Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [196,3,Mod(67,196)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(196, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("196.67");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 196 = 2^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 196.g (of order \(6\), degree \(2\), 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: | \(5.34061318146\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.1728283481971641.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 4 x^{10} - 6 x^{9} + 6 x^{8} - 8 x^{7} + 9 x^{6} - 16 x^{5} + 24 x^{4} - 48 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 67.3 | ||
Root | \(-1.24688 - 0.667301i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 196.67 |
Dual form | 196.3.g.j.79.3 |
$q$-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 \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).
\(n\) | \(99\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.259316 | − | 1.98312i | 0.129658 | − | 0.991559i | ||||
\(3\) | −2.58484 | − | 1.49236i | −0.861614 | − | 0.497453i | 0.00293865 | − | 0.999996i | \(-0.499065\pi\) |
−0.864552 | + | 0.502543i | \(0.832398\pi\) | |||||||
\(4\) | −3.86551 | − | 1.02851i | −0.966378 | − | 0.257127i | ||||
\(5\) | −3.40268 | − | 5.89361i | −0.680536 | − | 1.17872i | −0.974818 | − | 0.223004i | \(-0.928414\pi\) |
0.294282 | − | 0.955719i | \(-0.404920\pi\) | |||||||
\(6\) | −3.62981 | + | 4.73905i | −0.604969 | + | 0.789842i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.04204 | + | 7.39905i | −0.380255 | + | 0.924882i | ||||
\(9\) | −0.0457311 | − | 0.0792086i | −0.00508124 | − | 0.00880096i | ||||
\(10\) | −12.5701 | + | 5.21960i | −1.25701 | + | 0.521960i | ||||
\(11\) | 12.4211 | + | 7.17132i | 1.12919 | + | 0.651938i | 0.943731 | − | 0.330714i | \(-0.107290\pi\) |
0.185459 | + | 0.982652i | \(0.440623\pi\) | |||||||
\(12\) | 8.45683 | + | 8.42726i | 0.704736 | + | 0.702272i | ||||
\(13\) | −4.62243 | −0.355572 | −0.177786 | − | 0.984069i | \(-0.556893\pi\) | ||||
−0.177786 | + | 0.984069i | \(0.556893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.3121i | 1.35414i | ||||||||
\(16\) | 13.8843 | + | 7.95142i | 0.867771 | + | 0.496964i | ||||
\(17\) | 5.80536 | − | 10.0552i | 0.341492 | − | 0.591481i | −0.643218 | − | 0.765683i | \(-0.722401\pi\) |
0.984710 | + | 0.174202i | \(0.0557346\pi\) | |||||||
\(18\) | −0.168939 | + | 0.0701501i | −0.00938549 | + | 0.00389723i | ||||
\(19\) | −19.4361 | + | 11.2214i | −1.02295 | + | 0.590601i | −0.914957 | − | 0.403550i | \(-0.867776\pi\) |
−0.107994 | + | 0.994152i | \(0.534443\pi\) | |||||||
\(20\) | 7.09146 | + | 26.2815i | 0.354573 | + | 1.31408i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 17.4426 | − | 22.7728i | 0.792843 | − | 1.03513i | ||||
\(23\) | 0.739535 | − | 0.426971i | 0.0321537 | − | 0.0185639i | −0.483837 | − | 0.875158i | \(-0.660757\pi\) |
0.515991 | + | 0.856594i | \(0.327424\pi\) | |||||||
\(24\) | 18.9052 | − | 14.5856i | 0.787718 | − | 0.607732i | ||||
\(25\) | −10.6564 | + | 18.4575i | −0.426258 | + | 0.738300i | ||||
\(26\) | −1.19867 | + | 9.16683i | −0.0461027 | + | 0.352570i | ||||
\(27\) | 27.1354i | 1.00502i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −42.8321 | −1.47697 | −0.738485 | − | 0.674270i | \(-0.764459\pi\) | ||||
−0.738485 | + | 0.674270i | \(0.764459\pi\) | |||||||
\(30\) | 40.2812 | + | 5.26724i | 1.34271 | + | 0.175575i | ||||
\(31\) | −1.34219 | − | 0.774912i | −0.0432963 | − | 0.0249972i | 0.478196 | − | 0.878253i | \(-0.341291\pi\) |
−0.521492 | + | 0.853256i | \(0.674624\pi\) | |||||||
\(32\) | 19.3690 | − | 25.4724i | 0.605282 | − | 0.796011i | ||||
\(33\) | −21.4044 | − | 37.0734i | −0.648617 | − | 1.12344i | ||||
\(34\) | −18.4352 | − | 14.1202i | −0.542211 | − | 0.415299i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0953074 | + | 0.353217i | 0.00264743 | + | 0.00981157i | ||||
\(37\) | −22.5075 | − | 38.9842i | −0.608312 | − | 1.05363i | −0.991519 | − | 0.129964i | \(-0.958514\pi\) |
0.383207 | − | 0.923663i | \(-0.374820\pi\) | |||||||
\(38\) | 17.2133 | + | 41.4539i | 0.452982 | + | 1.09089i | ||||
\(39\) | 11.9483 | + | 6.89833i | 0.306366 | + | 0.176880i | ||||
\(40\) | 53.9582 | − | 7.24799i | 1.34896 | − | 0.181200i | ||||
\(41\) | 36.6492 | 0.893883 | 0.446942 | − | 0.894563i | \(-0.352513\pi\) | ||||
0.446942 | + | 0.894563i | \(0.352513\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 27.9894i | − | 0.650916i | −0.945557 | − | 0.325458i | \(-0.894482\pi\) | ||
0.945557 | − | 0.325458i | \(-0.105518\pi\) | |||||||
\(44\) | −40.6381 | − | 40.4960i | −0.923593 | − | 0.920363i | ||||
\(45\) | −0.311217 | + | 0.539043i | −0.00691592 | + | 0.0119787i | ||||
\(46\) | −0.654960 | − | 1.57730i | −0.0142383 | − | 0.0342892i | ||||
\(47\) | −36.5237 | + | 21.0870i | −0.777100 | + | 0.448659i | −0.835402 | − | 0.549640i | \(-0.814765\pi\) |
0.0583012 | + | 0.998299i | \(0.481432\pi\) | |||||||
\(48\) | −24.0225 | − | 41.2736i | −0.500468 | − | 0.859866i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 33.8400 | + | 25.9193i | 0.676800 | + | 0.518386i | ||||
\(51\) | −30.0119 | + | 17.3274i | −0.588468 | + | 0.339752i | ||||
\(52\) | 17.8681 | + | 4.75421i | 0.343617 | + | 0.0914271i | ||||
\(53\) | −21.7022 | + | 37.5893i | −0.409475 | + | 0.709232i | −0.994831 | − | 0.101545i | \(-0.967621\pi\) |
0.585356 | + | 0.810776i | \(0.300955\pi\) | |||||||
\(54\) | 53.8128 | + | 7.03665i | 0.996533 | + | 0.130308i | ||||
\(55\) | − | 97.6068i | − | 1.77467i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 66.9856 | 1.17519 | ||||||||
\(58\) | −11.1071 | + | 84.9412i | −0.191501 | + | 1.46450i | ||||
\(59\) | −46.7636 | − | 26.9990i | −0.792603 | − | 0.457609i | 0.0482754 | − | 0.998834i | \(-0.484627\pi\) |
−0.840878 | + | 0.541225i | \(0.817961\pi\) | |||||||
\(60\) | 20.8911 | − | 78.5165i | 0.348185 | − | 1.30861i | ||||
\(61\) | −7.97489 | − | 13.8129i | −0.130736 | − | 0.226441i | 0.793225 | − | 0.608929i | \(-0.208401\pi\) |
−0.923960 | + | 0.382488i | \(0.875067\pi\) | |||||||
\(62\) | −1.88479 | + | 2.46077i | −0.0303999 | + | 0.0396898i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −45.4920 | − | 45.0164i | −0.710812 | − | 0.703382i | ||||
\(65\) | 15.7287 | + | 27.2428i | 0.241979 | + | 0.419120i | ||||
\(66\) | −79.0715 | + | 32.8336i | −1.19805 | + | 0.497479i | ||||
\(67\) | −79.6270 | − | 45.9726i | −1.18846 | − | 0.686159i | −0.230505 | − | 0.973071i | \(-0.574038\pi\) |
−0.957957 | + | 0.286912i | \(0.907371\pi\) | |||||||
\(68\) | −32.7825 | + | 32.8975i | −0.482096 | + | 0.483787i | ||||
\(69\) | −2.54877 | −0.0369387 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 16.3585i | 0.230401i | 0.993342 | + | 0.115201i | \(0.0367511\pi\) | ||||
−0.993342 | + | 0.115201i | \(0.963249\pi\) | |||||||
\(72\) | 0.725185 | − | 0.0974111i | 0.0100720 | − | 0.00135293i | ||||
\(73\) | 4.79364 | − | 8.30283i | 0.0656663 | − | 0.113737i | −0.831323 | − | 0.555790i | \(-0.812416\pi\) |
0.896989 | + | 0.442052i | \(0.145749\pi\) | |||||||
\(74\) | −83.1468 | + | 34.5259i | −1.12361 | + | 0.466566i | ||||
\(75\) | 55.0904 | − | 31.8065i | 0.734539 | − | 0.424086i | ||||
\(76\) | 86.6717 | − | 23.3864i | 1.14042 | − | 0.307715i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.7786 | − | 21.9059i | 0.215110 | − | 0.280845i | ||||
\(79\) | −49.3484 | + | 28.4913i | −0.624663 | + | 0.360649i | −0.778682 | − | 0.627418i | \(-0.784112\pi\) |
0.154019 | + | 0.988068i | \(0.450778\pi\) | |||||||
\(80\) | −0.381382 | − | 108.885i | −0.00476727 | − | 1.36106i | ||||
\(81\) | 40.0842 | − | 69.4279i | 0.494867 | − | 0.857135i | ||||
\(82\) | 9.50373 | − | 72.6797i | 0.115899 | − | 0.886338i | ||||
\(83\) | − | 14.3077i | − | 0.172381i | −0.996279 | − | 0.0861907i | \(-0.972531\pi\) | ||
0.996279 | − | 0.0861907i | \(-0.0274694\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −79.0151 | −0.929589 | ||||||||
\(86\) | −55.5062 | − | 7.25809i | −0.645421 | − | 0.0843965i | ||||
\(87\) | 110.714 | + | 63.9209i | 1.27258 | + | 0.734723i | ||||
\(88\) | −90.8464 | + | 70.0888i | −1.03235 | + | 0.796464i | ||||
\(89\) | 50.0680 | + | 86.7204i | 0.562562 | + | 0.974386i | 0.997272 | + | 0.0738155i | \(0.0235176\pi\) |
−0.434710 | + | 0.900571i | \(0.643149\pi\) | |||||||
\(90\) | 0.988282 | + | 0.756962i | 0.0109809 | + | 0.00841068i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.29782 | + | 0.889842i | −0.0358459 | + | 0.00967219i | ||||
\(93\) | 2.31289 | + | 4.00605i | 0.0248698 | + | 0.0430758i | ||||
\(94\) | 32.3468 | + | 77.8990i | 0.344115 | + | 0.828713i | ||||
\(95\) | 132.269 | + | 76.3658i | 1.39231 | + | 0.803850i | ||||
\(96\) | −88.0797 | + | 36.9364i | −0.917497 | + | 0.384755i | ||||
\(97\) | −68.2834 | −0.703952 | −0.351976 | − | 0.936009i | \(-0.614490\pi\) | ||||
−0.351976 | + | 0.936009i | \(0.614490\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.31181i | − | 0.0132506i | ||||||
\(100\) | 60.1763 | − | 60.3874i | 0.601763 | − | 0.603874i | ||||
\(101\) | −14.0814 | + | 24.3897i | −0.139420 | + | 0.241483i | −0.927277 | − | 0.374375i | \(-0.877857\pi\) |
0.787857 | + | 0.615858i | \(0.211190\pi\) | |||||||
\(102\) | 26.5796 | + | 64.0103i | 0.260585 | + | 0.627552i | ||||
\(103\) | 138.774 | − | 80.1213i | 1.34732 | − | 0.777877i | 0.359453 | − | 0.933163i | \(-0.382963\pi\) |
0.987870 | + | 0.155286i | \(0.0496299\pi\) | |||||||
\(104\) | 14.0616 | − | 34.2016i | 0.135208 | − | 0.328862i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 68.9162 | + | 52.7855i | 0.650153 | + | 0.497976i | ||||
\(107\) | 102.990 | − | 59.4613i | 0.962524 | − | 0.555713i | 0.0655750 | − | 0.997848i | \(-0.479112\pi\) |
0.896949 | + | 0.442134i | \(0.145779\pi\) | |||||||
\(108\) | 27.9090 | − | 104.892i | 0.258417 | − | 0.971225i | ||||
\(109\) | 49.1333 | − | 85.1014i | 0.450764 | − | 0.780747i | −0.547669 | − | 0.836695i | \(-0.684485\pi\) |
0.998434 | + | 0.0559480i | \(0.0178181\pi\) | |||||||
\(110\) | −193.566 | − | 25.3110i | −1.75969 | − | 0.230100i | ||||
\(111\) | 134.357i | 1.21043i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 96.9977 | 0.858387 | 0.429193 | − | 0.903213i | \(-0.358798\pi\) | ||||
0.429193 | + | 0.903213i | \(0.358798\pi\) | |||||||
\(114\) | 17.3704 | − | 132.840i | 0.152372 | − | 1.16527i | ||||
\(115\) | −5.03280 | − | 2.90569i | −0.0437635 | − | 0.0252669i | ||||
\(116\) | 165.568 | + | 44.0532i | 1.42731 | + | 0.379769i | ||||
\(117\) | 0.211389 | + | 0.366137i | 0.00180674 | + | 0.00312937i | ||||
\(118\) | −65.6686 | + | 85.7364i | −0.556514 | + | 0.726579i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −150.290 | − | 61.7901i | −1.25242 | − | 0.514918i | ||||
\(121\) | 42.3556 | + | 73.3620i | 0.350046 | + | 0.606298i | ||||
\(122\) | −29.4606 | + | 12.2332i | −0.241481 | + | 0.100272i | ||||
\(123\) | −94.7324 | − | 54.6938i | −0.770182 | − | 0.444665i | ||||
\(124\) | 4.39123 | + | 4.37588i | 0.0354132 | + | 0.0352894i | ||||
\(125\) | −25.0921 | −0.200737 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 71.8712i | − | 0.565915i | −0.959132 | − | 0.282958i | \(-0.908684\pi\) | ||
0.959132 | − | 0.282958i | \(-0.0913156\pi\) | |||||||
\(128\) | −101.070 | + | 78.5424i | −0.789607 | + | 0.613613i | ||||
\(129\) | −41.7702 | + | 72.3481i | −0.323800 | + | 0.560838i | ||||
\(130\) | 58.1044 | − | 24.1273i | 0.446957 | − | 0.185594i | ||||
\(131\) | −181.724 | + | 104.919i | −1.38721 | + | 0.800906i | −0.993000 | − | 0.118115i | \(-0.962315\pi\) |
−0.394209 | + | 0.919021i | \(0.628982\pi\) | |||||||
\(132\) | 44.6084 | + | 165.322i | 0.337943 | + | 1.25244i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −111.818 | + | 145.988i | −0.834460 | + | 1.08946i | ||||
\(135\) | 159.926 | − | 92.3332i | 1.18464 | − | 0.683950i | ||||
\(136\) | 56.7386 | + | 73.5424i | 0.417196 | + | 0.540753i | ||||
\(137\) | 9.08248 | − | 15.7313i | 0.0662954 | − | 0.114827i | −0.830972 | − | 0.556314i | \(-0.812215\pi\) |
0.897268 | + | 0.441486i | \(0.145549\pi\) | |||||||
\(138\) | −0.660938 | + | 5.05452i | −0.00478940 | + | 0.0366269i | ||||
\(139\) | 134.084i | 0.964635i | 0.875996 | + | 0.482318i | \(0.160205\pi\) | ||||
−0.875996 | + | 0.482318i | \(0.839795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 125.877 | 0.892747 | ||||||||
\(142\) | 32.4408 | + | 4.24202i | 0.228456 | + | 0.0298733i | ||||
\(143\) | −57.4156 | − | 33.1489i | −0.401508 | − | 0.231811i | ||||
\(144\) | −0.00512567 | − | 1.46339i | −3.55949e−5 | − | 0.0101624i | ||||
\(145\) | 145.744 | + | 252.436i | 1.00513 | + | 1.74094i | ||||
\(146\) | −15.2224 | − | 11.6594i | −0.104263 | − | 0.0798590i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 46.9076 | + | 173.843i | 0.316943 | + | 1.17461i | ||||
\(149\) | 10.3809 | + | 17.9803i | 0.0696706 | + | 0.120673i | 0.898756 | − | 0.438449i | \(-0.144472\pi\) |
−0.829086 | + | 0.559122i | \(0.811139\pi\) | |||||||
\(150\) | −48.7902 | − | 117.499i | −0.325268 | − | 0.783325i | ||||
\(151\) | −80.6348 | − | 46.5545i | −0.534005 | − | 0.308308i | 0.208641 | − | 0.977992i | \(-0.433096\pi\) |
−0.742646 | + | 0.669684i | \(0.766429\pi\) | |||||||
\(152\) | −23.9026 | − | 177.945i | −0.157254 | − | 1.17069i | ||||
\(153\) | −1.06194 | −0.00694080 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.5471i | 0.0680458i | ||||||||
\(156\) | −39.0911 | − | 38.9544i | −0.250584 | − | 0.249708i | ||||
\(157\) | 79.6687 | − | 137.990i | 0.507444 | − | 0.878919i | −0.492519 | − | 0.870302i | \(-0.663924\pi\) |
0.999963 | − | 0.00861697i | \(-0.00274290\pi\) | |||||||
\(158\) | 43.7048 | + | 105.252i | 0.276613 | + | 0.666151i | ||||
\(159\) | 112.193 | − | 64.7749i | 0.705619 | − | 0.407389i | ||||
\(160\) | −216.031 | − | 27.4793i | −1.35019 | − | 0.171746i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −127.289 | − | 97.4955i | −0.785736 | − | 0.601824i | ||||
\(163\) | 39.6880 | − | 22.9139i | 0.243485 | − | 0.140576i | −0.373293 | − | 0.927714i | \(-0.621771\pi\) |
0.616777 | + | 0.787138i | \(0.288438\pi\) | |||||||
\(164\) | −141.668 | − | 37.6940i | −0.863829 | − | 0.229842i | ||||
\(165\) | −145.664 | + | 252.298i | −0.882814 | + | 1.52908i | ||||
\(166\) | −28.3738 | − | 3.71020i | −0.170926 | − | 0.0223506i | ||||
\(167\) | 15.5845i | 0.0933203i | 0.998911 | + | 0.0466602i | \(0.0148578\pi\) | ||||
−0.998911 | + | 0.0466602i | \(0.985142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −147.633 | −0.873569 | ||||||||
\(170\) | −20.4899 | + | 156.696i | −0.120529 | + | 0.921742i | ||||
\(171\) | 1.77767 | + | 1.02634i | 0.0103957 | + | 0.00600197i | ||||
\(172\) | −28.7873 | + | 108.193i | −0.167368 | + | 0.629031i | ||||
\(173\) | −133.011 | − | 230.381i | −0.768848 | − | 1.33168i | −0.938188 | − | 0.346126i | \(-0.887497\pi\) |
0.169340 | − | 0.985558i | \(-0.445836\pi\) | |||||||
\(174\) | 155.473 | − | 202.984i | 0.893521 | − | 1.16657i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 115.436 | + | 198.334i | 0.655889 | + | 1.12690i | ||||
\(177\) | 80.5842 | + | 139.576i | 0.455278 | + | 0.788565i | ||||
\(178\) | 184.960 | − | 76.8028i | 1.03910 | − | 0.431476i | ||||
\(179\) | −38.5433 | − | 22.2530i | −0.215325 | − | 0.124318i | 0.388458 | − | 0.921466i | \(-0.373008\pi\) |
−0.603784 | + | 0.797148i | \(0.706341\pi\) | |||||||
\(180\) | 1.75742 | − | 1.76359i | 0.00976345 | − | 0.00979771i | ||||
\(181\) | 168.111 | 0.928787 | 0.464394 | − | 0.885629i | \(-0.346272\pi\) | ||||
0.464394 | + | 0.885629i | \(0.346272\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 47.6056i | 0.260140i | ||||||||
\(184\) | 0.909483 | + | 6.77072i | 0.00494284 | + | 0.0367974i | ||||
\(185\) | −153.172 | + | 265.301i | −0.827956 | + | 1.43406i | ||||
\(186\) | 8.54423 | − | 3.54791i | 0.0459367 | − | 0.0190748i | ||||
\(187\) | 144.218 | − | 83.2641i | 0.771218 | − | 0.445263i | ||||
\(188\) | 162.871 | − | 43.9470i | 0.866335 | − | 0.233761i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 185.742 | − | 242.503i | 0.977589 | − | 1.27633i | ||||
\(191\) | −306.232 | + | 176.803i | −1.60331 | + | 0.925672i | −0.612491 | + | 0.790477i | \(0.709833\pi\) |
−0.990819 | + | 0.135194i | \(0.956834\pi\) | |||||||
\(192\) | 50.4088 | + | 184.251i | 0.262546 | + | 0.959639i | ||||
\(193\) | 174.287 | − | 301.874i | 0.903042 | − | 1.56411i | 0.0795170 | − | 0.996834i | \(-0.474662\pi\) |
0.823525 | − | 0.567280i | \(-0.192004\pi\) | |||||||
\(194\) | −17.7070 | + | 135.414i | −0.0912730 | + | 0.698010i | ||||
\(195\) | − | 93.8912i | − | 0.481493i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.9314 | −0.136707 | −0.0683537 | − | 0.997661i | \(-0.521775\pi\) | ||||
−0.0683537 | + | 0.997661i | \(0.521775\pi\) | |||||||
\(198\) | −2.60147 | − | 0.340173i | −0.0131387 | − | 0.00171805i | ||||
\(199\) | −200.537 | − | 115.780i | −1.00772 | − | 0.581809i | −0.0971981 | − | 0.995265i | \(-0.530988\pi\) |
−0.910524 | + | 0.413457i | \(0.864321\pi\) | |||||||
\(200\) | −104.151 | − | 134.996i | −0.520754 | − | 0.674981i | ||||
\(201\) | 137.215 | + | 237.664i | 0.682663 | + | 1.18241i | ||||
\(202\) | 44.7162 | + | 34.2498i | 0.221367 | + | 0.169553i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 133.832 | − | 36.1116i | 0.656041 | − | 0.177018i | ||||
\(205\) | −124.706 | − | 215.996i | −0.608320 | − | 1.05364i | ||||
\(206\) | −122.904 | − | 295.982i | −0.596620 | − | 1.43681i | ||||
\(207\) | −0.0676395 | − | 0.0390517i | −0.000326761 | − | 0.000188655i | ||||
\(208\) | −64.1794 | − | 36.7549i | −0.308555 | − | 0.176706i | ||||
\(209\) | −321.890 | −1.54014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 79.6903i | 0.377679i | 0.982008 | + | 0.188840i | \(0.0604726\pi\) | ||||
−0.982008 | + | 0.188840i | \(0.939527\pi\) | |||||||
\(212\) | 122.551 | − | 122.981i | 0.578070 | − | 0.580098i | ||||
\(213\) | 24.4127 | − | 42.2841i | 0.114614 | − | 0.198517i | ||||
\(214\) | −91.2119 | − | 219.661i | −0.426224 | − | 1.02645i | ||||
\(215\) | −164.959 | + | 95.2389i | −0.767249 | + | 0.442972i | ||||
\(216\) | −200.777 | − | 82.5471i | −0.929521 | − | 0.382163i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −156.025 | − | 119.505i | −0.715711 | − | 0.548189i | ||||
\(219\) | −24.7816 | + | 14.3077i | −0.113158 | + | 0.0653318i | ||||
\(220\) | −100.389 | + | 377.300i | −0.456315 | + | 1.71500i | ||||
\(221\) | −26.8349 | + | 46.4794i | −0.121425 | + | 0.210314i | ||||
\(222\) | 266.446 | + | 34.8410i | 1.20021 | + | 0.156941i | ||||
\(223\) | − | 264.367i | − | 1.18550i | −0.805386 | − | 0.592750i | \(-0.798042\pi\) | ||
0.805386 | − | 0.592750i | \(-0.201958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.94932 | 0.00866367 | ||||||||
\(226\) | 25.1531 | − | 192.358i | 0.111297 | − | 0.851141i | ||||
\(227\) | 373.538 | + | 215.662i | 1.64554 | + | 0.950053i | 0.978814 | + | 0.204750i | \(0.0656383\pi\) |
0.666726 | + | 0.745303i | \(0.267695\pi\) | |||||||
\(228\) | −258.933 | − | 68.8952i | −1.13567 | − | 0.302172i | ||||
\(229\) | −212.451 | − | 367.975i | −0.927732 | − | 1.60688i | −0.787107 | − | 0.616816i | \(-0.788422\pi\) |
−0.140625 | − | 0.990063i | \(-0.544911\pi\) | |||||||
\(230\) | −7.06741 | + | 9.22714i | −0.0307279 | + | 0.0401180i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 130.297 | − | 316.917i | 0.561626 | − | 1.36602i | ||||
\(233\) | −109.414 | − | 189.511i | −0.469588 | − | 0.813350i | 0.529808 | − | 0.848118i | \(-0.322264\pi\) |
−0.999395 | + | 0.0347679i | \(0.988931\pi\) | |||||||
\(234\) | 0.780908 | − | 0.324264i | 0.00333722 | − | 0.00138574i | ||||
\(235\) | 248.557 | + | 143.504i | 1.05769 | + | 0.610657i | ||||
\(236\) | 152.996 | + | 152.461i | 0.648290 | + | 0.646023i | ||||
\(237\) | 170.077 | 0.717625 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 90.1656i | − | 0.377262i | −0.982048 | − | 0.188631i | \(-0.939595\pi\) | ||
0.982048 | − | 0.188631i | \(-0.0604050\pi\) | |||||||
\(240\) | −161.510 | + | 282.020i | −0.672957 | + | 1.17508i | ||||
\(241\) | 187.972 | − | 325.577i | 0.779968 | − | 1.35094i | −0.151992 | − | 0.988382i | \(-0.548569\pi\) |
0.931960 | − | 0.362562i | \(-0.118098\pi\) | |||||||
\(242\) | 156.469 | − | 64.9722i | 0.646566 | − | 0.268480i | ||||
\(243\) | 4.27710 | − | 2.46938i | 0.0176012 | − | 0.0101621i | ||||
\(244\) | 16.6203 | + | 61.5962i | 0.0681161 | + | 0.252443i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −133.030 | + | 173.683i | −0.540772 | + | 0.706027i | ||||
\(247\) | 89.8420 | − | 51.8703i | 0.363733 | − | 0.210001i | ||||
\(248\) | 9.81660 | − | 7.57360i | 0.0395831 | − | 0.0305387i | ||||
\(249\) | −21.3522 | + | 36.9830i | −0.0857516 | + | 0.148526i | ||||
\(250\) | −6.50678 | + | 49.7605i | −0.0260271 | + | 0.199042i | ||||
\(251\) | − | 319.525i | − | 1.27301i | −0.771274 | − | 0.636503i | \(-0.780380\pi\) | ||
0.771274 | − | 0.636503i | \(-0.219620\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.2478 | 0.0484101 | ||||||||
\(254\) | −142.529 | − | 18.6374i | −0.561138 | − | 0.0733754i | ||||
\(255\) | 204.241 | + | 117.919i | 0.800947 | + | 0.462427i | ||||
\(256\) | 129.550 | + | 220.800i | 0.506054 | + | 0.862502i | ||||
\(257\) | −83.7329 | − | 145.030i | −0.325809 | − | 0.564318i | 0.655867 | − | 0.754877i | \(-0.272303\pi\) |
−0.981676 | + | 0.190559i | \(0.938970\pi\) | |||||||
\(258\) | 132.643 | + | 101.596i | 0.514121 | + | 0.393784i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −32.7798 | − | 121.484i | −0.126076 | − | 0.467248i | ||||
\(261\) | 1.95876 | + | 3.39267i | 0.00750483 | + | 0.0129988i | ||||
\(262\) | 160.942 | + | 387.588i | 0.614282 | + | 1.47934i | ||||
\(263\) | 74.5887 | + | 43.0638i | 0.283607 | + | 0.163741i | 0.635055 | − | 0.772467i | \(-0.280977\pi\) |
−0.351448 | + | 0.936207i | \(0.614311\pi\) | |||||||
\(264\) | 339.421 | − | 45.5931i | 1.28569 | − | 0.172701i | ||||
\(265\) | 295.382 | 1.11465 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 298.878i | − | 1.11939i | ||||||
\(268\) | 260.516 | + | 259.605i | 0.972073 | + | 0.968674i | ||||
\(269\) | 134.672 | − | 233.258i | 0.500638 | − | 0.867130i | −0.499362 | − | 0.866394i | \(-0.666432\pi\) |
1.00000 | 0.000736768i | \(-0.000234520\pi\) | ||||||||
\(270\) | −141.636 | − | 341.095i | −0.524579 | − | 1.26332i | ||||
\(271\) | −275.671 | + | 159.159i | −1.01724 | + | 0.587302i | −0.913302 | − | 0.407282i | \(-0.866477\pi\) |
−0.103935 | + | 0.994584i | \(0.533143\pi\) | |||||||
\(272\) | 160.556 | − | 93.4487i | 0.590281 | − | 0.343561i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −28.8418 | − | 22.0910i | −0.105262 | − | 0.0806241i | ||||
\(275\) | −264.729 | + | 152.842i | −0.962652 | + | 0.555787i | ||||
\(276\) | 9.85231 | + | 2.62143i | 0.0356968 | + | 0.00949795i | ||||
\(277\) | −178.298 | + | 308.822i | −0.643677 | + | 1.11488i | 0.340929 | + | 0.940089i | \(0.389259\pi\) |
−0.984605 | + | 0.174792i | \(0.944075\pi\) | |||||||
\(278\) | 265.905 | + | 34.7702i | 0.956492 | + | 0.125073i | ||||
\(279\) | 0.141750i | 0.000508066i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 109.846 | 0.390911 | 0.195455 | − | 0.980713i | \(-0.437381\pi\) | ||||
0.195455 | + | 0.980713i | \(0.437381\pi\) | |||||||
\(282\) | 32.6420 | − | 249.630i | 0.115752 | − | 0.885211i | ||||
\(283\) | −445.641 | − | 257.291i | −1.57470 | − | 0.909155i | −0.995580 | − | 0.0939154i | \(-0.970062\pi\) |
−0.579123 | − | 0.815240i | \(-0.696605\pi\) | |||||||
\(284\) | 16.8248 | − | 63.2339i | 0.0592424 | − | 0.222654i | ||||
\(285\) | −227.930 | − | 394.787i | −0.799755 | − | 1.38522i | ||||
\(286\) | −80.6270 | + | 105.266i | −0.281913 | + | 0.368063i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.90340 | − | 0.369315i | −0.0100812 | − | 0.00128234i | ||||
\(289\) | 77.0956 | + | 133.534i | 0.266767 | + | 0.462054i | ||||
\(290\) | 538.404 | − | 223.567i | 1.85657 | − | 0.770920i | ||||
\(291\) | 176.502 | + | 101.903i | 0.606535 | + | 0.350183i | ||||
\(292\) | −27.0694 | + | 27.1644i | −0.0927034 | + | 0.0930287i | ||||
\(293\) | 133.002 | 0.453931 | 0.226965 | − | 0.973903i | \(-0.427120\pi\) | ||||
0.226965 | + | 0.973903i | \(0.427120\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 367.475i | 1.24568i | ||||||||
\(296\) | 356.915 | − | 47.9429i | 1.20579 | − | 0.161969i | ||||
\(297\) | −194.597 | + | 337.052i | −0.655208 | + | 1.13485i | ||||
\(298\) | 38.3489 | − | 15.9240i | 0.128688 | − | 0.0534363i | ||||
\(299\) | −3.41845 | + | 1.97364i | −0.0114329 | + | 0.00660081i | ||||
\(300\) | −245.666 | + | 66.2873i | −0.818886 | + | 0.220958i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −113.233 | + | 147.836i | −0.374944 | + | 0.489523i | ||||
\(303\) | 72.7965 | − | 42.0291i | 0.240252 | − | 0.138710i | ||||
\(304\) | −359.083 | + | 1.25773i | −1.18120 | + | 0.00413726i | ||||
\(305\) | −54.2720 | + | 94.0018i | −0.177941 | + | 0.308203i | ||||
\(306\) | −0.275379 | + | 2.10596i | −0.000899930 | + | 0.00688221i | ||||
\(307\) | 382.811i | 1.24694i | 0.781847 | + | 0.623471i | \(0.214278\pi\) | ||||
−0.781847 | + | 0.623471i | \(0.785722\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −478.279 | −1.54783 | ||||||||
\(310\) | 20.9161 | + | 2.73503i | 0.0674714 | + | 0.00882269i | ||||
\(311\) | −170.064 | − | 98.1868i | −0.546831 | − | 0.315713i | 0.201012 | − | 0.979589i | \(-0.435577\pi\) |
−0.747843 | + | 0.663876i | \(0.768910\pi\) | |||||||
\(312\) | −87.3882 | + | 67.4208i | −0.280090 | + | 0.216092i | ||||
\(313\) | 213.523 | + | 369.832i | 0.682181 | + | 1.18157i | 0.974314 | + | 0.225194i | \(0.0723017\pi\) |
−0.292133 | + | 0.956378i | \(0.594365\pi\) | |||||||
\(314\) | −252.991 | − | 193.775i | −0.805705 | − | 0.617119i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 220.060 | − | 59.3782i | 0.696393 | − | 0.187906i | ||||
\(317\) | −55.5247 | − | 96.1716i | −0.175157 | − | 0.303381i | 0.765059 | − | 0.643961i | \(-0.222710\pi\) |
−0.940216 | + | 0.340580i | \(0.889377\pi\) | |||||||
\(318\) | −99.3626 | − | 239.290i | −0.312461 | − | 0.752484i | ||||
\(319\) | −532.022 | − | 307.163i | −1.66778 | − | 0.962893i | ||||
\(320\) | −110.515 | + | 421.289i | −0.345359 | + | 1.31653i | ||||
\(321\) | −354.951 | −1.10577 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 260.577i | 0.806741i | ||||||||
\(324\) | −226.353 | + | 227.147i | −0.698621 | + | 0.701072i | ||||
\(325\) | 49.2587 | − | 85.3186i | 0.151565 | − | 0.262519i | ||||
\(326\) | −35.1492 | − | 84.6479i | −0.107820 | − | 0.259656i | ||||
\(327\) | −254.004 | + | 146.649i | −0.776770 | + | 0.448468i | ||||
\(328\) | −111.488 | + | 271.170i | −0.339904 | + | 0.826736i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 462.563 | + | 354.294i | 1.40171 | + | 1.07362i | ||||
\(331\) | −103.601 | + | 59.8143i | −0.312995 | + | 0.180708i | −0.648266 | − | 0.761414i | \(-0.724505\pi\) |
0.335271 | + | 0.942122i | \(0.391172\pi\) | |||||||
\(332\) | −14.7155 | + | 55.3064i | −0.0443239 | + | 0.166586i | ||||
\(333\) | −2.05859 | + | 3.56558i | −0.00618195 | + | 0.0107075i | ||||
\(334\) | 30.9059 | + | 4.04131i | 0.0925326 | + | 0.0120997i | ||||
\(335\) | 625.721i | 1.86782i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −57.3636 | −0.170218 | −0.0851092 | − | 0.996372i | \(-0.527124\pi\) | ||||
−0.0851092 | + | 0.996372i | \(0.527124\pi\) | |||||||
\(338\) | −38.2836 | + | 292.774i | −0.113265 | + | 0.866195i | ||||
\(339\) | −250.724 | − | 144.755i | −0.739598 | − | 0.427007i | ||||
\(340\) | 305.434 | + | 81.2676i | 0.898334 | + | 0.239022i | ||||
\(341\) | −11.1143 | − | 19.2505i | −0.0325932 | − | 0.0564531i | ||||
\(342\) | 2.49632 | − | 3.25918i | 0.00729919 | − | 0.00952976i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 207.095 | + | 85.1449i | 0.602020 | + | 0.247514i | ||||
\(345\) | 8.67266 | + | 15.0215i | 0.0251381 | + | 0.0435405i | ||||
\(346\) | −491.365 | + | 204.034i | −1.42013 | + | 0.589694i | ||||
\(347\) | 232.766 | + | 134.387i | 0.670794 | + | 0.387283i | 0.796377 | − | 0.604800i | \(-0.206747\pi\) |
−0.125583 | + | 0.992083i | \(0.540080\pi\) | |||||||
\(348\) | −362.224 | − | 360.958i | −1.04087 | − | 1.03723i | ||||
\(349\) | −97.0498 | −0.278080 | −0.139040 | − | 0.990287i | \(-0.544402\pi\) | ||||
−0.139040 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 125.432i | − | 0.357356i | ||||||
\(352\) | 423.255 | − | 177.493i | 1.20243 | − | 0.504241i | ||||
\(353\) | −158.464 | + | 274.468i | −0.448907 | + | 0.777529i | −0.998315 | − | 0.0580249i | \(-0.981520\pi\) |
0.549409 | + | 0.835554i | \(0.314853\pi\) | |||||||
\(354\) | 297.692 | − | 123.614i | 0.840939 | − | 0.349191i | ||||
\(355\) | 96.4105 | − | 55.6627i | 0.271579 | − | 0.156796i | ||||
\(356\) | −104.346 | − | 386.714i | −0.293106 | − | 1.08627i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −54.1251 | + | 70.6653i | −0.151187 | + | 0.197389i | ||||
\(359\) | 511.123 | − | 295.097i | 1.42374 | − | 0.821997i | 0.427124 | − | 0.904193i | \(-0.359527\pi\) |
0.996616 | + | 0.0821961i | \(0.0261934\pi\) | |||||||
\(360\) | −3.04167 | − | 3.94250i | −0.00844909 | − | 0.0109514i | ||||
\(361\) | 71.3407 | − | 123.566i | 0.197620 | − | 0.342287i | ||||
\(362\) | 43.5937 | − | 333.383i | 0.120425 | − | 0.920947i | ||||
\(363\) | − | 252.839i | − | 0.696526i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −65.2449 | −0.178753 | ||||||||
\(366\) | 94.4074 | + | 12.3449i | 0.257944 | + | 0.0337292i | ||||
\(367\) | 152.025 | + | 87.7718i | 0.414238 | + | 0.239160i | 0.692609 | − | 0.721313i | \(-0.256461\pi\) |
−0.278371 | + | 0.960474i | \(0.589795\pi\) | |||||||
\(368\) | 13.6630 | − | 0.0478560i | 0.0371277 | − | 0.000130044i | ||||
\(369\) | −1.67601 | − | 2.90293i | −0.00454203 | − | 0.00786703i | ||||
\(370\) | 486.404 | + | 372.555i | 1.31461 | + | 1.00690i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.82026 | − | 17.8642i | −0.0129577 | − | 0.0480222i | ||||
\(373\) | −277.008 | − | 479.792i | −0.742649 | − | 1.28631i | −0.951285 | − | 0.308312i | \(-0.900236\pi\) |
0.208637 | − | 0.977993i | \(-0.433097\pi\) | |||||||
\(374\) | −127.725 | − | 307.592i | −0.341510 | − | 0.822439i | ||||
\(375\) | 64.8590 | + | 37.4464i | 0.172957 | + | 0.0998570i | ||||
\(376\) | −44.9170 | − | 334.388i | −0.119460 | − | 0.889331i | ||||
\(377\) | 197.989 | 0.525169 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 749.909i | 1.97865i | 0.145723 | + | 0.989325i | \(0.453449\pi\) | ||||
−0.145723 | + | 0.989325i | \(0.546551\pi\) | |||||||
\(380\) | −432.746 | − | 431.233i | −1.13881 | − | 1.13482i | ||||
\(381\) | −107.258 | + | 185.776i | −0.281516 | + | 0.487600i | ||||
\(382\) | 271.211 | + | 653.143i | 0.709976 | + | 1.70980i | ||||
\(383\) | 213.242 | − | 123.115i | 0.556767 | − | 0.321450i | −0.195080 | − | 0.980787i | \(-0.562497\pi\) |
0.751847 | + | 0.659338i | \(0.229163\pi\) | |||||||
\(384\) | 378.463 | − | 52.1875i | 0.985580 | − | 0.135905i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −553.456 | − | 423.912i | −1.43382 | − | 1.09822i | ||||
\(387\) | −2.21700 | + | 1.27999i | −0.00572868 | + | 0.00330746i | ||||
\(388\) | 263.950 | + | 70.2300i | 0.680284 | + | 0.181005i | ||||
\(389\) | −149.009 | + | 258.092i | −0.383058 | + | 0.663475i | −0.991498 | − | 0.130125i | \(-0.958462\pi\) |
0.608440 | + | 0.793600i | \(0.291796\pi\) | |||||||
\(390\) | −186.197 | − | 24.3475i | −0.477429 | − | 0.0624294i | ||||
\(391\) | − | 9.91487i | − | 0.0253577i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 626.305 | 1.59365 | ||||||||
\(394\) | −6.98373 | + | 53.4080i | −0.0177252 | + | 0.135553i | ||||
\(395\) | 335.833 | + | 193.894i | 0.850211 | + | 0.490870i | ||||
\(396\) | −1.34921 | + | 5.07081i | −0.00340709 | + | 0.0128051i | ||||
\(397\) | 63.9113 | + | 110.698i | 0.160986 | + | 0.278835i | 0.935222 | − | 0.354061i | \(-0.115199\pi\) |
−0.774237 | + | 0.632896i | \(0.781866\pi\) | |||||||
\(398\) | −281.608 | + | 367.664i | −0.707557 | + | 0.923779i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −294.721 | + | 171.536i | −0.736803 | + | 0.428841i | ||||
\(401\) | 387.143 | + | 670.552i | 0.965444 | + | 1.67220i | 0.708416 | + | 0.705795i | \(0.249410\pi\) |
0.257028 | + | 0.966404i | \(0.417257\pi\) | |||||||
\(402\) | 506.898 | − | 210.484i | 1.26094 | − | 0.523592i | ||||
\(403\) | 6.20417 | + | 3.58198i | 0.0153950 | + | 0.00888828i | ||||
\(404\) | 79.5169 | − | 79.7959i | 0.196824 | − | 0.197515i | ||||
\(405\) | −545.575 | −1.34710 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 645.635i | − | 1.58633i | ||||||
\(408\) | −36.9087 | − | 274.770i | −0.0904625 | − | 0.673455i | ||||
\(409\) | 333.442 | − | 577.538i | 0.815262 | − | 1.41207i | −0.0938783 | − | 0.995584i | \(-0.529926\pi\) |
0.909140 | − | 0.416491i | \(-0.136740\pi\) | |||||||
\(410\) | −460.684 | + | 191.294i | −1.12362 | + | 0.466572i | ||||
\(411\) | −46.9535 | + | 27.1086i | −0.114242 | + | 0.0659577i | ||||
\(412\) | −618.839 | + | 166.979i | −1.50204 | + | 0.405290i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.0949841 | + | 0.124010i | −0.000229430 | + | 0.000299542i | ||||
\(415\) | −84.3238 | + | 48.6844i | −0.203190 | + | 0.117312i | ||||
\(416\) | −89.5320 | + | 117.744i | −0.215221 | + | 0.283039i | ||||
\(417\) | 200.102 | − | 346.587i | 0.479861 | − | 0.831143i | ||||
\(418\) | −83.4711 | + | 638.345i | −0.199692 | + | 1.52714i | ||||
\(419\) | 95.3634i | 0.227598i | 0.993504 | + | 0.113799i | \(0.0363019\pi\) | ||||
−0.993504 | + | 0.113799i | \(0.963698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −279.158 | −0.663083 | −0.331541 | − | 0.943441i | \(-0.607569\pi\) | ||||
−0.331541 | + | 0.943441i | \(0.607569\pi\) | |||||||
\(422\) | 158.035 | + | 20.6650i | 0.374491 | + | 0.0489691i | ||||
\(423\) | 3.34054 | + | 1.92866i | 0.00789726 | + | 0.00455949i | ||||
\(424\) | −212.106 | − | 274.924i | −0.500250 | − | 0.648405i | ||||
\(425\) | 123.729 | + | 214.305i | 0.291127 | + | 0.504247i | ||||
\(426\) | −77.5237 | − | 59.3782i | −0.181980 | − | 0.139386i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −459.266 | + | 123.922i | −1.07305 | + | 0.289538i | ||||
\(429\) | 98.9402 | + | 171.369i | 0.230630 | + | 0.399463i | ||||
\(430\) | 146.094 | + | 351.829i | 0.339752 | + | 0.818208i | ||||
\(431\) | −146.682 | − | 84.6868i | −0.340329 | − | 0.196489i | 0.320088 | − | 0.947388i | \(-0.396287\pi\) |
−0.660418 | + | 0.750899i | \(0.729621\pi\) | |||||||
\(432\) | −215.765 | + | 376.758i | −0.499457 | + | 0.872125i | ||||
\(433\) | 295.214 | 0.681787 | 0.340894 | − | 0.940102i | \(-0.389270\pi\) | ||||
0.340894 | + | 0.940102i | \(0.389270\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 870.010i | − | 2.00002i | ||||||
\(436\) | −277.453 | + | 278.426i | −0.636360 | + | 0.638593i | ||||
\(437\) | −9.58244 | + | 16.5973i | −0.0219278 | + | 0.0379800i | ||||
\(438\) | 21.9475 | + | 52.8550i | 0.0501085 | + | 0.120674i | ||||
\(439\) | 282.994 | − | 163.386i | 0.644632 | − | 0.372179i | −0.141764 | − | 0.989900i | \(-0.545278\pi\) |
0.786397 | + | 0.617722i | \(0.211944\pi\) | |||||||
\(440\) | 722.198 | + | 296.924i | 1.64136 | + | 0.674827i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 85.2153 | + | 65.2696i | 0.192795 | + | 0.147669i | ||||
\(443\) | 445.821 | − | 257.395i | 1.00637 | − | 0.581026i | 0.0962414 | − | 0.995358i | \(-0.469318\pi\) |
0.910126 | + | 0.414332i | \(0.135985\pi\) | |||||||
\(444\) | 138.188 | − | 519.359i | 0.311233 | − | 1.16973i | ||||
\(445\) | 340.731 | − | 590.163i | 0.765687 | − | 1.32621i | ||||
\(446\) | −524.270 | − | 68.5545i | −1.17549 | − | 0.153710i | ||||
\(447\) | − | 61.9682i | − | 0.138631i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 602.217 | 1.34124 | 0.670620 | − | 0.741801i | \(-0.266028\pi\) | ||||
0.670620 | + | 0.741801i | \(0.266028\pi\) | |||||||
\(450\) | 0.505491 | − | 3.86574i | 0.00112331 | − | 0.00859053i | ||||
\(451\) | 455.223 | + | 262.823i | 1.00936 | + | 0.582757i | ||||
\(452\) | −374.946 | − | 99.7629i | −0.829526 | − | 0.220714i | ||||
\(453\) | 138.952 | + | 240.672i | 0.306738 | + | 0.531285i | ||||
\(454\) | 524.548 | − | 684.845i | 1.15539 | − | 1.50847i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −203.773 | + | 495.630i | −0.446870 | + | 1.08691i | ||||
\(457\) | 132.317 | + | 229.180i | 0.289534 | + | 0.501488i | 0.973699 | − | 0.227840i | \(-0.0731662\pi\) |
−0.684164 | + | 0.729328i | \(0.739833\pi\) | |||||||
\(458\) | −784.830 | + | 325.893i | −1.71360 | + | 0.711556i | ||||
\(459\) | 272.852 | + | 157.531i | 0.594448 | + | 0.343205i | ||||
\(460\) | 16.4658 | + | 16.4082i | 0.0357952 | + | 0.0356701i | ||||
\(461\) | 434.788 | 0.943140 | 0.471570 | − | 0.881829i | \(-0.343687\pi\) | ||||
0.471570 | + | 0.881829i | \(0.343687\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 193.258i | − | 0.417403i | −0.977979 | − | 0.208702i | \(-0.933076\pi\) | ||
0.977979 | − | 0.208702i | \(-0.0669237\pi\) | |||||||
\(464\) | −594.696 | − | 340.576i | −1.28167 | − | 0.734001i | ||||
\(465\) | 15.7401 | − | 27.2626i | 0.0338496 | − | 0.0586292i | ||||
\(466\) | −404.194 | + | 167.838i | −0.867370 | + | 0.360167i | ||||
\(467\) | 567.503 | − | 327.648i | 1.21521 | − | 0.701602i | 0.251321 | − | 0.967904i | \(-0.419135\pi\) |
0.963890 | + | 0.266301i | \(0.0858017\pi\) | |||||||
\(468\) | −0.440552 | − | 1.63272i | −0.000941351 | − | 0.00348872i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 349.041 | − | 455.705i | 0.742640 | − | 0.969585i | ||||
\(471\) | −411.862 | + | 237.789i | −0.874441 | + | 0.504859i | ||||
\(472\) | 342.023 | − | 263.874i | 0.724626 | − | 0.559055i | ||||
\(473\) | 200.721 | − | 347.659i | 0.424357 | − | 0.735008i | ||||
\(474\) | 44.1037 | − | 337.283i | 0.0930458 | − | 0.711567i | ||||
\(475\) | − | 478.322i | − | 1.00699i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.96986 | 0.00832256 | ||||||||
\(478\) | −178.809 | − | 23.3814i | −0.374077 | − | 0.0489150i | ||||
\(479\) | −88.9066 | − | 51.3302i | −0.185609 | − | 0.107161i | 0.404316 | − | 0.914619i | \(-0.367509\pi\) |
−0.589925 | + | 0.807458i | \(0.700843\pi\) | |||||||
\(480\) | 517.396 | + | 393.425i | 1.07791 | + | 0.819635i | ||||
\(481\) | 104.040 | + | 180.202i | 0.216298 | + | 0.374640i | ||||
\(482\) | −596.914 | − | 457.198i | −1.23841 | − | 0.948544i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −88.2725 | − | 327.145i | −0.182381 | − | 0.675919i | ||||
\(485\) | 232.346 | + | 402.436i | 0.479065 | + | 0.829764i | ||||
\(486\) | −3.78796 | − | 9.12234i | −0.00779415 | − | 0.0187702i | ||||
\(487\) | 130.469 | + | 75.3260i | 0.267903 | + | 0.154674i | 0.627934 | − | 0.778267i | \(-0.283901\pi\) |
−0.360032 | + | 0.932940i | \(0.617234\pi\) | |||||||
\(488\) | 126.462 | − | 16.9872i | 0.259144 | − | 0.0348098i | ||||
\(489\) | −136.783 | −0.279720 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 118.795i | 0.241946i | 0.992656 | + | 0.120973i | \(0.0386014\pi\) | ||||
−0.992656 | + | 0.120973i | \(0.961399\pi\) | |||||||
\(492\) | 309.936 | + | 308.852i | 0.629951 | + | 0.627749i | ||||
\(493\) | −248.656 | + | 430.685i | −0.504373 | + | 0.873600i | ||||
\(494\) | −79.5674 | − | 191.618i | −0.161068 | − | 0.387891i | ||||
\(495\) | −7.73130 | + | 4.46367i | −0.0156188 | + | 0.00901751i | ||||
\(496\) | −12.4737 | − | 21.4314i | −0.0251487 | − | 0.0432085i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 67.8047 | + | 51.9341i | 0.136154 | + | 0.104285i | ||||
\(499\) | −473.223 | + | 273.215i | −0.948343 | + | 0.547526i | −0.892566 | − | 0.450917i | \(-0.851097\pi\) |
−0.0557769 | + | 0.998443i | \(0.517764\pi\) | |||||||
\(500\) | 96.9937 | + | 25.8074i | 0.193987 | + | 0.0516148i | ||||
\(501\) | 23.2577 | − | 40.2834i | 0.0464225 | − | 0.0804061i | ||||
\(502\) | −633.655 | − | 82.8578i | −1.26226 | − | 0.165055i | ||||
\(503\) | − | 520.718i | − | 1.03522i | −0.855615 | − | 0.517612i | \(-0.826821\pi\) | ||
0.855615 | − | 0.517612i | \(-0.173179\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 191.658 | 0.379521 | ||||||||
\(506\) | 3.17604 | − | 24.2888i | 0.00627676 | − | 0.0480015i | ||||
\(507\) | 381.608 | + | 220.322i | 0.752679 | + | 0.434559i | ||||
\(508\) | −73.9201 | + | 277.819i | −0.145512 | + | 0.546888i | ||||
\(509\) | 300.714 | + | 520.851i | 0.590793 | + | 1.02328i | 0.994126 | + | 0.108230i | \(0.0345183\pi\) |
−0.403333 | + | 0.915053i | \(0.632148\pi\) | |||||||
\(510\) | 286.810 | − | 374.456i | 0.562372 | − | 0.734228i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 471.468 | − | 199.656i | 0.920835 | − | 0.389952i | ||||
\(513\) | −304.498 | − | 527.407i | −0.593564 | − | 1.02808i | ||||
\(514\) | −309.324 | + | 128.444i | −0.601798 | + | 0.249891i | ||||
\(515\) | −944.408 | − | 545.254i | −1.83380 | − | 1.05875i | ||||
\(516\) | 235.874 | − | 236.701i | 0.457120 | − | 0.458724i | ||||
\(517\) | −604.886 | −1.16999 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 793.998i | 1.52986i | ||||||||
\(520\) | −249.418 | + | 33.5033i | −0.479651 | + | 0.0644295i | ||||
\(521\) | −291.134 | + | 504.259i | −0.558798 | + | 0.967867i | 0.438799 | + | 0.898585i | \(0.355404\pi\) |
−0.997597 | + | 0.0692818i | \(0.977929\pi\) | |||||||
\(522\) | 7.23601 | − | 3.00468i | 0.0138621 | − | 0.00575609i | ||||
\(523\) | 124.355 | − | 71.7965i | 0.237773 | − | 0.137278i | −0.376380 | − | 0.926465i | \(-0.622831\pi\) |
0.614153 | + | 0.789187i | \(0.289498\pi\) | |||||||
\(524\) | 810.367 | − | 218.659i | 1.54650 | − | 0.417288i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 104.743 | − | 136.751i | 0.199130 | − | 0.259983i | ||||
\(527\) | −15.5837 | + | 8.99728i | −0.0295707 | + | 0.0170726i | ||||
\(528\) | −2.39906 | − | 684.935i | −0.00454367 | − | 1.29723i | ||||
\(529\) | −264.135 | + | 457.496i | −0.499311 | + | 0.864832i | ||||
\(530\) | 76.5973 | − | 585.778i | 0.144523 | − | 1.10524i | ||||
\(531\) | 4.93877i | 0.00930088i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −169.409 | −0.317840 | ||||||||
\(534\) | −592.710 | − | 77.5038i | −1.10994 | − | 0.145138i | ||||
\(535\) | −700.884 | − | 404.656i | −1.31006 | − | 0.756366i | ||||
\(536\) | 582.382 | − | 449.313i | 1.08653 | − | 0.838271i | ||||
\(537\) | 66.4188 | + | 115.041i | 0.123685 | + | 0.214229i | ||||
\(538\) | −427.656 | − | 327.557i | −0.794899 | − | 0.608842i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −713.160 | + | 192.430i | −1.32067 | + | 0.356352i | ||||
\(541\) | −416.548 | − | 721.483i | −0.769960 | − | 1.33361i | −0.937584 | − | 0.347759i | \(-0.886943\pi\) |
0.167624 | − | 0.985851i | \(-0.446391\pi\) | |||||||
\(542\) | 244.145 | + | 587.961i | 0.450452 | + | 1.08480i | ||||
\(543\) | −434.539 | − | 250.881i | −0.800256 | − | 0.462028i | ||||
\(544\) | −143.685 | − | 342.635i | −0.264127 | − | 0.629844i | ||||
\(545\) | −668.740 | −1.22705 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 356.858i | − | 0.652391i | −0.945302 | − | 0.326196i | \(-0.894233\pi\) | ||
0.945302 | − | 0.326196i | \(-0.105767\pi\) | |||||||
\(548\) | −51.2882 | + | 51.4681i | −0.0935916 | + | 0.0939200i | ||||
\(549\) | −0.729401 | + | 1.26336i | −0.00132860 | + | 0.00230120i | ||||
\(550\) | 234.454 | + | 564.624i | 0.426280 | + | 1.02659i | ||||
\(551\) | 832.489 | − | 480.638i | 1.51087 | − | 0.872301i | ||||
\(552\) | 7.75347 | − | 18.8585i | 0.0140461 | − | 0.0341640i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 566.195 | + | 433.669i | 1.02201 | + | 0.782796i | ||||
\(555\) | 791.850 | − | 457.175i | 1.42676 | − | 0.823738i | ||||
\(556\) | 137.907 | − | 518.304i | 0.248034 | − | 0.932202i | ||||
\(557\) | −162.430 | + | 281.336i | −0.291615 | + | 0.505092i | −0.974192 | − | 0.225722i | \(-0.927526\pi\) |
0.682577 | + | 0.730814i | \(0.260859\pi\) | |||||||
\(558\) | 0.281108 | + | 0.0367581i | 0.000503777 | + | 6.58748e-5i | ||||
\(559\) | 129.379i | 0.231447i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −497.040 | −0.885989 | ||||||||
\(562\) | 28.4848 | − | 217.837i | 0.0506847 | − | 0.387611i | ||||
\(563\) | −73.8314 | − | 42.6266i | −0.131139 | − | 0.0757133i | 0.432995 | − | 0.901396i | \(-0.357457\pi\) |
−0.564134 | + | 0.825683i | \(0.690790\pi\) | |||||||
\(564\) | −486.580 | − | 129.466i | −0.862731 | − | 0.229549i | ||||
\(565\) | −330.052 | − | 571.667i | −0.584163 | − | 1.01180i | ||||
\(566\) | −625.800 | + | 817.039i | −1.10565 | + | 1.44353i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −121.037 | − | 49.7632i | −0.213094 | − | 0.0876112i | ||||
\(569\) | 14.3756 | + | 24.8993i | 0.0252647 | + | 0.0437597i | 0.878381 | − | 0.477961i | \(-0.158624\pi\) |
−0.853117 | + | 0.521720i | \(0.825290\pi\) | |||||||
\(570\) | −842.015 | + | 349.638i | −1.47722 | + | 0.613400i | ||||
\(571\) | −586.760 | − | 338.766i | −1.02760 | − | 0.593286i | −0.111304 | − | 0.993786i | \(-0.535503\pi\) |
−0.916296 | + | 0.400501i | \(0.868836\pi\) | |||||||
\(572\) | 187.847 | + | 187.190i | 0.328404 | + | 0.327255i | ||||
\(573\) | 1055.42 | 1.84191 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.2000i | 0.0316521i | ||||||||
\(576\) | −1.48529 | + | 5.66201i | −0.00257863 | + | 0.00982988i | ||||
\(577\) | −10.3338 | + | 17.8986i | −0.0179095 | + | 0.0310201i | −0.874841 | − | 0.484410i | \(-0.839034\pi\) |
0.856932 | + | 0.515430i | \(0.172368\pi\) | |||||||
\(578\) | 284.805 | − | 118.262i | 0.492742 | − | 0.204606i | ||||
\(579\) | −901.009 | + | 520.198i | −1.55615 | + | 0.898441i | ||||
\(580\) | −303.743 | − | 1125.69i | −0.523694 | − | 1.94085i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 247.856 | − | 323.598i | 0.425869 | − | 0.556011i | ||||
\(583\) | −539.129 | + | 311.266i | −0.924750 | + | 0.533905i | ||||
\(584\) | 46.8506 | + | 60.7259i | 0.0802237 | + | 0.103983i | ||||
\(585\) | 1.43858 | − | 2.49169i | 0.00245911 | − | 0.00425930i | ||||
\(586\) | 34.4895 | − | 263.758i | 0.0588557 | − | 0.450099i | ||||
\(587\) | 551.489i | 0.939504i | 0.882798 | + | 0.469752i | \(0.155657\pi\) | ||||
−0.882798 | + | 0.469752i | \(0.844343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 34.7825 | 0.0590534 | ||||||||
\(590\) | 728.746 | + | 95.2921i | 1.23516 | + | 0.161512i | ||||
\(591\) | 69.6133 | + | 40.1912i | 0.117789 | + | 0.0680055i | ||||
\(592\) | −2.52271 | − | 720.237i | −0.00426133 | − | 1.21662i | ||||
\(593\) | 22.9656 | + | 39.7776i | 0.0387279 | + | 0.0670787i | 0.884740 | − | 0.466086i | \(-0.154336\pi\) |
−0.846012 | + | 0.533164i | \(0.821003\pi\) | |||||||
\(594\) | 617.951 | + | 473.311i | 1.04032 | + | 0.796821i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.6347 | − | 80.1798i | −0.0362998 | − | 0.134530i | ||||
\(597\) | 345.570 | + | 598.545i | 0.578845 | + | 1.00259i | ||||
\(598\) | 3.02751 | + | 7.29099i | 0.00506272 | + | 0.0121923i | ||||
\(599\) | 573.698 | + | 331.225i | 0.957759 | + | 0.552963i | 0.895483 | − | 0.445096i | \(-0.146831\pi\) |
0.0622766 | + | 0.998059i | \(0.480164\pi\) | |||||||
\(600\) | 67.7505 | + | 504.374i | 0.112917 | + | 0.840623i | ||||
\(601\) | 840.257 | 1.39810 | 0.699049 | − | 0.715074i | \(-0.253607\pi\) | ||||
0.699049 | + | 0.715074i | \(0.253607\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.40952i | 0.0139461i | ||||||||
\(604\) | 263.813 | + | 262.891i | 0.436776 | + | 0.435249i | ||||
\(605\) | 288.245 | − | 499.255i | 0.476438 | − | 0.825215i | ||||
\(606\) | −64.4713 | − | 155.263i | −0.106388 | − | 0.256209i | ||||
\(607\) | −887.606 | + | 512.459i | −1.46228 | + | 0.844249i | −0.999117 | − | 0.0420222i | \(-0.986620\pi\) |
−0.463166 | + | 0.886272i | \(0.653287\pi\) | |||||||
\(608\) | −90.6218 | + | 712.431i | −0.149049 | + | 1.17176i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 172.343 | + | 132.004i | 0.282530 | + | 0.216400i | ||||
\(611\) | 168.828 | − | 97.4732i | 0.276315 | − | 0.159531i | ||||
\(612\) | 4.10495 | + | 1.09222i | 0.00670743 | + | 0.00178467i | ||||
\(613\) | 54.5739 | − | 94.5248i | 0.0890276 | − | 0.154200i | −0.818073 | − | 0.575115i | \(-0.804957\pi\) |
0.907100 | + | 0.420914i | \(0.138291\pi\) | |||||||
\(614\) | 759.159 | + | 99.2690i | 1.23642 | + | 0.161676i | ||||
\(615\) | 744.422i | 1.21044i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 78.9177 | 0.127905 | 0.0639527 | − | 0.997953i | \(-0.479629\pi\) | ||||
0.0639527 | + | 0.997953i | \(0.479629\pi\) | |||||||
\(618\) | −124.025 | + | 948.484i | −0.200688 | + | 1.53476i | ||||
\(619\) | −620.070 | − | 357.997i | −1.00173 | − | 0.578348i | −0.0929689 | − | 0.995669i | \(-0.529636\pi\) |
−0.908759 | + | 0.417321i | \(0.862969\pi\) | |||||||
\(620\) | 10.8478 | − | 40.7699i | 0.0174964 | − | 0.0657580i | ||||
\(621\) | 11.5860 | + | 20.0676i | 0.0186571 | + | 0.0323150i | ||||
\(622\) | −238.816 | + | 311.796i | −0.383949 | + | 0.501281i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 111.042 | + | 190.784i | 0.177952 | + | 0.305744i | ||||
\(625\) | 351.791 | + | 609.321i | 0.562866 | + | 0.974913i | ||||
\(626\) | 788.790 | − | 327.537i | 1.26005 | − | 0.523222i | ||||
\(627\) | 832.033 | + | 480.375i | 1.32701 | + | 0.766148i | ||||
\(628\) | −449.884 | + | 451.463i | −0.716376 | + | 0.718890i | ||||
\(629\) | −522.657 | −0.830933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 849.316i | − | 1.34598i | −0.739650 | − | 0.672992i | \(-0.765009\pi\) | ||
0.739650 | − | 0.672992i | \(-0.234991\pi\) | |||||||
\(632\) | −60.6889 | − | 451.803i | −0.0960267 | − | 0.714878i | ||||
\(633\) | 118.927 | − | 205.987i | 0.187878 | − | 0.325414i | ||||
\(634\) | −205.118 | + | 85.1732i | −0.323530 | + | 0.134343i | ||||
\(635\) | −423.581 | + | 244.555i | −0.667057 | + | 0.385126i | ||||
\(636\) | −500.306 | + | 134.996i | −0.786645 | + | 0.212258i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −747.102 | + | 975.409i | −1.17101 | + | 1.52885i | ||||
\(639\) | 1.29573 | − | 0.748092i | 0.00202775 | − | 0.00117072i | ||||
\(640\) | 806.806 | + | 328.411i | 1.26064 | + | 0.513142i | ||||
\(641\) | −244.045 | + | 422.698i | −0.380725 | + | 0.659435i | −0.991166 | − | 0.132627i | \(-0.957659\pi\) |
0.610441 | + | 0.792062i | \(0.290992\pi\) | |||||||
\(642\) | −92.0444 | + | 703.909i | −0.143371 | + | 1.09643i | ||||
\(643\) | − | 257.106i | − | 0.399854i | −0.979811 | − | 0.199927i | \(-0.935930\pi\) | ||
0.979811 | − | 0.199927i | \(-0.0640705\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 568.522 | 0.881430 | ||||||||
\(646\) | 516.756 | + | 67.5719i | 0.799932 | + | 0.104600i | ||||
\(647\) | 605.816 | + | 349.768i | 0.936346 | + | 0.540600i | 0.888813 | − | 0.458270i | \(-0.151531\pi\) |
0.0475329 | + | 0.998870i | \(0.484864\pi\) | |||||||
\(648\) | 391.763 | + | 507.788i | 0.604573 | + | 0.783624i | ||||
\(649\) | −387.236 | − | 670.713i | −0.596666 | − | 1.03346i | ||||
\(650\) | −156.423 | − | 119.810i | −0.240651 | − | 0.184324i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −176.981 | + | 47.7544i | −0.271444 | + | 0.0732429i | ||||
\(653\) | −138.815 | − | 240.434i | −0.212580 | − | 0.368199i | 0.739941 | − | 0.672671i | \(-0.234853\pi\) |
−0.952521 | + | 0.304472i | \(0.901520\pi\) | |||||||
\(654\) | 224.955 | + | 541.748i | 0.343968 | + | 0.828360i | ||||
\(655\) | 1236.70 | + | 714.009i | 1.88809 | + | 1.09009i | ||||
\(656\) | 508.850 | + | 291.413i | 0.775686 | + | 0.444228i | ||||
\(657\) | −0.876874 | −0.00133466 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 522.721i | 0.793204i | 0.917991 | + | 0.396602i | \(0.129811\pi\) | ||||
−0.917991 | + | 0.396602i | \(0.870189\pi\) | |||||||
\(660\) | 822.557 | − | 825.443i | 1.24630 | − | 1.25067i | ||||
\(661\) | 257.961 | − | 446.802i | 0.390259 | − | 0.675948i | −0.602224 | − | 0.798327i | \(-0.705719\pi\) |
0.992484 | + | 0.122378i | \(0.0390521\pi\) | |||||||
\(662\) | 91.7533 | + | 220.964i | 0.138600 | + | 0.333783i | ||||
\(663\) | 138.728 | − | 80.0945i | 0.209243 | − | 0.120806i | ||||
\(664\) | 105.863 | + | 43.5245i | 0.159432 | + | 0.0655489i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 6.53714 | + | 5.00704i | 0.00981553 | + | 0.00751807i | ||||
\(667\) | −31.6759 | + | 18.2881i | −0.0474901 | + | 0.0274184i | ||||
\(668\) | 16.0288 | − | 60.2420i | 0.0239952 | − | 0.0901827i | ||||
\(669\) | −394.530 | + | 683.346i | −0.589731 | + | 1.02144i | ||||
\(670\) | 1240.88 | + | 162.259i | 1.85206 | + | 0.242178i | ||||
\(671\) | − | 228.762i | − | 0.340927i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1231.64 | −1.83008 | −0.915041 | − | 0.403361i | \(-0.867842\pi\) | ||||
−0.915041 | + | 0.403361i | \(0.867842\pi\) | |||||||
\(674\) | −14.8753 | + | 113.759i | −0.0220702 | + | 0.168781i | ||||
\(675\) | −500.853 | − | 289.167i | −0.742004 | − | 0.428396i | ||||
\(676\) | 570.677 | + | 151.842i | 0.844197 | + | 0.224618i | ||||
\(677\) | −288.282 | − | 499.319i | −0.425822 | − | 0.737546i | 0.570674 | − | 0.821176i | \(-0.306682\pi\) |
−0.996497 | + | 0.0836304i | \(0.973348\pi\) | |||||||
\(678\) | −352.084 | + | 459.677i | −0.519297 | + | 0.677990i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 240.367 | − | 584.637i | 0.353481 | − | 0.859760i | ||||
\(681\) | −643.690 | − | 1114.90i | −0.945213 | − | 1.63716i | ||||
\(682\) | −41.0581 | + | 17.0490i | −0.0602025 | + | 0.0249985i | ||||
\(683\) | −139.772 | − | 80.6973i | −0.204644 | − | 0.118151i | 0.394176 | − | 0.919035i | \(-0.371030\pi\) |
−0.598820 | + | 0.800884i | \(0.704363\pi\) | |||||||
\(684\) | −5.81599 | − | 5.79566i | −0.00850292 | − | 0.00847318i | ||||
\(685\) | −123.619 | −0.180466 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1268.21i | 1.84601i | ||||||||
\(688\) | 222.555 | − | 388.614i | 0.323482 | − | 0.564846i | ||||
\(689\) | 100.317 | − | 173.754i | 0.145598 | − | 0.252183i | ||||
\(690\) | 32.0383 | − | 13.3036i | 0.0464324 | − | 0.0192806i | ||||
\(691\) | −98.4337 | + | 56.8307i | −0.142451 | + | 0.0822442i | −0.569532 | − | 0.821969i | \(-0.692875\pi\) |
0.427081 | + | 0.904214i | \(0.359542\pi\) | |||||||
\(692\) | 277.205 | + | 1027.34i | 0.400585 | + | 1.48460i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 326.865 | − | 426.753i | 0.470988 | − | 0.614917i | ||||
\(695\) | 790.241 | − | 456.246i | 1.13704 | − | 0.656469i | ||||
\(696\) | −809.752 | + | 624.731i | −1.16344 | + | 0.897602i | ||||
\(697\) | 212.762 | − | 368.514i | 0.305254 | − | 0.528715i | ||||
\(698\) | −25.1666 | + | 192.461i | −0.0360552 | + | 0.275732i | ||||
\(699\) | 653.140i | 0.934391i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 331.011 | 0.472198 | 0.236099 | − | 0.971729i | \(-0.424131\pi\) | ||||
0.236099 | + | 0.971729i | \(0.424131\pi\) | |||||||
\(702\) | −248.746 | − | 32.5265i | −0.354339 | − | 0.0463340i | ||||
\(703\) | 874.916 | + | 505.133i | 1.24455 | + | 0.718539i | ||||
\(704\) | −242.232 | − | 885.391i | −0.344080 | − | 1.25766i | ||||
\(705\) | −428.320 | − | 741.872i | −0.607546 | − | 1.05230i | ||||
\(706\) | 503.210 | + | 385.427i | 0.712761 | + | 0.545930i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −167.944 | − | 622.414i | −0.237209 | − | 0.879116i | ||||
\(709\) | 295.675 | + | 512.125i | 0.417032 | + | 0.722320i | 0.995639 | − | 0.0932861i | \(-0.0297371\pi\) |
−0.578608 | + | 0.815606i | \(0.696404\pi\) | |||||||
\(710\) | −85.3848 | − | 205.628i | −0.120260 | − | 0.289616i | ||||
\(711\) | 4.51351 | + | 2.60588i | 0.00634812 | + | 0.00366509i | ||||
\(712\) | −793.958 | + | 106.649i | −1.11511 | + | 0.149788i | ||||
\(713\) | −1.32346 | −0.00185618 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 451.181i | 0.631022i | ||||||||
\(716\) | 126.102 | + | 125.661i | 0.176120 | + | 0.175504i | ||||
\(717\) | −134.559 | + | 233.064i | −0.187670 | + | 0.325054i | ||||
\(718\) | −452.669 | − | 1090.14i | −0.630459 | − | 1.51830i | ||||
\(719\) | −418.810 | + | 241.800i | −0.582489 | + | 0.336300i | −0.762122 | − | 0.647433i | \(-0.775842\pi\) |
0.179633 | + | 0.983734i | \(0.442509\pi\) | |||||||
\(720\) | −8.60719 | + | 5.00964i | −0.0119544 | + | 0.00695784i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −226.545 | − | 173.519i | −0.313775 | − | 0.240332i | ||||
\(723\) | −971.756 | + | 561.044i | −1.34406 | + | 0.775994i | ||||
\(724\) | −649.833 | − | 172.903i | −0.897559 | − | 0.238816i | ||||
\(725\) | 456.438 | − | 790.575i | 0.629570 | − | 1.09045i | ||||
\(726\) | −501.409 | − | 65.5652i | −0.690646 | − | 0.0903101i | ||||
\(727\) | − | 659.508i | − | 0.907163i | −0.891215 | − | 0.453582i | \(-0.850146\pi\) | ||
0.891215 | − | 0.453582i | \(-0.149854\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −736.257 | −1.00995 | ||||||||
\(730\) | −16.9190 | + | 129.388i | −0.0231768 | + | 0.177244i | ||||
\(731\) | −281.438 | − | 162.488i | −0.385004 | − | 0.222282i | ||||
\(732\) | 48.9627 | − | 184.020i | 0.0668890 | − | 0.251393i | ||||
\(733\) | 105.888 | + | 183.403i | 0.144458 | + | 0.250209i | 0.929171 | − | 0.369651i | \(-0.120523\pi\) |
−0.784713 | + | 0.619860i | \(0.787189\pi\) | |||||||
\(734\) | 213.484 | − | 278.723i | 0.290851 | − | 0.379732i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.44812 | − | 27.1077i | 0.00468495 | − | 0.0368311i | ||||
\(737\) | −659.369 | − | 1142.06i | −0.894666 | − | 1.54961i | ||||
\(738\) | −6.19148 | + | 2.57095i | −0.00838953 | + | 0.00348367i | ||||
\(739\) | 213.832 | + | 123.456i | 0.289353 | + | 0.167058i | 0.637650 | − | 0.770326i | \(-0.279907\pi\) |
−0.348297 | + | 0.937384i | \(0.613240\pi\) | |||||||
\(740\) | 864.952 | − | 867.987i | 1.16885 | − | 1.17296i | ||||
\(741\) | −309.636 | −0.417863 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 333.126i | − | 0.448352i | −0.974549 | − | 0.224176i | \(-0.928031\pi\) | ||
0.974549 | − | 0.224176i | \(-0.0719691\pi\) | |||||||
\(744\) | −36.6769 | + | 4.92665i | −0.0492969 | + | 0.00662185i | ||||
\(745\) | 70.6459 | − | 122.362i | 0.0948267 | − | 0.164245i | ||||
\(746\) | −1023.32 | + | 424.922i | −1.37174 | + | 0.569600i | ||||
\(747\) | −1.13329 | + | 0.654305i | −0.00151712 | + | 0.000875911i | ||||
\(748\) | −643.113 | + | 173.529i | −0.859776 | + | 0.231991i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 91.0796 | − | 118.913i | 0.121439 | − | 0.158550i | ||||
\(751\) | 528.203 | − | 304.958i | 0.703333 | − | 0.406069i | −0.105255 | − | 0.994445i | \(-0.533566\pi\) |
0.808588 | + | 0.588376i | \(0.200232\pi\) | |||||||
\(752\) | −674.779 | + | 2.36349i | −0.897313 | + | 0.00314293i | ||||
\(753\) | −476.845 | + | 825.920i | −0.633261 | + | 1.09684i | ||||
\(754\) | 51.3416 | − | 392.635i | 0.0680924 | − | 0.520736i | ||||
\(755\) | 633.640i | 0.839259i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 439.344 | 0.580375 | 0.290187 | − | 0.956970i | \(-0.406282\pi\) | ||||
0.290187 | + | 0.956970i | \(0.406282\pi\) | |||||||
\(758\) | 1487.16 | + | 194.463i | 1.96195 | + | 0.256548i | ||||
\(759\) | −31.6585 | − | 18.2781i | −0.0417108 | − | 0.0240818i | ||||
\(760\) | −967.404 | + | 746.361i | −1.27290 | + | 0.982054i | ||||
\(761\) | −230.484 | − | 399.210i | −0.302870 | − | 0.524586i | 0.673915 | − | 0.738809i | \(-0.264611\pi\) |
−0.976785 | + | 0.214223i | \(0.931278\pi\) | |||||||
\(762\) | 340.601 | + | 260.879i | 0.446984 | + | 0.342361i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1365.59 | − | 368.473i | 1.78742 | − | 0.482294i | ||||
\(765\) | 3.61345 | + | 6.25867i | 0.00472346 | + | 0.00818127i | ||||
\(766\) | −188.855 | − | 454.809i | −0.246547 | − | 0.593746i | ||||
\(767\) | 216.161 | + | 124.801i | 0.281827 | + | 0.162713i | ||||
\(768\) | −5.35253 | − | 764.069i | −0.00696944 | − | 0.994881i | ||||
\(769\) | −1431.37 | −1.86134 | −0.930670 | − | 0.365859i | \(-0.880775\pi\) | ||||
−0.930670 | + | 0.365859i | \(0.880775\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 499.838i | 0.648299i | ||||||||
\(772\) | −984.188 | + | 987.641i | −1.27486 | + | 1.27933i | ||||
\(773\) | 122.740 | − | 212.592i | 0.158784 | − | 0.275022i | −0.775646 | − | 0.631168i | \(-0.782576\pi\) |
0.934430 | + | 0.356146i | \(0.115909\pi\) | |||||||
\(774\) | 1.96346 | + | 4.72849i | 0.00253677 | + | 0.00610916i | ||||
\(775\) | 28.6059 | − | 16.5156i | 0.0369108 | − | 0.0213105i | ||||
\(776\) | 207.721 | − | 505.232i | 0.267681 | − | 0.651073i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 473.186 | + | 362.431i | 0.608208 | + | 0.465849i | ||||
\(779\) | −712.317 | + | 411.256i | −0.914399 | + | 0.527929i | ||||
\(780\) | −96.5678 | + | 362.937i | −0.123805 | + | 0.465304i | ||||
\(781\) | −117.312 | + | 203.190i | −0.150207 | + | 0.260167i | ||||
\(782\) | −19.6624 | − | 2.57108i | −0.0251437 | − | 0.00328783i | ||||
\(783\) | − | 1162.27i | − | 1.48438i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1084.35 | −1.38134 | ||||||||
\(786\) | 162.411 | − | 1242.04i | 0.206630 | − | 1.58020i | ||||
\(787\) | −502.289 | − | 289.997i | −0.638232 | − | 0.368483i | 0.145701 | − | 0.989329i | \(-0.453456\pi\) |
−0.783933 | + | 0.620845i | \(0.786790\pi\) | |||||||
\(788\) | 104.103 | + | 27.6991i | 0.132111 | + | 0.0351512i | ||||
\(789\) | −128.533 | − | 222.626i | −0.162907 | − | 0.282162i | ||||
\(790\) | 471.601 | − | 615.718i | 0.596963 | − | 0.779389i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.70615 | + | 3.99058i | 0.0122552 | + | 0.00503861i | ||||
\(793\) | 36.8634 | + | 63.8493i | 0.0464860 | + | 0.0805161i | ||||
\(794\) | 236.100 | − | 98.0379i | 0.297355 | − | 0.123473i | ||||
\(795\) | −763.516 | − | 440.816i | −0.960397 | − | 0.554486i | ||||
\(796\) | 656.096 | + | 653.802i | 0.824241 | + | 0.821359i | ||||
\(797\) | 1348.22 | 1.69162 | 0.845810 | − | 0.533484i | \(-0.179118\pi\) | ||||
0.845810 | + | 0.533484i | \(0.179118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 489.670i | 0.612853i | ||||||||
\(800\) | 263.751 | + | 628.949i | 0.329689 | + | 0.786186i | ||||
\(801\) | 4.57933 | − | 7.93164i | 0.00571702 | − | 0.00990217i | ||||
\(802\) | 1430.18 | − | 593.866i | 1.78326 | − | 0.740481i | ||||
\(803\) | 119.084 | − | 68.7534i | 0.148299 | − | 0.0856207i | ||||
\(804\) | −285.968 | − | 1059.82i | −0.355682 | − | 1.31818i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.71232 | − | 11.3747i | 0.0108093 | − | 0.0141126i | ||||
\(807\) | −696.209 | + | 401.957i | −0.862713 | + | 0.498088i | ||||
\(808\) | −137.625 | − | 178.384i | −0.170328 | − | 0.220772i | ||||
\(809\) | 348.732 | − | 604.022i | 0.431066 | − | 0.746628i | −0.565899 | − | 0.824474i | \(-0.691471\pi\) |
0.996965 | + | 0.0778461i | \(0.0248043\pi\) | |||||||
\(810\) | −141.476 | + | 1081.94i | −0.174662 | + | 1.33573i | ||||
\(811\) | − | 482.271i | − | 0.594662i | −0.954774 | − | 0.297331i | \(-0.903903\pi\) | ||
0.954774 | − | 0.297331i | \(-0.0960965\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 950.089 | 1.16862 | ||||||||
\(814\) | −1280.37 | − | 167.423i | −1.57294 | − | 0.205680i | ||||
\(815\) | −270.091 | − | 155.937i | −0.331400 | − | 0.191334i | ||||
\(816\) | −554.472 | + | 1.94210i | −0.679500 | + | 0.00238002i | ||||
\(817\) | 314.081 | + | 544.004i | 0.384432 | + | 0.665855i | ||||
\(818\) | −1058.86 | − | 811.020i | −1.29445 | − | 0.991467i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 259.897 | + | 963.197i | 0.316947 | + | 1.17463i | ||||
\(821\) | 193.173 | + | 334.585i | 0.235289 | + | 0.407533i | 0.959357 | − | 0.282196i | \(-0.0910629\pi\) |
−0.724067 | + | 0.689729i | \(0.757730\pi\) | |||||||
\(822\) | 41.5838 | + | 100.144i | 0.0505886 | + | 0.121830i | ||||
\(823\) | −306.907 | − | 177.193i | −0.372913 | − | 0.215301i | 0.301817 | − | 0.953366i | \(-0.402407\pi\) |
−0.674730 | + | 0.738064i | \(0.735740\pi\) | |||||||
\(824\) | 170.665 | + | 1270.53i | 0.207118 | + | 1.54191i | ||||
\(825\) | 912.377 | 1.10591 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1260.47i | − | 1.52414i | −0.647493 | − | 0.762072i | \(-0.724182\pi\) | ||
0.647493 | − | 0.762072i | \(-0.275818\pi\) | |||||||
\(828\) | 0.221296 | + | 0.220522i | 0.000267266 | + | 0.000266332i | ||||
\(829\) | −721.843 | + | 1250.27i | −0.870739 | + | 1.50816i | −0.00950526 | + | 0.999955i | \(0.503026\pi\) |
−0.861234 | + | 0.508209i | \(0.830308\pi\) | |||||||
\(830\) | 74.6803 | + | 179.849i | 0.0899763 | + | 0.216685i | ||||
\(831\) | 921.746 | − | 532.170i | 1.10920 | − | 0.640398i | ||||
\(832\) | 210.284 | + | 208.086i | 0.252745 | + | 0.250103i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −635.432 | − | 486.701i | −0.761909 | − | 0.583574i | ||||
\(835\) | 91.8490 | − | 53.0290i | 0.109999 | − | 0.0635078i | ||||
\(836\) | 1244.27 | + | 331.066i | 1.48836 | + | 0.396012i | ||||
\(837\) | 21.0276 | − | 36.4208i | 0.0251226 | − | 0.0435135i | ||||
\(838\) | 189.117 | + | 24.7293i | 0.225676 | + | 0.0295099i | ||||
\(839\) | − | 44.6511i | − | 0.0532194i | −0.999646 | − | 0.0266097i | \(-0.991529\pi\) | ||
0.999646 | − | 0.0266097i | \(-0.00847114\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 993.593 | 1.18144 | ||||||||
\(842\) | −72.3901 | + | 553.603i | −0.0859740 | + | 0.657485i | ||||
\(843\) | −283.934 | − | 163.930i | −0.336814 | − | 0.194460i | ||||
\(844\) | 81.9621 | − | 308.044i | 0.0971115 | − | 0.364981i | ||||
\(845\) | 502.348 | + | 870.092i | 0.594495 | + | 1.02970i | ||||
\(846\) | 4.69102 | − | 6.12455i | 0.00554494 | − | 0.00723942i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −600.208 | + | 349.339i | −0.707793 | + | 0.411957i | ||||
\(849\) | 767.941 | + | 1330.11i | 0.904524 | + | 1.56668i | ||||
\(850\) | 457.077 | − | 189.796i | 0.537737 | − | 0.223290i | ||||
\(851\) | −33.2902 | − | 19.2201i | −0.0391189 | − | 0.0225853i | ||||
\(852\) | −137.857 | + | 138.341i | −0.161804 | + | 0.162372i | ||||
\(853\) | 118.167 | 0.138531 | 0.0692655 | − | 0.997598i | \(-0.477934\pi\) | ||||
0.0692655 | + | 0.997598i | \(0.477934\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 13.9692i | − | 0.0163382i | ||||||
\(856\) | 126.658 | + | 942.913i | 0.147964 | + | 1.10153i | ||||
\(857\) | −76.5651 | + | 132.615i | −0.0893408 | + | 0.154743i | −0.907233 | − | 0.420629i | \(-0.861809\pi\) |
0.817892 | + | 0.575372i | \(0.195143\pi\) | |||||||
\(858\) | 365.503 | − | 151.771i | 0.425994 | − | 0.176890i | ||||
\(859\) | 118.348 | − | 68.3281i | 0.137774 | − | 0.0795437i | −0.429529 | − | 0.903053i | \(-0.641320\pi\) |
0.567303 | + | 0.823509i | \(0.307987\pi\) | |||||||
\(860\) | 735.603 | − | 198.486i | 0.855353 | − | 0.230797i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −205.981 | + | 268.927i | −0.238957 | + | 0.311980i | ||||
\(863\) | −1266.58 | + | 731.262i | −1.46765 | + | 0.847349i | −0.999344 | − | 0.0362164i | \(-0.988469\pi\) |
−0.468308 | + | 0.883565i | \(0.655136\pi\) | |||||||
\(864\) | 691.204 | + | 525.587i | 0.800004 | + | 0.608319i | ||||
\(865\) | −905.185 | + | 1567.83i | −1.04646 | + | 1.81252i | ||||
\(866\) | 76.5537 | − | 585.444i | 0.0883992 | − | 0.676032i | ||||
\(867\) | − | 460.217i | − | 0.530816i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −817.281 | −0.940484 | ||||||||
\(870\) | −1725.33 | − | 225.607i | −1.98314 | − | 0.259319i | ||||
\(871\) | 368.070 | + | 212.505i | 0.422584 | + | 0.243979i | ||||
\(872\) | 480.204 | + | 622.422i | 0.550693 | + | 0.713787i | ||||
\(873\) | 3.12267 | + | 5.40863i | 0.00357695 | + | 0.00619545i | ||||
\(874\) | 30.4295 | + | 23.3070i | 0.0348163 | + | 0.0266671i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 110.509 | − | 29.8183i | 0.126152 | − | 0.0340392i | ||||
\(877\) | −14.9440 | − | 25.8838i | −0.0170399 | − | 0.0295140i | 0.857380 | − | 0.514684i | \(-0.172091\pi\) |
−0.874420 | + | 0.485170i | \(0.838758\pi\) | |||||||
\(878\) | −250.630 | − | 603.578i | −0.285455 | − | 0.687447i | ||||
\(879\) | −343.788 | − | 198.486i | −0.391113 | − | 0.225809i | ||||
\(880\) | 776.112 | − | 1355.21i | 0.881946 | − | 1.54001i | ||||
\(881\) | 497.832 | 0.565076 | 0.282538 | − | 0.959256i | \(-0.408824\pi\) | ||||
0.282538 | + | 0.959256i | \(0.408824\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1430.98i | − | 1.62059i | −0.586022 | − | 0.810295i | \(-0.699307\pi\) | ||
0.586022 | − | 0.810295i | \(-0.300693\pi\) | |||||||
\(884\) | 151.535 | − | 152.067i | 0.171420 | − | 0.172021i | ||||
\(885\) | 548.405 | − | 949.865i | 0.619666 | − | 1.07329i | ||||
\(886\) | −394.836 | − | 950.862i | −0.445638 | − | 1.07321i | ||||
\(887\) | −1028.15 | + | 593.605i | −1.15914 | + | 0.669228i | −0.951097 | − | 0.308892i | \(-0.900042\pi\) |
−0.208040 | + | 0.978120i | \(0.566708\pi\) | |||||||
\(888\) | −994.117 | − | 408.720i | −1.11950 | − | 0.460271i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1082.01 | − | 828.748i | −1.21574 | − | 0.931178i | ||||
\(891\) | 995.780 | − | 574.914i | 1.11760 | − | 0.645245i | ||||
\(892\) | −271.903 | + | 1021.91i | −0.304824 | + | 1.14564i | ||||
\(893\) | 473.252 | − | 819.696i | 0.529957 | − | 0.917913i | ||||
\(894\) | −122.890 | − | 16.0693i | −0.137461 | − | 0.0179747i | ||||
\(895\) | 302.879i | 0.338412i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 11.7815 | 0.0131344 | ||||||||
\(898\) | 156.164 | − | 1194.27i | 0.173902 | − | 1.32992i | ||||
\(899\) | 57.4887 | + | 33.1911i | 0.0639474 | + | 0.0369201i | ||||
\(900\) | −7.53514 | − | 2.00490i | −0.00837237 | − | 0.00222766i | ||||
\(901\) | 251.978 | + | 436.438i | 0.279665 | + | 0.484393i | ||||
\(902\) | 639.256 | − | 834.607i | 0.708709 | − | 0.925285i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −295.071 | + | 717.691i | −0.326406 | + | 0.793906i | ||||
\(905\) | −572.026 | − | 990.778i | −0.632073 | − | 1.09478i | ||||
\(906\) | 513.314 | − | 213.148i | 0.566571 | − | 0.235263i | ||||
\(907\) | −708.980 | − | 409.330i | −0.781676 | − | 0.451301i | 0.0553481 | − | 0.998467i | \(-0.482373\pi\) |
−0.837024 | + | 0.547166i | \(0.815706\pi\) | |||||||
\(908\) | −1222.10 | − | 1217.83i | −1.34593 | − | 1.34122i | ||||
\(909\) | 2.57584 | 0.00283370 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 774.905i | − | 0.850610i | −0.905050 | − | 0.425305i | \(-0.860167\pi\) | ||
0.905050 | − | 0.425305i | \(-0.139833\pi\) | |||||||
\(912\) | 930.050 | + | 532.630i | 1.01979 | + | 0.584024i | ||||
\(913\) | 102.605 | − | 177.717i | 0.112382 | − | 0.194651i | ||||
\(914\) | 488.803 | − | 202.970i | 0.534795 | − | 0.222068i | ||||
\(915\) | 280.569 | − | 161.986i | 0.306633 | − | 0.177034i | ||||
\(916\) | 442.765 | + | 1640.92i | 0.483367 | + | 1.79140i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 383.157 | − | 500.247i | 0.417383 | − | 0.544931i | ||||
\(919\) | 1468.77 | − | 847.993i | 1.59822 | − | 0.922734i | 0.606393 | − | 0.795165i | \(-0.292616\pi\) |
0.991830 | − | 0.127569i | \(-0.0407175\pi\) | |||||||
\(920\) | 36.8093 | − | 28.3987i | 0.0400101 | − | 0.0308682i | ||||
\(921\) | 571.291 | − | 989.506i | 0.620295 | − | 1.07438i | ||||
\(922\) | 112.747 | − | 862.235i | 0.122286 | − | 0.935179i | ||||
\(923\) | − | 75.6160i | − | 0.0819241i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 959.401 | 1.03719 | ||||||||
\(926\) | −383.253 | − | 50.1148i | −0.413880 | − | 0.0541196i | ||||
\(927\) | −12.6926 | − | 7.32808i | −0.0136921 | − | 0.00790515i | ||||
\(928\) | −829.617 | + | 1091.04i | −0.893984 | + | 1.17568i | ||||
\(929\) | −586.655 | − | 1016.12i | −0.631491 | − | 1.09378i | −0.987247 | − | 0.159196i | \(-0.949110\pi\) |
0.355756 | − | 0.934579i | \(-0.384224\pi\) | |||||||
\(930\) | −49.9833 | − | 38.2840i | −0.0537455 | − | 0.0411656i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 228.028 | + | 845.088i | 0.244665 | + | 0.906747i | ||||
\(933\) | 293.060 | + | 507.594i | 0.314105 | + | 0.544046i | ||||
\(934\) | −502.602 | − | 1210.39i | −0.538118 | − | 1.29592i | ||||
\(935\) | −981.453 | − | 566.642i | −1.04968 | − | 0.606034i | ||||
\(936\) | −3.35212 | + | 0.450276i | −0.00358132 | + | 0.000481064i | ||||
\(937\) | 315.505 | 0.336719 | 0.168359 | − | 0.985726i | \(-0.446153\pi\) | ||||
0.168359 | + | 0.985726i | \(0.446153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 1274.61i | − | 1.35741i | ||||||
\(940\) | −813.204 | − | 810.361i | −0.865111 | − | 0.862086i | ||||
\(941\) | −211.752 | + | 366.766i | −0.225029 | + | 0.389762i | −0.956328 | − | 0.292295i | \(-0.905581\pi\) |
0.731299 | + | 0.682057i | \(0.238914\pi\) | |||||||
\(942\) | 364.760 | + | 878.433i | 0.387219 | + | 0.932519i | ||||
\(943\) | 27.1034 | − | 15.6481i | 0.0287417 | − | 0.0165940i | ||||
\(944\) | −434.601 | − | 746.699i | −0.460383 | − | 0.790995i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −637.398 | − | 488.206i | −0.673782 | − | 0.516074i | ||||
\(947\) | 993.572 | − | 573.639i | 1.04918 | − | 0.605743i | 0.126759 | − | 0.991934i | \(-0.459542\pi\) |
0.922419 | + | 0.386190i | \(0.126209\pi\) | |||||||
\(948\) | −657.434 | − | 174.926i | −0.693496 | − | 0.184521i | ||||
\(949\) | −22.1583 | + | 38.3793i | −0.0233491 | + | 0.0404418i | ||||
\(950\) | −948.569 | − | 124.037i | −0.998493 | − | 0.130565i | ||||
\(951\) | 331.451i | 0.348529i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 736.494 | 0.772816 | 0.386408 | − | 0.922328i | \(-0.373716\pi\) | ||||
0.386408 | + | 0.922328i | \(0.373716\pi\) | |||||||
\(954\) | 1.02945 | − | 7.87270i | 0.00107909 | − | 0.00825230i | ||||
\(955\) | 2084.02 | + | 1203.21i | 2.18222 | + | 1.25991i | ||||
\(956\) | −92.7361 | + | 348.536i | −0.0970042 | + | 0.364577i | ||||
\(957\) | 916.794 | + | 1587.93i | 0.957988 | + | 1.65928i | ||||
\(958\) | −124.849 | + | 163.001i | −0.130322 | + | 0.170148i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 914.377 | − | 924.036i | 0.952476 | − | 0.962538i | ||||
\(961\) | −479.299 | − | 830.170i | −0.498750 | − | 0.863861i | ||||
\(962\) | 384.341 | − | 159.593i | 0.399522 | − | 0.165898i | ||||
\(963\) | −9.41970 | − | 5.43847i | −0.00978162 | − | 0.00564742i | ||||
\(964\) | −1061.47 | + | 1065.19i | −1.10111 | + | 1.10497i | ||||
\(965\) | −2372.17 | −2.45821 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1147.66i | 1.18682i | 0.804899 | + | 0.593411i | \(0.202219\pi\) | ||||
−0.804899 | + | 0.593411i | \(0.797781\pi\) | |||||||
\(968\) | −671.657 | + | 90.2209i | −0.693860 | + | 0.0932034i | ||||
\(969\) | 388.875 | − | 673.551i | 0.401316 | − | 0.695099i | ||||
\(970\) | 858.329 | − | 356.412i | 0.884875 | − | 0.367435i | ||||
\(971\) | 960.111 | − | 554.321i | 0.988786 | − | 0.570876i | 0.0838750 | − | 0.996476i | \(-0.473270\pi\) |
0.904911 | + | 0.425600i | \(0.139937\pi\) | |||||||
\(972\) | −19.0730 | + | 5.14640i | −0.0196224 | + | 0.00529465i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 183.213 | − | 239.201i | 0.188104 | − | 0.245586i | ||||
\(975\) | −254.652 | + | 147.023i | −0.261181 | + | 0.150793i | ||||
\(976\) | −0.893847 | − | 255.195i | −0.000915827 | − | 0.261470i | ||||
\(977\) | −389.513 | + | 674.657i | −0.398683 | + | 0.690539i | −0.993564 | − | 0.113275i | \(-0.963866\pi\) |
0.594881 | + | 0.803814i | \(0.297199\pi\) | |||||||
\(978\) | −35.4700 | + | 271.256i | −0.0362679 | + | 0.277358i | ||||
\(979\) | 1436.21i | 1.46702i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.98769 | −0.00916176 | ||||||||
\(982\) | 235.585 | + | 30.8055i | 0.239903 | + | 0.0313702i | ||||
\(983\) | −68.9305 | − | 39.7970i | −0.0701225 | − | 0.0404853i | 0.464529 | − | 0.885558i | \(-0.346224\pi\) |
−0.534651 | + | 0.845073i | \(0.679557\pi\) | |||||||
\(984\) | 692.862 | − | 534.549i | 0.704128 | − | 0.543241i | ||||
\(985\) | 91.6387 | + | 158.723i | 0.0930343 | + | 0.161140i | ||||
\(986\) | 789.618 | + | 604.797i | 0.800830 | + | 0.613385i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −400.634 | + | 108.102i | −0.405500 | + | 0.109415i | ||||
\(989\) | −11.9506 | − | 20.6991i | −0.0120836 | − | 0.0209293i | ||||
\(990\) | 6.84713 | + | 16.4896i | 0.00691629 | + | 0.0166561i | ||||
\(991\) | 557.931 | + | 322.122i | 0.562998 | + | 0.325047i | 0.754348 | − | 0.656475i | \(-0.227953\pi\) |
−0.191350 | + | 0.981522i | \(0.561286\pi\) | |||||||
\(992\) | −45.7357 | + | 19.1794i | −0.0461045 | + | 0.0193340i | ||||
\(993\) | 357.057 | 0.359574 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1575.85i | 1.58377i | ||||||||
\(996\) | 120.574 | − | 120.997i | 0.121059 | − | 0.121483i | ||||
\(997\) | −869.997 | + | 1506.88i | −0.872615 | + | 1.51141i | −0.0133331 | + | 0.999911i | \(0.504244\pi\) |
−0.859282 | + | 0.511502i | \(0.829089\pi\) | |||||||
\(998\) | 419.104 | + | 1009.31i | 0.419944 | + | 1.01133i | ||||
\(999\) | 1057.85 | − | 610.752i | 1.05891 | − | 0.611363i |
(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 | 196.3.g.j.67.3 | 12 | ||
4.3 | odd | 2 | inner | 196.3.g.j.67.1 | 12 | ||
7.2 | even | 3 | inner | 196.3.g.j.79.1 | 12 | ||
7.3 | odd | 6 | 28.3.c.a.15.6 | yes | 6 | ||
7.4 | even | 3 | 196.3.c.g.99.6 | 6 | |||
7.5 | odd | 6 | 196.3.g.k.79.1 | 12 | |||
7.6 | odd | 2 | 196.3.g.k.67.3 | 12 | |||
21.17 | even | 6 | 252.3.g.a.127.1 | 6 | |||
28.3 | even | 6 | 28.3.c.a.15.5 | ✓ | 6 | ||
28.11 | odd | 6 | 196.3.c.g.99.5 | 6 | |||
28.19 | even | 6 | 196.3.g.k.79.3 | 12 | |||
28.23 | odd | 6 | inner | 196.3.g.j.79.3 | 12 | ||
28.27 | even | 2 | 196.3.g.k.67.1 | 12 | |||
56.3 | even | 6 | 448.3.d.d.127.2 | 6 | |||
56.45 | odd | 6 | 448.3.d.d.127.5 | 6 | |||
84.59 | odd | 6 | 252.3.g.a.127.2 | 6 | |||
112.3 | even | 12 | 1792.3.g.g.127.4 | 12 | |||
112.45 | odd | 12 | 1792.3.g.g.127.10 | 12 | |||
112.59 | even | 12 | 1792.3.g.g.127.9 | 12 | |||
112.101 | odd | 12 | 1792.3.g.g.127.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.3.c.a.15.5 | ✓ | 6 | 28.3 | even | 6 | ||
28.3.c.a.15.6 | yes | 6 | 7.3 | odd | 6 | ||
196.3.c.g.99.5 | 6 | 28.11 | odd | 6 | |||
196.3.c.g.99.6 | 6 | 7.4 | even | 3 | |||
196.3.g.j.67.1 | 12 | 4.3 | odd | 2 | inner | ||
196.3.g.j.67.3 | 12 | 1.1 | even | 1 | trivial | ||
196.3.g.j.79.1 | 12 | 7.2 | even | 3 | inner | ||
196.3.g.j.79.3 | 12 | 28.23 | odd | 6 | inner | ||
196.3.g.k.67.1 | 12 | 28.27 | even | 2 | |||
196.3.g.k.67.3 | 12 | 7.6 | odd | 2 | |||
196.3.g.k.79.1 | 12 | 7.5 | odd | 6 | |||
196.3.g.k.79.3 | 12 | 28.19 | even | 6 | |||
252.3.g.a.127.1 | 6 | 21.17 | even | 6 | |||
252.3.g.a.127.2 | 6 | 84.59 | odd | 6 | |||
448.3.d.d.127.2 | 6 | 56.3 | even | 6 | |||
448.3.d.d.127.5 | 6 | 56.45 | odd | 6 | |||
1792.3.g.g.127.3 | 12 | 112.101 | odd | 12 | |||
1792.3.g.g.127.4 | 12 | 112.3 | even | 12 | |||
1792.3.g.g.127.9 | 12 | 112.59 | even | 12 | |||
1792.3.g.g.127.10 | 12 | 112.45 | odd | 12 |