Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(14.4129975648\) |
Analytic rank: | \(2\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.381966 | −0.270091 | −0.135045 | − | 0.990839i | \(-0.543118\pi\) | ||||
−0.135045 | + | 0.990839i | \(0.543118\pi\) | |||||||
\(3\) | −0.381966 | −0.220528 | −0.110264 | − | 0.993902i | \(-0.535170\pi\) | ||||
−0.110264 | + | 0.993902i | \(0.535170\pi\) | |||||||
\(4\) | −1.85410 | −0.927051 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.145898 | 0.0595626 | ||||||||
\(7\) | −4.23607 | −1.60108 | −0.800542 | − | 0.599277i | \(-0.795455\pi\) | ||||
−0.800542 | + | 0.599277i | \(0.795455\pi\) | |||||||
\(8\) | 1.47214 | 0.520479 | ||||||||
\(9\) | −2.85410 | −0.951367 | ||||||||
\(10\) | 0.381966 | 0.120788 | ||||||||
\(11\) | −2.38197 | −0.718190 | −0.359095 | − | 0.933301i | \(-0.616915\pi\) | ||||
−0.359095 | + | 0.933301i | \(0.616915\pi\) | |||||||
\(12\) | 0.708204 | 0.204441 | ||||||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 1.61803 | 0.432438 | ||||||||
\(15\) | 0.381966 | 0.0986232 | ||||||||
\(16\) | 3.14590 | 0.786475 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 1.09017 | 0.256956 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 1.85410 | 0.414590 | ||||||||
\(21\) | 1.61803 | 0.353084 | ||||||||
\(22\) | 0.909830 | 0.193976 | ||||||||
\(23\) | 0.618034 | 0.128869 | 0.0644345 | − | 0.997922i | \(-0.479476\pi\) | ||||
0.0644345 | + | 0.997922i | \(0.479476\pi\) | |||||||
\(24\) | −0.562306 | −0.114780 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.90983 | 0.374548 | ||||||||
\(27\) | 2.23607 | 0.430331 | ||||||||
\(28\) | 7.85410 | 1.48429 | ||||||||
\(29\) | −4.85410 | −0.901384 | −0.450692 | − | 0.892679i | \(-0.648823\pi\) | ||||
−0.450692 | + | 0.892679i | \(0.648823\pi\) | |||||||
\(30\) | −0.145898 | −0.0266372 | ||||||||
\(31\) | −10.8541 | −1.94945 | −0.974727 | − | 0.223399i | \(-0.928285\pi\) | ||||
−0.974727 | + | 0.223399i | \(0.928285\pi\) | |||||||
\(32\) | −4.14590 | −0.732898 | ||||||||
\(33\) | 0.909830 | 0.158381 | ||||||||
\(34\) | 2.29180 | 0.393040 | ||||||||
\(35\) | 4.23607 | 0.716026 | ||||||||
\(36\) | 5.29180 | 0.881966 | ||||||||
\(37\) | −4.85410 | −0.798009 | −0.399005 | − | 0.916949i | \(-0.630644\pi\) | ||||
−0.399005 | + | 0.916949i | \(0.630644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.90983 | 0.305818 | ||||||||
\(40\) | −1.47214 | −0.232765 | ||||||||
\(41\) | 11.1803 | 1.74608 | 0.873038 | − | 0.487652i | \(-0.162147\pi\) | ||||
0.873038 | + | 0.487652i | \(0.162147\pi\) | |||||||
\(42\) | −0.618034 | −0.0953647 | ||||||||
\(43\) | 3.85410 | 0.587745 | 0.293873 | − | 0.955845i | \(-0.405056\pi\) | ||||
0.293873 | + | 0.955845i | \(0.405056\pi\) | |||||||
\(44\) | 4.41641 | 0.665799 | ||||||||
\(45\) | 2.85410 | 0.425464 | ||||||||
\(46\) | −0.236068 | −0.0348063 | ||||||||
\(47\) | −5.76393 | −0.840756 | −0.420378 | − | 0.907349i | \(-0.638103\pi\) | ||||
−0.420378 | + | 0.907349i | \(0.638103\pi\) | |||||||
\(48\) | −1.20163 | −0.173440 | ||||||||
\(49\) | 10.9443 | 1.56347 | ||||||||
\(50\) | −0.381966 | −0.0540182 | ||||||||
\(51\) | 2.29180 | 0.320916 | ||||||||
\(52\) | 9.27051 | 1.28559 | ||||||||
\(53\) | −3.38197 | −0.464549 | −0.232274 | − | 0.972650i | \(-0.574617\pi\) | ||||
−0.232274 | + | 0.972650i | \(0.574617\pi\) | |||||||
\(54\) | −0.854102 | −0.116229 | ||||||||
\(55\) | 2.38197 | 0.321184 | ||||||||
\(56\) | −6.23607 | −0.833330 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.85410 | 0.243456 | ||||||||
\(59\) | 11.0902 | 1.44382 | 0.721909 | − | 0.691988i | \(-0.243265\pi\) | ||||
0.721909 | + | 0.691988i | \(0.243265\pi\) | |||||||
\(60\) | −0.708204 | −0.0914287 | ||||||||
\(61\) | −3.00000 | −0.384111 | −0.192055 | − | 0.981384i | \(-0.561515\pi\) | ||||
−0.192055 | + | 0.981384i | \(0.561515\pi\) | |||||||
\(62\) | 4.14590 | 0.526530 | ||||||||
\(63\) | 12.0902 | 1.52322 | ||||||||
\(64\) | −4.70820 | −0.588525 | ||||||||
\(65\) | 5.00000 | 0.620174 | ||||||||
\(66\) | −0.347524 | −0.0427773 | ||||||||
\(67\) | −8.70820 | −1.06388 | −0.531938 | − | 0.846783i | \(-0.678536\pi\) | ||||
−0.531938 | + | 0.846783i | \(0.678536\pi\) | |||||||
\(68\) | 11.1246 | 1.34906 | ||||||||
\(69\) | −0.236068 | −0.0284192 | ||||||||
\(70\) | −1.61803 | −0.193392 | ||||||||
\(71\) | −8.23607 | −0.977441 | −0.488721 | − | 0.872440i | \(-0.662536\pi\) | ||||
−0.488721 | + | 0.872440i | \(0.662536\pi\) | |||||||
\(72\) | −4.20163 | −0.495166 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | 1.85410 | 0.215535 | ||||||||
\(75\) | −0.381966 | −0.0441056 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.0902 | 1.14988 | ||||||||
\(78\) | −0.729490 | −0.0825985 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | −3.14590 | −0.351722 | ||||||||
\(81\) | 7.70820 | 0.856467 | ||||||||
\(82\) | −4.27051 | −0.471599 | ||||||||
\(83\) | −4.47214 | −0.490881 | −0.245440 | − | 0.969412i | \(-0.578933\pi\) | ||||
−0.245440 | + | 0.969412i | \(0.578933\pi\) | |||||||
\(84\) | −3.00000 | −0.327327 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | −1.47214 | −0.158745 | ||||||||
\(87\) | 1.85410 | 0.198781 | ||||||||
\(88\) | −3.50658 | −0.373802 | ||||||||
\(89\) | −6.70820 | −0.711068 | −0.355534 | − | 0.934663i | \(-0.615701\pi\) | ||||
−0.355534 | + | 0.934663i | \(0.615701\pi\) | |||||||
\(90\) | −1.09017 | −0.114914 | ||||||||
\(91\) | 21.1803 | 2.22030 | ||||||||
\(92\) | −1.14590 | −0.119468 | ||||||||
\(93\) | 4.14590 | 0.429910 | ||||||||
\(94\) | 2.20163 | 0.227080 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.58359 | 0.161625 | ||||||||
\(97\) | 5.09017 | 0.516828 | 0.258414 | − | 0.966034i | \(-0.416800\pi\) | ||||
0.258414 | + | 0.966034i | \(0.416800\pi\) | |||||||
\(98\) | −4.18034 | −0.422278 | ||||||||
\(99\) | 6.79837 | 0.683262 | ||||||||
\(100\) | −1.85410 | −0.185410 | ||||||||
\(101\) | 5.94427 | 0.591477 | 0.295739 | − | 0.955269i | \(-0.404434\pi\) | ||||
0.295739 | + | 0.955269i | \(0.404434\pi\) | |||||||
\(102\) | −0.875388 | −0.0866763 | ||||||||
\(103\) | −1.67376 | −0.164921 | −0.0824603 | − | 0.996594i | \(-0.526278\pi\) | ||||
−0.0824603 | + | 0.996594i | \(0.526278\pi\) | |||||||
\(104\) | −7.36068 | −0.721774 | ||||||||
\(105\) | −1.61803 | −0.157904 | ||||||||
\(106\) | 1.29180 | 0.125470 | ||||||||
\(107\) | −3.00000 | −0.290021 | −0.145010 | − | 0.989430i | \(-0.546322\pi\) | ||||
−0.145010 | + | 0.989430i | \(0.546322\pi\) | |||||||
\(108\) | −4.14590 | −0.398939 | ||||||||
\(109\) | −1.76393 | −0.168954 | −0.0844770 | − | 0.996425i | \(-0.526922\pi\) | ||||
−0.0844770 | + | 0.996425i | \(0.526922\pi\) | |||||||
\(110\) | −0.909830 | −0.0867489 | ||||||||
\(111\) | 1.85410 | 0.175984 | ||||||||
\(112\) | −13.3262 | −1.25921 | ||||||||
\(113\) | 14.9443 | 1.40584 | 0.702919 | − | 0.711269i | \(-0.251879\pi\) | ||||
0.702919 | + | 0.711269i | \(0.251879\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.618034 | −0.0576320 | ||||||||
\(116\) | 9.00000 | 0.835629 | ||||||||
\(117\) | 14.2705 | 1.31931 | ||||||||
\(118\) | −4.23607 | −0.389962 | ||||||||
\(119\) | 25.4164 | 2.32992 | ||||||||
\(120\) | 0.562306 | 0.0513313 | ||||||||
\(121\) | −5.32624 | −0.484203 | ||||||||
\(122\) | 1.14590 | 0.103745 | ||||||||
\(123\) | −4.27051 | −0.385059 | ||||||||
\(124\) | 20.1246 | 1.80724 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −4.61803 | −0.411407 | ||||||||
\(127\) | −10.7082 | −0.950199 | −0.475100 | − | 0.879932i | \(-0.657588\pi\) | ||||
−0.475100 | + | 0.879932i | \(0.657588\pi\) | |||||||
\(128\) | 10.0902 | 0.891853 | ||||||||
\(129\) | −1.47214 | −0.129614 | ||||||||
\(130\) | −1.90983 | −0.167503 | ||||||||
\(131\) | −7.85410 | −0.686216 | −0.343108 | − | 0.939296i | \(-0.611480\pi\) | ||||
−0.343108 | + | 0.939296i | \(0.611480\pi\) | |||||||
\(132\) | −1.68692 | −0.146827 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.32624 | 0.287343 | ||||||||
\(135\) | −2.23607 | −0.192450 | ||||||||
\(136\) | −8.83282 | −0.757408 | ||||||||
\(137\) | 1.18034 | 0.100843 | 0.0504216 | − | 0.998728i | \(-0.483943\pi\) | ||||
0.0504216 | + | 0.998728i | \(0.483943\pi\) | |||||||
\(138\) | 0.0901699 | 0.00767578 | ||||||||
\(139\) | 8.14590 | 0.690926 | 0.345463 | − | 0.938432i | \(-0.387722\pi\) | ||||
0.345463 | + | 0.938432i | \(0.387722\pi\) | |||||||
\(140\) | −7.85410 | −0.663793 | ||||||||
\(141\) | 2.20163 | 0.185410 | ||||||||
\(142\) | 3.14590 | 0.263998 | ||||||||
\(143\) | 11.9098 | 0.995950 | ||||||||
\(144\) | −8.97871 | −0.748226 | ||||||||
\(145\) | 4.85410 | 0.403111 | ||||||||
\(146\) | 0.381966 | 0.0316117 | ||||||||
\(147\) | −4.18034 | −0.344789 | ||||||||
\(148\) | 9.00000 | 0.739795 | ||||||||
\(149\) | −7.61803 | −0.624094 | −0.312047 | − | 0.950067i | \(-0.601015\pi\) | ||||
−0.312047 | + | 0.950067i | \(0.601015\pi\) | |||||||
\(150\) | 0.145898 | 0.0119125 | ||||||||
\(151\) | 7.38197 | 0.600736 | 0.300368 | − | 0.953823i | \(-0.402891\pi\) | ||||
0.300368 | + | 0.953823i | \(0.402891\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.1246 | 1.38444 | ||||||||
\(154\) | −3.85410 | −0.310572 | ||||||||
\(155\) | 10.8541 | 0.871822 | ||||||||
\(156\) | −3.54102 | −0.283508 | ||||||||
\(157\) | −24.0344 | −1.91816 | −0.959079 | − | 0.283140i | \(-0.908624\pi\) | ||||
−0.959079 | + | 0.283140i | \(0.908624\pi\) | |||||||
\(158\) | 3.05573 | 0.243101 | ||||||||
\(159\) | 1.29180 | 0.102446 | ||||||||
\(160\) | 4.14590 | 0.327762 | ||||||||
\(161\) | −2.61803 | −0.206330 | ||||||||
\(162\) | −2.94427 | −0.231324 | ||||||||
\(163\) | 8.52786 | 0.667954 | 0.333977 | − | 0.942581i | \(-0.391609\pi\) | ||||
0.333977 | + | 0.942581i | \(0.391609\pi\) | |||||||
\(164\) | −20.7295 | −1.61870 | ||||||||
\(165\) | −0.909830 | −0.0708302 | ||||||||
\(166\) | 1.70820 | 0.132582 | ||||||||
\(167\) | −8.23607 | −0.637326 | −0.318663 | − | 0.947868i | \(-0.603234\pi\) | ||||
−0.318663 | + | 0.947868i | \(0.603234\pi\) | |||||||
\(168\) | 2.38197 | 0.183773 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | −2.29180 | −0.175773 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.14590 | −0.544870 | ||||||||
\(173\) | −13.8885 | −1.05593 | −0.527963 | − | 0.849267i | \(-0.677044\pi\) | ||||
−0.527963 | + | 0.849267i | \(0.677044\pi\) | |||||||
\(174\) | −0.708204 | −0.0536888 | ||||||||
\(175\) | −4.23607 | −0.320217 | ||||||||
\(176\) | −7.49342 | −0.564838 | ||||||||
\(177\) | −4.23607 | −0.318402 | ||||||||
\(178\) | 2.56231 | 0.192053 | ||||||||
\(179\) | −10.5279 | −0.786890 | −0.393445 | − | 0.919348i | \(-0.628717\pi\) | ||||
−0.393445 | + | 0.919348i | \(0.628717\pi\) | |||||||
\(180\) | −5.29180 | −0.394427 | ||||||||
\(181\) | −8.29180 | −0.616324 | −0.308162 | − | 0.951334i | \(-0.599714\pi\) | ||||
−0.308162 | + | 0.951334i | \(0.599714\pi\) | |||||||
\(182\) | −8.09017 | −0.599683 | ||||||||
\(183\) | 1.14590 | 0.0847072 | ||||||||
\(184\) | 0.909830 | 0.0670736 | ||||||||
\(185\) | 4.85410 | 0.356881 | ||||||||
\(186\) | −1.58359 | −0.116115 | ||||||||
\(187\) | 14.2918 | 1.04512 | ||||||||
\(188\) | 10.6869 | 0.779424 | ||||||||
\(189\) | −9.47214 | −0.688997 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.05573 | 0.438177 | 0.219089 | − | 0.975705i | \(-0.429692\pi\) | ||||
0.219089 | + | 0.975705i | \(0.429692\pi\) | |||||||
\(192\) | 1.79837 | 0.129786 | ||||||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | −1.94427 | −0.139591 | ||||||||
\(195\) | −1.90983 | −0.136766 | ||||||||
\(196\) | −20.2918 | −1.44941 | ||||||||
\(197\) | 16.5279 | 1.17756 | 0.588781 | − | 0.808293i | \(-0.299608\pi\) | ||||
0.588781 | + | 0.808293i | \(0.299608\pi\) | |||||||
\(198\) | −2.59675 | −0.184543 | ||||||||
\(199\) | 13.4164 | 0.951064 | 0.475532 | − | 0.879698i | \(-0.342256\pi\) | ||||
0.475532 | + | 0.879698i | \(0.342256\pi\) | |||||||
\(200\) | 1.47214 | 0.104096 | ||||||||
\(201\) | 3.32624 | 0.234615 | ||||||||
\(202\) | −2.27051 | −0.159753 | ||||||||
\(203\) | 20.5623 | 1.44319 | ||||||||
\(204\) | −4.24922 | −0.297505 | ||||||||
\(205\) | −11.1803 | −0.780869 | ||||||||
\(206\) | 0.639320 | 0.0445436 | ||||||||
\(207\) | −1.76393 | −0.122602 | ||||||||
\(208\) | −15.7295 | −1.09064 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0.618034 | 0.0426484 | ||||||||
\(211\) | 6.90983 | 0.475692 | 0.237846 | − | 0.971303i | \(-0.423559\pi\) | ||||
0.237846 | + | 0.971303i | \(0.423559\pi\) | |||||||
\(212\) | 6.27051 | 0.430660 | ||||||||
\(213\) | 3.14590 | 0.215553 | ||||||||
\(214\) | 1.14590 | 0.0783320 | ||||||||
\(215\) | −3.85410 | −0.262848 | ||||||||
\(216\) | 3.29180 | 0.223978 | ||||||||
\(217\) | 45.9787 | 3.12124 | ||||||||
\(218\) | 0.673762 | 0.0456329 | ||||||||
\(219\) | 0.381966 | 0.0258109 | ||||||||
\(220\) | −4.41641 | −0.297754 | ||||||||
\(221\) | 30.0000 | 2.01802 | ||||||||
\(222\) | −0.708204 | −0.0475315 | ||||||||
\(223\) | −10.2361 | −0.685458 | −0.342729 | − | 0.939434i | \(-0.611351\pi\) | ||||
−0.342729 | + | 0.939434i | \(0.611351\pi\) | |||||||
\(224\) | 17.5623 | 1.17343 | ||||||||
\(225\) | −2.85410 | −0.190273 | ||||||||
\(226\) | −5.70820 | −0.379704 | ||||||||
\(227\) | −17.6525 | −1.17164 | −0.585818 | − | 0.810443i | \(-0.699227\pi\) | ||||
−0.585818 | + | 0.810443i | \(0.699227\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.6180 | −1.42856 | −0.714280 | − | 0.699860i | \(-0.753246\pi\) | ||||
−0.714280 | + | 0.699860i | \(0.753246\pi\) | |||||||
\(230\) | 0.236068 | 0.0155659 | ||||||||
\(231\) | −3.85410 | −0.253581 | ||||||||
\(232\) | −7.14590 | −0.469151 | ||||||||
\(233\) | −6.81966 | −0.446771 | −0.223385 | − | 0.974730i | \(-0.571711\pi\) | ||||
−0.223385 | + | 0.974730i | \(0.571711\pi\) | |||||||
\(234\) | −5.45085 | −0.356333 | ||||||||
\(235\) | 5.76393 | 0.375997 | ||||||||
\(236\) | −20.5623 | −1.33849 | ||||||||
\(237\) | 3.05573 | 0.198491 | ||||||||
\(238\) | −9.70820 | −0.629289 | ||||||||
\(239\) | 23.5623 | 1.52412 | 0.762059 | − | 0.647507i | \(-0.224188\pi\) | ||||
0.762059 | + | 0.647507i | \(0.224188\pi\) | |||||||
\(240\) | 1.20163 | 0.0775646 | ||||||||
\(241\) | −18.1246 | −1.16751 | −0.583754 | − | 0.811930i | \(-0.698417\pi\) | ||||
−0.583754 | + | 0.811930i | \(0.698417\pi\) | |||||||
\(242\) | 2.03444 | 0.130779 | ||||||||
\(243\) | −9.65248 | −0.619207 | ||||||||
\(244\) | 5.56231 | 0.356090 | ||||||||
\(245\) | −10.9443 | −0.699204 | ||||||||
\(246\) | 1.63119 | 0.104001 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −15.9787 | −1.01465 | ||||||||
\(249\) | 1.70820 | 0.108253 | ||||||||
\(250\) | 0.381966 | 0.0241577 | ||||||||
\(251\) | 15.1803 | 0.958175 | 0.479087 | − | 0.877767i | \(-0.340968\pi\) | ||||
0.479087 | + | 0.877767i | \(0.340968\pi\) | |||||||
\(252\) | −22.4164 | −1.41210 | ||||||||
\(253\) | −1.47214 | −0.0925524 | ||||||||
\(254\) | 4.09017 | 0.256640 | ||||||||
\(255\) | −2.29180 | −0.143518 | ||||||||
\(256\) | 5.56231 | 0.347644 | ||||||||
\(257\) | −13.5279 | −0.843845 | −0.421922 | − | 0.906632i | \(-0.638645\pi\) | ||||
−0.421922 | + | 0.906632i | \(0.638645\pi\) | |||||||
\(258\) | 0.562306 | 0.0350076 | ||||||||
\(259\) | 20.5623 | 1.27768 | ||||||||
\(260\) | −9.27051 | −0.574933 | ||||||||
\(261\) | 13.8541 | 0.857547 | ||||||||
\(262\) | 3.00000 | 0.185341 | ||||||||
\(263\) | −19.8885 | −1.22638 | −0.613190 | − | 0.789935i | \(-0.710114\pi\) | ||||
−0.613190 | + | 0.789935i | \(0.710114\pi\) | |||||||
\(264\) | 1.33939 | 0.0824340 | ||||||||
\(265\) | 3.38197 | 0.207753 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.56231 | 0.156811 | ||||||||
\(268\) | 16.1459 | 0.986268 | ||||||||
\(269\) | −1.67376 | −0.102051 | −0.0510255 | − | 0.998697i | \(-0.516249\pi\) | ||||
−0.0510255 | + | 0.998697i | \(0.516249\pi\) | |||||||
\(270\) | 0.854102 | 0.0519790 | ||||||||
\(271\) | 16.3820 | 0.995134 | 0.497567 | − | 0.867426i | \(-0.334227\pi\) | ||||
0.497567 | + | 0.867426i | \(0.334227\pi\) | |||||||
\(272\) | −18.8754 | −1.14449 | ||||||||
\(273\) | −8.09017 | −0.489639 | ||||||||
\(274\) | −0.450850 | −0.0272368 | ||||||||
\(275\) | −2.38197 | −0.143638 | ||||||||
\(276\) | 0.437694 | 0.0263461 | ||||||||
\(277\) | −25.4164 | −1.52712 | −0.763562 | − | 0.645735i | \(-0.776551\pi\) | ||||
−0.763562 | + | 0.645735i | \(0.776551\pi\) | |||||||
\(278\) | −3.11146 | −0.186613 | ||||||||
\(279\) | 30.9787 | 1.85465 | ||||||||
\(280\) | 6.23607 | 0.372676 | ||||||||
\(281\) | −27.5066 | −1.64090 | −0.820452 | − | 0.571715i | \(-0.806278\pi\) | ||||
−0.820452 | + | 0.571715i | \(0.806278\pi\) | |||||||
\(282\) | −0.840946 | −0.0500776 | ||||||||
\(283\) | 4.61803 | 0.274514 | 0.137257 | − | 0.990535i | \(-0.456171\pi\) | ||||
0.137257 | + | 0.990535i | \(0.456171\pi\) | |||||||
\(284\) | 15.2705 | 0.906138 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.54915 | −0.268997 | ||||||||
\(287\) | −47.3607 | −2.79561 | ||||||||
\(288\) | 11.8328 | 0.697255 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | −1.85410 | −0.108877 | ||||||||
\(291\) | −1.94427 | −0.113975 | ||||||||
\(292\) | 1.85410 | 0.108503 | ||||||||
\(293\) | −22.0344 | −1.28727 | −0.643633 | − | 0.765334i | \(-0.722574\pi\) | ||||
−0.643633 | + | 0.765334i | \(0.722574\pi\) | |||||||
\(294\) | 1.59675 | 0.0931242 | ||||||||
\(295\) | −11.0902 | −0.645695 | ||||||||
\(296\) | −7.14590 | −0.415347 | ||||||||
\(297\) | −5.32624 | −0.309060 | ||||||||
\(298\) | 2.90983 | 0.168562 | ||||||||
\(299\) | −3.09017 | −0.178709 | ||||||||
\(300\) | 0.708204 | 0.0408882 | ||||||||
\(301\) | −16.3262 | −0.941029 | ||||||||
\(302\) | −2.81966 | −0.162253 | ||||||||
\(303\) | −2.27051 | −0.130437 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | 0.171780 | ||||||||
\(306\) | −6.54102 | −0.373925 | ||||||||
\(307\) | 12.2705 | 0.700315 | 0.350157 | − | 0.936691i | \(-0.386128\pi\) | ||||
0.350157 | + | 0.936691i | \(0.386128\pi\) | |||||||
\(308\) | −18.7082 | −1.06600 | ||||||||
\(309\) | 0.639320 | 0.0363697 | ||||||||
\(310\) | −4.14590 | −0.235471 | ||||||||
\(311\) | −7.05573 | −0.400094 | −0.200047 | − | 0.979786i | \(-0.564109\pi\) | ||||
−0.200047 | + | 0.979786i | \(0.564109\pi\) | |||||||
\(312\) | 2.81153 | 0.159172 | ||||||||
\(313\) | −9.79837 | −0.553837 | −0.276918 | − | 0.960893i | \(-0.589313\pi\) | ||||
−0.276918 | + | 0.960893i | \(0.589313\pi\) | |||||||
\(314\) | 9.18034 | 0.518077 | ||||||||
\(315\) | −12.0902 | −0.681204 | ||||||||
\(316\) | 14.8328 | 0.834411 | ||||||||
\(317\) | 13.2361 | 0.743412 | 0.371706 | − | 0.928351i | \(-0.378773\pi\) | ||||
0.371706 | + | 0.928351i | \(0.378773\pi\) | |||||||
\(318\) | −0.493422 | −0.0276697 | ||||||||
\(319\) | 11.5623 | 0.647365 | ||||||||
\(320\) | 4.70820 | 0.263197 | ||||||||
\(321\) | 1.14590 | 0.0639578 | ||||||||
\(322\) | 1.00000 | 0.0557278 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −14.2918 | −0.793989 | ||||||||
\(325\) | −5.00000 | −0.277350 | ||||||||
\(326\) | −3.25735 | −0.180408 | ||||||||
\(327\) | 0.673762 | 0.0372591 | ||||||||
\(328\) | 16.4590 | 0.908795 | ||||||||
\(329\) | 24.4164 | 1.34612 | ||||||||
\(330\) | 0.347524 | 0.0191306 | ||||||||
\(331\) | 0.291796 | 0.0160386 | 0.00801928 | − | 0.999968i | \(-0.497447\pi\) | ||||
0.00801928 | + | 0.999968i | \(0.497447\pi\) | |||||||
\(332\) | 8.29180 | 0.455071 | ||||||||
\(333\) | 13.8541 | 0.759200 | ||||||||
\(334\) | 3.14590 | 0.172136 | ||||||||
\(335\) | 8.70820 | 0.475780 | ||||||||
\(336\) | 5.09017 | 0.277692 | ||||||||
\(337\) | −28.0000 | −1.52526 | −0.762629 | − | 0.646837i | \(-0.776092\pi\) | ||||
−0.762629 | + | 0.646837i | \(0.776092\pi\) | |||||||
\(338\) | −4.58359 | −0.249315 | ||||||||
\(339\) | −5.70820 | −0.310027 | ||||||||
\(340\) | −11.1246 | −0.603317 | ||||||||
\(341\) | 25.8541 | 1.40008 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.7082 | −0.902158 | ||||||||
\(344\) | 5.67376 | 0.305909 | ||||||||
\(345\) | 0.236068 | 0.0127095 | ||||||||
\(346\) | 5.30495 | 0.285196 | ||||||||
\(347\) | −19.8885 | −1.06767 | −0.533836 | − | 0.845588i | \(-0.679250\pi\) | ||||
−0.533836 | + | 0.845588i | \(0.679250\pi\) | |||||||
\(348\) | −3.43769 | −0.184280 | ||||||||
\(349\) | 21.7426 | 1.16386 | 0.581929 | − | 0.813240i | \(-0.302298\pi\) | ||||
0.581929 | + | 0.813240i | \(0.302298\pi\) | |||||||
\(350\) | 1.61803 | 0.0864876 | ||||||||
\(351\) | −11.1803 | −0.596762 | ||||||||
\(352\) | 9.87539 | 0.526360 | ||||||||
\(353\) | −36.1591 | −1.92455 | −0.962276 | − | 0.272075i | \(-0.912290\pi\) | ||||
−0.962276 | + | 0.272075i | \(0.912290\pi\) | |||||||
\(354\) | 1.61803 | 0.0859975 | ||||||||
\(355\) | 8.23607 | 0.437125 | ||||||||
\(356\) | 12.4377 | 0.659196 | ||||||||
\(357\) | −9.70820 | −0.513813 | ||||||||
\(358\) | 4.02129 | 0.212532 | ||||||||
\(359\) | 26.3820 | 1.39239 | 0.696193 | − | 0.717854i | \(-0.254876\pi\) | ||||
0.696193 | + | 0.717854i | \(0.254876\pi\) | |||||||
\(360\) | 4.20163 | 0.221445 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 3.16718 | 0.166464 | ||||||||
\(363\) | 2.03444 | 0.106781 | ||||||||
\(364\) | −39.2705 | −2.05833 | ||||||||
\(365\) | 1.00000 | 0.0523424 | ||||||||
\(366\) | −0.437694 | −0.0228786 | ||||||||
\(367\) | 1.65248 | 0.0862585 | 0.0431293 | − | 0.999070i | \(-0.486267\pi\) | ||||
0.0431293 | + | 0.999070i | \(0.486267\pi\) | |||||||
\(368\) | 1.94427 | 0.101352 | ||||||||
\(369\) | −31.9098 | −1.66116 | ||||||||
\(370\) | −1.85410 | −0.0963902 | ||||||||
\(371\) | 14.3262 | 0.743781 | ||||||||
\(372\) | −7.68692 | −0.398548 | ||||||||
\(373\) | 6.70820 | 0.347338 | 0.173669 | − | 0.984804i | \(-0.444438\pi\) | ||||
0.173669 | + | 0.984804i | \(0.444438\pi\) | |||||||
\(374\) | −5.45898 | −0.282277 | ||||||||
\(375\) | 0.381966 | 0.0197246 | ||||||||
\(376\) | −8.48529 | −0.437596 | ||||||||
\(377\) | 24.2705 | 1.24999 | ||||||||
\(378\) | 3.61803 | 0.186092 | ||||||||
\(379\) | 26.8328 | 1.37831 | 0.689155 | − | 0.724614i | \(-0.257982\pi\) | ||||
0.689155 | + | 0.724614i | \(0.257982\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.09017 | 0.209546 | ||||||||
\(382\) | −2.31308 | −0.118348 | ||||||||
\(383\) | −32.9230 | −1.68229 | −0.841143 | − | 0.540813i | \(-0.818117\pi\) | ||||
−0.841143 | + | 0.540813i | \(0.818117\pi\) | |||||||
\(384\) | −3.85410 | −0.196679 | ||||||||
\(385\) | −10.0902 | −0.514243 | ||||||||
\(386\) | 1.52786 | 0.0777662 | ||||||||
\(387\) | −11.0000 | −0.559161 | ||||||||
\(388\) | −9.43769 | −0.479126 | ||||||||
\(389\) | −24.3262 | −1.23339 | −0.616695 | − | 0.787202i | \(-0.711529\pi\) | ||||
−0.616695 | + | 0.787202i | \(0.711529\pi\) | |||||||
\(390\) | 0.729490 | 0.0369392 | ||||||||
\(391\) | −3.70820 | −0.187532 | ||||||||
\(392\) | 16.1115 | 0.813751 | ||||||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | −6.31308 | −0.318048 | ||||||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | −12.6049 | −0.633419 | ||||||||
\(397\) | −16.8885 | −0.847612 | −0.423806 | − | 0.905753i | \(-0.639306\pi\) | ||||
−0.423806 | + | 0.905753i | \(0.639306\pi\) | |||||||
\(398\) | −5.12461 | −0.256874 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.14590 | 0.157295 | ||||||||
\(401\) | −6.76393 | −0.337775 | −0.168887 | − | 0.985635i | \(-0.554017\pi\) | ||||
−0.168887 | + | 0.985635i | \(0.554017\pi\) | |||||||
\(402\) | −1.27051 | −0.0633673 | ||||||||
\(403\) | 54.2705 | 2.70341 | ||||||||
\(404\) | −11.0213 | −0.548329 | ||||||||
\(405\) | −7.70820 | −0.383024 | ||||||||
\(406\) | −7.85410 | −0.389793 | ||||||||
\(407\) | 11.5623 | 0.573122 | ||||||||
\(408\) | 3.37384 | 0.167030 | ||||||||
\(409\) | 1.70820 | 0.0844652 | 0.0422326 | − | 0.999108i | \(-0.486553\pi\) | ||||
0.0422326 | + | 0.999108i | \(0.486553\pi\) | |||||||
\(410\) | 4.27051 | 0.210905 | ||||||||
\(411\) | −0.450850 | −0.0222388 | ||||||||
\(412\) | 3.10333 | 0.152890 | ||||||||
\(413\) | −46.9787 | −2.31167 | ||||||||
\(414\) | 0.673762 | 0.0331136 | ||||||||
\(415\) | 4.47214 | 0.219529 | ||||||||
\(416\) | 20.7295 | 1.01635 | ||||||||
\(417\) | −3.11146 | −0.152369 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.05573 | 0.0515757 | 0.0257878 | − | 0.999667i | \(-0.491791\pi\) | ||||
0.0257878 | + | 0.999667i | \(0.491791\pi\) | |||||||
\(420\) | 3.00000 | 0.146385 | ||||||||
\(421\) | −26.1246 | −1.27324 | −0.636618 | − | 0.771179i | \(-0.719667\pi\) | ||||
−0.636618 | + | 0.771179i | \(0.719667\pi\) | |||||||
\(422\) | −2.63932 | −0.128480 | ||||||||
\(423\) | 16.4508 | 0.799868 | ||||||||
\(424\) | −4.97871 | −0.241788 | ||||||||
\(425\) | −6.00000 | −0.291043 | ||||||||
\(426\) | −1.20163 | −0.0582190 | ||||||||
\(427\) | 12.7082 | 0.614993 | ||||||||
\(428\) | 5.56231 | 0.268864 | ||||||||
\(429\) | −4.54915 | −0.219635 | ||||||||
\(430\) | 1.47214 | 0.0709927 | ||||||||
\(431\) | 25.1803 | 1.21289 | 0.606447 | − | 0.795124i | \(-0.292594\pi\) | ||||
0.606447 | + | 0.795124i | \(0.292594\pi\) | |||||||
\(432\) | 7.03444 | 0.338445 | ||||||||
\(433\) | 29.2148 | 1.40397 | 0.701986 | − | 0.712190i | \(-0.252297\pi\) | ||||
0.701986 | + | 0.712190i | \(0.252297\pi\) | |||||||
\(434\) | −17.5623 | −0.843018 | ||||||||
\(435\) | −1.85410 | −0.0888974 | ||||||||
\(436\) | 3.27051 | 0.156629 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −0.145898 | −0.00697128 | ||||||||
\(439\) | −3.47214 | −0.165716 | −0.0828580 | − | 0.996561i | \(-0.526405\pi\) | ||||
−0.0828580 | + | 0.996561i | \(0.526405\pi\) | |||||||
\(440\) | 3.50658 | 0.167170 | ||||||||
\(441\) | −31.2361 | −1.48743 | ||||||||
\(442\) | −11.4590 | −0.545048 | ||||||||
\(443\) | −29.3607 | −1.39497 | −0.697484 | − | 0.716600i | \(-0.745697\pi\) | ||||
−0.697484 | + | 0.716600i | \(0.745697\pi\) | |||||||
\(444\) | −3.43769 | −0.163146 | ||||||||
\(445\) | 6.70820 | 0.317999 | ||||||||
\(446\) | 3.90983 | 0.185136 | ||||||||
\(447\) | 2.90983 | 0.137630 | ||||||||
\(448\) | 19.9443 | 0.942278 | ||||||||
\(449\) | −41.4721 | −1.95719 | −0.978596 | − | 0.205793i | \(-0.934023\pi\) | ||||
−0.978596 | + | 0.205793i | \(0.934023\pi\) | |||||||
\(450\) | 1.09017 | 0.0513911 | ||||||||
\(451\) | −26.6312 | −1.25401 | ||||||||
\(452\) | −27.7082 | −1.30328 | ||||||||
\(453\) | −2.81966 | −0.132479 | ||||||||
\(454\) | 6.74265 | 0.316448 | ||||||||
\(455\) | −21.1803 | −0.992950 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.00000 | −0.280668 | −0.140334 | − | 0.990104i | \(-0.544818\pi\) | ||||
−0.140334 | + | 0.990104i | \(0.544818\pi\) | |||||||
\(458\) | 8.25735 | 0.385841 | ||||||||
\(459\) | −13.4164 | −0.626224 | ||||||||
\(460\) | 1.14590 | 0.0534278 | ||||||||
\(461\) | −1.05573 | −0.0491702 | −0.0245851 | − | 0.999698i | \(-0.507826\pi\) | ||||
−0.0245851 | + | 0.999698i | \(0.507826\pi\) | |||||||
\(462\) | 1.47214 | 0.0684900 | ||||||||
\(463\) | 33.0344 | 1.53524 | 0.767620 | − | 0.640905i | \(-0.221441\pi\) | ||||
0.767620 | + | 0.640905i | \(0.221441\pi\) | |||||||
\(464\) | −15.2705 | −0.708916 | ||||||||
\(465\) | −4.14590 | −0.192261 | ||||||||
\(466\) | 2.60488 | 0.120669 | ||||||||
\(467\) | −24.7082 | −1.14336 | −0.571680 | − | 0.820477i | \(-0.693708\pi\) | ||||
−0.571680 | + | 0.820477i | \(0.693708\pi\) | |||||||
\(468\) | −26.4590 | −1.22307 | ||||||||
\(469\) | 36.8885 | 1.70335 | ||||||||
\(470\) | −2.20163 | −0.101553 | ||||||||
\(471\) | 9.18034 | 0.423008 | ||||||||
\(472\) | 16.3262 | 0.751476 | ||||||||
\(473\) | −9.18034 | −0.422112 | ||||||||
\(474\) | −1.16718 | −0.0536105 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −47.1246 | −2.15995 | ||||||||
\(477\) | 9.65248 | 0.441957 | ||||||||
\(478\) | −9.00000 | −0.411650 | ||||||||
\(479\) | −10.6180 | −0.485150 | −0.242575 | − | 0.970133i | \(-0.577992\pi\) | ||||
−0.242575 | + | 0.970133i | \(0.577992\pi\) | |||||||
\(480\) | −1.58359 | −0.0722808 | ||||||||
\(481\) | 24.2705 | 1.10664 | ||||||||
\(482\) | 6.92299 | 0.315333 | ||||||||
\(483\) | 1.00000 | 0.0455016 | ||||||||
\(484\) | 9.87539 | 0.448881 | ||||||||
\(485\) | −5.09017 | −0.231133 | ||||||||
\(486\) | 3.68692 | 0.167242 | ||||||||
\(487\) | 35.4164 | 1.60487 | 0.802435 | − | 0.596739i | \(-0.203537\pi\) | ||||
0.802435 | + | 0.596739i | \(0.203537\pi\) | |||||||
\(488\) | −4.41641 | −0.199921 | ||||||||
\(489\) | −3.25735 | −0.147303 | ||||||||
\(490\) | 4.18034 | 0.188849 | ||||||||
\(491\) | 8.67376 | 0.391441 | 0.195721 | − | 0.980660i | \(-0.437295\pi\) | ||||
0.195721 | + | 0.980660i | \(0.437295\pi\) | |||||||
\(492\) | 7.91796 | 0.356969 | ||||||||
\(493\) | 29.1246 | 1.31171 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.79837 | −0.305564 | ||||||||
\(496\) | −34.1459 | −1.53320 | ||||||||
\(497\) | 34.8885 | 1.56497 | ||||||||
\(498\) | −0.652476 | −0.0292381 | ||||||||
\(499\) | 26.6525 | 1.19313 | 0.596564 | − | 0.802565i | \(-0.296532\pi\) | ||||
0.596564 | + | 0.802565i | \(0.296532\pi\) | |||||||
\(500\) | 1.85410 | 0.0829180 | ||||||||
\(501\) | 3.14590 | 0.140548 | ||||||||
\(502\) | −5.79837 | −0.258794 | ||||||||
\(503\) | −2.05573 | −0.0916604 | −0.0458302 | − | 0.998949i | \(-0.514593\pi\) | ||||
−0.0458302 | + | 0.998949i | \(0.514593\pi\) | |||||||
\(504\) | 17.7984 | 0.792803 | ||||||||
\(505\) | −5.94427 | −0.264517 | ||||||||
\(506\) | 0.562306 | 0.0249975 | ||||||||
\(507\) | −4.58359 | −0.203564 | ||||||||
\(508\) | 19.8541 | 0.880883 | ||||||||
\(509\) | −10.7984 | −0.478630 | −0.239315 | − | 0.970942i | \(-0.576923\pi\) | ||||
−0.239315 | + | 0.970942i | \(0.576923\pi\) | |||||||
\(510\) | 0.875388 | 0.0387628 | ||||||||
\(511\) | 4.23607 | 0.187393 | ||||||||
\(512\) | −22.3050 | −0.985749 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.16718 | 0.227915 | ||||||||
\(515\) | 1.67376 | 0.0737548 | ||||||||
\(516\) | 2.72949 | 0.120159 | ||||||||
\(517\) | 13.7295 | 0.603822 | ||||||||
\(518\) | −7.85410 | −0.345089 | ||||||||
\(519\) | 5.30495 | 0.232862 | ||||||||
\(520\) | 7.36068 | 0.322787 | ||||||||
\(521\) | 0.381966 | 0.0167342 | 0.00836712 | − | 0.999965i | \(-0.497337\pi\) | ||||
0.00836712 | + | 0.999965i | \(0.497337\pi\) | |||||||
\(522\) | −5.29180 | −0.231616 | ||||||||
\(523\) | −10.5967 | −0.463363 | −0.231682 | − | 0.972792i | \(-0.574423\pi\) | ||||
−0.231682 | + | 0.972792i | \(0.574423\pi\) | |||||||
\(524\) | 14.5623 | 0.636157 | ||||||||
\(525\) | 1.61803 | 0.0706168 | ||||||||
\(526\) | 7.59675 | 0.331234 | ||||||||
\(527\) | 65.1246 | 2.83687 | ||||||||
\(528\) | 2.86223 | 0.124563 | ||||||||
\(529\) | −22.6180 | −0.983393 | ||||||||
\(530\) | −1.29180 | −0.0561120 | ||||||||
\(531\) | −31.6525 | −1.37360 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −55.9017 | −2.42137 | ||||||||
\(534\) | −0.978714 | −0.0423531 | ||||||||
\(535\) | 3.00000 | 0.129701 | ||||||||
\(536\) | −12.8197 | −0.553725 | ||||||||
\(537\) | 4.02129 | 0.173531 | ||||||||
\(538\) | 0.639320 | 0.0275631 | ||||||||
\(539\) | −26.0689 | −1.12287 | ||||||||
\(540\) | 4.14590 | 0.178411 | ||||||||
\(541\) | 32.5967 | 1.40144 | 0.700722 | − | 0.713435i | \(-0.252861\pi\) | ||||
0.700722 | + | 0.713435i | \(0.252861\pi\) | |||||||
\(542\) | −6.25735 | −0.268776 | ||||||||
\(543\) | 3.16718 | 0.135917 | ||||||||
\(544\) | 24.8754 | 1.06652 | ||||||||
\(545\) | 1.76393 | 0.0755585 | ||||||||
\(546\) | 3.09017 | 0.132247 | ||||||||
\(547\) | −37.9787 | −1.62385 | −0.811926 | − | 0.583760i | \(-0.801581\pi\) | ||||
−0.811926 | + | 0.583760i | \(0.801581\pi\) | |||||||
\(548\) | −2.18847 | −0.0934868 | ||||||||
\(549\) | 8.56231 | 0.365430 | ||||||||
\(550\) | 0.909830 | 0.0387953 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −0.347524 | −0.0147916 | ||||||||
\(553\) | 33.8885 | 1.44109 | ||||||||
\(554\) | 9.70820 | 0.412462 | ||||||||
\(555\) | −1.85410 | −0.0787022 | ||||||||
\(556\) | −15.1033 | −0.640524 | ||||||||
\(557\) | −21.4721 | −0.909804 | −0.454902 | − | 0.890542i | \(-0.650326\pi\) | ||||
−0.454902 | + | 0.890542i | \(0.650326\pi\) | |||||||
\(558\) | −11.8328 | −0.500923 | ||||||||
\(559\) | −19.2705 | −0.815056 | ||||||||
\(560\) | 13.3262 | 0.563136 | ||||||||
\(561\) | −5.45898 | −0.230478 | ||||||||
\(562\) | 10.5066 | 0.443193 | ||||||||
\(563\) | 30.1803 | 1.27195 | 0.635975 | − | 0.771710i | \(-0.280598\pi\) | ||||
0.635975 | + | 0.771710i | \(0.280598\pi\) | |||||||
\(564\) | −4.08204 | −0.171885 | ||||||||
\(565\) | −14.9443 | −0.628710 | ||||||||
\(566\) | −1.76393 | −0.0741436 | ||||||||
\(567\) | −32.6525 | −1.37128 | ||||||||
\(568\) | −12.1246 | −0.508737 | ||||||||
\(569\) | 0.437694 | 0.0183491 | 0.00917455 | − | 0.999958i | \(-0.497080\pi\) | ||||
0.00917455 | + | 0.999958i | \(0.497080\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.8541 | 1.12381 | 0.561905 | − | 0.827202i | \(-0.310069\pi\) | ||||
0.561905 | + | 0.827202i | \(0.310069\pi\) | |||||||
\(572\) | −22.0820 | −0.923296 | ||||||||
\(573\) | −2.31308 | −0.0966304 | ||||||||
\(574\) | 18.0902 | 0.755069 | ||||||||
\(575\) | 0.618034 | 0.0257738 | ||||||||
\(576\) | 13.4377 | 0.559904 | ||||||||
\(577\) | 19.7639 | 0.822783 | 0.411392 | − | 0.911459i | \(-0.365043\pi\) | ||||
0.411392 | + | 0.911459i | \(0.365043\pi\) | |||||||
\(578\) | −7.25735 | −0.301866 | ||||||||
\(579\) | 1.52786 | 0.0634959 | ||||||||
\(580\) | −9.00000 | −0.373705 | ||||||||
\(581\) | 18.9443 | 0.785941 | ||||||||
\(582\) | 0.742646 | 0.0307837 | ||||||||
\(583\) | 8.05573 | 0.333634 | ||||||||
\(584\) | −1.47214 | −0.0609174 | ||||||||
\(585\) | −14.2705 | −0.590013 | ||||||||
\(586\) | 8.41641 | 0.347679 | ||||||||
\(587\) | −42.2361 | −1.74327 | −0.871635 | − | 0.490156i | \(-0.836940\pi\) | ||||
−0.871635 | + | 0.490156i | \(0.836940\pi\) | |||||||
\(588\) | 7.75078 | 0.319637 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 4.23607 | 0.174396 | ||||||||
\(591\) | −6.31308 | −0.259686 | ||||||||
\(592\) | −15.2705 | −0.627614 | ||||||||
\(593\) | −15.6525 | −0.642770 | −0.321385 | − | 0.946949i | \(-0.604148\pi\) | ||||
−0.321385 | + | 0.946949i | \(0.604148\pi\) | |||||||
\(594\) | 2.03444 | 0.0834742 | ||||||||
\(595\) | −25.4164 | −1.04197 | ||||||||
\(596\) | 14.1246 | 0.578567 | ||||||||
\(597\) | −5.12461 | −0.209736 | ||||||||
\(598\) | 1.18034 | 0.0482677 | ||||||||
\(599\) | −7.36068 | −0.300749 | −0.150375 | − | 0.988629i | \(-0.548048\pi\) | ||||
−0.150375 | + | 0.988629i | \(0.548048\pi\) | |||||||
\(600\) | −0.562306 | −0.0229560 | ||||||||
\(601\) | −22.0000 | −0.897399 | −0.448699 | − | 0.893683i | \(-0.648113\pi\) | ||||
−0.448699 | + | 0.893683i | \(0.648113\pi\) | |||||||
\(602\) | 6.23607 | 0.254163 | ||||||||
\(603\) | 24.8541 | 1.01214 | ||||||||
\(604\) | −13.6869 | −0.556913 | ||||||||
\(605\) | 5.32624 | 0.216542 | ||||||||
\(606\) | 0.867258 | 0.0352299 | ||||||||
\(607\) | 16.5623 | 0.672243 | 0.336122 | − | 0.941819i | \(-0.390885\pi\) | ||||
0.336122 | + | 0.941819i | \(0.390885\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.85410 | −0.318264 | ||||||||
\(610\) | −1.14590 | −0.0463961 | ||||||||
\(611\) | 28.8197 | 1.16592 | ||||||||
\(612\) | −31.7508 | −1.28345 | ||||||||
\(613\) | 4.05573 | 0.163809 | 0.0819047 | − | 0.996640i | \(-0.473900\pi\) | ||||
0.0819047 | + | 0.996640i | \(0.473900\pi\) | |||||||
\(614\) | −4.68692 | −0.189149 | ||||||||
\(615\) | 4.27051 | 0.172204 | ||||||||
\(616\) | 14.8541 | 0.598489 | ||||||||
\(617\) | −12.9098 | −0.519730 | −0.259865 | − | 0.965645i | \(-0.583678\pi\) | ||||
−0.259865 | + | 0.965645i | \(0.583678\pi\) | |||||||
\(618\) | −0.244199 | −0.00982311 | ||||||||
\(619\) | −8.05573 | −0.323787 | −0.161894 | − | 0.986808i | \(-0.551760\pi\) | ||||
−0.161894 | + | 0.986808i | \(0.551760\pi\) | |||||||
\(620\) | −20.1246 | −0.808224 | ||||||||
\(621\) | 1.38197 | 0.0554564 | ||||||||
\(622\) | 2.69505 | 0.108062 | ||||||||
\(623\) | 28.4164 | 1.13848 | ||||||||
\(624\) | 6.00813 | 0.240518 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 3.74265 | 0.149586 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.5623 | 1.77823 | ||||||||
\(629\) | 29.1246 | 1.16127 | ||||||||
\(630\) | 4.61803 | 0.183987 | ||||||||
\(631\) | 15.0000 | 0.597141 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(632\) | −11.7771 | −0.468467 | ||||||||
\(633\) | −2.63932 | −0.104904 | ||||||||
\(634\) | −5.05573 | −0.200789 | ||||||||
\(635\) | 10.7082 | 0.424942 | ||||||||
\(636\) | −2.39512 | −0.0949728 | ||||||||
\(637\) | −54.7214 | −2.16814 | ||||||||
\(638\) | −4.41641 | −0.174847 | ||||||||
\(639\) | 23.5066 | 0.929906 | ||||||||
\(640\) | −10.0902 | −0.398849 | ||||||||
\(641\) | −5.72949 | −0.226301 | −0.113151 | − | 0.993578i | \(-0.536094\pi\) | ||||
−0.113151 | + | 0.993578i | \(0.536094\pi\) | |||||||
\(642\) | −0.437694 | −0.0172744 | ||||||||
\(643\) | 31.5967 | 1.24605 | 0.623027 | − | 0.782200i | \(-0.285903\pi\) | ||||
0.623027 | + | 0.782200i | \(0.285903\pi\) | |||||||
\(644\) | 4.85410 | 0.191278 | ||||||||
\(645\) | 1.47214 | 0.0579653 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.3050 | 1.42729 | 0.713647 | − | 0.700505i | \(-0.247042\pi\) | ||||
0.713647 | + | 0.700505i | \(0.247042\pi\) | |||||||
\(648\) | 11.3475 | 0.445773 | ||||||||
\(649\) | −26.4164 | −1.03693 | ||||||||
\(650\) | 1.90983 | 0.0749097 | ||||||||
\(651\) | −17.5623 | −0.688321 | ||||||||
\(652\) | −15.8115 | −0.619227 | ||||||||
\(653\) | 7.85410 | 0.307355 | 0.153677 | − | 0.988121i | \(-0.450888\pi\) | ||||
0.153677 | + | 0.988121i | \(0.450888\pi\) | |||||||
\(654\) | −0.257354 | −0.0100633 | ||||||||
\(655\) | 7.85410 | 0.306885 | ||||||||
\(656\) | 35.1722 | 1.37324 | ||||||||
\(657\) | 2.85410 | 0.111349 | ||||||||
\(658\) | −9.32624 | −0.363575 | ||||||||
\(659\) | −42.4721 | −1.65448 | −0.827240 | − | 0.561849i | \(-0.810090\pi\) | ||||
−0.827240 | + | 0.561849i | \(0.810090\pi\) | |||||||
\(660\) | 1.68692 | 0.0656632 | ||||||||
\(661\) | 3.70820 | 0.144232 | 0.0721162 | − | 0.997396i | \(-0.477025\pi\) | ||||
0.0721162 | + | 0.997396i | \(0.477025\pi\) | |||||||
\(662\) | −0.111456 | −0.00433187 | ||||||||
\(663\) | −11.4590 | −0.445030 | ||||||||
\(664\) | −6.58359 | −0.255493 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.29180 | −0.205053 | ||||||||
\(667\) | −3.00000 | −0.116160 | ||||||||
\(668\) | 15.2705 | 0.590834 | ||||||||
\(669\) | 3.90983 | 0.151163 | ||||||||
\(670\) | −3.32624 | −0.128504 | ||||||||
\(671\) | 7.14590 | 0.275864 | ||||||||
\(672\) | −6.70820 | −0.258775 | ||||||||
\(673\) | 11.1115 | 0.428315 | 0.214158 | − | 0.976799i | \(-0.431299\pi\) | ||||
0.214158 | + | 0.976799i | \(0.431299\pi\) | |||||||
\(674\) | 10.6950 | 0.411958 | ||||||||
\(675\) | 2.23607 | 0.0860663 | ||||||||
\(676\) | −22.2492 | −0.855739 | ||||||||
\(677\) | 8.38197 | 0.322145 | 0.161073 | − | 0.986943i | \(-0.448505\pi\) | ||||
0.161073 | + | 0.986943i | \(0.448505\pi\) | |||||||
\(678\) | 2.18034 | 0.0837354 | ||||||||
\(679\) | −21.5623 | −0.827485 | ||||||||
\(680\) | 8.83282 | 0.338723 | ||||||||
\(681\) | 6.74265 | 0.258379 | ||||||||
\(682\) | −9.87539 | −0.378148 | ||||||||
\(683\) | −23.4721 | −0.898136 | −0.449068 | − | 0.893498i | \(-0.648244\pi\) | ||||
−0.449068 | + | 0.893498i | \(0.648244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.18034 | −0.0450985 | ||||||||
\(686\) | 6.38197 | 0.243665 | ||||||||
\(687\) | 8.25735 | 0.315038 | ||||||||
\(688\) | 12.1246 | 0.462246 | ||||||||
\(689\) | 16.9098 | 0.644213 | ||||||||
\(690\) | −0.0901699 | −0.00343271 | ||||||||
\(691\) | 21.4721 | 0.816839 | 0.408419 | − | 0.912794i | \(-0.366080\pi\) | ||||
0.408419 | + | 0.912794i | \(0.366080\pi\) | |||||||
\(692\) | 25.7508 | 0.978898 | ||||||||
\(693\) | −28.7984 | −1.09396 | ||||||||
\(694\) | 7.59675 | 0.288369 | ||||||||
\(695\) | −8.14590 | −0.308992 | ||||||||
\(696\) | 2.72949 | 0.103461 | ||||||||
\(697\) | −67.0820 | −2.54091 | ||||||||
\(698\) | −8.30495 | −0.314347 | ||||||||
\(699\) | 2.60488 | 0.0985255 | ||||||||
\(700\) | 7.85410 | 0.296857 | ||||||||
\(701\) | 48.5755 | 1.83467 | 0.917335 | − | 0.398116i | \(-0.130336\pi\) | ||||
0.917335 | + | 0.398116i | \(0.130336\pi\) | |||||||
\(702\) | 4.27051 | 0.161180 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 11.2148 | 0.422673 | ||||||||
\(705\) | −2.20163 | −0.0829180 | ||||||||
\(706\) | 13.8115 | 0.519804 | ||||||||
\(707\) | −25.1803 | −0.947004 | ||||||||
\(708\) | 7.85410 | 0.295175 | ||||||||
\(709\) | −15.7082 | −0.589934 | −0.294967 | − | 0.955507i | \(-0.595309\pi\) | ||||
−0.294967 | + | 0.955507i | \(0.595309\pi\) | |||||||
\(710\) | −3.14590 | −0.118063 | ||||||||
\(711\) | 22.8328 | 0.856297 | ||||||||
\(712\) | −9.87539 | −0.370096 | ||||||||
\(713\) | −6.70820 | −0.251224 | ||||||||
\(714\) | 3.70820 | 0.138776 | ||||||||
\(715\) | −11.9098 | −0.445402 | ||||||||
\(716\) | 19.5197 | 0.729487 | ||||||||
\(717\) | −9.00000 | −0.336111 | ||||||||
\(718\) | −10.0770 | −0.376071 | ||||||||
\(719\) | 12.2016 | 0.455044 | 0.227522 | − | 0.973773i | \(-0.426938\pi\) | ||||
0.227522 | + | 0.973773i | \(0.426938\pi\) | |||||||
\(720\) | 8.97871 | 0.334617 | ||||||||
\(721\) | 7.09017 | 0.264052 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.92299 | 0.257469 | ||||||||
\(724\) | 15.3738 | 0.571364 | ||||||||
\(725\) | −4.85410 | −0.180277 | ||||||||
\(726\) | −0.777088 | −0.0288404 | ||||||||
\(727\) | −10.5836 | −0.392524 | −0.196262 | − | 0.980552i | \(-0.562880\pi\) | ||||
−0.196262 | + | 0.980552i | \(0.562880\pi\) | |||||||
\(728\) | 31.1803 | 1.15562 | ||||||||
\(729\) | −19.4377 | −0.719915 | ||||||||
\(730\) | −0.381966 | −0.0141372 | ||||||||
\(731\) | −23.1246 | −0.855295 | ||||||||
\(732\) | −2.12461 | −0.0785279 | ||||||||
\(733\) | 0.236068 | 0.00871937 | 0.00435968 | − | 0.999990i | \(-0.498612\pi\) | ||||
0.00435968 | + | 0.999990i | \(0.498612\pi\) | |||||||
\(734\) | −0.631190 | −0.0232976 | ||||||||
\(735\) | 4.18034 | 0.154194 | ||||||||
\(736\) | −2.56231 | −0.0944478 | ||||||||
\(737\) | 20.7426 | 0.764065 | ||||||||
\(738\) | 12.1885 | 0.448664 | ||||||||
\(739\) | −21.8328 | −0.803133 | −0.401567 | − | 0.915830i | \(-0.631534\pi\) | ||||
−0.401567 | + | 0.915830i | \(0.631534\pi\) | |||||||
\(740\) | −9.00000 | −0.330847 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.47214 | −0.200888 | ||||||||
\(743\) | −36.2361 | −1.32937 | −0.664686 | − | 0.747123i | \(-0.731435\pi\) | ||||
−0.664686 | + | 0.747123i | \(0.731435\pi\) | |||||||
\(744\) | 6.10333 | 0.223759 | ||||||||
\(745\) | 7.61803 | 0.279103 | ||||||||
\(746\) | −2.56231 | −0.0938127 | ||||||||
\(747\) | 12.7639 | 0.467008 | ||||||||
\(748\) | −26.4984 | −0.968879 | ||||||||
\(749\) | 12.7082 | 0.464348 | ||||||||
\(750\) | −0.145898 | −0.00532744 | ||||||||
\(751\) | 2.56231 | 0.0934999 | 0.0467499 | − | 0.998907i | \(-0.485114\pi\) | ||||
0.0467499 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(752\) | −18.1327 | −0.661233 | ||||||||
\(753\) | −5.79837 | −0.211304 | ||||||||
\(754\) | −9.27051 | −0.337612 | ||||||||
\(755\) | −7.38197 | −0.268657 | ||||||||
\(756\) | 17.5623 | 0.638735 | ||||||||
\(757\) | −14.3820 | −0.522721 | −0.261361 | − | 0.965241i | \(-0.584171\pi\) | ||||
−0.261361 | + | 0.965241i | \(0.584171\pi\) | |||||||
\(758\) | −10.2492 | −0.372269 | ||||||||
\(759\) | 0.562306 | 0.0204104 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.3607 | 1.35432 | 0.677162 | − | 0.735834i | \(-0.263210\pi\) | ||||
0.677162 | + | 0.735834i | \(0.263210\pi\) | |||||||
\(762\) | −1.56231 | −0.0565964 | ||||||||
\(763\) | 7.47214 | 0.270509 | ||||||||
\(764\) | −11.2279 | −0.406213 | ||||||||
\(765\) | −17.1246 | −0.619142 | ||||||||
\(766\) | 12.5755 | 0.454370 | ||||||||
\(767\) | −55.4508 | −2.00221 | ||||||||
\(768\) | −2.12461 | −0.0766653 | ||||||||
\(769\) | 13.6869 | 0.493563 | 0.246781 | − | 0.969071i | \(-0.420627\pi\) | ||||
0.246781 | + | 0.969071i | \(0.420627\pi\) | |||||||
\(770\) | 3.85410 | 0.138892 | ||||||||
\(771\) | 5.16718 | 0.186092 | ||||||||
\(772\) | 7.41641 | 0.266922 | ||||||||
\(773\) | 39.7426 | 1.42944 | 0.714722 | − | 0.699409i | \(-0.246553\pi\) | ||||
0.714722 | + | 0.699409i | \(0.246553\pi\) | |||||||
\(774\) | 4.20163 | 0.151024 | ||||||||
\(775\) | −10.8541 | −0.389891 | ||||||||
\(776\) | 7.49342 | 0.268998 | ||||||||
\(777\) | −7.85410 | −0.281764 | ||||||||
\(778\) | 9.29180 | 0.333127 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 3.54102 | 0.126789 | ||||||||
\(781\) | 19.6180 | 0.701988 | ||||||||
\(782\) | 1.41641 | 0.0506506 | ||||||||
\(783\) | −10.8541 | −0.387894 | ||||||||
\(784\) | 34.4296 | 1.22963 | ||||||||
\(785\) | 24.0344 | 0.857826 | ||||||||
\(786\) | −1.14590 | −0.0408728 | ||||||||
\(787\) | 35.4853 | 1.26491 | 0.632457 | − | 0.774595i | \(-0.282046\pi\) | ||||
0.632457 | + | 0.774595i | \(0.282046\pi\) | |||||||
\(788\) | −30.6443 | −1.09166 | ||||||||
\(789\) | 7.59675 | 0.270451 | ||||||||
\(790\) | −3.05573 | −0.108718 | ||||||||
\(791\) | −63.3050 | −2.25086 | ||||||||
\(792\) | 10.0081 | 0.355623 | ||||||||
\(793\) | 15.0000 | 0.532666 | ||||||||
\(794\) | 6.45085 | 0.228932 | ||||||||
\(795\) | −1.29180 | −0.0458153 | ||||||||
\(796\) | −24.8754 | −0.881685 | ||||||||
\(797\) | 2.18034 | 0.0772316 | 0.0386158 | − | 0.999254i | \(-0.487705\pi\) | ||||
0.0386158 | + | 0.999254i | \(0.487705\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.5836 | 1.22348 | ||||||||
\(800\) | −4.14590 | −0.146580 | ||||||||
\(801\) | 19.1459 | 0.676487 | ||||||||
\(802\) | 2.58359 | 0.0912298 | ||||||||
\(803\) | 2.38197 | 0.0840578 | ||||||||
\(804\) | −6.16718 | −0.217500 | ||||||||
\(805\) | 2.61803 | 0.0922736 | ||||||||
\(806\) | −20.7295 | −0.730165 | ||||||||
\(807\) | 0.639320 | 0.0225051 | ||||||||
\(808\) | 8.75078 | 0.307851 | ||||||||
\(809\) | 28.9098 | 1.01642 | 0.508208 | − | 0.861235i | \(-0.330308\pi\) | ||||
0.508208 | + | 0.861235i | \(0.330308\pi\) | |||||||
\(810\) | 2.94427 | 0.103451 | ||||||||
\(811\) | −40.3262 | −1.41605 | −0.708023 | − | 0.706190i | \(-0.750413\pi\) | ||||
−0.708023 | + | 0.706190i | \(0.750413\pi\) | |||||||
\(812\) | −38.1246 | −1.33791 | ||||||||
\(813\) | −6.25735 | −0.219455 | ||||||||
\(814\) | −4.41641 | −0.154795 | ||||||||
\(815\) | −8.52786 | −0.298718 | ||||||||
\(816\) | 7.20976 | 0.252392 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −0.652476 | −0.0228133 | ||||||||
\(819\) | −60.4508 | −2.11232 | ||||||||
\(820\) | 20.7295 | 0.723905 | ||||||||
\(821\) | 12.3820 | 0.432134 | 0.216067 | − | 0.976379i | \(-0.430677\pi\) | ||||
0.216067 | + | 0.976379i | \(0.430677\pi\) | |||||||
\(822\) | 0.172209 | 0.00600649 | ||||||||
\(823\) | 8.36068 | 0.291435 | 0.145717 | − | 0.989326i | \(-0.453451\pi\) | ||||
0.145717 | + | 0.989326i | \(0.453451\pi\) | |||||||
\(824\) | −2.46401 | −0.0858377 | ||||||||
\(825\) | 0.909830 | 0.0316762 | ||||||||
\(826\) | 17.9443 | 0.624361 | ||||||||
\(827\) | 35.8328 | 1.24603 | 0.623015 | − | 0.782210i | \(-0.285908\pi\) | ||||
0.623015 | + | 0.782210i | \(0.285908\pi\) | |||||||
\(828\) | 3.27051 | 0.113658 | ||||||||
\(829\) | −43.3951 | −1.50717 | −0.753587 | − | 0.657348i | \(-0.771678\pi\) | ||||
−0.753587 | + | 0.657348i | \(0.771678\pi\) | |||||||
\(830\) | −1.70820 | −0.0592926 | ||||||||
\(831\) | 9.70820 | 0.336774 | ||||||||
\(832\) | 23.5410 | 0.816138 | ||||||||
\(833\) | −65.6656 | −2.27518 | ||||||||
\(834\) | 1.18847 | 0.0411534 | ||||||||
\(835\) | 8.23607 | 0.285021 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −24.2705 | −0.838912 | ||||||||
\(838\) | −0.403252 | −0.0139301 | ||||||||
\(839\) | 13.3820 | 0.461997 | 0.230998 | − | 0.972954i | \(-0.425801\pi\) | ||||
0.230998 | + | 0.972954i | \(0.425801\pi\) | |||||||
\(840\) | −2.38197 | −0.0821856 | ||||||||
\(841\) | −5.43769 | −0.187507 | ||||||||
\(842\) | 9.97871 | 0.343889 | ||||||||
\(843\) | 10.5066 | 0.361866 | ||||||||
\(844\) | −12.8115 | −0.440991 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | −6.28367 | −0.216037 | ||||||||
\(847\) | 22.5623 | 0.775250 | ||||||||
\(848\) | −10.6393 | −0.365356 | ||||||||
\(849\) | −1.76393 | −0.0605380 | ||||||||
\(850\) | 2.29180 | 0.0786080 | ||||||||
\(851\) | −3.00000 | −0.102839 | ||||||||
\(852\) | −5.83282 | −0.199829 | ||||||||
\(853\) | 52.9574 | 1.81323 | 0.906614 | − | 0.421961i | \(-0.138658\pi\) | ||||
0.906614 | + | 0.421961i | \(0.138658\pi\) | |||||||
\(854\) | −4.85410 | −0.166104 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.41641 | −0.150950 | ||||||||
\(857\) | 32.6180 | 1.11421 | 0.557105 | − | 0.830442i | \(-0.311912\pi\) | ||||
0.557105 | + | 0.830442i | \(0.311912\pi\) | |||||||
\(858\) | 1.73762 | 0.0593214 | ||||||||
\(859\) | 13.5967 | 0.463915 | 0.231958 | − | 0.972726i | \(-0.425487\pi\) | ||||
0.231958 | + | 0.972726i | \(0.425487\pi\) | |||||||
\(860\) | 7.14590 | 0.243673 | ||||||||
\(861\) | 18.0902 | 0.616511 | ||||||||
\(862\) | −9.61803 | −0.327592 | ||||||||
\(863\) | 4.65248 | 0.158372 | 0.0791861 | − | 0.996860i | \(-0.474768\pi\) | ||||
0.0791861 | + | 0.996860i | \(0.474768\pi\) | |||||||
\(864\) | −9.27051 | −0.315389 | ||||||||
\(865\) | 13.8885 | 0.472225 | ||||||||
\(866\) | −11.1591 | −0.379200 | ||||||||
\(867\) | −7.25735 | −0.246473 | ||||||||
\(868\) | −85.2492 | −2.89355 | ||||||||
\(869\) | 19.0557 | 0.646421 | ||||||||
\(870\) | 0.708204 | 0.0240104 | ||||||||
\(871\) | 43.5410 | 1.47533 | ||||||||
\(872\) | −2.59675 | −0.0879370 | ||||||||
\(873\) | −14.5279 | −0.491694 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.23607 | 0.143205 | ||||||||
\(876\) | −0.708204 | −0.0239280 | ||||||||
\(877\) | 7.81966 | 0.264051 | 0.132026 | − | 0.991246i | \(-0.457852\pi\) | ||||
0.132026 | + | 0.991246i | \(0.457852\pi\) | |||||||
\(878\) | 1.32624 | 0.0447584 | ||||||||
\(879\) | 8.41641 | 0.283878 | ||||||||
\(880\) | 7.49342 | 0.252603 | ||||||||
\(881\) | 25.0344 | 0.843432 | 0.421716 | − | 0.906728i | \(-0.361428\pi\) | ||||
0.421716 | + | 0.906728i | \(0.361428\pi\) | |||||||
\(882\) | 11.9311 | 0.401742 | ||||||||
\(883\) | 46.9230 | 1.57908 | 0.789542 | − | 0.613696i | \(-0.210318\pi\) | ||||
0.789542 | + | 0.613696i | \(0.210318\pi\) | |||||||
\(884\) | −55.6231 | −1.87081 | ||||||||
\(885\) | 4.23607 | 0.142394 | ||||||||
\(886\) | 11.2148 | 0.376768 | ||||||||
\(887\) | −12.4721 | −0.418773 | −0.209387 | − | 0.977833i | \(-0.567147\pi\) | ||||
−0.209387 | + | 0.977833i | \(0.567147\pi\) | |||||||
\(888\) | 2.72949 | 0.0915957 | ||||||||
\(889\) | 45.3607 | 1.52135 | ||||||||
\(890\) | −2.56231 | −0.0858887 | ||||||||
\(891\) | −18.3607 | −0.615106 | ||||||||
\(892\) | 18.9787 | 0.635454 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.11146 | −0.0371727 | ||||||||
\(895\) | 10.5279 | 0.351908 | ||||||||
\(896\) | −42.7426 | −1.42793 | ||||||||
\(897\) | 1.18034 | 0.0394104 | ||||||||
\(898\) | 15.8409 | 0.528619 | ||||||||
\(899\) | 52.6869 | 1.75721 | ||||||||
\(900\) | 5.29180 | 0.176393 | ||||||||
\(901\) | 20.2918 | 0.676018 | ||||||||
\(902\) | 10.1722 | 0.338698 | ||||||||
\(903\) | 6.23607 | 0.207523 | ||||||||
\(904\) | 22.0000 | 0.731709 | ||||||||
\(905\) | 8.29180 | 0.275629 | ||||||||
\(906\) | 1.07701 | 0.0357814 | ||||||||
\(907\) | 32.2492 | 1.07082 | 0.535409 | − | 0.844593i | \(-0.320158\pi\) | ||||
0.535409 | + | 0.844593i | \(0.320158\pi\) | |||||||
\(908\) | 32.7295 | 1.08617 | ||||||||
\(909\) | −16.9656 | −0.562712 | ||||||||
\(910\) | 8.09017 | 0.268187 | ||||||||
\(911\) | −36.1033 | −1.19616 | −0.598078 | − | 0.801438i | \(-0.704069\pi\) | ||||
−0.598078 | + | 0.801438i | \(0.704069\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6525 | 0.352545 | ||||||||
\(914\) | 2.29180 | 0.0758059 | ||||||||
\(915\) | −1.14590 | −0.0378822 | ||||||||
\(916\) | 40.0820 | 1.32435 | ||||||||
\(917\) | 33.2705 | 1.09869 | ||||||||
\(918\) | 5.12461 | 0.169137 | ||||||||
\(919\) | 22.8885 | 0.755023 | 0.377512 | − | 0.926005i | \(-0.376780\pi\) | ||||
0.377512 | + | 0.926005i | \(0.376780\pi\) | |||||||
\(920\) | −0.909830 | −0.0299962 | ||||||||
\(921\) | −4.68692 | −0.154439 | ||||||||
\(922\) | 0.403252 | 0.0132804 | ||||||||
\(923\) | 41.1803 | 1.35547 | ||||||||
\(924\) | 7.14590 | 0.235083 | ||||||||
\(925\) | −4.85410 | −0.159602 | ||||||||
\(926\) | −12.6180 | −0.414654 | ||||||||
\(927\) | 4.77709 | 0.156900 | ||||||||
\(928\) | 20.1246 | 0.660623 | ||||||||
\(929\) | 11.6180 | 0.381175 | 0.190588 | − | 0.981670i | \(-0.438961\pi\) | ||||
0.190588 | + | 0.981670i | \(0.438961\pi\) | |||||||
\(930\) | 1.58359 | 0.0519280 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.6443 | 0.414179 | ||||||||
\(933\) | 2.69505 | 0.0882319 | ||||||||
\(934\) | 9.43769 | 0.308811 | ||||||||
\(935\) | −14.2918 | −0.467392 | ||||||||
\(936\) | 21.0081 | 0.686672 | ||||||||
\(937\) | 2.56231 | 0.0837069 | 0.0418534 | − | 0.999124i | \(-0.486674\pi\) | ||||
0.0418534 | + | 0.999124i | \(0.486674\pi\) | |||||||
\(938\) | −14.0902 | −0.460060 | ||||||||
\(939\) | 3.74265 | 0.122137 | ||||||||
\(940\) | −10.6869 | −0.348569 | ||||||||
\(941\) | −10.5066 | −0.342505 | −0.171252 | − | 0.985227i | \(-0.554781\pi\) | ||||
−0.171252 | + | 0.985227i | \(0.554781\pi\) | |||||||
\(942\) | −3.50658 | −0.114250 | ||||||||
\(943\) | 6.90983 | 0.225015 | ||||||||
\(944\) | 34.8885 | 1.13553 | ||||||||
\(945\) | 9.47214 | 0.308129 | ||||||||
\(946\) | 3.50658 | 0.114009 | ||||||||
\(947\) | 48.0000 | 1.55979 | 0.779895 | − | 0.625910i | \(-0.215272\pi\) | ||||
0.779895 | + | 0.625910i | \(0.215272\pi\) | |||||||
\(948\) | −5.66563 | −0.184011 | ||||||||
\(949\) | 5.00000 | 0.162307 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.05573 | −0.163943 | ||||||||
\(952\) | 37.4164 | 1.21267 | ||||||||
\(953\) | 11.8328 | 0.383302 | 0.191651 | − | 0.981463i | \(-0.438616\pi\) | ||||
0.191651 | + | 0.981463i | \(0.438616\pi\) | |||||||
\(954\) | −3.68692 | −0.119368 | ||||||||
\(955\) | −6.05573 | −0.195959 | ||||||||
\(956\) | −43.6869 | −1.41294 | ||||||||
\(957\) | −4.41641 | −0.142762 | ||||||||
\(958\) | 4.05573 | 0.131035 | ||||||||
\(959\) | −5.00000 | −0.161458 | ||||||||
\(960\) | −1.79837 | −0.0580423 | ||||||||
\(961\) | 86.8115 | 2.80037 | ||||||||
\(962\) | −9.27051 | −0.298893 | ||||||||
\(963\) | 8.56231 | 0.275916 | ||||||||
\(964\) | 33.6049 | 1.08234 | ||||||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | −0.381966 | −0.0122896 | ||||||||
\(967\) | 28.7639 | 0.924986 | 0.462493 | − | 0.886623i | \(-0.346955\pi\) | ||||
0.462493 | + | 0.886623i | \(0.346955\pi\) | |||||||
\(968\) | −7.84095 | −0.252018 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.94427 | 0.0624268 | ||||||||
\(971\) | 37.7984 | 1.21301 | 0.606504 | − | 0.795081i | \(-0.292572\pi\) | ||||
0.606504 | + | 0.795081i | \(0.292572\pi\) | |||||||
\(972\) | 17.8967 | 0.574036 | ||||||||
\(973\) | −34.5066 | −1.10623 | ||||||||
\(974\) | −13.5279 | −0.433461 | ||||||||
\(975\) | 1.90983 | 0.0611635 | ||||||||
\(976\) | −9.43769 | −0.302093 | ||||||||
\(977\) | −53.6525 | −1.71649 | −0.858247 | − | 0.513236i | \(-0.828446\pi\) | ||||
−0.858247 | + | 0.513236i | \(0.828446\pi\) | |||||||
\(978\) | 1.24420 | 0.0397851 | ||||||||
\(979\) | 15.9787 | 0.510682 | ||||||||
\(980\) | 20.2918 | 0.648198 | ||||||||
\(981\) | 5.03444 | 0.160737 | ||||||||
\(982\) | −3.31308 | −0.105725 | ||||||||
\(983\) | −13.8541 | −0.441877 | −0.220939 | − | 0.975288i | \(-0.570912\pi\) | ||||
−0.220939 | + | 0.975288i | \(0.570912\pi\) | |||||||
\(984\) | −6.28677 | −0.200415 | ||||||||
\(985\) | −16.5279 | −0.526622 | ||||||||
\(986\) | −11.1246 | −0.354280 | ||||||||
\(987\) | −9.32624 | −0.296857 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.38197 | 0.0757421 | ||||||||
\(990\) | 2.59675 | 0.0825301 | ||||||||
\(991\) | −18.1459 | −0.576423 | −0.288212 | − | 0.957567i | \(-0.593061\pi\) | ||||
−0.288212 | + | 0.957567i | \(0.593061\pi\) | |||||||
\(992\) | 45.0000 | 1.42875 | ||||||||
\(993\) | −0.111456 | −0.00353695 | ||||||||
\(994\) | −13.3262 | −0.422683 | ||||||||
\(995\) | −13.4164 | −0.425329 | ||||||||
\(996\) | −3.16718 | −0.100356 | ||||||||
\(997\) | −3.23607 | −0.102487 | −0.0512437 | − | 0.998686i | \(-0.516319\pi\) | ||||
−0.0512437 | + | 0.998686i | \(0.516319\pi\) | |||||||
\(998\) | −10.1803 | −0.322253 | ||||||||
\(999\) | −10.8541 | −0.343409 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1805.2.a.c.1.2 | ✓ | 2 | |
5.4 | even | 2 | 9025.2.a.v.1.1 | 2 | |||
19.18 | odd | 2 | 1805.2.a.e.1.1 | yes | 2 | ||
95.94 | odd | 2 | 9025.2.a.k.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1805.2.a.e.1.1 | yes | 2 | 19.18 | odd | 2 | ||
9025.2.a.k.1.2 | 2 | 95.94 | odd | 2 | |||
9025.2.a.v.1.1 | 2 | 5.4 | even | 2 |