Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(17,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([21, 25]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.bg (of order \(42\), degree \(12\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(216\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{42})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{42}]$ |
Embedding invariants
Embedding label | 17.4 | ||
Character | \(\chi\) | \(=\) | 441.17 |
Dual form | 441.2.bg.a.26.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(e\left(\frac{25}{42}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.57786 | + | 0.118244i | −1.11571 | + | 0.0836111i | −0.619799 | − | 0.784761i | \(-0.712786\pi\) |
−0.495914 | + | 0.868372i | \(0.665167\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.497985 | − | 0.0750592i | 0.248993 | − | 0.0375296i | ||||
\(5\) | −2.70933 | + | 2.51389i | −1.21165 | + | 1.12425i | −0.222874 | + | 0.974847i | \(0.571544\pi\) |
−0.988777 | + | 0.149401i | \(0.952266\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.38562 | − | 2.25390i | 0.523713 | − | 0.851894i | ||||
\(8\) | 2.30834 | − | 0.526865i | 0.816123 | − | 0.186275i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.97769 | − | 4.28693i | 1.25785 | − | 1.35564i | ||||
\(11\) | 2.08781 | + | 3.06225i | 0.629498 | + | 0.923304i | 0.999985 | − | 0.00553360i | \(-0.00176141\pi\) |
−0.370487 | + | 0.928838i | \(0.620809\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.81859 | + | 3.77635i | −0.504387 | + | 1.04737i | 0.480949 | + | 0.876748i | \(0.340292\pi\) |
−0.985336 | + | 0.170622i | \(0.945422\pi\) | |||||||
\(14\) | −1.91979 | + | 3.72017i | −0.513086 | + | 0.994258i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.54241 | + | 1.40115i | −1.13560 | + | 0.350287i | ||||
\(17\) | −0.686097 | − | 1.74815i | −0.166403 | − | 0.423988i | 0.823212 | − | 0.567735i | \(-0.192180\pi\) |
−0.989614 | + | 0.143747i | \(0.954085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.369695 | + | 0.213443i | −0.0848137 | + | 0.0489672i | −0.541807 | − | 0.840503i | \(-0.682260\pi\) |
0.456993 | + | 0.889470i | \(0.348926\pi\) | |||||||
\(20\) | −1.16052 | + | 1.45524i | −0.259500 | + | 0.325402i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.65635 | − | 4.58492i | −0.779537 | − | 0.977509i | ||||
\(23\) | −8.16396 | − | 3.20412i | −1.70230 | − | 0.668105i | −0.703222 | − | 0.710970i | \(-0.748256\pi\) |
−0.999081 | + | 0.0428658i | \(0.986351\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.647174 | − | 8.63594i | 0.129435 | − | 1.72719i | ||||
\(26\) | 2.42295 | − | 6.17357i | 0.475179 | − | 1.21074i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.520840 | − | 1.22641i | 0.0984295 | − | 0.231770i | ||||
\(29\) | −7.23589 | − | 5.77043i | −1.34367 | − | 1.07154i | −0.990723 | − | 0.135899i | \(-0.956608\pi\) |
−0.352948 | − | 0.935643i | \(-0.614821\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.63700 | + | 0.945120i | 0.294013 | + | 0.169749i | 0.639750 | − | 0.768583i | \(-0.279038\pi\) |
−0.345737 | + | 0.938331i | \(0.612371\pi\) | |||||||
\(32\) | 2.59351 | − | 1.01788i | 0.458473 | − | 0.179937i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.28927 | + | 2.67720i | 0.221108 | + | 0.459135i | ||||
\(35\) | 1.91197 | + | 9.58986i | 0.323183 | + | 1.62098i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.99050 | − | 0.902922i | −0.984832 | − | 0.148440i | −0.363168 | − | 0.931724i | \(-0.618305\pi\) |
−0.621664 | + | 0.783284i | \(0.713543\pi\) | |||||||
\(38\) | 0.558086 | − | 0.380497i | 0.0905335 | − | 0.0617247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.92959 | + | 7.23039i | −0.779437 | + | 1.14322i | ||||
\(41\) | −0.210940 | − | 0.924187i | −0.0329433 | − | 0.144334i | 0.955782 | − | 0.294077i | \(-0.0950123\pi\) |
−0.988725 | + | 0.149744i | \(0.952155\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.484253 | + | 2.12165i | −0.0738479 | + | 0.323549i | −0.998336 | − | 0.0576617i | \(-0.981636\pi\) |
0.924488 | + | 0.381210i | \(0.124493\pi\) | |||||||
\(44\) | 1.26955 | + | 1.36825i | 0.191392 | + | 0.206271i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 13.2604 | + | 4.09030i | 1.95514 | + | 0.603081i | ||||
\(47\) | −0.0205569 | − | 0.274312i | −0.00299853 | − | 0.0400126i | 0.995504 | − | 0.0947213i | \(-0.0301960\pi\) |
−0.998502 | + | 0.0547088i | \(0.982577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.16014 | − | 6.24608i | −0.451448 | − | 0.892297i | ||||
\(50\) | 13.7028i | 1.93787i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.622183 | + | 2.01707i | −0.0862813 | + | 0.279717i | ||||
\(53\) | −1.01410 | − | 6.72809i | −0.139297 | − | 0.924174i | −0.943869 | − | 0.330319i | \(-0.892844\pi\) |
0.804572 | − | 0.593854i | \(-0.202395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.3548 | − | 3.04814i | −1.80075 | − | 0.411011i | ||||
\(56\) | 2.01098 | − | 5.93281i | 0.268728 | − | 0.792805i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 12.0995 | + | 8.24930i | 1.58874 | + | 1.08319i | ||||
\(59\) | 3.04988 | + | 2.82987i | 0.397060 | + | 0.368418i | 0.853284 | − | 0.521447i | \(-0.174608\pi\) |
−0.456223 | + | 0.889865i | \(0.650798\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00731 | + | 13.3177i | −0.257010 | + | 1.70515i | 0.372395 | + | 0.928074i | \(0.378537\pi\) |
−0.629405 | + | 0.777077i | \(0.716701\pi\) | |||||||
\(62\) | −2.69470 | − | 1.29770i | −0.342227 | − | 0.164808i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.59385 | − | 2.21228i | 0.574232 | − | 0.276535i | ||||
\(65\) | −4.56617 | − | 14.8031i | −0.566363 | − | 1.83610i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.116151 | + | 0.201179i | −0.0141900 | + | 0.0245779i | −0.873033 | − | 0.487661i | \(-0.837850\pi\) |
0.858843 | + | 0.512239i | \(0.171184\pi\) | |||||||
\(68\) | −0.472881 | − | 0.819053i | −0.0573452 | − | 0.0993248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.15076 | − | 14.9053i | −0.496111 | − | 1.78153i | ||||
\(71\) | −9.97267 | + | 7.95294i | −1.18354 | + | 0.943840i | −0.999238 | − | 0.0390297i | \(-0.987573\pi\) |
−0.184300 | + | 0.982870i | \(0.559002\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.4185 | − | 1.23040i | −1.92164 | − | 0.144007i | −0.940819 | − | 0.338909i | \(-0.889942\pi\) |
−0.980823 | + | 0.194901i | \(0.937561\pi\) | |||||||
\(74\) | 9.55891 | + | 0.716341i | 1.11120 | + | 0.0832730i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.168082 | + | 0.134041i | −0.0192803 | + | 0.0153755i | ||||
\(77\) | 9.79492 | − | 0.462609i | 1.11623 | − | 0.0527192i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.31826 | − | 5.74740i | −0.373334 | − | 0.646633i | 0.616743 | − | 0.787165i | \(-0.288452\pi\) |
−0.990076 | + | 0.140532i | \(0.955119\pi\) | |||||||
\(80\) | 8.78456 | − | 15.2153i | 0.982144 | − | 1.70112i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.442112 | + | 1.43329i | 0.0488231 | + | 0.158281i | ||||
\(83\) | 11.8980 | − | 5.72975i | 1.30597 | − | 0.628922i | 0.354038 | − | 0.935231i | \(-0.384808\pi\) |
0.951932 | + | 0.306309i | \(0.0990941\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.25352 | + | 3.01154i | 0.678290 | + | 0.326647i | ||||
\(86\) | 0.513209 | − | 3.40492i | 0.0553407 | − | 0.367162i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.43278 | + | 5.96874i | 0.685736 | + | 0.636270i | ||||
\(89\) | 10.1016 | + | 6.88713i | 1.07076 | + | 0.730034i | 0.964441 | − | 0.264298i | \(-0.0851402\pi\) |
0.106322 | + | 0.994332i | \(0.466093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.99165 | + | 9.33150i | 0.628095 | + | 0.978207i | ||||
\(92\) | −4.30603 | − | 0.982823i | −0.448935 | − | 0.102466i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.0648716 | + | 0.430395i | 0.00669099 | + | 0.0443918i | ||||
\(95\) | 0.465052 | − | 1.50766i | 0.0477133 | − | 0.154683i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.46635i | − | 0.250420i | −0.992130 | − | 0.125210i | \(-0.960040\pi\) | ||
0.992130 | − | 0.125210i | \(-0.0399604\pi\) | |||||||
\(98\) | 5.72480 | + | 9.48175i | 0.578293 | + | 0.957801i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.325924 | − | 4.34915i | −0.0325924 | − | 0.434915i | ||||
\(101\) | −3.51151 | − | 1.08316i | −0.349408 | − | 0.107778i | 0.115083 | − | 0.993356i | \(-0.463287\pi\) |
−0.464491 | + | 0.885578i | \(0.653763\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.75257 | + | 4.04431i | 0.369752 | + | 0.398498i | 0.890330 | − | 0.455316i | \(-0.150474\pi\) |
−0.520578 | + | 0.853814i | \(0.674283\pi\) | |||||||
\(104\) | −2.20832 | + | 9.67527i | −0.216543 | + | 0.948738i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.39565 | + | 10.4960i | 0.232686 | + | 1.01947i | ||||
\(107\) | −4.30053 | + | 6.30771i | −0.415748 | + | 0.609790i | −0.975799 | − | 0.218668i | \(-0.929829\pi\) |
0.560052 | + | 0.828458i | \(0.310781\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0919472 | + | 0.0626885i | −0.00880694 | + | 0.00600447i | −0.567716 | − | 0.823225i | \(-0.692173\pi\) |
0.558909 | + | 0.829229i | \(0.311220\pi\) | |||||||
\(110\) | 21.4323 | + | 3.23040i | 2.04349 | + | 0.308007i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.13598 | + | 12.1796i | −0.296323 | + | 1.15086i | ||||
\(113\) | 3.22553 | + | 6.69787i | 0.303432 | + | 0.630083i | 0.995809 | − | 0.0914525i | \(-0.0291510\pi\) |
−0.692378 | + | 0.721535i | \(0.743437\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.1737 | − | 11.8423i | 2.81371 | − | 1.10430i | ||||
\(116\) | −4.03649 | − | 2.33047i | −0.374779 | − | 0.216379i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.14688 | − | 4.10450i | −0.473809 | − | 0.377850i | ||||
\(119\) | −4.89082 | − | 0.875864i | −0.448340 | − | 0.0802904i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.999699 | + | 2.54719i | −0.0908817 | + | 0.231563i | ||||
\(122\) | 1.59252 | − | 21.2507i | 0.144180 | − | 1.92395i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.886140 | + | 0.347784i | 0.0795777 | + | 0.0312320i | ||||
\(125\) | 8.43445 | + | 10.5765i | 0.754400 | + | 0.945988i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.27637 | − | 11.6322i | 0.823145 | − | 1.03219i | −0.175714 | − | 0.984441i | \(-0.556224\pi\) |
0.998859 | − | 0.0477498i | \(-0.0152050\pi\) | |||||||
\(128\) | −11.8125 | + | 6.81997i | −1.04409 | + | 0.602806i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.95513 | + | 22.8173i | 0.785417 | + | 2.00121i | ||||
\(131\) | −17.6370 | + | 5.44031i | −1.54096 | + | 0.475322i | −0.944828 | − | 0.327567i | \(-0.893771\pi\) |
−0.596128 | + | 0.802889i | \(0.703295\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0311746 | + | 1.12901i | −0.00270318 | + | 0.0978972i | ||||
\(134\) | 0.159481 | − | 0.331165i | 0.0137770 | − | 0.0286083i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.50478 | − | 3.67384i | −0.214783 | − | 0.315030i | ||||
\(137\) | 3.45520 | − | 3.72382i | 0.295198 | − | 0.318148i | −0.567985 | − | 0.823039i | \(-0.692277\pi\) |
0.863183 | + | 0.504891i | \(0.168467\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.9111 | + | 3.17511i | −1.17992 | + | 0.269310i | −0.767116 | − | 0.641509i | \(-0.778309\pi\) |
−0.412807 | + | 0.910818i | \(0.635452\pi\) | |||||||
\(140\) | 1.67194 | + | 4.63210i | 0.141305 | + | 0.391484i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 14.7950 | − | 13.7278i | 1.24157 | − | 1.15201i | ||||
\(143\) | −15.3610 | + | 2.31530i | −1.28455 | + | 0.193615i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 34.1107 | − | 2.55624i | 2.83274 | − | 0.212284i | ||||
\(146\) | 26.0515 | 2.15604 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.05095 | −0.250787 | ||||||||
\(149\) | 15.7536 | − | 1.18057i | 1.29059 | − | 0.0967161i | 0.588319 | − | 0.808629i | \(-0.299790\pi\) |
0.702268 | + | 0.711913i | \(0.252171\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.9058 | + | 2.09596i | −1.13164 | + | 0.170567i | −0.688049 | − | 0.725664i | \(-0.741533\pi\) |
−0.443588 | + | 0.896231i | \(0.646294\pi\) | |||||||
\(152\) | −0.740927 | + | 0.687479i | −0.0600971 | + | 0.0557619i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −15.4003 | + | 1.88812i | −1.24099 | + | 0.152149i | ||||
\(155\) | −6.81110 | + | 1.55459i | −0.547081 | + | 0.124868i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.807372 | − | 0.870140i | 0.0644353 | − | 0.0694448i | −0.700011 | − | 0.714132i | \(-0.746822\pi\) |
0.764447 | + | 0.644687i | \(0.223012\pi\) | |||||||
\(158\) | 5.91533 | + | 8.67620i | 0.470599 | + | 0.690241i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.46785 | + | 9.27759i | −0.353215 | + | 0.733458i | ||||
\(161\) | −18.5339 | + | 13.9611i | −1.46067 | + | 1.10029i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.50588 | − | 2.62372i | 0.666232 | − | 0.205505i | 0.0568506 | − | 0.998383i | \(-0.481894\pi\) |
0.609381 | + | 0.792877i | \(0.291418\pi\) | |||||||
\(164\) | −0.174414 | − | 0.444399i | −0.0136194 | − | 0.0347017i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.0957 | + | 10.4476i | −1.40450 | + | 0.810890i | ||||
\(167\) | 6.78697 | − | 8.51059i | 0.525191 | − | 0.658569i | −0.446511 | − | 0.894778i | \(-0.647334\pi\) |
0.971702 | + | 0.236209i | \(0.0759051\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.84816 | − | 3.57148i | −0.219090 | − | 0.274730i | ||||
\(170\) | −10.2233 | − | 4.01233i | −0.784088 | − | 0.307732i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0819014 | + | 1.09290i | −0.00624492 | + | 0.0833327i | ||||
\(173\) | 2.15991 | − | 5.50336i | 0.164215 | − | 0.418412i | −0.824953 | − | 0.565201i | \(-0.808799\pi\) |
0.989168 | + | 0.146789i | \(0.0468938\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −18.5678 | − | 13.4248i | −1.40360 | − | 1.01482i | ||||
\(176\) | −13.7744 | − | 10.9847i | −1.03828 | − | 0.828001i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −16.7532 | − | 9.67244i | −1.25570 | − | 0.724980i | ||||
\(179\) | −4.34885 | + | 1.70680i | −0.325049 | + | 0.127572i | −0.522254 | − | 0.852790i | \(-0.674909\pi\) |
0.197205 | + | 0.980362i | \(0.436813\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.59066 | − | 5.37956i | −0.192562 | − | 0.399859i | 0.782225 | − | 0.622996i | \(-0.214085\pi\) |
−0.974787 | + | 0.223137i | \(0.928370\pi\) | |||||||
\(182\) | −10.5573 | − | 14.0153i | −0.782562 | − | 1.03888i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −20.5334 | − | 3.09491i | −1.51374 | − | 0.228160i | ||||
\(185\) | 18.5001 | − | 12.6132i | 1.36016 | − | 0.927338i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.92083 | − | 5.75080i | 0.286719 | − | 0.420540i | ||||
\(188\) | −0.0308267 | − | 0.135061i | −0.00224827 | − | 0.00985030i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.555513 | + | 2.43386i | −0.0403012 | + | 0.176571i | ||||
\(191\) | −1.13621 | − | 1.22454i | −0.0822133 | − | 0.0886049i | 0.690605 | − | 0.723232i | \(-0.257344\pi\) |
−0.772819 | + | 0.634627i | \(0.781154\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.68813 | − | 1.13764i | −0.265477 | − | 0.0818889i | 0.159159 | − | 0.987253i | \(-0.449122\pi\) |
−0.424636 | + | 0.905364i | \(0.639598\pi\) | |||||||
\(194\) | 0.291631 | + | 3.89154i | 0.0209379 | + | 0.279396i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.04253 | − | 2.87326i | −0.145895 | − | 0.205233i | ||||
\(197\) | 3.58713i | 0.255572i | 0.991802 | + | 0.127786i | \(0.0407871\pi\) | ||||
−0.991802 | + | 0.127786i | \(0.959213\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.179176 | − | 0.580875i | 0.0127015 | − | 0.0411771i | −0.949000 | − | 0.315275i | \(-0.897903\pi\) |
0.961702 | + | 0.274098i | \(0.0883793\pi\) | |||||||
\(200\) | −3.05607 | − | 20.2757i | −0.216097 | − | 1.43371i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.66873 | + | 1.29385i | 0.398850 | + | 0.0910350i | ||||
\(203\) | −23.0321 | + | 8.31338i | −1.61654 | + | 0.583485i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.89482 | + | 1.97365i | 0.202183 | + | 0.137846i | ||||
\(206\) | −6.39923 | − | 5.93762i | −0.445856 | − | 0.413694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.96957 | − | 19.7018i | 0.205903 | − | 1.36608i | ||||
\(209\) | −1.42547 | − | 0.686470i | −0.0986018 | − | 0.0474841i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.38006 | + | 3.55405i | −0.508064 | + | 0.244671i | −0.670312 | − | 0.742079i | \(-0.733840\pi\) |
0.162248 | + | 0.986750i | \(0.448126\pi\) | |||||||
\(212\) | −1.01001 | − | 3.27437i | −0.0693677 | − | 0.224885i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.03976 | − | 10.4612i | 0.412870 | − | 0.715111i | ||||
\(215\) | −4.02160 | − | 6.96562i | −0.274271 | − | 0.475051i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.39846 | − | 2.38005i | 0.298587 | − | 0.161569i | ||||
\(218\) | 0.137667 | − | 0.109786i | 0.00932397 | − | 0.00743562i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.87926 | − | 0.515529i | −0.463800 | − | 0.0347570i | ||||
\(221\) | 7.84934 | + | 0.588227i | 0.528004 | + | 0.0395684i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.481571 | + | 0.384040i | −0.0322484 | + | 0.0257172i | −0.639481 | − | 0.768807i | \(-0.720851\pi\) |
0.607233 | + | 0.794524i | \(0.292279\pi\) | |||||||
\(224\) | 1.29941 | − | 7.25591i | 0.0868208 | − | 0.484806i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.88140 | − | 10.1869i | −0.391225 | − | 0.677621i | ||||
\(227\) | −5.95885 | + | 10.3210i | −0.395503 | + | 0.685031i | −0.993165 | − | 0.116717i | \(-0.962763\pi\) |
0.597662 | + | 0.801748i | \(0.296096\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.24281 | + | 26.7225i | 0.544700 | + | 1.76587i | 0.637783 | + | 0.770216i | \(0.279852\pi\) |
−0.0930829 | + | 0.995658i | \(0.529672\pi\) | |||||||
\(230\) | −46.2095 | + | 22.2533i | −3.04696 | + | 1.46734i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.7432 | − | 9.50780i | −1.29620 | − | 0.624218i | ||||
\(233\) | 0.695670 | − | 4.61547i | 0.0455749 | − | 0.302370i | −0.954418 | − | 0.298475i | \(-0.903522\pi\) |
0.999992 | − | 0.00389485i | \(-0.00123977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.745288 | + | 0.691526i | 0.0486172 | + | 0.0451102i | ||||
\(236\) | 1.73120 | + | 1.18031i | 0.112692 | + | 0.0768319i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.82057 | + | 0.803678i | 0.506932 | + | 0.0520947i | ||||
\(239\) | −8.96689 | − | 2.04663i | −0.580020 | − | 0.132386i | −0.0775621 | − | 0.996988i | \(-0.524714\pi\) |
−0.502458 | + | 0.864602i | \(0.667571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.51065 | + | 29.9262i | 0.290557 | + | 1.92772i | 0.366102 | + | 0.930575i | \(0.380692\pi\) |
−0.0755452 | + | 0.997142i | \(0.524070\pi\) | |||||||
\(242\) | 1.27619 | − | 4.13731i | 0.0820367 | − | 0.265956i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.78267i | 0.434216i | ||||||||
\(245\) | 24.2639 | + | 8.97846i | 1.55016 | + | 0.573613i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.133712 | − | 1.78426i | −0.00850789 | − | 0.113530i | ||||
\(248\) | 4.27670 | + | 1.31919i | 0.271571 | + | 0.0837685i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.5590 | − | 15.6908i | −0.920789 | − | 0.992374i | ||||
\(251\) | −3.19381 | + | 13.9930i | −0.201591 | + | 0.883229i | 0.768377 | + | 0.639997i | \(0.221065\pi\) |
−0.969968 | + | 0.243231i | \(0.921793\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.23297 | − | 31.6897i | −0.454733 | − | 1.99231i | ||||
\(254\) | −13.2613 | + | 19.4508i | −0.832090 | + | 1.22045i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.40640 | − | 6.41318i | 0.587900 | − | 0.400824i | ||||
\(257\) | 4.77127 | + | 0.719153i | 0.297624 | + | 0.0448595i | 0.296157 | − | 0.955139i | \(-0.404295\pi\) |
0.00146698 | + | 0.999999i | \(0.499533\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.3356 | + | 12.2509i | −0.642224 | + | 0.761233i | ||||
\(260\) | −3.38500 | − | 7.02902i | −0.209929 | − | 0.435921i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 27.1854 | − | 10.6695i | 1.67952 | − | 0.659164i | ||||
\(263\) | 20.2728 | + | 11.7045i | 1.25008 | + | 0.721732i | 0.971124 | − | 0.238573i | \(-0.0766797\pi\) |
0.278952 | + | 0.960305i | \(0.410013\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 19.6612 | + | 15.6793i | 1.20778 | + | 0.963172i | ||||
\(266\) | −0.0843090 | − | 1.78509i | −0.00516932 | − | 0.109451i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.0427410 | + | 0.108902i | −0.00261082 | + | 0.00665226i | ||||
\(269\) | −0.822144 | + | 10.9708i | −0.0501270 | + | 0.668899i | 0.914383 | + | 0.404851i | \(0.132677\pi\) |
−0.964510 | + | 0.264048i | \(0.914942\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.6381 | − | 10.0622i | −1.55741 | − | 0.611237i | −0.578524 | − | 0.815665i | \(-0.696371\pi\) |
−0.978881 | + | 0.204429i | \(0.934466\pi\) | |||||||
\(272\) | 5.56594 | + | 6.97947i | 0.337485 | + | 0.423193i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.01149 | + | 6.28421i | −0.302755 | + | 0.379643i | ||||
\(275\) | 27.7966 | − | 16.0484i | 1.67620 | − | 0.967754i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.17380 | + | 5.53876i | 0.130611 | + | 0.332792i | 0.981187 | − | 0.193061i | \(-0.0618415\pi\) |
−0.850576 | + | 0.525853i | \(0.823746\pi\) | |||||||
\(278\) | 21.5742 | − | 6.65477i | 1.29394 | − | 0.399127i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 9.46605 | + | 21.1294i | 0.565705 | + | 1.26272i | ||||
\(281\) | −9.10986 | + | 18.9168i | −0.543449 | + | 1.12848i | 0.430683 | + | 0.902503i | \(0.358273\pi\) |
−0.974132 | + | 0.225980i | \(0.927442\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.58714 | + | 14.0617i | 0.569896 | + | 0.835884i | 0.997686 | − | 0.0679943i | \(-0.0216600\pi\) |
−0.427790 | + | 0.903878i | \(0.640708\pi\) | |||||||
\(284\) | −4.36930 | + | 4.70899i | −0.259270 | + | 0.279427i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.9637 | − | 5.46956i | 1.41700 | − | 0.323422i | ||||
\(287\) | −2.37531 | − | 0.805131i | −0.140210 | − | 0.0475254i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.87659 | − | 9.16414i | 0.580976 | − | 0.539067i | ||||
\(290\) | −53.5195 | + | 8.06676i | −3.14277 | + | 0.473697i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.26853 | + | 0.619641i | −0.483879 | + | 0.0362617i | ||||
\(293\) | −15.9997 | −0.934711 | −0.467356 | − | 0.884069i | \(-0.654793\pi\) | ||||
−0.467356 | + | 0.884069i | \(0.654793\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.3771 | −0.895292 | ||||||||
\(296\) | −14.3039 | + | 1.07193i | −0.831394 | + | 0.0623044i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −24.7173 | + | 3.72554i | −1.43184 | + | 0.215815i | ||||
\(299\) | 26.9468 | − | 25.0030i | 1.55837 | − | 1.44596i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.11100 | + | 4.03125i | 0.236954 | + | 0.232357i | ||||
\(302\) | 21.6935 | − | 4.95140i | 1.24832 | − | 0.284921i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.38024 | − | 1.48754i | 0.0791621 | − | 0.0853164i | ||||
\(305\) | −28.0407 | − | 41.1282i | −1.60561 | − | 2.35499i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.92187 | − | 18.5265i | 0.509198 | − | 1.05736i | −0.474950 | − | 0.880013i | \(-0.657534\pi\) |
0.984148 | − | 0.177348i | \(-0.0567519\pi\) | |||||||
\(308\) | 4.84300 | − | 0.965571i | 0.275956 | − | 0.0550185i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 10.5631 | − | 3.25829i | 0.599945 | − | 0.185058i | ||||
\(311\) | 6.50779 | + | 16.5816i | 0.369023 | + | 0.940255i | 0.987945 | + | 0.154803i | \(0.0494742\pi\) |
−0.618923 | + | 0.785452i | \(0.712431\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6742 | + | 6.74008i | −0.659863 | + | 0.380972i | −0.792225 | − | 0.610229i | \(-0.791077\pi\) |
0.132362 | + | 0.991201i | \(0.457744\pi\) | |||||||
\(314\) | −1.17103 | + | 1.46842i | −0.0660849 | + | 0.0828679i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.08384 | − | 2.61305i | −0.117225 | − | 0.146996i | ||||
\(317\) | −16.5602 | − | 6.49940i | −0.930114 | − | 0.365043i | −0.148576 | − | 0.988901i | \(-0.547469\pi\) |
−0.781538 | + | 0.623858i | \(0.785564\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.56336 | − | 34.2057i | 0.143521 | − | 1.91515i | ||||
\(320\) | −6.88484 | + | 17.5423i | −0.384874 | + | 0.980643i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 27.5930 | − | 24.2201i | 1.53770 | − | 1.34973i | ||||
\(323\) | 0.626776 | + | 0.499837i | 0.0348748 | + | 0.0278117i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 31.4354 | + | 18.1492i | 1.74372 | + | 1.00674i | ||||
\(326\) | −13.1108 | + | 5.14561i | −0.726140 | + | 0.284989i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.973843 | − | 2.02221i | −0.0537715 | − | 0.111658i | ||||
\(329\) | −0.646757 | − | 0.333758i | −0.0356569 | − | 0.0184007i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.3216 | + | 2.91227i | 1.06201 | + | 0.160073i | 0.656735 | − | 0.754121i | \(-0.271937\pi\) |
0.405277 | + | 0.914194i | \(0.367175\pi\) | |||||||
\(332\) | 5.49493 | − | 3.74638i | 0.301574 | − | 0.205609i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.70253 | + | 14.2310i | −0.530899 | + | 0.778685i | ||||
\(335\) | −0.191051 | − | 0.837050i | −0.0104382 | − | 0.0457330i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.93386 | − | 12.8541i | 0.159817 | − | 0.700206i | −0.829988 | − | 0.557781i | \(-0.811653\pi\) |
0.989806 | − | 0.142425i | \(-0.0454899\pi\) | |||||||
\(338\) | 4.91630 | + | 5.29851i | 0.267411 | + | 0.288201i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.34021 | + | 1.03032i | 0.181148 | + | 0.0558768i | ||||
\(341\) | 0.523538 | + | 6.98613i | 0.0283512 | + | 0.378320i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4568 | − | 1.53203i | −0.996573 | − | 0.0827216i | ||||
\(344\) | 5.15264i | 0.277811i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.75729 | + | 8.93890i | −0.148233 | + | 0.480558i | ||||
\(347\) | −2.43939 | − | 16.1843i | −0.130953 | − | 0.868819i | −0.953776 | − | 0.300520i | \(-0.902840\pi\) |
0.822822 | − | 0.568299i | \(-0.192398\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.7346 | + | 2.90660i | 0.681669 | + | 0.155587i | 0.549314 | − | 0.835616i | \(-0.314889\pi\) |
0.132355 | + | 0.991202i | \(0.457746\pi\) | |||||||
\(350\) | 30.8847 | + | 18.9868i | 1.65086 | + | 1.01489i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.53177 | + | 5.81686i | 0.454745 | + | 0.310040i | ||||
\(353\) | 9.44447 | + | 8.76319i | 0.502679 | + | 0.466418i | 0.890283 | − | 0.455408i | \(-0.150507\pi\) |
−0.387604 | + | 0.921826i | \(0.626697\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.02644 | − | 46.6174i | 0.372925 | − | 2.47420i | ||||
\(356\) | 5.54737 | + | 2.67147i | 0.294010 | + | 0.141588i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.66005 | − | 3.20731i | 0.351994 | − | 0.169512i | ||||
\(359\) | 4.74043 | + | 15.3681i | 0.250190 | + | 0.811097i | 0.990341 | + | 0.138655i | \(0.0442780\pi\) |
−0.740151 | + | 0.672441i | \(0.765246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.40888 | + | 16.2967i | −0.495204 | + | 0.857719i | ||||
\(362\) | 4.72378 | + | 8.18184i | 0.248277 | + | 0.430028i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.68417 | + | 4.19722i | 0.193103 | + | 0.219994i | ||||
\(365\) | 47.5763 | − | 37.9409i | 2.49026 | − | 1.98592i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.3415 | − | 1.82414i | −1.27061 | − | 0.0952194i | −0.577706 | − | 0.816245i | \(-0.696052\pi\) |
−0.692909 | + | 0.721025i | \(0.743671\pi\) | |||||||
\(368\) | 41.5735 | + | 3.11550i | 2.16717 | + | 0.162407i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −27.6991 | + | 22.0893i | −1.44001 | + | 1.14837i | ||||
\(371\) | −16.5696 | − | 7.03687i | −0.860250 | − | 0.365336i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.52813 | + | 6.11090i | 0.182680 | + | 0.316411i | 0.942792 | − | 0.333381i | \(-0.108190\pi\) |
−0.760112 | + | 0.649792i | \(0.774856\pi\) | |||||||
\(374\) | −5.50650 | + | 9.53755i | −0.284735 | + | 0.493175i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.191978 | − | 0.622377i | −0.00990050 | − | 0.0320966i | ||||
\(377\) | 34.9503 | − | 16.8312i | 1.80003 | − | 0.866850i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.8626 | − | 6.19432i | −0.660709 | − | 0.318181i | 0.0733102 | − | 0.997309i | \(-0.476644\pi\) |
−0.734020 | + | 0.679128i | \(0.762358\pi\) | |||||||
\(380\) | 0.118425 | − | 0.785700i | 0.00607509 | − | 0.0403056i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.93757 | + | 1.79780i | 0.0991348 | + | 0.0919836i | ||||
\(383\) | −17.5153 | − | 11.9417i | −0.894991 | − | 0.610194i | 0.0260499 | − | 0.999661i | \(-0.491707\pi\) |
−0.921041 | + | 0.389466i | \(0.872660\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −25.3748 | + | 25.8768i | −1.29322 | + | 1.31880i | ||||
\(386\) | 5.95385 | + | 1.35893i | 0.303043 | + | 0.0691676i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.185122 | − | 1.22820i | −0.00939815 | − | 0.0623526i | ||||
\(389\) | −7.88011 | + | 25.5467i | −0.399537 | + | 1.29527i | 0.502862 | + | 0.864367i | \(0.332280\pi\) |
−0.902399 | + | 0.430901i | \(0.858196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.4701i | 0.832930i | ||||||||
\(392\) | −10.5855 | − | 12.7531i | −0.534650 | − | 0.644131i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.424156 | − | 5.65997i | −0.0213687 | − | 0.285145i | ||||
\(395\) | 23.4386 | + | 7.22986i | 1.17933 | + | 0.363774i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3190 | + | 11.1212i | 0.517894 | + | 0.558157i | 0.936797 | − | 0.349874i | \(-0.113776\pi\) |
−0.418903 | + | 0.908031i | \(0.637585\pi\) | |||||||
\(398\) | −0.214029 | + | 0.937723i | −0.0107283 | + | 0.0470038i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.16050 | + | 40.1348i | 0.458025 | + | 2.00674i | ||||
\(401\) | 5.57969 | − | 8.18391i | 0.278637 | − | 0.408685i | −0.661253 | − | 0.750163i | \(-0.729975\pi\) |
0.939890 | + | 0.341478i | \(0.110927\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.54614 | + | 4.46308i | −0.326086 | + | 0.222322i | ||||
\(404\) | −1.82998 | − | 0.275825i | −0.0910449 | − | 0.0137228i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 35.3584 | − | 15.8407i | 1.75481 | − | 0.786162i | ||||
\(407\) | −9.74204 | − | 20.2296i | −0.482895 | − | 1.00274i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.75843 | + | 3.04496i | −0.383630 | + | 0.150564i | −0.549316 | − | 0.835615i | \(-0.685112\pi\) |
0.165686 | + | 0.986179i | \(0.447016\pi\) | |||||||
\(410\) | −4.80097 | − | 2.77184i | −0.237103 | − | 0.136892i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.17229 | + | 1.73234i | 0.107021 | + | 0.0853464i | ||||
\(413\) | 10.6042 | − | 2.95301i | 0.521799 | − | 0.145308i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.8315 | + | 45.4340i | −0.875316 | + | 2.23027i | ||||
\(416\) | −0.872681 | + | 11.6451i | −0.0427867 | + | 0.570949i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.33036 | + | 0.914597i | 0.113981 | + | 0.0447344i | ||||
\(419\) | 13.3451 | + | 16.7342i | 0.651948 | + | 0.817517i | 0.992440 | − | 0.122730i | \(-0.0391650\pi\) |
−0.340492 | + | 0.940248i | \(0.610594\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.2516 | − | 22.8867i | 0.889527 | − | 1.11543i | −0.103154 | − | 0.994665i | \(-0.532893\pi\) |
0.992681 | − | 0.120766i | \(-0.0385351\pi\) | |||||||
\(422\) | 11.2244 | − | 6.48043i | 0.546396 | − | 0.315462i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.88567 | − | 14.9964i | −0.285834 | − | 0.728292i | ||||
\(425\) | −15.5409 | + | 4.79374i | −0.753845 | + | 0.232530i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 27.2353 | + | 22.9774i | 1.31801 | + | 1.11196i | ||||
\(428\) | −1.66815 | + | 3.46394i | −0.0806329 | + | 0.167436i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 7.16915 | + | 10.5152i | 0.345727 | + | 0.507089i | ||||
\(431\) | −2.98851 | + | 3.22084i | −0.143951 | + | 0.155143i | −0.800912 | − | 0.598783i | \(-0.795651\pi\) |
0.656960 | + | 0.753925i | \(0.271842\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.5036 | − | 5.59278i | 1.17757 | − | 0.268772i | 0.411425 | − | 0.911444i | \(-0.365031\pi\) |
0.766141 | + | 0.642672i | \(0.222174\pi\) | |||||||
\(434\) | −6.65870 | + | 4.27547i | −0.319628 | + | 0.205229i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0410830 | + | 0.0381194i | −0.00196752 | + | 0.00182559i | ||||
\(437\) | 3.70207 | − | 0.557997i | 0.177094 | − | 0.0266926i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.75124 | + | 0.505936i | −0.322219 | + | 0.0241470i | −0.234858 | − | 0.972030i | \(-0.575463\pi\) |
−0.0873613 | + | 0.996177i | \(0.527843\pi\) | |||||||
\(440\) | −32.4333 | −1.54620 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −12.4547 | −0.592409 | ||||||||
\(443\) | −16.6583 | + | 1.24837i | −0.791461 | + | 0.0593118i | −0.464324 | − | 0.885665i | \(-0.653703\pi\) |
−0.327137 | + | 0.944977i | \(0.606084\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −44.6820 | + | 6.73473i | −2.11813 | + | 0.319257i | ||||
\(446\) | 0.714440 | − | 0.662903i | 0.0338297 | − | 0.0313894i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.37905 | − | 13.4195i | 0.0651539 | − | 0.634010i | ||||
\(449\) | 32.3488 | − | 7.38340i | 1.52663 | − | 0.348444i | 0.624890 | − | 0.780713i | \(-0.285144\pi\) |
0.901745 | + | 0.432269i | \(0.142287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.38969 | − | 2.57548i | 0.112526 | − | 0.121275i | ||||
\(452\) | 2.10900 | + | 3.09334i | 0.0991991 | + | 0.145498i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.18181 | − | 16.9897i | 0.383991 | − | 0.797366i | ||||
\(455\) | −39.6918 | − | 10.2198i | −1.86078 | − | 0.479111i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.8928 | + | 6.75304i | −1.02410 | + | 0.315894i | −0.760916 | − | 0.648851i | \(-0.775250\pi\) |
−0.263187 | + | 0.964745i | \(0.584774\pi\) | |||||||
\(458\) | −16.1657 | − | 41.1896i | −0.755375 | − | 1.92467i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.1372 | − | 8.16211i | 0.659150 | − | 0.380560i | ||||
\(461\) | 12.1939 | − | 15.2907i | 0.567928 | − | 0.712159i | −0.412073 | − | 0.911151i | \(-0.635195\pi\) |
0.980001 | + | 0.198992i | \(0.0637667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.3266 | + | 26.7427i | 0.991132 | + | 1.24284i | 0.970010 | + | 0.243064i | \(0.0781524\pi\) |
0.0211221 | + | 0.999777i | \(0.493276\pi\) | |||||||
\(464\) | 40.9536 | + | 16.0731i | 1.90122 | + | 0.746175i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.551916 | + | 7.36481i | −0.0255670 | + | 0.341168i | ||||
\(467\) | 12.4824 | − | 31.8045i | 0.577615 | − | 1.47174i | −0.281300 | − | 0.959620i | \(-0.590766\pi\) |
0.858915 | − | 0.512119i | \(-0.171139\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.292497 | + | 0.540548i | 0.0135062 | + | 0.0249602i | ||||
\(470\) | −1.25773 | − | 1.00300i | −0.0580146 | − | 0.0462651i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.53113 | + | 4.92545i | 0.392677 | + | 0.226712i | ||||
\(473\) | −7.50806 | + | 2.94670i | −0.345221 | + | 0.135489i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.60403 | + | 3.33080i | 0.0735978 | + | 0.152827i | ||||
\(476\) | −2.50130 | − | 0.0690669i | −0.114647 | − | 0.00316567i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.3905 | + | 2.16901i | 0.658204 | + | 0.0992083i | ||||
\(479\) | 0.503579 | − | 0.343335i | 0.0230091 | − | 0.0156874i | −0.551761 | − | 0.834002i | \(-0.686044\pi\) |
0.574770 | + | 0.818315i | \(0.305092\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.3040 | − | 20.9802i | 0.652208 | − | 0.956613i | ||||
\(482\) | −10.6558 | − | 46.6859i | −0.485356 | − | 2.12648i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.306645 | + | 1.34350i | −0.0139384 | + | 0.0610682i | ||||
\(485\) | 6.20014 | + | 6.68216i | 0.281534 | + | 0.303421i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.1670 | − | 3.13609i | −0.460709 | − | 0.142110i | 0.0557079 | − | 0.998447i | \(-0.482258\pi\) |
−0.516417 | + | 0.856337i | \(0.672735\pi\) | |||||||
\(488\) | 2.38303 | + | 31.7993i | 0.107875 | + | 1.43949i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −39.3465 | − | 11.2977i | −1.77749 | − | 0.510376i | ||||
\(491\) | − | 17.6897i | − | 0.798323i | −0.916881 | − | 0.399162i | \(-0.869301\pi\) | ||
0.916881 | − | 0.399162i | \(-0.130699\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.12303 | + | 16.6085i | −0.230730 | + | 0.748008i | ||||
\(494\) | 0.421956 | + | 2.79950i | 0.0189847 | + | 0.125955i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.76016 | − | 1.99945i | −0.393343 | − | 0.0897779i | ||||
\(497\) | 4.10685 | + | 33.4971i | 0.184217 | + | 1.50255i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.2187 | − | 16.5120i | −1.08418 | − | 0.739180i | −0.116963 | − | 0.993136i | \(-0.537316\pi\) |
−0.967216 | + | 0.253956i | \(0.918268\pi\) | |||||||
\(500\) | 4.99409 | + | 4.63384i | 0.223343 | + | 0.207232i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.38478 | − | 22.4565i | 0.151070 | − | 1.00228i | ||||
\(503\) | 14.5378 | + | 7.00104i | 0.648209 | + | 0.312161i | 0.728943 | − | 0.684575i | \(-0.240012\pi\) |
−0.0807339 | + | 0.996736i | \(0.525726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2368 | − | 5.89292i | 0.544530 | − | 0.262232i | ||||
\(506\) | 15.1597 | + | 49.1465i | 0.673930 | + | 2.18483i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.74639 | − | 6.48894i | 0.166219 | − | 0.287900i | ||||
\(509\) | −7.20106 | − | 12.4726i | −0.319181 | − | 0.552838i | 0.661136 | − | 0.750266i | \(-0.270075\pi\) |
−0.980317 | + | 0.197428i | \(0.936741\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.5229 | + | 35.3009i | −1.12907 | + | 1.56162i | ||||
\(512\) | 7.24463 | − | 5.77740i | 0.320170 | − | 0.255327i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.61341 | − | 0.570546i | −0.335813 | − | 0.0251657i | ||||
\(515\) | −20.3339 | − | 1.52382i | −0.896021 | − | 0.0671475i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.797095 | − | 0.635662i | 0.0350562 | − | 0.0279564i | ||||
\(518\) | 14.8595 | − | 20.5523i | 0.652890 | − | 0.903014i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.3395 | − | 31.7650i | −0.804242 | − | 1.39299i | ||||
\(521\) | 8.06844 | − | 13.9749i | 0.353485 | − | 0.612254i | −0.633373 | − | 0.773847i | \(-0.718330\pi\) |
0.986857 | + | 0.161593i | \(0.0516633\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.46609 | + | 27.4464i | 0.370196 | + | 1.20015i | 0.928759 | + | 0.370685i | \(0.120877\pi\) |
−0.558563 | + | 0.829462i | \(0.688647\pi\) | |||||||
\(524\) | −8.37465 | + | 4.03302i | −0.365848 | + | 0.176183i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −33.3716 | − | 16.0709i | −1.45507 | − | 0.700725i | ||||
\(527\) | 0.529071 | − | 3.51015i | 0.0230467 | − | 0.152905i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 39.5236 | + | 36.6726i | 1.71842 | + | 1.59446i | ||||
\(530\) | −32.8766 | − | 22.4149i | −1.42807 | − | 0.973639i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.0692177 | + | 0.564568i | 0.00300097 | + | 0.0244771i | ||||
\(533\) | 3.87367 | + | 0.884140i | 0.167787 | + | 0.0382963i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.20537 | − | 27.9008i | −0.181814 | − | 1.20626i | ||||
\(536\) | −0.162122 | + | 0.525585i | −0.00700259 | + | 0.0227018i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 17.4075i | − | 0.750490i | ||||||
\(539\) | 12.5293 | − | 22.7178i | 0.539676 | − | 0.978524i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.08248 | + | 14.4447i | 0.0465395 | + | 0.621027i | 0.970897 | + | 0.239499i | \(0.0769830\pi\) |
−0.924357 | + | 0.381528i | \(0.875398\pi\) | |||||||
\(542\) | 41.6431 | + | 12.8452i | 1.78872 | + | 0.551748i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.55880 | − | 3.83548i | −0.152582 | − | 0.164445i | ||||
\(545\) | 0.0915233 | − | 0.400990i | 0.00392043 | − | 0.0171765i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.09694 | + | 22.3311i | 0.217929 | + | 0.954810i | 0.959005 | + | 0.283389i | \(0.0914588\pi\) |
−0.741076 | + | 0.671421i | \(0.765684\pi\) | |||||||
\(548\) | 1.44113 | − | 2.11375i | 0.0615621 | − | 0.0902951i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −41.9614 | + | 28.6088i | −1.78924 | + | 1.21988i | ||||
\(551\) | 3.90673 | + | 0.588844i | 0.166432 | + | 0.0250856i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.5519 | − | 0.484651i | −0.746383 | − | 0.0206094i | ||||
\(554\) | −4.08487 | − | 8.48232i | −0.173550 | − | 0.360379i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.68919 | + | 2.62532i | −0.283685 | + | 0.111338i | ||||
\(557\) | −11.6819 | − | 6.74456i | −0.494979 | − | 0.285776i | 0.231659 | − | 0.972797i | \(-0.425585\pi\) |
−0.726638 | + | 0.687021i | \(0.758918\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.13143 | − | 5.68713i | −0.301628 | − | 0.240540i | ||||
\(560\) | −22.1218 | − | 40.8821i | −0.934816 | − | 1.72758i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.1373 | − | 30.9252i | 0.511979 | − | 1.30450i | ||||
\(563\) | −3.05208 | + | 40.7272i | −0.128630 | + | 1.71645i | 0.443493 | + | 0.896278i | \(0.353739\pi\) |
−0.572123 | + | 0.820168i | \(0.693880\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −25.5768 | − | 10.0381i | −1.07602 | − | 0.422308i | ||||
\(566\) | −16.7898 | − | 21.0538i | −0.705729 | − | 0.884957i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −18.8302 | + | 23.6124i | −0.790099 | + | 0.990753i | ||||
\(569\) | −0.886893 | + | 0.512048i | −0.0371805 | + | 0.0214662i | −0.518475 | − | 0.855093i | \(-0.673500\pi\) |
0.481295 | + | 0.876559i | \(0.340167\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.297902 | + | 0.759041i | 0.0124668 | + | 0.0317649i | 0.936972 | − | 0.349405i | \(-0.113616\pi\) |
−0.924505 | + | 0.381170i | \(0.875521\pi\) | |||||||
\(572\) | −7.47578 | + | 2.30597i | −0.312578 | + | 0.0964175i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.84310 | + | 0.989515i | 0.160408 | + | 0.0413016i | ||||
\(575\) | −32.9541 | + | 68.4298i | −1.37428 | + | 2.85372i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −25.9073 | − | 37.9990i | −1.07853 | − | 1.58192i | −0.778127 | − | 0.628107i | \(-0.783830\pi\) |
−0.300407 | − | 0.953811i | \(-0.597123\pi\) | |||||||
\(578\) | −14.5002 | + | 15.6275i | −0.603130 | + | 0.650020i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.7948 | − | 3.83329i | 0.697364 | − | 0.159169i | ||||
\(581\) | 3.57169 | − | 34.7560i | 0.148179 | − | 1.44192i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.4859 | − | 17.1524i | 0.765607 | − | 0.710379i | ||||
\(584\) | −38.5478 | + | 5.81015i | −1.59512 | + | 0.240426i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.2452 | − | 1.89186i | 1.04287 | − | 0.0781522i | ||||
\(587\) | 16.9176 | 0.698266 | 0.349133 | − | 0.937073i | \(-0.386476\pi\) | ||||
0.349133 | + | 0.937073i | \(0.386476\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.806918 | −0.0332485 | ||||||||
\(590\) | 24.2629 | − | 1.81825i | 0.998889 | − | 0.0748564i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 28.4764 | − | 4.29213i | 1.17037 | − | 0.176405i | ||||
\(593\) | −19.1336 | + | 17.7534i | −0.785722 | + | 0.729044i | −0.967107 | − | 0.254368i | \(-0.918132\pi\) |
0.181385 | + | 0.983412i | \(0.441942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.4527 | − | 9.92199i | 0.633498 | − | 0.406762i | ||||
\(596\) | 7.75646 | − | 1.77036i | 0.317717 | − | 0.0725168i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −39.5617 | + | 42.6374i | −1.61780 | + | 1.74357i | ||||
\(599\) | 14.6447 | + | 21.4799i | 0.598368 | + | 0.877644i | 0.999259 | − | 0.0384812i | \(-0.0122520\pi\) |
−0.400892 | + | 0.916126i | \(0.631300\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.05090 | − | 18.7944i | 0.369194 | − | 0.766639i | −0.630763 | − | 0.775976i | \(-0.717258\pi\) |
0.999956 | + | 0.00933691i | \(0.00297207\pi\) | |||||||
\(602\) | −6.96324 | − | 5.87463i | −0.283800 | − | 0.239432i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.76755 | + | 2.08751i | −0.275368 | + | 0.0849397i | ||||
\(605\) | −3.69485 | − | 9.41433i | −0.150217 | − | 0.382747i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.8025 | − | 16.0518i | 1.12847 | − | 0.651521i | 0.184919 | − | 0.982754i | \(-0.440798\pi\) |
0.943549 | + | 0.331232i | \(0.107464\pi\) | |||||||
\(608\) | −0.741548 | + | 0.929872i | −0.0300738 | + | 0.0377113i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 49.1073 | + | 61.5787i | 1.98830 | + | 2.49325i | ||||
\(611\) | 1.07328 | + | 0.421233i | 0.0434204 | + | 0.0170413i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.24518 | − | 43.3039i | 0.131072 | − | 1.74903i | −0.413673 | − | 0.910426i | \(-0.635754\pi\) |
0.544744 | − | 0.838602i | \(-0.316627\pi\) | |||||||
\(614\) | −11.8868 | + | 30.2870i | −0.479712 | + | 1.22229i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 22.3663 | − | 6.22846i | 0.901164 | − | 0.250952i | ||||
\(617\) | −16.7016 | − | 13.3191i | −0.672382 | − | 0.536207i | 0.226712 | − | 0.973962i | \(-0.427202\pi\) |
−0.899094 | + | 0.437755i | \(0.855774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.9448 | − | 17.8660i | −1.24378 | − | 0.718095i | −0.273916 | − | 0.961754i | \(-0.588319\pi\) |
−0.969861 | + | 0.243658i | \(0.921652\pi\) | |||||||
\(620\) | −3.27514 | + | 1.28540i | −0.131533 | + | 0.0516229i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.2290 | − | 25.3938i | −0.490339 | − | 1.01820i | ||||
\(623\) | 29.5198 | − | 13.2250i | 1.18268 | − | 0.529849i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.62272 | − | 0.998215i | −0.264909 | − | 0.0399286i | ||||
\(626\) | 17.6232 | − | 12.0153i | 0.704364 | − | 0.480227i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.336747 | − | 0.493918i | 0.0134377 | − | 0.0197095i | ||||
\(629\) | 2.53162 | + | 11.0918i | 0.100942 | + | 0.442257i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.787058 | − | 3.44833i | 0.0313323 | − | 0.137276i | −0.956843 | − | 0.290607i | \(-0.906143\pi\) |
0.988175 | + | 0.153331i | \(0.0490000\pi\) | |||||||
\(632\) | −10.6878 | − | 11.5187i | −0.425137 | − | 0.458189i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26.8981 | + | 8.29698i | 1.06826 | + | 0.329515i | ||||
\(635\) | 4.10934 | + | 54.8353i | 0.163074 | + | 2.17607i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.3344 | − | 0.574705i | 1.16227 | − | 0.0227706i | ||||
\(638\) | 54.2747i | 2.14876i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 14.8594 | − | 48.1730i | 0.587370 | − | 1.90421i | ||||
\(641\) | 2.62231 | + | 17.3979i | 0.103575 | + | 0.687176i | 0.979006 | + | 0.203833i | \(0.0653398\pi\) |
−0.875431 | + | 0.483344i | \(0.839422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.49763 | − | 0.798310i | −0.137933 | − | 0.0314823i | 0.152997 | − | 0.988227i | \(-0.451108\pi\) |
−0.290930 | + | 0.956744i | \(0.593965\pi\) | |||||||
\(644\) | −8.18169 | + | 8.34355i | −0.322404 | + | 0.328782i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.04807 | − | 0.714559i | −0.0412356 | − | 0.0281139i | ||||
\(647\) | −9.27890 | − | 8.60956i | −0.364791 | − | 0.338477i | 0.476386 | − | 0.879236i | \(-0.341946\pi\) |
−0.841177 | + | 0.540760i | \(0.818137\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.29823 | + | 15.2477i | −0.0902133 | + | 0.598526i | ||||
\(650\) | −51.7465 | − | 24.9198i | −2.02967 | − | 0.977436i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.03887 | − | 1.94502i | 0.158174 | − | 0.0761727i | ||||
\(653\) | −5.99595 | − | 19.4384i | −0.234640 | − | 0.760684i | −0.993938 | − | 0.109941i | \(-0.964934\pi\) |
0.759298 | − | 0.650743i | \(-0.225542\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.1083 | − | 59.0773i | 1.33272 | − | 2.30834i | ||||
\(656\) | 2.25310 | + | 3.90248i | 0.0879687 | + | 0.152366i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.05995 | + | 0.450147i | 0.0413213 | + | 0.0175486i | ||||
\(659\) | −3.85986 | + | 3.07813i | −0.150359 | + | 0.119907i | −0.695780 | − | 0.718255i | \(-0.744941\pi\) |
0.545421 | + | 0.838162i | \(0.316370\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9885 | − | 2.17239i | −1.12752 | − | 0.0844961i | −0.502119 | − | 0.864798i | \(-0.667446\pi\) |
−0.625402 | + | 0.780302i | \(0.715065\pi\) | |||||||
\(662\) | −30.8311 | − | 2.31047i | −1.19828 | − | 0.0897990i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 24.4458 | − | 19.4948i | 0.948680 | − | 0.756547i | ||||
\(665\) | −2.75374 | − | 3.13722i | −0.106785 | − | 0.121656i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 40.5844 | + | 70.2942i | 1.57143 | + | 2.72180i | ||||
\(668\) | 2.74101 | − | 4.74757i | 0.106053 | − | 0.183689i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.400428 | + | 1.29815i | 0.0154699 | + | 0.0501521i | ||||
\(671\) | −44.9729 | + | 21.6578i | −1.73616 | + | 0.836091i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.4825 | + | 17.0875i | 1.36775 | + | 0.658673i | 0.966350 | − | 0.257230i | \(-0.0828099\pi\) |
0.401399 | + | 0.915903i | \(0.368524\pi\) | |||||||
\(674\) | −3.10929 | + | 20.6288i | −0.119765 | + | 0.794591i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.68642 | − | 1.56477i | −0.0648622 | − | 0.0601833i | ||||
\(677\) | −12.9080 | − | 8.80049i | −0.496093 | − | 0.338230i | 0.289289 | − | 0.957242i | \(-0.406581\pi\) |
−0.785382 | + | 0.619011i | \(0.787533\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.55890 | − | 3.41741i | −0.213331 | − | 0.131148i | ||||
\(680\) | 16.0220 | + | 3.65691i | 0.614414 | + | 0.140236i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.65213 | − | 10.9612i | −0.0632635 | − | 0.419726i | ||||
\(683\) | −5.65164 | + | 18.3222i | −0.216254 | + | 0.701078i | 0.780828 | + | 0.624746i | \(0.214797\pi\) |
−0.997082 | + | 0.0763327i | \(0.975679\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.7751i | 0.717359i | ||||||||
\(686\) | 29.3033 | + | 0.234913i | 1.11881 | + | 0.00896901i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.773071 | − | 10.3159i | −0.0294730 | − | 0.393290i | ||||
\(689\) | 27.2518 | + | 8.40608i | 1.03821 | + | 0.320246i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.36039 | + | 5.77713i | 0.203919 | + | 0.219772i | 0.826728 | − | 0.562601i | \(-0.190199\pi\) |
−0.622810 | + | 0.782373i | \(0.714009\pi\) | |||||||
\(692\) | 0.662525 | − | 2.90271i | 0.0251854 | − | 0.110345i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.76270 | + | 25.2480i | 0.218749 | + | 0.958403i | ||||
\(695\) | 29.7079 | − | 43.5734i | 1.12688 | − | 1.65283i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.47089 | + | 1.00284i | −0.0557139 | + | 0.0379851i | ||||
\(698\) | −20.4371 | − | 3.08040i | −0.773556 | − | 0.116595i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.2542 | − | 5.29165i | −0.387571 | − | 0.200005i | ||||
\(701\) | −13.8180 | − | 28.6935i | −0.521900 | − | 1.08374i | −0.980758 | − | 0.195227i | \(-0.937456\pi\) |
0.458858 | − | 0.888510i | \(-0.348259\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.40738 | − | 0.944826i | 0.0907959 | − | 0.0356348i | ||||
\(704\) | 16.3657 | + | 9.44872i | 0.616804 | + | 0.356112i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.9382 | − | 12.7103i | −0.599842 | − | 0.478358i | ||||
\(707\) | −7.30692 | + | 6.41375i | −0.274805 | + | 0.241214i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.01627 | − | 12.7813i | 0.188390 | − | 0.480010i | −0.805207 | − | 0.592994i | \(-0.797946\pi\) |
0.993597 | + | 0.112984i | \(0.0360409\pi\) | |||||||
\(710\) | −5.57449 | + | 74.3864i | −0.209207 | + | 2.79167i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 26.9465 | + | 10.5757i | 1.00986 | + | 0.396341i | ||||
\(713\) | −10.3361 | − | 12.9611i | −0.387090 | − | 0.485395i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.7977 | − | 44.8889i | 1.33876 | − | 1.67875i | ||||
\(716\) | −2.03755 | + | 1.17638i | −0.0761470 | + | 0.0439635i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.29689 | − | 23.6881i | −0.346957 | − | 0.884032i | ||||
\(719\) | −42.4928 | + | 13.1073i | −1.58472 | + | 0.488820i | −0.957113 | − | 0.289714i | \(-0.906440\pi\) |
−0.627602 | + | 0.778534i | \(0.715963\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3151 | − | 2.85407i | 0.533122 | − | 0.106291i | ||||
\(722\) | 12.9189 | − | 26.8263i | 0.480791 | − | 0.998373i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.69389 | − | 2.48449i | −0.0629531 | − | 0.0923353i | ||||
\(725\) | −54.5160 | + | 58.7542i | −2.02467 | + | 2.18208i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.7733 | + | 7.25205i | −1.17841 | + | 0.268964i | −0.766489 | − | 0.642257i | \(-0.777998\pi\) |
−0.411918 | + | 0.911221i | \(0.635141\pi\) | |||||||
\(728\) | 18.7472 | + | 18.3835i | 0.694818 | + | 0.681339i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −70.5823 | + | 65.4908i | −2.61237 | + | 2.42392i | ||||
\(731\) | 4.04120 | − | 0.609113i | 0.149469 | − | 0.0225289i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −16.3986 | + | 1.22891i | −0.605697 | + | 0.0453907i | −0.374049 | − | 0.927409i | \(-0.622031\pi\) |
−0.231648 | + | 0.972800i | \(0.574412\pi\) | |||||||
\(734\) | 38.6230 | 1.42560 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.4347 | −0.900676 | ||||||||
\(737\) | −0.858560 | + | 0.0643402i | −0.0316255 | + | 0.00237000i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.1029 | + | 3.03003i | −0.739498 | + | 0.111461i | −0.507980 | − | 0.861369i | \(-0.669608\pi\) |
−0.231519 | + | 0.972830i | \(0.574369\pi\) | |||||||
\(740\) | 8.26605 | − | 7.66977i | 0.303866 | − | 0.281946i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 26.9765 | + | 9.14391i | 0.990338 | + | 0.335684i | ||||
\(743\) | 0.819561 | − | 0.187060i | 0.0300668 | − | 0.00686255i | −0.207461 | − | 0.978243i | \(-0.566520\pi\) |
0.237528 | + | 0.971381i | \(0.423663\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.7140 | + | 42.8015i | −1.45501 | + | 1.56813i | ||||
\(746\) | −6.28946 | − | 9.22494i | −0.230273 | − | 0.337749i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.52086 | − | 3.15811i | 0.0556083 | − | 0.115472i | ||||
\(749\) | 8.25809 | + | 18.4330i | 0.301744 | + | 0.673528i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.6040 | − | 9.74854i | 1.15325 | − | 0.355729i | 0.341581 | − | 0.939852i | \(-0.389038\pi\) |
0.811665 | + | 0.584123i | \(0.198561\pi\) | |||||||
\(752\) | 0.477730 | + | 1.21724i | 0.0174210 | + | 0.0443880i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −53.1563 | + | 30.6898i | −1.93584 | + | 1.11766i | ||||
\(755\) | 32.4064 | − | 40.6363i | 1.17939 | − | 1.47891i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.0169 | − | 23.8464i | −0.691180 | − | 0.866712i | 0.305150 | − | 0.952304i | \(-0.401293\pi\) |
−0.996330 | + | 0.0855920i | \(0.972722\pi\) | |||||||
\(758\) | 21.0278 | + | 8.25281i | 0.763765 | + | 0.299756i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.279167 | − | 3.72522i | 0.0101264 | − | 0.135128i | ||||
\(761\) | 13.0112 | − | 33.1520i | 0.471656 | − | 1.20176i | −0.475136 | − | 0.879912i | \(-0.657601\pi\) |
0.946792 | − | 0.321847i | \(-0.104304\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.0138903 | + | 0.294102i | 0.000502862 | + | 0.0106472i | ||||
\(764\) | −0.657730 | − | 0.524522i | −0.0237958 | − | 0.0189765i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.0487 | + | 16.7713i | 1.04957 | + | 0.605970i | ||||
\(767\) | −16.2331 | + | 6.37102i | −0.586143 | + | 0.230044i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.2443 | − | 27.5020i | −0.477601 | − | 0.991749i | −0.991033 | − | 0.133619i | \(-0.957340\pi\) |
0.513432 | − | 0.858131i | \(-0.328374\pi\) | |||||||
\(770\) | 36.9779 | − | 43.8302i | 1.33259 | − | 1.57953i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.92202 | − | 0.289698i | −0.0691751 | − | 0.0104265i | ||||
\(773\) | 6.52978 | − | 4.45193i | 0.234860 | − | 0.160125i | −0.440172 | − | 0.897914i | \(-0.645082\pi\) |
0.675032 | + | 0.737789i | \(0.264130\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.22143 | − | 13.5253i | 0.331243 | − | 0.485845i | ||||
\(776\) | −1.29943 | − | 5.69318i | −0.0466469 | − | 0.204373i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.41293 | − | 41.2408i | 0.337470 | − | 1.47855i | ||||
\(779\) | 0.275245 | + | 0.296643i | 0.00986167 | + | 0.0106284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −45.1750 | − | 13.9346i | −1.61649 | − | 0.498620i | ||||
\(782\) | −1.94749 | − | 25.9875i | −0.0696422 | − | 0.929311i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 23.1063 | + | 23.9444i | 0.825226 | + | 0.855158i | ||||
\(785\) | 4.38715i | 0.156584i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.67101 | − | 31.3526i | 0.344734 | − | 1.11760i | −0.602785 | − | 0.797903i | \(-0.705942\pi\) |
0.947520 | − | 0.319698i | \(-0.103581\pi\) | |||||||
\(788\) | 0.269247 | + | 1.78634i | 0.00959153 | + | 0.0636356i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −37.8377 | − | 8.63620i | −1.34620 | − | 0.307262i | ||||
\(791\) | 19.5657 | + | 2.01066i | 0.695676 | + | 0.0714909i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.6416 | − | 31.7997i | −1.65629 | − | 1.12924i | ||||
\(794\) | −17.5968 | − | 16.3275i | −0.624488 | − | 0.579441i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.0456271 | − | 0.302716i | 0.00161721 | − | 0.0107295i | ||||
\(797\) | −35.9376 | − | 17.3066i | −1.27297 | − | 0.613032i | −0.329399 | − | 0.944191i | \(-0.606846\pi\) |
−0.943575 | + | 0.331159i | \(0.892560\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.465434 | + | 0.224141i | −0.0164659 | + | 0.00792955i | ||||
\(800\) | −7.11189 | − | 23.0562i | −0.251443 | − | 0.815159i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.83625 | + | 13.5728i | −0.276708 | + | 0.479272i | ||||
\(803\) | −30.5109 | − | 52.8465i | −1.07671 | − | 1.86491i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.1178 | − | 84.4174i | 0.532831 | − | 2.97532i | ||||
\(806\) | 9.80113 | − | 7.81614i | 0.345230 | − | 0.275312i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.67644 | − | 0.650209i | −0.305236 | − | 0.0228743i | ||||
\(809\) | 5.36904 | + | 0.402354i | 0.188765 | + | 0.0141460i | 0.168777 | − | 0.985654i | \(-0.446018\pi\) |
0.0199880 | + | 0.999800i | \(0.493637\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −12.0024 | + | 9.57160i | −0.421462 | + | 0.336104i | −0.811146 | − | 0.584844i | \(-0.801156\pi\) |
0.389684 | + | 0.920949i | \(0.372584\pi\) | |||||||
\(812\) | −10.8457 | + | 5.86872i | −0.380608 | + | 0.205952i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 17.7636 | + | 30.7674i | 0.622612 | + | 1.07840i | ||||
\(815\) | −16.4495 | + | 28.4914i | −0.576201 | + | 0.998010i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.273826 | − | 0.887723i | −0.00957997 | − | 0.0310575i | ||||
\(818\) | 11.8816 | − | 5.72190i | 0.415432 | − | 0.200061i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.58972 | + | 0.765567i | 0.0555153 | + | 0.0267348i | ||||
\(821\) | −0.838008 | + | 5.55982i | −0.0292467 | + | 0.194039i | −0.998683 | − | 0.0513036i | \(-0.983662\pi\) |
0.969436 | + | 0.245343i | \(0.0789005\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.6016 | + | 9.83684i | 0.369548 | + | 0.342891i | 0.842985 | − | 0.537937i | \(-0.180796\pi\) |
−0.473437 | + | 0.880828i | \(0.656987\pi\) | |||||||
\(824\) | 10.7930 | + | 7.35857i | 0.375993 | + | 0.256348i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.3827 | + | 5.91330i | −0.570029 | + | 0.205750i | ||||
\(827\) | −16.7531 | − | 3.82379i | −0.582562 | − | 0.132966i | −0.0789240 | − | 0.996881i | \(-0.525148\pi\) |
−0.503638 | + | 0.863915i | \(0.668006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.15913 | − | 27.5940i | −0.144453 | − | 0.958380i | −0.937191 | − | 0.348818i | \(-0.886583\pi\) |
0.792738 | − | 0.609563i | \(-0.208655\pi\) | |||||||
\(830\) | 22.7633 | − | 73.7968i | 0.790125 | − | 2.56152i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.3712i | 0.740915i | ||||||||
\(833\) | −8.75090 | + | 9.80980i | −0.303201 | + | 0.339890i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.00656 | + | 40.1197i | 0.104046 | + | 1.38840i | ||||
\(836\) | −0.761388 | − | 0.234857i | −0.0263332 | − | 0.00812271i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.0353 | − | 24.8261i | −0.795740 | − | 0.857604i | ||||
\(839\) | −5.12198 | + | 22.4409i | −0.176830 | + | 0.774745i | 0.806251 | + | 0.591574i | \(0.201493\pi\) |
−0.983081 | + | 0.183171i | \(0.941364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6071 | + | 55.2355i | 0.434729 | + | 1.90467i | ||||
\(842\) | −26.0921 | + | 38.2701i | −0.899194 | + | 1.31888i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.40840 | + | 2.32381i | −0.117322 | + | 0.0799887i | ||||
\(845\) | 16.6950 | + | 2.51636i | 0.574324 | + | 0.0865654i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.35592 | + | 5.78265i | 0.149671 | + | 0.198694i | ||||
\(848\) | 14.0335 | + | 29.1408i | 0.481912 | + | 1.00070i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 23.9545 | − | 9.40144i | 0.821632 | − | 0.322467i | ||||
\(851\) | 46.0131 | + | 26.5657i | 1.57731 | + | 0.910660i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.2780 | + | 36.1080i | 1.55029 | + | 1.23631i | 0.856519 | + | 0.516115i | \(0.172622\pi\) |
0.693768 | + | 0.720198i | \(0.255949\pi\) | |||||||
\(854\) | −45.6903 | − | 33.0347i | −1.56349 | − | 1.13042i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.60379 | + | 16.8262i | −0.225713 | + | 0.575107i | ||||
\(857\) | 1.05092 | − | 14.0236i | 0.0358988 | − | 0.479036i | −0.950062 | − | 0.312061i | \(-0.898981\pi\) |
0.985961 | − | 0.166976i | \(-0.0534001\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.1206 | − | 9.07416i | −0.788864 | − | 0.309606i | −0.0635090 | − | 0.997981i | \(-0.520229\pi\) |
−0.725355 | + | 0.688375i | \(0.758324\pi\) | |||||||
\(860\) | −2.52553 | − | 3.16692i | −0.0861200 | − | 0.107991i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.33459 | − | 5.43540i | 0.147637 | − | 0.185130i | ||||
\(863\) | −35.8904 | + | 20.7213i | −1.22172 | + | 0.705363i | −0.965285 | − | 0.261198i | \(-0.915882\pi\) |
−0.256438 | + | 0.966561i | \(0.582549\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.98295 | + | 20.3402i | 0.271428 | + | 0.691588i | ||||
\(866\) | −38.0018 | + | 11.7220i | −1.29135 | + | 0.398330i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.01172 | − | 1.51538i | 0.0682823 | − | 0.0514352i | ||||
\(869\) | 10.6721 | − | 22.1608i | 0.362026 | − | 0.751755i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.548490 | − | 0.804487i | −0.0185849 | − | 0.0272590i | ||||
\(872\) | −0.179217 | + | 0.193150i | −0.00606907 | + | 0.00654090i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.77535 | + | 1.31819i | −0.195354 | + | 0.0445883i | ||||
\(875\) | 35.5252 | − | 4.35550i | 1.20097 | − | 0.147243i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.9057 | + | 30.5320i | −1.11115 | + | 1.03099i | −0.111840 | + | 0.993726i | \(0.535674\pi\) |
−0.999305 | + | 0.0372659i | \(0.988135\pi\) | |||||||
\(878\) | 10.5927 | − | 1.59659i | 0.357485 | − | 0.0538822i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 64.9336 | − | 4.86610i | 2.18891 | − | 0.164036i | ||||
\(881\) | 41.6366 | 1.40277 | 0.701387 | − | 0.712781i | \(-0.252564\pi\) | ||||
0.701387 | + | 0.712781i | \(0.252564\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.6568 | −0.964379 | −0.482190 | − | 0.876067i | \(-0.660158\pi\) | ||||
−0.482190 | + | 0.876067i | \(0.660158\pi\) | |||||||
\(884\) | 3.95301 | − | 0.296237i | 0.132954 | − | 0.00996353i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 26.1368 | − | 3.93949i | 0.878084 | − | 0.132350i | ||||
\(887\) | −15.9961 | + | 14.8422i | −0.537095 | + | 0.498352i | −0.901435 | − | 0.432914i | \(-0.857485\pi\) |
0.364340 | + | 0.931266i | \(0.381295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.3643 | − | 37.0258i | −0.448226 | − | 1.24180i | ||||
\(890\) | 69.7054 | − | 15.9098i | 2.33653 | − | 0.533298i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.210990 | + | 0.227393i | −0.00706446 | + | 0.00761367i | ||||
\(893\) | 0.0661499 | + | 0.0970241i | 0.00221362 | + | 0.00324679i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.49178 | − | 15.5568i | 0.250423 | − | 0.520008i | ||||
\(896\) | −0.996094 | + | 36.0741i | −0.0332772 | + | 1.20515i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −50.1687 | + | 15.4750i | −1.67415 | + | 0.516407i | ||||
\(899\) | −6.39137 | − | 16.2850i | −0.213164 | − | 0.543134i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.0659 | + | 6.38891i | −0.368659 | + | 0.212845i | ||||
\(902\) | −3.46606 | + | 4.34630i | −0.115407 | + | 0.144716i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.9745 | + | 13.7616i | 0.365006 | + | 0.457703i | ||||
\(905\) | 20.5426 | + | 8.06238i | 0.682859 | + | 0.268002i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.16496 | + | 42.2334i | −0.105091 | + | 1.40234i | 0.656522 | + | 0.754307i | \(0.272027\pi\) |
−0.761613 | + | 0.648032i | \(0.775592\pi\) | |||||||
\(908\) | −2.19273 | + | 5.58699i | −0.0727683 | + | 0.185411i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 63.8363 | + | 11.4320i | 2.11615 | + | 0.378968i | ||||
\(911\) | 17.7832 | + | 14.1816i | 0.589184 | + | 0.469859i | 0.872128 | − | 0.489278i | \(-0.162740\pi\) |
−0.282944 | + | 0.959136i | \(0.591311\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.3866 | + | 24.4719i | 1.40279 | + | 0.809902i | ||||
\(914\) | 33.7452 | − | 13.2440i | 1.11619 | − | 0.438073i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.11057 | + | 12.6887i | 0.201899 | + | 0.419247i | ||||
\(917\) | −12.1763 | + | 47.2903i | −0.402095 | + | 1.56166i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.3160 | + | 2.45924i | 0.538215 | + | 0.0811229i | 0.412524 | − | 0.910947i | \(-0.364647\pi\) |
0.125691 | + | 0.992069i | \(0.459885\pi\) | |||||||
\(920\) | 63.4120 | − | 43.2336i | 2.09063 | − | 1.42537i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.4322 | + | 25.5684i | −0.574100 | + | 0.842050i | ||||
\(923\) | −11.8968 | − | 52.1235i | −0.391589 | − | 1.71566i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.6745 | + | 51.1492i | −0.383855 | + | 1.68178i | ||||
\(926\) | −36.8125 | − | 39.6744i | −1.20973 | − | 1.30378i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −24.6400 | − | 7.60043i | −0.808847 | − | 0.249496i | ||||
\(929\) | −3.24578 | − | 43.3120i | −0.106491 | − | 1.42102i | −0.752953 | − | 0.658074i | \(-0.771371\pi\) |
0.646463 | − | 0.762946i | \(-0.276248\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.50147 | + | 1.63463i | 0.0819824 | + | 0.0535729i | ||||
\(932\) | − | 2.35065i | − | 0.0769982i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.9347 | + | 51.6589i | −0.521398 | + | 1.69033i | ||||
\(935\) | 3.83407 | + | 25.4374i | 0.125387 | + | 0.831891i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −21.1113 | − | 4.81853i | −0.689677 | − | 0.157414i | −0.136702 | − | 0.990612i | \(-0.543650\pi\) |
−0.552975 | + | 0.833198i | \(0.686508\pi\) | |||||||
\(938\) | −0.525434 | − | 0.818321i | −0.0171560 | − | 0.0267191i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.423048 | + | 0.288429i | 0.0137983 | + | 0.00940752i | ||||
\(941\) | 22.4245 | + | 20.8069i | 0.731019 | + | 0.678286i | 0.955100 | − | 0.296284i | \(-0.0957476\pi\) |
−0.224081 | + | 0.974571i | \(0.571938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.23910 | + | 8.22090i | −0.0403507 | + | 0.267709i | ||||
\(944\) | −17.8189 | − | 8.58111i | −0.579955 | − | 0.279291i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.4982 | − | 5.53724i | 0.373839 | − | 0.180031i | ||||
\(947\) | −1.34716 | − | 4.36738i | −0.0437768 | − | 0.141921i | 0.931046 | − | 0.364902i | \(-0.118897\pi\) |
−0.974823 | + | 0.222981i | \(0.928421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 34.5050 | − | 59.7645i | 1.12008 | − | 1.94004i | ||||
\(950\) | −2.92477 | − | 5.06585i | −0.0948920 | − | 0.164358i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.7511 | + | 0.555001i | −0.380857 | + | 0.0179877i | ||||
\(953\) | −27.4267 | + | 21.8721i | −0.888439 | + | 0.708506i | −0.957293 | − | 0.289120i | \(-0.906637\pi\) |
0.0688538 | + | 0.997627i | \(0.478066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.15675 | + | 0.461385i | 0.199228 | + | 0.0149301i | ||||
\(956\) | −4.61900 | − | 0.346146i | −0.149389 | − | 0.0111952i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.753978 | + | 0.601278i | −0.0243599 | + | 0.0194264i | ||||
\(959\) | −3.60554 | − | 12.9475i | −0.116429 | − | 0.418096i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7135 | − | 23.7525i | −0.442371 | − | 0.766209i | ||||
\(962\) | −20.0889 | + | 34.7950i | −0.647693 | + | 1.12184i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.49248 | + | 14.5643i | 0.144693 | + | 0.469083i | ||||
\(965\) | 12.8523 | − | 6.18933i | 0.413729 | − | 0.199241i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.17747 | − | 3.93806i | −0.262970 | − | 0.126640i | 0.297754 | − | 0.954643i | \(-0.403763\pi\) |
−0.560723 | + | 0.828003i | \(0.689477\pi\) | |||||||
\(968\) | −0.965625 | + | 6.40650i | −0.0310364 | + | 0.205913i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.5730 | − | 9.81035i | −0.339480 | − | 0.314991i | ||||
\(971\) | 10.2557 | + | 6.99225i | 0.329123 | + | 0.224392i | 0.716595 | − | 0.697489i | \(-0.245699\pi\) |
−0.387473 | + | 0.921881i | \(0.626652\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.1190 | + | 35.7537i | −0.388518 | + | 1.14621i | ||||
\(974\) | 16.4128 | + | 3.74612i | 0.525901 | + | 0.120033i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.54196 | − | 63.3068i | −0.305431 | − | 2.02640i | ||||
\(977\) | −9.66937 | + | 31.3473i | −0.309350 | + | 1.00289i | 0.658757 | + | 0.752355i | \(0.271082\pi\) |
−0.968108 | + | 0.250534i | \(0.919394\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.3125i | 1.44819i | ||||||||
\(980\) | 12.7570 | + | 2.64992i | 0.407506 | + | 0.0846485i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.09169 | + | 27.9117i | 0.0667487 | + | 0.890699i | ||||
\(983\) | 5.95985 | + | 1.83837i | 0.190090 | + | 0.0586349i | 0.388338 | − | 0.921517i | \(-0.373049\pi\) |
−0.198249 | + | 0.980152i | \(0.563525\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.01766 | − | 9.71873i | −0.287327 | − | 0.309665i | ||||
\(986\) | 6.11956 | − | 26.8115i | 0.194886 | − | 0.853853i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.200512 | − | 0.878500i | −0.00637913 | − | 0.0279488i | ||||
\(989\) | 10.7514 | − | 15.7695i | 0.341876 | − | 0.501440i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.72667 | + | 1.17722i | −0.0548493 | + | 0.0373956i | −0.590434 | − | 0.807086i | \(-0.701044\pi\) |
0.535585 | + | 0.844481i | \(0.320091\pi\) | |||||||
\(992\) | 5.20759 | + | 0.784918i | 0.165341 | + | 0.0249212i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −10.4408 | − | 52.3680i | −0.331164 | − | 1.66101i | ||||
\(995\) | 0.974810 | + | 2.02421i | 0.0309036 | + | 0.0641719i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.1794 | − | 10.6671i | 0.860779 | − | 0.337831i | 0.106443 | − | 0.994319i | \(-0.466054\pi\) |
0.754337 | + | 0.656488i | \(0.227959\pi\) | |||||||
\(998\) | 40.1661 | + | 23.1899i | 1.27143 | + | 0.734063i | ||||
\(999\) | 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 | 441.2.bg.a.17.4 | ✓ | 216 | |
3.2 | odd | 2 | inner | 441.2.bg.a.17.15 | yes | 216 | |
49.26 | odd | 42 | inner | 441.2.bg.a.26.15 | yes | 216 | |
147.26 | even | 42 | inner | 441.2.bg.a.26.4 | yes | 216 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.bg.a.17.4 | ✓ | 216 | 1.1 | even | 1 | trivial | |
441.2.bg.a.17.15 | yes | 216 | 3.2 | odd | 2 | inner | |
441.2.bg.a.26.4 | yes | 216 | 147.26 | even | 42 | inner | |
441.2.bg.a.26.15 | yes | 216 | 49.26 | odd | 42 | inner |