Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [845,2,Mod(506,845)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(845, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("845.506");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 845 = 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 845.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.74735897080\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.22581504.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 506.2 | ||
Root | \(1.20036 + 0.747754i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 845.506 |
Dual form | 845.2.c.g.506.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/845\mathbb{Z}\right)^\times\).
\(n\) | \(171\) | \(677\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.49551i | − 1.05748i | −0.848783 | − | 0.528742i | \(-0.822664\pi\) | ||||
0.848783 | − | 0.528742i | \(-0.177336\pi\) | |||||||
\(3\) | 0.0947876 | 0.0547256 | 0.0273628 | − | 0.999626i | \(-0.491289\pi\) | ||||
0.0273628 | + | 0.999626i | \(0.491289\pi\) | |||||||
\(4\) | −0.236543 | −0.118272 | ||||||||
\(5\) | − 1.00000i | − 0.447214i | ||||||||
\(6\) | − 0.141756i | − 0.0578715i | ||||||||
\(7\) | − 4.82684i | − 1.82437i | −0.409775 | − | 0.912187i | \(-0.634393\pi\) | ||||
0.409775 | − | 0.912187i | \(-0.365607\pi\) | |||||||
\(8\) | − 2.63726i | − 0.932413i | ||||||||
\(9\) | −2.99102 | −0.997005 | ||||||||
\(10\) | −1.49551 | −0.472921 | ||||||||
\(11\) | 1.06939i | 0.322433i | 0.986919 | + | 0.161217i | \(0.0515417\pi\) | ||||
−0.986919 | + | 0.161217i | \(0.948458\pi\) | |||||||
\(12\) | −0.0224214 | −0.00647249 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −7.21857 | −1.92924 | ||||||||
\(15\) | − 0.0947876i | − 0.0244740i | ||||||||
\(16\) | −4.41713 | −1.10428 | ||||||||
\(17\) | −3.55889 | −0.863157 | −0.431579 | − | 0.902075i | \(-0.642043\pi\) | ||||
−0.431579 | + | 0.902075i | \(0.642043\pi\) | |||||||
\(18\) | 4.47309i | 1.05432i | ||||||||
\(19\) | 5.73205i | 1.31502i | 0.753445 | + | 0.657511i | \(0.228391\pi\) | ||||
−0.753445 | + | 0.657511i | \(0.771609\pi\) | |||||||
\(20\) | 0.236543i | 0.0528927i | ||||||||
\(21\) | − 0.457524i | − 0.0998400i | ||||||||
\(22\) | 1.59928 | 0.340968 | ||||||||
\(23\) | 7.08580 | 1.47749 | 0.738746 | − | 0.673984i | \(-0.235418\pi\) | ||||
0.738746 | + | 0.673984i | \(0.235418\pi\) | |||||||
\(24\) | − 0.249980i | − 0.0510269i | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.567874 | −0.109287 | ||||||||
\(28\) | 1.14176i | 0.215772i | ||||||||
\(29\) | 1.47309 | 0.273545 | 0.136773 | − | 0.990602i | \(-0.456327\pi\) | ||||
0.136773 | + | 0.990602i | \(0.456327\pi\) | |||||||
\(30\) | −0.141756 | −0.0258809 | ||||||||
\(31\) | − 1.46410i | − 0.262960i | −0.991319 | − | 0.131480i | \(-0.958027\pi\) | ||||
0.991319 | − | 0.131480i | \(-0.0419730\pi\) | |||||||
\(32\) | 1.33133i | 0.235348i | ||||||||
\(33\) | 0.101365i | 0.0176454i | ||||||||
\(34\) | 5.32235i | 0.912775i | ||||||||
\(35\) | −4.82684 | −0.815885 | ||||||||
\(36\) | 0.707504 | 0.117917 | ||||||||
\(37\) | 0.0253983i | 0.00417545i | 0.999998 | + | 0.00208772i | \(0.000664544\pi\) | ||||
−0.999998 | + | 0.00208772i | \(0.999335\pi\) | |||||||
\(38\) | 8.57233 | 1.39061 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.63726 | −0.416988 | ||||||||
\(41\) | 0.267949i | 0.0418466i | 0.999781 | + | 0.0209233i | \(0.00666058\pi\) | ||||
−0.999781 | + | 0.0209233i | \(0.993339\pi\) | |||||||
\(42\) | −0.684231 | −0.105579 | ||||||||
\(43\) | −3.55889 | −0.542726 | −0.271363 | − | 0.962477i | \(-0.587474\pi\) | ||||
−0.271363 | + | 0.962477i | \(0.587474\pi\) | |||||||
\(44\) | − 0.252957i | − 0.0381347i | ||||||||
\(45\) | 2.99102i | 0.445874i | ||||||||
\(46\) | − 10.5969i | − 1.56242i | ||||||||
\(47\) | − 6.51793i | − 0.950738i | −0.879787 | − | 0.475369i | \(-0.842315\pi\) | ||||
0.879787 | − | 0.475369i | \(-0.157685\pi\) | |||||||
\(48\) | −0.418689 | −0.0604326 | ||||||||
\(49\) | −16.2984 | −2.32834 | ||||||||
\(50\) | 1.49551i | 0.211497i | ||||||||
\(51\) | −0.337339 | −0.0472368 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.991015 | 0.136126 | 0.0680632 | − | 0.997681i | \(-0.478318\pi\) | ||||
0.0680632 | + | 0.997681i | \(0.478318\pi\) | |||||||
\(54\) | 0.849260i | 0.115570i | ||||||||
\(55\) | 1.06939 | 0.144196 | ||||||||
\(56\) | −12.7296 | −1.70107 | ||||||||
\(57\) | 0.543327i | 0.0719655i | ||||||||
\(58\) | − 2.20301i | − 0.289270i | ||||||||
\(59\) | − 8.72307i | − 1.13565i | −0.823151 | − | 0.567823i | \(-0.807786\pi\) | ||||
0.823151 | − | 0.567823i | \(-0.192214\pi\) | |||||||
\(60\) | 0.0224214i | 0.00289458i | ||||||||
\(61\) | 6.33734 | 0.811413 | 0.405707 | − | 0.914003i | \(-0.367026\pi\) | ||||
0.405707 | + | 0.914003i | \(0.367026\pi\) | |||||||
\(62\) | −2.18958 | −0.278076 | ||||||||
\(63\) | 14.4371i | 1.81891i | ||||||||
\(64\) | −6.84325 | −0.855406 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.151592 | 0.0186597 | ||||||||
\(67\) | 5.17316i | 0.632002i | 0.948759 | + | 0.316001i | \(0.102340\pi\) | ||||
−0.948759 | + | 0.316001i | \(0.897660\pi\) | |||||||
\(68\) | 0.841831 | 0.102087 | ||||||||
\(69\) | 0.671646 | 0.0808567 | ||||||||
\(70\) | 7.21857i | 0.862785i | ||||||||
\(71\) | − 7.76488i | − 0.921521i | −0.887524 | − | 0.460761i | \(-0.847577\pi\) | ||||
0.887524 | − | 0.460761i | \(-0.152423\pi\) | |||||||
\(72\) | 7.88809i | 0.929621i | ||||||||
\(73\) | − 10.1088i | − 1.18314i | −0.806252 | − | 0.591572i | \(-0.798507\pi\) | ||||
0.806252 | − | 0.591572i | \(-0.201493\pi\) | |||||||
\(74\) | 0.0379833 | 0.00441547 | ||||||||
\(75\) | −0.0947876 | −0.0109451 | ||||||||
\(76\) | − 1.35588i | − 0.155530i | ||||||||
\(77\) | 5.16177 | 0.588238 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.78347 | 0.988218 | 0.494109 | − | 0.869400i | \(-0.335494\pi\) | ||||
0.494109 | + | 0.869400i | \(0.335494\pi\) | |||||||
\(80\) | 4.41713i | 0.493851i | ||||||||
\(81\) | 8.91922 | 0.991024 | ||||||||
\(82\) | 0.400720 | 0.0442521 | ||||||||
\(83\) | − 0.725474i | − 0.0796311i | −0.999207 | − | 0.0398155i | \(-0.987323\pi\) | ||||
0.999207 | − | 0.0398155i | \(-0.0126770\pi\) | |||||||
\(84\) | 0.108224i | 0.0118082i | ||||||||
\(85\) | 3.55889i | 0.386016i | ||||||||
\(86\) | 5.32235i | 0.573923i | ||||||||
\(87\) | 0.139630 | 0.0149699 | ||||||||
\(88\) | 2.82026 | 0.300641 | ||||||||
\(89\) | − 13.5065i | − 1.43169i | −0.698259 | − | 0.715845i | \(-0.746042\pi\) | ||||
0.698259 | − | 0.715845i | \(-0.253958\pi\) | |||||||
\(90\) | 4.47309 | 0.471505 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −1.67610 | −0.174745 | ||||||||
\(93\) | − 0.138779i | − 0.0143907i | ||||||||
\(94\) | −9.74761 | −1.00539 | ||||||||
\(95\) | 5.73205 | 0.588096 | ||||||||
\(96\) | 0.126194i | 0.0128796i | ||||||||
\(97\) | − 3.43870i | − 0.349147i | −0.984644 | − | 0.174574i | \(-0.944145\pi\) | ||||
0.984644 | − | 0.174574i | \(-0.0558547\pi\) | |||||||
\(98\) | 24.3743i | 2.46218i | ||||||||
\(99\) | − 3.19856i | − 0.321467i | ||||||||
\(100\) | 0.236543 | 0.0236543 | ||||||||
\(101\) | −2.85527 | −0.284110 | −0.142055 | − | 0.989859i | \(-0.545371\pi\) | ||||
−0.142055 | + | 0.989859i | \(0.545371\pi\) | |||||||
\(102\) | 0.504492i | 0.0499522i | ||||||||
\(103\) | 5.54488 | 0.546354 | 0.273177 | − | 0.961964i | \(-0.411926\pi\) | ||||
0.273177 | + | 0.961964i | \(0.411926\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.457524 | −0.0446498 | ||||||||
\(106\) | − 1.48207i | − 0.143951i | ||||||||
\(107\) | −4.44111 | −0.429338 | −0.214669 | − | 0.976687i | \(-0.568867\pi\) | ||||
−0.214669 | + | 0.976687i | \(0.568867\pi\) | |||||||
\(108\) | 0.134327 | 0.0129256 | ||||||||
\(109\) | 13.7804i | 1.31993i | 0.751298 | + | 0.659963i | \(0.229428\pi\) | ||||
−0.751298 | + | 0.659963i | \(0.770572\pi\) | |||||||
\(110\) | − 1.59928i | − 0.152485i | ||||||||
\(111\) | 0.00240744i | 0 0.000228504i | ||||||||
\(112\) | 21.3208i | 2.01463i | ||||||||
\(113\) | −8.04399 | −0.756715 | −0.378358 | − | 0.925660i | \(-0.623511\pi\) | ||||
−0.378358 | + | 0.925660i | \(0.623511\pi\) | |||||||
\(114\) | 0.812550 | 0.0761023 | ||||||||
\(115\) | − 7.08580i | − 0.660755i | ||||||||
\(116\) | −0.348448 | −0.0323526 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −13.0454 | −1.20093 | ||||||||
\(119\) | 17.1782i | 1.57472i | ||||||||
\(120\) | −0.249980 | −0.0228199 | ||||||||
\(121\) | 9.85641 | 0.896037 | ||||||||
\(122\) | − 9.47754i | − 0.858056i | ||||||||
\(123\) | 0.0253983i | 0.00229008i | ||||||||
\(124\) | 0.346323i | 0.0311007i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 21.5909 | 1.92347 | ||||||||
\(127\) | −0.706653 | −0.0627053 | −0.0313526 | − | 0.999508i | \(-0.509981\pi\) | ||||
−0.0313526 | + | 0.999508i | \(0.509981\pi\) | |||||||
\(128\) | 12.8968i | 1.13993i | ||||||||
\(129\) | −0.337339 | −0.0297010 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.26554 | 0.547423 | 0.273711 | − | 0.961812i | \(-0.411749\pi\) | ||||
0.273711 | + | 0.961812i | \(0.411749\pi\) | |||||||
\(132\) | − 0.0239772i | − 0.00208694i | ||||||||
\(133\) | 27.6677 | 2.39909 | ||||||||
\(134\) | 7.73650 | 0.668332 | ||||||||
\(135\) | 0.567874i | 0.0488748i | ||||||||
\(136\) | 9.38573i | 0.804820i | ||||||||
\(137\) | − 16.3058i | − 1.39310i | −0.717509 | − | 0.696549i | \(-0.754718\pi\) | ||||
0.717509 | − | 0.696549i | \(-0.245282\pi\) | |||||||
\(138\) | − 1.00445i | − 0.0855046i | ||||||||
\(139\) | −6.82528 | −0.578913 | −0.289456 | − | 0.957191i | \(-0.593475\pi\) | ||||
−0.289456 | + | 0.957191i | \(0.593475\pi\) | |||||||
\(140\) | 1.14176 | 0.0964960 | ||||||||
\(141\) | − 0.617819i | − 0.0520297i | ||||||||
\(142\) | −11.6124 | −0.974494 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 13.2117 | 1.10098 | ||||||||
\(145\) | − 1.47309i | − 0.122333i | ||||||||
\(146\) | −15.1178 | −1.25116 | ||||||||
\(147\) | −1.54488 | −0.127420 | ||||||||
\(148\) | − 0.00600778i | 0 0.000493837i | ||||||||
\(149\) | − 8.43955i | − 0.691395i | −0.938346 | − | 0.345698i | \(-0.887642\pi\) | ||||
0.938346 | − | 0.345698i | \(-0.112358\pi\) | |||||||
\(150\) | 0.141756i | 0.0115743i | ||||||||
\(151\) | 1.37017i | 0.111503i | 0.998445 | + | 0.0557513i | \(0.0177554\pi\) | ||||
−0.998445 | + | 0.0557513i | \(0.982245\pi\) | |||||||
\(152\) | 15.1169 | 1.22614 | ||||||||
\(153\) | 10.6447 | 0.860572 | ||||||||
\(154\) | − 7.71947i | − 0.622052i | ||||||||
\(155\) | −1.46410 | −0.117599 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.9700 | 0.955311 | 0.477656 | − | 0.878547i | \(-0.341487\pi\) | ||||
0.477656 | + | 0.878547i | \(0.341487\pi\) | |||||||
\(158\) | − 13.1357i | − 1.04502i | ||||||||
\(159\) | 0.0939360 | 0.00744961 | ||||||||
\(160\) | 1.33133 | 0.105251 | ||||||||
\(161\) | − 34.2020i | − 2.69550i | ||||||||
\(162\) | − 13.3388i | − 1.04799i | ||||||||
\(163\) | 22.5713i | 1.76792i | 0.467559 | + | 0.883962i | \(0.345134\pi\) | ||||
−0.467559 | + | 0.883962i | \(0.654866\pi\) | |||||||
\(164\) | − 0.0633815i | − 0.00494927i | ||||||||
\(165\) | 0.101365 | 0.00789124 | ||||||||
\(166\) | −1.08495 | −0.0842085 | ||||||||
\(167\) | − 8.19700i | − 0.634303i | −0.948375 | − | 0.317152i | \(-0.897274\pi\) | ||||
0.948375 | − | 0.317152i | \(-0.102726\pi\) | |||||||
\(168\) | −1.20661 | −0.0930922 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 5.32235 | 0.408205 | ||||||||
\(171\) | − 17.1447i | − 1.31108i | ||||||||
\(172\) | 0.841831 | 0.0641890 | ||||||||
\(173\) | 9.16772 | 0.697009 | 0.348505 | − | 0.937307i | \(-0.386690\pi\) | ||||
0.348505 | + | 0.937307i | \(0.386690\pi\) | |||||||
\(174\) | − 0.208818i | − 0.0158305i | ||||||||
\(175\) | 4.82684i | 0.364875i | ||||||||
\(176\) | − 4.72364i | − 0.356057i | ||||||||
\(177\) | − 0.826838i | − 0.0621490i | ||||||||
\(178\) | −20.1991 | −1.51399 | ||||||||
\(179\) | 10.0370 | 0.750200 | 0.375100 | − | 0.926984i | \(-0.377608\pi\) | ||||
0.375100 | + | 0.926984i | \(0.377608\pi\) | |||||||
\(180\) | − 0.707504i | − 0.0527342i | ||||||||
\(181\) | −17.0238 | −1.26537 | −0.632686 | − | 0.774408i | \(-0.718048\pi\) | ||||
−0.632686 | + | 0.774408i | \(0.718048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.600701 | 0.0444051 | ||||||||
\(184\) | − 18.6871i | − 1.37763i | ||||||||
\(185\) | 0.0253983 | 0.00186732 | ||||||||
\(186\) | −0.207545 | −0.0152179 | ||||||||
\(187\) | − 3.80584i | − 0.278310i | ||||||||
\(188\) | 1.54177i | 0.112445i | ||||||||
\(189\) | 2.74104i | 0.199381i | ||||||||
\(190\) | − 8.57233i | − 0.621902i | ||||||||
\(191\) | −3.87741 | −0.280559 | −0.140280 | − | 0.990112i | \(-0.544800\pi\) | ||||
−0.140280 | + | 0.990112i | \(0.544800\pi\) | |||||||
\(192\) | −0.648655 | −0.0468127 | ||||||||
\(193\) | − 1.25394i | − 0.0902608i | −0.998981 | − | 0.0451304i | \(-0.985630\pi\) | ||||
0.998981 | − | 0.0451304i | \(-0.0143703\pi\) | |||||||
\(194\) | −5.14261 | −0.369218 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.85527 | 0.275376 | ||||||||
\(197\) | − 15.2820i | − 1.08879i | −0.838828 | − | 0.544397i | \(-0.816758\pi\) | ||||
0.838828 | − | 0.544397i | \(-0.183242\pi\) | |||||||
\(198\) | −4.78347 | −0.339946 | ||||||||
\(199\) | 13.2296 | 0.937822 | 0.468911 | − | 0.883246i | \(-0.344647\pi\) | ||||
0.468911 | + | 0.883246i | \(0.344647\pi\) | |||||||
\(200\) | 2.63726i | 0.186483i | ||||||||
\(201\) | 0.490352i | 0.0345867i | ||||||||
\(202\) | 4.27007i | 0.300441i | ||||||||
\(203\) | − 7.11035i | − 0.499049i | ||||||||
\(204\) | 0.0797951 | 0.00558678 | ||||||||
\(205\) | 0.267949 | 0.0187144 | ||||||||
\(206\) | − 8.29242i | − 0.577760i | ||||||||
\(207\) | −21.1937 | −1.47307 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.12979 | −0.424007 | ||||||||
\(210\) | 0.684231i | 0.0472164i | ||||||||
\(211\) | −4.81042 | −0.331163 | −0.165582 | − | 0.986196i | \(-0.552950\pi\) | ||||
−0.165582 | + | 0.986196i | \(0.552950\pi\) | |||||||
\(212\) | −0.234418 | −0.0160999 | ||||||||
\(213\) | − 0.736014i | − 0.0504309i | ||||||||
\(214\) | 6.64172i | 0.454018i | ||||||||
\(215\) | 3.55889i | 0.242714i | ||||||||
\(216\) | 1.49763i | 0.101901i | ||||||||
\(217\) | −7.06698 | −0.479738 | ||||||||
\(218\) | 20.6088 | 1.39580 | ||||||||
\(219\) | − 0.958188i | − 0.0647484i | ||||||||
\(220\) | −0.252957 | −0.0170543 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0.00360034 | 0.000241639 0 | ||||||||
\(223\) | 14.7132i | 0.985271i | 0.870236 | + | 0.492635i | \(0.163966\pi\) | ||||
−0.870236 | + | 0.492635i | \(0.836034\pi\) | |||||||
\(224\) | 6.42612 | 0.429363 | ||||||||
\(225\) | 2.99102 | 0.199401 | ||||||||
\(226\) | 12.0299i | 0.800214i | ||||||||
\(227\) | 14.9028i | 0.989134i | 0.869140 | + | 0.494567i | \(0.164673\pi\) | ||||
−0.869140 | + | 0.494567i | \(0.835327\pi\) | |||||||
\(228\) | − 0.128520i | − 0.00851147i | ||||||||
\(229\) | 19.3074i | 1.27587i | 0.770092 | + | 0.637933i | \(0.220210\pi\) | ||||
−0.770092 | + | 0.637933i | \(0.779790\pi\) | |||||||
\(230\) | −10.5969 | −0.698737 | ||||||||
\(231\) | 0.489272 | 0.0321917 | ||||||||
\(232\) | − 3.88492i | − 0.255057i | ||||||||
\(233\) | 21.1937 | 1.38845 | 0.694224 | − | 0.719759i | \(-0.255748\pi\) | ||||
0.694224 | + | 0.719759i | \(0.255748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.51793 | −0.425183 | ||||||||
\(236\) | 2.06338i | 0.134315i | ||||||||
\(237\) | 0.832564 | 0.0540808 | ||||||||
\(238\) | 25.6901 | 1.66524 | ||||||||
\(239\) | − 14.8971i | − 0.963612i | −0.876278 | − | 0.481806i | \(-0.839981\pi\) | ||||
0.876278 | − | 0.481806i | \(-0.160019\pi\) | |||||||
\(240\) | 0.418689i | 0.0270263i | ||||||||
\(241\) | − 9.39168i | − 0.604971i | −0.953154 | − | 0.302486i | \(-0.902184\pi\) | ||||
0.953154 | − | 0.302486i | \(-0.0978164\pi\) | |||||||
\(242\) | − 14.7403i | − 0.947544i | ||||||||
\(243\) | 2.54905 | 0.163522 | ||||||||
\(244\) | −1.49905 | −0.0959671 | ||||||||
\(245\) | 16.2984i | 1.04126i | ||||||||
\(246\) | 0.0379833 | 0.00242173 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.86122 | −0.245188 | ||||||||
\(249\) | − 0.0687659i | − 0.00435786i | ||||||||
\(250\) | 1.49551 | 0.0945842 | ||||||||
\(251\) | −11.3163 | −0.714281 | −0.357140 | − | 0.934051i | \(-0.616248\pi\) | ||||
−0.357140 | + | 0.934051i | \(0.616248\pi\) | |||||||
\(252\) | − 3.41501i | − 0.215125i | ||||||||
\(253\) | 7.57748i | 0.476392i | ||||||||
\(254\) | 1.05680i | 0.0663098i | ||||||||
\(255\) | 0.337339i | 0.0211250i | ||||||||
\(256\) | 5.60076 | 0.350047 | ||||||||
\(257\) | 26.5319 | 1.65502 | 0.827508 | − | 0.561453i | \(-0.189758\pi\) | ||||
0.827508 | + | 0.561453i | \(0.189758\pi\) | |||||||
\(258\) | 0.504492i | 0.0314083i | ||||||||
\(259\) | 0.122593 | 0.00761758 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.40602 | −0.272726 | ||||||||
\(262\) | − 9.37017i | − 0.578891i | ||||||||
\(263\) | −14.1408 | −0.871957 | −0.435979 | − | 0.899957i | \(-0.643598\pi\) | ||||
−0.435979 | + | 0.899957i | \(0.643598\pi\) | |||||||
\(264\) | 0.267326 | 0.0164528 | ||||||||
\(265\) | − 0.991015i | − 0.0608776i | ||||||||
\(266\) | − 41.3772i | − 2.53700i | ||||||||
\(267\) | − 1.28025i | − 0.0783502i | ||||||||
\(268\) | − 1.22368i | − 0.0747479i | ||||||||
\(269\) | 24.7745 | 1.51053 | 0.755264 | − | 0.655421i | \(-0.227509\pi\) | ||||
0.755264 | + | 0.655421i | \(0.227509\pi\) | |||||||
\(270\) | 0.849260 | 0.0516843 | ||||||||
\(271\) | − 18.7171i | − 1.13698i | −0.822689 | − | 0.568492i | \(-0.807527\pi\) | ||||
0.822689 | − | 0.568492i | \(-0.192473\pi\) | |||||||
\(272\) | 15.7201 | 0.953170 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −24.3854 | −1.47318 | ||||||||
\(275\) | − 1.06939i | − 0.0644866i | ||||||||
\(276\) | −0.158873 | −0.00956305 | ||||||||
\(277\) | 22.6647 | 1.36179 | 0.680893 | − | 0.732382i | \(-0.261592\pi\) | ||||
0.680893 | + | 0.732382i | \(0.261592\pi\) | |||||||
\(278\) | 10.2073i | 0.612191i | ||||||||
\(279\) | 4.37915i | 0.262173i | ||||||||
\(280\) | 12.7296i | 0.760742i | ||||||||
\(281\) | 27.8384i | 1.66070i | 0.557241 | + | 0.830351i | \(0.311860\pi\) | ||||
−0.557241 | + | 0.830351i | \(0.688140\pi\) | |||||||
\(282\) | −0.923953 | −0.0550206 | ||||||||
\(283\) | −7.92007 | −0.470799 | −0.235400 | − | 0.971899i | \(-0.575640\pi\) | ||||
−0.235400 | + | 0.971899i | \(0.575640\pi\) | |||||||
\(284\) | 1.83673i | 0.108990i | ||||||||
\(285\) | 0.543327 | 0.0321839 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.29335 | 0.0763439 | ||||||||
\(288\) | − 3.98203i | − 0.234643i | ||||||||
\(289\) | −4.33431 | −0.254959 | ||||||||
\(290\) | −2.20301 | −0.129365 | ||||||||
\(291\) | − 0.325946i | − 0.0191073i | ||||||||
\(292\) | 2.39117i | 0.139932i | ||||||||
\(293\) | 0.272971i | 0.0159471i | 0.999968 | + | 0.00797356i | \(0.00253809\pi\) | ||||
−0.999968 | + | 0.00797356i | \(0.997462\pi\) | |||||||
\(294\) | 2.31038i | 0.134744i | ||||||||
\(295\) | −8.72307 | −0.507877 | ||||||||
\(296\) | 0.0669819 | 0.00389324 | ||||||||
\(297\) | − 0.607278i | − 0.0352379i | ||||||||
\(298\) | −12.6214 | −0.731139 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.0224214 | 0.00129450 | ||||||||
\(301\) | 17.1782i | 0.990134i | ||||||||
\(302\) | 2.04909 | 0.117912 | ||||||||
\(303\) | −0.270644 | −0.0155481 | ||||||||
\(304\) | − 25.3192i | − 1.45216i | ||||||||
\(305\) | − 6.33734i | − 0.362875i | ||||||||
\(306\) | − 15.9192i | − 0.910041i | ||||||||
\(307\) | − 6.85224i | − 0.391078i | −0.980696 | − | 0.195539i | \(-0.937354\pi\) | ||||
0.980696 | − | 0.195539i | \(-0.0626456\pi\) | |||||||
\(308\) | −1.22098 | −0.0695719 | ||||||||
\(309\) | 0.525586 | 0.0298995 | ||||||||
\(310\) | 2.18958i | 0.124360i | ||||||||
\(311\) | −10.6447 | −0.603605 | −0.301803 | − | 0.953370i | \(-0.597588\pi\) | ||||
−0.301803 | + | 0.953370i | \(0.597588\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.8236 | 1.00745 | 0.503724 | − | 0.863865i | \(-0.331963\pi\) | ||||
0.503724 | + | 0.863865i | \(0.331963\pi\) | |||||||
\(314\) | − 17.9012i | − 1.01023i | ||||||||
\(315\) | 14.4371 | 0.813441 | ||||||||
\(316\) | −2.07767 | −0.116878 | ||||||||
\(317\) | 8.17161i | 0.458963i | 0.973313 | + | 0.229482i | \(0.0737031\pi\) | ||||
−0.973313 | + | 0.229482i | \(0.926297\pi\) | |||||||
\(318\) | − 0.140482i | − 0.00787784i | ||||||||
\(319\) | 1.57530i | 0.0882000i | ||||||||
\(320\) | 6.84325i | 0.382549i | ||||||||
\(321\) | −0.420962 | −0.0234958 | ||||||||
\(322\) | −51.1494 | −2.85044 | ||||||||
\(323\) | − 20.3997i | − 1.13507i | ||||||||
\(324\) | −2.10978 | −0.117210 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 33.7556 | 1.86955 | ||||||||
\(327\) | 1.30621i | 0.0722338i | ||||||||
\(328\) | 0.706653 | 0.0390184 | ||||||||
\(329\) | −31.4610 | −1.73450 | ||||||||
\(330\) | − 0.151592i | − 0.00834486i | ||||||||
\(331\) | 24.9395i | 1.37080i | 0.728167 | + | 0.685400i | \(0.240373\pi\) | ||||
−0.728167 | + | 0.685400i | \(0.759627\pi\) | |||||||
\(332\) | 0.171606i | 0.00941809i | ||||||||
\(333\) | − 0.0759666i | − 0.00416294i | ||||||||
\(334\) | −12.2587 | −0.670765 | ||||||||
\(335\) | 5.17316 | 0.282640 | ||||||||
\(336\) | 2.02095i | 0.110252i | ||||||||
\(337\) | 19.6057 | 1.06799 | 0.533996 | − | 0.845487i | \(-0.320690\pi\) | ||||
0.533996 | + | 0.845487i | \(0.320690\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.762471 | −0.0414117 | ||||||||
\(340\) | − 0.841831i | − 0.0456547i | ||||||||
\(341\) | 1.56569 | 0.0847871 | ||||||||
\(342\) | −25.6400 | −1.38645 | ||||||||
\(343\) | 44.8817i | 2.42339i | ||||||||
\(344\) | 9.38573i | 0.506045i | ||||||||
\(345\) | − 0.671646i | − 0.0361602i | ||||||||
\(346\) | − 13.7104i | − 0.737076i | ||||||||
\(347\) | 17.0810 | 0.916955 | 0.458478 | − | 0.888706i | \(-0.348395\pi\) | ||||
0.458478 | + | 0.888706i | \(0.348395\pi\) | |||||||
\(348\) | −0.0330286 | −0.00177052 | ||||||||
\(349\) | 28.3719i | 1.51871i | 0.650674 | + | 0.759357i | \(0.274486\pi\) | ||||
−0.650674 | + | 0.759357i | \(0.725514\pi\) | |||||||
\(350\) | 7.21857 | 0.385849 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.42371 | −0.0758840 | ||||||||
\(353\) | 21.2520i | 1.13113i | 0.824704 | + | 0.565564i | \(0.191342\pi\) | ||||
−0.824704 | + | 0.565564i | \(0.808658\pi\) | |||||||
\(354\) | −1.23654 | −0.0657215 | ||||||||
\(355\) | −7.76488 | −0.412117 | ||||||||
\(356\) | 3.19488i | 0.169328i | ||||||||
\(357\) | 1.62828i | 0.0861776i | ||||||||
\(358\) | − 15.0104i | − 0.793325i | ||||||||
\(359\) | − 32.6519i | − 1.72330i | −0.507502 | − | 0.861650i | \(-0.669431\pi\) | ||||
0.507502 | − | 0.861650i | \(-0.330569\pi\) | |||||||
\(360\) | 7.88809 | 0.415739 | ||||||||
\(361\) | −13.8564 | −0.729285 | ||||||||
\(362\) | 25.4593i | 1.33811i | ||||||||
\(363\) | 0.934265 | 0.0490362 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.1088 | −0.529118 | ||||||||
\(366\) | − 0.898353i | − 0.0469577i | ||||||||
\(367\) | −5.91837 | −0.308936 | −0.154468 | − | 0.987998i | \(-0.549366\pi\) | ||||
−0.154468 | + | 0.987998i | \(0.549366\pi\) | |||||||
\(368\) | −31.2989 | −1.63157 | ||||||||
\(369\) | − 0.801440i | − 0.0417213i | ||||||||
\(370\) | − 0.0379833i | − 0.00197466i | ||||||||
\(371\) | − 4.78347i | − 0.248345i | ||||||||
\(372\) | 0.0328271i | 0.00170201i | ||||||||
\(373\) | −13.3185 | −0.689607 | −0.344803 | − | 0.938675i | \(-0.612054\pi\) | ||||
−0.344803 | + | 0.938675i | \(0.612054\pi\) | |||||||
\(374\) | −5.69166 | −0.294309 | ||||||||
\(375\) | 0.0947876i | 0.00489481i | ||||||||
\(376\) | −17.1895 | −0.886480 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 4.09924 | 0.210842 | ||||||||
\(379\) | 25.4186i | 1.30566i | 0.757503 | + | 0.652832i | \(0.226419\pi\) | ||||
−0.757503 | + | 0.652832i | \(0.773581\pi\) | |||||||
\(380\) | −1.35588 | −0.0695550 | ||||||||
\(381\) | −0.0669819 | −0.00343159 | ||||||||
\(382\) | 5.79869i | 0.296687i | ||||||||
\(383\) | − 10.8268i | − 0.553226i | −0.960981 | − | 0.276613i | \(-0.910788\pi\) | ||||
0.960981 | − | 0.276613i | \(-0.0892119\pi\) | |||||||
\(384\) | 1.22246i | 0.0623832i | ||||||||
\(385\) | − 5.16177i | − 0.263068i | ||||||||
\(386\) | −1.87528 | −0.0954493 | ||||||||
\(387\) | 10.6447 | 0.541100 | ||||||||
\(388\) | 0.813402i | 0.0412942i | ||||||||
\(389\) | 23.0370 | 1.16802 | 0.584011 | − | 0.811746i | \(-0.301482\pi\) | ||||
0.584011 | + | 0.811746i | \(0.301482\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.2176 | −1.27531 | ||||||||
\(392\) | 42.9831i | 2.17097i | ||||||||
\(393\) | 0.593896 | 0.0299581 | ||||||||
\(394\) | −22.8543 | −1.15138 | ||||||||
\(395\) | − 8.78347i | − 0.441944i | ||||||||
\(396\) | 0.756597i | 0.0380205i | ||||||||
\(397\) | − 21.0864i | − 1.05830i | −0.848529 | − | 0.529149i | \(-0.822511\pi\) | ||||
0.848529 | − | 0.529149i | \(-0.177489\pi\) | |||||||
\(398\) | − 19.7850i | − 0.991731i | ||||||||
\(399\) | 2.62255 | 0.131292 | ||||||||
\(400\) | 4.41713 | 0.220857 | ||||||||
\(401\) | 19.7769i | 0.987611i | 0.869572 | + | 0.493805i | \(0.164395\pi\) | ||||
−0.869572 | + | 0.493805i | \(0.835605\pi\) | |||||||
\(402\) | 0.733324 | 0.0365749 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.675394 | 0.0336021 | ||||||||
\(405\) | − 8.91922i | − 0.443200i | ||||||||
\(406\) | −10.6336 | −0.527736 | ||||||||
\(407\) | −0.0271606 | −0.00134630 | ||||||||
\(408\) | 0.889650i | 0.0440443i | ||||||||
\(409\) | − 31.8809i | − 1.57641i | −0.615414 | − | 0.788204i | \(-0.711011\pi\) | ||||
0.615414 | − | 0.788204i | \(-0.288989\pi\) | |||||||
\(410\) | − 0.400720i | − 0.0197902i | ||||||||
\(411\) | − 1.54559i | − 0.0762382i | ||||||||
\(412\) | −1.31160 | −0.0646181 | ||||||||
\(413\) | −42.1048 | −2.07184 | ||||||||
\(414\) | 31.6954i | 1.55774i | ||||||||
\(415\) | −0.725474 | −0.0356121 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.646952 | −0.0316814 | ||||||||
\(418\) | 9.16715i | 0.448380i | ||||||||
\(419\) | 30.7296 | 1.50124 | 0.750621 | − | 0.660733i | \(-0.229755\pi\) | ||||
0.750621 | + | 0.660733i | \(0.229755\pi\) | |||||||
\(420\) | 0.108224 | 0.00528080 | ||||||||
\(421\) | 17.9820i | 0.876391i | 0.898880 | + | 0.438195i | \(0.144382\pi\) | ||||
−0.898880 | + | 0.438195i | \(0.855618\pi\) | |||||||
\(422\) | 7.19403i | 0.350200i | ||||||||
\(423\) | 19.4952i | 0.947890i | ||||||||
\(424\) | − 2.61357i | − 0.126926i | ||||||||
\(425\) | 3.55889 | 0.172631 | ||||||||
\(426\) | −1.10071 | −0.0533298 | ||||||||
\(427\) | − 30.5893i | − 1.48032i | ||||||||
\(428\) | 1.05051 | 0.0507785 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.32235 | 0.256666 | ||||||||
\(431\) | 4.89949i | 0.236000i | 0.993014 | + | 0.118000i | \(0.0376483\pi\) | ||||
−0.993014 | + | 0.118000i | \(0.962352\pi\) | |||||||
\(432\) | 2.50837 | 0.120684 | ||||||||
\(433\) | 19.2394 | 0.924588 | 0.462294 | − | 0.886727i | \(-0.347026\pi\) | ||||
0.462294 | + | 0.886727i | \(0.347026\pi\) | |||||||
\(434\) | 10.5687i | 0.507315i | ||||||||
\(435\) | − 0.139630i | − 0.00669476i | ||||||||
\(436\) | − 3.25967i | − 0.156110i | ||||||||
\(437\) | 40.6162i | 1.94294i | ||||||||
\(438\) | −1.43298 | −0.0684703 | ||||||||
\(439\) | 8.55974 | 0.408534 | 0.204267 | − | 0.978915i | \(-0.434519\pi\) | ||||
0.204267 | + | 0.978915i | \(0.434519\pi\) | |||||||
\(440\) | − 2.82026i | − 0.134451i | ||||||||
\(441\) | 48.7487 | 2.32137 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.9652 | −1.80378 | −0.901891 | − | 0.431965i | \(-0.857821\pi\) | ||||
−0.901891 | + | 0.431965i | \(0.857821\pi\) | |||||||
\(444\) | 0 0.000569463i | 0 2.70255e-5i | ||||||||
\(445\) | −13.5065 | −0.640271 | ||||||||
\(446\) | 22.0037 | 1.04191 | ||||||||
\(447\) | − 0.799965i | − 0.0378370i | ||||||||
\(448\) | 33.0313i | 1.56058i | ||||||||
\(449\) | 26.7062i | 1.26035i | 0.776455 | + | 0.630173i | \(0.217016\pi\) | ||||
−0.776455 | + | 0.630173i | \(0.782984\pi\) | |||||||
\(450\) | − 4.47309i | − 0.210863i | ||||||||
\(451\) | −0.286542 | −0.0134927 | ||||||||
\(452\) | 1.90275 | 0.0894979 | ||||||||
\(453\) | 0.129875i | 0.00610205i | ||||||||
\(454\) | 22.2873 | 1.04599 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.43290 | 0.0671016 | ||||||||
\(457\) | − 4.27127i | − 0.199801i | −0.994997 | − | 0.0999007i | \(-0.968147\pi\) | ||||
0.994997 | − | 0.0999007i | \(-0.0318525\pi\) | |||||||
\(458\) | 28.8743 | 1.34921 | ||||||||
\(459\) | 2.02100 | 0.0943322 | ||||||||
\(460\) | 1.67610i | 0.0781485i | ||||||||
\(461\) | 20.6423i | 0.961407i | 0.876883 | + | 0.480704i | \(0.159619\pi\) | ||||
−0.876883 | + | 0.480704i | \(0.840381\pi\) | |||||||
\(462\) | − 0.731710i | − 0.0340422i | ||||||||
\(463\) | 32.1040i | 1.49200i | 0.665947 | + | 0.745999i | \(0.268028\pi\) | ||||
−0.665947 | + | 0.745999i | \(0.731972\pi\) | |||||||
\(464\) | −6.50682 | −0.302071 | ||||||||
\(465\) | −0.138779 | −0.00643571 | ||||||||
\(466\) | − 31.6954i | − 1.46826i | ||||||||
\(467\) | −23.3774 | −1.08178 | −0.540888 | − | 0.841095i | \(-0.681912\pi\) | ||||
−0.540888 | + | 0.841095i | \(0.681912\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.9700 | 1.15301 | ||||||||
\(470\) | 9.74761i | 0.449624i | ||||||||
\(471\) | 1.13461 | 0.0522800 | ||||||||
\(472\) | −23.0050 | −1.05889 | ||||||||
\(473\) | − 3.80584i | − 0.174993i | ||||||||
\(474\) | − 1.24511i | − 0.0571896i | ||||||||
\(475\) | − 5.73205i | − 0.263005i | ||||||||
\(476\) | − 4.06338i | − 0.186245i | ||||||||
\(477\) | −2.96414 | −0.135719 | ||||||||
\(478\) | −22.2787 | −1.01900 | ||||||||
\(479\) | 5.17534i | 0.236467i | 0.992986 | + | 0.118234i | \(0.0377232\pi\) | ||||
−0.992986 | + | 0.118234i | \(0.962277\pi\) | |||||||
\(480\) | 0.126194 | 0.00575992 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −14.0453 | −0.639747 | ||||||||
\(483\) | − 3.24193i | − 0.147513i | ||||||||
\(484\) | −2.33147 | −0.105976 | ||||||||
\(485\) | −3.43870 | −0.156143 | ||||||||
\(486\) | − 3.81213i | − 0.172922i | ||||||||
\(487\) | − 30.7729i | − 1.39445i | −0.716850 | − | 0.697227i | \(-0.754417\pi\) | ||||
0.716850 | − | 0.697227i | \(-0.245583\pi\) | |||||||
\(488\) | − 16.7132i | − 0.756572i | ||||||||
\(489\) | 2.13948i | 0.0967508i | ||||||||
\(490\) | 24.3743 | 1.10112 | ||||||||
\(491\) | −35.7983 | −1.61556 | −0.807778 | − | 0.589487i | \(-0.799330\pi\) | ||||
−0.807778 | + | 0.589487i | \(0.799330\pi\) | |||||||
\(492\) | − 0.00600778i | 0 0.000270852i | ||||||||
\(493\) | −5.24255 | −0.236113 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.19856 | −0.143765 | ||||||||
\(496\) | 6.46713i | 0.290383i | ||||||||
\(497\) | −37.4798 | −1.68120 | ||||||||
\(498\) | −0.102840 | −0.00460837 | ||||||||
\(499\) | 28.8971i | 1.29361i | 0.762655 | + | 0.646805i | \(0.223895\pi\) | ||||
−0.762655 | + | 0.646805i | \(0.776105\pi\) | |||||||
\(500\) | − 0.236543i | − 0.0105785i | ||||||||
\(501\) | − 0.776974i | − 0.0347126i | ||||||||
\(502\) | 16.9237i | 0.755340i | ||||||||
\(503\) | −7.86321 | −0.350603 | −0.175302 | − | 0.984515i | \(-0.556090\pi\) | ||||
−0.175302 | + | 0.984515i | \(0.556090\pi\) | |||||||
\(504\) | 38.0746 | 1.69598 | ||||||||
\(505\) | 2.85527i | 0.127058i | ||||||||
\(506\) | 11.3322 | 0.503777 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.167154 | 0.00741625 | ||||||||
\(509\) | − 28.0113i | − 1.24158i | −0.783977 | − | 0.620790i | \(-0.786812\pi\) | ||||
0.783977 | − | 0.620790i | \(-0.213188\pi\) | |||||||
\(510\) | 0.504492 | 0.0223393 | ||||||||
\(511\) | −48.7935 | −2.15850 | ||||||||
\(512\) | 17.4176i | 0.769757i | ||||||||
\(513\) | − 3.25508i | − 0.143715i | ||||||||
\(514\) | − 39.6787i | − 1.75015i | ||||||||
\(515\) | − 5.54488i | − 0.244337i | ||||||||
\(516\) | 0.0797951 | 0.00351278 | ||||||||
\(517\) | 6.97020 | 0.306549 | ||||||||
\(518\) | − 0.183339i | − 0.00805546i | ||||||||
\(519\) | 0.868986 | 0.0381443 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.5609 | −1.64557 | −0.822786 | − | 0.568351i | \(-0.807581\pi\) | ||||
−0.822786 | + | 0.568351i | \(0.807581\pi\) | |||||||
\(522\) | 6.58924i | 0.288403i | ||||||||
\(523\) | −45.3106 | −1.98129 | −0.990647 | − | 0.136450i | \(-0.956431\pi\) | ||||
−0.990647 | + | 0.136450i | \(0.956431\pi\) | |||||||
\(524\) | −1.48207 | −0.0647446 | ||||||||
\(525\) | 0.457524i | 0.0199680i | ||||||||
\(526\) | 21.1476i | 0.922080i | ||||||||
\(527\) | 5.21058i | 0.226976i | ||||||||
\(528\) | − 0.447742i | − 0.0194855i | ||||||||
\(529\) | 27.2086 | 1.18298 | ||||||||
\(530\) | −1.48207 | −0.0643770 | ||||||||
\(531\) | 26.0908i | 1.13225i | ||||||||
\(532\) | −6.54460 | −0.283744 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −1.91463 | −0.0828540 | ||||||||
\(535\) | 4.44111i | 0.192006i | ||||||||
\(536\) | 13.6430 | 0.589287 | ||||||||
\(537\) | 0.951383 | 0.0410552 | ||||||||
\(538\) | − 37.0504i | − 1.59736i | ||||||||
\(539\) | − 17.4293i | − 0.750733i | ||||||||
\(540\) | − 0.134327i | − 0.00578050i | ||||||||
\(541\) | − 19.7445i | − 0.848882i | −0.905456 | − | 0.424441i | \(-0.860471\pi\) | ||||
0.905456 | − | 0.424441i | \(-0.139529\pi\) | |||||||
\(542\) | −27.9916 | −1.20234 | ||||||||
\(543\) | −1.61365 | −0.0692483 | ||||||||
\(544\) | − 4.73806i | − 0.203143i | ||||||||
\(545\) | 13.7804 | 0.590289 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8312 | −0.505867 | −0.252934 | − | 0.967484i | \(-0.581395\pi\) | ||||
−0.252934 | + | 0.967484i | \(0.581395\pi\) | |||||||
\(548\) | 3.85702i | 0.164764i | ||||||||
\(549\) | −18.9551 | −0.808983 | ||||||||
\(550\) | −1.59928 | −0.0681935 | ||||||||
\(551\) | 8.44381i | 0.359718i | ||||||||
\(552\) | − 1.77131i | − 0.0753919i | ||||||||
\(553\) | − 42.3964i | − 1.80288i | ||||||||
\(554\) | − 33.8952i | − 1.44007i | ||||||||
\(555\) | 0.00240744 | 0.000102190 0 | ||||||||
\(556\) | 1.61447 | 0.0684689 | ||||||||
\(557\) | 4.04621i | 0.171443i | 0.996319 | + | 0.0857217i | \(0.0273196\pi\) | ||||
−0.996319 | + | 0.0857217i | \(0.972680\pi\) | |||||||
\(558\) | 6.54905 | 0.277244 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 21.3208 | 0.900968 | ||||||||
\(561\) | − 0.360746i | − 0.0152307i | ||||||||
\(562\) | 41.6326 | 1.75617 | ||||||||
\(563\) | −3.89926 | −0.164334 | −0.0821671 | − | 0.996619i | \(-0.526184\pi\) | ||||
−0.0821671 | + | 0.996619i | \(0.526184\pi\) | |||||||
\(564\) | 0.146141i | 0.00615364i | ||||||||
\(565\) | 8.04399i | 0.338413i | ||||||||
\(566\) | 11.8445i | 0.497863i | ||||||||
\(567\) | − 43.0516i | − 1.80800i | ||||||||
\(568\) | −20.4780 | −0.859239 | ||||||||
\(569\) | 17.3356 | 0.726744 | 0.363372 | − | 0.931644i | \(-0.381625\pi\) | ||||
0.363372 | + | 0.931644i | \(0.381625\pi\) | |||||||
\(570\) | − 0.812550i | − 0.0340340i | ||||||||
\(571\) | −29.5118 | −1.23503 | −0.617515 | − | 0.786559i | \(-0.711860\pi\) | ||||
−0.617515 | + | 0.786559i | \(0.711860\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.367530 | −0.0153538 | ||||||||
\(574\) | − 1.93421i | − 0.0807324i | ||||||||
\(575\) | −7.08580 | −0.295498 | ||||||||
\(576\) | 20.4683 | 0.852845 | ||||||||
\(577\) | − 28.3684i | − 1.18099i | −0.807041 | − | 0.590496i | \(-0.798932\pi\) | ||||
0.807041 | − | 0.590496i | \(-0.201068\pi\) | |||||||
\(578\) | 6.48199i | 0.269615i | ||||||||
\(579\) | − 0.118858i | − 0.00493958i | ||||||||
\(580\) | 0.348448i | 0.0144685i | ||||||||
\(581\) | −3.50174 | −0.145277 | ||||||||
\(582\) | −0.487455 | −0.0202057 | ||||||||
\(583\) | 1.05978i | 0.0438917i | ||||||||
\(584\) | −26.6595 | −1.10318 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.408230 | 0.0168638 | ||||||||
\(587\) | − 34.3877i | − 1.41933i | −0.704538 | − | 0.709667i | \(-0.748846\pi\) | ||||
0.704538 | − | 0.709667i | \(-0.251154\pi\) | |||||||
\(588\) | 0.365432 | 0.0150701 | ||||||||
\(589\) | 8.39230 | 0.345799 | ||||||||
\(590\) | 13.0454i | 0.537071i | ||||||||
\(591\) | − 1.44854i | − 0.0595850i | ||||||||
\(592\) | − 0.112187i | − 0.00461088i | ||||||||
\(593\) | 5.47612i | 0.224877i | 0.993659 | + | 0.112439i | \(0.0358662\pi\) | ||||
−0.993659 | + | 0.112439i | \(0.964134\pi\) | |||||||
\(594\) | −0.908189 | −0.0372635 | ||||||||
\(595\) | 17.1782 | 0.704237 | ||||||||
\(596\) | 1.99632i | 0.0817724i | ||||||||
\(597\) | 1.25400 | 0.0513229 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 38.6039 | 1.57731 | 0.788657 | − | 0.614833i | \(-0.210777\pi\) | ||||
0.788657 | + | 0.614833i | \(0.210777\pi\) | |||||||
\(600\) | 0.249980i | 0.0102054i | ||||||||
\(601\) | 6.57896 | 0.268361 | 0.134181 | − | 0.990957i | \(-0.457160\pi\) | ||||
0.134181 | + | 0.990957i | \(0.457160\pi\) | |||||||
\(602\) | 25.6901 | 1.04705 | ||||||||
\(603\) | − 15.4730i | − 0.630109i | ||||||||
\(604\) | − 0.324103i | − 0.0131876i | ||||||||
\(605\) | − 9.85641i | − 0.400720i | ||||||||
\(606\) | 0.404750i | 0.0164418i | ||||||||
\(607\) | −16.7664 | −0.680525 | −0.340263 | − | 0.940330i | \(-0.610516\pi\) | ||||
−0.340263 | + | 0.940330i | \(0.610516\pi\) | |||||||
\(608\) | −7.63126 | −0.309488 | ||||||||
\(609\) | − 0.673973i | − 0.0273108i | ||||||||
\(610\) | −9.47754 | −0.383734 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2.51793 | −0.101781 | ||||||||
\(613\) | − 28.7789i | − 1.16237i | −0.813772 | − | 0.581184i | \(-0.802590\pi\) | ||||
0.813772 | − | 0.581184i | \(-0.197410\pi\) | |||||||
\(614\) | −10.2476 | −0.413558 | ||||||||
\(615\) | 0.0253983 | 0.00102416 | ||||||||
\(616\) | − 13.6129i | − 0.548481i | ||||||||
\(617\) | 37.3291i | 1.50281i | 0.659840 | + | 0.751406i | \(0.270624\pi\) | ||||
−0.659840 | + | 0.751406i | \(0.729376\pi\) | |||||||
\(618\) | − 0.786018i | − 0.0316183i | ||||||||
\(619\) | 12.7535i | 0.512606i | 0.966597 | + | 0.256303i | \(0.0825045\pi\) | ||||
−0.966597 | + | 0.256303i | \(0.917496\pi\) | |||||||
\(620\) | 0.346323 | 0.0139087 | ||||||||
\(621\) | −4.02384 | −0.161471 | ||||||||
\(622\) | 15.9192i | 0.638303i | ||||||||
\(623\) | −65.1939 | −2.61194 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | − 26.6553i | − 1.06536i | ||||||||
\(627\) | −0.581028 | −0.0232040 | ||||||||
\(628\) | −2.83143 | −0.112986 | ||||||||
\(629\) | − 0.0903896i | − 0.00360407i | ||||||||
\(630\) | − 21.5909i | − 0.860201i | ||||||||
\(631\) | 28.7242i | 1.14349i | 0.820430 | + | 0.571746i | \(0.193734\pi\) | ||||
−0.820430 | + | 0.571746i | \(0.806266\pi\) | |||||||
\(632\) | − 23.1643i | − 0.921427i | ||||||||
\(633\) | −0.455969 | −0.0181231 | ||||||||
\(634\) | 12.2207 | 0.485346 | ||||||||
\(635\) | 0.706653i | 0.0280427i | ||||||||
\(636\) | −0.0222199 | −0.000881077 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.35588 | 0.0932701 | ||||||||
\(639\) | 23.2249i | 0.918762i | ||||||||
\(640\) | 12.8968 | 0.509791 | ||||||||
\(641\) | 22.3970 | 0.884630 | 0.442315 | − | 0.896860i | \(-0.354157\pi\) | ||||
0.442315 | + | 0.896860i | \(0.354157\pi\) | |||||||
\(642\) | 0.629552i | 0.0248464i | ||||||||
\(643\) | 14.1642i | 0.558581i | 0.960207 | + | 0.279290i | \(0.0900992\pi\) | ||||
−0.960207 | + | 0.279290i | \(0.909901\pi\) | |||||||
\(644\) | 8.09025i | 0.318801i | ||||||||
\(645\) | 0.337339i | 0.0132827i | ||||||||
\(646\) | −30.5080 | −1.20032 | ||||||||
\(647\) | 23.6097 | 0.928193 | 0.464096 | − | 0.885785i | \(-0.346379\pi\) | ||||
0.464096 | + | 0.885785i | \(0.346379\pi\) | |||||||
\(648\) | − 23.5223i | − 0.924044i | ||||||||
\(649\) | 9.32835 | 0.366170 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.669862 | −0.0262540 | ||||||||
\(652\) | − 5.33910i | − 0.209095i | ||||||||
\(653\) | 33.2765 | 1.30221 | 0.651105 | − | 0.758987i | \(-0.274306\pi\) | ||||
0.651105 | + | 0.758987i | \(0.274306\pi\) | |||||||
\(654\) | 1.95345 | 0.0763861 | ||||||||
\(655\) | − 6.26554i | − 0.244815i | ||||||||
\(656\) | − 1.18357i | − 0.0462105i | ||||||||
\(657\) | 30.2356i | 1.17960i | ||||||||
\(658\) | 47.0502i | 1.83421i | ||||||||
\(659\) | 23.0908 | 0.899491 | 0.449745 | − | 0.893157i | \(-0.351515\pi\) | ||||
0.449745 | + | 0.893157i | \(0.351515\pi\) | |||||||
\(660\) | −0.0239772 | −0.000933310 0 | ||||||||
\(661\) | − 13.4365i | − 0.522620i | −0.965255 | − | 0.261310i | \(-0.915845\pi\) | ||||
0.965255 | − | 0.261310i | \(-0.0841545\pi\) | |||||||
\(662\) | 37.2972 | 1.44960 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.91326 | −0.0742491 | ||||||||
\(665\) | − 27.6677i | − 1.07291i | ||||||||
\(666\) | −0.113609 | −0.00440224 | ||||||||
\(667\) | 10.4380 | 0.404161 | ||||||||
\(668\) | 1.93895i | 0.0750200i | ||||||||
\(669\) | 1.39463i | 0.0539196i | ||||||||
\(670\) | − 7.73650i | − 0.298887i | ||||||||
\(671\) | 6.77708i | 0.261626i | ||||||||
\(672\) | 0.609116 | 0.0234972 | ||||||||
\(673\) | 1.94524 | 0.0749835 | 0.0374918 | − | 0.999297i | \(-0.488063\pi\) | ||||
0.0374918 | + | 0.999297i | \(0.488063\pi\) | |||||||
\(674\) | − 29.3205i | − 1.12938i | ||||||||
\(675\) | 0.567874 | 0.0218575 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.8683 | 0.955768 | 0.477884 | − | 0.878423i | \(-0.341404\pi\) | ||||
0.477884 | + | 0.878423i | \(0.341404\pi\) | |||||||
\(678\) | 1.14028i | 0.0437922i | ||||||||
\(679\) | −16.5981 | −0.636975 | ||||||||
\(680\) | 9.38573 | 0.359926 | ||||||||
\(681\) | 1.41260i | 0.0541310i | ||||||||
\(682\) | − 2.34151i | − 0.0896610i | ||||||||
\(683\) | − 14.6221i | − 0.559500i | −0.960073 | − | 0.279750i | \(-0.909748\pi\) | ||||
0.960073 | − | 0.279750i | \(-0.0902517\pi\) | |||||||
\(684\) | 4.05545i | 0.155064i | ||||||||
\(685\) | −16.3058 | −0.623013 | ||||||||
\(686\) | 67.1210 | 2.56269 | ||||||||
\(687\) | 1.83010i | 0.0698226i | ||||||||
\(688\) | 15.7201 | 0.599323 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.00445 | −0.0382388 | ||||||||
\(691\) | 3.52451i | 0.134079i | 0.997750 | + | 0.0670393i | \(0.0213553\pi\) | ||||
−0.997750 | + | 0.0670393i | \(0.978645\pi\) | |||||||
\(692\) | −2.16856 | −0.0824364 | ||||||||
\(693\) | −15.4389 | −0.586477 | ||||||||
\(694\) | − 25.5447i | − 0.969665i | ||||||||
\(695\) | 6.82528i | 0.258898i | ||||||||
\(696\) | − 0.368242i | − 0.0139582i | ||||||||
\(697\) | − 0.953601i | − 0.0361202i | ||||||||
\(698\) | 42.4304 | 1.60602 | ||||||||
\(699\) | 2.00890 | 0.0759837 | ||||||||
\(700\) | − 1.14176i | − 0.0431543i | ||||||||
\(701\) | 1.53457 | 0.0579599 | 0.0289800 | − | 0.999580i | \(-0.490774\pi\) | ||||
0.0289800 | + | 0.999580i | \(0.490774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.145584 | −0.00549081 | ||||||||
\(704\) | − 7.31810i | − 0.275811i | ||||||||
\(705\) | −0.617819 | −0.0232684 | ||||||||
\(706\) | 31.7825 | 1.19615 | ||||||||
\(707\) | 13.7819i | 0.518322i | ||||||||
\(708\) | 0.195583i | 0.00735046i | ||||||||
\(709\) | 14.0052i | 0.525978i | 0.964799 | + | 0.262989i | \(0.0847083\pi\) | ||||
−0.964799 | + | 0.262989i | \(0.915292\pi\) | |||||||
\(710\) | 11.6124i | 0.435807i | ||||||||
\(711\) | −26.2715 | −0.985258 | ||||||||
\(712\) | −35.6203 | −1.33493 | ||||||||
\(713\) | − 10.3743i | − 0.388522i | ||||||||
\(714\) | 2.43510 | 0.0911314 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.37418 | −0.0887274 | ||||||||
\(717\) | − 1.41206i | − 0.0527343i | ||||||||
\(718\) | −48.8312 | −1.82236 | ||||||||
\(719\) | −22.4761 | −0.838218 | −0.419109 | − | 0.907936i | \(-0.637657\pi\) | ||||
−0.419109 | + | 0.907936i | \(0.637657\pi\) | |||||||
\(720\) | − 13.2117i | − 0.492372i | ||||||||
\(721\) | − 26.7643i | − 0.996753i | ||||||||
\(722\) | 20.7224i | 0.771206i | ||||||||
\(723\) | − 0.890215i | − 0.0331074i | ||||||||
\(724\) | 4.02687 | 0.149658 | ||||||||
\(725\) | −1.47309 | −0.0547091 | ||||||||
\(726\) | − 1.39720i | − 0.0518550i | ||||||||
\(727\) | 10.3421 | 0.383566 | 0.191783 | − | 0.981437i | \(-0.438573\pi\) | ||||
0.191783 | + | 0.981437i | \(0.438573\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5160 | −0.982075 | ||||||||
\(730\) | 15.1178i | 0.559534i | ||||||||
\(731\) | 12.6657 | 0.468458 | ||||||||
\(732\) | −0.142092 | −0.00525186 | ||||||||
\(733\) | − 27.3533i | − 1.01032i | −0.863026 | − | 0.505159i | \(-0.831434\pi\) | ||||
0.863026 | − | 0.505159i | \(-0.168566\pi\) | |||||||
\(734\) | 8.85096i | 0.326695i | ||||||||
\(735\) | 1.54488i | 0.0569839i | ||||||||
\(736\) | 9.43355i | 0.347725i | ||||||||
\(737\) | −5.53212 | −0.203778 | ||||||||
\(738\) | −1.19856 | −0.0441196 | ||||||||
\(739\) | − 13.4517i | − 0.494827i | −0.968910 | − | 0.247413i | \(-0.920419\pi\) | ||||
0.968910 | − | 0.247413i | \(-0.0795806\pi\) | |||||||
\(740\) | −0.00600778 | −0.000220851 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.15372 | −0.262621 | ||||||||
\(743\) | − 16.3926i | − 0.601388i | −0.953721 | − | 0.300694i | \(-0.902782\pi\) | ||||
0.953721 | − | 0.300694i | \(-0.0972182\pi\) | |||||||
\(744\) | −0.365996 | −0.0134181 | ||||||||
\(745\) | −8.43955 | −0.309201 | ||||||||
\(746\) | 19.9179i | 0.729248i | ||||||||
\(747\) | 2.16990i | 0.0793926i | ||||||||
\(748\) | 0.900245i | 0.0329162i | ||||||||
\(749\) | 21.4365i | 0.783274i | ||||||||
\(750\) | 0.141756 | 0.00517618 | ||||||||
\(751\) | 27.6655 | 1.00953 | 0.504764 | − | 0.863257i | \(-0.331579\pi\) | ||||
0.504764 | + | 0.863257i | \(0.331579\pi\) | |||||||
\(752\) | 28.7906i | 1.04988i | ||||||||
\(753\) | −1.07265 | −0.0390895 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.37017 | 0.0498654 | ||||||||
\(756\) | − 0.648373i | − 0.0235811i | ||||||||
\(757\) | 22.9978 | 0.835870 | 0.417935 | − | 0.908477i | \(-0.362754\pi\) | ||||
0.417935 | + | 0.908477i | \(0.362754\pi\) | |||||||
\(758\) | 38.0136 | 1.38072 | ||||||||
\(759\) | 0.718251i | 0.0260709i | ||||||||
\(760\) | − 15.1169i | − 0.548349i | ||||||||
\(761\) | 7.66442i | 0.277835i | 0.990304 | + | 0.138918i | \(0.0443623\pi\) | ||||
−0.990304 | + | 0.138918i | \(0.955638\pi\) | |||||||
\(762\) | 0.100172i | 0.00362885i | ||||||||
\(763\) | 66.5160 | 2.40804 | ||||||||
\(764\) | 0.917174 | 0.0331822 | ||||||||
\(765\) | − 10.6447i | − 0.384860i | ||||||||
\(766\) | −16.1916 | −0.585027 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.530882 | 0.0191566 | ||||||||
\(769\) | − 7.23095i | − 0.260755i | −0.991464 | − | 0.130377i | \(-0.958381\pi\) | ||||
0.991464 | − | 0.130377i | \(-0.0416189\pi\) | |||||||
\(770\) | −7.71947 | −0.278190 | ||||||||
\(771\) | 2.51490 | 0.0905718 | ||||||||
\(772\) | 0.296612i | 0.0106753i | ||||||||
\(773\) | − 33.5995i | − 1.20849i | −0.796798 | − | 0.604246i | \(-0.793475\pi\) | ||||
0.796798 | − | 0.604246i | \(-0.206525\pi\) | |||||||
\(774\) | − 15.9192i | − 0.572204i | ||||||||
\(775\) | 1.46410i | 0.0525921i | ||||||||
\(776\) | −9.06877 | −0.325550 | ||||||||
\(777\) | 0.0116203 | 0.000416877 0 | ||||||||
\(778\) | − 34.4520i | − 1.23516i | ||||||||
\(779\) | −1.53590 | −0.0550293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.30368 | 0.297129 | ||||||||
\(782\) | 37.7131i | 1.34862i | ||||||||
\(783\) | −0.836527 | −0.0298950 | ||||||||
\(784\) | 71.9921 | 2.57115 | ||||||||
\(785\) | − 11.9700i | − 0.427228i | ||||||||
\(786\) | − 0.888175i | − 0.0316802i | ||||||||
\(787\) | 2.97168i | 0.105929i | 0.998596 | + | 0.0529645i | \(0.0168670\pi\) | ||||
−0.998596 | + | 0.0529645i | \(0.983133\pi\) | |||||||
\(788\) | 3.61484i | 0.128773i | ||||||||
\(789\) | −1.34037 | −0.0477184 | ||||||||
\(790\) | −13.1357 | −0.467349 | ||||||||
\(791\) | 38.8270i | 1.38053i | ||||||||
\(792\) | −8.43544 | −0.299740 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −31.5349 | −1.11913 | ||||||||
\(795\) | − 0.0939360i | − 0.00333156i | ||||||||
\(796\) | −3.12937 | −0.110918 | ||||||||
\(797\) | 22.5751 | 0.799650 | 0.399825 | − | 0.916591i | \(-0.369071\pi\) | ||||
0.399825 | + | 0.916591i | \(0.369071\pi\) | |||||||
\(798\) | − 3.92205i | − 0.138839i | ||||||||
\(799\) | 23.1966i | 0.820636i | ||||||||
\(800\) | − 1.33133i | − 0.0470696i | ||||||||
\(801\) | 40.3983i | 1.42740i | ||||||||
\(802\) | 29.5765 | 1.04438 | ||||||||
\(803\) | 10.8102 | 0.381485 | ||||||||
\(804\) | − 0.115989i | − 0.00409063i | ||||||||
\(805\) | −34.2020 | −1.20546 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.34831 | 0.0826646 | ||||||||
\(808\) | 7.53009i | 0.264908i | ||||||||
\(809\) | 13.6584 | 0.480204 | 0.240102 | − | 0.970748i | \(-0.422819\pi\) | ||||
0.240102 | + | 0.970748i | \(0.422819\pi\) | |||||||
\(810\) | −13.3388 | −0.468676 | ||||||||
\(811\) | 14.1147i | 0.495636i | 0.968807 | + | 0.247818i | \(0.0797135\pi\) | ||||
−0.968807 | + | 0.247818i | \(0.920287\pi\) | |||||||
\(812\) | 1.68190i | 0.0590233i | ||||||||
\(813\) | − 1.77415i | − 0.0622222i | ||||||||
\(814\) | 0.0406189i | 0.00142369i | ||||||||
\(815\) | 22.5713 | 0.790640 | ||||||||
\(816\) | 1.49007 | 0.0521629 | ||||||||
\(817\) | − 20.3997i | − 0.713696i | ||||||||
\(818\) | −47.6781 | −1.66703 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.0633815 | −0.00221338 | ||||||||
\(821\) | 1.58562i | 0.0553383i | 0.999617 | + | 0.0276692i | \(0.00880850\pi\) | ||||
−0.999617 | + | 0.0276692i | \(0.991192\pi\) | |||||||
\(822\) | −2.31144 | −0.0806206 | ||||||||
\(823\) | −18.5648 | −0.647127 | −0.323563 | − | 0.946206i | \(-0.604881\pi\) | ||||
−0.323563 | + | 0.946206i | \(0.604881\pi\) | |||||||
\(824\) | − 14.6233i | − 0.509427i | ||||||||
\(825\) | − 0.101365i | − 0.00352907i | ||||||||
\(826\) | 62.9681i | 2.19094i | ||||||||
\(827\) | − 9.01023i | − 0.313316i | −0.987653 | − | 0.156658i | \(-0.949928\pi\) | ||||
0.987653 | − | 0.156658i | \(-0.0500721\pi\) | |||||||
\(828\) | 5.01324 | 0.174222 | ||||||||
\(829\) | −47.1177 | −1.63647 | −0.818233 | − | 0.574887i | \(-0.805046\pi\) | ||||
−0.818233 | + | 0.574887i | \(0.805046\pi\) | |||||||
\(830\) | 1.08495i | 0.0376592i | ||||||||
\(831\) | 2.14833 | 0.0745247 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 58.0041 | 2.00972 | ||||||||
\(834\) | 0.967522i | 0.0335025i | ||||||||
\(835\) | −8.19700 | −0.283669 | ||||||||
\(836\) | 1.44996 | 0.0501479 | ||||||||
\(837\) | 0.831425i | 0.0287383i | ||||||||
\(838\) | − 45.9564i | − 1.58754i | ||||||||
\(839\) | 53.4766i | 1.84622i | 0.384541 | + | 0.923108i | \(0.374360\pi\) | ||||
−0.384541 | + | 0.923108i | \(0.625640\pi\) | |||||||
\(840\) | 1.20661i | 0.0416321i | ||||||||
\(841\) | −26.8300 | −0.925173 | ||||||||
\(842\) | 26.8923 | 0.926769 | ||||||||
\(843\) | 2.63874i | 0.0908830i | ||||||||
\(844\) | 1.13787 | 0.0391672 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 29.1553 | 1.00238 | ||||||||
\(847\) | − 47.5753i | − 1.63471i | ||||||||
\(848\) | −4.37745 | −0.150322 | ||||||||
\(849\) | −0.750724 | −0.0257648 | ||||||||
\(850\) | − 5.32235i | − 0.182555i | ||||||||
\(851\) | 0.179967i | 0.00616919i | ||||||||
\(852\) | 0.174099i | 0.00596454i | ||||||||
\(853\) | − 27.7756i | − 0.951019i | −0.879711 | − | 0.475510i | \(-0.842264\pi\) | ||||
0.879711 | − | 0.475510i | \(-0.157736\pi\) | |||||||
\(854\) | −45.7465 | −1.56541 | ||||||||
\(855\) | −17.1447 | −0.586335 | ||||||||
\(856\) | 11.7124i | 0.400321i | ||||||||
\(857\) | −53.6917 | −1.83407 | −0.917037 | − | 0.398801i | \(-0.869426\pi\) | ||||
−0.917037 | + | 0.398801i | \(0.869426\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.08958 | 0.0712955 | 0.0356477 | − | 0.999364i | \(-0.488651\pi\) | ||||
0.0356477 | + | 0.999364i | \(0.488651\pi\) | |||||||
\(860\) | − 0.841831i | − 0.0287062i | ||||||||
\(861\) | 0.122593 | 0.00417797 | ||||||||
\(862\) | 7.32722 | 0.249566 | ||||||||
\(863\) | 1.75413i | 0.0597113i | 0.999554 | + | 0.0298557i | \(0.00950476\pi\) | ||||
−0.999554 | + | 0.0298557i | \(0.990495\pi\) | |||||||
\(864\) | − 0.756028i | − 0.0257206i | ||||||||
\(865\) | − 9.16772i | − 0.311712i | ||||||||
\(866\) | − 28.7727i | − 0.977737i | ||||||||
\(867\) | −0.410839 | −0.0139528 | ||||||||
\(868\) | 1.67165 | 0.0567394 | ||||||||
\(869\) | 9.39295i | 0.318634i | ||||||||
\(870\) | −0.208818 | −0.00707960 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 36.3426 | 1.23072 | ||||||||
\(873\) | 10.2852i | 0.348102i | ||||||||
\(874\) | 60.7418 | 2.05462 | ||||||||
\(875\) | 4.82684 | 0.163177 | ||||||||
\(876\) | 0.226653i | 0.00765789i | ||||||||
\(877\) | − 21.5672i | − 0.728272i | −0.931346 | − | 0.364136i | \(-0.881364\pi\) | ||||
0.931346 | − | 0.364136i | \(-0.118636\pi\) | |||||||
\(878\) | − 12.8012i | − 0.432018i | ||||||||
\(879\) | 0.0258742i | 0 0.000872716i | ||||||||
\(880\) | −4.72364 | −0.159234 | ||||||||
\(881\) | −25.0263 | −0.843158 | −0.421579 | − | 0.906792i | \(-0.638524\pi\) | ||||
−0.421579 | + | 0.906792i | \(0.638524\pi\) | |||||||
\(882\) | − 72.9040i | − 2.45481i | ||||||||
\(883\) | 48.7832 | 1.64169 | 0.820843 | − | 0.571154i | \(-0.193504\pi\) | ||||
0.820843 | + | 0.571154i | \(0.193504\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.826838 | −0.0277939 | ||||||||
\(886\) | 56.7772i | 1.90747i | ||||||||
\(887\) | −33.7933 | −1.13467 | −0.567334 | − | 0.823488i | \(-0.692025\pi\) | ||||
−0.567334 | + | 0.823488i | \(0.692025\pi\) | |||||||
\(888\) | 0.00634905 | 0.000213060 0 | ||||||||
\(889\) | 3.41090i | 0.114398i | ||||||||
\(890\) | 20.1991i | 0.677076i | ||||||||
\(891\) | 9.53812i | 0.319539i | ||||||||
\(892\) | − 3.48031i | − 0.116530i | ||||||||
\(893\) | 37.3611 | 1.25024 | ||||||||
\(894\) | −1.19635 | −0.0400121 | ||||||||
\(895\) | − 10.0370i | − 0.335500i | ||||||||
\(896\) | 62.2508 | 2.07965 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.9394 | 1.33279 | ||||||||
\(899\) | − 2.15675i | − 0.0719316i | ||||||||
\(900\) | −0.707504 | −0.0235835 | ||||||||
\(901\) | −3.52691 | −0.117499 | ||||||||
\(902\) | 0.428526i | 0.0142683i | ||||||||
\(903\) | 1.62828i | 0.0541857i | ||||||||
\(904\) | 21.2141i | 0.705571i | ||||||||
\(905\) | 17.0238i | 0.565892i | ||||||||
\(906\) | 0.194229 | 0.00645281 | ||||||||
\(907\) | 34.6270 | 1.14977 | 0.574885 | − | 0.818234i | \(-0.305047\pi\) | ||||
0.574885 | + | 0.818234i | \(0.305047\pi\) | |||||||
\(908\) | − 3.52516i | − 0.116986i | ||||||||
\(909\) | 8.54015 | 0.283259 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.1865 | 1.03326 | 0.516628 | − | 0.856210i | \(-0.327187\pi\) | ||||
0.516628 | + | 0.856210i | \(0.327187\pi\) | |||||||
\(912\) | − 2.39995i | − 0.0794703i | ||||||||
\(913\) | 0.775814 | 0.0256757 | ||||||||
\(914\) | −6.38771 | −0.211287 | ||||||||
\(915\) | − 0.600701i | − 0.0198586i | ||||||||
\(916\) | − 4.56702i | − 0.150899i | ||||||||
\(917\) | − 30.2428i | − 0.998704i | ||||||||
\(918\) | − 3.02242i | − 0.0997548i | ||||||||
\(919\) | −51.9220 | −1.71275 | −0.856374 | − | 0.516356i | \(-0.827288\pi\) | ||||
−0.856374 | + | 0.516356i | \(0.827288\pi\) | |||||||
\(920\) | −18.6871 | −0.616096 | ||||||||
\(921\) | − 0.649507i | − 0.0214020i | ||||||||
\(922\) | 30.8707 | 1.01667 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.115734 | −0.00380736 | ||||||||
\(925\) | − 0.0253983i | 0 0.000835090i | ||||||||
\(926\) | 48.0117 | 1.57776 | ||||||||
\(927\) | −16.5848 | −0.544717 | ||||||||
\(928\) | 1.96117i | 0.0643784i | ||||||||
\(929\) | − 20.4915i | − 0.672304i | −0.941808 | − | 0.336152i | \(-0.890874\pi\) | ||||
0.941808 | − | 0.336152i | \(-0.109126\pi\) | |||||||
\(930\) | 0.207545i | 0.00680565i | ||||||||
\(931\) | − 93.4231i | − 3.06182i | ||||||||
\(932\) | −5.01324 | −0.164214 | ||||||||
\(933\) | −1.00898 | −0.0330327 | ||||||||
\(934\) | 34.9610i | 1.14396i | ||||||||
\(935\) | −3.80584 | −0.124464 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −39.6806 | −1.29631 | −0.648154 | − | 0.761510i | \(-0.724459\pi\) | ||||
−0.648154 | + | 0.761510i | \(0.724459\pi\) | |||||||
\(938\) | − 37.3428i | − 1.21929i | ||||||||
\(939\) | 1.68945 | 0.0551333 | ||||||||
\(940\) | 1.54177 | 0.0502870 | ||||||||
\(941\) | 19.6189i | 0.639557i | 0.947492 | + | 0.319779i | \(0.103609\pi\) | ||||
−0.947492 | + | 0.319779i | \(0.896391\pi\) | |||||||
\(942\) | − 1.69682i | − 0.0552853i | ||||||||
\(943\) | 1.89864i | 0.0618281i | ||||||||
\(944\) | 38.5309i | 1.25408i | ||||||||
\(945\) | 2.74104 | 0.0891659 | ||||||||
\(946\) | −5.69166 | −0.185052 | ||||||||
\(947\) | 57.2124i | 1.85915i | 0.368631 | + | 0.929576i | \(0.379827\pi\) | ||||
−0.368631 | + | 0.929576i | \(0.620173\pi\) | |||||||
\(948\) | −0.196937 | −0.00639623 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.57233 | −0.278123 | ||||||||
\(951\) | 0.774567i | 0.0251170i | ||||||||
\(952\) | 45.3034 | 1.46829 | ||||||||
\(953\) | −27.4770 | −0.890066 | −0.445033 | − | 0.895514i | \(-0.646808\pi\) | ||||
−0.445033 | + | 0.895514i | \(0.646808\pi\) | |||||||
\(954\) | 4.43290i | 0.143520i | ||||||||
\(955\) | 3.87741i | 0.125470i | ||||||||
\(956\) | 3.52380i | 0.113968i | ||||||||
\(957\) | 0.149319i | 0.00482680i | ||||||||
\(958\) | 7.73976 | 0.250060 | ||||||||
\(959\) | −78.7055 | −2.54153 | ||||||||
\(960\) | 0.648655i | 0.0209353i | ||||||||
\(961\) | 28.8564 | 0.930852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13.2834 | 0.428053 | ||||||||
\(964\) | 2.22154i | 0.0715509i | ||||||||
\(965\) | −1.25394 | −0.0403659 | ||||||||
\(966\) | −4.84833 | −0.155992 | ||||||||
\(967\) | 10.3643i | 0.333293i | 0.986017 | + | 0.166647i | \(0.0532939\pi\) | ||||
−0.986017 | + | 0.166647i | \(0.946706\pi\) | |||||||
\(968\) | − 25.9939i | − 0.835477i | ||||||||
\(969\) | − 1.93364i | − 0.0621175i | ||||||||
\(970\) | 5.14261i | 0.165119i | ||||||||
\(971\) | 41.7515 | 1.33987 | 0.669935 | − | 0.742420i | \(-0.266322\pi\) | ||||
0.669935 | + | 0.742420i | \(0.266322\pi\) | |||||||
\(972\) | −0.602961 | −0.0193400 | ||||||||
\(973\) | 32.9445i | 1.05615i | ||||||||
\(974\) | −46.0212 | −1.47461 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −27.9929 | −0.896030 | ||||||||
\(977\) | 13.7938i | 0.441303i | 0.975353 | + | 0.220652i | \(0.0708184\pi\) | ||||
−0.975353 | + | 0.220652i | \(0.929182\pi\) | |||||||
\(978\) | 3.19961 | 0.102312 | ||||||||
\(979\) | 14.4437 | 0.461624 | ||||||||
\(980\) | − 3.85527i | − 0.123152i | ||||||||
\(981\) | − 41.2175i | − 1.31597i | ||||||||
\(982\) | 53.5367i | 1.70842i | ||||||||
\(983\) | 37.9997i | 1.21200i | 0.795463 | + | 0.606002i | \(0.207227\pi\) | ||||
−0.795463 | + | 0.606002i | \(0.792773\pi\) | |||||||
\(984\) | 0.0669819 | 0.00213530 | ||||||||
\(985\) | −15.2820 | −0.486924 | ||||||||
\(986\) | 7.84028i | 0.249685i | ||||||||
\(987\) | −2.98211 | −0.0949217 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.2176 | −0.801873 | ||||||||
\(990\) | 4.78347i | 0.152029i | ||||||||
\(991\) | −52.5530 | −1.66940 | −0.834700 | − | 0.550705i | \(-0.814359\pi\) | ||||
−0.834700 | + | 0.550705i | \(0.814359\pi\) | |||||||
\(992\) | 1.94920 | 0.0618873 | ||||||||
\(993\) | 2.36396i | 0.0750179i | ||||||||
\(994\) | 56.0513i | 1.77784i | ||||||||
\(995\) | − 13.2296i | − 0.419407i | ||||||||
\(996\) | 0.0162661i | 0 0.000515411i | ||||||||
\(997\) | 18.5899 | 0.588749 | 0.294375 | − | 0.955690i | \(-0.404889\pi\) | ||||
0.294375 | + | 0.955690i | \(0.404889\pi\) | |||||||
\(998\) | 43.2158 | 1.36797 | ||||||||
\(999\) | − 0.0144230i | 0 0.000456324i |
(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 | 845.2.c.g.506.2 | 8 | ||
13.2 | odd | 12 | 845.2.e.m.191.4 | 8 | |||
13.3 | even | 3 | 65.2.m.a.56.4 | yes | 8 | ||
13.4 | even | 6 | 65.2.m.a.36.4 | ✓ | 8 | ||
13.5 | odd | 4 | 845.2.a.m.1.1 | 4 | |||
13.6 | odd | 12 | 845.2.e.m.146.4 | 8 | |||
13.7 | odd | 12 | 845.2.e.n.146.1 | 8 | |||
13.8 | odd | 4 | 845.2.a.l.1.4 | 4 | |||
13.9 | even | 3 | 845.2.m.g.361.1 | 8 | |||
13.10 | even | 6 | 845.2.m.g.316.1 | 8 | |||
13.11 | odd | 12 | 845.2.e.n.191.1 | 8 | |||
13.12 | even | 2 | inner | 845.2.c.g.506.7 | 8 | ||
39.5 | even | 4 | 7605.2.a.cf.1.4 | 4 | |||
39.8 | even | 4 | 7605.2.a.cj.1.1 | 4 | |||
39.17 | odd | 6 | 585.2.bu.c.361.1 | 8 | |||
39.29 | odd | 6 | 585.2.bu.c.316.1 | 8 | |||
52.3 | odd | 6 | 1040.2.da.b.641.3 | 8 | |||
52.43 | odd | 6 | 1040.2.da.b.881.3 | 8 | |||
65.3 | odd | 12 | 325.2.m.b.199.4 | 8 | |||
65.4 | even | 6 | 325.2.n.d.101.1 | 8 | |||
65.17 | odd | 12 | 325.2.m.b.49.4 | 8 | |||
65.29 | even | 6 | 325.2.n.d.251.1 | 8 | |||
65.34 | odd | 4 | 4225.2.a.bl.1.1 | 4 | |||
65.42 | odd | 12 | 325.2.m.c.199.1 | 8 | |||
65.43 | odd | 12 | 325.2.m.c.49.1 | 8 | |||
65.44 | odd | 4 | 4225.2.a.bi.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.m.a.36.4 | ✓ | 8 | 13.4 | even | 6 | ||
65.2.m.a.56.4 | yes | 8 | 13.3 | even | 3 | ||
325.2.m.b.49.4 | 8 | 65.17 | odd | 12 | |||
325.2.m.b.199.4 | 8 | 65.3 | odd | 12 | |||
325.2.m.c.49.1 | 8 | 65.43 | odd | 12 | |||
325.2.m.c.199.1 | 8 | 65.42 | odd | 12 | |||
325.2.n.d.101.1 | 8 | 65.4 | even | 6 | |||
325.2.n.d.251.1 | 8 | 65.29 | even | 6 | |||
585.2.bu.c.316.1 | 8 | 39.29 | odd | 6 | |||
585.2.bu.c.361.1 | 8 | 39.17 | odd | 6 | |||
845.2.a.l.1.4 | 4 | 13.8 | odd | 4 | |||
845.2.a.m.1.1 | 4 | 13.5 | odd | 4 | |||
845.2.c.g.506.2 | 8 | 1.1 | even | 1 | trivial | ||
845.2.c.g.506.7 | 8 | 13.12 | even | 2 | inner | ||
845.2.e.m.146.4 | 8 | 13.6 | odd | 12 | |||
845.2.e.m.191.4 | 8 | 13.2 | odd | 12 | |||
845.2.e.n.146.1 | 8 | 13.7 | odd | 12 | |||
845.2.e.n.191.1 | 8 | 13.11 | odd | 12 | |||
845.2.m.g.316.1 | 8 | 13.10 | even | 6 | |||
845.2.m.g.361.1 | 8 | 13.9 | even | 3 | |||
1040.2.da.b.641.3 | 8 | 52.3 | odd | 6 | |||
1040.2.da.b.881.3 | 8 | 52.43 | odd | 6 | |||
4225.2.a.bi.1.4 | 4 | 65.44 | odd | 4 | |||
4225.2.a.bl.1.1 | 4 | 65.34 | odd | 4 | |||
7605.2.a.cf.1.4 | 4 | 39.5 | even | 4 | |||
7605.2.a.cj.1.1 | 4 | 39.8 | even | 4 |