.161803 | ||||||||
\(101\) | 3.29180 | 0.327546 | 0.163773 | − | 0.986498i | \(-0.447634\pi\) | ||||
0.163773 | + | 0.986498i | \(0.447634\pi\) | |||||||
\(102\) | 18.9443 | 1.87576 | ||||||||
\(103\) | −14.9394 | −1.47202 | −0.736011 | − | 0.676970i | \(-0.763293\pi\) | ||||
−0.736011 | + | 0.676970i | \(0.763293\pi\) | |||||||
\(104\) | 2.23607 | 0.219265 | ||||||||
\(105\) | −8.05748 | −0.786330 | ||||||||
\(106\) | −21.1803 | −2.05722 | ||||||||
\(107\) | −8.33499 | −0.805774 | −0.402887 | − | 0.915250i | \(-0.631993\pi\) | ||||
−0.402887 | + | 0.915250i | \(0.631993\pi\) | |||||||
\(108\) | 7.33094 | 0.705420 | ||||||||
\(109\) | −2.17963 | −0.208770 | −0.104385 | − | 0.994537i | \(-0.533287\pi\) | ||||
−0.104385 | + | 0.994537i | \(0.533287\pi\) | |||||||
\(110\) | −11.1352 | −1.06170 | ||||||||
\(111\) | 5.32624 | 0.505544 | ||||||||
\(112\) | 19.5623 | 1.84846 | ||||||||
\(113\) | 18.4661 | 1.73714 | 0.868572 | − | 0.495562i | \(-0.165038\pi\) | ||||
0.868572 | + | 0.495562i | \(0.165038\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.09017 | −0.381410 | ||||||||
\(116\) | −4.53077 | −0.420671 | ||||||||
\(117\) | 1.90211 | 0.175850 | ||||||||
\(118\) | −26.7082 | −2.45869 | ||||||||
\(119\) | −22.1803 | −2.03327 | ||||||||
\(120\) | 1.38197 | 0.126156 | ||||||||
\(121\) | 23.2705 | 2.11550 | ||||||||
\(122\) | −7.50245 | −0.679240 | ||||||||
\(123\) | 13.0902 | 1.18030 | ||||||||
\(124\) | 3.07768 | 0.276384 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 4.97980 | 0.443636 | ||||||||
\(127\) | 9.23305 | 0.819301 | 0.409650 | − | 0.912243i | \(-0.365651\pi\) | ||||
0.409650 | + | 0.912243i | \(0.365651\pi\) | |||||||
\(128\) | −5.70634 | −0.504374 | ||||||||
\(129\) | −0.726543 | −0.0639685 | ||||||||
\(130\) | 5.85410 | 0.513439 | ||||||||
\(131\) | −15.6180 | −1.36455 | −0.682277 | − | 0.731094i | \(-0.739010\pi\) | ||||
−0.682277 | + | 0.731094i | \(0.739010\pi\) | |||||||
\(132\) | 18.0171 | 1.56818 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −11.3820 | −0.983252 | ||||||||
\(135\) | −4.53077 | −0.389946 | ||||||||
\(136\) | 3.80423 | 0.326210 | ||||||||
\(137\) | 9.76393 | 0.834189 | 0.417095 | − | 0.908863i | \(-0.363048\pi\) | ||||
0.417095 | + | 0.908863i | \(0.363048\pi\) | |||||||
\(138\) | 14.7984 | 1.25972 | ||||||||
\(139\) | −22.0902 | −1.87366 | −0.936832 | − | 0.349780i | \(-0.886256\pi\) | ||||
−0.936832 | + | 0.349780i | \(0.886256\pi\) | |||||||
\(140\) | 6.85410 | 0.579277 | ||||||||
\(141\) | 2.80017 | 0.235817 | ||||||||
\(142\) | −0.326238 | −0.0273773 | ||||||||
\(143\) | −18.0171 | −1.50666 | ||||||||
\(144\) | −2.85410 | −0.237842 | ||||||||
\(145\) | 2.80017 | 0.232541 | ||||||||
\(146\) | 1.90211 | 0.157420 | ||||||||
\(147\) | −20.8172 | −1.71698 | ||||||||
\(148\) | −4.53077 | −0.372427 | ||||||||
\(149\) | 7.09017 | 0.580849 | 0.290425 | − | 0.956898i | \(-0.406203\pi\) | ||||
0.290425 | + | 0.956898i | \(0.406203\pi\) | |||||||
\(150\) | 3.61803 | 0.295411 | ||||||||
\(151\) | 0.620541 | 0.0504989 | 0.0252495 | − | 0.999681i | \(-0.491962\pi\) | ||||
0.0252495 | + | 0.999681i | \(0.491962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.23607 | 0.261621 | ||||||||
\(154\) | −47.1693 | −3.80101 | ||||||||
\(155\) | −1.90211 | −0.152781 | ||||||||
\(156\) | −9.47214 | −0.758378 | ||||||||
\(157\) | −16.2705 | −1.29853 | −0.649264 | − | 0.760563i | \(-0.724923\pi\) | ||||
−0.649264 | + | 0.760563i | \(0.724923\pi\) | |||||||
\(158\) | 10.0000 | 0.795557 | ||||||||
\(159\) | −21.1803 | −1.67971 | ||||||||
\(160\) | −7.33094 | −0.579562 | ||||||||
\(161\) | −17.3262 | −1.36550 | ||||||||
\(162\) | 19.9192 | 1.56500 | ||||||||
\(163\) | −25.1803 | −1.97228 | −0.986138 | − | 0.165926i | \(-0.946939\pi\) | ||||
−0.986138 | + | 0.165926i | \(0.946939\pi\) | |||||||
\(164\) | −11.1352 | −0.869510 | ||||||||
\(165\) | −11.1352 | −0.866871 | ||||||||
\(166\) | 16.6700 | 1.29384 | ||||||||
\(167\) | 0.171513 | 0.0132721 | 0.00663605 | − | 0.999978i | \(-0.497888\pi\) | ||||
0.00663605 | + | 0.999978i | \(0.497888\pi\) | |||||||
\(168\) | 5.85410 | 0.451654 | ||||||||
\(169\) | −3.52786 | −0.271374 | ||||||||
\(170\) | 9.95959 | 0.763866 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.618034 | 0.0471246 | ||||||||
\(173\) | −13.2088 | −1.00425 | −0.502123 | − | 0.864796i | \(-0.667447\pi\) | ||||
−0.502123 | + | 0.864796i | \(0.667447\pi\) | |||||||
\(174\) | −10.1311 | −0.768037 | ||||||||
\(175\) | −4.23607 | −0.320217 | ||||||||
\(176\) | 27.0344 | 2.03780 | ||||||||
\(177\) | −26.7082 | −2.00751 | ||||||||
\(178\) | −14.7984 | −1.10919 | ||||||||
\(179\) | 10.1311 | 0.757234 | 0.378617 | − | 0.925553i | \(-0.376400\pi\) | ||||
0.378617 | + | 0.925553i | \(0.376400\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | −6.71040 | −0.498780 | −0.249390 | − | 0.968403i | \(-0.580230\pi\) | ||||
−0.249390 | + | 0.968403i | \(0.580230\pi\) | |||||||
\(182\) | 24.7984 | 1.83818 | ||||||||
\(183\) | −7.50245 | −0.554597 | ||||||||
\(184\) | 2.97168 | 0.219075 | ||||||||
\(185\) | 2.80017 | 0.205873 | ||||||||
\(186\) | 6.88191 | 0.504606 | ||||||||
\(187\) | −30.6525 | −2.24153 | ||||||||
\(188\) | −2.38197 | −0.173723 | ||||||||
\(189\) | −19.1926 | −1.39606 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.0000 | 0.940647 | 0.470323 | − | 0.882494i | \(-0.344137\pi\) | ||||
0.470323 | + | 0.882494i | \(0.344137\pi\) | |||||||
\(192\) | 8.95554 | 0.646310 | ||||||||
\(193\) | 1.45309 | 0.104595 | 0.0522977 | − | 0.998632i | \(-0.483346\pi\) | ||||
0.0522977 | + | 0.998632i | \(0.483346\pi\) | |||||||
\(194\) | 5.00000 | 0.358979 | ||||||||
\(195\) | 5.85410 | 0.419221 | ||||||||
\(196\) | 17.7082 | 1.26487 | ||||||||
\(197\) | 14.8885 | 1.06076 | 0.530382 | − | 0.847759i | \(-0.322048\pi\) | ||||
0.530382 | + | 0.847759i | \(0.322048\pi\) | |||||||
\(198\) | 6.88191 | 0.489076 | ||||||||
\(199\) | 13.4164 | 0.951064 | 0.475532 | − | 0.879698i | \(-0.342256\pi\) | ||||
0.475532 | + | 0.879698i | \(0.342256\pi\) | |||||||
\(200\) | 0.726543 | 0.0513743 | ||||||||
\(201\) | −11.3820 | −0.802822 | ||||||||
\(202\) | −6.26137 | −0.440548 | ||||||||
\(203\) | 11.8617 | 0.832529 | ||||||||
\(204\) | −16.1150 | −1.12827 | ||||||||
\(205\) | 6.88191 | 0.480653 | ||||||||
\(206\) | 28.4164 | 1.97986 | ||||||||
\(207\) | 2.52786 | 0.175699 | ||||||||
\(208\) | −14.2128 | −0.985484 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 15.3262 | 1.05761 | ||||||||
\(211\) | −1.73060 | −0.119139 | −0.0595697 | − | 0.998224i | \(-0.518973\pi\) | ||||
−0.0595697 | + | 0.998224i | \(0.518973\pi\) | |||||||
\(212\) | 18.0171 | 1.23742 | ||||||||
\(213\) | −0.326238 | −0.0223535 | ||||||||
\(214\) | 15.8541 | 1.08376 | ||||||||
\(215\) | −0.381966 | −0.0260499 | ||||||||
\(216\) | 3.29180 | 0.223978 | ||||||||
\(217\) | −8.05748 | −0.546977 | ||||||||
\(218\) | 4.14590 | 0.280796 | ||||||||
\(219\) | 1.90211 | 0.128533 | ||||||||
\(220\) | 9.47214 | 0.638611 | ||||||||
\(221\) | 16.1150 | 1.08401 | ||||||||
\(222\) | −10.1311 | −0.679955 | ||||||||
\(223\) | −14.8334 | −0.993317 | −0.496659 | − | 0.867946i | \(-0.665440\pi\) | ||||
−0.496659 | + | 0.867946i | \(0.665440\pi\) | |||||||
\(224\) | −31.0543 | −2.07491 | ||||||||
\(225\) | 0.618034 | 0.0412023 | ||||||||
\(226\) | −35.1246 | −2.33645 | ||||||||
\(227\) | 17.3965 | 1.15465 | 0.577324 | − | 0.816515i | \(-0.304097\pi\) | ||||
0.577324 | + | 0.816515i | \(0.304097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.1459 | −1.19911 | −0.599557 | − | 0.800332i | \(-0.704657\pi\) | ||||
−0.599557 | + | 0.800332i | \(0.704657\pi\) | |||||||
\(230\) | 7.77997 | 0.512996 | ||||||||
\(231\) | −47.1693 | −3.10351 | ||||||||
\(232\) | −2.03444 | −0.133568 | ||||||||
\(233\) | 1.76393 | 0.115559 | 0.0577795 | − | 0.998329i | \(-0.481598\pi\) | ||||
0.0577795 | + | 0.998329i | \(0.481598\pi\) | |||||||
\(234\) | −3.61803 | −0.236518 | ||||||||
\(235\) | 1.47214 | 0.0960316 | ||||||||
\(236\) | 22.7194 | 1.47890 | ||||||||
\(237\) | 10.0000 | 0.649570 | ||||||||
\(238\) | 42.1895 | 2.73474 | ||||||||
\(239\) | −23.2148 | −1.50164 | −0.750820 | − | 0.660507i | \(-0.770341\pi\) | ||||
−0.750820 | + | 0.660507i | \(0.770341\pi\) | |||||||
\(240\) | −8.78402 | −0.567006 | ||||||||
\(241\) | −6.32688 | −0.407550 | −0.203775 | − | 0.979018i | \(-0.565321\pi\) | ||||
−0.203775 | + | 0.979018i | \(0.565321\pi\) | |||||||
\(242\) | −44.2631 | −2.84534 | ||||||||
\(243\) | 6.32688 | 0.405870 | ||||||||
\(244\) | 6.38197 | 0.408564 | ||||||||
\(245\) | −10.9443 | −0.699204 | ||||||||
\(246\) | −24.8990 | −1.58750 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1.38197 | 0.0877549 | ||||||||
\(249\) | 16.6700 | 1.05642 | ||||||||
\(250\) | 1.90211 | 0.120300 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | −4.23607 | −0.266847 | ||||||||
\(253\) | −23.9443 | −1.50536 | ||||||||
\(254\) | −17.5623 | −1.10196 | ||||||||
\(255\) | 9.95959 | 0.623694 | ||||||||
\(256\) | 20.2705 | 1.26691 | ||||||||
\(257\) | −3.24920 | −0.202679 | −0.101340 | − | 0.994852i | \(-0.532313\pi\) | ||||
−0.101340 | + | 0.994852i | \(0.532313\pi\) | |||||||
\(258\) | 1.38197 | 0.0860374 | ||||||||
\(259\) | 11.8617 | 0.737051 | ||||||||
\(260\) | −4.97980 | −0.308834 | ||||||||
\(261\) | −1.73060 | −0.107121 | ||||||||
\(262\) | 29.7073 | 1.83532 | ||||||||
\(263\) | −6.00000 | −0.369976 | −0.184988 | − | 0.982741i | \(-0.559225\pi\) | ||||
−0.184988 | + | 0.982741i | \(0.559225\pi\) | |||||||
\(264\) | 8.09017 | 0.497916 | ||||||||
\(265\) | −11.1352 | −0.684028 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.7984 | −0.905646 | ||||||||
\(268\) | 9.68208 | 0.591427 | ||||||||
\(269\) | 19.6417 | 1.19757 | 0.598787 | − | 0.800908i | \(-0.295650\pi\) | ||||
0.598787 | + | 0.800908i | \(0.295650\pi\) | |||||||
\(270\) | 8.61803 | 0.524477 | ||||||||
\(271\) | 8.61803 | 0.523508 | 0.261754 | − | 0.965135i | \(-0.415699\pi\) | ||||
0.261754 | + | 0.965135i | \(0.415699\pi\) | |||||||
\(272\) | −24.1803 | −1.46615 | ||||||||
\(273\) | 24.7984 | 1.50087 | ||||||||
\(274\) | −18.5721 | −1.12198 | ||||||||
\(275\) | −5.85410 | −0.353016 | ||||||||
\(276\) | −12.5882 | −0.757724 | ||||||||
\(277\) | 24.8328 | 1.49206 | 0.746030 | − | 0.665913i | \(-0.231958\pi\) | ||||
0.746030 | + | 0.665913i | \(0.231958\pi\) | |||||||
\(278\) | 42.0180 | 2.52007 | ||||||||
\(279\) | 1.17557 | 0.0703796 | ||||||||
\(280\) | 3.07768 | 0.183927 | ||||||||
\(281\) | −25.0705 | −1.49558 | −0.747790 | − | 0.663935i | \(-0.768885\pi\) | ||||
−0.747790 | + | 0.663935i | \(0.768885\pi\) | |||||||
\(282\) | −5.32624 | −0.317173 | ||||||||
\(283\) | −28.2705 | −1.68051 | −0.840254 | − | 0.542193i | \(-0.817594\pi\) | ||||
−0.840254 | + | 0.542193i | \(0.817594\pi\) | |||||||
\(284\) | 0.277515 | 0.0164675 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 34.2705 | 2.02646 | ||||||||
\(287\) | 29.1522 | 1.72080 | ||||||||
\(288\) | 4.53077 | 0.266978 | ||||||||
\(289\) | 10.4164 | 0.612730 | ||||||||
\(290\) | −5.32624 | −0.312767 | ||||||||
\(291\) | 5.00000 | 0.293105 | ||||||||
\(292\) | −1.61803 | −0.0946883 | ||||||||
\(293\) | 13.8293 | 0.807918 | 0.403959 | − | 0.914777i | \(-0.367634\pi\) | ||||
0.403959 | + | 0.914777i | \(0.367634\pi\) | |||||||
\(294\) | 39.5967 | 2.30933 | ||||||||
\(295\) | −14.0413 | −0.817518 | ||||||||
\(296\) | −2.03444 | −0.118250 | ||||||||
\(297\) | −26.5236 | −1.53905 | ||||||||
\(298\) | −13.4863 | −0.781241 | ||||||||
\(299\) | 12.5882 | 0.727997 | ||||||||
\(300\) | −3.07768 | −0.177690 | ||||||||
\(301\) | −1.61803 | −0.0932619 | ||||||||
\(302\) | −1.18034 | −0.0679209 | ||||||||
\(303\) | −6.26137 | −0.359706 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.94427 | −0.225848 | ||||||||
\(306\) | −6.15537 | −0.351879 | ||||||||
\(307\) | 18.3601 | 1.04787 | 0.523933 | − | 0.851759i | \(-0.324464\pi\) | ||||
0.523933 | + | 0.851759i | \(0.324464\pi\) | |||||||
\(308\) | 40.1246 | 2.28631 | ||||||||
\(309\) | 28.4164 | 1.61655 | ||||||||
\(310\) | 3.61803 | 0.205491 | ||||||||
\(311\) | −2.76393 | −0.156728 | −0.0783641 | − | 0.996925i | \(-0.524970\pi\) | ||||
−0.0783641 | + | 0.996925i | \(0.524970\pi\) | |||||||
\(312\) | −4.25325 | −0.240793 | ||||||||
\(313\) | 3.27051 | 0.184860 | 0.0924301 | − | 0.995719i | \(-0.470537\pi\) | ||||
0.0924301 | + | 0.995719i | \(0.470537\pi\) | |||||||
\(314\) | 30.9483 | 1.74652 | ||||||||
\(315\) | 2.61803 | 0.147510 | ||||||||
\(316\) | −8.50651 | −0.478528 | ||||||||
\(317\) | −16.4580 | −0.924373 | −0.462186 | − | 0.886783i | \(-0.652935\pi\) | ||||
−0.462186 | + | 0.886783i | \(0.652935\pi\) | |||||||
\(318\) | 40.2874 | 2.25921 | ||||||||
\(319\) | 16.3925 | 0.917802 | ||||||||
\(320\) | 4.70820 | 0.263197 | ||||||||
\(321\) | 15.8541 | 0.884890 | ||||||||
\(322\) | 32.9565 | 1.83659 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −16.9443 | −0.941348 | ||||||||
\(325\) | 3.07768 | 0.170719 | ||||||||
\(326\) | 47.8959 | 2.65271 | ||||||||
\(327\) | 4.14590 | 0.229269 | ||||||||
\(328\) | −5.00000 | −0.276079 | ||||||||
\(329\) | 6.23607 | 0.343806 | ||||||||
\(330\) | 21.1803 | 1.16594 | ||||||||
\(331\) | −19.9192 | −1.09486 | −0.547429 | − | 0.836852i | \(-0.684393\pi\) | ||||
−0.547429 | + | 0.836852i | \(0.684393\pi\) | |||||||
\(332\) | −14.1803 | −0.778247 | ||||||||
\(333\) | −1.73060 | −0.0948363 | ||||||||
\(334\) | −0.326238 | −0.0178509 | ||||||||
\(335\) | −5.98385 | −0.326933 | ||||||||
\(336\) | −37.2097 | −2.02996 | ||||||||
\(337\) | 28.4257 | 1.54845 | 0.774223 | − | 0.632913i | \(-0.218141\pi\) | ||||
0.774223 | + | 0.632913i | \(0.218141\pi\) | |||||||
\(338\) | 6.71040 | 0.364997 | ||||||||
\(339\) | −35.1246 | −1.90771 | ||||||||
\(340\) | −8.47214 | −0.459466 | ||||||||
\(341\) | −11.1352 | −0.603003 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | 0.277515 | 0.0149626 | ||||||||
\(345\) | 7.77997 | 0.418859 | ||||||||
\(346\) | 25.1246 | 1.35071 | ||||||||
\(347\) | 16.4721 | 0.884271 | 0.442135 | − | 0.896948i | \(-0.354221\pi\) | ||||
0.442135 | + | 0.896948i | \(0.354221\pi\) | |||||||
\(348\) | 8.61803 | 0.461975 | ||||||||
\(349\) | −2.56231 | −0.137157 | −0.0685785 | − | 0.997646i | \(-0.521846\pi\) | ||||
−0.0685785 | + | 0.997646i | \(0.521846\pi\) | |||||||
\(350\) | 8.05748 | 0.430690 | ||||||||
\(351\) | 13.9443 | 0.744290 | ||||||||
\(352\) | −42.9161 | −2.28743 | ||||||||
\(353\) | 3.67376 | 0.195535 | 0.0977673 | − | 0.995209i | \(-0.468830\pi\) | ||||
0.0977673 | + | 0.995209i | \(0.468830\pi\) | |||||||
\(354\) | 50.8020 | 2.70010 | ||||||||
\(355\) | −0.171513 | −0.00910299 | ||||||||
\(356\) | 12.5882 | 0.667176 | ||||||||
\(357\) | 42.1895 | 2.23291 | ||||||||
\(358\) | −19.2705 | −1.01848 | ||||||||
\(359\) | 7.38197 | 0.389605 | 0.194803 | − | 0.980842i | \(-0.437593\pi\) | ||||
0.194803 | + | 0.980842i | \(0.437593\pi\) | |||||||
\(360\) | −0.449028 | −0.0236659 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 12.7639 | 0.670857 | ||||||||
\(363\) | −44.2631 | −2.32321 | ||||||||
\(364\) | −21.0948 | −1.10567 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | 14.2705 | 0.745931 | ||||||||
\(367\) | 31.0689 | 1.62178 | 0.810891 | − | 0.585197i | \(-0.198983\pi\) | ||||
0.810891 | + | 0.585197i | \(0.198983\pi\) | |||||||
\(368\) | −18.8885 | −0.984633 | ||||||||
\(369\) | −4.25325 | −0.221416 | ||||||||
\(370\) | −5.32624 | −0.276898 | ||||||||
\(371\) | −47.1693 | −2.44891 | ||||||||
\(372\) | −5.85410 | −0.303521 | ||||||||
\(373\) | 5.42882 | 0.281094 | 0.140547 | − | 0.990074i | \(-0.455114\pi\) | ||||
0.140547 | + | 0.990074i | \(0.455114\pi\) | |||||||
\(374\) | 58.3045 | 3.01485 | ||||||||
\(375\) | 1.90211 | 0.0982247 | ||||||||
\(376\) | −1.06957 | −0.0551588 | ||||||||
\(377\) | −8.61803 | −0.443851 | ||||||||
\(378\) | 36.5066 | 1.87770 | ||||||||
\(379\) | −12.8658 | −0.660870 | −0.330435 | − | 0.943829i | \(-0.607195\pi\) | ||||
−0.330435 | + | 0.943829i | \(0.607195\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.5623 | −0.899744 | ||||||||
\(382\) | −24.7275 | −1.26517 | ||||||||
\(383\) | −4.25325 | −0.217331 | −0.108666 | − | 0.994078i | \(-0.534658\pi\) | ||||
−0.108666 | + | 0.994078i | \(0.534658\pi\) | |||||||
\(384\) | 10.8541 | 0.553896 | ||||||||
\(385\) | −24.7984 | −1.26384 | ||||||||
\(386\) | −2.76393 | −0.140680 | ||||||||
\(387\) | 0.236068 | 0.0120000 | ||||||||
\(388\) | −4.25325 | −0.215926 | ||||||||
\(389\) | −20.8541 | −1.05734 | −0.528672 | − | 0.848826i | \(-0.677310\pi\) | ||||
−0.528672 | + | 0.848826i | \(0.677310\pi\) | |||||||
\(390\) | −11.1352 | −0.563851 | ||||||||
\(391\) | 21.4164 | 1.08307 | ||||||||
\(392\) | 7.95148 | 0.401610 | ||||||||
\(393\) | 29.7073 | 1.49853 | ||||||||
\(394\) | −28.3197 | −1.42673 | ||||||||
\(395\) | 5.25731 | 0.264524 | ||||||||
\(396\) | −5.85410 | −0.294180 | ||||||||
\(397\) | −23.8328 | −1.19613 | −0.598067 | − | 0.801446i | \(-0.704064\pi\) | ||||
−0.598067 | + | 0.801446i | \(0.704064\pi\) | |||||||
\(398\) | −25.5195 | −1.27918 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.61803 | −0.230902 | ||||||||
\(401\) | 9.06154 | 0.452512 | 0.226256 | − | 0.974068i | \(-0.427351\pi\) | ||||
0.226256 | + | 0.974068i | \(0.427351\pi\) | |||||||
\(402\) | 21.6498 | 1.07979 | ||||||||
\(403\) | 5.85410 | 0.291614 | ||||||||
\(404\) | 5.32624 | 0.264990 | ||||||||
\(405\) | 10.4721 | 0.520365 | ||||||||
\(406\) | −22.5623 | −1.11975 | ||||||||
\(407\) | 16.3925 | 0.812545 | ||||||||
\(408\) | −7.23607 | −0.358239 | ||||||||
\(409\) | 21.7153 | 1.07375 | 0.536876 | − | 0.843661i | \(-0.319604\pi\) | ||||
0.536876 | + | 0.843661i | \(0.319604\pi\) | |||||||
\(410\) | −13.0902 | −0.646477 | ||||||||
\(411\) | −18.5721 | −0.916094 | ||||||||
\(412\) | −24.1724 | −1.19089 | ||||||||
\(413\) | −59.4800 | −2.92682 | ||||||||
\(414\) | −4.80828 | −0.236314 | ||||||||
\(415\) | 8.76393 | 0.430205 | ||||||||
\(416\) | 22.5623 | 1.10621 | ||||||||
\(417\) | 42.0180 | 2.05763 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.1803 | 1.27899 | 0.639497 | − | 0.768794i | \(-0.279143\pi\) | ||||
0.639497 | + | 0.768794i | \(0.279143\pi\) | |||||||
\(420\) | −13.0373 | −0.636154 | ||||||||
\(421\) | −11.5842 | −0.564579 | −0.282289 | − | 0.959329i | \(-0.591094\pi\) | ||||
−0.282289 | + | 0.959329i | \(0.591094\pi\) | |||||||
\(422\) | 3.29180 | 0.160242 | ||||||||
\(423\) | −0.909830 | −0.0442375 | ||||||||
\(424\) | 8.09017 | 0.392893 | ||||||||
\(425\) | 5.23607 | 0.253987 | ||||||||
\(426\) | 0.620541 | 0.0300653 | ||||||||
\(427\) | −16.7082 | −0.808567 | ||||||||
\(428\) | −13.4863 | −0.651885 | ||||||||
\(429\) | 34.2705 | 1.65460 | ||||||||
\(430\) | 0.726543 | 0.0350370 | ||||||||
\(431\) | 6.88191 | 0.331490 | 0.165745 | − | 0.986169i | \(-0.446997\pi\) | ||||
0.165745 | + | 0.986169i | \(0.446997\pi\) | |||||||
\(432\) | −20.9232 | −1.00667 | ||||||||
\(433\) | −6.04937 | −0.290714 | −0.145357 | − | 0.989379i | \(-0.546433\pi\) | ||||
−0.145357 | + | 0.989379i | \(0.546433\pi\) | |||||||
\(434\) | 15.3262 | 0.735683 | ||||||||
\(435\) | −5.32624 | −0.255374 | ||||||||
\(436\) | −3.52671 | −0.168899 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.61803 | −0.172876 | ||||||||
\(439\) | 5.64083 | 0.269222 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(440\) | 4.25325 | 0.202766 | ||||||||
\(441\) | 6.76393 | 0.322092 | ||||||||
\(442\) | −30.6525 | −1.45799 | ||||||||
\(443\) | 34.7771 | 1.65231 | 0.826155 | − | 0.563443i | \(-0.190524\pi\) | ||||
0.826155 | + | 0.563443i | \(0.190524\pi\) | |||||||
\(444\) | 8.61803 | 0.408994 | ||||||||
\(445\) | −7.77997 | −0.368806 | ||||||||
\(446\) | 28.2148 | 1.33601 | ||||||||
\(447\) | −13.4863 | −0.637880 | ||||||||
\(448\) | 19.9443 | 0.942278 | ||||||||
\(449\) | 5.64083 | 0.266207 | 0.133104 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133104 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(450\) | −1.17557 | −0.0554169 | ||||||||
\(451\) | 40.2874 | 1.89706 | ||||||||
\(452\) | 29.8788 | 1.40538 | ||||||||
\(453\) | −1.18034 | −0.0554572 | ||||||||
\(454\) | −33.0902 | −1.55300 | ||||||||
\(455\) | 13.0373 | 0.611197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.23607 | 0.244933 | 0.122466 | − | 0.992473i | \(-0.460920\pi\) | ||||
0.122466 | + | 0.992473i | \(0.460920\pi\) | |||||||
\(458\) | 34.5155 | 1.61281 | ||||||||
\(459\) | 23.7234 | 1.10731 | ||||||||
\(460\) | −6.61803 | −0.308567 | ||||||||
\(461\) | −8.00000 | −0.372597 | −0.186299 | − | 0.982493i | \(-0.559649\pi\) | ||||
−0.186299 | + | 0.982493i | \(0.559649\pi\) | |||||||
\(462\) | 89.7214 | 4.17422 | ||||||||
\(463\) | 0.145898 | 0.00678046 | 0.00339023 | − | 0.999994i | \(-0.498921\pi\) | ||||
0.00339023 | + | 0.999994i | \(0.498921\pi\) | |||||||
\(464\) | 12.9313 | 0.600319 | ||||||||
\(465\) | 3.61803 | 0.167782 | ||||||||
\(466\) | −3.35520 | −0.155427 | ||||||||
\(467\) | −9.18034 | −0.424815 | −0.212408 | − | 0.977181i | \(-0.568130\pi\) | ||||
−0.212408 | + | 0.977181i | \(0.568130\pi\) | |||||||
\(468\) | 3.07768 | 0.142266 | ||||||||
\(469\) | −25.3480 | −1.17046 | ||||||||
\(470\) | −2.80017 | −0.129162 | ||||||||
\(471\) | 30.9483 | 1.42602 | ||||||||
\(472\) | 10.2016 | 0.469568 | ||||||||
\(473\) | −2.23607 | −0.102815 | ||||||||
\(474\) | −19.0211 | −0.873669 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −35.8885 | −1.64495 | ||||||||
\(477\) | 6.88191 | 0.315101 | ||||||||
\(478\) | 44.1571 | 2.01970 | ||||||||
\(479\) | −11.4377 | −0.522602 | −0.261301 | − | 0.965257i | \(-0.584151\pi\) | ||||
−0.261301 | + | 0.965257i | \(0.584151\pi\) | |||||||
\(480\) | 13.9443 | 0.636466 | ||||||||
\(481\) | −8.61803 | −0.392949 | ||||||||
\(482\) | 12.0344 | 0.548154 | ||||||||
\(483\) | 32.9565 | 1.49957 | ||||||||
\(484\) | 37.6525 | 1.71148 | ||||||||
\(485\) | 2.62866 | 0.119361 | ||||||||
\(486\) | −12.0344 | −0.545893 | ||||||||
\(487\) | −21.0292 | −0.952926 | −0.476463 | − | 0.879195i | \(-0.658081\pi\) | ||||
−0.476463 | + | 0.879195i | \(0.658081\pi\) | |||||||
\(488\) | 2.86568 | 0.129723 | ||||||||
\(489\) | 47.8959 | 2.16593 | ||||||||
\(490\) | 20.8172 | 0.940427 | ||||||||
\(491\) | 37.2705 | 1.68199 | 0.840997 | − | 0.541039i | \(-0.181969\pi\) | ||||
0.840997 | + | 0.541039i | \(0.181969\pi\) | |||||||
\(492\) | 21.1803 | 0.954883 | ||||||||
\(493\) | −14.6619 | −0.660338 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.61803 | 0.162619 | ||||||||
\(496\) | −8.78402 | −0.394414 | ||||||||
\(497\) | −0.726543 | −0.0325899 | ||||||||
\(498\) | −31.7082 | −1.42088 | ||||||||
\(499\) | −29.5279 | −1.32185 | −0.660924 | − | 0.750453i | \(-0.729836\pi\) | ||||
−0.660924 | + | 0.750453i | \(0.729836\pi\) | |||||||
\(500\) | −1.61803 | −0.0723607 | ||||||||
\(501\) | −0.326238 | −0.0145752 | ||||||||
\(502\) | 5.70634 | 0.254686 | ||||||||
\(503\) | 31.6525 | 1.41131 | 0.705657 | − | 0.708554i | \(-0.250652\pi\) | ||||
0.705657 | + | 0.708554i | \(0.250652\pi\) | |||||||
\(504\) | −1.90211 | −0.0847268 | ||||||||
\(505\) | −3.29180 | −0.146483 | ||||||||
\(506\) | 45.5447 | 2.02471 | ||||||||
\(507\) | 6.71040 | 0.298019 | ||||||||
\(508\) | 14.9394 | 0.662828 | ||||||||
\(509\) | 30.1563 | 1.33665 | 0.668327 | − | 0.743868i | \(-0.267011\pi\) | ||||
0.668327 | + | 0.743868i | \(0.267011\pi\) | |||||||
\(510\) | −18.9443 | −0.838866 | ||||||||
\(511\) | 4.23607 | 0.187393 | ||||||||
\(512\) | −27.1441 | −1.19961 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.18034 | 0.272603 | ||||||||
\(515\) | 14.9394 | 0.658308 | ||||||||
\(516\) | −1.17557 | −0.0517516 | ||||||||
\(517\) | 8.61803 | 0.379021 | ||||||||
\(518\) | −22.5623 | −0.991331 | ||||||||
\(519\) | 25.1246 | 1.10285 | ||||||||
\(520\) | −2.23607 | −0.0980581 | ||||||||
\(521\) | −32.6789 | −1.43169 | −0.715845 | − | 0.698259i | \(-0.753958\pi\) | ||||
−0.715845 | + | 0.698259i | \(0.753958\pi\) | |||||||
\(522\) | 3.29180 | 0.144078 | ||||||||
\(523\) | −6.53888 | −0.285925 | −0.142963 | − | 0.989728i | \(-0.545663\pi\) | ||||
−0.142963 | + | 0.989728i | \(0.545663\pi\) | |||||||
\(524\) | −25.2705 | −1.10395 | ||||||||
\(525\) | 8.05748 | 0.351657 | ||||||||
\(526\) | 11.4127 | 0.497616 | ||||||||
\(527\) | 9.95959 | 0.433847 | ||||||||
\(528\) | −51.4226 | −2.23788 | ||||||||
\(529\) | −6.27051 | −0.272631 | ||||||||
\(530\) | 21.1803 | 0.920015 | ||||||||
\(531\) | 8.67802 | 0.376594 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −21.1803 | −0.917422 | ||||||||
\(534\) | 28.1482 | 1.21809 | ||||||||
\(535\) | 8.33499 | 0.360353 | ||||||||
\(536\) | 4.34752 | 0.187784 | ||||||||
\(537\) | −19.2705 | −0.831584 | ||||||||
\(538\) | −37.3607 | −1.61073 | ||||||||
\(539\) | −64.0689 | −2.75964 | ||||||||
\(540\) | −7.33094 | −0.315473 | ||||||||
\(541\) | −24.5967 | −1.05750 | −0.528748 | − | 0.848779i | \(-0.677338\pi\) | ||||
−0.528748 | + | 0.848779i | \(0.677338\pi\) | |||||||
\(542\) | −16.3925 | −0.704117 | ||||||||
\(543\) | 12.7639 | 0.547753 | ||||||||
\(544\) | 38.3853 | 1.64576 | ||||||||
\(545\) | 2.17963 | 0.0933650 | ||||||||
\(546\) | −47.1693 | −2.01866 | ||||||||
\(547\) | −21.2663 | −0.909280 | −0.454640 | − | 0.890675i | \(-0.650232\pi\) | ||||
−0.454640 | + | 0.890675i | \(0.650232\pi\) | |||||||
\(548\) | 15.7984 | 0.674873 | ||||||||
\(549\) | 2.43769 | 0.104038 | ||||||||
\(550\) | 11.1352 | 0.474805 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −5.65248 | −0.240585 | ||||||||
\(553\) | 22.2703 | 0.947031 | ||||||||
\(554\) | −47.2348 | −2.00682 | ||||||||
\(555\) | −5.32624 | −0.226086 | ||||||||
\(556\) | −35.7426 | −1.51583 | ||||||||
\(557\) | −31.0689 | −1.31643 | −0.658215 | − | 0.752830i | \(-0.728688\pi\) | ||||
−0.658215 | + | 0.752830i | \(0.728688\pi\) | |||||||
\(558\) | −2.23607 | −0.0946603 | ||||||||
\(559\) | 1.17557 | 0.0497213 | ||||||||
\(560\) | −19.5623 | −0.826658 | ||||||||
\(561\) | 58.3045 | 2.46162 | ||||||||
\(562\) | 47.6869 | 2.01155 | ||||||||
\(563\) | −4.35926 | −0.183721 | −0.0918604 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918604 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(564\) | 4.53077 | 0.190780 | ||||||||
\(565\) | −18.4661 | −0.776875 | ||||||||
\(566\) | 53.7737 | 2.26028 | ||||||||
\(567\) | 44.3607 | 1.86297 | ||||||||
\(568\) | 0.124612 | 0.00522859 | ||||||||
\(569\) | −25.7970 | −1.08147 | −0.540734 | − | 0.841194i | \(-0.681853\pi\) | ||||
−0.540734 | + | 0.841194i | \(0.681853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.8541 | −1.08196 | −0.540980 | − | 0.841035i | \(-0.681947\pi\) | ||||
−0.540980 | + | 0.841035i | \(0.681947\pi\) | |||||||
\(572\) | −29.1522 | −1.21892 | ||||||||
\(573\) | −24.7275 | −1.03300 | ||||||||
\(574\) | −55.4508 | −2.31447 | ||||||||
\(575\) | 4.09017 | 0.170572 | ||||||||
\(576\) | −2.90983 | −0.121243 | ||||||||
\(577\) | 8.52786 | 0.355020 | 0.177510 | − | 0.984119i | \(-0.443196\pi\) | ||||
0.177510 | + | 0.984119i | \(0.443196\pi\) | |||||||
\(578\) | −19.8132 | −0.824120 | ||||||||
\(579\) | −2.76393 | −0.114865 | ||||||||
\(580\) | 4.53077 | 0.188130 | ||||||||
\(581\) | 37.1246 | 1.54019 | ||||||||
\(582\) | −9.51057 | −0.394226 | ||||||||
\(583\) | −65.1864 | −2.69974 | ||||||||
\(584\) | −0.726543 | −0.0300645 | ||||||||
\(585\) | −1.90211 | −0.0786427 | ||||||||
\(586\) | −26.3050 | −1.08665 | ||||||||
\(587\) | 36.4164 | 1.50307 | 0.751533 | − | 0.659695i | \(-0.229315\pi\) | ||||
0.751533 | + | 0.659695i | \(0.229315\pi\) | |||||||
\(588\) | −33.6830 | −1.38906 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 26.7082 | 1.09956 | ||||||||
\(591\) | −28.3197 | −1.16492 | ||||||||
\(592\) | 12.9313 | 0.531472 | ||||||||
\(593\) | 20.7082 | 0.850384 | 0.425192 | − | 0.905103i | \(-0.360207\pi\) | ||||
0.425192 | + | 0.905103i | \(0.360207\pi\) | |||||||
\(594\) | 50.4508 | 2.07002 | ||||||||
\(595\) | 22.1803 | 0.909305 | ||||||||
\(596\) | 11.4721 | 0.469917 | ||||||||
\(597\) | −25.5195 | −1.04444 | ||||||||
\(598\) | −23.9443 | −0.979154 | ||||||||
\(599\) | −30.0503 | −1.22782 | −0.613911 | − | 0.789375i | \(-0.710405\pi\) | ||||
−0.613911 | + | 0.789375i | \(0.710405\pi\) | |||||||
\(600\) | −1.38197 | −0.0564185 | ||||||||
\(601\) | 10.5146 | 0.428900 | 0.214450 | − | 0.976735i | \(-0.431204\pi\) | ||||
0.214450 | + | 0.976735i | \(0.431204\pi\) | |||||||
\(602\) | 3.07768 | 0.125437 | ||||||||
\(603\) | 3.69822 | 0.150603 | ||||||||
\(604\) | 1.00406 | 0.0408545 | ||||||||
\(605\) | −23.2705 | −0.946081 | ||||||||
\(606\) | 11.9098 | 0.483804 | ||||||||
\(607\) | −16.2210 | −0.658389 | −0.329194 | − | 0.944262i | \(-0.606777\pi\) | ||||
−0.329194 | + | 0.944262i | \(0.606777\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −22.5623 | −0.914271 | ||||||||
\(610\) | 7.50245 | 0.303765 | ||||||||
\(611\) | −4.53077 | −0.183295 | ||||||||
\(612\) | 5.23607 | 0.211656 | ||||||||
\(613\) | 26.5279 | 1.07145 | 0.535725 | − | 0.844392i | \(-0.320038\pi\) | ||||
0.535725 | + | 0.844392i | \(0.320038\pi\) | |||||||
\(614\) | −34.9230 | −1.40938 | ||||||||
\(615\) | −13.0902 | −0.527847 | ||||||||
\(616\) | 18.0171 | 0.725929 | ||||||||
\(617\) | 21.6180 | 0.870309 | 0.435155 | − | 0.900356i | \(-0.356694\pi\) | ||||
0.435155 | + | 0.900356i | \(0.356694\pi\) | |||||||
\(618\) | −54.0512 | −2.17426 | ||||||||
\(619\) | 39.5410 | 1.58929 | 0.794644 | − | 0.607076i | \(-0.207658\pi\) | ||||
0.794644 | + | 0.607076i | \(0.207658\pi\) | |||||||
\(620\) | −3.07768 | −0.123603 | ||||||||
\(621\) | 18.5316 | 0.743648 | ||||||||
\(622\) | 5.25731 | 0.210799 | ||||||||
\(623\) | −32.9565 | −1.32037 | ||||||||
\(624\) | 27.0344 | 1.08224 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −6.22088 | −0.248636 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −26.3262 | −1.05053 | ||||||||
\(629\) | −14.6619 | −0.584607 | ||||||||
\(630\) | −4.97980 | −0.198400 | ||||||||
\(631\) | −41.1803 | −1.63936 | −0.819682 | − | 0.572819i | \(-0.805850\pi\) | ||||
−0.819682 | + | 0.572819i | \(0.805850\pi\) | |||||||
\(632\) | −3.81966 | −0.151938 | ||||||||
\(633\) | 3.29180 | 0.130837 | ||||||||
\(634\) | 31.3050 | 1.24328 | ||||||||
\(635\) | −9.23305 | −0.366402 | ||||||||
\(636\) | −34.2705 | −1.35891 | ||||||||
\(637\) | 33.6830 | 1.33457 | ||||||||
\(638\) | −31.1803 | −1.23444 | ||||||||
\(639\) | 0.106001 | 0.00419334 | ||||||||
\(640\) | 5.70634 | 0.225563 | ||||||||
\(641\) | −36.6952 | −1.44937 | −0.724686 | − | 0.689079i | \(-0.758015\pi\) | ||||
−0.724686 | + | 0.689079i | \(0.758015\pi\) | |||||||
\(642\) | −30.1563 | −1.19017 | ||||||||
\(643\) | −38.4721 | −1.51719 | −0.758596 | − | 0.651561i | \(-0.774115\pi\) | ||||
−0.758596 | + | 0.651561i | \(0.774115\pi\) | |||||||
\(644\) | −28.0344 | −1.10471 | ||||||||
\(645\) | 0.726543 | 0.0286076 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.52786 | 0.335265 | 0.167632 | − | 0.985850i | \(-0.446388\pi\) | ||||
0.167632 | + | 0.985850i | \(0.446388\pi\) | |||||||
\(648\) | −7.60845 | −0.298888 | ||||||||
\(649\) | −82.1994 | −3.22661 | ||||||||
\(650\) | −5.85410 | −0.229617 | ||||||||
\(651\) | 15.3262 | 0.600683 | ||||||||
\(652\) | −40.7426 | −1.59561 | ||||||||
\(653\) | −13.7984 | −0.539972 | −0.269986 | − | 0.962864i | \(-0.587019\pi\) | ||||
−0.269986 | + | 0.962864i | \(0.587019\pi\) | |||||||
\(654\) | −7.88597 | −0.308366 | ||||||||
\(655\) | 15.6180 | 0.610247 | ||||||||
\(656\) | 31.7809 | 1.24084 | ||||||||
\(657\) | −0.618034 | −0.0241118 | ||||||||
\(658\) | −11.8617 | −0.462417 | ||||||||
\(659\) | 7.26543 | 0.283021 | 0.141510 | − | 0.989937i | \(-0.454804\pi\) | ||||
0.141510 | + | 0.989937i | \(0.454804\pi\) | |||||||
\(660\) | −18.0171 | −0.701314 | ||||||||
\(661\) | −29.3238 | −1.14056 | −0.570281 | − | 0.821450i | \(-0.693166\pi\) | ||||
−0.570281 | + | 0.821450i | \(0.693166\pi\) | |||||||
\(662\) | 37.8885 | 1.47258 | ||||||||
\(663\) | −30.6525 | −1.19044 | ||||||||
\(664\) | −6.36737 | −0.247102 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.29180 | 0.127555 | ||||||||
\(667\) | −11.4532 | −0.443468 | ||||||||
\(668\) | 0.277515 | 0.0107374 | ||||||||
\(669\) | 28.2148 | 1.09085 | ||||||||
\(670\) | 11.3820 | 0.439724 | ||||||||
\(671\) | −23.0902 | −0.891386 | ||||||||
\(672\) | 59.0689 | 2.27863 | ||||||||
\(673\) | 24.2380 | 0.934304 | 0.467152 | − | 0.884177i | \(-0.345280\pi\) | ||||
0.467152 | + | 0.884177i | \(0.345280\pi\) | |||||||
\(674\) | −54.0689 | −2.08266 | ||||||||
\(675\) | 4.53077 | 0.174389 | ||||||||
\(676\) | −5.70820 | −0.219546 | ||||||||
\(677\) | 33.5770 | 1.29047 | 0.645235 | − | 0.763985i | \(-0.276760\pi\) | ||||
0.645235 | + | 0.763985i | \(0.276760\pi\) | |||||||
\(678\) | 66.8110 | 2.56586 | ||||||||
\(679\) | 11.1352 | 0.427328 | ||||||||
\(680\) | −3.80423 | −0.145885 | ||||||||
\(681\) | −33.0902 | −1.26802 | ||||||||
\(682\) | 21.1803 | 0.811037 | ||||||||
\(683\) | 28.0422 | 1.07300 | 0.536502 | − | 0.843899i | \(-0.319745\pi\) | ||||
0.536502 | + | 0.843899i | \(0.319745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.76393 | −0.373061 | ||||||||
\(686\) | 31.7809 | 1.21340 | ||||||||
\(687\) | 34.5155 | 1.31685 | ||||||||
\(688\) | −1.76393 | −0.0672493 | ||||||||
\(689\) | 34.2705 | 1.30560 | ||||||||
\(690\) | −14.7984 | −0.563364 | ||||||||
\(691\) | −12.2361 | −0.465482 | −0.232741 | − | 0.972539i | \(-0.574769\pi\) | ||||
−0.232741 | + | 0.972539i | \(0.574769\pi\) | |||||||
\(692\) | −21.3723 | −0.812452 | ||||||||
\(693\) | 15.3262 | 0.582196 | ||||||||
\(694\) | −31.3319 | −1.18934 | ||||||||
\(695\) | 22.0902 | 0.837928 | ||||||||
\(696\) | 3.86974 | 0.146682 | ||||||||
\(697\) | −36.0341 | −1.36489 | ||||||||
\(698\) | 4.87380 | 0.184476 | ||||||||
\(699\) | −3.35520 | −0.126905 | ||||||||
\(700\) | −6.85410 | −0.259061 | ||||||||
\(701\) | −31.9098 | −1.20522 | −0.602609 | − | 0.798037i | \(-0.705872\pi\) | ||||
−0.602609 | + | 0.798037i | \(0.705872\pi\) | |||||||
\(702\) | −26.5236 | −1.00107 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 27.5623 | 1.03879 | ||||||||
\(705\) | −2.80017 | −0.105460 | ||||||||
\(706\) | −6.98791 | −0.262993 | ||||||||
\(707\) | −13.9443 | −0.524428 | ||||||||
\(708\) | −43.2148 | −1.62411 | ||||||||
\(709\) | 36.1803 | 1.35878 | 0.679391 | − | 0.733777i | \(-0.262244\pi\) | ||||
0.679391 | + | 0.733777i | \(0.262244\pi\) | |||||||
\(710\) | 0.326238 | 0.0122435 | ||||||||
\(711\) | −3.24920 | −0.121854 | ||||||||
\(712\) | 5.65248 | 0.211835 | ||||||||
\(713\) | 7.77997 | 0.291362 | ||||||||
\(714\) | −80.2492 | −3.00325 | ||||||||
\(715\) | 18.0171 | 0.673800 | ||||||||
\(716\) | 16.3925 | 0.612616 | ||||||||
\(717\) | 44.1571 | 1.64908 | ||||||||
\(718\) | −14.0413 | −0.524018 | ||||||||
\(719\) | −30.9098 | −1.15274 | −0.576371 | − | 0.817188i | \(-0.695532\pi\) | ||||
−0.576371 | + | 0.817188i | \(0.695532\pi\) | |||||||
\(720\) | 2.85410 | 0.106366 | ||||||||
\(721\) | 63.2843 | 2.35683 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.0344 | 0.447566 | ||||||||
\(724\) | −10.8576 | −0.403521 | ||||||||
\(725\) | −2.80017 | −0.103996 | ||||||||
\(726\) | 84.1935 | 3.12471 | ||||||||
\(727\) | 34.3607 | 1.27437 | 0.637184 | − | 0.770712i | \(-0.280099\pi\) | ||||
0.637184 | + | 0.770712i | \(0.280099\pi\) | |||||||
\(728\) | −9.47214 | −0.351061 | ||||||||
\(729\) | 19.3820 | 0.717851 | ||||||||
\(730\) | −1.90211 | −0.0704004 | ||||||||
\(731\) | 2.00000 | 0.0739727 | ||||||||
\(732\) | −12.1392 | −0.448679 | ||||||||
\(733\) | −11.0000 | −0.406294 | −0.203147 | − | 0.979148i | \(-0.565117\pi\) | ||||
−0.203147 | + | 0.979148i | \(0.565117\pi\) | |||||||
\(734\) | −59.0965 | −2.18129 | ||||||||
\(735\) | 20.8172 | 0.767856 | ||||||||
\(736\) | 29.9848 | 1.10525 | ||||||||
\(737\) | −35.0301 | −1.29035 | ||||||||
\(738\) | 8.09017 | 0.297803 | ||||||||
\(739\) | −27.7639 | −1.02131 | −0.510656 | − | 0.859785i | \(-0.670598\pi\) | ||||
−0.510656 | + | 0.859785i | \(0.670598\pi\) | |||||||
\(740\) | 4.53077 | 0.166554 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 89.7214 | 3.29377 | ||||||||
\(743\) | −5.98385 | −0.219526 | −0.109763 | − | 0.993958i | \(-0.535009\pi\) | ||||
−0.109763 | + | 0.993958i | \(0.535009\pi\) | |||||||
\(744\) | −2.62866 | −0.0963712 | ||||||||
\(745\) | −7.09017 | −0.259764 | ||||||||
\(746\) | −10.3262 | −0.378070 | ||||||||
\(747\) | −5.41641 | −0.198176 | ||||||||
\(748\) | −49.5967 | −1.81344 | ||||||||
\(749\) | 35.3076 | 1.29011 | ||||||||
\(750\) | −3.61803 | −0.132112 | ||||||||
\(751\) | 50.4590 | 1.84127 | 0.920637 | − | 0.390419i | \(-0.127670\pi\) | ||||
0.920637 | + | 0.390419i | \(0.127670\pi\) | |||||||
\(752\) | 6.79837 | 0.247911 | ||||||||
\(753\) | 5.70634 | 0.207951 | ||||||||
\(754\) | 16.3925 | 0.596979 | ||||||||
\(755\) | −0.620541 | −0.0225838 | ||||||||
\(756\) | −31.0543 | −1.12944 | ||||||||
\(757\) | 2.97871 | 0.108263 | 0.0541316 | − | 0.998534i | \(-0.482761\pi\) | ||||
0.0541316 | + | 0.998534i | \(0.482761\pi\) | |||||||
\(758\) | 24.4721 | 0.888868 | ||||||||
\(759\) | 45.5447 | 1.65317 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −18.8197 | −0.682212 | −0.341106 | − | 0.940025i | \(-0.610802\pi\) | ||||
−0.341106 | + | 0.940025i | \(0.610802\pi\) | |||||||
\(762\) | 33.4055 | 1.21015 | ||||||||
\(763\) | 9.23305 | 0.334259 | ||||||||
\(764\) | 21.0344 | 0.760999 | ||||||||
\(765\) | −3.23607 | −0.117000 | ||||||||
\(766\) | 8.09017 | 0.292310 | ||||||||
\(767\) | 43.2148 | 1.56040 | ||||||||
\(768\) | −38.5568 | −1.39130 | ||||||||
\(769\) | −13.2705 | −0.478547 | −0.239273 | − | 0.970952i | \(-0.576909\pi\) | ||||
−0.239273 | + | 0.970952i | \(0.576909\pi\) | |||||||
\(770\) | 47.1693 | 1.69986 | ||||||||
\(771\) | 6.18034 | 0.222580 | ||||||||
\(772\) | 2.35114 | 0.0846194 | ||||||||
\(773\) | −32.5074 | −1.16921 | −0.584606 | − | 0.811318i | \(-0.698751\pi\) | ||||
−0.584606 | + | 0.811318i | \(0.698751\pi\) | |||||||
\(774\) | −0.449028 | −0.0161400 | ||||||||
\(775\) | 1.90211 | 0.0683259 | ||||||||
\(776\) | −1.90983 | −0.0685589 | ||||||||
\(777\) | −22.5623 | −0.809418 | ||||||||
\(778\) | 39.6669 | 1.42213 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 9.47214 | 0.339157 | ||||||||
\(781\) | −1.00406 | −0.0359280 | ||||||||
\(782\) | −40.7364 | −1.45673 | ||||||||
\(783\) | −12.6869 | −0.453393 | ||||||||
\(784\) | −50.5410 | −1.80504 | ||||||||
\(785\) | 16.2705 | 0.580719 | ||||||||
\(786\) | −56.5066 | −2.01552 | ||||||||
\(787\) | 20.1312 | 0.717599 | 0.358800 | − | 0.933415i | \(-0.383186\pi\) | ||||
0.358800 | + | 0.933415i | \(0.383186\pi\) | |||||||
\(788\) | 24.0902 | 0.858177 | ||||||||
\(789\) | 11.4127 | 0.406302 | ||||||||
\(790\) | −10.0000 | −0.355784 | ||||||||
\(791\) | −78.2237 | −2.78131 | ||||||||
\(792\) | −2.62866 | −0.0934052 | ||||||||
\(793\) | 12.1392 | 0.431076 | ||||||||
\(794\) | 45.3327 | 1.60880 | ||||||||
\(795\) | 21.1803 | 0.751189 | ||||||||
\(796\) | 21.7082 | 0.769427 | ||||||||
\(797\) | −23.7234 | −0.840326 | −0.420163 | − | 0.907449i | \(-0.638027\pi\) | ||||
−0.420163 | + | 0.907449i | \(0.638027\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.70820 | −0.272697 | ||||||||
\(800\) | 7.33094 | 0.259188 | ||||||||
\(801\) | 4.80828 | 0.169892 | ||||||||
\(802\) | −17.2361 | −0.608627 | ||||||||
\(803\) | 5.85410 | 0.206587 | ||||||||
\(804\) | −18.4164 | −0.649497 | ||||||||
\(805\) | 17.3262 | 0.610670 | ||||||||
\(806\) | −11.1352 | −0.392219 | ||||||||
\(807\) | −37.3607 | −1.31516 | ||||||||
\(808\) | 2.39163 | 0.0841372 | ||||||||
\(809\) | −53.2148 | −1.87093 | −0.935466 | − | 0.353417i | \(-0.885020\pi\) | ||||
−0.935466 | + | 0.353417i | \(0.885020\pi\) | |||||||
\(810\) | −19.9192 | −0.699889 | ||||||||
\(811\) | −13.1433 | −0.461523 | −0.230761 | − | 0.973010i | \(-0.574122\pi\) | ||||
−0.230761 | + | 0.973010i | \(0.574122\pi\) | |||||||
\(812\) | 19.1926 | 0.673530 | ||||||||
\(813\) | −16.3925 | −0.574909 | ||||||||
\(814\) | −31.1803 | −1.09287 | ||||||||
\(815\) | 25.1803 | 0.882029 | ||||||||
\(816\) | 45.9937 | 1.61010 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −41.3050 | −1.44419 | ||||||||
\(819\) | −8.05748 | −0.281551 | ||||||||
\(820\) | 11.1352 | 0.388857 | ||||||||
\(821\) | −27.4508 | −0.958041 | −0.479021 | − | 0.877804i | \(-0.659008\pi\) | ||||
−0.479021 | + | 0.877804i | \(0.659008\pi\) | |||||||
\(822\) | 35.3262 | 1.23214 | ||||||||
\(823\) | −16.7639 | −0.584354 | −0.292177 | − | 0.956364i | \(-0.594380\pi\) | ||||
−0.292177 | + | 0.956364i | \(0.594380\pi\) | |||||||
\(824\) | −10.8541 | −0.378121 | ||||||||
\(825\) | 11.1352 | 0.387677 | ||||||||
\(826\) | 113.138 | 3.93657 | ||||||||
\(827\) | −9.23305 | −0.321065 | −0.160532 | − | 0.987031i | \(-0.551321\pi\) | ||||
−0.160532 | + | 0.987031i | \(0.551321\pi\) | |||||||
\(828\) | 4.09017 | 0.142143 | ||||||||
\(829\) | 25.9686 | 0.901925 | 0.450963 | − | 0.892543i | \(-0.351081\pi\) | ||||
0.450963 | + | 0.892543i | \(0.351081\pi\) | |||||||
\(830\) | −16.6700 | −0.578624 | ||||||||
\(831\) | −47.2348 | −1.63856 | ||||||||
\(832\) | −14.4904 | −0.502363 | ||||||||
\(833\) | 57.3050 | 1.98550 | ||||||||
\(834\) | −79.9230 | −2.76751 | ||||||||
\(835\) | −0.171513 | −0.00593547 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.61803 | 0.297883 | ||||||||
\(838\) | −49.7980 | −1.72024 | ||||||||
\(839\) | −4.08174 | −0.140917 | −0.0704587 | − | 0.997515i | \(-0.522446\pi\) | ||||
−0.0704587 | + | 0.997515i | \(0.522446\pi\) | |||||||
\(840\) | −5.85410 | −0.201986 | ||||||||
\(841\) | −21.1591 | −0.729623 | ||||||||
\(842\) | 22.0344 | 0.759357 | ||||||||
\(843\) | 47.6869 | 1.64242 | ||||||||
\(844\) | −2.80017 | −0.0963858 | ||||||||
\(845\) | 3.52786 | 0.121362 | ||||||||
\(846\) | 1.73060 | 0.0594992 | ||||||||
\(847\) | −98.5755 | −3.38709 | ||||||||
\(848\) | −51.4226 | −1.76586 | ||||||||
\(849\) | 53.7737 | 1.84551 | ||||||||
\(850\) | −9.95959 | −0.341611 | ||||||||
\(851\) | −11.4532 | −0.392610 | ||||||||
\(852\) | −0.527864 | −0.0180843 | ||||||||
\(853\) | −15.4721 | −0.529756 | −0.264878 | − | 0.964282i | \(-0.585332\pi\) | ||||
−0.264878 | + | 0.964282i | \(0.585332\pi\) | |||||||
\(854\) | 31.7809 | 1.08752 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.05573 | −0.206981 | ||||||||
\(857\) | 6.22088 | 0.212501 | 0.106251 | − | 0.994339i | \(-0.466115\pi\) | ||||
0.106251 | + | 0.994339i | \(0.466115\pi\) | |||||||
\(858\) | −65.1864 | −2.22543 | ||||||||
\(859\) | −22.7639 | −0.776695 | −0.388348 | − | 0.921513i | \(-0.626954\pi\) | ||||
−0.388348 | + | 0.921513i | \(0.626954\pi\) | |||||||
\(860\) | −0.618034 | −0.0210748 | ||||||||
\(861\) | −55.4508 | −1.88976 | ||||||||
\(862\) | −13.0902 | −0.445853 | ||||||||
\(863\) | 36.3772 | 1.23829 | 0.619147 | − | 0.785275i | \(-0.287479\pi\) | ||||
0.619147 | + | 0.785275i | \(0.287479\pi\) | |||||||
\(864\) | 33.2148 | 1.12999 | ||||||||
\(865\) | 13.2088 | 0.449112 | ||||||||
\(866\) | 11.5066 | 0.391009 | ||||||||
\(867\) | −19.8132 | −0.672891 | ||||||||
\(868\) | −13.0373 | −0.442514 | ||||||||
\(869\) | 30.7768 | 1.04403 | ||||||||
\(870\) | 10.1311 | 0.343477 | ||||||||
\(871\) | 18.4164 | 0.624016 | ||||||||
\(872\) | −1.58359 | −0.0536272 | ||||||||
\(873\) | −1.62460 | −0.0549843 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.23607 | 0.143205 | ||||||||
\(876\) | 3.07768 | 0.103985 | ||||||||
\(877\) | −11.9677 | −0.404121 | −0.202060 | − | 0.979373i | \(-0.564764\pi\) | ||||
−0.202060 | + | 0.979373i | \(0.564764\pi\) | |||||||
\(878\) | −10.7295 | −0.362103 | ||||||||
\(879\) | −26.3050 | −0.887244 | ||||||||
\(880\) | −27.0344 | −0.911331 | ||||||||
\(881\) | 10.3262 | 0.347900 | 0.173950 | − | 0.984755i | \(-0.444347\pi\) | ||||
0.173950 | + | 0.984755i | \(0.444347\pi\) | |||||||
\(882\) | −12.8658 | −0.433213 | ||||||||
\(883\) | −5.78522 | −0.194688 | −0.0973440 | − | 0.995251i | \(-0.531035\pi\) | ||||
−0.0973440 | + | 0.995251i | \(0.531035\pi\) | |||||||
\(884\) | 26.0746 | 0.876982 | ||||||||
\(885\) | 26.7082 | 0.897786 | ||||||||
\(886\) | −66.1500 | −2.22235 | ||||||||
\(887\) | −14.3188 | −0.480780 | −0.240390 | − | 0.970676i | \(-0.577275\pi\) | ||||
−0.240390 | + | 0.970676i | \(0.577275\pi\) | |||||||
\(888\) | 3.86974 | 0.129860 | ||||||||
\(889\) | −39.1118 | −1.31177 | ||||||||
\(890\) | 14.7984 | 0.496043 | ||||||||
\(891\) | 61.3050 | 2.05379 | ||||||||
\(892\) | −24.0009 | −0.803610 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 25.6525 | 0.857947 | ||||||||
\(895\) | −10.1311 | −0.338646 | ||||||||
\(896\) | 24.1724 | 0.807545 | ||||||||
\(897\) | −23.9443 | −0.799476 | ||||||||
\(898\) | −10.7295 | −0.358048 | ||||||||
\(899\) | −5.32624 | −0.177640 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 58.3045 | 1.94240 | ||||||||
\(902\) | −76.6312 | −2.55154 | ||||||||
\(903\) | 3.07768 | 0.102419 | ||||||||
\(904\) | 13.4164 | 0.446223 | ||||||||
\(905\) | 6.71040 | 0.223061 | ||||||||
\(906\) | 2.24514 | 0.0745898 | ||||||||
\(907\) | −51.9371 | −1.72454 | −0.862272 | − | 0.506446i | \(-0.830959\pi\) | ||||
−0.862272 | + | 0.506446i | \(0.830959\pi\) | |||||||
\(908\) | 28.1482 | 0.934130 | ||||||||
\(909\) | 2.03444 | 0.0674782 | ||||||||
\(910\) | −24.7984 | −0.822058 | ||||||||
\(911\) | 34.3035 | 1.13653 | 0.568264 | − | 0.822847i | \(-0.307615\pi\) | ||||
0.568264 | + | 0.822847i | \(0.307615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.3050 | 1.69795 | ||||||||
\(914\) | −9.95959 | −0.329434 | ||||||||
\(915\) | 7.50245 | 0.248023 | ||||||||
\(916\) | −29.3607 | −0.970104 | ||||||||
\(917\) | 66.1591 | 2.18476 | ||||||||
\(918\) | −45.1246 | −1.48933 | ||||||||
\(919\) | 7.36068 | 0.242806 | 0.121403 | − | 0.992603i | \(-0.461261\pi\) | ||||
0.121403 | + | 0.992603i | \(0.461261\pi\) | |||||||
\(920\) | −2.97168 | −0.0979735 | ||||||||
\(921\) | −34.9230 | −1.15075 | ||||||||
\(922\) | 15.2169 | 0.501142 | ||||||||
\(923\) | 0.527864 | 0.0173749 | ||||||||
\(924\) | −76.3215 | −2.51079 | ||||||||
\(925\) | −2.80017 | −0.0920690 | ||||||||
\(926\) | −0.277515 | −0.00911969 | ||||||||
\(927\) | −9.23305 | −0.303253 | ||||||||
\(928\) | −20.5279 | −0.673860 | ||||||||
\(929\) | 37.5623 | 1.23238 | 0.616190 | − | 0.787598i | \(-0.288675\pi\) | ||||
0.616190 | + | 0.787598i | \(0.288675\pi\) | |||||||
\(930\) | −6.88191 | −0.225667 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.85410 | 0.0934892 | ||||||||
\(933\) | 5.25731 | 0.172117 | ||||||||
\(934\) | 17.4620 | 0.571376 | ||||||||
\(935\) | 30.6525 | 1.00244 | ||||||||
\(936\) | 1.38197 | 0.0451710 | ||||||||
\(937\) | 23.2016 | 0.757964 | 0.378982 | − | 0.925404i | \(-0.376274\pi\) | ||||
0.378982 | + | 0.925404i | \(0.376274\pi\) | |||||||
\(938\) | 48.2148 | 1.57427 | ||||||||
\(939\) | −6.22088 | −0.203011 | ||||||||
\(940\) | 2.38197 | 0.0776912 | ||||||||
\(941\) | −50.7615 | −1.65478 | −0.827389 | − | 0.561629i | \(-0.810175\pi\) | ||||
−0.827389 | + | 0.561629i | \(0.810175\pi\) | |||||||
\(942\) | −58.8673 | −1.91800 | ||||||||
\(943\) | −28.1482 | −0.916631 | ||||||||
\(944\) | −64.8434 | −2.11047 | ||||||||
\(945\) | 19.1926 | 0.624337 | ||||||||
\(946\) | 4.25325 | 0.138285 | ||||||||
\(947\) | 1.41641 | 0.0460271 | 0.0230135 | − | 0.999735i | \(-0.492674\pi\) | ||||
0.0230135 | + | 0.999735i | \(0.492674\pi\) | |||||||
\(948\) | 16.1803 | 0.525513 | ||||||||
\(949\) | −3.07768 | −0.0999058 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.3050 | 1.01513 | ||||||||
\(952\) | −16.1150 | −0.522289 | ||||||||
\(953\) | 42.2300 | 1.36796 | 0.683982 | − | 0.729499i | \(-0.260247\pi\) | ||||
0.683982 | + | 0.729499i | \(0.260247\pi\) | |||||||
\(954\) | −13.0902 | −0.423810 | ||||||||
\(955\) | −13.0000 | −0.420670 | ||||||||
\(956\) | −37.5623 | −1.21485 | ||||||||
\(957\) | −31.1803 | −1.00792 | ||||||||
\(958\) | 21.7558 | 0.702898 | ||||||||
\(959\) | −41.3607 | −1.33561 | ||||||||
\(960\) | −8.95554 | −0.289039 | ||||||||
\(961\) | −27.3820 | −0.883289 | ||||||||
\(962\) | 16.3925 | 0.528515 | ||||||||
\(963\) | −5.15131 | −0.165999 | ||||||||
\(964\) | −10.2371 | −0.329715 | ||||||||
\(965\) | −1.45309 | −0.0467765 | ||||||||
\(966\) | −62.6869 | −2.01692 | ||||||||
\(967\) | −29.0557 | −0.934369 | −0.467185 | − | 0.884160i | \(-0.654732\pi\) | ||||
−0.467185 | + | 0.884160i | \(0.654732\pi\) | |||||||
\(968\) | 16.9070 | 0.543412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.00000 | −0.160540 | ||||||||
\(971\) | −27.4216 | −0.880002 | −0.440001 | − | 0.897997i | \(-0.645022\pi\) | ||||
−0.440001 | + | 0.897997i | \(0.645022\pi\) | |||||||
\(972\) | 10.2371 | 0.328355 | ||||||||
\(973\) | 93.5755 | 2.99989 | ||||||||
\(974\) | 40.0000 | 1.28168 | ||||||||
\(975\) | −5.85410 | −0.187481 | ||||||||
\(976\) | −18.2148 | −0.583041 | ||||||||
\(977\) | −36.7607 | −1.17608 | −0.588039 | − | 0.808832i | \(-0.700100\pi\) | ||||
−0.588039 | + | 0.808832i | \(0.700100\pi\) | |||||||
\(978\) | −91.1033 | −2.91316 | ||||||||
\(979\) | −45.5447 | −1.45562 | ||||||||
\(980\) | −17.7082 | −0.565668 | ||||||||
\(981\) | −1.34708 | −0.0430091 | ||||||||
\(982\) | −70.8927 | −2.26228 | ||||||||
\(983\) | −19.6417 | −0.626472 | −0.313236 | − | 0.949675i | \(-0.601413\pi\) | ||||
−0.313236 | + | 0.949675i | \(0.601413\pi\) | |||||||
\(984\) | 9.51057 | 0.303186 | ||||||||
\(985\) | −14.8885 | −0.474388 | ||||||||
\(986\) | 27.8885 | 0.888152 | ||||||||
\(987\) | −11.8617 | −0.377562 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.56231 | 0.0496784 | ||||||||
\(990\) | −6.88191 | −0.218721 | ||||||||
\(991\) | 57.6839 | 1.83239 | 0.916195 | − | 0.400732i | \(-0.131244\pi\) | ||||
0.916195 | + | 0.400732i | \(0.131244\pi\) | |||||||
\(992\) | 13.9443 | 0.442731 | ||||||||
\(993\) | 37.8885 | 1.20236 | ||||||||
\(994\) | 1.38197 | 0.0438333 | ||||||||
\(995\) | −13.4164 | −0.425329 | ||||||||
\(996\) | 26.9726 | 0.854660 | ||||||||
\(997\) | −36.9443 | −1.17004 | −0.585018 | − | 0.811020i | \(-0.698913\pi\) | ||||
−0.585018 | + | 0.811020i | \(0.698913\pi\) | |||||||
\(998\) | 56.1653 | 1.77788 | ||||||||
\(999\) | −12.6869 | −0.401396 |
(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 | 1805.2.a.l.1.1 | ✓ | 4 | |
5.4 | even | 2 | 9025.2.a.bl.1.4 | 4 | |||
19.18 | odd | 2 | inner | 1805.2.a.l.1.4 | yes | 4 | |
95.94 | odd | 2 | 9025.2.a.bl.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.l.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1805.2.a.l.1.4 | yes | 4 | 19.18 | odd | 2 | inner | |
9025.2.a.bl.1.1 | 4 | 95.94 | odd | 2 | |||
9025.2.a.bl.1.4 | 4 | 5.4 | even | 2 |