Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.61803 | 0.934172 | 0.467086 | − | 0.884212i | \(-0.345304\pi\) | ||||
0.467086 | + | 0.884212i | \(0.345304\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.61803 | −0.660560 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.381966 | −0.127322 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.61803 | 0.467086 | ||||||||
\(13\) | −5.23607 | −1.45222 | −0.726112 | − | 0.687576i | \(-0.758675\pi\) | ||||
−0.726112 | + | 0.687576i | \(0.758675\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.61803 | −0.417775 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.61803 | 0.634967 | 0.317483 | − | 0.948264i | \(-0.397162\pi\) | ||||
0.317483 | + | 0.948264i | \(0.397162\pi\) | |||||||
\(18\) | 0.381966 | 0.0900303 | ||||||||
\(19\) | 7.85410 | 1.80185 | 0.900927 | − | 0.433970i | \(-0.142888\pi\) | ||||
0.900927 | + | 0.433970i | \(0.142888\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.472136 | −0.0984472 | −0.0492236 | − | 0.998788i | \(-0.515675\pi\) | ||||
−0.0492236 | + | 0.998788i | \(0.515675\pi\) | |||||||
\(24\) | −1.61803 | −0.330280 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.23607 | 1.02688 | ||||||||
\(27\) | −5.47214 | −1.05311 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.47214 | 0.830455 | 0.415227 | − | 0.909718i | \(-0.363702\pi\) | ||||
0.415227 | + | 0.909718i | \(0.363702\pi\) | |||||||
\(30\) | 1.61803 | 0.295411 | ||||||||
\(31\) | 2.47214 | 0.444009 | 0.222004 | − | 0.975046i | \(-0.428740\pi\) | ||||
0.222004 | + | 0.975046i | \(0.428740\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.61803 | −0.448989 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −0.381966 | −0.0636610 | ||||||||
\(37\) | −11.2361 | −1.84720 | −0.923599 | − | 0.383360i | \(-0.874767\pi\) | ||||
−0.923599 | + | 0.383360i | \(0.874767\pi\) | |||||||
\(38\) | −7.85410 | −1.27410 | ||||||||
\(39\) | −8.47214 | −1.35663 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.85410 | 0.445736 | 0.222868 | − | 0.974849i | \(-0.428458\pi\) | ||||
0.222868 | + | 0.974849i | \(0.428458\pi\) | |||||||
\(42\) | −1.61803 | −0.249668 | ||||||||
\(43\) | −2.09017 | −0.318748 | −0.159374 | − | 0.987218i | \(-0.550948\pi\) | ||||
−0.159374 | + | 0.987218i | \(0.550948\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.381966 | 0.0569401 | ||||||||
\(46\) | 0.472136 | 0.0696126 | ||||||||
\(47\) | 4.76393 | 0.694891 | 0.347445 | − | 0.937700i | \(-0.387049\pi\) | ||||
0.347445 | + | 0.937700i | \(0.387049\pi\) | |||||||
\(48\) | 1.61803 | 0.233543 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 4.23607 | 0.593168 | ||||||||
\(52\) | −5.23607 | −0.726112 | ||||||||
\(53\) | −2.76393 | −0.379655 | −0.189828 | − | 0.981817i | \(-0.560793\pi\) | ||||
−0.189828 | + | 0.981817i | \(0.560793\pi\) | |||||||
\(54\) | 5.47214 | 0.744663 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 12.7082 | 1.68324 | ||||||||
\(58\) | −4.47214 | −0.587220 | ||||||||
\(59\) | 4.14590 | 0.539750 | 0.269875 | − | 0.962895i | \(-0.413018\pi\) | ||||
0.269875 | + | 0.962895i | \(0.413018\pi\) | |||||||
\(60\) | −1.61803 | −0.208887 | ||||||||
\(61\) | 13.7082 | 1.75516 | 0.877578 | − | 0.479434i | \(-0.159158\pi\) | ||||
0.877578 | + | 0.479434i | \(0.159158\pi\) | |||||||
\(62\) | −2.47214 | −0.313962 | ||||||||
\(63\) | −0.381966 | −0.0481232 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.23607 | 0.649454 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.38197 | −0.413173 | −0.206586 | − | 0.978428i | \(-0.566235\pi\) | ||||
−0.206586 | + | 0.978428i | \(0.566235\pi\) | |||||||
\(68\) | 2.61803 | 0.317483 | ||||||||
\(69\) | −0.763932 | −0.0919666 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 10.9443 | 1.29885 | 0.649423 | − | 0.760427i | \(-0.275010\pi\) | ||||
0.649423 | + | 0.760427i | \(0.275010\pi\) | |||||||
\(72\) | 0.381966 | 0.0450151 | ||||||||
\(73\) | 2.85410 | 0.334047 | 0.167024 | − | 0.985953i | \(-0.446584\pi\) | ||||
0.167024 | + | 0.985953i | \(0.446584\pi\) | |||||||
\(74\) | 11.2361 | 1.30617 | ||||||||
\(75\) | 1.61803 | 0.186834 | ||||||||
\(76\) | 7.85410 | 0.900927 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.47214 | 0.959280 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −7.70820 | −0.856467 | ||||||||
\(82\) | −2.85410 | −0.315183 | ||||||||
\(83\) | −8.85410 | −0.971864 | −0.485932 | − | 0.873997i | \(-0.661520\pi\) | ||||
−0.485932 | + | 0.873997i | \(0.661520\pi\) | |||||||
\(84\) | 1.61803 | 0.176542 | ||||||||
\(85\) | −2.61803 | −0.283966 | ||||||||
\(86\) | 2.09017 | 0.225389 | ||||||||
\(87\) | 7.23607 | 0.775788 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.8541 | −1.57453 | −0.787266 | − | 0.616614i | \(-0.788504\pi\) | ||||
−0.787266 | + | 0.616614i | \(0.788504\pi\) | |||||||
\(90\) | −0.381966 | −0.0402628 | ||||||||
\(91\) | −5.23607 | −0.548889 | ||||||||
\(92\) | −0.472136 | −0.0492236 | ||||||||
\(93\) | 4.00000 | 0.414781 | ||||||||
\(94\) | −4.76393 | −0.491362 | ||||||||
\(95\) | −7.85410 | −0.805814 | ||||||||
\(96\) | −1.61803 | −0.165140 | ||||||||
\(97\) | −8.38197 | −0.851060 | −0.425530 | − | 0.904944i | \(-0.639912\pi\) | ||||
−0.425530 | + | 0.904944i | \(0.639912\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.9443 | −1.48701 | −0.743505 | − | 0.668730i | \(-0.766838\pi\) | ||||
−0.743505 | + | 0.668730i | \(0.766838\pi\) | |||||||
\(102\) | −4.23607 | −0.419433 | ||||||||
\(103\) | −6.00000 | −0.591198 | −0.295599 | − | 0.955312i | \(-0.595519\pi\) | ||||
−0.295599 | + | 0.955312i | \(0.595519\pi\) | |||||||
\(104\) | 5.23607 | 0.513439 | ||||||||
\(105\) | −1.61803 | −0.157904 | ||||||||
\(106\) | 2.76393 | 0.268457 | ||||||||
\(107\) | 2.85410 | 0.275916 | 0.137958 | − | 0.990438i | \(-0.455946\pi\) | ||||
0.137958 | + | 0.990438i | \(0.455946\pi\) | |||||||
\(108\) | −5.47214 | −0.526557 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.1803 | −1.72560 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 4.32624 | 0.406978 | 0.203489 | − | 0.979077i | \(-0.434772\pi\) | ||||
0.203489 | + | 0.979077i | \(0.434772\pi\) | |||||||
\(114\) | −12.7082 | −1.19023 | ||||||||
\(115\) | 0.472136 | 0.0440269 | ||||||||
\(116\) | 4.47214 | 0.415227 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | −4.14590 | −0.381661 | ||||||||
\(119\) | 2.61803 | 0.239995 | ||||||||
\(120\) | 1.61803 | 0.147706 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −13.7082 | −1.24108 | ||||||||
\(123\) | 4.61803 | 0.416394 | ||||||||
\(124\) | 2.47214 | 0.222004 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.381966 | 0.0340282 | ||||||||
\(127\) | 12.4721 | 1.10672 | 0.553362 | − | 0.832941i | \(-0.313345\pi\) | ||||
0.553362 | + | 0.832941i | \(0.313345\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −3.38197 | −0.297766 | ||||||||
\(130\) | −5.23607 | −0.459234 | ||||||||
\(131\) | 5.09017 | 0.444730 | 0.222365 | − | 0.974963i | \(-0.428622\pi\) | ||||
0.222365 | + | 0.974963i | \(0.428622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.85410 | 0.681037 | ||||||||
\(134\) | 3.38197 | 0.292157 | ||||||||
\(135\) | 5.47214 | 0.470966 | ||||||||
\(136\) | −2.61803 | −0.224495 | ||||||||
\(137\) | 4.85410 | 0.414714 | 0.207357 | − | 0.978265i | \(-0.433514\pi\) | ||||
0.207357 | + | 0.978265i | \(0.433514\pi\) | |||||||
\(138\) | 0.763932 | 0.0650302 | ||||||||
\(139\) | −4.94427 | −0.419368 | −0.209684 | − | 0.977769i | \(-0.567243\pi\) | ||||
−0.209684 | + | 0.977769i | \(0.567243\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 7.70820 | 0.649148 | ||||||||
\(142\) | −10.9443 | −0.918423 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.381966 | −0.0318305 | ||||||||
\(145\) | −4.47214 | −0.371391 | ||||||||
\(146\) | −2.85410 | −0.236207 | ||||||||
\(147\) | 1.61803 | 0.133453 | ||||||||
\(148\) | −11.2361 | −0.923599 | ||||||||
\(149\) | 11.7082 | 0.959173 | 0.479587 | − | 0.877494i | \(-0.340787\pi\) | ||||
0.479587 | + | 0.877494i | \(0.340787\pi\) | |||||||
\(150\) | −1.61803 | −0.132112 | ||||||||
\(151\) | 18.4721 | 1.50324 | 0.751621 | − | 0.659596i | \(-0.229272\pi\) | ||||
0.751621 | + | 0.659596i | \(0.229272\pi\) | |||||||
\(152\) | −7.85410 | −0.637052 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.47214 | −0.198567 | ||||||||
\(156\) | −8.47214 | −0.678314 | ||||||||
\(157\) | −14.9443 | −1.19268 | −0.596341 | − | 0.802731i | \(-0.703380\pi\) | ||||
−0.596341 | + | 0.802731i | \(0.703380\pi\) | |||||||
\(158\) | −4.00000 | −0.318223 | ||||||||
\(159\) | −4.47214 | −0.354663 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −0.472136 | −0.0372095 | ||||||||
\(162\) | 7.70820 | 0.605614 | ||||||||
\(163\) | 22.7984 | 1.78571 | 0.892853 | − | 0.450348i | \(-0.148700\pi\) | ||||
0.892853 | + | 0.450348i | \(0.148700\pi\) | |||||||
\(164\) | 2.85410 | 0.222868 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.85410 | 0.687212 | ||||||||
\(167\) | 8.29180 | 0.641638 | 0.320819 | − | 0.947140i | \(-0.396042\pi\) | ||||
0.320819 | + | 0.947140i | \(0.396042\pi\) | |||||||
\(168\) | −1.61803 | −0.124834 | ||||||||
\(169\) | 14.4164 | 1.10895 | ||||||||
\(170\) | 2.61803 | 0.200794 | ||||||||
\(171\) | −3.00000 | −0.229416 | ||||||||
\(172\) | −2.09017 | −0.159374 | ||||||||
\(173\) | 19.8885 | 1.51210 | 0.756049 | − | 0.654515i | \(-0.227127\pi\) | ||||
0.756049 | + | 0.654515i | \(0.227127\pi\) | |||||||
\(174\) | −7.23607 | −0.548565 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.70820 | 0.504219 | ||||||||
\(178\) | 14.8541 | 1.11336 | ||||||||
\(179\) | 2.14590 | 0.160392 | 0.0801960 | − | 0.996779i | \(-0.474445\pi\) | ||||
0.0801960 | + | 0.996779i | \(0.474445\pi\) | |||||||
\(180\) | 0.381966 | 0.0284701 | ||||||||
\(181\) | 20.9443 | 1.55678 | 0.778388 | − | 0.627784i | \(-0.216038\pi\) | ||||
0.778388 | + | 0.627784i | \(0.216038\pi\) | |||||||
\(182\) | 5.23607 | 0.388123 | ||||||||
\(183\) | 22.1803 | 1.63962 | ||||||||
\(184\) | 0.472136 | 0.0348063 | ||||||||
\(185\) | 11.2361 | 0.826092 | ||||||||
\(186\) | −4.00000 | −0.293294 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.76393 | 0.347445 | ||||||||
\(189\) | −5.47214 | −0.398039 | ||||||||
\(190\) | 7.85410 | 0.569796 | ||||||||
\(191\) | −1.23607 | −0.0894387 | −0.0447194 | − | 0.999000i | \(-0.514239\pi\) | ||||
−0.0447194 | + | 0.999000i | \(0.514239\pi\) | |||||||
\(192\) | 1.61803 | 0.116772 | ||||||||
\(193\) | −21.4164 | −1.54159 | −0.770793 | − | 0.637085i | \(-0.780140\pi\) | ||||
−0.770793 | + | 0.637085i | \(0.780140\pi\) | |||||||
\(194\) | 8.38197 | 0.601790 | ||||||||
\(195\) | 8.47214 | 0.606702 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 11.5279 | 0.821326 | 0.410663 | − | 0.911787i | \(-0.365297\pi\) | ||||
0.410663 | + | 0.911787i | \(0.365297\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.05573 | 0.358391 | 0.179196 | − | 0.983813i | \(-0.442651\pi\) | ||||
0.179196 | + | 0.983813i | \(0.442651\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −5.47214 | −0.385975 | ||||||||
\(202\) | 14.9443 | 1.05148 | ||||||||
\(203\) | 4.47214 | 0.313882 | ||||||||
\(204\) | 4.23607 | 0.296584 | ||||||||
\(205\) | −2.85410 | −0.199339 | ||||||||
\(206\) | 6.00000 | 0.418040 | ||||||||
\(207\) | 0.180340 | 0.0125345 | ||||||||
\(208\) | −5.23607 | −0.363056 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.61803 | 0.111655 | ||||||||
\(211\) | 10.6738 | 0.734812 | 0.367406 | − | 0.930061i | \(-0.380246\pi\) | ||||
0.367406 | + | 0.930061i | \(0.380246\pi\) | |||||||
\(212\) | −2.76393 | −0.189828 | ||||||||
\(213\) | 17.7082 | 1.21335 | ||||||||
\(214\) | −2.85410 | −0.195102 | ||||||||
\(215\) | 2.09017 | 0.142548 | ||||||||
\(216\) | 5.47214 | 0.372332 | ||||||||
\(217\) | 2.47214 | 0.167820 | ||||||||
\(218\) | −4.00000 | −0.270914 | ||||||||
\(219\) | 4.61803 | 0.312058 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.7082 | −0.922114 | ||||||||
\(222\) | 18.1803 | 1.22018 | ||||||||
\(223\) | 13.1246 | 0.878889 | 0.439445 | − | 0.898270i | \(-0.355175\pi\) | ||||
0.439445 | + | 0.898270i | \(0.355175\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −0.381966 | −0.0254644 | ||||||||
\(226\) | −4.32624 | −0.287777 | ||||||||
\(227\) | 13.6738 | 0.907559 | 0.453780 | − | 0.891114i | \(-0.350075\pi\) | ||||
0.453780 | + | 0.891114i | \(0.350075\pi\) | |||||||
\(228\) | 12.7082 | 0.841621 | ||||||||
\(229\) | 22.3607 | 1.47764 | 0.738818 | − | 0.673905i | \(-0.235384\pi\) | ||||
0.738818 | + | 0.673905i | \(0.235384\pi\) | |||||||
\(230\) | −0.472136 | −0.0311317 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.47214 | −0.293610 | ||||||||
\(233\) | 0.673762 | 0.0441396 | 0.0220698 | − | 0.999756i | \(-0.492974\pi\) | ||||
0.0220698 | + | 0.999756i | \(0.492974\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | −4.76393 | −0.310765 | ||||||||
\(236\) | 4.14590 | 0.269875 | ||||||||
\(237\) | 6.47214 | 0.420410 | ||||||||
\(238\) | −2.61803 | −0.169702 | ||||||||
\(239\) | 6.29180 | 0.406982 | 0.203491 | − | 0.979077i | \(-0.434771\pi\) | ||||
0.203491 | + | 0.979077i | \(0.434771\pi\) | |||||||
\(240\) | −1.61803 | −0.104444 | ||||||||
\(241\) | −30.9787 | −1.99551 | −0.997757 | − | 0.0669372i | \(-0.978677\pi\) | ||||
−0.997757 | + | 0.0669372i | \(0.978677\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.94427 | 0.253025 | ||||||||
\(244\) | 13.7082 | 0.877578 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | −4.61803 | −0.294435 | ||||||||
\(247\) | −41.1246 | −2.61670 | ||||||||
\(248\) | −2.47214 | −0.156981 | ||||||||
\(249\) | −14.3262 | −0.907888 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 20.0000 | 1.26239 | 0.631194 | − | 0.775625i | \(-0.282565\pi\) | ||||
0.631194 | + | 0.775625i | \(0.282565\pi\) | |||||||
\(252\) | −0.381966 | −0.0240616 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −12.4721 | −0.782571 | ||||||||
\(255\) | −4.23607 | −0.265273 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.8541 | 0.926573 | 0.463287 | − | 0.886208i | \(-0.346670\pi\) | ||||
0.463287 | + | 0.886208i | \(0.346670\pi\) | |||||||
\(258\) | 3.38197 | 0.210552 | ||||||||
\(259\) | −11.2361 | −0.698175 | ||||||||
\(260\) | 5.23607 | 0.324727 | ||||||||
\(261\) | −1.70820 | −0.105735 | ||||||||
\(262\) | −5.09017 | −0.314472 | ||||||||
\(263\) | 26.3607 | 1.62547 | 0.812735 | − | 0.582634i | \(-0.197978\pi\) | ||||
0.812735 | + | 0.582634i | \(0.197978\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.76393 | 0.169787 | ||||||||
\(266\) | −7.85410 | −0.481566 | ||||||||
\(267\) | −24.0344 | −1.47088 | ||||||||
\(268\) | −3.38197 | −0.206586 | ||||||||
\(269\) | −18.6525 | −1.13726 | −0.568631 | − | 0.822593i | \(-0.692527\pi\) | ||||
−0.568631 | + | 0.822593i | \(0.692527\pi\) | |||||||
\(270\) | −5.47214 | −0.333024 | ||||||||
\(271\) | −6.18034 | −0.375429 | −0.187714 | − | 0.982224i | \(-0.560108\pi\) | ||||
−0.187714 | + | 0.982224i | \(0.560108\pi\) | |||||||
\(272\) | 2.61803 | 0.158742 | ||||||||
\(273\) | −8.47214 | −0.512757 | ||||||||
\(274\) | −4.85410 | −0.293247 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.763932 | −0.0459833 | ||||||||
\(277\) | −12.0000 | −0.721010 | −0.360505 | − | 0.932757i | \(-0.617396\pi\) | ||||
−0.360505 | + | 0.932757i | \(0.617396\pi\) | |||||||
\(278\) | 4.94427 | 0.296538 | ||||||||
\(279\) | −0.944272 | −0.0565321 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 11.3262 | 0.675667 | 0.337833 | − | 0.941206i | \(-0.390306\pi\) | ||||
0.337833 | + | 0.941206i | \(0.390306\pi\) | |||||||
\(282\) | −7.70820 | −0.459017 | ||||||||
\(283\) | 16.3607 | 0.972541 | 0.486271 | − | 0.873808i | \(-0.338357\pi\) | ||||
0.486271 | + | 0.873808i | \(0.338357\pi\) | |||||||
\(284\) | 10.9443 | 0.649423 | ||||||||
\(285\) | −12.7082 | −0.752769 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.85410 | 0.168472 | ||||||||
\(288\) | 0.381966 | 0.0225076 | ||||||||
\(289\) | −10.1459 | −0.596818 | ||||||||
\(290\) | 4.47214 | 0.262613 | ||||||||
\(291\) | −13.5623 | −0.795036 | ||||||||
\(292\) | 2.85410 | 0.167024 | ||||||||
\(293\) | 18.4721 | 1.07915 | 0.539577 | − | 0.841936i | \(-0.318584\pi\) | ||||
0.539577 | + | 0.841936i | \(0.318584\pi\) | |||||||
\(294\) | −1.61803 | −0.0943657 | ||||||||
\(295\) | −4.14590 | −0.241384 | ||||||||
\(296\) | 11.2361 | 0.653083 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.7082 | −0.678238 | ||||||||
\(299\) | 2.47214 | 0.142967 | ||||||||
\(300\) | 1.61803 | 0.0934172 | ||||||||
\(301\) | −2.09017 | −0.120475 | ||||||||
\(302\) | −18.4721 | −1.06295 | ||||||||
\(303\) | −24.1803 | −1.38912 | ||||||||
\(304\) | 7.85410 | 0.450464 | ||||||||
\(305\) | −13.7082 | −0.784929 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 18.5623 | 1.05941 | 0.529703 | − | 0.848183i | \(-0.322303\pi\) | ||||
0.529703 | + | 0.848183i | \(0.322303\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.70820 | −0.552280 | ||||||||
\(310\) | 2.47214 | 0.140408 | ||||||||
\(311\) | −2.18034 | −0.123636 | −0.0618179 | − | 0.998087i | \(-0.519690\pi\) | ||||
−0.0618179 | + | 0.998087i | \(0.519690\pi\) | |||||||
\(312\) | 8.47214 | 0.479640 | ||||||||
\(313\) | −31.2705 | −1.76751 | −0.883757 | − | 0.467946i | \(-0.844994\pi\) | ||||
−0.883757 | + | 0.467946i | \(0.844994\pi\) | |||||||
\(314\) | 14.9443 | 0.843354 | ||||||||
\(315\) | 0.381966 | 0.0215213 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | 30.3607 | 1.70523 | 0.852613 | − | 0.522543i | \(-0.175017\pi\) | ||||
0.852613 | + | 0.522543i | \(0.175017\pi\) | |||||||
\(318\) | 4.47214 | 0.250785 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 4.61803 | 0.257754 | ||||||||
\(322\) | 0.472136 | 0.0263111 | ||||||||
\(323\) | 20.5623 | 1.14412 | ||||||||
\(324\) | −7.70820 | −0.428234 | ||||||||
\(325\) | −5.23607 | −0.290445 | ||||||||
\(326\) | −22.7984 | −1.26269 | ||||||||
\(327\) | 6.47214 | 0.357910 | ||||||||
\(328\) | −2.85410 | −0.157591 | ||||||||
\(329\) | 4.76393 | 0.262644 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.965558 | −0.0530719 | −0.0265359 | − | 0.999648i | \(-0.508448\pi\) | ||||
−0.0265359 | + | 0.999648i | \(0.508448\pi\) | |||||||
\(332\) | −8.85410 | −0.485932 | ||||||||
\(333\) | 4.29180 | 0.235189 | ||||||||
\(334\) | −8.29180 | −0.453707 | ||||||||
\(335\) | 3.38197 | 0.184777 | ||||||||
\(336\) | 1.61803 | 0.0882710 | ||||||||
\(337\) | −1.20163 | −0.0654567 | −0.0327284 | − | 0.999464i | \(-0.510420\pi\) | ||||
−0.0327284 | + | 0.999464i | \(0.510420\pi\) | |||||||
\(338\) | −14.4164 | −0.784149 | ||||||||
\(339\) | 7.00000 | 0.380188 | ||||||||
\(340\) | −2.61803 | −0.141983 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 2.09017 | 0.112694 | ||||||||
\(345\) | 0.763932 | 0.0411287 | ||||||||
\(346\) | −19.8885 | −1.06921 | ||||||||
\(347\) | 15.0902 | 0.810083 | 0.405041 | − | 0.914298i | \(-0.367257\pi\) | ||||
0.405041 | + | 0.914298i | \(0.367257\pi\) | |||||||
\(348\) | 7.23607 | 0.387894 | ||||||||
\(349\) | −19.4164 | −1.03934 | −0.519668 | − | 0.854368i | \(-0.673944\pi\) | ||||
−0.519668 | + | 0.854368i | \(0.673944\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 28.6525 | 1.52936 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.5623 | −0.615399 | −0.307700 | − | 0.951484i | \(-0.599559\pi\) | ||||
−0.307700 | + | 0.951484i | \(0.599559\pi\) | |||||||
\(354\) | −6.70820 | −0.356537 | ||||||||
\(355\) | −10.9443 | −0.580862 | ||||||||
\(356\) | −14.8541 | −0.787266 | ||||||||
\(357\) | 4.23607 | 0.224196 | ||||||||
\(358\) | −2.14590 | −0.113414 | ||||||||
\(359\) | 29.5967 | 1.56206 | 0.781028 | − | 0.624496i | \(-0.214695\pi\) | ||||
0.781028 | + | 0.624496i | \(0.214695\pi\) | |||||||
\(360\) | −0.381966 | −0.0201314 | ||||||||
\(361\) | 42.6869 | 2.24668 | ||||||||
\(362\) | −20.9443 | −1.10081 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.23607 | −0.274445 | ||||||||
\(365\) | −2.85410 | −0.149391 | ||||||||
\(366\) | −22.1803 | −1.15938 | ||||||||
\(367\) | 15.8885 | 0.829375 | 0.414688 | − | 0.909964i | \(-0.363891\pi\) | ||||
0.414688 | + | 0.909964i | \(0.363891\pi\) | |||||||
\(368\) | −0.472136 | −0.0246118 | ||||||||
\(369\) | −1.09017 | −0.0567520 | ||||||||
\(370\) | −11.2361 | −0.584135 | ||||||||
\(371\) | −2.76393 | −0.143496 | ||||||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | 14.6525 | 0.758676 | 0.379338 | − | 0.925258i | \(-0.376152\pi\) | ||||
0.379338 | + | 0.925258i | \(0.376152\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.61803 | −0.0835549 | ||||||||
\(376\) | −4.76393 | −0.245681 | ||||||||
\(377\) | −23.4164 | −1.20601 | ||||||||
\(378\) | 5.47214 | 0.281456 | ||||||||
\(379\) | 15.6180 | 0.802245 | 0.401122 | − | 0.916025i | \(-0.368620\pi\) | ||||
0.401122 | + | 0.916025i | \(0.368620\pi\) | |||||||
\(380\) | −7.85410 | −0.402907 | ||||||||
\(381\) | 20.1803 | 1.03387 | ||||||||
\(382\) | 1.23607 | 0.0632427 | ||||||||
\(383\) | −20.1803 | −1.03117 | −0.515584 | − | 0.856839i | \(-0.672425\pi\) | ||||
−0.515584 | + | 0.856839i | \(0.672425\pi\) | |||||||
\(384\) | −1.61803 | −0.0825700 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.4164 | 1.09007 | ||||||||
\(387\) | 0.798374 | 0.0405836 | ||||||||
\(388\) | −8.38197 | −0.425530 | ||||||||
\(389\) | 25.7082 | 1.30346 | 0.651729 | − | 0.758452i | \(-0.274044\pi\) | ||||
0.651729 | + | 0.758452i | \(0.274044\pi\) | |||||||
\(390\) | −8.47214 | −0.429003 | ||||||||
\(391\) | −1.23607 | −0.0625106 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 8.23607 | 0.415455 | ||||||||
\(394\) | −11.5279 | −0.580765 | ||||||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.111456 | 0.00559383 | 0.00279691 | − | 0.999996i | \(-0.499110\pi\) | ||||
0.00279691 | + | 0.999996i | \(0.499110\pi\) | |||||||
\(398\) | −5.05573 | −0.253421 | ||||||||
\(399\) | 12.7082 | 0.636206 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 2.56231 | 0.127955 | 0.0639777 | − | 0.997951i | \(-0.479621\pi\) | ||||
0.0639777 | + | 0.997951i | \(0.479621\pi\) | |||||||
\(402\) | 5.47214 | 0.272925 | ||||||||
\(403\) | −12.9443 | −0.644800 | ||||||||
\(404\) | −14.9443 | −0.743505 | ||||||||
\(405\) | 7.70820 | 0.383024 | ||||||||
\(406\) | −4.47214 | −0.221948 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.23607 | −0.209717 | ||||||||
\(409\) | −22.9443 | −1.13452 | −0.567261 | − | 0.823538i | \(-0.691997\pi\) | ||||
−0.567261 | + | 0.823538i | \(0.691997\pi\) | |||||||
\(410\) | 2.85410 | 0.140954 | ||||||||
\(411\) | 7.85410 | 0.387414 | ||||||||
\(412\) | −6.00000 | −0.295599 | ||||||||
\(413\) | 4.14590 | 0.204006 | ||||||||
\(414\) | −0.180340 | −0.00886322 | ||||||||
\(415\) | 8.85410 | 0.434631 | ||||||||
\(416\) | 5.23607 | 0.256719 | ||||||||
\(417\) | −8.00000 | −0.391762 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 22.5623 | 1.10224 | 0.551120 | − | 0.834426i | \(-0.314200\pi\) | ||||
0.551120 | + | 0.834426i | \(0.314200\pi\) | |||||||
\(420\) | −1.61803 | −0.0789520 | ||||||||
\(421\) | −36.8328 | −1.79512 | −0.897561 | − | 0.440891i | \(-0.854663\pi\) | ||||
−0.897561 | + | 0.440891i | \(0.854663\pi\) | |||||||
\(422\) | −10.6738 | −0.519591 | ||||||||
\(423\) | −1.81966 | −0.0884749 | ||||||||
\(424\) | 2.76393 | 0.134228 | ||||||||
\(425\) | 2.61803 | 0.126993 | ||||||||
\(426\) | −17.7082 | −0.857965 | ||||||||
\(427\) | 13.7082 | 0.663386 | ||||||||
\(428\) | 2.85410 | 0.137958 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.09017 | −0.100797 | ||||||||
\(431\) | −0.652476 | −0.0314287 | −0.0157143 | − | 0.999877i | \(-0.505002\pi\) | ||||
−0.0157143 | + | 0.999877i | \(0.505002\pi\) | |||||||
\(432\) | −5.47214 | −0.263278 | ||||||||
\(433\) | −8.79837 | −0.422823 | −0.211411 | − | 0.977397i | \(-0.567806\pi\) | ||||
−0.211411 | + | 0.977397i | \(0.567806\pi\) | |||||||
\(434\) | −2.47214 | −0.118666 | ||||||||
\(435\) | −7.23607 | −0.346943 | ||||||||
\(436\) | 4.00000 | 0.191565 | ||||||||
\(437\) | −3.70820 | −0.177387 | ||||||||
\(438\) | −4.61803 | −0.220658 | ||||||||
\(439\) | 30.5410 | 1.45764 | 0.728822 | − | 0.684704i | \(-0.240068\pi\) | ||||
0.728822 | + | 0.684704i | \(0.240068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.381966 | −0.0181889 | ||||||||
\(442\) | 13.7082 | 0.652033 | ||||||||
\(443\) | −28.5623 | −1.35704 | −0.678518 | − | 0.734584i | \(-0.737377\pi\) | ||||
−0.678518 | + | 0.734584i | \(0.737377\pi\) | |||||||
\(444\) | −18.1803 | −0.862801 | ||||||||
\(445\) | 14.8541 | 0.704152 | ||||||||
\(446\) | −13.1246 | −0.621468 | ||||||||
\(447\) | 18.9443 | 0.896033 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −20.0344 | −0.945484 | −0.472742 | − | 0.881201i | \(-0.656736\pi\) | ||||
−0.472742 | + | 0.881201i | \(0.656736\pi\) | |||||||
\(450\) | 0.381966 | 0.0180061 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.32624 | 0.203489 | ||||||||
\(453\) | 29.8885 | 1.40429 | ||||||||
\(454\) | −13.6738 | −0.641741 | ||||||||
\(455\) | 5.23607 | 0.245471 | ||||||||
\(456\) | −12.7082 | −0.595116 | ||||||||
\(457\) | −25.9787 | −1.21523 | −0.607616 | − | 0.794231i | \(-0.707874\pi\) | ||||
−0.607616 | + | 0.794231i | \(0.707874\pi\) | |||||||
\(458\) | −22.3607 | −1.04485 | ||||||||
\(459\) | −14.3262 | −0.668692 | ||||||||
\(460\) | 0.472136 | 0.0220135 | ||||||||
\(461\) | 23.0557 | 1.07381 | 0.536906 | − | 0.843642i | \(-0.319593\pi\) | ||||
0.536906 | + | 0.843642i | \(0.319593\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.9443 | −0.508623 | −0.254312 | − | 0.967122i | \(-0.581849\pi\) | ||||
−0.254312 | + | 0.967122i | \(0.581849\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | −4.00000 | −0.185496 | ||||||||
\(466\) | −0.673762 | −0.0312114 | ||||||||
\(467\) | 12.9443 | 0.598989 | 0.299495 | − | 0.954098i | \(-0.403182\pi\) | ||||
0.299495 | + | 0.954098i | \(0.403182\pi\) | |||||||
\(468\) | 2.00000 | 0.0924500 | ||||||||
\(469\) | −3.38197 | −0.156165 | ||||||||
\(470\) | 4.76393 | 0.219744 | ||||||||
\(471\) | −24.1803 | −1.11417 | ||||||||
\(472\) | −4.14590 | −0.190830 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.47214 | −0.297275 | ||||||||
\(475\) | 7.85410 | 0.360371 | ||||||||
\(476\) | 2.61803 | 0.119997 | ||||||||
\(477\) | 1.05573 | 0.0483385 | ||||||||
\(478\) | −6.29180 | −0.287780 | ||||||||
\(479\) | 22.2918 | 1.01854 | 0.509269 | − | 0.860607i | \(-0.329916\pi\) | ||||
0.509269 | + | 0.860607i | \(0.329916\pi\) | |||||||
\(480\) | 1.61803 | 0.0738528 | ||||||||
\(481\) | 58.8328 | 2.68255 | ||||||||
\(482\) | 30.9787 | 1.41104 | ||||||||
\(483\) | −0.763932 | −0.0347601 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.38197 | 0.380605 | ||||||||
\(486\) | −3.94427 | −0.178916 | ||||||||
\(487\) | 38.1803 | 1.73012 | 0.865058 | − | 0.501672i | \(-0.167281\pi\) | ||||
0.865058 | + | 0.501672i | \(0.167281\pi\) | |||||||
\(488\) | −13.7082 | −0.620541 | ||||||||
\(489\) | 36.8885 | 1.66816 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | −19.2148 | −0.867151 | −0.433575 | − | 0.901117i | \(-0.642748\pi\) | ||||
−0.433575 | + | 0.901117i | \(0.642748\pi\) | |||||||
\(492\) | 4.61803 | 0.208197 | ||||||||
\(493\) | 11.7082 | 0.527311 | ||||||||
\(494\) | 41.1246 | 1.85028 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.47214 | 0.111002 | ||||||||
\(497\) | 10.9443 | 0.490918 | ||||||||
\(498\) | 14.3262 | 0.641974 | ||||||||
\(499\) | −19.9787 | −0.894370 | −0.447185 | − | 0.894441i | \(-0.647573\pi\) | ||||
−0.447185 | + | 0.894441i | \(0.647573\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 13.4164 | 0.599401 | ||||||||
\(502\) | −20.0000 | −0.892644 | ||||||||
\(503\) | −20.6525 | −0.920848 | −0.460424 | − | 0.887699i | \(-0.652303\pi\) | ||||
−0.460424 | + | 0.887699i | \(0.652303\pi\) | |||||||
\(504\) | 0.381966 | 0.0170141 | ||||||||
\(505\) | 14.9443 | 0.665011 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 23.3262 | 1.03595 | ||||||||
\(508\) | 12.4721 | 0.553362 | ||||||||
\(509\) | 13.1246 | 0.581738 | 0.290869 | − | 0.956763i | \(-0.406056\pi\) | ||||
0.290869 | + | 0.956763i | \(0.406056\pi\) | |||||||
\(510\) | 4.23607 | 0.187576 | ||||||||
\(511\) | 2.85410 | 0.126258 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −42.9787 | −1.89756 | ||||||||
\(514\) | −14.8541 | −0.655186 | ||||||||
\(515\) | 6.00000 | 0.264392 | ||||||||
\(516\) | −3.38197 | −0.148883 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 11.2361 | 0.493684 | ||||||||
\(519\) | 32.1803 | 1.41256 | ||||||||
\(520\) | −5.23607 | −0.229617 | ||||||||
\(521\) | −9.67376 | −0.423815 | −0.211908 | − | 0.977290i | \(-0.567968\pi\) | ||||
−0.211908 | + | 0.977290i | \(0.567968\pi\) | |||||||
\(522\) | 1.70820 | 0.0747661 | ||||||||
\(523\) | −20.7984 | −0.909449 | −0.454725 | − | 0.890632i | \(-0.650262\pi\) | ||||
−0.454725 | + | 0.890632i | \(0.650262\pi\) | |||||||
\(524\) | 5.09017 | 0.222365 | ||||||||
\(525\) | 1.61803 | 0.0706168 | ||||||||
\(526\) | −26.3607 | −1.14938 | ||||||||
\(527\) | 6.47214 | 0.281931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7771 | −0.990308 | ||||||||
\(530\) | −2.76393 | −0.120058 | ||||||||
\(531\) | −1.58359 | −0.0687220 | ||||||||
\(532\) | 7.85410 | 0.340519 | ||||||||
\(533\) | −14.9443 | −0.647308 | ||||||||
\(534\) | 24.0344 | 1.04007 | ||||||||
\(535\) | −2.85410 | −0.123394 | ||||||||
\(536\) | 3.38197 | 0.146079 | ||||||||
\(537\) | 3.47214 | 0.149834 | ||||||||
\(538\) | 18.6525 | 0.804165 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.47214 | 0.235483 | ||||||||
\(541\) | −43.0132 | −1.84928 | −0.924640 | − | 0.380842i | \(-0.875634\pi\) | ||||
−0.924640 | + | 0.380842i | \(0.875634\pi\) | |||||||
\(542\) | 6.18034 | 0.265468 | ||||||||
\(543\) | 33.8885 | 1.45430 | ||||||||
\(544\) | −2.61803 | −0.112247 | ||||||||
\(545\) | −4.00000 | −0.171341 | ||||||||
\(546\) | 8.47214 | 0.362574 | ||||||||
\(547\) | −22.1459 | −0.946890 | −0.473445 | − | 0.880823i | \(-0.656990\pi\) | ||||
−0.473445 | + | 0.880823i | \(0.656990\pi\) | |||||||
\(548\) | 4.85410 | 0.207357 | ||||||||
\(549\) | −5.23607 | −0.223470 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.1246 | 1.49636 | ||||||||
\(552\) | 0.763932 | 0.0325151 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 12.0000 | 0.509831 | ||||||||
\(555\) | 18.1803 | 0.771712 | ||||||||
\(556\) | −4.94427 | −0.209684 | ||||||||
\(557\) | 18.7639 | 0.795053 | 0.397527 | − | 0.917591i | \(-0.369869\pi\) | ||||
0.397527 | + | 0.917591i | \(0.369869\pi\) | |||||||
\(558\) | 0.944272 | 0.0399742 | ||||||||
\(559\) | 10.9443 | 0.462893 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.3262 | −0.477769 | ||||||||
\(563\) | 29.6180 | 1.24825 | 0.624126 | − | 0.781324i | \(-0.285455\pi\) | ||||
0.624126 | + | 0.781324i | \(0.285455\pi\) | |||||||
\(564\) | 7.70820 | 0.324574 | ||||||||
\(565\) | −4.32624 | −0.182006 | ||||||||
\(566\) | −16.3607 | −0.687691 | ||||||||
\(567\) | −7.70820 | −0.323714 | ||||||||
\(568\) | −10.9443 | −0.459211 | ||||||||
\(569\) | 44.3262 | 1.85825 | 0.929126 | − | 0.369763i | \(-0.120561\pi\) | ||||
0.929126 | + | 0.369763i | \(0.120561\pi\) | |||||||
\(570\) | 12.7082 | 0.532288 | ||||||||
\(571\) | −34.8328 | −1.45771 | −0.728854 | − | 0.684669i | \(-0.759947\pi\) | ||||
−0.728854 | + | 0.684669i | \(0.759947\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.00000 | −0.0835512 | ||||||||
\(574\) | −2.85410 | −0.119128 | ||||||||
\(575\) | −0.472136 | −0.0196894 | ||||||||
\(576\) | −0.381966 | −0.0159153 | ||||||||
\(577\) | −26.3951 | −1.09884 | −0.549422 | − | 0.835545i | \(-0.685152\pi\) | ||||
−0.549422 | + | 0.835545i | \(0.685152\pi\) | |||||||
\(578\) | 10.1459 | 0.422014 | ||||||||
\(579\) | −34.6525 | −1.44011 | ||||||||
\(580\) | −4.47214 | −0.185695 | ||||||||
\(581\) | −8.85410 | −0.367330 | ||||||||
\(582\) | 13.5623 | 0.562176 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −2.85410 | −0.118104 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | −18.4721 | −0.763077 | ||||||||
\(587\) | −8.21478 | −0.339060 | −0.169530 | − | 0.985525i | \(-0.554225\pi\) | ||||
−0.169530 | + | 0.985525i | \(0.554225\pi\) | |||||||
\(588\) | 1.61803 | 0.0667266 | ||||||||
\(589\) | 19.4164 | 0.800039 | ||||||||
\(590\) | 4.14590 | 0.170684 | ||||||||
\(591\) | 18.6525 | 0.767260 | ||||||||
\(592\) | −11.2361 | −0.461800 | ||||||||
\(593\) | −34.0344 | −1.39763 | −0.698814 | − | 0.715304i | \(-0.746288\pi\) | ||||
−0.698814 | + | 0.715304i | \(0.746288\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.61803 | −0.107329 | ||||||||
\(596\) | 11.7082 | 0.479587 | ||||||||
\(597\) | 8.18034 | 0.334799 | ||||||||
\(598\) | −2.47214 | −0.101093 | ||||||||
\(599\) | −36.0689 | −1.47373 | −0.736867 | − | 0.676037i | \(-0.763696\pi\) | ||||
−0.736867 | + | 0.676037i | \(0.763696\pi\) | |||||||
\(600\) | −1.61803 | −0.0660560 | ||||||||
\(601\) | −33.3262 | −1.35941 | −0.679703 | − | 0.733488i | \(-0.737891\pi\) | ||||
−0.679703 | + | 0.733488i | \(0.737891\pi\) | |||||||
\(602\) | 2.09017 | 0.0851890 | ||||||||
\(603\) | 1.29180 | 0.0526060 | ||||||||
\(604\) | 18.4721 | 0.751621 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 24.1803 | 0.982259 | ||||||||
\(607\) | −6.83282 | −0.277335 | −0.138668 | − | 0.990339i | \(-0.544282\pi\) | ||||
−0.138668 | + | 0.990339i | \(0.544282\pi\) | |||||||
\(608\) | −7.85410 | −0.318526 | ||||||||
\(609\) | 7.23607 | 0.293220 | ||||||||
\(610\) | 13.7082 | 0.555029 | ||||||||
\(611\) | −24.9443 | −1.00914 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −10.4721 | −0.422966 | −0.211483 | − | 0.977382i | \(-0.567829\pi\) | ||||
−0.211483 | + | 0.977382i | \(0.567829\pi\) | |||||||
\(614\) | −18.5623 | −0.749114 | ||||||||
\(615\) | −4.61803 | −0.186217 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.56231 | −0.223930 | −0.111965 | − | 0.993712i | \(-0.535714\pi\) | ||||
−0.111965 | + | 0.993712i | \(0.535714\pi\) | |||||||
\(618\) | 9.70820 | 0.390521 | ||||||||
\(619\) | 43.2705 | 1.73919 | 0.869594 | − | 0.493767i | \(-0.164380\pi\) | ||||
0.869594 | + | 0.493767i | \(0.164380\pi\) | |||||||
\(620\) | −2.47214 | −0.0992834 | ||||||||
\(621\) | 2.58359 | 0.103676 | ||||||||
\(622\) | 2.18034 | 0.0874237 | ||||||||
\(623\) | −14.8541 | −0.595117 | ||||||||
\(624\) | −8.47214 | −0.339157 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 31.2705 | 1.24982 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −14.9443 | −0.596341 | ||||||||
\(629\) | −29.4164 | −1.17291 | ||||||||
\(630\) | −0.381966 | −0.0152179 | ||||||||
\(631\) | 25.1246 | 1.00020 | 0.500098 | − | 0.865969i | \(-0.333297\pi\) | ||||
0.500098 | + | 0.865969i | \(0.333297\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | 17.2705 | 0.686441 | ||||||||
\(634\) | −30.3607 | −1.20578 | ||||||||
\(635\) | −12.4721 | −0.494942 | ||||||||
\(636\) | −4.47214 | −0.177332 | ||||||||
\(637\) | −5.23607 | −0.207461 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.18034 | −0.165372 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −40.8541 | −1.61364 | −0.806820 | − | 0.590797i | \(-0.798813\pi\) | ||||
−0.806820 | + | 0.590797i | \(0.798813\pi\) | |||||||
\(642\) | −4.61803 | −0.182259 | ||||||||
\(643\) | −14.2016 | −0.560057 | −0.280029 | − | 0.959992i | \(-0.590344\pi\) | ||||
−0.280029 | + | 0.959992i | \(0.590344\pi\) | |||||||
\(644\) | −0.472136 | −0.0186048 | ||||||||
\(645\) | 3.38197 | 0.133165 | ||||||||
\(646\) | −20.5623 | −0.809013 | ||||||||
\(647\) | 37.7082 | 1.48246 | 0.741231 | − | 0.671250i | \(-0.234242\pi\) | ||||
0.741231 | + | 0.671250i | \(0.234242\pi\) | |||||||
\(648\) | 7.70820 | 0.302807 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5.23607 | 0.205375 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | 22.7984 | 0.892853 | ||||||||
\(653\) | 44.6525 | 1.74739 | 0.873693 | − | 0.486477i | \(-0.161718\pi\) | ||||
0.873693 | + | 0.486477i | \(0.161718\pi\) | |||||||
\(654\) | −6.47214 | −0.253081 | ||||||||
\(655\) | −5.09017 | −0.198889 | ||||||||
\(656\) | 2.85410 | 0.111434 | ||||||||
\(657\) | −1.09017 | −0.0425316 | ||||||||
\(658\) | −4.76393 | −0.185717 | ||||||||
\(659\) | −20.9787 | −0.817215 | −0.408607 | − | 0.912710i | \(-0.633985\pi\) | ||||
−0.408607 | + | 0.912710i | \(0.633985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.81966 | 0.0707766 | 0.0353883 | − | 0.999374i | \(-0.488733\pi\) | ||||
0.0353883 | + | 0.999374i | \(0.488733\pi\) | |||||||
\(662\) | 0.965558 | 0.0375275 | ||||||||
\(663\) | −22.1803 | −0.861413 | ||||||||
\(664\) | 8.85410 | 0.343606 | ||||||||
\(665\) | −7.85410 | −0.304569 | ||||||||
\(666\) | −4.29180 | −0.166304 | ||||||||
\(667\) | −2.11146 | −0.0817559 | ||||||||
\(668\) | 8.29180 | 0.320819 | ||||||||
\(669\) | 21.2361 | 0.821034 | ||||||||
\(670\) | −3.38197 | −0.130657 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.61803 | −0.0624170 | ||||||||
\(673\) | 15.4508 | 0.595586 | 0.297793 | − | 0.954630i | \(-0.403749\pi\) | ||||
0.297793 | + | 0.954630i | \(0.403749\pi\) | |||||||
\(674\) | 1.20163 | 0.0462849 | ||||||||
\(675\) | −5.47214 | −0.210623 | ||||||||
\(676\) | 14.4164 | 0.554477 | ||||||||
\(677\) | 11.4164 | 0.438768 | 0.219384 | − | 0.975639i | \(-0.429595\pi\) | ||||
0.219384 | + | 0.975639i | \(0.429595\pi\) | |||||||
\(678\) | −7.00000 | −0.268833 | ||||||||
\(679\) | −8.38197 | −0.321670 | ||||||||
\(680\) | 2.61803 | 0.100397 | ||||||||
\(681\) | 22.1246 | 0.847817 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.5279 | 0.823741 | 0.411870 | − | 0.911242i | \(-0.364876\pi\) | ||||
0.411870 | + | 0.911242i | \(0.364876\pi\) | |||||||
\(684\) | −3.00000 | −0.114708 | ||||||||
\(685\) | −4.85410 | −0.185466 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 36.1803 | 1.38037 | ||||||||
\(688\) | −2.09017 | −0.0796870 | ||||||||
\(689\) | 14.4721 | 0.551344 | ||||||||
\(690\) | −0.763932 | −0.0290824 | ||||||||
\(691\) | −7.56231 | −0.287684 | −0.143842 | − | 0.989601i | \(-0.545946\pi\) | ||||
−0.143842 | + | 0.989601i | \(0.545946\pi\) | |||||||
\(692\) | 19.8885 | 0.756049 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −15.0902 | −0.572815 | ||||||||
\(695\) | 4.94427 | 0.187547 | ||||||||
\(696\) | −7.23607 | −0.274282 | ||||||||
\(697\) | 7.47214 | 0.283027 | ||||||||
\(698\) | 19.4164 | 0.734922 | ||||||||
\(699\) | 1.09017 | 0.0412340 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −34.8328 | −1.31562 | −0.657809 | − | 0.753185i | \(-0.728516\pi\) | ||||
−0.657809 | + | 0.753185i | \(0.728516\pi\) | |||||||
\(702\) | −28.6525 | −1.08142 | ||||||||
\(703\) | −88.2492 | −3.32838 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.70820 | −0.290308 | ||||||||
\(706\) | 11.5623 | 0.435153 | ||||||||
\(707\) | −14.9443 | −0.562037 | ||||||||
\(708\) | 6.70820 | 0.252110 | ||||||||
\(709\) | 33.7771 | 1.26853 | 0.634263 | − | 0.773118i | \(-0.281304\pi\) | ||||
0.634263 | + | 0.773118i | \(0.281304\pi\) | |||||||
\(710\) | 10.9443 | 0.410731 | ||||||||
\(711\) | −1.52786 | −0.0572994 | ||||||||
\(712\) | 14.8541 | 0.556681 | ||||||||
\(713\) | −1.16718 | −0.0437114 | ||||||||
\(714\) | −4.23607 | −0.158531 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.14590 | 0.0801960 | ||||||||
\(717\) | 10.1803 | 0.380192 | ||||||||
\(718\) | −29.5967 | −1.10454 | ||||||||
\(719\) | 24.0689 | 0.897618 | 0.448809 | − | 0.893628i | \(-0.351848\pi\) | ||||
0.448809 | + | 0.893628i | \(0.351848\pi\) | |||||||
\(720\) | 0.381966 | 0.0142350 | ||||||||
\(721\) | −6.00000 | −0.223452 | ||||||||
\(722\) | −42.6869 | −1.58864 | ||||||||
\(723\) | −50.1246 | −1.86415 | ||||||||
\(724\) | 20.9443 | 0.778388 | ||||||||
\(725\) | 4.47214 | 0.166091 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.2492 | 1.86364 | 0.931820 | − | 0.362920i | \(-0.118220\pi\) | ||||
0.931820 | + | 0.362920i | \(0.118220\pi\) | |||||||
\(728\) | 5.23607 | 0.194062 | ||||||||
\(729\) | 29.5066 | 1.09284 | ||||||||
\(730\) | 2.85410 | 0.105635 | ||||||||
\(731\) | −5.47214 | −0.202394 | ||||||||
\(732\) | 22.1803 | 0.819809 | ||||||||
\(733\) | −35.5967 | −1.31480 | −0.657398 | − | 0.753544i | \(-0.728343\pi\) | ||||
−0.657398 | + | 0.753544i | \(0.728343\pi\) | |||||||
\(734\) | −15.8885 | −0.586457 | ||||||||
\(735\) | −1.61803 | −0.0596821 | ||||||||
\(736\) | 0.472136 | 0.0174032 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 1.09017 | 0.0401297 | ||||||||
\(739\) | 10.1459 | 0.373223 | 0.186611 | − | 0.982434i | \(-0.440249\pi\) | ||||
0.186611 | + | 0.982434i | \(0.440249\pi\) | |||||||
\(740\) | 11.2361 | 0.413046 | ||||||||
\(741\) | −66.5410 | −2.44445 | ||||||||
\(742\) | 2.76393 | 0.101467 | ||||||||
\(743\) | −40.2492 | −1.47660 | −0.738300 | − | 0.674472i | \(-0.764371\pi\) | ||||
−0.738300 | + | 0.674472i | \(0.764371\pi\) | |||||||
\(744\) | −4.00000 | −0.146647 | ||||||||
\(745\) | −11.7082 | −0.428955 | ||||||||
\(746\) | −14.6525 | −0.536465 | ||||||||
\(747\) | 3.38197 | 0.123740 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.85410 | 0.104287 | ||||||||
\(750\) | 1.61803 | 0.0590822 | ||||||||
\(751\) | −45.3050 | −1.65320 | −0.826601 | − | 0.562789i | \(-0.809728\pi\) | ||||
−0.826601 | + | 0.562789i | \(0.809728\pi\) | |||||||
\(752\) | 4.76393 | 0.173723 | ||||||||
\(753\) | 32.3607 | 1.17929 | ||||||||
\(754\) | 23.4164 | 0.852775 | ||||||||
\(755\) | −18.4721 | −0.672270 | ||||||||
\(756\) | −5.47214 | −0.199020 | ||||||||
\(757\) | 44.6525 | 1.62292 | 0.811461 | − | 0.584407i | \(-0.198673\pi\) | ||||
0.811461 | + | 0.584407i | \(0.198673\pi\) | |||||||
\(758\) | −15.6180 | −0.567273 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.85410 | 0.284898 | ||||||||
\(761\) | −49.8115 | −1.80567 | −0.902833 | − | 0.429991i | \(-0.858517\pi\) | ||||
−0.902833 | + | 0.429991i | \(0.858517\pi\) | |||||||
\(762\) | −20.1803 | −0.731057 | ||||||||
\(763\) | 4.00000 | 0.144810 | ||||||||
\(764\) | −1.23607 | −0.0447194 | ||||||||
\(765\) | 1.00000 | 0.0361551 | ||||||||
\(766\) | 20.1803 | 0.729145 | ||||||||
\(767\) | −21.7082 | −0.783838 | ||||||||
\(768\) | 1.61803 | 0.0583858 | ||||||||
\(769\) | 31.3050 | 1.12889 | 0.564443 | − | 0.825472i | \(-0.309091\pi\) | ||||
0.564443 | + | 0.825472i | \(0.309091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.0344 | 0.865579 | ||||||||
\(772\) | −21.4164 | −0.770793 | ||||||||
\(773\) | 34.7639 | 1.25037 | 0.625186 | − | 0.780476i | \(-0.285023\pi\) | ||||
0.625186 | + | 0.780476i | \(0.285023\pi\) | |||||||
\(774\) | −0.798374 | −0.0286970 | ||||||||
\(775\) | 2.47214 | 0.0888017 | ||||||||
\(776\) | 8.38197 | 0.300895 | ||||||||
\(777\) | −18.1803 | −0.652216 | ||||||||
\(778\) | −25.7082 | −0.921684 | ||||||||
\(779\) | 22.4164 | 0.803151 | ||||||||
\(780\) | 8.47214 | 0.303351 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.23607 | 0.0442017 | ||||||||
\(783\) | −24.4721 | −0.874563 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 14.9443 | 0.533384 | ||||||||
\(786\) | −8.23607 | −0.293771 | ||||||||
\(787\) | 43.2705 | 1.54243 | 0.771214 | − | 0.636577i | \(-0.219650\pi\) | ||||
0.771214 | + | 0.636577i | \(0.219650\pi\) | |||||||
\(788\) | 11.5279 | 0.410663 | ||||||||
\(789\) | 42.6525 | 1.51847 | ||||||||
\(790\) | 4.00000 | 0.142314 | ||||||||
\(791\) | 4.32624 | 0.153823 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −71.7771 | −2.54888 | ||||||||
\(794\) | −0.111456 | −0.00395543 | ||||||||
\(795\) | 4.47214 | 0.158610 | ||||||||
\(796\) | 5.05573 | 0.179196 | ||||||||
\(797\) | −8.18034 | −0.289763 | −0.144881 | − | 0.989449i | \(-0.546280\pi\) | ||||
−0.144881 | + | 0.989449i | \(0.546280\pi\) | |||||||
\(798\) | −12.7082 | −0.449866 | ||||||||
\(799\) | 12.4721 | 0.441232 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 5.67376 | 0.200473 | ||||||||
\(802\) | −2.56231 | −0.0904782 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −5.47214 | −0.192987 | ||||||||
\(805\) | 0.472136 | 0.0166406 | ||||||||
\(806\) | 12.9443 | 0.455943 | ||||||||
\(807\) | −30.1803 | −1.06240 | ||||||||
\(808\) | 14.9443 | 0.525738 | ||||||||
\(809\) | 27.1591 | 0.954861 | 0.477431 | − | 0.878669i | \(-0.341568\pi\) | ||||
0.477431 | + | 0.878669i | \(0.341568\pi\) | |||||||
\(810\) | −7.70820 | −0.270839 | ||||||||
\(811\) | 35.6869 | 1.25314 | 0.626569 | − | 0.779366i | \(-0.284459\pi\) | ||||
0.626569 | + | 0.779366i | \(0.284459\pi\) | |||||||
\(812\) | 4.47214 | 0.156941 | ||||||||
\(813\) | −10.0000 | −0.350715 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.7984 | −0.798592 | ||||||||
\(816\) | 4.23607 | 0.148292 | ||||||||
\(817\) | −16.4164 | −0.574337 | ||||||||
\(818\) | 22.9443 | 0.802228 | ||||||||
\(819\) | 2.00000 | 0.0698857 | ||||||||
\(820\) | −2.85410 | −0.0996696 | ||||||||
\(821\) | −0.111456 | −0.00388985 | −0.00194492 | − | 0.999998i | \(-0.500619\pi\) | ||||
−0.00194492 | + | 0.999998i | \(0.500619\pi\) | |||||||
\(822\) | −7.85410 | −0.273943 | ||||||||
\(823\) | −3.81966 | −0.133145 | −0.0665725 | − | 0.997782i | \(-0.521206\pi\) | ||||
−0.0665725 | + | 0.997782i | \(0.521206\pi\) | |||||||
\(824\) | 6.00000 | 0.209020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.14590 | −0.144254 | ||||||||
\(827\) | 52.3262 | 1.81956 | 0.909781 | − | 0.415089i | \(-0.136250\pi\) | ||||
0.909781 | + | 0.415089i | \(0.136250\pi\) | |||||||
\(828\) | 0.180340 | 0.00626724 | ||||||||
\(829\) | 33.5279 | 1.16447 | 0.582235 | − | 0.813020i | \(-0.302178\pi\) | ||||
0.582235 | + | 0.813020i | \(0.302178\pi\) | |||||||
\(830\) | −8.85410 | −0.307330 | ||||||||
\(831\) | −19.4164 | −0.673548 | ||||||||
\(832\) | −5.23607 | −0.181528 | ||||||||
\(833\) | 2.61803 | 0.0907095 | ||||||||
\(834\) | 8.00000 | 0.277017 | ||||||||
\(835\) | −8.29180 | −0.286949 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.5279 | −0.467591 | ||||||||
\(838\) | −22.5623 | −0.779402 | ||||||||
\(839\) | 36.2918 | 1.25293 | 0.626466 | − | 0.779449i | \(-0.284501\pi\) | ||||
0.626466 | + | 0.779449i | \(0.284501\pi\) | |||||||
\(840\) | 1.61803 | 0.0558275 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | 36.8328 | 1.26934 | ||||||||
\(843\) | 18.3262 | 0.631189 | ||||||||
\(844\) | 10.6738 | 0.367406 | ||||||||
\(845\) | −14.4164 | −0.495940 | ||||||||
\(846\) | 1.81966 | 0.0625612 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.76393 | −0.0949138 | ||||||||
\(849\) | 26.4721 | 0.908521 | ||||||||
\(850\) | −2.61803 | −0.0897978 | ||||||||
\(851\) | 5.30495 | 0.181851 | ||||||||
\(852\) | 17.7082 | 0.606673 | ||||||||
\(853\) | −13.4164 | −0.459369 | −0.229685 | − | 0.973265i | \(-0.573769\pi\) | ||||
−0.229685 | + | 0.973265i | \(0.573769\pi\) | |||||||
\(854\) | −13.7082 | −0.469085 | ||||||||
\(855\) | 3.00000 | 0.102598 | ||||||||
\(856\) | −2.85410 | −0.0975512 | ||||||||
\(857\) | 24.5623 | 0.839032 | 0.419516 | − | 0.907748i | \(-0.362200\pi\) | ||||
0.419516 | + | 0.907748i | \(0.362200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.3262 | 0.488805 | 0.244402 | − | 0.969674i | \(-0.421408\pi\) | ||||
0.244402 | + | 0.969674i | \(0.421408\pi\) | |||||||
\(860\) | 2.09017 | 0.0712742 | ||||||||
\(861\) | 4.61803 | 0.157382 | ||||||||
\(862\) | 0.652476 | 0.0222234 | ||||||||
\(863\) | −14.1115 | −0.480360 | −0.240180 | − | 0.970728i | \(-0.577206\pi\) | ||||
−0.240180 | + | 0.970728i | \(0.577206\pi\) | |||||||
\(864\) | 5.47214 | 0.186166 | ||||||||
\(865\) | −19.8885 | −0.676231 | ||||||||
\(866\) | 8.79837 | 0.298981 | ||||||||
\(867\) | −16.4164 | −0.557530 | ||||||||
\(868\) | 2.47214 | 0.0839098 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 7.23607 | 0.245326 | ||||||||
\(871\) | 17.7082 | 0.600020 | ||||||||
\(872\) | −4.00000 | −0.135457 | ||||||||
\(873\) | 3.20163 | 0.108359 | ||||||||
\(874\) | 3.70820 | 0.125432 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 4.61803 | 0.156029 | ||||||||
\(877\) | −2.76393 | −0.0933314 | −0.0466657 | − | 0.998911i | \(-0.514860\pi\) | ||||
−0.0466657 | + | 0.998911i | \(0.514860\pi\) | |||||||
\(878\) | −30.5410 | −1.03071 | ||||||||
\(879\) | 29.8885 | 1.00812 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.6738 | 0.494372 | 0.247186 | − | 0.968968i | \(-0.420494\pi\) | ||||
0.247186 | + | 0.968968i | \(0.420494\pi\) | |||||||
\(882\) | 0.381966 | 0.0128615 | ||||||||
\(883\) | −43.2148 | −1.45429 | −0.727147 | − | 0.686482i | \(-0.759154\pi\) | ||||
−0.727147 | + | 0.686482i | \(0.759154\pi\) | |||||||
\(884\) | −13.7082 | −0.461057 | ||||||||
\(885\) | −6.70820 | −0.225494 | ||||||||
\(886\) | 28.5623 | 0.959569 | ||||||||
\(887\) | 26.5410 | 0.891160 | 0.445580 | − | 0.895242i | \(-0.352997\pi\) | ||||
0.445580 | + | 0.895242i | \(0.352997\pi\) | |||||||
\(888\) | 18.1803 | 0.610092 | ||||||||
\(889\) | 12.4721 | 0.418302 | ||||||||
\(890\) | −14.8541 | −0.497911 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.1246 | 0.439445 | ||||||||
\(893\) | 37.4164 | 1.25209 | ||||||||
\(894\) | −18.9443 | −0.633591 | ||||||||
\(895\) | −2.14590 | −0.0717295 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 4.00000 | 0.133556 | ||||||||
\(898\) | 20.0344 | 0.668558 | ||||||||
\(899\) | 11.0557 | 0.368729 | ||||||||
\(900\) | −0.381966 | −0.0127322 | ||||||||
\(901\) | −7.23607 | −0.241068 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.38197 | −0.112545 | ||||||||
\(904\) | −4.32624 | −0.143889 | ||||||||
\(905\) | −20.9443 | −0.696211 | ||||||||
\(906\) | −29.8885 | −0.992980 | ||||||||
\(907\) | 25.8541 | 0.858471 | 0.429236 | − | 0.903193i | \(-0.358783\pi\) | ||||
0.429236 | + | 0.903193i | \(0.358783\pi\) | |||||||
\(908\) | 13.6738 | 0.453780 | ||||||||
\(909\) | 5.70820 | 0.189329 | ||||||||
\(910\) | −5.23607 | −0.173574 | ||||||||
\(911\) | 9.52786 | 0.315672 | 0.157836 | − | 0.987465i | \(-0.449548\pi\) | ||||
0.157836 | + | 0.987465i | \(0.449548\pi\) | |||||||
\(912\) | 12.7082 | 0.420811 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 25.9787 | 0.859299 | ||||||||
\(915\) | −22.1803 | −0.733259 | ||||||||
\(916\) | 22.3607 | 0.738818 | ||||||||
\(917\) | 5.09017 | 0.168092 | ||||||||
\(918\) | 14.3262 | 0.472836 | ||||||||
\(919\) | 7.05573 | 0.232747 | 0.116373 | − | 0.993206i | \(-0.462873\pi\) | ||||
0.116373 | + | 0.993206i | \(0.462873\pi\) | |||||||
\(920\) | −0.472136 | −0.0155659 | ||||||||
\(921\) | 30.0344 | 0.989669 | ||||||||
\(922\) | −23.0557 | −0.759300 | ||||||||
\(923\) | −57.3050 | −1.88622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.2361 | −0.369440 | ||||||||
\(926\) | 10.9443 | 0.359651 | ||||||||
\(927\) | 2.29180 | 0.0752725 | ||||||||
\(928\) | −4.47214 | −0.146805 | ||||||||
\(929\) | 10.9098 | 0.357940 | 0.178970 | − | 0.983855i | \(-0.442724\pi\) | ||||
0.178970 | + | 0.983855i | \(0.442724\pi\) | |||||||
\(930\) | 4.00000 | 0.131165 | ||||||||
\(931\) | 7.85410 | 0.257408 | ||||||||
\(932\) | 0.673762 | 0.0220698 | ||||||||
\(933\) | −3.52786 | −0.115497 | ||||||||
\(934\) | −12.9443 | −0.423550 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.00000 | −0.0653720 | ||||||||
\(937\) | −28.5066 | −0.931269 | −0.465635 | − | 0.884977i | \(-0.654174\pi\) | ||||
−0.465635 | + | 0.884977i | \(0.654174\pi\) | |||||||
\(938\) | 3.38197 | 0.110425 | ||||||||
\(939\) | −50.5967 | −1.65116 | ||||||||
\(940\) | −4.76393 | −0.155382 | ||||||||
\(941\) | −24.3607 | −0.794135 | −0.397068 | − | 0.917789i | \(-0.629972\pi\) | ||||
−0.397068 | + | 0.917789i | \(0.629972\pi\) | |||||||
\(942\) | 24.1803 | 0.787838 | ||||||||
\(943\) | −1.34752 | −0.0438814 | ||||||||
\(944\) | 4.14590 | 0.134937 | ||||||||
\(945\) | 5.47214 | 0.178009 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.6312 | −1.74278 | −0.871390 | − | 0.490591i | \(-0.836781\pi\) | ||||
−0.871390 | + | 0.490591i | \(0.836781\pi\) | |||||||
\(948\) | 6.47214 | 0.210205 | ||||||||
\(949\) | −14.9443 | −0.485112 | ||||||||
\(950\) | −7.85410 | −0.254821 | ||||||||
\(951\) | 49.1246 | 1.59297 | ||||||||
\(952\) | −2.61803 | −0.0848510 | ||||||||
\(953\) | 0.854102 | 0.0276671 | 0.0138335 | − | 0.999904i | \(-0.495597\pi\) | ||||
0.0138335 | + | 0.999904i | \(0.495597\pi\) | |||||||
\(954\) | −1.05573 | −0.0341805 | ||||||||
\(955\) | 1.23607 | 0.0399982 | ||||||||
\(956\) | 6.29180 | 0.203491 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.2918 | −0.720215 | ||||||||
\(959\) | 4.85410 | 0.156747 | ||||||||
\(960\) | −1.61803 | −0.0522218 | ||||||||
\(961\) | −24.8885 | −0.802856 | ||||||||
\(962\) | −58.8328 | −1.89685 | ||||||||
\(963\) | −1.09017 | −0.0351302 | ||||||||
\(964\) | −30.9787 | −0.997757 | ||||||||
\(965\) | 21.4164 | 0.689419 | ||||||||
\(966\) | 0.763932 | 0.0245791 | ||||||||
\(967\) | 17.3475 | 0.557859 | 0.278929 | − | 0.960312i | \(-0.410020\pi\) | ||||
0.278929 | + | 0.960312i | \(0.410020\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 33.2705 | 1.06880 | ||||||||
\(970\) | −8.38197 | −0.269129 | ||||||||
\(971\) | −34.8328 | −1.11784 | −0.558919 | − | 0.829222i | \(-0.688784\pi\) | ||||
−0.558919 | + | 0.829222i | \(0.688784\pi\) | |||||||
\(972\) | 3.94427 | 0.126513 | ||||||||
\(973\) | −4.94427 | −0.158506 | ||||||||
\(974\) | −38.1803 | −1.22338 | ||||||||
\(975\) | −8.47214 | −0.271325 | ||||||||
\(976\) | 13.7082 | 0.438789 | ||||||||
\(977\) | −37.1935 | −1.18993 | −0.594963 | − | 0.803753i | \(-0.702833\pi\) | ||||
−0.594963 | + | 0.803753i | \(0.702833\pi\) | |||||||
\(978\) | −36.8885 | −1.17957 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −1.52786 | −0.0487809 | ||||||||
\(982\) | 19.2148 | 0.613168 | ||||||||
\(983\) | −8.94427 | −0.285278 | −0.142639 | − | 0.989775i | \(-0.545559\pi\) | ||||
−0.142639 | + | 0.989775i | \(0.545559\pi\) | |||||||
\(984\) | −4.61803 | −0.147218 | ||||||||
\(985\) | −11.5279 | −0.367308 | ||||||||
\(986\) | −11.7082 | −0.372865 | ||||||||
\(987\) | 7.70820 | 0.245355 | ||||||||
\(988\) | −41.1246 | −1.30835 | ||||||||
\(989\) | 0.986844 | 0.0313798 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 34.3607 | 1.09150 | 0.545751 | − | 0.837947i | \(-0.316244\pi\) | ||||
0.545751 | + | 0.837947i | \(0.316244\pi\) | |||||||
\(992\) | −2.47214 | −0.0784904 | ||||||||
\(993\) | −1.56231 | −0.0495783 | ||||||||
\(994\) | −10.9443 | −0.347131 | ||||||||
\(995\) | −5.05573 | −0.160277 | ||||||||
\(996\) | −14.3262 | −0.453944 | ||||||||
\(997\) | −48.8328 | −1.54655 | −0.773275 | − | 0.634070i | \(-0.781383\pi\) | ||||
−0.773275 | + | 0.634070i | \(0.781383\pi\) | |||||||
\(998\) | 19.9787 | 0.632415 | ||||||||
\(999\) | 61.4853 | 1.94531 |
(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 | 8470.2.a.bp.1.2 | 2 | ||
11.5 | even | 5 | 770.2.n.d.421.1 | ✓ | 4 | ||
11.9 | even | 5 | 770.2.n.d.631.1 | yes | 4 | ||
11.10 | odd | 2 | 8470.2.a.cb.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.n.d.421.1 | ✓ | 4 | 11.5 | even | 5 | ||
770.2.n.d.631.1 | yes | 4 | 11.9 | even | 5 | ||
8470.2.a.bp.1.2 | 2 | 1.1 | even | 1 | trivial | ||
8470.2.a.cb.1.2 | 2 | 11.10 | odd | 2 |