Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [750,2,Mod(151,750)]
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, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("750.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 750 = 2 \cdot 3 \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 750.g (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.98878015160\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 750.151 |
Dual form | 750.2.g.b.601.1 |
$q$-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 \(\left(\mathbb{Z}/750\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(251\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | − | 0.951057i | −0.218508 | − | 0.672499i | ||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | + | 0.587785i | −0.404508 | + | 0.293893i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.809017 | + | 0.587785i | 0.330280 | + | 0.239962i | ||||
\(7\) | −0.381966 | −0.144370 | −0.0721848 | − | 0.997391i | \(-0.522997\pi\) | ||||
−0.0721848 | + | 0.997391i | \(0.522997\pi\) | |||||||
\(8\) | 0.809017 | + | 0.587785i | 0.286031 | + | 0.207813i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.427051 | + | 1.31433i | 0.128761 | + | 0.396285i | 0.994567 | − | 0.104094i | \(-0.0331942\pi\) |
−0.865807 | + | 0.500378i | \(0.833194\pi\) | |||||||
\(12\) | 0.309017 | − | 0.951057i | 0.0892055 | − | 0.274546i | ||||
\(13\) | −0.763932 | + | 2.35114i | −0.211877 | + | 0.652089i | 0.787484 | + | 0.616335i | \(0.211383\pi\) |
−0.999361 | + | 0.0357541i | \(0.988617\pi\) | |||||||
\(14\) | 0.118034 | + | 0.363271i | 0.0315459 | + | 0.0970883i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | − | 0.951057i | 0.0772542 | − | 0.237764i | ||||
\(17\) | −2.61803 | − | 1.90211i | −0.634967 | − | 0.461330i | 0.223151 | − | 0.974784i | \(-0.428366\pi\) |
−0.858117 | + | 0.513454i | \(0.828366\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −6.23607 | − | 4.53077i | −1.43065 | − | 1.03943i | −0.989895 | − | 0.141803i | \(-0.954710\pi\) |
−0.440757 | − | 0.897626i | \(-0.645290\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.309017 | − | 0.224514i | 0.0674330 | − | 0.0489930i | ||||
\(22\) | 1.11803 | − | 0.812299i | 0.238366 | − | 0.173183i | ||||
\(23\) | 1.38197 | + | 4.25325i | 0.288160 | + | 0.886865i | 0.985434 | + | 0.170060i | \(0.0543961\pi\) |
−0.697274 | + | 0.716805i | \(0.745604\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.47214 | 0.484826 | ||||||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | 0.309017 | − | 0.224514i | 0.0583987 | − | 0.0424292i | ||||
\(29\) | 0.381966 | − | 0.277515i | 0.0709293 | − | 0.0515332i | −0.551756 | − | 0.834006i | \(-0.686042\pi\) |
0.622685 | + | 0.782473i | \(0.286042\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.54508 | − | 2.57565i | −0.636716 | − | 0.462601i | 0.222004 | − | 0.975046i | \(-0.428740\pi\) |
−0.858720 | + | 0.512444i | \(0.828740\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.11803 | − | 0.812299i | −0.194625 | − | 0.141403i | ||||
\(34\) | −1.00000 | + | 3.07768i | −0.171499 | + | 0.527818i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.309017 | + | 0.951057i | 0.0515028 | + | 0.158509i | ||||
\(37\) | −2.47214 | + | 7.60845i | −0.406417 | + | 1.25082i | 0.513290 | + | 0.858215i | \(0.328427\pi\) |
−0.919707 | + | 0.392607i | \(0.871573\pi\) | |||||||
\(38\) | −2.38197 | + | 7.33094i | −0.386406 | + | 1.18924i | ||||
\(39\) | −0.763932 | − | 2.35114i | −0.122327 | − | 0.376484i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.38197 | + | 7.33094i | −0.372001 | + | 1.14490i | 0.573479 | + | 0.819220i | \(0.305593\pi\) |
−0.945480 | + | 0.325680i | \(0.894407\pi\) | |||||||
\(42\) | −0.309017 | − | 0.224514i | −0.0476824 | − | 0.0346433i | ||||
\(43\) | −5.70820 | −0.870493 | −0.435246 | − | 0.900311i | \(-0.643339\pi\) | ||||
−0.435246 | + | 0.900311i | \(0.643339\pi\) | |||||||
\(44\) | −1.11803 | − | 0.812299i | −0.168550 | − | 0.122459i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.61803 | − | 2.62866i | 0.533450 | − | 0.387574i | ||||
\(47\) | −9.47214 | + | 6.88191i | −1.38165 | + | 1.00383i | −0.384929 | + | 0.922946i | \(0.625774\pi\) |
−0.996724 | + | 0.0808837i | \(0.974226\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −6.85410 | −0.979157 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.23607 | 0.453140 | ||||||||
\(52\) | −0.763932 | − | 2.35114i | −0.105938 | − | 0.326045i | ||||
\(53\) | 7.35410 | − | 5.34307i | 1.01016 | − | 0.733927i | 0.0459202 | − | 0.998945i | \(-0.485378\pi\) |
0.964243 | + | 0.265018i | \(0.0853780\pi\) | |||||||
\(54\) | 0.809017 | − | 0.587785i | 0.110093 | − | 0.0799874i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.309017 | − | 0.224514i | −0.0412941 | − | 0.0300019i | ||||
\(57\) | 7.70820 | 1.02098 | ||||||||
\(58\) | −0.381966 | − | 0.277515i | −0.0501546 | − | 0.0364394i | ||||
\(59\) | −0.427051 | + | 1.31433i | −0.0555973 | + | 0.171111i | −0.974999 | − | 0.222209i | \(-0.928673\pi\) |
0.919402 | + | 0.393320i | \(0.128673\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.23607 | + | 6.88191i | 0.286299 | + | 0.881138i | 0.986006 | + | 0.166708i | \(0.0533138\pi\) |
−0.699707 | + | 0.714430i | \(0.746686\pi\) | |||||||
\(62\) | −1.35410 | + | 4.16750i | −0.171971 | + | 0.529273i | ||||
\(63\) | −0.118034 | + | 0.363271i | −0.0148709 | + | 0.0457679i | ||||
\(64\) | 0.309017 | + | 0.951057i | 0.0386271 | + | 0.118882i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.427051 | + | 1.31433i | −0.0525663 | + | 0.161783i | ||||
\(67\) | −8.47214 | − | 6.15537i | −1.03504 | − | 0.751998i | −0.0657257 | − | 0.997838i | \(-0.520936\pi\) |
−0.969310 | + | 0.245840i | \(0.920936\pi\) | |||||||
\(68\) | 3.23607 | 0.392431 | ||||||||
\(69\) | −3.61803 | − | 2.62866i | −0.435560 | − | 0.316453i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.7082 | + | 8.50651i | −1.38951 | + | 1.00954i | −0.393589 | + | 0.919286i | \(0.628767\pi\) |
−0.995919 | + | 0.0902503i | \(0.971233\pi\) | |||||||
\(72\) | 0.809017 | − | 0.587785i | 0.0953436 | − | 0.0692712i | ||||
\(73\) | −3.85410 | − | 11.8617i | −0.451089 | − | 1.38831i | −0.875667 | − | 0.482916i | \(-0.839578\pi\) |
0.424578 | − | 0.905391i | \(-0.360422\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.70820 | 0.884192 | ||||||||
\(77\) | −0.163119 | − | 0.502029i | −0.0185891 | − | 0.0572115i | ||||
\(78\) | −2.00000 | + | 1.45309i | −0.226455 | + | 0.164529i | ||||
\(79\) | 2.73607 | − | 1.98787i | 0.307832 | − | 0.223653i | −0.423134 | − | 0.906067i | \(-0.639070\pi\) |
0.730966 | + | 0.682414i | \(0.239070\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 7.70820 | 0.851229 | ||||||||
\(83\) | 7.16312 | + | 5.20431i | 0.786254 | + | 0.571247i | 0.906850 | − | 0.421454i | \(-0.138480\pi\) |
−0.120595 | + | 0.992702i | \(0.538480\pi\) | |||||||
\(84\) | −0.118034 | + | 0.363271i | −0.0128786 | + | 0.0396361i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.76393 | + | 5.42882i | 0.190210 | + | 0.585405i | ||||
\(87\) | −0.145898 | + | 0.449028i | −0.0156419 | + | 0.0481409i | ||||
\(88\) | −0.427051 | + | 1.31433i | −0.0455238 | + | 0.140108i | ||||
\(89\) | 3.85410 | + | 11.8617i | 0.408534 | + | 1.25734i | 0.917908 | + | 0.396793i | \(0.129877\pi\) |
−0.509374 | + | 0.860545i | \(0.670123\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.291796 | − | 0.898056i | 0.0305885 | − | 0.0941418i | ||||
\(92\) | −3.61803 | − | 2.62866i | −0.377206 | − | 0.274056i | ||||
\(93\) | 4.38197 | 0.454389 | ||||||||
\(94\) | 9.47214 | + | 6.88191i | 0.976976 | + | 0.709815i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.809017 | − | 0.587785i | 0.0825700 | − | 0.0599906i | ||||
\(97\) | −4.54508 | + | 3.30220i | −0.461483 | + | 0.335287i | −0.794113 | − | 0.607770i | \(-0.792064\pi\) |
0.332629 | + | 0.943058i | \(0.392064\pi\) | |||||||
\(98\) | 2.11803 | + | 6.51864i | 0.213954 | + | 0.658482i | ||||
\(99\) | 1.38197 | 0.138893 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.61803 | 0.658519 | 0.329259 | − | 0.944239i | \(-0.393201\pi\) | ||||
0.329259 | + | 0.944239i | \(0.393201\pi\) | |||||||
\(102\) | −1.00000 | − | 3.07768i | −0.0990148 | − | 0.304736i | ||||
\(103\) | −1.07295 | + | 0.779543i | −0.105721 | + | 0.0768107i | −0.639390 | − | 0.768883i | \(-0.720813\pi\) |
0.533669 | + | 0.845694i | \(0.320813\pi\) | |||||||
\(104\) | −2.00000 | + | 1.45309i | −0.196116 | + | 0.142487i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.35410 | − | 5.34307i | −0.714294 | − | 0.518965i | ||||
\(107\) | 9.38197 | 0.906989 | 0.453494 | − | 0.891259i | \(-0.350177\pi\) | ||||
0.453494 | + | 0.891259i | \(0.350177\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 3.94427 | − | 12.1392i | 0.377793 | − | 1.16273i | −0.563782 | − | 0.825923i | \(-0.690654\pi\) |
0.941575 | − | 0.336803i | \(-0.109346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.47214 | − | 7.60845i | −0.234645 | − | 0.722162i | ||||
\(112\) | −0.118034 | + | 0.363271i | −0.0111532 | + | 0.0343259i | ||||
\(113\) | 4.56231 | − | 14.0413i | 0.429186 | − | 1.32090i | −0.469743 | − | 0.882803i | \(-0.655654\pi\) |
0.898929 | − | 0.438095i | \(-0.144346\pi\) | |||||||
\(114\) | −2.38197 | − | 7.33094i | −0.223092 | − | 0.686605i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.145898 | + | 0.449028i | −0.0135463 | + | 0.0416912i | ||||
\(117\) | 2.00000 | + | 1.45309i | 0.184900 | + | 0.134338i | ||||
\(118\) | 1.38197 | 0.127220 | ||||||||
\(119\) | 1.00000 | + | 0.726543i | 0.0916698 | + | 0.0666020i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.35410 | − | 5.34307i | 0.668555 | − | 0.485733i | ||||
\(122\) | 5.85410 | − | 4.25325i | 0.530005 | − | 0.385072i | ||||
\(123\) | −2.38197 | − | 7.33094i | −0.214775 | − | 0.661008i | ||||
\(124\) | 4.38197 | 0.393512 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.381966 | 0.0340282 | ||||||||
\(127\) | −3.51722 | − | 10.8249i | −0.312103 | − | 0.960554i | −0.976931 | − | 0.213557i | \(-0.931495\pi\) |
0.664828 | − | 0.746997i | \(-0.268505\pi\) | |||||||
\(128\) | 0.809017 | − | 0.587785i | 0.0715077 | − | 0.0519534i | ||||
\(129\) | 4.61803 | − | 3.35520i | 0.406595 | − | 0.295409i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.4721 | − | 10.5146i | −1.26444 | − | 0.918667i | −0.265470 | − | 0.964119i | \(-0.585527\pi\) |
−0.998967 | + | 0.0454523i | \(0.985527\pi\) | |||||||
\(132\) | 1.38197 | 0.120285 | ||||||||
\(133\) | 2.38197 | + | 1.73060i | 0.206543 | + | 0.150062i | ||||
\(134\) | −3.23607 | + | 9.95959i | −0.279554 | + | 0.860378i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | − | 3.07768i | −0.0857493 | − | 0.263909i | ||||
\(137\) | −3.14590 | + | 9.68208i | −0.268772 | + | 0.827196i | 0.722028 | + | 0.691864i | \(0.243210\pi\) |
−0.990800 | + | 0.135332i | \(0.956790\pi\) | |||||||
\(138\) | −1.38197 | + | 4.25325i | −0.117641 | + | 0.362061i | ||||
\(139\) | 0.472136 | + | 1.45309i | 0.0400460 | + | 0.123249i | 0.969081 | − | 0.246743i | \(-0.0793604\pi\) |
−0.929035 | + | 0.369992i | \(0.879360\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.61803 | − | 11.1352i | 0.304693 | − | 0.937750i | ||||
\(142\) | 11.7082 | + | 8.50651i | 0.982531 | + | 0.713850i | ||||
\(143\) | −3.41641 | −0.285694 | ||||||||
\(144\) | −0.809017 | − | 0.587785i | −0.0674181 | − | 0.0489821i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.0902 | + | 7.33094i | −0.835068 | + | 0.606713i | ||||
\(147\) | 5.54508 | − | 4.02874i | 0.457351 | − | 0.332285i | ||||
\(148\) | −2.47214 | − | 7.60845i | −0.203208 | − | 0.625411i | ||||
\(149\) | 10.9098 | 0.893768 | 0.446884 | − | 0.894592i | \(-0.352534\pi\) | ||||
0.446884 | + | 0.894592i | \(0.352534\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.67376 | 0.217588 | 0.108794 | − | 0.994064i | \(-0.465301\pi\) | ||||
0.108794 | + | 0.994064i | \(0.465301\pi\) | |||||||
\(152\) | −2.38197 | − | 7.33094i | −0.193203 | − | 0.594618i | ||||
\(153\) | −2.61803 | + | 1.90211i | −0.211656 | + | 0.153777i | ||||
\(154\) | −0.427051 | + | 0.310271i | −0.0344127 | + | 0.0250023i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | + | 1.45309i | 0.160128 | + | 0.116340i | ||||
\(157\) | 22.6525 | 1.80786 | 0.903932 | − | 0.427676i | \(-0.140668\pi\) | ||||
0.903932 | + | 0.427676i | \(0.140668\pi\) | |||||||
\(158\) | −2.73607 | − | 1.98787i | −0.217670 | − | 0.158146i | ||||
\(159\) | −2.80902 | + | 8.64527i | −0.222770 | + | 0.685614i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.527864 | − | 1.62460i | −0.0416015 | − | 0.128036i | ||||
\(162\) | −0.309017 | + | 0.951057i | −0.0242787 | + | 0.0747221i | ||||
\(163\) | −2.61803 | + | 8.05748i | −0.205060 | + | 0.631111i | 0.794651 | + | 0.607067i | \(0.207654\pi\) |
−0.999711 | + | 0.0240436i | \(0.992346\pi\) | |||||||
\(164\) | −2.38197 | − | 7.33094i | −0.186000 | − | 0.572450i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.73607 | − | 8.42075i | 0.212360 | − | 0.653577i | ||||
\(167\) | −1.38197 | − | 1.00406i | −0.106940 | − | 0.0776963i | 0.533030 | − | 0.846096i | \(-0.321053\pi\) |
−0.639970 | + | 0.768400i | \(0.721053\pi\) | |||||||
\(168\) | 0.381966 | 0.0294693 | ||||||||
\(169\) | 5.57295 | + | 4.04898i | 0.428688 | + | 0.311460i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.23607 | + | 4.53077i | −0.476884 | + | 0.346477i | ||||
\(172\) | 4.61803 | − | 3.35520i | 0.352122 | − | 0.255831i | ||||
\(173\) | 1.88197 | + | 5.79210i | 0.143083 | + | 0.440365i | 0.996760 | − | 0.0804391i | \(-0.0256322\pi\) |
−0.853676 | + | 0.520804i | \(0.825632\pi\) | |||||||
\(174\) | 0.472136 | 0.0357925 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.38197 | 0.104170 | ||||||||
\(177\) | −0.427051 | − | 1.31433i | −0.0320991 | − | 0.0987909i | ||||
\(178\) | 10.0902 | − | 7.33094i | 0.756290 | − | 0.549477i | ||||
\(179\) | −2.54508 | + | 1.84911i | −0.190229 | + | 0.138209i | −0.678823 | − | 0.734302i | \(-0.737510\pi\) |
0.488595 | + | 0.872511i | \(0.337510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.9443 | − | 14.4904i | −1.48245 | − | 1.07706i | −0.976758 | − | 0.214344i | \(-0.931239\pi\) |
−0.505688 | − | 0.862717i | \(-0.668761\pi\) | |||||||
\(182\) | −0.944272 | −0.0699941 | ||||||||
\(183\) | −5.85410 | − | 4.25325i | −0.432748 | − | 0.314410i | ||||
\(184\) | −1.38197 | + | 4.25325i | −0.101880 | + | 0.313554i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.35410 | − | 4.16750i | −0.0992876 | − | 0.305576i | ||||
\(187\) | 1.38197 | − | 4.25325i | 0.101059 | − | 0.311029i | ||||
\(188\) | 3.61803 | − | 11.1352i | 0.263872 | − | 0.812115i | ||||
\(189\) | −0.118034 | − | 0.363271i | −0.00858571 | − | 0.0264241i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.47214 | − | 16.8415i | 0.395950 | − | 1.21861i | −0.532269 | − | 0.846575i | \(-0.678661\pi\) |
0.928219 | − | 0.372033i | \(-0.121339\pi\) | |||||||
\(192\) | −0.809017 | − | 0.587785i | −0.0583858 | − | 0.0424197i | ||||
\(193\) | −11.1459 | −0.802299 | −0.401150 | − | 0.916013i | \(-0.631389\pi\) | ||||
−0.401150 | + | 0.916013i | \(0.631389\pi\) | |||||||
\(194\) | 4.54508 | + | 3.30220i | 0.326318 | + | 0.237084i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.54508 | − | 4.02874i | 0.396077 | − | 0.287767i | ||||
\(197\) | −4.78115 | + | 3.47371i | −0.340643 | + | 0.247492i | −0.744933 | − | 0.667139i | \(-0.767519\pi\) |
0.404290 | + | 0.914631i | \(0.367519\pi\) | |||||||
\(198\) | −0.427051 | − | 1.31433i | −0.0303492 | − | 0.0934052i | ||||
\(199\) | −18.5066 | −1.31190 | −0.655948 | − | 0.754806i | \(-0.727731\pi\) | ||||
−0.655948 | + | 0.754806i | \(0.727731\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.4721 | 0.738648 | ||||||||
\(202\) | −2.04508 | − | 6.29412i | −0.143892 | − | 0.442853i | ||||
\(203\) | −0.145898 | + | 0.106001i | −0.0102400 | + | 0.00743982i | ||||
\(204\) | −2.61803 | + | 1.90211i | −0.183299 | + | 0.133175i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.07295 | + | 0.779543i | 0.0747559 | + | 0.0543133i | ||||
\(207\) | 4.47214 | 0.310835 | ||||||||
\(208\) | 2.00000 | + | 1.45309i | 0.138675 | + | 0.100753i | ||||
\(209\) | 3.29180 | − | 10.1311i | 0.227698 | − | 0.700783i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.23607 | + | 22.2703i | 0.498151 | + | 1.53315i | 0.811987 | + | 0.583675i | \(0.198386\pi\) |
−0.313836 | + | 0.949477i | \(0.601614\pi\) | |||||||
\(212\) | −2.80902 | + | 8.64527i | −0.192924 | + | 0.593759i | ||||
\(213\) | 4.47214 | − | 13.7638i | 0.306426 | − | 0.943081i | ||||
\(214\) | −2.89919 | − | 8.92278i | −0.198184 | − | 0.609949i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.309017 | + | 0.951057i | −0.0210259 | + | 0.0647112i | ||||
\(217\) | 1.35410 | + | 0.983813i | 0.0919224 | + | 0.0667856i | ||||
\(218\) | −12.7639 | −0.864483 | ||||||||
\(219\) | 10.0902 | + | 7.33094i | 0.681830 | + | 0.495379i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.47214 | − | 4.70228i | 0.435363 | − | 0.316310i | ||||
\(222\) | −6.47214 | + | 4.70228i | −0.434381 | + | 0.315597i | ||||
\(223\) | −0.954915 | − | 2.93893i | −0.0639458 | − | 0.196805i | 0.913979 | − | 0.405761i | \(-0.132993\pi\) |
−0.977925 | + | 0.208956i | \(0.932993\pi\) | |||||||
\(224\) | 0.381966 | 0.0255212 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −14.7639 | −0.982082 | ||||||||
\(227\) | −3.48278 | − | 10.7189i | −0.231160 | − | 0.711438i | −0.997608 | − | 0.0691308i | \(-0.977977\pi\) |
0.766447 | − | 0.642307i | \(-0.222023\pi\) | |||||||
\(228\) | −6.23607 | + | 4.53077i | −0.412994 | + | 0.300057i | ||||
\(229\) | 11.7082 | − | 8.50651i | 0.773700 | − | 0.562126i | −0.129382 | − | 0.991595i | \(-0.541299\pi\) |
0.903082 | + | 0.429469i | \(0.141299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.427051 | + | 0.310271i | 0.0280979 | + | 0.0204143i | ||||
\(232\) | 0.472136 | 0.0309972 | ||||||||
\(233\) | −10.2361 | − | 7.43694i | −0.670587 | − | 0.487210i | 0.199635 | − | 0.979870i | \(-0.436024\pi\) |
−0.870222 | + | 0.492660i | \(0.836024\pi\) | |||||||
\(234\) | 0.763932 | − | 2.35114i | 0.0499398 | − | 0.153699i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.427051 | − | 1.31433i | −0.0277987 | − | 0.0855555i | ||||
\(237\) | −1.04508 | + | 3.21644i | −0.0678856 | + | 0.208930i | ||||
\(238\) | 0.381966 | − | 1.17557i | 0.0247592 | − | 0.0762009i | ||||
\(239\) | 7.94427 | + | 24.4500i | 0.513872 | + | 1.58154i | 0.785325 | + | 0.619084i | \(0.212496\pi\) |
−0.271452 | + | 0.962452i | \(0.587504\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.26393 | + | 10.0453i | −0.210248 | + | 0.647078i | 0.789209 | + | 0.614125i | \(0.210491\pi\) |
−0.999457 | + | 0.0329526i | \(0.989509\pi\) | |||||||
\(242\) | −7.35410 | − | 5.34307i | −0.472740 | − | 0.343465i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −5.85410 | − | 4.25325i | −0.374770 | − | 0.272287i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.23607 | + | 4.53077i | −0.397597 | + | 0.288871i | ||||
\(247\) | 15.4164 | − | 11.2007i | 0.980923 | − | 0.712682i | ||||
\(248\) | −1.35410 | − | 4.16750i | −0.0859856 | − | 0.264636i | ||||
\(249\) | −8.85410 | −0.561106 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.56231 | −0.414209 | −0.207105 | − | 0.978319i | \(-0.566404\pi\) | ||||
−0.207105 | + | 0.978319i | \(0.566404\pi\) | |||||||
\(252\) | −0.118034 | − | 0.363271i | −0.00743544 | − | 0.0228839i | ||||
\(253\) | −5.00000 | + | 3.63271i | −0.314347 | + | 0.228387i | ||||
\(254\) | −9.20820 | + | 6.69015i | −0.577774 | + | 0.419777i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | − | 0.587785i | −0.0505636 | − | 0.0367366i | ||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | −4.61803 | − | 3.35520i | −0.287506 | − | 0.208886i | ||||
\(259\) | 0.944272 | − | 2.90617i | 0.0586742 | − | 0.180581i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.145898 | − | 0.449028i | −0.00903086 | − | 0.0277941i | ||||
\(262\) | −5.52786 | + | 17.0130i | −0.341513 | + | 1.05107i | ||||
\(263\) | −0.527864 | + | 1.62460i | −0.0325495 | + | 0.100177i | −0.966011 | − | 0.258500i | \(-0.916772\pi\) |
0.933462 | + | 0.358677i | \(0.116772\pi\) | |||||||
\(264\) | −0.427051 | − | 1.31433i | −0.0262832 | − | 0.0808913i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.909830 | − | 2.80017i | 0.0557853 | − | 0.171689i | ||||
\(267\) | −10.0902 | − | 7.33094i | −0.617508 | − | 0.448646i | ||||
\(268\) | 10.4721 | 0.639688 | ||||||||
\(269\) | −1.69098 | − | 1.22857i | −0.103101 | − | 0.0749073i | 0.535040 | − | 0.844827i | \(-0.320296\pi\) |
−0.638141 | + | 0.769919i | \(0.720296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.92705 | + | 6.48588i | −0.542280 | + | 0.393989i | −0.824931 | − | 0.565233i | \(-0.808786\pi\) |
0.282651 | + | 0.959223i | \(0.408786\pi\) | |||||||
\(272\) | −2.61803 | + | 1.90211i | −0.158742 | + | 0.115333i | ||||
\(273\) | 0.291796 | + | 0.898056i | 0.0176603 | + | 0.0543528i | ||||
\(274\) | 10.1803 | 0.615017 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.47214 | 0.269191 | ||||||||
\(277\) | 0.291796 | + | 0.898056i | 0.0175323 | + | 0.0539590i | 0.959440 | − | 0.281913i | \(-0.0909690\pi\) |
−0.941908 | + | 0.335872i | \(0.890969\pi\) | |||||||
\(278\) | 1.23607 | − | 0.898056i | 0.0741344 | − | 0.0538618i | ||||
\(279\) | −3.54508 | + | 2.57565i | −0.212239 | + | 0.154200i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1803 | + | 17.5680i | 1.44248 | + | 1.04802i | 0.987517 | + | 0.157510i | \(0.0503467\pi\) |
0.454961 | + | 0.890511i | \(0.349653\pi\) | |||||||
\(282\) | −11.7082 | −0.697213 | ||||||||
\(283\) | 25.4164 | + | 18.4661i | 1.51085 | + | 1.09770i | 0.965799 | + | 0.259292i | \(0.0834892\pi\) |
0.545050 | + | 0.838404i | \(0.316511\pi\) | |||||||
\(284\) | 4.47214 | − | 13.7638i | 0.265372 | − | 0.816732i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.05573 | + | 3.24920i | 0.0624265 | + | 0.192129i | ||||
\(287\) | 0.909830 | − | 2.80017i | 0.0537056 | − | 0.165289i | ||||
\(288\) | −0.309017 | + | 0.951057i | −0.0182090 | + | 0.0560415i | ||||
\(289\) | −2.01722 | − | 6.20837i | −0.118660 | − | 0.365198i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.73607 | − | 5.34307i | 0.101770 | − | 0.313216i | ||||
\(292\) | 10.0902 | + | 7.33094i | 0.590483 | + | 0.429011i | ||||
\(293\) | 10.9098 | 0.637359 | 0.318680 | − | 0.947863i | \(-0.396761\pi\) | ||||
0.318680 | + | 0.947863i | \(0.396761\pi\) | |||||||
\(294\) | −5.54508 | − | 4.02874i | −0.323396 | − | 0.234961i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.47214 | + | 4.70228i | −0.376185 | + | 0.273315i | ||||
\(297\) | −1.11803 | + | 0.812299i | −0.0648749 | + | 0.0471344i | ||||
\(298\) | −3.37132 | − | 10.3759i | −0.195295 | − | 0.601058i | ||||
\(299\) | −11.0557 | −0.639369 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.18034 | 0.125673 | ||||||||
\(302\) | −0.826238 | − | 2.54290i | −0.0475446 | − | 0.146327i | ||||
\(303\) | −5.35410 | + | 3.88998i | −0.307585 | + | 0.223474i | ||||
\(304\) | −6.23607 | + | 4.53077i | −0.357663 | + | 0.259857i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.61803 | + | 1.90211i | 0.149663 | + | 0.108737i | ||||
\(307\) | −10.0000 | −0.570730 | −0.285365 | − | 0.958419i | \(-0.592115\pi\) | ||||
−0.285365 | + | 0.958419i | \(0.592115\pi\) | |||||||
\(308\) | 0.427051 | + | 0.310271i | 0.0243335 | + | 0.0176793i | ||||
\(309\) | 0.409830 | − | 1.26133i | 0.0233144 | − | 0.0717544i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.85410 | − | 18.0171i | −0.331956 | − | 1.02165i | −0.968202 | − | 0.250169i | \(-0.919514\pi\) |
0.636247 | − | 0.771486i | \(-0.280486\pi\) | |||||||
\(312\) | 0.763932 | − | 2.35114i | 0.0432491 | − | 0.133107i | ||||
\(313\) | −5.33688 | + | 16.4252i | −0.301658 | + | 0.928409i | 0.679245 | + | 0.733912i | \(0.262307\pi\) |
−0.980903 | + | 0.194497i | \(0.937693\pi\) | |||||||
\(314\) | −7.00000 | − | 21.5438i | −0.395033 | − | 1.21579i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.04508 | + | 3.21644i | −0.0587906 | + | 0.180939i | ||||
\(317\) | −0.354102 | − | 0.257270i | −0.0198883 | − | 0.0144497i | 0.577797 | − | 0.816181i | \(-0.303913\pi\) |
−0.597685 | + | 0.801731i | \(0.703913\pi\) | |||||||
\(318\) | 9.09017 | 0.509751 | ||||||||
\(319\) | 0.527864 | + | 0.383516i | 0.0295547 | + | 0.0214728i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.59017 | + | 5.51458i | −0.423642 | + | 0.307794i | ||||
\(322\) | −1.38197 | + | 1.00406i | −0.0770140 | + | 0.0559539i | ||||
\(323\) | 7.70820 | + | 23.7234i | 0.428896 | + | 1.32001i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.47214 | 0.469228 | ||||||||
\(327\) | 3.94427 | + | 12.1392i | 0.218119 | + | 0.671300i | ||||
\(328\) | −6.23607 | + | 4.53077i | −0.344329 | + | 0.250170i | ||||
\(329\) | 3.61803 | − | 2.62866i | 0.199469 | − | 0.144922i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.5623 | + | 10.5801i | 0.800417 | + | 0.581537i | 0.911036 | − | 0.412326i | \(-0.135284\pi\) |
−0.110620 | + | 0.993863i | \(0.535284\pi\) | |||||||
\(332\) | −8.85410 | −0.485932 | ||||||||
\(333\) | 6.47214 | + | 4.70228i | 0.354671 | + | 0.257683i | ||||
\(334\) | −0.527864 | + | 1.62460i | −0.0288834 | + | 0.0888941i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.118034 | − | 0.363271i | −0.00643928 | − | 0.0198181i | ||||
\(337\) | −3.73607 | + | 11.4984i | −0.203517 | + | 0.626360i | 0.796254 | + | 0.604962i | \(0.206812\pi\) |
−0.999771 | + | 0.0213978i | \(0.993188\pi\) | |||||||
\(338\) | 2.12868 | − | 6.55139i | 0.115785 | − | 0.356349i | ||||
\(339\) | 4.56231 | + | 14.0413i | 0.247790 | + | 0.762621i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.87132 | − | 5.75934i | 0.101338 | − | 0.311886i | ||||
\(342\) | 6.23607 | + | 4.53077i | 0.337208 | + | 0.244996i | ||||
\(343\) | 5.29180 | 0.285730 | ||||||||
\(344\) | −4.61803 | − | 3.35520i | −0.248988 | − | 0.180900i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.92705 | − | 3.57971i | 0.264880 | − | 0.192447i | ||||
\(347\) | 0.354102 | − | 0.257270i | 0.0190092 | − | 0.0138110i | −0.578240 | − | 0.815867i | \(-0.696260\pi\) |
0.597249 | + | 0.802056i | \(0.296260\pi\) | |||||||
\(348\) | −0.145898 | − | 0.449028i | −0.00782096 | − | 0.0240704i | ||||
\(349\) | 7.88854 | 0.422264 | 0.211132 | − | 0.977458i | \(-0.432285\pi\) | ||||
0.211132 | + | 0.977458i | \(0.432285\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.47214 | −0.131953 | ||||||||
\(352\) | −0.427051 | − | 1.31433i | −0.0227619 | − | 0.0700539i | ||||
\(353\) | −7.09017 | + | 5.15131i | −0.377372 | + | 0.274177i | −0.760261 | − | 0.649618i | \(-0.774929\pi\) |
0.382889 | + | 0.923794i | \(0.374929\pi\) | |||||||
\(354\) | −1.11803 | + | 0.812299i | −0.0594228 | + | 0.0431732i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.0902 | − | 7.33094i | −0.534778 | − | 0.388539i | ||||
\(357\) | −1.23607 | −0.0654197 | ||||||||
\(358\) | 2.54508 | + | 1.84911i | 0.134512 | + | 0.0977286i | ||||
\(359\) | −0.0557281 | + | 0.171513i | −0.00294122 | + | 0.00905213i | −0.952516 | − | 0.304487i | \(-0.901515\pi\) |
0.949575 | + | 0.313540i | \(0.101515\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.4894 | + | 38.4383i | 0.657335 | + | 2.02307i | ||||
\(362\) | −7.61803 | + | 23.4459i | −0.400395 | + | 1.23229i | ||||
\(363\) | −2.80902 | + | 8.64527i | −0.147435 | + | 0.453759i | ||||
\(364\) | 0.291796 | + | 0.898056i | 0.0152943 | + | 0.0470709i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.23607 | + | 6.88191i | −0.116881 | + | 0.359723i | ||||
\(367\) | −22.9615 | − | 16.6825i | −1.19858 | − | 0.870819i | −0.204436 | − | 0.978880i | \(-0.565536\pi\) |
−0.994144 | + | 0.108060i | \(0.965536\pi\) | |||||||
\(368\) | 4.47214 | 0.233126 | ||||||||
\(369\) | 6.23607 | + | 4.53077i | 0.324637 | + | 0.235862i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.80902 | + | 2.04087i | −0.145837 | + | 0.105957i | ||||
\(372\) | −3.54508 | + | 2.57565i | −0.183804 | + | 0.133541i | ||||
\(373\) | 6.32624 | + | 19.4702i | 0.327560 | + | 1.00813i | 0.970272 | + | 0.242018i | \(0.0778094\pi\) |
−0.642712 | + | 0.766108i | \(0.722191\pi\) | |||||||
\(374\) | −4.47214 | −0.231249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −11.7082 | −0.603805 | ||||||||
\(377\) | 0.360680 | + | 1.11006i | 0.0185760 | + | 0.0571709i | ||||
\(378\) | −0.309017 | + | 0.224514i | −0.0158941 | + | 0.0115478i | ||||
\(379\) | −1.76393 | + | 1.28157i | −0.0906071 | + | 0.0658299i | −0.632166 | − | 0.774833i | \(-0.717834\pi\) |
0.541559 | + | 0.840662i | \(0.317834\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.20820 | + | 6.69015i | 0.471751 | + | 0.342747i | ||||
\(382\) | −17.7082 | −0.906031 | ||||||||
\(383\) | −16.1803 | − | 11.7557i | −0.826777 | − | 0.600688i | 0.0918688 | − | 0.995771i | \(-0.470716\pi\) |
−0.918646 | + | 0.395083i | \(0.870716\pi\) | |||||||
\(384\) | −0.309017 | + | 0.951057i | −0.0157695 | + | 0.0485334i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.44427 | + | 10.6004i | 0.175309 | + | 0.539545i | ||||
\(387\) | −1.76393 | + | 5.42882i | −0.0896657 | + | 0.275963i | ||||
\(388\) | 1.73607 | − | 5.34307i | 0.0881355 | − | 0.271253i | ||||
\(389\) | −4.51722 | − | 13.9026i | −0.229032 | − | 0.704889i | −0.997857 | − | 0.0654294i | \(-0.979158\pi\) |
0.768825 | − | 0.639459i | \(-0.220842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.47214 | − | 13.7638i | 0.226166 | − | 0.696066i | ||||
\(392\) | −5.54508 | − | 4.02874i | −0.280069 | − | 0.203482i | ||||
\(393\) | 17.8885 | 0.902358 | ||||||||
\(394\) | 4.78115 | + | 3.47371i | 0.240871 | + | 0.175003i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.11803 | + | 0.812299i | −0.0561833 | + | 0.0408196i | ||||
\(397\) | −28.5066 | + | 20.7112i | −1.43070 | + | 1.03947i | −0.440819 | + | 0.897596i | \(0.645312\pi\) |
−0.989885 | + | 0.141871i | \(0.954688\pi\) | |||||||
\(398\) | 5.71885 | + | 17.6008i | 0.286660 | + | 0.882248i | ||||
\(399\) | −2.94427 | −0.147398 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.2918 | 0.613823 | 0.306912 | − | 0.951738i | \(-0.400704\pi\) | ||||
0.306912 | + | 0.951738i | \(0.400704\pi\) | |||||||
\(402\) | −3.23607 | − | 9.95959i | −0.161400 | − | 0.496739i | ||||
\(403\) | 8.76393 | − | 6.36737i | 0.436563 | − | 0.317181i | ||||
\(404\) | −5.35410 | + | 3.88998i | −0.266377 | + | 0.193534i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.145898 | + | 0.106001i | 0.00724080 | + | 0.00526075i | ||||
\(407\) | −11.0557 | −0.548012 | ||||||||
\(408\) | 2.61803 | + | 1.90211i | 0.129612 | + | 0.0941686i | ||||
\(409\) | −5.80902 | + | 17.8783i | −0.287237 | + | 0.884026i | 0.698482 | + | 0.715628i | \(0.253859\pi\) |
−0.985719 | + | 0.168398i | \(0.946141\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.14590 | − | 9.68208i | −0.155176 | − | 0.477582i | ||||
\(412\) | 0.409830 | − | 1.26133i | 0.0201909 | − | 0.0621411i | ||||
\(413\) | 0.163119 | − | 0.502029i | 0.00802656 | − | 0.0247032i | ||||
\(414\) | −1.38197 | − | 4.25325i | −0.0679199 | − | 0.209036i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.763932 | − | 2.35114i | 0.0374548 | − | 0.115274i | ||||
\(417\) | −1.23607 | − | 0.898056i | −0.0605305 | − | 0.0439780i | ||||
\(418\) | −10.6525 | −0.521030 | ||||||||
\(419\) | −6.54508 | − | 4.75528i | −0.319748 | − | 0.232311i | 0.416320 | − | 0.909218i | \(-0.363320\pi\) |
−0.736068 | + | 0.676908i | \(0.763320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0344 | − | 16.0090i | 1.07389 | − | 0.780229i | 0.0972850 | − | 0.995257i | \(-0.468984\pi\) |
0.976608 | + | 0.215028i | \(0.0689842\pi\) | |||||||
\(422\) | 18.9443 | − | 13.7638i | 0.922193 | − | 0.670012i | ||||
\(423\) | 3.61803 | + | 11.1352i | 0.175915 | + | 0.541410i | ||||
\(424\) | 9.09017 | 0.441458 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.4721 | −0.701177 | ||||||||
\(427\) | −0.854102 | − | 2.62866i | −0.0413329 | − | 0.127210i | ||||
\(428\) | −7.59017 | + | 5.51458i | −0.366885 | + | 0.266557i | ||||
\(429\) | 2.76393 | − | 2.00811i | 0.133444 | − | 0.0969527i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.7984 | + | 21.6498i | 1.43534 | + | 1.04283i | 0.988991 | + | 0.147973i | \(0.0472748\pi\) |
0.446346 | + | 0.894861i | \(0.352725\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −18.2082 | − | 13.2290i | −0.875030 | − | 0.635747i | 0.0569016 | − | 0.998380i | \(-0.481878\pi\) |
−0.931932 | + | 0.362633i | \(0.881878\pi\) | |||||||
\(434\) | 0.517221 | − | 1.59184i | 0.0248274 | − | 0.0764109i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.94427 | + | 12.1392i | 0.188896 | + | 0.581363i | ||||
\(437\) | 10.6525 | − | 32.7849i | 0.509577 | − | 1.56832i | ||||
\(438\) | 3.85410 | − | 11.8617i | 0.184156 | − | 0.566774i | ||||
\(439\) | 4.48278 | + | 13.7966i | 0.213951 | + | 0.658475i | 0.999226 | + | 0.0393275i | \(0.0125216\pi\) |
−0.785275 | + | 0.619147i | \(0.787478\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.11803 | + | 6.51864i | −0.100859 | + | 0.310411i | ||||
\(442\) | −6.47214 | − | 4.70228i | −0.307848 | − | 0.223665i | ||||
\(443\) | −14.3820 | −0.683308 | −0.341654 | − | 0.939826i | \(-0.610987\pi\) | ||||
−0.341654 | + | 0.939826i | \(0.610987\pi\) | |||||||
\(444\) | 6.47214 | + | 4.70228i | 0.307154 | + | 0.223160i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.50000 | + | 1.81636i | −0.118378 | + | 0.0860070i | ||||
\(447\) | −8.82624 | + | 6.41264i | −0.417467 | + | 0.303307i | ||||
\(448\) | −0.118034 | − | 0.363271i | −0.00557658 | − | 0.0171630i | ||||
\(449\) | −14.2918 | −0.674472 | −0.337236 | − | 0.941420i | \(-0.609492\pi\) | ||||
−0.337236 | + | 0.941420i | \(0.609492\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6525 | −0.501605 | ||||||||
\(452\) | 4.56231 | + | 14.0413i | 0.214593 | + | 0.660449i | ||||
\(453\) | −2.16312 | + | 1.57160i | −0.101632 | + | 0.0738401i | ||||
\(454\) | −9.11803 | + | 6.62464i | −0.427931 | + | 0.310910i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.23607 | + | 4.53077i | 0.292031 | + | 0.212173i | ||||
\(457\) | −7.09017 | −0.331664 | −0.165832 | − | 0.986154i | \(-0.553031\pi\) | ||||
−0.165832 | + | 0.986154i | \(0.553031\pi\) | |||||||
\(458\) | −11.7082 | − | 8.50651i | −0.547088 | − | 0.397483i | ||||
\(459\) | 1.00000 | − | 3.07768i | 0.0466760 | − | 0.143654i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.88197 | − | 11.9475i | −0.180801 | − | 0.556449i | 0.819050 | − | 0.573723i | \(-0.194501\pi\) |
−0.999851 | + | 0.0172739i | \(0.994501\pi\) | |||||||
\(462\) | 0.163119 | − | 0.502029i | 0.00758898 | − | 0.0233565i | ||||
\(463\) | −9.52786 | + | 29.3238i | −0.442797 | + | 1.36279i | 0.442084 | + | 0.896974i | \(0.354239\pi\) |
−0.884881 | + | 0.465817i | \(0.845761\pi\) | |||||||
\(464\) | −0.145898 | − | 0.449028i | −0.00677315 | − | 0.0208456i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.90983 | + | 12.0332i | −0.181119 | + | 0.557428i | ||||
\(467\) | 21.2984 | + | 15.4742i | 0.985571 | + | 0.716059i | 0.958947 | − | 0.283586i | \(-0.0915242\pi\) |
0.0266244 | + | 0.999646i | \(0.491524\pi\) | |||||||
\(468\) | −2.47214 | −0.114275 | ||||||||
\(469\) | 3.23607 | + | 2.35114i | 0.149428 | + | 0.108566i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −18.3262 | + | 13.3148i | −0.844428 | + | 0.613513i | ||||
\(472\) | −1.11803 | + | 0.812299i | −0.0514617 | + | 0.0373891i | ||||
\(473\) | −2.43769 | − | 7.50245i | −0.112085 | − | 0.344963i | ||||
\(474\) | 3.38197 | 0.155339 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.23607 | −0.0566551 | ||||||||
\(477\) | −2.80902 | − | 8.64527i | −0.128616 | − | 0.395840i | ||||
\(478\) | 20.7984 | − | 15.1109i | 0.951295 | − | 0.691157i | ||||
\(479\) | −9.00000 | + | 6.53888i | −0.411220 | + | 0.298769i | −0.774096 | − | 0.633069i | \(-0.781795\pi\) |
0.362875 | + | 0.931838i | \(0.381795\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −16.0000 | − | 11.6247i | −0.729537 | − | 0.530040i | ||||
\(482\) | 10.5623 | 0.481100 | ||||||||
\(483\) | 1.38197 | + | 1.00406i | 0.0628816 | + | 0.0456862i | ||||
\(484\) | −2.80902 | + | 8.64527i | −0.127683 | + | 0.392967i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.309017 | − | 0.951057i | −0.0140173 | − | 0.0431408i | ||||
\(487\) | 2.10081 | − | 6.46564i | 0.0951969 | − | 0.292986i | −0.892108 | − | 0.451822i | \(-0.850774\pi\) |
0.987305 | + | 0.158836i | \(0.0507742\pi\) | |||||||
\(488\) | −2.23607 | + | 6.88191i | −0.101222 | + | 0.311529i | ||||
\(489\) | −2.61803 | − | 8.05748i | −0.118392 | − | 0.364372i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.55573 | − | 7.86572i | 0.115338 | − | 0.354975i | −0.876679 | − | 0.481076i | \(-0.840246\pi\) |
0.992017 | + | 0.126101i | \(0.0402462\pi\) | |||||||
\(492\) | 6.23607 | + | 4.53077i | 0.281144 | + | 0.204263i | ||||
\(493\) | −1.52786 | −0.0688115 | ||||||||
\(494\) | −15.4164 | − | 11.2007i | −0.693617 | − | 0.503942i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.54508 | + | 2.57565i | −0.159179 | + | 0.115650i | ||||
\(497\) | 4.47214 | − | 3.24920i | 0.200603 | − | 0.145746i | ||||
\(498\) | 2.73607 | + | 8.42075i | 0.122606 | + | 0.377343i | ||||
\(499\) | −13.5967 | −0.608674 | −0.304337 | − | 0.952564i | \(-0.598435\pi\) | ||||
−0.304337 | + | 0.952564i | \(0.598435\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.70820 | 0.0763169 | ||||||||
\(502\) | 2.02786 | + | 6.24112i | 0.0905080 | + | 0.278555i | ||||
\(503\) | −9.61803 | + | 6.98791i | −0.428847 | + | 0.311576i | −0.781188 | − | 0.624296i | \(-0.785386\pi\) |
0.352341 | + | 0.935872i | \(0.385386\pi\) | |||||||
\(504\) | −0.309017 | + | 0.224514i | −0.0137647 | + | 0.0100006i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.00000 | + | 3.63271i | 0.222277 | + | 0.161494i | ||||
\(507\) | −6.88854 | −0.305931 | ||||||||
\(508\) | 9.20820 | + | 6.69015i | 0.408548 | + | 0.296827i | ||||
\(509\) | 6.33688 | − | 19.5029i | 0.280877 | − | 0.864451i | −0.706727 | − | 0.707487i | \(-0.749829\pi\) |
0.987604 | − | 0.156965i | \(-0.0501710\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.47214 | + | 4.53077i | 0.0651235 | + | 0.200429i | ||||
\(512\) | −0.309017 | + | 0.951057i | −0.0136568 | + | 0.0420312i | ||||
\(513\) | 2.38197 | − | 7.33094i | 0.105166 | − | 0.323669i | ||||
\(514\) | −6.79837 | − | 20.9232i | −0.299863 | − | 0.922885i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.76393 | + | 5.42882i | −0.0776528 | + | 0.238991i | ||||
\(517\) | −13.0902 | − | 9.51057i | −0.575705 | − | 0.418274i | ||||
\(518\) | −3.05573 | −0.134261 | ||||||||
\(519\) | −4.92705 | − | 3.57971i | −0.216274 | − | 0.157132i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.61803 | − | 4.80828i | 0.289941 | − | 0.210655i | −0.433301 | − | 0.901249i | \(-0.642651\pi\) |
0.723242 | + | 0.690595i | \(0.242651\pi\) | |||||||
\(522\) | −0.381966 | + | 0.277515i | −0.0167182 | + | 0.0121465i | ||||
\(523\) | −8.94427 | − | 27.5276i | −0.391106 | − | 1.20370i | −0.931953 | − | 0.362579i | \(-0.881896\pi\) |
0.540847 | − | 0.841121i | \(-0.318104\pi\) | |||||||
\(524\) | 17.8885 | 0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.70820 | 0.0744812 | ||||||||
\(527\) | 4.38197 | + | 13.4863i | 0.190881 | + | 0.587473i | ||||
\(528\) | −1.11803 | + | 0.812299i | −0.0486562 | + | 0.0353508i | ||||
\(529\) | 2.42705 | − | 1.76336i | 0.105524 | − | 0.0766676i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.11803 | + | 0.812299i | 0.0485185 | + | 0.0352508i | ||||
\(532\) | −2.94427 | −0.127650 | ||||||||
\(533\) | −15.4164 | − | 11.2007i | −0.667759 | − | 0.485155i | ||||
\(534\) | −3.85410 | + | 11.8617i | −0.166783 | + | 0.513306i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.23607 | − | 9.95959i | −0.139777 | − | 0.430189i | ||||
\(537\) | 0.972136 | − | 2.99193i | 0.0419508 | − | 0.129111i | ||||
\(538\) | −0.645898 | + | 1.98787i | −0.0278466 | + | 0.0857032i | ||||
\(539\) | −2.92705 | − | 9.00854i | −0.126077 | − | 0.388025i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.18034 | + | 3.63271i | −0.0507468 | + | 0.156183i | −0.973218 | − | 0.229882i | \(-0.926166\pi\) |
0.922472 | + | 0.386065i | \(0.126166\pi\) | |||||||
\(542\) | 8.92705 | + | 6.48588i | 0.383450 | + | 0.278592i | ||||
\(543\) | 24.6525 | 1.05794 | ||||||||
\(544\) | 2.61803 | + | 1.90211i | 0.112247 | + | 0.0815524i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.763932 | − | 0.555029i | 0.0326933 | − | 0.0237531i | ||||
\(547\) | −3.00000 | + | 2.17963i | −0.128271 | + | 0.0931941i | −0.650071 | − | 0.759874i | \(-0.725261\pi\) |
0.521800 | + | 0.853068i | \(0.325261\pi\) | |||||||
\(548\) | −3.14590 | − | 9.68208i | −0.134386 | − | 0.413598i | ||||
\(549\) | 7.23607 | 0.308828 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.63932 | −0.155040 | ||||||||
\(552\) | −1.38197 | − | 4.25325i | −0.0588204 | − | 0.181031i | ||||
\(553\) | −1.04508 | + | 0.759299i | −0.0444415 | + | 0.0322887i | ||||
\(554\) | 0.763932 | − | 0.555029i | 0.0324564 | − | 0.0235809i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.23607 | − | 0.898056i | −0.0524210 | − | 0.0380861i | ||||
\(557\) | 2.67376 | 0.113291 | 0.0566455 | − | 0.998394i | \(-0.481960\pi\) | ||||
0.0566455 | + | 0.998394i | \(0.481960\pi\) | |||||||
\(558\) | 3.54508 | + | 2.57565i | 0.150075 | + | 0.109036i | ||||
\(559\) | 4.36068 | − | 13.4208i | 0.184437 | − | 0.567639i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.38197 | + | 4.25325i | 0.0583467 | + | 0.179573i | ||||
\(562\) | 9.23607 | − | 28.4257i | 0.389600 | − | 1.19907i | ||||
\(563\) | 3.79180 | − | 11.6699i | 0.159805 | − | 0.491830i | −0.838811 | − | 0.544423i | \(-0.816749\pi\) |
0.998616 | + | 0.0525933i | \(0.0167487\pi\) | |||||||
\(564\) | 3.61803 | + | 11.1352i | 0.152347 | + | 0.468875i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.70820 | − | 29.8788i | 0.408066 | − | 1.25590i | ||||
\(567\) | 0.309017 | + | 0.224514i | 0.0129775 | + | 0.00942870i | ||||
\(568\) | −14.4721 | −0.607237 | ||||||||
\(569\) | −35.4164 | − | 25.7315i | −1.48473 | − | 1.07872i | −0.975993 | − | 0.217801i | \(-0.930111\pi\) |
−0.508740 | − | 0.860920i | \(-0.669889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.5623 | − | 16.3925i | 0.944203 | − | 0.686004i | −0.00522561 | − | 0.999986i | \(-0.501663\pi\) |
0.949429 | + | 0.313983i | \(0.101663\pi\) | |||||||
\(572\) | 2.76393 | − | 2.00811i | 0.115566 | − | 0.0839635i | ||||
\(573\) | 5.47214 | + | 16.8415i | 0.228602 | + | 0.703564i | ||||
\(574\) | −2.94427 | −0.122892 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 11.7361 | + | 36.1199i | 0.488579 | + | 1.50369i | 0.826730 | + | 0.562599i | \(0.190199\pi\) |
−0.338151 | + | 0.941092i | \(0.609801\pi\) | |||||||
\(578\) | −5.28115 | + | 3.83698i | −0.219667 | + | 0.159597i | ||||
\(579\) | 9.01722 | − | 6.55139i | 0.374743 | − | 0.272267i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.73607 | − | 1.98787i | −0.113511 | − | 0.0824707i | ||||
\(582\) | −5.61803 | −0.232875 | ||||||||
\(583\) | 10.1631 | + | 7.38394i | 0.420913 | + | 0.305811i | ||||
\(584\) | 3.85410 | − | 11.8617i | 0.159484 | − | 0.490841i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.37132 | − | 10.3759i | −0.139268 | − | 0.428623i | ||||
\(587\) | 9.28115 | − | 28.5645i | 0.383074 | − | 1.17898i | −0.554794 | − | 0.831988i | \(-0.687203\pi\) |
0.937868 | − | 0.346993i | \(-0.112797\pi\) | |||||||
\(588\) | −2.11803 | + | 6.51864i | −0.0873462 | + | 0.268824i | ||||
\(589\) | 10.4377 | + | 32.1239i | 0.430078 | + | 1.32364i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.82624 | − | 5.62058i | 0.0751214 | − | 0.231200i | ||||
\(592\) | 6.47214 | + | 4.70228i | 0.266003 | + | 0.193263i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 1.11803 | + | 0.812299i | 0.0458735 | + | 0.0333290i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.82624 | + | 6.41264i | −0.361537 | + | 0.262672i | ||||
\(597\) | 14.9721 | − | 10.8779i | 0.612769 | − | 0.445203i | ||||
\(598\) | 3.41641 | + | 10.5146i | 0.139707 | + | 0.429975i | ||||
\(599\) | −8.47214 | −0.346162 | −0.173081 | − | 0.984908i | \(-0.555372\pi\) | ||||
−0.173081 | + | 0.984908i | \(0.555372\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.2705 | −1.68346 | −0.841730 | − | 0.539899i | \(-0.818462\pi\) | ||||
−0.841730 | + | 0.539899i | \(0.818462\pi\) | |||||||
\(602\) | −0.673762 | − | 2.07363i | −0.0274605 | − | 0.0845147i | ||||
\(603\) | −8.47214 | + | 6.15537i | −0.345012 | + | 0.250666i | ||||
\(604\) | −2.16312 | + | 1.57160i | −0.0880161 | + | 0.0639474i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.35410 | + | 3.88998i | 0.217496 | + | 0.158020i | ||||
\(607\) | 13.5623 | 0.550477 | 0.275239 | − | 0.961376i | \(-0.411243\pi\) | ||||
0.275239 | + | 0.961376i | \(0.411243\pi\) | |||||||
\(608\) | 6.23607 | + | 4.53077i | 0.252906 | + | 0.183747i | ||||
\(609\) | 0.0557281 | − | 0.171513i | 0.00225822 | − | 0.00695007i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.94427 | − | 27.5276i | −0.361847 | − | 1.11365i | ||||
\(612\) | 1.00000 | − | 3.07768i | 0.0404226 | − | 0.124408i | ||||
\(613\) | 9.96556 | − | 30.6708i | 0.402505 | − | 1.23878i | −0.520455 | − | 0.853889i | \(-0.674238\pi\) |
0.922961 | − | 0.384895i | \(-0.125762\pi\) | |||||||
\(614\) | 3.09017 | + | 9.51057i | 0.124709 | + | 0.383815i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.163119 | − | 0.502029i | 0.00657225 | − | 0.0202273i | ||||
\(617\) | 30.6525 | + | 22.2703i | 1.23402 | + | 0.896570i | 0.997185 | − | 0.0749797i | \(-0.0238892\pi\) |
0.236837 | + | 0.971549i | \(0.423889\pi\) | |||||||
\(618\) | −1.32624 | −0.0533491 | ||||||||
\(619\) | −14.0902 | − | 10.2371i | −0.566332 | − | 0.411464i | 0.267439 | − | 0.963575i | \(-0.413823\pi\) |
−0.833771 | + | 0.552111i | \(0.813823\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.61803 | + | 2.62866i | −0.145187 | + | 0.105484i | ||||
\(622\) | −15.3262 | + | 11.1352i | −0.614526 | + | 0.446479i | ||||
\(623\) | −1.47214 | − | 4.53077i | −0.0589799 | − | 0.181521i | ||||
\(624\) | −2.47214 | −0.0989646 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17.2705 | 0.690268 | ||||||||
\(627\) | 3.29180 | + | 10.1311i | 0.131462 | + | 0.404597i | ||||
\(628\) | −18.3262 | + | 13.3148i | −0.731297 | + | 0.531318i | ||||
\(629\) | 20.9443 | − | 15.2169i | 0.835103 | − | 0.606738i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.3607 | − | 22.0583i | −1.20864 | − | 0.878128i | −0.213533 | − | 0.976936i | \(-0.568497\pi\) |
−0.995107 | + | 0.0988078i | \(0.968497\pi\) | |||||||
\(632\) | 3.38197 | 0.134527 | ||||||||
\(633\) | −18.9443 | − | 13.7638i | −0.752967 | − | 0.547063i | ||||
\(634\) | −0.135255 | + | 0.416272i | −0.00537166 | + | 0.0165323i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.80902 | − | 8.64527i | −0.111385 | − | 0.342807i | ||||
\(637\) | 5.23607 | − | 16.1150i | 0.207461 | − | 0.638498i | ||||
\(638\) | 0.201626 | − | 0.620541i | 0.00798245 | − | 0.0245675i | ||||
\(639\) | 4.47214 | + | 13.7638i | 0.176915 | + | 0.544488i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.1803 | + | 34.4095i | −0.441597 | + | 1.35910i | 0.444576 | + | 0.895741i | \(0.353354\pi\) |
−0.886173 | + | 0.463354i | \(0.846646\pi\) | |||||||
\(642\) | 7.59017 | + | 5.51458i | 0.299560 | + | 0.217643i | ||||
\(643\) | 13.8885 | 0.547711 | 0.273855 | − | 0.961771i | \(-0.411701\pi\) | ||||
0.273855 | + | 0.961771i | \(0.411701\pi\) | |||||||
\(644\) | 1.38197 | + | 1.00406i | 0.0544571 | + | 0.0395654i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.1803 | − | 14.6619i | 0.793985 | − | 0.576864i | ||||
\(647\) | −4.09017 | + | 2.97168i | −0.160801 | + | 0.116829i | −0.665276 | − | 0.746598i | \(-0.731686\pi\) |
0.504475 | + | 0.863426i | \(0.331686\pi\) | |||||||
\(648\) | −0.309017 | − | 0.951057i | −0.0121393 | − | 0.0373610i | ||||
\(649\) | −1.90983 | −0.0749674 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.67376 | −0.0655999 | ||||||||
\(652\) | −2.61803 | − | 8.05748i | −0.102530 | − | 0.315555i | ||||
\(653\) | 2.30902 | − | 1.67760i | 0.0903588 | − | 0.0656495i | −0.541689 | − | 0.840579i | \(-0.682215\pi\) |
0.632047 | + | 0.774930i | \(0.282215\pi\) | |||||||
\(654\) | 10.3262 | − | 7.50245i | 0.403788 | − | 0.293369i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.23607 | + | 4.53077i | 0.243478 | + | 0.176897i | ||||
\(657\) | −12.4721 | −0.486584 | ||||||||
\(658\) | −3.61803 | − | 2.62866i | −0.141046 | − | 0.102476i | ||||
\(659\) | −5.68034 | + | 17.4823i | −0.221275 | + | 0.681013i | 0.777374 | + | 0.629039i | \(0.216551\pi\) |
−0.998648 | + | 0.0519743i | \(0.983449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.65248 | − | 20.4742i | −0.258751 | − | 0.796355i | −0.993067 | − | 0.117547i | \(-0.962497\pi\) |
0.734316 | − | 0.678808i | \(-0.237503\pi\) | |||||||
\(662\) | 5.56231 | − | 17.1190i | 0.216185 | − | 0.665350i | ||||
\(663\) | −2.47214 | + | 7.60845i | −0.0960098 | + | 0.295488i | ||||
\(664\) | 2.73607 | + | 8.42075i | 0.106180 | + | 0.326789i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.47214 | − | 7.60845i | 0.0957933 | − | 0.294822i | ||||
\(667\) | 1.70820 | + | 1.24108i | 0.0661419 | + | 0.0480549i | ||||
\(668\) | 1.70820 | 0.0660924 | ||||||||
\(669\) | 2.50000 | + | 1.81636i | 0.0966556 | + | 0.0702244i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.09017 | + | 5.87785i | −0.312318 | + | 0.226912i | ||||
\(672\) | −0.309017 | + | 0.224514i | −0.0119206 | + | 0.00866082i | ||||
\(673\) | −7.55573 | − | 23.2541i | −0.291252 | − | 0.896381i | −0.984455 | − | 0.175639i | \(-0.943801\pi\) |
0.693203 | − | 0.720743i | \(-0.256199\pi\) | |||||||
\(674\) | 12.0902 | 0.465696 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.88854 | −0.264944 | ||||||||
\(677\) | −5.53444 | − | 17.0333i | −0.212706 | − | 0.654641i | −0.999309 | − | 0.0371818i | \(-0.988162\pi\) |
0.786603 | − | 0.617460i | \(-0.211838\pi\) | |||||||
\(678\) | 11.9443 | − | 8.67802i | 0.458717 | − | 0.333277i | ||||
\(679\) | 1.73607 | − | 1.26133i | 0.0666242 | − | 0.0484053i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.11803 | + | 6.62464i | 0.349404 | + | 0.253857i | ||||
\(682\) | −6.05573 | −0.231886 | ||||||||
\(683\) | −3.64590 | − | 2.64890i | −0.139506 | − | 0.101357i | 0.515843 | − | 0.856683i | \(-0.327479\pi\) |
−0.655350 | + | 0.755326i | \(0.727479\pi\) | |||||||
\(684\) | 2.38197 | − | 7.33094i | 0.0910767 | − | 0.280305i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.63525 | − | 5.03280i | −0.0624343 | − | 0.192153i | ||||
\(687\) | −4.47214 | + | 13.7638i | −0.170623 | + | 0.525122i | ||||
\(688\) | −1.76393 | + | 5.42882i | −0.0672493 | + | 0.206972i | ||||
\(689\) | 6.94427 | + | 21.3723i | 0.264556 | + | 0.814219i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.09017 | − | 6.43288i | 0.0795138 | − | 0.244718i | −0.903396 | − | 0.428808i | \(-0.858934\pi\) |
0.982909 | + | 0.184090i | \(0.0589337\pi\) | |||||||
\(692\) | −4.92705 | − | 3.57971i | −0.187298 | − | 0.136080i | ||||
\(693\) | −0.527864 | −0.0200519 | ||||||||
\(694\) | −0.354102 | − | 0.257270i | −0.0134415 | − | 0.00976584i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.381966 | + | 0.277515i | −0.0144784 | + | 0.0105192i | ||||
\(697\) | 20.1803 | − | 14.6619i | 0.764385 | − | 0.555358i | ||||
\(698\) | −2.43769 | − | 7.50245i | −0.0922681 | − | 0.283972i | ||||
\(699\) | 12.6525 | 0.478561 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.8328 | −0.484689 | −0.242344 | − | 0.970190i | \(-0.577916\pi\) | ||||
−0.242344 | + | 0.970190i | \(0.577916\pi\) | |||||||
\(702\) | 0.763932 | + | 2.35114i | 0.0288328 | + | 0.0887381i | ||||
\(703\) | 49.8885 | − | 36.2461i | 1.88158 | − | 1.36705i | ||||
\(704\) | −1.11803 | + | 0.812299i | −0.0421375 | + | 0.0306147i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.09017 | + | 5.15131i | 0.266842 | + | 0.193872i | ||||
\(707\) | −2.52786 | −0.0950701 | ||||||||
\(708\) | 1.11803 | + | 0.812299i | 0.0420183 | + | 0.0305281i | ||||
\(709\) | −9.36068 | + | 28.8092i | −0.351548 | + | 1.08195i | 0.606437 | + | 0.795132i | \(0.292598\pi\) |
−0.957984 | + | 0.286821i | \(0.907402\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.04508 | − | 3.21644i | −0.0391937 | − | 0.120626i | ||||
\(712\) | −3.85410 | + | 11.8617i | −0.144439 | + | 0.444536i | ||||
\(713\) | 6.05573 | − | 18.6376i | 0.226789 | − | 0.697984i | ||||
\(714\) | 0.381966 | + | 1.17557i | 0.0142947 | + | 0.0439946i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.972136 | − | 2.99193i | 0.0363304 | − | 0.111814i | ||||
\(717\) | −20.7984 | − | 15.1109i | −0.776730 | − | 0.564327i | ||||
\(718\) | 0.180340 | 0.00673022 | ||||||||
\(719\) | 35.1246 | + | 25.5195i | 1.30993 | + | 0.951718i | 1.00000 | 0.000957448i | \(0.000304765\pi\) | |
0.309927 | + | 0.950760i | \(0.399695\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.409830 | − | 0.297759i | 0.0152629 | − | 0.0110891i | ||||
\(722\) | 32.6976 | − | 23.7562i | 1.21688 | − | 0.884113i | ||||
\(723\) | −3.26393 | − | 10.0453i | −0.121387 | − | 0.373591i | ||||
\(724\) | 24.6525 | 0.916202 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 9.09017 | 0.337368 | ||||||||
\(727\) | 10.9443 | + | 33.6830i | 0.405901 | + | 1.24923i | 0.920141 | + | 0.391587i | \(0.128074\pi\) |
−0.514240 | + | 0.857646i | \(0.671926\pi\) | |||||||
\(728\) | 0.763932 | − | 0.555029i | 0.0283132 | − | 0.0205707i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.9443 | + | 10.8576i | 0.552734 | + | 0.401585i | ||||
\(732\) | 7.23607 | 0.267453 | ||||||||
\(733\) | −0.0901699 | − | 0.0655123i | −0.00333050 | − | 0.00241975i | 0.586119 | − | 0.810225i | \(-0.300655\pi\) |
−0.589449 | + | 0.807805i | \(0.700655\pi\) | |||||||
\(734\) | −8.77051 | + | 26.9929i | −0.323725 | + | 0.996324i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.38197 | − | 4.25325i | −0.0509399 | − | 0.156777i | ||||
\(737\) | 4.47214 | − | 13.7638i | 0.164733 | − | 0.506997i | ||||
\(738\) | 2.38197 | − | 7.33094i | 0.0876814 | − | 0.269856i | ||||
\(739\) | −7.97871 | − | 24.5560i | −0.293502 | − | 0.903305i | −0.983721 | − | 0.179705i | \(-0.942486\pi\) |
0.690219 | − | 0.723601i | \(-0.257514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.88854 | + | 18.1231i | −0.216321 | + | 0.665768i | ||||
\(742\) | 2.80902 | + | 2.04087i | 0.103122 | + | 0.0749227i | ||||
\(743\) | −37.0132 | −1.35788 | −0.678940 | − | 0.734193i | \(-0.737561\pi\) | ||||
−0.678940 | + | 0.734193i | \(0.737561\pi\) | |||||||
\(744\) | 3.54508 | + | 2.57565i | 0.129969 | + | 0.0944281i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.5623 | − | 12.0332i | 0.606389 | − | 0.440567i | ||||
\(747\) | 7.16312 | − | 5.20431i | 0.262085 | − | 0.190416i | ||||
\(748\) | 1.38197 | + | 4.25325i | 0.0505297 | + | 0.155514i | ||||
\(749\) | −3.58359 | −0.130942 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.201626 | 0.00735744 | 0.00367872 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00367872 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(752\) | 3.61803 | + | 11.1352i | 0.131936 | + | 0.406058i | ||||
\(753\) | 5.30902 | − | 3.85723i | 0.193471 | − | 0.140565i | ||||
\(754\) | 0.944272 | − | 0.686054i | 0.0343884 | − | 0.0249846i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.309017 | + | 0.224514i | 0.0112388 | + | 0.00816549i | ||||
\(757\) | −23.1246 | −0.840478 | −0.420239 | − | 0.907413i | \(-0.638054\pi\) | ||||
−0.420239 | + | 0.907413i | \(0.638054\pi\) | |||||||
\(758\) | 1.76393 | + | 1.28157i | 0.0640689 | + | 0.0465488i | ||||
\(759\) | 1.90983 | − | 5.87785i | 0.0693224 | − | 0.213353i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.85410 | − | 24.1724i | −0.284711 | − | 0.876250i | −0.986485 | − | 0.163851i | \(-0.947608\pi\) |
0.701774 | − | 0.712399i | \(-0.252392\pi\) | |||||||
\(762\) | 3.51722 | − | 10.8249i | 0.127415 | − | 0.392144i | ||||
\(763\) | −1.50658 | + | 4.63677i | −0.0545418 | + | 0.167862i | ||||
\(764\) | 5.47214 | + | 16.8415i | 0.197975 | + | 0.609304i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.18034 | + | 19.0211i | −0.223305 | + | 0.687261i | ||||
\(767\) | −2.76393 | − | 2.00811i | −0.0997998 | − | 0.0725088i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 28.8713 | + | 20.9762i | 1.04113 | + | 0.756423i | 0.970505 | − | 0.241080i | \(-0.0775018\pi\) |
0.0706214 | + | 0.997503i | \(0.477502\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.7984 | + | 12.9313i | −0.640993 | + | 0.465709i | ||||
\(772\) | 9.01722 | − | 6.55139i | 0.324537 | − | 0.235790i | ||||
\(773\) | 2.42705 | + | 7.46969i | 0.0872950 | + | 0.268666i | 0.985169 | − | 0.171586i | \(-0.0548891\pi\) |
−0.897874 | + | 0.440252i | \(0.854889\pi\) | |||||||
\(774\) | 5.70820 | 0.205177 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.61803 | −0.201676 | ||||||||
\(777\) | 0.944272 | + | 2.90617i | 0.0338756 | + | 0.104258i | ||||
\(778\) | −11.8262 | + | 8.59226i | −0.423991 | + | 0.308048i | ||||
\(779\) | 48.0689 | − | 34.9241i | 1.72225 | − | 1.25129i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.1803 | − | 11.7557i | −0.578978 | − | 0.420652i | ||||
\(782\) | −14.4721 | −0.517523 | ||||||||
\(783\) | 0.381966 | + | 0.277515i | 0.0136504 | + | 0.00991756i | ||||
\(784\) | −2.11803 | + | 6.51864i | −0.0756441 | + | 0.232809i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.52786 | − | 17.0130i | −0.197172 | − | 0.606834i | ||||
\(787\) | 9.29180 | − | 28.5972i | 0.331217 | − | 1.01938i | −0.637339 | − | 0.770584i | \(-0.719965\pi\) |
0.968556 | − | 0.248797i | \(-0.0800351\pi\) | |||||||
\(788\) | 1.82624 | − | 5.62058i | 0.0650570 | − | 0.200225i | ||||
\(789\) | −0.527864 | − | 1.62460i | −0.0187925 | − | 0.0578372i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.74265 | + | 5.36331i | −0.0619614 | + | 0.190697i | ||||
\(792\) | 1.11803 | + | 0.812299i | 0.0397276 | + | 0.0288638i | ||||
\(793\) | −17.8885 | −0.635241 | ||||||||
\(794\) | 28.5066 | + | 20.7112i | 1.01166 | + | 0.735014i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.9721 | − | 10.8779i | 0.530673 | − | 0.385557i | ||||
\(797\) | −29.5344 | + | 21.4580i | −1.04616 | + | 0.760082i | −0.971479 | − | 0.237125i | \(-0.923795\pi\) |
−0.0746844 | + | 0.997207i | \(0.523795\pi\) | |||||||
\(798\) | 0.909830 | + | 2.80017i | 0.0322076 | + | 0.0991249i | ||||
\(799\) | 37.8885 | 1.34040 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.4721 | 0.440681 | ||||||||
\(802\) | −3.79837 | − | 11.6902i | −0.134125 | − | 0.412795i | ||||
\(803\) | 13.9443 | − | 10.1311i | 0.492083 | − | 0.357519i | ||||
\(804\) | −8.47214 | + | 6.15537i | −0.298789 | + | 0.217083i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.76393 | − | 6.36737i | −0.308696 | − | 0.224281i | ||||
\(807\) | 2.09017 | 0.0735775 | ||||||||
\(808\) | 5.35410 | + | 3.88998i | 0.188357 | + | 0.136849i | ||||
\(809\) | 7.05573 | − | 21.7153i | 0.248066 | − | 0.763469i | −0.747051 | − | 0.664767i | \(-0.768531\pi\) |
0.995117 | − | 0.0987023i | \(-0.0314692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.38197 | + | 7.33094i | 0.0836421 | + | 0.257424i | 0.984128 | − | 0.177462i | \(-0.0567887\pi\) |
−0.900486 | + | 0.434886i | \(0.856789\pi\) | |||||||
\(812\) | 0.0557281 | − | 0.171513i | 0.00195567 | − | 0.00601894i | ||||
\(813\) | 3.40983 | − | 10.4944i | 0.119588 | − | 0.368054i | ||||
\(814\) | 3.41641 | + | 10.5146i | 0.119745 | + | 0.368537i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | − | 3.07768i | 0.0350070 | − | 0.107740i | ||||
\(817\) | 35.5967 | + | 25.8626i | 1.24537 | + | 0.904816i | ||||
\(818\) | 18.7984 | 0.657270 | ||||||||
\(819\) | −0.763932 | − | 0.555029i | −0.0266939 | − | 0.0193943i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.4336 | − | 19.9317i | 0.957440 | − | 0.695621i | 0.00488541 | − | 0.999988i | \(-0.498445\pi\) |
0.952555 | + | 0.304367i | \(0.0984449\pi\) | |||||||
\(822\) | −8.23607 | + | 5.98385i | −0.287266 | + | 0.208711i | ||||
\(823\) | −9.89919 | − | 30.4666i | −0.345064 | − | 1.06200i | −0.961550 | − | 0.274631i | \(-0.911444\pi\) |
0.616486 | − | 0.787366i | \(-0.288556\pi\) | |||||||
\(824\) | −1.32624 | −0.0462017 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.527864 | −0.0183667 | ||||||||
\(827\) | 13.3197 | + | 40.9937i | 0.463170 | + | 1.42549i | 0.861270 | + | 0.508148i | \(0.169670\pi\) |
−0.398100 | + | 0.917342i | \(0.630330\pi\) | |||||||
\(828\) | −3.61803 | + | 2.62866i | −0.125735 | + | 0.0913521i | ||||
\(829\) | 8.00000 | − | 5.81234i | 0.277851 | − | 0.201871i | −0.440128 | − | 0.897935i | \(-0.645067\pi\) |
0.717980 | + | 0.696064i | \(0.245067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.763932 | − | 0.555029i | −0.0265005 | − | 0.0192537i | ||||
\(832\) | −2.47214 | −0.0857059 | ||||||||
\(833\) | 17.9443 | + | 13.0373i | 0.621732 | + | 0.451715i | ||||
\(834\) | −0.472136 | + | 1.45309i | −0.0163487 | + | 0.0503162i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.29180 | + | 10.1311i | 0.113849 | + | 0.350392i | ||||
\(837\) | 1.35410 | − | 4.16750i | 0.0468046 | − | 0.144050i | ||||
\(838\) | −2.50000 | + | 7.69421i | −0.0863611 | + | 0.265792i | ||||
\(839\) | −11.8541 | − | 36.4832i | −0.409249 | − | 1.25954i | −0.917295 | − | 0.398209i | \(-0.869632\pi\) |
0.508046 | − | 0.861330i | \(-0.330368\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.89261 | + | 27.3686i | −0.306642 | + | 0.943746i | ||||
\(842\) | −22.0344 | − | 16.0090i | −0.759357 | − | 0.551705i | ||||
\(843\) | −29.8885 | −1.02942 | ||||||||
\(844\) | −18.9443 | − | 13.7638i | −0.652089 | − | 0.473770i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 9.47214 | − | 6.88191i | 0.325659 | − | 0.236605i | ||||
\(847\) | −2.80902 | + | 2.04087i | −0.0965190 | + | 0.0701251i | ||||
\(848\) | −2.80902 | − | 8.64527i | −0.0964620 | − | 0.296880i | ||||
\(849\) | −31.4164 | −1.07821 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −35.7771 | −1.22642 | ||||||||
\(852\) | 4.47214 | + | 13.7638i | 0.153213 | + | 0.471541i | ||||
\(853\) | 4.52786 | − | 3.28969i | 0.155031 | − | 0.112637i | −0.507565 | − | 0.861613i | \(-0.669454\pi\) |
0.662597 | + | 0.748977i | \(0.269454\pi\) | |||||||
\(854\) | −2.23607 | + | 1.62460i | −0.0765167 | + | 0.0555926i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.59017 | + | 5.51458i | 0.259427 | + | 0.188485i | ||||
\(857\) | −42.0689 | −1.43705 | −0.718523 | − | 0.695503i | \(-0.755181\pi\) | ||||
−0.718523 | + | 0.695503i | \(0.755181\pi\) | |||||||
\(858\) | −2.76393 | − | 2.00811i | −0.0943591 | − | 0.0685559i | ||||
\(859\) | −4.85410 | + | 14.9394i | −0.165620 | + | 0.509725i | −0.999081 | − | 0.0428520i | \(-0.986356\pi\) |
0.833462 | + | 0.552577i | \(0.186356\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.909830 | + | 2.80017i | 0.0310069 | + | 0.0954295i | ||||
\(862\) | 11.3820 | − | 35.0301i | 0.387671 | − | 1.19313i | ||||
\(863\) | −3.76393 | + | 11.5842i | −0.128126 | + | 0.394330i | −0.994458 | − | 0.105138i | \(-0.966471\pi\) |
0.866332 | + | 0.499469i | \(0.166471\pi\) | |||||||
\(864\) | −0.309017 | − | 0.951057i | −0.0105130 | − | 0.0323556i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −6.95492 | + | 21.4050i | −0.236338 | + | 0.727372i | ||||
\(867\) | 5.28115 | + | 3.83698i | 0.179357 | + | 0.130311i | ||||
\(868\) | −1.67376 | −0.0568112 | ||||||||
\(869\) | 3.78115 | + | 2.74717i | 0.128267 | + | 0.0931913i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.9443 | − | 15.2169i | 0.709670 | − | 0.515605i | ||||
\(872\) | 10.3262 | − | 7.50245i | 0.349691 | − | 0.254065i | ||||
\(873\) | 1.73607 | + | 5.34307i | 0.0587570 | + | 0.180835i | ||||
\(874\) | −34.4721 | −1.16604 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.4721 | −0.421394 | ||||||||
\(877\) | −0.965558 | − | 2.97168i | −0.0326046 | − | 0.100347i | 0.933430 | − | 0.358760i | \(-0.116800\pi\) |
−0.966034 | + | 0.258413i | \(0.916800\pi\) | |||||||
\(878\) | 11.7361 | − | 8.52675i | 0.396073 | − | 0.287764i | ||||
\(879\) | −8.82624 | + | 6.41264i | −0.297702 | + | 0.216293i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.7082 | − | 15.0454i | −0.697677 | − | 0.506892i | 0.181498 | − | 0.983391i | \(-0.441905\pi\) |
−0.879175 | + | 0.476499i | \(0.841905\pi\) | |||||||
\(882\) | 6.85410 | 0.230790 | ||||||||
\(883\) | 22.7082 | + | 16.4985i | 0.764192 | + | 0.555218i | 0.900193 | − | 0.435491i | \(-0.143425\pi\) |
−0.136001 | + | 0.990709i | \(0.543425\pi\) | |||||||
\(884\) | −2.47214 | + | 7.60845i | −0.0831469 | + | 0.255900i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.44427 | + | 13.6781i | 0.149308 | + | 0.459523i | ||||
\(887\) | 1.05573 | − | 3.24920i | 0.0354479 | − | 0.109097i | −0.931767 | − | 0.363057i | \(-0.881733\pi\) |
0.967215 | + | 0.253960i | \(0.0817330\pi\) | |||||||
\(888\) | 2.47214 | − | 7.60845i | 0.0829595 | − | 0.255323i | ||||
\(889\) | 1.34346 | + | 4.13474i | 0.0450582 | + | 0.138675i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.427051 | − | 1.31433i | 0.0143067 | − | 0.0440316i | ||||
\(892\) | 2.50000 | + | 1.81636i | 0.0837062 | + | 0.0608161i | ||||
\(893\) | 90.2492 | 3.02008 | ||||||||
\(894\) | 8.82624 | + | 6.41264i | 0.295194 | + | 0.214471i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.309017 | + | 0.224514i | −0.0103235 | + | 0.00750049i | ||||
\(897\) | 8.94427 | − | 6.49839i | 0.298641 | − | 0.216975i | ||||
\(898\) | 4.41641 | + | 13.5923i | 0.147377 | + | 0.453581i | ||||
\(899\) | −2.06888 | −0.0690011 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.4164 | −0.980003 | ||||||||
\(902\) | 3.29180 | + | 10.1311i | 0.109605 | + | 0.337329i | ||||
\(903\) | −1.76393 | + | 1.28157i | −0.0587000 | + | 0.0426480i | ||||
\(904\) | 11.9443 | − | 8.67802i | 0.397261 | − | 0.288627i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.16312 | + | 1.57160i | 0.0718648 | + | 0.0522128i | ||||
\(907\) | −21.5279 | −0.714821 | −0.357410 | − | 0.933947i | \(-0.616340\pi\) | ||||
−0.357410 | + | 0.933947i | \(0.616340\pi\) | |||||||
\(908\) | 9.11803 | + | 6.62464i | 0.302593 | + | 0.219846i | ||||
\(909\) | 2.04508 | − | 6.29412i | 0.0678312 | − | 0.208763i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.29180 | − | 3.97574i | −0.0427991 | − | 0.131722i | 0.927374 | − | 0.374136i | \(-0.122061\pi\) |
−0.970173 | + | 0.242414i | \(0.922061\pi\) | |||||||
\(912\) | 2.38197 | − | 7.33094i | 0.0788748 | − | 0.242752i | ||||
\(913\) | −3.78115 | + | 11.6372i | −0.125138 | + | 0.385135i | ||||
\(914\) | 2.19098 | + | 6.74315i | 0.0724713 | + | 0.223044i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.47214 | + | 13.7638i | −0.147764 | + | 0.454769i | ||||
\(917\) | 5.52786 | + | 4.01623i | 0.182546 | + | 0.132628i | ||||
\(918\) | −3.23607 | −0.106806 | ||||||||
\(919\) | −39.4164 | − | 28.6377i | −1.30023 | − | 0.944670i | −0.300269 | − | 0.953854i | \(-0.597077\pi\) |
−0.999958 | + | 0.00918396i | \(0.997077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.09017 | − | 5.87785i | 0.266580 | − | 0.193682i | ||||
\(922\) | −10.1631 | + | 7.38394i | −0.334704 | + | 0.243177i | ||||
\(923\) | −11.0557 | − | 34.0260i | −0.363904 | − | 1.11998i | ||||
\(924\) | −0.527864 | −0.0173655 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 30.8328 | 1.01323 | ||||||||
\(927\) | 0.409830 | + | 1.26133i | 0.0134606 | + | 0.0414274i | ||||
\(928\) | −0.381966 | + | 0.277515i | −0.0125386 | + | 0.00910986i | ||||
\(929\) | −46.1246 | + | 33.5115i | −1.51330 | + | 1.09948i | −0.548613 | + | 0.836077i | \(0.684844\pi\) |
−0.964687 | + | 0.263400i | \(0.915156\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 42.7426 | + | 31.0543i | 1.40083 | + | 1.01777i | ||||
\(932\) | 12.6525 | 0.414446 | ||||||||
\(933\) | 15.3262 | + | 11.1352i | 0.501759 | + | 0.364549i | ||||
\(934\) | 8.13525 | − | 25.0377i | 0.266194 | − | 0.819260i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.763932 | + | 2.35114i | 0.0249699 | + | 0.0768494i | ||||
\(937\) | −15.9721 | + | 49.1572i | −0.521787 | + | 1.60590i | 0.248796 | + | 0.968556i | \(0.419965\pi\) |
−0.770583 | + | 0.637339i | \(0.780035\pi\) | |||||||
\(938\) | 1.23607 | − | 3.80423i | 0.0403591 | − | 0.124212i | ||||
\(939\) | −5.33688 | − | 16.4252i | −0.174163 | − | 0.536017i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.59017 | + | 23.3601i | −0.247432 | + | 0.761519i | 0.747794 | + | 0.663930i | \(0.231113\pi\) |
−0.995227 | + | 0.0975885i | \(0.968887\pi\) | |||||||
\(942\) | 18.3262 | + | 13.3148i | 0.597101 | + | 0.433819i | ||||
\(943\) | −34.4721 | −1.12257 | ||||||||
\(944\) | 1.11803 | + | 0.812299i | 0.0363889 | + | 0.0264381i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.38197 | + | 4.63677i | −0.207496 | + | 0.150754i | ||||
\(947\) | −10.8713 | + | 7.89848i | −0.353271 | + | 0.256666i | −0.750240 | − | 0.661166i | \(-0.770062\pi\) |
0.396969 | + | 0.917832i | \(0.370062\pi\) | |||||||
\(948\) | −1.04508 | − | 3.21644i | −0.0339428 | − | 0.104465i | ||||
\(949\) | 30.8328 | 1.00088 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.437694 | 0.0141932 | ||||||||
\(952\) | 0.381966 | + | 1.17557i | 0.0123796 | + | 0.0381005i | ||||
\(953\) | −46.3607 | + | 33.6830i | −1.50177 | + | 1.09110i | −0.532100 | + | 0.846682i | \(0.678597\pi\) |
−0.969670 | + | 0.244418i | \(0.921403\pi\) | |||||||
\(954\) | −7.35410 | + | 5.34307i | −0.238098 | + | 0.172988i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −20.7984 | − | 15.1109i | −0.672667 | − | 0.488722i | ||||
\(957\) | −0.652476 | −0.0210915 | ||||||||
\(958\) | 9.00000 | + | 6.53888i | 0.290777 | + | 0.211262i | ||||
\(959\) | 1.20163 | − | 3.69822i | 0.0388025 | − | 0.119422i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.64590 | − | 11.2209i | −0.117610 | − | 0.361965i | ||||
\(962\) | −6.11146 | + | 18.8091i | −0.197041 | + | 0.606431i | ||||
\(963\) | 2.89919 | − | 8.92278i | 0.0934250 | − | 0.287533i | ||||
\(964\) | −3.26393 | − | 10.0453i | −0.105124 | − | 0.323539i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.527864 | − | 1.62460i | 0.0169837 | − | 0.0522706i | ||||
\(967\) | 17.8713 | + | 12.9843i | 0.574703 | + | 0.417546i | 0.836811 | − | 0.547492i | \(-0.184418\pi\) |
−0.262108 | + | 0.965039i | \(0.584418\pi\) | |||||||
\(968\) | 9.09017 | 0.292169 | ||||||||
\(969\) | −20.1803 | − | 14.6619i | −0.648286 | − | 0.471007i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.1074 | + | 21.8743i | −0.966192 | + | 0.701980i | −0.954581 | − | 0.297953i | \(-0.903696\pi\) |
−0.0116116 | + | 0.999933i | \(0.503696\pi\) | |||||||
\(972\) | −0.809017 | + | 0.587785i | −0.0259492 | + | 0.0188532i | ||||
\(973\) | −0.180340 | − | 0.555029i | −0.00578143 | − | 0.0177934i | ||||
\(974\) | −6.79837 | −0.217834 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.23607 | 0.231621 | ||||||||
\(977\) | 1.61803 | + | 4.97980i | 0.0517655 | + | 0.159318i | 0.973597 | − | 0.228272i | \(-0.0733076\pi\) |
−0.921832 | + | 0.387590i | \(0.873308\pi\) | |||||||
\(978\) | −6.85410 | + | 4.97980i | −0.219170 | + | 0.159236i | ||||
\(979\) | −13.9443 | + | 10.1311i | −0.445661 | + | 0.323792i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.3262 | − | 7.50245i | −0.329691 | − | 0.239535i | ||||
\(982\) | −8.27051 | −0.263923 | ||||||||
\(983\) | 14.4164 | + | 10.4741i | 0.459812 | + | 0.334073i | 0.793458 | − | 0.608626i | \(-0.208279\pi\) |
−0.333646 | + | 0.942699i | \(0.608279\pi\) | |||||||
\(984\) | 2.38197 | − | 7.33094i | 0.0759343 | − | 0.233702i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.472136 | + | 1.45309i | 0.0150359 | + | 0.0462757i | ||||
\(987\) | −1.38197 | + | 4.25325i | −0.0439885 | + | 0.135383i | ||||
\(988\) | −5.88854 | + | 18.1231i | −0.187340 | + | 0.576572i | ||||
\(989\) | −7.88854 | − | 24.2784i | −0.250841 | − | 0.772010i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.17376 | + | 25.1563i | −0.259648 | + | 0.799115i | 0.733230 | + | 0.679981i | \(0.238012\pi\) |
−0.992878 | + | 0.119134i | \(0.961988\pi\) | |||||||
\(992\) | 3.54508 | + | 2.57565i | 0.112557 | + | 0.0817771i | ||||
\(993\) | −18.0000 | −0.571213 | ||||||||
\(994\) | −4.47214 | − | 3.24920i | −0.141848 | − | 0.103058i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7.16312 | − | 5.20431i | 0.226972 | − | 0.164905i | ||||
\(997\) | 35.2705 | − | 25.6255i | 1.11703 | − | 0.811569i | 0.133272 | − | 0.991079i | \(-0.457452\pi\) |
0.983756 | + | 0.179511i | \(0.0574515\pi\) | |||||||
\(998\) | 4.20163 | + | 12.9313i | 0.133000 | + | 0.409332i | ||||
\(999\) | −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.g.b.151.1 | 4 | ||
5.2 | odd | 4 | 750.2.h.b.349.2 | 8 | |||
5.3 | odd | 4 | 750.2.h.b.349.1 | 8 | |||
5.4 | even | 2 | 150.2.g.a.31.1 | ✓ | 4 | ||
15.14 | odd | 2 | 450.2.h.c.181.1 | 4 | |||
25.2 | odd | 20 | 3750.2.c.b.1249.2 | 4 | |||
25.3 | odd | 20 | 750.2.h.b.649.2 | 8 | |||
25.4 | even | 10 | 150.2.g.a.121.1 | yes | 4 | ||
25.11 | even | 5 | 3750.2.a.d.1.2 | 2 | |||
25.14 | even | 10 | 3750.2.a.f.1.1 | 2 | |||
25.21 | even | 5 | inner | 750.2.g.b.601.1 | 4 | ||
25.22 | odd | 20 | 750.2.h.b.649.1 | 8 | |||
25.23 | odd | 20 | 3750.2.c.b.1249.3 | 4 | |||
75.29 | odd | 10 | 450.2.h.c.271.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.2.g.a.31.1 | ✓ | 4 | 5.4 | even | 2 | ||
150.2.g.a.121.1 | yes | 4 | 25.4 | even | 10 | ||
450.2.h.c.181.1 | 4 | 15.14 | odd | 2 | |||
450.2.h.c.271.1 | 4 | 75.29 | odd | 10 | |||
750.2.g.b.151.1 | 4 | 1.1 | even | 1 | trivial | ||
750.2.g.b.601.1 | 4 | 25.21 | even | 5 | inner | ||
750.2.h.b.349.1 | 8 | 5.3 | odd | 4 | |||
750.2.h.b.349.2 | 8 | 5.2 | odd | 4 | |||
750.2.h.b.649.1 | 8 | 25.22 | odd | 20 | |||
750.2.h.b.649.2 | 8 | 25.3 | odd | 20 | |||
3750.2.a.d.1.2 | 2 | 25.11 | even | 5 | |||
3750.2.a.f.1.1 | 2 | 25.14 | even | 10 | |||
3750.2.c.b.1249.2 | 4 | 25.2 | odd | 20 | |||
3750.2.c.b.1249.3 | 4 | 25.23 | odd | 20 |