Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(49,750)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(750, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.h (of order \(10\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | \(\Q(\zeta_{20})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 649.1 | ||
Root | \(-0.951057 - 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.649 |
Dual form | 750.2.h.b.349.1 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.951057 | − | 0.309017i | −0.672499 | − | 0.218508i | ||||
\(3\) | −0.587785 | + | 0.809017i | −0.339358 | + | 0.467086i | ||||
\(4\) | 0.809017 | + | 0.587785i | 0.404508 | + | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.809017 | − | 0.587785i | 0.330280 | − | 0.239962i | ||||
\(7\) | − | 0.381966i | − | 0.144370i | −0.997391 | − | 0.0721848i | \(-0.977003\pi\) | ||
0.997391 | − | 0.0721848i | \(-0.0229971\pi\) | |||||||
\(8\) | −0.587785 | − | 0.809017i | −0.207813 | − | 0.286031i | ||||
\(9\) | −0.309017 | − | 0.951057i | −0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.427051 | − | 1.31433i | 0.128761 | − | 0.396285i | −0.865807 | − | 0.500378i | \(-0.833194\pi\) |
0.994567 | + | 0.104094i | \(0.0331942\pi\) | |||||||
\(12\) | −0.951057 | + | 0.309017i | −0.274546 | + | 0.0892055i | ||||
\(13\) | −2.35114 | + | 0.763932i | −0.652089 | + | 0.211877i | −0.616335 | − | 0.787484i | \(-0.711383\pi\) |
−0.0357541 | + | 0.999361i | \(0.511383\pi\) | |||||||
\(14\) | −0.118034 | + | 0.363271i | −0.0315459 | + | 0.0970883i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | −1.90211 | − | 2.61803i | −0.461330 | − | 0.634967i | 0.513454 | − | 0.858117i | \(-0.328366\pi\) |
−0.974784 | + | 0.223151i | \(0.928366\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 6.23607 | − | 4.53077i | 1.43065 | − | 1.03943i | 0.440757 | − | 0.897626i | \(-0.354710\pi\) |
0.989895 | − | 0.141803i | \(-0.0452900\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.309017 | + | 0.224514i | 0.0674330 | + | 0.0489930i | ||||
\(22\) | −0.812299 | + | 1.11803i | −0.173183 | + | 0.238366i | ||||
\(23\) | −4.25325 | − | 1.38197i | −0.886865 | − | 0.288160i | −0.170060 | − | 0.985434i | \(-0.554396\pi\) |
−0.716805 | + | 0.697274i | \(0.754396\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.47214 | 0.484826 | ||||||||
\(27\) | 0.951057 | + | 0.309017i | 0.183031 | + | 0.0594703i | ||||
\(28\) | 0.224514 | − | 0.309017i | 0.0424292 | − | 0.0583987i | ||||
\(29\) | −0.381966 | − | 0.277515i | −0.0709293 | − | 0.0515332i | 0.551756 | − | 0.834006i | \(-0.313958\pi\) |
−0.622685 | + | 0.782473i | \(0.713958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.54508 | + | 2.57565i | −0.636716 | + | 0.462601i | −0.858720 | − | 0.512444i | \(-0.828740\pi\) |
0.222004 | + | 0.975046i | \(0.428740\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0.812299 | + | 1.11803i | 0.141403 | + | 0.194625i | ||||
\(34\) | 1.00000 | + | 3.07768i | 0.171499 | + | 0.527818i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.309017 | − | 0.951057i | 0.0515028 | − | 0.158509i | ||||
\(37\) | 7.60845 | − | 2.47214i | 1.25082 | − | 0.406417i | 0.392607 | − | 0.919707i | \(-0.371573\pi\) |
0.858215 | + | 0.513290i | \(0.171573\pi\) | |||||||
\(38\) | −7.33094 | + | 2.38197i | −1.18924 | + | 0.386406i | ||||
\(39\) | 0.763932 | − | 2.35114i | 0.122327 | − | 0.376484i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.38197 | − | 7.33094i | −0.372001 | − | 1.14490i | −0.945480 | − | 0.325680i | \(-0.894407\pi\) |
0.573479 | − | 0.819220i | \(-0.305593\pi\) | |||||||
\(42\) | −0.224514 | − | 0.309017i | −0.0346433 | − | 0.0476824i | ||||
\(43\) | 5.70820i | 0.870493i | 0.900311 | + | 0.435246i | \(0.143339\pi\) | ||||
−0.900311 | + | 0.435246i | \(0.856661\pi\) | |||||||
\(44\) | 1.11803 | − | 0.812299i | 0.168550 | − | 0.122459i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.61803 | + | 2.62866i | 0.533450 | + | 0.387574i | ||||
\(47\) | 6.88191 | − | 9.47214i | 1.00383 | − | 1.38165i | 0.0808837 | − | 0.996724i | \(-0.474226\pi\) |
0.922946 | − | 0.384929i | \(-0.125774\pi\) | |||||||
\(48\) | −0.951057 | − | 0.309017i | −0.137273 | − | 0.0446028i | ||||
\(49\) | 6.85410 | 0.979157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.23607 | 0.453140 | ||||||||
\(52\) | −2.35114 | − | 0.763932i | −0.326045 | − | 0.105938i | ||||
\(53\) | 5.34307 | − | 7.35410i | 0.733927 | − | 1.01016i | −0.265018 | − | 0.964243i | \(-0.585378\pi\) |
0.998945 | − | 0.0459202i | \(-0.0146220\pi\) | |||||||
\(54\) | −0.809017 | − | 0.587785i | −0.110093 | − | 0.0799874i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.309017 | + | 0.224514i | −0.0412941 | + | 0.0300019i | ||||
\(57\) | 7.70820i | 1.02098i | ||||||||
\(58\) | 0.277515 | + | 0.381966i | 0.0364394 | + | 0.0501546i | ||||
\(59\) | 0.427051 | + | 1.31433i | 0.0555973 | + | 0.171111i | 0.974999 | − | 0.222209i | \(-0.0713266\pi\) |
−0.919402 | + | 0.393320i | \(0.871327\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.23607 | − | 6.88191i | 0.286299 | − | 0.881138i | −0.699707 | − | 0.714430i | \(-0.746686\pi\) |
0.986006 | − | 0.166708i | \(-0.0533138\pi\) | |||||||
\(62\) | 4.16750 | − | 1.35410i | 0.529273 | − | 0.171971i | ||||
\(63\) | −0.363271 | + | 0.118034i | −0.0457679 | + | 0.0148709i | ||||
\(64\) | −0.309017 | + | 0.951057i | −0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.427051 | − | 1.31433i | −0.0525663 | − | 0.161783i | ||||
\(67\) | −6.15537 | − | 8.47214i | −0.751998 | − | 1.03504i | −0.997838 | − | 0.0657257i | \(-0.979064\pi\) |
0.245840 | − | 0.969310i | \(-0.420936\pi\) | |||||||
\(68\) | − | 3.23607i | − | 0.392431i | ||||||
\(69\) | 3.61803 | − | 2.62866i | 0.435560 | − | 0.316453i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7082 | − | 8.50651i | −1.38951 | − | 1.00954i | −0.995919 | − | 0.0902503i | \(-0.971233\pi\) |
−0.393589 | − | 0.919286i | \(-0.628767\pi\) | |||||||
\(72\) | −0.587785 | + | 0.809017i | −0.0692712 | + | 0.0953436i | ||||
\(73\) | 11.8617 | + | 3.85410i | 1.38831 | + | 0.451089i | 0.905391 | − | 0.424578i | \(-0.139578\pi\) |
0.482916 | + | 0.875667i | \(0.339578\pi\) | |||||||
\(74\) | −8.00000 | −0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.70820 | 0.884192 | ||||||||
\(77\) | −0.502029 | − | 0.163119i | −0.0572115 | − | 0.0185891i | ||||
\(78\) | −1.45309 | + | 2.00000i | −0.164529 | + | 0.226455i | ||||
\(79\) | −2.73607 | − | 1.98787i | −0.307832 | − | 0.223653i | 0.423134 | − | 0.906067i | \(-0.360930\pi\) |
−0.730966 | + | 0.682414i | \(0.760930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | + | 0.587785i | −0.0898908 | + | 0.0653095i | ||||
\(82\) | 7.70820i | 0.851229i | ||||||||
\(83\) | −5.20431 | − | 7.16312i | −0.571247 | − | 0.786254i | 0.421454 | − | 0.906850i | \(-0.361520\pi\) |
−0.992702 | + | 0.120595i | \(0.961520\pi\) | |||||||
\(84\) | 0.118034 | + | 0.363271i | 0.0128786 | + | 0.0396361i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.76393 | − | 5.42882i | 0.190210 | − | 0.585405i | ||||
\(87\) | 0.449028 | − | 0.145898i | 0.0481409 | − | 0.0156419i | ||||
\(88\) | −1.31433 | + | 0.427051i | −0.140108 | + | 0.0455238i | ||||
\(89\) | −3.85410 | + | 11.8617i | −0.408534 | + | 1.25734i | 0.509374 | + | 0.860545i | \(0.329877\pi\) |
−0.917908 | + | 0.396793i | \(0.870123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.291796 | + | 0.898056i | 0.0305885 | + | 0.0941418i | ||||
\(92\) | −2.62866 | − | 3.61803i | −0.274056 | − | 0.377206i | ||||
\(93\) | − | 4.38197i | − | 0.454389i | ||||||
\(94\) | −9.47214 | + | 6.88191i | −0.976976 | + | 0.709815i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.809017 | + | 0.587785i | 0.0825700 | + | 0.0599906i | ||||
\(97\) | 3.30220 | − | 4.54508i | 0.335287 | − | 0.461483i | −0.607770 | − | 0.794113i | \(-0.707936\pi\) |
0.943058 | + | 0.332629i | \(0.107936\pi\) | |||||||
\(98\) | −6.51864 | − | 2.11803i | −0.658482 | − | 0.213954i | ||||
\(99\) | −1.38197 | −0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.61803 | 0.658519 | 0.329259 | − | 0.944239i | \(-0.393201\pi\) | ||||
0.329259 | + | 0.944239i | \(0.393201\pi\) | |||||||
\(102\) | −3.07768 | − | 1.00000i | −0.304736 | − | 0.0990148i | ||||
\(103\) | −0.779543 | + | 1.07295i | −0.0768107 | + | 0.105721i | −0.845694 | − | 0.533669i | \(-0.820813\pi\) |
0.768883 | + | 0.639390i | \(0.220813\pi\) | |||||||
\(104\) | 2.00000 | + | 1.45309i | 0.196116 | + | 0.142487i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.35410 | + | 5.34307i | −0.714294 | + | 0.518965i | ||||
\(107\) | 9.38197i | 0.906989i | 0.891259 | + | 0.453494i | \(0.149823\pi\) | ||||
−0.891259 | + | 0.453494i | \(0.850177\pi\) | |||||||
\(108\) | 0.587785 | + | 0.809017i | 0.0565597 | + | 0.0778477i | ||||
\(109\) | −3.94427 | − | 12.1392i | −0.377793 | − | 1.16273i | −0.941575 | − | 0.336803i | \(-0.890654\pi\) |
0.563782 | − | 0.825923i | \(-0.309346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.47214 | + | 7.60845i | −0.234645 | + | 0.722162i | ||||
\(112\) | 0.363271 | − | 0.118034i | 0.0343259 | − | 0.0111532i | ||||
\(113\) | 14.0413 | − | 4.56231i | 1.32090 | − | 0.429186i | 0.438095 | − | 0.898929i | \(-0.355654\pi\) |
0.882803 | + | 0.469743i | \(0.155654\pi\) | |||||||
\(114\) | 2.38197 | − | 7.33094i | 0.223092 | − | 0.686605i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.145898 | − | 0.449028i | −0.0135463 | − | 0.0416912i | ||||
\(117\) | 1.45309 | + | 2.00000i | 0.134338 | + | 0.184900i | ||||
\(118\) | − | 1.38197i | − | 0.127220i | ||||||
\(119\) | −1.00000 | + | 0.726543i | −0.0916698 | + | 0.0666020i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.35410 | + | 5.34307i | 0.668555 | + | 0.485733i | ||||
\(122\) | −4.25325 | + | 5.85410i | −0.385072 | + | 0.530005i | ||||
\(123\) | 7.33094 | + | 2.38197i | 0.661008 | + | 0.214775i | ||||
\(124\) | −4.38197 | −0.393512 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.381966 | 0.0340282 | ||||||||
\(127\) | −10.8249 | − | 3.51722i | −0.960554 | − | 0.312103i | −0.213557 | − | 0.976931i | \(-0.568505\pi\) |
−0.746997 | + | 0.664828i | \(0.768505\pi\) | |||||||
\(128\) | 0.587785 | − | 0.809017i | 0.0519534 | − | 0.0715077i | ||||
\(129\) | −4.61803 | − | 3.35520i | −0.406595 | − | 0.295409i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.4721 | + | 10.5146i | −1.26444 | + | 0.918667i | −0.998967 | − | 0.0454523i | \(-0.985527\pi\) |
−0.265470 | + | 0.964119i | \(0.585527\pi\) | |||||||
\(132\) | 1.38197i | 0.120285i | ||||||||
\(133\) | −1.73060 | − | 2.38197i | −0.150062 | − | 0.206543i | ||||
\(134\) | 3.23607 | + | 9.95959i | 0.279554 | + | 0.860378i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 3.07768i | −0.0857493 | + | 0.263909i | ||||
\(137\) | 9.68208 | − | 3.14590i | 0.827196 | − | 0.268772i | 0.135332 | − | 0.990800i | \(-0.456790\pi\) |
0.691864 | + | 0.722028i | \(0.256790\pi\) | |||||||
\(138\) | −4.25325 | + | 1.38197i | −0.362061 | + | 0.117641i | ||||
\(139\) | −0.472136 | + | 1.45309i | −0.0400460 | + | 0.123249i | −0.969081 | − | 0.246743i | \(-0.920640\pi\) |
0.929035 | + | 0.369992i | \(0.120640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.61803 | + | 11.1352i | 0.304693 | + | 0.937750i | ||||
\(142\) | 8.50651 | + | 11.7082i | 0.713850 | + | 0.982531i | ||||
\(143\) | 3.41641i | 0.285694i | ||||||||
\(144\) | 0.809017 | − | 0.587785i | 0.0674181 | − | 0.0489821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.0902 | − | 7.33094i | −0.835068 | − | 0.606713i | ||||
\(147\) | −4.02874 | + | 5.54508i | −0.332285 | + | 0.457351i | ||||
\(148\) | 7.60845 | + | 2.47214i | 0.625411 | + | 0.203208i | ||||
\(149\) | −10.9098 | −0.893768 | −0.446884 | − | 0.894592i | \(-0.647466\pi\) | ||||
−0.446884 | + | 0.894592i | \(0.647466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.67376 | 0.217588 | 0.108794 | − | 0.994064i | \(-0.465301\pi\) | ||||
0.108794 | + | 0.994064i | \(0.465301\pi\) | |||||||
\(152\) | −7.33094 | − | 2.38197i | −0.594618 | − | 0.193203i | ||||
\(153\) | −1.90211 | + | 2.61803i | −0.153777 | + | 0.211656i | ||||
\(154\) | 0.427051 | + | 0.310271i | 0.0344127 | + | 0.0250023i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | − | 1.45309i | 0.160128 | − | 0.116340i | ||||
\(157\) | 22.6525i | 1.80786i | 0.427676 | + | 0.903932i | \(0.359332\pi\) | ||||
−0.427676 | + | 0.903932i | \(0.640668\pi\) | |||||||
\(158\) | 1.98787 | + | 2.73607i | 0.158146 | + | 0.217670i | ||||
\(159\) | 2.80902 | + | 8.64527i | 0.222770 | + | 0.685614i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.527864 | + | 1.62460i | −0.0416015 | + | 0.128036i | ||||
\(162\) | 0.951057 | − | 0.309017i | 0.0747221 | − | 0.0242787i | ||||
\(163\) | −8.05748 | + | 2.61803i | −0.631111 | + | 0.205060i | −0.607067 | − | 0.794651i | \(-0.707654\pi\) |
−0.0240436 | + | 0.999711i | \(0.507654\pi\) | |||||||
\(164\) | 2.38197 | − | 7.33094i | 0.186000 | − | 0.572450i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.73607 | + | 8.42075i | 0.212360 | + | 0.653577i | ||||
\(167\) | −1.00406 | − | 1.38197i | −0.0776963 | − | 0.106940i | 0.768400 | − | 0.639970i | \(-0.221053\pi\) |
−0.846096 | + | 0.533030i | \(0.821053\pi\) | |||||||
\(168\) | − | 0.381966i | − | 0.0294693i | ||||||
\(169\) | −5.57295 | + | 4.04898i | −0.428688 | + | 0.311460i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.23607 | − | 4.53077i | −0.476884 | − | 0.346477i | ||||
\(172\) | −3.35520 | + | 4.61803i | −0.255831 | + | 0.352122i | ||||
\(173\) | −5.79210 | − | 1.88197i | −0.440365 | − | 0.143083i | 0.0804391 | − | 0.996760i | \(-0.474368\pi\) |
−0.520804 | + | 0.853676i | \(0.674368\pi\) | |||||||
\(174\) | −0.472136 | −0.0357925 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.38197 | 0.104170 | ||||||||
\(177\) | −1.31433 | − | 0.427051i | −0.0987909 | − | 0.0320991i | ||||
\(178\) | 7.33094 | − | 10.0902i | 0.549477 | − | 0.756290i | ||||
\(179\) | 2.54508 | + | 1.84911i | 0.190229 | + | 0.138209i | 0.678823 | − | 0.734302i | \(-0.262490\pi\) |
−0.488595 | + | 0.872511i | \(0.662490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9443 | + | 14.4904i | −1.48245 | + | 1.07706i | −0.505688 | + | 0.862717i | \(0.668761\pi\) |
−0.976758 | + | 0.214344i | \(0.931239\pi\) | |||||||
\(182\) | − | 0.944272i | − | 0.0699941i | ||||||
\(183\) | 4.25325 | + | 5.85410i | 0.314410 | + | 0.432748i | ||||
\(184\) | 1.38197 | + | 4.25325i | 0.101880 | + | 0.313554i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.35410 | + | 4.16750i | −0.0992876 | + | 0.305576i | ||||
\(187\) | −4.25325 | + | 1.38197i | −0.311029 | + | 0.101059i | ||||
\(188\) | 11.1352 | − | 3.61803i | 0.812115 | − | 0.263872i | ||||
\(189\) | 0.118034 | − | 0.363271i | 0.00858571 | − | 0.0264241i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.47214 | + | 16.8415i | 0.395950 | + | 1.21861i | 0.928219 | + | 0.372033i | \(0.121339\pi\) |
−0.532269 | + | 0.846575i | \(0.678661\pi\) | |||||||
\(192\) | −0.587785 | − | 0.809017i | −0.0424197 | − | 0.0583858i | ||||
\(193\) | 11.1459i | 0.802299i | 0.916013 | + | 0.401150i | \(0.131389\pi\) | ||||
−0.916013 | + | 0.401150i | \(0.868611\pi\) | |||||||
\(194\) | −4.54508 | + | 3.30220i | −0.326318 | + | 0.237084i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.54508 | + | 4.02874i | 0.396077 | + | 0.287767i | ||||
\(197\) | 3.47371 | − | 4.78115i | 0.247492 | − | 0.340643i | −0.667139 | − | 0.744933i | \(-0.732481\pi\) |
0.914631 | + | 0.404290i | \(0.132481\pi\) | |||||||
\(198\) | 1.31433 | + | 0.427051i | 0.0934052 | + | 0.0303492i | ||||
\(199\) | 18.5066 | 1.31190 | 0.655948 | − | 0.754806i | \(-0.272269\pi\) | ||||
0.655948 | + | 0.754806i | \(0.272269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.4721 | 0.738648 | ||||||||
\(202\) | −6.29412 | − | 2.04508i | −0.442853 | − | 0.143892i | ||||
\(203\) | −0.106001 | + | 0.145898i | −0.00743982 | + | 0.0102400i | ||||
\(204\) | 2.61803 | + | 1.90211i | 0.183299 | + | 0.133175i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.07295 | − | 0.779543i | 0.0747559 | − | 0.0543133i | ||||
\(207\) | 4.47214i | 0.310835i | ||||||||
\(208\) | −1.45309 | − | 2.00000i | −0.100753 | − | 0.138675i | ||||
\(209\) | −3.29180 | − | 10.1311i | −0.227698 | − | 0.700783i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.23607 | − | 22.2703i | 0.498151 | − | 1.53315i | −0.313836 | − | 0.949477i | \(-0.601614\pi\) |
0.811987 | − | 0.583675i | \(-0.198386\pi\) | |||||||
\(212\) | 8.64527 | − | 2.80902i | 0.593759 | − | 0.192924i | ||||
\(213\) | 13.7638 | − | 4.47214i | 0.943081 | − | 0.306426i | ||||
\(214\) | 2.89919 | − | 8.92278i | 0.198184 | − | 0.609949i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.309017 | − | 0.951057i | −0.0210259 | − | 0.0647112i | ||||
\(217\) | 0.983813 | + | 1.35410i | 0.0667856 | + | 0.0919224i | ||||
\(218\) | 12.7639i | 0.864483i | ||||||||
\(219\) | −10.0902 | + | 7.33094i | −0.681830 | + | 0.495379i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47214 | + | 4.70228i | 0.435363 | + | 0.316310i | ||||
\(222\) | 4.70228 | − | 6.47214i | 0.315597 | − | 0.434381i | ||||
\(223\) | 2.93893 | + | 0.954915i | 0.196805 | + | 0.0639458i | 0.405761 | − | 0.913979i | \(-0.367007\pi\) |
−0.208956 | + | 0.977925i | \(0.567007\pi\) | |||||||
\(224\) | −0.381966 | −0.0255212 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.7639 | −0.982082 | ||||||||
\(227\) | −10.7189 | − | 3.48278i | −0.711438 | − | 0.231160i | −0.0691308 | − | 0.997608i | \(-0.522023\pi\) |
−0.642307 | + | 0.766447i | \(0.722023\pi\) | |||||||
\(228\) | −4.53077 | + | 6.23607i | −0.300057 | + | 0.412994i | ||||
\(229\) | −11.7082 | − | 8.50651i | −0.773700 | − | 0.562126i | 0.129382 | − | 0.991595i | \(-0.458701\pi\) |
−0.903082 | + | 0.429469i | \(0.858701\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.427051 | − | 0.310271i | 0.0280979 | − | 0.0204143i | ||||
\(232\) | 0.472136i | 0.0309972i | ||||||||
\(233\) | 7.43694 | + | 10.2361i | 0.487210 | + | 0.670587i | 0.979870 | − | 0.199635i | \(-0.0639755\pi\) |
−0.492660 | + | 0.870222i | \(0.663976\pi\) | |||||||
\(234\) | −0.763932 | − | 2.35114i | −0.0499398 | − | 0.153699i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.427051 | + | 1.31433i | −0.0277987 | + | 0.0855555i | ||||
\(237\) | 3.21644 | − | 1.04508i | 0.208930 | − | 0.0678856i | ||||
\(238\) | 1.17557 | − | 0.381966i | 0.0762009 | − | 0.0247592i | ||||
\(239\) | −7.94427 | + | 24.4500i | −0.513872 | + | 1.58154i | 0.271452 | + | 0.962452i | \(0.412496\pi\) |
−0.785325 | + | 0.619084i | \(0.787504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.26393 | − | 10.0453i | −0.210248 | − | 0.647078i | −0.999457 | − | 0.0329526i | \(-0.989509\pi\) |
0.789209 | − | 0.614125i | \(-0.210491\pi\) | |||||||
\(242\) | −5.34307 | − | 7.35410i | −0.343465 | − | 0.472740i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 5.85410 | − | 4.25325i | 0.374770 | − | 0.272287i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.23607 | − | 4.53077i | −0.397597 | − | 0.288871i | ||||
\(247\) | −11.2007 | + | 15.4164i | −0.712682 | + | 0.980923i | ||||
\(248\) | 4.16750 | + | 1.35410i | 0.264636 | + | 0.0859856i | ||||
\(249\) | 8.85410 | 0.561106 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.56231 | −0.414209 | −0.207105 | − | 0.978319i | \(-0.566404\pi\) | ||||
−0.207105 | + | 0.978319i | \(0.566404\pi\) | |||||||
\(252\) | −0.363271 | − | 0.118034i | −0.0228839 | − | 0.00743544i | ||||
\(253\) | −3.63271 | + | 5.00000i | −0.228387 | + | 0.314347i | ||||
\(254\) | 9.20820 | + | 6.69015i | 0.577774 | + | 0.419777i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 22.0000i | 1.37232i | 0.727450 | + | 0.686161i | \(0.240706\pi\) | ||||
−0.727450 | + | 0.686161i | \(0.759294\pi\) | |||||||
\(258\) | 3.35520 | + | 4.61803i | 0.208886 | + | 0.287506i | ||||
\(259\) | −0.944272 | − | 2.90617i | −0.0586742 | − | 0.180581i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.145898 | + | 0.449028i | −0.00903086 | + | 0.0277941i | ||||
\(262\) | 17.0130 | − | 5.52786i | 1.05107 | − | 0.341513i | ||||
\(263\) | −1.62460 | + | 0.527864i | −0.100177 | + | 0.0325495i | −0.358677 | − | 0.933462i | \(-0.616772\pi\) |
0.258500 | + | 0.966011i | \(0.416772\pi\) | |||||||
\(264\) | 0.427051 | − | 1.31433i | 0.0262832 | − | 0.0808913i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.909830 | + | 2.80017i | 0.0557853 | + | 0.171689i | ||||
\(267\) | −7.33094 | − | 10.0902i | −0.448646 | − | 0.617508i | ||||
\(268\) | − | 10.4721i | − | 0.639688i | ||||||
\(269\) | 1.69098 | − | 1.22857i | 0.103101 | − | 0.0749073i | −0.535040 | − | 0.844827i | \(-0.679704\pi\) |
0.638141 | + | 0.769919i | \(0.279704\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.92705 | − | 6.48588i | −0.542280 | − | 0.393989i | 0.282651 | − | 0.959223i | \(-0.408786\pi\) |
−0.824931 | + | 0.565233i | \(0.808786\pi\) | |||||||
\(272\) | 1.90211 | − | 2.61803i | 0.115333 | − | 0.158742i | ||||
\(273\) | −0.898056 | − | 0.291796i | −0.0543528 | − | 0.0176603i | ||||
\(274\) | −10.1803 | −0.615017 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.47214 | 0.269191 | ||||||||
\(277\) | 0.898056 | + | 0.291796i | 0.0539590 | + | 0.0175323i | 0.335872 | − | 0.941908i | \(-0.390969\pi\) |
−0.281913 | + | 0.959440i | \(0.590969\pi\) | |||||||
\(278\) | 0.898056 | − | 1.23607i | 0.0538618 | − | 0.0741344i | ||||
\(279\) | 3.54508 | + | 2.57565i | 0.212239 | + | 0.154200i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1803 | − | 17.5680i | 1.44248 | − | 1.04802i | 0.454961 | − | 0.890511i | \(-0.349653\pi\) |
0.987517 | − | 0.157510i | \(-0.0503467\pi\) | |||||||
\(282\) | − | 11.7082i | − | 0.697213i | ||||||
\(283\) | −18.4661 | − | 25.4164i | −1.09770 | − | 1.51085i | −0.838404 | − | 0.545050i | \(-0.816511\pi\) |
−0.259292 | − | 0.965799i | \(-0.583489\pi\) | |||||||
\(284\) | −4.47214 | − | 13.7638i | −0.265372 | − | 0.816732i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.05573 | − | 3.24920i | 0.0624265 | − | 0.192129i | ||||
\(287\) | −2.80017 | + | 0.909830i | −0.165289 | + | 0.0537056i | ||||
\(288\) | −0.951057 | + | 0.309017i | −0.0560415 | + | 0.0182090i | ||||
\(289\) | 2.01722 | − | 6.20837i | 0.118660 | − | 0.365198i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.73607 | + | 5.34307i | 0.101770 | + | 0.313216i | ||||
\(292\) | 7.33094 | + | 10.0902i | 0.429011 | + | 0.590483i | ||||
\(293\) | − | 10.9098i | − | 0.637359i | −0.947863 | − | 0.318680i | \(-0.896761\pi\) | ||
0.947863 | − | 0.318680i | \(-0.103239\pi\) | |||||||
\(294\) | 5.54508 | − | 4.02874i | 0.323396 | − | 0.234961i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.47214 | − | 4.70228i | −0.376185 | − | 0.273315i | ||||
\(297\) | 0.812299 | − | 1.11803i | 0.0471344 | − | 0.0648749i | ||||
\(298\) | 10.3759 | + | 3.37132i | 0.601058 | + | 0.195295i | ||||
\(299\) | 11.0557 | 0.639369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18034 | 0.125673 | ||||||||
\(302\) | −2.54290 | − | 0.826238i | −0.146327 | − | 0.0475446i | ||||
\(303\) | −3.88998 | + | 5.35410i | −0.223474 | + | 0.307585i | ||||
\(304\) | 6.23607 | + | 4.53077i | 0.357663 | + | 0.259857i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.61803 | − | 1.90211i | 0.149663 | − | 0.108737i | ||||
\(307\) | − | 10.0000i | − | 0.570730i | −0.958419 | − | 0.285365i | \(-0.907885\pi\) | ||
0.958419 | − | 0.285365i | \(-0.0921148\pi\) | |||||||
\(308\) | −0.310271 | − | 0.427051i | −0.0176793 | − | 0.0243335i | ||||
\(309\) | −0.409830 | − | 1.26133i | −0.0233144 | − | 0.0717544i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.85410 | + | 18.0171i | −0.331956 | + | 1.02165i | 0.636247 | + | 0.771486i | \(0.280486\pi\) |
−0.968202 | + | 0.250169i | \(0.919514\pi\) | |||||||
\(312\) | −2.35114 | + | 0.763932i | −0.133107 | + | 0.0432491i | ||||
\(313\) | −16.4252 | + | 5.33688i | −0.928409 | + | 0.301658i | −0.733912 | − | 0.679245i | \(-0.762307\pi\) |
−0.194497 | + | 0.980903i | \(0.562307\pi\) | |||||||
\(314\) | 7.00000 | − | 21.5438i | 0.395033 | − | 1.21579i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.04508 | − | 3.21644i | −0.0587906 | − | 0.180939i | ||||
\(317\) | −0.257270 | − | 0.354102i | −0.0144497 | − | 0.0198883i | 0.801731 | − | 0.597685i | \(-0.203913\pi\) |
−0.816181 | + | 0.577797i | \(0.803913\pi\) | |||||||
\(318\) | − | 9.09017i | − | 0.509751i | ||||||
\(319\) | −0.527864 | + | 0.383516i | −0.0295547 | + | 0.0214728i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.59017 | − | 5.51458i | −0.423642 | − | 0.307794i | ||||
\(322\) | 1.00406 | − | 1.38197i | 0.0559539 | − | 0.0770140i | ||||
\(323\) | −23.7234 | − | 7.70820i | −1.32001 | − | 0.428896i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.47214 | 0.469228 | ||||||||
\(327\) | 12.1392 | + | 3.94427i | 0.671300 | + | 0.218119i | ||||
\(328\) | −4.53077 | + | 6.23607i | −0.250170 | + | 0.344329i | ||||
\(329\) | −3.61803 | − | 2.62866i | −0.199469 | − | 0.144922i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5623 | − | 10.5801i | 0.800417 | − | 0.581537i | −0.110620 | − | 0.993863i | \(-0.535284\pi\) |
0.911036 | + | 0.412326i | \(0.135284\pi\) | |||||||
\(332\) | − | 8.85410i | − | 0.485932i | ||||||
\(333\) | −4.70228 | − | 6.47214i | −0.257683 | − | 0.354671i | ||||
\(334\) | 0.527864 | + | 1.62460i | 0.0288834 | + | 0.0888941i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.118034 | + | 0.363271i | −0.00643928 | + | 0.0198181i | ||||
\(337\) | 11.4984 | − | 3.73607i | 0.626360 | − | 0.203517i | 0.0213978 | − | 0.999771i | \(-0.493188\pi\) |
0.604962 | + | 0.796254i | \(0.293188\pi\) | |||||||
\(338\) | 6.55139 | − | 2.12868i | 0.356349 | − | 0.115785i | ||||
\(339\) | −4.56231 | + | 14.0413i | −0.247790 | + | 0.762621i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.87132 | + | 5.75934i | 0.101338 | + | 0.311886i | ||||
\(342\) | 4.53077 | + | 6.23607i | 0.244996 | + | 0.337208i | ||||
\(343\) | − | 5.29180i | − | 0.285730i | ||||||
\(344\) | 4.61803 | − | 3.35520i | 0.248988 | − | 0.180900i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.92705 | + | 3.57971i | 0.264880 | + | 0.192447i | ||||
\(347\) | −0.257270 | + | 0.354102i | −0.0138110 | + | 0.0190092i | −0.815867 | − | 0.578240i | \(-0.803740\pi\) |
0.802056 | + | 0.597249i | \(0.203740\pi\) | |||||||
\(348\) | 0.449028 | + | 0.145898i | 0.0240704 | + | 0.00782096i | ||||
\(349\) | −7.88854 | −0.422264 | −0.211132 | − | 0.977458i | \(-0.567715\pi\) | ||||
−0.211132 | + | 0.977458i | \(0.567715\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.47214 | −0.131953 | ||||||||
\(352\) | −1.31433 | − | 0.427051i | −0.0700539 | − | 0.0227619i | ||||
\(353\) | −5.15131 | + | 7.09017i | −0.274177 | + | 0.377372i | −0.923794 | − | 0.382889i | \(-0.874929\pi\) |
0.649618 | + | 0.760261i | \(0.274929\pi\) | |||||||
\(354\) | 1.11803 | + | 0.812299i | 0.0594228 | + | 0.0431732i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0902 | + | 7.33094i | −0.534778 | + | 0.388539i | ||||
\(357\) | − | 1.23607i | − | 0.0654197i | ||||||
\(358\) | −1.84911 | − | 2.54508i | −0.0977286 | − | 0.134512i | ||||
\(359\) | 0.0557281 | + | 0.171513i | 0.00294122 | + | 0.00905213i | 0.952516 | − | 0.304487i | \(-0.0984852\pi\) |
−0.949575 | + | 0.313540i | \(0.898485\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4894 | − | 38.4383i | 0.657335 | − | 2.02307i | ||||
\(362\) | 23.4459 | − | 7.61803i | 1.23229 | − | 0.400395i | ||||
\(363\) | −8.64527 | + | 2.80902i | −0.453759 | + | 0.147435i | ||||
\(364\) | −0.291796 | + | 0.898056i | −0.0152943 | + | 0.0470709i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.23607 | − | 6.88191i | −0.116881 | − | 0.359723i | ||||
\(367\) | −16.6825 | − | 22.9615i | −0.870819 | − | 1.19858i | −0.978880 | − | 0.204436i | \(-0.934464\pi\) |
0.108060 | − | 0.994144i | \(-0.465536\pi\) | |||||||
\(368\) | − | 4.47214i | − | 0.233126i | ||||||
\(369\) | −6.23607 | + | 4.53077i | −0.324637 | + | 0.235862i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.80902 | − | 2.04087i | −0.145837 | − | 0.105957i | ||||
\(372\) | 2.57565 | − | 3.54508i | 0.133541 | − | 0.183804i | ||||
\(373\) | −19.4702 | − | 6.32624i | −1.00813 | − | 0.327560i | −0.242018 | − | 0.970272i | \(-0.577809\pi\) |
−0.766108 | + | 0.642712i | \(0.777809\pi\) | |||||||
\(374\) | 4.47214 | 0.231249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.7082 | −0.603805 | ||||||||
\(377\) | 1.11006 | + | 0.360680i | 0.0571709 | + | 0.0185760i | ||||
\(378\) | −0.224514 | + | 0.309017i | −0.0115478 | + | 0.0158941i | ||||
\(379\) | 1.76393 | + | 1.28157i | 0.0906071 | + | 0.0658299i | 0.632166 | − | 0.774833i | \(-0.282166\pi\) |
−0.541559 | + | 0.840662i | \(0.682166\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.20820 | − | 6.69015i | 0.471751 | − | 0.342747i | ||||
\(382\) | − | 17.7082i | − | 0.906031i | ||||||
\(383\) | 11.7557 | + | 16.1803i | 0.600688 | + | 0.826777i | 0.995771 | − | 0.0918688i | \(-0.0292840\pi\) |
−0.395083 | + | 0.918646i | \(0.629284\pi\) | |||||||
\(384\) | 0.309017 | + | 0.951057i | 0.0157695 | + | 0.0485334i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.44427 | − | 10.6004i | 0.175309 | − | 0.539545i | ||||
\(387\) | 5.42882 | − | 1.76393i | 0.275963 | − | 0.0896657i | ||||
\(388\) | 5.34307 | − | 1.73607i | 0.271253 | − | 0.0881355i | ||||
\(389\) | 4.51722 | − | 13.9026i | 0.229032 | − | 0.704889i | −0.768825 | − | 0.639459i | \(-0.779158\pi\) |
0.997857 | − | 0.0654294i | \(-0.0208417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.47214 | + | 13.7638i | 0.226166 | + | 0.696066i | ||||
\(392\) | −4.02874 | − | 5.54508i | −0.203482 | − | 0.280069i | ||||
\(393\) | − | 17.8885i | − | 0.902358i | ||||||
\(394\) | −4.78115 | + | 3.47371i | −0.240871 | + | 0.175003i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.11803 | − | 0.812299i | −0.0561833 | − | 0.0408196i | ||||
\(397\) | 20.7112 | − | 28.5066i | 1.03947 | − | 1.43070i | 0.141871 | − | 0.989885i | \(-0.454688\pi\) |
0.897596 | − | 0.440819i | \(-0.145312\pi\) | |||||||
\(398\) | −17.6008 | − | 5.71885i | −0.882248 | − | 0.286660i | ||||
\(399\) | 2.94427 | 0.147398 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2918 | 0.613823 | 0.306912 | − | 0.951738i | \(-0.400704\pi\) | ||||
0.306912 | + | 0.951738i | \(0.400704\pi\) | |||||||
\(402\) | −9.95959 | − | 3.23607i | −0.496739 | − | 0.161400i | ||||
\(403\) | 6.36737 | − | 8.76393i | 0.317181 | − | 0.436563i | ||||
\(404\) | 5.35410 | + | 3.88998i | 0.266377 | + | 0.193534i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.145898 | − | 0.106001i | 0.00724080 | − | 0.00526075i | ||||
\(407\) | − | 11.0557i | − | 0.548012i | ||||||
\(408\) | −1.90211 | − | 2.61803i | −0.0941686 | − | 0.129612i | ||||
\(409\) | 5.80902 | + | 17.8783i | 0.287237 | + | 0.884026i | 0.985719 | + | 0.168398i | \(0.0538594\pi\) |
−0.698482 | + | 0.715628i | \(0.746141\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.14590 | + | 9.68208i | −0.155176 | + | 0.477582i | ||||
\(412\) | −1.26133 | + | 0.409830i | −0.0621411 | + | 0.0201909i | ||||
\(413\) | 0.502029 | − | 0.163119i | 0.0247032 | − | 0.00802656i | ||||
\(414\) | 1.38197 | − | 4.25325i | 0.0679199 | − | 0.209036i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.763932 | + | 2.35114i | 0.0374548 | + | 0.115274i | ||||
\(417\) | −0.898056 | − | 1.23607i | −0.0439780 | − | 0.0605305i | ||||
\(418\) | 10.6525i | 0.521030i | ||||||||
\(419\) | 6.54508 | − | 4.75528i | 0.319748 | − | 0.232311i | −0.416320 | − | 0.909218i | \(-0.636680\pi\) |
0.736068 | + | 0.676908i | \(0.236680\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0344 | + | 16.0090i | 1.07389 | + | 0.780229i | 0.976608 | − | 0.215028i | \(-0.0689842\pi\) |
0.0972850 | + | 0.995257i | \(0.468984\pi\) | |||||||
\(422\) | −13.7638 | + | 18.9443i | −0.670012 | + | 0.922193i | ||||
\(423\) | −11.1352 | − | 3.61803i | −0.541410 | − | 0.175915i | ||||
\(424\) | −9.09017 | −0.441458 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4721 | −0.701177 | ||||||||
\(427\) | −2.62866 | − | 0.854102i | −0.127210 | − | 0.0413329i | ||||
\(428\) | −5.51458 | + | 7.59017i | −0.266557 | + | 0.366885i | ||||
\(429\) | −2.76393 | − | 2.00811i | −0.133444 | − | 0.0969527i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.7984 | − | 21.6498i | 1.43534 | − | 1.04283i | 0.446346 | − | 0.894861i | \(-0.352725\pi\) |
0.988991 | − | 0.147973i | \(-0.0472748\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 13.2290 | + | 18.2082i | 0.635747 | + | 0.875030i | 0.998380 | − | 0.0569016i | \(-0.0181221\pi\) |
−0.362633 | + | 0.931932i | \(0.618122\pi\) | |||||||
\(434\) | −0.517221 | − | 1.59184i | −0.0248274 | − | 0.0764109i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.94427 | − | 12.1392i | 0.188896 | − | 0.581363i | ||||
\(437\) | −32.7849 | + | 10.6525i | −1.56832 | + | 0.509577i | ||||
\(438\) | 11.8617 | − | 3.85410i | 0.566774 | − | 0.184156i | ||||
\(439\) | −4.48278 | + | 13.7966i | −0.213951 | + | 0.658475i | 0.785275 | + | 0.619147i | \(0.212522\pi\) |
−0.999226 | + | 0.0393275i | \(0.987478\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.11803 | − | 6.51864i | −0.100859 | − | 0.310411i | ||||
\(442\) | −4.70228 | − | 6.47214i | −0.223665 | − | 0.307848i | ||||
\(443\) | 14.3820i | 0.683308i | 0.939826 | + | 0.341654i | \(0.110987\pi\) | ||||
−0.939826 | + | 0.341654i | \(0.889013\pi\) | |||||||
\(444\) | −6.47214 | + | 4.70228i | −0.307154 | + | 0.223160i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.50000 | − | 1.81636i | −0.118378 | − | 0.0860070i | ||||
\(447\) | 6.41264 | − | 8.82624i | 0.303307 | − | 0.417467i | ||||
\(448\) | 0.363271 | + | 0.118034i | 0.0171630 | + | 0.00557658i | ||||
\(449\) | 14.2918 | 0.674472 | 0.337236 | − | 0.941420i | \(-0.390508\pi\) | ||||
0.337236 | + | 0.941420i | \(0.390508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6525 | −0.501605 | ||||||||
\(452\) | 14.0413 | + | 4.56231i | 0.660449 | + | 0.214593i | ||||
\(453\) | −1.57160 | + | 2.16312i | −0.0738401 | + | 0.101632i | ||||
\(454\) | 9.11803 | + | 6.62464i | 0.427931 | + | 0.310910i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.23607 | − | 4.53077i | 0.292031 | − | 0.212173i | ||||
\(457\) | − | 7.09017i | − | 0.331664i | −0.986154 | − | 0.165832i | \(-0.946969\pi\) | ||
0.986154 | − | 0.165832i | \(-0.0530310\pi\) | |||||||
\(458\) | 8.50651 | + | 11.7082i | 0.397483 | + | 0.547088i | ||||
\(459\) | −1.00000 | − | 3.07768i | −0.0466760 | − | 0.143654i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.88197 | + | 11.9475i | −0.180801 | + | 0.556449i | −0.999851 | − | 0.0172739i | \(-0.994501\pi\) |
0.819050 | + | 0.573723i | \(0.194501\pi\) | |||||||
\(462\) | −0.502029 | + | 0.163119i | −0.0233565 | + | 0.00758898i | ||||
\(463\) | −29.3238 | + | 9.52786i | −1.36279 | + | 0.442797i | −0.896974 | − | 0.442084i | \(-0.854239\pi\) |
−0.465817 | + | 0.884881i | \(0.654239\pi\) | |||||||
\(464\) | 0.145898 | − | 0.449028i | 0.00677315 | − | 0.0208456i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.90983 | − | 12.0332i | −0.181119 | − | 0.557428i | ||||
\(467\) | 15.4742 | + | 21.2984i | 0.716059 | + | 0.985571i | 0.999646 | + | 0.0266244i | \(0.00847582\pi\) |
−0.283586 | + | 0.958947i | \(0.591524\pi\) | |||||||
\(468\) | 2.47214i | 0.114275i | ||||||||
\(469\) | −3.23607 | + | 2.35114i | −0.149428 | + | 0.108566i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.3262 | − | 13.3148i | −0.844428 | − | 0.613513i | ||||
\(472\) | 0.812299 | − | 1.11803i | 0.0373891 | − | 0.0514617i | ||||
\(473\) | 7.50245 | + | 2.43769i | 0.344963 | + | 0.112085i | ||||
\(474\) | −3.38197 | −0.155339 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.23607 | −0.0566551 | ||||||||
\(477\) | −8.64527 | − | 2.80902i | −0.395840 | − | 0.128616i | ||||
\(478\) | 15.1109 | − | 20.7984i | 0.691157 | − | 0.951295i | ||||
\(479\) | 9.00000 | + | 6.53888i | 0.411220 | + | 0.298769i | 0.774096 | − | 0.633069i | \(-0.218205\pi\) |
−0.362875 | + | 0.931838i | \(0.618205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | + | 11.6247i | −0.729537 | + | 0.530040i | ||||
\(482\) | 10.5623i | 0.481100i | ||||||||
\(483\) | −1.00406 | − | 1.38197i | −0.0456862 | − | 0.0628816i | ||||
\(484\) | 2.80902 | + | 8.64527i | 0.127683 | + | 0.392967i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.309017 | + | 0.951057i | −0.0140173 | + | 0.0431408i | ||||
\(487\) | −6.46564 | + | 2.10081i | −0.292986 | + | 0.0951969i | −0.451822 | − | 0.892108i | \(-0.649226\pi\) |
0.158836 | + | 0.987305i | \(0.449226\pi\) | |||||||
\(488\) | −6.88191 | + | 2.23607i | −0.311529 | + | 0.101222i | ||||
\(489\) | 2.61803 | − | 8.05748i | 0.118392 | − | 0.364372i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.55573 | + | 7.86572i | 0.115338 | + | 0.354975i | 0.992017 | − | 0.126101i | \(-0.0402462\pi\) |
−0.876679 | + | 0.481076i | \(0.840246\pi\) | |||||||
\(492\) | 4.53077 | + | 6.23607i | 0.204263 | + | 0.281144i | ||||
\(493\) | 1.52786i | 0.0688115i | ||||||||
\(494\) | 15.4164 | − | 11.2007i | 0.693617 | − | 0.503942i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.54508 | − | 2.57565i | −0.159179 | − | 0.115650i | ||||
\(497\) | −3.24920 | + | 4.47214i | −0.145746 | + | 0.200603i | ||||
\(498\) | −8.42075 | − | 2.73607i | −0.377343 | − | 0.122606i | ||||
\(499\) | 13.5967 | 0.608674 | 0.304337 | − | 0.952564i | \(-0.401565\pi\) | ||||
0.304337 | + | 0.952564i | \(0.401565\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.70820 | 0.0763169 | ||||||||
\(502\) | 6.24112 | + | 2.02786i | 0.278555 | + | 0.0905080i | ||||
\(503\) | −6.98791 | + | 9.61803i | −0.311576 | + | 0.428847i | −0.935872 | − | 0.352341i | \(-0.885386\pi\) |
0.624296 | + | 0.781188i | \(0.285386\pi\) | |||||||
\(504\) | 0.309017 | + | 0.224514i | 0.0137647 | + | 0.0100006i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.00000 | − | 3.63271i | 0.222277 | − | 0.161494i | ||||
\(507\) | − | 6.88854i | − | 0.305931i | ||||||
\(508\) | −6.69015 | − | 9.20820i | −0.296827 | − | 0.408548i | ||||
\(509\) | −6.33688 | − | 19.5029i | −0.280877 | − | 0.864451i | −0.987604 | − | 0.156965i | \(-0.949829\pi\) |
0.706727 | − | 0.707487i | \(-0.250171\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.47214 | − | 4.53077i | 0.0651235 | − | 0.200429i | ||||
\(512\) | 0.951057 | − | 0.309017i | 0.0420312 | − | 0.0136568i | ||||
\(513\) | 7.33094 | − | 2.38197i | 0.323669 | − | 0.105166i | ||||
\(514\) | 6.79837 | − | 20.9232i | 0.299863 | − | 0.922885i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.76393 | − | 5.42882i | −0.0776528 | − | 0.238991i | ||||
\(517\) | −9.51057 | − | 13.0902i | −0.418274 | − | 0.575705i | ||||
\(518\) | 3.05573i | 0.134261i | ||||||||
\(519\) | 4.92705 | − | 3.57971i | 0.216274 | − | 0.157132i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.61803 | + | 4.80828i | 0.289941 | + | 0.210655i | 0.723242 | − | 0.690595i | \(-0.242651\pi\) |
−0.433301 | + | 0.901249i | \(0.642651\pi\) | |||||||
\(522\) | 0.277515 | − | 0.381966i | 0.0121465 | − | 0.0167182i | ||||
\(523\) | 27.5276 | + | 8.94427i | 1.20370 | + | 0.391106i | 0.841121 | − | 0.540847i | \(-0.181896\pi\) |
0.362579 | + | 0.931953i | \(0.381896\pi\) | |||||||
\(524\) | −17.8885 | −0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.70820 | 0.0744812 | ||||||||
\(527\) | 13.4863 | + | 4.38197i | 0.587473 | + | 0.190881i | ||||
\(528\) | −0.812299 | + | 1.11803i | −0.0353508 | + | 0.0486562i | ||||
\(529\) | −2.42705 | − | 1.76336i | −0.105524 | − | 0.0766676i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.11803 | − | 0.812299i | 0.0485185 | − | 0.0352508i | ||||
\(532\) | − | 2.94427i | − | 0.127650i | ||||||
\(533\) | 11.2007 | + | 15.4164i | 0.485155 | + | 0.667759i | ||||
\(534\) | 3.85410 | + | 11.8617i | 0.166783 | + | 0.513306i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.23607 | + | 9.95959i | −0.139777 | + | 0.430189i | ||||
\(537\) | −2.99193 | + | 0.972136i | −0.129111 | + | 0.0419508i | ||||
\(538\) | −1.98787 | + | 0.645898i | −0.0857032 | + | 0.0278466i | ||||
\(539\) | 2.92705 | − | 9.00854i | 0.126077 | − | 0.388025i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.18034 | − | 3.63271i | −0.0507468 | − | 0.156183i | 0.922472 | − | 0.386065i | \(-0.126166\pi\) |
−0.973218 | + | 0.229882i | \(0.926166\pi\) | |||||||
\(542\) | 6.48588 | + | 8.92705i | 0.278592 | + | 0.383450i | ||||
\(543\) | − | 24.6525i | − | 1.05794i | ||||||
\(544\) | −2.61803 | + | 1.90211i | −0.112247 | + | 0.0815524i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.763932 | + | 0.555029i | 0.0326933 | + | 0.0237531i | ||||
\(547\) | 2.17963 | − | 3.00000i | 0.0931941 | − | 0.128271i | −0.759874 | − | 0.650071i | \(-0.774739\pi\) |
0.853068 | + | 0.521800i | \(0.174739\pi\) | |||||||
\(548\) | 9.68208 | + | 3.14590i | 0.413598 | + | 0.134386i | ||||
\(549\) | −7.23607 | −0.308828 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.63932 | −0.155040 | ||||||||
\(552\) | −4.25325 | − | 1.38197i | −0.181031 | − | 0.0588204i | ||||
\(553\) | −0.759299 | + | 1.04508i | −0.0322887 | + | 0.0444415i | ||||
\(554\) | −0.763932 | − | 0.555029i | −0.0324564 | − | 0.0235809i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.23607 | + | 0.898056i | −0.0524210 | + | 0.0380861i | ||||
\(557\) | 2.67376i | 0.113291i | 0.998394 | + | 0.0566455i | \(0.0180405\pi\) | ||||
−0.998394 | + | 0.0566455i | \(0.981960\pi\) | |||||||
\(558\) | −2.57565 | − | 3.54508i | −0.109036 | − | 0.150075i | ||||
\(559\) | −4.36068 | − | 13.4208i | −0.184437 | − | 0.567639i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.38197 | − | 4.25325i | 0.0583467 | − | 0.179573i | ||||
\(562\) | −28.4257 | + | 9.23607i | −1.19907 | + | 0.389600i | ||||
\(563\) | 11.6699 | − | 3.79180i | 0.491830 | − | 0.159805i | −0.0525933 | − | 0.998616i | \(-0.516749\pi\) |
0.544423 | + | 0.838811i | \(0.316749\pi\) | |||||||
\(564\) | −3.61803 | + | 11.1352i | −0.152347 | + | 0.468875i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.70820 | + | 29.8788i | 0.408066 | + | 1.25590i | ||||
\(567\) | 0.224514 | + | 0.309017i | 0.00942870 | + | 0.0129775i | ||||
\(568\) | 14.4721i | 0.607237i | ||||||||
\(569\) | 35.4164 | − | 25.7315i | 1.48473 | − | 1.07872i | 0.508740 | − | 0.860920i | \(-0.330111\pi\) |
0.975993 | − | 0.217801i | \(-0.0698885\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5623 | + | 16.3925i | 0.944203 | + | 0.686004i | 0.949429 | − | 0.313983i | \(-0.101663\pi\) |
−0.00522561 | + | 0.999986i | \(0.501663\pi\) | |||||||
\(572\) | −2.00811 | + | 2.76393i | −0.0839635 | + | 0.115566i | ||||
\(573\) | −16.8415 | − | 5.47214i | −0.703564 | − | 0.228602i | ||||
\(574\) | 2.94427 | 0.122892 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 36.1199 | + | 11.7361i | 1.50369 | + | 0.488579i | 0.941092 | − | 0.338151i | \(-0.109801\pi\) |
0.562599 | + | 0.826730i | \(0.309801\pi\) | |||||||
\(578\) | −3.83698 | + | 5.28115i | −0.159597 | + | 0.219667i | ||||
\(579\) | −9.01722 | − | 6.55139i | −0.374743 | − | 0.272267i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.73607 | + | 1.98787i | −0.113511 | + | 0.0824707i | ||||
\(582\) | − | 5.61803i | − | 0.232875i | ||||||
\(583\) | −7.38394 | − | 10.1631i | −0.305811 | − | 0.420913i | ||||
\(584\) | −3.85410 | − | 11.8617i | −0.159484 | − | 0.490841i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.37132 | + | 10.3759i | −0.139268 | + | 0.428623i | ||||
\(587\) | −28.5645 | + | 9.28115i | −1.17898 | + | 0.383074i | −0.831988 | − | 0.554794i | \(-0.812797\pi\) |
−0.346993 | + | 0.937868i | \(0.612797\pi\) | |||||||
\(588\) | −6.51864 | + | 2.11803i | −0.268824 | + | 0.0873462i | ||||
\(589\) | −10.4377 | + | 32.1239i | −0.430078 | + | 1.32364i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.82624 | + | 5.62058i | 0.0751214 | + | 0.231200i | ||||
\(592\) | 4.70228 | + | 6.47214i | 0.193263 | + | 0.266003i | ||||
\(593\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(594\) | −1.11803 | + | 0.812299i | −0.0458735 | + | 0.0333290i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.82624 | − | 6.41264i | −0.361537 | − | 0.262672i | ||||
\(597\) | −10.8779 | + | 14.9721i | −0.445203 | + | 0.612769i | ||||
\(598\) | −10.5146 | − | 3.41641i | −0.429975 | − | 0.139707i | ||||
\(599\) | 8.47214 | 0.346162 | 0.173081 | − | 0.984908i | \(-0.444628\pi\) | ||||
0.173081 | + | 0.984908i | \(0.444628\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.2705 | −1.68346 | −0.841730 | − | 0.539899i | \(-0.818462\pi\) | ||||
−0.841730 | + | 0.539899i | \(0.818462\pi\) | |||||||
\(602\) | −2.07363 | − | 0.673762i | −0.0845147 | − | 0.0274605i | ||||
\(603\) | −6.15537 | + | 8.47214i | −0.250666 | + | 0.345012i | ||||
\(604\) | 2.16312 | + | 1.57160i | 0.0880161 | + | 0.0639474i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.35410 | − | 3.88998i | 0.217496 | − | 0.158020i | ||||
\(607\) | 13.5623i | 0.550477i | 0.961376 | + | 0.275239i | \(0.0887568\pi\) | ||||
−0.961376 | + | 0.275239i | \(0.911243\pi\) | |||||||
\(608\) | −4.53077 | − | 6.23607i | −0.183747 | − | 0.252906i | ||||
\(609\) | −0.0557281 | − | 0.171513i | −0.00225822 | − | 0.00695007i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.94427 | + | 27.5276i | −0.361847 | + | 1.11365i | ||||
\(612\) | −3.07768 | + | 1.00000i | −0.124408 | + | 0.0404226i | ||||
\(613\) | 30.6708 | − | 9.96556i | 1.23878 | − | 0.402505i | 0.384895 | − | 0.922961i | \(-0.374238\pi\) |
0.853889 | + | 0.520455i | \(0.174238\pi\) | |||||||
\(614\) | −3.09017 | + | 9.51057i | −0.124709 | + | 0.383815i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.163119 | + | 0.502029i | 0.00657225 | + | 0.0202273i | ||||
\(617\) | 22.2703 | + | 30.6525i | 0.896570 | + | 1.23402i | 0.971549 | + | 0.236837i | \(0.0761108\pi\) |
−0.0749797 | + | 0.997185i | \(0.523889\pi\) | |||||||
\(618\) | 1.32624i | 0.0533491i | ||||||||
\(619\) | 14.0902 | − | 10.2371i | 0.566332 | − | 0.411464i | −0.267439 | − | 0.963575i | \(-0.586177\pi\) |
0.833771 | + | 0.552111i | \(0.186177\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.61803 | − | 2.62866i | −0.145187 | − | 0.105484i | ||||
\(622\) | 11.1352 | − | 15.3262i | 0.446479 | − | 0.614526i | ||||
\(623\) | 4.53077 | + | 1.47214i | 0.181521 | + | 0.0589799i | ||||
\(624\) | 2.47214 | 0.0989646 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.2705 | 0.690268 | ||||||||
\(627\) | 10.1311 | + | 3.29180i | 0.404597 | + | 0.131462i | ||||
\(628\) | −13.3148 | + | 18.3262i | −0.531318 | + | 0.731297i | ||||
\(629\) | −20.9443 | − | 15.2169i | −0.835103 | − | 0.606738i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.3607 | + | 22.0583i | −1.20864 | + | 0.878128i | −0.995107 | − | 0.0988078i | \(-0.968497\pi\) |
−0.213533 | + | 0.976936i | \(0.568497\pi\) | |||||||
\(632\) | 3.38197i | 0.134527i | ||||||||
\(633\) | 13.7638 | + | 18.9443i | 0.547063 | + | 0.752967i | ||||
\(634\) | 0.135255 | + | 0.416272i | 0.00537166 | + | 0.0165323i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.80902 | + | 8.64527i | −0.111385 | + | 0.342807i | ||||
\(637\) | −16.1150 | + | 5.23607i | −0.638498 | + | 0.207461i | ||||
\(638\) | 0.620541 | − | 0.201626i | 0.0245675 | − | 0.00798245i | ||||
\(639\) | −4.47214 | + | 13.7638i | −0.176915 | + | 0.544488i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1803 | − | 34.4095i | −0.441597 | − | 1.35910i | −0.886173 | − | 0.463354i | \(-0.846646\pi\) |
0.444576 | − | 0.895741i | \(-0.353354\pi\) | |||||||
\(642\) | 5.51458 | + | 7.59017i | 0.217643 | + | 0.299560i | ||||
\(643\) | − | 13.8885i | − | 0.547711i | −0.961771 | − | 0.273855i | \(-0.911701\pi\) | ||
0.961771 | − | 0.273855i | \(-0.0882990\pi\) | |||||||
\(644\) | −1.38197 | + | 1.00406i | −0.0544571 | + | 0.0395654i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.1803 | + | 14.6619i | 0.793985 | + | 0.576864i | ||||
\(647\) | 2.97168 | − | 4.09017i | 0.116829 | − | 0.160801i | −0.746598 | − | 0.665276i | \(-0.768314\pi\) |
0.863426 | + | 0.504475i | \(0.168314\pi\) | |||||||
\(648\) | 0.951057 | + | 0.309017i | 0.0373610 | + | 0.0121393i | ||||
\(649\) | 1.90983 | 0.0749674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.67376 | −0.0655999 | ||||||||
\(652\) | −8.05748 | − | 2.61803i | −0.315555 | − | 0.102530i | ||||
\(653\) | 1.67760 | − | 2.30902i | 0.0656495 | − | 0.0903588i | −0.774930 | − | 0.632047i | \(-0.782215\pi\) |
0.840579 | + | 0.541689i | \(0.182215\pi\) | |||||||
\(654\) | −10.3262 | − | 7.50245i | −0.403788 | − | 0.293369i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.23607 | − | 4.53077i | 0.243478 | − | 0.176897i | ||||
\(657\) | − | 12.4721i | − | 0.486584i | ||||||
\(658\) | 2.62866 | + | 3.61803i | 0.102476 | + | 0.141046i | ||||
\(659\) | 5.68034 | + | 17.4823i | 0.221275 | + | 0.681013i | 0.998648 | + | 0.0519743i | \(0.0165514\pi\) |
−0.777374 | + | 0.629039i | \(0.783449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.65248 | + | 20.4742i | −0.258751 | + | 0.796355i | 0.734316 | + | 0.678808i | \(0.237503\pi\) |
−0.993067 | + | 0.117547i | \(0.962497\pi\) | |||||||
\(662\) | −17.1190 | + | 5.56231i | −0.665350 | + | 0.216185i | ||||
\(663\) | −7.60845 | + | 2.47214i | −0.295488 | + | 0.0960098i | ||||
\(664\) | −2.73607 | + | 8.42075i | −0.106180 | + | 0.326789i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.47214 | + | 7.60845i | 0.0957933 | + | 0.294822i | ||||
\(667\) | 1.24108 | + | 1.70820i | 0.0480549 | + | 0.0661419i | ||||
\(668\) | − | 1.70820i | − | 0.0660924i | ||||||
\(669\) | −2.50000 | + | 1.81636i | −0.0966556 | + | 0.0702244i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.09017 | − | 5.87785i | −0.312318 | − | 0.226912i | ||||
\(672\) | 0.224514 | − | 0.309017i | 0.00866082 | − | 0.0119206i | ||||
\(673\) | 23.2541 | + | 7.55573i | 0.896381 | + | 0.291252i | 0.720743 | − | 0.693203i | \(-0.243801\pi\) |
0.175639 | + | 0.984455i | \(0.443801\pi\) | |||||||
\(674\) | −12.0902 | −0.465696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.88854 | −0.264944 | ||||||||
\(677\) | −17.0333 | − | 5.53444i | −0.654641 | − | 0.212706i | −0.0371818 | − | 0.999309i | \(-0.511838\pi\) |
−0.617460 | + | 0.786603i | \(0.711838\pi\) | |||||||
\(678\) | 8.67802 | − | 11.9443i | 0.333277 | − | 0.458717i | ||||
\(679\) | −1.73607 | − | 1.26133i | −0.0666242 | − | 0.0484053i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.11803 | − | 6.62464i | 0.349404 | − | 0.253857i | ||||
\(682\) | − | 6.05573i | − | 0.231886i | ||||||
\(683\) | 2.64890 | + | 3.64590i | 0.101357 | + | 0.139506i | 0.856683 | − | 0.515843i | \(-0.172521\pi\) |
−0.755326 | + | 0.655350i | \(0.772521\pi\) | |||||||
\(684\) | −2.38197 | − | 7.33094i | −0.0910767 | − | 0.280305i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.63525 | + | 5.03280i | −0.0624343 | + | 0.192153i | ||||
\(687\) | 13.7638 | − | 4.47214i | 0.525122 | − | 0.170623i | ||||
\(688\) | −5.42882 | + | 1.76393i | −0.206972 | + | 0.0672493i | ||||
\(689\) | −6.94427 | + | 21.3723i | −0.264556 | + | 0.814219i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.09017 | + | 6.43288i | 0.0795138 | + | 0.244718i | 0.982909 | − | 0.184090i | \(-0.0589337\pi\) |
−0.903396 | + | 0.428808i | \(0.858934\pi\) | |||||||
\(692\) | −3.57971 | − | 4.92705i | −0.136080 | − | 0.187298i | ||||
\(693\) | 0.527864i | 0.0200519i | ||||||||
\(694\) | 0.354102 | − | 0.257270i | 0.0134415 | − | 0.00976584i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.381966 | − | 0.277515i | −0.0144784 | − | 0.0105192i | ||||
\(697\) | −14.6619 | + | 20.1803i | −0.555358 | + | 0.764385i | ||||
\(698\) | 7.50245 | + | 2.43769i | 0.283972 | + | 0.0922681i | ||||
\(699\) | −12.6525 | −0.478561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.8328 | −0.484689 | −0.242344 | − | 0.970190i | \(-0.577916\pi\) | ||||
−0.242344 | + | 0.970190i | \(0.577916\pi\) | |||||||
\(702\) | 2.35114 | + | 0.763932i | 0.0887381 | + | 0.0288328i | ||||
\(703\) | 36.2461 | − | 49.8885i | 1.36705 | − | 1.88158i | ||||
\(704\) | 1.11803 | + | 0.812299i | 0.0421375 | + | 0.0306147i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.09017 | − | 5.15131i | 0.266842 | − | 0.193872i | ||||
\(707\) | − | 2.52786i | − | 0.0950701i | ||||||
\(708\) | −0.812299 | − | 1.11803i | −0.0305281 | − | 0.0420183i | ||||
\(709\) | 9.36068 | + | 28.8092i | 0.351548 | + | 1.08195i | 0.957984 | + | 0.286821i | \(0.0925984\pi\) |
−0.606437 | + | 0.795132i | \(0.707402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04508 | + | 3.21644i | −0.0391937 | + | 0.120626i | ||||
\(712\) | 11.8617 | − | 3.85410i | 0.444536 | − | 0.144439i | ||||
\(713\) | 18.6376 | − | 6.05573i | 0.697984 | − | 0.226789i | ||||
\(714\) | −0.381966 | + | 1.17557i | −0.0142947 | + | 0.0439946i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.972136 | + | 2.99193i | 0.0363304 | + | 0.111814i | ||||
\(717\) | −15.1109 | − | 20.7984i | −0.564327 | − | 0.776730i | ||||
\(718\) | − | 0.180340i | − | 0.00673022i | ||||||
\(719\) | −35.1246 | + | 25.5195i | −1.30993 | + | 0.951718i | −0.309927 | + | 0.950760i | \(0.600305\pi\) |
−1.00000 | 0.000957448i | \(0.999695\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.409830 | + | 0.297759i | 0.0152629 | + | 0.0110891i | ||||
\(722\) | −23.7562 | + | 32.6976i | −0.884113 | + | 1.21688i | ||||
\(723\) | 10.0453 | + | 3.26393i | 0.373591 | + | 0.121387i | ||||
\(724\) | −24.6525 | −0.916202 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.09017 | 0.337368 | ||||||||
\(727\) | 33.6830 | + | 10.9443i | 1.24923 | + | 0.405901i | 0.857646 | − | 0.514240i | \(-0.171926\pi\) |
0.391587 | + | 0.920141i | \(0.371926\pi\) | |||||||
\(728\) | 0.555029 | − | 0.763932i | 0.0205707 | − | 0.0283132i | ||||
\(729\) | 0.809017 | + | 0.587785i | 0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9443 | − | 10.8576i | 0.552734 | − | 0.401585i | ||||
\(732\) | 7.23607i | 0.267453i | ||||||||
\(733\) | 0.0655123 | + | 0.0901699i | 0.00241975 | + | 0.00333050i | 0.810225 | − | 0.586119i | \(-0.199345\pi\) |
−0.807805 | + | 0.589449i | \(0.799345\pi\) | |||||||
\(734\) | 8.77051 | + | 26.9929i | 0.323725 | + | 0.996324i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.38197 | + | 4.25325i | −0.0509399 | + | 0.156777i | ||||
\(737\) | −13.7638 | + | 4.47214i | −0.506997 | + | 0.164733i | ||||
\(738\) | 7.33094 | − | 2.38197i | 0.269856 | − | 0.0876814i | ||||
\(739\) | 7.97871 | − | 24.5560i | 0.293502 | − | 0.903305i | −0.690219 | − | 0.723601i | \(-0.742486\pi\) |
0.983721 | − | 0.179705i | \(-0.0575142\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.88854 | − | 18.1231i | −0.216321 | − | 0.665768i | ||||
\(742\) | 2.04087 | + | 2.80902i | 0.0749227 | + | 0.103122i | ||||
\(743\) | 37.0132i | 1.35788i | 0.734193 | + | 0.678940i | \(0.237561\pi\) | ||||
−0.734193 | + | 0.678940i | \(0.762439\pi\) | |||||||
\(744\) | −3.54508 | + | 2.57565i | −0.129969 | + | 0.0944281i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.5623 | + | 12.0332i | 0.606389 | + | 0.440567i | ||||
\(747\) | −5.20431 | + | 7.16312i | −0.190416 | + | 0.262085i | ||||
\(748\) | −4.25325 | − | 1.38197i | −0.155514 | − | 0.0505297i | ||||
\(749\) | 3.58359 | 0.130942 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.201626 | 0.00735744 | 0.00367872 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00367872 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(752\) | 11.1352 | + | 3.61803i | 0.406058 | + | 0.131936i | ||||
\(753\) | 3.85723 | − | 5.30902i | 0.140565 | − | 0.193471i | ||||
\(754\) | −0.944272 | − | 0.686054i | −0.0343884 | − | 0.0249846i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.309017 | − | 0.224514i | 0.0112388 | − | 0.00816549i | ||||
\(757\) | − | 23.1246i | − | 0.840478i | −0.907413 | − | 0.420239i | \(-0.861946\pi\) | ||
0.907413 | − | 0.420239i | \(-0.138054\pi\) | |||||||
\(758\) | −1.28157 | − | 1.76393i | −0.0465488 | − | 0.0640689i | ||||
\(759\) | −1.90983 | − | 5.87785i | −0.0693224 | − | 0.213353i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.85410 | + | 24.1724i | −0.284711 | + | 0.876250i | 0.701774 | + | 0.712399i | \(0.252392\pi\) |
−0.986485 | + | 0.163851i | \(0.947608\pi\) | |||||||
\(762\) | −10.8249 | + | 3.51722i | −0.392144 | + | 0.127415i | ||||
\(763\) | −4.63677 | + | 1.50658i | −0.167862 | + | 0.0545418i | ||||
\(764\) | −5.47214 | + | 16.8415i | −0.197975 | + | 0.609304i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.18034 | − | 19.0211i | −0.223305 | − | 0.687261i | ||||
\(767\) | −2.00811 | − | 2.76393i | −0.0725088 | − | 0.0997998i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −28.8713 | + | 20.9762i | −1.04113 | + | 0.756423i | −0.970505 | − | 0.241080i | \(-0.922498\pi\) |
−0.0706214 | + | 0.997503i | \(0.522498\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.7984 | − | 12.9313i | −0.640993 | − | 0.465709i | ||||
\(772\) | −6.55139 | + | 9.01722i | −0.235790 | + | 0.324537i | ||||
\(773\) | −7.46969 | − | 2.42705i | −0.268666 | − | 0.0872950i | 0.171586 | − | 0.985169i | \(-0.445111\pi\) |
−0.440252 | + | 0.897874i | \(0.645111\pi\) | |||||||
\(774\) | −5.70820 | −0.205177 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.61803 | −0.201676 | ||||||||
\(777\) | 2.90617 | + | 0.944272i | 0.104258 | + | 0.0338756i | ||||
\(778\) | −8.59226 | + | 11.8262i | −0.308048 | + | 0.423991i | ||||
\(779\) | −48.0689 | − | 34.9241i | −1.72225 | − | 1.25129i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.1803 | + | 11.7557i | −0.578978 | + | 0.420652i | ||||
\(782\) | − | 14.4721i | − | 0.517523i | ||||||
\(783\) | −0.277515 | − | 0.381966i | −0.00991756 | − | 0.0136504i | ||||
\(784\) | 2.11803 | + | 6.51864i | 0.0756441 | + | 0.232809i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.52786 | + | 17.0130i | −0.197172 | + | 0.606834i | ||||
\(787\) | −28.5972 | + | 9.29180i | −1.01938 | + | 0.331217i | −0.770584 | − | 0.637339i | \(-0.780035\pi\) |
−0.248797 | + | 0.968556i | \(0.580035\pi\) | |||||||
\(788\) | 5.62058 | − | 1.82624i | 0.200225 | − | 0.0650570i | ||||
\(789\) | 0.527864 | − | 1.62460i | 0.0187925 | − | 0.0578372i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.74265 | − | 5.36331i | −0.0619614 | − | 0.190697i | ||||
\(792\) | 0.812299 | + | 1.11803i | 0.0288638 | + | 0.0397276i | ||||
\(793\) | 17.8885i | 0.635241i | ||||||||
\(794\) | −28.5066 | + | 20.7112i | −1.01166 | + | 0.735014i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9721 | + | 10.8779i | 0.530673 | + | 0.385557i | ||||
\(797\) | 21.4580 | − | 29.5344i | 0.760082 | − | 1.04616i | −0.237125 | − | 0.971479i | \(-0.576205\pi\) |
0.997207 | − | 0.0746844i | \(-0.0237949\pi\) | |||||||
\(798\) | −2.80017 | − | 0.909830i | −0.0991249 | − | 0.0322076i | ||||
\(799\) | −37.8885 | −1.34040 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.4721 | 0.440681 | ||||||||
\(802\) | −11.6902 | − | 3.79837i | −0.412795 | − | 0.134125i | ||||
\(803\) | 10.1311 | − | 13.9443i | 0.357519 | − | 0.492083i | ||||
\(804\) | 8.47214 | + | 6.15537i | 0.298789 | + | 0.217083i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.76393 | + | 6.36737i | −0.308696 | + | 0.224281i | ||||
\(807\) | 2.09017i | 0.0735775i | ||||||||
\(808\) | −3.88998 | − | 5.35410i | −0.136849 | − | 0.188357i | ||||
\(809\) | −7.05573 | − | 21.7153i | −0.248066 | − | 0.763469i | −0.995117 | − | 0.0987023i | \(-0.968531\pi\) |
0.747051 | − | 0.664767i | \(-0.231469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.38197 | − | 7.33094i | 0.0836421 | − | 0.257424i | −0.900486 | − | 0.434886i | \(-0.856789\pi\) |
0.984128 | + | 0.177462i | \(0.0567887\pi\) | |||||||
\(812\) | −0.171513 | + | 0.0557281i | −0.00601894 | + | 0.00195567i | ||||
\(813\) | 10.4944 | − | 3.40983i | 0.368054 | − | 0.119588i | ||||
\(814\) | −3.41641 | + | 10.5146i | −0.119745 | + | 0.368537i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | + | 3.07768i | 0.0350070 | + | 0.107740i | ||||
\(817\) | 25.8626 | + | 35.5967i | 0.904816 | + | 1.24537i | ||||
\(818\) | − | 18.7984i | − | 0.657270i | ||||||
\(819\) | 0.763932 | − | 0.555029i | 0.0266939 | − | 0.0193943i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.4336 | + | 19.9317i | 0.957440 | + | 0.695621i | 0.952555 | − | 0.304367i | \(-0.0984449\pi\) |
0.00488541 | + | 0.999988i | \(0.498445\pi\) | |||||||
\(822\) | 5.98385 | − | 8.23607i | 0.208711 | − | 0.287266i | ||||
\(823\) | 30.4666 | + | 9.89919i | 1.06200 | + | 0.345064i | 0.787366 | − | 0.616486i | \(-0.211444\pi\) |
0.274631 | + | 0.961550i | \(0.411444\pi\) | |||||||
\(824\) | 1.32624 | 0.0462017 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.527864 | −0.0183667 | ||||||||
\(827\) | 40.9937 | + | 13.3197i | 1.42549 | + | 0.463170i | 0.917342 | − | 0.398100i | \(-0.130330\pi\) |
0.508148 | + | 0.861270i | \(0.330330\pi\) | |||||||
\(828\) | −2.62866 | + | 3.61803i | −0.0913521 | + | 0.125735i | ||||
\(829\) | −8.00000 | − | 5.81234i | −0.277851 | − | 0.201871i | 0.440128 | − | 0.897935i | \(-0.354933\pi\) |
−0.717980 | + | 0.696064i | \(0.754933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.763932 | + | 0.555029i | −0.0265005 | + | 0.0192537i | ||||
\(832\) | − | 2.47214i | − | 0.0857059i | ||||||
\(833\) | −13.0373 | − | 17.9443i | −0.451715 | − | 0.621732i | ||||
\(834\) | 0.472136 | + | 1.45309i | 0.0163487 | + | 0.0503162i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.29180 | − | 10.1311i | 0.113849 | − | 0.350392i | ||||
\(837\) | −4.16750 | + | 1.35410i | −0.144050 | + | 0.0468046i | ||||
\(838\) | −7.69421 | + | 2.50000i | −0.265792 | + | 0.0863611i | ||||
\(839\) | 11.8541 | − | 36.4832i | 0.409249 | − | 1.25954i | −0.508046 | − | 0.861330i | \(-0.669632\pi\) |
0.917295 | − | 0.398209i | \(-0.130368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.89261 | − | 27.3686i | −0.306642 | − | 0.943746i | ||||
\(842\) | −16.0090 | − | 22.0344i | −0.551705 | − | 0.759357i | ||||
\(843\) | 29.8885i | 1.02942i | ||||||||
\(844\) | 18.9443 | − | 13.7638i | 0.652089 | − | 0.473770i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.47214 | + | 6.88191i | 0.325659 | + | 0.236605i | ||||
\(847\) | 2.04087 | − | 2.80902i | 0.0701251 | − | 0.0965190i | ||||
\(848\) | 8.64527 | + | 2.80902i | 0.296880 | + | 0.0964620i | ||||
\(849\) | 31.4164 | 1.07821 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.7771 | −1.22642 | ||||||||
\(852\) | 13.7638 | + | 4.47214i | 0.471541 | + | 0.153213i | ||||
\(853\) | 3.28969 | − | 4.52786i | 0.112637 | − | 0.155031i | −0.748977 | − | 0.662597i | \(-0.769454\pi\) |
0.861613 | + | 0.507565i | \(0.169454\pi\) | |||||||
\(854\) | 2.23607 | + | 1.62460i | 0.0765167 | + | 0.0555926i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.59017 | − | 5.51458i | 0.259427 | − | 0.188485i | ||||
\(857\) | − | 42.0689i | − | 1.43705i | −0.695503 | − | 0.718523i | \(-0.744819\pi\) | ||
0.695503 | − | 0.718523i | \(-0.255181\pi\) | |||||||
\(858\) | 2.00811 | + | 2.76393i | 0.0685559 | + | 0.0943591i | ||||
\(859\) | 4.85410 | + | 14.9394i | 0.165620 | + | 0.509725i | 0.999081 | − | 0.0428520i | \(-0.0136444\pi\) |
−0.833462 | + | 0.552577i | \(0.813644\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.909830 | − | 2.80017i | 0.0310069 | − | 0.0954295i | ||||
\(862\) | −35.0301 | + | 11.3820i | −1.19313 | + | 0.387671i | ||||
\(863\) | −11.5842 | + | 3.76393i | −0.394330 | + | 0.128126i | −0.499469 | − | 0.866332i | \(-0.666471\pi\) |
0.105138 | + | 0.994458i | \(0.466471\pi\) | |||||||
\(864\) | 0.309017 | − | 0.951057i | 0.0105130 | − | 0.0323556i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.95492 | − | 21.4050i | −0.236338 | − | 0.727372i | ||||
\(867\) | 3.83698 | + | 5.28115i | 0.130311 | + | 0.179357i | ||||
\(868\) | 1.67376i | 0.0568112i | ||||||||
\(869\) | −3.78115 | + | 2.74717i | −0.128267 | + | 0.0931913i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.9443 | + | 15.2169i | 0.709670 | + | 0.515605i | ||||
\(872\) | −7.50245 | + | 10.3262i | −0.254065 | + | 0.349691i | ||||
\(873\) | −5.34307 | − | 1.73607i | −0.180835 | − | 0.0587570i | ||||
\(874\) | 34.4721 | 1.16604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.4721 | −0.421394 | ||||||||
\(877\) | −2.97168 | − | 0.965558i | −0.100347 | − | 0.0326046i | 0.258413 | − | 0.966034i | \(-0.416800\pi\) |
−0.358760 | + | 0.933430i | \(0.616800\pi\) | |||||||
\(878\) | 8.52675 | − | 11.7361i | 0.287764 | − | 0.396073i | ||||
\(879\) | 8.82624 | + | 6.41264i | 0.297702 | + | 0.216293i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.7082 | + | 15.0454i | −0.697677 | + | 0.506892i | −0.879175 | − | 0.476499i | \(-0.841905\pi\) |
0.181498 | + | 0.983391i | \(0.441905\pi\) | |||||||
\(882\) | 6.85410i | 0.230790i | ||||||||
\(883\) | −16.4985 | − | 22.7082i | −0.555218 | − | 0.764192i | 0.435491 | − | 0.900193i | \(-0.356575\pi\) |
−0.990709 | + | 0.136001i | \(0.956575\pi\) | |||||||
\(884\) | 2.47214 | + | 7.60845i | 0.0831469 | + | 0.255900i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.44427 | − | 13.6781i | 0.149308 | − | 0.459523i | ||||
\(887\) | −3.24920 | + | 1.05573i | −0.109097 | + | 0.0354479i | −0.363057 | − | 0.931767i | \(-0.618267\pi\) |
0.253960 | + | 0.967215i | \(0.418267\pi\) | |||||||
\(888\) | 7.60845 | − | 2.47214i | 0.255323 | − | 0.0829595i | ||||
\(889\) | −1.34346 | + | 4.13474i | −0.0450582 | + | 0.138675i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.427051 | + | 1.31433i | 0.0143067 | + | 0.0440316i | ||||
\(892\) | 1.81636 | + | 2.50000i | 0.0608161 | + | 0.0837062i | ||||
\(893\) | − | 90.2492i | − | 3.02008i | ||||||
\(894\) | −8.82624 | + | 6.41264i | −0.295194 | + | 0.214471i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.309017 | − | 0.224514i | −0.0103235 | − | 0.00750049i | ||||
\(897\) | −6.49839 | + | 8.94427i | −0.216975 | + | 0.298641i | ||||
\(898\) | −13.5923 | − | 4.41641i | −0.453581 | − | 0.147377i | ||||
\(899\) | 2.06888 | 0.0690011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.4164 | −0.980003 | ||||||||
\(902\) | 10.1311 | + | 3.29180i | 0.337329 | + | 0.109605i | ||||
\(903\) | −1.28157 | + | 1.76393i | −0.0426480 | + | 0.0587000i | ||||
\(904\) | −11.9443 | − | 8.67802i | −0.397261 | − | 0.288627i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.16312 | − | 1.57160i | 0.0718648 | − | 0.0522128i | ||||
\(907\) | − | 21.5279i | − | 0.714821i | −0.933947 | − | 0.357410i | \(-0.883660\pi\) | ||
0.933947 | − | 0.357410i | \(-0.116340\pi\) | |||||||
\(908\) | −6.62464 | − | 9.11803i | −0.219846 | − | 0.302593i | ||||
\(909\) | −2.04508 | − | 6.29412i | −0.0678312 | − | 0.208763i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.29180 | + | 3.97574i | −0.0427991 | + | 0.131722i | −0.970173 | − | 0.242414i | \(-0.922061\pi\) |
0.927374 | + | 0.374136i | \(0.122061\pi\) | |||||||
\(912\) | −7.33094 | + | 2.38197i | −0.242752 | + | 0.0788748i | ||||
\(913\) | −11.6372 | + | 3.78115i | −0.385135 | + | 0.125138i | ||||
\(914\) | −2.19098 | + | 6.74315i | −0.0724713 | + | 0.223044i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.47214 | − | 13.7638i | −0.147764 | − | 0.454769i | ||||
\(917\) | 4.01623 | + | 5.52786i | 0.132628 | + | 0.182546i | ||||
\(918\) | 3.23607i | 0.106806i | ||||||||
\(919\) | 39.4164 | − | 28.6377i | 1.30023 | − | 0.944670i | 0.300269 | − | 0.953854i | \(-0.402923\pi\) |
0.999958 | + | 0.00918396i | \(0.00292339\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.09017 | + | 5.87785i | 0.266580 | + | 0.193682i | ||||
\(922\) | 7.38394 | − | 10.1631i | 0.243177 | − | 0.334704i | ||||
\(923\) | 34.0260 | + | 11.0557i | 1.11998 | + | 0.363904i | ||||
\(924\) | 0.527864 | 0.0173655 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.8328 | 1.01323 | ||||||||
\(927\) | 1.26133 | + | 0.409830i | 0.0414274 | + | 0.0134606i | ||||
\(928\) | −0.277515 | + | 0.381966i | −0.00910986 | + | 0.0125386i | ||||
\(929\) | 46.1246 | + | 33.5115i | 1.51330 | + | 1.09948i | 0.964687 | + | 0.263400i | \(0.0848438\pi\) |
0.548613 | + | 0.836077i | \(0.315156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.7426 | − | 31.0543i | 1.40083 | − | 1.01777i | ||||
\(932\) | 12.6525i | 0.414446i | ||||||||
\(933\) | −11.1352 | − | 15.3262i | −0.364549 | − | 0.501759i | ||||
\(934\) | −8.13525 | − | 25.0377i | −0.266194 | − | 0.819260i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.763932 | − | 2.35114i | 0.0249699 | − | 0.0768494i | ||||
\(937\) | 49.1572 | − | 15.9721i | 1.60590 | − | 0.521787i | 0.637339 | − | 0.770583i | \(-0.280035\pi\) |
0.968556 | + | 0.248796i | \(0.0800350\pi\) | |||||||
\(938\) | 3.80423 | − | 1.23607i | 0.124212 | − | 0.0403591i | ||||
\(939\) | 5.33688 | − | 16.4252i | 0.174163 | − | 0.536017i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.59017 | − | 23.3601i | −0.247432 | − | 0.761519i | −0.995227 | − | 0.0975885i | \(-0.968887\pi\) |
0.747794 | − | 0.663930i | \(-0.231113\pi\) | |||||||
\(942\) | 13.3148 | + | 18.3262i | 0.433819 | + | 0.597101i | ||||
\(943\) | 34.4721i | 1.12257i | ||||||||
\(944\) | −1.11803 | + | 0.812299i | −0.0363889 | + | 0.0264381i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.38197 | − | 4.63677i | −0.207496 | − | 0.150754i | ||||
\(947\) | 7.89848 | − | 10.8713i | 0.256666 | − | 0.353271i | −0.661166 | − | 0.750240i | \(-0.729938\pi\) |
0.917832 | + | 0.396969i | \(0.129938\pi\) | |||||||
\(948\) | 3.21644 | + | 1.04508i | 0.104465 | + | 0.0339428i | ||||
\(949\) | −30.8328 | −1.00088 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.437694 | 0.0141932 | ||||||||
\(952\) | 1.17557 | + | 0.381966i | 0.0381005 | + | 0.0123796i | ||||
\(953\) | −33.6830 | + | 46.3607i | −1.09110 | + | 1.50177i | −0.244418 | + | 0.969670i | \(0.578597\pi\) |
−0.846682 | + | 0.532100i | \(0.821403\pi\) | |||||||
\(954\) | 7.35410 | + | 5.34307i | 0.238098 | + | 0.172988i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.7984 | + | 15.1109i | −0.672667 | + | 0.488722i | ||||
\(957\) | − | 0.652476i | − | 0.0210915i | ||||||
\(958\) | −6.53888 | − | 9.00000i | −0.211262 | − | 0.290777i | ||||
\(959\) | −1.20163 | − | 3.69822i | −0.0388025 | − | 0.119422i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.64590 | + | 11.2209i | −0.117610 | + | 0.361965i | ||||
\(962\) | 18.8091 | − | 6.11146i | 0.606431 | − | 0.197041i | ||||
\(963\) | 8.92278 | − | 2.89919i | 0.287533 | − | 0.0934250i | ||||
\(964\) | 3.26393 | − | 10.0453i | 0.105124 | − | 0.323539i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.527864 | + | 1.62460i | 0.0169837 | + | 0.0522706i | ||||
\(967\) | 12.9843 | + | 17.8713i | 0.417546 | + | 0.574703i | 0.965039 | − | 0.262108i | \(-0.0844175\pi\) |
−0.547492 | + | 0.836811i | \(0.684418\pi\) | |||||||
\(968\) | − | 9.09017i | − | 0.292169i | ||||||
\(969\) | 20.1803 | − | 14.6619i | 0.648286 | − | 0.471007i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.1074 | − | 21.8743i | −0.966192 | − | 0.701980i | −0.0116116 | − | 0.999933i | \(-0.503696\pi\) |
−0.954581 | + | 0.297953i | \(0.903696\pi\) | |||||||
\(972\) | 0.587785 | − | 0.809017i | 0.0188532 | − | 0.0259492i | ||||
\(973\) | 0.555029 | + | 0.180340i | 0.0177934 | + | 0.00578143i | ||||
\(974\) | 6.79837 | 0.217834 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.23607 | 0.231621 | ||||||||
\(977\) | 4.97980 | + | 1.61803i | 0.159318 | + | 0.0517655i | 0.387590 | − | 0.921832i | \(-0.373308\pi\) |
−0.228272 | + | 0.973597i | \(0.573308\pi\) | |||||||
\(978\) | −4.97980 | + | 6.85410i | −0.159236 | + | 0.219170i | ||||
\(979\) | 13.9443 | + | 10.1311i | 0.445661 | + | 0.323792i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3262 | + | 7.50245i | −0.329691 | + | 0.239535i | ||||
\(982\) | − | 8.27051i | − | 0.263923i | ||||||
\(983\) | −10.4741 | − | 14.4164i | −0.334073 | − | 0.459812i | 0.608626 | − | 0.793458i | \(-0.291721\pi\) |
−0.942699 | + | 0.333646i | \(0.891721\pi\) | |||||||
\(984\) | −2.38197 | − | 7.33094i | −0.0759343 | − | 0.233702i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.472136 | − | 1.45309i | 0.0150359 | − | 0.0462757i | ||||
\(987\) | 4.25325 | − | 1.38197i | 0.135383 | − | 0.0439885i | ||||
\(988\) | −18.1231 | + | 5.88854i | −0.576572 | + | 0.187340i | ||||
\(989\) | 7.88854 | − | 24.2784i | 0.250841 | − | 0.772010i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.17376 | − | 25.1563i | −0.259648 | − | 0.799115i | −0.992878 | − | 0.119134i | \(-0.961988\pi\) |
0.733230 | − | 0.679981i | \(-0.238012\pi\) | |||||||
\(992\) | 2.57565 | + | 3.54508i | 0.0817771 | + | 0.112557i | ||||
\(993\) | 18.0000i | 0.571213i | ||||||||
\(994\) | 4.47214 | − | 3.24920i | 0.141848 | − | 0.103058i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.16312 | + | 5.20431i | 0.226972 | + | 0.164905i | ||||
\(997\) | −25.6255 | + | 35.2705i | −0.811569 | + | 1.11703i | 0.179511 | + | 0.983756i | \(0.442548\pi\) |
−0.991079 | + | 0.133272i | \(0.957452\pi\) | |||||||
\(998\) | −12.9313 | − | 4.20163i | −0.409332 | − | 0.133000i | ||||
\(999\) | 8.00000 | 0.253109 |
(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 | 750.2.h.b.649.1 | 8 | ||
5.2 | odd | 4 | 150.2.g.a.121.1 | yes | 4 | ||
5.3 | odd | 4 | 750.2.g.b.601.1 | 4 | |||
5.4 | even | 2 | inner | 750.2.h.b.649.2 | 8 | ||
15.2 | even | 4 | 450.2.h.c.271.1 | 4 | |||
25.6 | even | 5 | inner | 750.2.h.b.349.2 | 8 | ||
25.8 | odd | 20 | 750.2.g.b.151.1 | 4 | |||
25.9 | even | 10 | 3750.2.c.b.1249.3 | 4 | |||
25.12 | odd | 20 | 3750.2.a.f.1.1 | 2 | |||
25.13 | odd | 20 | 3750.2.a.d.1.2 | 2 | |||
25.16 | even | 5 | 3750.2.c.b.1249.2 | 4 | |||
25.17 | odd | 20 | 150.2.g.a.31.1 | ✓ | 4 | ||
25.19 | even | 10 | inner | 750.2.h.b.349.1 | 8 | ||
75.17 | even | 20 | 450.2.h.c.181.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.a.31.1 | ✓ | 4 | 25.17 | odd | 20 | ||
150.2.g.a.121.1 | yes | 4 | 5.2 | odd | 4 | ||
450.2.h.c.181.1 | 4 | 75.17 | even | 20 | |||
450.2.h.c.271.1 | 4 | 15.2 | even | 4 | |||
750.2.g.b.151.1 | 4 | 25.8 | odd | 20 | |||
750.2.g.b.601.1 | 4 | 5.3 | odd | 4 | |||
750.2.h.b.349.1 | 8 | 25.19 | even | 10 | inner | ||
750.2.h.b.349.2 | 8 | 25.6 | even | 5 | inner | ||
750.2.h.b.649.1 | 8 | 1.1 | even | 1 | trivial | ||
750.2.h.b.649.2 | 8 | 5.4 | even | 2 | inner | ||
3750.2.a.d.1.2 | 2 | 25.13 | odd | 20 | |||
3750.2.a.f.1.1 | 2 | 25.12 | odd | 20 | |||
3750.2.c.b.1249.2 | 4 | 25.16 | even | 5 | |||
3750.2.c.b.1249.3 | 4 | 25.9 | even | 10 |