Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 729.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.729 |
Dual form | 847.2.f.b.323.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.80902 | + | 1.31433i | −1.27917 | + | 0.929370i | −0.999528 | − | 0.0307347i | \(-0.990215\pi\) |
−0.279641 | + | 0.960105i | \(0.590215\pi\) | |||||||
\(3\) | 1.00000 | + | 3.07768i | 0.577350 | + | 1.77690i | 0.628033 | + | 0.778187i | \(0.283860\pi\) |
−0.0506828 | + | 0.998715i | \(0.516140\pi\) | |||||||
\(4\) | 0.927051 | − | 2.85317i | 0.463525 | − | 1.42658i | ||||
\(5\) | 1.61803 | + | 1.17557i | 0.723607 | + | 0.525731i | 0.887535 | − | 0.460741i | \(-0.152416\pi\) |
−0.163928 | + | 0.986472i | \(0.552416\pi\) | |||||||
\(6\) | −5.85410 | − | 4.25325i | −2.38993 | − | 1.73638i | ||||
\(7\) | −0.309017 | + | 0.951057i | −0.116797 | + | 0.359466i | ||||
\(8\) | 0.690983 | + | 2.12663i | 0.244299 | + | 0.751876i | ||||
\(9\) | −6.04508 | + | 4.39201i | −2.01503 | + | 1.46400i | ||||
\(10\) | −4.47214 | −1.41421 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 9.70820 | 2.80252 | ||||||||
\(13\) | −1.00000 | + | 0.726543i | −0.277350 | + | 0.201507i | −0.717761 | − | 0.696290i | \(-0.754833\pi\) |
0.440411 | + | 0.897796i | \(0.354833\pi\) | |||||||
\(14\) | −0.690983 | − | 2.12663i | −0.184673 | − | 0.568365i | ||||
\(15\) | −2.00000 | + | 6.15537i | −0.516398 | + | 1.58931i | ||||
\(16\) | 0.809017 | + | 0.587785i | 0.202254 | + | 0.146946i | ||||
\(17\) | 1.00000 | + | 0.726543i | 0.242536 | + | 0.176212i | 0.702412 | − | 0.711770i | \(-0.252106\pi\) |
−0.459877 | + | 0.887983i | \(0.652106\pi\) | |||||||
\(18\) | 5.16312 | − | 15.8904i | 1.21696 | − | 3.74541i | ||||
\(19\) | 0.763932 | + | 2.35114i | 0.175258 | + | 0.539389i | 0.999645 | − | 0.0266376i | \(-0.00848003\pi\) |
−0.824387 | + | 0.566026i | \(0.808480\pi\) | |||||||
\(20\) | 4.85410 | − | 3.52671i | 1.08541 | − | 0.788597i | ||||
\(21\) | −3.23607 | −0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | −5.85410 | + | 4.25325i | −1.19496 | + | 0.868192i | ||||
\(25\) | −0.309017 | − | 0.951057i | −0.0618034 | − | 0.190211i | ||||
\(26\) | 0.854102 | − | 2.62866i | 0.167503 | − | 0.515522i | ||||
\(27\) | −11.7082 | − | 8.50651i | −2.25324 | − | 1.63708i | ||||
\(28\) | 2.42705 | + | 1.76336i | 0.458670 | + | 0.333243i | ||||
\(29\) | 0.145898 | − | 0.449028i | 0.0270926 | − | 0.0833824i | −0.936596 | − | 0.350411i | \(-0.886042\pi\) |
0.963689 | + | 0.267029i | \(0.0860419\pi\) | |||||||
\(30\) | −4.47214 | − | 13.7638i | −0.816497 | − | 2.51292i | ||||
\(31\) | 5.85410 | − | 4.25325i | 1.05143 | − | 0.763907i | 0.0789443 | − | 0.996879i | \(-0.474845\pi\) |
0.972483 | + | 0.232972i | \(0.0748451\pi\) | |||||||
\(32\) | −6.70820 | −1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.76393 | −0.474010 | ||||||||
\(35\) | −1.61803 | + | 1.17557i | −0.273498 | + | 0.198708i | ||||
\(36\) | 6.92705 | + | 21.3193i | 1.15451 | + | 3.55321i | ||||
\(37\) | 0.145898 | − | 0.449028i | 0.0239855 | − | 0.0738197i | −0.938347 | − | 0.345694i | \(-0.887644\pi\) |
0.962333 | + | 0.271874i | \(0.0876435\pi\) | |||||||
\(38\) | −4.47214 | − | 3.24920i | −0.725476 | − | 0.527089i | ||||
\(39\) | −3.23607 | − | 2.35114i | −0.518186 | − | 0.376484i | ||||
\(40\) | −1.38197 | + | 4.25325i | −0.218508 | + | 0.672499i | ||||
\(41\) | 2.09017 | + | 6.43288i | 0.326430 | + | 1.00465i | 0.970791 | + | 0.239926i | \(0.0771233\pi\) |
−0.644361 | + | 0.764721i | \(0.722877\pi\) | |||||||
\(42\) | 5.85410 | − | 4.25325i | 0.903308 | − | 0.656291i | ||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.9443 | −2.22776 | ||||||||
\(46\) | 11.7082 | − | 8.50651i | 1.72628 | − | 1.25422i | ||||
\(47\) | 2.23607 | + | 6.88191i | 0.326164 | + | 1.00383i | 0.970912 | + | 0.239435i | \(0.0769621\pi\) |
−0.644748 | + | 0.764395i | \(0.723038\pi\) | |||||||
\(48\) | −1.00000 | + | 3.07768i | −0.144338 | + | 0.444225i | ||||
\(49\) | −0.809017 | − | 0.587785i | −0.115574 | − | 0.0839693i | ||||
\(50\) | 1.80902 | + | 1.31433i | 0.255834 | + | 0.185874i | ||||
\(51\) | −1.23607 | + | 3.80423i | −0.173084 | + | 0.532698i | ||||
\(52\) | 1.14590 | + | 3.52671i | 0.158907 | + | 0.489067i | ||||
\(53\) | −6.85410 | + | 4.97980i | −0.941483 | + | 0.684028i | −0.948777 | − | 0.315946i | \(-0.897678\pi\) |
0.00729395 | + | 0.999973i | \(0.497678\pi\) | |||||||
\(54\) | 32.3607 | 4.40373 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | −6.47214 | + | 4.70228i | −0.857255 | + | 0.622832i | ||||
\(58\) | 0.326238 | + | 1.00406i | 0.0428371 | + | 0.131839i | ||||
\(59\) | 1.00000 | − | 3.07768i | 0.130189 | − | 0.400680i | −0.864622 | − | 0.502423i | \(-0.832442\pi\) |
0.994811 | + | 0.101743i | \(0.0324419\pi\) | |||||||
\(60\) | 15.7082 | + | 11.4127i | 2.02792 | + | 1.47337i | ||||
\(61\) | −2.23607 | − | 1.62460i | −0.286299 | − | 0.208009i | 0.435361 | − | 0.900256i | \(-0.356621\pi\) |
−0.721660 | + | 0.692247i | \(0.756621\pi\) | |||||||
\(62\) | −5.00000 | + | 15.3884i | −0.635001 | + | 1.95433i | ||||
\(63\) | −2.30902 | − | 7.10642i | −0.290909 | − | 0.895325i | ||||
\(64\) | 10.5172 | − | 7.64121i | 1.31465 | − | 0.955151i | ||||
\(65\) | −2.47214 | −0.306631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.52786 | 0.675336 | 0.337668 | − | 0.941265i | \(-0.390362\pi\) | ||||
0.337668 | + | 0.941265i | \(0.390362\pi\) | |||||||
\(68\) | 3.00000 | − | 2.17963i | 0.363803 | − | 0.264319i | ||||
\(69\) | −6.47214 | − | 19.9192i | −0.779154 | − | 2.39799i | ||||
\(70\) | 1.38197 | − | 4.25325i | 0.165177 | − | 0.508361i | ||||
\(71\) | 1.23607 | + | 0.898056i | 0.146694 | + | 0.106580i | 0.658712 | − | 0.752395i | \(-0.271102\pi\) |
−0.512017 | + | 0.858975i | \(0.671102\pi\) | |||||||
\(72\) | −13.5172 | − | 9.82084i | −1.59302 | − | 1.15740i | ||||
\(73\) | 1.61803 | − | 4.97980i | 0.189377 | − | 0.582841i | −0.810620 | − | 0.585573i | \(-0.800870\pi\) |
0.999996 | + | 0.00273185i | \(0.000869575\pi\) | |||||||
\(74\) | 0.326238 | + | 1.00406i | 0.0379244 | + | 0.116719i | ||||
\(75\) | 2.61803 | − | 1.90211i | 0.302305 | − | 0.219637i | ||||
\(76\) | 7.41641 | 0.850720 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.94427 | 1.01274 | ||||||||
\(79\) | 7.23607 | − | 5.25731i | 0.814121 | − | 0.591494i | −0.100901 | − | 0.994896i | \(-0.532173\pi\) |
0.915023 | + | 0.403403i | \(0.132173\pi\) | |||||||
\(80\) | 0.618034 | + | 1.90211i | 0.0690983 | + | 0.212663i | ||||
\(81\) | 7.54508 | − | 23.2214i | 0.838343 | − | 2.58015i | ||||
\(82\) | −12.2361 | − | 8.89002i | −1.35125 | − | 0.981739i | ||||
\(83\) | 12.4721 | + | 9.06154i | 1.36899 | + | 0.994633i | 0.997815 | + | 0.0660720i | \(0.0210467\pi\) |
0.371180 | + | 0.928561i | \(0.378953\pi\) | |||||||
\(84\) | −3.00000 | + | 9.23305i | −0.327327 | + | 1.00741i | ||||
\(85\) | 0.763932 | + | 2.35114i | 0.0828601 | + | 0.255017i | ||||
\(86\) | 14.4721 | − | 10.5146i | 1.56057 | − | 1.13382i | ||||
\(87\) | 1.52786 | 0.163804 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 27.0344 | − | 19.6417i | 2.84968 | − | 2.07041i | ||||
\(91\) | −0.381966 | − | 1.17557i | −0.0400409 | − | 0.123233i | ||||
\(92\) | −6.00000 | + | 18.4661i | −0.625543 | + | 1.92522i | ||||
\(93\) | 18.9443 | + | 13.7638i | 1.96443 | + | 1.42724i | ||||
\(94\) | −13.0902 | − | 9.51057i | −1.35015 | − | 0.980940i | ||||
\(95\) | −1.52786 | + | 4.70228i | −0.156756 | + | 0.482444i | ||||
\(96\) | −6.70820 | − | 20.6457i | −0.684653 | − | 2.10715i | ||||
\(97\) | 7.61803 | − | 5.53483i | 0.773494 | − | 0.561976i | −0.129525 | − | 0.991576i | \(-0.541345\pi\) |
0.903019 | + | 0.429600i | \(0.141345\pi\) | |||||||
\(98\) | 2.23607 | 0.225877 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −7.47214 | + | 5.42882i | −0.743505 | + | 0.540188i | −0.893807 | − | 0.448452i | \(-0.851976\pi\) |
0.150302 | + | 0.988640i | \(0.451976\pi\) | |||||||
\(102\) | −2.76393 | − | 8.50651i | −0.273670 | − | 0.842270i | ||||
\(103\) | −1.76393 | + | 5.42882i | −0.173805 | + | 0.534918i | −0.999577 | − | 0.0290868i | \(-0.990740\pi\) |
0.825772 | + | 0.564005i | \(0.190740\pi\) | |||||||
\(104\) | −2.23607 | − | 1.62460i | −0.219265 | − | 0.159305i | ||||
\(105\) | −5.23607 | − | 3.80423i | −0.510988 | − | 0.371254i | ||||
\(106\) | 5.85410 | − | 18.0171i | 0.568601 | − | 1.74997i | ||||
\(107\) | 1.23607 | + | 3.80423i | 0.119495 | + | 0.367768i | 0.992858 | − | 0.119302i | \(-0.0380656\pi\) |
−0.873363 | + | 0.487070i | \(0.838066\pi\) | |||||||
\(108\) | −35.1246 | + | 25.5195i | −3.37987 | + | 2.45562i | ||||
\(109\) | −4.47214 | −0.428353 | −0.214176 | − | 0.976795i | \(-0.568707\pi\) | ||||
−0.214176 | + | 0.976795i | \(0.568707\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.52786 | 0.145018 | ||||||||
\(112\) | −0.809017 | + | 0.587785i | −0.0764449 | + | 0.0555405i | ||||
\(113\) | 0.618034 | + | 1.90211i | 0.0581397 | + | 0.178936i | 0.975909 | − | 0.218179i | \(-0.0700116\pi\) |
−0.917769 | + | 0.397114i | \(0.870012\pi\) | |||||||
\(114\) | 5.52786 | − | 17.0130i | 0.517732 | − | 1.59341i | ||||
\(115\) | −10.4721 | − | 7.60845i | −0.976532 | − | 0.709492i | ||||
\(116\) | −1.14590 | − | 0.832544i | −0.106394 | − | 0.0772997i | ||||
\(117\) | 2.85410 | − | 8.78402i | 0.263862 | − | 0.812083i | ||||
\(118\) | 2.23607 | + | 6.88191i | 0.205847 | + | 0.633531i | ||||
\(119\) | −1.00000 | + | 0.726543i | −0.0916698 | + | 0.0666020i | ||||
\(120\) | −14.4721 | −1.32112 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.18034 | 0.559542 | ||||||||
\(123\) | −17.7082 | + | 12.8658i | −1.59669 | + | 1.16007i | ||||
\(124\) | −6.70820 | − | 20.6457i | −0.602414 | − | 1.85404i | ||||
\(125\) | 3.70820 | − | 11.4127i | 0.331672 | − | 1.02078i | ||||
\(126\) | 13.5172 | + | 9.82084i | 1.20421 | + | 0.874910i | ||||
\(127\) | 16.9443 | + | 12.3107i | 1.50356 | + | 1.09240i | 0.968936 | + | 0.247312i | \(0.0795471\pi\) |
0.534625 | + | 0.845089i | \(0.320453\pi\) | |||||||
\(128\) | −4.83688 | + | 14.8864i | −0.427524 | + | 1.31578i | ||||
\(129\) | −8.00000 | − | 24.6215i | −0.704361 | − | 2.16780i | ||||
\(130\) | 4.47214 | − | 3.24920i | 0.392232 | − | 0.284973i | ||||
\(131\) | 13.8885 | 1.21345 | 0.606724 | − | 0.794913i | \(-0.292483\pi\) | ||||
0.606724 | + | 0.794913i | \(0.292483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.47214 | −0.214361 | ||||||||
\(134\) | −10.0000 | + | 7.26543i | −0.863868 | + | 0.627637i | ||||
\(135\) | −8.94427 | − | 27.5276i | −0.769800 | − | 2.36920i | ||||
\(136\) | −0.854102 | + | 2.62866i | −0.0732386 | + | 0.225405i | ||||
\(137\) | −6.09017 | − | 4.42477i | −0.520318 | − | 0.378033i | 0.296405 | − | 0.955062i | \(-0.404212\pi\) |
−0.816724 | + | 0.577029i | \(0.804212\pi\) | |||||||
\(138\) | 37.8885 | + | 27.5276i | 3.22529 | + | 2.34331i | ||||
\(139\) | 3.23607 | − | 9.95959i | 0.274480 | − | 0.844762i | −0.714877 | − | 0.699250i | \(-0.753517\pi\) |
0.989357 | − | 0.145511i | \(-0.0464827\pi\) | |||||||
\(140\) | 1.85410 | + | 5.70634i | 0.156700 | + | 0.482274i | ||||
\(141\) | −18.9443 | + | 13.7638i | −1.59540 | + | 1.15912i | ||||
\(142\) | −3.41641 | −0.286699 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.47214 | −0.622678 | ||||||||
\(145\) | 0.763932 | − | 0.555029i | 0.0634411 | − | 0.0460927i | ||||
\(146\) | 3.61803 | + | 11.1352i | 0.299431 | + | 0.921553i | ||||
\(147\) | 1.00000 | − | 3.07768i | 0.0824786 | − | 0.253843i | ||||
\(148\) | −1.14590 | − | 0.832544i | −0.0941922 | − | 0.0684347i | ||||
\(149\) | 11.3262 | + | 8.22899i | 0.927882 | + | 0.674145i | 0.945473 | − | 0.325700i | \(-0.105600\pi\) |
−0.0175917 | + | 0.999845i | \(0.505600\pi\) | |||||||
\(150\) | −2.23607 | + | 6.88191i | −0.182574 | + | 0.561906i | ||||
\(151\) | 2.76393 | + | 8.50651i | 0.224926 | + | 0.692250i | 0.998299 | + | 0.0582992i | \(0.0185677\pi\) |
−0.773374 | + | 0.633951i | \(0.781432\pi\) | |||||||
\(152\) | −4.47214 | + | 3.24920i | −0.362738 | + | 0.263545i | ||||
\(153\) | −9.23607 | −0.746692 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4721 | 1.16243 | ||||||||
\(156\) | −9.70820 | + | 7.05342i | −0.777278 | + | 0.564726i | ||||
\(157\) | −2.14590 | − | 6.60440i | −0.171261 | − | 0.527088i | 0.828182 | − | 0.560460i | \(-0.189376\pi\) |
−0.999443 | + | 0.0333716i | \(0.989376\pi\) | |||||||
\(158\) | −6.18034 | + | 19.0211i | −0.491681 | + | 1.51324i | ||||
\(159\) | −22.1803 | − | 16.1150i | −1.75902 | − | 1.27800i | ||||
\(160\) | −10.8541 | − | 7.88597i | −0.858092 | − | 0.623440i | ||||
\(161\) | 2.00000 | − | 6.15537i | 0.157622 | − | 0.485111i | ||||
\(162\) | 16.8713 | + | 51.9246i | 1.32554 | + | 4.07958i | ||||
\(163\) | −18.9443 | + | 13.7638i | −1.48383 | + | 1.07807i | −0.507532 | + | 0.861633i | \(0.669442\pi\) |
−0.976298 | + | 0.216433i | \(0.930558\pi\) | |||||||
\(164\) | 20.2918 | 1.58452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −34.4721 | −2.67556 | ||||||||
\(167\) | −10.4721 | + | 7.60845i | −0.810358 | + | 0.588760i | −0.913934 | − | 0.405862i | \(-0.866971\pi\) |
0.103576 | + | 0.994622i | \(0.466971\pi\) | |||||||
\(168\) | −2.23607 | − | 6.88191i | −0.172516 | − | 0.530951i | ||||
\(169\) | −3.54508 | + | 10.9106i | −0.272699 | + | 0.839281i | ||||
\(170\) | −4.47214 | − | 3.24920i | −0.342997 | − | 0.249202i | ||||
\(171\) | −14.9443 | − | 10.8576i | −1.14282 | − | 0.830305i | ||||
\(172\) | −7.41641 | + | 22.8254i | −0.565496 | + | 1.74042i | ||||
\(173\) | 5.32624 | + | 16.3925i | 0.404946 | + | 1.24630i | 0.920940 | + | 0.389704i | \(0.127423\pi\) |
−0.515994 | + | 0.856592i | \(0.672577\pi\) | |||||||
\(174\) | −2.76393 | + | 2.00811i | −0.209533 | + | 0.152235i | ||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.4721 | 0.787134 | ||||||||
\(178\) | −3.61803 | + | 2.62866i | −0.271183 | + | 0.197026i | ||||
\(179\) | 2.76393 | + | 8.50651i | 0.206586 | + | 0.635806i | 0.999645 | + | 0.0266609i | \(0.00848742\pi\) |
−0.793059 | + | 0.609145i | \(0.791513\pi\) | |||||||
\(180\) | −13.8541 | + | 42.6385i | −1.03262 | + | 3.17809i | ||||
\(181\) | −1.14590 | − | 0.832544i | −0.0851739 | − | 0.0618825i | 0.544383 | − | 0.838837i | \(-0.316764\pi\) |
−0.629557 | + | 0.776954i | \(0.716764\pi\) | |||||||
\(182\) | 2.23607 | + | 1.62460i | 0.165748 | + | 0.120423i | ||||
\(183\) | 2.76393 | − | 8.50651i | 0.204316 | − | 0.628819i | ||||
\(184\) | −4.47214 | − | 13.7638i | −0.329690 | − | 1.01468i | ||||
\(185\) | 0.763932 | − | 0.555029i | 0.0561654 | − | 0.0408066i | ||||
\(186\) | −52.3607 | −3.83927 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 21.7082 | 1.58323 | ||||||||
\(189\) | 11.7082 | − | 8.50651i | 0.851647 | − | 0.618757i | ||||
\(190\) | −3.41641 | − | 10.5146i | −0.247852 | − | 0.762811i | ||||
\(191\) | −6.47214 | + | 19.9192i | −0.468307 | + | 1.44130i | 0.386468 | + | 0.922303i | \(0.373695\pi\) |
−0.854775 | + | 0.518999i | \(0.826305\pi\) | |||||||
\(192\) | 34.0344 | + | 24.7275i | 2.45622 | + | 1.78455i | ||||
\(193\) | −19.3262 | − | 14.0413i | −1.39113 | − | 1.01072i | −0.995740 | − | 0.0922053i | \(-0.970608\pi\) |
−0.395393 | − | 0.918512i | \(-0.629392\pi\) | |||||||
\(194\) | −6.50658 | + | 20.0252i | −0.467145 | + | 1.43772i | ||||
\(195\) | −2.47214 | − | 7.60845i | −0.177033 | − | 0.544853i | ||||
\(196\) | −2.42705 | + | 1.76336i | −0.173361 | + | 0.125954i | ||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1803 | 1.43055 | 0.715273 | − | 0.698845i | \(-0.246302\pi\) | ||||
0.715273 | + | 0.698845i | \(0.246302\pi\) | |||||||
\(200\) | 1.80902 | − | 1.31433i | 0.127917 | − | 0.0929370i | ||||
\(201\) | 5.52786 | + | 17.0130i | 0.389905 | + | 1.20001i | ||||
\(202\) | 6.38197 | − | 19.6417i | 0.449034 | − | 1.38198i | ||||
\(203\) | 0.381966 | + | 0.277515i | 0.0268088 | + | 0.0194777i | ||||
\(204\) | 9.70820 | + | 7.05342i | 0.679710 | + | 0.493838i | ||||
\(205\) | −4.18034 | + | 12.8658i | −0.291968 | + | 0.898584i | ||||
\(206\) | −3.94427 | − | 12.1392i | −0.274810 | − | 0.845780i | ||||
\(207\) | 39.1246 | − | 28.4257i | 2.71935 | − | 1.97572i | ||||
\(208\) | −1.23607 | −0.0857059 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 14.4721 | 0.998672 | ||||||||
\(211\) | 17.7082 | − | 12.8658i | 1.21908 | − | 0.885716i | 0.223059 | − | 0.974805i | \(-0.428396\pi\) |
0.996024 | + | 0.0890892i | \(0.0283956\pi\) | |||||||
\(212\) | 7.85410 | + | 24.1724i | 0.539422 | + | 1.66017i | ||||
\(213\) | −1.52786 | + | 4.70228i | −0.104688 | + | 0.322195i | ||||
\(214\) | −7.23607 | − | 5.25731i | −0.494647 | − | 0.359382i | ||||
\(215\) | −12.9443 | − | 9.40456i | −0.882792 | − | 0.641386i | ||||
\(216\) | 10.0000 | − | 30.7768i | 0.680414 | − | 2.09410i | ||||
\(217\) | 2.23607 | + | 6.88191i | 0.151794 | + | 0.467174i | ||||
\(218\) | 8.09017 | − | 5.87785i | 0.547935 | − | 0.398098i | ||||
\(219\) | 16.9443 | 1.14499 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.52786 | −0.102775 | ||||||||
\(222\) | −2.76393 | + | 2.00811i | −0.185503 | + | 0.134776i | ||||
\(223\) | 3.76393 | + | 11.5842i | 0.252052 | + | 0.775735i | 0.994396 | + | 0.105717i | \(0.0337137\pi\) |
−0.742345 | + | 0.670018i | \(0.766286\pi\) | |||||||
\(224\) | 2.07295 | − | 6.37988i | 0.138505 | − | 0.426274i | ||||
\(225\) | 6.04508 | + | 4.39201i | 0.403006 | + | 0.292801i | ||||
\(226\) | −3.61803 | − | 2.62866i | −0.240668 | − | 0.174856i | ||||
\(227\) | 9.23607 | − | 28.4257i | 0.613019 | − | 1.88668i | 0.185603 | − | 0.982625i | \(-0.440576\pi\) |
0.427417 | − | 0.904055i | \(-0.359424\pi\) | |||||||
\(228\) | 7.41641 | + | 22.8254i | 0.491164 | + | 1.51165i | ||||
\(229\) | −3.61803 | + | 2.62866i | −0.239086 | + | 0.173706i | −0.700876 | − | 0.713283i | \(-0.747207\pi\) |
0.461790 | + | 0.886989i | \(0.347207\pi\) | |||||||
\(230\) | 28.9443 | 1.90853 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.05573 | 0.0693119 | ||||||||
\(233\) | −14.0902 | + | 10.2371i | −0.923078 | + | 0.670655i | −0.944288 | − | 0.329120i | \(-0.893248\pi\) |
0.0212104 | + | 0.999775i | \(0.493248\pi\) | |||||||
\(234\) | 6.38197 | + | 19.6417i | 0.417202 | + | 1.28402i | ||||
\(235\) | −4.47214 | + | 13.7638i | −0.291730 | + | 0.897853i | ||||
\(236\) | −7.85410 | − | 5.70634i | −0.511258 | − | 0.371451i | ||||
\(237\) | 23.4164 | + | 17.0130i | 1.52106 | + | 1.10511i | ||||
\(238\) | 0.854102 | − | 2.62866i | 0.0553632 | − | 0.170390i | ||||
\(239\) | −8.00000 | − | 24.6215i | −0.517477 | − | 1.59263i | −0.778729 | − | 0.627360i | \(-0.784136\pi\) |
0.261252 | − | 0.965271i | \(-0.415864\pi\) | |||||||
\(240\) | −5.23607 | + | 3.80423i | −0.337987 | + | 0.245562i | ||||
\(241\) | −27.1246 | −1.74725 | −0.873625 | − | 0.486600i | \(-0.838237\pi\) | ||||
−0.873625 | + | 0.486600i | \(0.838237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 35.5967 | 2.28353 | ||||||||
\(244\) | −6.70820 | + | 4.87380i | −0.429449 | + | 0.312013i | ||||
\(245\) | −0.618034 | − | 1.90211i | −0.0394847 | − | 0.121522i | ||||
\(246\) | 15.1246 | − | 46.5488i | 0.964310 | − | 2.96784i | ||||
\(247\) | −2.47214 | − | 1.79611i | −0.157298 | − | 0.114284i | ||||
\(248\) | 13.0902 | + | 9.51057i | 0.831227 | + | 0.603921i | ||||
\(249\) | −15.4164 | + | 47.4468i | −0.976975 | + | 3.00682i | ||||
\(250\) | 8.29180 | + | 25.5195i | 0.524419 | + | 1.61400i | ||||
\(251\) | −14.3262 | + | 10.4086i | −0.904264 | + | 0.656986i | −0.939558 | − | 0.342391i | \(-0.888763\pi\) |
0.0352936 | + | 0.999377i | \(0.488763\pi\) | |||||||
\(252\) | −22.4164 | −1.41210 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −46.8328 | −2.93855 | ||||||||
\(255\) | −6.47214 | + | 4.70228i | −0.405301 | + | 0.294468i | ||||
\(256\) | −2.78115 | − | 8.55951i | −0.173822 | − | 0.534969i | ||||
\(257\) | −1.85410 | + | 5.70634i | −0.115656 | + | 0.355952i | −0.992083 | − | 0.125582i | \(-0.959920\pi\) |
0.876428 | + | 0.481534i | \(0.159920\pi\) | |||||||
\(258\) | 46.8328 | + | 34.0260i | 2.91568 | + | 2.11837i | ||||
\(259\) | 0.381966 | + | 0.277515i | 0.0237342 | + | 0.0172439i | ||||
\(260\) | −2.29180 | + | 7.05342i | −0.142131 | + | 0.437435i | ||||
\(261\) | 1.09017 | + | 3.35520i | 0.0674798 | + | 0.207682i | ||||
\(262\) | −25.1246 | + | 18.2541i | −1.55220 | + | 1.12774i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.9443 | −1.04088 | ||||||||
\(266\) | 4.47214 | − | 3.24920i | 0.274204 | − | 0.199221i | ||||
\(267\) | 2.00000 | + | 6.15537i | 0.122398 | + | 0.376702i | ||||
\(268\) | 5.12461 | − | 15.7719i | 0.313035 | − | 0.963424i | ||||
\(269\) | 10.8541 | + | 7.88597i | 0.661786 | + | 0.480816i | 0.867266 | − | 0.497846i | \(-0.165875\pi\) |
−0.205479 | + | 0.978661i | \(0.565875\pi\) | |||||||
\(270\) | 52.3607 | + | 38.0423i | 3.18657 | + | 2.31518i | ||||
\(271\) | 0.472136 | − | 1.45309i | 0.0286802 | − | 0.0882686i | −0.935692 | − | 0.352818i | \(-0.885223\pi\) |
0.964372 | + | 0.264550i | \(0.0852233\pi\) | |||||||
\(272\) | 0.381966 | + | 1.17557i | 0.0231601 | + | 0.0712794i | ||||
\(273\) | 3.23607 | − | 2.35114i | 0.195856 | − | 0.142298i | ||||
\(274\) | 16.8328 | 1.01691 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −62.8328 | −3.78209 | ||||||||
\(277\) | 12.8541 | − | 9.33905i | 0.772328 | − | 0.561129i | −0.130339 | − | 0.991470i | \(-0.541606\pi\) |
0.902667 | + | 0.430340i | \(0.141606\pi\) | |||||||
\(278\) | 7.23607 | + | 22.2703i | 0.433991 | + | 1.33569i | ||||
\(279\) | −16.7082 | + | 51.4226i | −1.00029 | + | 3.07859i | ||||
\(280\) | −3.61803 | − | 2.62866i | −0.216219 | − | 0.157092i | ||||
\(281\) | −10.0902 | − | 7.33094i | −0.601929 | − | 0.437327i | 0.244634 | − | 0.969615i | \(-0.421332\pi\) |
−0.846563 | + | 0.532288i | \(0.821332\pi\) | |||||||
\(282\) | 16.1803 | − | 49.7980i | 0.963525 | − | 2.96543i | ||||
\(283\) | 1.81966 | + | 5.60034i | 0.108168 | + | 0.332906i | 0.990461 | − | 0.137795i | \(-0.0440014\pi\) |
−0.882293 | + | 0.470700i | \(0.844001\pi\) | |||||||
\(284\) | 3.70820 | − | 2.69417i | 0.220041 | − | 0.159869i | ||||
\(285\) | −16.0000 | −0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.76393 | −0.399262 | ||||||||
\(288\) | 40.5517 | − | 29.4625i | 2.38953 | − | 1.73609i | ||||
\(289\) | −4.78115 | − | 14.7149i | −0.281244 | − | 0.865581i | ||||
\(290\) | −0.652476 | + | 2.00811i | −0.0383147 | + | 0.117921i | ||||
\(291\) | 24.6525 | + | 17.9111i | 1.44515 | + | 1.04997i | ||||
\(292\) | −12.7082 | − | 9.23305i | −0.743691 | − | 0.540323i | ||||
\(293\) | −4.67376 | + | 14.3844i | −0.273044 | + | 0.840343i | 0.716686 | + | 0.697396i | \(0.245658\pi\) |
−0.989730 | + | 0.142948i | \(0.954342\pi\) | |||||||
\(294\) | 2.23607 | + | 6.88191i | 0.130410 | + | 0.401361i | ||||
\(295\) | 5.23607 | − | 3.80423i | 0.304856 | − | 0.221491i | ||||
\(296\) | 1.05573 | 0.0613629 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −31.3050 | −1.81345 | ||||||||
\(299\) | 6.47214 | − | 4.70228i | 0.374293 | − | 0.271940i | ||||
\(300\) | −3.00000 | − | 9.23305i | −0.173205 | − | 0.533070i | ||||
\(301\) | 2.47214 | − | 7.60845i | 0.142492 | − | 0.438544i | ||||
\(302\) | −16.1803 | − | 11.7557i | −0.931074 | − | 0.676465i | ||||
\(303\) | −24.1803 | − | 17.5680i | −1.38912 | − | 1.00926i | ||||
\(304\) | −0.763932 | + | 2.35114i | −0.0438145 | + | 0.134847i | ||||
\(305\) | −1.70820 | − | 5.25731i | −0.0978115 | − | 0.301033i | ||||
\(306\) | 16.7082 | − | 12.1392i | 0.955144 | − | 0.693953i | ||||
\(307\) | −8.94427 | −0.510477 | −0.255238 | − | 0.966878i | \(-0.582154\pi\) | ||||
−0.255238 | + | 0.966878i | \(0.582154\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4721 | −1.05084 | ||||||||
\(310\) | −26.1803 | + | 19.0211i | −1.48694 | + | 1.08033i | ||||
\(311\) | −6.70820 | − | 20.6457i | −0.380387 | − | 1.17071i | −0.939772 | − | 0.341803i | \(-0.888962\pi\) |
0.559384 | − | 0.828909i | \(-0.311038\pi\) | |||||||
\(312\) | 2.76393 | − | 8.50651i | 0.156477 | − | 0.481586i | ||||
\(313\) | 2.38197 | + | 1.73060i | 0.134637 | + | 0.0978193i | 0.653065 | − | 0.757302i | \(-0.273483\pi\) |
−0.518428 | + | 0.855121i | \(0.673483\pi\) | |||||||
\(314\) | 12.5623 | + | 9.12705i | 0.708932 | + | 0.515069i | ||||
\(315\) | 4.61803 | − | 14.2128i | 0.260197 | − | 0.800803i | ||||
\(316\) | −8.29180 | − | 25.5195i | −0.466450 | − | 1.43559i | ||||
\(317\) | −11.3262 | + | 8.22899i | −0.636145 | + | 0.462186i | −0.858524 | − | 0.512774i | \(-0.828618\pi\) |
0.222379 | + | 0.974960i | \(0.428618\pi\) | |||||||
\(318\) | 61.3050 | 3.43781 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 26.0000 | 1.45344 | ||||||||
\(321\) | −10.4721 | + | 7.60845i | −0.584498 | + | 0.424662i | ||||
\(322\) | 4.47214 | + | 13.7638i | 0.249222 | + | 0.767028i | ||||
\(323\) | −0.944272 | + | 2.90617i | −0.0525407 | + | 0.161704i | ||||
\(324\) | −59.2599 | − | 43.0548i | −3.29221 | − | 2.39193i | ||||
\(325\) | 1.00000 | + | 0.726543i | 0.0554700 | + | 0.0403013i | ||||
\(326\) | 16.1803 | − | 49.7980i | 0.896146 | − | 2.75805i | ||||
\(327\) | −4.47214 | − | 13.7638i | −0.247310 | − | 0.761141i | ||||
\(328\) | −12.2361 | + | 8.89002i | −0.675624 | + | 0.490869i | ||||
\(329\) | −7.23607 | −0.398937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8885 | 1.20310 | 0.601552 | − | 0.798834i | \(-0.294549\pi\) | ||||
0.601552 | + | 0.798834i | \(0.294549\pi\) | |||||||
\(332\) | 37.4164 | − | 27.1846i | 2.05349 | − | 1.49195i | ||||
\(333\) | 1.09017 | + | 3.35520i | 0.0597409 | + | 0.183864i | ||||
\(334\) | 8.94427 | − | 27.5276i | 0.489409 | − | 1.50625i | ||||
\(335\) | 8.94427 | + | 6.49839i | 0.488678 | + | 0.355045i | ||||
\(336\) | −2.61803 | − | 1.90211i | −0.142825 | − | 0.103769i | ||||
\(337\) | 6.32624 | − | 19.4702i | 0.344612 | − | 1.06061i | −0.617179 | − | 0.786823i | \(-0.711725\pi\) |
0.961791 | − | 0.273784i | \(-0.0882754\pi\) | |||||||
\(338\) | −7.92705 | − | 24.3970i | −0.431175 | − | 1.32702i | ||||
\(339\) | −5.23607 | + | 3.80423i | −0.284384 | + | 0.206617i | ||||
\(340\) | 7.41641 | 0.402211 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 41.3050 | 2.23352 | ||||||||
\(343\) | 0.809017 | − | 0.587785i | 0.0436828 | − | 0.0317374i | ||||
\(344\) | −5.52786 | − | 17.0130i | −0.298042 | − | 0.917280i | ||||
\(345\) | 12.9443 | − | 39.8384i | 0.696896 | − | 2.14483i | ||||
\(346\) | −31.1803 | − | 22.6538i | −1.67627 | − | 1.21788i | ||||
\(347\) | 2.47214 | + | 1.79611i | 0.132711 | + | 0.0964203i | 0.652160 | − | 0.758081i | \(-0.273863\pi\) |
−0.519449 | + | 0.854501i | \(0.673863\pi\) | |||||||
\(348\) | 1.41641 | − | 4.35926i | 0.0759274 | − | 0.233681i | ||||
\(349\) | 0.854102 | + | 2.62866i | 0.0457190 | + | 0.140709i | 0.971310 | − | 0.237816i | \(-0.0764315\pi\) |
−0.925591 | + | 0.378525i | \(0.876432\pi\) | |||||||
\(350\) | −1.80902 | + | 1.31433i | −0.0966960 | + | 0.0702538i | ||||
\(351\) | 17.8885 | 0.954820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8885 | −0.845662 | −0.422831 | − | 0.906209i | \(-0.638964\pi\) | ||||
−0.422831 | + | 0.906209i | \(0.638964\pi\) | |||||||
\(354\) | −18.9443 | + | 13.7638i | −1.00688 | + | 0.731539i | ||||
\(355\) | 0.944272 | + | 2.90617i | 0.0501167 | + | 0.154243i | ||||
\(356\) | 1.85410 | − | 5.70634i | 0.0982672 | − | 0.302435i | ||||
\(357\) | −3.23607 | − | 2.35114i | −0.171271 | − | 0.124436i | ||||
\(358\) | −16.1803 | − | 11.7557i | −0.855158 | − | 0.621308i | ||||
\(359\) | 2.18034 | − | 6.71040i | 0.115074 | − | 0.354161i | −0.876889 | − | 0.480694i | \(-0.840385\pi\) |
0.991962 | + | 0.126533i | \(0.0403849\pi\) | |||||||
\(360\) | −10.3262 | − | 31.7809i | −0.544241 | − | 1.67500i | ||||
\(361\) | 10.4271 | − | 7.57570i | 0.548792 | − | 0.398721i | ||||
\(362\) | 3.16718 | 0.166464 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.70820 | −0.194363 | ||||||||
\(365\) | 8.47214 | − | 6.15537i | 0.443452 | − | 0.322187i | ||||
\(366\) | 6.18034 | + | 19.0211i | 0.323052 | + | 0.994250i | ||||
\(367\) | 5.29180 | − | 16.2865i | 0.276230 | − | 0.850147i | −0.712662 | − | 0.701508i | \(-0.752511\pi\) |
0.988891 | − | 0.148639i | \(-0.0474894\pi\) | |||||||
\(368\) | −5.23607 | − | 3.80423i | −0.272949 | − | 0.198309i | ||||
\(369\) | −40.8885 | − | 29.7073i | −2.12857 | − | 1.54650i | ||||
\(370\) | −0.652476 | + | 2.00811i | −0.0339206 | + | 0.104397i | ||||
\(371\) | −2.61803 | − | 8.05748i | −0.135922 | − | 0.418324i | ||||
\(372\) | 56.8328 | − | 41.2915i | 2.94664 | − | 2.14086i | ||||
\(373\) | −6.00000 | −0.310668 | −0.155334 | − | 0.987862i | \(-0.549645\pi\) | ||||
−0.155334 | + | 0.987862i | \(0.549645\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38.8328 | 2.00532 | ||||||||
\(376\) | −13.0902 | + | 9.51057i | −0.675074 | + | 0.490470i | ||||
\(377\) | 0.180340 | + | 0.555029i | 0.00928798 | + | 0.0285855i | ||||
\(378\) | −10.0000 | + | 30.7768i | −0.514344 | + | 1.58299i | ||||
\(379\) | 20.4721 | + | 14.8739i | 1.05158 | + | 0.764020i | 0.972513 | − | 0.232849i | \(-0.0748049\pi\) |
0.0790702 | + | 0.996869i | \(0.474805\pi\) | |||||||
\(380\) | 12.0000 | + | 8.71851i | 0.615587 | + | 0.447250i | ||||
\(381\) | −20.9443 | + | 64.4598i | −1.07301 | + | 3.30238i | ||||
\(382\) | −14.4721 | − | 44.5407i | −0.740459 | − | 2.27890i | ||||
\(383\) | −21.5623 | + | 15.6659i | −1.10178 | + | 0.800492i | −0.981350 | − | 0.192230i | \(-0.938428\pi\) |
−0.120432 | + | 0.992722i | \(0.538428\pi\) | |||||||
\(384\) | −50.6525 | −2.58485 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.4164 | 2.71882 | ||||||||
\(387\) | 48.3607 | − | 35.1361i | 2.45831 | − | 1.78607i | ||||
\(388\) | −8.72949 | − | 26.8666i | −0.443173 | − | 1.36395i | ||||
\(389\) | −6.14590 | + | 18.9151i | −0.311609 | + | 0.959035i | 0.665518 | + | 0.746382i | \(0.268211\pi\) |
−0.977128 | + | 0.212654i | \(0.931789\pi\) | |||||||
\(390\) | 14.4721 | + | 10.5146i | 0.732825 | + | 0.532429i | ||||
\(391\) | −6.47214 | − | 4.70228i | −0.327310 | − | 0.237805i | ||||
\(392\) | 0.690983 | − | 2.12663i | 0.0348999 | − | 0.107411i | ||||
\(393\) | 13.8885 | + | 42.7445i | 0.700584 | + | 2.15618i | ||||
\(394\) | −3.61803 | + | 2.62866i | −0.182274 | + | 0.132430i | ||||
\(395\) | 17.8885 | 0.900070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.111456 | −0.00559383 | −0.00279691 | − | 0.999996i | \(-0.500890\pi\) | ||||
−0.00279691 | + | 0.999996i | \(0.500890\pi\) | |||||||
\(398\) | −36.5066 | + | 26.5236i | −1.82991 | + | 1.32951i | ||||
\(399\) | −2.47214 | − | 7.60845i | −0.123762 | − | 0.380899i | ||||
\(400\) | 0.309017 | − | 0.951057i | 0.0154508 | − | 0.0475528i | ||||
\(401\) | −4.09017 | − | 2.97168i | −0.204253 | − | 0.148399i | 0.480956 | − | 0.876744i | \(-0.340290\pi\) |
−0.685210 | + | 0.728346i | \(0.740290\pi\) | |||||||
\(402\) | −32.3607 | − | 23.5114i | −1.61400 | − | 1.17264i | ||||
\(403\) | −2.76393 | + | 8.50651i | −0.137681 | + | 0.423739i | ||||
\(404\) | 8.56231 | + | 26.3521i | 0.425991 | + | 1.31106i | ||||
\(405\) | 39.5066 | − | 28.7032i | 1.96310 | − | 1.42627i | ||||
\(406\) | −1.05573 | −0.0523949 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −8.94427 | −0.442807 | ||||||||
\(409\) | −25.1803 | + | 18.2946i | −1.24509 | + | 0.904609i | −0.997926 | − | 0.0643652i | \(-0.979498\pi\) |
−0.247161 | + | 0.968974i | \(0.579498\pi\) | |||||||
\(410\) | −9.34752 | − | 28.7687i | −0.461641 | − | 1.42079i | ||||
\(411\) | 7.52786 | − | 23.1684i | 0.371322 | − | 1.14281i | ||||
\(412\) | 13.8541 | + | 10.0656i | 0.682543 | + | 0.495896i | ||||
\(413\) | 2.61803 | + | 1.90211i | 0.128825 | + | 0.0935969i | ||||
\(414\) | −33.4164 | + | 102.845i | −1.64233 | + | 5.05456i | ||||
\(415\) | 9.52786 | + | 29.3238i | 0.467704 | + | 1.43945i | ||||
\(416\) | 6.70820 | − | 4.87380i | 0.328897 | − | 0.238957i | ||||
\(417\) | 33.8885 | 1.65953 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.65248 | −0.324995 | −0.162497 | − | 0.986709i | \(-0.551955\pi\) | ||||
−0.162497 | + | 0.986709i | \(0.551955\pi\) | |||||||
\(420\) | −15.7082 | + | 11.4127i | −0.766482 | + | 0.556882i | ||||
\(421\) | −6.90983 | − | 21.2663i | −0.336765 | − | 1.03645i | −0.965846 | − | 0.259116i | \(-0.916569\pi\) |
0.629082 | − | 0.777339i | \(-0.283431\pi\) | |||||||
\(422\) | −15.1246 | + | 46.5488i | −0.736255 | + | 2.26596i | ||||
\(423\) | −43.7426 | − | 31.7809i | −2.12684 | − | 1.54524i | ||||
\(424\) | −15.3262 | − | 11.1352i | −0.744308 | − | 0.540771i | ||||
\(425\) | 0.381966 | − | 1.17557i | 0.0185281 | − | 0.0570235i | ||||
\(426\) | −3.41641 | − | 10.5146i | −0.165526 | − | 0.509435i | ||||
\(427\) | 2.23607 | − | 1.62460i | 0.108211 | − | 0.0786198i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 35.7771 | 1.72532 | ||||||||
\(431\) | 9.70820 | − | 7.05342i | 0.467628 | − | 0.339751i | −0.328888 | − | 0.944369i | \(-0.606674\pi\) |
0.796516 | + | 0.604617i | \(0.206674\pi\) | |||||||
\(432\) | −4.47214 | − | 13.7638i | −0.215166 | − | 0.662212i | ||||
\(433\) | 0.145898 | − | 0.449028i | 0.00701141 | − | 0.0215789i | −0.947490 | − | 0.319787i | \(-0.896389\pi\) |
0.954501 | + | 0.298208i | \(0.0963888\pi\) | |||||||
\(434\) | −13.0902 | − | 9.51057i | −0.628348 | − | 0.456522i | ||||
\(435\) | 2.47214 | + | 1.79611i | 0.118530 | + | 0.0861170i | ||||
\(436\) | −4.14590 | + | 12.7598i | −0.198553 | + | 0.611082i | ||||
\(437\) | −4.94427 | − | 15.2169i | −0.236517 | − | 0.727923i | ||||
\(438\) | −30.6525 | + | 22.2703i | −1.46463 | + | 1.06412i | ||||
\(439\) | −1.52786 | −0.0729210 | −0.0364605 | − | 0.999335i | \(-0.511608\pi\) | ||||
−0.0364605 | + | 0.999335i | \(0.511608\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | 2.76393 | − | 2.00811i | 0.131467 | − | 0.0955163i | ||||
\(443\) | −2.18034 | − | 6.71040i | −0.103591 | − | 0.318821i | 0.885806 | − | 0.464056i | \(-0.153606\pi\) |
−0.989397 | + | 0.145235i | \(0.953606\pi\) | |||||||
\(444\) | 1.41641 | − | 4.35926i | 0.0672197 | − | 0.206881i | ||||
\(445\) | 3.23607 | + | 2.35114i | 0.153404 | + | 0.111455i | ||||
\(446\) | −22.0344 | − | 16.0090i | −1.04336 | − | 0.758046i | ||||
\(447\) | −14.0000 | + | 43.0876i | −0.662177 | + | 2.03797i | ||||
\(448\) | 4.01722 | + | 12.3637i | 0.189796 | + | 0.584132i | ||||
\(449\) | 15.7984 | − | 11.4782i | 0.745571 | − | 0.541689i | −0.148880 | − | 0.988855i | \(-0.547567\pi\) |
0.894451 | + | 0.447166i | \(0.147567\pi\) | |||||||
\(450\) | −16.7082 | −0.787632 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | −23.4164 | + | 17.0130i | −1.10020 | + | 0.799341i | ||||
\(454\) | 20.6525 | + | 63.5618i | 0.969269 | + | 2.98310i | ||||
\(455\) | 0.763932 | − | 2.35114i | 0.0358137 | − | 0.110223i | ||||
\(456\) | −14.4721 | − | 10.5146i | −0.677720 | − | 0.492392i | ||||
\(457\) | 20.0902 | + | 14.5964i | 0.939779 | + | 0.682789i | 0.948367 | − | 0.317174i | \(-0.102734\pi\) |
−0.00858883 | + | 0.999963i | \(0.502734\pi\) | |||||||
\(458\) | 3.09017 | − | 9.51057i | 0.144394 | − | 0.444400i | ||||
\(459\) | −5.52786 | − | 17.0130i | −0.258019 | − | 0.794100i | ||||
\(460\) | −31.4164 | + | 22.8254i | −1.46480 | + | 1.06424i | ||||
\(461\) | −10.1803 | −0.474146 | −0.237073 | − | 0.971492i | \(-0.576188\pi\) | ||||
−0.237073 | + | 0.971492i | \(0.576188\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.4721 | −0.672577 | −0.336289 | − | 0.941759i | \(-0.609172\pi\) | ||||
−0.336289 | + | 0.941759i | \(0.609172\pi\) | |||||||
\(464\) | 0.381966 | − | 0.277515i | 0.0177323 | − | 0.0128833i | ||||
\(465\) | 14.4721 | + | 44.5407i | 0.671129 | + | 2.06552i | ||||
\(466\) | 12.0344 | − | 37.0382i | 0.557485 | − | 1.71576i | ||||
\(467\) | 27.5623 | + | 20.0252i | 1.27543 | + | 0.926655i | 0.999405 | − | 0.0344949i | \(-0.0109822\pi\) |
0.276027 | + | 0.961150i | \(0.410982\pi\) | |||||||
\(468\) | −22.4164 | − | 16.2865i | −1.03620 | − | 0.752843i | ||||
\(469\) | −1.70820 | + | 5.25731i | −0.0788775 | + | 0.242760i | ||||
\(470\) | −10.0000 | − | 30.7768i | −0.461266 | − | 1.41963i | ||||
\(471\) | 18.1803 | − | 13.2088i | 0.837706 | − | 0.608629i | ||||
\(472\) | 7.23607 | 0.333067 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −64.7214 | −2.97275 | ||||||||
\(475\) | 2.00000 | − | 1.45309i | 0.0917663 | − | 0.0666721i | ||||
\(476\) | 1.14590 | + | 3.52671i | 0.0525222 | + | 0.161647i | ||||
\(477\) | 19.5623 | − | 60.2066i | 0.895696 | − | 2.75667i | ||||
\(478\) | 46.8328 | + | 34.0260i | 2.14208 | + | 1.55631i | ||||
\(479\) | 18.1803 | + | 13.2088i | 0.830681 | + | 0.603525i | 0.919752 | − | 0.392500i | \(-0.128390\pi\) |
−0.0890710 | + | 0.996025i | \(0.528390\pi\) | |||||||
\(480\) | 13.4164 | − | 41.2915i | 0.612372 | − | 1.88469i | ||||
\(481\) | 0.180340 | + | 0.555029i | 0.00822279 | + | 0.0253071i | ||||
\(482\) | 49.0689 | − | 35.6506i | 2.23503 | − | 1.62384i | ||||
\(483\) | 20.9443 | 0.952997 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.8328 | 0.855154 | ||||||||
\(486\) | −64.3951 | + | 46.7858i | −2.92102 | + | 2.12225i | ||||
\(487\) | 2.58359 | + | 7.95148i | 0.117074 | + | 0.360316i | 0.992374 | − | 0.123264i | \(-0.0393362\pi\) |
−0.875300 | + | 0.483580i | \(0.839336\pi\) | |||||||
\(488\) | 1.90983 | − | 5.87785i | 0.0864539 | − | 0.266078i | ||||
\(489\) | −61.3050 | − | 44.5407i | −2.77231 | − | 2.01420i | ||||
\(490\) | 3.61803 | + | 2.62866i | 0.163446 | + | 0.118751i | ||||
\(491\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(492\) | 20.2918 | + | 62.4517i | 0.914825 | + | 2.81554i | ||||
\(493\) | 0.472136 | − | 0.343027i | 0.0212639 | − | 0.0154492i | ||||
\(494\) | 6.83282 | 0.307423 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.23607 | 0.324909 | ||||||||
\(497\) | −1.23607 | + | 0.898056i | −0.0554452 | + | 0.0402833i | ||||
\(498\) | −34.4721 | − | 106.094i | −1.54473 | − | 4.75420i | ||||
\(499\) | 3.23607 | − | 9.95959i | 0.144866 | − | 0.445853i | −0.852127 | − | 0.523334i | \(-0.824688\pi\) |
0.996994 | + | 0.0774816i | \(0.0246879\pi\) | |||||||
\(500\) | −29.1246 | − | 21.1603i | −1.30249 | − | 0.946316i | ||||
\(501\) | −33.8885 | − | 24.6215i | −1.51403 | − | 1.10001i | ||||
\(502\) | 12.2361 | − | 37.6587i | 0.546122 | − | 1.68079i | ||||
\(503\) | 1.05573 | + | 3.24920i | 0.0470726 | + | 0.144875i | 0.971830 | − | 0.235682i | \(-0.0757324\pi\) |
−0.924758 | + | 0.380557i | \(0.875732\pi\) | |||||||
\(504\) | 13.5172 | − | 9.82084i | 0.602105 | − | 0.437455i | ||||
\(505\) | −18.4721 | −0.821999 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.1246 | −1.64876 | ||||||||
\(508\) | 50.8328 | − | 36.9322i | 2.25534 | − | 1.63860i | ||||
\(509\) | 9.74265 | + | 29.9848i | 0.431835 | + | 1.32905i | 0.896295 | + | 0.443458i | \(0.146248\pi\) |
−0.464460 | + | 0.885594i | \(0.653752\pi\) | |||||||
\(510\) | 5.52786 | − | 17.0130i | 0.244778 | − | 0.753349i | ||||
\(511\) | 4.23607 | + | 3.07768i | 0.187393 | + | 0.136149i | ||||
\(512\) | −9.04508 | − | 6.57164i | −0.399740 | − | 0.290428i | ||||
\(513\) | 11.0557 | − | 34.0260i | 0.488122 | − | 1.50229i | ||||
\(514\) | −4.14590 | − | 12.7598i | −0.182868 | − | 0.562809i | ||||
\(515\) | −9.23607 | + | 6.71040i | −0.406990 | + | 0.295695i | ||||
\(516\) | −77.6656 | −3.41904 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.05573 | −0.0463860 | ||||||||
\(519\) | −45.1246 | + | 32.7849i | −1.98075 | + | 1.43910i | ||||
\(520\) | −1.70820 | − | 5.25731i | −0.0749097 | − | 0.230548i | ||||
\(521\) | −4.43769 | + | 13.6578i | −0.194419 | + | 0.598360i | 0.805564 | + | 0.592509i | \(0.201862\pi\) |
−0.999983 | + | 0.00585107i | \(0.998138\pi\) | |||||||
\(522\) | −6.38197 | − | 4.63677i | −0.279331 | − | 0.202946i | ||||
\(523\) | 35.5967 | + | 25.8626i | 1.55654 | + | 1.13089i | 0.938778 | + | 0.344523i | \(0.111959\pi\) |
0.617759 | + | 0.786367i | \(0.288041\pi\) | |||||||
\(524\) | 12.8754 | − | 39.6264i | 0.562464 | − | 1.73109i | ||||
\(525\) | 1.00000 | + | 3.07768i | 0.0436436 | + | 0.134321i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.94427 | 0.389619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 30.6525 | − | 22.2703i | 1.33146 | − | 0.967361i | ||||
\(531\) | 7.47214 | + | 22.9969i | 0.324263 | + | 0.997979i | ||||
\(532\) | −2.29180 | + | 7.05342i | −0.0993620 | + | 0.305805i | ||||
\(533\) | −6.76393 | − | 4.91428i | −0.292978 | − | 0.212861i | ||||
\(534\) | −11.7082 | − | 8.50651i | −0.506664 | − | 0.368113i | ||||
\(535\) | −2.47214 | + | 7.60845i | −0.106880 | + | 0.328942i | ||||
\(536\) | 3.81966 | + | 11.7557i | 0.164984 | + | 0.507769i | ||||
\(537\) | −23.4164 | + | 17.0130i | −1.01049 | + | 0.734166i | ||||
\(538\) | −30.0000 | −1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −86.8328 | −3.73669 | ||||||||
\(541\) | −26.5623 | + | 19.2986i | −1.14200 | + | 0.829714i | −0.987397 | − | 0.158263i | \(-0.949411\pi\) |
−0.154606 | + | 0.987976i | \(0.549411\pi\) | |||||||
\(542\) | 1.05573 | + | 3.24920i | 0.0453474 | + | 0.139565i | ||||
\(543\) | 1.41641 | − | 4.35926i | 0.0607839 | − | 0.187074i | ||||
\(544\) | −6.70820 | − | 4.87380i | −0.287612 | − | 0.208962i | ||||
\(545\) | −7.23607 | − | 5.25731i | −0.309959 | − | 0.225198i | ||||
\(546\) | −2.76393 | + | 8.50651i | −0.118285 | + | 0.364045i | ||||
\(547\) | −8.65248 | − | 26.6296i | −0.369953 | − | 1.13860i | −0.946821 | − | 0.321761i | \(-0.895725\pi\) |
0.576868 | − | 0.816838i | \(-0.304275\pi\) | |||||||
\(548\) | −18.2705 | + | 13.2743i | −0.780477 | + | 0.567050i | ||||
\(549\) | 20.6525 | 0.881426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.16718 | 0.0497237 | ||||||||
\(552\) | 37.8885 | − | 27.5276i | 1.61264 | − | 1.17165i | ||||
\(553\) | 2.76393 | + | 8.50651i | 0.117534 | + | 0.361734i | ||||
\(554\) | −10.9787 | + | 33.7890i | −0.466441 | + | 1.43556i | ||||
\(555\) | 2.47214 | + | 1.79611i | 0.104936 | + | 0.0762407i | ||||
\(556\) | −25.4164 | − | 18.4661i | −1.07790 | − | 0.783137i | ||||
\(557\) | 6.50658 | − | 20.0252i | 0.275693 | − | 0.848494i | −0.713343 | − | 0.700815i | \(-0.752820\pi\) |
0.989035 | − | 0.147679i | \(-0.0471803\pi\) | |||||||
\(558\) | −37.3607 | − | 114.984i | −1.58160 | − | 4.86768i | ||||
\(559\) | 8.00000 | − | 5.81234i | 0.338364 | − | 0.245836i | ||||
\(560\) | −2.00000 | −0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.8885 | 1.17641 | ||||||||
\(563\) | 31.8885 | − | 23.1684i | 1.34394 | − | 0.976431i | 0.344653 | − | 0.938730i | \(-0.387997\pi\) |
0.999289 | − | 0.0377007i | \(-0.0120034\pi\) | |||||||
\(564\) | 21.7082 | + | 66.8110i | 0.914080 | + | 2.81325i | ||||
\(565\) | −1.23607 | + | 3.80423i | −0.0520018 | + | 0.160045i | ||||
\(566\) | −10.6525 | − | 7.73948i | −0.447757 | − | 0.325314i | ||||
\(567\) | 19.7533 | + | 14.3516i | 0.829560 | + | 0.602711i | ||||
\(568\) | −1.05573 | + | 3.24920i | −0.0442974 | + | 0.136333i | ||||
\(569\) | −5.09017 | − | 15.6659i | −0.213391 | − | 0.656750i | −0.999264 | − | 0.0383620i | \(-0.987786\pi\) |
0.785873 | − | 0.618388i | \(-0.212214\pi\) | |||||||
\(570\) | 28.9443 | − | 21.0292i | 1.21234 | − | 0.880818i | ||||
\(571\) | 32.9443 | 1.37867 | 0.689337 | − | 0.724440i | \(-0.257902\pi\) | ||||
0.689337 | + | 0.724440i | \(0.257902\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −67.7771 | −2.83143 | ||||||||
\(574\) | 12.2361 | − | 8.89002i | 0.510724 | − | 0.371062i | ||||
\(575\) | 2.00000 | + | 6.15537i | 0.0834058 | + | 0.256697i | ||||
\(576\) | −30.0172 | + | 92.3835i | −1.25072 | + | 3.84931i | ||||
\(577\) | 23.0344 | + | 16.7355i | 0.958936 | + | 0.696708i | 0.952903 | − | 0.303274i | \(-0.0980797\pi\) |
0.00603289 | + | 0.999982i | \(0.498080\pi\) | |||||||
\(578\) | 27.9894 | + | 20.3355i | 1.16420 | + | 0.845844i | ||||
\(579\) | 23.8885 | − | 73.5214i | 0.992774 | − | 3.05544i | ||||
\(580\) | −0.875388 | − | 2.69417i | −0.0363485 | − | 0.111869i | ||||
\(581\) | −12.4721 | + | 9.06154i | −0.517431 | + | 0.375936i | ||||
\(582\) | −68.1378 | −2.82440 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.7082 | 0.484489 | ||||||||
\(585\) | 14.9443 | − | 10.8576i | 0.617870 | − | 0.448909i | ||||
\(586\) | −10.4508 | − | 32.1644i | −0.431721 | − | 1.32870i | ||||
\(587\) | −4.05573 | + | 12.4822i | −0.167398 | + | 0.515197i | −0.999205 | − | 0.0398672i | \(-0.987307\pi\) |
0.831807 | + | 0.555065i | \(0.187307\pi\) | |||||||
\(588\) | −7.85410 | − | 5.70634i | −0.323898 | − | 0.235325i | ||||
\(589\) | 14.4721 | + | 10.5146i | 0.596314 | + | 0.433247i | ||||
\(590\) | −4.47214 | + | 13.7638i | −0.184115 | + | 0.566647i | ||||
\(591\) | 2.00000 | + | 6.15537i | 0.0822690 | + | 0.253198i | ||||
\(592\) | 0.381966 | − | 0.277515i | 0.0156987 | − | 0.0114058i | ||||
\(593\) | 32.2918 | 1.32607 | 0.663033 | − | 0.748591i | \(-0.269269\pi\) | ||||
0.663033 | + | 0.748591i | \(0.269269\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47214 | −0.101348 | ||||||||
\(596\) | 33.9787 | − | 24.6870i | 1.39182 | − | 1.01122i | ||||
\(597\) | 20.1803 | + | 62.1087i | 0.825926 | + | 2.54194i | ||||
\(598\) | −5.52786 | + | 17.0130i | −0.226051 | + | 0.695714i | ||||
\(599\) | −2.76393 | − | 2.00811i | −0.112931 | − | 0.0820493i | 0.529886 | − | 0.848069i | \(-0.322235\pi\) |
−0.642817 | + | 0.766019i | \(0.722235\pi\) | |||||||
\(600\) | 5.85410 | + | 4.25325i | 0.238993 | + | 0.173638i | ||||
\(601\) | −0.965558 | + | 2.97168i | −0.0393859 | + | 0.121217i | −0.968816 | − | 0.247780i | \(-0.920299\pi\) |
0.929430 | + | 0.368998i | \(0.120299\pi\) | |||||||
\(602\) | 5.52786 | + | 17.0130i | 0.225299 | + | 0.693399i | ||||
\(603\) | −33.4164 | + | 24.2784i | −1.36082 | + | 0.988695i | ||||
\(604\) | 26.8328 | 1.09181 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 66.8328 | 2.71490 | ||||||||
\(607\) | −4.00000 | + | 2.90617i | −0.162355 | + | 0.117958i | −0.665996 | − | 0.745955i | \(-0.731993\pi\) |
0.503641 | + | 0.863913i | \(0.331993\pi\) | |||||||
\(608\) | −5.12461 | − | 15.7719i | −0.207830 | − | 0.639636i | ||||
\(609\) | −0.472136 | + | 1.45309i | −0.0191319 | + | 0.0588820i | ||||
\(610\) | 10.0000 | + | 7.26543i | 0.404888 | + | 0.294168i | ||||
\(611\) | −7.23607 | − | 5.25731i | −0.292740 | − | 0.212688i | ||||
\(612\) | −8.56231 | + | 26.3521i | −0.346111 | + | 1.06522i | ||||
\(613\) | 14.6180 | + | 44.9897i | 0.590417 | + | 1.81712i | 0.576332 | + | 0.817215i | \(0.304483\pi\) |
0.0140844 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(614\) | 16.1803 | − | 11.7557i | 0.652985 | − | 0.474422i | ||||
\(615\) | −43.7771 | −1.76526 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4164 | 1.34529 | 0.672647 | − | 0.739964i | \(-0.265157\pi\) | ||||
0.672647 | + | 0.739964i | \(0.265157\pi\) | |||||||
\(618\) | 33.4164 | − | 24.2784i | 1.34421 | − | 0.976622i | ||||
\(619\) | −9.00000 | − | 27.6992i | −0.361741 | − | 1.11332i | −0.951997 | − | 0.306107i | \(-0.900973\pi\) |
0.590257 | − | 0.807216i | \(-0.299027\pi\) | |||||||
\(620\) | 13.4164 | − | 41.2915i | 0.538816 | − | 1.65830i | ||||
\(621\) | 75.7771 | + | 55.0553i | 3.04083 | + | 2.20929i | ||||
\(622\) | 39.2705 | + | 28.5317i | 1.57460 | + | 1.14402i | ||||
\(623\) | −0.618034 | + | 1.90211i | −0.0247610 | + | 0.0762065i | ||||
\(624\) | −1.23607 | − | 3.80423i | −0.0494823 | − | 0.152291i | ||||
\(625\) | 15.3713 | − | 11.1679i | 0.614853 | − | 0.446717i | ||||
\(626\) | −6.58359 | −0.263133 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.8328 | −0.831320 | ||||||||
\(629\) | 0.472136 | − | 0.343027i | 0.0188253 | − | 0.0136774i | ||||
\(630\) | 10.3262 | + | 31.7809i | 0.411407 | + | 1.26618i | ||||
\(631\) | −7.41641 | + | 22.8254i | −0.295243 | + | 0.908663i | 0.687897 | + | 0.725808i | \(0.258534\pi\) |
−0.983140 | + | 0.182855i | \(0.941466\pi\) | |||||||
\(632\) | 16.1803 | + | 11.7557i | 0.643619 | + | 0.467617i | ||||
\(633\) | 57.3050 | + | 41.6345i | 2.27767 | + | 1.65482i | ||||
\(634\) | 9.67376 | − | 29.7728i | 0.384194 | − | 1.18243i | ||||
\(635\) | 12.9443 | + | 39.8384i | 0.513678 | + | 1.58094i | ||||
\(636\) | −66.5410 | + | 48.3449i | −2.63852 | + | 1.91700i | ||||
\(637\) | 1.23607 | 0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.4164 | −0.451626 | ||||||||
\(640\) | −25.3262 | + | 18.4006i | −1.00111 | + | 0.727347i | ||||
\(641\) | −7.56231 | − | 23.2744i | −0.298693 | − | 0.919283i | −0.981956 | − | 0.189110i | \(-0.939440\pi\) |
0.683263 | − | 0.730173i | \(-0.260560\pi\) | |||||||
\(642\) | 8.94427 | − | 27.5276i | 0.353002 | − | 1.08643i | ||||
\(643\) | 23.5623 | + | 17.1190i | 0.929207 | + | 0.675108i | 0.945798 | − | 0.324754i | \(-0.105282\pi\) |
−0.0165918 | + | 0.999862i | \(0.505282\pi\) | |||||||
\(644\) | −15.7082 | − | 11.4127i | −0.618990 | − | 0.449723i | ||||
\(645\) | 16.0000 | − | 49.2429i | 0.629999 | − | 1.93894i | ||||
\(646\) | −2.11146 | − | 6.49839i | −0.0830741 | − | 0.255676i | ||||
\(647\) | 17.8541 | − | 12.9718i | 0.701917 | − | 0.509973i | −0.178639 | − | 0.983915i | \(-0.557169\pi\) |
0.880556 | + | 0.473942i | \(0.157169\pi\) | |||||||
\(648\) | 54.5967 | 2.14476 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.76393 | −0.108410 | ||||||||
\(651\) | −18.9443 | + | 13.7638i | −0.742485 | + | 0.539447i | ||||
\(652\) | 21.7082 | + | 66.8110i | 0.850159 | + | 2.61652i | ||||
\(653\) | 13.2705 | − | 40.8424i | 0.519315 | − | 1.59829i | −0.255976 | − | 0.966683i | \(-0.582397\pi\) |
0.775291 | − | 0.631605i | \(-0.217603\pi\) | |||||||
\(654\) | 26.1803 | + | 19.0211i | 1.02373 | + | 0.743785i | ||||
\(655\) | 22.4721 | + | 16.3270i | 0.878059 | + | 0.637947i | ||||
\(656\) | −2.09017 | + | 6.43288i | −0.0816074 | + | 0.251162i | ||||
\(657\) | 12.0902 | + | 37.2097i | 0.471682 | + | 1.45169i | ||||
\(658\) | 13.0902 | − | 9.51057i | 0.510308 | − | 0.370760i | ||||
\(659\) | −17.8885 | −0.696839 | −0.348419 | − | 0.937339i | \(-0.613281\pi\) | ||||
−0.348419 | + | 0.937339i | \(0.613281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8328 | 0.499139 | 0.249569 | − | 0.968357i | \(-0.419711\pi\) | ||||
0.249569 | + | 0.968357i | \(0.419711\pi\) | |||||||
\(662\) | −39.5967 | + | 28.7687i | −1.53897 | + | 1.11813i | ||||
\(663\) | −1.52786 | − | 4.70228i | −0.0593373 | − | 0.182622i | ||||
\(664\) | −10.6525 | + | 32.7849i | −0.413396 | + | 1.27230i | ||||
\(665\) | −4.00000 | − | 2.90617i | −0.155113 | − | 0.112696i | ||||
\(666\) | −6.38197 | − | 4.63677i | −0.247296 | − | 0.179671i | ||||
\(667\) | −0.944272 | + | 2.90617i | −0.0365624 | + | 0.112527i | ||||
\(668\) | 12.0000 | + | 36.9322i | 0.464294 | + | 1.42895i | ||||
\(669\) | −31.8885 | + | 23.1684i | −1.23288 | + | 0.895741i | ||||
\(670\) | −24.7214 | −0.955069 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 21.7082 | 0.837412 | ||||||||
\(673\) | 4.38197 | − | 3.18368i | 0.168912 | − | 0.122722i | −0.500117 | − | 0.865958i | \(-0.666710\pi\) |
0.669030 | + | 0.743236i | \(0.266710\pi\) | |||||||
\(674\) | 14.1459 | + | 43.5366i | 0.544880 | + | 1.67697i | ||||
\(675\) | −4.47214 | + | 13.7638i | −0.172133 | + | 0.529770i | ||||
\(676\) | 27.8435 | + | 20.2295i | 1.07090 | + | 0.778056i | ||||
\(677\) | 3.00000 | + | 2.17963i | 0.115299 | + | 0.0837699i | 0.643941 | − | 0.765075i | \(-0.277298\pi\) |
−0.528641 | + | 0.848845i | \(0.677298\pi\) | |||||||
\(678\) | 4.47214 | − | 13.7638i | 0.171751 | − | 0.528596i | ||||
\(679\) | 2.90983 | + | 8.95554i | 0.111669 | + | 0.343682i | ||||
\(680\) | −4.47214 | + | 3.24920i | −0.171499 | + | 0.124601i | ||||
\(681\) | 96.7214 | 3.70637 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.8885 | 1.14365 | 0.571827 | − | 0.820374i | \(-0.306235\pi\) | ||||
0.571827 | + | 0.820374i | \(0.306235\pi\) | |||||||
\(684\) | −44.8328 | + | 32.5729i | −1.71423 | + | 1.24546i | ||||
\(685\) | −4.65248 | − | 14.3188i | −0.177762 | − | 0.547095i | ||||
\(686\) | −0.690983 | + | 2.12663i | −0.0263819 | + | 0.0811950i | ||||
\(687\) | −11.7082 | − | 8.50651i | −0.446696 | − | 0.324544i | ||||
\(688\) | −6.47214 | − | 4.70228i | −0.246748 | − | 0.179273i | ||||
\(689\) | 3.23607 | − | 9.95959i | 0.123284 | − | 0.379430i | ||||
\(690\) | 28.9443 | + | 89.0813i | 1.10189 | + | 3.39127i | ||||
\(691\) | 39.2705 | − | 28.5317i | 1.49392 | − | 1.08540i | 0.521195 | − | 0.853438i | \(-0.325486\pi\) |
0.972725 | − | 0.231959i | \(-0.0745136\pi\) | |||||||
\(692\) | 51.7082 | 1.96565 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.83282 | −0.259370 | ||||||||
\(695\) | 16.9443 | − | 12.3107i | 0.642733 | − | 0.466973i | ||||
\(696\) | 1.05573 | + | 3.24920i | 0.0400173 | + | 0.123160i | ||||
\(697\) | −2.58359 | + | 7.95148i | −0.0978605 | + | 0.301184i | ||||
\(698\) | −5.00000 | − | 3.63271i | −0.189253 | − | 0.137500i | ||||
\(699\) | −45.5967 | − | 33.1280i | −1.72463 | − | 1.25302i | ||||
\(700\) | 0.927051 | − | 2.85317i | 0.0350392 | − | 0.107840i | ||||
\(701\) | 7.56231 | + | 23.2744i | 0.285624 | + | 0.879061i | 0.986211 | + | 0.165494i | \(0.0529218\pi\) |
−0.700586 | + | 0.713568i | \(0.747078\pi\) | |||||||
\(702\) | −32.3607 | + | 23.5114i | −1.22138 | + | 0.887381i | ||||
\(703\) | 1.16718 | 0.0440212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −46.8328 | −1.76383 | ||||||||
\(706\) | 28.7426 | − | 20.8828i | 1.08174 | − | 0.785933i | ||||
\(707\) | −2.85410 | − | 8.78402i | −0.107340 | − | 0.330357i | ||||
\(708\) | 9.70820 | − | 29.8788i | 0.364857 | − | 1.12291i | ||||
\(709\) | −2.38197 | − | 1.73060i | −0.0894566 | − | 0.0649940i | 0.542158 | − | 0.840277i | \(-0.317607\pi\) |
−0.631615 | + | 0.775283i | \(0.717607\pi\) | |||||||
\(710\) | −5.52786 | − | 4.01623i | −0.207457 | − | 0.150726i | ||||
\(711\) | −20.6525 | + | 63.5618i | −0.774528 | + | 2.38375i | ||||
\(712\) | 1.38197 | + | 4.25325i | 0.0517914 | + | 0.159397i | ||||
\(713\) | −37.8885 | + | 27.5276i | −1.41894 | + | 1.03092i | ||||
\(714\) | 8.94427 | 0.334731 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.8328 | 1.00279 | ||||||||
\(717\) | 67.7771 | − | 49.2429i | 2.53118 | − | 1.83901i | ||||
\(718\) | 4.87539 | + | 15.0049i | 0.181948 | + | 0.559978i | ||||
\(719\) | 10.3475 | − | 31.8464i | 0.385898 | − | 1.18767i | −0.549930 | − | 0.835211i | \(-0.685345\pi\) |
0.935827 | − | 0.352459i | \(-0.114655\pi\) | |||||||
\(720\) | −12.0902 | − | 8.78402i | −0.450574 | − | 0.327361i | ||||
\(721\) | −4.61803 | − | 3.35520i | −0.171985 | − | 0.124954i | ||||
\(722\) | −8.90576 | + | 27.4091i | −0.331438 | + | 1.02006i | ||||
\(723\) | −27.1246 | − | 83.4810i | −1.00878 | − | 3.10469i | ||||
\(724\) | −3.43769 | + | 2.49763i | −0.127761 | + | 0.0928237i | ||||
\(725\) | −0.472136 | −0.0175347 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.0132 | −1.89197 | −0.945987 | − | 0.324206i | \(-0.894903\pi\) | ||||
−0.945987 | + | 0.324206i | \(0.894903\pi\) | |||||||
\(728\) | 2.23607 | − | 1.62460i | 0.0828742 | − | 0.0602116i | ||||
\(729\) | 12.9615 | + | 39.8914i | 0.480055 | + | 1.47746i | ||||
\(730\) | −7.23607 | + | 22.2703i | −0.267819 | + | 0.824262i | ||||
\(731\) | −8.00000 | − | 5.81234i | −0.295891 | − | 0.214977i | ||||
\(732\) | −21.7082 | − | 15.7719i | −0.802358 | − | 0.582947i | ||||
\(733\) | −4.09017 | + | 12.5882i | −0.151074 | + | 0.464958i | −0.997742 | − | 0.0671638i | \(-0.978605\pi\) |
0.846668 | + | 0.532121i | \(0.178605\pi\) | |||||||
\(734\) | 11.8328 | + | 36.4177i | 0.436757 | + | 1.34420i | ||||
\(735\) | 5.23607 | − | 3.80423i | 0.193135 | − | 0.140321i | ||||
\(736\) | 43.4164 | 1.60035 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 113.013 | 4.16007 | ||||||||
\(739\) | 5.70820 | − | 4.14725i | 0.209980 | − | 0.152559i | −0.477825 | − | 0.878455i | \(-0.658575\pi\) |
0.687804 | + | 0.725896i | \(0.258575\pi\) | |||||||
\(740\) | −0.875388 | − | 2.69417i | −0.0321799 | − | 0.0990396i | ||||
\(741\) | 3.05573 | − | 9.40456i | 0.112255 | − | 0.345485i | ||||
\(742\) | 15.3262 | + | 11.1352i | 0.562644 | + | 0.408785i | ||||
\(743\) | −27.4164 | − | 19.9192i | −1.00581 | − | 0.730764i | −0.0424843 | − | 0.999097i | \(-0.513527\pi\) |
−0.963326 | + | 0.268333i | \(0.913527\pi\) | |||||||
\(744\) | −16.1803 | + | 49.7980i | −0.593200 | + | 1.82568i | ||||
\(745\) | 8.65248 | + | 26.6296i | 0.317002 | + | 0.975632i | ||||
\(746\) | 10.8541 | − | 7.88597i | 0.397397 | − | 0.288726i | ||||
\(747\) | −115.193 | −4.21471 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | −70.2492 | + | 51.0390i | −2.56514 | + | 1.86368i | ||||
\(751\) | 11.8885 | + | 36.5892i | 0.433819 | + | 1.33516i | 0.894292 | + | 0.447484i | \(0.147680\pi\) |
−0.460473 | + | 0.887674i | \(0.652320\pi\) | |||||||
\(752\) | −2.23607 | + | 6.88191i | −0.0815410 | + | 0.250957i | ||||
\(753\) | −46.3607 | − | 33.6830i | −1.68948 | − | 1.22748i | ||||
\(754\) | −1.05573 | − | 0.767031i | −0.0384473 | − | 0.0279336i | ||||
\(755\) | −5.52786 | + | 17.0130i | −0.201180 | + | 0.619167i | ||||
\(756\) | −13.4164 | − | 41.2915i | −0.487950 | − | 1.50176i | ||||
\(757\) | 16.0902 | − | 11.6902i | 0.584807 | − | 0.424887i | −0.255647 | − | 0.966770i | \(-0.582288\pi\) |
0.840454 | + | 0.541883i | \(0.182288\pi\) | |||||||
\(758\) | −56.5836 | −2.05521 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.0557 | −0.401033 | ||||||||
\(761\) | 14.2361 | − | 10.3431i | 0.516057 | − | 0.374937i | −0.299059 | − | 0.954234i | \(-0.596673\pi\) |
0.815116 | + | 0.579297i | \(0.196673\pi\) | |||||||
\(762\) | −46.8328 | − | 144.137i | −1.69657 | − | 5.22152i | ||||
\(763\) | 1.38197 | − | 4.25325i | 0.0500305 | − | 0.153978i | ||||
\(764\) | 50.8328 | + | 36.9322i | 1.83907 | + | 1.33616i | ||||
\(765\) | −14.9443 | − | 10.8576i | −0.540311 | − | 0.392559i | ||||
\(766\) | 18.4164 | − | 56.6799i | 0.665412 | − | 2.04793i | ||||
\(767\) | 1.23607 | + | 3.80423i | 0.0446318 | + | 0.137363i | ||||
\(768\) | 23.5623 | − | 17.1190i | 0.850231 | − | 0.617729i | ||||
\(769\) | −31.7082 | −1.14343 | −0.571714 | − | 0.820453i | \(-0.693721\pi\) | ||||
−0.571714 | + | 0.820453i | \(0.693721\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.4164 | −0.699265 | ||||||||
\(772\) | −57.9787 | + | 42.1240i | −2.08670 | + | 1.51608i | ||||
\(773\) | 1.96556 | + | 6.04937i | 0.0706962 | + | 0.217581i | 0.980162 | − | 0.198198i | \(-0.0635090\pi\) |
−0.909466 | + | 0.415779i | \(0.863509\pi\) | |||||||
\(774\) | −41.3050 | + | 127.124i | −1.48468 | + | 4.56936i | ||||
\(775\) | −5.85410 | − | 4.25325i | −0.210286 | − | 0.152781i | ||||
\(776\) | 17.0344 | + | 12.3762i | 0.611501 | + | 0.444281i | ||||
\(777\) | −0.472136 | + | 1.45309i | −0.0169378 | + | 0.0521291i | ||||
\(778\) | −13.7426 | − | 42.2955i | −0.492698 | − | 1.51637i | ||||
\(779\) | −13.5279 | + | 9.82857i | −0.484686 | + | 0.352145i | ||||
\(780\) | −24.0000 | −0.859338 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 17.8885 | 0.639693 | ||||||||
\(783\) | −5.52786 | + | 4.01623i | −0.197550 | + | 0.143528i | ||||
\(784\) | −0.309017 | − | 0.951057i | −0.0110363 | − | 0.0339663i | ||||
\(785\) | 4.29180 | − | 13.2088i | 0.153181 | − | 0.471442i | ||||
\(786\) | −81.3050 | − | 59.0715i | −2.90005 | − | 2.10701i | ||||
\(787\) | −13.4164 | − | 9.74759i | −0.478243 | − | 0.347464i | 0.322402 | − | 0.946603i | \(-0.395510\pi\) |
−0.800645 | + | 0.599139i | \(0.795510\pi\) | |||||||
\(788\) | 1.85410 | − | 5.70634i | 0.0660496 | − | 0.203280i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.3607 | + | 23.5114i | −1.15134 | + | 0.836498i | ||||
\(791\) | −2.00000 | −0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.41641 | 0.121320 | ||||||||
\(794\) | 0.201626 | − | 0.146490i | 0.00715544 | − | 0.00519873i | ||||
\(795\) | −16.9443 | − | 52.1491i | −0.600951 | − | 1.84954i | ||||
\(796\) | 18.7082 | − | 57.5779i | 0.663095 | − | 2.04080i | ||||
\(797\) | −2.38197 | − | 1.73060i | −0.0843736 | − | 0.0613010i | 0.544799 | − | 0.838567i | \(-0.316606\pi\) |
−0.629172 | + | 0.777266i | \(0.716606\pi\) | |||||||
\(798\) | 14.4721 | + | 10.5146i | 0.512308 | + | 0.372214i | ||||
\(799\) | −2.76393 | + | 8.50651i | −0.0977809 | + | 0.300939i | ||||
\(800\) | 2.07295 | + | 6.37988i | 0.0732898 | + | 0.225563i | ||||
\(801\) | −12.0902 | + | 8.78402i | −0.427185 | + | 0.310368i | ||||
\(802\) | 11.3050 | 0.399192 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 53.6656 | 1.89264 | ||||||||
\(805\) | 10.4721 | − | 7.60845i | 0.369094 | − | 0.268163i | ||||
\(806\) | −6.18034 | − | 19.0211i | −0.217693 | − | 0.669991i | ||||
\(807\) | −13.4164 | + | 41.2915i | −0.472280 | + | 1.45353i | ||||
\(808\) | −16.7082 | − | 12.1392i | −0.587793 | − | 0.427056i | ||||
\(809\) | 31.5066 | + | 22.8909i | 1.10771 | + | 0.804800i | 0.982302 | − | 0.187305i | \(-0.0599752\pi\) |
0.125410 | + | 0.992105i | \(0.459975\pi\) | |||||||
\(810\) | −33.7426 | + | 103.849i | −1.18560 | + | 3.64889i | ||||
\(811\) | −5.81966 | − | 17.9111i | −0.204356 | − | 0.628943i | −0.999739 | − | 0.0228361i | \(-0.992730\pi\) |
0.795383 | − | 0.606107i | \(-0.207270\pi\) | |||||||
\(812\) | 1.14590 | − | 0.832544i | 0.0402131 | − | 0.0292166i | ||||
\(813\) | 4.94427 | 0.173403 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46.8328 | −1.64048 | ||||||||
\(816\) | −3.23607 | + | 2.35114i | −0.113285 | + | 0.0823064i | ||||
\(817\) | −6.11146 | − | 18.8091i | −0.213813 | − | 0.658048i | ||||
\(818\) | 21.5066 | − | 66.1904i | 0.751960 | − | 2.31429i | ||||
\(819\) | 7.47214 | + | 5.42882i | 0.261098 | + | 0.189698i | ||||
\(820\) | 32.8328 | + | 23.8544i | 1.14657 | + | 0.833033i | ||||
\(821\) | 2.72949 | − | 8.40051i | 0.0952599 | − | 0.293180i | −0.892061 | − | 0.451914i | \(-0.850741\pi\) |
0.987321 | + | 0.158734i | \(0.0507413\pi\) | |||||||
\(822\) | 16.8328 | + | 51.8061i | 0.587112 | + | 1.80694i | ||||
\(823\) | 40.3607 | − | 29.3238i | 1.40688 | − | 1.02216i | 0.413119 | − | 0.910677i | \(-0.364439\pi\) |
0.993766 | − | 0.111484i | \(-0.0355605\pi\) | |||||||
\(824\) | −12.7639 | −0.444653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.23607 | −0.251775 | ||||||||
\(827\) | 4.00000 | − | 2.90617i | 0.139094 | − | 0.101057i | −0.516063 | − | 0.856551i | \(-0.672603\pi\) |
0.655156 | + | 0.755493i | \(0.272603\pi\) | |||||||
\(828\) | −44.8328 | − | 137.981i | −1.55805 | − | 4.79518i | ||||
\(829\) | −5.20163 | + | 16.0090i | −0.180660 | + | 0.556014i | −0.999847 | − | 0.0175128i | \(-0.994425\pi\) |
0.819187 | + | 0.573527i | \(0.194425\pi\) | |||||||
\(830\) | −55.7771 | − | 40.5244i | −1.93605 | − | 1.40662i | ||||
\(831\) | 41.5967 | + | 30.2218i | 1.44298 | + | 1.04838i | ||||
\(832\) | −4.96556 | + | 15.2824i | −0.172150 | + | 0.529822i | ||||
\(833\) | −0.381966 | − | 1.17557i | −0.0132343 | − | 0.0407311i | ||||
\(834\) | −61.3050 | + | 44.5407i | −2.12282 | + | 1.54232i | ||||
\(835\) | −25.8885 | −0.895910 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −104.721 | −3.61970 | ||||||||
\(838\) | 12.0344 | − | 8.74353i | 0.415723 | − | 0.302040i | ||||
\(839\) | −4.34752 | − | 13.3803i | −0.150093 | − | 0.461939i | 0.847538 | − | 0.530735i | \(-0.178084\pi\) |
−0.997631 | + | 0.0687961i | \(0.978084\pi\) | |||||||
\(840\) | 4.47214 | − | 13.7638i | 0.154303 | − | 0.474897i | ||||
\(841\) | 23.2812 | + | 16.9147i | 0.802798 | + | 0.583267i | ||||
\(842\) | 40.4508 | + | 29.3893i | 1.39403 | + | 1.01282i | ||||
\(843\) | 12.4721 | − | 38.3853i | 0.429563 | − | 1.32206i | ||||
\(844\) | −20.2918 | − | 62.4517i | −0.698472 | − | 2.14968i | ||||
\(845\) | −18.5623 | + | 13.4863i | −0.638563 | + | 0.463943i | ||||
\(846\) | 120.902 | 4.15669 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.47214 | −0.290934 | ||||||||
\(849\) | −15.4164 | + | 11.2007i | −0.529090 | + | 0.384406i | ||||
\(850\) | 0.854102 | + | 2.62866i | 0.0292955 | + | 0.0901621i | ||||
\(851\) | −0.944272 | + | 2.90617i | −0.0323692 | + | 0.0996222i | ||||
\(852\) | 12.0000 | + | 8.71851i | 0.411113 | + | 0.298691i | ||||
\(853\) | 0.527864 | + | 0.383516i | 0.0180737 | + | 0.0131313i | 0.596785 | − | 0.802401i | \(-0.296444\pi\) |
−0.578712 | + | 0.815532i | \(0.696444\pi\) | |||||||
\(854\) | −1.90983 | + | 5.87785i | −0.0653530 | + | 0.201136i | ||||
\(855\) | −11.4164 | − | 35.1361i | −0.390433 | − | 1.20163i | ||||
\(856\) | −7.23607 | + | 5.25731i | −0.247324 | + | 0.179691i | ||||
\(857\) | −10.7639 | −0.367689 | −0.183844 | − | 0.982955i | \(-0.558854\pi\) | ||||
−0.183844 | + | 0.982955i | \(0.558854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.5410 | 1.38324 | 0.691621 | − | 0.722261i | \(-0.256897\pi\) | ||||
0.691621 | + | 0.722261i | \(0.256897\pi\) | |||||||
\(860\) | −38.8328 | + | 28.2137i | −1.32419 | + | 0.962079i | ||||
\(861\) | −6.76393 | − | 20.8172i | −0.230514 | − | 0.709450i | ||||
\(862\) | −8.29180 | + | 25.5195i | −0.282420 | + | 0.869198i | ||||
\(863\) | 16.9443 | + | 12.3107i | 0.576790 | + | 0.419062i | 0.837565 | − | 0.546337i | \(-0.183978\pi\) |
−0.260776 | + | 0.965399i | \(0.583978\pi\) | |||||||
\(864\) | 78.5410 | + | 57.0634i | 2.67202 | + | 1.94134i | ||||
\(865\) | −10.6525 | + | 32.7849i | −0.362195 | + | 1.11472i | ||||
\(866\) | 0.326238 | + | 1.00406i | 0.0110860 | + | 0.0341192i | ||||
\(867\) | 40.5066 | − | 29.4298i | 1.37568 | − | 0.999487i | ||||
\(868\) | 21.7082 | 0.736824 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.83282 | −0.231654 | ||||||||
\(871\) | −5.52786 | + | 4.01623i | −0.187305 | + | 0.136085i | ||||
\(872\) | −3.09017 | − | 9.51057i | −0.104646 | − | 0.322068i | ||||
\(873\) | −21.7426 | + | 66.9170i | −0.735877 | + | 2.26480i | ||||
\(874\) | 28.9443 | + | 21.0292i | 0.979055 | + | 0.711325i | ||||
\(875\) | 9.70820 | + | 7.05342i | 0.328197 | + | 0.238449i | ||||
\(876\) | 15.7082 | − | 48.3449i | 0.530731 | − | 1.63342i | ||||
\(877\) | −12.7984 | − | 39.3893i | −0.432170 | − | 1.33008i | −0.895959 | − | 0.444138i | \(-0.853510\pi\) |
0.463788 | − | 0.885946i | \(-0.346490\pi\) | |||||||
\(878\) | 2.76393 | − | 2.00811i | 0.0932782 | − | 0.0677706i | ||||
\(879\) | −48.9443 | −1.65085 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.4164 | 0.991064 | 0.495532 | − | 0.868590i | \(-0.334973\pi\) | ||||
0.495532 | + | 0.868590i | \(0.334973\pi\) | |||||||
\(882\) | −13.5172 | + | 9.82084i | −0.455149 | + | 0.330685i | ||||
\(883\) | 2.76393 | + | 8.50651i | 0.0930137 | + | 0.286267i | 0.986731 | − | 0.162364i | \(-0.0519119\pi\) |
−0.893717 | + | 0.448631i | \(0.851912\pi\) | |||||||
\(884\) | −1.41641 | + | 4.35926i | −0.0476390 | + | 0.146618i | ||||
\(885\) | 16.9443 | + | 12.3107i | 0.569575 | + | 0.413821i | ||||
\(886\) | 12.7639 | + | 9.27354i | 0.428813 | + | 0.311551i | ||||
\(887\) | −12.4721 | + | 38.3853i | −0.418773 | + | 1.28885i | 0.490059 | + | 0.871689i | \(0.336975\pi\) |
−0.908832 | + | 0.417162i | \(0.863025\pi\) | |||||||
\(888\) | 1.05573 | + | 3.24920i | 0.0354279 | + | 0.109036i | ||||
\(889\) | −16.9443 | + | 12.3107i | −0.568293 | + | 0.412889i | ||||
\(890\) | −8.94427 | −0.299813 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.5410 | 1.22348 | ||||||||
\(893\) | −14.4721 | + | 10.5146i | −0.484292 | + | 0.351858i | ||||
\(894\) | −31.3050 | − | 96.3467i | −1.04699 | − | 3.22232i | ||||
\(895\) | −5.52786 | + | 17.0130i | −0.184776 | + | 0.568682i | ||||
\(896\) | −12.6631 | − | 9.20029i | −0.423045 | − | 0.307360i | ||||
\(897\) | 20.9443 | + | 15.2169i | 0.699309 | + | 0.508078i | ||||
\(898\) | −13.4934 | + | 41.5285i | −0.450281 | + | 1.38582i | ||||
\(899\) | −1.05573 | − | 3.24920i | −0.0352105 | − | 0.108367i | ||||
\(900\) | 18.1353 | − | 13.1760i | 0.604508 | − | 0.439201i | ||||
\(901\) | −10.4721 | −0.348877 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.8885 | 0.861517 | ||||||||
\(904\) | −3.61803 | + | 2.62866i | −0.120334 | + | 0.0874278i | ||||
\(905\) | −0.875388 | − | 2.69417i | −0.0290989 | − | 0.0895572i | ||||
\(906\) | 20.0000 | − | 61.5537i | 0.664455 | − | 2.04498i | ||||
\(907\) | −10.9443 | − | 7.95148i | −0.363399 | − | 0.264025i | 0.391070 | − | 0.920361i | \(-0.372105\pi\) |
−0.754468 | + | 0.656337i | \(0.772105\pi\) | |||||||
\(908\) | −72.5410 | − | 52.7041i | −2.40736 | − | 1.74905i | ||||
\(909\) | 21.3262 | − | 65.6354i | 0.707347 | − | 2.17699i | ||||
\(910\) | 1.70820 | + | 5.25731i | 0.0566264 | + | 0.174278i | ||||
\(911\) | −27.1246 | + | 19.7072i | −0.898678 | + | 0.652928i | −0.938126 | − | 0.346293i | \(-0.887440\pi\) |
0.0394477 | + | 0.999222i | \(0.487440\pi\) | |||||||
\(912\) | −8.00000 | −0.264906 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −55.5279 | −1.83670 | ||||||||
\(915\) | 14.4721 | − | 10.5146i | 0.478434 | − | 0.347603i | ||||
\(916\) | 4.14590 | + | 12.7598i | 0.136984 | + | 0.421594i | ||||
\(917\) | −4.29180 | + | 13.2088i | −0.141728 | + | 0.436193i | ||||
\(918\) | 32.3607 | + | 23.5114i | 1.06806 | + | 0.775992i | ||||
\(919\) | 4.94427 | + | 3.59222i | 0.163096 | + | 0.118497i | 0.666340 | − | 0.745648i | \(-0.267860\pi\) |
−0.503243 | + | 0.864145i | \(0.667860\pi\) | |||||||
\(920\) | 8.94427 | − | 27.5276i | 0.294884 | − | 0.907559i | ||||
\(921\) | −8.94427 | − | 27.5276i | −0.294724 | − | 0.907067i | ||||
\(922\) | 18.4164 | − | 13.3803i | 0.606512 | − | 0.440657i | ||||
\(923\) | −1.88854 | −0.0621622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.472136 | −0.0155237 | ||||||||
\(926\) | 26.1803 | − | 19.0211i | 0.860339 | − | 0.625073i | ||||
\(927\) | −13.1803 | − | 40.5649i | −0.432899 | − | 1.33233i | ||||
\(928\) | −0.978714 | + | 3.01217i | −0.0321279 | + | 0.0988794i | ||||
\(929\) | −22.8541 | − | 16.6045i | −0.749819 | − | 0.544775i | 0.145952 | − | 0.989292i | \(-0.453376\pi\) |
−0.895771 | + | 0.444516i | \(0.853376\pi\) | |||||||
\(930\) | −84.7214 | − | 61.5537i | −2.77812 | − | 2.01842i | ||||
\(931\) | 0.763932 | − | 2.35114i | 0.0250369 | − | 0.0770555i | ||||
\(932\) | 16.1459 | + | 49.6920i | 0.528876 | + | 1.62771i | ||||
\(933\) | 56.8328 | − | 41.2915i | 1.86062 | − | 1.35182i | ||||
\(934\) | −76.1803 | −2.49270 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.6525 | 0.675047 | ||||||||
\(937\) | 16.7082 | − | 12.1392i | 0.545833 | − | 0.396571i | −0.280414 | − | 0.959879i | \(-0.590472\pi\) |
0.826247 | + | 0.563308i | \(0.190472\pi\) | |||||||
\(938\) | −3.81966 | − | 11.7557i | −0.124716 | − | 0.383837i | ||||
\(939\) | −2.94427 | + | 9.06154i | −0.0960827 | + | 0.295712i | ||||
\(940\) | 35.1246 | + | 25.5195i | 1.14564 | + | 0.832355i | ||||
\(941\) | −33.6525 | − | 24.4500i | −1.09704 | − | 0.797046i | −0.116465 | − | 0.993195i | \(-0.537156\pi\) |
−0.980574 | + | 0.196149i | \(0.937156\pi\) | |||||||
\(942\) | −15.5279 | + | 47.7899i | −0.505925 | + | 1.55708i | ||||
\(943\) | −13.5279 | − | 41.6345i | −0.440528 | − | 1.35581i | ||||
\(944\) | 2.61803 | − | 1.90211i | 0.0852097 | − | 0.0619085i | ||||
\(945\) | 28.9443 | 0.941557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −58.8328 | −1.91181 | −0.955905 | − | 0.293677i | \(-0.905121\pi\) | ||||
−0.955905 | + | 0.293677i | \(0.905121\pi\) | |||||||
\(948\) | 70.2492 | − | 51.0390i | 2.28159 | − | 1.65767i | ||||
\(949\) | 2.00000 | + | 6.15537i | 0.0649227 | + | 0.199812i | ||||
\(950\) | −1.70820 | + | 5.25731i | −0.0554215 | + | 0.170570i | ||||
\(951\) | −36.6525 | − | 26.6296i | −1.18854 | − | 0.863523i | ||||
\(952\) | −2.23607 | − | 1.62460i | −0.0724714 | − | 0.0526535i | ||||
\(953\) | −1.56231 | + | 4.80828i | −0.0506081 | + | 0.155756i | −0.973167 | − | 0.230101i | \(-0.926094\pi\) |
0.922559 | + | 0.385857i | \(0.126094\pi\) | |||||||
\(954\) | 43.7426 | + | 134.626i | 1.41622 | + | 4.35868i | ||||
\(955\) | −33.8885 | + | 24.6215i | −1.09661 | + | 0.796732i | ||||
\(956\) | −77.6656 | −2.51189 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50.2492 | −1.62348 | ||||||||
\(959\) | 6.09017 | − | 4.42477i | 0.196662 | − | 0.142883i | ||||
\(960\) | 26.0000 | + | 80.0198i | 0.839146 | + | 2.58263i | ||||
\(961\) | 6.60081 | − | 20.3152i | 0.212929 | − | 0.655329i | ||||
\(962\) | −1.05573 | − | 0.767031i | −0.0340380 | − | 0.0247301i | ||||
\(963\) | −24.1803 | − | 17.5680i | −0.779201 | − | 0.566122i | ||||
\(964\) | −25.1459 | + | 77.3911i | −0.809895 | + | 2.49260i | ||||
\(965\) | −14.7639 | − | 45.4387i | −0.475268 | − | 1.46272i | ||||
\(966\) | −37.8885 | + | 27.5276i | −1.21904 | + | 0.885687i | ||||
\(967\) | −21.8885 | −0.703888 | −0.351944 | − | 0.936021i | \(-0.614479\pi\) | ||||
−0.351944 | + | 0.936021i | \(0.614479\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.88854 | −0.317666 | ||||||||
\(970\) | −34.0689 | + | 24.7525i | −1.09389 | + | 0.794755i | ||||
\(971\) | −9.00000 | − | 27.6992i | −0.288824 | − | 0.888908i | −0.985226 | − | 0.171257i | \(-0.945217\pi\) |
0.696403 | − | 0.717651i | \(-0.254783\pi\) | |||||||
\(972\) | 33.0000 | − | 101.564i | 1.05848 | − | 3.25765i | ||||
\(973\) | 8.47214 | + | 6.15537i | 0.271604 | + | 0.197332i | ||||
\(974\) | −15.1246 | − | 10.9887i | −0.484624 | − | 0.352100i | ||||
\(975\) | −1.23607 | + | 3.80423i | −0.0395859 | + | 0.121833i | ||||
\(976\) | −0.854102 | − | 2.62866i | −0.0273391 | − | 0.0841412i | ||||
\(977\) | −4.09017 | + | 2.97168i | −0.130856 | + | 0.0950725i | −0.651288 | − | 0.758831i | \(-0.725771\pi\) |
0.520432 | + | 0.853903i | \(0.325771\pi\) | |||||||
\(978\) | 169.443 | 5.41818 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 27.0344 | − | 19.6417i | 0.863143 | − | 0.627110i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.6525 | − | 42.0180i | 0.435446 | − | 1.34017i | −0.457182 | − | 0.889373i | \(-0.651141\pi\) |
0.892629 | − | 0.450793i | \(-0.148859\pi\) | |||||||
\(984\) | −39.5967 | − | 28.7687i | −1.26230 | − | 0.917113i | ||||
\(985\) | 3.23607 | + | 2.35114i | 0.103110 | + | 0.0749136i | ||||
\(986\) | −0.403252 | + | 1.24108i | −0.0128422 | + | 0.0395241i | ||||
\(987\) | −7.23607 | − | 22.2703i | −0.230327 | − | 0.708872i | ||||
\(988\) | −7.41641 | + | 5.38834i | −0.235947 | + | 0.171426i | ||||
\(989\) | 51.7771 | 1.64642 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.2492 | −0.833834 | −0.416917 | − | 0.908945i | \(-0.636889\pi\) | ||||
−0.416917 | + | 0.908945i | \(0.636889\pi\) | |||||||
\(992\) | −39.2705 | + | 28.5317i | −1.24684 | + | 0.905882i | ||||
\(993\) | 21.8885 | + | 67.3660i | 0.694612 | + | 2.13780i | ||||
\(994\) | 1.05573 | − | 3.24920i | 0.0334857 | − | 0.103058i | ||||
\(995\) | 32.6525 | + | 23.7234i | 1.03515 | + | 0.752083i | ||||
\(996\) | 121.082 | + | 87.9713i | 3.83663 | + | 2.78748i | ||||
\(997\) | −10.0902 | + | 31.0543i | −0.319559 | + | 0.983501i | 0.654278 | + | 0.756254i | \(0.272973\pi\) |
−0.973837 | + | 0.227247i | \(0.927027\pi\) | |||||||
\(998\) | 7.23607 | + | 22.2703i | 0.229054 | + | 0.704955i | ||||
\(999\) | −5.52786 | + | 4.01623i | −0.174894 | + | 0.127068i |
(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 | 847.2.f.b.729.1 | 4 | ||
11.2 | odd | 10 | 77.2.a.d.1.1 | ✓ | 2 | ||
11.3 | even | 5 | 847.2.f.m.148.1 | 4 | |||
11.4 | even | 5 | inner | 847.2.f.b.323.1 | 4 | ||
11.5 | even | 5 | 847.2.f.m.372.1 | 4 | |||
11.6 | odd | 10 | 847.2.f.a.372.1 | 4 | |||
11.7 | odd | 10 | 847.2.f.n.323.1 | 4 | |||
11.8 | odd | 10 | 847.2.f.a.148.1 | 4 | |||
11.9 | even | 5 | 847.2.a.f.1.2 | 2 | |||
11.10 | odd | 2 | 847.2.f.n.729.1 | 4 | |||
33.2 | even | 10 | 693.2.a.h.1.2 | 2 | |||
33.20 | odd | 10 | 7623.2.a.bl.1.1 | 2 | |||
44.35 | even | 10 | 1232.2.a.m.1.1 | 2 | |||
55.2 | even | 20 | 1925.2.b.h.1849.1 | 4 | |||
55.13 | even | 20 | 1925.2.b.h.1849.4 | 4 | |||
55.24 | odd | 10 | 1925.2.a.r.1.2 | 2 | |||
77.2 | odd | 30 | 539.2.e.i.67.2 | 4 | |||
77.13 | even | 10 | 539.2.a.f.1.1 | 2 | |||
77.20 | odd | 10 | 5929.2.a.m.1.2 | 2 | |||
77.24 | even | 30 | 539.2.e.j.177.2 | 4 | |||
77.46 | odd | 30 | 539.2.e.i.177.2 | 4 | |||
77.68 | even | 30 | 539.2.e.j.67.2 | 4 | |||
88.13 | odd | 10 | 4928.2.a.bm.1.1 | 2 | |||
88.35 | even | 10 | 4928.2.a.bv.1.2 | 2 | |||
231.167 | odd | 10 | 4851.2.a.y.1.2 | 2 | |||
308.167 | odd | 10 | 8624.2.a.ce.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.1 | ✓ | 2 | 11.2 | odd | 10 | ||
539.2.a.f.1.1 | 2 | 77.13 | even | 10 | |||
539.2.e.i.67.2 | 4 | 77.2 | odd | 30 | |||
539.2.e.i.177.2 | 4 | 77.46 | odd | 30 | |||
539.2.e.j.67.2 | 4 | 77.68 | even | 30 | |||
539.2.e.j.177.2 | 4 | 77.24 | even | 30 | |||
693.2.a.h.1.2 | 2 | 33.2 | even | 10 | |||
847.2.a.f.1.2 | 2 | 11.9 | even | 5 | |||
847.2.f.a.148.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.a.372.1 | 4 | 11.6 | odd | 10 | |||
847.2.f.b.323.1 | 4 | 11.4 | even | 5 | inner | ||
847.2.f.b.729.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.m.148.1 | 4 | 11.3 | even | 5 | |||
847.2.f.m.372.1 | 4 | 11.5 | even | 5 | |||
847.2.f.n.323.1 | 4 | 11.7 | odd | 10 | |||
847.2.f.n.729.1 | 4 | 11.10 | odd | 2 | |||
1232.2.a.m.1.1 | 2 | 44.35 | even | 10 | |||
1925.2.a.r.1.2 | 2 | 55.24 | odd | 10 | |||
1925.2.b.h.1849.1 | 4 | 55.2 | even | 20 | |||
1925.2.b.h.1849.4 | 4 | 55.13 | even | 20 | |||
4851.2.a.y.1.2 | 2 | 231.167 | odd | 10 | |||
4928.2.a.bm.1.1 | 2 | 88.13 | odd | 10 | |||
4928.2.a.bv.1.2 | 2 | 88.35 | even | 10 | |||
5929.2.a.m.1.2 | 2 | 77.20 | odd | 10 | |||
7623.2.a.bl.1.1 | 2 | 33.20 | odd | 10 | |||
8624.2.a.ce.1.2 | 2 | 308.167 | odd | 10 |