Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.5 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.e.47.5 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0.471935 | + | 1.66652i | 0.272472 | + | 0.962164i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.55923 | + | 1.60274i | −0.697311 | + | 0.716769i | ||||
\(6\) | 0.844697 | − | 1.51211i | 0.344846 | − | 0.617318i | ||||
\(7\) | −3.44975 | + | 3.44975i | −1.30388 | + | 1.30388i | −0.378129 | + | 0.925753i | \(0.623432\pi\) |
−0.925753 | + | 0.378129i | \(0.876568\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −2.55455 | + | 1.57298i | −0.851518 | + | 0.524325i | ||||
\(10\) | 2.23586 | − | 0.0307665i | 0.707040 | − | 0.00972923i | ||||
\(11\) | − | 3.84509i | − | 1.15934i | −0.814852 | − | 0.579670i | \(-0.803182\pi\) | ||
0.814852 | − | 0.579670i | \(-0.196818\pi\) | |||||||
\(12\) | −1.66652 | + | 0.471935i | −0.481082 | + | 0.136236i | ||||
\(13\) | 0.875224 | + | 0.875224i | 0.242743 | + | 0.242743i | 0.817984 | − | 0.575241i | \(-0.195092\pi\) |
−0.575241 | + | 0.817984i | \(0.695092\pi\) | |||||||
\(14\) | 4.87868 | 1.30388 | ||||||||
\(15\) | −3.40686 | − | 1.84210i | −0.879647 | − | 0.475628i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.35706 | + | 1.35706i | 0.329135 | + | 0.329135i | 0.852258 | − | 0.523122i | \(-0.175233\pi\) |
−0.523122 | + | 0.852258i | \(0.675233\pi\) | |||||||
\(18\) | 2.91860 | + | 0.694081i | 0.687922 | + | 0.163597i | ||||
\(19\) | − | 3.81508i | − | 0.875239i | −0.899160 | − | 0.437619i | \(-0.855822\pi\) | ||
0.899160 | − | 0.437619i | \(-0.144178\pi\) | |||||||
\(20\) | −1.60274 | − | 1.55923i | −0.358385 | − | 0.348655i | ||||
\(21\) | −7.37712 | − | 4.12100i | −1.60982 | − | 0.899277i | ||||
\(22\) | −2.71889 | + | 2.71889i | −0.579670 | + | 0.579670i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | 1.51211 | + | 0.844697i | 0.308659 | + | 0.172423i | ||||
\(25\) | −0.137579 | − | 4.99811i | −0.0275158 | − | 0.999621i | ||||
\(26\) | − | 1.23775i | − | 0.242743i | ||||||
\(27\) | −3.82697 | − | 3.51487i | −0.736501 | − | 0.676436i | ||||
\(28\) | −3.44975 | − | 3.44975i | −0.651941 | − | 0.651941i | ||||
\(29\) | −7.78450 | −1.44554 | −0.722772 | − | 0.691086i | \(-0.757133\pi\) | ||||
−0.722772 | + | 0.691086i | \(0.757133\pi\) | |||||||
\(30\) | 1.10645 | + | 3.71157i | 0.202010 | + | 0.677637i | ||||
\(31\) | 5.58131 | 1.00243 | 0.501217 | − | 0.865322i | \(-0.332886\pi\) | ||||
0.501217 | + | 0.865322i | \(0.332886\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 6.40791 | − | 1.81463i | 1.11547 | − | 0.315887i | ||||
\(34\) | − | 1.91917i | − | 0.329135i | ||||||
\(35\) | −0.150100 | − | 10.9080i | −0.0253715 | − | 1.84379i | ||||
\(36\) | −1.57298 | − | 2.55455i | −0.262163 | − | 0.425759i | ||||
\(37\) | 1.86954 | − | 1.86954i | 0.307351 | − | 0.307351i | −0.536530 | − | 0.843881i | \(-0.680265\pi\) |
0.843881 | + | 0.536530i | \(0.180265\pi\) | |||||||
\(38\) | −2.69767 | + | 2.69767i | −0.437619 | + | 0.437619i | ||||
\(39\) | −1.04553 | + | 1.87162i | −0.167418 | + | 0.299700i | ||||
\(40\) | 0.0307665 | + | 2.23586i | 0.00486461 | + | 0.353520i | ||||
\(41\) | 4.29759i | 0.671170i | 0.942010 | + | 0.335585i | \(0.108934\pi\) | ||||
−0.942010 | + | 0.335585i | \(0.891066\pi\) | |||||||
\(42\) | 2.30242 | + | 8.13040i | 0.355271 | + | 1.25455i | ||||
\(43\) | 0.142657 | + | 0.142657i | 0.0217549 | + | 0.0217549i | 0.717901 | − | 0.696146i | \(-0.245103\pi\) |
−0.696146 | + | 0.717901i | \(0.745103\pi\) | |||||||
\(44\) | 3.84509 | 0.579670 | ||||||||
\(45\) | 1.46207 | − | 6.54693i | 0.217953 | − | 0.975959i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 3.63185 | + | 3.63185i | 0.529760 | + | 0.529760i | 0.920501 | − | 0.390741i | \(-0.127781\pi\) |
−0.390741 | + | 0.920501i | \(0.627781\pi\) | |||||||
\(48\) | −0.471935 | − | 1.66652i | −0.0681180 | − | 0.240541i | ||||
\(49\) | − | 16.8015i | − | 2.40022i | ||||||
\(50\) | −3.43691 | + | 3.63148i | −0.486053 | + | 0.513569i | ||||
\(51\) | −1.62112 | + | 2.90201i | −0.227002 | + | 0.406362i | ||||
\(52\) | −0.875224 | + | 0.875224i | −0.121372 | + | 0.121372i | ||||
\(53\) | −3.62512 | + | 3.62512i | −0.497949 | + | 0.497949i | −0.910799 | − | 0.412850i | \(-0.864533\pi\) |
0.412850 | + | 0.910799i | \(0.364533\pi\) | |||||||
\(54\) | 0.220693 | + | 5.19146i | 0.0300326 | + | 0.706469i | ||||
\(55\) | 6.16270 | + | 5.99540i | 0.830979 | + | 0.808420i | ||||
\(56\) | 4.87868i | 0.651941i | ||||||||
\(57\) | 6.35789 | − | 1.80047i | 0.842123 | − | 0.238478i | ||||
\(58\) | 5.50447 | + | 5.50447i | 0.722772 | + | 0.722772i | ||||
\(59\) | −3.87315 | −0.504241 | −0.252120 | − | 0.967696i | \(-0.581128\pi\) | ||||
−0.252120 | + | 0.967696i | \(0.581128\pi\) | |||||||
\(60\) | 1.84210 | − | 3.40686i | 0.237814 | − | 0.439823i | ||||
\(61\) | −13.5655 | −1.73688 | −0.868442 | − | 0.495791i | \(-0.834878\pi\) | ||||
−0.868442 | + | 0.495791i | \(0.834878\pi\) | |||||||
\(62\) | −3.94659 | − | 3.94659i | −0.501217 | − | 0.501217i | ||||
\(63\) | 3.38620 | − | 14.2389i | 0.426621 | − | 1.79394i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −2.76744 | + | 0.0380814i | −0.343259 | + | 0.00472341i | ||||
\(66\) | −5.81422 | − | 3.24794i | −0.715681 | − | 0.399794i | ||||
\(67\) | −2.77087 | + | 2.77087i | −0.338515 | + | 0.338515i | −0.855808 | − | 0.517293i | \(-0.826940\pi\) |
0.517293 | + | 0.855808i | \(0.326940\pi\) | |||||||
\(68\) | −1.35706 | + | 1.35706i | −0.164568 | + | 0.164568i | ||||
\(69\) | 1.51211 | + | 0.844697i | 0.182037 | + | 0.101690i | ||||
\(70\) | −7.60700 | + | 7.81928i | −0.909211 | + | 0.934582i | ||||
\(71\) | 6.15174i | 0.730077i | 0.930992 | + | 0.365039i | \(0.118944\pi\) | ||||
−0.930992 | + | 0.365039i | \(0.881056\pi\) | |||||||
\(72\) | −0.694081 | + | 2.91860i | −0.0817983 | + | 0.343961i | ||||
\(73\) | −9.60788 | − | 9.60788i | −1.12452 | − | 1.12452i | −0.991054 | − | 0.133463i | \(-0.957390\pi\) |
−0.133463 | − | 0.991054i | \(-0.542610\pi\) | |||||||
\(74\) | −2.64393 | −0.307351 | ||||||||
\(75\) | 8.26450 | − | 2.58806i | 0.954302 | − | 0.298843i | ||||
\(76\) | 3.81508 | 0.437619 | ||||||||
\(77\) | 13.2646 | + | 13.2646i | 1.51164 | + | 1.51164i | ||||
\(78\) | 2.06274 | − | 0.584139i | 0.233559 | − | 0.0661408i | ||||
\(79\) | 17.1956i | 1.93466i | 0.253525 | + | 0.967329i | \(0.418410\pi\) | ||||
−0.253525 | + | 0.967329i | \(0.581590\pi\) | |||||||
\(80\) | 1.55923 | − | 1.60274i | 0.174328 | − | 0.179192i | ||||
\(81\) | 4.05150 | − | 8.03650i | 0.450166 | − | 0.892945i | ||||
\(82\) | 3.03885 | − | 3.03885i | 0.335585 | − | 0.335585i | ||||
\(83\) | −2.00448 | + | 2.00448i | −0.220021 | + | 0.220021i | −0.808507 | − | 0.588486i | \(-0.799724\pi\) |
0.588486 | + | 0.808507i | \(0.299724\pi\) | |||||||
\(84\) | 4.12100 | − | 7.37712i | 0.449638 | − | 0.804910i | ||||
\(85\) | −4.29100 | + | 0.0590463i | −0.465424 | + | 0.00640447i | ||||
\(86\) | − | 0.201747i | − | 0.0217549i | ||||||
\(87\) | −3.67378 | − | 12.9730i | −0.393870 | − | 1.39085i | ||||
\(88\) | −2.71889 | − | 2.71889i | −0.289835 | − | 0.289835i | ||||
\(89\) | −12.5987 | −1.33546 | −0.667728 | − | 0.744406i | \(-0.732733\pi\) | ||||
−0.667728 | + | 0.744406i | \(0.732733\pi\) | |||||||
\(90\) | −5.66322 | + | 3.59554i | −0.596956 | + | 0.379003i | ||||
\(91\) | −6.03860 | −0.633018 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 2.63402 | + | 9.30135i | 0.273135 | + | 0.964505i | ||||
\(94\) | − | 5.13622i | − | 0.529760i | ||||||
\(95\) | 6.11459 | + | 5.94860i | 0.627344 | + | 0.610313i | ||||
\(96\) | −0.844697 | + | 1.51211i | −0.0862115 | + | 0.154329i | ||||
\(97\) | −3.36602 | + | 3.36602i | −0.341767 | + | 0.341767i | −0.857032 | − | 0.515264i | \(-0.827694\pi\) |
0.515264 | + | 0.857032i | \(0.327694\pi\) | |||||||
\(98\) | −11.8805 | + | 11.8805i | −1.20011 | + | 1.20011i | ||||
\(99\) | 6.04824 | + | 9.82250i | 0.607871 | + | 0.987199i | ||||
\(100\) | 4.99811 | − | 0.137579i | 0.499811 | − | 0.0137579i | ||||
\(101\) | − | 11.2944i | − | 1.12383i | −0.827194 | − | 0.561916i | \(-0.810064\pi\) | ||
0.827194 | − | 0.561916i | \(-0.189936\pi\) | |||||||
\(102\) | 3.19833 | − | 0.905725i | 0.316682 | − | 0.0896801i | ||||
\(103\) | −8.36819 | − | 8.36819i | −0.824542 | − | 0.824542i | 0.162214 | − | 0.986756i | \(-0.448137\pi\) |
−0.986756 | + | 0.162214i | \(0.948137\pi\) | |||||||
\(104\) | 1.23775 | 0.121372 | ||||||||
\(105\) | 18.1076 | − | 5.39802i | 1.76712 | − | 0.526793i | ||||
\(106\) | 5.12670 | 0.497949 | ||||||||
\(107\) | 7.21940 | + | 7.21940i | 0.697925 | + | 0.697925i | 0.963963 | − | 0.266037i | \(-0.0857145\pi\) |
−0.266037 | + | 0.963963i | \(0.585714\pi\) | |||||||
\(108\) | 3.51487 | − | 3.82697i | 0.338218 | − | 0.368251i | ||||
\(109\) | 2.16073i | 0.206960i | 0.994632 | + | 0.103480i | \(0.0329978\pi\) | ||||
−0.994632 | + | 0.103480i | \(0.967002\pi\) | |||||||
\(110\) | −0.118300 | − | 8.59708i | −0.0112795 | − | 0.819699i | ||||
\(111\) | 3.99792 | + | 2.23332i | 0.379466 | + | 0.211977i | ||||
\(112\) | 3.44975 | − | 3.44975i | 0.325971 | − | 0.325971i | ||||
\(113\) | −8.63760 | + | 8.63760i | −0.812557 | + | 0.812557i | −0.985017 | − | 0.172459i | \(-0.944829\pi\) |
0.172459 | + | 0.985017i | \(0.444829\pi\) | |||||||
\(114\) | −5.76883 | − | 3.22258i | −0.540301 | − | 0.301823i | ||||
\(115\) | 0.0307665 | + | 2.23586i | 0.00286899 | + | 0.208495i | ||||
\(116\) | − | 7.78450i | − | 0.722772i | ||||||
\(117\) | −3.61251 | − | 0.859102i | −0.333977 | − | 0.0794240i | ||||
\(118\) | 2.73873 | + | 2.73873i | 0.252120 | + | 0.252120i | ||||
\(119\) | −9.36303 | −0.858308 | ||||||||
\(120\) | −3.71157 | + | 1.10645i | −0.338819 | + | 0.101005i | ||||
\(121\) | −3.78475 | −0.344068 | ||||||||
\(122\) | 9.59226 | + | 9.59226i | 0.868442 | + | 0.868442i | ||||
\(123\) | −7.16200 | + | 2.02818i | −0.645775 | + | 0.182875i | ||||
\(124\) | 5.58131i | 0.501217i | ||||||||
\(125\) | 8.22521 | + | 7.57271i | 0.735685 | + | 0.677324i | ||||
\(126\) | −12.4629 | + | 7.67404i | −1.11028 | + | 0.683658i | ||||
\(127\) | −10.4407 | + | 10.4407i | −0.926462 | + | 0.926462i | −0.997475 | − | 0.0710131i | \(-0.977377\pi\) |
0.0710131 | + | 0.997475i | \(0.477377\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −0.170415 | + | 0.305064i | −0.0150042 | + | 0.0268594i | ||||
\(130\) | 1.98380 | + | 1.92995i | 0.173991 | + | 0.169268i | ||||
\(131\) | 11.2466i | 0.982617i | 0.870985 | + | 0.491309i | \(0.163481\pi\) | ||||
−0.870985 | + | 0.491309i | \(0.836519\pi\) | |||||||
\(132\) | 1.81463 | + | 6.40791i | 0.157944 | + | 0.557737i | ||||
\(133\) | 13.1611 | + | 13.1611i | 1.14121 | + | 1.14121i | ||||
\(134\) | 3.91860 | 0.338515 | ||||||||
\(135\) | 11.6006 | − | 0.653162i | 0.998419 | − | 0.0562152i | ||||
\(136\) | 1.91917 | 0.164568 | ||||||||
\(137\) | −10.4263 | − | 10.4263i | −0.890776 | − | 0.890776i | 0.103820 | − | 0.994596i | \(-0.466893\pi\) |
−0.994596 | + | 0.103820i | \(0.966893\pi\) | |||||||
\(138\) | −0.471935 | − | 1.66652i | −0.0401738 | − | 0.141863i | ||||
\(139\) | − | 14.6451i | − | 1.24218i | −0.783738 | − | 0.621092i | \(-0.786689\pi\) | ||
0.783738 | − | 0.621092i | \(-0.213311\pi\) | |||||||
\(140\) | 10.9080 | − | 0.150100i | 0.921897 | − | 0.0126858i | ||||
\(141\) | −4.33854 | + | 7.76654i | −0.365371 | + | 0.654061i | ||||
\(142\) | 4.34994 | − | 4.34994i | 0.365039 | − | 0.365039i | ||||
\(143\) | 3.36532 | − | 3.36532i | 0.281422 | − | 0.281422i | ||||
\(144\) | 2.55455 | − | 1.57298i | 0.212880 | − | 0.131081i | ||||
\(145\) | 12.1379 | − | 12.4766i | 1.00799 | − | 1.03612i | ||||
\(146\) | 13.5876i | 1.12452i | ||||||||
\(147\) | 28.0000 | − | 7.92922i | 2.30940 | − | 0.653991i | ||||
\(148\) | 1.86954 | + | 1.86954i | 0.153675 | + | 0.153675i | ||||
\(149\) | −1.21978 | −0.0999285 | −0.0499642 | − | 0.998751i | \(-0.515911\pi\) | ||||
−0.0499642 | + | 0.998751i | \(0.515911\pi\) | |||||||
\(150\) | −7.67392 | − | 4.01385i | −0.626573 | − | 0.327729i | ||||
\(151\) | 6.92084 | 0.563210 | 0.281605 | − | 0.959530i | \(-0.409133\pi\) | ||||
0.281605 | + | 0.959530i | \(0.409133\pi\) | |||||||
\(152\) | −2.69767 | − | 2.69767i | −0.218810 | − | 0.218810i | ||||
\(153\) | −5.60131 | − | 1.33206i | −0.452839 | − | 0.107691i | ||||
\(154\) | − | 18.7590i | − | 1.51164i | ||||||
\(155\) | −8.70257 | + | 8.94542i | −0.699008 | + | 0.718513i | ||||
\(156\) | −1.87162 | − | 1.04553i | −0.149850 | − | 0.0837091i | ||||
\(157\) | 1.67127 | − | 1.67127i | 0.133382 | − | 0.133382i | −0.637264 | − | 0.770646i | \(-0.719934\pi\) |
0.770646 | + | 0.637264i | \(0.219934\pi\) | |||||||
\(158\) | 12.1591 | − | 12.1591i | 0.967329 | − | 0.967329i | ||||
\(159\) | −7.75215 | − | 4.33051i | −0.614786 | − | 0.343431i | ||||
\(160\) | −2.23586 | + | 0.0307665i | −0.176760 | + | 0.00243231i | ||||
\(161\) | 4.87868i | 0.384494i | ||||||||
\(162\) | −8.54751 | + | 2.81782i | −0.671556 | + | 0.221389i | ||||
\(163\) | 9.29670 | + | 9.29670i | 0.728173 | + | 0.728173i | 0.970256 | − | 0.242082i | \(-0.0778304\pi\) |
−0.242082 | + | 0.970256i | \(0.577830\pi\) | |||||||
\(164\) | −4.29759 | −0.335585 | ||||||||
\(165\) | −7.08304 | + | 13.0997i | −0.551414 | + | 1.01981i | ||||
\(166\) | 2.83477 | 0.220021 | ||||||||
\(167\) | 10.9776 | + | 10.9776i | 0.849475 | + | 0.849475i | 0.990068 | − | 0.140593i | \(-0.0449008\pi\) |
−0.140593 | + | 0.990068i | \(0.544901\pi\) | |||||||
\(168\) | −8.13040 | + | 2.30242i | −0.627274 | + | 0.177636i | ||||
\(169\) | − | 11.4680i | − | 0.882151i | ||||||
\(170\) | 3.07594 | + | 2.99244i | 0.235914 | + | 0.229510i | ||||
\(171\) | 6.00102 | + | 9.74582i | 0.458910 | + | 0.745282i | ||||
\(172\) | −0.142657 | + | 0.142657i | −0.0108775 | + | 0.0108775i | ||||
\(173\) | 17.3398 | − | 17.3398i | 1.31832 | − | 1.31832i | 0.403212 | − | 0.915107i | \(-0.367894\pi\) |
0.915107 | − | 0.403212i | \(-0.132106\pi\) | |||||||
\(174\) | −6.57554 | + | 11.7710i | −0.498490 | + | 0.892361i | ||||
\(175\) | 17.7168 | + | 16.7676i | 1.33927 | + | 1.26751i | ||||
\(176\) | 3.84509i | 0.289835i | ||||||||
\(177\) | −1.82787 | − | 6.45466i | −0.137391 | − | 0.485162i | ||||
\(178\) | 8.90860 | + | 8.90860i | 0.667728 | + | 0.667728i | ||||
\(179\) | 1.47094 | 0.109943 | 0.0549715 | − | 0.998488i | \(-0.482493\pi\) | ||||
0.0549715 | + | 0.998488i | \(0.482493\pi\) | |||||||
\(180\) | 6.54693 | + | 1.46207i | 0.487980 | + | 0.108976i | ||||
\(181\) | −15.6852 | −1.16587 | −0.582936 | − | 0.812518i | \(-0.698096\pi\) | ||||
−0.582936 | + | 0.812518i | \(0.698096\pi\) | |||||||
\(182\) | 4.26994 | + | 4.26994i | 0.316509 | + | 0.316509i | ||||
\(183\) | −6.40203 | − | 22.6071i | −0.473252 | − | 1.67117i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 0.0813446 | + | 5.91145i | 0.00598057 | + | 0.434618i | ||||
\(186\) | 4.71452 | − | 8.43958i | 0.345685 | − | 0.618820i | ||||
\(187\) | 5.21802 | − | 5.21802i | 0.381580 | − | 0.381580i | ||||
\(188\) | −3.63185 | + | 3.63185i | −0.264880 | + | 0.264880i | ||||
\(189\) | 25.3275 | − | 1.07669i | 1.84230 | − | 0.0783179i | ||||
\(190\) | −0.117377 | − | 8.52997i | −0.00851540 | − | 0.618829i | ||||
\(191\) | − | 21.7200i | − | 1.57160i | −0.618480 | − | 0.785800i | \(-0.712251\pi\) | ||
0.618480 | − | 0.785800i | \(-0.287749\pi\) | |||||||
\(192\) | 1.66652 | − | 0.471935i | 0.120270 | − | 0.0340590i | ||||
\(193\) | 17.8302 | + | 17.8302i | 1.28345 | + | 1.28345i | 0.938694 | + | 0.344751i | \(0.112037\pi\) |
0.344751 | + | 0.938694i | \(0.387963\pi\) | |||||||
\(194\) | 4.76027 | 0.341767 | ||||||||
\(195\) | −1.36951 | − | 4.59401i | −0.0980730 | − | 0.328984i | ||||
\(196\) | 16.8015 | 1.20011 | ||||||||
\(197\) | 0.806128 | + | 0.806128i | 0.0574342 | + | 0.0574342i | 0.735241 | − | 0.677806i | \(-0.237069\pi\) |
−0.677806 | + | 0.735241i | \(0.737069\pi\) | |||||||
\(198\) | 2.66881 | − | 11.2223i | 0.189664 | − | 0.797535i | ||||
\(199\) | − | 18.0493i | − | 1.27948i | −0.768590 | − | 0.639742i | \(-0.779041\pi\) | ||
0.768590 | − | 0.639742i | \(-0.220959\pi\) | |||||||
\(200\) | −3.63148 | − | 3.43691i | −0.256784 | − | 0.243026i | ||||
\(201\) | −5.92537 | − | 3.31003i | −0.417943 | − | 0.233471i | ||||
\(202\) | −7.98633 | + | 7.98633i | −0.561916 | + | 0.561916i | ||||
\(203\) | 26.8546 | − | 26.8546i | 1.88482 | − | 1.88482i | ||||
\(204\) | −2.90201 | − | 1.62112i | −0.203181 | − | 0.113501i | ||||
\(205\) | −6.88793 | − | 6.70094i | −0.481074 | − | 0.468014i | ||||
\(206\) | 11.8344i | 0.824542i | ||||||||
\(207\) | −0.694081 | + | 2.91860i | −0.0482420 | + | 0.202857i | ||||
\(208\) | −0.875224 | − | 0.875224i | −0.0606859 | − | 0.0606859i | ||||
\(209\) | −14.6693 | −1.01470 | ||||||||
\(210\) | −16.6210 | − | 8.98701i | −1.14696 | − | 0.620162i | ||||
\(211\) | 7.95847 | 0.547884 | 0.273942 | − | 0.961746i | \(-0.411672\pi\) | ||||
0.273942 | + | 0.961746i | \(0.411672\pi\) | |||||||
\(212\) | −3.62512 | − | 3.62512i | −0.248975 | − | 0.248975i | ||||
\(213\) | −10.2520 | + | 2.90322i | −0.702454 | + | 0.198925i | ||||
\(214\) | − | 10.2098i | − | 0.697925i | ||||||
\(215\) | −0.451077 | + | 0.00620705i | −0.0307632 | + | 0.000423317i | ||||
\(216\) | −5.19146 | + | 0.220693i | −0.353234 | + | 0.0150163i | ||||
\(217\) | −19.2541 | + | 19.2541i | −1.30706 | + | 1.30706i | ||||
\(218\) | 1.52786 | − | 1.52786i | 0.103480 | − | 0.103480i | ||||
\(219\) | 11.4774 | − | 20.5460i | 0.775570 | − | 1.38837i | ||||
\(220\) | −5.99540 | + | 6.16270i | −0.404210 | + | 0.415489i | ||||
\(221\) | 2.37546i | 0.159791i | ||||||||
\(222\) | −1.24776 | − | 4.40615i | −0.0837444 | − | 0.295722i | ||||
\(223\) | 16.5940 | + | 16.5940i | 1.11122 | + | 1.11122i | 0.992986 | + | 0.118233i | \(0.0377228\pi\) |
0.118233 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(224\) | −4.87868 | −0.325971 | ||||||||
\(225\) | 8.21335 | + | 12.5515i | 0.547557 | + | 0.836769i | ||||
\(226\) | 12.2154 | 0.812557 | ||||||||
\(227\) | −4.89140 | − | 4.89140i | −0.324653 | − | 0.324653i | 0.525896 | − | 0.850549i | \(-0.323730\pi\) |
−0.850549 | + | 0.525896i | \(0.823730\pi\) | |||||||
\(228\) | 1.80047 | + | 6.35789i | 0.119239 | + | 0.421062i | ||||
\(229\) | 4.39356i | 0.290335i | 0.989407 | + | 0.145167i | \(0.0463721\pi\) | ||||
−0.989407 | + | 0.145167i | \(0.953628\pi\) | |||||||
\(230\) | 1.55923 | − | 1.60274i | 0.102813 | − | 0.105682i | ||||
\(231\) | −15.8456 | + | 28.3657i | −1.04257 | + | 1.86633i | ||||
\(232\) | −5.50447 | + | 5.50447i | −0.361386 | + | 0.361386i | ||||
\(233\) | −8.94095 | + | 8.94095i | −0.585741 | + | 0.585741i | −0.936475 | − | 0.350734i | \(-0.885932\pi\) |
0.350734 | + | 0.936475i | \(0.385932\pi\) | |||||||
\(234\) | 1.94696 | + | 3.16191i | 0.127276 | + | 0.206700i | ||||
\(235\) | −11.4838 | + | 0.158024i | −0.749123 | + | 0.0103083i | ||||
\(236\) | − | 3.87315i | − | 0.252120i | ||||||
\(237\) | −28.6568 | + | 8.11521i | −1.86146 | + | 0.527140i | ||||
\(238\) | 6.62066 | + | 6.62066i | 0.429154 | + | 0.429154i | ||||
\(239\) | −7.07155 | −0.457420 | −0.228710 | − | 0.973495i | \(-0.573451\pi\) | ||||
−0.228710 | + | 0.973495i | \(0.573451\pi\) | |||||||
\(240\) | 3.40686 | + | 1.84210i | 0.219912 | + | 0.118907i | ||||
\(241\) | −4.22605 | −0.272224 | −0.136112 | − | 0.990693i | \(-0.543461\pi\) | ||||
−0.136112 | + | 0.990693i | \(0.543461\pi\) | |||||||
\(242\) | 2.67622 | + | 2.67622i | 0.172034 | + | 0.172034i | ||||
\(243\) | 15.3050 | + | 2.95918i | 0.981817 | + | 0.189832i | ||||
\(244\) | − | 13.5655i | − | 0.868442i | ||||||
\(245\) | 26.9285 | + | 26.1975i | 1.72040 | + | 1.67370i | ||||
\(246\) | 6.49844 | + | 3.63016i | 0.414325 | + | 0.231450i | ||||
\(247\) | 3.33905 | − | 3.33905i | 0.212459 | − | 0.212459i | ||||
\(248\) | 3.94659 | − | 3.94659i | 0.250608 | − | 0.250608i | ||||
\(249\) | −4.28649 | − | 2.39452i | −0.271645 | − | 0.151747i | ||||
\(250\) | −0.461381 | − | 11.1708i | −0.0291803 | − | 0.706504i | ||||
\(251\) | − | 0.318931i | − | 0.0201307i | −0.999949 | − | 0.0100654i | \(-0.996796\pi\) | ||
0.999949 | − | 0.0100654i | \(-0.00320396\pi\) | |||||||
\(252\) | 14.2389 | + | 3.38620i | 0.896969 | + | 0.213311i | ||||
\(253\) | −2.71889 | − | 2.71889i | −0.170935 | − | 0.170935i | ||||
\(254\) | 14.7654 | 0.926462 | ||||||||
\(255\) | −2.12347 | − | 7.12315i | −0.132977 | − | 0.446069i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.89138 | + | 9.89138i | 0.617007 | + | 0.617007i | 0.944763 | − | 0.327755i | \(-0.106292\pi\) |
−0.327755 | + | 0.944763i | \(0.606292\pi\) | |||||||
\(258\) | 0.336214 | − | 0.0952114i | 0.0209318 | − | 0.00592760i | ||||
\(259\) | 12.8989i | 0.801498i | ||||||||
\(260\) | −0.0380814 | − | 2.76744i | −0.00236171 | − | 0.171629i | ||||
\(261\) | 19.8859 | − | 12.2448i | 1.23091 | − | 0.757935i | ||||
\(262\) | 7.95253 | − | 7.95253i | 0.491309 | − | 0.491309i | ||||
\(263\) | −6.24409 | + | 6.24409i | −0.385027 | + | 0.385027i | −0.872909 | − | 0.487882i | \(-0.837769\pi\) |
0.487882 | + | 0.872909i | \(0.337769\pi\) | |||||||
\(264\) | 3.24794 | − | 5.81422i | 0.199897 | − | 0.357840i | ||||
\(265\) | −0.157731 | − | 11.4626i | −0.00968932 | − | 0.704140i | ||||
\(266\) | − | 18.6125i | − | 1.14121i | ||||||
\(267\) | −5.94575 | − | 20.9959i | −0.363874 | − | 1.28493i | ||||
\(268\) | −2.77087 | − | 2.77087i | −0.169258 | − | 0.169258i | ||||
\(269\) | −11.4973 | −0.701002 | −0.350501 | − | 0.936562i | \(-0.613989\pi\) | ||||
−0.350501 | + | 0.936562i | \(0.613989\pi\) | |||||||
\(270\) | −8.66470 | − | 7.74099i | −0.527317 | − | 0.471102i | ||||
\(271\) | 14.4129 | 0.875519 | 0.437760 | − | 0.899092i | \(-0.355772\pi\) | ||||
0.437760 | + | 0.899092i | \(0.355772\pi\) | |||||||
\(272\) | −1.35706 | − | 1.35706i | −0.0822839 | − | 0.0822839i | ||||
\(273\) | −2.84983 | − | 10.0634i | −0.172479 | − | 0.609067i | ||||
\(274\) | 14.7450i | 0.890776i | ||||||||
\(275\) | −19.2182 | + | 0.529004i | −1.15890 | + | 0.0319002i | ||||
\(276\) | −0.844697 | + | 1.51211i | −0.0508448 | + | 0.0910185i | ||||
\(277\) | −21.8386 | + | 21.8386i | −1.31215 | + | 1.31215i | −0.392325 | + | 0.919827i | \(0.628329\pi\) |
−0.919827 | + | 0.392325i | \(0.871671\pi\) | |||||||
\(278\) | −10.3557 | + | 10.3557i | −0.621092 | + | 0.621092i | ||||
\(279\) | −14.2578 | + | 8.77927i | −0.853590 | + | 0.525601i | ||||
\(280\) | −7.81928 | − | 7.60700i | −0.467291 | − | 0.454605i | ||||
\(281\) | 32.5667i | 1.94277i | 0.237517 | + | 0.971383i | \(0.423666\pi\) | ||||
−0.237517 | + | 0.971383i | \(0.576334\pi\) | |||||||
\(282\) | 8.55959 | − | 2.42396i | 0.509716 | − | 0.144345i | ||||
\(283\) | −18.1562 | − | 18.1562i | −1.07927 | − | 1.07927i | −0.996574 | − | 0.0827000i | \(-0.973646\pi\) |
−0.0827000 | − | 0.996574i | \(-0.526354\pi\) | |||||||
\(284\) | −6.15174 | −0.365039 | ||||||||
\(285\) | −7.02775 | + | 12.9974i | −0.416288 | + | 0.769901i | ||||
\(286\) | −4.75928 | −0.281422 | ||||||||
\(287\) | −14.8256 | − | 14.8256i | −0.875127 | − | 0.875127i | ||||
\(288\) | −2.91860 | − | 0.694081i | −0.171980 | − | 0.0408991i | ||||
\(289\) | − | 13.3168i | − | 0.783340i | ||||||
\(290\) | −17.4050 | + | 0.239502i | −1.02206 | + | 0.0140640i | ||||
\(291\) | −7.19807 | − | 4.02098i | −0.421958 | − | 0.235714i | ||||
\(292\) | 9.60788 | − | 9.60788i | 0.562258 | − | 0.562258i | ||||
\(293\) | −9.83546 | + | 9.83546i | −0.574594 | + | 0.574594i | −0.933409 | − | 0.358815i | \(-0.883181\pi\) |
0.358815 | + | 0.933409i | \(0.383181\pi\) | |||||||
\(294\) | −25.4058 | − | 14.1922i | −1.48170 | − | 0.827705i | ||||
\(295\) | 6.03914 | − | 6.20766i | 0.351612 | − | 0.361424i | ||||
\(296\) | − | 2.64393i | − | 0.153675i | ||||||
\(297\) | −13.5150 | + | 14.7151i | −0.784219 | + | 0.853855i | ||||
\(298\) | 0.862517 | + | 0.862517i | 0.0499642 | + | 0.0499642i | ||||
\(299\) | 1.23775 | 0.0715811 | ||||||||
\(300\) | 2.58806 | + | 8.26450i | 0.149422 | + | 0.477151i | ||||
\(301\) | −0.984258 | −0.0567317 | ||||||||
\(302\) | −4.89377 | − | 4.89377i | −0.281605 | − | 0.281605i | ||||
\(303\) | 18.8223 | − | 5.33021i | 1.08131 | − | 0.306213i | ||||
\(304\) | 3.81508i | 0.218810i | ||||||||
\(305\) | 21.1518 | − | 21.7420i | 1.21115 | − | 1.24494i | ||||
\(306\) | 3.01881 | + | 4.90263i | 0.172574 | + | 0.280265i | ||||
\(307\) | −16.7681 | + | 16.7681i | −0.957004 | + | 0.957004i | −0.999113 | − | 0.0421088i | \(-0.986592\pi\) |
0.0421088 | + | 0.999113i | \(0.486592\pi\) | |||||||
\(308\) | −13.2646 | + | 13.2646i | −0.755821 | + | 0.755821i | ||||
\(309\) | 9.99648 | − | 17.8950i | 0.568680 | − | 1.01801i | ||||
\(310\) | 12.4790 | − | 0.171718i | 0.708760 | − | 0.00975291i | ||||
\(311\) | 6.36857i | 0.361128i | 0.983563 | + | 0.180564i | \(0.0577924\pi\) | ||||
−0.983563 | + | 0.180564i | \(0.942208\pi\) | |||||||
\(312\) | 0.584139 | + | 2.06274i | 0.0330704 | + | 0.116779i | ||||
\(313\) | −16.8425 | − | 16.8425i | −0.951993 | − | 0.951993i | 0.0469067 | − | 0.998899i | \(-0.485064\pi\) |
−0.998899 | + | 0.0469067i | \(0.985064\pi\) | |||||||
\(314\) | −2.36353 | −0.133382 | ||||||||
\(315\) | 17.5415 | + | 27.6290i | 0.988351 | + | 1.55672i | ||||
\(316\) | −17.1956 | −0.967329 | ||||||||
\(317\) | −17.8078 | − | 17.8078i | −1.00018 | − | 1.00018i | −1.00000 | 0.000184598i | \(-0.999941\pi\) | |
−0.000184598 | − | 1.00000i | \(-0.500059\pi\) | |||||||
\(318\) | 2.41947 | + | 8.54373i | 0.135677 | + | 0.479108i | ||||
\(319\) | 29.9321i | 1.67588i | ||||||||
\(320\) | 1.60274 | + | 1.55923i | 0.0895961 | + | 0.0871638i | ||||
\(321\) | −8.62416 | + | 15.4383i | −0.481353 | + | 0.861683i | ||||
\(322\) | 3.44975 | − | 3.44975i | 0.192247 | − | 0.192247i | ||||
\(323\) | 5.17729 | − | 5.17729i | 0.288072 | − | 0.288072i | ||||
\(324\) | 8.03650 | + | 4.05150i | 0.446472 | + | 0.225083i | ||||
\(325\) | 4.25405 | − | 4.49488i | 0.235972 | − | 0.249331i | ||||
\(326\) | − | 13.1475i | − | 0.728173i | ||||||
\(327\) | −3.60089 | + | 1.01972i | −0.199129 | + | 0.0563908i | ||||
\(328\) | 3.03885 | + | 3.03885i | 0.167793 | + | 0.167793i | ||||
\(329\) | −25.0580 | −1.38149 | ||||||||
\(330\) | 14.2713 | − | 4.25441i | 0.785611 | − | 0.234198i | ||||
\(331\) | −5.76581 | −0.316918 | −0.158459 | − | 0.987366i | \(-0.550653\pi\) | ||||
−0.158459 | + | 0.987366i | \(0.550653\pi\) | |||||||
\(332\) | −2.00448 | − | 2.00448i | −0.110010 | − | 0.110010i | ||||
\(333\) | −1.83510 | + | 7.71659i | −0.100563 | + | 0.422866i | ||||
\(334\) | − | 15.5247i | − | 0.849475i | ||||||
\(335\) | −0.120562 | − | 8.76143i | −0.00658699 | − | 0.478688i | ||||
\(336\) | 7.37712 | + | 4.12100i | 0.402455 | + | 0.224819i | ||||
\(337\) | −11.3239 | + | 11.3239i | −0.616851 | + | 0.616851i | −0.944722 | − | 0.327871i | \(-0.893669\pi\) |
0.327871 | + | 0.944722i | \(0.393669\pi\) | |||||||
\(338\) | −8.10908 | + | 8.10908i | −0.441076 | + | 0.441076i | ||||
\(339\) | −18.4711 | − | 10.3183i | −1.00321 | − | 0.560414i | ||||
\(340\) | −0.0590463 | − | 4.29100i | −0.00320223 | − | 0.232712i | ||||
\(341\) | − | 21.4607i | − | 1.16216i | ||||||
\(342\) | 2.64797 | − | 11.1347i | 0.143186 | − | 0.602096i | ||||
\(343\) | 33.8128 | + | 33.8128i | 1.82572 | + | 1.82572i | ||||
\(344\) | 0.201747 | 0.0108775 | ||||||||
\(345\) | −3.71157 | + | 1.10645i | −0.199824 | + | 0.0595694i | ||||
\(346\) | −24.5221 | −1.31832 | ||||||||
\(347\) | 6.47445 | + | 6.47445i | 0.347567 | + | 0.347567i | 0.859203 | − | 0.511636i | \(-0.170960\pi\) |
−0.511636 | + | 0.859203i | \(0.670960\pi\) | |||||||
\(348\) | 12.9730 | − | 3.67378i | 0.695425 | − | 0.196935i | ||||
\(349\) | − | 11.4593i | − | 0.613401i | −0.951806 | − | 0.306701i | \(-0.900775\pi\) | ||
0.951806 | − | 0.306701i | \(-0.0992251\pi\) | |||||||
\(350\) | −0.671204 | − | 24.3842i | −0.0358774 | − | 1.30339i | ||||
\(351\) | −0.273164 | − | 6.42575i | −0.0145804 | − | 0.342981i | ||||
\(352\) | 2.71889 | − | 2.71889i | 0.144917 | − | 0.144917i | ||||
\(353\) | 14.6045 | − | 14.6045i | 0.777319 | − | 0.777319i | −0.202055 | − | 0.979374i | \(-0.564762\pi\) |
0.979374 | + | 0.202055i | \(0.0647621\pi\) | |||||||
\(354\) | −3.27163 | + | 5.85664i | −0.173885 | + | 0.311277i | ||||
\(355\) | −9.85967 | − | 9.59200i | −0.523297 | − | 0.509091i | ||||
\(356\) | − | 12.5987i | − | 0.667728i | ||||||
\(357\) | −4.41874 | − | 15.6036i | −0.233865 | − | 0.825833i | ||||
\(358\) | −1.04011 | − | 1.04011i | −0.0549715 | − | 0.0549715i | ||||
\(359\) | 3.30519 | 0.174441 | 0.0872207 | − | 0.996189i | \(-0.472201\pi\) | ||||
0.0872207 | + | 0.996189i | \(0.472201\pi\) | |||||||
\(360\) | −3.59554 | − | 5.66322i | −0.189502 | − | 0.298478i | ||||
\(361\) | 4.44518 | 0.233957 | ||||||||
\(362\) | 11.0911 | + | 11.0911i | 0.582936 | + | 0.582936i | ||||
\(363\) | −1.78615 | − | 6.30734i | −0.0937488 | − | 0.331050i | ||||
\(364\) | − | 6.03860i | − | 0.316509i | ||||||
\(365\) | 30.3799 | − | 0.418043i | 1.59016 | − | 0.0218814i | ||||
\(366\) | −11.4587 | + | 20.5126i | −0.598957 | + | 1.07221i | ||||
\(367\) | −12.2911 | + | 12.2911i | −0.641591 | + | 0.641591i | −0.950946 | − | 0.309355i | \(-0.899887\pi\) |
0.309355 | + | 0.950946i | \(0.399887\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | −6.75999 | − | 10.9784i | −0.351911 | − | 0.571513i | ||||
\(370\) | 4.12251 | − | 4.23754i | 0.214319 | − | 0.220299i | ||||
\(371\) | − | 25.0115i | − | 1.29853i | ||||||
\(372\) | −9.30135 | + | 2.63402i | −0.482253 | + | 0.136567i | ||||
\(373\) | 4.21951 | + | 4.21951i | 0.218478 | + | 0.218478i | 0.807857 | − | 0.589379i | \(-0.200627\pi\) |
−0.589379 | + | 0.807857i | \(0.700627\pi\) | |||||||
\(374\) | −7.37940 | −0.381580 | ||||||||
\(375\) | −8.73829 | + | 17.2813i | −0.451243 | + | 0.892401i | ||||
\(376\) | 5.13622 | 0.264880 | ||||||||
\(377\) | −6.81318 | − | 6.81318i | −0.350897 | − | 0.350897i | ||||
\(378\) | −18.6706 | − | 17.1479i | −0.960311 | − | 0.881993i | ||||
\(379\) | 24.7674i | 1.27221i | 0.771601 | + | 0.636107i | \(0.219456\pi\) | ||||
−0.771601 | + | 0.636107i | \(0.780544\pi\) | |||||||
\(380\) | −5.94860 | + | 6.11459i | −0.305157 | + | 0.313672i | ||||
\(381\) | −22.3269 | − | 12.4723i | −1.14384 | − | 0.638974i | ||||
\(382\) | −15.3583 | + | 15.3583i | −0.785800 | + | 0.785800i | ||||
\(383\) | 12.2872 | − | 12.2872i | 0.627846 | − | 0.627846i | −0.319680 | − | 0.947526i | \(-0.603575\pi\) |
0.947526 | + | 0.319680i | \(0.103575\pi\) | |||||||
\(384\) | −1.51211 | − | 0.844697i | −0.0771647 | − | 0.0431057i | ||||
\(385\) | −41.9424 | + | 0.577149i | −2.13758 | + | 0.0294142i | ||||
\(386\) | − | 25.2157i | − | 1.28345i | ||||||
\(387\) | −0.588819 | − | 0.140029i | −0.0299314 | − | 0.00711806i | ||||
\(388\) | −3.36602 | − | 3.36602i | −0.170884 | − | 0.170884i | ||||
\(389\) | 15.4882 | 0.785281 | 0.392640 | − | 0.919692i | \(-0.371562\pi\) | ||||
0.392640 | + | 0.919692i | \(0.371562\pi\) | |||||||
\(390\) | −2.28006 | + | 4.21685i | −0.115456 | + | 0.213529i | ||||
\(391\) | 1.91917 | 0.0970568 | ||||||||
\(392\) | −11.8805 | − | 11.8805i | −0.600054 | − | 0.600054i | ||||
\(393\) | −18.7426 | + | 5.30765i | −0.945439 | + | 0.267736i | ||||
\(394\) | − | 1.14004i | − | 0.0574342i | ||||||
\(395\) | −27.5602 | − | 26.8120i | −1.38670 | − | 1.34906i | ||||
\(396\) | −9.82250 | + | 6.04824i | −0.493599 | + | 0.303935i | ||||
\(397\) | −14.2745 | + | 14.2745i | −0.716415 | + | 0.716415i | −0.967869 | − | 0.251454i | \(-0.919091\pi\) |
0.251454 | + | 0.967869i | \(0.419091\pi\) | |||||||
\(398\) | −12.7628 | + | 12.7628i | −0.639742 | + | 0.639742i | ||||
\(399\) | −15.7220 | + | 28.1443i | −0.787082 | + | 1.40898i | ||||
\(400\) | 0.137579 | + | 4.99811i | 0.00687895 | + | 0.249905i | ||||
\(401\) | − | 3.26739i | − | 0.163166i | −0.996667 | − | 0.0815829i | \(-0.974002\pi\) | ||
0.996667 | − | 0.0815829i | \(-0.0259975\pi\) | |||||||
\(402\) | 1.84932 | + | 6.53041i | 0.0922359 | + | 0.325707i | ||||
\(403\) | 4.88490 | + | 4.88490i | 0.243334 | + | 0.243334i | ||||
\(404\) | 11.2944 | 0.561916 | ||||||||
\(405\) | 6.56322 | + | 19.0243i | 0.326129 | + | 0.945325i | ||||
\(406\) | −37.9781 | −1.88482 | ||||||||
\(407\) | −7.18856 | − | 7.18856i | −0.356324 | − | 0.356324i | ||||
\(408\) | 0.905725 | + | 3.19833i | 0.0448401 | + | 0.158341i | ||||
\(409\) | 33.7644i | 1.66954i | 0.550596 | + | 0.834772i | \(0.314400\pi\) | ||||
−0.550596 | + | 0.834772i | \(0.685600\pi\) | |||||||
\(410\) | 0.132222 | + | 9.60878i | 0.00652997 | + | 0.474544i | ||||
\(411\) | 12.4550 | − | 22.2961i | 0.614361 | − | 1.09978i | ||||
\(412\) | 8.36819 | − | 8.36819i | 0.412271 | − | 0.412271i | ||||
\(413\) | 13.3614 | − | 13.3614i | 0.657470 | − | 0.657470i | ||||
\(414\) | 2.55455 | − | 1.57298i | 0.125550 | − | 0.0773075i | ||||
\(415\) | −0.0872160 | − | 6.33814i | −0.00428126 | − | 0.311127i | ||||
\(416\) | 1.23775i | 0.0606859i | ||||||||
\(417\) | 24.4063 | − | 6.91155i | 1.19518 | − | 0.338460i | ||||
\(418\) | 10.3728 | + | 10.3728i | 0.507349 | + | 0.507349i | ||||
\(419\) | 20.6323 | 1.00795 | 0.503977 | − | 0.863717i | \(-0.331870\pi\) | ||||
0.503977 | + | 0.863717i | \(0.331870\pi\) | |||||||
\(420\) | 5.39802 | + | 18.1076i | 0.263397 | + | 0.883559i | ||||
\(421\) | −33.8481 | −1.64966 | −0.824828 | − | 0.565383i | \(-0.808728\pi\) | ||||
−0.824828 | + | 0.565383i | \(0.808728\pi\) | |||||||
\(422\) | −5.62749 | − | 5.62749i | −0.273942 | − | 0.273942i | ||||
\(423\) | −14.9906 | − | 3.56495i | −0.728867 | − | 0.173334i | ||||
\(424\) | 5.12670i | 0.248975i | ||||||||
\(425\) | 6.59603 | − | 6.96944i | 0.319954 | − | 0.338067i | ||||
\(426\) | 9.30213 | + | 5.19635i | 0.450690 | + | 0.251764i | ||||
\(427\) | 46.7975 | − | 46.7975i | 2.26469 | − | 2.26469i | ||||
\(428\) | −7.21940 | + | 7.21940i | −0.348963 | + | 0.348963i | ||||
\(429\) | 7.19657 | + | 4.02015i | 0.347454 | + | 0.194095i | ||||
\(430\) | 0.323349 | + | 0.314570i | 0.0155932 | + | 0.0151699i | ||||
\(431\) | 11.9724i | 0.576690i | 0.957527 | + | 0.288345i | \(0.0931051\pi\) | ||||
−0.957527 | + | 0.288345i | \(0.906895\pi\) | |||||||
\(432\) | 3.82697 | + | 3.51487i | 0.184125 | + | 0.169109i | ||||
\(433\) | 13.6433 | + | 13.6433i | 0.655655 | + | 0.655655i | 0.954349 | − | 0.298694i | \(-0.0965511\pi\) |
−0.298694 | + | 0.954349i | \(0.596551\pi\) | |||||||
\(434\) | 27.2294 | 1.30706 | ||||||||
\(435\) | 26.5207 | + | 14.3398i | 1.27157 | + | 0.687541i | ||||
\(436\) | −2.16073 | −0.103480 | ||||||||
\(437\) | −2.69767 | − | 2.69767i | −0.129047 | − | 0.129047i | ||||
\(438\) | −22.6439 | + | 6.41246i | −1.08197 | + | 0.306399i | ||||
\(439\) | 12.4463i | 0.594027i | 0.954873 | + | 0.297014i | \(0.0959907\pi\) | ||||
−0.954873 | + | 0.297014i | \(0.904009\pi\) | |||||||
\(440\) | 8.59708 | − | 0.118300i | 0.409850 | − | 0.00563974i | ||||
\(441\) | 26.4284 | + | 42.9204i | 1.25849 | + | 2.04383i | ||||
\(442\) | 1.67971 | − | 1.67971i | 0.0798955 | − | 0.0798955i | ||||
\(443\) | −8.23721 | + | 8.23721i | −0.391362 | + | 0.391362i | −0.875173 | − | 0.483811i | \(-0.839252\pi\) |
0.483811 | + | 0.875173i | \(0.339252\pi\) | |||||||
\(444\) | −2.23332 | + | 3.99792i | −0.105989 | + | 0.189733i | ||||
\(445\) | 19.6443 | − | 20.1924i | 0.931227 | − | 0.957213i | ||||
\(446\) | − | 23.4675i | − | 1.11122i | ||||||
\(447\) | −0.575658 | − | 2.03279i | −0.0272277 | − | 0.0961476i | ||||
\(448\) | 3.44975 | + | 3.44975i | 0.162985 | + | 0.162985i | ||||
\(449\) | 16.4715 | 0.777340 | 0.388670 | − | 0.921377i | \(-0.372935\pi\) | ||||
0.388670 | + | 0.921377i | \(0.372935\pi\) | |||||||
\(450\) | 3.06755 | − | 14.6830i | 0.144606 | − | 0.692163i | ||||
\(451\) | 16.5246 | 0.778114 | ||||||||
\(452\) | −8.63760 | − | 8.63760i | −0.406279 | − | 0.406279i | ||||
\(453\) | 3.26619 | + | 11.5337i | 0.153459 | + | 0.541900i | ||||
\(454\) | 6.91748i | 0.324653i | ||||||||
\(455\) | 9.41560 | − | 9.67834i | 0.441410 | − | 0.453728i | ||||
\(456\) | 3.22258 | − | 5.76883i | 0.150911 | − | 0.270150i | ||||
\(457\) | −8.60752 | + | 8.60752i | −0.402643 | + | 0.402643i | −0.879163 | − | 0.476520i | \(-0.841898\pi\) |
0.476520 | + | 0.879163i | \(0.341898\pi\) | |||||||
\(458\) | 3.10672 | − | 3.10672i | 0.145167 | − | 0.145167i | ||||
\(459\) | −0.423549 | − | 9.96332i | −0.0197696 | − | 0.465048i | ||||
\(460\) | −2.23586 | + | 0.0307665i | −0.104247 | + | 0.00143450i | ||||
\(461\) | 37.7905i | 1.76008i | 0.474898 | + | 0.880041i | \(0.342485\pi\) | ||||
−0.474898 | + | 0.880041i | \(0.657515\pi\) | |||||||
\(462\) | 31.2622 | − | 8.85302i | 1.45445 | − | 0.411880i | ||||
\(463\) | −7.64424 | − | 7.64424i | −0.355258 | − | 0.355258i | 0.506804 | − | 0.862062i | \(-0.330827\pi\) |
−0.862062 | + | 0.506804i | \(0.830827\pi\) | |||||||
\(464\) | 7.78450 | 0.361386 | ||||||||
\(465\) | −19.0147 | − | 10.2813i | −0.881787 | − | 0.476785i | ||||
\(466\) | 12.6444 | 0.585741 | ||||||||
\(467\) | 5.24131 | + | 5.24131i | 0.242539 | + | 0.242539i | 0.817900 | − | 0.575361i | \(-0.195138\pi\) |
−0.575361 | + | 0.817900i | \(0.695138\pi\) | |||||||
\(468\) | 0.859102 | − | 3.61251i | 0.0397120 | − | 0.166988i | ||||
\(469\) | − | 19.1176i | − | 0.882768i | ||||||
\(470\) | 8.23204 | + | 8.00856i | 0.379716 | + | 0.369407i | ||||
\(471\) | 3.57393 | + | 1.99647i | 0.164678 | + | 0.0919923i | ||||
\(472\) | −2.73873 | + | 2.73873i | −0.126060 | + | 0.126060i | ||||
\(473\) | 0.548528 | − | 0.548528i | 0.0252213 | − | 0.0252213i | ||||
\(474\) | 26.0017 | + | 14.5251i | 1.19430 | + | 0.667159i | ||||
\(475\) | −19.0682 | + | 0.524875i | −0.874907 | + | 0.0240829i | ||||
\(476\) | − | 9.36303i | − | 0.429154i | ||||||
\(477\) | 3.55835 | − | 14.9628i | 0.162926 | − | 0.685100i | ||||
\(478\) | 5.00034 | + | 5.00034i | 0.228710 | + | 0.228710i | ||||
\(479\) | 26.6043 | 1.21558 | 0.607790 | − | 0.794098i | \(-0.292056\pi\) | ||||
0.607790 | + | 0.794098i | \(0.292056\pi\) | |||||||
\(480\) | −1.10645 | − | 3.71157i | −0.0505024 | − | 0.169409i | ||||
\(481\) | 3.27254 | 0.149215 | ||||||||
\(482\) | 2.98827 | + | 2.98827i | 0.136112 | + | 0.136112i | ||||
\(483\) | −8.13040 | + | 2.30242i | −0.369946 | + | 0.104764i | ||||
\(484\) | − | 3.78475i | − | 0.172034i | ||||||
\(485\) | −0.146457 | − | 10.6433i | −0.00665027 | − | 0.483286i | ||||
\(486\) | −8.72982 | − | 12.9147i | −0.395993 | − | 0.585824i | ||||
\(487\) | −5.61285 | + | 5.61285i | −0.254342 | + | 0.254342i | −0.822748 | − | 0.568406i | \(-0.807560\pi\) |
0.568406 | + | 0.822748i | \(0.307560\pi\) | |||||||
\(488\) | −9.59226 | + | 9.59226i | −0.434221 | + | 0.434221i | ||||
\(489\) | −11.1057 | + | 19.8805i | −0.502215 | + | 0.899029i | ||||
\(490\) | −0.516924 | − | 37.5658i | −0.0233523 | − | 1.69705i | ||||
\(491\) | − | 35.1263i | − | 1.58523i | −0.609724 | − | 0.792614i | \(-0.708720\pi\) | ||
0.609724 | − | 0.792614i | \(-0.291280\pi\) | |||||||
\(492\) | −2.02818 | − | 7.16200i | −0.0914375 | − | 0.322888i | ||||
\(493\) | −10.5640 | − | 10.5640i | −0.475780 | − | 0.475780i | ||||
\(494\) | −4.72213 | −0.212459 | ||||||||
\(495\) | −25.1736 | − | 5.62180i | −1.13147 | − | 0.252681i | ||||
\(496\) | −5.58131 | −0.250608 | ||||||||
\(497\) | −21.2219 | − | 21.2219i | −0.951934 | − | 0.951934i | ||||
\(498\) | 1.33783 | + | 4.72419i | 0.0599495 | + | 0.211696i | ||||
\(499\) | − | 10.0259i | − | 0.448822i | −0.974495 | − | 0.224411i | \(-0.927954\pi\) | ||
0.974495 | − | 0.224411i | \(-0.0720458\pi\) | |||||||
\(500\) | −7.57271 | + | 8.22521i | −0.338662 | + | 0.367842i | ||||
\(501\) | −13.1137 | + | 23.4751i | −0.585876 | + | 1.04879i | ||||
\(502\) | −0.225518 | + | 0.225518i | −0.0100654 | + | 0.0100654i | ||||
\(503\) | −14.7345 | + | 14.7345i | −0.656979 | + | 0.656979i | −0.954664 | − | 0.297685i | \(-0.903785\pi\) |
0.297685 | + | 0.954664i | \(0.403785\pi\) | |||||||
\(504\) | −7.67404 | − | 12.4629i | −0.341829 | − | 0.555140i | ||||
\(505\) | 18.1020 | + | 17.6106i | 0.805528 | + | 0.783660i | ||||
\(506\) | 3.84509i | 0.170935i | ||||||||
\(507\) | 19.1116 | − | 5.41214i | 0.848774 | − | 0.240361i | ||||
\(508\) | −10.4407 | − | 10.4407i | −0.463231 | − | 0.463231i | ||||
\(509\) | 29.8800 | 1.32441 | 0.662205 | − | 0.749323i | \(-0.269621\pi\) | ||||
0.662205 | + | 0.749323i | \(0.269621\pi\) | |||||||
\(510\) | −3.53530 | + | 6.53835i | −0.156546 | + | 0.289523i | ||||
\(511\) | 66.2895 | 2.93247 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −13.4095 | + | 14.6002i | −0.592043 | + | 0.644615i | ||||
\(514\) | − | 13.9885i | − | 0.617007i | ||||||
\(515\) | 26.4600 | − | 0.364103i | 1.16597 | − | 0.0160443i | ||||
\(516\) | −0.305064 | − | 0.170415i | −0.0134297 | − | 0.00750209i | ||||
\(517\) | 13.9648 | − | 13.9648i | 0.614172 | − | 0.614172i | ||||
\(518\) | 9.12089 | − | 9.12089i | 0.400749 | − | 0.400749i | ||||
\(519\) | 37.0803 | + | 20.7138i | 1.62764 | + | 0.909234i | ||||
\(520\) | −1.92995 | + | 1.98380i | −0.0846338 | + | 0.0869955i | ||||
\(521\) | 1.39433i | 0.0610866i | 0.999533 | + | 0.0305433i | \(0.00972375\pi\) | ||||
−0.999533 | + | 0.0305433i | \(0.990276\pi\) | |||||||
\(522\) | −22.7199 | − | 5.40308i | −0.994422 | − | 0.236486i | ||||
\(523\) | −25.8878 | − | 25.8878i | −1.13199 | − | 1.13199i | −0.989845 | − | 0.142148i | \(-0.954599\pi\) |
−0.142148 | − | 0.989845i | \(-0.545401\pi\) | |||||||
\(524\) | −11.2466 | −0.491309 | ||||||||
\(525\) | −19.5823 | + | 37.4386i | −0.854641 | + | 1.63395i | ||||
\(526\) | 8.83047 | 0.385027 | ||||||||
\(527\) | 7.57418 | + | 7.57418i | 0.329936 | + | 0.329936i | ||||
\(528\) | −6.40791 | + | 1.81463i | −0.278869 | + | 0.0789718i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −7.99372 | + | 8.21679i | −0.347225 | + | 0.356914i | ||||
\(531\) | 9.89417 | − | 6.09236i | 0.429370 | − | 0.264386i | ||||
\(532\) | −13.1611 | + | 13.1611i | −0.570604 | + | 0.570604i | ||||
\(533\) | −3.76135 | + | 3.76135i | −0.162922 | + | 0.162922i | ||||
\(534\) | −10.6420 | + | 19.0506i | −0.460526 | + | 0.824400i | ||||
\(535\) | −22.8276 | + | 0.314119i | −0.986922 | + | 0.0135805i | ||||
\(536\) | 3.91860i | 0.169258i | ||||||||
\(537\) | 0.694187 | + | 2.45134i | 0.0299564 | + | 0.105783i | ||||
\(538\) | 8.12981 | + | 8.12981i | 0.350501 | + | 0.350501i | ||||
\(539\) | −64.6034 | −2.78267 | ||||||||
\(540\) | 0.653162 | + | 11.6006i | 0.0281076 | + | 0.499209i | ||||
\(541\) | 18.7230 | 0.804966 | 0.402483 | − | 0.915427i | \(-0.368147\pi\) | ||||
0.402483 | + | 0.915427i | \(0.368147\pi\) | |||||||
\(542\) | −10.1914 | − | 10.1914i | −0.437760 | − | 0.437760i | ||||
\(543\) | −7.40239 | − | 26.1396i | −0.317667 | − | 1.12176i | ||||
\(544\) | 1.91917i | 0.0822839i | ||||||||
\(545\) | −3.46309 | − | 3.36908i | −0.148343 | − | 0.144315i | ||||
\(546\) | −5.10079 | + | 9.13106i | −0.218294 | + | 0.390773i | ||||
\(547\) | 17.9273 | − | 17.9273i | 0.766517 | − | 0.766517i | −0.210974 | − | 0.977492i | \(-0.567664\pi\) |
0.977492 | + | 0.210974i | \(0.0676636\pi\) | |||||||
\(548\) | 10.4263 | − | 10.4263i | 0.445388 | − | 0.445388i | ||||
\(549\) | 34.6538 | − | 21.3382i | 1.47899 | − | 0.910692i | ||||
\(550\) | 13.9634 | + | 13.2152i | 0.595400 | + | 0.563500i | ||||
\(551\) | 29.6985i | 1.26520i | ||||||||
\(552\) | 1.66652 | − | 0.471935i | 0.0709317 | − | 0.0200869i | ||||
\(553\) | −59.3205 | − | 59.3205i | −2.52257 | − | 2.52257i | ||||
\(554\) | 30.8844 | 1.31215 | ||||||||
\(555\) | −9.81314 | + | 2.92538i | −0.416545 | + | 0.124176i | ||||
\(556\) | 14.6451 | 0.621092 | ||||||||
\(557\) | −18.5689 | − | 18.5689i | −0.786789 | − | 0.786789i | 0.194178 | − | 0.980966i | \(-0.437796\pi\) |
−0.980966 | + | 0.194178i | \(0.937796\pi\) | |||||||
\(558\) | 16.2896 | + | 3.87389i | 0.689596 | + | 0.163995i | ||||
\(559\) | 0.249713i | 0.0105617i | ||||||||
\(560\) | 0.150100 | + | 10.9080i | 0.00634288 | + | 0.460948i | ||||
\(561\) | 11.1585 | + | 6.23336i | 0.471112 | + | 0.263172i | ||||
\(562\) | 23.0281 | − | 23.0281i | 0.971383 | − | 0.971383i | ||||
\(563\) | 9.38961 | − | 9.38961i | 0.395725 | − | 0.395725i | −0.480997 | − | 0.876722i | \(-0.659725\pi\) |
0.876722 | + | 0.480997i | \(0.159725\pi\) | |||||||
\(564\) | −7.76654 | − | 4.33854i | −0.327030 | − | 0.182686i | ||||
\(565\) | −0.375826 | − | 27.3119i | −0.0158111 | − | 1.14902i | ||||
\(566\) | 25.6768i | 1.07927i | ||||||||
\(567\) | 13.7473 | + | 41.7005i | 0.577330 | + | 1.75126i | ||||
\(568\) | 4.34994 | + | 4.34994i | 0.182519 | + | 0.182519i | ||||
\(569\) | −9.13075 | −0.382781 | −0.191390 | − | 0.981514i | \(-0.561300\pi\) | ||||
−0.191390 | + | 0.981514i | \(0.561300\pi\) | |||||||
\(570\) | 14.1599 | − | 4.22120i | 0.593094 | − | 0.176807i | ||||
\(571\) | 33.9459 | 1.42059 | 0.710296 | − | 0.703903i | \(-0.248561\pi\) | ||||
0.710296 | + | 0.703903i | \(0.248561\pi\) | |||||||
\(572\) | 3.36532 | + | 3.36532i | 0.140711 | + | 0.140711i | ||||
\(573\) | 36.1967 | − | 10.2504i | 1.51214 | − | 0.428217i | ||||
\(574\) | 20.9665i | 0.875127i | ||||||||
\(575\) | −3.63148 | − | 3.43691i | −0.151443 | − | 0.143329i | ||||
\(576\) | 1.57298 | + | 2.55455i | 0.0655406 | + | 0.106440i | ||||
\(577\) | −3.14294 | + | 3.14294i | −0.130842 | + | 0.130842i | −0.769495 | − | 0.638653i | \(-0.779492\pi\) |
0.638653 | + | 0.769495i | \(0.279492\pi\) | |||||||
\(578\) | −9.41638 | + | 9.41638i | −0.391670 | + | 0.391670i | ||||
\(579\) | −21.2996 | + | 38.1290i | −0.885182 | + | 1.58459i | ||||
\(580\) | 12.4766 | + | 12.1379i | 0.518061 | + | 0.503997i | ||||
\(581\) | − | 13.8299i | − | 0.573762i | ||||||
\(582\) | 2.24654 | + | 7.93307i | 0.0931220 | + | 0.328836i | ||||
\(583\) | 13.9389 | + | 13.9389i | 0.577292 | + | 0.577292i | ||||
\(584\) | −13.5876 | −0.562258 | ||||||||
\(585\) | 7.00967 | − | 4.45039i | 0.289814 | − | 0.184001i | ||||
\(586\) | 13.9094 | 0.574594 | ||||||||
\(587\) | −15.2589 | − | 15.2589i | −0.629804 | − | 0.629804i | 0.318215 | − | 0.948019i | \(-0.396917\pi\) |
−0.948019 | + | 0.318215i | \(0.896917\pi\) | |||||||
\(588\) | 7.92922 | + | 28.0000i | 0.326996 | + | 1.15470i | ||||
\(589\) | − | 21.2931i | − | 0.877369i | ||||||
\(590\) | −8.65980 | + | 0.119163i | −0.356518 | + | 0.00490587i | ||||
\(591\) | −0.962985 | + | 1.72387i | −0.0396119 | + | 0.0709103i | ||||
\(592\) | −1.86954 | + | 1.86954i | −0.0768377 | + | 0.0768377i | ||||
\(593\) | −23.4549 | + | 23.4549i | −0.963176 | + | 0.963176i | −0.999346 | − | 0.0361698i | \(-0.988484\pi\) |
0.0361698 | + | 0.999346i | \(0.488484\pi\) | |||||||
\(594\) | 19.9617 | − | 0.848587i | 0.819037 | − | 0.0348179i | ||||
\(595\) | 14.5992 | − | 15.0065i | 0.598507 | − | 0.615208i | ||||
\(596\) | − | 1.21978i | − | 0.0499642i | ||||||
\(597\) | 30.0795 | − | 8.51811i | 1.23107 | − | 0.348623i | ||||
\(598\) | −0.875224 | − | 0.875224i | −0.0357906 | − | 0.0357906i | ||||
\(599\) | 10.6390 | 0.434697 | 0.217349 | − | 0.976094i | \(-0.430259\pi\) | ||||
0.217349 | + | 0.976094i | \(0.430259\pi\) | |||||||
\(600\) | 4.01385 | − | 7.67392i | 0.163865 | − | 0.313286i | ||||
\(601\) | −24.4899 | −0.998966 | −0.499483 | − | 0.866324i | \(-0.666477\pi\) | ||||
−0.499483 | + | 0.866324i | \(0.666477\pi\) | |||||||
\(602\) | 0.695975 | + | 0.695975i | 0.0283658 | + | 0.0283658i | ||||
\(603\) | 2.71983 | − | 11.4368i | 0.110760 | − | 0.465744i | ||||
\(604\) | 6.92084i | 0.281605i | ||||||||
\(605\) | 5.90131 | − | 6.06598i | 0.239922 | − | 0.246617i | ||||
\(606\) | −17.0784 | − | 9.54032i | −0.693761 | − | 0.387549i | ||||
\(607\) | −20.6737 | + | 20.6737i | −0.839120 | + | 0.839120i | −0.988743 | − | 0.149623i | \(-0.952194\pi\) |
0.149623 | + | 0.988743i | \(0.452194\pi\) | |||||||
\(608\) | 2.69767 | − | 2.69767i | 0.109405 | − | 0.109405i | ||||
\(609\) | 57.4272 | + | 32.0799i | 2.32707 | + | 1.29995i | ||||
\(610\) | −30.3305 | + | 0.417363i | −1.22805 | + | 0.0168985i | ||||
\(611\) | 6.35737i | 0.257192i | ||||||||
\(612\) | 1.33206 | − | 5.60131i | 0.0538454 | − | 0.226419i | ||||
\(613\) | 14.6753 | + | 14.6753i | 0.592731 | + | 0.592731i | 0.938368 | − | 0.345637i | \(-0.112337\pi\) |
−0.345637 | + | 0.938368i | \(0.612337\pi\) | |||||||
\(614\) | 23.7136 | 0.957004 | ||||||||
\(615\) | 7.91657 | − | 14.6413i | 0.319227 | − | 0.590393i | ||||
\(616\) | 18.7590 | 0.755821 | ||||||||
\(617\) | −9.12773 | − | 9.12773i | −0.367469 | − | 0.367469i | 0.499085 | − | 0.866553i | \(-0.333670\pi\) |
−0.866553 | + | 0.499085i | \(0.833670\pi\) | |||||||
\(618\) | −19.7222 | + | 5.58507i | −0.793344 | + | 0.224664i | ||||
\(619\) | − | 14.8927i | − | 0.598587i | −0.954161 | − | 0.299294i | \(-0.903249\pi\) | ||
0.954161 | − | 0.299294i | \(-0.0967510\pi\) | |||||||
\(620\) | −8.94542 | − | 8.70257i | −0.359257 | − | 0.349504i | ||||
\(621\) | −5.19146 | + | 0.220693i | −0.208326 | + | 0.00885612i | ||||
\(622\) | 4.50326 | − | 4.50326i | 0.180564 | − | 0.180564i | ||||
\(623\) | 43.4622 | − | 43.4622i | 1.74128 | − | 1.74128i | ||||
\(624\) | 1.04553 | − | 1.87162i | 0.0418546 | − | 0.0749249i | ||||
\(625\) | −24.9621 | + | 1.37527i | −0.998486 | + | 0.0550108i | ||||
\(626\) | 23.8188i | 0.951993i | ||||||||
\(627\) | −6.92297 | − | 24.4467i | −0.276477 | − | 0.976307i | ||||
\(628\) | 1.67127 | + | 1.67127i | 0.0666909 | + | 0.0666909i | ||||
\(629\) | 5.07416 | 0.202320 | ||||||||
\(630\) | 7.13298 | − | 31.9404i | 0.284185 | − | 1.27254i | ||||
\(631\) | −5.19423 | −0.206779 | −0.103390 | − | 0.994641i | \(-0.532969\pi\) | ||||
−0.103390 | + | 0.994641i | \(0.532969\pi\) | |||||||
\(632\) | 12.1591 | + | 12.1591i | 0.483664 | + | 0.483664i | ||||
\(633\) | 3.75588 | + | 13.2629i | 0.149283 | + | 0.527154i | ||||
\(634\) | 25.1840i | 1.00018i | ||||||||
\(635\) | −0.454279 | − | 33.0133i | −0.0180275 | − | 1.31009i | ||||
\(636\) | 4.33051 | − | 7.75215i | 0.171716 | − | 0.307393i | ||||
\(637\) | 14.7051 | − | 14.7051i | 0.582637 | − | 0.582637i | ||||
\(638\) | 21.1652 | − | 21.1652i | 0.837939 | − | 0.837939i | ||||
\(639\) | −9.67653 | − | 15.7150i | −0.382798 | − | 0.621674i | ||||
\(640\) | −0.0307665 | − | 2.23586i | −0.00121615 | − | 0.0883800i | ||||
\(641\) | 37.8880i | 1.49649i | 0.663425 | + | 0.748243i | \(0.269102\pi\) | ||||
−0.663425 | + | 0.748243i | \(0.730898\pi\) | |||||||
\(642\) | 17.0147 | − | 4.81835i | 0.671518 | − | 0.190165i | ||||
\(643\) | −8.06700 | − | 8.06700i | −0.318131 | − | 0.318131i | 0.529918 | − | 0.848049i | \(-0.322223\pi\) |
−0.848049 | + | 0.529918i | \(0.822223\pi\) | |||||||
\(644\) | −4.87868 | −0.192247 | ||||||||
\(645\) | −0.223223 | − | 0.748798i | −0.00878940 | − | 0.0294839i | ||||
\(646\) | −7.32179 | −0.288072 | ||||||||
\(647\) | 19.7436 | + | 19.7436i | 0.776203 | + | 0.776203i | 0.979183 | − | 0.202980i | \(-0.0650626\pi\) |
−0.202980 | + | 0.979183i | \(0.565063\pi\) | |||||||
\(648\) | −2.81782 | − | 8.54751i | −0.110695 | − | 0.335778i | ||||
\(649\) | 14.8926i | 0.584586i | ||||||||
\(650\) | −6.18643 | + | 0.170289i | −0.242652 | + | 0.00667928i | ||||
\(651\) | −41.1740 | − | 23.0006i | −1.61374 | − | 0.901465i | ||||
\(652\) | −9.29670 | + | 9.29670i | −0.364087 | + | 0.364087i | ||||
\(653\) | 1.55428 | − | 1.55428i | 0.0608235 | − | 0.0608235i | −0.676041 | − | 0.736864i | \(-0.736306\pi\) |
0.736864 | + | 0.676041i | \(0.236306\pi\) | |||||||
\(654\) | 3.26726 | + | 1.82516i | 0.127760 | + | 0.0713693i | ||||
\(655\) | −18.0254 | − | 17.5360i | −0.704310 | − | 0.685190i | ||||
\(656\) | − | 4.29759i | − | 0.167793i | ||||||
\(657\) | 39.6568 | + | 9.43089i | 1.54716 | + | 0.367934i | ||||
\(658\) | 17.7187 | + | 17.7187i | 0.690745 | + | 0.690745i | ||||
\(659\) | −10.6771 | −0.415921 | −0.207960 | − | 0.978137i | \(-0.566682\pi\) | ||||
−0.207960 | + | 0.978137i | \(0.566682\pi\) | |||||||
\(660\) | −13.0997 | − | 7.08304i | −0.509905 | − | 0.275707i | ||||
\(661\) | 40.2271 | 1.56465 | 0.782326 | − | 0.622869i | \(-0.214033\pi\) | ||||
0.782326 | + | 0.622869i | \(0.214033\pi\) | |||||||
\(662\) | 4.07705 | + | 4.07705i | 0.158459 | + | 0.158459i | ||||
\(663\) | −3.95875 | + | 1.12106i | −0.153745 | + | 0.0435385i | ||||
\(664\) | 2.83477i | 0.110010i | ||||||||
\(665\) | −41.6150 | + | 0.572643i | −1.61376 | + | 0.0222062i | ||||
\(666\) | 6.75407 | − | 4.15884i | 0.261715 | − | 0.161152i | ||||
\(667\) | −5.50447 | + | 5.50447i | −0.213134 | + | 0.213134i | ||||
\(668\) | −10.9776 | + | 10.9776i | −0.424738 | + | 0.424738i | ||||
\(669\) | −19.8229 | + | 35.4855i | −0.766398 | + | 1.37195i | ||||
\(670\) | −6.11001 | + | 6.28051i | −0.236050 | + | 0.242637i | ||||
\(671\) | 52.1606i | 2.01364i | ||||||||
\(672\) | −2.30242 | − | 8.13040i | −0.0888178 | − | 0.313637i | ||||
\(673\) | −24.3131 | − | 24.3131i | −0.937203 | − | 0.937203i | 0.0609388 | − | 0.998142i | \(-0.480591\pi\) |
−0.998142 | + | 0.0609388i | \(0.980591\pi\) | |||||||
\(674\) | 16.0144 | 0.616851 | ||||||||
\(675\) | −17.0412 | + | 19.6112i | −0.655915 | + | 0.754835i | ||||
\(676\) | 11.4680 | 0.441076 | ||||||||
\(677\) | 32.4421 | + | 32.4421i | 1.24685 | + | 1.24685i | 0.957103 | + | 0.289749i | \(0.0935719\pi\) |
0.289749 | + | 0.957103i | \(0.406428\pi\) | |||||||
\(678\) | 5.76488 | + | 20.3572i | 0.221399 | + | 0.781813i | ||||
\(679\) | − | 23.2238i | − | 0.891249i | ||||||
\(680\) | −2.99244 | + | 3.07594i | −0.114755 | + | 0.117957i | ||||
\(681\) | 5.84317 | − | 10.4600i | 0.223911 | − | 0.400829i | ||||
\(682\) | −15.1750 | + | 15.1750i | −0.581080 | + | 0.581080i | ||||
\(683\) | −30.8958 | + | 30.8958i | −1.18219 | + | 1.18219i | −0.203020 | + | 0.979175i | \(0.565076\pi\) |
−0.979175 | + | 0.203020i | \(0.934924\pi\) | |||||||
\(684\) | −9.74582 | + | 6.00102i | −0.372641 | + | 0.229455i | ||||
\(685\) | 32.9676 | − | 0.453651i | 1.25963 | − | 0.0173331i | ||||
\(686\) | − | 47.8185i | − | 1.82572i | ||||||
\(687\) | −7.32194 | + | 2.07348i | −0.279350 | + | 0.0791081i | ||||
\(688\) | −0.142657 | − | 0.142657i | −0.00543873 | − | 0.00543873i | ||||
\(689\) | −6.34559 | −0.241748 | ||||||||
\(690\) | 3.40686 | + | 1.84210i | 0.129697 | + | 0.0701275i | ||||
\(691\) | −4.89262 | −0.186124 | −0.0930620 | − | 0.995660i | \(-0.529665\pi\) | ||||
−0.0930620 | + | 0.995660i | \(0.529665\pi\) | |||||||
\(692\) | 17.3398 | + | 17.3398i | 0.659159 | + | 0.659159i | ||||
\(693\) | −54.7500 | − | 13.0203i | −2.07978 | − | 0.494599i | ||||
\(694\) | − | 9.15626i | − | 0.347567i | ||||||
\(695\) | 23.4724 | + | 22.8352i | 0.890359 | + | 0.866188i | ||||
\(696\) | −11.7710 | − | 6.57554i | −0.446180 | − | 0.249245i | ||||
\(697\) | −5.83208 | + | 5.83208i | −0.220906 | + | 0.220906i | ||||
\(698\) | −8.10294 | + | 8.10294i | −0.306701 | + | 0.306701i | ||||
\(699\) | −19.1198 | − | 10.6807i | −0.723177 | − | 0.403981i | ||||
\(700\) | −16.7676 | + | 17.7168i | −0.633755 | + | 0.669633i | ||||
\(701\) | − | 12.6440i | − | 0.477556i | −0.971074 | − | 0.238778i | \(-0.923253\pi\) | ||
0.971074 | − | 0.238778i | \(-0.0767468\pi\) | |||||||
\(702\) | −4.35054 | + | 4.73685i | −0.164200 | + | 0.178781i | ||||
\(703\) | −7.13245 | − | 7.13245i | −0.269005 | − | 0.269005i | ||||
\(704\) | −3.84509 | −0.144917 | ||||||||
\(705\) | −5.68298 | − | 19.0634i | −0.214033 | − | 0.717971i | ||||
\(706\) | −20.6539 | −0.777319 | ||||||||
\(707\) | 38.9627 | + | 38.9627i | 1.46534 | + | 1.46534i | ||||
\(708\) | 6.45466 | − | 1.82787i | 0.242581 | − | 0.0686957i | ||||
\(709\) | 18.0882i | 0.679317i | 0.940549 | + | 0.339658i | \(0.110311\pi\) | ||||
−0.940549 | + | 0.339658i | \(0.889689\pi\) | |||||||
\(710\) | 0.189268 | + | 13.7544i | 0.00710309 | + | 0.516194i | ||||
\(711\) | −27.0483 | − | 43.9271i | −1.01439 | − | 1.64740i | ||||
\(712\) | −8.90860 | + | 8.90860i | −0.333864 | + | 0.333864i | ||||
\(713\) | 3.94659 | − | 3.94659i | 0.147801 | − | 0.147801i | ||||
\(714\) | −7.90892 | + | 14.1580i | −0.295984 | + | 0.529849i | ||||
\(715\) | 0.146426 | + | 10.6411i | 0.00547604 | + | 0.397953i | ||||
\(716\) | 1.47094i | 0.0549715i | ||||||||
\(717\) | −3.33731 | − | 11.7849i | −0.124634 | − | 0.440113i | ||||
\(718\) | −2.33713 | − | 2.33713i | −0.0872207 | − | 0.0872207i | ||||
\(719\) | −18.9895 | −0.708188 | −0.354094 | − | 0.935210i | \(-0.615211\pi\) | ||||
−0.354094 | + | 0.935210i | \(0.615211\pi\) | |||||||
\(720\) | −1.46207 | + | 6.54693i | −0.0544882 | + | 0.243990i | ||||
\(721\) | 57.7363 | 2.15021 | ||||||||
\(722\) | −3.14322 | − | 3.14322i | −0.116978 | − | 0.116978i | ||||
\(723\) | −1.99442 | − | 7.04278i | −0.0741733 | − | 0.261924i | ||||
\(724\) | − | 15.6852i | − | 0.582936i | ||||||
\(725\) | 1.07098 | + | 38.9078i | 0.0397753 | + | 1.44500i | ||||
\(726\) | −3.19696 | + | 5.72297i | −0.118650 | + | 0.212399i | ||||
\(727\) | −2.21531 | + | 2.21531i | −0.0821613 | + | 0.0821613i | −0.746993 | − | 0.664832i | \(-0.768503\pi\) |
0.664832 | + | 0.746993i | \(0.268503\pi\) | |||||||
\(728\) | −4.26994 | + | 4.26994i | −0.158254 | + | 0.158254i | ||||
\(729\) | 2.29144 | + | 26.9026i | 0.0848683 | + | 0.996392i | ||||
\(730\) | −21.7774 | − | 21.1862i | −0.806019 | − | 0.784138i | ||||
\(731\) | 0.387187i | 0.0143206i | ||||||||
\(732\) | 22.6071 | − | 6.40203i | 0.835583 | − | 0.236626i | ||||
\(733\) | 23.0122 | + | 23.0122i | 0.849976 | + | 0.849976i | 0.990130 | − | 0.140154i | \(-0.0447597\pi\) |
−0.140154 | + | 0.990130i | \(0.544760\pi\) | |||||||
\(734\) | 17.3823 | 0.641591 | ||||||||
\(735\) | −30.9500 | + | 57.2404i | −1.14161 | + | 2.11134i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 10.6542 | + | 10.6542i | 0.392454 | + | 0.392454i | ||||
\(738\) | −2.98287 | + | 12.5430i | −0.109801 | + | 0.461712i | ||||
\(739\) | 10.0080i | 0.368151i | 0.982912 | + | 0.184076i | \(0.0589291\pi\) | ||||
−0.982912 | + | 0.184076i | \(0.941071\pi\) | |||||||
\(740\) | −5.91145 | + | 0.0813446i | −0.217309 | + | 0.00299029i | ||||
\(741\) | 7.14039 | + | 3.98876i | 0.262309 | + | 0.146531i | ||||
\(742\) | −17.6858 | + | 17.6858i | −0.649267 | + | 0.649267i | ||||
\(743\) | −23.6306 | + | 23.6306i | −0.866922 | + | 0.866922i | −0.992130 | − | 0.125208i | \(-0.960040\pi\) |
0.125208 | + | 0.992130i | \(0.460040\pi\) | |||||||
\(744\) | 8.43958 | + | 4.71452i | 0.309410 | + | 0.172843i | ||||
\(745\) | 1.90193 | − | 1.95500i | 0.0696812 | − | 0.0716257i | ||||
\(746\) | − | 5.96729i | − | 0.218478i | ||||||
\(747\) | 1.96756 | − | 8.27357i | 0.0719893 | − | 0.302714i | ||||
\(748\) | 5.21802 | + | 5.21802i | 0.190790 | + | 0.190790i | ||||
\(749\) | −49.8102 | −1.82002 | ||||||||
\(750\) | 18.3986 | − | 6.04080i | 0.671822 | − | 0.220579i | ||||
\(751\) | 17.4785 | 0.637798 | 0.318899 | − | 0.947789i | \(-0.396687\pi\) | ||||
0.318899 | + | 0.947789i | \(0.396687\pi\) | |||||||
\(752\) | −3.63185 | − | 3.63185i | −0.132440 | − | 0.132440i | ||||
\(753\) | 0.531504 | − | 0.150515i | 0.0193691 | − | 0.00548506i | ||||
\(754\) | 9.63529i | 0.350897i | ||||||||
\(755\) | −10.7912 | + | 11.0923i | −0.392732 | + | 0.403691i | ||||
\(756\) | 1.07669 | + | 25.3275i | 0.0391589 | + | 0.921152i | ||||
\(757\) | 7.37005 | − | 7.37005i | 0.267869 | − | 0.267869i | −0.560372 | − | 0.828241i | \(-0.689342\pi\) |
0.828241 | + | 0.560372i | \(0.189342\pi\) | |||||||
\(758\) | 17.5132 | − | 17.5132i | 0.636107 | − | 0.636107i | ||||
\(759\) | 3.24794 | − | 5.81422i | 0.117893 | − | 0.211043i | ||||
\(760\) | 8.52997 | − | 0.117377i | 0.309414 | − | 0.00425770i | ||||
\(761\) | − | 49.0359i | − | 1.77755i | −0.458345 | − | 0.888774i | \(-0.651558\pi\) | ||
0.458345 | − | 0.888774i | \(-0.348442\pi\) | |||||||
\(762\) | 6.96830 | + | 24.6067i | 0.252435 | + | 0.891408i | ||||
\(763\) | −7.45396 | − | 7.45396i | −0.269851 | − | 0.269851i | ||||
\(764\) | 21.7200 | 0.785800 | ||||||||
\(765\) | 10.8687 | − | 6.90047i | 0.392959 | − | 0.249487i | ||||
\(766\) | −17.3767 | −0.627846 | ||||||||
\(767\) | −3.38987 | − | 3.38987i | −0.122401 | − | 0.122401i | ||||
\(768\) | 0.471935 | + | 1.66652i | 0.0170295 | + | 0.0601352i | ||||
\(769\) | 24.0936i | 0.868838i | 0.900711 | + | 0.434419i | \(0.143046\pi\) | ||||
−0.900711 | + | 0.434419i | \(0.856954\pi\) | |||||||
\(770\) | 30.0659 | + | 29.2496i | 1.08350 | + | 1.05408i | ||||
\(771\) | −11.8161 | + | 21.1522i | −0.425545 | + | 0.761779i | ||||
\(772\) | −17.8302 | + | 17.8302i | −0.641723 | + | 0.641723i | ||||
\(773\) | −12.6293 | + | 12.6293i | −0.454243 | + | 0.454243i | −0.896760 | − | 0.442517i | \(-0.854086\pi\) |
0.442517 | + | 0.896760i | \(0.354086\pi\) | |||||||
\(774\) | 0.317343 | + | 0.515373i | 0.0114066 | + | 0.0185247i | ||||
\(775\) | −0.767872 | − | 27.8960i | −0.0275828 | − | 1.00205i | ||||
\(776\) | 4.76027i | 0.170884i | ||||||||
\(777\) | −21.4962 | + | 6.08744i | −0.771172 | + | 0.218386i | ||||
\(778\) | −10.9518 | − | 10.9518i | −0.392640 | − | 0.392640i | ||||
\(779\) | 16.3956 | 0.587434 | ||||||||
\(780\) | 4.59401 | − | 1.36951i | 0.164492 | − | 0.0490365i | ||||
\(781\) | 23.6540 | 0.846407 | ||||||||
\(782\) | −1.35706 | − | 1.35706i | −0.0485284 | − | 0.0485284i | ||||
\(783\) | 29.7911 | + | 27.3615i | 1.06465 | + | 0.977819i | ||||
\(784\) | 16.8015i | 0.600054i | ||||||||
\(785\) | 0.0727176 | + | 5.28452i | 0.00259540 | + | 0.188612i | ||||
\(786\) | 17.0061 | + | 9.49994i | 0.606587 | + | 0.338852i | ||||
\(787\) | −1.79982 | + | 1.79982i | −0.0641566 | + | 0.0641566i | −0.738457 | − | 0.674300i | \(-0.764445\pi\) |
0.674300 | + | 0.738457i | \(0.264445\pi\) | |||||||
\(788\) | −0.806128 | + | 0.806128i | −0.0287171 | + | 0.0287171i | ||||
\(789\) | −13.3527 | − | 7.45907i | −0.475368 | − | 0.265550i | ||||
\(790\) | 0.529049 | + | 38.4469i | 0.0188227 | + | 1.36788i | ||||
\(791\) | − | 59.5951i | − | 2.11896i | ||||||
\(792\) | 11.2223 | + | 2.66881i | 0.398767 | + | 0.0948320i | ||||
\(793\) | −11.8729 | − | 11.8729i | −0.421617 | − | 0.421617i | ||||
\(794\) | 20.1872 | 0.716415 | ||||||||
\(795\) | 19.0281 | − | 5.67245i | 0.674858 | − | 0.201181i | ||||
\(796\) | 18.0493 | 0.639742 | ||||||||
\(797\) | −30.9163 | − | 30.9163i | −1.09511 | − | 1.09511i | −0.994974 | − | 0.100136i | \(-0.968072\pi\) |
−0.100136 | − | 0.994974i | \(-0.531928\pi\) | |||||||
\(798\) | 31.0181 | − | 8.78391i | 1.09803 | − | 0.310947i | ||||
\(799\) | 9.85729i | 0.348726i | ||||||||
\(800\) | 3.43691 | − | 3.63148i | 0.121513 | − | 0.128392i | ||||
\(801\) | 32.1840 | − | 19.8174i | 1.13716 | − | 0.700213i | ||||
\(802\) | −2.31040 | + | 2.31040i | −0.0815829 | + | 0.0815829i | ||||
\(803\) | −36.9432 | + | 36.9432i | −1.30370 | + | 1.30370i | ||||
\(804\) | 3.31003 | − | 5.92537i | 0.116736 | − | 0.208972i | ||||
\(805\) | −7.81928 | − | 7.60700i | −0.275593 | − | 0.268112i | ||||
\(806\) | − | 6.90829i | − | 0.243334i | ||||||
\(807\) | −5.42598 | − | 19.1604i | −0.191003 | − | 0.674479i | ||||
\(808\) | −7.98633 | − | 7.98633i | −0.280958 | − | 0.280958i | ||||
\(809\) | 48.5806 | 1.70800 | 0.854001 | − | 0.520272i | \(-0.174169\pi\) | ||||
0.854001 | + | 0.520272i | \(0.174169\pi\) | |||||||
\(810\) | 8.81131 | − | 18.0931i | 0.309598 | − | 0.635727i | ||||
\(811\) | 12.0582 | 0.423419 | 0.211710 | − | 0.977333i | \(-0.432097\pi\) | ||||
0.211710 | + | 0.977333i | \(0.432097\pi\) | |||||||
\(812\) | 26.8546 | + | 26.8546i | 0.942410 | + | 0.942410i | ||||
\(813\) | 6.80194 | + | 24.0193i | 0.238554 | + | 0.842393i | ||||
\(814\) | 10.1662i | 0.356324i | ||||||||
\(815\) | −29.3960 | + | 0.404503i | −1.02970 | + | 0.0141691i | ||||
\(816\) | 1.62112 | − | 2.90201i | 0.0567505 | − | 0.101591i | ||||
\(817\) | 0.544246 | − | 0.544246i | 0.0190407 | − | 0.0190407i | ||||
\(818\) | 23.8751 | − | 23.8751i | 0.834772 | − | 0.834772i | ||||
\(819\) | 15.4259 | − | 9.49857i | 0.539026 | − | 0.331907i | ||||
\(820\) | 6.70094 | − | 6.88793i | 0.234007 | − | 0.240537i | ||||
\(821\) | 4.47010i | 0.156008i | 0.996953 | + | 0.0780038i | \(0.0248546\pi\) | ||||
−0.996953 | + | 0.0780038i | \(0.975145\pi\) | |||||||
\(822\) | −24.5727 | + | 6.95867i | −0.857072 | + | 0.242711i | ||||
\(823\) | −12.8565 | − | 12.8565i | −0.448148 | − | 0.448148i | 0.446590 | − | 0.894739i | \(-0.352638\pi\) |
−0.894739 | + | 0.446590i | \(0.852638\pi\) | |||||||
\(824\) | −11.8344 | −0.412271 | ||||||||
\(825\) | −9.95133 | − | 31.7778i | −0.346461 | − | 1.10636i | ||||
\(826\) | −18.8958 | −0.657470 | ||||||||
\(827\) | 19.8305 | + | 19.8305i | 0.689573 | + | 0.689573i | 0.962138 | − | 0.272564i | \(-0.0878717\pi\) |
−0.272564 | + | 0.962138i | \(0.587872\pi\) | |||||||
\(828\) | −2.91860 | − | 0.694081i | −0.101429 | − | 0.0241210i | ||||
\(829\) | − | 32.9160i | − | 1.14322i | −0.820526 | − | 0.571610i | \(-0.806319\pi\) | ||
0.820526 | − | 0.571610i | \(-0.193681\pi\) | |||||||
\(830\) | −4.42007 | + | 4.54341i | −0.153423 | + | 0.157704i | ||||
\(831\) | −46.7007 | − | 26.0879i | −1.62003 | − | 0.904981i | ||||
\(832\) | 0.875224 | − | 0.875224i | 0.0303429 | − | 0.0303429i | ||||
\(833\) | 22.8007 | − | 22.8007i | 0.789996 | − | 0.789996i | ||||
\(834\) | −22.1451 | − | 12.3707i | −0.766822 | − | 0.428362i | ||||
\(835\) | −34.7110 | + | 0.477642i | −1.20123 | + | 0.0165295i | ||||
\(836\) | − | 14.6693i | − | 0.507349i | ||||||
\(837\) | −21.3595 | − | 19.6176i | −0.738294 | − | 0.678082i | ||||
\(838\) | −14.5892 | − | 14.5892i | −0.503977 | − | 0.503977i | ||||
\(839\) | −36.9410 | −1.27535 | −0.637673 | − | 0.770307i | \(-0.720103\pi\) | ||||
−0.637673 | + | 0.770307i | \(0.720103\pi\) | |||||||
\(840\) | 8.98701 | − | 16.6210i | 0.310081 | − | 0.573478i | ||||
\(841\) | 31.5984 | 1.08960 | ||||||||
\(842\) | 23.9342 | + | 23.9342i | 0.824828 | + | 0.824828i | ||||
\(843\) | −54.2729 | + | 15.3694i | −1.86926 | + | 0.529349i | ||||
\(844\) | 7.95847i | 0.273942i | ||||||||
\(845\) | 18.3802 | + | 17.8812i | 0.632299 | + | 0.615133i | ||||
\(846\) | 8.07914 | + | 13.1207i | 0.277767 | + | 0.451101i | ||||
\(847\) | 13.0564 | − | 13.0564i | 0.448624 | − | 0.448624i | ||||
\(848\) | 3.62512 | − | 3.62512i | 0.124487 | − | 0.124487i | ||||
\(849\) | 21.6891 | − | 38.8262i | 0.744367 | − | 1.33251i | ||||
\(850\) | −9.59223 | + | 0.264038i | −0.329011 | + | 0.00905643i | ||||
\(851\) | − | 2.64393i | − | 0.0906328i | ||||||
\(852\) | −2.90322 | − | 10.2520i | −0.0994627 | − | 0.351227i | ||||
\(853\) | 1.30323 | + | 1.30323i | 0.0446219 | + | 0.0446219i | 0.729066 | − | 0.684444i | \(-0.239955\pi\) |
−0.684444 | + | 0.729066i | \(0.739955\pi\) | |||||||
\(854\) | −66.1817 | −2.26469 | ||||||||
\(855\) | −24.9771 | − | 5.57792i | −0.854198 | − | 0.190761i | ||||
\(856\) | 10.2098 | 0.348963 | ||||||||
\(857\) | −27.5259 | − | 27.5259i | −0.940268 | − | 0.940268i | 0.0580457 | − | 0.998314i | \(-0.481513\pi\) |
−0.998314 | + | 0.0580457i | \(0.981513\pi\) | |||||||
\(858\) | −2.24607 | − | 7.93142i | −0.0766796 | − | 0.270774i | ||||
\(859\) | − | 11.6992i | − | 0.399172i | −0.979880 | − | 0.199586i | \(-0.936040\pi\) | ||
0.979880 | − | 0.199586i | \(-0.0639597\pi\) | |||||||
\(860\) | −0.00620705 | − | 0.451077i | −0.000211659 | − | 0.0153816i | ||||
\(861\) | 17.7104 | − | 31.7038i | 0.603568 | − | 1.08046i | ||||
\(862\) | 8.46577 | − | 8.46577i | 0.288345 | − | 0.288345i | ||||
\(863\) | 25.3452 | − | 25.3452i | 0.862762 | − | 0.862762i | −0.128896 | − | 0.991658i | \(-0.541143\pi\) |
0.991658 | + | 0.128896i | \(0.0411435\pi\) | |||||||
\(864\) | −0.220693 | − | 5.19146i | −0.00750814 | − | 0.176617i | ||||
\(865\) | 0.754461 | + | 54.8280i | 0.0256524 | + | 1.86421i | ||||
\(866\) | − | 19.2945i | − | 0.655655i | ||||||
\(867\) | 22.1926 | − | 6.28465i | 0.753701 | − | 0.213438i | ||||
\(868\) | −19.2541 | − | 19.2541i | −0.653528 | − | 0.653528i | ||||
\(869\) | 66.1187 | 2.24292 | ||||||||
\(870\) | −8.61317 | − | 28.8927i | −0.292014 | − | 0.979555i | ||||
\(871\) | −4.85026 | −0.164345 | ||||||||
\(872\) | 1.52786 | + | 1.52786i | 0.0517400 | + | 0.0517400i | ||||
\(873\) | 3.30402 | − | 13.8933i | 0.111824 | − | 0.470219i | ||||
\(874\) | 3.81508i | 0.129047i | ||||||||
\(875\) | −54.4988 | + | 2.25093i | −1.84240 | + | 0.0760954i | ||||
\(876\) | 20.5460 | + | 11.4774i | 0.694184 | + | 0.387785i | ||||
\(877\) | −5.23787 | + | 5.23787i | −0.176870 | + | 0.176870i | −0.789990 | − | 0.613120i | \(-0.789914\pi\) |
0.613120 | + | 0.789990i | \(0.289914\pi\) | |||||||
\(878\) | 8.80083 | − | 8.80083i | 0.297014 | − | 0.297014i | ||||
\(879\) | −21.0327 | − | 11.7493i | −0.709414 | − | 0.396293i | ||||
\(880\) | −6.16270 | − | 5.99540i | −0.207745 | − | 0.202105i | ||||
\(881\) | 50.3328i | 1.69575i | 0.530193 | + | 0.847877i | \(0.322120\pi\) | ||||
−0.530193 | + | 0.847877i | \(0.677880\pi\) | |||||||
\(882\) | 11.6616 | − | 49.0370i | 0.392667 | − | 1.65116i | ||||
\(883\) | 22.4165 | + | 22.4165i | 0.754377 | + | 0.754377i | 0.975293 | − | 0.220916i | \(-0.0709047\pi\) |
−0.220916 | + | 0.975293i | \(0.570905\pi\) | |||||||
\(884\) | −2.37546 | −0.0798955 | ||||||||
\(885\) | 13.1953 | + | 7.13472i | 0.443554 | + | 0.239831i | ||||
\(886\) | 11.6492 | 0.391362 | ||||||||
\(887\) | 7.53529 | + | 7.53529i | 0.253010 | + | 0.253010i | 0.822204 | − | 0.569193i | \(-0.192744\pi\) |
−0.569193 | + | 0.822204i | \(0.692744\pi\) | |||||||
\(888\) | 4.40615 | − | 1.24776i | 0.147861 | − | 0.0418722i | ||||
\(889\) | − | 72.0356i | − | 2.41599i | ||||||
\(890\) | −28.1688 | + | 0.387617i | −0.944220 | + | 0.0129929i | ||||
\(891\) | −30.9011 | − | 15.5784i | −1.03523 | − | 0.521896i | ||||
\(892\) | −16.5940 | + | 16.5940i | −0.555609 | + | 0.555609i | ||||
\(893\) | 13.8558 | − | 13.8558i | 0.463667 | − | 0.463667i | ||||
\(894\) | −1.03035 | + | 1.84445i | −0.0344599 | + | 0.0616876i | ||||
\(895\) | −2.29354 | + | 2.35754i | −0.0766644 | + | 0.0788038i | ||||
\(896\) | − | 4.87868i | − | 0.162985i | ||||||
\(897\) | 0.584139 | + | 2.06274i | 0.0195038 | + | 0.0688728i | ||||
\(898\) | −11.6471 | − | 11.6471i | −0.388670 | − | 0.388670i | ||||
\(899\) | −43.4477 | −1.44906 | ||||||||
\(900\) | −12.5515 | + | 8.21335i | −0.418384 | + | 0.273778i | ||||
\(901\) | −9.83902 | −0.327785 | ||||||||
\(902\) | −11.6847 | − | 11.6847i | −0.389057 | − | 0.389057i | ||||
\(903\) | −0.464506 | − | 1.64028i | −0.0154578 | − | 0.0545852i | ||||
\(904\) | 12.2154i | 0.406279i | ||||||||
\(905\) | 24.4569 | − | 25.1394i | 0.812975 | − | 0.835661i | ||||
\(906\) | 5.84601 | − | 10.4651i | 0.194221 | − | 0.347679i | ||||
\(907\) | 30.7230 | − | 30.7230i | 1.02014 | − | 1.02014i | 0.0203465 | − | 0.999793i | \(-0.493523\pi\) |
0.999793 | − | 0.0203465i | \(-0.00647695\pi\) | |||||||
\(908\) | 4.89140 | − | 4.89140i | 0.162327 | − | 0.162327i | ||||
\(909\) | 17.7658 | + | 28.8521i | 0.589253 | + | 0.956963i | ||||
\(910\) | −13.5015 | + | 0.185787i | −0.447569 | + | 0.00615877i | ||||
\(911\) | − | 22.0603i | − | 0.730892i | −0.930833 | − | 0.365446i | \(-0.880917\pi\) | ||
0.930833 | − | 0.365446i | \(-0.119083\pi\) | |||||||
\(912\) | −6.35789 | + | 1.80047i | −0.210531 | + | 0.0596195i | ||||
\(913\) | 7.70743 | + | 7.70743i | 0.255079 | + | 0.255079i | ||||
\(914\) | 12.1729 | 0.402643 | ||||||||
\(915\) | 46.2157 | + | 24.9890i | 1.52784 | + | 0.826110i | ||||
\(916\) | −4.39356 | −0.145167 | ||||||||
\(917\) | −38.7978 | − | 38.7978i | −1.28122 | − | 1.28122i | ||||
\(918\) | −6.74564 | + | 7.34462i | −0.222639 | + | 0.242409i | ||||
\(919\) | 3.88895i | 0.128285i | 0.997941 | + | 0.0641423i | \(0.0204312\pi\) | ||||
−0.997941 | + | 0.0641423i | \(0.979569\pi\) | |||||||
\(920\) | 1.60274 | + | 1.55923i | 0.0528409 | + | 0.0514064i | ||||
\(921\) | −35.8577 | − | 20.0308i | −1.18155 | − | 0.660038i | ||||
\(922\) | 26.7220 | − | 26.7220i | 0.880041 | − | 0.880041i | ||||
\(923\) | −5.38415 | + | 5.38415i | −0.177221 | + | 0.177221i | ||||
\(924\) | −28.3657 | − | 15.8456i | −0.933163 | − | 0.521284i | ||||
\(925\) | −9.60138 | − | 9.08696i | −0.315691 | − | 0.298777i | ||||
\(926\) | 10.8106i | 0.355258i | ||||||||
\(927\) | 34.5399 | + | 8.21404i | 1.13444 | + | 0.269784i | ||||
\(928\) | −5.50447 | − | 5.50447i | −0.180693 | − | 0.180693i | ||||
\(929\) | 23.5939 | 0.774091 | 0.387045 | − | 0.922061i | \(-0.373496\pi\) | ||||
0.387045 | + | 0.922061i | \(0.373496\pi\) | |||||||
\(930\) | 6.17546 | + | 20.7154i | 0.202501 | + | 0.679286i | ||||
\(931\) | −64.0991 | −2.10076 | ||||||||
\(932\) | −8.94095 | − | 8.94095i | −0.292870 | − | 0.292870i | ||||
\(933\) | −10.6133 | + | 3.00555i | −0.347465 | + | 0.0983973i | ||||
\(934\) | − | 7.41233i | − | 0.242539i | ||||||
\(935\) | 0.227038 | + | 16.4993i | 0.00742495 | + | 0.539584i | ||||
\(936\) | −3.16191 | + | 1.94696i | −0.103350 | + | 0.0636382i | ||||
\(937\) | 13.8791 | − | 13.8791i | 0.453411 | − | 0.453411i | −0.443074 | − | 0.896485i | \(-0.646112\pi\) |
0.896485 | + | 0.443074i | \(0.146112\pi\) | |||||||
\(938\) | −13.5182 | + | 13.5182i | −0.441384 | + | 0.441384i | ||||
\(939\) | 20.1197 | − | 36.0168i | 0.656582 | − | 1.17536i | ||||
\(940\) | −0.158024 | − | 11.4838i | −0.00515416 | − | 0.374562i | ||||
\(941\) | − | 28.8322i | − | 0.939903i | −0.882692 | − | 0.469952i | \(-0.844271\pi\) | ||
0.882692 | − | 0.469952i | \(-0.155729\pi\) | |||||||
\(942\) | −1.11543 | − | 3.93886i | −0.0363428 | − | 0.128335i | ||||
\(943\) | 3.03885 | + | 3.03885i | 0.0989586 | + | 0.0989586i | ||||
\(944\) | 3.87315 | 0.126060 | ||||||||
\(945\) | −37.7658 | + | 42.2723i | −1.22852 | + | 1.37512i | ||||
\(946\) | −0.775735 | −0.0252213 | ||||||||
\(947\) | 18.6992 | + | 18.6992i | 0.607644 | + | 0.607644i | 0.942330 | − | 0.334686i | \(-0.108630\pi\) |
−0.334686 | + | 0.942330i | \(0.608630\pi\) | |||||||
\(948\) | −8.11521 | − | 28.6568i | −0.263570 | − | 0.930729i | ||||
\(949\) | − | 16.8181i | − | 0.545938i | ||||||
\(950\) | 13.8544 | + | 13.1121i | 0.449495 | + | 0.425412i | ||||
\(951\) | 21.2728 | − | 38.0811i | 0.689819 | − | 1.23486i | ||||
\(952\) | −6.62066 | + | 6.62066i | −0.214577 | + | 0.214577i | ||||
\(953\) | 20.6730 | − | 20.6730i | 0.669664 | − | 0.669664i | −0.287974 | − | 0.957638i | \(-0.592982\pi\) |
0.957638 | + | 0.287974i | \(0.0929816\pi\) | |||||||
\(954\) | −13.0964 | + | 8.06417i | −0.424013 | + | 0.261087i | ||||
\(955\) | 34.8115 | + | 33.8665i | 1.12647 | + | 1.09589i | ||||
\(956\) | − | 7.07155i | − | 0.228710i | ||||||
\(957\) | −49.8824 | + | 14.1260i | −1.61247 | + | 0.456629i | ||||
\(958\) | −18.8121 | − | 18.8121i | −0.607790 | − | 0.607790i | ||||
\(959\) | 71.9360 | 2.32293 | ||||||||
\(960\) | −1.84210 | + | 3.40686i | −0.0594535 | + | 0.109956i | ||||
\(961\) | 0.151067 | 0.00487312 | ||||||||
\(962\) | −2.31403 | − | 2.31403i | −0.0746074 | − | 0.0746074i | ||||
\(963\) | −29.7983 | − | 7.08641i | −0.960236 | − | 0.228356i | ||||
\(964\) | − | 4.22605i | − | 0.136112i | ||||||
\(965\) | −56.3787 | + | 0.775799i | −1.81489 | + | 0.0249739i | ||||
\(966\) | 7.37712 | + | 4.12100i | 0.237355 | + | 0.132591i | ||||
\(967\) | −10.4942 | + | 10.4942i | −0.337471 | + | 0.337471i | −0.855415 | − | 0.517944i | \(-0.826698\pi\) |
0.517944 | + | 0.855415i | \(0.326698\pi\) | |||||||
\(968\) | −2.67622 | + | 2.67622i | −0.0860170 | + | 0.0860170i | ||||
\(969\) | 11.0714 | + | 6.18470i | 0.355664 | + | 0.198681i | ||||
\(970\) | −7.42238 | + | 7.62950i | −0.238318 | + | 0.244968i | ||||
\(971\) | − | 3.41196i | − | 0.109495i | −0.998500 | − | 0.0547475i | \(-0.982565\pi\) | ||
0.998500 | − | 0.0547475i | \(-0.0174354\pi\) | |||||||
\(972\) | −2.95918 | + | 15.3050i | −0.0949158 | + | 0.490908i | ||||
\(973\) | 50.5220 | + | 50.5220i | 1.61966 | + | 1.61966i | ||||
\(974\) | 7.93776 | 0.254342 | ||||||||
\(975\) | 9.49842 | + | 4.96816i | 0.304193 | + | 0.159108i | ||||
\(976\) | 13.5655 | 0.434221 | ||||||||
\(977\) | 2.16215 | + | 2.16215i | 0.0691735 | + | 0.0691735i | 0.740847 | − | 0.671674i | \(-0.234424\pi\) |
−0.671674 | + | 0.740847i | \(0.734424\pi\) | |||||||
\(978\) | 21.9105 | − | 6.20477i | 0.700622 | − | 0.198407i | ||||
\(979\) | 48.4430i | 1.54825i | ||||||||
\(980\) | −26.1975 | + | 26.9285i | −0.836848 | + | 0.860200i | ||||
\(981\) | −3.39877 | − | 5.51969i | −0.108514 | − | 0.176230i | ||||
\(982\) | −24.8380 | + | 24.8380i | −0.792614 | + | 0.792614i | ||||
\(983\) | 15.0702 | − | 15.0702i | 0.480665 | − | 0.480665i | −0.424679 | − | 0.905344i | \(-0.639613\pi\) |
0.905344 | + | 0.424679i | \(0.139613\pi\) | |||||||
\(984\) | −3.63016 | + | 6.49844i | −0.115725 | + | 0.207163i | ||||
\(985\) | −2.54896 | + | 0.0350750i | −0.0812166 | + | 0.00111758i | ||||
\(986\) | 14.9398i | 0.475780i | ||||||||
\(987\) | −11.8257 | − | 41.7595i | −0.376417 | − | 1.32922i | ||||
\(988\) | 3.33905 | + | 3.33905i | 0.106229 | + | 0.106229i | ||||
\(989\) | 0.201747 | 0.00641517 | ||||||||
\(990\) | 13.8252 | + | 21.7756i | 0.439393 | + | 0.692075i | ||||
\(991\) | −38.6581 | −1.22802 | −0.614008 | − | 0.789300i | \(-0.710444\pi\) | ||||
−0.614008 | + | 0.789300i | \(0.710444\pi\) | |||||||
\(992\) | 3.94659 | + | 3.94659i | 0.125304 | + | 0.125304i | ||||
\(993\) | −2.72109 | − | 9.60883i | −0.0863512 | − | 0.304927i | ||||
\(994\) | 30.0124i | 0.951934i | ||||||||
\(995\) | 28.9285 | + | 28.1431i | 0.917094 | + | 0.892197i | ||||
\(996\) | 2.39452 | − | 4.28649i | 0.0758733 | − | 0.135823i | ||||
\(997\) | 9.32310 | − | 9.32310i | 0.295266 | − | 0.295266i | −0.543891 | − | 0.839156i | \(-0.683049\pi\) |
0.839156 | + | 0.543891i | \(0.183049\pi\) | |||||||
\(998\) | −7.08939 | + | 7.08939i | −0.224411 | + | 0.224411i | ||||
\(999\) | −13.7259 | + | 0.583498i | −0.434267 | + | 0.0184611i |
(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 | 690.2.i.e.323.5 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.e.323.16 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.e.47.16 | yes | 32 | |
15.2 | even | 4 | inner | 690.2.i.e.47.5 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.e.47.5 | ✓ | 32 | 15.2 | even | 4 | inner | |
690.2.i.e.47.16 | yes | 32 | 5.2 | odd | 4 | inner | |
690.2.i.e.323.5 | yes | 32 | 1.1 | even | 1 | trivial | |
690.2.i.e.323.16 | yes | 32 | 3.2 | odd | 2 | inner |