Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1530,2,Mod(647,1530)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1530, 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("1530.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1530.m (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: | \(12.2171115093\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.1573541673494879666176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{16} - 4 x^{15} - 2 x^{14} + 24 x^{13} + 2 x^{12} - 48 x^{11} + 88 x^{10} - 72 x^{9} + 18 x^{8} + \cdots + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 647.4 | ||
Root | \(1.29693 + 0.537207i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1530.647 |
Dual form | 1530.2.m.i.953.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times\).
\(n\) | \(307\) | \(1261\) | \(1361\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 2.23580 | + | 0.0345211i | 0.999881 | + | 0.0154383i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.796815 | + | 0.796815i | 0.301168 | + | 0.301168i | 0.841471 | − | 0.540303i | \(-0.181690\pi\) |
−0.540303 | + | 0.841471i | \(0.681690\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.60536 | + | 1.55654i | −0.507660 | + | 0.492221i | ||||
\(11\) | − | 2.14883i | − | 0.647896i | −0.946075 | − | 0.323948i | \(-0.894990\pi\) | ||
0.946075 | − | 0.323948i | \(-0.105010\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.95872 | − | 3.95872i | 1.09795 | − | 1.09795i | 0.103300 | − | 0.994650i | \(-0.467060\pi\) |
0.994650 | − | 0.103300i | \(-0.0329402\pi\) | |||||||
\(14\) | −1.12687 | −0.301168 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.707107 | + | 0.707107i | −0.171499 | + | 0.171499i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.73017i | − | 1.08518i | −0.839999 | − | 0.542588i | \(-0.817445\pi\) | ||
0.839999 | − | 0.542588i | \(-0.182555\pi\) | |||||||
\(20\) | 0.0345211 | − | 2.23580i | 0.00771915 | − | 0.499940i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.51945 | + | 1.51945i | 0.323948 | + | 0.323948i | ||||
\(23\) | −5.76432 | − | 5.76432i | −1.20194 | − | 1.20194i | −0.973575 | − | 0.228370i | \(-0.926661\pi\) |
−0.228370 | − | 0.973575i | \(-0.573339\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99762 | + | 0.154365i | 0.999523 | + | 0.0308729i | ||||
\(26\) | 5.59847i | 1.09795i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.796815 | − | 0.796815i | 0.150584 | − | 0.150584i | ||||
\(29\) | 6.62043 | 1.22938 | 0.614692 | − | 0.788768i | \(-0.289281\pi\) | ||||
0.614692 | + | 0.788768i | \(0.289281\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.21072 | −0.217452 | −0.108726 | − | 0.994072i | \(-0.534677\pi\) | ||||
−0.108726 | + | 0.994072i | \(0.534677\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.00000i | − | 0.171499i | ||||||
\(35\) | 1.75401 | + | 1.80903i | 0.296482 | + | 0.305781i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.37262 | − | 8.37262i | −1.37645 | − | 1.37645i | −0.850540 | − | 0.525911i | \(-0.823725\pi\) |
−0.525911 | − | 0.850540i | \(-0.676275\pi\) | |||||||
\(38\) | 3.34474 | + | 3.34474i | 0.542588 | + | 0.542588i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.55654 | + | 1.60536i | 0.246111 | + | 0.253830i | ||||
\(41\) | 9.89612i | 1.54551i | 0.634701 | + | 0.772757i | \(0.281123\pi\) | ||||
−0.634701 | + | 0.772757i | \(0.718877\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.47817 | − | 2.47817i | 0.377917 | − | 0.377917i | −0.492433 | − | 0.870350i | \(-0.663892\pi\) |
0.870350 | + | 0.492433i | \(0.163892\pi\) | |||||||
\(44\) | −2.14883 | −0.323948 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.15198 | 1.20194 | ||||||||
\(47\) | −8.42690 | + | 8.42690i | −1.22919 | + | 1.22919i | −0.264918 | + | 0.964271i | \(0.585345\pi\) |
−0.964271 | + | 0.264918i | \(0.914655\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.73017i | − | 0.818596i | ||||||
\(50\) | −3.64300 | + | 3.42470i | −0.515198 | + | 0.484325i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.95872 | − | 3.95872i | −0.548975 | − | 0.548975i | ||||
\(53\) | −0.461295 | − | 0.461295i | −0.0633638 | − | 0.0633638i | 0.674715 | − | 0.738079i | \(-0.264267\pi\) |
−0.738079 | + | 0.674715i | \(0.764267\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0741799 | − | 4.80435i | 0.0100024 | − | 0.647819i | ||||
\(56\) | 1.12687i | 0.150584i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.68135 | + | 4.68135i | −0.614692 | + | 0.614692i | ||||
\(59\) | −4.07935 | −0.531086 | −0.265543 | − | 0.964099i | \(-0.585551\pi\) | ||||
−0.265543 | + | 0.964099i | \(0.585551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.7456 | 1.50387 | 0.751936 | − | 0.659236i | \(-0.229120\pi\) | ||||
0.751936 | + | 0.659236i | \(0.229120\pi\) | |||||||
\(62\) | 0.856109 | − | 0.856109i | 0.108726 | − | 0.108726i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 8.98756 | − | 8.71424i | 1.11477 | − | 1.08087i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.22854 | + | 2.22854i | 0.272260 | + | 0.272260i | 0.830009 | − | 0.557749i | \(-0.188335\pi\) |
−0.557749 | + | 0.830009i | \(0.688335\pi\) | |||||||
\(68\) | 0.707107 | + | 0.707107i | 0.0857493 | + | 0.0857493i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.51945 | − | 0.0389007i | −0.301132 | − | 0.00464952i | ||||
\(71\) | − | 3.51868i | − | 0.417591i | −0.977959 | − | 0.208796i | \(-0.933046\pi\) | ||
0.977959 | − | 0.208796i | \(-0.0669543\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.15436 | + | 3.15436i | −0.369190 | + | 0.369190i | −0.867182 | − | 0.497991i | \(-0.834071\pi\) |
0.497991 | + | 0.867182i | \(0.334071\pi\) | |||||||
\(74\) | 11.8407 | 1.37645 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.73017 | −0.542588 | ||||||||
\(77\) | 1.71222 | − | 1.71222i | 0.195125 | − | 0.195125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 16.2647i | − | 1.82992i | −0.403543 | − | 0.914961i | \(-0.632222\pi\) | ||
0.403543 | − | 0.914961i | \(-0.367778\pi\) | |||||||
\(80\) | −2.23580 | − | 0.0345211i | −0.249970 | − | 0.00385958i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.99762 | − | 6.99762i | −0.772757 | − | 0.772757i | ||||
\(83\) | 11.0370 | + | 11.0370i | 1.21147 | + | 1.21147i | 0.970543 | + | 0.240927i | \(0.0774514\pi\) |
0.240927 | + | 0.970543i | \(0.422549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.60536 | + | 1.55654i | −0.174126 | + | 0.168830i | ||||
\(86\) | 3.50466i | 0.377917i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.51945 | − | 1.51945i | 0.161974 | − | 0.161974i | ||||
\(89\) | −10.8272 | −1.14768 | −0.573841 | − | 0.818967i | \(-0.694547\pi\) | ||||
−0.573841 | + | 0.818967i | \(0.694547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.30873 | 0.661335 | ||||||||
\(92\) | −5.76432 | + | 5.76432i | −0.600972 | + | 0.600972i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 11.9174i | − | 1.22919i | ||||||
\(95\) | 0.163291 | − | 10.5757i | 0.0167533 | − | 1.08505i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.47817 | + | 1.47817i | 0.150085 | + | 0.150085i | 0.778156 | − | 0.628071i | \(-0.216155\pi\) |
−0.628071 | + | 0.778156i | \(0.716155\pi\) | |||||||
\(98\) | 4.05184 | + | 4.05184i | 0.409298 | + | 0.409298i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.154365 | − | 4.99762i | 0.0154365 | − | 0.499762i | ||||
\(101\) | − | 4.02434i | − | 0.400436i | −0.979751 | − | 0.200218i | \(-0.935835\pi\) | ||
0.979751 | − | 0.200218i | \(-0.0641651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.24962 | + | 6.24962i | −0.615794 | + | 0.615794i | −0.944450 | − | 0.328656i | \(-0.893404\pi\) |
0.328656 | + | 0.944450i | \(0.393404\pi\) | |||||||
\(104\) | 5.59847 | 0.548975 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.652370 | 0.0633638 | ||||||||
\(107\) | 11.3654 | − | 11.3654i | 1.09873 | − | 1.09873i | 0.104171 | − | 0.994559i | \(-0.466781\pi\) |
0.994559 | − | 0.104171i | \(-0.0332188\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.10831i | 0.872418i | 0.899845 | + | 0.436209i | \(0.143679\pi\) | ||||
−0.899845 | + | 0.436209i | \(0.856321\pi\) | |||||||
\(110\) | 3.34474 | + | 3.44964i | 0.318908 | + | 0.328911i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.796815 | − | 0.796815i | −0.0752920 | − | 0.0752920i | ||||
\(113\) | 5.30047 | + | 5.30047i | 0.498626 | + | 0.498626i | 0.911010 | − | 0.412384i | \(-0.135304\pi\) |
−0.412384 | + | 0.911010i | \(0.635304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6889 | − | 13.0869i | −1.18324 | − | 1.22036i | ||||
\(116\) | − | 6.62043i | − | 0.614692i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.88454 | − | 2.88454i | 0.265543 | − | 0.265543i | ||||
\(119\) | −1.12687 | −0.103300 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.38254 | 0.580231 | ||||||||
\(122\) | −8.30540 | + | 8.30540i | −0.751936 | + | 0.751936i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.21072i | 0.108726i | ||||||||
\(125\) | 11.1683 | + | 0.517652i | 0.998928 | + | 0.0463002i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.4170 | + | 13.4170i | 1.19057 | + | 1.19057i | 0.976908 | + | 0.213663i | \(0.0685393\pi\) |
0.213663 | + | 0.976908i | \(0.431461\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.193265 | + | 12.5171i | −0.0169505 | + | 1.09782i | ||||
\(131\) | − | 19.1126i | − | 1.66988i | −0.550341 | − | 0.834940i | \(-0.685502\pi\) | ||
0.550341 | − | 0.834940i | \(-0.314498\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.76907 | − | 3.76907i | 0.326820 | − | 0.326820i | ||||
\(134\) | −3.15164 | −0.272260 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −8.18391 | + | 8.18391i | −0.699198 | + | 0.699198i | −0.964238 | − | 0.265039i | \(-0.914615\pi\) |
0.265039 | + | 0.964238i | \(0.414615\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.95633i | 0.590028i | 0.955493 | + | 0.295014i | \(0.0953244\pi\) | ||||
−0.955493 | + | 0.295014i | \(0.904676\pi\) | |||||||
\(140\) | 1.80903 | − | 1.75401i | 0.152891 | − | 0.148241i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.48809 | + | 2.48809i | 0.208796 | + | 0.208796i | ||||
\(143\) | −8.50660 | − | 8.50660i | −0.711357 | − | 0.711357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.8020 | + | 0.228545i | 1.22924 | + | 0.0189796i | ||||
\(146\) | − | 4.46095i | − | 0.369190i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.37262 | + | 8.37262i | −0.688225 | + | 0.688225i | ||||
\(149\) | 12.0450 | 0.986761 | 0.493380 | − | 0.869814i | \(-0.335761\pi\) | ||||
0.493380 | + | 0.869814i | \(0.335761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9174 | 0.969827 | 0.484913 | − | 0.874562i | \(-0.338851\pi\) | ||||
0.484913 | + | 0.874562i | \(0.338851\pi\) | |||||||
\(152\) | 3.34474 | − | 3.34474i | 0.271294 | − | 0.271294i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.42144i | 0.195125i | ||||||||
\(155\) | −2.70693 | − | 0.0417954i | −0.217426 | − | 0.00335709i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.09526 | + | 5.09526i | 0.406646 | + | 0.406646i | 0.880567 | − | 0.473921i | \(-0.157162\pi\) |
−0.473921 | + | 0.880567i | \(0.657162\pi\) | |||||||
\(158\) | 11.5009 | + | 11.5009i | 0.914961 | + | 0.914961i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.60536 | − | 1.55654i | 0.126915 | − | 0.123055i | ||||
\(161\) | − | 9.18620i | − | 0.723974i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.6476 | − | 10.6476i | 0.833985 | − | 0.833985i | −0.154075 | − | 0.988059i | \(-0.549240\pi\) |
0.988059 | + | 0.154075i | \(0.0492396\pi\) | |||||||
\(164\) | 9.89612 | 0.772757 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.6087 | −1.21147 | ||||||||
\(167\) | −8.28357 | + | 8.28357i | −0.641002 | + | 0.641002i | −0.950802 | − | 0.309800i | \(-0.899738\pi\) |
0.309800 | + | 0.950802i | \(0.399738\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 18.3429i | − | 1.41099i | ||||||
\(170\) | 0.0345211 | − | 2.23580i | 0.00264765 | − | 0.171478i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.47817 | − | 2.47817i | −0.188958 | − | 0.188958i | ||||
\(173\) | 8.92662 | + | 8.92662i | 0.678678 | + | 0.678678i | 0.959701 | − | 0.281023i | \(-0.0906737\pi\) |
−0.281023 | + | 0.959701i | \(0.590674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.85918 | + | 4.10518i | 0.291726 | + | 0.310322i | ||||
\(176\) | 2.14883i | 0.161974i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.65599 | − | 7.65599i | 0.573841 | − | 0.573841i | ||||
\(179\) | 16.9885 | 1.26978 | 0.634890 | − | 0.772602i | \(-0.281045\pi\) | ||||
0.634890 | + | 0.772602i | \(0.281045\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.2258 | 0.834407 | 0.417203 | − | 0.908813i | \(-0.363010\pi\) | ||||
0.417203 | + | 0.908813i | \(0.363010\pi\) | |||||||
\(182\) | −4.46095 | + | 4.46095i | −0.330667 | + | 0.330667i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 8.15198i | − | 0.600972i | ||||||
\(185\) | −18.4305 | − | 19.0086i | −1.35504 | − | 1.39754i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.51945 | + | 1.51945i | 0.111113 | + | 0.111113i | ||||
\(188\) | 8.42690 | + | 8.42690i | 0.614595 | + | 0.614595i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.36270 | + | 7.59363i | 0.534147 | + | 0.550900i | ||||
\(191\) | 4.43574i | 0.320959i | 0.987039 | + | 0.160479i | \(0.0513040\pi\) | ||||
−0.987039 | + | 0.160479i | \(0.948696\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0869 | + | 19.0869i | −1.37390 | + | 1.37390i | −0.519328 | + | 0.854575i | \(0.673818\pi\) |
−0.854575 | + | 0.519328i | \(0.826182\pi\) | |||||||
\(194\) | −2.09044 | −0.150085 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.73017 | −0.409298 | ||||||||
\(197\) | −2.74011 | + | 2.74011i | −0.195225 | + | 0.195225i | −0.797949 | − | 0.602725i | \(-0.794082\pi\) |
0.602725 | + | 0.797949i | \(0.294082\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7408i | 0.832286i | 0.909299 | + | 0.416143i | \(0.136619\pi\) | ||||
−0.909299 | + | 0.416143i | \(0.863381\pi\) | |||||||
\(200\) | 3.42470 | + | 3.64300i | 0.242163 | + | 0.257599i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.84564 | + | 2.84564i | 0.200218 | + | 0.200218i | ||||
\(203\) | 5.27526 | + | 5.27526i | 0.370251 | + | 0.370251i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.341625 | + | 22.1258i | −0.0238601 | + | 1.54533i | ||||
\(206\) | − | 8.83830i | − | 0.615794i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.95872 | + | 3.95872i | −0.274488 | + | 0.274488i | ||||
\(209\) | −10.1643 | −0.703081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.37452 | −0.163469 | −0.0817344 | − | 0.996654i | \(-0.526046\pi\) | ||||
−0.0817344 | + | 0.996654i | \(0.526046\pi\) | |||||||
\(212\) | −0.461295 | + | 0.461295i | −0.0316819 | + | 0.0316819i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.0730i | 1.09873i | ||||||||
\(215\) | 5.62624 | − | 5.45514i | 0.383706 | − | 0.372037i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.964721 | − | 0.964721i | −0.0654895 | − | 0.0654895i | ||||
\(218\) | −6.44055 | − | 6.44055i | −0.436209 | − | 0.436209i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −4.80435 | − | 0.0741799i | −0.323909 | − | 0.00500121i | ||||
\(221\) | 5.59847i | 0.376594i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.0154 | + | 11.0154i | −0.737648 | + | 0.737648i | −0.972122 | − | 0.234474i | \(-0.924663\pi\) |
0.234474 | + | 0.972122i | \(0.424663\pi\) | |||||||
\(224\) | 1.12687 | 0.0752920 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.49599 | −0.498626 | ||||||||
\(227\) | −14.1938 | + | 14.1938i | −0.942074 | + | 0.942074i | −0.998412 | − | 0.0563376i | \(-0.982058\pi\) |
0.0563376 | + | 0.998412i | \(0.482058\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 0.0705584i | − | 0.00466263i | −0.999997 | − | 0.00233132i | \(-0.999258\pi\) | ||
0.999997 | − | 0.00233132i | \(-0.000742081\pi\) | |||||||
\(230\) | 18.2262 | + | 0.281415i | 1.20180 | + | 0.0185560i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.68135 | + | 4.68135i | 0.307346 | + | 0.307346i | ||||
\(233\) | 4.10456 | + | 4.10456i | 0.268898 | + | 0.268898i | 0.828656 | − | 0.559758i | \(-0.189106\pi\) |
−0.559758 | + | 0.828656i | \(0.689106\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.1318 | + | 18.5500i | −1.24802 | + | 1.21007i | ||||
\(236\) | 4.07935i | 0.265543i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.796815 | − | 0.796815i | 0.0516499 | − | 0.0516499i | ||||
\(239\) | −19.2176 | −1.24308 | −0.621540 | − | 0.783382i | \(-0.713493\pi\) | ||||
−0.621540 | + | 0.783382i | \(0.713493\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.0221 | 1.86948 | 0.934740 | − | 0.355333i | \(-0.115633\pi\) | ||||
0.934740 | + | 0.355333i | \(0.115633\pi\) | |||||||
\(242\) | −4.51314 | + | 4.51314i | −0.290116 | + | 0.290116i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.7456i | − | 0.751936i | ||||||
\(245\) | 0.197812 | − | 12.8115i | 0.0126377 | − | 0.818498i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.7254 | − | 18.7254i | −1.19147 | − | 1.19147i | ||||
\(248\) | −0.856109 | − | 0.856109i | −0.0543630 | − | 0.0543630i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.26325 | + | 7.53118i | −0.522614 | + | 0.476314i | ||||
\(251\) | − | 11.1723i | − | 0.705186i | −0.935777 | − | 0.352593i | \(-0.885300\pi\) | ||
0.935777 | − | 0.352593i | \(-0.114700\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.3865 | + | 12.3865i | −0.778735 | + | 0.778735i | ||||
\(254\) | −18.9746 | −1.19057 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.7951 | − | 20.7951i | 1.29716 | − | 1.29716i | 0.366900 | − | 0.930261i | \(-0.380419\pi\) |
0.930261 | − | 0.366900i | \(-0.119581\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 13.3429i | − | 0.829085i | ||||||
\(260\) | −8.71424 | − | 8.98756i | −0.540434 | − | 0.557385i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.5147 | + | 13.5147i | 0.834940 | + | 0.834940i | ||||
\(263\) | −8.36851 | − | 8.36851i | −0.516025 | − | 0.516025i | 0.400341 | − | 0.916366i | \(-0.368892\pi\) |
−0.916366 | + | 0.400341i | \(0.868892\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.01544 | − | 1.04729i | −0.0623780 | − | 0.0643345i | ||||
\(266\) | 5.33027i | 0.326820i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.22854 | − | 2.22854i | 0.136130 | − | 0.136130i | ||||
\(269\) | −1.70441 | −0.103920 | −0.0519599 | − | 0.998649i | \(-0.516547\pi\) | ||||
−0.0519599 | + | 0.998649i | \(0.516547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.8301 | −0.840119 | −0.420059 | − | 0.907497i | \(-0.637991\pi\) | ||||
−0.420059 | + | 0.907497i | \(0.637991\pi\) | |||||||
\(272\) | 0.707107 | − | 0.707107i | 0.0428746 | − | 0.0428746i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 11.5738i | − | 0.699198i | ||||||
\(275\) | 0.331703 | − | 10.7390i | 0.0200024 | − | 0.647587i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.00552 | − | 4.00552i | −0.240668 | − | 0.240668i | 0.576458 | − | 0.817127i | \(-0.304434\pi\) |
−0.817127 | + | 0.576458i | \(0.804434\pi\) | |||||||
\(278\) | −4.91887 | − | 4.91887i | −0.295014 | − | 0.295014i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.0389007 | + | 2.51945i | −0.00232476 | + | 0.150566i | ||||
\(281\) | 8.96504i | 0.534810i | 0.963584 | + | 0.267405i | \(0.0861661\pi\) | ||||
−0.963584 | + | 0.267405i | \(0.913834\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.32857 | + | 2.32857i | −0.138419 | + | 0.138419i | −0.772921 | − | 0.634502i | \(-0.781205\pi\) |
0.634502 | + | 0.772921i | \(0.281205\pi\) | |||||||
\(284\) | −3.51868 | −0.208796 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.0301 | 0.711357 | ||||||||
\(287\) | −7.88538 | + | 7.88538i | −0.465459 | + | 0.465459i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 1.00000i | − | 0.0588235i | ||||||
\(290\) | −10.6282 | + | 10.3050i | −0.624108 | + | 0.605128i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.15436 | + | 3.15436i | 0.184595 | + | 0.184595i | ||||
\(293\) | −19.5156 | − | 19.5156i | −1.14011 | − | 1.14011i | −0.988429 | − | 0.151682i | \(-0.951531\pi\) |
−0.151682 | − | 0.988429i | \(-0.548469\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.12062 | − | 0.140824i | −0.531023 | − | 0.00819907i | ||||
\(296\) | − | 11.8407i | − | 0.688225i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.51707 | + | 8.51707i | −0.493380 | + | 0.493380i | ||||
\(299\) | −45.6386 | −2.63935 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.94928 | 0.227633 | ||||||||
\(302\) | −8.42690 | + | 8.42690i | −0.484913 | + | 0.484913i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.73017i | 0.271294i | ||||||||
\(305\) | 26.2609 | + | 0.405471i | 1.50369 | + | 0.0232172i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.5090 | − | 18.5090i | −1.05637 | − | 1.05637i | −0.998313 | − | 0.0580536i | \(-0.981511\pi\) |
−0.0580536 | − | 0.998313i | \(-0.518489\pi\) | |||||||
\(308\) | −1.71222 | − | 1.71222i | −0.0975627 | − | 0.0975627i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.94364 | − | 1.88454i | 0.110392 | − | 0.107034i | ||||
\(311\) | 23.5658i | 1.33629i | 0.744030 | + | 0.668147i | \(0.232912\pi\) | ||||
−0.744030 | + | 0.668147i | \(0.767088\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0869 | + | 15.0869i | −0.852760 | + | 0.852760i | −0.990472 | − | 0.137712i | \(-0.956025\pi\) |
0.137712 | + | 0.990472i | \(0.456025\pi\) | |||||||
\(314\) | −7.20578 | −0.406646 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.2647 | −0.914961 | ||||||||
\(317\) | 9.89019 | − | 9.89019i | 0.555489 | − | 0.555489i | −0.372531 | − | 0.928020i | \(-0.621510\pi\) |
0.928020 | + | 0.372531i | \(0.121510\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14.2262i | − | 0.796512i | ||||||
\(320\) | −0.0345211 | + | 2.23580i | −0.00192979 | + | 0.124985i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.49562 | + | 6.49562i | 0.361987 | + | 0.361987i | ||||
\(323\) | 3.34474 | + | 3.34474i | 0.186106 | + | 0.186106i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.3952 | − | 19.1731i | 1.13132 | − | 1.06353i | ||||
\(326\) | 15.0580i | 0.833985i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.99762 | + | 6.99762i | −0.386379 | + | 0.386379i | ||||
\(329\) | −13.4294 | −0.740384 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.77709 | −0.152643 | −0.0763214 | − | 0.997083i | \(-0.524318\pi\) | ||||
−0.0763214 | + | 0.997083i | \(0.524318\pi\) | |||||||
\(332\) | 11.0370 | − | 11.0370i | 0.605735 | − | 0.605735i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 11.7147i | − | 0.641002i | ||||||
\(335\) | 4.90565 | + | 5.05952i | 0.268024 | + | 0.276431i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.52889 | − | 1.52889i | −0.0832837 | − | 0.0832837i | 0.664238 | − | 0.747521i | \(-0.268756\pi\) |
−0.747521 | + | 0.664238i | \(0.768756\pi\) | |||||||
\(338\) | 12.9704 | + | 12.9704i | 0.705495 | + | 0.705495i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.55654 | + | 1.60536i | 0.0844152 | + | 0.0870629i | ||||
\(341\) | 2.60163i | 0.140886i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.1436 | − | 10.1436i | 0.547703 | − | 0.547703i | ||||
\(344\) | 3.50466 | 0.188958 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.6241 | −0.678678 | ||||||||
\(347\) | −9.34949 | + | 9.34949i | −0.501907 | + | 0.501907i | −0.912030 | − | 0.410123i | \(-0.865486\pi\) |
0.410123 | + | 0.912030i | \(0.365486\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.26983i | 0.496203i | 0.968734 | + | 0.248101i | \(0.0798066\pi\) | ||||
−0.968734 | + | 0.248101i | \(0.920193\pi\) | |||||||
\(350\) | −5.63165 | − | 0.173948i | −0.301024 | − | 0.00929793i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.51945 | − | 1.51945i | −0.0809870 | − | 0.0809870i | ||||
\(353\) | 6.47454 | + | 6.47454i | 0.344605 | + | 0.344605i | 0.858095 | − | 0.513490i | \(-0.171648\pi\) |
−0.513490 | + | 0.858095i | \(0.671648\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.121469 | − | 7.86708i | 0.00644690 | − | 0.417541i | ||||
\(356\) | 10.8272i | 0.573841i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.0127 | + | 12.0127i | −0.634890 | + | 0.634890i | ||||
\(359\) | −11.1533 | −0.588647 | −0.294323 | − | 0.955706i | \(-0.595094\pi\) | ||||
−0.294323 | + | 0.955706i | \(0.595094\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.37452 | −0.177606 | ||||||||
\(362\) | −7.93783 | + | 7.93783i | −0.417203 | + | 0.417203i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 6.30873i | − | 0.330667i | ||||||
\(365\) | −7.16143 | + | 6.94364i | −0.374846 | + | 0.363447i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.92534 | + | 2.92534i | 0.152701 | + | 0.152701i | 0.779323 | − | 0.626622i | \(-0.215563\pi\) |
−0.626622 | + | 0.779323i | \(0.715563\pi\) | |||||||
\(368\) | 5.76432 | + | 5.76432i | 0.300486 | + | 0.300486i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.4734 | + | 0.408753i | 1.37629 | + | 0.0212501i | ||||
\(371\) | − | 0.735134i | − | 0.0381663i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.2707 | + | 23.2707i | −1.20491 | + | 1.20491i | −0.232257 | + | 0.972655i | \(0.574611\pi\) |
−0.972655 | + | 0.232257i | \(0.925389\pi\) | |||||||
\(374\) | −2.14883 | −0.111113 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.9174 | −0.614595 | ||||||||
\(377\) | 26.2084 | − | 26.2084i | 1.34980 | − | 1.34980i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 0.957068i | − | 0.0491613i | −0.999698 | − | 0.0245806i | \(-0.992175\pi\) | ||
0.999698 | − | 0.0245806i | \(-0.00782505\pi\) | |||||||
\(380\) | −10.5757 | − | 0.163291i | −0.542523 | − | 0.00837664i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.13654 | − | 3.13654i | −0.160479 | − | 0.160479i | ||||
\(383\) | 14.0585 | + | 14.0585i | 0.718358 | + | 0.718358i | 0.968269 | − | 0.249911i | \(-0.0804013\pi\) |
−0.249911 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.88729 | − | 3.76907i | 0.198115 | − | 0.192090i | ||||
\(386\) | − | 26.9929i | − | 1.37390i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.47817 | − | 1.47817i | 0.0750425 | − | 0.0750425i | ||||
\(389\) | 3.39923 | 0.172348 | 0.0861739 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861739 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.15198 | 0.412263 | ||||||||
\(392\) | 4.05184 | − | 4.05184i | 0.204649 | − | 0.204649i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 3.87510i | − | 0.195225i | ||||||
\(395\) | 0.561475 | − | 36.3646i | 0.0282509 | − | 1.82970i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.319017 | − | 0.319017i | −0.0160110 | − | 0.0160110i | 0.699056 | − | 0.715067i | \(-0.253604\pi\) |
−0.715067 | + | 0.699056i | \(0.753604\pi\) | |||||||
\(398\) | −8.30203 | − | 8.30203i | −0.416143 | − | 0.416143i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.99762 | − | 0.154365i | −0.249881 | − | 0.00771823i | ||||
\(401\) | − | 16.9054i | − | 0.844217i | −0.906545 | − | 0.422109i | \(-0.861290\pi\) | ||
0.906545 | − | 0.422109i | \(-0.138710\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.79290 | + | 4.79290i | −0.238751 | + | 0.238751i | ||||
\(404\) | −4.02434 | −0.200218 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.46034 | −0.370251 | ||||||||
\(407\) | −17.9913 | + | 17.9913i | −0.891797 | + | 0.891797i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.6421i | 1.91073i | 0.295430 | + | 0.955364i | \(0.404537\pi\) | ||||
−0.295430 | + | 0.955364i | \(0.595463\pi\) | |||||||
\(410\) | −15.4037 | − | 15.8868i | −0.760735 | − | 0.784595i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.24962 | + | 6.24962i | 0.307897 | + | 0.307897i | ||||
\(413\) | −3.25049 | − | 3.25049i | −0.159946 | − | 0.159946i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.2956 | + | 25.0576i | 1.19262 | + | 1.23003i | ||||
\(416\) | − | 5.59847i | − | 0.274488i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.18726 | − | 7.18726i | 0.351540 | − | 0.351540i | ||||
\(419\) | −18.9813 | −0.927297 | −0.463649 | − | 0.886019i | \(-0.653460\pi\) | ||||
−0.463649 | + | 0.886019i | \(0.653460\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.695260 | 0.0338849 | 0.0169425 | − | 0.999856i | \(-0.494607\pi\) | ||||
0.0169425 | + | 0.999856i | \(0.494607\pi\) | |||||||
\(422\) | 1.67904 | − | 1.67904i | 0.0817344 | − | 0.0817344i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 0.652370i | − | 0.0316819i | ||||||
\(425\) | −3.64300 | + | 3.42470i | −0.176711 | + | 0.166122i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.35908 | + | 9.35908i | 0.452918 | + | 0.452918i | ||||
\(428\) | −11.3654 | − | 11.3654i | −0.549365 | − | 0.549365i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.120985 | + | 7.83572i | −0.00583440 | + | 0.377872i | ||||
\(431\) | 14.1579i | 0.681963i | 0.940070 | + | 0.340981i | \(0.110759\pi\) | ||||
−0.940070 | + | 0.340981i | \(0.889241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.79633 | + | 6.79633i | −0.326611 | + | 0.326611i | −0.851296 | − | 0.524685i | \(-0.824183\pi\) |
0.524685 | + | 0.851296i | \(0.324183\pi\) | |||||||
\(434\) | 1.36432 | 0.0654895 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.10831 | 0.436209 | ||||||||
\(437\) | −27.2662 | + | 27.2662i | −1.30432 | + | 1.30432i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 16.7265i | − | 0.798315i | −0.916882 | − | 0.399157i | \(-0.869303\pi\) | ||
0.916882 | − | 0.399157i | \(-0.130697\pi\) | |||||||
\(440\) | 3.44964 | − | 3.34474i | 0.164455 | − | 0.159454i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.95872 | − | 3.95872i | −0.188297 | − | 0.188297i | ||||
\(443\) | 7.42694 | + | 7.42694i | 0.352864 | + | 0.352864i | 0.861174 | − | 0.508310i | \(-0.169730\pi\) |
−0.508310 | + | 0.861174i | \(0.669730\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.2075 | − | 0.373767i | −1.14754 | − | 0.0177183i | ||||
\(446\) | − | 15.5782i | − | 0.737648i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.796815 | + | 0.796815i | −0.0376460 | + | 0.0376460i | ||||
\(449\) | 5.09550 | 0.240472 | 0.120236 | − | 0.992745i | \(-0.461635\pi\) | ||||
0.120236 | + | 0.992745i | \(0.461635\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.2651 | 1.00133 | ||||||||
\(452\) | 5.30047 | − | 5.30047i | 0.249313 | − | 0.249313i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 20.0730i | − | 0.942074i | ||||||
\(455\) | 14.1051 | + | 0.217784i | 0.661256 | + | 0.0102099i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.3742 | − | 20.3742i | −0.953063 | − | 0.953063i | 0.0458841 | − | 0.998947i | \(-0.485390\pi\) |
−0.998947 | + | 0.0458841i | \(0.985390\pi\) | |||||||
\(458\) | 0.0498923 | + | 0.0498923i | 0.00233132 | + | 0.00233132i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.0869 | + | 12.6889i | −0.610178 | + | 0.591622i | ||||
\(461\) | − | 15.8779i | − | 0.739509i | −0.929129 | − | 0.369755i | \(-0.879442\pi\) | ||
0.929129 | − | 0.369755i | \(-0.120558\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.0504 | + | 21.0504i | −0.978293 | + | 0.978293i | −0.999769 | − | 0.0214766i | \(-0.993163\pi\) |
0.0214766 | + | 0.999769i | \(0.493163\pi\) | |||||||
\(464\) | −6.62043 | −0.307346 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.80472 | −0.268898 | ||||||||
\(467\) | 4.07086 | − | 4.07086i | 0.188377 | − | 0.188377i | −0.606617 | − | 0.794994i | \(-0.707474\pi\) |
0.794994 | + | 0.606617i | \(0.207474\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.55148i | 0.163992i | ||||||||
\(470\) | 0.411403 | − | 26.6450i | 0.0189766 | − | 1.22904i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.88454 | − | 2.88454i | −0.132772 | − | 0.132772i | ||||
\(473\) | −5.32515 | − | 5.32515i | −0.244851 | − | 0.244851i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.730171 | − | 23.6396i | 0.0335026 | − | 1.08466i | ||||
\(476\) | 1.12687i | 0.0516499i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.5889 | − | 13.5889i | 0.621540 | − | 0.621540i | ||||
\(479\) | 0.442145 | 0.0202021 | 0.0101011 | − | 0.999949i | \(-0.496785\pi\) | ||||
0.0101011 | + | 0.999949i | \(0.496785\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −66.2897 | −3.02255 | ||||||||
\(482\) | −20.5217 | + | 20.5217i | −0.934740 | + | 0.934740i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 6.38254i | − | 0.290116i | ||||||
\(485\) | 3.25386 | + | 3.35591i | 0.147750 | + | 0.152384i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.58133 | + | 1.58133i | 0.0716568 | + | 0.0716568i | 0.742027 | − | 0.670370i | \(-0.233865\pi\) |
−0.670370 | + | 0.742027i | \(0.733865\pi\) | |||||||
\(488\) | 8.30540 | + | 8.30540i | 0.375968 | + | 0.375968i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.91924 | + | 9.19899i | 0.402930 | + | 0.415568i | ||||
\(491\) | 29.7714i | 1.34357i | 0.740748 | + | 0.671783i | \(0.234471\pi\) | ||||
−0.740748 | + | 0.671783i | \(0.765529\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.68135 | + | 4.68135i | −0.210837 | + | 0.210837i | ||||
\(494\) | 26.4817 | 1.19147 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.21072 | 0.0543630 | ||||||||
\(497\) | 2.80374 | − | 2.80374i | 0.125765 | − | 0.125765i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.14034i | − | 0.140581i | −0.997527 | − | 0.0702904i | \(-0.977607\pi\) | ||
0.997527 | − | 0.0702904i | \(-0.0223926\pi\) | |||||||
\(500\) | 0.517652 | − | 11.1683i | 0.0231501 | − | 0.499464i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.89998 | + | 7.89998i | 0.352593 | + | 0.352593i | ||||
\(503\) | −21.7449 | − | 21.7449i | −0.969557 | − | 0.969557i | 0.0299931 | − | 0.999550i | \(-0.490451\pi\) |
−0.999550 | + | 0.0299931i | \(0.990451\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.138925 | − | 8.99762i | 0.00618206 | − | 0.400389i | ||||
\(506\) | − | 17.5172i | − | 0.778735i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.4170 | − | 13.4170i | 0.595285 | − | 0.595285i | ||||
\(509\) | 10.8452 | 0.480703 | 0.240351 | − | 0.970686i | \(-0.422737\pi\) | ||||
0.240351 | + | 0.970686i | \(0.422737\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.02689 | −0.222377 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 29.4087i | 1.29716i | ||||||||
\(515\) | −14.1887 | + | 13.7572i | −0.625227 | + | 0.606213i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.1079 | + | 18.1079i | 0.796387 | + | 0.796387i | ||||
\(518\) | 9.43483 | + | 9.43483i | 0.414543 | + | 0.414543i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.5171 | + | 0.193265i | 0.548910 | + | 0.00847525i | ||||
\(521\) | − | 34.6381i | − | 1.51752i | −0.651367 | − | 0.758762i | \(-0.725804\pi\) | ||
0.651367 | − | 0.758762i | \(-0.274196\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.6111 | + | 11.6111i | −0.507717 | + | 0.507717i | −0.913825 | − | 0.406108i | \(-0.866886\pi\) |
0.406108 | + | 0.913825i | \(0.366886\pi\) | |||||||
\(524\) | −19.1126 | −0.834940 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.8349 | 0.516025 | ||||||||
\(527\) | 0.856109 | − | 0.856109i | 0.0372927 | − | 0.0372927i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.4548i | 1.88934i | ||||||||
\(530\) | 1.45857 | + | 0.0225205i | 0.0633562 | + | 0.000978229i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.76907 | − | 3.76907i | −0.163410 | − | 0.163410i | ||||
\(533\) | 39.1759 | + | 39.1759i | 1.69690 | + | 1.69690i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.8030 | − | 25.0183i | 1.11556 | − | 1.08164i | ||||
\(536\) | 3.15164i | 0.136130i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.20520 | − | 1.20520i | 0.0519599 | − | 0.0519599i | ||||
\(539\) | −12.3131 | −0.530365 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.0893 | 0.863704 | 0.431852 | − | 0.901944i | \(-0.357860\pi\) | ||||
0.431852 | + | 0.901944i | \(0.357860\pi\) | |||||||
\(542\) | 9.77936 | − | 9.77936i | 0.420059 | − | 0.420059i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.00000i | 0.0428746i | ||||||||
\(545\) | −0.314429 | + | 20.3644i | −0.0134687 | + | 0.872314i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.3539 | − | 20.3539i | −0.870272 | − | 0.870272i | 0.122230 | − | 0.992502i | \(-0.460995\pi\) |
−0.992502 | + | 0.122230i | \(0.960995\pi\) | |||||||
\(548\) | 8.18391 | + | 8.18391i | 0.349599 | + | 0.349599i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 7.35908 | + | 7.82818i | 0.313792 | + | 0.333795i | ||||
\(551\) | − | 31.3158i | − | 1.33410i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9600 | − | 12.9600i | 0.551113 | − | 0.551113i | ||||
\(554\) | 5.66466 | 0.240668 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.95633 | 0.295014 | ||||||||
\(557\) | −9.44817 | + | 9.44817i | −0.400332 | + | 0.400332i | −0.878350 | − | 0.478018i | \(-0.841355\pi\) |
0.478018 | + | 0.878350i | \(0.341355\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 19.6207i | − | 0.829868i | ||||||
\(560\) | −1.75401 | − | 1.80903i | −0.0741206 | − | 0.0764454i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.33924 | − | 6.33924i | −0.267405 | − | 0.267405i | ||||
\(563\) | 18.4112 | + | 18.4112i | 0.775940 | + | 0.775940i | 0.979138 | − | 0.203198i | \(-0.0651334\pi\) |
−0.203198 | + | 0.979138i | \(0.565133\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6678 | + | 12.0338i | 0.490868 | + | 0.506264i | ||||
\(566\) | − | 3.29309i | − | 0.138419i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.48809 | − | 2.48809i | 0.104398 | − | 0.104398i | ||||
\(569\) | 8.03733 | 0.336942 | 0.168471 | − | 0.985707i | \(-0.446117\pi\) | ||||
0.168471 | + | 0.985707i | \(0.446117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.7992 | 1.49815 | 0.749075 | − | 0.662485i | \(-0.230498\pi\) | ||||
0.749075 | + | 0.662485i | \(0.230498\pi\) | |||||||
\(572\) | −8.50660 | + | 8.50660i | −0.355679 | + | 0.355679i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 11.1516i | − | 0.465459i | ||||||
\(575\) | −27.9181 | − | 29.6977i | −1.16426 | − | 1.23848i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.30396 | + | 3.30396i | 0.137546 | + | 0.137546i | 0.772527 | − | 0.634982i | \(-0.218992\pi\) |
−0.634982 | + | 0.772527i | \(0.718992\pi\) | |||||||
\(578\) | 0.707107 | + | 0.707107i | 0.0294118 | + | 0.0294118i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.228545 | − | 14.8020i | 0.00948980 | − | 0.614618i | ||||
\(581\) | 17.5889i | 0.729712i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.991244 | + | 0.991244i | −0.0410531 | + | 0.0410531i | ||||
\(584\) | −4.46095 | −0.184595 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.5992 | 1.14011 | ||||||||
\(587\) | −23.4735 | + | 23.4735i | −0.968857 | + | 0.968857i | −0.999529 | − | 0.0306728i | \(-0.990235\pi\) |
0.0306728 | + | 0.999529i | \(0.490235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.72692i | 0.235974i | ||||||||
\(590\) | 6.54883 | − | 6.34967i | 0.269611 | − | 0.261412i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.37262 | + | 8.37262i | 0.344113 | + | 0.344113i | ||||
\(593\) | 8.12889 | + | 8.12889i | 0.333814 | + | 0.333814i | 0.854033 | − | 0.520219i | \(-0.174150\pi\) |
−0.520219 | + | 0.854033i | \(0.674150\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.51945 | − | 0.0389007i | −0.103287 | − | 0.00159477i | ||||
\(596\) | − | 12.0450i | − | 0.493380i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 32.2714 | − | 32.2714i | 1.31967 | − | 1.31967i | ||||
\(599\) | −23.0136 | −0.940311 | −0.470155 | − | 0.882584i | \(-0.655802\pi\) | ||||
−0.470155 | + | 0.882584i | \(0.655802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.1508 | −0.495643 | −0.247821 | − | 0.968806i | \(-0.579715\pi\) | ||||
−0.247821 | + | 0.968806i | \(0.579715\pi\) | |||||||
\(602\) | −2.79256 | + | 2.79256i | −0.113816 | + | 0.113816i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 11.9174i | − | 0.484913i | ||||||
\(605\) | 14.2701 | + | 0.220332i | 0.580162 | + | 0.00895778i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.2099 | + | 21.2099i | 0.860882 | + | 0.860882i | 0.991441 | − | 0.130559i | \(-0.0416771\pi\) |
−0.130559 | + | 0.991441i | \(0.541677\pi\) | |||||||
\(608\) | −3.34474 | − | 3.34474i | −0.135647 | − | 0.135647i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.8559 | + | 18.2825i | −0.763455 | + | 0.740237i | ||||
\(611\) | 66.7194i | 2.69918i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.02145 | − | 6.02145i | 0.243204 | − | 0.243204i | −0.574970 | − | 0.818174i | \(-0.694986\pi\) |
0.818174 | + | 0.574970i | \(0.194986\pi\) | |||||||
\(614\) | 26.1757 | 1.05637 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.42144 | 0.0975627 | ||||||||
\(617\) | 8.91625 | − | 8.91625i | 0.358955 | − | 0.358955i | −0.504473 | − | 0.863428i | \(-0.668313\pi\) |
0.863428 | + | 0.504473i | \(0.168313\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.11670i | − | 0.205658i | −0.994699 | − | 0.102829i | \(-0.967211\pi\) | ||
0.994699 | − | 0.102829i | \(-0.0327894\pi\) | |||||||
\(620\) | −0.0417954 | + | 2.70693i | −0.00167854 | + | 0.108713i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −16.6635 | − | 16.6635i | −0.668147 | − | 0.668147i | ||||
\(623\) | −8.62728 | − | 8.62728i | −0.345645 | − | 0.345645i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9523 | + | 1.54291i | 0.998094 | + | 0.0617164i | ||||
\(626\) | − | 21.3361i | − | 0.852760i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.09526 | − | 5.09526i | 0.203323 | − | 0.203323i | ||||
\(629\) | 11.8407 | 0.472119 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.4508 | 1.80937 | 0.904684 | − | 0.426083i | \(-0.140107\pi\) | ||||
0.904684 | + | 0.426083i | \(0.140107\pi\) | |||||||
\(632\) | 11.5009 | − | 11.5009i | 0.457480 | − | 0.457480i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.9868i | 0.555489i | ||||||||
\(635\) | 29.5347 | + | 30.4610i | 1.17205 | + | 1.20881i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.6841 | − | 22.6841i | −0.898778 | − | 0.898778i | ||||
\(638\) | 10.0594 | + | 10.0594i | 0.398256 | + | 0.398256i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.55654 | − | 1.60536i | −0.0615277 | − | 0.0634574i | ||||
\(641\) | 34.4653i | 1.36130i | 0.732611 | + | 0.680648i | \(0.238302\pi\) | ||||
−0.732611 | + | 0.680648i | \(0.761698\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.57379 | + | 9.57379i | −0.377553 | + | 0.377553i | −0.870219 | − | 0.492665i | \(-0.836023\pi\) |
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(644\) | −9.18620 | −0.361987 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.73017 | −0.186106 | ||||||||
\(647\) | 10.3356 | − | 10.3356i | 0.406334 | − | 0.406334i | −0.474124 | − | 0.880458i | \(-0.657235\pi\) |
0.880458 | + | 0.474124i | \(0.157235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.76582i | 0.344088i | ||||||||
\(650\) | −0.864206 | + | 27.9790i | −0.0338969 | + | 1.09743i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10.6476 | − | 10.6476i | −0.416992 | − | 0.416992i | ||||
\(653\) | 17.1902 | + | 17.1902i | 0.672705 | + | 0.672705i | 0.958339 | − | 0.285634i | \(-0.0922040\pi\) |
−0.285634 | + | 0.958339i | \(0.592204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.659790 | − | 42.7321i | 0.0257801 | − | 1.66968i | ||||
\(656\) | − | 9.89612i | − | 0.386379i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.49599 | − | 9.49599i | 0.370192 | − | 0.370192i | ||||
\(659\) | −9.62048 | −0.374761 | −0.187380 | − | 0.982287i | \(-0.560000\pi\) | ||||
−0.187380 | + | 0.982287i | \(0.560000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.45558 | 0.367779 | 0.183890 | − | 0.982947i | \(-0.441131\pi\) | ||||
0.183890 | + | 0.982947i | \(0.441131\pi\) | |||||||
\(662\) | 1.96370 | − | 1.96370i | 0.0763214 | − | 0.0763214i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.6087i | 0.605735i | ||||||||
\(665\) | 8.55701 | − | 8.29678i | 0.331827 | − | 0.321735i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.1623 | − | 38.1623i | −1.47765 | − | 1.47765i | ||||
\(668\) | 8.28357 | + | 8.28357i | 0.320501 | + | 0.320501i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.04644 | − | 0.108798i | −0.272228 | − | 0.00420323i | ||||
\(671\) | − | 25.2393i | − | 0.974352i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.09562 | + | 6.09562i | −0.234969 | + | 0.234969i | −0.814763 | − | 0.579794i | \(-0.803133\pi\) |
0.579794 | + | 0.814763i | \(0.303133\pi\) | |||||||
\(674\) | 2.16217 | 0.0832837 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.3429 | −0.705495 | ||||||||
\(677\) | 13.9397 | − | 13.9397i | 0.535748 | − | 0.535748i | −0.386529 | − | 0.922277i | \(-0.626326\pi\) |
0.922277 | + | 0.386529i | \(0.126326\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.35565i | 0.0904016i | ||||||||
\(680\) | −2.23580 | − | 0.0345211i | −0.0857391 | − | 0.00132382i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.83963 | − | 1.83963i | −0.0704431 | − | 0.0704431i | ||||
\(683\) | 6.53953 | + | 6.53953i | 0.250228 | + | 0.250228i | 0.821064 | − | 0.570836i | \(-0.193381\pi\) |
−0.570836 | + | 0.821064i | \(0.693381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.5801 | + | 18.0151i | −0.709909 | + | 0.688321i | ||||
\(686\) | 14.3452i | 0.547703i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.47817 | + | 2.47817i | −0.0944792 | + | 0.0944792i | ||||
\(689\) | −3.65227 | −0.139141 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.0469211 | −0.00178496 | −0.000892481 | − | 1.00000i | \(-0.500284\pi\) | ||||
−0.000892481 | 1.00000i | \(0.500284\pi\) | ||||||||
\(692\) | 8.92662 | − | 8.92662i | 0.339339 | − | 0.339339i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 13.2222i | − | 0.501907i | ||||||
\(695\) | −0.240140 | + | 15.5530i | −0.00910904 | + | 0.589958i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.99762 | − | 6.99762i | −0.265054 | − | 0.265054i | ||||
\(698\) | −6.55476 | − | 6.55476i | −0.248101 | − | 0.248101i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.10518 | − | 3.85918i | 0.155161 | − | 0.145863i | ||||
\(701\) | − | 14.7343i | − | 0.556505i | −0.960508 | − | 0.278253i | \(-0.910245\pi\) | ||
0.960508 | − | 0.278253i | \(-0.0897552\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.6039 | + | 39.6039i | −1.49369 | + | 1.49369i | ||||
\(704\) | 2.14883 | 0.0809870 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.15638 | −0.344605 | ||||||||
\(707\) | 3.20665 | − | 3.20665i | 0.120599 | − | 0.120599i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.4527i | 0.730561i | 0.930897 | + | 0.365281i | \(0.119027\pi\) | ||||
−0.930897 | + | 0.365281i | \(0.880973\pi\) | |||||||
\(710\) | 5.47697 | + | 5.64876i | 0.205547 | + | 0.211994i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.65599 | − | 7.65599i | −0.286920 | − | 0.286920i | ||||
\(713\) | 6.97898 | + | 6.97898i | 0.261365 | + | 0.261365i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.7254 | − | 19.3127i | −0.700290 | − | 0.722255i | ||||
\(716\) | − | 16.9885i | − | 0.634890i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.88655 | − | 7.88655i | 0.294323 | − | 0.294323i | ||||
\(719\) | 8.28101 | 0.308829 | 0.154415 | − | 0.988006i | \(-0.450651\pi\) | ||||
0.154415 | + | 0.988006i | \(0.450651\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.95959 | −0.370914 | ||||||||
\(722\) | 2.38615 | − | 2.38615i | 0.0888032 | − | 0.0888032i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 11.2258i | − | 0.417203i | ||||||
\(725\) | 33.0864 | + | 1.02196i | 1.22880 | + | 0.0379547i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.5606 | + | 27.5606i | 1.02217 | + | 1.02217i | 0.999749 | + | 0.0224187i | \(0.00713671\pi\) |
0.0224187 | + | 0.999749i | \(0.492863\pi\) | |||||||
\(728\) | 4.46095 | + | 4.46095i | 0.165334 | + | 0.165334i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.153997 | − | 9.97379i | 0.00569968 | − | 0.369146i | ||||
\(731\) | 3.50466i | 0.129624i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.458695 | + | 0.458695i | −0.0169423 | + | 0.0169423i | −0.715527 | − | 0.698585i | \(-0.753813\pi\) |
0.698585 | + | 0.715527i | \(0.253813\pi\) | |||||||
\(734\) | −4.13705 | −0.152701 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.15198 | −0.300486 | ||||||||
\(737\) | 4.78876 | − | 4.78876i | 0.176396 | − | 0.176396i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30.0206i | − | 1.10433i | −0.833736 | − | 0.552163i | \(-0.813803\pi\) | ||
0.833736 | − | 0.552163i | \(-0.186197\pi\) | |||||||
\(740\) | −19.0086 | + | 18.4305i | −0.698768 | + | 0.677518i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.519818 | + | 0.519818i | 0.0190831 | + | 0.0190831i | ||||
\(743\) | −13.4426 | − | 13.4426i | −0.493160 | − | 0.493160i | 0.416140 | − | 0.909300i | \(-0.363383\pi\) |
−0.909300 | + | 0.416140i | \(0.863383\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.9301 | + | 0.415805i | 0.986643 | + | 0.0152339i | ||||
\(746\) | − | 32.9097i | − | 1.20491i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.51945 | − | 1.51945i | 0.0555566 | − | 0.0555566i | ||||
\(749\) | 18.1122 | 0.661804 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.9203 | −1.09181 | −0.545904 | − | 0.837848i | \(-0.683814\pi\) | ||||
−0.545904 | + | 0.837848i | \(0.683814\pi\) | |||||||
\(752\) | 8.42690 | − | 8.42690i | 0.307297 | − | 0.307297i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.0643i | 1.34980i | ||||||||
\(755\) | 26.6450 | + | 0.411403i | 0.969711 | + | 0.0149725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.86584 | − | 3.86584i | −0.140506 | − | 0.140506i | 0.633355 | − | 0.773861i | \(-0.281677\pi\) |
−0.773861 | + | 0.633355i | \(0.781677\pi\) | |||||||
\(758\) | 0.676749 | + | 0.676749i | 0.0245806 | + | 0.0245806i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.59363 | − | 7.36270i | 0.275450 | − | 0.267073i | ||||
\(761\) | 28.1664i | 1.02103i | 0.859868 | + | 0.510516i | \(0.170545\pi\) | ||||
−0.859868 | + | 0.510516i | \(0.829455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.25764 | + | 7.25764i | −0.262744 | + | 0.262744i | ||||
\(764\) | 4.43574 | 0.160479 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.8818 | −0.718358 | ||||||||
\(767\) | −16.1490 | + | 16.1490i | −0.583106 | + | 0.583106i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.43020i | 0.267940i | 0.990985 | + | 0.133970i | \(0.0427725\pi\) | ||||
−0.990985 | + | 0.133970i | \(0.957227\pi\) | |||||||
\(770\) | −0.0835909 | + | 5.41386i | −0.00301241 | + | 0.195102i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.0869 | + | 19.0869i | 0.686951 | + | 0.686951i | ||||
\(773\) | −28.8769 | − | 28.8769i | −1.03863 | − | 1.03863i | −0.999223 | − | 0.0394070i | \(-0.987453\pi\) |
−0.0394070 | − | 0.999223i | \(-0.512547\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.05072 | − | 0.186893i | −0.217348 | − | 0.00671338i | ||||
\(776\) | 2.09044i | 0.0750425i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.40362 | + | 2.40362i | −0.0861739 | + | 0.0861739i | ||||
\(779\) | 46.8104 | 1.67716 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.56105 | −0.270555 | ||||||||
\(782\) | −5.76432 | + | 5.76432i | −0.206132 | + | 0.206132i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.73017i | 0.204649i | ||||||||
\(785\) | 11.2161 | + | 11.5679i | 0.400319 | + | 0.412875i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.72312 | + | 1.72312i | 0.0614226 | + | 0.0614226i | 0.737151 | − | 0.675728i | \(-0.236171\pi\) |
−0.675728 | + | 0.737151i | \(0.736171\pi\) | |||||||
\(788\) | 2.74011 | + | 2.74011i | 0.0976124 | + | 0.0976124i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 25.3167 | + | 26.1107i | 0.900726 | + | 0.928977i | ||||
\(791\) | 8.44698i | 0.300340i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 46.4975 | − | 46.4975i | 1.65118 | − | 1.65118i | ||||
\(794\) | 0.451158 | 0.0160110 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.7408 | 0.416143 | ||||||||
\(797\) | 11.4513 | − | 11.4513i | 0.405625 | − | 0.405625i | −0.474585 | − | 0.880210i | \(-0.657402\pi\) |
0.880210 | + | 0.474585i | \(0.157402\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.9174i | − | 0.421608i | ||||||
\(800\) | 3.64300 | − | 3.42470i | 0.128800 | − | 0.121081i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 11.9539 | + | 11.9539i | 0.422109 | + | 0.422109i | ||||
\(803\) | 6.77818 | + | 6.77818i | 0.239197 | + | 0.239197i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.317118 | − | 20.5385i | 0.0111769 | − | 0.723887i | ||||
\(806\) | − | 6.77818i | − | 0.238751i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.84564 | − | 2.84564i | 0.100109 | − | 0.100109i | ||||
\(809\) | 34.0791 | 1.19816 | 0.599078 | − | 0.800691i | \(-0.295534\pi\) | ||||
0.599078 | + | 0.800691i | \(0.295534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.9872 | −0.596502 | −0.298251 | − | 0.954488i | \(-0.596403\pi\) | ||||
−0.298251 | + | 0.954488i | \(0.596403\pi\) | |||||||
\(812\) | 5.27526 | − | 5.27526i | 0.185125 | − | 0.185125i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 25.4436i | − | 0.891797i | ||||||
\(815\) | 24.1735 | − | 23.4384i | 0.846761 | − | 0.821010i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.7222 | − | 11.7222i | −0.410106 | − | 0.410106i | ||||
\(818\) | −27.3241 | − | 27.3241i | −0.955364 | − | 0.955364i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 22.1258 | + | 0.341625i | 0.772665 | + | 0.0119301i | ||||
\(821\) | − | 17.7259i | − | 0.618640i | −0.950958 | − | 0.309320i | \(-0.899899\pi\) | ||
0.950958 | − | 0.309320i | \(-0.100101\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21.2135 | − | 21.2135i | 0.739456 | − | 0.739456i | −0.233017 | − | 0.972473i | \(-0.574860\pi\) |
0.972473 | + | 0.233017i | \(0.0748597\pi\) | |||||||
\(824\) | −8.83830 | −0.307897 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.59688 | 0.159946 | ||||||||
\(827\) | 9.94265 | − | 9.94265i | 0.345740 | − | 0.345740i | −0.512780 | − | 0.858520i | \(-0.671384\pi\) |
0.858520 | + | 0.512780i | \(0.171384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 30.9159i | − | 1.07375i | −0.843660 | − | 0.536877i | \(-0.819604\pi\) | ||
0.843660 | − | 0.536877i | \(-0.180396\pi\) | |||||||
\(830\) | −34.8980 | − | 0.538830i | −1.21133 | − | 0.0187030i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.95872 | + | 3.95872i | 0.137244 | + | 0.137244i | ||||
\(833\) | 4.05184 | + | 4.05184i | 0.140388 | + | 0.140388i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.8064 | + | 18.2345i | −0.650821 | + | 0.631029i | ||||
\(836\) | 10.1643i | 0.351540i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.4218 | − | 13.4218i | 0.463649 | − | 0.463649i | ||||
\(839\) | −10.3354 | −0.356818 | −0.178409 | − | 0.983956i | \(-0.557095\pi\) | ||||
−0.178409 | + | 0.983956i | \(0.557095\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.8301 | 0.511383 | ||||||||
\(842\) | −0.491623 | + | 0.491623i | −0.0169425 | + | 0.0169425i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.37452i | 0.0817344i | ||||||||
\(845\) | 0.633216 | − | 41.0110i | 0.0217833 | − | 1.41082i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.08571 | + | 5.08571i | 0.174747 | + | 0.174747i | ||||
\(848\) | 0.461295 | + | 0.461295i | 0.0158409 | + | 0.0158409i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.154365 | − | 4.99762i | 0.00529466 | − | 0.171417i | ||||
\(851\) | 96.5250i | 3.30883i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.6249 | − | 34.6249i | 1.18553 | − | 1.18553i | 0.207245 | − | 0.978289i | \(-0.433550\pi\) |
0.978289 | − | 0.207245i | \(-0.0664496\pi\) | |||||||
\(854\) | −13.2357 | −0.452918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.0730 | 0.549365 | ||||||||
\(857\) | −6.14336 | + | 6.14336i | −0.209853 | + | 0.209853i | −0.804205 | − | 0.594352i | \(-0.797409\pi\) |
0.594352 | + | 0.804205i | \(0.297409\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 12.3389i | − | 0.420997i | −0.977594 | − | 0.210498i | \(-0.932491\pi\) | ||
0.977594 | − | 0.210498i | \(-0.0675087\pi\) | |||||||
\(860\) | −5.45514 | − | 5.62624i | −0.186019 | − | 0.191853i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.0112 | − | 10.0112i | −0.340981 | − | 0.340981i | ||||
\(863\) | 7.27751 | + | 7.27751i | 0.247729 | + | 0.247729i | 0.820038 | − | 0.572309i | \(-0.193952\pi\) |
−0.572309 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.6500 | + | 20.2663i | 0.668120 | + | 0.689075i | ||||
\(866\) | − | 9.61146i | − | 0.326611i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.964721 | + | 0.964721i | −0.0327448 | + | 0.0327448i | ||||
\(869\) | −34.9500 | −1.18560 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.6443 | 0.597856 | ||||||||
\(872\) | −6.44055 | + | 6.44055i | −0.218105 | + | 0.218105i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 38.5603i | − | 1.30432i | ||||||
\(875\) | 8.48664 | + | 9.31158i | 0.286901 | + | 0.314789i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.963967 | − | 0.963967i | −0.0325509 | − | 0.0325509i | 0.690644 | − | 0.723195i | \(-0.257327\pi\) |
−0.723195 | + | 0.690644i | \(0.757327\pi\) | |||||||
\(878\) | 11.8275 | + | 11.8275i | 0.399157 | + | 0.399157i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.0741799 | + | 4.80435i | −0.00250060 | + | 0.161955i | ||||
\(881\) | 32.0589i | 1.08009i | 0.841636 | + | 0.540045i | \(0.181593\pi\) | ||||
−0.841636 | + | 0.540045i | \(0.818407\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.7318 | + | 12.7318i | −0.428460 | + | 0.428460i | −0.888103 | − | 0.459644i | \(-0.847977\pi\) |
0.459644 | + | 0.888103i | \(0.347977\pi\) | |||||||
\(884\) | 5.59847 | 0.188297 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.5033 | −0.352864 | ||||||||
\(887\) | 9.48728 | − | 9.48728i | 0.318552 | − | 0.318552i | −0.529659 | − | 0.848211i | \(-0.677680\pi\) |
0.848211 | + | 0.529659i | \(0.177680\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21.3818i | 0.717123i | ||||||||
\(890\) | 17.3816 | − | 16.8530i | 0.582632 | − | 0.564913i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.0154 | + | 11.0154i | 0.368824 | + | 0.368824i | ||||
\(893\) | 39.8607 | + | 39.8607i | 1.33389 | + | 1.33389i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.9829 | + | 0.586462i | 1.26963 | + | 0.0196033i | ||||
\(896\) | − | 1.12687i | − | 0.0376460i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.60307 | + | 3.60307i | −0.120236 | + | 0.120236i | ||||
\(899\) | −8.01549 | −0.267332 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.652370 | 0.0217336 | ||||||||
\(902\) | −15.0367 | + | 15.0367i | −0.500666 | + | 0.500666i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.49599i | 0.249313i | ||||||||
\(905\) | 25.0986 | + | 0.387527i | 0.834307 | + | 0.0128818i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.1634 | − | 12.1634i | −0.403880 | − | 0.403880i | 0.475718 | − | 0.879598i | \(-0.342188\pi\) |
−0.879598 | + | 0.475718i | \(0.842188\pi\) | |||||||
\(908\) | 14.1938 | + | 14.1938i | 0.471037 | + | 0.471037i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −10.1278 | + | 9.81979i | −0.335733 | + | 0.325523i | ||||
\(911\) | − | 45.4286i | − | 1.50512i | −0.658525 | − | 0.752559i | \(-0.728819\pi\) | ||
0.658525 | − | 0.752559i | \(-0.271181\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.7166 | − | 23.7166i | 0.784906 | − | 0.784906i | ||||
\(914\) | 28.8134 | 0.953063 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.0705584 | −0.00233132 | ||||||||
\(917\) | 15.2292 | − | 15.2292i | 0.502914 | − | 0.502914i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.0422i | 1.51879i | 0.650630 | + | 0.759395i | \(0.274505\pi\) | ||||
−0.650630 | + | 0.759395i | \(0.725495\pi\) | |||||||
\(920\) | 0.281415 | − | 18.2262i | 0.00927799 | − | 0.600900i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.2274 | + | 11.2274i | 0.369755 | + | 0.369755i | ||||
\(923\) | −13.9295 | − | 13.9295i | −0.458494 | − | 0.458494i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.5507 | − | 43.1356i | −1.33330 | − | 1.41829i | ||||
\(926\) | − | 29.7697i | − | 0.978293i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.68135 | − | 4.68135i | 0.153673 | − | 0.153673i | ||||
\(929\) | −46.2717 | −1.51813 | −0.759063 | − | 0.651018i | \(-0.774342\pi\) | ||||
−0.759063 | + | 0.651018i | \(0.774342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.1047 | −0.888320 | ||||||||
\(932\) | 4.10456 | − | 4.10456i | 0.134449 | − | 0.134449i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.75706i | 0.188377i | ||||||||
\(935\) | 3.34474 | + | 3.44964i | 0.109385 | + | 0.112815i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9043 | + | 18.9043i | 0.617576 | + | 0.617576i | 0.944909 | − | 0.327333i | \(-0.106150\pi\) |
−0.327333 | + | 0.944909i | \(0.606150\pi\) | |||||||
\(938\) | −2.51127 | − | 2.51127i | −0.0819960 | − | 0.0819960i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 18.5500 | + | 19.1318i | 0.605033 | + | 0.624010i | ||||
\(941\) | − | 21.0595i | − | 0.686519i | −0.939241 | − | 0.343260i | \(-0.888469\pi\) | ||
0.939241 | − | 0.343260i | \(-0.111531\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.0444 | − | 57.0444i | 1.85762 | − | 1.85762i | ||||
\(944\) | 4.07935 | 0.132772 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.53090 | 0.244851 | ||||||||
\(947\) | 10.4376 | − | 10.4376i | 0.339178 | − | 0.339178i | −0.516880 | − | 0.856058i | \(-0.672907\pi\) |
0.856058 | + | 0.516880i | \(0.172907\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 24.9745i | 0.810706i | ||||||||
\(950\) | 16.1994 | + | 17.2320i | 0.525578 | + | 0.559081i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.796815 | − | 0.796815i | −0.0258249 | − | 0.0258249i | ||||
\(953\) | 38.1698 | + | 38.1698i | 1.23644 | + | 1.23644i | 0.961446 | + | 0.274994i | \(0.0886759\pi\) |
0.274994 | + | 0.961446i | \(0.411324\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.153127 | + | 9.91743i | −0.00495506 | + | 0.320921i | ||||
\(956\) | 19.2176i | 0.621540i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.312644 | + | 0.312644i | −0.0101011 | + | 0.0101011i | ||||
\(959\) | −13.0421 | −0.421152 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5342 | −0.952715 | ||||||||
\(962\) | 46.8739 | − | 46.8739i | 1.51127 | − | 1.51127i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 29.0221i | − | 0.934740i | ||||||
\(965\) | −43.3333 | + | 42.0155i | −1.39495 | + | 1.35253i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25.2765 | + | 25.2765i | 0.812838 | + | 0.812838i | 0.985058 | − | 0.172221i | \(-0.0550942\pi\) |
−0.172221 | + | 0.985058i | \(0.555094\pi\) | |||||||
\(968\) | 4.51314 | + | 4.51314i | 0.145058 | + | 0.145058i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.67382 | − | 0.0721644i | −0.150067 | − | 0.00231706i | ||||
\(971\) | − | 8.47005i | − | 0.271817i | −0.990721 | − | 0.135908i | \(-0.956605\pi\) | ||
0.990721 | − | 0.135908i | \(-0.0433953\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.54291 | + | 5.54291i | −0.177698 | + | 0.177698i | ||||
\(974\) | −2.23633 | −0.0716568 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.7456 | −0.375968 | ||||||||
\(977\) | 28.3027 | − | 28.3027i | 0.905485 | − | 0.905485i | −0.0904191 | − | 0.995904i | \(-0.528821\pi\) |
0.995904 | + | 0.0904191i | \(0.0288206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.2658i | 0.743578i | ||||||||
\(980\) | −12.8115 | − | 0.197812i | −0.409249 | − | 0.00631887i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −21.0516 | − | 21.0516i | −0.671783 | − | 0.671783i | ||||
\(983\) | −13.4971 | − | 13.4971i | −0.430490 | − | 0.430490i | 0.458305 | − | 0.888795i | \(-0.348457\pi\) |
−0.888795 | + | 0.458305i | \(0.848457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.22093 | + | 6.03175i | −0.198215 | + | 0.192188i | ||||
\(986\) | − | 6.62043i | − | 0.210837i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.7254 | + | 18.7254i | −0.595734 | + | 0.595734i | ||||
\(989\) | −28.5699 | −0.908470 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.7401 | 0.595298 | 0.297649 | − | 0.954675i | \(-0.403798\pi\) | ||||
0.297649 | + | 0.954675i | \(0.403798\pi\) | |||||||
\(992\) | −0.856109 | + | 0.856109i | −0.0271815 | + | 0.0271815i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.96509i | 0.125765i | ||||||||
\(995\) | −0.405307 | + | 26.2502i | −0.0128491 | + | 0.832187i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −31.6882 | − | 31.6882i | −1.00358 | − | 1.00358i | −0.999994 | − | 0.00358261i | \(-0.998860\pi\) |
−0.00358261 | − | 0.999994i | \(-0.501140\pi\) | |||||||
\(998\) | 2.22056 | + | 2.22056i | 0.0702904 | + | 0.0702904i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1530.2.m.i.647.4 | ✓ | 16 | |
3.2 | odd | 2 | inner | 1530.2.m.i.647.5 | yes | 16 | |
5.3 | odd | 4 | inner | 1530.2.m.i.953.5 | yes | 16 | |
15.8 | even | 4 | inner | 1530.2.m.i.953.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1530.2.m.i.647.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1530.2.m.i.647.5 | yes | 16 | 3.2 | odd | 2 | inner | |
1530.2.m.i.953.4 | yes | 16 | 15.8 | even | 4 | inner | |
1530.2.m.i.953.5 | yes | 16 | 5.3 | odd | 4 | inner |