Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 169.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.169 |
Dual form | 462.2.j.c.421.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 0.587785i | 0.572061 | + | 0.415627i | ||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 2.92705 | − | 2.12663i | 1.30902 | − | 0.951057i | 0.309017 | − | 0.951057i | \(-0.400000\pi\) |
1.00000 | \(0\) | |||||||||
\(6\) | 0.809017 | − | 0.587785i | 0.330280 | − | 0.239962i | ||||
\(7\) | −0.309017 | − | 0.951057i | −0.116797 | − | 0.359466i | ||||
\(8\) | −0.309017 | + | 0.951057i | −0.109254 | + | 0.336249i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | 3.61803 | 1.14412 | ||||||||
\(11\) | 0.809017 | − | 3.21644i | 0.243928 | − | 0.969793i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −2.61803 | − | 1.90211i | −0.726112 | − | 0.527551i | 0.162219 | − | 0.986755i | \(-0.448135\pi\) |
−0.888331 | + | 0.459204i | \(0.848135\pi\) | |||||||
\(14\) | 0.309017 | − | 0.951057i | 0.0825883 | − | 0.254181i | ||||
\(15\) | −1.11803 | − | 3.44095i | −0.288675 | − | 0.888451i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −4.35410 | + | 3.16344i | −1.05602 | + | 0.767247i | −0.973349 | − | 0.229330i | \(-0.926347\pi\) |
−0.0826760 | + | 0.996576i | \(0.526347\pi\) | |||||||
\(18\) | −0.309017 | − | 0.951057i | −0.0728360 | − | 0.224166i | ||||
\(19\) | −2.19098 | + | 6.74315i | −0.502646 | + | 1.54699i | 0.302046 | + | 0.953293i | \(0.402330\pi\) |
−0.804692 | + | 0.593692i | \(0.797670\pi\) | |||||||
\(20\) | 2.92705 | + | 2.12663i | 0.654508 | + | 0.475528i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 2.54508 | − | 2.12663i | 0.542614 | − | 0.453398i | ||||
\(23\) | 6.32624 | 1.31911 | 0.659556 | − | 0.751656i | \(-0.270744\pi\) | ||||
0.659556 | + | 0.751656i | \(0.270744\pi\) | |||||||
\(24\) | 0.809017 | + | 0.587785i | 0.165140 | + | 0.119981i | ||||
\(25\) | 2.50000 | − | 7.69421i | 0.500000 | − | 1.53884i | ||||
\(26\) | −1.00000 | − | 3.07768i | −0.196116 | − | 0.603583i | ||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | 0.809017 | − | 0.587785i | 0.152890 | − | 0.111081i | ||||
\(29\) | 1.00000 | + | 3.07768i | 0.185695 | + | 0.571511i | 0.999960 | − | 0.00898281i | \(-0.00285936\pi\) |
−0.814264 | + | 0.580494i | \(0.802859\pi\) | |||||||
\(30\) | 1.11803 | − | 3.44095i | 0.204124 | − | 0.628230i | ||||
\(31\) | 8.16312 | + | 5.93085i | 1.46614 | + | 1.06521i | 0.981710 | + | 0.190382i | \(0.0609728\pi\) |
0.484429 | + | 0.874830i | \(0.339027\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.80902 | − | 1.76336i | −0.488987 | − | 0.306961i | ||||
\(34\) | −5.38197 | −0.923000 | ||||||||
\(35\) | −2.92705 | − | 2.12663i | −0.494762 | − | 0.359466i | ||||
\(36\) | 0.309017 | − | 0.951057i | 0.0515028 | − | 0.158509i | ||||
\(37\) | −1.97214 | − | 6.06961i | −0.324217 | − | 0.997838i | −0.971793 | − | 0.235837i | \(-0.924217\pi\) |
0.647576 | − | 0.762001i | \(-0.275783\pi\) | |||||||
\(38\) | −5.73607 | + | 4.16750i | −0.930513 | + | 0.676057i | ||||
\(39\) | −2.61803 | + | 1.90211i | −0.419221 | + | 0.304582i | ||||
\(40\) | 1.11803 | + | 3.44095i | 0.176777 | + | 0.544063i | ||||
\(41\) | 1.59017 | − | 4.89404i | 0.248343 | − | 0.764321i | −0.746726 | − | 0.665132i | \(-0.768375\pi\) |
0.995069 | − | 0.0991886i | \(-0.0316247\pi\) | |||||||
\(42\) | −0.809017 | − | 0.587785i | −0.124834 | − | 0.0906972i | ||||
\(43\) | 0.763932 | 0.116499 | 0.0582493 | − | 0.998302i | \(-0.481448\pi\) | ||||
0.0582493 | + | 0.998302i | \(0.481448\pi\) | |||||||
\(44\) | 3.30902 | − | 0.224514i | 0.498853 | − | 0.0338468i | ||||
\(45\) | −3.61803 | −0.539345 | ||||||||
\(46\) | 5.11803 | + | 3.71847i | 0.754613 | + | 0.548258i | ||||
\(47\) | −3.76393 | + | 11.5842i | −0.549026 | + | 1.68973i | 0.162194 | + | 0.986759i | \(0.448143\pi\) |
−0.711220 | + | 0.702969i | \(0.751857\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | 6.54508 | − | 4.75528i | 0.925615 | − | 0.672499i | ||||
\(51\) | 1.66312 | + | 5.11855i | 0.232883 | + | 0.716741i | ||||
\(52\) | 1.00000 | − | 3.07768i | 0.138675 | − | 0.426798i | ||||
\(53\) | 7.23607 | + | 5.25731i | 0.993950 | + | 0.722147i | 0.960783 | − | 0.277303i | \(-0.0894404\pi\) |
0.0331677 | + | 0.999450i | \(0.489440\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −4.47214 | − | 11.1352i | −0.603023 | − | 1.50147i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 5.73607 | + | 4.16750i | 0.759761 | + | 0.551999i | ||||
\(58\) | −1.00000 | + | 3.07768i | −0.131306 | + | 0.404120i | ||||
\(59\) | 2.76393 | + | 8.50651i | 0.359833 | + | 1.10745i | 0.953154 | + | 0.302487i | \(0.0978167\pi\) |
−0.593320 | + | 0.804966i | \(0.702183\pi\) | |||||||
\(60\) | 2.92705 | − | 2.12663i | 0.377881 | − | 0.274546i | ||||
\(61\) | 3.85410 | − | 2.80017i | 0.493467 | − | 0.358525i | −0.313049 | − | 0.949737i | \(-0.601350\pi\) |
0.806516 | + | 0.591212i | \(0.201350\pi\) | |||||||
\(62\) | 3.11803 | + | 9.59632i | 0.395991 | + | 1.21873i | ||||
\(63\) | −0.309017 | + | 0.951057i | −0.0389325 | + | 0.119822i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | −11.7082 | −1.45222 | ||||||||
\(66\) | −1.23607 | − | 3.07768i | −0.152149 | − | 0.378837i | ||||
\(67\) | 3.23607 | 0.395349 | 0.197674 | − | 0.980268i | \(-0.436661\pi\) | ||||
0.197674 | + | 0.980268i | \(0.436661\pi\) | |||||||
\(68\) | −4.35410 | − | 3.16344i | −0.528012 | − | 0.383623i | ||||
\(69\) | 1.95492 | − | 6.01661i | 0.235344 | − | 0.724315i | ||||
\(70\) | −1.11803 | − | 3.44095i | −0.133631 | − | 0.411273i | ||||
\(71\) | −8.47214 | + | 6.15537i | −1.00546 | + | 0.730508i | −0.963251 | − | 0.268601i | \(-0.913439\pi\) |
−0.0422061 | + | 0.999109i | \(0.513439\pi\) | |||||||
\(72\) | 0.809017 | − | 0.587785i | 0.0953436 | − | 0.0692712i | ||||
\(73\) | −2.47214 | − | 7.60845i | −0.289342 | − | 0.890502i | −0.985064 | − | 0.172191i | \(-0.944915\pi\) |
0.695722 | − | 0.718311i | \(-0.255085\pi\) | |||||||
\(74\) | 1.97214 | − | 6.06961i | 0.229256 | − | 0.705578i | ||||
\(75\) | −6.54508 | − | 4.75528i | −0.755761 | − | 0.549093i | ||||
\(76\) | −7.09017 | −0.813298 | ||||||||
\(77\) | −3.30902 | + | 0.224514i | −0.377097 | + | 0.0255857i | ||||
\(78\) | −3.23607 | −0.366413 | ||||||||
\(79\) | −4.61803 | − | 3.35520i | −0.519569 | − | 0.377489i | 0.296872 | − | 0.954917i | \(-0.404056\pi\) |
−0.816442 | + | 0.577428i | \(0.804056\pi\) | |||||||
\(80\) | −1.11803 | + | 3.44095i | −0.125000 | + | 0.384710i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | 4.16312 | − | 3.02468i | 0.459740 | − | 0.334020i | ||||
\(83\) | −8.70820 | + | 6.32688i | −0.955850 | + | 0.694465i | −0.952183 | − | 0.305528i | \(-0.901167\pi\) |
−0.00366644 | + | 0.999993i | \(0.501167\pi\) | |||||||
\(84\) | −0.309017 | − | 0.951057i | −0.0337165 | − | 0.103769i | ||||
\(85\) | −6.01722 | + | 18.5191i | −0.652659 | + | 2.00868i | ||||
\(86\) | 0.618034 | + | 0.449028i | 0.0666443 | + | 0.0484199i | ||||
\(87\) | 3.23607 | 0.346943 | ||||||||
\(88\) | 2.80902 | + | 1.76336i | 0.299442 | + | 0.187974i | ||||
\(89\) | −11.8541 | −1.25653 | −0.628266 | − | 0.777998i | \(-0.716235\pi\) | ||||
−0.628266 | + | 0.777998i | \(0.716235\pi\) | |||||||
\(90\) | −2.92705 | − | 2.12663i | −0.308538 | − | 0.224166i | ||||
\(91\) | −1.00000 | + | 3.07768i | −0.104828 | + | 0.322629i | ||||
\(92\) | 1.95492 | + | 6.01661i | 0.203814 | + | 0.627275i | ||||
\(93\) | 8.16312 | − | 5.93085i | 0.846476 | − | 0.615001i | ||||
\(94\) | −9.85410 | + | 7.15942i | −1.01637 | + | 0.738438i | ||||
\(95\) | 7.92705 | + | 24.3970i | 0.813298 | + | 2.50307i | ||||
\(96\) | −0.309017 | + | 0.951057i | −0.0315389 | + | 0.0970668i | ||||
\(97\) | −5.47214 | − | 3.97574i | −0.555611 | − | 0.403675i | 0.274239 | − | 0.961662i | \(-0.411574\pi\) |
−0.829850 | + | 0.557986i | \(0.811574\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −2.54508 | + | 2.12663i | −0.255791 | + | 0.213734i | ||||
\(100\) | 8.09017 | 0.809017 | ||||||||
\(101\) | −4.16312 | − | 3.02468i | −0.414246 | − | 0.300967i | 0.361073 | − | 0.932538i | \(-0.382411\pi\) |
−0.775318 | + | 0.631570i | \(0.782411\pi\) | |||||||
\(102\) | −1.66312 | + | 5.11855i | −0.164673 | + | 0.506812i | ||||
\(103\) | −5.80902 | − | 17.8783i | −0.572379 | − | 1.76160i | −0.644934 | − | 0.764238i | \(-0.723115\pi\) |
0.0725544 | − | 0.997364i | \(-0.476885\pi\) | |||||||
\(104\) | 2.61803 | − | 1.90211i | 0.256719 | − | 0.186518i | ||||
\(105\) | −2.92705 | + | 2.12663i | −0.285651 | + | 0.207538i | ||||
\(106\) | 2.76393 | + | 8.50651i | 0.268457 | + | 0.826225i | ||||
\(107\) | 3.10081 | − | 9.54332i | 0.299767 | − | 0.922588i | −0.681811 | − | 0.731528i | \(-0.738808\pi\) |
0.981578 | − | 0.191060i | \(-0.0611924\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 2.38197 | 0.228151 | 0.114075 | − | 0.993472i | \(-0.463609\pi\) | ||||
0.114075 | + | 0.993472i | \(0.463609\pi\) | |||||||
\(110\) | 2.92705 | − | 11.6372i | 0.279083 | − | 1.10956i | ||||
\(111\) | −6.38197 | −0.605749 | ||||||||
\(112\) | 0.809017 | + | 0.587785i | 0.0764449 | + | 0.0555405i | ||||
\(113\) | 0.763932 | − | 2.35114i | 0.0718647 | − | 0.221177i | −0.908673 | − | 0.417509i | \(-0.862903\pi\) |
0.980537 | + | 0.196332i | \(0.0629032\pi\) | |||||||
\(114\) | 2.19098 | + | 6.74315i | 0.205204 | + | 0.631554i | ||||
\(115\) | 18.5172 | − | 13.4535i | 1.72674 | − | 1.25455i | ||||
\(116\) | −2.61803 | + | 1.90211i | −0.243078 | + | 0.176607i | ||||
\(117\) | 1.00000 | + | 3.07768i | 0.0924500 | + | 0.284532i | ||||
\(118\) | −2.76393 | + | 8.50651i | −0.254441 | + | 0.783088i | ||||
\(119\) | 4.35410 | + | 3.16344i | 0.399140 | + | 0.289992i | ||||
\(120\) | 3.61803 | 0.330280 | ||||||||
\(121\) | −9.69098 | − | 5.20431i | −0.880998 | − | 0.473119i | ||||
\(122\) | 4.76393 | 0.431306 | ||||||||
\(123\) | −4.16312 | − | 3.02468i | −0.375376 | − | 0.272726i | ||||
\(124\) | −3.11803 | + | 9.59632i | −0.280008 | + | 0.861775i | ||||
\(125\) | −3.45492 | − | 10.6331i | −0.309017 | − | 0.951057i | ||||
\(126\) | −0.809017 | + | 0.587785i | −0.0720730 | + | 0.0523641i | ||||
\(127\) | −5.47214 | + | 3.97574i | −0.485574 | + | 0.352790i | −0.803480 | − | 0.595332i | \(-0.797020\pi\) |
0.317906 | + | 0.948122i | \(0.397020\pi\) | |||||||
\(128\) | −0.309017 | − | 0.951057i | −0.0273135 | − | 0.0840623i | ||||
\(129\) | 0.236068 | − | 0.726543i | 0.0207846 | − | 0.0639685i | ||||
\(130\) | −9.47214 | − | 6.88191i | −0.830761 | − | 0.603583i | ||||
\(131\) | 10.7639 | 0.940449 | 0.470225 | − | 0.882547i | \(-0.344173\pi\) | ||||
0.470225 | + | 0.882547i | \(0.344173\pi\) | |||||||
\(132\) | 0.809017 | − | 3.21644i | 0.0704159 | − | 0.279955i | ||||
\(133\) | 7.09017 | 0.614796 | ||||||||
\(134\) | 2.61803 | + | 1.90211i | 0.226164 | + | 0.164318i | ||||
\(135\) | −1.11803 | + | 3.44095i | −0.0962250 | + | 0.296150i | ||||
\(136\) | −1.66312 | − | 5.11855i | −0.142611 | − | 0.438912i | ||||
\(137\) | 2.00000 | − | 1.45309i | 0.170872 | − | 0.124145i | −0.499063 | − | 0.866566i | \(-0.666322\pi\) |
0.669934 | + | 0.742420i | \(0.266322\pi\) | |||||||
\(138\) | 5.11803 | − | 3.71847i | 0.435676 | − | 0.316537i | ||||
\(139\) | 3.13525 | + | 9.64932i | 0.265929 | + | 0.818445i | 0.991478 | + | 0.130274i | \(0.0415858\pi\) |
−0.725549 | + | 0.688170i | \(0.758414\pi\) | |||||||
\(140\) | 1.11803 | − | 3.44095i | 0.0944911 | − | 0.290814i | ||||
\(141\) | 9.85410 | + | 7.15942i | 0.829865 | + | 0.602932i | ||||
\(142\) | −10.4721 | −0.878802 | ||||||||
\(143\) | −8.23607 | + | 6.88191i | −0.688735 | + | 0.575494i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 9.47214 | + | 6.88191i | 0.786618 | + | 0.571511i | ||||
\(146\) | 2.47214 | − | 7.60845i | 0.204595 | − | 0.629680i | ||||
\(147\) | 0.309017 | + | 0.951057i | 0.0254873 | + | 0.0784418i | ||||
\(148\) | 5.16312 | − | 3.75123i | 0.424406 | − | 0.308349i | ||||
\(149\) | −6.00000 | + | 4.35926i | −0.491539 | + | 0.357124i | −0.805776 | − | 0.592221i | \(-0.798251\pi\) |
0.314237 | + | 0.949345i | \(0.398251\pi\) | |||||||
\(150\) | −2.50000 | − | 7.69421i | −0.204124 | − | 0.628230i | ||||
\(151\) | 2.76393 | − | 8.50651i | 0.224926 | − | 0.692250i | −0.773374 | − | 0.633951i | \(-0.781432\pi\) |
0.998299 | − | 0.0582992i | \(-0.0185677\pi\) | |||||||
\(152\) | −5.73607 | − | 4.16750i | −0.465257 | − | 0.338029i | ||||
\(153\) | 5.38197 | 0.435106 | ||||||||
\(154\) | −2.80902 | − | 1.76336i | −0.226357 | − | 0.142095i | ||||
\(155\) | 36.5066 | 2.93228 | ||||||||
\(156\) | −2.61803 | − | 1.90211i | −0.209610 | − | 0.152291i | ||||
\(157\) | −3.00000 | + | 9.23305i | −0.239426 | + | 0.736878i | 0.757077 | + | 0.653325i | \(0.226627\pi\) |
−0.996503 | + | 0.0835524i | \(0.973373\pi\) | |||||||
\(158\) | −1.76393 | − | 5.42882i | −0.140331 | − | 0.431894i | ||||
\(159\) | 7.23607 | − | 5.25731i | 0.573858 | − | 0.416932i | ||||
\(160\) | −2.92705 | + | 2.12663i | −0.231404 | + | 0.168125i | ||||
\(161\) | −1.95492 | − | 6.01661i | −0.154069 | − | 0.474175i | ||||
\(162\) | −0.309017 | + | 0.951057i | −0.0242787 | + | 0.0747221i | ||||
\(163\) | −9.32624 | − | 6.77591i | −0.730487 | − | 0.530730i | 0.159230 | − | 0.987241i | \(-0.449099\pi\) |
−0.889718 | + | 0.456511i | \(0.849099\pi\) | |||||||
\(164\) | 5.14590 | 0.401827 | ||||||||
\(165\) | −11.9721 | + | 0.812299i | −0.932030 | + | 0.0632374i | ||||
\(166\) | −10.7639 | −0.835443 | ||||||||
\(167\) | −13.3262 | − | 9.68208i | −1.03122 | − | 0.749222i | −0.0626637 | − | 0.998035i | \(-0.519960\pi\) |
−0.968552 | + | 0.248813i | \(0.919960\pi\) | |||||||
\(168\) | 0.309017 | − | 0.951057i | 0.0238412 | − | 0.0733756i | ||||
\(169\) | −0.781153 | − | 2.40414i | −0.0600887 | − | 0.184934i | ||||
\(170\) | −15.7533 | + | 11.4454i | −1.20822 | + | 0.877825i | ||||
\(171\) | 5.73607 | − | 4.16750i | 0.438648 | − | 0.318696i | ||||
\(172\) | 0.236068 | + | 0.726543i | 0.0180000 | + | 0.0553983i | ||||
\(173\) | 0.0450850 | − | 0.138757i | 0.00342775 | − | 0.0105495i | −0.949328 | − | 0.314287i | \(-0.898235\pi\) |
0.952756 | + | 0.303737i | \(0.0982346\pi\) | |||||||
\(174\) | 2.61803 | + | 1.90211i | 0.198473 | + | 0.144199i | ||||
\(175\) | −8.09017 | −0.611559 | ||||||||
\(176\) | 1.23607 | + | 3.07768i | 0.0931721 | + | 0.231989i | ||||
\(177\) | 8.94427 | 0.672293 | ||||||||
\(178\) | −9.59017 | − | 6.96767i | −0.718814 | − | 0.522249i | ||||
\(179\) | 0.444272 | − | 1.36733i | 0.0332064 | − | 0.102199i | −0.933080 | − | 0.359670i | \(-0.882889\pi\) |
0.966286 | + | 0.257471i | \(0.0828892\pi\) | |||||||
\(180\) | −1.11803 | − | 3.44095i | −0.0833333 | − | 0.256474i | ||||
\(181\) | −6.47214 | + | 4.70228i | −0.481070 | + | 0.349518i | −0.801740 | − | 0.597673i | \(-0.796092\pi\) |
0.320670 | + | 0.947191i | \(0.396092\pi\) | |||||||
\(182\) | −2.61803 | + | 1.90211i | −0.194062 | + | 0.140994i | ||||
\(183\) | −1.47214 | − | 4.53077i | −0.108823 | − | 0.334924i | ||||
\(184\) | −1.95492 | + | 6.01661i | −0.144118 | + | 0.443550i | ||||
\(185\) | −18.6803 | − | 13.5721i | −1.37341 | − | 0.997838i | ||||
\(186\) | 10.0902 | 0.739847 | ||||||||
\(187\) | 6.65248 | + | 16.5640i | 0.486477 | + | 1.21128i | ||||
\(188\) | −12.1803 | −0.888343 | ||||||||
\(189\) | 0.809017 | + | 0.587785i | 0.0588473 | + | 0.0427551i | ||||
\(190\) | −7.92705 | + | 24.3970i | −0.575089 | + | 1.76994i | ||||
\(191\) | −0.0278640 | − | 0.0857567i | −0.00201617 | − | 0.00620514i | 0.950043 | − | 0.312118i | \(-0.101038\pi\) |
−0.952060 | + | 0.305913i | \(0.901038\pi\) | |||||||
\(192\) | −0.809017 | + | 0.587785i | −0.0583858 | + | 0.0424197i | ||||
\(193\) | −3.92705 | + | 2.85317i | −0.282675 | + | 0.205376i | −0.720083 | − | 0.693887i | \(-0.755897\pi\) |
0.437408 | + | 0.899263i | \(0.355897\pi\) | |||||||
\(194\) | −2.09017 | − | 6.43288i | −0.150065 | − | 0.461854i | ||||
\(195\) | −3.61803 | + | 11.1352i | −0.259093 | + | 0.797406i | ||||
\(196\) | −0.809017 | − | 0.587785i | −0.0577869 | − | 0.0419847i | ||||
\(197\) | 23.2361 | 1.65550 | 0.827751 | − | 0.561096i | \(-0.189620\pi\) | ||||
0.827751 | + | 0.561096i | \(0.189620\pi\) | |||||||
\(198\) | −3.30902 | + | 0.224514i | −0.235162 | + | 0.0159555i | ||||
\(199\) | 25.2705 | 1.79138 | 0.895689 | − | 0.444680i | \(-0.146683\pi\) | ||||
0.895689 | + | 0.444680i | \(0.146683\pi\) | |||||||
\(200\) | 6.54508 | + | 4.75528i | 0.462807 | + | 0.336249i | ||||
\(201\) | 1.00000 | − | 3.07768i | 0.0705346 | − | 0.217083i | ||||
\(202\) | −1.59017 | − | 4.89404i | −0.111884 | − | 0.344343i | ||||
\(203\) | 2.61803 | − | 1.90211i | 0.183750 | − | 0.133502i | ||||
\(204\) | −4.35410 | + | 3.16344i | −0.304848 | + | 0.221485i | ||||
\(205\) | −5.75329 | − | 17.7068i | −0.401827 | − | 1.23670i | ||||
\(206\) | 5.80902 | − | 17.8783i | 0.404733 | − | 1.24564i | ||||
\(207\) | −5.11803 | − | 3.71847i | −0.355728 | − | 0.258451i | ||||
\(208\) | 3.23607 | 0.224381 | ||||||||
\(209\) | 19.9164 | + | 12.5025i | 1.37765 | + | 0.864815i | ||||
\(210\) | −3.61803 | −0.249668 | ||||||||
\(211\) | −4.23607 | − | 3.07768i | −0.291623 | − | 0.211876i | 0.432348 | − | 0.901707i | \(-0.357685\pi\) |
−0.723971 | + | 0.689830i | \(0.757685\pi\) | |||||||
\(212\) | −2.76393 | + | 8.50651i | −0.189828 | + | 0.584229i | ||||
\(213\) | 3.23607 | + | 9.95959i | 0.221732 | + | 0.682420i | ||||
\(214\) | 8.11803 | − | 5.89810i | 0.554937 | − | 0.403186i | ||||
\(215\) | 2.23607 | − | 1.62460i | 0.152499 | − | 0.110797i | ||||
\(216\) | −0.309017 | − | 0.951057i | −0.0210259 | − | 0.0647112i | ||||
\(217\) | 3.11803 | − | 9.59632i | 0.211666 | − | 0.651441i | ||||
\(218\) | 1.92705 | + | 1.40008i | 0.130516 | + | 0.0948257i | ||||
\(219\) | −8.00000 | −0.540590 | ||||||||
\(220\) | 9.20820 | − | 7.69421i | 0.620817 | − | 0.518743i | ||||
\(221\) | 17.4164 | 1.17155 | ||||||||
\(222\) | −5.16312 | − | 3.75123i | −0.346526 | − | 0.251766i | ||||
\(223\) | 3.04508 | − | 9.37181i | 0.203914 | − | 0.627583i | −0.795842 | − | 0.605504i | \(-0.792972\pi\) |
0.999756 | − | 0.0220787i | \(-0.00702843\pi\) | |||||||
\(224\) | 0.309017 | + | 0.951057i | 0.0206471 | + | 0.0635451i | ||||
\(225\) | −6.54508 | + | 4.75528i | −0.436339 | + | 0.317019i | ||||
\(226\) | 2.00000 | − | 1.45309i | 0.133038 | − | 0.0966578i | ||||
\(227\) | 6.94427 | + | 21.3723i | 0.460908 | + | 1.41853i | 0.864057 | + | 0.503393i | \(0.167915\pi\) |
−0.403150 | + | 0.915134i | \(0.632085\pi\) | |||||||
\(228\) | −2.19098 | + | 6.74315i | −0.145101 | + | 0.446576i | ||||
\(229\) | −20.0902 | − | 14.5964i | −1.32760 | − | 0.964555i | −0.999804 | − | 0.0198049i | \(-0.993696\pi\) |
−0.327792 | − | 0.944750i | \(-0.606304\pi\) | |||||||
\(230\) | 22.8885 | 1.50923 | ||||||||
\(231\) | −0.809017 | + | 3.21644i | −0.0532294 | + | 0.211626i | ||||
\(232\) | −3.23607 | −0.212458 | ||||||||
\(233\) | 12.8541 | + | 9.33905i | 0.842100 | + | 0.611822i | 0.922957 | − | 0.384904i | \(-0.125765\pi\) |
−0.0808563 | + | 0.996726i | \(0.525765\pi\) | |||||||
\(234\) | −1.00000 | + | 3.07768i | −0.0653720 | + | 0.201194i | ||||
\(235\) | 13.6180 | + | 41.9120i | 0.888343 | + | 2.73404i | ||||
\(236\) | −7.23607 | + | 5.25731i | −0.471028 | + | 0.342222i | ||||
\(237\) | −4.61803 | + | 3.35520i | −0.299974 | + | 0.217944i | ||||
\(238\) | 1.66312 | + | 5.11855i | 0.107804 | + | 0.331787i | ||||
\(239\) | 2.89919 | − | 8.92278i | 0.187533 | − | 0.577167i | −0.812450 | − | 0.583031i | \(-0.801867\pi\) |
0.999983 | + | 0.00586423i | \(0.00186665\pi\) | |||||||
\(240\) | 2.92705 | + | 2.12663i | 0.188940 | + | 0.137273i | ||||
\(241\) | 16.1803 | 1.04227 | 0.521134 | − | 0.853475i | \(-0.325509\pi\) | ||||
0.521134 | + | 0.853475i | \(0.325509\pi\) | |||||||
\(242\) | −4.78115 | − | 9.90659i | −0.307344 | − | 0.636820i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 3.85410 | + | 2.80017i | 0.246734 | + | 0.179262i | ||||
\(245\) | −1.11803 | + | 3.44095i | −0.0714286 | + | 0.219835i | ||||
\(246\) | −1.59017 | − | 4.89404i | −0.101386 | − | 0.312033i | ||||
\(247\) | 18.5623 | − | 13.4863i | 1.18109 | − | 0.858113i | ||||
\(248\) | −8.16312 | + | 5.93085i | −0.518359 | + | 0.376610i | ||||
\(249\) | 3.32624 | + | 10.2371i | 0.210792 | + | 0.648750i | ||||
\(250\) | 3.45492 | − | 10.6331i | 0.218508 | − | 0.672499i | ||||
\(251\) | −7.23607 | − | 5.25731i | −0.456737 | − | 0.331839i | 0.335513 | − | 0.942036i | \(-0.391090\pi\) |
−0.792250 | + | 0.610197i | \(0.791090\pi\) | |||||||
\(252\) | −1.00000 | −0.0629941 | ||||||||
\(253\) | 5.11803 | − | 20.3480i | 0.321768 | − | 1.27927i | ||||
\(254\) | −6.76393 | −0.424407 | ||||||||
\(255\) | 15.7533 | + | 11.4454i | 0.986509 | + | 0.716741i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | −4.89919 | − | 15.0781i | −0.305603 | − | 0.940549i | −0.979452 | − | 0.201680i | \(-0.935360\pi\) |
0.673849 | − | 0.738869i | \(-0.264640\pi\) | |||||||
\(258\) | 0.618034 | − | 0.449028i | 0.0384771 | − | 0.0279553i | ||||
\(259\) | −5.16312 | + | 3.75123i | −0.320821 | + | 0.233090i | ||||
\(260\) | −3.61803 | − | 11.1352i | −0.224381 | − | 0.690574i | ||||
\(261\) | 1.00000 | − | 3.07768i | 0.0618984 | − | 0.190504i | ||||
\(262\) | 8.70820 | + | 6.32688i | 0.537995 | + | 0.390876i | ||||
\(263\) | −22.0344 | −1.35870 | −0.679351 | − | 0.733814i | \(-0.737739\pi\) | ||||
−0.679351 | + | 0.733814i | \(0.737739\pi\) | |||||||
\(264\) | 2.54508 | − | 2.12663i | 0.156639 | − | 0.130885i | ||||
\(265\) | 32.3607 | 1.98790 | ||||||||
\(266\) | 5.73607 | + | 4.16750i | 0.351701 | + | 0.255526i | ||||
\(267\) | −3.66312 | + | 11.2739i | −0.224179 | + | 0.689953i | ||||
\(268\) | 1.00000 | + | 3.07768i | 0.0610847 | + | 0.187999i | ||||
\(269\) | −4.85410 | + | 3.52671i | −0.295960 | + | 0.215027i | −0.725849 | − | 0.687854i | \(-0.758553\pi\) |
0.429889 | + | 0.902882i | \(0.358553\pi\) | |||||||
\(270\) | −2.92705 | + | 2.12663i | −0.178135 | + | 0.129422i | ||||
\(271\) | −1.88197 | − | 5.79210i | −0.114321 | − | 0.351845i | 0.877484 | − | 0.479607i | \(-0.159221\pi\) |
−0.991805 | + | 0.127762i | \(0.959221\pi\) | |||||||
\(272\) | 1.66312 | − | 5.11855i | 0.100841 | − | 0.310358i | ||||
\(273\) | 2.61803 | + | 1.90211i | 0.158451 | + | 0.115121i | ||||
\(274\) | 2.47214 | 0.149347 | ||||||||
\(275\) | −22.7254 | − | 14.2658i | −1.37039 | − | 0.860263i | ||||
\(276\) | 6.32624 | 0.380795 | ||||||||
\(277\) | −7.97214 | − | 5.79210i | −0.478999 | − | 0.348013i | 0.321939 | − | 0.946760i | \(-0.395665\pi\) |
−0.800938 | + | 0.598747i | \(0.795665\pi\) | |||||||
\(278\) | −3.13525 | + | 9.64932i | −0.188040 | + | 0.578728i | ||||
\(279\) | −3.11803 | − | 9.59632i | −0.186672 | − | 0.574517i | ||||
\(280\) | 2.92705 | − | 2.12663i | 0.174925 | − | 0.127090i | ||||
\(281\) | 13.4721 | − | 9.78808i | 0.803680 | − | 0.583908i | −0.108311 | − | 0.994117i | \(-0.534544\pi\) |
0.911991 | + | 0.410209i | \(0.134544\pi\) | |||||||
\(282\) | 3.76393 | + | 11.5842i | 0.224139 | + | 0.689829i | ||||
\(283\) | −3.11803 | + | 9.59632i | −0.185348 | + | 0.570442i | −0.999954 | − | 0.00957216i | \(-0.996953\pi\) |
0.814606 | + | 0.580014i | \(0.196953\pi\) | |||||||
\(284\) | −8.47214 | − | 6.15537i | −0.502729 | − | 0.365254i | ||||
\(285\) | 25.6525 | 1.51952 | ||||||||
\(286\) | −10.7082 | + | 0.726543i | −0.633189 | + | 0.0429614i | ||||
\(287\) | −5.14590 | −0.303753 | ||||||||
\(288\) | 0.809017 | + | 0.587785i | 0.0476718 | + | 0.0346356i | ||||
\(289\) | 3.69756 | − | 11.3799i | 0.217504 | − | 0.669407i | ||||
\(290\) | 3.61803 | + | 11.1352i | 0.212458 | + | 0.653879i | ||||
\(291\) | −5.47214 | + | 3.97574i | −0.320782 | + | 0.233062i | ||||
\(292\) | 6.47214 | − | 4.70228i | 0.378753 | − | 0.275180i | ||||
\(293\) | −4.88197 | − | 15.0251i | −0.285207 | − | 0.877778i | −0.986336 | − | 0.164744i | \(-0.947320\pi\) |
0.701129 | − | 0.713035i | \(-0.252680\pi\) | |||||||
\(294\) | −0.309017 | + | 0.951057i | −0.0180222 | + | 0.0554667i | ||||
\(295\) | 26.1803 | + | 19.0211i | 1.52428 | + | 1.10745i | ||||
\(296\) | 6.38197 | 0.370944 | ||||||||
\(297\) | 1.23607 | + | 3.07768i | 0.0717239 | + | 0.178585i | ||||
\(298\) | −7.41641 | −0.429621 | ||||||||
\(299\) | −16.5623 | − | 12.0332i | −0.957823 | − | 0.695899i | ||||
\(300\) | 2.50000 | − | 7.69421i | 0.144338 | − | 0.444225i | ||||
\(301\) | −0.236068 | − | 0.726543i | −0.0136067 | − | 0.0418772i | ||||
\(302\) | 7.23607 | − | 5.25731i | 0.416389 | − | 0.302524i | ||||
\(303\) | −4.16312 | + | 3.02468i | −0.239165 | + | 0.173763i | ||||
\(304\) | −2.19098 | − | 6.74315i | −0.125661 | − | 0.386746i | ||||
\(305\) | 5.32624 | − | 16.3925i | 0.304979 | − | 0.938630i | ||||
\(306\) | 4.35410 | + | 3.16344i | 0.248907 | + | 0.180842i | ||||
\(307\) | 9.14590 | 0.521984 | 0.260992 | − | 0.965341i | \(-0.415950\pi\) | ||||
0.260992 | + | 0.965341i | \(0.415950\pi\) | |||||||
\(308\) | −1.23607 | − | 3.07768i | −0.0704315 | − | 0.175367i | ||||
\(309\) | −18.7984 | −1.06940 | ||||||||
\(310\) | 29.5344 | + | 21.4580i | 1.67744 | + | 1.21873i | ||||
\(311\) | −6.94427 | + | 21.3723i | −0.393774 | + | 1.21191i | 0.536139 | + | 0.844130i | \(0.319882\pi\) |
−0.929913 | + | 0.367781i | \(0.880118\pi\) | |||||||
\(312\) | −1.00000 | − | 3.07768i | −0.0566139 | − | 0.174240i | ||||
\(313\) | −22.4164 | + | 16.2865i | −1.26705 | + | 0.920566i | −0.999081 | − | 0.0428615i | \(-0.986353\pi\) |
−0.267969 | + | 0.963427i | \(0.586353\pi\) | |||||||
\(314\) | −7.85410 | + | 5.70634i | −0.443233 | + | 0.322027i | ||||
\(315\) | 1.11803 | + | 3.44095i | 0.0629941 | + | 0.193876i | ||||
\(316\) | 1.76393 | − | 5.42882i | 0.0992289 | − | 0.305395i | ||||
\(317\) | −9.70820 | − | 7.05342i | −0.545267 | − | 0.396160i | 0.280770 | − | 0.959775i | \(-0.409410\pi\) |
−0.826037 | + | 0.563615i | \(0.809410\pi\) | |||||||
\(318\) | 8.94427 | 0.501570 | ||||||||
\(319\) | 10.7082 | − | 0.726543i | 0.599544 | − | 0.0406786i | ||||
\(320\) | −3.61803 | −0.202254 | ||||||||
\(321\) | −8.11803 | − | 5.89810i | −0.453104 | − | 0.329200i | ||||
\(322\) | 1.95492 | − | 6.01661i | 0.108943 | − | 0.335293i | ||||
\(323\) | −11.7918 | − | 36.2914i | −0.656113 | − | 2.01931i | ||||
\(324\) | −0.809017 | + | 0.587785i | −0.0449454 | + | 0.0326547i | ||||
\(325\) | −21.1803 | + | 15.3884i | −1.17487 | + | 0.853596i | ||||
\(326\) | −3.56231 | − | 10.9637i | −0.197298 | − | 0.607220i | ||||
\(327\) | 0.736068 | − | 2.26538i | 0.0407047 | − | 0.125276i | ||||
\(328\) | 4.16312 | + | 3.02468i | 0.229870 | + | 0.167010i | ||||
\(329\) | 12.1803 | 0.671524 | ||||||||
\(330\) | −10.1631 | − | 6.37988i | −0.559461 | − | 0.351201i | ||||
\(331\) | 22.1803 | 1.21914 | 0.609571 | − | 0.792732i | \(-0.291342\pi\) | ||||
0.609571 | + | 0.792732i | \(0.291342\pi\) | |||||||
\(332\) | −8.70820 | − | 6.32688i | −0.477925 | − | 0.347233i | ||||
\(333\) | −1.97214 | + | 6.06961i | −0.108072 | + | 0.332613i | ||||
\(334\) | −5.09017 | − | 15.6659i | −0.278522 | − | 0.857202i | ||||
\(335\) | 9.47214 | − | 6.88191i | 0.517518 | − | 0.375999i | ||||
\(336\) | 0.809017 | − | 0.587785i | 0.0441355 | − | 0.0320663i | ||||
\(337\) | 2.26393 | + | 6.96767i | 0.123324 | + | 0.379553i | 0.993592 | − | 0.113026i | \(-0.0360543\pi\) |
−0.870268 | + | 0.492579i | \(0.836054\pi\) | |||||||
\(338\) | 0.781153 | − | 2.40414i | 0.0424891 | − | 0.130768i | ||||
\(339\) | −2.00000 | − | 1.45309i | −0.108625 | − | 0.0789207i | ||||
\(340\) | −19.4721 | −1.05602 | ||||||||
\(341\) | 25.6803 | − | 21.4580i | 1.39067 | − | 1.16202i | ||||
\(342\) | 7.09017 | 0.383392 | ||||||||
\(343\) | 0.809017 | + | 0.587785i | 0.0436828 | + | 0.0317374i | ||||
\(344\) | −0.236068 | + | 0.726543i | −0.0127279 | + | 0.0391725i | ||||
\(345\) | −7.07295 | − | 21.7683i | −0.380795 | − | 1.17197i | ||||
\(346\) | 0.118034 | − | 0.0857567i | 0.00634555 | − | 0.00461031i | ||||
\(347\) | 11.1631 | − | 8.11048i | 0.599268 | − | 0.435393i | −0.246351 | − | 0.969181i | \(-0.579232\pi\) |
0.845619 | + | 0.533787i | \(0.179232\pi\) | |||||||
\(348\) | 1.00000 | + | 3.07768i | 0.0536056 | + | 0.164981i | ||||
\(349\) | −5.70820 | + | 17.5680i | −0.305553 | + | 0.940396i | 0.673917 | + | 0.738807i | \(0.264610\pi\) |
−0.979470 | + | 0.201589i | \(0.935390\pi\) | |||||||
\(350\) | −6.54508 | − | 4.75528i | −0.349850 | − | 0.254181i | ||||
\(351\) | 3.23607 | 0.172729 | ||||||||
\(352\) | −0.809017 | + | 3.21644i | −0.0431208 | + | 0.171437i | ||||
\(353\) | 5.05573 | 0.269089 | 0.134545 | − | 0.990908i | \(-0.457043\pi\) | ||||
0.134545 | + | 0.990908i | \(0.457043\pi\) | |||||||
\(354\) | 7.23607 | + | 5.25731i | 0.384593 | + | 0.279423i | ||||
\(355\) | −11.7082 | + | 36.0341i | −0.621407 | + | 1.91249i | ||||
\(356\) | −3.66312 | − | 11.2739i | −0.194145 | − | 0.597517i | ||||
\(357\) | 4.35410 | − | 3.16344i | 0.230444 | − | 0.167427i | ||||
\(358\) | 1.16312 | − | 0.845055i | 0.0614727 | − | 0.0446626i | ||||
\(359\) | 6.55573 | + | 20.1765i | 0.345998 | + | 1.06487i | 0.961047 | + | 0.276384i | \(0.0891361\pi\) |
−0.615049 | + | 0.788489i | \(0.710864\pi\) | |||||||
\(360\) | 1.11803 | − | 3.44095i | 0.0589256 | − | 0.181354i | ||||
\(361\) | −25.2984 | − | 18.3803i | −1.33149 | − | 0.967387i | ||||
\(362\) | −8.00000 | −0.420471 | ||||||||
\(363\) | −7.94427 | + | 7.60845i | −0.416966 | + | 0.399340i | ||||
\(364\) | −3.23607 | −0.169616 | ||||||||
\(365\) | −23.4164 | − | 17.0130i | −1.22567 | − | 0.890502i | ||||
\(366\) | 1.47214 | − | 4.53077i | 0.0769498 | − | 0.236827i | ||||
\(367\) | 0.173762 | + | 0.534785i | 0.00907031 | + | 0.0279155i | 0.955489 | − | 0.295026i | \(-0.0953283\pi\) |
−0.946419 | + | 0.322941i | \(0.895328\pi\) | |||||||
\(368\) | −5.11803 | + | 3.71847i | −0.266796 | + | 0.193839i | ||||
\(369\) | −4.16312 | + | 3.02468i | −0.216723 | + | 0.157459i | ||||
\(370\) | −7.13525 | − | 21.9601i | −0.370944 | − | 1.14165i | ||||
\(371\) | 2.76393 | − | 8.50651i | 0.143496 | − | 0.441636i | ||||
\(372\) | 8.16312 | + | 5.93085i | 0.423238 | + | 0.307500i | ||||
\(373\) | −11.5066 | −0.595788 | −0.297894 | − | 0.954599i | \(-0.596284\pi\) | ||||
−0.297894 | + | 0.954599i | \(0.596284\pi\) | |||||||
\(374\) | −4.35410 | + | 17.3108i | −0.225145 | + | 0.895119i | ||||
\(375\) | −11.1803 | −0.577350 | ||||||||
\(376\) | −9.85410 | − | 7.15942i | −0.508187 | − | 0.369219i | ||||
\(377\) | 3.23607 | − | 9.95959i | 0.166666 | − | 0.512945i | ||||
\(378\) | 0.309017 | + | 0.951057i | 0.0158941 | + | 0.0489171i | ||||
\(379\) | −6.70820 | + | 4.87380i | −0.344577 | + | 0.250350i | −0.746591 | − | 0.665284i | \(-0.768311\pi\) |
0.402013 | + | 0.915634i | \(0.368311\pi\) | |||||||
\(380\) | −20.7533 | + | 15.0781i | −1.06462 | + | 0.773493i | ||||
\(381\) | 2.09017 | + | 6.43288i | 0.107083 | + | 0.329567i | ||||
\(382\) | 0.0278640 | − | 0.0857567i | 0.00142565 | − | 0.00438770i | ||||
\(383\) | −4.85410 | − | 3.52671i | −0.248033 | − | 0.180207i | 0.456822 | − | 0.889558i | \(-0.348988\pi\) |
−0.704855 | + | 0.709352i | \(0.748988\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −9.20820 | + | 7.69421i | −0.469294 | + | 0.392133i | ||||
\(386\) | −4.85410 | −0.247067 | ||||||||
\(387\) | −0.618034 | − | 0.449028i | −0.0314164 | − | 0.0228254i | ||||
\(388\) | 2.09017 | − | 6.43288i | 0.106112 | − | 0.326580i | ||||
\(389\) | 1.18034 | + | 3.63271i | 0.0598456 | + | 0.184186i | 0.976510 | − | 0.215472i | \(-0.0691290\pi\) |
−0.916664 | + | 0.399658i | \(0.869129\pi\) | |||||||
\(390\) | −9.47214 | + | 6.88191i | −0.479640 | + | 0.348479i | ||||
\(391\) | −27.5451 | + | 20.0127i | −1.39301 | + | 1.01208i | ||||
\(392\) | −0.309017 | − | 0.951057i | −0.0156077 | − | 0.0480356i | ||||
\(393\) | 3.32624 | − | 10.2371i | 0.167787 | − | 0.516394i | ||||
\(394\) | 18.7984 | + | 13.6578i | 0.947048 | + | 0.688071i | ||||
\(395\) | −20.6525 | −1.03914 | ||||||||
\(396\) | −2.80902 | − | 1.76336i | −0.141158 | − | 0.0886120i | ||||
\(397\) | 16.0000 | 0.803017 | 0.401508 | − | 0.915855i | \(-0.368486\pi\) | ||||
0.401508 | + | 0.915855i | \(0.368486\pi\) | |||||||
\(398\) | 20.4443 | + | 14.8536i | 1.02478 | + | 0.744545i | ||||
\(399\) | 2.19098 | − | 6.74315i | 0.109686 | − | 0.337580i | ||||
\(400\) | 2.50000 | + | 7.69421i | 0.125000 | + | 0.384710i | ||||
\(401\) | −1.38197 | + | 1.00406i | −0.0690121 | + | 0.0501402i | −0.621756 | − | 0.783211i | \(-0.713581\pi\) |
0.552744 | + | 0.833351i | \(0.313581\pi\) | |||||||
\(402\) | 2.61803 | − | 1.90211i | 0.130576 | − | 0.0948688i | ||||
\(403\) | −10.0902 | − | 31.0543i | −0.502627 | − | 1.54693i | ||||
\(404\) | 1.59017 | − | 4.89404i | 0.0791139 | − | 0.243488i | ||||
\(405\) | 2.92705 | + | 2.12663i | 0.145446 | + | 0.105673i | ||||
\(406\) | 3.23607 | 0.160603 | ||||||||
\(407\) | −21.1180 | + | 1.43284i | −1.04678 | + | 0.0710233i | ||||
\(408\) | −5.38197 | −0.266447 | ||||||||
\(409\) | 18.0344 | + | 13.1028i | 0.891746 | + | 0.647891i | 0.936333 | − | 0.351114i | \(-0.114197\pi\) |
−0.0445868 | + | 0.999006i | \(0.514197\pi\) | |||||||
\(410\) | 5.75329 | − | 17.7068i | 0.284135 | − | 0.874477i | ||||
\(411\) | −0.763932 | − | 2.35114i | −0.0376820 | − | 0.115973i | ||||
\(412\) | 15.2082 | − | 11.0494i | 0.749254 | − | 0.544365i | ||||
\(413\) | 7.23607 | − | 5.25731i | 0.356064 | − | 0.258695i | ||||
\(414\) | −1.95492 | − | 6.01661i | −0.0960788 | − | 0.295700i | ||||
\(415\) | −12.0344 | + | 37.0382i | −0.590748 | + | 1.81813i | ||||
\(416\) | 2.61803 | + | 1.90211i | 0.128360 | + | 0.0932588i | ||||
\(417\) | 10.1459 | 0.496847 | ||||||||
\(418\) | 8.76393 | + | 21.8213i | 0.428658 | + | 1.06731i | ||||
\(419\) | −14.9443 | −0.730075 | −0.365038 | − | 0.930993i | \(-0.618944\pi\) | ||||
−0.365038 | + | 0.930993i | \(0.618944\pi\) | |||||||
\(420\) | −2.92705 | − | 2.12663i | −0.142825 | − | 0.103769i | ||||
\(421\) | 0.100813 | − | 0.310271i | 0.00491333 | − | 0.0151217i | −0.948570 | − | 0.316568i | \(-0.897469\pi\) |
0.953483 | + | 0.301446i | \(0.0974694\pi\) | |||||||
\(422\) | −1.61803 | − | 4.97980i | −0.0787647 | − | 0.242413i | ||||
\(423\) | 9.85410 | − | 7.15942i | 0.479123 | − | 0.348103i | ||||
\(424\) | −7.23607 | + | 5.25731i | −0.351415 | + | 0.255318i | ||||
\(425\) | 13.4549 | + | 41.4100i | 0.652659 | + | 2.00868i | ||||
\(426\) | −3.23607 | + | 9.95959i | −0.156788 | + | 0.482544i | ||||
\(427\) | −3.85410 | − | 2.80017i | −0.186513 | − | 0.135510i | ||||
\(428\) | 10.0344 | 0.485033 | ||||||||
\(429\) | 4.00000 | + | 9.95959i | 0.193122 | + | 0.480854i | ||||
\(430\) | 2.76393 | 0.133289 | ||||||||
\(431\) | 19.6353 | + | 14.2658i | 0.945797 | + | 0.687162i | 0.949809 | − | 0.312830i | \(-0.101277\pi\) |
−0.00401210 | + | 0.999992i | \(0.501277\pi\) | |||||||
\(432\) | 0.309017 | − | 0.951057i | 0.0148676 | − | 0.0457577i | ||||
\(433\) | −10.7082 | − | 32.9565i | −0.514603 | − | 1.58379i | −0.784002 | − | 0.620758i | \(-0.786825\pi\) |
0.269399 | − | 0.963029i | \(-0.413175\pi\) | |||||||
\(434\) | 8.16312 | − | 5.93085i | 0.391842 | − | 0.284690i | ||||
\(435\) | 9.47214 | − | 6.88191i | 0.454154 | − | 0.329962i | ||||
\(436\) | 0.736068 | + | 2.26538i | 0.0352513 | + | 0.108492i | ||||
\(437\) | −13.8607 | + | 42.6588i | −0.663046 | + | 2.04065i | ||||
\(438\) | −6.47214 | − | 4.70228i | −0.309251 | − | 0.224684i | ||||
\(439\) | −7.03444 | −0.335736 | −0.167868 | − | 0.985810i | \(-0.553688\pi\) | ||||
−0.167868 | + | 0.985810i | \(0.553688\pi\) | |||||||
\(440\) | 11.9721 | − | 0.812299i | 0.570749 | − | 0.0387248i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 14.0902 | + | 10.2371i | 0.670201 | + | 0.486930i | ||||
\(443\) | 8.33688 | − | 25.6583i | 0.396097 | − | 1.21906i | −0.532007 | − | 0.846740i | \(-0.678562\pi\) |
0.928104 | − | 0.372322i | \(-0.121438\pi\) | |||||||
\(444\) | −1.97214 | − | 6.06961i | −0.0935934 | − | 0.288051i | ||||
\(445\) | −34.6976 | + | 25.2093i | −1.64482 | + | 1.19503i | ||||
\(446\) | 7.97214 | − | 5.79210i | 0.377492 | − | 0.274264i | ||||
\(447\) | 2.29180 | + | 7.05342i | 0.108398 | + | 0.333615i | ||||
\(448\) | −0.309017 | + | 0.951057i | −0.0145997 | + | 0.0449332i | ||||
\(449\) | 8.23607 | + | 5.98385i | 0.388684 | + | 0.282396i | 0.764916 | − | 0.644130i | \(-0.222780\pi\) |
−0.376232 | + | 0.926526i | \(0.622780\pi\) | |||||||
\(450\) | −8.09017 | −0.381374 | ||||||||
\(451\) | −14.4549 | − | 9.07405i | −0.680655 | − | 0.427280i | ||||
\(452\) | 2.47214 | 0.116279 | ||||||||
\(453\) | −7.23607 | − | 5.25731i | −0.339980 | − | 0.247010i | ||||
\(454\) | −6.94427 | + | 21.3723i | −0.325911 | + | 1.00305i | ||||
\(455\) | 3.61803 | + | 11.1352i | 0.169616 | + | 0.522025i | ||||
\(456\) | −5.73607 | + | 4.16750i | −0.268616 | + | 0.195161i | ||||
\(457\) | 27.0344 | − | 19.6417i | 1.26462 | − | 0.918799i | 0.265643 | − | 0.964071i | \(-0.414416\pi\) |
0.998975 | + | 0.0452728i | \(0.0144157\pi\) | |||||||
\(458\) | −7.67376 | − | 23.6174i | −0.358571 | − | 1.10357i | ||||
\(459\) | 1.66312 | − | 5.11855i | 0.0776277 | − | 0.238914i | ||||
\(460\) | 18.5172 | + | 13.4535i | 0.863370 | + | 0.627275i | ||||
\(461\) | −15.8885 | −0.740003 | −0.370002 | − | 0.929031i | \(-0.620643\pi\) | ||||
−0.370002 | + | 0.929031i | \(0.620643\pi\) | |||||||
\(462\) | −2.54508 | + | 2.12663i | −0.118408 | + | 0.0989396i | ||||
\(463\) | −10.5836 | −0.491861 | −0.245931 | − | 0.969287i | \(-0.579094\pi\) | ||||
−0.245931 | + | 0.969287i | \(0.579094\pi\) | |||||||
\(464\) | −2.61803 | − | 1.90211i | −0.121539 | − | 0.0883034i | ||||
\(465\) | 11.2812 | − | 34.7198i | 0.523151 | − | 1.61009i | ||||
\(466\) | 4.90983 | + | 15.1109i | 0.227443 | + | 0.699999i | ||||
\(467\) | −6.47214 | + | 4.70228i | −0.299495 | + | 0.217596i | −0.727376 | − | 0.686239i | \(-0.759260\pi\) |
0.427881 | + | 0.903835i | \(0.359260\pi\) | |||||||
\(468\) | −2.61803 | + | 1.90211i | −0.121019 | + | 0.0879252i | ||||
\(469\) | −1.00000 | − | 3.07768i | −0.0461757 | − | 0.142114i | ||||
\(470\) | −13.6180 | + | 41.9120i | −0.628153 | + | 1.93326i | ||||
\(471\) | 7.85410 | + | 5.70634i | 0.361898 | + | 0.262934i | ||||
\(472\) | −8.94427 | −0.411693 | ||||||||
\(473\) | 0.618034 | − | 2.45714i | 0.0284172 | − | 0.112980i | ||||
\(474\) | −5.70820 | −0.262186 | ||||||||
\(475\) | 46.4058 | + | 33.7158i | 2.12924 | + | 1.54699i | ||||
\(476\) | −1.66312 | + | 5.11855i | −0.0762289 | + | 0.234609i | ||||
\(477\) | −2.76393 | − | 8.50651i | −0.126552 | − | 0.389486i | ||||
\(478\) | 7.59017 | − | 5.51458i | 0.347166 | − | 0.252231i | ||||
\(479\) | 10.4721 | − | 7.60845i | 0.478484 | − | 0.347639i | −0.322254 | − | 0.946653i | \(-0.604441\pi\) |
0.800739 | + | 0.599014i | \(0.204441\pi\) | |||||||
\(480\) | 1.11803 | + | 3.44095i | 0.0510310 | + | 0.157057i | ||||
\(481\) | −6.38197 | + | 19.6417i | −0.290993 | + | 0.895583i | ||||
\(482\) | 13.0902 | + | 9.51057i | 0.596241 | + | 0.433194i | ||||
\(483\) | −6.32624 | −0.287854 | ||||||||
\(484\) | 1.95492 | − | 10.8249i | 0.0888598 | − | 0.492041i | ||||
\(485\) | −24.4721 | −1.11122 | ||||||||
\(486\) | 0.809017 | + | 0.587785i | 0.0366978 | + | 0.0266625i | ||||
\(487\) | −3.81966 | + | 11.7557i | −0.173085 | + | 0.532702i | −0.999541 | − | 0.0303002i | \(-0.990354\pi\) |
0.826456 | + | 0.563002i | \(0.190354\pi\) | |||||||
\(488\) | 1.47214 | + | 4.53077i | 0.0666405 | + | 0.205098i | ||||
\(489\) | −9.32624 | + | 6.77591i | −0.421747 | + | 0.306417i | ||||
\(490\) | −2.92705 | + | 2.12663i | −0.132231 | + | 0.0960712i | ||||
\(491\) | 12.4271 | + | 38.2465i | 0.560825 | + | 1.72604i | 0.680042 | + | 0.733173i | \(0.261962\pi\) |
−0.119217 | + | 0.992868i | \(0.538038\pi\) | |||||||
\(492\) | 1.59017 | − | 4.89404i | 0.0716904 | − | 0.220640i | ||||
\(493\) | −14.0902 | − | 10.2371i | −0.634589 | − | 0.461056i | ||||
\(494\) | 22.9443 | 1.03231 | ||||||||
\(495\) | −2.92705 | + | 11.6372i | −0.131561 | + | 0.523053i | ||||
\(496\) | −10.0902 | −0.453062 | ||||||||
\(497\) | 8.47214 | + | 6.15537i | 0.380027 | + | 0.276106i | ||||
\(498\) | −3.32624 | + | 10.2371i | −0.149052 | + | 0.458736i | ||||
\(499\) | 2.70820 | + | 8.33499i | 0.121236 | + | 0.373126i | 0.993197 | − | 0.116450i | \(-0.0371516\pi\) |
−0.871961 | + | 0.489576i | \(0.837152\pi\) | |||||||
\(500\) | 9.04508 | − | 6.57164i | 0.404508 | − | 0.293893i | ||||
\(501\) | −13.3262 | + | 9.68208i | −0.595372 | + | 0.432563i | ||||
\(502\) | −2.76393 | − | 8.50651i | −0.123360 | − | 0.379664i | ||||
\(503\) | 11.4721 | − | 35.3076i | 0.511517 | − | 1.57429i | −0.278013 | − | 0.960577i | \(-0.589676\pi\) |
0.789531 | − | 0.613711i | \(-0.210324\pi\) | |||||||
\(504\) | −0.809017 | − | 0.587785i | −0.0360365 | − | 0.0261820i | ||||
\(505\) | −18.6180 | −0.828492 | ||||||||
\(506\) | 16.1008 | − | 13.4535i | 0.715768 | − | 0.598083i | ||||
\(507\) | −2.52786 | −0.112266 | ||||||||
\(508\) | −5.47214 | − | 3.97574i | −0.242787 | − | 0.176395i | ||||
\(509\) | −6.06231 | + | 18.6579i | −0.268707 | + | 0.826995i | 0.722109 | + | 0.691779i | \(0.243173\pi\) |
−0.990816 | + | 0.135216i | \(0.956827\pi\) | |||||||
\(510\) | 6.01722 | + | 18.5191i | 0.266447 | + | 0.820040i | ||||
\(511\) | −6.47214 | + | 4.70228i | −0.286310 | + | 0.208017i | ||||
\(512\) | 0.809017 | − | 0.587785i | 0.0357538 | − | 0.0259767i | ||||
\(513\) | −2.19098 | − | 6.74315i | −0.0967343 | − | 0.297717i | ||||
\(514\) | 4.89919 | − | 15.0781i | 0.216094 | − | 0.665069i | ||||
\(515\) | −55.0238 | − | 39.9771i | −2.42464 | − | 1.76160i | ||||
\(516\) | 0.763932 | 0.0336302 | ||||||||
\(517\) | 34.2148 | + | 21.4783i | 1.50476 | + | 0.944613i | ||||
\(518\) | −6.38197 | −0.280407 | ||||||||
\(519\) | −0.118034 | − | 0.0857567i | −0.00518112 | − | 0.00376430i | ||||
\(520\) | 3.61803 | − | 11.1352i | 0.158661 | − | 0.488309i | ||||
\(521\) | −2.93769 | − | 9.04129i | −0.128703 | − | 0.396106i | 0.865855 | − | 0.500295i | \(-0.166775\pi\) |
−0.994557 | + | 0.104189i | \(0.966775\pi\) | |||||||
\(522\) | 2.61803 | − | 1.90211i | 0.114588 | − | 0.0832532i | ||||
\(523\) | −5.73607 | + | 4.16750i | −0.250821 | + | 0.182232i | −0.706090 | − | 0.708122i | \(-0.749543\pi\) |
0.455270 | + | 0.890354i | \(0.349543\pi\) | |||||||
\(524\) | 3.32624 | + | 10.2371i | 0.145307 | + | 0.447210i | ||||
\(525\) | −2.50000 | + | 7.69421i | −0.109109 | + | 0.335803i | ||||
\(526\) | −17.8262 | − | 12.9515i | −0.777261 | − | 0.564713i | ||||
\(527\) | −54.3050 | −2.36556 | ||||||||
\(528\) | 3.30902 | − | 0.224514i | 0.144006 | − | 0.00977072i | ||||
\(529\) | 17.0213 | 0.740056 | ||||||||
\(530\) | 26.1803 | + | 19.0211i | 1.13720 | + | 0.826225i | ||||
\(531\) | 2.76393 | − | 8.50651i | 0.119944 | − | 0.369151i | ||||
\(532\) | 2.19098 | + | 6.74315i | 0.0949912 | + | 0.292353i | ||||
\(533\) | −13.4721 | + | 9.78808i | −0.583543 | + | 0.423969i | ||||
\(534\) | −9.59017 | + | 6.96767i | −0.415007 | + | 0.301520i | ||||
\(535\) | −11.2188 | − | 34.5281i | −0.485033 | − | 1.49278i | ||||
\(536\) | −1.00000 | + | 3.07768i | −0.0431934 | + | 0.132936i | ||||
\(537\) | −1.16312 | − | 0.845055i | −0.0501923 | − | 0.0364668i | ||||
\(538\) | −6.00000 | −0.258678 | ||||||||
\(539\) | 1.23607 | + | 3.07768i | 0.0532412 | + | 0.132565i | ||||
\(540\) | −3.61803 | −0.155695 | ||||||||
\(541\) | −13.7812 | − | 10.0126i | −0.592498 | − | 0.430475i | 0.250710 | − | 0.968062i | \(-0.419336\pi\) |
−0.843208 | + | 0.537587i | \(0.819336\pi\) | |||||||
\(542\) | 1.88197 | − | 5.79210i | 0.0808374 | − | 0.248792i | ||||
\(543\) | 2.47214 | + | 7.60845i | 0.106090 | + | 0.326510i | ||||
\(544\) | 4.35410 | − | 3.16344i | 0.186681 | − | 0.135631i | ||||
\(545\) | 6.97214 | − | 5.06555i | 0.298653 | − | 0.216984i | ||||
\(546\) | 1.00000 | + | 3.07768i | 0.0427960 | + | 0.131713i | ||||
\(547\) | 8.18034 | − | 25.1765i | 0.349766 | − | 1.07647i | −0.609216 | − | 0.793004i | \(-0.708516\pi\) |
0.958982 | − | 0.283465i | \(-0.0914841\pi\) | |||||||
\(548\) | 2.00000 | + | 1.45309i | 0.0854358 | + | 0.0620727i | ||||
\(549\) | −4.76393 | −0.203320 | ||||||||
\(550\) | −10.0000 | − | 24.8990i | −0.426401 | − | 1.06170i | ||||
\(551\) | −22.9443 | −0.977459 | ||||||||
\(552\) | 5.11803 | + | 3.71847i | 0.217838 | + | 0.158269i | ||||
\(553\) | −1.76393 | + | 5.42882i | −0.0750100 | + | 0.230857i | ||||
\(554\) | −3.04508 | − | 9.37181i | −0.129373 | − | 0.398170i | ||||
\(555\) | −18.6803 | + | 13.5721i | −0.792936 | + | 0.576102i | ||||
\(556\) | −8.20820 | + | 5.96361i | −0.348105 | + | 0.252913i | ||||
\(557\) | 7.67376 | + | 23.6174i | 0.325148 | + | 1.00070i | 0.971374 | + | 0.237556i | \(0.0763463\pi\) |
−0.646226 | + | 0.763146i | \(0.723654\pi\) | |||||||
\(558\) | 3.11803 | − | 9.59632i | 0.131997 | − | 0.406245i | ||||
\(559\) | −2.00000 | − | 1.45309i | −0.0845910 | − | 0.0614589i | ||||
\(560\) | 3.61803 | 0.152890 | ||||||||
\(561\) | 17.8090 | − | 1.20833i | 0.751897 | − | 0.0510156i | ||||
\(562\) | 16.6525 | 0.702442 | ||||||||
\(563\) | −2.85410 | − | 2.07363i | −0.120286 | − | 0.0873929i | 0.526016 | − | 0.850475i | \(-0.323685\pi\) |
−0.646302 | + | 0.763082i | \(0.723685\pi\) | |||||||
\(564\) | −3.76393 | + | 11.5842i | −0.158490 | + | 0.487782i | ||||
\(565\) | −2.76393 | − | 8.50651i | −0.116279 | − | 0.357871i | ||||
\(566\) | −8.16312 | + | 5.93085i | −0.343121 | + | 0.249292i | ||||
\(567\) | 0.809017 | − | 0.587785i | 0.0339755 | − | 0.0246847i | ||||
\(568\) | −3.23607 | − | 9.95959i | −0.135782 | − | 0.417895i | ||||
\(569\) | −5.29180 | + | 16.2865i | −0.221844 | + | 0.682764i | 0.776753 | + | 0.629805i | \(0.216865\pi\) |
−0.998597 | + | 0.0529592i | \(0.983135\pi\) | |||||||
\(570\) | 20.7533 | + | 15.0781i | 0.869260 | + | 0.631554i | ||||
\(571\) | −6.29180 | −0.263303 | −0.131652 | − | 0.991296i | \(-0.542028\pi\) | ||||
−0.131652 | + | 0.991296i | \(0.542028\pi\) | |||||||
\(572\) | −9.09017 | − | 5.70634i | −0.380079 | − | 0.238594i | ||||
\(573\) | −0.0901699 | −0.00376690 | ||||||||
\(574\) | −4.16312 | − | 3.02468i | −0.173765 | − | 0.126248i | ||||
\(575\) | 15.8156 | − | 48.6754i | 0.659556 | − | 2.02990i | ||||
\(576\) | 0.309017 | + | 0.951057i | 0.0128757 | + | 0.0396274i | ||||
\(577\) | −8.47214 | + | 6.15537i | −0.352700 | + | 0.256251i | −0.750001 | − | 0.661437i | \(-0.769947\pi\) |
0.397301 | + | 0.917688i | \(0.369947\pi\) | |||||||
\(578\) | 9.68034 | − | 7.03318i | 0.402649 | − | 0.292542i | ||||
\(579\) | 1.50000 | + | 4.61653i | 0.0623379 | + | 0.191856i | ||||
\(580\) | −3.61803 | + | 11.1352i | −0.150231 | + | 0.462363i | ||||
\(581\) | 8.70820 | + | 6.32688i | 0.361277 | + | 0.262483i | ||||
\(582\) | −6.76393 | −0.280374 | ||||||||
\(583\) | 22.7639 | − | 19.0211i | 0.942786 | − | 0.787775i | ||||
\(584\) | 8.00000 | 0.331042 | ||||||||
\(585\) | 9.47214 | + | 6.88191i | 0.391625 | + | 0.284532i | ||||
\(586\) | 4.88197 | − | 15.0251i | 0.201672 | − | 0.620683i | ||||
\(587\) | 3.67376 | + | 11.3067i | 0.151632 | + | 0.466677i | 0.997804 | − | 0.0662338i | \(-0.0210983\pi\) |
−0.846172 | + | 0.532910i | \(0.821098\pi\) | |||||||
\(588\) | −0.809017 | + | 0.587785i | −0.0333633 | + | 0.0242399i | ||||
\(589\) | −57.8779 | + | 42.0508i | −2.38482 | + | 1.73267i | ||||
\(590\) | 10.0000 | + | 30.7768i | 0.411693 | + | 1.26706i | ||||
\(591\) | 7.18034 | − | 22.0988i | 0.295360 | − | 0.909024i | ||||
\(592\) | 5.16312 | + | 3.75123i | 0.212203 | + | 0.154174i | ||||
\(593\) | 28.7426 | 1.18032 | 0.590159 | − | 0.807287i | \(-0.299065\pi\) | ||||
0.590159 | + | 0.807287i | \(0.299065\pi\) | |||||||
\(594\) | −0.809017 | + | 3.21644i | −0.0331944 | + | 0.131972i | ||||
\(595\) | 19.4721 | 0.798280 | ||||||||
\(596\) | −6.00000 | − | 4.35926i | −0.245770 | − | 0.178562i | ||||
\(597\) | 7.80902 | − | 24.0337i | 0.319602 | − | 0.983633i | ||||
\(598\) | −6.32624 | − | 19.4702i | −0.258699 | − | 0.796194i | ||||
\(599\) | −12.8262 | + | 9.31881i | −0.524066 | + | 0.380756i | −0.818133 | − | 0.575029i | \(-0.804991\pi\) |
0.294067 | + | 0.955785i | \(0.404991\pi\) | |||||||
\(600\) | 6.54508 | − | 4.75528i | 0.267202 | − | 0.194134i | ||||
\(601\) | −5.09017 | − | 15.6659i | −0.207632 | − | 0.639027i | −0.999595 | − | 0.0284572i | \(-0.990941\pi\) |
0.791963 | − | 0.610570i | \(-0.209059\pi\) | |||||||
\(602\) | 0.236068 | − | 0.726543i | 0.00962141 | − | 0.0296117i | ||||
\(603\) | −2.61803 | − | 1.90211i | −0.106615 | − | 0.0774600i | ||||
\(604\) | 8.94427 | 0.363937 | ||||||||
\(605\) | −39.4336 | + | 5.37582i | −1.60320 | + | 0.218558i | ||||
\(606\) | −5.14590 | −0.209038 | ||||||||
\(607\) | −26.3885 | − | 19.1724i | −1.07108 | − | 0.778184i | −0.0949722 | − | 0.995480i | \(-0.530276\pi\) |
−0.976106 | + | 0.217296i | \(0.930276\pi\) | |||||||
\(608\) | 2.19098 | − | 6.74315i | 0.0888561 | − | 0.273471i | ||||
\(609\) | −1.00000 | − | 3.07768i | −0.0405220 | − | 0.124714i | ||||
\(610\) | 13.9443 | − | 10.1311i | 0.564587 | − | 0.410197i | ||||
\(611\) | 31.8885 | − | 23.1684i | 1.29007 | − | 0.937292i | ||||
\(612\) | 1.66312 | + | 5.11855i | 0.0672276 | + | 0.206905i | ||||
\(613\) | 7.51722 | − | 23.1356i | 0.303618 | − | 0.934439i | −0.676572 | − | 0.736377i | \(-0.736535\pi\) |
0.980189 | − | 0.198062i | \(-0.0634649\pi\) | |||||||
\(614\) | 7.39919 | + | 5.37582i | 0.298607 | + | 0.216951i | ||||
\(615\) | −18.6180 | −0.750752 | ||||||||
\(616\) | 0.809017 | − | 3.21644i | 0.0325962 | − | 0.129594i | ||||
\(617\) | −6.58359 | −0.265045 | −0.132523 | − | 0.991180i | \(-0.542308\pi\) | ||||
−0.132523 | + | 0.991180i | \(0.542308\pi\) | |||||||
\(618\) | −15.2082 | − | 11.0494i | −0.611764 | − | 0.444472i | ||||
\(619\) | 10.1180 | − | 31.1401i | 0.406678 | − | 1.25163i | −0.512808 | − | 0.858503i | \(-0.671395\pi\) |
0.919486 | − | 0.393123i | \(-0.128605\pi\) | |||||||
\(620\) | 11.2812 | + | 34.7198i | 0.453062 | + | 1.39438i | ||||
\(621\) | −5.11803 | + | 3.71847i | −0.205380 | + | 0.149217i | ||||
\(622\) | −18.1803 | + | 13.2088i | −0.728965 | + | 0.529624i | ||||
\(623\) | 3.66312 | + | 11.2739i | 0.146760 | + | 0.451680i | ||||
\(624\) | 1.00000 | − | 3.07768i | 0.0400320 | − | 0.123206i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.7082 | −1.10744 | ||||||||
\(627\) | 18.0451 | − | 15.0781i | 0.720651 | − | 0.602163i | ||||
\(628\) | −9.70820 | −0.387400 | ||||||||
\(629\) | 27.7877 | + | 20.1890i | 1.10797 | + | 0.804987i | ||||
\(630\) | −1.11803 | + | 3.44095i | −0.0445435 | + | 0.137091i | ||||
\(631\) | −9.94427 | − | 30.6053i | −0.395875 | − | 1.21838i | −0.928278 | − | 0.371887i | \(-0.878711\pi\) |
0.532403 | − | 0.846491i | \(-0.321289\pi\) | |||||||
\(632\) | 4.61803 | − | 3.35520i | 0.183696 | − | 0.133463i | ||||
\(633\) | −4.23607 | + | 3.07768i | −0.168369 | + | 0.122327i | ||||
\(634\) | −3.70820 | − | 11.4127i | −0.147272 | − | 0.453255i | ||||
\(635\) | −7.56231 | + | 23.2744i | −0.300101 | + | 0.923616i | ||||
\(636\) | 7.23607 | + | 5.25731i | 0.286929 | + | 0.208466i | ||||
\(637\) | 3.23607 | 0.128218 | ||||||||
\(638\) | 9.09017 | + | 5.70634i | 0.359883 | + | 0.225916i | ||||
\(639\) | 10.4721 | 0.414271 | ||||||||
\(640\) | −2.92705 | − | 2.12663i | −0.115702 | − | 0.0840623i | ||||
\(641\) | 3.88854 | − | 11.9677i | 0.153588 | − | 0.472696i | −0.844427 | − | 0.535671i | \(-0.820059\pi\) |
0.998015 | + | 0.0629748i | \(0.0200588\pi\) | |||||||
\(642\) | −3.10081 | − | 9.54332i | −0.122379 | − | 0.376645i | ||||
\(643\) | 29.1525 | − | 21.1805i | 1.14966 | − | 0.835278i | 0.161226 | − | 0.986918i | \(-0.448455\pi\) |
0.988436 | + | 0.151640i | \(0.0484553\pi\) | |||||||
\(644\) | 5.11803 | − | 3.71847i | 0.201679 | − | 0.146528i | ||||
\(645\) | −0.854102 | − | 2.62866i | −0.0336302 | − | 0.103503i | ||||
\(646\) | 11.7918 | − | 36.2914i | 0.463942 | − | 1.42787i | ||||
\(647\) | −2.61803 | − | 1.90211i | −0.102926 | − | 0.0747798i | 0.535132 | − | 0.844768i | \(-0.320262\pi\) |
−0.638058 | + | 0.769989i | \(0.720262\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 29.5967 | − | 2.00811i | 1.16177 | − | 0.0788254i | ||||
\(650\) | −26.1803 | −1.02688 | ||||||||
\(651\) | −8.16312 | − | 5.93085i | −0.319938 | − | 0.232448i | ||||
\(652\) | 3.56231 | − | 10.9637i | 0.139511 | − | 0.429370i | ||||
\(653\) | 10.9098 | + | 33.5770i | 0.426935 | + | 1.31397i | 0.901130 | + | 0.433550i | \(0.142739\pi\) |
−0.474195 | + | 0.880420i | \(0.657261\pi\) | |||||||
\(654\) | 1.92705 | − | 1.40008i | 0.0753537 | − | 0.0547476i | ||||
\(655\) | 31.5066 | − | 22.8909i | 1.23106 | − | 0.894420i | ||||
\(656\) | 1.59017 | + | 4.89404i | 0.0620857 | + | 0.191080i | ||||
\(657\) | −2.47214 | + | 7.60845i | −0.0964472 | + | 0.296834i | ||||
\(658\) | 9.85410 | + | 7.15942i | 0.384153 | + | 0.279103i | ||||
\(659\) | 38.1591 | 1.48647 | 0.743233 | − | 0.669033i | \(-0.233291\pi\) | ||||
0.743233 | + | 0.669033i | \(0.233291\pi\) | |||||||
\(660\) | −4.47214 | − | 11.1352i | −0.174078 | − | 0.433436i | ||||
\(661\) | −19.8885 | −0.773575 | −0.386787 | − | 0.922169i | \(-0.626415\pi\) | ||||
−0.386787 | + | 0.922169i | \(0.626415\pi\) | |||||||
\(662\) | 17.9443 | + | 13.0373i | 0.697424 | + | 0.506708i | ||||
\(663\) | 5.38197 | − | 16.5640i | 0.209018 | − | 0.643292i | ||||
\(664\) | −3.32624 | − | 10.2371i | −0.129083 | − | 0.397277i | ||||
\(665\) | 20.7533 | − | 15.0781i | 0.804778 | − | 0.584705i | ||||
\(666\) | −5.16312 | + | 3.75123i | −0.200067 | + | 0.145357i | ||||
\(667\) | 6.32624 | + | 19.4702i | 0.244953 | + | 0.753888i | ||||
\(668\) | 5.09017 | − | 15.6659i | 0.196945 | − | 0.606133i | ||||
\(669\) | −7.97214 | − | 5.79210i | −0.308221 | − | 0.223935i | ||||
\(670\) | 11.7082 | 0.452327 | ||||||||
\(671\) | −5.88854 | − | 14.6619i | −0.227325 | − | 0.566015i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −28.5623 | − | 20.7517i | −1.10100 | − | 0.799920i | −0.119774 | − | 0.992801i | \(-0.538217\pi\) |
−0.981222 | + | 0.192881i | \(0.938217\pi\) | |||||||
\(674\) | −2.26393 | + | 6.96767i | −0.0872034 | + | 0.268384i | ||||
\(675\) | 2.50000 | + | 7.69421i | 0.0962250 | + | 0.296150i | ||||
\(676\) | 2.04508 | − | 1.48584i | 0.0786571 | − | 0.0571477i | ||||
\(677\) | 10.8541 | − | 7.88597i | 0.417157 | − | 0.303082i | −0.359336 | − | 0.933208i | \(-0.616997\pi\) |
0.776493 | + | 0.630126i | \(0.216997\pi\) | |||||||
\(678\) | −0.763932 | − | 2.35114i | −0.0293386 | − | 0.0902950i | ||||
\(679\) | −2.09017 | + | 6.43288i | −0.0802134 | + | 0.246871i | ||||
\(680\) | −15.7533 | − | 11.4454i | −0.604111 | − | 0.438912i | ||||
\(681\) | 22.4721 | 0.861134 | ||||||||
\(682\) | 33.3885 | − | 2.26538i | 1.27851 | − | 0.0867460i | ||||
\(683\) | 38.5623 | 1.47555 | 0.737773 | − | 0.675049i | \(-0.235878\pi\) | ||||
0.737773 | + | 0.675049i | \(0.235878\pi\) | |||||||
\(684\) | 5.73607 | + | 4.16750i | 0.219324 | + | 0.159348i | ||||
\(685\) | 2.76393 | − | 8.50651i | 0.105604 | − | 0.325017i | ||||
\(686\) | 0.309017 | + | 0.951057i | 0.0117983 | + | 0.0363115i | ||||
\(687\) | −20.0902 | + | 14.5964i | −0.766488 | + | 0.556886i | ||||
\(688\) | −0.618034 | + | 0.449028i | −0.0235623 | + | 0.0171190i | ||||
\(689\) | −8.94427 | − | 27.5276i | −0.340750 | − | 1.04872i | ||||
\(690\) | 7.07295 | − | 21.7683i | 0.269263 | − | 0.828705i | ||||
\(691\) | −7.50000 | − | 5.44907i | −0.285313 | − | 0.207292i | 0.435918 | − | 0.899986i | \(-0.356424\pi\) |
−0.721232 | + | 0.692694i | \(0.756424\pi\) | |||||||
\(692\) | 0.145898 | 0.00554621 | ||||||||
\(693\) | 2.80902 | + | 1.76336i | 0.106706 | + | 0.0669843i | ||||
\(694\) | 13.7984 | 0.523779 | ||||||||
\(695\) | 29.6976 | + | 21.5765i | 1.12649 | + | 0.818445i | ||||
\(696\) | −1.00000 | + | 3.07768i | −0.0379049 | + | 0.116659i | ||||
\(697\) | 8.55824 | + | 26.3396i | 0.324166 | + | 0.997682i | ||||
\(698\) | −14.9443 | + | 10.8576i | −0.565649 | + | 0.410968i | ||||
\(699\) | 12.8541 | − | 9.33905i | 0.486187 | − | 0.353235i | ||||
\(700\) | −2.50000 | − | 7.69421i | −0.0944911 | − | 0.290814i | ||||
\(701\) | −12.9098 | + | 39.7324i | −0.487598 | + | 1.50067i | 0.340586 | + | 0.940213i | \(0.389375\pi\) |
−0.828183 | + | 0.560457i | \(0.810625\pi\) | |||||||
\(702\) | 2.61803 | + | 1.90211i | 0.0988113 | + | 0.0717906i | ||||
\(703\) | 45.2492 | 1.70661 | ||||||||
\(704\) | −2.54508 | + | 2.12663i | −0.0959215 | + | 0.0801503i | ||||
\(705\) | 44.0689 | 1.65973 | ||||||||
\(706\) | 4.09017 | + | 2.97168i | 0.153936 | + | 0.111841i | ||||
\(707\) | −1.59017 | + | 4.89404i | −0.0598045 | + | 0.184059i | ||||
\(708\) | 2.76393 | + | 8.50651i | 0.103875 | + | 0.319694i | ||||
\(709\) | −16.3992 | + | 11.9147i | −0.615884 | + | 0.447466i | −0.851482 | − | 0.524385i | \(-0.824295\pi\) |
0.235597 | + | 0.971851i | \(0.424295\pi\) | |||||||
\(710\) | −30.6525 | + | 22.2703i | −1.15037 | + | 0.835790i | ||||
\(711\) | 1.76393 | + | 5.42882i | 0.0661526 | + | 0.203597i | ||||
\(712\) | 3.66312 | − | 11.2739i | 0.137281 | − | 0.422508i | ||||
\(713\) | 51.6418 | + | 37.5200i | 1.93400 | + | 1.40513i | ||||
\(714\) | 5.38197 | 0.201415 | ||||||||
\(715\) | −9.47214 | + | 37.6587i | −0.354238 | + | 1.40836i | ||||
\(716\) | 1.43769 | 0.0537292 | ||||||||
\(717\) | −7.59017 | − | 5.51458i | −0.283460 | − | 0.205946i | ||||
\(718\) | −6.55573 | + | 20.1765i | −0.244658 | + | 0.752979i | ||||
\(719\) | 13.0902 | + | 40.2874i | 0.488181 | + | 1.50247i | 0.827320 | + | 0.561730i | \(0.189864\pi\) |
−0.339139 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(720\) | 2.92705 | − | 2.12663i | 0.109085 | − | 0.0792547i | ||||
\(721\) | −15.2082 | + | 11.0494i | −0.566383 | + | 0.411501i | ||||
\(722\) | −9.66312 | − | 29.7400i | −0.359624 | − | 1.10681i | ||||
\(723\) | 5.00000 | − | 15.3884i | 0.185952 | − | 0.572301i | ||||
\(724\) | −6.47214 | − | 4.70228i | −0.240535 | − | 0.174759i | ||||
\(725\) | 26.1803 | 0.972313 | ||||||||
\(726\) | −10.8992 | + | 1.48584i | −0.404507 | + | 0.0551447i | ||||
\(727\) | −14.5066 | −0.538019 | −0.269010 | − | 0.963137i | \(-0.586696\pi\) | ||||
−0.269010 | + | 0.963137i | \(0.586696\pi\) | |||||||
\(728\) | −2.61803 | − | 1.90211i | −0.0970308 | − | 0.0704970i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −8.94427 | − | 27.5276i | −0.331042 | − | 1.01884i | ||||
\(731\) | −3.32624 | + | 2.41665i | −0.123025 | + | 0.0893832i | ||||
\(732\) | 3.85410 | − | 2.80017i | 0.142452 | − | 0.103497i | ||||
\(733\) | 10.4721 | + | 32.2299i | 0.386797 | + | 1.19044i | 0.935168 | + | 0.354204i | \(0.115248\pi\) |
−0.548371 | + | 0.836235i | \(0.684752\pi\) | |||||||
\(734\) | −0.173762 | + | 0.534785i | −0.00641368 | + | 0.0197393i | ||||
\(735\) | 2.92705 | + | 2.12663i | 0.107966 | + | 0.0784418i | ||||
\(736\) | −6.32624 | −0.233188 | ||||||||
\(737\) | 2.61803 | − | 10.4086i | 0.0964365 | − | 0.383406i | ||||
\(738\) | −5.14590 | −0.189423 | ||||||||
\(739\) | −4.23607 | − | 3.07768i | −0.155826 | − | 0.113214i | 0.507140 | − | 0.861864i | \(-0.330703\pi\) |
−0.662966 | + | 0.748649i | \(0.730703\pi\) | |||||||
\(740\) | 7.13525 | − | 21.9601i | 0.262297 | − | 0.807268i | ||||
\(741\) | −7.09017 | − | 21.8213i | −0.260464 | − | 0.801625i | ||||
\(742\) | 7.23607 | − | 5.25731i | 0.265644 | − | 0.193002i | ||||
\(743\) | 32.8713 | − | 23.8824i | 1.20593 | − | 0.876161i | 0.211077 | − | 0.977469i | \(-0.432303\pi\) |
0.994855 | + | 0.101309i | \(0.0323030\pi\) | |||||||
\(744\) | 3.11803 | + | 9.59632i | 0.114313 | + | 0.351818i | ||||
\(745\) | −8.29180 | + | 25.5195i | −0.303788 | + | 0.934963i | ||||
\(746\) | −9.30902 | − | 6.76340i | −0.340827 | − | 0.247626i | ||||
\(747\) | 10.7639 | 0.393832 | ||||||||
\(748\) | −13.6976 | + | 11.4454i | −0.500832 | + | 0.418487i | ||||
\(749\) | −10.0344 | −0.366651 | ||||||||
\(750\) | −9.04508 | − | 6.57164i | −0.330280 | − | 0.239962i | ||||
\(751\) | −2.32624 | + | 7.15942i | −0.0848856 | + | 0.261251i | −0.984486 | − | 0.175463i | \(-0.943858\pi\) |
0.899600 | + | 0.436714i | \(0.143858\pi\) | |||||||
\(752\) | −3.76393 | − | 11.5842i | −0.137256 | − | 0.422432i | ||||
\(753\) | −7.23607 | + | 5.25731i | −0.263697 | + | 0.191587i | ||||
\(754\) | 8.47214 | − | 6.15537i | 0.308537 | − | 0.224165i | ||||
\(755\) | −10.0000 | − | 30.7768i | −0.363937 | − | 1.12008i | ||||
\(756\) | −0.309017 | + | 0.951057i | −0.0112388 | + | 0.0345896i | ||||
\(757\) | −10.9721 | − | 7.97172i | −0.398789 | − | 0.289737i | 0.370259 | − | 0.928929i | \(-0.379269\pi\) |
−0.769048 | + | 0.639192i | \(0.779269\pi\) | |||||||
\(758\) | −8.29180 | −0.301172 | ||||||||
\(759\) | −17.7705 | − | 11.1554i | −0.645029 | − | 0.404916i | ||||
\(760\) | −25.6525 | −0.930513 | ||||||||
\(761\) | 23.3262 | + | 16.9475i | 0.845575 | + | 0.614347i | 0.923923 | − | 0.382580i | \(-0.124964\pi\) |
−0.0783471 | + | 0.996926i | \(0.524964\pi\) | |||||||
\(762\) | −2.09017 | + | 6.43288i | −0.0757189 | + | 0.233039i | ||||
\(763\) | −0.736068 | − | 2.26538i | −0.0266474 | − | 0.0820124i | ||||
\(764\) | 0.0729490 | − | 0.0530006i | 0.00263920 | − | 0.00191749i | ||||
\(765\) | 15.7533 | − | 11.4454i | 0.569561 | − | 0.413811i | ||||
\(766\) | −1.85410 | − | 5.70634i | −0.0669914 | − | 0.206178i | ||||
\(767\) | 8.94427 | − | 27.5276i | 0.322959 | − | 0.993965i | ||||
\(768\) | −0.809017 | − | 0.587785i | −0.0291929 | − | 0.0212099i | ||||
\(769\) | 1.52786 | 0.0550962 | 0.0275481 | − | 0.999620i | \(-0.491230\pi\) | ||||
0.0275481 | + | 0.999620i | \(0.491230\pi\) | |||||||
\(770\) | −11.9721 | + | 0.812299i | −0.431446 | + | 0.0292732i | ||||
\(771\) | −15.8541 | −0.570972 | ||||||||
\(772\) | −3.92705 | − | 2.85317i | −0.141338 | − | 0.102688i | ||||
\(773\) | 12.4377 | − | 38.2793i | 0.447353 | − | 1.37681i | −0.432530 | − | 0.901620i | \(-0.642379\pi\) |
0.879883 | − | 0.475191i | \(-0.157621\pi\) | |||||||
\(774\) | −0.236068 | − | 0.726543i | −0.00848529 | − | 0.0261150i | ||||
\(775\) | 66.0410 | − | 47.9816i | 2.37226 | − | 1.72355i | ||||
\(776\) | 5.47214 | − | 3.97574i | 0.196438 | − | 0.142721i | ||||
\(777\) | 1.97214 | + | 6.06961i | 0.0707500 | + | 0.217746i | ||||
\(778\) | −1.18034 | + | 3.63271i | −0.0423172 | + | 0.130239i | ||||
\(779\) | 29.5172 | + | 21.4455i | 1.05756 | + | 0.768365i | ||||
\(780\) | −11.7082 | −0.419221 | ||||||||
\(781\) | 12.9443 | + | 32.2299i | 0.463182 | + | 1.15328i | ||||
\(782\) | −34.0476 | −1.21754 | ||||||||
\(783\) | −2.61803 | − | 1.90211i | −0.0935609 | − | 0.0679760i | ||||
\(784\) | 0.309017 | − | 0.951057i | 0.0110363 | − | 0.0339663i | ||||
\(785\) | 10.8541 | + | 33.4055i | 0.387400 | + | 1.19229i | ||||
\(786\) | 8.70820 | − | 6.32688i | 0.310611 | − | 0.225672i | ||||
\(787\) | 21.1074 | − | 15.3354i | 0.752397 | − | 0.546649i | −0.144172 | − | 0.989553i | \(-0.546052\pi\) |
0.896569 | + | 0.442904i | \(0.146052\pi\) | |||||||
\(788\) | 7.18034 | + | 22.0988i | 0.255789 | + | 0.787238i | ||||
\(789\) | −6.80902 | + | 20.9560i | −0.242407 | + | 0.746053i | ||||
\(790\) | −16.7082 | − | 12.1392i | −0.594451 | − | 0.431894i | ||||
\(791\) | −2.47214 | −0.0878990 | ||||||||
\(792\) | −1.23607 | − | 3.07768i | −0.0439218 | − | 0.109361i | ||||
\(793\) | −15.4164 | −0.547453 | ||||||||
\(794\) | 12.9443 | + | 9.40456i | 0.459375 | + | 0.333755i | ||||
\(795\) | 10.0000 | − | 30.7768i | 0.354663 | − | 1.09154i | ||||
\(796\) | 7.80902 | + | 24.0337i | 0.276783 | + | 0.851851i | ||||
\(797\) | −33.5795 | + | 24.3970i | −1.18945 | + | 0.864184i | −0.993206 | − | 0.116371i | \(-0.962874\pi\) |
−0.196242 | + | 0.980555i | \(0.562874\pi\) | |||||||
\(798\) | 5.73607 | − | 4.16750i | 0.203055 | − | 0.147528i | ||||
\(799\) | −20.2574 | − | 62.3457i | −0.716654 | − | 2.20563i | ||||
\(800\) | −2.50000 | + | 7.69421i | −0.0883883 | + | 0.272031i | ||||
\(801\) | 9.59017 | + | 6.96767i | 0.338852 | + | 0.246190i | ||||
\(802\) | −1.70820 | −0.0603188 | ||||||||
\(803\) | −26.4721 | + | 1.79611i | −0.934181 | + | 0.0633834i | ||||
\(804\) | 3.23607 | 0.114127 | ||||||||
\(805\) | −18.5172 | − | 13.4535i | −0.652646 | − | 0.474175i | ||||
\(806\) | 10.0902 | − | 31.0543i | 0.355411 | − | 1.09384i | ||||
\(807\) | 1.85410 | + | 5.70634i | 0.0652675 | + | 0.200873i | ||||
\(808\) | 4.16312 | − | 3.02468i | 0.146458 | − | 0.106408i | ||||
\(809\) | 13.8541 | − | 10.0656i | 0.487084 | − | 0.353887i | −0.316978 | − | 0.948433i | \(-0.602668\pi\) |
0.804062 | + | 0.594546i | \(0.202668\pi\) | |||||||
\(810\) | 1.11803 | + | 3.44095i | 0.0392837 | + | 0.120903i | ||||
\(811\) | −15.4164 | + | 47.4468i | −0.541343 | + | 1.66608i | 0.188186 | + | 0.982133i | \(0.439739\pi\) |
−0.729529 | + | 0.683950i | \(0.760261\pi\) | |||||||
\(812\) | 2.61803 | + | 1.90211i | 0.0918750 | + | 0.0667511i | ||||
\(813\) | −6.09017 | −0.213592 | ||||||||
\(814\) | −17.9271 | − | 11.2537i | −0.628343 | − | 0.394441i | ||||
\(815\) | −41.7082 | −1.46097 | ||||||||
\(816\) | −4.35410 | − | 3.16344i | −0.152424 | − | 0.110743i | ||||
\(817\) | −1.67376 | + | 5.15131i | −0.0585575 | + | 0.180222i | ||||
\(818\) | 6.88854 | + | 21.2008i | 0.240852 | + | 0.741267i | ||||
\(819\) | 2.61803 | − | 1.90211i | 0.0914815 | − | 0.0664652i | ||||
\(820\) | 15.0623 | − | 10.9434i | 0.525999 | − | 0.382160i | ||||
\(821\) | −1.94427 | − | 5.98385i | −0.0678556 | − | 0.208838i | 0.911379 | − | 0.411568i | \(-0.135019\pi\) |
−0.979235 | + | 0.202730i | \(0.935019\pi\) | |||||||
\(822\) | 0.763932 | − | 2.35114i | 0.0266452 | − | 0.0820055i | ||||
\(823\) | 41.4164 | + | 30.0908i | 1.44369 | + | 1.04890i | 0.987256 | + | 0.159139i | \(0.0508718\pi\) |
0.456429 | + | 0.889760i | \(0.349128\pi\) | |||||||
\(824\) | 18.7984 | 0.654872 | ||||||||
\(825\) | −20.5902 | + | 17.2048i | −0.716858 | + | 0.598993i | ||||
\(826\) | 8.94427 | 0.311211 | ||||||||
\(827\) | −39.2984 | − | 28.5519i | −1.36654 | − | 0.992848i | −0.997999 | − | 0.0632362i | \(-0.979858\pi\) |
−0.368540 | − | 0.929612i | \(-0.620142\pi\) | |||||||
\(828\) | 1.95492 | − | 6.01661i | 0.0679380 | − | 0.209092i | ||||
\(829\) | 0.381966 | + | 1.17557i | 0.0132662 | + | 0.0408293i | 0.957471 | − | 0.288531i | \(-0.0931669\pi\) |
−0.944204 | + | 0.329360i | \(0.893167\pi\) | |||||||
\(830\) | −31.5066 | + | 22.8909i | −1.09361 | + | 0.794554i | ||||
\(831\) | −7.97214 | + | 5.79210i | −0.276550 | + | 0.200926i | ||||
\(832\) | 1.00000 | + | 3.07768i | 0.0346688 | + | 0.106699i | ||||
\(833\) | 1.66312 | − | 5.11855i | 0.0576237 | − | 0.177347i | ||||
\(834\) | 8.20820 | + | 5.96361i | 0.284227 | + | 0.206503i | ||||
\(835\) | −59.5967 | −2.06243 | ||||||||
\(836\) | −5.73607 | + | 22.8051i | −0.198386 | + | 0.788731i | ||||
\(837\) | −10.0902 | −0.348767 | ||||||||
\(838\) | −12.0902 | − | 8.78402i | −0.417648 | − | 0.303439i | ||||
\(839\) | −9.88854 | + | 30.4338i | −0.341390 | + | 1.05069i | 0.622097 | + | 0.782940i | \(0.286281\pi\) |
−0.963488 | + | 0.267752i | \(0.913719\pi\) | |||||||
\(840\) | −1.11803 | − | 3.44095i | −0.0385758 | − | 0.118724i | ||||
\(841\) | 14.9894 | − | 10.8904i | 0.516874 | − | 0.375531i | ||||
\(842\) | 0.263932 | − | 0.191758i | 0.00909570 | − | 0.00660841i | ||||
\(843\) | −5.14590 | − | 15.8374i | −0.177234 | − | 0.545471i | ||||
\(844\) | 1.61803 | − | 4.97980i | 0.0556950 | − | 0.171412i | ||||
\(845\) | −7.39919 | − | 5.37582i | −0.254540 | − | 0.184934i | ||||
\(846\) | 12.1803 | 0.418769 | ||||||||
\(847\) | −1.95492 | + | 10.8249i | −0.0671717 | + | 0.371948i | ||||
\(848\) | −8.94427 | −0.307148 | ||||||||
\(849\) | 8.16312 | + | 5.93085i | 0.280158 | + | 0.203546i | ||||
\(850\) | −13.4549 | + | 41.4100i | −0.461500 | + | 1.42035i | ||||
\(851\) | −12.4762 | − | 38.3978i | −0.427679 | − | 1.31626i | ||||
\(852\) | −8.47214 | + | 6.15537i | −0.290251 | + | 0.210879i | ||||
\(853\) | 29.1803 | − | 21.2008i | 0.999116 | − | 0.725900i | 0.0372174 | − | 0.999307i | \(-0.488151\pi\) |
0.961898 | + | 0.273407i | \(0.0881506\pi\) | |||||||
\(854\) | −1.47214 | − | 4.53077i | −0.0503755 | − | 0.155040i | ||||
\(855\) | 7.92705 | − | 24.3970i | 0.271099 | − | 0.834358i | ||||
\(856\) | 8.11803 | + | 5.89810i | 0.277469 | + | 0.201593i | ||||
\(857\) | 55.3050 | 1.88918 | 0.944591 | − | 0.328251i | \(-0.106459\pi\) | ||||
0.944591 | + | 0.328251i | \(0.106459\pi\) | |||||||
\(858\) | −2.61803 | + | 10.4086i | −0.0893782 | + | 0.355344i | ||||
\(859\) | 34.4721 | 1.17617 | 0.588087 | − | 0.808798i | \(-0.299881\pi\) | ||||
0.588087 | + | 0.808798i | \(0.299881\pi\) | |||||||
\(860\) | 2.23607 | + | 1.62460i | 0.0762493 | + | 0.0553983i | ||||
\(861\) | −1.59017 | + | 4.89404i | −0.0541928 | + | 0.166788i | ||||
\(862\) | 7.50000 | + | 23.0826i | 0.255451 | + | 0.786197i | ||||
\(863\) | −0.0729490 | + | 0.0530006i | −0.00248321 | + | 0.00180416i | −0.589026 | − | 0.808114i | \(-0.700489\pi\) |
0.586543 | + | 0.809918i | \(0.300489\pi\) | |||||||
\(864\) | 0.809017 | − | 0.587785i | 0.0275233 | − | 0.0199969i | ||||
\(865\) | −0.163119 | − | 0.502029i | −0.00554621 | − | 0.0170695i | ||||
\(866\) | 10.7082 | − | 32.9565i | 0.363880 | − | 1.11991i | ||||
\(867\) | −9.68034 | − | 7.03318i | −0.328762 | − | 0.238859i | ||||
\(868\) | 10.0902 | 0.342483 | ||||||||
\(869\) | −14.5279 | + | 12.1392i | −0.492824 | + | 0.411795i | ||||
\(870\) | 11.7082 | 0.396945 | ||||||||
\(871\) | −8.47214 | − | 6.15537i | −0.287067 | − | 0.208567i | ||||
\(872\) | −0.736068 | + | 2.26538i | −0.0249264 | + | 0.0767156i | ||||
\(873\) | 2.09017 | + | 6.43288i | 0.0707415 | + | 0.217720i | ||||
\(874\) | −36.2877 | + | 26.3646i | −1.22745 | + | 0.891795i | ||||
\(875\) | −9.04508 | + | 6.57164i | −0.305780 | + | 0.222162i | ||||
\(876\) | −2.47214 | − | 7.60845i | −0.0835257 | − | 0.257066i | ||||
\(877\) | −7.20163 | + | 22.1643i | −0.243182 | + | 0.748436i | 0.752749 | + | 0.658308i | \(0.228728\pi\) |
−0.995930 | + | 0.0901280i | \(0.971272\pi\) | |||||||
\(878\) | −5.69098 | − | 4.13474i | −0.192061 | − | 0.139541i | ||||
\(879\) | −15.7984 | −0.532866 | ||||||||
\(880\) | 10.1631 | + | 6.37988i | 0.342599 | + | 0.215066i | ||||
\(881\) | 28.2148 | 0.950580 | 0.475290 | − | 0.879829i | \(-0.342343\pi\) | ||||
0.475290 | + | 0.879829i | \(0.342343\pi\) | |||||||
\(882\) | 0.809017 | + | 0.587785i | 0.0272410 | + | 0.0197918i | ||||
\(883\) | 0.618034 | − | 1.90211i | 0.0207985 | − | 0.0640112i | −0.940119 | − | 0.340848i | \(-0.889286\pi\) |
0.960917 | + | 0.276836i | \(0.0892860\pi\) | |||||||
\(884\) | 5.38197 | + | 16.5640i | 0.181015 | + | 0.557107i | ||||
\(885\) | 26.1803 | − | 19.0211i | 0.880042 | − | 0.639388i | ||||
\(886\) | 21.8262 | − | 15.8577i | 0.733267 | − | 0.532750i | ||||
\(887\) | −6.00000 | − | 18.4661i | −0.201460 | − | 0.620031i | −0.999840 | − | 0.0178769i | \(-0.994309\pi\) |
0.798380 | − | 0.602154i | \(-0.205691\pi\) | |||||||
\(888\) | 1.97214 | − | 6.06961i | 0.0661805 | − | 0.203683i | ||||
\(889\) | 5.47214 | + | 3.97574i | 0.183530 | + | 0.133342i | ||||
\(890\) | −42.8885 | −1.43763 | ||||||||
\(891\) | 3.30902 | − | 0.224514i | 0.110856 | − | 0.00752150i | ||||
\(892\) | 9.85410 | 0.329940 | ||||||||
\(893\) | −69.8673 | − | 50.7615i | −2.33802 | − | 1.69867i | ||||
\(894\) | −2.29180 | + | 7.05342i | −0.0766491 | + | 0.235902i | ||||
\(895\) | −1.60739 | − | 4.94704i | −0.0537292 | − | 0.165361i | ||||
\(896\) | −0.809017 | + | 0.587785i | −0.0270274 | + | 0.0196365i | ||||
\(897\) | −16.5623 | + | 12.0332i | −0.552999 | + | 0.401778i | ||||
\(898\) | 3.14590 | + | 9.68208i | 0.104980 | + | 0.323095i | ||||
\(899\) | −10.0902 | + | 31.0543i | −0.336526 | + | 1.03572i | ||||
\(900\) | −6.54508 | − | 4.75528i | −0.218169 | − | 0.158509i | ||||
\(901\) | −48.1378 | −1.60370 | ||||||||
\(902\) | −6.36068 | − | 15.8374i | −0.211787 | − | 0.527329i | ||||
\(903\) | −0.763932 | −0.0254221 | ||||||||
\(904\) | 2.00000 | + | 1.45309i | 0.0665190 | + | 0.0483289i | ||||
\(905\) | −8.94427 | + | 27.5276i | −0.297318 | + | 0.915050i | ||||
\(906\) | −2.76393 | − | 8.50651i | −0.0918255 | − | 0.282610i | ||||
\(907\) | −11.3820 | + | 8.26948i | −0.377932 | + | 0.274584i | −0.760492 | − | 0.649347i | \(-0.775042\pi\) |
0.382560 | + | 0.923930i | \(0.375042\pi\) | |||||||
\(908\) | −18.1803 | + | 13.2088i | −0.603336 | + | 0.438349i | ||||
\(909\) | 1.59017 | + | 4.89404i | 0.0527426 | + | 0.162325i | ||||
\(910\) | −3.61803 | + | 11.1352i | −0.119937 | + | 0.369127i | ||||
\(911\) | −31.5967 | − | 22.9564i | −1.04685 | − | 0.760579i | −0.0752366 | − | 0.997166i | \(-0.523971\pi\) |
−0.971610 | + | 0.236587i | \(0.923971\pi\) | |||||||
\(912\) | −7.09017 | −0.234779 | ||||||||
\(913\) | 13.3050 | + | 33.1280i | 0.440330 | + | 1.09638i | ||||
\(914\) | 33.4164 | 1.10532 | ||||||||
\(915\) | −13.9443 | − | 10.1311i | −0.460983 | − | 0.334924i | ||||
\(916\) | 7.67376 | − | 23.6174i | 0.253548 | − | 0.780341i | ||||
\(917\) | −3.32624 | − | 10.2371i | −0.109842 | − | 0.338059i | ||||
\(918\) | 4.35410 | − | 3.16344i | 0.143707 | − | 0.104409i | ||||
\(919\) | −28.3262 | + | 20.5802i | −0.934396 | + | 0.678879i | −0.947065 | − | 0.321041i | \(-0.895967\pi\) |
0.0126689 | + | 0.999920i | \(0.495967\pi\) | |||||||
\(920\) | 7.07295 | + | 21.7683i | 0.233188 | + | 0.717680i | ||||
\(921\) | 2.82624 | − | 8.69827i | 0.0931277 | − | 0.286618i | ||||
\(922\) | −12.8541 | − | 9.33905i | −0.423327 | − | 0.307565i | ||||
\(923\) | 33.8885 | 1.11546 | ||||||||
\(924\) | −3.30902 | + | 0.224514i | −0.108859 | + | 0.00738597i | ||||
\(925\) | −51.6312 | −1.69762 | ||||||||
\(926\) | −8.56231 | − | 6.22088i | −0.281375 | − | 0.204431i | ||||
\(927\) | −5.80902 | + | 17.8783i | −0.190793 | + | 0.587201i | ||||
\(928\) | −1.00000 | − | 3.07768i | −0.0328266 | − | 0.101030i | ||||
\(929\) | 45.1869 | − | 32.8302i | 1.48253 | − | 1.07712i | 0.505806 | − | 0.862647i | \(-0.331195\pi\) |
0.976729 | − | 0.214477i | \(-0.0688047\pi\) | |||||||
\(930\) | 29.5344 | − | 21.4580i | 0.968473 | − | 0.703636i | ||||
\(931\) | −2.19098 | − | 6.74315i | −0.0718066 | − | 0.220998i | ||||
\(932\) | −4.90983 | + | 15.1109i | −0.160827 | + | 0.494974i | ||||
\(933\) | 18.1803 | + | 13.2088i | 0.595198 | + | 0.432436i | ||||
\(934\) | −8.00000 | −0.261768 | ||||||||
\(935\) | 54.6976 | + | 34.3363i | 1.78880 | + | 1.12292i | ||||
\(936\) | −3.23607 | −0.105774 | ||||||||
\(937\) | −28.1803 | − | 20.4742i | −0.920612 | − | 0.668863i | 0.0230646 | − | 0.999734i | \(-0.492658\pi\) |
−0.943676 | + | 0.330871i | \(0.892658\pi\) | |||||||
\(938\) | 1.00000 | − | 3.07768i | 0.0326512 | − | 0.100490i | ||||
\(939\) | 8.56231 | + | 26.3521i | 0.279420 | + | 0.859967i | ||||
\(940\) | −35.6525 | + | 25.9030i | −1.16286 | + | 0.844864i | ||||
\(941\) | −6.35410 | + | 4.61653i | −0.207138 | + | 0.150494i | −0.686518 | − | 0.727113i | \(-0.740862\pi\) |
0.479380 | + | 0.877607i | \(0.340862\pi\) | |||||||
\(942\) | 3.00000 | + | 9.23305i | 0.0977453 | + | 0.300829i | ||||
\(943\) | 10.0598 | − | 30.9609i | 0.327592 | − | 1.00822i | ||||
\(944\) | −7.23607 | − | 5.25731i | −0.235514 | − | 0.171111i | ||||
\(945\) | 3.61803 | 0.117695 | ||||||||
\(946\) | 1.94427 | − | 1.62460i | 0.0632137 | − | 0.0528203i | ||||
\(947\) | 5.61803 | 0.182562 | 0.0912808 | − | 0.995825i | \(-0.470904\pi\) | ||||
0.0912808 | + | 0.995825i | \(0.470904\pi\) | |||||||
\(948\) | −4.61803 | − | 3.35520i | −0.149987 | − | 0.108972i | ||||
\(949\) | −8.00000 | + | 24.6215i | −0.259691 | + | 0.799247i | ||||
\(950\) | 17.7254 | + | 54.5532i | 0.575089 | + | 1.76994i | ||||
\(951\) | −9.70820 | + | 7.05342i | −0.314810 | + | 0.228723i | ||||
\(952\) | −4.35410 | + | 3.16344i | −0.141117 | + | 0.102528i | ||||
\(953\) | 7.47214 | + | 22.9969i | 0.242046 | + | 0.744942i | 0.996108 | + | 0.0881385i | \(0.0280918\pi\) |
−0.754062 | + | 0.656803i | \(0.771908\pi\) | |||||||
\(954\) | 2.76393 | − | 8.50651i | 0.0894856 | − | 0.275408i | ||||
\(955\) | −0.263932 | − | 0.191758i | −0.00854064 | − | 0.00620514i | ||||
\(956\) | 9.38197 | 0.303434 | ||||||||
\(957\) | 2.61803 | − | 10.4086i | 0.0846290 | − | 0.336463i | ||||
\(958\) | 12.9443 | 0.418210 | ||||||||
\(959\) | −2.00000 | − | 1.45309i | −0.0645834 | − | 0.0469226i | ||||
\(960\) | −1.11803 | + | 3.44095i | −0.0360844 | + | 0.111056i | ||||
\(961\) | 21.8820 | + | 67.3458i | 0.705870 | + | 2.17244i | ||||
\(962\) | −16.7082 | + | 12.1392i | −0.538694 | + | 0.391384i | ||||
\(963\) | −8.11803 | + | 5.89810i | −0.261600 | + | 0.190064i | ||||
\(964\) | 5.00000 | + | 15.3884i | 0.161039 | + | 0.495628i | ||||
\(965\) | −5.42705 | + | 16.7027i | −0.174703 | + | 0.537680i | ||||
\(966\) | −5.11803 | − | 3.71847i | −0.164670 | − | 0.119640i | ||||
\(967\) | −2.18034 | −0.0701150 | −0.0350575 | − | 0.999385i | \(-0.511161\pi\) | ||||
−0.0350575 | + | 0.999385i | \(0.511161\pi\) | |||||||
\(968\) | 7.94427 | − | 7.60845i | 0.255339 | − | 0.244545i | ||||
\(969\) | −38.1591 | −1.22585 | ||||||||
\(970\) | −19.7984 | − | 14.3844i | −0.635687 | − | 0.461854i | ||||
\(971\) | −12.4377 | + | 38.2793i | −0.399145 | + | 1.22844i | 0.526542 | + | 0.850149i | \(0.323488\pi\) |
−0.925686 | + | 0.378292i | \(0.876512\pi\) | |||||||
\(972\) | 0.309017 | + | 0.951057i | 0.00991172 | + | 0.0305052i | ||||
\(973\) | 8.20820 | − | 5.96361i | 0.263143 | − | 0.191185i | ||||
\(974\) | −10.0000 | + | 7.26543i | −0.320421 | + | 0.232799i | ||||
\(975\) | 8.09017 | + | 24.8990i | 0.259093 | + | 0.797406i | ||||
\(976\) | −1.47214 | + | 4.53077i | −0.0471219 | + | 0.145026i | ||||
\(977\) | −21.8541 | − | 15.8779i | −0.699175 | − | 0.507980i | 0.180489 | − | 0.983577i | \(-0.442232\pi\) |
−0.879663 | + | 0.475597i | \(0.842232\pi\) | |||||||
\(978\) | −11.5279 | −0.368620 | ||||||||
\(979\) | −9.59017 | + | 38.1280i | −0.306503 | + | 1.21858i | ||||
\(980\) | −3.61803 | −0.115574 | ||||||||
\(981\) | −1.92705 | − | 1.40008i | −0.0615260 | − | 0.0447013i | ||||
\(982\) | −12.4271 | + | 38.2465i | −0.396563 | + | 1.22050i | ||||
\(983\) | 7.56231 | + | 23.2744i | 0.241200 | + | 0.742338i | 0.996238 | + | 0.0866567i | \(0.0276183\pi\) |
−0.755038 | + | 0.655681i | \(0.772382\pi\) | |||||||
\(984\) | 4.16312 | − | 3.02468i | 0.132715 | − | 0.0964234i | ||||
\(985\) | 68.0132 | − | 49.4145i | 2.16708 | − | 1.57448i | ||||
\(986\) | −5.38197 | − | 16.5640i | −0.171397 | − | 0.527505i | ||||
\(987\) | 3.76393 | − | 11.5842i | 0.119807 | − | 0.368729i | ||||
\(988\) | 18.5623 | + | 13.4863i | 0.590546 | + | 0.429057i | ||||
\(989\) | 4.83282 | 0.153675 | ||||||||
\(990\) | −9.20820 | + | 7.69421i | −0.292656 | + | 0.244538i | ||||
\(991\) | 17.7082 | 0.562520 | 0.281260 | − | 0.959632i | \(-0.409248\pi\) | ||||
0.281260 | + | 0.959632i | \(0.409248\pi\) | |||||||
\(992\) | −8.16312 | − | 5.93085i | −0.259179 | − | 0.188305i | ||||
\(993\) | 6.85410 | − | 21.0948i | 0.217508 | − | 0.669422i | ||||
\(994\) | 3.23607 | + | 9.95959i | 0.102642 | + | 0.315899i | ||||
\(995\) | 73.9681 | − | 53.7409i | 2.34495 | − | 1.70370i | ||||
\(996\) | −8.70820 | + | 6.32688i | −0.275930 | + | 0.200475i | ||||
\(997\) | −5.67376 | − | 17.4620i | −0.179690 | − | 0.553028i | 0.820127 | − | 0.572182i | \(-0.193903\pi\) |
−0.999817 | + | 0.0191535i | \(0.993903\pi\) | |||||||
\(998\) | −2.70820 | + | 8.33499i | −0.0857267 | + | 0.263840i | ||||
\(999\) | 5.16312 | + | 3.75123i | 0.163354 | + | 0.118684i |
(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 | 462.2.j.c.169.1 | ✓ | 4 | |
11.3 | even | 5 | inner | 462.2.j.c.421.1 | yes | 4 | |
11.5 | even | 5 | 5082.2.a.bh.1.1 | 2 | |||
11.6 | odd | 10 | 5082.2.a.br.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.c.169.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
462.2.j.c.421.1 | yes | 4 | 11.3 | even | 5 | inner | |
5082.2.a.bh.1.1 | 2 | 11.5 | even | 5 | |||
5082.2.a.br.1.1 | 2 | 11.6 | odd | 10 |