Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [560,2,Mod(141,560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(560, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("560.141");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 560 = 2^{4} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 560.bd (of order \(4\), 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: | \(4.47162251319\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Relative dimension: | \(26\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 141.9 | ||
Character | \(\chi\) | \(=\) | 560.141 |
Dual form | 560.2.bd.b.421.9 |
$q$-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 \(\left(\mathbb{Z}/560\mathbb{Z}\right)^\times\).
\(n\) | \(241\) | \(337\) | \(351\) | \(421\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.557588 | + | 1.29965i | −0.394275 | + | 0.918993i | ||||
\(3\) | −2.40733 | − | 2.40733i | −1.38987 | − | 1.38987i | −0.825567 | − | 0.564304i | \(-0.809144\pi\) |
−0.564304 | − | 0.825567i | \(-0.690856\pi\) | |||||||
\(4\) | −1.37819 | − | 1.44934i | −0.689095 | − | 0.724671i | ||||
\(5\) | −0.707107 | + | 0.707107i | −0.316228 | + | 0.316228i | ||||
\(6\) | 4.47099 | − | 1.78639i | 1.82527 | − | 0.729291i | ||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 2.65210 | − | 0.983032i | 0.937660 | − | 0.347554i | ||||
\(9\) | 8.59045i | 2.86348i | ||||||||
\(10\) | −0.524718 | − | 1.31327i | −0.165930 | − | 0.415292i | ||||
\(11\) | −2.37243 | + | 2.37243i | −0.715314 | + | 0.715314i | −0.967642 | − | 0.252327i | \(-0.918804\pi\) |
0.252327 | + | 0.967642i | \(0.418804\pi\) | |||||||
\(12\) | −0.171285 | + | 6.80680i | −0.0494456 | + | 1.96495i | ||||
\(13\) | −0.459738 | − | 0.459738i | −0.127508 | − | 0.127508i | 0.640473 | − | 0.767981i | \(-0.278738\pi\) |
−0.767981 | + | 0.640473i | \(0.778738\pi\) | |||||||
\(14\) | −1.29965 | − | 0.557588i | −0.347347 | − | 0.149022i | ||||
\(15\) | 3.40448 | 0.879032 | ||||||||
\(16\) | −0.201183 | + | 3.99494i | −0.0502957 | + | 0.998734i | ||||
\(17\) | 6.60890 | 1.60289 | 0.801447 | − | 0.598066i | \(-0.204064\pi\) | ||||
0.801447 | + | 0.598066i | \(0.204064\pi\) | |||||||
\(18\) | −11.1646 | − | 4.78994i | −2.63152 | − | 1.12900i | ||||
\(19\) | −2.56181 | − | 2.56181i | −0.587721 | − | 0.587721i | 0.349293 | − | 0.937014i | \(-0.386422\pi\) |
−0.937014 | + | 0.349293i | \(0.886422\pi\) | |||||||
\(20\) | 1.99937 | + | 0.0503116i | 0.447072 | + | 0.0112500i | ||||
\(21\) | 2.40733 | − | 2.40733i | 0.525322 | − | 0.525322i | ||||
\(22\) | −1.76049 | − | 4.40617i | −0.375338 | − | 0.939399i | ||||
\(23\) | − | 7.04981i | − | 1.46999i | −0.678074 | − | 0.734994i | \(-0.737185\pi\) | ||
0.678074 | − | 0.734994i | \(-0.262815\pi\) | |||||||
\(24\) | −8.75096 | − | 4.01800i | −1.78628 | − | 0.820171i | ||||
\(25\) | − | 1.00000i | − | 0.200000i | ||||||
\(26\) | 0.853844 | − | 0.341155i | 0.167453 | − | 0.0669060i | ||||
\(27\) | 13.4580 | − | 13.4580i | 2.59000 | − | 2.59000i | ||||
\(28\) | 1.44934 | − | 1.37819i | 0.273900 | − | 0.260453i | ||||
\(29\) | −1.21927 | − | 1.21927i | −0.226413 | − | 0.226413i | 0.584779 | − | 0.811192i | \(-0.301181\pi\) |
−0.811192 | + | 0.584779i | \(0.801181\pi\) | |||||||
\(30\) | −1.89830 | + | 4.42463i | −0.346580 | + | 0.807824i | ||||
\(31\) | 0.0789065 | 0.0141720 | 0.00708601 | − | 0.999975i | \(-0.497744\pi\) | ||||
0.00708601 | + | 0.999975i | \(0.497744\pi\) | |||||||
\(32\) | −5.07985 | − | 2.48900i | −0.897999 | − | 0.439997i | ||||
\(33\) | 11.4224 | 1.98839 | ||||||||
\(34\) | −3.68505 | + | 8.58927i | −0.631980 | + | 1.47305i | ||||
\(35\) | −0.707107 | − | 0.707107i | −0.119523 | − | 0.119523i | ||||
\(36\) | 12.4505 | − | 11.8393i | 2.07508 | − | 1.97321i | ||||
\(37\) | 0.585796 | − | 0.585796i | 0.0963043 | − | 0.0963043i | −0.657313 | − | 0.753617i | \(-0.728307\pi\) |
0.753617 | + | 0.657313i | \(0.228307\pi\) | |||||||
\(38\) | 4.75791 | − | 1.90103i | 0.771834 | − | 0.308388i | ||||
\(39\) | 2.21348i | 0.354440i | ||||||||
\(40\) | −1.18021 | + | 2.57043i | −0.186608 | + | 0.406420i | ||||
\(41\) | − | 0.548655i | − | 0.0856855i | −0.999082 | − | 0.0428428i | \(-0.986359\pi\) | ||
0.999082 | − | 0.0428428i | \(-0.0136415\pi\) | |||||||
\(42\) | 1.78639 | + | 4.47099i | 0.275646 | + | 0.689888i | ||||
\(43\) | −2.40716 | + | 2.40716i | −0.367088 | + | 0.367088i | −0.866414 | − | 0.499326i | \(-0.833581\pi\) |
0.499326 | + | 0.866414i | \(0.333581\pi\) | |||||||
\(44\) | 6.70812 | + | 0.168802i | 1.01129 | + | 0.0254478i | ||||
\(45\) | −6.07437 | − | 6.07437i | −0.905513 | − | 0.905513i | ||||
\(46\) | 9.16231 | + | 3.93090i | 1.35091 | + | 0.579579i | ||||
\(47\) | 9.79702 | 1.42904 | 0.714521 | − | 0.699614i | \(-0.246645\pi\) | ||||
0.714521 | + | 0.699614i | \(0.246645\pi\) | |||||||
\(48\) | 10.1014 | − | 9.13281i | 1.45802 | − | 1.31821i | ||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.29965 | + | 0.557588i | 0.183799 | + | 0.0788549i | ||||
\(51\) | −15.9098 | − | 15.9098i | −2.22782 | − | 2.22782i | ||||
\(52\) | −0.0327110 | + | 1.29992i | −0.00453620 | + | 0.180267i | ||||
\(53\) | 0.805532 | − | 0.805532i | 0.110648 | − | 0.110648i | −0.649615 | − | 0.760263i | \(-0.725070\pi\) |
0.760263 | + | 0.649615i | \(0.225070\pi\) | |||||||
\(54\) | 9.98673 | + | 24.9948i | 1.35902 | + | 3.40137i | ||||
\(55\) | − | 3.35512i | − | 0.452405i | ||||||
\(56\) | 0.983032 | + | 2.65210i | 0.131363 | + | 0.354402i | ||||
\(57\) | 12.3343i | 1.63371i | ||||||||
\(58\) | 2.26448 | − | 0.904778i | 0.297341 | − | 0.118803i | ||||
\(59\) | 10.3251 | − | 10.3251i | 1.34421 | − | 1.34421i | 0.452392 | − | 0.891819i | \(-0.350571\pi\) |
0.891819 | − | 0.452392i | \(-0.149429\pi\) | |||||||
\(60\) | −4.69201 | − | 4.93425i | −0.605737 | − | 0.637009i | ||||
\(61\) | 5.24714 | + | 5.24714i | 0.671828 | + | 0.671828i | 0.958137 | − | 0.286309i | \(-0.0924285\pi\) |
−0.286309 | + | 0.958137i | \(0.592429\pi\) | |||||||
\(62\) | −0.0439974 | + | 0.102551i | −0.00558767 | + | 0.0130240i | ||||
\(63\) | −8.59045 | −1.08230 | ||||||||
\(64\) | 6.06730 | − | 5.21420i | 0.758412 | − | 0.651775i | ||||
\(65\) | 0.650168 | 0.0806434 | ||||||||
\(66\) | −6.36902 | + | 14.8452i | −0.783972 | + | 1.82732i | ||||
\(67\) | −1.05522 | − | 1.05522i | −0.128915 | − | 0.128915i | 0.639705 | − | 0.768620i | \(-0.279057\pi\) |
−0.768620 | + | 0.639705i | \(0.779057\pi\) | |||||||
\(68\) | −9.10832 | − | 9.57855i | −1.10455 | − | 1.16157i | ||||
\(69\) | −16.9712 | + | 16.9712i | −2.04309 | + | 2.04309i | ||||
\(70\) | 1.31327 | − | 0.524718i | 0.156965 | − | 0.0627158i | ||||
\(71\) | 7.97855i | 0.946880i | 0.880826 | + | 0.473440i | \(0.156988\pi\) | ||||
−0.880826 | + | 0.473440i | \(0.843012\pi\) | |||||||
\(72\) | 8.44469 | + | 22.7828i | 0.995216 | + | 2.68497i | ||||
\(73\) | − | 13.8380i | − | 1.61962i | −0.586695 | − | 0.809808i | \(-0.699571\pi\) | ||
0.586695 | − | 0.809808i | \(-0.300429\pi\) | |||||||
\(74\) | 0.434698 | + | 1.08796i | 0.0505326 | + | 0.126473i | ||||
\(75\) | −2.40733 | + | 2.40733i | −0.277974 | + | 0.277974i | ||||
\(76\) | −0.182277 | + | 7.24361i | −0.0209086 | + | 0.830899i | ||||
\(77\) | −2.37243 | − | 2.37243i | −0.270363 | − | 0.270363i | ||||
\(78\) | −2.87675 | − | 1.23421i | −0.325728 | − | 0.139747i | ||||
\(79\) | 7.50113 | 0.843943 | 0.421971 | − | 0.906609i | \(-0.361338\pi\) | ||||
0.421971 | + | 0.906609i | \(0.361338\pi\) | |||||||
\(80\) | −2.68259 | − | 2.96711i | −0.299923 | − | 0.331732i | ||||
\(81\) | −39.0245 | −4.33606 | ||||||||
\(82\) | 0.713061 | + | 0.305924i | 0.0787444 | + | 0.0337836i | ||||
\(83\) | 0.984319 | + | 0.984319i | 0.108043 | + | 0.108043i | 0.759062 | − | 0.651019i | \(-0.225658\pi\) |
−0.651019 | + | 0.759062i | \(0.725658\pi\) | |||||||
\(84\) | −6.80680 | − | 0.171285i | −0.742682 | − | 0.0186887i | ||||
\(85\) | −4.67320 | + | 4.67320i | −0.506879 | + | 0.506879i | ||||
\(86\) | −1.78626 | − | 4.47067i | −0.192618 | − | 0.482084i | ||||
\(87\) | 5.87038i | 0.629371i | ||||||||
\(88\) | −3.95975 | + | 8.62410i | −0.422111 | + | 0.919332i | ||||
\(89\) | − | 7.03304i | − | 0.745501i | −0.927932 | − | 0.372751i | \(-0.878415\pi\) | ||
0.927932 | − | 0.372751i | \(-0.121585\pi\) | |||||||
\(90\) | 11.2816 | − | 4.50757i | 1.18918 | − | 0.475139i | ||||
\(91\) | 0.459738 | − | 0.459738i | 0.0481936 | − | 0.0481936i | ||||
\(92\) | −10.2176 | + | 9.71599i | −1.06526 | + | 1.01296i | ||||
\(93\) | −0.189954 | − | 0.189954i | −0.0196973 | − | 0.0196973i | ||||
\(94\) | −5.46270 | + | 12.7327i | −0.563435 | + | 1.31328i | ||||
\(95\) | 3.62295 | 0.371707 | ||||||||
\(96\) | 6.23703 | + | 18.2207i | 0.636564 | + | 1.85964i | ||||
\(97\) | −6.77139 | −0.687531 | −0.343765 | − | 0.939056i | \(-0.611703\pi\) | ||||
−0.343765 | + | 0.939056i | \(0.611703\pi\) | |||||||
\(98\) | 0.557588 | − | 1.29965i | 0.0563249 | − | 0.131285i | ||||
\(99\) | −20.3802 | − | 20.3802i | −2.04829 | − | 2.04829i | ||||
\(100\) | −1.44934 | + | 1.37819i | −0.144934 | + | 0.137819i | ||||
\(101\) | 5.49510 | − | 5.49510i | 0.546783 | − | 0.546783i | −0.378726 | − | 0.925509i | \(-0.623638\pi\) |
0.925509 | + | 0.378726i | \(0.123638\pi\) | |||||||
\(102\) | 29.5483 | − | 11.8061i | 2.92572 | − | 1.16898i | ||||
\(103\) | − | 0.602751i | − | 0.0593908i | −0.999559 | − | 0.0296954i | \(-0.990546\pi\) | ||
0.999559 | − | 0.0296954i | \(-0.00945373\pi\) | |||||||
\(104\) | −1.67121 | − | 0.767335i | −0.163876 | − | 0.0752434i | ||||
\(105\) | 3.40448i | 0.332243i | ||||||||
\(106\) | 0.597756 | + | 1.49607i | 0.0580592 | + | 0.145311i | ||||
\(107\) | 9.56811 | − | 9.56811i | 0.924984 | − | 0.924984i | −0.0723925 | − | 0.997376i | \(-0.523063\pi\) |
0.997376 | + | 0.0723925i | \(0.0230634\pi\) | |||||||
\(108\) | −38.0531 | − | 0.957559i | −3.66166 | − | 0.0921411i | ||||
\(109\) | 14.7149 | + | 14.7149i | 1.40944 | + | 1.40944i | 0.762789 | + | 0.646647i | \(0.223829\pi\) |
0.646647 | + | 0.762789i | \(0.276171\pi\) | |||||||
\(110\) | 4.36049 | + | 1.87078i | 0.415757 | + | 0.178372i | ||||
\(111\) | −2.82041 | −0.267701 | ||||||||
\(112\) | −3.99494 | − | 0.201183i | −0.377486 | − | 0.0190100i | ||||
\(113\) | 15.5240 | 1.46038 | 0.730189 | − | 0.683245i | \(-0.239432\pi\) | ||||
0.730189 | + | 0.683245i | \(0.239432\pi\) | |||||||
\(114\) | −16.0302 | − | 6.87744i | −1.50137 | − | 0.644131i | ||||
\(115\) | 4.98497 | + | 4.98497i | 0.464851 | + | 0.464851i | ||||
\(116\) | −0.0867529 | + | 3.44753i | −0.00805481 | + | 0.320095i | ||||
\(117\) | 3.94936 | − | 3.94936i | 0.365118 | − | 0.365118i | ||||
\(118\) | 7.66187 | + | 19.1762i | 0.705332 | + | 1.76531i | ||||
\(119\) | 6.60890i | 0.605837i | ||||||||
\(120\) | 9.02902 | − | 3.34671i | 0.824233 | − | 0.305511i | ||||
\(121\) | − | 0.256846i | − | 0.0233496i | ||||||
\(122\) | −9.74521 | + | 3.89371i | −0.882290 | + | 0.352520i | ||||
\(123\) | −1.32079 | + | 1.32079i | −0.119092 | + | 0.119092i | ||||
\(124\) | −0.108748 | − | 0.114362i | −0.00976587 | − | 0.0102701i | ||||
\(125\) | 0.707107 | + | 0.707107i | 0.0632456 | + | 0.0632456i | ||||
\(126\) | 4.78994 | − | 11.1646i | 0.426721 | − | 0.994621i | ||||
\(127\) | −12.4812 | −1.10752 | −0.553762 | − | 0.832675i | \(-0.686808\pi\) | ||||
−0.553762 | + | 0.832675i | \(0.686808\pi\) | |||||||
\(128\) | 3.39359 | + | 10.7928i | 0.299954 | + | 0.953954i | ||||
\(129\) | 11.5896 | 1.02041 | ||||||||
\(130\) | −0.362526 | + | 0.844992i | −0.0317956 | + | 0.0741107i | ||||
\(131\) | −0.940145 | − | 0.940145i | −0.0821408 | − | 0.0821408i | 0.664843 | − | 0.746983i | \(-0.268499\pi\) |
−0.746983 | + | 0.664843i | \(0.768499\pi\) | |||||||
\(132\) | −15.7423 | − | 16.5550i | −1.37019 | − | 1.44093i | ||||
\(133\) | 2.56181 | − | 2.56181i | 0.222137 | − | 0.222137i | ||||
\(134\) | 1.95979 | − | 0.783039i | 0.169300 | − | 0.0676443i | ||||
\(135\) | 19.0326i | 1.63806i | ||||||||
\(136\) | 17.5275 | − | 6.49676i | 1.50297 | − | 0.557092i | ||||
\(137\) | − | 6.37076i | − | 0.544291i | −0.962256 | − | 0.272145i | \(-0.912267\pi\) | ||
0.962256 | − | 0.272145i | \(-0.0877332\pi\) | |||||||
\(138\) | −12.5937 | − | 31.5196i | −1.07205 | − | 2.68313i | ||||
\(139\) | −0.486651 | + | 0.486651i | −0.0412772 | + | 0.0412772i | −0.727444 | − | 0.686167i | \(-0.759292\pi\) |
0.686167 | + | 0.727444i | \(0.259292\pi\) | |||||||
\(140\) | −0.0503116 | + | 1.99937i | −0.00425211 | + | 0.168977i | ||||
\(141\) | −23.5846 | − | 23.5846i | −1.98618 | − | 1.98618i | ||||
\(142\) | −10.3693 | − | 4.44875i | −0.870176 | − | 0.373331i | ||||
\(143\) | 2.18139 | 0.182417 | ||||||||
\(144\) | −34.3183 | − | 1.72825i | −2.85986 | − | 0.144021i | ||||
\(145\) | 1.72431 | 0.143196 | ||||||||
\(146\) | 17.9846 | + | 7.71591i | 1.48841 | + | 0.638573i | ||||
\(147\) | 2.40733 | + | 2.40733i | 0.198553 | + | 0.198553i | ||||
\(148\) | −1.65636 | − | 0.0416802i | −0.136152 | − | 0.00342609i | ||||
\(149\) | 11.4185 | − | 11.4185i | 0.935443 | − | 0.935443i | −0.0625964 | − | 0.998039i | \(-0.519938\pi\) |
0.998039 | + | 0.0625964i | \(0.0199381\pi\) | |||||||
\(150\) | −1.78639 | − | 4.47099i | −0.145858 | − | 0.365054i | ||||
\(151\) | 11.2483i | 0.915377i | 0.889113 | + | 0.457689i | \(0.151323\pi\) | ||||
−0.889113 | + | 0.457689i | \(0.848677\pi\) | |||||||
\(152\) | −9.31254 | − | 4.27585i | −0.755347 | − | 0.346817i | ||||
\(153\) | 56.7734i | 4.58986i | ||||||||
\(154\) | 4.40617 | − | 1.76049i | 0.355059 | − | 0.141865i | ||||
\(155\) | −0.0557953 | + | 0.0557953i | −0.00448159 | + | 0.00448159i | ||||
\(156\) | 3.20809 | − | 3.05060i | 0.256853 | − | 0.244243i | ||||
\(157\) | −7.65513 | − | 7.65513i | −0.610946 | − | 0.610946i | 0.332247 | − | 0.943193i | \(-0.392193\pi\) |
−0.943193 | + | 0.332247i | \(0.892193\pi\) | |||||||
\(158\) | −4.18254 | + | 9.74886i | −0.332745 | + | 0.775577i | ||||
\(159\) | −3.87836 | −0.307574 | ||||||||
\(160\) | 5.35198 | − | 1.83201i | 0.423112 | − | 0.144833i | ||||
\(161\) | 7.04981 | 0.555603 | ||||||||
\(162\) | 21.7596 | − | 50.7183i | 1.70960 | − | 3.98480i | ||||
\(163\) | 8.49444 | + | 8.49444i | 0.665336 | + | 0.665336i | 0.956633 | − | 0.291297i | \(-0.0940868\pi\) |
−0.291297 | + | 0.956633i | \(0.594087\pi\) | |||||||
\(164\) | −0.795189 | + | 0.756151i | −0.0620938 | + | 0.0590455i | ||||
\(165\) | −8.07688 | + | 8.07688i | −0.628784 | + | 0.628784i | ||||
\(166\) | −1.82812 | + | 0.730427i | −0.141889 | + | 0.0566921i | ||||
\(167\) | 10.1424i | 0.784843i | 0.919785 | + | 0.392422i | \(0.128363\pi\) | ||||
−0.919785 | + | 0.392422i | \(0.871637\pi\) | |||||||
\(168\) | 4.01800 | − | 8.75096i | 0.309996 | − | 0.675151i | ||||
\(169\) | − | 12.5773i | − | 0.967483i | ||||||
\(170\) | −3.46781 | − | 8.67925i | −0.265969 | − | 0.665668i | ||||
\(171\) | 22.0071 | − | 22.0071i | 1.68293 | − | 1.68293i | ||||
\(172\) | 6.80631 | + | 0.171272i | 0.518976 | + | 0.0130594i | ||||
\(173\) | 3.05165 | + | 3.05165i | 0.232013 | + | 0.232013i | 0.813532 | − | 0.581520i | \(-0.197542\pi\) |
−0.581520 | + | 0.813532i | \(0.697542\pi\) | |||||||
\(174\) | −7.62945 | − | 3.27325i | −0.578387 | − | 0.248145i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −9.00042 | − | 9.95500i | −0.678432 | − | 0.750386i | ||||
\(177\) | −49.7117 | −3.73656 | ||||||||
\(178\) | 9.14051 | + | 3.92154i | 0.685110 | + | 0.293932i | ||||
\(179\) | −3.38310 | − | 3.38310i | −0.252865 | − | 0.252865i | 0.569279 | − | 0.822144i | \(-0.307222\pi\) |
−0.822144 | + | 0.569279i | \(0.807222\pi\) | |||||||
\(180\) | −0.432200 | + | 17.1755i | −0.0322143 | + | 1.28018i | ||||
\(181\) | 6.90132 | − | 6.90132i | 0.512971 | − | 0.512971i | −0.402465 | − | 0.915436i | \(-0.631846\pi\) |
0.915436 | + | 0.402465i | \(0.131846\pi\) | |||||||
\(182\) | 0.341155 | + | 0.853844i | 0.0252881 | + | 0.0632911i | ||||
\(183\) | − | 25.2632i | − | 1.86751i | ||||||
\(184\) | −6.93019 | − | 18.6968i | −0.510900 | − | 1.37835i | ||||
\(185\) | 0.828441i | 0.0609082i | ||||||||
\(186\) | 0.352790 | − | 0.140958i | 0.0258678 | − | 0.0103355i | ||||
\(187\) | −15.6791 | + | 15.6791i | −1.14657 | + | 1.14657i | ||||
\(188\) | −13.5022 | − | 14.1992i | −0.984746 | − | 1.03558i | ||||
\(189\) | 13.4580 | + | 13.4580i | 0.978929 | + | 0.978929i | ||||
\(190\) | −2.02012 | + | 4.70858i | −0.146555 | + | 0.341596i | ||||
\(191\) | −9.25297 | −0.669522 | −0.334761 | − | 0.942303i | \(-0.608656\pi\) | ||||
−0.334761 | + | 0.942303i | \(0.608656\pi\) | |||||||
\(192\) | −27.1583 | − | 2.05368i | −1.95998 | − | 0.148212i | ||||
\(193\) | −18.2876 | −1.31637 | −0.658185 | − | 0.752856i | \(-0.728675\pi\) | ||||
−0.658185 | + | 0.752856i | \(0.728675\pi\) | |||||||
\(194\) | 3.77565 | − | 8.80046i | 0.271076 | − | 0.631836i | ||||
\(195\) | −1.56517 | − | 1.56517i | −0.112084 | − | 0.112084i | ||||
\(196\) | 1.37819 | + | 1.44934i | 0.0984422 | + | 0.103524i | ||||
\(197\) | 4.05457 | − | 4.05457i | 0.288876 | − | 0.288876i | −0.547760 | − | 0.836636i | \(-0.684519\pi\) |
0.836636 | + | 0.547760i | \(0.184519\pi\) | |||||||
\(198\) | 37.8510 | − | 15.1234i | 2.68995 | − | 1.07478i | ||||
\(199\) | 8.19764i | 0.581115i | 0.956858 | + | 0.290558i | \(0.0938408\pi\) | ||||
−0.956858 | + | 0.290558i | \(0.906159\pi\) | |||||||
\(200\) | −0.983032 | − | 2.65210i | −0.0695108 | − | 0.187532i | ||||
\(201\) | 5.08051i | 0.358352i | ||||||||
\(202\) | 4.07771 | + | 10.2057i | 0.286907 | + | 0.718072i | ||||
\(203\) | 1.21927 | − | 1.21927i | 0.0855762 | − | 0.0855762i | ||||
\(204\) | −1.13200 | + | 44.9854i | −0.0792561 | + | 3.14961i | ||||
\(205\) | 0.387958 | + | 0.387958i | 0.0270961 | + | 0.0270961i | ||||
\(206\) | 0.783366 | + | 0.336087i | 0.0545797 | + | 0.0234163i | ||||
\(207\) | 60.5611 | 4.20929 | ||||||||
\(208\) | 1.92912 | − | 1.74413i | 0.133760 | − | 0.120934i | ||||
\(209\) | 12.1555 | 0.840810 | ||||||||
\(210\) | −4.42463 | − | 1.89830i | −0.305329 | − | 0.130995i | ||||
\(211\) | 8.21521 | + | 8.21521i | 0.565558 | + | 0.565558i | 0.930881 | − | 0.365323i | \(-0.119041\pi\) |
−0.365323 | + | 0.930881i | \(0.619041\pi\) | |||||||
\(212\) | −2.27767 | − | 0.0573147i | −0.156431 | − | 0.00393639i | ||||
\(213\) | 19.2070 | − | 19.2070i | 1.31604 | − | 1.31604i | ||||
\(214\) | 7.10014 | + | 17.7703i | 0.485356 | + | 1.21475i | ||||
\(215\) | − | 3.40423i | − | 0.232167i | ||||||
\(216\) | 22.4624 | − | 48.9218i | 1.52838 | − | 3.32871i | ||||
\(217\) | 0.0789065i | 0.00535652i | ||||||||
\(218\) | −27.3292 | + | 10.9194i | −1.85097 | + | 0.739557i | ||||
\(219\) | −33.3126 | + | 33.3126i | −2.25106 | + | 2.25106i | ||||
\(220\) | −4.86272 | + | 4.62400i | −0.327844 | + | 0.311750i | ||||
\(221\) | −3.03836 | − | 3.03836i | −0.204382 | − | 0.204382i | ||||
\(222\) | 1.57263 | − | 3.66555i | 0.105548 | − | 0.246015i | ||||
\(223\) | 22.1333 | 1.48215 | 0.741077 | − | 0.671420i | \(-0.234315\pi\) | ||||
0.741077 | + | 0.671420i | \(0.234315\pi\) | |||||||
\(224\) | 2.48900 | − | 5.07985i | 0.166303 | − | 0.339412i | ||||
\(225\) | 8.59045 | 0.572697 | ||||||||
\(226\) | −8.65602 | + | 20.1758i | −0.575790 | + | 1.34208i | ||||
\(227\) | −13.4268 | − | 13.4268i | −0.891169 | − | 0.891169i | 0.103464 | − | 0.994633i | \(-0.467007\pi\) |
−0.994633 | + | 0.103464i | \(0.967007\pi\) | |||||||
\(228\) | 17.8765 | − | 16.9989i | 1.18390 | − | 1.12578i | ||||
\(229\) | −15.1501 | + | 15.1501i | −1.00115 | + | 1.00115i | −0.00114841 | + | 0.999999i | \(0.500366\pi\) |
−0.999999 | + | 0.00114841i | \(0.999634\pi\) | |||||||
\(230\) | −9.25829 | + | 3.69917i | −0.610474 | + | 0.243916i | ||||
\(231\) | 11.4224i | 0.751541i | ||||||||
\(232\) | −4.43222 | − | 2.03505i | −0.290990 | − | 0.133608i | ||||
\(233\) | 2.07514i | 0.135947i | 0.997687 | + | 0.0679735i | \(0.0216533\pi\) | ||||
−0.997687 | + | 0.0679735i | \(0.978347\pi\) | |||||||
\(234\) | 2.93067 | + | 7.33491i | 0.191584 | + | 0.479498i | ||||
\(235\) | −6.92754 | + | 6.92754i | −0.451903 | + | 0.451903i | ||||
\(236\) | −29.1945 | − | 0.734644i | −1.90040 | − | 0.0478212i | ||||
\(237\) | −18.0577 | − | 18.0577i | −1.17297 | − | 1.17297i | ||||
\(238\) | −8.58927 | − | 3.68505i | −0.556760 | − | 0.238866i | ||||
\(239\) | −14.9463 | −0.966795 | −0.483397 | − | 0.875401i | \(-0.660597\pi\) | ||||
−0.483397 | + | 0.875401i | \(0.660597\pi\) | |||||||
\(240\) | −0.684922 | + | 13.6007i | −0.0442115 | + | 0.877919i | ||||
\(241\) | 8.77461 | 0.565222 | 0.282611 | − | 0.959235i | \(-0.408799\pi\) | ||||
0.282611 | + | 0.959235i | \(0.408799\pi\) | |||||||
\(242\) | 0.333810 | + | 0.143214i | 0.0214581 | + | 0.00920615i | ||||
\(243\) | 53.5706 | + | 53.5706i | 3.43656 | + | 3.43656i | ||||
\(244\) | 0.373341 | − | 14.8365i | 0.0239007 | − | 0.949807i | ||||
\(245\) | 0.707107 | − | 0.707107i | 0.0451754 | − | 0.0451754i | ||||
\(246\) | −0.980112 | − | 2.45303i | −0.0624897 | − | 0.156399i | ||||
\(247\) | 2.35553i | 0.149879i | ||||||||
\(248\) | 0.209268 | − | 0.0775676i | 0.0132885 | − | 0.00492555i | ||||
\(249\) | − | 4.73916i | − | 0.300332i | ||||||
\(250\) | −1.31327 | + | 0.524718i | −0.0830583 | + | 0.0331861i | ||||
\(251\) | −15.3667 | + | 15.3667i | −0.969937 | + | 0.969937i | −0.999561 | − | 0.0296242i | \(-0.990569\pi\) |
0.0296242 | + | 0.999561i | \(0.490569\pi\) | |||||||
\(252\) | 11.8393 | + | 12.4505i | 0.745804 | + | 0.784308i | ||||
\(253\) | 16.7252 | + | 16.7252i | 1.05150 | + | 1.05150i | ||||
\(254\) | 6.95935 | − | 16.2212i | 0.436668 | − | 1.01781i | ||||
\(255\) | 22.4998 | 1.40899 | ||||||||
\(256\) | −15.9191 | − | 1.60743i | −0.994941 | − | 0.100464i | ||||
\(257\) | 12.1822 | 0.759907 | 0.379954 | − | 0.925006i | \(-0.375940\pi\) | ||||
0.379954 | + | 0.925006i | \(0.375940\pi\) | |||||||
\(258\) | −6.46224 | + | 15.0625i | −0.402322 | + | 0.937749i | ||||
\(259\) | 0.585796 | + | 0.585796i | 0.0363996 | + | 0.0363996i | ||||
\(260\) | −0.896055 | − | 0.942315i | −0.0555710 | − | 0.0584399i | ||||
\(261\) | 10.4741 | − | 10.4741i | 0.648331 | − | 0.648331i | ||||
\(262\) | 1.74608 | − | 0.697647i | 0.107873 | − | 0.0431008i | ||||
\(263\) | − | 18.4787i | − | 1.13944i | −0.821837 | − | 0.569722i | \(-0.807051\pi\) | ||
0.821837 | − | 0.569722i | \(-0.192949\pi\) | |||||||
\(264\) | 30.2935 | − | 11.2286i | 1.86443 | − | 0.691073i | ||||
\(265\) | 1.13919i | 0.0699801i | ||||||||
\(266\) | 1.90103 | + | 4.75791i | 0.116560 | + | 0.291726i | ||||
\(267\) | −16.9308 | + | 16.9308i | −1.03615 | + | 1.03615i | ||||
\(268\) | −0.0750802 | + | 2.98366i | −0.00458626 | + | 0.182256i | ||||
\(269\) | 18.2057 | + | 18.2057i | 1.11002 | + | 1.11002i | 0.993147 | + | 0.116875i | \(0.0372877\pi\) |
0.116875 | + | 0.993147i | \(0.462712\pi\) | |||||||
\(270\) | −24.7357 | − | 10.6123i | −1.50537 | − | 0.645846i | ||||
\(271\) | 7.57219 | 0.459978 | 0.229989 | − | 0.973193i | \(-0.426131\pi\) | ||||
0.229989 | + | 0.973193i | \(0.426131\pi\) | |||||||
\(272\) | −1.32960 | + | 26.4021i | −0.0806187 | + | 1.60086i | ||||
\(273\) | −2.21348 | −0.133966 | ||||||||
\(274\) | 8.27977 | + | 3.55226i | 0.500199 | + | 0.214600i | ||||
\(275\) | 2.37243 | + | 2.37243i | 0.143063 | + | 0.143063i | ||||
\(276\) | 47.9867 | + | 1.20753i | 2.88846 | + | 0.0726845i | ||||
\(277\) | 9.62303 | − | 9.62303i | 0.578192 | − | 0.578192i | −0.356213 | − | 0.934405i | \(-0.615932\pi\) |
0.934405 | + | 0.356213i | \(0.115932\pi\) | |||||||
\(278\) | −0.361126 | − | 0.903828i | −0.0216589 | − | 0.0542080i | ||||
\(279\) | 0.677843i | 0.0405814i | ||||||||
\(280\) | −2.57043 | − | 1.18021i | −0.153612 | − | 0.0705311i | ||||
\(281\) | − | 22.1150i | − | 1.31927i | −0.751585 | − | 0.659637i | \(-0.770710\pi\) | ||
0.751585 | − | 0.659637i | \(-0.229290\pi\) | |||||||
\(282\) | 43.8023 | − | 17.5013i | 2.60839 | − | 1.04219i | ||||
\(283\) | 8.73247 | − | 8.73247i | 0.519091 | − | 0.519091i | −0.398205 | − | 0.917296i | \(-0.630367\pi\) |
0.917296 | + | 0.398205i | \(0.130367\pi\) | |||||||
\(284\) | 11.5637 | − | 10.9960i | 0.686176 | − | 0.652491i | ||||
\(285\) | −8.72163 | − | 8.72163i | −0.516625 | − | 0.516625i | ||||
\(286\) | −1.21632 | + | 2.83505i | −0.0719225 | + | 0.167640i | ||||
\(287\) | 0.548655 | 0.0323861 | ||||||||
\(288\) | 21.3816 | − | 43.6382i | 1.25992 | − | 2.57141i | ||||
\(289\) | 26.6776 | 1.56927 | ||||||||
\(290\) | −0.961456 | + | 2.24101i | −0.0564587 | + | 0.131596i | ||||
\(291\) | 16.3010 | + | 16.3010i | 0.955579 | + | 0.955579i | ||||
\(292\) | −20.0560 | + | 19.0714i | −1.17369 | + | 1.11607i | ||||
\(293\) | 0.540807 | − | 0.540807i | 0.0315943 | − | 0.0315943i | −0.691133 | − | 0.722727i | \(-0.742888\pi\) |
0.722727 | + | 0.691133i | \(0.242888\pi\) | |||||||
\(294\) | −4.47099 | + | 1.78639i | −0.260753 | + | 0.104184i | ||||
\(295\) | 14.6019i | 0.850154i | ||||||||
\(296\) | 0.977735 | − | 2.12945i | 0.0568297 | − | 0.123772i | ||||
\(297\) | 63.8566i | 3.70533i | ||||||||
\(298\) | 8.47328 | + | 21.2070i | 0.490844 | + | 1.22849i | ||||
\(299\) | −3.24107 | + | 3.24107i | −0.187436 | + | 0.187436i | ||||
\(300\) | 6.80680 | + | 0.171285i | 0.392991 | + | 0.00988913i | ||||
\(301\) | −2.40716 | − | 2.40716i | −0.138746 | − | 0.138746i | ||||
\(302\) | −14.6189 | − | 6.27195i | −0.841225 | − | 0.360910i | ||||
\(303\) | −26.4570 | −1.51992 | ||||||||
\(304\) | 10.7497 | − | 9.71890i | 0.616537 | − | 0.557417i | ||||
\(305\) | −7.42058 | −0.424901 | ||||||||
\(306\) | −73.7857 | − | 31.6562i | −4.21805 | − | 1.80967i | ||||
\(307\) | −8.07455 | − | 8.07455i | −0.460839 | − | 0.460839i | 0.438092 | − | 0.898930i | \(-0.355655\pi\) |
−0.898930 | + | 0.438092i | \(0.855655\pi\) | |||||||
\(308\) | −0.168802 | + | 6.70812i | −0.00961837 | + | 0.382231i | ||||
\(309\) | −1.45102 | + | 1.45102i | −0.0825456 | + | 0.0825456i | ||||
\(310\) | −0.0414037 | − | 0.103625i | −0.00235157 | − | 0.00588552i | ||||
\(311\) | − | 30.3239i | − | 1.71951i | −0.510708 | − | 0.859754i | \(-0.670617\pi\) | ||
0.510708 | − | 0.859754i | \(-0.329383\pi\) | |||||||
\(312\) | 2.17592 | + | 5.87038i | 0.123187 | + | 0.332345i | ||||
\(313\) | 8.12409i | 0.459201i | 0.973285 | + | 0.229600i | \(0.0737419\pi\) | ||||
−0.973285 | + | 0.229600i | \(0.926258\pi\) | |||||||
\(314\) | 14.2174 | − | 5.68059i | 0.802335 | − | 0.320574i | ||||
\(315\) | 6.07437 | − | 6.07437i | 0.342252 | − | 0.342252i | ||||
\(316\) | −10.3380 | − | 10.8717i | −0.581557 | − | 0.611581i | ||||
\(317\) | 19.7163 | + | 19.7163i | 1.10738 | + | 1.10738i | 0.993494 | + | 0.113885i | \(0.0363296\pi\) |
0.113885 | + | 0.993494i | \(0.463670\pi\) | |||||||
\(318\) | 2.16253 | − | 5.04052i | 0.121269 | − | 0.282658i | ||||
\(319\) | 5.78528 | 0.323913 | ||||||||
\(320\) | −0.603230 | + | 7.97722i | −0.0337216 | + | 0.445940i | ||||
\(321\) | −46.0671 | −2.57122 | ||||||||
\(322\) | −3.93090 | + | 9.16231i | −0.219060 | + | 0.510595i | ||||
\(323\) | −16.9308 | − | 16.9308i | −0.942054 | − | 0.942054i | ||||
\(324\) | 53.7832 | + | 56.5598i | 2.98796 | + | 3.14221i | ||||
\(325\) | −0.459738 | + | 0.459738i | −0.0255017 | + | 0.0255017i | ||||
\(326\) | −15.7762 | + | 6.30341i | −0.873764 | + | 0.349114i | ||||
\(327\) | − | 70.8474i | − | 3.91787i | ||||||
\(328\) | −0.539345 | − | 1.45509i | −0.0297804 | − | 0.0803439i | ||||
\(329\) | 9.79702i | 0.540127i | ||||||||
\(330\) | −5.99356 | − | 15.0007i | −0.329934 | − | 0.825762i | ||||
\(331\) | 2.96634 | − | 2.96634i | 0.163045 | − | 0.163045i | −0.620869 | − | 0.783914i | \(-0.713220\pi\) |
0.783914 | + | 0.620869i | \(0.213220\pi\) | |||||||
\(332\) | 0.0700356 | − | 2.78319i | 0.00384371 | − | 0.152748i | ||||
\(333\) | 5.03225 | + | 5.03225i | 0.275766 | + | 0.275766i | ||||
\(334\) | −13.1816 | − | 5.65529i | −0.721265 | − | 0.309444i | ||||
\(335\) | 1.49230 | 0.0815333 | ||||||||
\(336\) | 9.13281 | + | 10.1014i | 0.498236 | + | 0.551079i | ||||
\(337\) | −8.40709 | −0.457964 | −0.228982 | − | 0.973431i | \(-0.573540\pi\) | ||||
−0.228982 | + | 0.973431i | \(0.573540\pi\) | |||||||
\(338\) | 16.3461 | + | 7.01295i | 0.889110 | + | 0.381454i | ||||
\(339\) | −37.3714 | − | 37.3714i | −2.02974 | − | 2.02974i | ||||
\(340\) | 13.2136 | + | 0.332504i | 0.716609 | + | 0.0180326i | ||||
\(341\) | −0.187200 | + | 0.187200i | −0.0101375 | + | 0.0101375i | ||||
\(342\) | 16.3307 | + | 40.8726i | 0.883063 | + | 2.21013i | ||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −4.01771 | + | 8.75034i | −0.216621 | + | 0.471786i | ||||
\(345\) | − | 24.0009i | − | 1.29217i | ||||||
\(346\) | −5.66765 | + | 2.26452i | −0.304695 | + | 0.121741i | ||||
\(347\) | 3.86718 | − | 3.86718i | 0.207601 | − | 0.207601i | −0.595646 | − | 0.803247i | \(-0.703104\pi\) |
0.803247 | + | 0.595646i | \(0.203104\pi\) | |||||||
\(348\) | 8.50818 | − | 8.09050i | 0.456087 | − | 0.433696i | ||||
\(349\) | −18.4321 | − | 18.4321i | −0.986646 | − | 0.986646i | 0.0132656 | − | 0.999912i | \(-0.495777\pi\) |
−0.999912 | + | 0.0132656i | \(0.995777\pi\) | |||||||
\(350\) | −0.557588 | + | 1.29965i | −0.0298044 | + | 0.0694693i | ||||
\(351\) | −12.3744 | −0.660494 | ||||||||
\(352\) | 17.9566 | − | 6.14662i | 0.957088 | − | 0.327616i | ||||
\(353\) | −31.9993 | −1.70315 | −0.851574 | − | 0.524234i | \(-0.824352\pi\) | ||||
−0.851574 | + | 0.524234i | \(0.824352\pi\) | |||||||
\(354\) | 27.7187 | − | 64.6079i | 1.47323 | − | 3.43387i | ||||
\(355\) | −5.64169 | − | 5.64169i | −0.299430 | − | 0.299430i | ||||
\(356\) | −10.1933 | + | 9.69287i | −0.540243 | + | 0.513721i | ||||
\(357\) | 15.9098 | − | 15.9098i | 0.842035 | − | 0.842035i | ||||
\(358\) | 6.28324 | − | 2.51048i | 0.332079 | − | 0.132683i | ||||
\(359\) | 37.0569i | 1.95579i | 0.209100 | + | 0.977894i | \(0.432946\pi\) | ||||
−0.209100 | + | 0.977894i | \(0.567054\pi\) | |||||||
\(360\) | −22.0811 | − | 10.1386i | −1.16378 | − | 0.534349i | ||||
\(361\) | − | 5.87421i | − | 0.309169i | ||||||
\(362\) | 5.12122 | + | 12.8174i | 0.269165 | + | 0.673668i | ||||
\(363\) | −0.618311 | + | 0.618311i | −0.0324529 | + | 0.0324529i | ||||
\(364\) | −1.29992 | − | 0.0327110i | −0.0681345 | − | 0.00171452i | ||||
\(365\) | 9.78495 | + | 9.78495i | 0.512167 | + | 0.512167i | ||||
\(366\) | 32.8333 | + | 14.0865i | 1.71623 | + | 0.736311i | ||||
\(367\) | −17.0503 | −0.890019 | −0.445010 | − | 0.895526i | \(-0.646800\pi\) | ||||
−0.445010 | + | 0.895526i | \(0.646800\pi\) | |||||||
\(368\) | 28.1636 | + | 1.41830i | 1.46813 | + | 0.0739341i | ||||
\(369\) | 4.71319 | 0.245359 | ||||||||
\(370\) | −1.07668 | − | 0.461929i | −0.0559742 | − | 0.0240145i | ||||
\(371\) | 0.805532 | + | 0.805532i | 0.0418211 | + | 0.0418211i | ||||
\(372\) | −0.0135155 | + | 0.537100i | −0.000700745 | + | 0.0278474i | ||||
\(373\) | 4.54035 | − | 4.54035i | 0.235090 | − | 0.235090i | −0.579723 | − | 0.814814i | \(-0.696839\pi\) |
0.814814 | + | 0.579723i | \(0.196839\pi\) | |||||||
\(374\) | −11.6349 | − | 29.1199i | −0.601628 | − | 1.50576i | ||||
\(375\) | − | 3.40448i | − | 0.175806i | ||||||
\(376\) | 25.9827 | − | 9.63078i | 1.33996 | − | 0.496669i | ||||
\(377\) | 1.12109i | 0.0577392i | ||||||||
\(378\) | −24.9948 | + | 9.98673i | −1.28560 | + | 0.513662i | ||||
\(379\) | −13.9534 | + | 13.9534i | −0.716736 | + | 0.716736i | −0.967935 | − | 0.251199i | \(-0.919175\pi\) |
0.251199 | + | 0.967935i | \(0.419175\pi\) | |||||||
\(380\) | −4.99312 | − | 5.25090i | −0.256142 | − | 0.269365i | ||||
\(381\) | 30.0462 | + | 30.0462i | 1.53931 | + | 1.53931i | ||||
\(382\) | 5.15935 | − | 12.0256i | 0.263975 | − | 0.615285i | ||||
\(383\) | −22.7548 | −1.16272 | −0.581358 | − | 0.813648i | \(-0.697479\pi\) | ||||
−0.581358 | + | 0.813648i | \(0.697479\pi\) | |||||||
\(384\) | 17.8122 | − | 34.1512i | 0.908975 | − | 1.74277i | ||||
\(385\) | 3.35512 | 0.170993 | ||||||||
\(386\) | 10.1969 | − | 23.7675i | 0.519011 | − | 1.20973i | ||||
\(387\) | −20.6786 | − | 20.6786i | −1.05115 | − | 1.05115i | ||||
\(388\) | 9.33227 | + | 9.81406i | 0.473774 | + | 0.498234i | ||||
\(389\) | 0.289788 | − | 0.289788i | 0.0146928 | − | 0.0146928i | −0.699722 | − | 0.714415i | \(-0.746693\pi\) |
0.714415 | + | 0.699722i | \(0.246693\pi\) | |||||||
\(390\) | 2.90689 | − | 1.16145i | 0.147196 | − | 0.0588125i | ||||
\(391\) | − | 46.5915i | − | 2.35623i | ||||||
\(392\) | −2.65210 | + | 0.983032i | −0.133951 | + | 0.0496506i | ||||
\(393\) | 4.52647i | 0.228330i | ||||||||
\(394\) | 3.00875 | + | 7.53031i | 0.151579 | + | 0.379372i | ||||
\(395\) | −5.30410 | + | 5.30410i | −0.266878 | + | 0.266878i | ||||
\(396\) | −1.45008 | + | 57.6258i | −0.0728694 | + | 2.89580i | ||||
\(397\) | −16.1773 | − | 16.1773i | −0.811914 | − | 0.811914i | 0.173006 | − | 0.984921i | \(-0.444652\pi\) |
−0.984921 | + | 0.173006i | \(0.944652\pi\) | |||||||
\(398\) | −10.6541 | − | 4.57091i | −0.534041 | − | 0.229119i | ||||
\(399\) | −12.3343 | −0.617485 | ||||||||
\(400\) | 3.99494 | + | 0.201183i | 0.199747 | + | 0.0100591i | ||||
\(401\) | 12.1093 | 0.604709 | 0.302355 | − | 0.953196i | \(-0.402227\pi\) | ||||
0.302355 | + | 0.953196i | \(0.402227\pi\) | |||||||
\(402\) | −6.60290 | − | 2.83283i | −0.329323 | − | 0.141289i | ||||
\(403\) | −0.0362763 | − | 0.0362763i | −0.00180705 | − | 0.00180705i | ||||
\(404\) | −15.5376 | − | 0.390984i | −0.773023 | − | 0.0194522i | ||||
\(405\) | 27.5945 | − | 27.5945i | 1.37118 | − | 1.37118i | ||||
\(406\) | 0.904778 | + | 2.26448i | 0.0449034 | + | 0.112384i | ||||
\(407\) | 2.77952i | 0.137776i | ||||||||
\(408\) | −57.8342 | − | 26.5546i | −2.86322 | − | 1.31465i | ||||
\(409\) | − | 14.9655i | − | 0.739998i | −0.929032 | − | 0.369999i | \(-0.879358\pi\) | ||
0.929032 | − | 0.369999i | \(-0.120642\pi\) | |||||||
\(410\) | −0.720531 | + | 0.287889i | −0.0355845 | + | 0.0142178i | ||||
\(411\) | −15.3365 | + | 15.3365i | −0.756494 | + | 0.756494i | ||||
\(412\) | −0.873592 | + | 0.830706i | −0.0430388 | + | 0.0409259i | ||||
\(413\) | 10.3251 | + | 10.3251i | 0.508064 | + | 0.508064i | ||||
\(414\) | −33.7682 | + | 78.7083i | −1.65961 | + | 3.86830i | ||||
\(415\) | −1.39204 | −0.0683324 | ||||||||
\(416\) | 1.19111 | + | 3.47969i | 0.0583991 | + | 0.170606i | ||||
\(417\) | 2.34306 | 0.114740 | ||||||||
\(418\) | −6.77774 | + | 15.7979i | −0.331510 | + | 0.772698i | ||||
\(419\) | −15.4782 | − | 15.4782i | −0.756159 | − | 0.756159i | 0.219462 | − | 0.975621i | \(-0.429570\pi\) |
−0.975621 | + | 0.219462i | \(0.929570\pi\) | |||||||
\(420\) | 4.93425 | − | 4.69201i | 0.240767 | − | 0.228947i | ||||
\(421\) | −4.06993 | + | 4.06993i | −0.198356 | + | 0.198356i | −0.799295 | − | 0.600939i | \(-0.794794\pi\) |
0.600939 | + | 0.799295i | \(0.294794\pi\) | |||||||
\(422\) | −15.2576 | + | 6.09621i | −0.742729 | + | 0.296759i | ||||
\(423\) | 84.1608i | 4.09204i | ||||||||
\(424\) | 1.34449 | − | 2.92822i | 0.0652942 | − | 0.142207i | ||||
\(425\) | − | 6.60890i | − | 0.320579i | ||||||
\(426\) | 14.2528 | + | 35.6720i | 0.690551 | + | 1.72831i | ||||
\(427\) | −5.24714 | + | 5.24714i | −0.253927 | + | 0.253927i | ||||
\(428\) | −27.0541 | − | 0.680784i | −1.30771 | − | 0.0329069i | ||||
\(429\) | −5.25133 | − | 5.25133i | −0.253536 | − | 0.253536i | ||||
\(430\) | 4.42432 | + | 1.89816i | 0.213360 | + | 0.0915374i | ||||
\(431\) | 25.4099 | 1.22395 | 0.611975 | − | 0.790877i | \(-0.290375\pi\) | ||||
0.611975 | + | 0.790877i | \(0.290375\pi\) | |||||||
\(432\) | 51.0565 | + | 56.4716i | 2.45646 | + | 2.71699i | ||||
\(433\) | −8.25231 | −0.396581 | −0.198290 | − | 0.980143i | \(-0.563539\pi\) | ||||
−0.198290 | + | 0.980143i | \(0.563539\pi\) | |||||||
\(434\) | −0.102551 | − | 0.0439974i | −0.00492261 | − | 0.00211194i | ||||
\(435\) | −4.15098 | − | 4.15098i | −0.199024 | − | 0.199024i | ||||
\(436\) | 1.04699 | − | 41.6070i | 0.0501417 | − | 1.99261i | ||||
\(437\) | −18.0603 | + | 18.0603i | −0.863942 | + | 0.863942i | ||||
\(438\) | −24.7201 | − | 61.8695i | −1.18117 | − | 2.95624i | ||||
\(439\) | − | 21.2883i | − | 1.01603i | −0.861347 | − | 0.508017i | \(-0.830379\pi\) | ||
0.861347 | − | 0.508017i | \(-0.169621\pi\) | |||||||
\(440\) | −3.29819 | − | 8.89813i | −0.157235 | − | 0.424202i | ||||
\(441\) | − | 8.59045i | − | 0.409069i | ||||||
\(442\) | 5.64297 | − | 2.25466i | 0.268409 | − | 0.107243i | ||||
\(443\) | 2.23347 | − | 2.23347i | 0.106115 | − | 0.106115i | −0.652056 | − | 0.758171i | \(-0.726093\pi\) |
0.758171 | + | 0.652056i | \(0.226093\pi\) | |||||||
\(444\) | 3.88706 | + | 4.08773i | 0.184471 | + | 0.193995i | ||||
\(445\) | 4.97311 | + | 4.97311i | 0.235748 | + | 0.235748i | ||||
\(446\) | −12.3413 | + | 28.7656i | −0.584376 | + | 1.36209i | ||||
\(447\) | −54.9763 | −2.60029 | ||||||||
\(448\) | 5.21420 | + | 6.06730i | 0.246348 | + | 0.286653i | ||||
\(449\) | 14.8424 | 0.700457 | 0.350229 | − | 0.936664i | \(-0.386104\pi\) | ||||
0.350229 | + | 0.936664i | \(0.386104\pi\) | |||||||
\(450\) | −4.78994 | + | 11.1646i | −0.225800 | + | 0.526304i | ||||
\(451\) | 1.30165 | + | 1.30165i | 0.0612921 | + | 0.0612921i | ||||
\(452\) | −21.3951 | − | 22.4996i | −1.00634 | − | 1.05829i | ||||
\(453\) | 27.0785 | − | 27.0785i | 1.27226 | − | 1.27226i | ||||
\(454\) | 24.9368 | − | 9.96355i | 1.17034 | − | 0.467613i | ||||
\(455\) | 0.650168i | 0.0304803i | ||||||||
\(456\) | 12.1250 | + | 32.7117i | 0.567803 | + | 1.53187i | ||||
\(457\) | − | 14.1926i | − | 0.663903i | −0.943296 | − | 0.331952i | \(-0.892293\pi\) | ||
0.943296 | − | 0.331952i | \(-0.107707\pi\) | |||||||
\(458\) | −11.2423 | − | 28.1374i | −0.525320 | − | 1.31477i | ||||
\(459\) | 88.9429 | − | 88.9429i | 4.15150 | − | 4.15150i | ||||
\(460\) | 0.354688 | − | 14.0952i | 0.0165374 | − | 0.657191i | ||||
\(461\) | 19.2200 | + | 19.2200i | 0.895167 | + | 0.895167i | 0.995004 | − | 0.0998372i | \(-0.0318322\pi\) |
−0.0998372 | + | 0.995004i | \(0.531832\pi\) | |||||||
\(462\) | −14.8452 | − | 6.36902i | −0.690660 | − | 0.296313i | ||||
\(463\) | 8.06592 | 0.374855 | 0.187428 | − | 0.982278i | \(-0.439985\pi\) | ||||
0.187428 | + | 0.982278i | \(0.439985\pi\) | |||||||
\(464\) | 5.11622 | − | 4.62562i | 0.237514 | − | 0.214739i | ||||
\(465\) | 0.268635 | 0.0124577 | ||||||||
\(466\) | −2.69696 | − | 1.15708i | −0.124934 | − | 0.0536005i | ||||
\(467\) | −7.83411 | − | 7.83411i | −0.362520 | − | 0.362520i | 0.502220 | − | 0.864740i | \(-0.332517\pi\) |
−0.864740 | + | 0.502220i | \(0.832517\pi\) | |||||||
\(468\) | −11.1669 | − | 0.281002i | −0.516192 | − | 0.0129893i | ||||
\(469\) | 1.05522 | − | 1.05522i | 0.0487255 | − | 0.0487255i | ||||
\(470\) | −5.14067 | − | 12.8661i | −0.237122 | − | 0.593469i | ||||
\(471\) | 36.8568i | 1.69827i | ||||||||
\(472\) | 17.2333 | − | 37.5331i | 0.793227 | − | 1.72760i | ||||
\(473\) | − | 11.4216i | − | 0.525167i | ||||||
\(474\) | 33.5374 | − | 13.3999i | 1.54043 | − | 0.615480i | ||||
\(475\) | −2.56181 | + | 2.56181i | −0.117544 | + | 0.117544i | ||||
\(476\) | 9.57855 | − | 9.10832i | 0.439032 | − | 0.417479i | ||||
\(477\) | 6.91988 | + | 6.91988i | 0.316840 | + | 0.316840i | ||||
\(478\) | 8.33388 | − | 19.4250i | 0.381183 | − | 0.888477i | ||||
\(479\) | 22.0416 | 1.00711 | 0.503554 | − | 0.863964i | \(-0.332026\pi\) | ||||
0.503554 | + | 0.863964i | \(0.332026\pi\) | |||||||
\(480\) | −17.2942 | − | 8.47373i | −0.789370 | − | 0.386771i | ||||
\(481\) | −0.538625 | −0.0245592 | ||||||||
\(482\) | −4.89262 | + | 11.4039i | −0.222853 | + | 0.519435i | ||||
\(483\) | −16.9712 | − | 16.9712i | −0.772217 | − | 0.772217i | ||||
\(484\) | −0.372257 | + | 0.353982i | −0.0169208 | + | 0.0160901i | ||||
\(485\) | 4.78810 | − | 4.78810i | 0.217416 | − | 0.217416i | ||||
\(486\) | −99.4935 | + | 39.7528i | −4.51312 | + | 1.80322i | ||||
\(487\) | 38.4601i | 1.74279i | 0.490580 | + | 0.871396i | \(0.336785\pi\) | ||||
−0.490580 | + | 0.871396i | \(0.663215\pi\) | |||||||
\(488\) | 19.0741 | + | 8.75786i | 0.863443 | + | 0.396449i | ||||
\(489\) | − | 40.8978i | − | 1.84946i | ||||||
\(490\) | 0.524718 | + | 1.31327i | 0.0237044 | + | 0.0593274i | ||||
\(491\) | −11.7492 | + | 11.7492i | −0.530232 | + | 0.530232i | −0.920641 | − | 0.390409i | \(-0.872334\pi\) |
0.390409 | + | 0.920641i | \(0.372334\pi\) | |||||||
\(492\) | 3.73458 | + | 0.0939762i | 0.168368 | + | 0.00423677i | ||||
\(493\) | −8.05805 | − | 8.05805i | −0.362916 | − | 0.362916i | ||||
\(494\) | −3.06137 | − | 1.31341i | −0.137737 | − | 0.0590933i | ||||
\(495\) | 28.8220 | 1.29545 | ||||||||
\(496\) | −0.0158746 | + | 0.315227i | −0.000712792 | + | 0.0141541i | ||||
\(497\) | −7.97855 | −0.357887 | ||||||||
\(498\) | 6.15925 | + | 2.64250i | 0.276003 | + | 0.118413i | ||||
\(499\) | 7.05189 | + | 7.05189i | 0.315686 | + | 0.315686i | 0.847108 | − | 0.531421i | \(-0.178342\pi\) |
−0.531421 | + | 0.847108i | \(0.678342\pi\) | |||||||
\(500\) | 0.0503116 | − | 1.99937i | 0.00225000 | − | 0.0894144i | ||||
\(501\) | 24.4161 | − | 24.4161i | 1.09083 | − | 1.09083i | ||||
\(502\) | −11.4031 | − | 28.5396i | −0.508944 | − | 1.27379i | ||||
\(503\) | − | 22.3743i | − | 0.997621i | −0.866711 | − | 0.498811i | \(-0.833770\pi\) | ||
0.866711 | − | 0.498811i | \(-0.166230\pi\) | |||||||
\(504\) | −22.7828 | + | 8.44469i | −1.01482 | + | 0.376156i | ||||
\(505\) | 7.77124i | 0.345816i | ||||||||
\(506\) | −31.0627 | + | 12.4112i | −1.38091 | + | 0.551743i | ||||
\(507\) | −30.2776 | + | 30.2776i | −1.34468 | + | 1.34468i | ||||
\(508\) | 17.2014 | + | 18.0895i | 0.763189 | + | 0.802590i | ||||
\(509\) | 13.7297 | + | 13.7297i | 0.608560 | + | 0.608560i | 0.942570 | − | 0.334009i | \(-0.108402\pi\) |
−0.334009 | + | 0.942570i | \(0.608402\pi\) | |||||||
\(510\) | −12.5456 | + | 29.2420i | −0.555531 | + | 1.29486i | ||||
\(511\) | 13.8380 | 0.612157 | ||||||||
\(512\) | 10.9654 | − | 19.7929i | 0.484606 | − | 0.874733i | ||||
\(513\) | −68.9541 | −3.04440 | ||||||||
\(514\) | −6.79268 | + | 15.8327i | −0.299612 | + | 0.698349i | ||||
\(515\) | 0.426209 | + | 0.426209i | 0.0187810 | + | 0.0187810i | ||||
\(516\) | −15.9727 | − | 16.7973i | −0.703159 | − | 0.739461i | ||||
\(517\) | −23.2427 | + | 23.2427i | −1.02221 | + | 1.02221i | ||||
\(518\) | −1.08796 | + | 0.434698i | −0.0478024 | + | 0.0190995i | ||||
\(519\) | − | 14.6927i | − | 0.644936i | ||||||
\(520\) | 1.72431 | − | 0.639135i | 0.0756161 | − | 0.0280279i | ||||
\(521\) | − | 29.6617i | − | 1.29950i | −0.760147 | − | 0.649751i | \(-0.774873\pi\) | ||
0.760147 | − | 0.649751i | \(-0.225127\pi\) | |||||||
\(522\) | 7.77245 | + | 19.4529i | 0.340191 | + | 0.851432i | ||||
\(523\) | 4.26196 | − | 4.26196i | 0.186362 | − | 0.186362i | −0.607759 | − | 0.794121i | \(-0.707931\pi\) |
0.794121 | + | 0.607759i | \(0.207931\pi\) | |||||||
\(524\) | −0.0668926 | + | 2.65829i | −0.00292222 | + | 0.116128i | ||||
\(525\) | −2.40733 | − | 2.40733i | −0.105064 | − | 0.105064i | ||||
\(526\) | 24.0159 | + | 10.3035i | 1.04714 | + | 0.449254i | ||||
\(527\) | 0.521485 | 0.0227163 | ||||||||
\(528\) | −2.29800 | + | 45.6319i | −0.100007 | + | 1.98587i | ||||
\(529\) | −26.6999 | −1.16086 | ||||||||
\(530\) | −1.48056 | − | 0.635201i | −0.0643112 | − | 0.0275914i | ||||
\(531\) | 88.6971 | + | 88.6971i | 3.84913 | + | 3.84913i | ||||
\(532\) | −7.24361 | − | 0.182277i | −0.314050 | − | 0.00790269i | ||||
\(533\) | −0.252238 | + | 0.252238i | −0.0109256 | + | 0.0109256i | ||||
\(534\) | −12.5638 | − | 31.4446i | −0.543687 | − | 1.36074i | ||||
\(535\) | 13.5313i | 0.585011i | ||||||||
\(536\) | −3.83586 | − | 1.76123i | −0.165684 | − | 0.0760737i | ||||
\(537\) | 16.2885i | 0.702900i | ||||||||
\(538\) | −33.8124 | + | 13.5098i | −1.45776 | + | 0.582449i | ||||
\(539\) | 2.37243 | − | 2.37243i | 0.102188 | − | 0.102188i | ||||
\(540\) | 27.5847 | − | 26.2305i | 1.18706 | − | 1.12878i | ||||
\(541\) | −21.2903 | − | 21.2903i | −0.915342 | − | 0.915342i | 0.0813437 | − | 0.996686i | \(-0.474079\pi\) |
−0.996686 | + | 0.0813437i | \(0.974079\pi\) | |||||||
\(542\) | −4.22217 | + | 9.84122i | −0.181358 | + | 0.422716i | ||||
\(543\) | −33.2275 | −1.42593 | ||||||||
\(544\) | −33.5722 | − | 16.4495i | −1.43940 | − | 0.705268i | ||||
\(545\) | −20.8101 | −0.891406 | ||||||||
\(546\) | 1.23421 | − | 2.87675i | 0.0528193 | − | 0.123114i | ||||
\(547\) | 14.5737 | + | 14.5737i | 0.623126 | + | 0.623126i | 0.946329 | − | 0.323204i | \(-0.104760\pi\) |
−0.323204 | + | 0.946329i | \(0.604760\pi\) | |||||||
\(548\) | −9.23341 | + | 8.78012i | −0.394432 | + | 0.375068i | ||||
\(549\) | −45.0753 | + | 45.0753i | −1.92377 | + | 1.92377i | ||||
\(550\) | −4.40617 | + | 1.76049i | −0.187880 | + | 0.0750677i | ||||
\(551\) | 6.24710i | 0.266135i | ||||||||
\(552\) | −28.3262 | + | 61.6926i | −1.20564 | + | 2.62581i | ||||
\(553\) | 7.50113i | 0.318980i | ||||||||
\(554\) | 7.14090 | + | 17.8723i | 0.303388 | + | 0.759320i | ||||
\(555\) | 1.99433 | − | 1.99433i | 0.0846545 | − | 0.0846545i | ||||
\(556\) | 1.37602 | + | 0.0346259i | 0.0583563 | + | 0.00146846i | ||||
\(557\) | −3.63217 | − | 3.63217i | −0.153900 | − | 0.153900i | 0.625957 | − | 0.779857i | \(-0.284708\pi\) |
−0.779857 | + | 0.625957i | \(0.784708\pi\) | |||||||
\(558\) | −0.880959 | − | 0.377957i | −0.0372940 | − | 0.0160002i | ||||
\(559\) | 2.21332 | 0.0936136 | ||||||||
\(560\) | 2.96711 | − | 2.68259i | 0.125383 | − | 0.113360i | ||||
\(561\) | 75.4897 | 3.18718 | ||||||||
\(562\) | 28.7419 | + | 12.3311i | 1.21240 | + | 0.520156i | ||||
\(563\) | 8.01210 | + | 8.01210i | 0.337670 | + | 0.337670i | 0.855490 | − | 0.517820i | \(-0.173256\pi\) |
−0.517820 | + | 0.855490i | \(0.673256\pi\) | |||||||
\(564\) | −1.67808 | + | 66.6863i | −0.0706599 | + | 2.80800i | ||||
\(565\) | −10.9771 | + | 10.9771i | −0.461812 | + | 0.461812i | ||||
\(566\) | 6.48004 | + | 16.2183i | 0.272377 | + | 0.681706i | ||||
\(567\) | − | 39.0245i | − | 1.63888i | ||||||
\(568\) | 7.84317 | + | 21.1599i | 0.329092 | + | 0.887852i | ||||
\(569\) | − | 22.6007i | − | 0.947469i | −0.880668 | − | 0.473735i | \(-0.842906\pi\) | ||
0.880668 | − | 0.473735i | \(-0.157094\pi\) | |||||||
\(570\) | 16.1982 | − | 6.47201i | 0.678467 | − | 0.271083i | ||||
\(571\) | −23.3563 | + | 23.3563i | −0.977432 | + | 0.977432i | −0.999751 | − | 0.0223187i | \(-0.992895\pi\) |
0.0223187 | + | 0.999751i | \(0.492895\pi\) | |||||||
\(572\) | −3.00637 | − | 3.16158i | −0.125703 | − | 0.132192i | ||||
\(573\) | 22.2749 | + | 22.2749i | 0.930549 | + | 0.930549i | ||||
\(574\) | −0.305924 | + | 0.713061i | −0.0127690 | + | 0.0297626i | ||||
\(575\) | −7.04981 | −0.293998 | ||||||||
\(576\) | 44.7923 | + | 52.1208i | 1.86635 | + | 2.17170i | ||||
\(577\) | −0.618797 | −0.0257609 | −0.0128804 | − | 0.999917i | \(-0.504100\pi\) | ||||
−0.0128804 | + | 0.999917i | \(0.504100\pi\) | |||||||
\(578\) | −14.8751 | + | 34.6715i | −0.618722 | + | 1.44215i | ||||
\(579\) | 44.0242 | + | 44.0242i | 1.82958 | + | 1.82958i | ||||
\(580\) | −2.37643 | − | 2.49912i | −0.0986759 | − | 0.103770i | ||||
\(581\) | −0.984319 | + | 0.984319i | −0.0408364 | + | 0.0408364i | ||||
\(582\) | −30.2748 | + | 12.0964i | −1.25493 | + | 0.501410i | ||||
\(583\) | 3.82214i | 0.158297i | ||||||||
\(584\) | −13.6032 | − | 36.6998i | −0.562904 | − | 1.51865i | ||||
\(585\) | 5.58523i | 0.230921i | ||||||||
\(586\) | 0.401313 | + | 1.00441i | 0.0165781 | + | 0.0414917i | ||||
\(587\) | −7.04144 | + | 7.04144i | −0.290631 | + | 0.290631i | −0.837330 | − | 0.546698i | \(-0.815884\pi\) |
0.546698 | + | 0.837330i | \(0.315884\pi\) | |||||||
\(588\) | 0.171285 | − | 6.80680i | 0.00706366 | − | 0.280708i | ||||
\(589\) | −0.202144 | − | 0.202144i | −0.00832919 | − | 0.00832919i | ||||
\(590\) | −18.9773 | − | 8.14183i | −0.781285 | − | 0.335194i | ||||
\(591\) | −19.5214 | −0.803001 | ||||||||
\(592\) | 2.22237 | + | 2.45807i | 0.0913387 | + | 0.101026i | ||||
\(593\) | 27.9722 | 1.14868 | 0.574340 | − | 0.818617i | \(-0.305259\pi\) | ||||
0.574340 | + | 0.818617i | \(0.305259\pi\) | |||||||
\(594\) | −82.9913 | − | 35.6057i | −3.40517 | − | 1.46092i | ||||
\(595\) | −4.67320 | − | 4.67320i | −0.191582 | − | 0.191582i | ||||
\(596\) | −32.2863 | − | 0.812444i | −1.32250 | − | 0.0332790i | ||||
\(597\) | 19.7344 | − | 19.7344i | 0.807675 | − | 0.807675i | ||||
\(598\) | −2.40508 | − | 6.01944i | −0.0983510 | − | 0.246153i | ||||
\(599\) | 27.6858i | 1.13121i | 0.824676 | + | 0.565605i | \(0.191357\pi\) | ||||
−0.824676 | + | 0.565605i | \(0.808643\pi\) | |||||||
\(600\) | −4.01800 | + | 8.75096i | −0.164034 | + | 0.357256i | ||||
\(601\) | − | 23.9255i | − | 0.975942i | −0.872860 | − | 0.487971i | \(-0.837737\pi\) | ||
0.872860 | − | 0.487971i | \(-0.162263\pi\) | |||||||
\(602\) | 4.47067 | − | 1.78626i | 0.182211 | − | 0.0728026i | ||||
\(603\) | 9.06480 | − | 9.06480i | 0.369147 | − | 0.369147i | ||||
\(604\) | 16.3027 | − | 15.5024i | 0.663347 | − | 0.630782i | ||||
\(605\) | 0.181617 | + | 0.181617i | 0.00738379 | + | 0.00738379i | ||||
\(606\) | 14.7521 | − | 34.3849i | 0.599264 | − | 1.39679i | ||||
\(607\) | −7.11335 | −0.288722 | −0.144361 | − | 0.989525i | \(-0.546113\pi\) | ||||
−0.144361 | + | 0.989525i | \(0.546113\pi\) | |||||||
\(608\) | 6.63728 | + | 19.3900i | 0.269177 | + | 0.786368i | ||||
\(609\) | −5.87038 | −0.237880 | ||||||||
\(610\) | 4.13763 | − | 9.64417i | 0.167528 | − | 0.390481i | ||||
\(611\) | −4.50406 | − | 4.50406i | −0.182215 | − | 0.182215i | ||||
\(612\) | 82.2841 | − | 78.2446i | 3.32614 | − | 3.16285i | ||||
\(613\) | −12.2698 | + | 12.2698i | −0.495571 | + | 0.495571i | −0.910056 | − | 0.414485i | \(-0.863962\pi\) |
0.414485 | + | 0.910056i | \(0.363962\pi\) | |||||||
\(614\) | 14.9964 | − | 5.99183i | 0.605205 | − | 0.241810i | ||||
\(615\) | − | 1.86788i | − | 0.0753203i | ||||||
\(616\) | −8.62410 | − | 3.95975i | −0.347475 | − | 0.159543i | ||||
\(617\) | 26.2983i | 1.05873i | 0.848394 | + | 0.529366i | \(0.177570\pi\) | ||||
−0.848394 | + | 0.529366i | \(0.822430\pi\) | |||||||
\(618\) | −1.07675 | − | 2.69489i | −0.0433132 | − | 0.108404i | ||||
\(619\) | 7.29239 | − | 7.29239i | 0.293106 | − | 0.293106i | −0.545200 | − | 0.838306i | \(-0.683546\pi\) |
0.838306 | + | 0.545200i | \(0.183546\pi\) | |||||||
\(620\) | 0.157763 | + | 0.00396991i | 0.00633592 | + | 0.000159436i | ||||
\(621\) | −94.8768 | − | 94.8768i | −3.80727 | − | 3.80727i | ||||
\(622\) | 39.4105 | + | 16.9082i | 1.58022 | + | 0.677958i | ||||
\(623\) | 7.03304 | 0.281773 | ||||||||
\(624\) | −8.84271 | − | 0.445314i | −0.353992 | − | 0.0178268i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | −10.5585 | − | 4.52990i | −0.422002 | − | 0.181051i | ||||
\(627\) | −29.2622 | − | 29.2622i | −1.16862 | − | 1.16862i | ||||
\(628\) | −0.544673 | + | 21.6451i | −0.0217348 | + | 0.863735i | ||||
\(629\) | 3.87147 | − | 3.87147i | 0.154365 | − | 0.154365i | ||||
\(630\) | 4.50757 | + | 11.2816i | 0.179586 | + | 0.449468i | ||||
\(631\) | 2.05090i | 0.0816448i | 0.999166 | + | 0.0408224i | \(0.0129978\pi\) | ||||
−0.999166 | + | 0.0408224i | \(0.987002\pi\) | |||||||
\(632\) | 19.8938 | − | 7.37385i | 0.791331 | − | 0.293316i | ||||
\(633\) | − | 39.5534i | − | 1.57211i | ||||||
\(634\) | −36.6180 | + | 14.6308i | −1.45428 | + | 0.581062i | ||||
\(635\) | 8.82551 | − | 8.82551i | 0.350230 | − | 0.350230i | ||||
\(636\) | 5.34512 | + | 5.62107i | 0.211948 | + | 0.222890i | ||||
\(637\) | 0.459738 | + | 0.459738i | 0.0182155 | + | 0.0182155i | ||||
\(638\) | −3.22580 | + | 7.51885i | −0.127711 | + | 0.297674i | ||||
\(639\) | −68.5394 | −2.71138 | ||||||||
\(640\) | −10.0313 | − | 5.23200i | −0.396520 | − | 0.206813i | ||||
\(641\) | −20.8338 | −0.822884 | −0.411442 | − | 0.911436i | \(-0.634975\pi\) | ||||
−0.411442 | + | 0.911436i | \(0.634975\pi\) | |||||||
\(642\) | 25.6865 | − | 59.8712i | 1.01377 | − | 2.36293i | ||||
\(643\) | −11.2607 | − | 11.2607i | −0.444079 | − | 0.444079i | 0.449301 | − | 0.893380i | \(-0.351673\pi\) |
−0.893380 | + | 0.449301i | \(0.851673\pi\) | |||||||
\(644\) | −9.71599 | − | 10.2176i | −0.382864 | − | 0.402629i | ||||
\(645\) | −8.19510 | + | 8.19510i | −0.322682 | + | 0.322682i | ||||
\(646\) | 31.4445 | − | 12.5637i | 1.23717 | − | 0.494313i | ||||
\(647\) | 25.3682i | 0.997326i | 0.866796 | + | 0.498663i | \(0.166175\pi\) | ||||
−0.866796 | + | 0.498663i | \(0.833825\pi\) | |||||||
\(648\) | −103.497 | + | 38.3623i | −4.06575 | + | 1.50701i | ||||
\(649\) | 48.9911i | 1.92307i | ||||||||
\(650\) | −0.341155 | − | 0.853844i | −0.0133812 | − | 0.0334905i | ||||
\(651\) | 0.189954 | − | 0.189954i | 0.00744488 | − | 0.00744488i | ||||
\(652\) | 0.604391 | − | 24.0183i | 0.0236698 | − | 0.940629i | ||||
\(653\) | 5.67998 | + | 5.67998i | 0.222275 | + | 0.222275i | 0.809456 | − | 0.587181i | \(-0.199762\pi\) |
−0.587181 | + | 0.809456i | \(0.699762\pi\) | |||||||
\(654\) | 92.0770 | + | 39.5037i | 3.60049 | + | 1.54472i | ||||
\(655\) | 1.32957 | 0.0519504 | ||||||||
\(656\) | 2.19184 | + | 0.110380i | 0.0855771 | + | 0.00430961i | ||||
\(657\) | 118.875 | 4.63774 | ||||||||
\(658\) | −12.7327 | − | 5.46270i | −0.496373 | − | 0.212958i | ||||
\(659\) | 21.2237 | + | 21.2237i | 0.826759 | + | 0.826759i | 0.987067 | − | 0.160308i | \(-0.0512487\pi\) |
−0.160308 | + | 0.987067i | \(0.551249\pi\) | |||||||
\(660\) | 22.8376 | + | 0.574681i | 0.888954 | + | 0.0223694i | ||||
\(661\) | 10.8284 | − | 10.8284i | 0.421176 | − | 0.421176i | −0.464433 | − | 0.885608i | \(-0.653742\pi\) |
0.885608 | + | 0.464433i | \(0.153742\pi\) | |||||||
\(662\) | 2.20122 | + | 5.50921i | 0.0855527 | + | 0.214122i | ||||
\(663\) | 14.6287i | 0.568130i | ||||||||
\(664\) | 3.57813 | + | 1.64290i | 0.138858 | + | 0.0637568i | ||||
\(665\) | 3.62295i | 0.140492i | ||||||||
\(666\) | −9.34610 | + | 3.73425i | −0.362154 | + | 0.144699i | ||||
\(667\) | −8.59565 | + | 8.59565i | −0.332825 | + | 0.332825i | ||||
\(668\) | 14.6998 | − | 13.9782i | 0.568753 | − | 0.540832i | ||||
\(669\) | −53.2821 | − | 53.2821i | −2.06000 | − | 2.06000i | ||||
\(670\) | −0.832091 | + | 1.93948i | −0.0321465 | + | 0.0749285i | ||||
\(671\) | −24.8970 | −0.961136 | ||||||||
\(672\) | −18.2207 | + | 6.23703i | −0.702879 | + | 0.240599i | ||||
\(673\) | −6.30782 | −0.243148 | −0.121574 | − | 0.992582i | \(-0.538794\pi\) | ||||
−0.121574 | + | 0.992582i | \(0.538794\pi\) | |||||||
\(674\) | 4.68770 | − | 10.9263i | 0.180563 | − | 0.420865i | ||||
\(675\) | −13.4580 | − | 13.4580i | −0.518001 | − | 0.518001i | ||||
\(676\) | −18.2288 | + | 17.3339i | −0.701107 | + | 0.666688i | ||||
\(677\) | 22.7752 | − | 22.7752i | 0.875320 | − | 0.875320i | −0.117726 | − | 0.993046i | \(-0.537560\pi\) |
0.993046 | + | 0.117726i | \(0.0375604\pi\) | |||||||
\(678\) | 69.4077 | − | 27.7320i | 2.66559 | − | 1.06504i | ||||
\(679\) | − | 6.77139i | − | 0.259862i | ||||||
\(680\) | −7.79990 | + | 16.9877i | −0.299112 | + | 0.651449i | ||||
\(681\) | 64.6455i | 2.47722i | ||||||||
\(682\) | −0.138914 | − | 0.347676i | −0.00531931 | − | 0.0133132i | ||||
\(683\) | 27.3383 | − | 27.3383i | 1.04607 | − | 1.04607i | 0.0471834 | − | 0.998886i | \(-0.484975\pi\) |
0.998886 | − | 0.0471834i | \(-0.0150245\pi\) | |||||||
\(684\) | −62.2259 | − | 1.56584i | −2.37927 | − | 0.0598713i | ||||
\(685\) | 4.50481 | + | 4.50481i | 0.172120 | + | 0.172120i | ||||
\(686\) | 1.29965 | + | 0.557588i | 0.0496209 | + | 0.0212888i | ||||
\(687\) | 72.9426 | 2.78293 | ||||||||
\(688\) | −9.13216 | − | 10.1007i | −0.348160 | − | 0.385086i | ||||
\(689\) | −0.740667 | −0.0282172 | ||||||||
\(690\) | 31.1928 | + | 13.3826i | 1.18749 | + | 0.509468i | ||||
\(691\) | 1.72857 | + | 1.72857i | 0.0657578 | + | 0.0657578i | 0.739221 | − | 0.673463i | \(-0.235194\pi\) |
−0.673463 | + | 0.739221i | \(0.735194\pi\) | |||||||
\(692\) | 0.217129 | − | 8.62864i | 0.00825402 | − | 0.328012i | ||||
\(693\) | 20.3802 | − | 20.3802i | 0.774181 | − | 0.774181i | ||||
\(694\) | 2.86969 | + | 7.18228i | 0.108932 | + | 0.272636i | ||||
\(695\) | − | 0.688228i | − | 0.0261060i | ||||||
\(696\) | 5.77077 | + | 15.5688i | 0.218740 | + | 0.590136i | ||||
\(697\) | − | 3.62601i | − | 0.137345i | ||||||
\(698\) | 34.2328 | − | 13.6778i | 1.29573 | − | 0.517711i | ||||
\(699\) | 4.99555 | − | 4.99555i | 0.188949 | − | 0.188949i | ||||
\(700\) | −1.37819 | − | 1.44934i | −0.0520907 | − | 0.0547800i | ||||
\(701\) | −11.7717 | − | 11.7717i | −0.444609 | − | 0.444609i | 0.448948 | − | 0.893558i | \(-0.351799\pi\) |
−0.893558 | + | 0.448948i | \(0.851799\pi\) | |||||||
\(702\) | 6.89980 | − | 16.0824i | 0.260416 | − | 0.606989i | ||||
\(703\) | −3.00140 | −0.113200 | ||||||||
\(704\) | −2.02391 | + | 26.7646i | −0.0762790 | + | 1.00873i | ||||
\(705\) | 33.3537 | 1.25617 | ||||||||
\(706\) | 17.8424 | − | 41.5879i | 0.671508 | − | 1.56518i | ||||
\(707\) | 5.49510 | + | 5.49510i | 0.206664 | + | 0.206664i | ||||
\(708\) | 68.5122 | + | 72.0493i | 2.57485 | + | 2.70778i | ||||
\(709\) | −10.0291 | + | 10.0291i | −0.376652 | + | 0.376652i | −0.869893 | − | 0.493241i | \(-0.835812\pi\) |
0.493241 | + | 0.869893i | \(0.335812\pi\) | |||||||
\(710\) | 10.4780 | − | 4.18649i | 0.393231 | − | 0.157116i | ||||
\(711\) | 64.4381i | 2.41662i | ||||||||
\(712\) | −6.91370 | − | 18.6524i | −0.259102 | − | 0.699027i | ||||
\(713\) | − | 0.556276i | − | 0.0208327i | ||||||
\(714\) | 11.8061 | + | 29.5483i | 0.441831 | + | 1.10582i | ||||
\(715\) | −1.54248 | + | 1.54248i | −0.0576854 | + | 0.0576854i | ||||
\(716\) | −0.240713 | + | 9.56584i | −0.00899585 | + | 0.357492i | ||||
\(717\) | 35.9806 | + | 35.9806i | 1.34372 | + | 1.34372i | ||||
\(718\) | −48.1611 | − | 20.6625i | −1.79736 | − | 0.771118i | ||||
\(719\) | 29.4371 | 1.09782 | 0.548909 | − | 0.835882i | \(-0.315043\pi\) | ||||
0.548909 | + | 0.835882i | \(0.315043\pi\) | |||||||
\(720\) | 25.4888 | − | 23.0447i | 0.949911 | − | 0.858824i | ||||
\(721\) | 0.602751 | 0.0224476 | ||||||||
\(722\) | 7.63443 | + | 3.27539i | 0.284124 | + | 0.121897i | ||||
\(723\) | −21.1234 | − | 21.1234i | −0.785586 | − | 0.785586i | ||||
\(724\) | −19.5137 | − | 0.491038i | −0.725221 | − | 0.0182493i | ||||
\(725\) | −1.21927 | + | 1.21927i | −0.0452827 | + | 0.0452827i | ||||
\(726\) | −0.458826 | − | 1.14835i | −0.0170286 | − | 0.0426194i | ||||
\(727\) | − | 29.1709i | − | 1.08189i | −0.841058 | − | 0.540945i | \(-0.818067\pi\) | ||
0.841058 | − | 0.540945i | \(-0.181933\pi\) | |||||||
\(728\) | 0.767335 | − | 1.67121i | 0.0284393 | − | 0.0619391i | ||||
\(729\) | − | 140.851i | − | 5.21669i | ||||||
\(730\) | −18.1730 | + | 7.26105i | −0.672613 | + | 0.268744i | ||||
\(731\) | −15.9087 | + | 15.9087i | −0.588403 | + | 0.588403i | ||||
\(732\) | −36.6150 | + | 34.8175i | −1.35333 | + | 1.28689i | ||||
\(733\) | −7.03839 | − | 7.03839i | −0.259969 | − | 0.259969i | 0.565072 | − | 0.825041i | \(-0.308848\pi\) |
−0.825041 | + | 0.565072i | \(0.808848\pi\) | |||||||
\(734\) | 9.50706 | − | 22.1595i | 0.350912 | − | 0.817921i | ||||
\(735\) | −3.40448 | −0.125576 | ||||||||
\(736\) | −17.5470 | + | 35.8120i | −0.646790 | + | 1.32005i | ||||
\(737\) | 5.00686 | 0.184430 | ||||||||
\(738\) | −2.62802 | + | 6.12551i | −0.0967389 | + | 0.225483i | ||||
\(739\) | −9.63082 | − | 9.63082i | −0.354276 | − | 0.354276i | 0.507422 | − | 0.861698i | \(-0.330599\pi\) |
−0.861698 | + | 0.507422i | \(0.830599\pi\) | |||||||
\(740\) | 1.20069 | − | 1.14175i | 0.0441384 | − | 0.0419715i | ||||
\(741\) | 5.67053 | − | 5.67053i | 0.208312 | − | 0.208312i | ||||
\(742\) | −1.49607 | + | 0.597756i | −0.0549223 | + | 0.0219443i | ||||
\(743\) | − | 1.94893i | − | 0.0714992i | −0.999361 | − | 0.0357496i | \(-0.988618\pi\) | ||
0.999361 | − | 0.0357496i | \(-0.0113819\pi\) | |||||||
\(744\) | −0.690508 | − | 0.317046i | −0.0253152 | − | 0.0116235i | ||||
\(745\) | 16.1482i | 0.591626i | ||||||||
\(746\) | 3.36923 | + | 8.43252i | 0.123356 | + | 0.308737i | ||||
\(747\) | −8.45574 | + | 8.45574i | −0.309379 | + | 0.309379i | ||||
\(748\) | 44.3333 | + | 1.11559i | 1.62099 | + | 0.0407901i | ||||
\(749\) | 9.56811 | + | 9.56811i | 0.349611 | + | 0.349611i | ||||
\(750\) | 4.42463 | + | 1.89830i | 0.161565 | + | 0.0693160i | ||||
\(751\) | 35.1964 | 1.28434 | 0.642168 | − | 0.766564i | \(-0.278035\pi\) | ||||
0.642168 | + | 0.766564i | \(0.278035\pi\) | |||||||
\(752\) | −1.97099 | + | 39.1385i | −0.0718747 | + | 1.42723i | ||||
\(753\) | 73.9853 | 2.69617 | ||||||||
\(754\) | −1.45703 | − | 0.625108i | −0.0530619 | − | 0.0227651i | ||||
\(755\) | −7.95378 | − | 7.95378i | −0.289468 | − | 0.289468i | ||||
\(756\) | 0.957559 | − | 38.0531i | 0.0348261 | − | 1.38398i | ||||
\(757\) | −15.7315 | + | 15.7315i | −0.571772 | + | 0.571772i | −0.932623 | − | 0.360852i | \(-0.882486\pi\) |
0.360852 | + | 0.932623i | \(0.382486\pi\) | |||||||
\(758\) | −10.3543 | − | 25.9148i | −0.376084 | − | 0.941266i | ||||
\(759\) | − | 80.5260i | − | 2.92291i | ||||||
\(760\) | 9.60844 | − | 3.56148i | 0.348535 | − | 0.129188i | ||||
\(761\) | − | 3.53285i | − | 0.128066i | −0.997948 | − | 0.0640329i | \(-0.979604\pi\) | ||
0.997948 | − | 0.0640329i | \(-0.0203963\pi\) | |||||||
\(762\) | −55.8031 | + | 22.2962i | −2.02153 | + | 0.807707i | ||||
\(763\) | −14.7149 | + | 14.7149i | −0.532717 | + | 0.532717i | ||||
\(764\) | 12.7524 | + | 13.4107i | 0.461364 | + | 0.485183i | ||||
\(765\) | −40.1449 | − | 40.1449i | −1.45144 | − | 1.45144i | ||||
\(766\) | 12.6878 | − | 29.5733i | 0.458430 | − | 1.06853i | ||||
\(767\) | −9.49367 | −0.342796 | ||||||||
\(768\) | 34.4528 | + | 42.1920i | 1.24321 | + | 1.52247i | ||||
\(769\) | 8.78487 | 0.316791 | 0.158395 | − | 0.987376i | \(-0.449368\pi\) | ||||
0.158395 | + | 0.987376i | \(0.449368\pi\) | |||||||
\(770\) | −1.87078 | + | 4.36049i | −0.0674181 | + | 0.157141i | ||||
\(771\) | −29.3266 | − | 29.3266i | −1.05617 | − | 1.05617i | ||||
\(772\) | 25.2038 | + | 26.5050i | 0.907104 | + | 0.953935i | ||||
\(773\) | 12.0940 | − | 12.0940i | 0.434991 | − | 0.434991i | −0.455331 | − | 0.890322i | \(-0.650479\pi\) |
0.890322 | + | 0.455331i | \(0.150479\pi\) | |||||||
\(774\) | 38.4051 | − | 15.3448i | 1.38044 | − | 0.551558i | ||||
\(775\) | − | 0.0789065i | − | 0.00283441i | ||||||
\(776\) | −17.9584 | + | 6.65649i | −0.644670 | + | 0.238954i | ||||
\(777\) | − | 2.82041i | − | 0.101181i | ||||||
\(778\) | 0.215041 | + | 0.538206i | 0.00770960 | + | 0.0192956i | ||||
\(779\) | −1.40555 | + | 1.40555i | −0.0503591 | + | 0.0503591i | ||||
\(780\) | −0.111364 | + | 4.42556i | −0.00398746 | + | 0.158460i | ||||
\(781\) | −18.9286 | − | 18.9286i | −0.677317 | − | 0.677317i | ||||
\(782\) | 60.5528 | + | 25.9789i | 2.16536 | + | 0.929003i | ||||
\(783\) | −32.8181 | −1.17282 | ||||||||
\(784\) | 0.201183 | − | 3.99494i | 0.00718510 | − | 0.142676i | ||||
\(785\) | 10.8260 | 0.386396 | ||||||||
\(786\) | −5.88284 | − | 2.52391i | −0.209834 | − | 0.0900249i | ||||
\(787\) | 2.37139 | + | 2.37139i | 0.0845310 | + | 0.0845310i | 0.748108 | − | 0.663577i | \(-0.230963\pi\) |
−0.663577 | + | 0.748108i | \(0.730963\pi\) | |||||||
\(788\) | −11.4644 | − | 0.288488i | −0.408403 | − | 0.0102770i | ||||
\(789\) | −44.4842 | + | 44.4842i | −1.58368 | + | 1.58368i | ||||
\(790\) | −3.93598 | − | 9.85099i | −0.140036 | − | 0.350482i | ||||
\(791\) | 15.5240i | 0.551971i | ||||||||
\(792\) | −74.0849 | − | 34.0161i | −2.63249 | − | 1.20871i | ||||
\(793\) | − | 4.82462i | − | 0.171327i | ||||||
\(794\) | 30.0451 | − | 12.0046i | 1.06626 | − | 0.426026i | ||||
\(795\) | 2.74241 | − | 2.74241i | 0.0972634 | − | 0.0972634i | ||||
\(796\) | 11.8812 | − | 11.2979i | 0.421117 | − | 0.400444i | ||||
\(797\) | −1.17474 | − | 1.17474i | −0.0416113 | − | 0.0416113i | 0.685995 | − | 0.727606i | \(-0.259367\pi\) |
−0.727606 | + | 0.685995i | \(0.759367\pi\) | |||||||
\(798\) | 6.87744 | − | 16.0302i | 0.243459 | − | 0.567464i | ||||
\(799\) | 64.7475 | 2.29060 | ||||||||
\(800\) | −2.48900 | + | 5.07985i | −0.0879994 | + | 0.179600i | ||||
\(801\) | 60.4170 | 2.13473 | ||||||||
\(802\) | −6.75200 | + | 15.7379i | −0.238421 | + | 0.555723i | ||||
\(803\) | 32.8297 | + | 32.8297i | 1.15853 | + | 1.15853i | ||||
\(804\) | 7.36340 | − | 7.00191i | 0.259687 | − | 0.246938i | ||||
\(805\) | −4.98497 | + | 4.98497i | −0.175697 | + | 0.175697i | ||||
\(806\) | 0.0673738 | − | 0.0269193i | 0.00237314 | − | 0.000948193i | ||||
\(807\) | − | 87.6542i | − | 3.08557i | ||||||
\(808\) | 9.17171 | − | 19.9754i | 0.322660 | − | 0.702733i | ||||
\(809\) | − | 5.70645i | − | 0.200628i | −0.994956 | − | 0.100314i | \(-0.968015\pi\) | ||
0.994956 | − | 0.100314i | \(-0.0319848\pi\) | |||||||
\(810\) | 20.4769 | + | 51.2496i | 0.719484 | + | 1.80073i | ||||
\(811\) | −26.8909 | + | 26.8909i | −0.944266 | + | 0.944266i | −0.998527 | − | 0.0542609i | \(-0.982720\pi\) |
0.0542609 | + | 0.998527i | \(0.482720\pi\) | |||||||
\(812\) | −3.44753 | − | 0.0867529i | −0.120985 | − | 0.00304443i | ||||
\(813\) | −18.2287 | − | 18.2287i | −0.639310 | − | 0.639310i | ||||
\(814\) | −3.61241 | − | 1.54983i | −0.126615 | − | 0.0543214i | ||||
\(815\) | −12.0129 | −0.420795 | ||||||||
\(816\) | 66.7594 | − | 60.3578i | 2.33705 | − | 2.11295i | ||||
\(817\) | 12.3334 | 0.431490 | ||||||||
\(818\) | 19.4500 | + | 8.34461i | 0.680053 | + | 0.291762i | ||||
\(819\) | 3.94936 | + | 3.94936i | 0.138002 | + | 0.138002i | ||||
\(820\) | 0.0276037 | − | 1.09696i | 0.000963964 | − | 0.0383076i | ||||
\(821\) | −36.8377 | + | 36.8377i | −1.28564 | + | 1.28564i | −0.348238 | + | 0.937406i | \(0.613220\pi\) |
−0.937406 | + | 0.348238i | \(0.886780\pi\) | |||||||
\(822\) | −11.3807 | − | 28.4836i | −0.396946 | − | 0.993479i | ||||
\(823\) | 26.3035i | 0.916883i | 0.888725 | + | 0.458442i | \(0.151592\pi\) | ||||
−0.888725 | + | 0.458442i | \(0.848408\pi\) | |||||||
\(824\) | −0.592523 | − | 1.59856i | −0.0206415 | − | 0.0556884i | ||||
\(825\) | − | 11.4224i | − | 0.397678i | ||||||
\(826\) | −19.1762 | + | 7.66187i | −0.667224 | + | 0.266590i | ||||
\(827\) | −6.37770 | + | 6.37770i | −0.221774 | + | 0.221774i | −0.809245 | − | 0.587471i | \(-0.800124\pi\) |
0.587471 | + | 0.809245i | \(0.300124\pi\) | |||||||
\(828\) | −83.4647 | − | 87.7737i | −2.90060 | − | 3.05035i | ||||
\(829\) | −23.0074 | − | 23.0074i | −0.799079 | − | 0.799079i | 0.183871 | − | 0.982950i | \(-0.441137\pi\) |
−0.982950 | + | 0.183871i | \(0.941137\pi\) | |||||||
\(830\) | 0.776184 | − | 1.80916i | 0.0269417 | − | 0.0627970i | ||||
\(831\) | −46.3316 | −1.60722 | ||||||||
\(832\) | −5.18653 | − | 0.392201i | −0.179811 | − | 0.0135971i | ||||
\(833\) | −6.60890 | −0.228985 | ||||||||
\(834\) | −1.30646 | + | 3.04516i | −0.0452390 | + | 0.105445i | ||||
\(835\) | −7.17177 | − | 7.17177i | −0.248189 | − | 0.248189i | ||||
\(836\) | −16.7525 | − | 17.6174i | −0.579398 | − | 0.609311i | ||||
\(837\) | 1.06193 | − | 1.06193i | 0.0367056 | − | 0.0367056i | ||||
\(838\) | 28.7467 | − | 11.4858i | 0.993039 | − | 0.396770i | ||||
\(839\) | 55.5878i | 1.91910i | 0.281531 | + | 0.959552i | \(0.409158\pi\) | ||||
−0.281531 | + | 0.959552i | \(0.590842\pi\) | |||||||
\(840\) | 3.34671 | + | 9.02902i | 0.115472 | + | 0.311531i | ||||
\(841\) | − | 26.0267i | − | 0.897474i | ||||||
\(842\) | −3.02015 | − | 7.55883i | −0.104081 | − | 0.260495i | ||||
\(843\) | −53.2382 | + | 53.2382i | −1.83362 | + | 1.83362i | ||||
\(844\) | 0.584523 | − | 23.2288i | 0.0201201 | − | 0.799567i | ||||
\(845\) | 8.89348 | + | 8.89348i | 0.305945 | + | 0.305945i | ||||
\(846\) | −109.380 | − | 46.9271i | −3.76055 | − | 1.61339i | ||||
\(847\) | 0.256846 | 0.00882532 | ||||||||
\(848\) | 3.05599 | + | 3.38011i | 0.104943 | + | 0.116073i | ||||
\(849\) | −42.0438 | −1.44294 | ||||||||
\(850\) | 8.58927 | + | 3.68505i | 0.294610 | + | 0.126396i | ||||
\(851\) | −4.12975 | − | 4.12975i | −0.141566 | − | 0.141566i | ||||
\(852\) | −54.3084 | − | 1.36660i | −1.86057 | − | 0.0468191i | ||||
\(853\) | −17.7059 | + | 17.7059i | −0.606238 | + | 0.606238i | −0.941961 | − | 0.335723i | \(-0.891020\pi\) |
0.335723 | + | 0.941961i | \(0.391020\pi\) | |||||||
\(854\) | −3.89371 | − | 9.74521i | −0.133240 | − | 0.333474i | ||||
\(855\) | 31.1228i | 1.06438i | ||||||||
\(856\) | 15.9699 | − | 34.7814i | 0.545838 | − | 1.18880i | ||||
\(857\) | − | 32.2502i | − | 1.10165i | −0.834622 | − | 0.550823i | \(-0.814314\pi\) | ||
0.834622 | − | 0.550823i | \(-0.185686\pi\) | |||||||
\(858\) | 9.75297 | − | 3.89682i | 0.332961 | − | 0.133035i | ||||
\(859\) | 1.87487 | − | 1.87487i | 0.0639696 | − | 0.0639696i | −0.674398 | − | 0.738368i | \(-0.735597\pi\) |
0.738368 | + | 0.674398i | \(0.235597\pi\) | |||||||
\(860\) | −4.93390 | + | 4.69168i | −0.168244 | + | 0.159985i | ||||
\(861\) | −1.32079 | − | 1.32079i | −0.0450125 | − | 0.0450125i | ||||
\(862\) | −14.1682 | + | 33.0240i | −0.482572 | + | 1.12480i | ||||
\(863\) | 3.59902 | 0.122512 | 0.0612560 | − | 0.998122i | \(-0.480489\pi\) | ||||
0.0612560 | + | 0.998122i | \(0.480489\pi\) | |||||||
\(864\) | −101.862 | + | 34.8678i | −3.46541 | + | 1.18623i | ||||
\(865\) | −4.31569 | −0.146738 | ||||||||
\(866\) | 4.60139 | − | 10.7251i | 0.156362 | − | 0.364455i | ||||
\(867\) | −64.2216 | − | 64.2216i | −2.18108 | − | 2.18108i | ||||
\(868\) | 0.114362 | − | 0.108748i | 0.00388172 | − | 0.00369115i | ||||
\(869\) | −17.7959 | + | 17.7959i | −0.603685 | + | 0.603685i | ||||
\(870\) | 7.70938 | − | 3.08029i | 0.261372 | − | 0.104432i | ||||
\(871\) | 0.970248i | 0.0328756i | ||||||||
\(872\) | 53.4908 | + | 24.5603i | 1.81143 | + | 0.831717i | ||||
\(873\) | − | 58.1693i | − | 1.96873i | ||||||
\(874\) | −13.4019 | − | 33.5424i | −0.453326 | − | 1.13459i | ||||
\(875\) | −0.707107 | + | 0.707107i | −0.0239046 | + | 0.0239046i | ||||
\(876\) | 94.1925 | + | 2.37024i | 3.18247 | + | 0.0800829i | ||||
\(877\) | 0.572209 | + | 0.572209i | 0.0193221 | + | 0.0193221i | 0.716702 | − | 0.697380i | \(-0.245651\pi\) |
−0.697380 | + | 0.716702i | \(0.745651\pi\) | |||||||
\(878\) | 27.6673 | + | 11.8701i | 0.933727 | + | 0.400596i | ||||
\(879\) | −2.60380 | −0.0878239 | ||||||||
\(880\) | 13.4035 | + | 0.674993i | 0.451832 | + | 0.0227540i | ||||
\(881\) | −25.7619 | −0.867940 | −0.433970 | − | 0.900927i | \(-0.642888\pi\) | ||||
−0.433970 | + | 0.900927i | \(0.642888\pi\) | |||||||
\(882\) | 11.1646 | + | 4.78994i | 0.375932 | + | 0.161286i | ||||
\(883\) | −21.9261 | − | 21.9261i | −0.737871 | − | 0.737871i | 0.234294 | − | 0.972166i | \(-0.424722\pi\) |
−0.972166 | + | 0.234294i | \(0.924722\pi\) | |||||||
\(884\) | −0.216184 | + | 8.59107i | −0.00727104 | + | 0.288949i | ||||
\(885\) | 35.1515 | − | 35.1515i | 1.18160 | − | 1.18160i | ||||
\(886\) | 1.65737 | + | 4.14808i | 0.0556806 | + | 0.139358i | ||||
\(887\) | 10.1484i | 0.340749i | 0.985379 | + | 0.170374i | \(0.0544977\pi\) | ||||
−0.985379 | + | 0.170374i | \(0.945502\pi\) | |||||||
\(888\) | −7.48001 | + | 2.77255i | −0.251013 | + | 0.0930406i | ||||
\(889\) | − | 12.4812i | − | 0.418605i | ||||||
\(890\) | −9.23627 | + | 3.69037i | −0.309600 | + | 0.123701i | ||||
\(891\) | 92.5829 | − | 92.5829i | 3.10164 | − | 3.10164i | ||||
\(892\) | −30.5039 | − | 32.0787i | −1.02135 | − | 1.07407i | ||||
\(893\) | −25.0981 | − | 25.0981i | −0.839877 | − | 0.839877i | ||||
\(894\) | 30.6541 | − | 71.4500i | 1.02523 | − | 2.38965i | ||||
\(895\) | 4.78443 | 0.159926 | ||||||||
\(896\) | −10.7928 | + | 3.39359i | −0.360561 | + | 0.113372i | ||||
\(897\) | 15.6046 | 0.521023 | ||||||||
\(898\) | −8.27596 | + | 19.2900i | −0.276172 | + | 0.643715i | ||||
\(899\) | −0.0962086 | − | 0.0962086i | −0.00320873 | − | 0.00320873i | ||||
\(900\) | −11.8393 | − | 12.4505i | −0.394643 | − | 0.415017i | ||||
\(901\) | 5.32368 | − | 5.32368i | 0.177357 | − | 0.177357i | ||||
\(902\) | −2.41747 | + | 0.965904i | −0.0804929 | + | 0.0321611i | ||||
\(903\) | 11.5896i | 0.385679i | ||||||||
\(904\) | 41.1713 | − | 15.2606i | 1.36934 | − | 0.507560i | ||||
\(905\) | 9.75994i | 0.324431i | ||||||||
\(906\) | 20.0939 | + | 50.2912i | 0.667576 | + | 1.67081i | ||||
\(907\) | 24.4321 | − | 24.4321i | 0.811253 | − | 0.811253i | −0.173568 | − | 0.984822i | \(-0.555530\pi\) |
0.984822 | + | 0.173568i | \(0.0555298\pi\) | |||||||
\(908\) | −0.955336 | + | 37.9647i | −0.0317040 | + | 1.25990i | ||||
\(909\) | 47.2054 | + | 47.2054i | 1.56570 | + | 1.56570i | ||||
\(910\) | −0.844992 | − | 0.362526i | −0.0280112 | − | 0.0120176i | ||||
\(911\) | −17.2393 | −0.571163 | −0.285581 | − | 0.958354i | \(-0.592187\pi\) | ||||
−0.285581 | + | 0.958354i | \(0.592187\pi\) | |||||||
\(912\) | −49.2746 | − | 2.48144i | −1.63164 | − | 0.0821687i | ||||
\(913\) | −4.67045 | −0.154569 | ||||||||
\(914\) | 18.4455 | + | 7.91365i | 0.610122 | + | 0.261760i | ||||
\(915\) | 17.8638 | + | 17.8638i | 0.590558 | + | 0.590558i | ||||
\(916\) | 42.8374 | + | 1.07795i | 1.41539 | + | 0.0356165i | ||||
\(917\) | 0.940145 | − | 0.940145i | 0.0310463 | − | 0.0310463i | ||||
\(918\) | 66.0013 | + | 165.188i | 2.17837 | + | 5.45203i | ||||
\(919\) | 18.0423i | 0.595162i | 0.954697 | + | 0.297581i | \(0.0961798\pi\) | ||||
−0.954697 | + | 0.297581i | \(0.903820\pi\) | |||||||
\(920\) | 18.1210 | + | 8.32027i | 0.597433 | + | 0.274311i | ||||
\(921\) | 38.8762i | 1.28101i | ||||||||
\(922\) | −35.6962 | + | 14.2625i | −1.17559 | + | 0.469710i | ||||
\(923\) | 3.66804 | − | 3.66804i | 0.120735 | − | 0.120735i | ||||
\(924\) | 16.5550 | − | 15.7423i | 0.544620 | − | 0.517883i | ||||
\(925\) | −0.585796 | − | 0.585796i | −0.0192609 | − | 0.0192609i | ||||
\(926\) | −4.49747 | + | 10.4829i | −0.147796 | + | 0.344489i | ||||
\(927\) | 5.17790 | 0.170065 | ||||||||
\(928\) | 3.15896 | + | 9.22849i | 0.103698 | + | 0.302940i | ||||
\(929\) | 0.815553 | 0.0267574 | 0.0133787 | − | 0.999911i | \(-0.495741\pi\) | ||||
0.0133787 | + | 0.999911i | \(0.495741\pi\) | |||||||
\(930\) | −0.149788 | + | 0.349132i | −0.00491174 | + | 0.0114485i | ||||
\(931\) | 2.56181 | + | 2.56181i | 0.0839601 | + | 0.0839601i | ||||
\(932\) | 3.00759 | − | 2.85994i | 0.0985169 | − | 0.0936805i | ||||
\(933\) | −72.9995 | + | 72.9995i | −2.38989 | + | 2.38989i | ||||
\(934\) | 14.5498 | − | 5.81341i | 0.476085 | − | 0.190221i | ||||
\(935\) | − | 22.1737i | − | 0.725156i | ||||||
\(936\) | 6.59176 | − | 14.3564i | 0.215458 | − | 0.469255i | ||||
\(937\) | 7.51159i | 0.245393i | 0.992444 | + | 0.122696i | \(0.0391542\pi\) | ||||
−0.992444 | + | 0.122696i | \(0.960846\pi\) | |||||||
\(938\) | 0.783039 | + | 1.95979i | 0.0255671 | + | 0.0639895i | ||||
\(939\) | 19.5573 | − | 19.5573i | 0.638230 | − | 0.638230i | ||||
\(940\) | 19.5878 | + | 0.492904i | 0.638885 | + | 0.0160767i | ||||
\(941\) | 20.2850 | + | 20.2850i | 0.661273 | + | 0.661273i | 0.955680 | − | 0.294407i | \(-0.0951221\pi\) |
−0.294407 | + | 0.955680i | \(0.595122\pi\) | |||||||
\(942\) | −47.9010 | − | 20.5509i | −1.56070 | − | 0.669586i | ||||
\(943\) | −3.86792 | −0.125957 | ||||||||
\(944\) | 39.1708 | + | 43.3253i | 1.27490 | + | 1.41012i | ||||
\(945\) | −19.0326 | −0.619129 | ||||||||
\(946\) | 14.8441 | + | 6.36856i | 0.482624 | + | 0.207060i | ||||
\(947\) | 36.6209 | + | 36.6209i | 1.19002 | + | 1.19002i | 0.977061 | + | 0.212959i | \(0.0683099\pi\) |
0.212959 | + | 0.977061i | \(0.431690\pi\) | |||||||
\(948\) | −1.28483 | + | 51.0586i | −0.0417293 | + | 1.65831i | ||||
\(949\) | −6.36186 | + | 6.36186i | −0.206515 | + | 0.206515i | ||||
\(950\) | −1.90103 | − | 4.75791i | −0.0616775 | − | 0.154367i | ||||
\(951\) | − | 94.9273i | − | 3.07823i | ||||||
\(952\) | 6.49676 | + | 17.5275i | 0.210561 | + | 0.568069i | ||||
\(953\) | 33.0932i | 1.07199i | 0.844220 | + | 0.535996i | \(0.180064\pi\) | ||||
−0.844220 | + | 0.535996i | \(0.819936\pi\) | |||||||
\(954\) | −12.8519 | + | 5.13499i | −0.416095 | + | 0.166252i | ||||
\(955\) | 6.54284 | − | 6.54284i | 0.211721 | − | 0.211721i | ||||
\(956\) | 20.5988 | + | 21.6623i | 0.666214 | + | 0.700608i | ||||
\(957\) | −13.9271 | − | 13.9271i | −0.450198 | − | 0.450198i | ||||
\(958\) | −12.2902 | + | 28.6464i | −0.397077 | + | 0.925525i | ||||
\(959\) | 6.37076 | 0.205723 | ||||||||
\(960\) | 20.6560 | − | 17.7516i | 0.666668 | − | 0.572931i | ||||
\(961\) | −30.9938 | −0.999799 | ||||||||
\(962\) | 0.300331 | − | 0.700026i | 0.00968307 | − | 0.0225697i | ||||
\(963\) | 82.1944 | + | 82.1944i | 2.64868 | + | 2.64868i | ||||
\(964\) | −12.0931 | − | 12.7174i | −0.389492 | − | 0.409600i | ||||
\(965\) | 12.9313 | − | 12.9313i | 0.416273 | − | 0.416273i | ||||
\(966\) | 31.5196 | − | 12.5937i | 1.01413 | − | 0.405196i | ||||
\(967\) | − | 13.4306i | − | 0.431899i | −0.976404 | − | 0.215950i | \(-0.930715\pi\) | ||
0.976404 | − | 0.215950i | \(-0.0692847\pi\) | |||||||
\(968\) | −0.252487 | − | 0.681181i | −0.00811525 | − | 0.0218940i | ||||
\(969\) | 81.5158i | 2.61867i | ||||||||
\(970\) | 3.55307 | + | 8.89265i | 0.114082 | + | 0.285526i | ||||
\(971\) | 23.6365 | − | 23.6365i | 0.758532 | − | 0.758532i | −0.217524 | − | 0.976055i | \(-0.569798\pi\) |
0.976055 | + | 0.217524i | \(0.0697979\pi\) | |||||||
\(972\) | 3.81162 | − | 151.473i | 0.122258 | − | 4.85849i | ||||
\(973\) | −0.486651 | − | 0.486651i | −0.0156013 | − | 0.0156013i | ||||
\(974\) | −49.9847 | − | 21.4449i | −1.60161 | − | 0.687139i | ||||
\(975\) | 2.21348 | 0.0708881 | ||||||||
\(976\) | −22.0176 | + | 19.9064i | −0.704768 | + | 0.637188i | ||||
\(977\) | 33.7394 | 1.07942 | 0.539710 | − | 0.841851i | \(-0.318534\pi\) | ||||
0.539710 | + | 0.841851i | \(0.318534\pi\) | |||||||
\(978\) | 53.1529 | + | 22.8041i | 1.69964 | + | 0.729196i | ||||
\(979\) | 16.6854 | + | 16.6854i | 0.533268 | + | 0.533268i | ||||
\(980\) | −1.99937 | − | 0.0503116i | −0.0638674 | − | 0.00160715i | ||||
\(981\) | −126.408 | + | 126.408i | −4.03590 | + | 4.03590i | ||||
\(982\) | −8.71862 | − | 21.8210i | −0.278222 | − | 0.696337i | ||||
\(983\) | 10.1795i | 0.324677i | 0.986735 | + | 0.162338i | \(0.0519036\pi\) | ||||
−0.986735 | + | 0.162338i | \(0.948096\pi\) | |||||||
\(984\) | −2.20450 | + | 4.80126i | −0.0702768 | + | 0.153059i | ||||
\(985\) | 5.73403i | 0.182701i | ||||||||
\(986\) | 14.9657 | − | 5.97959i | 0.476606 | − | 0.190429i | ||||
\(987\) | 23.5846 | − | 23.5846i | 0.750707 | − | 0.750707i | ||||
\(988\) | 3.41396 | − | 3.24636i | 0.108613 | − | 0.103281i | ||||
\(989\) | 16.9700 | + | 16.9700i | 0.539615 | + | 0.539615i | ||||
\(990\) | −16.0708 | + | 37.4586i | −0.510764 | + | 1.19051i | ||||
\(991\) | 28.5540 | 0.907049 | 0.453525 | − | 0.891244i | \(-0.350166\pi\) | ||||
0.453525 | + | 0.891244i | \(0.350166\pi\) | |||||||
\(992\) | −0.400833 | − | 0.196398i | −0.0127265 | − | 0.00623565i | ||||
\(993\) | −14.2819 | −0.453223 | ||||||||
\(994\) | 4.44875 | − | 10.3693i | 0.141106 | − | 0.328896i | ||||
\(995\) | −5.79660 | − | 5.79660i | −0.183765 | − | 0.183765i | ||||
\(996\) | −6.86866 | + | 6.53146i | −0.217642 | + | 0.206957i | ||||
\(997\) | −3.48225 | + | 3.48225i | −0.110284 | + | 0.110284i | −0.760096 | − | 0.649811i | \(-0.774848\pi\) |
0.649811 | + | 0.760096i | \(0.274848\pi\) | |||||||
\(998\) | −13.0971 | + | 5.23295i | −0.414580 | + | 0.165646i | ||||
\(999\) | − | 15.7673i | − | 0.498857i |
(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 | 560.2.bd.b.141.9 | ✓ | 52 | |
4.3 | odd | 2 | 2240.2.bd.b.1681.26 | 52 | |||
16.5 | even | 4 | inner | 560.2.bd.b.421.9 | yes | 52 | |
16.11 | odd | 4 | 2240.2.bd.b.561.26 | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
560.2.bd.b.141.9 | ✓ | 52 | 1.1 | even | 1 | trivial | |
560.2.bd.b.421.9 | yes | 52 | 16.5 | even | 4 | inner | |
2240.2.bd.b.561.26 | 52 | 16.11 | odd | 4 | |||
2240.2.bd.b.1681.26 | 52 | 4.3 | odd | 2 |