Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,3,Mod(27,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.27");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.03542500457\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.31 |
Dual form | 38.3.d.a.27.1 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | + | 0.707107i | −0.612372 | + | 0.353553i | ||||
\(3\) | 2.72474 | − | 1.57313i | 0.908248 | − | 0.524377i | 0.0283812 | − | 0.999597i | \(-0.490965\pi\) |
0.879867 | + | 0.475220i | \(0.157631\pi\) | |||||||
\(4\) | 1.00000 | − | 1.73205i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | 0.911684 | − | 0.410891i | \(-0.134782\pi\) |
−0.811684 | + | 0.584096i | \(0.801449\pi\) | |||||||
\(6\) | −2.22474 | + | 3.85337i | −0.370791 | + | 0.642229i | ||||
\(7\) | 6.89898 | 0.985568 | 0.492784 | − | 0.870152i | \(-0.335979\pi\) | ||||
0.492784 | + | 0.870152i | \(0.335979\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 0.449490 | − | 0.778539i | 0.0499433 | − | 0.0865043i | ||||
\(10\) | −1.22474 | − | 0.707107i | −0.122474 | − | 0.0707107i | ||||
\(11\) | −14.8990 | −1.35445 | −0.677226 | − | 0.735775i | \(-0.736818\pi\) | ||||
−0.677226 | + | 0.735775i | \(0.736818\pi\) | |||||||
\(12\) | − | 6.29253i | − | 0.524377i | ||||||
\(13\) | −14.8485 | − | 8.57277i | −1.14219 | − | 0.659444i | −0.195218 | − | 0.980760i | \(-0.562541\pi\) |
−0.946972 | + | 0.321316i | \(0.895875\pi\) | |||||||
\(14\) | −8.44949 | + | 4.87832i | −0.603535 | + | 0.348451i | ||||
\(15\) | 2.72474 | + | 1.57313i | 0.181650 | + | 0.104875i | ||||
\(16\) | −2.00000 | − | 3.46410i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.05051 | + | 1.81954i | 0.0617947 | + | 0.107032i | 0.895268 | − | 0.445529i | \(-0.146984\pi\) |
−0.833473 | + | 0.552560i | \(0.813651\pi\) | |||||||
\(18\) | 1.27135i | 0.0706305i | ||||||||
\(19\) | 11.3485 | + | 15.2385i | 0.597288 | + | 0.802027i | ||||
\(20\) | 2.00000 | 0.100000 | ||||||||
\(21\) | 18.7980 | − | 10.8530i | 0.895141 | − | 0.516810i | ||||
\(22\) | 18.2474 | − | 10.5352i | 0.829429 | − | 0.478871i | ||||
\(23\) | −13.5227 | + | 23.4220i | −0.587944 | + | 1.01835i | 0.406558 | + | 0.913625i | \(0.366729\pi\) |
−0.994501 | + | 0.104723i | \(0.966604\pi\) | |||||||
\(24\) | 4.44949 | + | 7.70674i | 0.185395 | + | 0.321114i | ||||
\(25\) | 12.0000 | − | 20.7846i | 0.480000 | − | 0.831384i | ||||
\(26\) | 24.2474 | 0.932594 | ||||||||
\(27\) | 25.4880i | 0.943998i | ||||||||
\(28\) | 6.89898 | − | 11.9494i | 0.246392 | − | 0.426764i | ||||
\(29\) | −5.54541 | − | 3.20164i | −0.191221 | − | 0.110401i | 0.401333 | − | 0.915932i | \(-0.368547\pi\) |
−0.592554 | + | 0.805531i | \(0.701880\pi\) | |||||||
\(30\) | −4.44949 | −0.148316 | ||||||||
\(31\) | − | 31.1769i | − | 1.00571i | −0.864372 | − | 0.502853i | \(-0.832284\pi\) | ||
0.864372 | − | 0.502853i | \(-0.167716\pi\) | |||||||
\(32\) | 4.89898 | + | 2.82843i | 0.153093 | + | 0.0883883i | ||||
\(33\) | −40.5959 | + | 23.4381i | −1.23018 | + | 0.710244i | ||||
\(34\) | −2.57321 | − | 1.48565i | −0.0756828 | − | 0.0436955i | ||||
\(35\) | 3.44949 | + | 5.97469i | 0.0985568 | + | 0.170705i | ||||
\(36\) | −0.898979 | − | 1.55708i | −0.0249717 | − | 0.0432522i | ||||
\(37\) | − | 28.9199i | − | 0.781620i | −0.920471 | − | 0.390810i | \(-0.872195\pi\) | ||
0.920471 | − | 0.390810i | \(-0.127805\pi\) | |||||||
\(38\) | −24.6742 | − | 10.6387i | −0.649322 | − | 0.279966i | ||||
\(39\) | −53.9444 | −1.38319 | ||||||||
\(40\) | −2.44949 | + | 1.41421i | −0.0612372 | + | 0.0353553i | ||||
\(41\) | 55.9393 | − | 32.2966i | 1.36437 | − | 0.787721i | 0.374170 | − | 0.927360i | \(-0.377928\pi\) |
0.990202 | + | 0.139639i | \(0.0445942\pi\) | |||||||
\(42\) | −15.3485 | + | 26.5843i | −0.365440 | + | 0.632960i | ||||
\(43\) | 37.6691 | + | 65.2449i | 0.876026 | + | 1.51732i | 0.855665 | + | 0.517529i | \(0.173148\pi\) |
0.0203609 | + | 0.999793i | \(0.493518\pi\) | |||||||
\(44\) | −14.8990 | + | 25.8058i | −0.338613 | + | 0.586495i | ||||
\(45\) | 0.898979 | 0.0199773 | ||||||||
\(46\) | − | 38.2480i | − | 0.831478i | ||||||
\(47\) | 5.77015 | − | 9.99420i | 0.122769 | − | 0.212642i | −0.798090 | − | 0.602539i | \(-0.794156\pi\) |
0.920859 | + | 0.389896i | \(0.127489\pi\) | |||||||
\(48\) | −10.8990 | − | 6.29253i | −0.227062 | − | 0.131094i | ||||
\(49\) | −1.40408 | −0.0286547 | ||||||||
\(50\) | 33.9411i | 0.678823i | ||||||||
\(51\) | 5.72474 | + | 3.30518i | 0.112250 | + | 0.0648075i | ||||
\(52\) | −29.6969 | + | 17.1455i | −0.571095 | + | 0.329722i | ||||
\(53\) | −69.2878 | − | 40.0033i | −1.30732 | − | 0.754779i | −0.325669 | − | 0.945484i | \(-0.605589\pi\) |
−0.981647 | + | 0.190705i | \(0.938923\pi\) | |||||||
\(54\) | −18.0227 | − | 31.2162i | −0.333754 | − | 0.578078i | ||||
\(55\) | −7.44949 | − | 12.9029i | −0.135445 | − | 0.234598i | ||||
\(56\) | 19.5133i | 0.348451i | ||||||||
\(57\) | 54.8939 | + | 23.6684i | 0.963050 | + | 0.415235i | ||||
\(58\) | 9.05561 | 0.156131 | ||||||||
\(59\) | 50.9166 | − | 29.3967i | 0.862993 | − | 0.498249i | −0.00202049 | − | 0.999998i | \(-0.500643\pi\) |
0.865013 | + | 0.501749i | \(0.167310\pi\) | |||||||
\(60\) | 5.44949 | − | 3.14626i | 0.0908248 | − | 0.0524377i | ||||
\(61\) | −1.09592 | + | 1.89819i | −0.0179659 | + | 0.0311178i | −0.874869 | − | 0.484360i | \(-0.839052\pi\) |
0.856903 | + | 0.515478i | \(0.172386\pi\) | |||||||
\(62\) | 22.0454 | + | 38.1838i | 0.355571 | + | 0.615867i | ||||
\(63\) | 3.10102 | − | 5.37113i | 0.0492225 | − | 0.0852560i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | − | 17.1455i | − | 0.263777i | ||||||
\(66\) | 33.1464 | − | 57.4113i | 0.502219 | − | 0.869868i | ||||
\(67\) | −51.6589 | − | 29.8253i | −0.771029 | − | 0.445154i | 0.0622127 | − | 0.998063i | \(-0.480184\pi\) |
−0.833241 | + | 0.552909i | \(0.813518\pi\) | |||||||
\(68\) | 4.20204 | 0.0617947 | ||||||||
\(69\) | 85.0920i | 1.23322i | ||||||||
\(70\) | −8.44949 | − | 4.87832i | −0.120707 | − | 0.0696902i | ||||
\(71\) | 87.5227 | − | 50.5313i | 1.23271 | − | 0.711708i | 0.265119 | − | 0.964216i | \(-0.414589\pi\) |
0.967595 | + | 0.252508i | \(0.0812553\pi\) | |||||||
\(72\) | 2.20204 | + | 1.27135i | 0.0305839 | + | 0.0176576i | ||||
\(73\) | 63.6918 | + | 110.317i | 0.872491 | + | 1.51120i | 0.859412 | + | 0.511284i | \(0.170830\pi\) |
0.0130791 | + | 0.999914i | \(0.495837\pi\) | |||||||
\(74\) | 20.4495 | + | 35.4196i | 0.276344 | + | 0.478643i | ||||
\(75\) | − | 75.5103i | − | 1.00680i | ||||||
\(76\) | 37.7423 | − | 4.41761i | 0.496610 | − | 0.0581265i | ||||
\(77\) | −102.788 | −1.33491 | ||||||||
\(78\) | 66.0681 | − | 38.1444i | 0.847027 | − | 0.489031i | ||||
\(79\) | −5.78036 | + | 3.33729i | −0.0731691 | + | 0.0422442i | −0.536138 | − | 0.844130i | \(-0.680117\pi\) |
0.462969 | + | 0.886374i | \(0.346784\pi\) | |||||||
\(80\) | 2.00000 | − | 3.46410i | 0.0250000 | − | 0.0433013i | ||||
\(81\) | 44.1413 | + | 76.4550i | 0.544955 | + | 0.943889i | ||||
\(82\) | −45.6742 | + | 79.1101i | −0.557003 | + | 0.964757i | ||||
\(83\) | −1.30306 | −0.0156995 | −0.00784977 | − | 0.999969i | \(-0.502499\pi\) | ||||
−0.00784977 | + | 0.999969i | \(0.502499\pi\) | |||||||
\(84\) | − | 43.4120i | − | 0.516810i | ||||||
\(85\) | −1.05051 | + | 1.81954i | −0.0123589 | + | 0.0214063i | ||||
\(86\) | −92.2702 | − | 53.2722i | −1.07291 | − | 0.619444i | ||||
\(87\) | −20.1464 | −0.231568 | ||||||||
\(88\) | − | 42.1407i | − | 0.478871i | ||||||
\(89\) | 5.84847 | + | 3.37662i | 0.0657131 | + | 0.0379395i | 0.532497 | − | 0.846432i | \(-0.321254\pi\) |
−0.466783 | + | 0.884372i | \(0.654587\pi\) | |||||||
\(90\) | −1.10102 | + | 0.635674i | −0.0122336 | + | 0.00706305i | ||||
\(91\) | −102.439 | − | 59.1433i | −1.12571 | − | 0.649927i | ||||
\(92\) | 27.0454 | + | 46.8440i | 0.293972 | + | 0.509174i | ||||
\(93\) | −49.0454 | − | 84.9491i | −0.527370 | − | 0.913432i | ||||
\(94\) | 16.3205i | 0.173622i | ||||||||
\(95\) | −7.52270 | + | 17.4473i | −0.0791864 | + | 0.183656i | ||||
\(96\) | 17.7980 | 0.185395 | ||||||||
\(97\) | −114.152 | + | 65.9054i | −1.17682 | + | 0.679437i | −0.955277 | − | 0.295713i | \(-0.904443\pi\) |
−0.221543 | + | 0.975151i | \(0.571109\pi\) | |||||||
\(98\) | 1.71964 | − | 0.992836i | 0.0175474 | − | 0.0101310i | ||||
\(99\) | −6.69694 | + | 11.5994i | −0.0676458 | + | 0.117166i | ||||
\(100\) | −24.0000 | − | 41.5692i | −0.240000 | − | 0.415692i | ||||
\(101\) | −3.24235 | + | 5.61591i | −0.0321024 | + | 0.0556031i | −0.881630 | − | 0.471941i | \(-0.843554\pi\) |
0.849528 | + | 0.527544i | \(0.176887\pi\) | |||||||
\(102\) | −9.34847 | −0.0916517 | ||||||||
\(103\) | 80.0243i | 0.776935i | 0.921462 | + | 0.388467i | \(0.126995\pi\) | ||||
−0.921462 | + | 0.388467i | \(0.873005\pi\) | |||||||
\(104\) | 24.2474 | − | 41.9978i | 0.233149 | − | 0.403825i | ||||
\(105\) | 18.7980 | + | 10.8530i | 0.179028 | + | 0.103362i | ||||
\(106\) | 113.146 | 1.06742 | ||||||||
\(107\) | 80.0243i | 0.747890i | 0.927451 | + | 0.373945i | \(0.121995\pi\) | ||||
−0.927451 | + | 0.373945i | \(0.878005\pi\) | |||||||
\(108\) | 44.1464 | + | 25.4880i | 0.408763 | + | 0.236000i | ||||
\(109\) | −14.2423 | + | 8.22282i | −0.130664 | + | 0.0754387i | −0.563907 | − | 0.825838i | \(-0.690702\pi\) |
0.433243 | + | 0.901277i | \(0.357369\pi\) | |||||||
\(110\) | 18.2474 | + | 10.5352i | 0.165886 | + | 0.0957743i | ||||
\(111\) | −45.4949 | − | 78.7995i | −0.409864 | − | 0.709905i | ||||
\(112\) | −13.7980 | − | 23.8988i | −0.123196 | − | 0.213382i | ||||
\(113\) | − | 132.843i | − | 1.17560i | −0.809006 | − | 0.587801i | \(-0.799994\pi\) | ||
0.809006 | − | 0.587801i | \(-0.200006\pi\) | |||||||
\(114\) | −83.9671 | + | 9.82806i | −0.736553 | + | 0.0862111i | ||||
\(115\) | −27.0454 | −0.235177 | ||||||||
\(116\) | −11.0908 | + | 6.40329i | −0.0956105 | + | 0.0552007i | ||||
\(117\) | −13.3485 | + | 7.70674i | −0.114089 | + | 0.0658696i | ||||
\(118\) | −41.5732 | + | 72.0069i | −0.352315 | + | 0.610228i | ||||
\(119\) | 7.24745 | + | 12.5529i | 0.0609029 | + | 0.105487i | ||||
\(120\) | −4.44949 | + | 7.70674i | −0.0370791 | + | 0.0642229i | ||||
\(121\) | 100.980 | 0.834542 | ||||||||
\(122\) | − | 3.09972i | − | 0.0254076i | ||||||
\(123\) | 101.614 | − | 176.000i | 0.826126 | − | 1.43089i | ||||
\(124\) | −54.0000 | − | 31.1769i | −0.435484 | − | 0.251427i | ||||
\(125\) | 49.0000 | 0.392000 | ||||||||
\(126\) | 8.77101i | 0.0696112i | ||||||||
\(127\) | 108.826 | + | 62.8306i | 0.856896 | + | 0.494729i | 0.862972 | − | 0.505253i | \(-0.168601\pi\) |
−0.00607575 | + | 0.999982i | \(0.501934\pi\) | |||||||
\(128\) | 9.79796 | − | 5.65685i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 205.278 | + | 118.517i | 1.59130 | + | 0.918737i | ||||
\(130\) | 12.1237 | + | 20.9989i | 0.0932594 | + | 0.161530i | ||||
\(131\) | −53.6237 | − | 92.8790i | −0.409341 | − | 0.709000i | 0.585475 | − | 0.810691i | \(-0.300908\pi\) |
−0.994816 | + | 0.101691i | \(0.967575\pi\) | |||||||
\(132\) | 93.7523i | 0.710244i | ||||||||
\(133\) | 78.2929 | + | 105.130i | 0.588668 | + | 0.790452i | ||||
\(134\) | 84.3587 | 0.629542 | ||||||||
\(135\) | −22.0732 | + | 12.7440i | −0.163505 | + | 0.0943998i | ||||
\(136\) | −5.14643 | + | 2.97129i | −0.0378414 | + | 0.0218477i | ||||
\(137\) | 1.05051 | − | 1.81954i | 0.00766796 | − | 0.0132813i | −0.862166 | − | 0.506626i | \(-0.830893\pi\) |
0.869834 | + | 0.493345i | \(0.164226\pi\) | |||||||
\(138\) | −60.1691 | − | 104.216i | −0.436008 | − | 0.755188i | ||||
\(139\) | 15.8712 | − | 27.4897i | 0.114181 | − | 0.197767i | −0.803271 | − | 0.595614i | \(-0.796909\pi\) |
0.917452 | + | 0.397846i | \(0.130242\pi\) | |||||||
\(140\) | 13.7980 | 0.0985568 | ||||||||
\(141\) | − | 36.3089i | − | 0.257510i | ||||||
\(142\) | −71.4620 | + | 123.776i | −0.503253 | + | 0.871661i | ||||
\(143\) | 221.227 | + | 127.725i | 1.54704 | + | 0.893185i | ||||
\(144\) | −3.59592 | −0.0249717 | ||||||||
\(145\) | − | 6.40329i | − | 0.0441606i | ||||||
\(146\) | −156.012 | − | 90.0739i | −1.06858 | − | 0.616944i | ||||
\(147\) | −3.82577 | + | 2.20881i | −0.0260256 | + | 0.0150259i | ||||
\(148\) | −50.0908 | − | 28.9199i | −0.338451 | − | 0.195405i | ||||
\(149\) | −94.8383 | − | 164.265i | −0.636498 | − | 1.10245i | −0.986196 | − | 0.165585i | \(-0.947049\pi\) |
0.349697 | − | 0.936863i | \(-0.386284\pi\) | |||||||
\(150\) | 53.3939 | + | 92.4809i | 0.355959 | + | 0.616539i | ||||
\(151\) | 16.2707i | 0.107753i | 0.998548 | + | 0.0538764i | \(0.0171577\pi\) | ||||
−0.998548 | + | 0.0538764i | \(0.982842\pi\) | |||||||
\(152\) | −43.1010 | + | 32.0983i | −0.283559 | + | 0.211173i | ||||
\(153\) | 1.88877 | 0.0123449 | ||||||||
\(154\) | 125.889 | − | 72.6819i | 0.817460 | − | 0.471961i | ||||
\(155\) | 27.0000 | − | 15.5885i | 0.174194 | − | 0.100571i | ||||
\(156\) | −53.9444 | + | 93.4344i | −0.345797 | + | 0.598939i | ||||
\(157\) | −135.076 | − | 233.958i | −0.860354 | − | 1.49018i | −0.871588 | − | 0.490239i | \(-0.836909\pi\) |
0.0112344 | − | 0.999937i | \(-0.496424\pi\) | |||||||
\(158\) | 4.71964 | − | 8.17466i | 0.0298712 | − | 0.0517384i | ||||
\(159\) | −251.722 | −1.58316 | ||||||||
\(160\) | 5.65685i | 0.0353553i | ||||||||
\(161\) | −93.2929 | + | 161.588i | −0.579459 | + | 1.00365i | ||||
\(162\) | −108.124 | − | 62.4253i | −0.667430 | − | 0.385341i | ||||
\(163\) | −156.697 | −0.961331 | −0.480665 | − | 0.876904i | \(-0.659605\pi\) | ||||
−0.480665 | + | 0.876904i | \(0.659605\pi\) | |||||||
\(164\) | − | 129.186i | − | 0.787721i | ||||||
\(165\) | −40.5959 | − | 23.4381i | −0.246036 | − | 0.142049i | ||||
\(166\) | 1.59592 | − | 0.921404i | 0.00961396 | − | 0.00555062i | ||||
\(167\) | −78.0834 | − | 45.0815i | −0.467565 | − | 0.269949i | 0.247655 | − | 0.968848i | \(-0.420340\pi\) |
−0.715220 | + | 0.698899i | \(0.753674\pi\) | |||||||
\(168\) | 30.6969 | + | 53.1687i | 0.182720 | + | 0.316480i | ||||
\(169\) | 62.4847 | + | 108.227i | 0.369732 | + | 0.640394i | ||||
\(170\) | − | 2.97129i | − | 0.0174782i | ||||||
\(171\) | 16.9648 | − | 1.98567i | 0.0992093 | − | 0.0116121i | ||||
\(172\) | 150.677 | 0.876026 | ||||||||
\(173\) | −263.379 | + | 152.062i | −1.52242 | + | 0.878969i | −0.522771 | + | 0.852473i | \(0.675102\pi\) |
−0.999649 | + | 0.0264959i | \(0.991565\pi\) | |||||||
\(174\) | 24.6742 | − | 14.2457i | 0.141806 | − | 0.0818717i | ||||
\(175\) | 82.7878 | − | 143.393i | 0.473073 | − | 0.819386i | ||||
\(176\) | 29.7980 | + | 51.6116i | 0.169307 | + | 0.293248i | ||||
\(177\) | 92.4898 | − | 160.197i | 0.522541 | − | 0.905068i | ||||
\(178\) | −9.55051 | −0.0536546 | ||||||||
\(179\) | 315.198i | 1.76088i | 0.474156 | + | 0.880441i | \(0.342753\pi\) | ||||
−0.474156 | + | 0.880441i | \(0.657247\pi\) | |||||||
\(180\) | 0.898979 | − | 1.55708i | 0.00499433 | − | 0.00865043i | ||||
\(181\) | −27.8939 | − | 16.1045i | −0.154110 | − | 0.0889753i | 0.420962 | − | 0.907078i | \(-0.361693\pi\) |
−0.575072 | + | 0.818103i | \(0.695026\pi\) | |||||||
\(182\) | 167.283 | 0.919135 | ||||||||
\(183\) | 6.89610i | 0.0376836i | ||||||||
\(184\) | −66.2474 | − | 38.2480i | −0.360040 | − | 0.207869i | ||||
\(185\) | 25.0454 | − | 14.4600i | 0.135381 | − | 0.0781620i | ||||
\(186\) | 120.136 | + | 69.3607i | 0.645894 | + | 0.372907i | ||||
\(187\) | −15.6515 | − | 27.1092i | −0.0836980 | − | 0.144969i | ||||
\(188\) | −11.5403 | − | 19.9884i | −0.0613846 | − | 0.106321i | ||||
\(189\) | 175.841i | 0.930375i | ||||||||
\(190\) | −3.12372 | − | 26.6879i | −0.0164407 | − | 0.140462i | ||||
\(191\) | 280.252 | 1.46729 | 0.733644 | − | 0.679534i | \(-0.237818\pi\) | ||||
0.733644 | + | 0.679534i | \(0.237818\pi\) | |||||||
\(192\) | −21.7980 | + | 12.5851i | −0.113531 | + | 0.0655472i | ||||
\(193\) | 42.0153 | − | 24.2575i | 0.217696 | − | 0.125687i | −0.387187 | − | 0.922001i | \(-0.626553\pi\) |
0.604883 | + | 0.796314i | \(0.293220\pi\) | |||||||
\(194\) | 93.2043 | − | 161.435i | 0.480435 | − | 0.832137i | ||||
\(195\) | −26.9722 | − | 46.7172i | −0.138319 | − | 0.239575i | ||||
\(196\) | −1.40408 | + | 2.43194i | −0.00716368 | + | 0.0124079i | ||||
\(197\) | 251.909 | 1.27873 | 0.639363 | − | 0.768905i | \(-0.279198\pi\) | ||||
0.639363 | + | 0.768905i | \(0.279198\pi\) | |||||||
\(198\) | − | 18.9418i | − | 0.0956657i | ||||||
\(199\) | −129.694 | + | 224.637i | −0.651729 | + | 1.12883i | 0.330974 | + | 0.943640i | \(0.392623\pi\) |
−0.982703 | + | 0.185188i | \(0.940710\pi\) | |||||||
\(200\) | 58.7878 | + | 33.9411i | 0.293939 | + | 0.169706i | ||||
\(201\) | −187.677 | −0.933714 | ||||||||
\(202\) | − | 9.17074i | − | 0.0453997i | ||||||
\(203\) | −38.2577 | − | 22.0881i | −0.188461 | − | 0.108808i | ||||
\(204\) | 11.4495 | − | 6.61037i | 0.0561249 | − | 0.0324038i | ||||
\(205\) | 55.9393 | + | 32.2966i | 0.272875 | + | 0.157544i | ||||
\(206\) | −56.5857 | − | 98.0093i | −0.274688 | − | 0.475773i | ||||
\(207\) | 12.1566 | + | 21.0559i | 0.0587277 | + | 0.101719i | ||||
\(208\) | 68.5821i | 0.329722i | ||||||||
\(209\) | −169.081 | − | 227.038i | −0.808998 | − | 1.08631i | ||||
\(210\) | −30.6969 | −0.146176 | ||||||||
\(211\) | 60.2503 | − | 34.7855i | 0.285546 | − | 0.164860i | −0.350385 | − | 0.936606i | \(-0.613949\pi\) |
0.635932 | + | 0.771745i | \(0.280616\pi\) | |||||||
\(212\) | −138.576 | + | 80.0066i | −0.653658 | + | 0.377390i | ||||
\(213\) | 158.985 | − | 275.370i | 0.746407 | − | 1.29281i | ||||
\(214\) | −56.5857 | − | 98.0093i | −0.264419 | − | 0.457988i | ||||
\(215\) | −37.6691 | + | 65.2449i | −0.175205 | + | 0.303464i | ||||
\(216\) | −72.0908 | −0.333754 | ||||||||
\(217\) | − | 215.089i | − | 0.991193i | ||||||
\(218\) | 11.6288 | − | 20.1417i | 0.0533432 | − | 0.0923932i | ||||
\(219\) | 347.088 | + | 200.391i | 1.58488 | + | 0.915029i | ||||
\(220\) | −29.7980 | −0.135445 | ||||||||
\(221\) | − | 36.0231i | − | 0.163001i | ||||||
\(222\) | 111.439 | + | 64.3395i | 0.501979 | + | 0.289818i | ||||
\(223\) | −5.47730 | + | 3.16232i | −0.0245619 | + | 0.0141808i | −0.512231 | − | 0.858848i | \(-0.671181\pi\) |
0.487669 | + | 0.873029i | \(0.337847\pi\) | |||||||
\(224\) | 33.7980 | + | 19.5133i | 0.150884 | + | 0.0871128i | ||||
\(225\) | −10.7878 | − | 18.6849i | −0.0479456 | − | 0.0830442i | ||||
\(226\) | 93.9342 | + | 162.699i | 0.415638 | + | 0.719906i | ||||
\(227\) | 55.7402i | 0.245552i | 0.992434 | + | 0.122776i | \(0.0391796\pi\) | ||||
−0.992434 | + | 0.122776i | \(0.960820\pi\) | |||||||
\(228\) | 95.8888 | − | 71.4106i | 0.420565 | − | 0.313204i | ||||
\(229\) | −132.313 | −0.577787 | −0.288894 | − | 0.957361i | \(-0.593287\pi\) | ||||
−0.288894 | + | 0.957361i | \(0.593287\pi\) | |||||||
\(230\) | 33.1237 | − | 19.1240i | 0.144016 | − | 0.0831478i | ||||
\(231\) | −280.070 | + | 161.699i | −1.21243 | + | 0.699994i | ||||
\(232\) | 9.05561 | − | 15.6848i | 0.0390328 | − | 0.0676068i | ||||
\(233\) | 111.859 | + | 193.745i | 0.480080 | + | 0.831523i | 0.999739 | − | 0.0228507i | \(-0.00727424\pi\) |
−0.519659 | + | 0.854374i | \(0.673941\pi\) | |||||||
\(234\) | 10.8990 | − | 18.8776i | 0.0465768 | − | 0.0806734i | ||||
\(235\) | 11.5403 | 0.0491077 | ||||||||
\(236\) | − | 117.587i | − | 0.498249i | ||||||
\(237\) | −10.5000 | + | 18.1865i | −0.0443038 | + | 0.0767364i | ||||
\(238\) | −17.7526 | − | 10.2494i | −0.0745906 | − | 0.0430649i | ||||
\(239\) | −71.3235 | −0.298425 | −0.149212 | − | 0.988805i | \(-0.547674\pi\) | ||||
−0.149212 | + | 0.988805i | \(0.547674\pi\) | |||||||
\(240\) | − | 12.5851i | − | 0.0524377i | ||||||
\(241\) | 120.727 | + | 69.7018i | 0.500942 | + | 0.289219i | 0.729103 | − | 0.684405i | \(-0.239938\pi\) |
−0.228160 | + | 0.973624i | \(0.573271\pi\) | |||||||
\(242\) | −123.674 | + | 71.4034i | −0.511051 | + | 0.295055i | ||||
\(243\) | 41.8888 | + | 24.1845i | 0.172382 | + | 0.0995247i | ||||
\(244\) | 2.19184 | + | 3.79637i | 0.00898293 | + | 0.0155589i | ||||
\(245\) | −0.702041 | − | 1.21597i | −0.00286547 | − | 0.00496315i | ||||
\(246\) | 287.406i | 1.16832i | ||||||||
\(247\) | −37.8712 | − | 323.556i | −0.153325 | − | 1.30994i | ||||
\(248\) | 88.1816 | 0.355571 | ||||||||
\(249\) | −3.55051 | + | 2.04989i | −0.0142591 | + | 0.00823248i | ||||
\(250\) | −60.0125 | + | 34.6482i | −0.240050 | + | 0.138593i | ||||
\(251\) | −120.038 | + | 207.912i | −0.478239 | + | 0.828334i | −0.999689 | − | 0.0249476i | \(-0.992058\pi\) |
0.521450 | + | 0.853282i | \(0.325391\pi\) | |||||||
\(252\) | −6.20204 | − | 10.7423i | −0.0246113 | − | 0.0426280i | ||||
\(253\) | 201.474 | − | 348.964i | 0.796342 | − | 1.37930i | ||||
\(254\) | −177.712 | −0.699652 | ||||||||
\(255\) | 6.61037i | 0.0259230i | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 8.37857 | + | 4.83737i | 0.0326014 | + | 0.0188224i | 0.516212 | − | 0.856461i | \(-0.327342\pi\) |
−0.483611 | + | 0.875283i | \(0.660675\pi\) | |||||||
\(258\) | −335.217 | −1.29929 | ||||||||
\(259\) | − | 199.518i | − | 0.770340i | ||||||
\(260\) | −29.6969 | − | 17.1455i | −0.114219 | − | 0.0659444i | ||||
\(261\) | −4.98521 | + | 2.87821i | −0.0191004 | + | 0.0110276i | ||||
\(262\) | 131.351 | + | 75.8354i | 0.501339 | + | 0.289448i | ||||
\(263\) | 56.9620 | + | 98.6611i | 0.216586 | + | 0.375137i | 0.953762 | − | 0.300563i | \(-0.0971747\pi\) |
−0.737176 | + | 0.675700i | \(0.763841\pi\) | |||||||
\(264\) | −66.2929 | − | 114.823i | −0.251109 | − | 0.434934i | ||||
\(265\) | − | 80.0066i | − | 0.301912i | ||||||
\(266\) | −170.227 | − | 73.3962i | −0.639951 | − | 0.275926i | ||||
\(267\) | 21.2474 | 0.0795785 | ||||||||
\(268\) | −103.318 | + | 59.6506i | −0.385514 | + | 0.222577i | ||||
\(269\) | −348.090 | + | 200.970i | −1.29402 | + | 0.747100i | −0.979364 | − | 0.202106i | \(-0.935221\pi\) |
−0.314652 | + | 0.949207i | \(0.601888\pi\) | |||||||
\(270\) | 18.0227 | − | 31.2162i | 0.0667508 | − | 0.115616i | ||||
\(271\) | −199.492 | − | 345.530i | −0.736133 | − | 1.27502i | −0.954224 | − | 0.299092i | \(-0.903316\pi\) |
0.218091 | − | 0.975928i | \(-0.430017\pi\) | |||||||
\(272\) | 4.20204 | − | 7.27815i | 0.0154487 | − | 0.0267579i | ||||
\(273\) | −372.161 | −1.36323 | ||||||||
\(274\) | 2.97129i | 0.0108441i | ||||||||
\(275\) | −178.788 | + | 309.669i | −0.650137 | + | 1.12607i | ||||
\(276\) | 147.384 | + | 85.0920i | 0.533999 | + | 0.308304i | ||||
\(277\) | 529.444 | 1.91135 | 0.955675 | − | 0.294424i | \(-0.0951278\pi\) | ||||
0.955675 | + | 0.294424i | \(0.0951278\pi\) | |||||||
\(278\) | 44.8905i | 0.161476i | ||||||||
\(279\) | −24.2724 | − | 14.0137i | −0.0869980 | − | 0.0502283i | ||||
\(280\) | −16.8990 | + | 9.75663i | −0.0603535 | + | 0.0348451i | ||||
\(281\) | 47.4092 | + | 27.3717i | 0.168716 | + | 0.0974082i | 0.581980 | − | 0.813203i | \(-0.302278\pi\) |
−0.413264 | + | 0.910611i | \(0.635611\pi\) | |||||||
\(282\) | 25.6742 | + | 44.4691i | 0.0910434 | + | 0.157692i | ||||
\(283\) | 74.4671 | + | 128.981i | 0.263135 | + | 0.455762i | 0.967073 | − | 0.254498i | \(-0.0819103\pi\) |
−0.703939 | + | 0.710261i | \(0.748577\pi\) | |||||||
\(284\) | − | 202.125i | − | 0.711708i | ||||||
\(285\) | 6.94949 | + | 59.3737i | 0.0243842 | + | 0.208329i | ||||
\(286\) | −361.262 | −1.26315 | ||||||||
\(287\) | 385.924 | − | 222.813i | 1.34468 | − | 0.776353i | ||||
\(288\) | 4.40408 | − | 2.54270i | 0.0152920 | − | 0.00882881i | ||||
\(289\) | 142.293 | − | 246.458i | 0.492363 | − | 0.852797i | ||||
\(290\) | 4.52781 | + | 7.84239i | 0.0156131 | + | 0.0270427i | ||||
\(291\) | −207.356 | + | 359.151i | −0.712563 | + | 1.23420i | ||||
\(292\) | 254.767 | 0.872491 | ||||||||
\(293\) | − | 145.685i | − | 0.497218i | −0.968604 | − | 0.248609i | \(-0.920027\pi\) | ||
0.968604 | − | 0.248609i | \(-0.0799734\pi\) | |||||||
\(294\) | 3.12372 | − | 5.41045i | 0.0106249 | − | 0.0184029i | ||||
\(295\) | 50.9166 | + | 29.3967i | 0.172599 | + | 0.0996498i | ||||
\(296\) | 81.7980 | 0.276344 | ||||||||
\(297\) | − | 379.744i | − | 1.27860i | ||||||
\(298\) | 232.305 | + | 134.122i | 0.779548 | + | 0.450072i | ||||
\(299\) | 401.583 | − | 231.854i | 1.34309 | − | 0.775431i | ||||
\(300\) | −130.788 | − | 75.5103i | −0.435959 | − | 0.251701i | ||||
\(301\) | 259.879 | + | 450.123i | 0.863384 | + | 1.49542i | ||||
\(302\) | −11.5051 | − | 19.9274i | −0.0380964 | − | 0.0659848i | ||||
\(303\) | 20.4026i | 0.0673352i | ||||||||
\(304\) | 30.0908 | − | 69.7893i | 0.0989829 | − | 0.229570i | ||||
\(305\) | −2.19184 | −0.00718635 | ||||||||
\(306\) | −2.31327 | + | 1.33557i | −0.00755970 | + | 0.00436459i | ||||
\(307\) | 98.0380 | − | 56.6023i | 0.319342 | − | 0.184372i | −0.331757 | − | 0.943365i | \(-0.607641\pi\) |
0.651099 | + | 0.758993i | \(0.274308\pi\) | |||||||
\(308\) | −102.788 | + | 178.034i | −0.333726 | + | 0.578031i | ||||
\(309\) | 125.889 | + | 218.046i | 0.407407 | + | 0.705650i | ||||
\(310\) | −22.0454 | + | 38.1838i | −0.0711142 | + | 0.123173i | ||||
\(311\) | −105.666 | −0.339763 | −0.169882 | − | 0.985464i | \(-0.554339\pi\) | ||||
−0.169882 | + | 0.985464i | \(0.554339\pi\) | |||||||
\(312\) | − | 152.578i | − | 0.489031i | ||||||
\(313\) | −124.121 | + | 214.984i | −0.396552 | + | 0.686849i | −0.993298 | − | 0.115582i | \(-0.963127\pi\) |
0.596746 | + | 0.802431i | \(0.296460\pi\) | |||||||
\(314\) | 330.866 | + | 191.026i | 1.05371 | + | 0.608362i | ||||
\(315\) | 6.20204 | 0.0196890 | ||||||||
\(316\) | 13.3492i | 0.0422442i | ||||||||
\(317\) | −196.061 | − | 113.196i | −0.618488 | − | 0.357084i | 0.157792 | − | 0.987472i | \(-0.449562\pi\) |
−0.776280 | + | 0.630388i | \(0.782896\pi\) | |||||||
\(318\) | 308.295 | − | 177.994i | 0.969482 | − | 0.559730i | ||||
\(319\) | 82.6209 | + | 47.7012i | 0.259000 | + | 0.149534i | ||||
\(320\) | −4.00000 | − | 6.92820i | −0.0125000 | − | 0.0216506i | ||||
\(321\) | 125.889 | + | 218.046i | 0.392177 | + | 0.679270i | ||||
\(322\) | − | 263.872i | − | 0.819478i | ||||||
\(323\) | −15.8054 | + | 36.6572i | −0.0489330 | + | 0.113490i | ||||
\(324\) | 176.565 | 0.544955 | ||||||||
\(325\) | −356.363 | + | 205.746i | −1.09650 | + | 0.633066i | ||||
\(326\) | 191.914 | − | 110.801i | 0.588693 | − | 0.339882i | ||||
\(327\) | −25.8712 | + | 44.8102i | −0.0791167 | + | 0.137034i | ||||
\(328\) | 91.3485 | + | 158.220i | 0.278501 | + | 0.482379i | ||||
\(329\) | 39.8082 | − | 68.9498i | 0.120997 | − | 0.209574i | ||||
\(330\) | 66.2929 | 0.200887 | ||||||||
\(331\) | − | 293.328i | − | 0.886188i | −0.896475 | − | 0.443094i | \(-0.853881\pi\) | ||
0.896475 | − | 0.443094i | \(-0.146119\pi\) | |||||||
\(332\) | −1.30306 | + | 2.25697i | −0.00392488 | + | 0.00679810i | ||||
\(333\) | −22.5153 | − | 12.9992i | −0.0676135 | − | 0.0390367i | ||||
\(334\) | 127.510 | 0.381766 | ||||||||
\(335\) | − | 59.6506i | − | 0.178061i | ||||||
\(336\) | −75.1918 | − | 43.4120i | −0.223785 | − | 0.129202i | ||||
\(337\) | −399.393 | + | 230.590i | −1.18514 | + | 0.684243i | −0.957199 | − | 0.289431i | \(-0.906534\pi\) |
−0.227945 | + | 0.973674i | \(0.573201\pi\) | |||||||
\(338\) | −153.056 | − | 88.3667i | −0.452827 | − | 0.261440i | ||||
\(339\) | −208.980 | − | 361.963i | −0.616459 | − | 1.06774i | ||||
\(340\) | 2.10102 | + | 3.63907i | 0.00617947 | + | 0.0107032i | ||||
\(341\) | 464.504i | 1.36218i | ||||||||
\(342\) | −19.3735 | + | 14.4279i | −0.0566476 | + | 0.0421867i | ||||
\(343\) | −347.737 | −1.01381 | ||||||||
\(344\) | −184.540 | + | 106.544i | −0.536454 | + | 0.309722i | ||||
\(345\) | −73.6918 | + | 42.5460i | −0.213600 | + | 0.123322i | ||||
\(346\) | 215.048 | − | 372.474i | 0.621525 | − | 1.07651i | ||||
\(347\) | −152.129 | − | 263.495i | −0.438412 | − | 0.759351i | 0.559156 | − | 0.829063i | \(-0.311125\pi\) |
−0.997567 | + | 0.0697116i | \(0.977792\pi\) | |||||||
\(348\) | −20.1464 | + | 34.8946i | −0.0578920 | + | 0.100272i | ||||
\(349\) | 50.4337 | 0.144509 | 0.0722545 | − | 0.997386i | \(-0.476981\pi\) | ||||
0.0722545 | + | 0.997386i | \(0.476981\pi\) | |||||||
\(350\) | 234.159i | 0.669026i | ||||||||
\(351\) | 218.502 | − | 378.457i | 0.622514 | − | 1.07823i | ||||
\(352\) | −72.9898 | − | 42.1407i | −0.207357 | − | 0.119718i | ||||
\(353\) | −316.817 | −0.897500 | −0.448750 | − | 0.893657i | \(-0.648131\pi\) | ||||
−0.448750 | + | 0.893657i | \(0.648131\pi\) | |||||||
\(354\) | 261.601i | 0.738985i | ||||||||
\(355\) | 87.5227 | + | 50.5313i | 0.246543 | + | 0.142342i | ||||
\(356\) | 11.6969 | − | 6.75323i | 0.0328566 | − | 0.0189697i | ||||
\(357\) | 39.4949 | + | 22.8024i | 0.110630 | + | 0.0638722i | ||||
\(358\) | −222.879 | − | 386.037i | −0.622566 | − | 1.07832i | ||||
\(359\) | −74.7043 | − | 129.392i | −0.208090 | − | 0.360423i | 0.743023 | − | 0.669266i | \(-0.233391\pi\) |
−0.951113 | + | 0.308844i | \(0.900058\pi\) | |||||||
\(360\) | 2.54270i | 0.00706305i | ||||||||
\(361\) | −103.424 | + | 345.868i | −0.286494 | + | 0.958082i | ||||
\(362\) | 45.5505 | 0.125830 | ||||||||
\(363\) | 275.144 | − | 158.854i | 0.757971 | − | 0.437615i | ||||
\(364\) | −204.879 | + | 118.287i | −0.562853 | + | 0.324963i | ||||
\(365\) | −63.6918 | + | 110.317i | −0.174498 | + | 0.302240i | ||||
\(366\) | −4.87628 | − | 8.44596i | −0.0133232 | − | 0.0230764i | ||||
\(367\) | −117.038 | + | 202.716i | −0.318905 | + | 0.552359i | −0.980260 | − | 0.197714i | \(-0.936648\pi\) |
0.661355 | + | 0.750073i | \(0.269982\pi\) | |||||||
\(368\) | 108.182 | 0.293972 | ||||||||
\(369\) | − | 58.0679i | − | 0.157366i | ||||||
\(370\) | −20.4495 | + | 35.4196i | −0.0552689 | + | 0.0957285i | ||||
\(371\) | −478.015 | − | 275.982i | −1.28845 | − | 0.743887i | ||||
\(372\) | −196.182 | −0.527370 | ||||||||
\(373\) | 639.738i | 1.71512i | 0.514387 | + | 0.857558i | \(0.328019\pi\) | ||||
−0.514387 | + | 0.857558i | \(0.671981\pi\) | |||||||
\(374\) | 38.3383 | + | 22.1346i | 0.102509 | + | 0.0591834i | ||||
\(375\) | 133.512 | − | 77.0835i | 0.356033 | − | 0.205556i | ||||
\(376\) | 28.2679 | + | 16.3205i | 0.0751805 | + | 0.0434055i | ||||
\(377\) | 54.8939 | + | 95.0790i | 0.145607 | + | 0.252199i | ||||
\(378\) | −124.338 | − | 215.360i | −0.328937 | − | 0.569736i | ||||
\(379\) | − | 108.366i | − | 0.285927i | −0.989728 | − | 0.142963i | \(-0.954337\pi\) | ||
0.989728 | − | 0.142963i | \(-0.0456631\pi\) | |||||||
\(380\) | 22.6969 | + | 30.4770i | 0.0597288 | + | 0.0802027i | ||||
\(381\) | 395.363 | 1.03770 | ||||||||
\(382\) | −343.237 | + | 198.168i | −0.898527 | + | 0.518765i | ||||
\(383\) | 215.552 | − | 124.449i | 0.562800 | − | 0.324933i | −0.191469 | − | 0.981499i | \(-0.561325\pi\) |
0.754268 | + | 0.656566i | \(0.227992\pi\) | |||||||
\(384\) | 17.7980 | − | 30.8270i | 0.0463489 | − | 0.0802786i | ||||
\(385\) | −51.3939 | − | 89.0168i | −0.133491 | − | 0.231212i | ||||
\(386\) | −34.3054 | + | 59.4186i | −0.0888740 | + | 0.153934i | ||||
\(387\) | 67.7276 | 0.175007 | ||||||||
\(388\) | 263.622i | 0.679437i | ||||||||
\(389\) | 335.560 | − | 581.207i | 0.862623 | − | 1.49411i | −0.00676592 | − | 0.999977i | \(-0.502154\pi\) |
0.869389 | − | 0.494129i | \(-0.164513\pi\) | |||||||
\(390\) | 66.0681 | + | 38.1444i | 0.169405 | + | 0.0978063i | ||||
\(391\) | −56.8230 | −0.145327 | ||||||||
\(392\) | − | 3.97134i | − | 0.0101310i | ||||||
\(393\) | −292.222 | − | 168.714i | −0.743567 | − | 0.429299i | ||||
\(394\) | −308.524 | + | 178.127i | −0.783057 | + | 0.452098i | ||||
\(395\) | −5.78036 | − | 3.33729i | −0.0146338 | − | 0.00844884i | ||||
\(396\) | 13.3939 | + | 23.1989i | 0.0338229 | + | 0.0585830i | ||||
\(397\) | 46.6816 | + | 80.8550i | 0.117586 | + | 0.203665i | 0.918811 | − | 0.394699i | \(-0.129151\pi\) |
−0.801225 | + | 0.598364i | \(0.795818\pi\) | |||||||
\(398\) | − | 366.830i | − | 0.921684i | ||||||
\(399\) | 378.712 | + | 163.288i | 0.949152 | + | 0.409243i | ||||
\(400\) | −96.0000 | −0.240000 | ||||||||
\(401\) | 242.484 | − | 139.998i | 0.604699 | − | 0.349123i | −0.166189 | − | 0.986094i | \(-0.553146\pi\) |
0.770888 | + | 0.636971i | \(0.219813\pi\) | |||||||
\(402\) | 229.856 | − | 132.707i | 0.571781 | − | 0.330118i | ||||
\(403\) | −267.272 | + | 462.929i | −0.663207 | + | 1.14871i | ||||
\(404\) | 6.48469 | + | 11.2318i | 0.0160512 | + | 0.0278015i | ||||
\(405\) | −44.1413 | + | 76.4550i | −0.108991 | + | 0.188778i | ||||
\(406\) | 62.4745 | 0.153878 | ||||||||
\(407\) | 430.878i | 1.05867i | ||||||||
\(408\) | −9.34847 | + | 16.1920i | −0.0229129 | + | 0.0396863i | ||||
\(409\) | −555.833 | − | 320.910i | −1.35900 | − | 0.784621i | −0.369514 | − | 0.929225i | \(-0.620476\pi\) |
−0.989490 | + | 0.144604i | \(0.953809\pi\) | |||||||
\(410\) | −91.3485 | −0.222801 | ||||||||
\(411\) | − | 6.61037i | − | 0.0160836i | ||||||
\(412\) | 138.606 | + | 80.0243i | 0.336423 | + | 0.194234i | ||||
\(413\) | 351.272 | − | 202.807i | 0.850539 | − | 0.491059i | ||||
\(414\) | −29.7775 | − | 17.1921i | −0.0719264 | − | 0.0415268i | ||||
\(415\) | −0.651531 | − | 1.12848i | −0.00156995 | − | 0.00271924i | ||||
\(416\) | −48.4949 | − | 83.9956i | −0.116574 | − | 0.201913i | ||||
\(417\) | − | 99.8698i | − | 0.239496i | ||||||
\(418\) | 367.621 | + | 158.506i | 0.879476 | + | 0.379201i | ||||
\(419\) | 668.879 | 1.59637 | 0.798184 | − | 0.602413i | \(-0.205794\pi\) | ||||
0.798184 | + | 0.602413i | \(0.205794\pi\) | |||||||
\(420\) | 37.5959 | − | 21.7060i | 0.0895141 | − | 0.0516810i | ||||
\(421\) | 433.711 | − | 250.403i | 1.03019 | − | 0.594782i | 0.113153 | − | 0.993578i | \(-0.463905\pi\) |
0.917040 | + | 0.398795i | \(0.130572\pi\) | |||||||
\(422\) | −49.1941 | + | 85.2067i | −0.116574 | + | 0.201912i | ||||
\(423\) | −5.18725 | − | 8.98458i | −0.0122630 | − | 0.0212401i | ||||
\(424\) | 113.146 | − | 195.975i | 0.266855 | − | 0.462206i | ||||
\(425\) | 50.4245 | 0.118646 | ||||||||
\(426\) | 449.677i | 1.05558i | ||||||||
\(427\) | −7.56072 | + | 13.0955i | −0.0177066 | + | 0.0306687i | ||||
\(428\) | 138.606 | + | 80.0243i | 0.323846 | + | 0.186973i | ||||
\(429\) | 803.716 | 1.87346 | ||||||||
\(430\) | − | 106.544i | − | 0.247778i | ||||||
\(431\) | 120.553 | + | 69.6015i | 0.279706 | + | 0.161488i | 0.633290 | − | 0.773914i | \(-0.281704\pi\) |
−0.353584 | + | 0.935403i | \(0.615037\pi\) | |||||||
\(432\) | 88.2929 | − | 50.9759i | 0.204382 | − | 0.118000i | ||||
\(433\) | 180.349 | + | 104.125i | 0.416510 | + | 0.240472i | 0.693583 | − | 0.720377i | \(-0.256031\pi\) |
−0.277073 | + | 0.960849i | \(0.589364\pi\) | |||||||
\(434\) | 152.091 | + | 263.429i | 0.350440 | + | 0.606979i | ||||
\(435\) | −10.0732 | − | 17.4473i | −0.0231568 | − | 0.0401088i | ||||
\(436\) | 32.8913i | 0.0754387i | ||||||||
\(437\) | −510.379 | + | 59.7381i | −1.16791 | + | 0.136700i | ||||
\(438\) | −566.792 | −1.29405 | ||||||||
\(439\) | 65.6748 | − | 37.9173i | 0.149601 | − | 0.0863721i | −0.423331 | − | 0.905975i | \(-0.639139\pi\) |
0.572932 | + | 0.819603i | \(0.305806\pi\) | |||||||
\(440\) | 36.4949 | − | 21.0703i | 0.0829429 | − | 0.0478871i | ||||
\(441\) | −0.631120 | + | 1.09313i | −0.00143111 | + | 0.00247876i | ||||
\(442\) | 25.4722 | + | 44.1191i | 0.0576294 | + | 0.0998170i | ||||
\(443\) | 227.628 | − | 394.264i | 0.513834 | − | 0.889986i | −0.486038 | − | 0.873938i | \(-0.661558\pi\) |
0.999871 | − | 0.0160481i | \(-0.00510848\pi\) | |||||||
\(444\) | −181.980 | −0.409864 | ||||||||
\(445\) | 6.75323i | 0.0151758i | ||||||||
\(446\) | 4.47219 | − | 7.74607i | 0.0100273 | − | 0.0173679i | ||||
\(447\) | −516.820 | − | 298.386i | −1.15620 | − | 0.667531i | ||||
\(448\) | −55.1918 | −0.123196 | ||||||||
\(449\) | − | 8.44993i | − | 0.0188194i | −0.999956 | − | 0.00940972i | \(-0.997005\pi\) | ||
0.999956 | − | 0.00940972i | \(-0.00299525\pi\) | |||||||
\(450\) | 26.4245 | + | 15.2562i | 0.0587211 | + | 0.0339026i | ||||
\(451\) | −833.438 | + | 481.186i | −1.84798 | + | 1.06693i | ||||
\(452\) | −230.091 | − | 132.843i | −0.509050 | − | 0.293900i | ||||
\(453\) | 25.5959 | + | 44.3334i | 0.0565031 | + | 0.0978663i | ||||
\(454\) | −39.4143 | − | 68.2675i | −0.0868156 | − | 0.150369i | ||||
\(455\) | − | 118.287i | − | 0.259971i | ||||||
\(456\) | −66.9444 | + | 155.263i | −0.146808 | + | 0.340490i | ||||
\(457\) | 208.424 | 0.456071 | 0.228036 | − | 0.973653i | \(-0.426770\pi\) | ||||
0.228036 | + | 0.973653i | \(0.426770\pi\) | |||||||
\(458\) | 162.050 | − | 93.5596i | 0.353821 | − | 0.204279i | ||||
\(459\) | −46.3763 | + | 26.7754i | −0.101038 | + | 0.0583341i | ||||
\(460\) | −27.0454 | + | 46.8440i | −0.0587944 | + | 0.101835i | ||||
\(461\) | 308.808 | + | 534.871i | 0.669865 | + | 1.16024i | 0.977942 | + | 0.208878i | \(0.0669813\pi\) |
−0.308077 | + | 0.951361i | \(0.599685\pi\) | |||||||
\(462\) | 228.677 | − | 396.079i | 0.494971 | − | 0.857315i | ||||
\(463\) | 640.958 | 1.38436 | 0.692179 | − | 0.721725i | \(-0.256651\pi\) | ||||
0.692179 | + | 0.721725i | \(0.256651\pi\) | |||||||
\(464\) | 25.6131i | 0.0552007i | ||||||||
\(465\) | 49.0454 | − | 84.9491i | 0.105474 | − | 0.182686i | ||||
\(466\) | −273.997 | − | 158.192i | −0.587976 | − | 0.339468i | ||||
\(467\) | 164.111 | 0.351416 | 0.175708 | − | 0.984442i | \(-0.443779\pi\) | ||||
0.175708 | + | 0.984442i | \(0.443779\pi\) | |||||||
\(468\) | 30.8270i | 0.0658696i | ||||||||
\(469\) | −356.394 | − | 205.764i | −0.759902 | − | 0.438729i | ||||
\(470\) | −14.1339 | + | 8.16023i | −0.0300722 | + | 0.0173622i | ||||
\(471\) | −736.093 | − | 424.983i | −1.56283 | − | 0.902300i | ||||
\(472\) | 83.1464 | + | 144.014i | 0.176158 | + | 0.305114i | ||||
\(473\) | −561.232 | − | 972.082i | −1.18654 | − | 2.05514i | ||||
\(474\) | − | 29.6985i | − | 0.0626550i | ||||||
\(475\) | 452.908 | − | 53.0114i | 0.953491 | − | 0.111603i | ||||
\(476\) | 28.9898 | 0.0609029 | ||||||||
\(477\) | −62.2883 | + | 35.9621i | −0.130583 | + | 0.0753923i | ||||
\(478\) | 87.3531 | − | 50.4333i | 0.182747 | − | 0.105509i | ||||
\(479\) | −401.401 | + | 695.247i | −0.837998 | + | 1.45146i | 0.0535671 | + | 0.998564i | \(0.482941\pi\) |
−0.891566 | + | 0.452892i | \(0.850392\pi\) | |||||||
\(480\) | 8.89898 | + | 15.4135i | 0.0185395 | + | 0.0321114i | ||||
\(481\) | −247.924 | + | 429.417i | −0.515434 | + | 0.892759i | ||||
\(482\) | −197.146 | −0.409017 | ||||||||
\(483\) | 587.048i | 1.21542i | ||||||||
\(484\) | 100.980 | − | 174.902i | 0.208636 | − | 0.361367i | ||||
\(485\) | −114.152 | − | 65.9054i | −0.235364 | − | 0.135887i | ||||
\(486\) | −68.4041 | −0.140749 | ||||||||
\(487\) | 454.391i | 0.933041i | 0.884510 | + | 0.466521i | \(0.154493\pi\) | ||||
−0.884510 | + | 0.466521i | \(0.845507\pi\) | |||||||
\(488\) | −5.36888 | − | 3.09972i | −0.0110018 | − | 0.00635189i | ||||
\(489\) | −426.959 | + | 246.505i | −0.873127 | + | 0.504100i | ||||
\(490\) | 1.71964 | + | 0.992836i | 0.00350947 | + | 0.00202620i | ||||
\(491\) | −259.826 | − | 450.031i | −0.529177 | − | 0.916561i | −0.999421 | − | 0.0340247i | \(-0.989168\pi\) |
0.470244 | − | 0.882536i | \(-0.344166\pi\) | |||||||
\(492\) | −203.227 | − | 352.000i | −0.413063 | − | 0.715446i | ||||
\(493\) | − | 13.4534i | − | 0.0272889i | ||||||
\(494\) | 275.171 | + | 369.495i | 0.557027 | + | 0.747966i | ||||
\(495\) | −13.3939 | −0.0270583 | ||||||||
\(496\) | −108.000 | + | 62.3538i | −0.217742 | + | 0.125713i | ||||
\(497\) | 603.817 | − | 348.614i | 1.21492 | − | 0.701437i | ||||
\(498\) | 2.89898 | − | 5.02118i | 0.00582124 | − | 0.0100827i | ||||
\(499\) | −221.543 | − | 383.724i | −0.443974 | − | 0.768986i | 0.554006 | − | 0.832513i | \(-0.313098\pi\) |
−0.997980 | + | 0.0635269i | \(0.979765\pi\) | |||||||
\(500\) | 49.0000 | − | 84.8705i | 0.0980000 | − | 0.169741i | ||||
\(501\) | −283.677 | −0.566221 | ||||||||
\(502\) | − | 339.519i | − | 0.676332i | ||||||
\(503\) | 120.841 | − | 209.302i | 0.240240 | − | 0.416107i | −0.720543 | − | 0.693410i | \(-0.756107\pi\) |
0.960782 | + | 0.277303i | \(0.0894406\pi\) | |||||||
\(504\) | 15.1918 | + | 8.77101i | 0.0301425 | + | 0.0174028i | ||||
\(505\) | −6.48469 | −0.0128410 | ||||||||
\(506\) | 569.856i | 1.12620i | ||||||||
\(507\) | 340.510 | + | 196.593i | 0.671617 | + | 0.387758i | ||||
\(508\) | 217.652 | − | 125.661i | 0.428448 | − | 0.247365i | ||||
\(509\) | 357.485 | + | 206.394i | 0.702329 | + | 0.405490i | 0.808214 | − | 0.588889i | \(-0.200434\pi\) |
−0.105886 | + | 0.994378i | \(0.533768\pi\) | |||||||
\(510\) | −4.67423 | − | 8.09601i | −0.00916517 | − | 0.0158745i | ||||
\(511\) | 439.409 | + | 761.078i | 0.859900 | + | 1.48939i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −388.398 | + | 289.249i | −0.757112 | + | 0.563839i | ||||
\(514\) | −13.6821 | −0.0266190 | ||||||||
\(515\) | −69.3031 | + | 40.0121i | −0.134569 | + | 0.0776935i | ||||
\(516\) | 410.555 | − | 237.034i | 0.795649 | − | 0.459368i | ||||
\(517\) | −85.9694 | + | 148.903i | −0.166285 | + | 0.288014i | ||||
\(518\) | 141.081 | + | 244.359i | 0.272356 | + | 0.471735i | ||||
\(519\) | −478.426 | + | 828.659i | −0.921823 | + | 1.59664i | ||||
\(520\) | 48.4949 | 0.0932594 | ||||||||
\(521\) | − | 888.839i | − | 1.70602i | −0.521891 | − | 0.853012i | \(-0.674773\pi\) | ||
0.521891 | − | 0.853012i | \(-0.325227\pi\) | |||||||
\(522\) | 4.07041 | − | 7.05015i | 0.00779771 | − | 0.0135060i | ||||
\(523\) | 132.856 | + | 76.7047i | 0.254027 | + | 0.146663i | 0.621607 | − | 0.783329i | \(-0.286480\pi\) |
−0.367580 | + | 0.929992i | \(0.619813\pi\) | |||||||
\(524\) | −214.495 | −0.409341 | ||||||||
\(525\) | − | 520.944i | − | 0.992275i | ||||||
\(526\) | −139.528 | − | 80.5564i | −0.265262 | − | 0.153149i | ||||
\(527\) | 56.7276 | − | 32.7517i | 0.107642 | − | 0.0621474i | ||||
\(528\) | 162.384 | + | 93.7523i | 0.307545 | + | 0.177561i | ||||
\(529\) | −101.227 | − | 175.330i | −0.191355 | − | 0.331437i | ||||
\(530\) | 56.5732 | + | 97.9877i | 0.106742 | + | 0.184882i | ||||
\(531\) | − | 52.8541i | − | 0.0995368i | ||||||
\(532\) | 260.384 | − | 30.4770i | 0.489443 | − | 0.0572876i | ||||
\(533\) | −1107.48 | −2.07783 | ||||||||
\(534\) | −26.0227 | + | 15.0242i | −0.0487317 | + | 0.0281352i | ||||
\(535\) | −69.3031 | + | 40.0121i | −0.129538 | + | 0.0747890i | ||||
\(536\) | 84.3587 | − | 146.114i | 0.157386 | − | 0.272600i | ||||
\(537\) | 495.848 | + | 858.834i | 0.923367 | + | 1.59932i | ||||
\(538\) | 284.215 | − | 492.274i | 0.528280 | − | 0.915007i | ||||
\(539\) | 20.9194 | 0.0388115 | ||||||||
\(540\) | 50.9759i | 0.0943998i | ||||||||
\(541\) | 446.424 | − | 773.229i | 0.825183 | − | 1.42926i | −0.0765964 | − | 0.997062i | \(-0.524405\pi\) |
0.901779 | − | 0.432197i | \(-0.142261\pi\) | |||||||
\(542\) | 488.654 | + | 282.124i | 0.901575 | + | 0.520525i | ||||
\(543\) | −101.338 | −0.186627 | ||||||||
\(544\) | 11.8852i | 0.0218477i | ||||||||
\(545\) | −14.2423 | − | 8.22282i | −0.0261327 | − | 0.0150877i | ||||
\(546\) | 455.803 | − | 263.158i | 0.834803 | − | 0.481974i | ||||
\(547\) | −748.841 | − | 432.343i | −1.36900 | − | 0.790390i | −0.378196 | − | 0.925726i | \(-0.623455\pi\) |
−0.990800 | + | 0.135336i | \(0.956789\pi\) | |||||||
\(548\) | −2.10102 | − | 3.63907i | −0.00383398 | − | 0.00664065i | ||||
\(549\) | 0.985208 | + | 1.70643i | 0.00179455 | + | 0.00310825i | ||||
\(550\) | − | 505.688i | − | 0.919433i | ||||||
\(551\) | −14.1436 | − | 120.838i | −0.0256690 | − | 0.219306i | ||||
\(552\) | −240.677 | −0.436008 | ||||||||
\(553\) | −39.8786 | + | 23.0239i | −0.0721131 | + | 0.0416345i | ||||
\(554\) | −648.434 | + | 374.373i | −1.17046 | + | 0.675764i | ||||
\(555\) | 45.4949 | − | 78.7995i | 0.0819728 | − | 0.141981i | ||||
\(556\) | −31.7423 | − | 54.9794i | −0.0570906 | − | 0.0988837i | ||||
\(557\) | −374.853 | + | 649.265i | −0.672986 | + | 1.16565i | 0.304068 | + | 0.952650i | \(0.401655\pi\) |
−0.977053 | + | 0.212995i | \(0.931678\pi\) | |||||||
\(558\) | 39.6367 | 0.0710336 | ||||||||
\(559\) | − | 1291.71i | − | 2.31076i | ||||||
\(560\) | 13.7980 | − | 23.8988i | 0.0246392 | − | 0.0426764i | ||||
\(561\) | −85.2929 | − | 49.2439i | −0.152037 | − | 0.0877787i | ||||
\(562\) | −77.4189 | −0.137756 | ||||||||
\(563\) | 162.777i | 0.289125i | 0.989496 | + | 0.144563i | \(0.0461775\pi\) | ||||
−0.989496 | + | 0.144563i | \(0.953823\pi\) | |||||||
\(564\) | −62.8888 | − | 36.3089i | −0.111505 | − | 0.0643774i | ||||
\(565\) | 115.045 | − | 66.4215i | 0.203620 | − | 0.117560i | ||||
\(566\) | −182.406 | − | 105.312i | −0.322273 | − | 0.186064i | ||||
\(567\) | 304.530 | + | 527.462i | 0.537090 | + | 0.930267i | ||||
\(568\) | 142.924 | + | 247.552i | 0.251627 | + | 0.435830i | ||||
\(569\) | 296.076i | 0.520345i | 0.965562 | + | 0.260173i | \(0.0837795\pi\) | ||||
−0.965562 | + | 0.260173i | \(0.916221\pi\) | |||||||
\(570\) | −50.4949 | − | 67.8036i | −0.0885875 | − | 0.118954i | ||||
\(571\) | 274.758 | 0.481188 | 0.240594 | − | 0.970626i | \(-0.422658\pi\) | ||||
0.240594 | + | 0.970626i | \(0.422658\pi\) | |||||||
\(572\) | 442.454 | − | 255.451i | 0.773521 | − | 0.446593i | ||||
\(573\) | 763.615 | − | 440.873i | 1.33266 | − | 0.769413i | ||||
\(574\) | −315.106 | + | 545.779i | −0.548964 | + | 0.950834i | ||||
\(575\) | 324.545 | + | 562.128i | 0.564426 | + | 0.977614i | ||||
\(576\) | −3.59592 | + | 6.22831i | −0.00624291 | + | 0.0108130i | ||||
\(577\) | 524.595 | 0.909177 | 0.454588 | − | 0.890702i | \(-0.349786\pi\) | ||||
0.454588 | + | 0.890702i | \(0.349786\pi\) | |||||||
\(578\) | 402.465i | 0.696306i | ||||||||
\(579\) | 76.3207 | − | 132.191i | 0.131815 | − | 0.228310i | ||||
\(580\) | −11.0908 | − | 6.40329i | −0.0191221 | − | 0.0110401i | ||||
\(581\) | −8.98979 | −0.0154730 | ||||||||
\(582\) | − | 586.491i | − | 1.00772i | ||||||
\(583\) | 1032.32 | + | 596.008i | 1.77070 | + | 1.02231i | ||||
\(584\) | −312.025 | + | 180.148i | −0.534289 | + | 0.308472i | ||||
\(585\) | −13.3485 | − | 7.70674i | −0.0228179 | − | 0.0131739i | ||||
\(586\) | 103.015 | + | 178.427i | 0.175793 | + | 0.304483i | ||||
\(587\) | 375.568 | + | 650.503i | 0.639809 | + | 1.10818i | 0.985474 | + | 0.169824i | \(0.0543200\pi\) |
−0.345665 | + | 0.938358i | \(0.612347\pi\) | |||||||
\(588\) | 8.83523i | 0.0150259i | ||||||||
\(589\) | 475.090 | − | 353.810i | 0.806604 | − | 0.600697i | ||||
\(590\) | −83.1464 | −0.140926 | ||||||||
\(591\) | 686.388 | − | 396.286i | 1.16140 | − | 0.670535i | ||||
\(592\) | −100.182 | + | 57.8399i | −0.169226 | + | 0.0977025i | ||||
\(593\) | 285.030 | − | 493.687i | 0.480658 | − | 0.832524i | −0.519096 | − | 0.854716i | \(-0.673731\pi\) |
0.999754 | + | 0.0221922i | \(0.00706458\pi\) | |||||||
\(594\) | 268.520 | + | 465.090i | 0.452054 | + | 0.782980i | ||||
\(595\) | −7.24745 | + | 12.5529i | −0.0121806 | + | 0.0210974i | ||||
\(596\) | −379.353 | −0.636498 | ||||||||
\(597\) | 816.104i | 1.36701i | ||||||||
\(598\) | −327.891 | + | 567.924i | −0.548313 | + | 0.949706i | ||||
\(599\) | −341.447 | − | 197.134i | −0.570028 | − | 0.329106i | 0.187133 | − | 0.982335i | \(-0.440081\pi\) |
−0.757160 | + | 0.653229i | \(0.773414\pi\) | |||||||
\(600\) | 213.576 | 0.355959 | ||||||||
\(601\) | − | 241.665i | − | 0.402105i | −0.979580 | − | 0.201053i | \(-0.935564\pi\) | ||
0.979580 | − | 0.201053i | \(-0.0644362\pi\) | |||||||
\(602\) | −636.570 | − | 367.524i | −1.05743 | − | 0.610505i | ||||
\(603\) | −46.4403 | + | 26.8123i | −0.0770154 | + | 0.0444649i | ||||
\(604\) | 28.1816 | + | 16.2707i | 0.0466583 | + | 0.0269382i | ||||
\(605\) | 50.4898 | + | 87.4509i | 0.0834542 | + | 0.144547i | ||||
\(606\) | −14.4268 | − | 24.9879i | −0.0238066 | − | 0.0412342i | ||||
\(607\) | − | 369.224i | − | 0.608276i | −0.952628 | − | 0.304138i | \(-0.901632\pi\) | ||
0.952628 | − | 0.304138i | \(-0.0983685\pi\) | |||||||
\(608\) | 12.4949 | + | 106.751i | 0.0205508 | + | 0.175578i | ||||
\(609\) | −138.990 | −0.228226 | ||||||||
\(610\) | 2.68444 | − | 1.54986i | 0.00440072 | − | 0.00254076i | ||||
\(611\) | −171.356 | + | 98.9324i | −0.280451 | + | 0.161919i | ||||
\(612\) | 1.88877 | − | 3.27145i | 0.00308623 | − | 0.00534551i | ||||
\(613\) | −190.171 | − | 329.386i | −0.310230 | − | 0.537334i | 0.668182 | − | 0.743998i | \(-0.267073\pi\) |
−0.978412 | + | 0.206664i | \(0.933739\pi\) | |||||||
\(614\) | −80.0477 | + | 138.647i | −0.130371 | + | 0.225809i | ||||
\(615\) | 203.227 | 0.330450 | ||||||||
\(616\) | − | 290.728i | − | 0.471961i | ||||||
\(617\) | −277.869 | + | 481.283i | −0.450355 | + | 0.780037i | −0.998408 | − | 0.0564062i | \(-0.982036\pi\) |
0.548053 | + | 0.836444i | \(0.315369\pi\) | |||||||
\(618\) | −308.363 | − | 178.034i | −0.498970 | − | 0.288080i | ||||
\(619\) | −624.152 | −1.00832 | −0.504162 | − | 0.863609i | \(-0.668198\pi\) | ||||
−0.504162 | + | 0.863609i | \(0.668198\pi\) | |||||||
\(620\) | − | 62.3538i | − | 0.100571i | ||||||
\(621\) | −596.979 | − | 344.666i | −0.961319 | − | 0.555018i | ||||
\(622\) | 129.414 | − | 74.7174i | 0.208062 | − | 0.120124i | ||||
\(623\) | 40.3485 | + | 23.2952i | 0.0647648 | + | 0.0373920i | ||||
\(624\) | 107.889 | + | 186.869i | 0.172899 | + | 0.299469i | ||||
\(625\) | −275.500 | − | 477.180i | −0.440800 | − | 0.763488i | ||||
\(626\) | − | 351.067i | − | 0.560810i | ||||||
\(627\) | −817.863 | − | 352.635i | −1.30441 | − | 0.562417i | ||||
\(628\) | −540.302 | −0.860354 | ||||||||
\(629\) | 52.6209 | − | 30.3807i | 0.0836581 | − | 0.0483000i | ||||
\(630\) | −7.59592 | + | 4.38551i | −0.0120570 | + | 0.00696112i | ||||
\(631\) | −42.7247 | + | 74.0014i | −0.0677096 | + | 0.117276i | −0.897893 | − | 0.440214i | \(-0.854902\pi\) |
0.830183 | + | 0.557491i | \(0.188236\pi\) | |||||||
\(632\) | −9.43928 | − | 16.3493i | −0.0149356 | − | 0.0258692i | ||||
\(633\) | 109.444 | − | 189.563i | 0.172898 | − | 0.299468i | ||||
\(634\) | 320.166 | 0.504993 | ||||||||
\(635\) | 125.661i | 0.197892i | ||||||||
\(636\) | −251.722 | + | 435.995i | −0.395789 | + | 0.685527i | ||||
\(637\) | 20.8485 | + | 12.0369i | 0.0327292 | + | 0.0188962i | ||||
\(638\) | −134.919 | −0.211472 | ||||||||
\(639\) | − | 90.8531i | − | 0.142180i | ||||||
\(640\) | 9.79796 | + | 5.65685i | 0.0153093 | + | 0.00883883i | ||||
\(641\) | 599.893 | − | 346.348i | 0.935870 | − | 0.540325i | 0.0472069 | − | 0.998885i | \(-0.484968\pi\) |
0.888663 | + | 0.458560i | \(0.151635\pi\) | |||||||
\(642\) | −308.363 | − | 178.034i | −0.480317 | − | 0.277311i | ||||
\(643\) | 252.123 | + | 436.690i | 0.392105 | + | 0.679145i | 0.992727 | − | 0.120388i | \(-0.0384138\pi\) |
−0.600622 | + | 0.799533i | \(0.705080\pi\) | |||||||
\(644\) | 186.586 | + | 323.176i | 0.289729 | + | 0.501826i | ||||
\(645\) | 237.034i | 0.367495i | ||||||||
\(646\) | −6.56301 | − | 56.0718i | −0.0101595 | − | 0.0867984i | ||||
\(647\) | −797.868 | −1.23318 | −0.616591 | − | 0.787284i | \(-0.711487\pi\) | ||||
−0.616591 | + | 0.787284i | \(0.711487\pi\) | |||||||
\(648\) | −216.247 | + | 124.851i | −0.333715 | + | 0.192671i | ||||
\(649\) | −758.605 | + | 437.981i | −1.16888 | + | 0.674855i | ||||
\(650\) | 290.969 | − | 503.974i | 0.447645 | − | 0.775344i | ||||
\(651\) | −338.363 | − | 586.062i | −0.519759 | − | 0.900249i | ||||
\(652\) | −156.697 | + | 271.407i | −0.240333 | + | 0.416268i | ||||
\(653\) | −651.383 | −0.997523 | −0.498762 | − | 0.866739i | \(-0.666212\pi\) | ||||
−0.498762 | + | 0.866739i | \(0.666212\pi\) | |||||||
\(654\) | − | 73.1747i | − | 0.111888i | ||||||
\(655\) | 53.6237 | − | 92.8790i | 0.0818683 | − | 0.141800i | ||||
\(656\) | −223.757 | − | 129.186i | −0.341093 | − | 0.196930i | ||||
\(657\) | 114.515 | 0.174300 | ||||||||
\(658\) | 112.594i | 0.171116i | ||||||||
\(659\) | −395.082 | − | 228.101i | −0.599518 | − | 0.346132i | 0.169334 | − | 0.985559i | \(-0.445838\pi\) |
−0.768852 | + | 0.639427i | \(0.779172\pi\) | |||||||
\(660\) | −81.1918 | + | 46.8761i | −0.123018 | + | 0.0710244i | ||||
\(661\) | 495.696 | + | 286.190i | 0.749919 | + | 0.432966i | 0.825665 | − | 0.564161i | \(-0.190800\pi\) |
−0.0757457 | + | 0.997127i | \(0.524134\pi\) | |||||||
\(662\) | 207.414 | + | 359.252i | 0.313315 | + | 0.542677i | ||||
\(663\) | −56.6691 | − | 98.1538i | −0.0854738 | − | 0.148045i | ||||
\(664\) | − | 3.68561i | − | 0.00555062i | ||||||
\(665\) | −51.8990 | + | 120.369i | −0.0780436 | + | 0.181006i | ||||
\(666\) | 36.7673 | 0.0552062 | ||||||||
\(667\) | 149.978 | − | 86.5897i | 0.224854 | − | 0.129820i | ||||
\(668\) | −156.167 | + | 90.1630i | −0.233783 | + | 0.134975i | ||||
\(669\) | −9.94949 | + | 17.2330i | −0.0148722 | + | 0.0257594i | ||||
\(670\) | 42.1793 | + | 73.0568i | 0.0629542 | + | 0.109040i | ||||
\(671\) | 16.3281 | − | 28.2810i | 0.0243339 | − | 0.0421476i | ||||
\(672\) | 122.788 | 0.182720 | ||||||||
\(673\) | − | 914.574i | − | 1.35895i | −0.733698 | − | 0.679476i | \(-0.762207\pi\) | ||
0.733698 | − | 0.679476i | \(-0.237793\pi\) | |||||||
\(674\) | 326.103 | − | 564.828i | 0.483833 | − | 0.838023i | ||||
\(675\) | 529.757 | + | 305.855i | 0.784825 | + | 0.453119i | ||||
\(676\) | 249.939 | 0.369732 | ||||||||
\(677\) | − | 272.492i | − | 0.402500i | −0.979540 | − | 0.201250i | \(-0.935500\pi\) | ||
0.979540 | − | 0.201250i | \(-0.0645003\pi\) | |||||||
\(678\) | 511.893 | + | 295.542i | 0.755005 | + | 0.435902i | ||||
\(679\) | −787.529 | + | 454.680i | −1.15984 | + | 0.669632i | ||||
\(680\) | −5.14643 | − | 2.97129i | −0.00756828 | − | 0.00436955i | ||||
\(681\) | 87.6867 | + | 151.878i | 0.128762 | + | 0.223022i | ||||
\(682\) | −328.454 | − | 568.899i | −0.481604 | − | 0.834163i | ||||
\(683\) | 164.842i | 0.241350i | 0.992692 | + | 0.120675i | \(0.0385058\pi\) | ||||
−0.992692 | + | 0.120675i | \(0.961494\pi\) | |||||||
\(684\) | 13.5255 | − | 31.3696i | 0.0197741 | − | 0.0458619i | ||||
\(685\) | 2.10102 | 0.00306718 | ||||||||
\(686\) | 425.889 | − | 245.887i | 0.620829 | − | 0.358436i | ||||
\(687\) | −360.520 | + | 208.146i | −0.524774 | + | 0.302979i | ||||
\(688\) | 150.677 | − | 260.979i | 0.219007 | − | 0.379331i | ||||
\(689\) | 685.878 | + | 1187.98i | 0.995469 | + | 1.72420i | ||||
\(690\) | 60.1691 | − | 104.216i | 0.0872016 | − | 0.151038i | ||||
\(691\) | 1040.21 | 1.50537 | 0.752685 | − | 0.658380i | \(-0.228758\pi\) | ||||
0.752685 | + | 0.658380i | \(0.228758\pi\) | |||||||
\(692\) | 608.247i | 0.878969i | ||||||||
\(693\) | −46.2020 | + | 80.0243i | −0.0666696 | + | 0.115475i | ||||
\(694\) | 372.638 | + | 215.143i | 0.536942 | + | 0.310004i | ||||
\(695\) | 31.7423 | 0.0456724 | ||||||||
\(696\) | − | 56.9827i | − | 0.0818717i | ||||||
\(697\) | 117.530 | + | 67.8557i | 0.168622 | + | 0.0973540i | ||||
\(698\) | −61.7684 | + | 35.6620i | −0.0884934 | + | 0.0510917i | ||||
\(699\) | 609.573 | + | 351.937i | 0.872064 | + | 0.503486i | ||||
\(700\) | −165.576 | − | 286.785i | −0.236536 | − | 0.409693i | ||||
\(701\) | 37.8179 | + | 65.5024i | 0.0539484 | + | 0.0934414i | 0.891738 | − | 0.452551i | \(-0.149486\pi\) |
−0.837790 | + | 0.545993i | \(0.816153\pi\) | |||||||
\(702\) | 618.018i | 0.880367i | ||||||||
\(703\) | 440.697 | − | 328.197i | 0.626880 | − | 0.466852i | ||||
\(704\) | 119.192 | 0.169307 | ||||||||
\(705\) | 31.4444 | − | 18.1544i | 0.0446020 | − | 0.0257510i | ||||
\(706\) | 388.020 | − | 224.024i | 0.549604 | − | 0.317314i | ||||
\(707\) | −22.3689 | + | 38.7440i | −0.0316392 | + | 0.0548006i | ||||
\(708\) | −184.980 | − | 320.394i | −0.261271 | − | 0.452534i | ||||
\(709\) | 451.379 | − | 781.811i | 0.636641 | − | 1.10269i | −0.349524 | − | 0.936928i | \(-0.613657\pi\) |
0.986165 | − | 0.165767i | \(-0.0530101\pi\) | |||||||
\(710\) | −142.924 | −0.201301 | ||||||||
\(711\) | 6.00031i | 0.00843926i | ||||||||
\(712\) | −9.55051 | + | 16.5420i | −0.0134136 | + | 0.0232331i | ||||
\(713\) | 730.226 | + | 421.596i | 1.02416 | + | 0.591299i | ||||
\(714\) | −64.4949 | −0.0903290 | ||||||||
\(715\) | 255.451i | 0.357274i | ||||||||
\(716\) | 545.939 | + | 315.198i | 0.762484 | + | 0.440221i | ||||
\(717\) | −194.338 | + | 112.201i | −0.271044 | + | 0.156487i | ||||
\(718\) | 182.988 | + | 105.648i | 0.254857 | + | 0.147142i | ||||
\(719\) | −586.734 | − | 1016.25i | −0.816042 | − | 1.41343i | −0.908578 | − | 0.417716i | \(-0.862831\pi\) |
0.0925359 | − | 0.995709i | \(-0.470503\pi\) | |||||||
\(720\) | −1.79796 | − | 3.11416i | −0.00249717 | − | 0.00432522i | ||||
\(721\) | 552.086i | 0.765722i | ||||||||
\(722\) | −117.897 | − | 496.732i | −0.163292 | − | 0.687994i | ||||
\(723\) | 438.601 | 0.606640 | ||||||||
\(724\) | −55.7878 | + | 32.2091i | −0.0770549 | + | 0.0444877i | ||||
\(725\) | −133.090 | + | 76.8394i | −0.183572 | + | 0.105985i | ||||
\(726\) | −224.654 | + | 389.112i | −0.309441 | + | 0.535967i | ||||
\(727\) | −288.552 | − | 499.787i | −0.396908 | − | 0.687465i | 0.596434 | − | 0.802662i | \(-0.296584\pi\) |
−0.993343 | + | 0.115197i | \(0.963250\pi\) | |||||||
\(728\) | 167.283 | − | 289.742i | 0.229784 | − | 0.397997i | ||||
\(729\) | −642.362 | −0.881155 | ||||||||
\(730\) | − | 180.148i | − | 0.246778i | ||||||
\(731\) | −79.1436 | + | 137.081i | −0.108268 | + | 0.187525i | ||||
\(732\) | 11.9444 | + | 6.89610i | 0.0163175 | + | 0.00942090i | ||||
\(733\) | −812.332 | −1.10823 | −0.554114 | − | 0.832441i | \(-0.686943\pi\) | ||||
−0.554114 | + | 0.832441i | \(0.686943\pi\) | |||||||
\(734\) | − | 331.033i | − | 0.450999i | ||||||
\(735\) | −3.82577 | − | 2.20881i | −0.00520512 | − | 0.00300518i | ||||
\(736\) | −132.495 | + | 76.4960i | −0.180020 | + | 0.103935i | ||||
\(737\) | 769.665 | + | 444.366i | 1.04432 | + | 0.602940i | ||||
\(738\) | 41.0602 | + | 71.1184i | 0.0556371 | + | 0.0963663i | ||||
\(739\) | 380.931 | + | 659.792i | 0.515469 | + | 0.892818i | 0.999839 | + | 0.0179548i | \(0.00571549\pi\) |
−0.484370 | + | 0.874863i | \(0.660951\pi\) | |||||||
\(740\) | − | 57.8399i | − | 0.0781620i | ||||||
\(741\) | −612.186 | − | 822.032i | −0.826162 | − | 1.10936i | ||||
\(742\) | 780.595 | 1.05201 | ||||||||
\(743\) | −118.810 | + | 68.5950i | −0.159906 | + | 0.0923216i | −0.577817 | − | 0.816166i | \(-0.696095\pi\) |
0.417912 | + | 0.908488i | \(0.362762\pi\) | |||||||
\(744\) | 240.272 | − | 138.721i | 0.322947 | − | 0.186453i | ||||
\(745\) | 94.8383 | − | 164.265i | 0.127300 | − | 0.220490i | ||||
\(746\) | −452.363 | − | 783.516i | −0.606385 | − | 1.05029i | ||||
\(747\) | −0.585713 | + | 1.01448i | −0.000784087 | + | 0.00135808i | ||||
\(748\) | −62.6061 | −0.0836980 | ||||||||
\(749\) | 552.086i | 0.737097i | ||||||||
\(750\) | −109.012 | + | 188.815i | −0.145350 | + | 0.251754i | ||||
\(751\) | 95.0686 | + | 54.8879i | 0.126589 | + | 0.0730864i | 0.561957 | − | 0.827166i | \(-0.310048\pi\) |
−0.435368 | + | 0.900253i | \(0.643382\pi\) | |||||||
\(752\) | −46.1612 | −0.0613846 | ||||||||
\(753\) | 755.343i | 1.00311i | ||||||||
\(754\) | −134.462 | − | 77.6317i | −0.178332 | − | 0.102960i | ||||
\(755\) | −14.0908 | + | 8.13534i | −0.0186633 | + | 0.0107753i | ||||
\(756\) | 304.565 | + | 175.841i | 0.402864 | + | 0.232594i | ||||
\(757\) | −133.257 | − | 230.808i | −0.176033 | − | 0.304898i | 0.764485 | − | 0.644641i | \(-0.222993\pi\) |
−0.940518 | + | 0.339743i | \(0.889660\pi\) | |||||||
\(758\) | 76.6265 | + | 132.721i | 0.101090 | + | 0.175094i | ||||
\(759\) | − | 1267.78i | − | 1.67033i | ||||||
\(760\) | −49.3485 | − | 21.2774i | −0.0649322 | − | 0.0279966i | ||||
\(761\) | 1227.85 | 1.61346 | 0.806732 | − | 0.590918i | \(-0.201234\pi\) | ||||
0.806732 | + | 0.590918i | \(0.201234\pi\) | |||||||
\(762\) | −484.219 | + | 279.564i | −0.635458 | + | 0.366882i | ||||
\(763\) | −98.2577 | + | 56.7291i | −0.128778 | + | 0.0743500i | ||||
\(764\) | 280.252 | − | 485.411i | 0.366822 | − | 0.635354i | ||||
\(765\) | 0.944387 | + | 1.63573i | 0.00123449 | + | 0.00213820i | ||||
\(766\) | −175.998 | + | 304.837i | −0.229762 | + | 0.397959i | ||||
\(767\) | −1008.04 | −1.31427 | ||||||||
\(768\) | 50.3402i | 0.0655472i | ||||||||
\(769\) | −334.115 | + | 578.705i | −0.434480 | + | 0.752542i | −0.997253 | − | 0.0740698i | \(-0.976401\pi\) |
0.562773 | + | 0.826612i | \(0.309735\pi\) | |||||||
\(770\) | 125.889 | + | 72.6819i | 0.163492 | + | 0.0943921i | ||||
\(771\) | 30.4393 | 0.0394803 | ||||||||
\(772\) | − | 97.0302i | − | 0.125687i | ||||||
\(773\) | −492.591 | − | 284.397i | −0.637246 | − | 0.367914i | 0.146307 | − | 0.989239i | \(-0.453261\pi\) |
−0.783553 | + | 0.621325i | \(0.786595\pi\) | |||||||
\(774\) | −82.9490 | + | 47.8906i | −0.107169 | + | 0.0618742i | ||||
\(775\) | −648.000 | − | 374.123i | −0.836129 | − | 0.482739i | ||||
\(776\) | −186.409 | − | 322.869i | −0.240217 | − | 0.416069i | ||||
\(777\) | −313.868 | − | 543.636i | −0.403949 | − | 0.699660i | ||||
\(778\) | 949.108i | 1.21993i | ||||||||
\(779\) | 1126.98 | + | 485.915i | 1.44670 | + | 0.623768i | ||||
\(780\) | −107.889 | −0.138319 | ||||||||
\(781\) | −1304.00 | + | 752.864i | −1.66965 | + | 0.963975i | ||||
\(782\) | 69.5936 | − | 40.1799i | 0.0889944 | − | 0.0513809i | ||||
\(783\) | 81.6033 | − | 141.341i | 0.104219 | − | 0.180512i | ||||
\(784\) | 2.80816 | + | 4.86388i | 0.00358184 | + | 0.00620393i | ||||
\(785\) | 135.076 | − | 233.958i | 0.172071 | − | 0.298035i | ||||
\(786\) | 477.196 | 0.607120 | ||||||||
\(787\) | 460.132i | 0.584665i | 0.956317 | + | 0.292333i | \(0.0944315\pi\) | ||||
−0.956317 | + | 0.292333i | \(0.905569\pi\) | |||||||
\(788\) | 251.909 | − | 436.320i | 0.319682 | − | 0.553705i | ||||
\(789\) | 310.414 | + | 179.217i | 0.393427 | + | 0.227145i | ||||
\(790\) | 9.43928 | 0.0119485 | ||||||||
\(791\) | − | 916.481i | − | 1.15864i | ||||||
\(792\) | −32.8082 | − | 18.9418i | −0.0414244 | − | 0.0239164i | ||||
\(793\) | 32.5454 | − | 18.7901i | 0.0410409 | − | 0.0236950i | ||||
\(794\) | −114.346 | − | 66.0178i | −0.144013 | − | 0.0831458i | ||||
\(795\) | −125.861 | − | 217.998i | −0.158316 | − | 0.274211i | ||||
\(796\) | 259.388 | + | 449.274i | 0.325865 | + | 0.564414i | ||||
\(797\) | 1211.02i | 1.51947i | 0.650234 | + | 0.759734i | \(0.274671\pi\) | ||||
−0.650234 | + | 0.759734i | \(0.725329\pi\) | |||||||
\(798\) | −579.287 | + | 67.8036i | −0.725924 | + | 0.0849669i | ||||
\(799\) | 24.2464 | 0.0303460 | ||||||||
\(800\) | 117.576 | − | 67.8823i | 0.146969 | − | 0.0848528i | ||||
\(801\) | 5.25765 | − | 3.03551i | 0.00656386 | − | 0.00378965i | ||||
\(802\) | −197.988 | + | 342.924i | −0.246867 | + | 0.427587i | ||||
\(803\) | −948.943 | − | 1643.62i | −1.18175 | − | 2.04685i | ||||
\(804\) | −187.677 | + | 325.065i | −0.233429 | + | 0.404310i | ||||
\(805\) | −186.586 | −0.231783 | ||||||||
\(806\) | − | 755.961i | − | 0.937916i | ||||||
\(807\) | −632.305 | + | 1095.18i | −0.783525 | + | 1.35711i | ||||
\(808\) | −15.8842 | − | 9.17074i | −0.0196586 | − | 0.0113499i | ||||
\(809\) | 914.089 | 1.12990 | 0.564950 | − | 0.825125i | \(-0.308896\pi\) | ||||
0.564950 | + | 0.825125i | \(0.308896\pi\) | |||||||
\(810\) | − | 124.851i | − | 0.154136i | ||||||
\(811\) | −403.234 | − | 232.808i | −0.497206 | − | 0.287062i | 0.230353 | − | 0.973107i | \(-0.426012\pi\) |
−0.727559 | + | 0.686045i | \(0.759345\pi\) | |||||||
\(812\) | −76.5153 | + | 44.1761i | −0.0942307 | + | 0.0544041i | ||||
\(813\) | −1087.13 | − | 627.655i | −1.33718 | − | 0.772023i | ||||
\(814\) | −304.677 | − | 527.715i | −0.374295 | − | 0.648299i | ||||
\(815\) | −78.3485 | − | 135.704i | −0.0961331 | − | 0.166507i | ||||
\(816\) | − | 26.4415i | − | 0.0324038i | ||||||
\(817\) | −566.747 | + | 1314.45i | −0.693693 | + | 1.60887i | ||||
\(818\) | 907.671 | 1.10962 | ||||||||
\(819\) | −92.0908 | + | 53.1687i | −0.112443 | + | 0.0649190i | ||||
\(820\) | 111.879 | − | 64.5931i | 0.136437 | − | 0.0787721i | ||||
\(821\) | 48.5556 | − | 84.1008i | 0.0591420 | − | 0.102437i | −0.834938 | − | 0.550343i | \(-0.814497\pi\) |
0.894081 | + | 0.447906i | \(0.147830\pi\) | |||||||
\(822\) | 4.67423 | + | 8.09601i | 0.00568642 | + | 0.00984916i | ||||
\(823\) | 562.052 | − | 973.502i | 0.682930 | − | 1.18287i | −0.291152 | − | 0.956677i | \(-0.594039\pi\) |
0.974082 | − | 0.226193i | \(-0.0726281\pi\) | |||||||
\(824\) | −226.343 | −0.274688 | ||||||||
\(825\) | 1125.03i | 1.36367i | ||||||||
\(826\) | −286.813 | + | 496.774i | −0.347231 | + | 0.601422i | ||||
\(827\) | −56.8722 | − | 32.8352i | −0.0687693 | − | 0.0397040i | 0.465221 | − | 0.885195i | \(-0.345975\pi\) |
−0.533990 | + | 0.845491i | \(0.679308\pi\) | |||||||
\(828\) | 48.6265 | 0.0587277 | ||||||||
\(829\) | − | 276.987i | − | 0.334121i | −0.985947 | − | 0.167061i | \(-0.946572\pi\) | ||
0.985947 | − | 0.167061i | \(-0.0534276\pi\) | |||||||
\(830\) | 1.59592 | + | 0.921404i | 0.00192279 | + | 0.00111012i | ||||
\(831\) | 1442.60 | − | 832.885i | 1.73598 | − | 1.00227i | ||||
\(832\) | 118.788 | + | 68.5821i | 0.142774 | + | 0.0824305i | ||||
\(833\) | −1.47500 | − | 2.55478i | −0.00177071 | − | 0.00306696i | ||||
\(834\) | 70.6186 | + | 122.315i | 0.0846746 | + | 0.146661i | ||||
\(835\) | − | 90.1630i | − | 0.107980i | ||||||
\(836\) | −562.322 | + | 65.8179i | −0.672634 | + | 0.0787296i | ||||
\(837\) | 794.636 | 0.949386 | ||||||||
\(838\) | −819.206 | + | 472.969i | −0.977572 | + | 0.564402i | ||||
\(839\) | −159.598 | + | 92.1438i | −0.190224 | + | 0.109826i | −0.592087 | − | 0.805874i | \(-0.701696\pi\) |
0.401864 | + | 0.915700i | \(0.368363\pi\) | |||||||
\(840\) | −30.6969 | + | 53.1687i | −0.0365440 | + | 0.0632960i | ||||
\(841\) | −399.999 | − | 692.819i | −0.475623 | − | 0.823803i | ||||
\(842\) | −354.124 | + | 613.360i | −0.420574 | + | 0.728456i | ||||
\(843\) | 172.237 | 0.204315 | ||||||||
\(844\) | − | 139.142i | − | 0.164860i | ||||||
\(845\) | −62.4847 | + | 108.227i | −0.0739464 | + | 0.128079i | ||||
\(846\) | 12.7061 | + | 7.33588i | 0.0150190 | + | 0.00867125i | ||||
\(847\) | 696.656 | 0.822498 | ||||||||
\(848\) | 320.026i | 0.377390i | ||||||||
\(849\) | 405.808 | + | 234.293i | 0.477983 | + | 0.275964i | ||||
\(850\) | −61.7571 | + | 35.6555i | −0.0726555 | + | 0.0419476i | ||||
\(851\) | 677.363 | + | 391.076i | 0.795962 | + | 0.459549i | ||||
\(852\) | −317.969 | − | 550.739i | −0.373204 | − | 0.646407i | ||||
\(853\) | 640.620 | + | 1109.59i | 0.751020 | + | 1.30081i | 0.947329 | + | 0.320263i | \(0.103771\pi\) |
−0.196308 | + | 0.980542i | \(0.562895\pi\) | |||||||
\(854\) | − | 21.3849i | − | 0.0250409i | ||||||
\(855\) | 10.2020 | + | 13.6991i | 0.0119322 | + | 0.0160224i | ||||
\(856\) | −226.343 | −0.264419 | ||||||||
\(857\) | 90.2265 | − | 52.0923i | 0.105282 | − | 0.0607845i | −0.446435 | − | 0.894816i | \(-0.647306\pi\) |
0.551716 | + | 0.834032i | \(0.313973\pi\) | |||||||
\(858\) | −984.347 | + | 568.313i | −1.14726 | + | 0.662370i | ||||
\(859\) | 374.183 | − | 648.105i | 0.435604 | − | 0.754487i | −0.561741 | − | 0.827313i | \(-0.689868\pi\) |
0.997345 | + | 0.0728256i | \(0.0232017\pi\) | |||||||
\(860\) | 75.3383 | + | 130.490i | 0.0876026 | + | 0.151732i | ||||
\(861\) | 701.030 | − | 1214.22i | 0.814204 | − | 1.41024i | ||||
\(862\) | −196.863 | −0.228379 | ||||||||
\(863\) | 19.3495i | 0.0224212i | 0.999937 | + | 0.0112106i | \(0.00356852\pi\) | ||||
−0.999937 | + | 0.0112106i | \(0.996431\pi\) | |||||||
\(864\) | −72.0908 | + | 124.865i | −0.0834384 | + | 0.144520i | ||||
\(865\) | −263.379 | − | 152.062i | −0.304484 | − | 0.175794i | ||||
\(866\) | −294.509 | −0.340079 | ||||||||
\(867\) | − | 895.382i | − | 1.03274i | ||||||
\(868\) | −372.545 | − | 215.089i | −0.429199 | − | 0.247798i | ||||
\(869\) | 86.1214 | − | 49.7222i | 0.0991041 | − | 0.0572178i | ||||
\(870\) | 24.6742 | + | 14.2457i | 0.0283612 | + | 0.0163743i | ||||
\(871\) | 511.371 | + | 885.720i | 0.587108 | + | 1.01690i | ||||
\(872\) | −23.2577 | − | 40.2834i | −0.0266716 | − | 0.0461966i | ||||
\(873\) | 118.495i | 0.135733i | ||||||||
\(874\) | 582.842 | − | 434.056i | 0.666868 | − | 0.496632i | ||||
\(875\) | 338.050 | 0.386343 | ||||||||
\(876\) | 694.176 | − | 400.783i | 0.792438 | − | 0.457515i | ||||
\(877\) | −303.060 | + | 174.972i | −0.345564 | + | 0.199512i | −0.662730 | − | 0.748859i | \(-0.730602\pi\) |
0.317166 | + | 0.948370i | \(0.397269\pi\) | |||||||
\(878\) | −53.6232 | + | 92.8781i | −0.0610743 | + | 0.105784i | ||||
\(879\) | −229.182 | − | 396.954i | −0.260730 | − | 0.451598i | ||||
\(880\) | −29.7980 | + | 51.6116i | −0.0338613 | + | 0.0586495i | ||||
\(881\) | −449.707 | −0.510451 | −0.255225 | − | 0.966882i | \(-0.582150\pi\) | ||||
−0.255225 | + | 0.966882i | \(0.582150\pi\) | |||||||
\(882\) | − | 1.78508i | − | 0.00202390i | ||||||
\(883\) | −557.532 | + | 965.674i | −0.631406 | + | 1.09363i | 0.355858 | + | 0.934540i | \(0.384189\pi\) |
−0.987264 | + | 0.159088i | \(0.949145\pi\) | |||||||
\(884\) | −62.3939 | − | 36.0231i | −0.0705813 | − | 0.0407501i | ||||
\(885\) | 184.980 | 0.209016 | ||||||||
\(886\) | 643.830i | 0.726671i | ||||||||
\(887\) | 818.675 | + | 472.662i | 0.922970 | + | 0.532877i | 0.884581 | − | 0.466386i | \(-0.154444\pi\) |
0.0383889 | + | 0.999263i | \(0.487777\pi\) | |||||||
\(888\) | 222.879 | − | 128.679i | 0.250989 | − | 0.144909i | ||||
\(889\) | 750.787 | + | 433.467i | 0.844529 | + | 0.487589i | ||||
\(890\) | −4.77526 | − | 8.27098i | −0.00536546 | − | 0.00929324i | ||||
\(891\) | −657.661 | − | 1139.10i | −0.738115 | − | 1.27845i | ||||
\(892\) | 12.6493i | 0.0141808i | ||||||||
\(893\) | 217.779 | − | 25.4903i | 0.243874 | − | 0.0285446i | ||||
\(894\) | 843.964 | 0.944031 | ||||||||
\(895\) | −272.969 | + | 157.599i | −0.304994 | + | 0.176088i | ||||
\(896\) | 67.5959 | − | 39.0265i | 0.0754419 | − | 0.0435564i | ||||
\(897\) | 729.474 | − | 1263.49i | 0.813237 | − | 1.40857i | ||||
\(898\) | 5.97500 | + | 10.3490i | 0.00665368 | + | 0.0115245i | ||||
\(899\) | −99.8173 | + | 172.889i | −0.111032 | + | 0.192312i | ||||
\(900\) | −43.1510 | −0.0479456 | ||||||||
\(901\) | − | 168.096i | − | 0.186566i | ||||||
\(902\) | 680.499 | − | 1178.66i | 0.754434 | − | 1.30672i | ||||
\(903\) | 1416.21 | + | 817.647i | 1.56833 | + | 0.905478i | ||||
\(904\) | 375.737 | 0.415638 | ||||||||
\(905\) | − | 32.2091i | − | 0.0355901i | ||||||
\(906\) | −62.6969 | − | 36.1981i | −0.0692019 | − | 0.0399537i | ||||
\(907\) | 617.886 | − | 356.737i | 0.681241 | − | 0.393315i | −0.119081 | − | 0.992885i | \(-0.537995\pi\) |
0.800323 | + | 0.599570i | \(0.204662\pi\) | |||||||
\(908\) | 96.5449 | + | 55.7402i | 0.106327 | + | 0.0613879i | ||||
\(909\) | 2.91480 | + | 5.04859i | 0.00320660 | + | 0.00555400i | ||||
\(910\) | 83.6413 | + | 144.871i | 0.0919135 | + | 0.159199i | ||||
\(911\) | 1490.37i | 1.63597i | 0.575242 | + | 0.817984i | \(0.304908\pi\) | ||||
−0.575242 | + | 0.817984i | \(0.695092\pi\) | |||||||
\(912\) | −27.7980 | − | 237.495i | −0.0304802 | − | 0.260411i | ||||
\(913\) | 19.4143 | 0.0212643 | ||||||||
\(914\) | −255.267 | + | 147.378i | −0.279285 | + | 0.161245i | ||||
\(915\) | −5.97219 | + | 3.44805i | −0.00652699 | + | 0.00376836i | ||||
\(916\) | −132.313 | + | 229.173i | −0.144447 | + | 0.250189i | ||||
\(917\) | −369.949 | − | 640.770i | −0.403434 | − | 0.698768i | ||||
\(918\) | 37.8661 | − | 65.5860i | 0.0412484 | − | 0.0714444i | ||||
\(919\) | −543.666 | −0.591585 | −0.295792 | − | 0.955252i | \(-0.595584\pi\) | ||||
−0.295792 | + | 0.955252i | \(0.595584\pi\) | |||||||
\(920\) | − | 76.4960i | − | 0.0831478i | ||||||
\(921\) | 178.086 | − | 308.454i | 0.193361 | − | 0.334912i | ||||
\(922\) | −756.421 | − | 436.720i | −0.820413 | − | 0.473666i | ||||
\(923\) | −1732.77 | −1.87732 | ||||||||
\(924\) | 646.795i | 0.699994i | ||||||||
\(925\) | −601.090 | − | 347.039i | −0.649827 | − | 0.375178i | ||||
\(926\) | −785.010 | + | 453.226i | −0.847743 | + | 0.489445i | ||||
\(927\) | 62.3020 | + | 35.9701i | 0.0672082 | + | 0.0388027i | ||||
\(928\) | −18.1112 | − | 31.3696i | −0.0195164 | − | 0.0338034i | ||||
\(929\) | −56.2582 | − | 97.4420i | −0.0605578 | − | 0.104889i | 0.834157 | − | 0.551527i | \(-0.185955\pi\) |
−0.894715 | + | 0.446638i | \(0.852621\pi\) | |||||||
\(930\) | 138.721i | 0.149163i | ||||||||
\(931\) | −15.9342 | − | 21.3961i | −0.0171151 | − | 0.0229819i | ||||
\(932\) | 447.435 | 0.480080 | ||||||||
\(933\) | −287.914 | + | 166.227i | −0.308589 | + | 0.178164i | ||||
\(934\) | −200.994 | + | 116.044i | −0.215197 | + | 0.124244i | ||||
\(935\) | 15.6515 | − | 27.1092i | 0.0167396 | − | 0.0289938i | ||||
\(936\) | −21.7980 | − | 37.7552i | −0.0232884 | − | 0.0403367i | ||||
\(937\) | 125.894 | − | 218.055i | 0.134358 | − | 0.232716i | −0.790994 | − | 0.611824i | \(-0.790436\pi\) |
0.925352 | + | 0.379109i | \(0.123769\pi\) | |||||||
\(938\) | 581.989 | 0.620457 | ||||||||
\(939\) | 781.034i | 0.831773i | ||||||||
\(940\) | 11.5403 | − | 19.9884i | 0.0122769 | − | 0.0212642i | ||||
\(941\) | −18.6520 | − | 10.7688i | −0.0198215 | − | 0.0114440i | 0.490057 | − | 0.871691i | \(-0.336976\pi\) |
−0.509878 | + | 0.860247i | \(0.670309\pi\) | |||||||
\(942\) | 1202.03 | 1.27604 | ||||||||
\(943\) | 1746.95i | 1.85254i | ||||||||
\(944\) | −203.666 | − | 117.587i | −0.215748 | − | 0.124562i | ||||
\(945\) | −152.283 | + | 87.9204i | −0.161146 | + | 0.0930375i | ||||
\(946\) | 1374.73 | + | 793.701i | 1.45320 | + | 0.839008i | ||||
\(947\) | −314.735 | − | 545.137i | −0.332349 | − | 0.575646i | 0.650623 | − | 0.759401i | \(-0.274508\pi\) |
−0.982972 | + | 0.183755i | \(0.941175\pi\) | |||||||
\(948\) | 21.0000 | + | 36.3731i | 0.0221519 | + | 0.0383682i | ||||
\(949\) | − | 2184.06i | − | 2.30143i | ||||||
\(950\) | −517.212 | + | 385.180i | −0.544434 | + | 0.405452i | ||||
\(951\) | −712.287 | −0.748988 | ||||||||
\(952\) | −35.5051 | + | 20.4989i | −0.0372953 | + | 0.0215324i | ||||
\(953\) | −420.863 | + | 242.986i | −0.441619 | + | 0.254969i | −0.704284 | − | 0.709918i | \(-0.748732\pi\) |
0.262665 | + | 0.964887i | \(0.415399\pi\) | |||||||
\(954\) | 50.8582 | − | 88.0889i | 0.0533104 | − | 0.0923364i | ||||
\(955\) | 140.126 | + | 242.705i | 0.146729 | + | 0.254142i | ||||
\(956\) | −71.3235 | + | 123.536i | −0.0746061 | + | 0.129222i | ||||
\(957\) | 300.161 | 0.313648 | ||||||||
\(958\) | − | 1135.33i | − | 1.18511i | ||||||
\(959\) | 7.24745 | − | 12.5529i | 0.00755730 | − | 0.0130896i | ||||
\(960\) | −21.7980 | − | 12.5851i | −0.0227062 | − | 0.0131094i | ||||
\(961\) | −11.0000 | −0.0114464 | ||||||||
\(962\) | − | 701.235i | − | 0.728934i | ||||||
\(963\) | 62.3020 | + | 35.9701i | 0.0646958 | + | 0.0373521i | ||||
\(964\) | 241.454 | − | 139.404i | 0.250471 | − | 0.144610i | ||||
\(965\) | 42.0153 | + | 24.2575i | 0.0435392 | + | 0.0251374i | ||||
\(966\) | −415.106 | − | 718.984i | −0.429716 | − | 0.744290i | ||||
\(967\) | −216.372 | − | 374.767i | −0.223756 | − | 0.387556i | 0.732190 | − | 0.681101i | \(-0.238498\pi\) |
−0.955945 | + | 0.293545i | \(0.905165\pi\) | |||||||
\(968\) | 285.613i | 0.295055i | ||||||||
\(969\) | 14.6010 | + | 124.745i | 0.0150681 | + | 0.128736i | ||||
\(970\) | 186.409 | 0.192174 | ||||||||
\(971\) | −1058.42 | + | 611.077i | −1.09003 | + | 0.629327i | −0.933584 | − | 0.358360i | \(-0.883336\pi\) |
−0.156443 | + | 0.987687i | \(0.550003\pi\) | |||||||
\(972\) | 83.7775 | − | 48.3690i | 0.0861909 | − | 0.0497623i | ||||
\(973\) | 109.495 | − | 189.651i | 0.112533 | − | 0.194913i | ||||
\(974\) | −321.303 | − | 556.513i | −0.329880 | − | 0.571369i | ||||
\(975\) | −647.333 | + | 1121.21i | −0.663931 | + | 1.14996i | ||||
\(976\) | 8.76734 | 0.00898293 | ||||||||
\(977\) | 867.932i | 0.888365i | 0.895936 | + | 0.444182i | \(0.146506\pi\) | ||||
−0.895936 | + | 0.444182i | \(0.853494\pi\) | |||||||
\(978\) | 348.611 | − | 603.811i | 0.356453 | − | 0.617394i | ||||
\(979\) | −87.1362 | − | 50.3081i | −0.0890053 | − | 0.0513873i | ||||
\(980\) | −2.80816 | −0.00286547 | ||||||||
\(981\) | 14.7843i | 0.0150706i | ||||||||
\(982\) | 636.441 | + | 367.449i | 0.648106 | + | 0.374184i | ||||
\(983\) | 930.158 | − | 537.027i | 0.946245 | − | 0.546315i | 0.0543322 | − | 0.998523i | \(-0.482697\pi\) |
0.891912 | + | 0.452208i | \(0.149364\pi\) | |||||||
\(984\) | 497.803 | + | 287.406i | 0.505897 | + | 0.292080i | ||||
\(985\) | 125.955 | + | 218.160i | 0.127873 | + | 0.221482i | ||||
\(986\) | 9.51301 | + | 16.4770i | 0.00964809 | + | 0.0167110i | ||||
\(987\) | − | 250.494i | − | 0.253793i | ||||||
\(988\) | −598.287 | − | 257.962i | −0.605554 | − | 0.261095i | ||||
\(989\) | −2037.55 | −2.06022 | ||||||||
\(990\) | 16.4041 | − | 9.47090i | 0.0165698 | − | 0.00956657i | ||||
\(991\) | −1527.57 | + | 881.941i | −1.54144 | + | 0.889951i | −0.542692 | + | 0.839932i | \(0.682595\pi\) |
−0.998748 | + | 0.0500189i | \(0.984072\pi\) | |||||||
\(992\) | 88.1816 | − | 152.735i | 0.0888928 | − | 0.153967i | ||||
\(993\) | −461.444 | − | 799.244i | −0.464697 | − | 0.804878i | ||||
\(994\) | −493.015 | + | 853.927i | −0.495991 | + | 0.859081i | ||||
\(995\) | −259.388 | −0.260692 | ||||||||
\(996\) | 8.19955i | 0.00823248i | ||||||||
\(997\) | 11.6214 | − | 20.1289i | 0.0116564 | − | 0.0201895i | −0.860138 | − | 0.510061i | \(-0.829623\pi\) |
0.871795 | + | 0.489871i | \(0.162956\pi\) | |||||||
\(998\) | 542.668 | + | 313.309i | 0.543755 | + | 0.313937i | ||||
\(999\) | 737.110 | 0.737848 |
(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 | 38.3.d.a.31.1 | yes | 4 | |
3.2 | odd | 2 | 342.3.m.a.145.2 | 4 | |||
4.3 | odd | 2 | 304.3.r.a.145.1 | 4 | |||
19.7 | even | 3 | 722.3.b.b.721.2 | 4 | |||
19.8 | odd | 6 | inner | 38.3.d.a.27.1 | ✓ | 4 | |
19.12 | odd | 6 | 722.3.b.b.721.3 | 4 | |||
57.8 | even | 6 | 342.3.m.a.217.2 | 4 | |||
76.27 | even | 6 | 304.3.r.a.65.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.3.d.a.27.1 | ✓ | 4 | 19.8 | odd | 6 | inner | |
38.3.d.a.31.1 | yes | 4 | 1.1 | even | 1 | trivial | |
304.3.r.a.65.1 | 4 | 76.27 | even | 6 | |||
304.3.r.a.145.1 | 4 | 4.3 | odd | 2 | |||
342.3.m.a.145.2 | 4 | 3.2 | odd | 2 | |||
342.3.m.a.217.2 | 4 | 57.8 | even | 6 | |||
722.3.b.b.721.2 | 4 | 19.7 | even | 3 | |||
722.3.b.b.721.3 | 4 | 19.12 | odd | 6 |