Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(406,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.406");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.k (of order \(3\), degree \(2\), 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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 406.3 | ||
Root | \(0.414953 + 0.718719i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.406 |
Dual form | 855.2.k.k.676.3 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0850473 | + | 0.147306i | 0.0601375 | + | 0.104161i | 0.894527 | − | 0.447014i | \(-0.147513\pi\) |
−0.834389 | + | 0.551176i | \(0.814179\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.985534 | − | 1.70699i | 0.492767 | − | 0.853497i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.218469 | −0.0825735 | −0.0412867 | − | 0.999147i | \(-0.513146\pi\) | ||||
−0.0412867 | + | 0.999147i | \(0.513146\pi\) | |||||||
\(8\) | 0.675457 | 0.238810 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.0850473 | + | 0.147306i | −0.0268943 | + | 0.0465823i | ||||
\(11\) | 5.33261 | 1.60784 | 0.803921 | − | 0.594737i | \(-0.202744\pi\) | ||||
0.803921 | + | 0.594737i | \(0.202744\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.01725 | + | 5.22603i | −0.836834 | + | 1.44944i | 0.0556936 | + | 0.998448i | \(0.482263\pi\) |
−0.892528 | + | 0.450992i | \(0.851070\pi\) | |||||||
\(14\) | −0.0185802 | − | 0.0321818i | −0.00496576 | − | 0.00860095i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.91362 | − | 3.31449i | −0.478406 | − | 0.828623i | ||||
\(17\) | 3.27554 | + | 5.67340i | 0.794435 | + | 1.37600i | 0.923198 | + | 0.384326i | \(0.125566\pi\) |
−0.128763 | + | 0.991675i | \(0.541101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.50507 | − | 4.09082i | 0.345286 | − | 0.938497i | ||||
\(20\) | 1.97107 | 0.440744 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.453524 | + | 0.785526i | 0.0966916 | + | 0.167475i | ||||
\(23\) | 1.90802 | − | 3.30478i | 0.397849 | − | 0.689094i | −0.595612 | − | 0.803273i | \(-0.703090\pi\) |
0.993460 | + | 0.114178i | \(0.0364236\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −1.02644 | −0.201301 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.215309 | + | 0.372925i | −0.0406895 | + | 0.0704763i | ||||
\(29\) | 0.525141 | − | 0.909571i | 0.0975162 | − | 0.168903i | −0.813140 | − | 0.582068i | \(-0.802244\pi\) |
0.910656 | + | 0.413165i | \(0.135577\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.65981 | 0.477716 | 0.238858 | − | 0.971054i | \(-0.423227\pi\) | ||||
0.238858 | + | 0.971054i | \(0.423227\pi\) | |||||||
\(32\) | 1.00095 | − | 1.73370i | 0.176945 | − | 0.306478i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.557151 | + | 0.965014i | −0.0955506 | + | 0.165499i | ||||
\(35\) | −0.109234 | − | 0.189200i | −0.0184640 | − | 0.0319806i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.10309 | 0.510145 | 0.255072 | − | 0.966922i | \(-0.417901\pi\) | ||||
0.255072 | + | 0.966922i | \(0.417901\pi\) | |||||||
\(38\) | 0.730604 | − | 0.126207i | 0.118520 | − | 0.0204735i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.337729 | + | 0.584963i | 0.0533996 | + | 0.0924908i | ||||
\(41\) | −1.75010 | − | 3.03127i | −0.273320 | − | 0.473404i | 0.696390 | − | 0.717664i | \(-0.254788\pi\) |
−0.969710 | + | 0.244259i | \(0.921455\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.39266 | − | 2.41216i | −0.212379 | − | 0.367852i | 0.740079 | − | 0.672519i | \(-0.234788\pi\) |
−0.952459 | + | 0.304668i | \(0.901455\pi\) | |||||||
\(44\) | 5.25546 | − | 9.10273i | 0.792291 | − | 1.37229i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.649086 | 0.0957025 | ||||||||
\(47\) | 4.26432 | − | 7.38603i | 0.622016 | − | 1.07736i | −0.367094 | − | 0.930184i | \(-0.619647\pi\) |
0.989110 | − | 0.147179i | \(-0.0470193\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.95227 | −0.993182 | ||||||||
\(50\) | −0.170095 | −0.0240550 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.94720 | + | 10.3009i | 0.824729 | + | 1.42847i | ||||
\(53\) | −2.57461 | + | 4.45936i | −0.353650 | + | 0.612540i | −0.986886 | − | 0.161419i | \(-0.948393\pi\) |
0.633236 | + | 0.773959i | \(0.281726\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.66630 | + | 4.61817i | 0.359524 | + | 0.622714i | ||||
\(56\) | −0.147566 | −0.0197194 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.178647 | 0.0234575 | ||||||||
\(59\) | 5.95070 | + | 10.3069i | 0.774715 | + | 1.34185i | 0.934954 | + | 0.354768i | \(0.115440\pi\) |
−0.160239 | + | 0.987078i | \(0.551227\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.25799 | − | 3.91096i | 0.289106 | − | 0.500747i | −0.684490 | − | 0.729022i | \(-0.739975\pi\) |
0.973597 | + | 0.228275i | \(0.0733085\pi\) | |||||||
\(62\) | 0.226210 | + | 0.391807i | 0.0287287 | + | 0.0497595i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.31397 | −0.914247 | ||||||||
\(65\) | −6.03450 | −0.748487 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.30165 | − | 5.71862i | 0.403360 | − | 0.698641i | −0.590769 | − | 0.806841i | \(-0.701175\pi\) |
0.994129 | + | 0.108200i | \(0.0345088\pi\) | |||||||
\(68\) | 12.9126 | 1.56588 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0185802 | − | 0.0321818i | 0.00222076 | − | 0.00384646i | ||||
\(71\) | 3.12329 | + | 5.40970i | 0.370666 | + | 0.642013i | 0.989668 | − | 0.143376i | \(-0.0457960\pi\) |
−0.619002 | + | 0.785390i | \(0.712463\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.31536 | − | 5.74237i | −0.388033 | − | 0.672093i | 0.604152 | − | 0.796869i | \(-0.293512\pi\) |
−0.992185 | + | 0.124776i | \(0.960179\pi\) | |||||||
\(74\) | 0.263909 | + | 0.457104i | 0.0306788 | + | 0.0531373i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.49971 | − | 6.60078i | −0.630859 | − | 0.757161i | ||||
\(77\) | −1.16501 | −0.132765 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.80793 | − | 3.13143i | −0.203409 | − | 0.352314i | 0.746216 | − | 0.665704i | \(-0.231869\pi\) |
−0.949624 | + | 0.313390i | \(0.898535\pi\) | |||||||
\(80\) | 1.91362 | − | 3.31449i | 0.213949 | − | 0.370571i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.297683 | − | 0.515602i | 0.0328736 | − | 0.0569387i | ||||
\(83\) | −8.39679 | −0.921668 | −0.460834 | − | 0.887486i | \(-0.652450\pi\) | ||||
−0.460834 | + | 0.887486i | \(0.652450\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.27554 | + | 5.67340i | −0.355282 | + | 0.615366i | ||||
\(86\) | 0.236884 | − | 0.410296i | 0.0255439 | − | 0.0442434i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.60195 | 0.383969 | ||||||||
\(89\) | −4.79182 | + | 8.29967i | −0.507932 | + | 0.879764i | 0.492026 | + | 0.870581i | \(0.336256\pi\) |
−0.999958 | + | 0.00918326i | \(0.997077\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.659175 | − | 1.14172i | 0.0691003 | − | 0.119685i | ||||
\(92\) | −3.76083 | − | 6.51394i | −0.392093 | − | 0.679126i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.45068 | 0.149626 | ||||||||
\(95\) | 4.29528 | − | 0.741981i | 0.440687 | − | 0.0761256i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.95622 | + | 13.7806i | 0.807832 | + | 1.39921i | 0.914362 | + | 0.404897i | \(0.132693\pi\) |
−0.106530 | + | 0.994309i | \(0.533974\pi\) | |||||||
\(98\) | −0.591272 | − | 1.02411i | −0.0597275 | − | 0.103451i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.985534 | + | 1.70699i | 0.0985534 | + | 0.170699i | ||||
\(101\) | 2.74154 | − | 4.74848i | 0.272793 | − | 0.472492i | −0.696783 | − | 0.717282i | \(-0.745386\pi\) |
0.969576 | + | 0.244791i | \(0.0787192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.51533 | −0.740508 | −0.370254 | − | 0.928931i | \(-0.620729\pi\) | ||||
−0.370254 | + | 0.928931i | \(0.620729\pi\) | |||||||
\(104\) | −2.03802 | + | 3.52996i | −0.199845 | + | 0.346141i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.875855 | −0.0850706 | ||||||||
\(107\) | −11.2010 | −1.08284 | −0.541421 | − | 0.840751i | \(-0.682114\pi\) | ||||
−0.541421 | + | 0.840751i | \(0.682114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.11443 | − | 7.12641i | −0.394091 | − | 0.682586i | 0.598894 | − | 0.800829i | \(-0.295607\pi\) |
−0.992985 | + | 0.118243i | \(0.962274\pi\) | |||||||
\(110\) | −0.453524 | + | 0.785526i | −0.0432418 | + | 0.0748970i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.418067 | + | 0.724113i | 0.0395036 | + | 0.0684223i | ||||
\(113\) | 11.2410 | 1.05746 | 0.528731 | − | 0.848789i | \(-0.322668\pi\) | ||||
0.528731 | + | 0.848789i | \(0.322668\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.81603 | 0.355847 | ||||||||
\(116\) | −1.03509 | − | 1.79283i | −0.0961055 | − | 0.166460i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.01218 | + | 1.75315i | −0.0931789 | + | 0.161391i | ||||
\(119\) | −0.715603 | − | 1.23946i | −0.0655992 | − | 0.113621i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.4367 | 1.58515 | ||||||||
\(122\) | 0.768145 | 0.0695446 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.62133 | − | 4.54028i | 0.235403 | − | 0.407729i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.99890 | + | 8.65834i | −0.443580 | + | 0.768304i | −0.997952 | − | 0.0639656i | \(-0.979625\pi\) |
0.554372 | + | 0.832269i | \(0.312959\pi\) | |||||||
\(128\) | −2.62394 | − | 4.54480i | −0.231926 | − | 0.401707i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.513218 | − | 0.888919i | −0.0450122 | − | 0.0779634i | ||||
\(131\) | 8.74252 | + | 15.1425i | 0.763837 | + | 1.32301i | 0.940859 | + | 0.338798i | \(0.110020\pi\) |
−0.177022 | + | 0.984207i | \(0.556646\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.328811 | + | 0.893716i | −0.0285115 | + | 0.0774950i | ||||
\(134\) | 1.12318 | 0.0970283 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.21248 | + | 3.83214i | 0.189719 | + | 0.328603i | ||||
\(137\) | −6.68642 | + | 11.5812i | −0.571259 | + | 0.989450i | 0.425178 | + | 0.905110i | \(0.360212\pi\) |
−0.996437 | + | 0.0843402i | \(0.973122\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.46095 | − | 7.72659i | 0.378373 | − | 0.655360i | −0.612453 | − | 0.790507i | \(-0.709817\pi\) |
0.990826 | + | 0.135146i | \(0.0431505\pi\) | |||||||
\(140\) | −0.430617 | −0.0363938 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.531255 | + | 0.920160i | −0.0445819 | + | 0.0772181i | ||||
\(143\) | −16.0898 | + | 27.8684i | −1.34550 | + | 2.33047i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.05028 | 0.0872212 | ||||||||
\(146\) | 0.563924 | − | 0.976745i | 0.0466707 | − | 0.0808360i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.05820 | − | 5.29696i | 0.251382 | − | 0.435407i | ||||
\(149\) | −8.59072 | − | 14.8796i | −0.703779 | − | 1.21898i | −0.967130 | − | 0.254281i | \(-0.918161\pi\) |
0.263351 | − | 0.964700i | \(-0.415172\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.4475 | −1.66399 | −0.831996 | − | 0.554781i | \(-0.812802\pi\) | ||||
−0.831996 | + | 0.554781i | \(0.812802\pi\) | |||||||
\(152\) | 1.01661 | − | 2.76317i | 0.0824578 | − | 0.224123i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0990808 | − | 0.171613i | −0.00798416 | − | 0.0138290i | ||||
\(155\) | 1.32991 | + | 2.30346i | 0.106821 | + | 0.185019i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.15365 | + | 5.46228i | 0.251689 | + | 0.435937i | 0.963991 | − | 0.265935i | \(-0.0856808\pi\) |
−0.712302 | + | 0.701873i | \(0.752347\pi\) | |||||||
\(158\) | 0.307520 | − | 0.532640i | 0.0244650 | − | 0.0423746i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.00191 | 0.158265 | ||||||||
\(161\) | −0.416842 | + | 0.721991i | −0.0328517 | + | 0.0569009i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.20330 | −0.329228 | −0.164614 | − | 0.986358i | \(-0.552638\pi\) | ||||
−0.164614 | + | 0.986358i | \(0.552638\pi\) | |||||||
\(164\) | −6.89914 | −0.538732 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.714124 | − | 1.23690i | −0.0554268 | − | 0.0960020i | ||||
\(167\) | −2.32721 | + | 4.03085i | −0.180085 | + | 0.311916i | −0.941909 | − | 0.335867i | \(-0.890971\pi\) |
0.761824 | + | 0.647784i | \(0.224304\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.7076 | − | 20.2781i | −0.900584 | − | 1.55986i | ||||
\(170\) | −1.11430 | −0.0854631 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.49007 | −0.418614 | ||||||||
\(173\) | −11.8837 | − | 20.5831i | −0.903500 | − | 1.56491i | −0.822919 | − | 0.568159i | \(-0.807656\pi\) |
−0.0805809 | − | 0.996748i | \(-0.525678\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.109234 | − | 0.189200i | 0.00825735 | − | 0.0143021i | ||||
\(176\) | −10.2046 | − | 17.6749i | −0.769200 | − | 1.33229i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.63012 | −0.122183 | ||||||||
\(179\) | −13.7265 | −1.02597 | −0.512984 | − | 0.858398i | \(-0.671460\pi\) | ||||
−0.512984 | + | 0.858398i | \(0.671460\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.9708 | + | 19.0020i | −0.815454 | + | 1.41241i | 0.0935470 | + | 0.995615i | \(0.470179\pi\) |
−0.909001 | + | 0.416793i | \(0.863154\pi\) | |||||||
\(182\) | 0.224244 | 0.0166221 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.28878 | − | 2.23224i | 0.0950103 | − | 0.164563i | ||||
\(185\) | 1.55154 | + | 2.68735i | 0.114072 | + | 0.197578i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.4672 | + | 30.2540i | 1.27732 | + | 2.21239i | ||||
\(188\) | −8.40527 | − | 14.5584i | −0.613017 | − | 1.06178i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.474601 | + | 0.569619i | 0.0344311 | + | 0.0413245i | ||||
\(191\) | −11.9978 | −0.868132 | −0.434066 | − | 0.900881i | \(-0.642921\pi\) | ||||
−0.434066 | + | 0.900881i | \(0.642921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.83782 | − | 10.1114i | −0.420216 | − | 0.727835i | 0.575745 | − | 0.817630i | \(-0.304712\pi\) |
−0.995960 | + | 0.0897947i | \(0.971379\pi\) | |||||||
\(194\) | −1.35331 | + | 2.34400i | −0.0971620 | + | 0.168290i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.85170 | + | 11.8675i | −0.489407 | + | 0.847678i | ||||
\(197\) | −10.3275 | −0.735801 | −0.367901 | − | 0.929865i | \(-0.619923\pi\) | ||||
−0.367901 | + | 0.929865i | \(0.619923\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.63560 | − | 8.02910i | 0.328609 | − | 0.569168i | −0.653627 | − | 0.756817i | \(-0.726753\pi\) |
0.982236 | + | 0.187649i | \(0.0600868\pi\) | |||||||
\(200\) | −0.337729 | + | 0.584963i | −0.0238810 | + | 0.0413631i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.932641 | 0.0656204 | ||||||||
\(203\) | −0.114727 | + | 0.198713i | −0.00805225 | + | 0.0139469i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.75010 | − | 3.03127i | 0.122232 | − | 0.211713i | ||||
\(206\) | −0.639159 | − | 1.10706i | −0.0445323 | − | 0.0771322i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 23.0955 | 1.60138 | ||||||||
\(209\) | 8.02593 | − | 21.8147i | 0.555166 | − | 1.50895i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.526860 | + | 0.912548i | 0.0362705 | + | 0.0628224i | 0.883591 | − | 0.468260i | \(-0.155119\pi\) |
−0.847320 | + | 0.531082i | \(0.821786\pi\) | |||||||
\(212\) | 5.07474 | + | 8.78970i | 0.348534 | + | 0.603679i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.952615 | − | 1.64998i | −0.0651195 | − | 0.112790i | ||||
\(215\) | 1.39266 | − | 2.41216i | 0.0949789 | − | 0.164508i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.581086 | −0.0394467 | ||||||||
\(218\) | 0.699843 | − | 1.21216i | 0.0473993 | − | 0.0820980i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.5109 | 0.708647 | ||||||||
\(221\) | −39.5325 | −2.65924 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0822 | − | 22.6591i | −0.876052 | − | 1.51737i | −0.855638 | − | 0.517574i | \(-0.826835\pi\) |
−0.0204133 | − | 0.999792i | \(-0.506498\pi\) | |||||||
\(224\) | −0.218677 | + | 0.378760i | −0.0146110 | + | 0.0253070i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.956015 | + | 1.65587i | 0.0635932 | + | 0.110147i | ||||
\(227\) | 15.2808 | 1.01422 | 0.507111 | − | 0.861881i | \(-0.330713\pi\) | ||||
0.507111 | + | 0.861881i | \(0.330713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5223 | −0.893581 | −0.446791 | − | 0.894639i | \(-0.647433\pi\) | ||||
−0.446791 | + | 0.894639i | \(0.647433\pi\) | |||||||
\(230\) | 0.324543 | + | 0.562125i | 0.0213997 | + | 0.0370654i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.354710 | − | 0.614376i | 0.0232879 | − | 0.0403358i | ||||
\(233\) | 2.45230 | + | 4.24751i | 0.160656 | + | 0.278264i | 0.935104 | − | 0.354373i | \(-0.115306\pi\) |
−0.774448 | + | 0.632637i | \(0.781972\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.52865 | 0.556348 | ||||||||
\(236\) | 23.4585 | 1.52702 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.121720 | − | 0.210826i | 0.00788995 | − | 0.0136658i | ||||
\(239\) | −18.0191 | −1.16556 | −0.582780 | − | 0.812630i | \(-0.698035\pi\) | ||||
−0.582780 | + | 0.812630i | \(0.698035\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.5193 | − | 25.1482i | 0.935273 | − | 1.61994i | 0.161125 | − | 0.986934i | \(-0.448488\pi\) |
0.774147 | − | 0.633006i | \(-0.218179\pi\) | |||||||
\(242\) | 1.48294 | + | 2.56853i | 0.0953272 | + | 0.165112i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.45066 | − | 7.70877i | −0.284924 | − | 0.493503i | ||||
\(245\) | −3.47614 | − | 6.02084i | −0.222082 | − | 0.384658i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.8376 | + | 20.2085i | 1.07135 | + | 1.28584i | ||||
\(248\) | 1.79659 | 0.114083 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.0850473 | − | 0.147306i | −0.00537886 | − | 0.00931646i | ||||
\(251\) | −14.4094 | + | 24.9578i | −0.909514 | + | 1.57532i | −0.0947735 | + | 0.995499i | \(0.530213\pi\) |
−0.814741 | + | 0.579826i | \(0.803121\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.1747 | − | 17.6231i | 0.639678 | − | 1.10795i | ||||
\(254\) | −1.70057 | −0.106703 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.86766 | + | 11.8951i | −0.429229 | + | 0.743446i | ||||
\(257\) | −5.87925 | + | 10.1832i | −0.366737 | + | 0.635208i | −0.989053 | − | 0.147558i | \(-0.952859\pi\) |
0.622316 | + | 0.782766i | \(0.286192\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.677928 | −0.0421244 | ||||||||
\(260\) | −5.94720 | + | 10.3009i | −0.368830 | + | 0.638832i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.48706 | + | 2.57565i | −0.0918706 | + | 0.159124i | ||||
\(263\) | 4.42603 | + | 7.66611i | 0.272921 | + | 0.472713i | 0.969608 | − | 0.244662i | \(-0.0786769\pi\) |
−0.696688 | + | 0.717375i | \(0.745344\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.14923 | −0.316314 | ||||||||
\(266\) | −0.159614 | + | 0.0275723i | −0.00978658 | + | 0.00169056i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.50777 | − | 11.2718i | −0.397525 | − | 0.688534i | ||||
\(269\) | 9.01236 | + | 15.6099i | 0.549493 | + | 0.951750i | 0.998309 | + | 0.0581261i | \(0.0185126\pi\) |
−0.448816 | + | 0.893624i | \(0.648154\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0833046 | − | 0.144288i | −0.00506040 | − | 0.00876486i | 0.863484 | − | 0.504376i | \(-0.168277\pi\) |
−0.868545 | + | 0.495611i | \(0.834944\pi\) | |||||||
\(272\) | 12.5363 | − | 21.7135i | 0.760124 | − | 1.31657i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.27465 | −0.137416 | ||||||||
\(275\) | −2.66630 | + | 4.61817i | −0.160784 | + | 0.278486i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.4262 | 1.10712 | 0.553560 | − | 0.832809i | \(-0.313269\pi\) | ||||
0.553560 | + | 0.832809i | \(0.313269\pi\) | |||||||
\(278\) | 1.51757 | 0.0910175 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.0737832 | − | 0.127796i | −0.00440939 | − | 0.00763728i | ||||
\(281\) | 15.0338 | − | 26.0394i | 0.896844 | − | 1.55338i | 0.0653383 | − | 0.997863i | \(-0.479187\pi\) |
0.831506 | − | 0.555516i | \(-0.187479\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.37959 | + | 5.85362i | 0.200896 | + | 0.347962i | 0.948817 | − | 0.315826i | \(-0.102281\pi\) |
−0.747922 | + | 0.663787i | \(0.768948\pi\) | |||||||
\(284\) | 12.3124 | 0.730609 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.47358 | −0.323659 | ||||||||
\(287\) | 0.382343 | + | 0.662237i | 0.0225690 | + | 0.0390906i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9583 | + | 22.4444i | −0.762253 | + | 1.32026i | ||||
\(290\) | 0.0893236 | + | 0.154713i | 0.00524526 | + | 0.00908506i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.0696 | −0.764840 | ||||||||
\(293\) | −26.0167 | −1.51991 | −0.759957 | − | 0.649973i | \(-0.774780\pi\) | ||||
−0.759957 | + | 0.649973i | \(0.774780\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.95070 | + | 10.3069i | −0.346463 | + | 0.600092i | ||||
\(296\) | 2.09600 | 0.121828 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.46123 | − | 2.53093i | 0.0846471 | − | 0.146613i | ||||
\(299\) | 11.5139 | + | 19.9427i | 0.665867 | + | 1.15332i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.304254 | + | 0.526983i | 0.0175369 | + | 0.0303748i | ||||
\(302\) | −1.73900 | − | 3.01204i | −0.100068 | − | 0.173323i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −16.4391 | + | 2.83974i | −0.942847 | + | 0.162870i | ||||
\(305\) | 4.51599 | 0.258585 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.57544 | − | 11.3890i | −0.375280 | − | 0.650004i | 0.615089 | − | 0.788458i | \(-0.289120\pi\) |
−0.990369 | + | 0.138454i | \(0.955787\pi\) | |||||||
\(308\) | −1.14816 | + | 1.98866i | −0.0654222 | + | 0.113315i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.226210 | + | 0.391807i | −0.0128478 | + | 0.0222531i | ||||
\(311\) | 3.98871 | 0.226179 | 0.113089 | − | 0.993585i | \(-0.463925\pi\) | ||||
0.113089 | + | 0.993585i | \(0.463925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.659360 | − | 1.14205i | 0.0372692 | − | 0.0645522i | −0.846789 | − | 0.531929i | \(-0.821467\pi\) |
0.884058 | + | 0.467377i | \(0.154801\pi\) | |||||||
\(314\) | −0.536418 | + | 0.929104i | −0.0302718 | + | 0.0524324i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.12712 | −0.400932 | ||||||||
\(317\) | −0.370562 | + | 0.641833i | −0.0208129 | + | 0.0360489i | −0.876244 | − | 0.481867i | \(-0.839959\pi\) |
0.855431 | + | 0.517916i | \(0.173292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.80037 | − | 4.85038i | 0.156791 | − | 0.271569i | ||||
\(320\) | −3.65699 | − | 6.33409i | −0.204432 | − | 0.354086i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.141805 | −0.00790249 | ||||||||
\(323\) | 28.1387 | − | 4.86077i | 1.56568 | − | 0.270461i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.01725 | − | 5.22603i | −0.167367 | − | 0.289888i | ||||
\(326\) | −0.357480 | − | 0.619173i | −0.0197990 | − | 0.0342928i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.18212 | − | 2.04749i | −0.0652716 | − | 0.113054i | ||||
\(329\) | −0.931622 | + | 1.61362i | −0.0513620 | + | 0.0889616i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3519 | 0.623958 | 0.311979 | − | 0.950089i | \(-0.399008\pi\) | ||||
0.311979 | + | 0.950089i | \(0.399008\pi\) | |||||||
\(332\) | −8.27532 | + | 14.3333i | −0.454167 | + | 0.786641i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.791692 | −0.0433195 | ||||||||
\(335\) | 6.60329 | 0.360776 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.3960 | + | 21.4705i | 0.675253 | + | 1.16957i | 0.976395 | + | 0.215993i | \(0.0692988\pi\) |
−0.301142 | + | 0.953579i | \(0.597368\pi\) | |||||||
\(338\) | 1.99140 | − | 3.44920i | 0.108318 | − | 0.187612i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.45631 | + | 11.1827i | 0.350142 | + | 0.606464i | ||||
\(341\) | 14.1837 | 0.768092 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.04814 | 0.164584 | ||||||||
\(344\) | −0.940684 | − | 1.62931i | −0.0507183 | − | 0.0878467i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.02135 | − | 3.50108i | 0.108668 | − | 0.188219i | ||||
\(347\) | −15.6066 | − | 27.0315i | −0.837807 | − | 1.45112i | −0.891724 | − | 0.452579i | \(-0.850504\pi\) |
0.0539174 | − | 0.998545i | \(-0.482829\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.67972 | 0.143442 | 0.0717212 | − | 0.997425i | \(-0.477151\pi\) | ||||
0.0717212 | + | 0.997425i | \(0.477151\pi\) | |||||||
\(350\) | 0.0371604 | 0.00198631 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.33769 | − | 9.24515i | 0.284500 | − | 0.492768i | ||||
\(353\) | 29.6238 | 1.57671 | 0.788357 | − | 0.615218i | \(-0.210932\pi\) | ||||
0.788357 | + | 0.615218i | \(0.210932\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.12329 | + | 5.40970i | −0.165767 | + | 0.287117i | ||||
\(356\) | 9.44500 | + | 16.3592i | 0.500584 | + | 0.867037i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.16740 | − | 2.02200i | −0.0616992 | − | 0.106866i | ||||
\(359\) | 10.9641 | + | 18.9904i | 0.578664 | + | 1.00228i | 0.995633 | + | 0.0933549i | \(0.0297591\pi\) |
−0.416969 | + | 0.908921i | \(0.636908\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4695 | − | 12.3139i | −0.761555 | − | 0.648100i | ||||
\(362\) | −3.73215 | −0.196158 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.29928 | − | 2.25042i | −0.0681007 | − | 0.117954i | ||||
\(365\) | 3.31536 | − | 5.74237i | 0.173534 | − | 0.300569i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.87305 | + | 11.9045i | −0.358770 | + | 0.621408i | −0.987756 | − | 0.156009i | \(-0.950137\pi\) |
0.628985 | + | 0.777417i | \(0.283470\pi\) | |||||||
\(368\) | −14.6049 | −0.761332 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.263909 | + | 0.457104i | −0.0137200 | + | 0.0237637i | ||||
\(371\) | 0.562473 | − | 0.974232i | 0.0292021 | − | 0.0505796i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.8295 | −1.18207 | −0.591034 | − | 0.806646i | \(-0.701280\pi\) | ||||
−0.591034 | + | 0.806646i | \(0.701280\pi\) | |||||||
\(374\) | −2.97107 | + | 5.14604i | −0.153630 | + | 0.266095i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.88037 | − | 4.98894i | 0.148544 | − | 0.257285i | ||||
\(377\) | 3.16896 | + | 5.48880i | 0.163210 | + | 0.282688i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.9938 | 1.48931 | 0.744656 | − | 0.667449i | \(-0.232614\pi\) | ||||
0.744656 | + | 0.667449i | \(0.232614\pi\) | |||||||
\(380\) | 2.96659 | − | 8.06327i | 0.152183 | − | 0.413637i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.02038 | − | 1.76735i | −0.0522073 | − | 0.0904257i | ||||
\(383\) | 13.0687 | + | 22.6357i | 0.667781 | + | 1.15663i | 0.978523 | + | 0.206137i | \(0.0660891\pi\) |
−0.310742 | + | 0.950494i | \(0.600578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.582504 | − | 1.00893i | −0.0296872 | − | 0.0514197i | ||||
\(386\) | 0.992982 | − | 1.71989i | 0.0505414 | − | 0.0875403i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 31.3645 | 1.59229 | ||||||||
\(389\) | 11.7728 | − | 20.3911i | 0.596906 | − | 1.03387i | −0.396369 | − | 0.918091i | \(-0.629730\pi\) |
0.993275 | − | 0.115780i | \(-0.0369369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9991 | 1.26426 | ||||||||
\(392\) | −4.69596 | −0.237182 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.878323 | − | 1.52130i | −0.0442493 | − | 0.0766420i | ||||
\(395\) | 1.80793 | − | 3.13143i | 0.0909670 | − | 0.157560i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.95863 | − | 13.7847i | −0.399432 | − | 0.691837i | 0.594224 | − | 0.804300i | \(-0.297459\pi\) |
−0.993656 | + | 0.112463i | \(0.964126\pi\) | |||||||
\(398\) | 1.57698 | 0.0790470 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.82724 | 0.191362 | ||||||||
\(401\) | 11.1575 | + | 19.3254i | 0.557179 | + | 0.965063i | 0.997730 | + | 0.0673353i | \(0.0214497\pi\) |
−0.440551 | + | 0.897728i | \(0.645217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.02531 | + | 13.9003i | −0.399769 | + | 0.692421i | ||||
\(404\) | −5.40376 | − | 9.35958i | −0.268847 | − | 0.465657i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0390289 | −0.00193697 | ||||||||
\(407\) | 16.5475 | 0.820232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.356179 | − | 0.616920i | 0.0176119 | − | 0.0305047i | −0.857085 | − | 0.515175i | \(-0.827727\pi\) |
0.874697 | + | 0.484670i | \(0.161060\pi\) | |||||||
\(410\) | 0.595366 | 0.0294030 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.40662 | + | 12.8286i | −0.364898 | + | 0.632022i | ||||
\(413\) | −1.30004 | − | 2.25174i | −0.0639709 | − | 0.110801i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.19840 | − | 7.27183i | −0.206091 | − | 0.356960i | ||||
\(416\) | 6.04025 | + | 10.4620i | 0.296148 | + | 0.512943i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.89603 | − | 0.673012i | 0.190561 | − | 0.0329181i | ||||
\(419\) | 30.0670 | 1.46887 | 0.734434 | − | 0.678681i | \(-0.237448\pi\) | ||||
0.734434 | + | 0.678681i | \(0.237448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4858 | + | 19.8939i | 0.559781 | + | 0.969570i | 0.997514 | + | 0.0704646i | \(0.0224482\pi\) |
−0.437733 | + | 0.899105i | \(0.644218\pi\) | |||||||
\(422\) | −0.0896160 | + | 0.155220i | −0.00436244 | + | 0.00755597i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.73904 | + | 3.01211i | −0.0844553 | + | 0.146281i | ||||
\(425\) | −6.55108 | −0.317774 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.493301 | + | 0.854423i | −0.0238725 | + | 0.0413484i | ||||
\(428\) | −11.0390 | + | 19.1201i | −0.533589 | + | 0.924203i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.473769 | 0.0228472 | ||||||||
\(431\) | 11.6935 | − | 20.2538i | 0.563258 | − | 0.975592i | −0.433951 | − | 0.900937i | \(-0.642881\pi\) |
0.997209 | − | 0.0746557i | \(-0.0237858\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.7300 | + | 28.9773i | −0.803994 | + | 1.39256i | 0.112974 | + | 0.993598i | \(0.463962\pi\) |
−0.916968 | + | 0.398961i | \(0.869371\pi\) | |||||||
\(434\) | −0.0494198 | − | 0.0855976i | −0.00237223 | − | 0.00410881i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.2197 | −0.776780 | ||||||||
\(437\) | −10.6475 | − | 12.7793i | −0.509341 | − | 0.611315i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.72611 | − | 15.1141i | −0.416474 | − | 0.721355i | 0.579108 | − | 0.815251i | \(-0.303401\pi\) |
−0.995582 | + | 0.0938963i | \(0.970068\pi\) | |||||||
\(440\) | 1.80097 | + | 3.11938i | 0.0858580 | + | 0.148710i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.36213 | − | 5.82338i | −0.159920 | − | 0.276990i | ||||
\(443\) | 7.57846 | − | 13.1263i | 0.360063 | − | 0.623648i | −0.627908 | − | 0.778288i | \(-0.716088\pi\) |
0.987971 | + | 0.154640i | \(0.0494218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.58364 | −0.454308 | ||||||||
\(446\) | 2.22522 | − | 3.85419i | 0.105367 | − | 0.182501i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.59788 | 0.0754925 | ||||||||
\(449\) | −13.1961 | −0.622762 | −0.311381 | − | 0.950285i | \(-0.600792\pi\) | ||||
−0.311381 | + | 0.950285i | \(0.600792\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.33261 | − | 16.1645i | −0.439455 | − | 0.761159i | ||||
\(452\) | 11.0784 | − | 19.1883i | 0.521083 | − | 0.902542i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.29959 | + | 2.25096i | 0.0609928 | + | 0.105643i | ||||
\(455\) | 1.31835 | 0.0618052 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.20019 | −0.196477 | −0.0982383 | − | 0.995163i | \(-0.531321\pi\) | ||||
−0.0982383 | + | 0.995163i | \(0.531321\pi\) | |||||||
\(458\) | −1.15004 | − | 1.99192i | −0.0537377 | − | 0.0930765i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.76083 | − | 6.51394i | 0.175349 | − | 0.303714i | ||||
\(461\) | −10.0039 | − | 17.3273i | −0.465928 | − | 0.807011i | 0.533315 | − | 0.845917i | \(-0.320946\pi\) |
−0.999243 | + | 0.0389056i | \(0.987613\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.4670 | −0.951183 | −0.475591 | − | 0.879666i | \(-0.657766\pi\) | ||||
−0.475591 | + | 0.879666i | \(0.657766\pi\) | |||||||
\(464\) | −4.01968 | −0.186609 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.417123 | + | 0.722479i | −0.0193229 | + | 0.0334682i | ||||
\(467\) | 39.2577 | 1.81663 | 0.908314 | − | 0.418288i | \(-0.137370\pi\) | ||||
0.908314 | + | 0.418288i | \(0.137370\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.721307 | + | 1.24934i | −0.0333069 | + | 0.0576892i | ||||
\(470\) | 0.725338 | + | 1.25632i | 0.0334574 | + | 0.0579498i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.01944 | + | 6.96188i | 0.185010 | + | 0.320446i | ||||
\(473\) | −7.42653 | − | 12.8631i | −0.341472 | − | 0.591447i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.79022 | + | 3.34883i | 0.128024 | + | 0.153655i | ||||
\(476\) | −2.82100 | −0.129301 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.53248 | − | 2.65433i | −0.0700939 | − | 0.121406i | ||||
\(479\) | 3.62557 | − | 6.27967i | 0.165656 | − | 0.286925i | −0.771232 | − | 0.636554i | \(-0.780359\pi\) |
0.936888 | + | 0.349629i | \(0.113692\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.36279 | + | 16.2168i | −0.426907 | + | 0.739424i | ||||
\(482\) | 4.93932 | 0.224980 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 17.1845 | − | 29.7643i | 0.781111 | − | 1.35292i | ||||
\(485\) | −7.95622 | + | 13.7806i | −0.361274 | + | 0.625744i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.16094 | −0.188550 | −0.0942751 | − | 0.995546i | \(-0.530053\pi\) | ||||
−0.0942751 | + | 0.995546i | \(0.530053\pi\) | |||||||
\(488\) | 1.52518 | − | 2.64169i | 0.0690415 | − | 0.119583i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.591272 | − | 1.02411i | 0.0267109 | − | 0.0462647i | ||||
\(491\) | −2.96842 | − | 5.14145i | −0.133963 | − | 0.232030i | 0.791238 | − | 0.611508i | \(-0.209437\pi\) |
−0.925201 | + | 0.379478i | \(0.876104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.88048 | 0.309881 | ||||||||
\(494\) | −1.54485 | + | 4.19896i | −0.0695063 | + | 0.188920i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.08987 | − | 8.81592i | −0.228542 | − | 0.395846i | ||||
\(497\) | −0.682342 | − | 1.18185i | −0.0306072 | − | 0.0530133i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.19537 | + | 2.07045i | 0.0535123 | + | 0.0926860i | 0.891541 | − | 0.452941i | \(-0.149625\pi\) |
−0.838028 | + | 0.545627i | \(0.816292\pi\) | |||||||
\(500\) | −0.985534 | + | 1.70699i | −0.0440744 | + | 0.0763391i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.90193 | −0.218784 | ||||||||
\(503\) | 10.0317 | − | 17.3754i | 0.447290 | − | 0.774729i | −0.550918 | − | 0.834559i | \(-0.685722\pi\) |
0.998209 | + | 0.0598298i | \(0.0190558\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.48308 | 0.243994 | ||||||||
\(506\) | 3.46132 | 0.153874 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 9.85316 | + | 17.0662i | 0.437163 | + | 0.757189i | ||||
\(509\) | 12.9575 | − | 22.4430i | 0.574329 | − | 0.994767i | −0.421785 | − | 0.906696i | \(-0.638596\pi\) |
0.996114 | − | 0.0880712i | \(-0.0280703\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.724302 | + | 1.25453i | 0.0320413 | + | 0.0554971i | ||||
\(512\) | −12.8321 | −0.567103 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.00006 | −0.0882187 | ||||||||
\(515\) | −3.75767 | − | 6.50847i | −0.165583 | − | 0.286797i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.7400 | − | 39.3868i | 1.00010 | − | 1.73223i | ||||
\(518\) | −0.0576560 | − | 0.0998630i | −0.00253326 | − | 0.00438773i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.07604 | −0.178746 | ||||||||
\(521\) | −21.0579 | −0.922562 | −0.461281 | − | 0.887254i | \(-0.652610\pi\) | ||||
−0.461281 | + | 0.887254i | \(0.652610\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.57494 | + | 16.5843i | −0.418683 | + | 0.725180i | −0.995807 | − | 0.0914762i | \(-0.970841\pi\) |
0.577124 | + | 0.816656i | \(0.304175\pi\) | |||||||
\(524\) | 34.4642 | 1.50558 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.752844 | + | 1.30396i | −0.0328256 | + | 0.0568555i | ||||
\(527\) | 8.71231 | + | 15.0902i | 0.379514 | + | 0.657338i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.21896 | + | 7.30745i | 0.183433 | + | 0.317715i | ||||
\(530\) | −0.437928 | − | 0.758513i | −0.0190224 | − | 0.0329477i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.20151 | + | 1.44207i | 0.0520923 | + | 0.0625215i | ||||
\(533\) | 21.1220 | 0.914895 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.60051 | − | 9.70036i | −0.242131 | − | 0.419383i | ||||
\(536\) | 2.23012 | − | 3.86268i | 0.0963265 | − | 0.166842i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.53295 | + | 2.65515i | −0.0660903 | + | 0.114472i | ||||
\(539\) | −37.0737 | −1.59688 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.84592 | − | 11.8575i | 0.294329 | − | 0.509793i | −0.680499 | − | 0.732749i | \(-0.738237\pi\) |
0.974829 | + | 0.222956i | \(0.0715705\pi\) | |||||||
\(542\) | 0.0141697 | − | 0.0245426i | 0.000608639 | − | 0.00105419i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.1146 | 0.562286 | ||||||||
\(545\) | 4.11443 | − | 7.12641i | 0.176243 | − | 0.305262i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.7556 | − | 22.0934i | 0.545391 | − | 0.944645i | −0.453191 | − | 0.891413i | \(-0.649714\pi\) |
0.998582 | − | 0.0532318i | \(-0.0169522\pi\) | |||||||
\(548\) | 13.1794 | + | 22.8274i | 0.562995 | + | 0.975137i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.907047 | −0.0386766 | ||||||||
\(551\) | −2.93051 | − | 3.51722i | −0.124844 | − | 0.149839i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.394977 | + | 0.684121i | 0.0167961 | + | 0.0290918i | ||||
\(554\) | 1.56710 | + | 2.71429i | 0.0665795 | + | 0.115319i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.79283 | − | 15.2296i | −0.372899 | − | 0.645880i | ||||
\(557\) | −5.49373 | + | 9.51541i | −0.232777 | + | 0.403181i | −0.958624 | − | 0.284675i | \(-0.908114\pi\) |
0.725848 | + | 0.687856i | \(0.241448\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.8081 | 0.710905 | ||||||||
\(560\) | −0.418067 | + | 0.724113i | −0.0176666 | + | 0.0305994i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.11435 | 0.215736 | ||||||||
\(563\) | −5.57158 | −0.234814 | −0.117407 | − | 0.993084i | \(-0.537458\pi\) | ||||
−0.117407 | + | 0.993084i | \(0.537458\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.62049 | + | 9.73498i | 0.236456 | + | 0.409553i | ||||
\(566\) | −0.574850 | + | 0.995669i | −0.0241627 | + | 0.0418511i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.10965 | + | 3.65402i | 0.0885189 | + | 0.153319i | ||||
\(569\) | −21.9856 | −0.921685 | −0.460843 | − | 0.887482i | \(-0.652453\pi\) | ||||
−0.460843 | + | 0.887482i | \(0.652453\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1104 | 1.51117 | 0.755586 | − | 0.655050i | \(-0.227352\pi\) | ||||
0.755586 | + | 0.655050i | \(0.227352\pi\) | |||||||
\(572\) | 31.7141 | + | 54.9304i | 1.32603 | + | 2.29676i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.0650344 | + | 0.112643i | −0.00271449 | + | 0.00470163i | ||||
\(575\) | 1.90802 | + | 3.30478i | 0.0795697 | + | 0.137819i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.0931 | −0.628333 | −0.314166 | − | 0.949368i | \(-0.601725\pi\) | ||||
−0.314166 | + | 0.949368i | \(0.601725\pi\) | |||||||
\(578\) | −4.40827 | −0.183360 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.03509 | − | 1.79283i | 0.0429797 | − | 0.0744430i | ||||
\(581\) | 1.83444 | 0.0761053 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.7294 | + | 23.7800i | −0.568614 | + | 0.984868i | ||||
\(584\) | −2.23938 | − | 3.87872i | −0.0926663 | − | 0.160503i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.21265 | − | 3.83243i | −0.0914039 | − | 0.158316i | ||||
\(587\) | 16.1610 | + | 27.9916i | 0.667034 | + | 1.15534i | 0.978729 | + | 0.205155i | \(0.0657699\pi\) |
−0.311695 | + | 0.950182i | \(0.600897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00320 | − | 10.8808i | 0.164949 | − | 0.448335i | ||||
\(590\) | −2.02436 | −0.0833417 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5.93814 | − | 10.2852i | −0.244056 | − | 0.422717i | ||||
\(593\) | 9.82932 | − | 17.0249i | 0.403642 | − | 0.699128i | −0.590520 | − | 0.807023i | \(-0.701077\pi\) |
0.994162 | + | 0.107894i | \(0.0344108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.715603 | − | 1.23946i | 0.0293369 | − | 0.0508129i | ||||
\(596\) | −33.8658 | −1.38720 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.95845 | + | 3.39214i | −0.0800872 | + | 0.138715i | ||||
\(599\) | −0.491006 | + | 0.850447i | −0.0200620 | + | 0.0347483i | −0.875882 | − | 0.482525i | \(-0.839720\pi\) |
0.855820 | + | 0.517274i | \(0.173053\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2561 | 1.47892 | 0.739458 | − | 0.673203i | \(-0.235082\pi\) | ||||
0.739458 | + | 0.673203i | \(0.235082\pi\) | |||||||
\(602\) | −0.0517519 | + | 0.0896369i | −0.00210925 | + | 0.00365333i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.1517 | + | 34.9037i | −0.819961 | + | 1.42021i | ||||
\(605\) | 8.71835 | + | 15.1006i | 0.354451 | + | 0.613927i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.5216 | −1.40119 | −0.700595 | − | 0.713559i | \(-0.747082\pi\) | ||||
−0.700595 | + | 0.713559i | \(0.747082\pi\) | |||||||
\(608\) | −5.58575 | − | 6.70406i | −0.226532 | − | 0.271885i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.384072 | + | 0.665233i | 0.0155506 | + | 0.0269345i | ||||
\(611\) | 25.7331 | + | 44.5710i | 1.04105 | + | 1.80315i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.5283 | + | 30.3599i | 0.707962 | + | 1.22623i | 0.965612 | + | 0.259988i | \(0.0837186\pi\) |
−0.257650 | + | 0.966238i | \(0.582948\pi\) | |||||||
\(614\) | 1.11845 | − | 1.93721i | 0.0451368 | − | 0.0781793i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.786913 | −0.0317056 | ||||||||
\(617\) | 20.0581 | − | 34.7417i | 0.807510 | − | 1.39865i | −0.107073 | − | 0.994251i | \(-0.534148\pi\) |
0.914583 | − | 0.404398i | \(-0.132519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.4071 | −1.58390 | −0.791952 | − | 0.610583i | \(-0.790935\pi\) | ||||
−0.791952 | + | 0.610583i | \(0.790935\pi\) | |||||||
\(620\) | 5.24267 | 0.210551 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.339229 | + | 0.587561i | 0.0136018 | + | 0.0235591i | ||||
\(623\) | 1.04686 | − | 1.81322i | 0.0419417 | − | 0.0726452i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0.224307 | 0.00896512 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 12.4321 | 0.496095 | ||||||||
\(629\) | 10.1643 | + | 17.6051i | 0.405276 | + | 0.701959i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.19428 | + | 7.26471i | −0.166972 | + | 0.289204i | −0.937354 | − | 0.348379i | \(-0.886732\pi\) |
0.770382 | + | 0.637583i | \(0.220066\pi\) | |||||||
\(632\) | −1.22118 | − | 2.11515i | −0.0485760 | − | 0.0841361i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.126061 | −0.00500653 | ||||||||
\(635\) | −9.99779 | −0.396750 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.9767 | − | 36.3328i | 0.831129 | − | 1.43956i | ||||
\(638\) | 0.952655 | 0.0377160 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.62394 | − | 4.54480i | 0.103720 | − | 0.179649i | ||||
\(641\) | −1.14214 | − | 1.97825i | −0.0451120 | − | 0.0781363i | 0.842588 | − | 0.538559i | \(-0.181031\pi\) |
−0.887700 | + | 0.460423i | \(0.847698\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.6063 | − | 35.6912i | −0.812635 | − | 1.40752i | −0.911014 | − | 0.412375i | \(-0.864699\pi\) |
0.0983795 | − | 0.995149i | \(-0.468634\pi\) | |||||||
\(644\) | 0.821624 | + | 1.42309i | 0.0323765 | + | 0.0560778i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.10914 | + | 3.73161i | 0.122328 | + | 0.146818i | ||||
\(647\) | 2.66299 | 0.104693 | 0.0523465 | − | 0.998629i | \(-0.483330\pi\) | ||||
0.0523465 | + | 0.998629i | \(0.483330\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 31.7327 | + | 54.9627i | 1.24562 | + | 2.15748i | ||||
\(650\) | 0.513218 | − | 0.888919i | 0.0201301 | − | 0.0348663i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.14250 | + | 7.17502i | −0.162233 | + | 0.280995i | ||||
\(653\) | −45.2522 | −1.77086 | −0.885428 | − | 0.464777i | \(-0.846135\pi\) | ||||
−0.885428 | + | 0.464777i | \(0.846135\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.74252 | + | 15.1425i | −0.341599 | + | 0.591666i | ||||
\(656\) | −6.69807 | + | 11.6014i | −0.261516 | + | 0.452958i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.316928 | −0.0123551 | ||||||||
\(659\) | 11.6414 | − | 20.1634i | 0.453483 | − | 0.785456i | −0.545116 | − | 0.838360i | \(-0.683515\pi\) |
0.998600 | + | 0.0529044i | \(0.0168478\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.0278 | − | 26.0289i | 0.584514 | − | 1.01241i | −0.410421 | − | 0.911896i | \(-0.634618\pi\) |
0.994936 | − | 0.100513i | \(-0.0320483\pi\) | |||||||
\(662\) | 0.965449 | + | 1.67221i | 0.0375233 | + | 0.0649922i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.67167 | −0.220104 | ||||||||
\(665\) | −0.938386 | + | 0.162100i | −0.0363890 | + | 0.00628596i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00395 | − | 3.47095i | −0.0775934 | − | 0.134396i | ||||
\(668\) | 4.58709 | + | 7.94508i | 0.177480 | + | 0.307404i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.561592 | + | 0.972706i | 0.0216962 | + | 0.0375789i | ||||
\(671\) | 12.0410 | − | 20.8556i | 0.464837 | − | 0.805122i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.4843 | −1.17508 | −0.587542 | − | 0.809194i | \(-0.699904\pi\) | ||||
−0.587542 | + | 0.809194i | \(0.699904\pi\) | |||||||
\(674\) | −2.10849 | + | 3.65201i | −0.0812160 | + | 0.140670i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.1529 | −1.77511 | ||||||||
\(677\) | −16.7595 | −0.644118 | −0.322059 | − | 0.946720i | \(-0.604375\pi\) | ||||
−0.322059 | + | 0.946720i | \(0.604375\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.73819 | − | 3.01063i | −0.0667055 | − | 0.115537i | ||||
\(680\) | −2.21248 | + | 3.83214i | −0.0848449 | + | 0.146956i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.20629 | + | 2.08935i | 0.0461911 | + | 0.0800054i | ||||
\(683\) | −28.1537 | −1.07727 | −0.538636 | − | 0.842538i | \(-0.681060\pi\) | ||||
−0.538636 | + | 0.842538i | \(0.681060\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.3728 | −0.510950 | ||||||||
\(686\) | 0.259236 | + | 0.449010i | 0.00989767 | + | 0.0171433i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.33006 | + | 9.23194i | −0.203207 | + | 0.351964i | ||||
\(689\) | −15.5365 | − | 26.9100i | −0.591894 | − | 1.02519i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.71714 | −0.141407 | −0.0707034 | − | 0.997497i | \(-0.522524\pi\) | ||||
−0.0707034 | + | 0.997497i | \(0.522524\pi\) | |||||||
\(692\) | −46.8471 | −1.78086 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.65460 | − | 4.59790i | 0.100767 | − | 0.174534i | ||||
\(695\) | 8.92189 | 0.338427 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.4651 | − | 19.8581i | 0.434270 | − | 0.752177i | ||||
\(698\) | 0.227903 | + | 0.394740i | 0.00862627 | + | 0.0149411i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.215309 | − | 0.372925i | −0.00813790 | − | 0.0140953i | ||||
\(701\) | −14.6085 | − | 25.3026i | −0.551754 | − | 0.955667i | −0.998148 | − | 0.0608301i | \(-0.980625\pi\) |
0.446394 | − | 0.894837i | \(-0.352708\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.67036 | − | 12.6942i | 0.176146 | − | 0.478769i | ||||
\(704\) | −39.0025 | −1.46996 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.51942 | + | 4.36377i | 0.0948197 | + | 0.164232i | ||||
\(707\) | −0.598941 | + | 1.03740i | −0.0225255 | + | 0.0390153i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.863639 | − | 1.49587i | 0.0324346 | − | 0.0561784i | −0.849352 | − | 0.527826i | \(-0.823007\pi\) |
0.881787 | + | 0.471648i | \(0.156341\pi\) | |||||||
\(710\) | −1.06251 | −0.0398753 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.23667 | + | 5.60607i | −0.121299 | + | 0.210096i | ||||
\(713\) | 5.07496 | − | 8.79009i | 0.190059 | − | 0.329191i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32.1796 | −1.20345 | ||||||||
\(716\) | −13.5279 | + | 23.4311i | −0.505563 | + | 0.875661i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.86494 | + | 3.23017i | −0.0695988 | + | 0.120549i | ||||
\(719\) | 10.6641 | + | 18.4708i | 0.397704 | + | 0.688843i | 0.993442 | − | 0.114336i | \(-0.0364739\pi\) |
−0.595739 | + | 0.803178i | \(0.703141\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.64187 | 0.0611463 | ||||||||
\(722\) | 0.583320 | − | 3.17872i | 0.0217089 | − | 0.118300i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 21.6242 | + | 37.4543i | 0.803658 | + | 1.39198i | ||||
\(725\) | 0.525141 | + | 0.909571i | 0.0195032 | + | 0.0337806i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.58913 | − | 16.6089i | −0.355641 | − | 0.615989i | 0.631586 | − | 0.775306i | \(-0.282404\pi\) |
−0.987227 | + | 0.159317i | \(0.949071\pi\) | |||||||
\(728\) | 0.445245 | − | 0.771186i | 0.0165019 | − | 0.0285821i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.12785 | 0.0417435 | ||||||||
\(731\) | 9.12344 | − | 15.8023i | 0.337443 | − | 0.584468i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.72949 | 0.100816 | 0.0504079 | − | 0.998729i | \(-0.483948\pi\) | ||||
0.0504079 | + | 0.998729i | \(0.483948\pi\) | |||||||
\(734\) | −2.33814 | −0.0863022 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.81967 | − | 6.61586i | −0.140795 | − | 0.243864i | ||||
\(737\) | 17.6064 | − | 30.4951i | 0.648539 | − | 1.12330i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.87026 | − | 6.70348i | −0.142370 | − | 0.246591i | 0.786019 | − | 0.618203i | \(-0.212139\pi\) |
−0.928389 | + | 0.371611i | \(0.878806\pi\) | |||||||
\(740\) | 6.11640 | 0.224843 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.191347 | 0.00702458 | ||||||||
\(743\) | 21.6349 | + | 37.4727i | 0.793707 | + | 1.37474i | 0.923657 | + | 0.383220i | \(0.125185\pi\) |
−0.129951 | + | 0.991520i | \(0.541482\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.59072 | − | 14.8796i | 0.314740 | − | 0.545145i | ||||
\(746\) | −1.94159 | − | 3.36293i | −0.0710867 | − | 0.123126i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 68.8579 | 2.51769 | ||||||||
\(749\) | 2.44707 | 0.0894141 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.9050 | − | 34.4766i | 0.726346 | − | 1.25807i | −0.232072 | − | 0.972699i | \(-0.574551\pi\) |
0.958418 | − | 0.285369i | \(-0.0921161\pi\) | |||||||
\(752\) | −32.6412 | −1.19030 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.539023 | + | 0.933616i | −0.0196301 | + | 0.0340003i | ||||
\(755\) | −10.2237 | − | 17.7080i | −0.372080 | − | 0.644462i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.9025 | − | 24.0798i | −0.505294 | − | 0.875196i | −0.999981 | − | 0.00612436i | \(-0.998051\pi\) |
0.494687 | − | 0.869071i | \(-0.335283\pi\) | |||||||
\(758\) | 2.46584 | + | 4.27097i | 0.0895635 | + | 0.155129i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.90128 | − | 0.501176i | 0.105240 | − | 0.0181796i | ||||
\(761\) | 34.2239 | 1.24061 | 0.620307 | − | 0.784359i | \(-0.287008\pi\) | ||||
0.620307 | + | 0.784359i | \(0.287008\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.898876 | + | 1.55690i | 0.0325415 | + | 0.0563635i | ||||
\(764\) | −11.8243 | + | 20.4802i | −0.427787 | + | 0.740948i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.22292 | + | 3.85021i | −0.0803174 | + | 0.139114i | ||||
\(767\) | −71.8190 | −2.59323 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.2857 | + | 31.6718i | −0.659401 | + | 1.14212i | 0.321371 | + | 0.946954i | \(0.395856\pi\) |
−0.980771 | + | 0.195162i | \(0.937477\pi\) | |||||||
\(770\) | 0.0990808 | − | 0.171613i | 0.00357063 | − | 0.00618450i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −23.0135 | −0.828274 | ||||||||
\(773\) | −16.0664 | + | 27.8278i | −0.577868 | + | 1.00090i | 0.417856 | + | 0.908513i | \(0.362782\pi\) |
−0.995724 | + | 0.0923831i | \(0.970552\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.32991 | + | 2.30346i | −0.0477716 | + | 0.0827429i | ||||
\(776\) | 5.37409 | + | 9.30819i | 0.192919 | + | 0.334145i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.00499 | 0.143586 | ||||||||
\(779\) | −15.0344 | + | 2.59708i | −0.538662 | + | 0.0930502i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.6553 | + | 28.8478i | 0.595973 | + | 1.03226i | ||||
\(782\) | 2.12611 | + | 3.68252i | 0.0760294 | + | 0.131687i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 13.3040 | + | 23.0432i | 0.475144 | + | 0.822973i | ||||
\(785\) | −3.15365 | + | 5.46228i | −0.112559 | + | 0.194957i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.0801 | −1.32176 | −0.660881 | − | 0.750491i | \(-0.729817\pi\) | ||||
−0.660881 | + | 0.750491i | \(0.729817\pi\) | |||||||
\(788\) | −10.1781 | + | 17.6289i | −0.362579 | + | 0.628005i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.615040 | 0.0218821 | ||||||||
\(791\) | −2.45580 | −0.0873184 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.6259 | + | 23.6007i | 0.483868 | + | 0.838085i | ||||
\(794\) | 1.35372 | − | 2.34471i | 0.0480417 | − | 0.0832107i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.13709 | − | 15.8259i | −0.323856 | − | 0.560934i | ||||
\(797\) | −13.6737 | −0.484347 | −0.242173 | − | 0.970233i | \(-0.577860\pi\) | ||||
−0.242173 | + | 0.970233i | \(0.577860\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.8718 | 1.97660 | ||||||||
\(800\) | 1.00095 | + | 1.73370i | 0.0353891 | + | 0.0612956i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.89783 | + | 3.28714i | −0.0670147 | + | 0.116073i | ||||
\(803\) | −17.6795 | − | 30.6218i | −0.623896 | − | 1.08062i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.833684 | −0.0293835 | ||||||||
\(806\) | −2.73012 | −0.0961645 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.85179 | − | 3.20740i | 0.0651458 | − | 0.112836i | ||||
\(809\) | 27.2716 | 0.958820 | 0.479410 | − | 0.877591i | \(-0.340851\pi\) | ||||
0.479410 | + | 0.877591i | \(0.340851\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.70684 | + | 15.0807i | −0.305738 | + | 0.529554i | −0.977425 | − | 0.211281i | \(-0.932237\pi\) |
0.671687 | + | 0.740835i | \(0.265570\pi\) | |||||||
\(812\) | 0.226135 | + | 0.391677i | 0.00793577 | + | 0.0137452i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.40732 | + | 2.43756i | 0.0493267 | + | 0.0854363i | ||||
\(815\) | −2.10165 | − | 3.64017i | −0.0736177 | − | 0.127510i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.9638 | + | 2.06666i | −0.418559 | + | 0.0723032i | ||||
\(818\) | 0.121168 | 0.00423654 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.44957 | − | 5.97483i | −0.120464 | − | 0.208650i | ||||
\(821\) | −13.1917 | + | 22.8487i | −0.460394 | + | 0.797425i | −0.998980 | − | 0.0451450i | \(-0.985625\pi\) |
0.538587 | + | 0.842570i | \(0.318958\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.6831 | − | 25.4318i | 0.511820 | − | 0.886498i | −0.488086 | − | 0.872795i | \(-0.662305\pi\) |
0.999906 | − | 0.0137024i | \(-0.00436173\pi\) | |||||||
\(824\) | −5.07628 | −0.176841 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.221130 | − | 0.383009i | 0.00769410 | − | 0.0133266i | ||||
\(827\) | −2.19866 | + | 3.80818i | −0.0764548 | + | 0.132424i | −0.901718 | − | 0.432325i | \(-0.857693\pi\) |
0.825263 | + | 0.564748i | \(0.191027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.68614 | 0.232219 | 0.116110 | − | 0.993236i | \(-0.462958\pi\) | ||||
0.116110 | + | 0.993236i | \(0.462958\pi\) | |||||||
\(830\) | 0.714124 | − | 1.23690i | 0.0247876 | − | 0.0429334i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.0681 | − | 38.2230i | 0.765073 | − | 1.32515i | ||||
\(833\) | −22.7724 | − | 39.4430i | −0.789018 | − | 1.36662i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.65442 | −0.161073 | ||||||||
\(836\) | −29.3278 | − | 35.1994i | −1.01432 | − | 1.21740i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.55711 | + | 4.42905i | 0.0883340 | + | 0.152999i | ||||
\(839\) | 17.7789 | + | 30.7939i | 0.613795 | + | 1.06312i | 0.990595 | + | 0.136829i | \(0.0436912\pi\) |
−0.376800 | + | 0.926295i | \(0.622975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.9485 | + | 24.1594i | 0.480981 | + | 0.833084i | ||||
\(842\) | −1.95366 | + | 3.38384i | −0.0673277 | + | 0.116615i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.07695 | 0.0714917 | ||||||||
\(845\) | 11.7076 | − | 20.2781i | 0.402753 | − | 0.697589i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.80938 | −0.130892 | ||||||||
\(848\) | 19.7073 | 0.676753 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.557151 | − | 0.965014i | −0.0191101 | − | 0.0330997i | ||||
\(851\) | 5.92074 | − | 10.2550i | 0.202960 | − | 0.351538i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.23270 | + | 9.06331i | 0.179164 | + | 0.310322i | 0.941595 | − | 0.336749i | \(-0.109327\pi\) |
−0.762430 | + | 0.647070i | \(0.775994\pi\) | |||||||
\(854\) | −0.167816 | −0.00574254 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.56580 | −0.258594 | ||||||||
\(857\) | −25.9250 | − | 44.9034i | −0.885580 | − | 1.53387i | −0.845047 | − | 0.534691i | \(-0.820428\pi\) |
−0.0405327 | − | 0.999178i | \(-0.512905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.93030 | + | 15.4677i | −0.304698 | + | 0.527752i | −0.977194 | − | 0.212349i | \(-0.931889\pi\) |
0.672496 | + | 0.740101i | \(0.265222\pi\) | |||||||
\(860\) | −2.74503 | − | 4.75454i | −0.0936049 | − | 0.162128i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.97802 | 0.135492 | ||||||||
\(863\) | −1.60981 | −0.0547986 | −0.0273993 | − | 0.999625i | \(-0.508723\pi\) | ||||
−0.0273993 | + | 0.999625i | \(0.508723\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.8837 | − | 20.5831i | 0.404057 | − | 0.699848i | ||||
\(866\) | −5.69138 | −0.193401 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.572680 | + | 0.991911i | −0.0194380 | + | 0.0336676i | ||||
\(869\) | −9.64100 | − | 16.6987i | −0.327049 | − | 0.566465i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.9238 | + | 34.5090i | 0.675092 | + | 1.16929i | ||||
\(872\) | −2.77912 | − | 4.81358i | −0.0941130 | − | 0.163008i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.976918 | − | 2.65529i | 0.0330448 | − | 0.0898166i | ||||
\(875\) | 0.218469 | 0.00738560 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.3628 | − | 24.8771i | −0.484997 | − | 0.840039i | 0.514855 | − | 0.857277i | \(-0.327846\pi\) |
−0.999851 | + | 0.0172388i | \(0.994512\pi\) | |||||||
\(878\) | 1.48426 | − | 2.57082i | 0.0500915 | − | 0.0867610i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.2046 | − | 17.6749i | 0.343997 | − | 0.595820i | ||||
\(881\) | −11.7794 | −0.396858 | −0.198429 | − | 0.980115i | \(-0.563584\pi\) | ||||
−0.198429 | + | 0.980115i | \(0.563584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.1435 | − | 41.8177i | 0.812493 | − | 1.40728i | −0.0986210 | − | 0.995125i | \(-0.531443\pi\) |
0.911114 | − | 0.412154i | \(-0.135224\pi\) | |||||||
\(884\) | −38.9606 | + | 67.4817i | −1.31039 | + | 2.26966i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.57811 | 0.0866132 | ||||||||
\(887\) | 14.0549 | − | 24.3438i | 0.471917 | − | 0.817384i | −0.527567 | − | 0.849514i | \(-0.676896\pi\) |
0.999484 | + | 0.0321295i | \(0.0102289\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.09210 | − | 1.89158i | 0.0366280 | − | 0.0634415i | ||||
\(890\) | −0.815062 | − | 1.41173i | −0.0273210 | − | 0.0473213i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −51.5720 | −1.72676 | ||||||||
\(893\) | −23.7968 | − | 28.5610i | −0.796329 | − | 0.955758i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.86326 | − | 11.8875i | −0.229413 | − | 0.397356i | ||||
\(896\) | 0.573250 | + | 0.992897i | 0.0191509 | + | 0.0331704i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.12229 | − | 1.94387i | −0.0374513 | − | 0.0648676i | ||||
\(899\) | 1.39678 | − | 2.41929i | 0.0465851 | − | 0.0806877i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33.7330 | −1.12381 | ||||||||
\(902\) | 1.58743 | − | 2.74950i | 0.0528555 | − | 0.0915484i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.59280 | 0.252533 | ||||||||
\(905\) | −21.9416 | −0.729364 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.04303 | − | 13.9309i | −0.267064 | − | 0.462569i | 0.701038 | − | 0.713124i | \(-0.252720\pi\) |
−0.968102 | + | 0.250555i | \(0.919387\pi\) | |||||||
\(908\) | 15.0597 | − | 26.0842i | 0.499775 | − | 0.865636i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.112122 | + | 0.194201i | 0.00371681 | + | 0.00643771i | ||||
\(911\) | −20.0946 | −0.665765 | −0.332882 | − | 0.942968i | \(-0.608021\pi\) | ||||
−0.332882 | + | 0.942968i | \(0.608021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.7768 | −1.48190 | ||||||||
\(914\) | −0.357215 | − | 0.618714i | −0.0118156 | − | 0.0204652i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.3267 | + | 23.0826i | −0.440327 | + | 0.762669i | ||||
\(917\) | −1.90997 | − | 3.30816i | −0.0630727 | − | 0.109245i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.6524 | 0.516324 | 0.258162 | − | 0.966102i | \(-0.416883\pi\) | ||||
0.258162 | + | 0.966102i | \(0.416883\pi\) | |||||||
\(920\) | 2.57756 | 0.0849798 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.70161 | − | 2.94727i | 0.0560395 | − | 0.0970633i | ||||
\(923\) | −37.6950 | −1.24075 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.55154 | + | 2.68735i | −0.0510145 | + | 0.0883596i | ||||
\(926\) | −1.74066 | − | 3.01492i | −0.0572018 | − | 0.0990764i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.05128 | − | 1.82088i | −0.0345101 | − | 0.0597732i | ||||
\(929\) | −16.6822 | − | 28.8944i | −0.547325 | − | 0.947995i | −0.998457 | − | 0.0555375i | \(-0.982313\pi\) |
0.451131 | − | 0.892458i | \(-0.351021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.4636 | + | 28.4405i | −0.342932 | + | 0.932098i | ||||
\(932\) | 9.66731 | 0.316663 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.33876 | + | 5.78290i | 0.109248 | + | 0.189222i | ||||
\(935\) | −17.4672 | + | 30.2540i | −0.571237 | + | 0.989412i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.298419 | + | 0.516876i | −0.00974892 | + | 0.0168856i | −0.870859 | − | 0.491533i | \(-0.836437\pi\) |
0.861110 | + | 0.508419i | \(0.169770\pi\) | |||||||
\(938\) | −0.245381 | −0.00801197 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.40527 | − | 14.5584i | 0.274150 | − | 0.474841i | ||||
\(941\) | −2.38306 | + | 4.12759i | −0.0776857 | + | 0.134556i | −0.902251 | − | 0.431211i | \(-0.858086\pi\) |
0.824565 | + | 0.565767i | \(0.191420\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.3569 | −0.434960 | ||||||||
\(944\) | 22.7748 | − | 39.4471i | 0.741256 | − | 1.28389i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.26321 | − | 2.18795i | 0.0410706 | − | 0.0711363i | ||||
\(947\) | 7.51096 | + | 13.0094i | 0.244073 | + | 0.422748i | 0.961871 | − | 0.273505i | \(-0.0881829\pi\) |
−0.717797 | + | 0.696252i | \(0.754850\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.0130 | 1.29888 | ||||||||
\(950\) | −0.256004 | + | 0.695825i | −0.00830586 | + | 0.0225756i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.483359 | − | 0.837203i | −0.0156658 | − | 0.0271339i | ||||
\(953\) | 24.3255 | + | 42.1330i | 0.787980 | + | 1.36482i | 0.927203 | + | 0.374560i | \(0.122206\pi\) |
−0.139223 | + | 0.990261i | \(0.544460\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.99891 | − | 10.3904i | −0.194120 | − | 0.336226i | ||||
\(956\) | −17.7585 | + | 30.7586i | −0.574350 | + | 0.994803i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.23338 | 0.0398487 | ||||||||
\(959\) | 1.46077 | − | 2.53014i | 0.0471709 | − | 0.0817023i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9254 | −0.771787 | ||||||||
\(962\) | −3.18512 | −0.102692 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −28.6186 | − | 49.5689i | −0.921743 | − | 1.59651i | ||||
\(965\) | 5.83782 | − | 10.1114i | 0.187926 | − | 0.325498i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.5079 | + | 37.2527i | 0.691647 | + | 1.19797i | 0.971298 | + | 0.237866i | \(0.0764479\pi\) |
−0.279651 | + | 0.960102i | \(0.590219\pi\) | |||||||
\(968\) | 11.7777 | 0.378551 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.70662 | −0.0869044 | ||||||||
\(971\) | 3.45564 | + | 5.98535i | 0.110897 | + | 0.192079i | 0.916132 | − | 0.400876i | \(-0.131294\pi\) |
−0.805235 | + | 0.592955i | \(0.797961\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.974578 | + | 1.68802i | −0.0312435 | + | 0.0541154i | ||||
\(974\) | −0.353877 | − | 0.612932i | −0.0113389 | − | 0.0196396i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.2838 | −0.553240 | ||||||||
\(977\) | 0.706172 | 0.0225924 | 0.0112962 | − | 0.999936i | \(-0.496404\pi\) | ||||
0.0112962 | + | 0.999936i | \(0.496404\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.5529 | + | 44.2589i | −0.816674 | + | 1.41452i | ||||
\(980\) | −13.7034 | −0.437739 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.504912 | − | 0.874533i | 0.0161124 | − | 0.0279075i | ||||
\(983\) | 23.7111 | + | 41.0689i | 0.756267 | + | 1.30989i | 0.944742 | + | 0.327815i | \(0.106312\pi\) |
−0.188474 | + | 0.982078i | \(0.560354\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.16373 | − | 8.94385i | −0.164530 | − | 0.284975i | ||||
\(986\) | 0.585166 | + | 1.01354i | 0.0186355 | + | 0.0322776i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 51.0899 | − | 8.82542i | 1.62538 | − | 0.280774i | ||||
\(989\) | −10.6289 | −0.337979 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.75338 | + | 11.6972i | 0.214528 | + | 0.371574i | 0.953127 | − | 0.302572i | \(-0.0978453\pi\) |
−0.738598 | + | 0.674146i | \(0.764512\pi\) | |||||||
\(992\) | 2.66235 | − | 4.61132i | 0.0845296 | − | 0.146410i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.116063 | − | 0.201026i | 0.00368128 | − | 0.00637617i | ||||
\(995\) | 9.27121 | 0.293917 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9706 | + | 29.3939i | −0.537464 | + | 0.930915i | 0.461576 | + | 0.887101i | \(0.347284\pi\) |
−0.999040 | + | 0.0438139i | \(0.986049\pi\) | |||||||
\(998\) | −0.203327 | + | 0.352172i | −0.00643619 | + | 0.0111478i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 855.2.k.k.406.3 | yes | 12 | |
3.2 | odd | 2 | 855.2.k.j.406.4 | ✓ | 12 | ||
19.11 | even | 3 | inner | 855.2.k.k.676.3 | yes | 12 | |
57.11 | odd | 6 | 855.2.k.j.676.4 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
855.2.k.j.406.4 | ✓ | 12 | 3.2 | odd | 2 | ||
855.2.k.j.676.4 | yes | 12 | 57.11 | odd | 6 | ||
855.2.k.k.406.3 | yes | 12 | 1.1 | even | 1 | trivial | |
855.2.k.k.676.3 | yes | 12 | 19.11 | even | 3 | inner |