Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(101,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | 12.0.4767670494822400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + \cdots + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 101.4 | ||
Root | \(0.618969 + 1.27156i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.101 |
Dual form | 400.2.l.f.301.4 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618969 | − | 1.27156i | −0.437677 | − | 0.899132i | ||||
\(3\) | −2.16859 | + | 2.16859i | −1.25203 | + | 1.25203i | −0.297227 | + | 0.954807i | \(0.596062\pi\) |
−0.954807 | + | 0.297227i | \(0.903938\pi\) | |||||||
\(4\) | −1.23375 | + | 1.57412i | −0.616877 | + | 0.787060i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.09979 | + | 1.41521i | 1.67373 | + | 0.577757i | ||||
\(7\) | 3.30519i | 1.24924i | 0.780927 | + | 0.624622i | \(0.214747\pi\) | ||||
−0.780927 | + | 0.624622i | \(0.785253\pi\) | |||||||
\(8\) | 2.76525 | + | 0.594467i | 0.977664 | + | 0.210176i | ||||
\(9\) | − | 6.40553i | − | 2.13518i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.01163 | + | 2.01163i | 0.606530 | + | 0.606530i | 0.942038 | − | 0.335507i | \(-0.108908\pi\) |
−0.335507 | + | 0.942038i | \(0.608908\pi\) | |||||||
\(12\) | −0.738111 | − | 6.08911i | −0.213074 | − | 1.75778i | ||||
\(13\) | −0.794042 | + | 0.794042i | −0.220228 | + | 0.220228i | −0.808594 | − | 0.588367i | \(-0.799771\pi\) |
0.588367 | + | 0.808594i | \(0.299771\pi\) | |||||||
\(14\) | 4.20276 | − | 2.04581i | 1.12324 | − | 0.546766i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.955702 | − | 3.88415i | −0.238926 | − | 0.971038i | ||||
\(17\) | −4.61575 | −1.11948 | −0.559741 | − | 0.828667i | \(-0.689100\pi\) | ||||
−0.559741 | + | 0.828667i | \(0.689100\pi\) | |||||||
\(18\) | −8.14504 | + | 3.96483i | −1.91981 | + | 0.934518i | ||||
\(19\) | −3.48786 | + | 3.48786i | −0.800169 | + | 0.800169i | −0.983122 | − | 0.182953i | \(-0.941434\pi\) |
0.182953 | + | 0.983122i | \(0.441434\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.16759 | − | 7.16759i | −1.56410 | − | 1.56410i | ||||
\(22\) | 1.31278 | − | 3.80306i | 0.279886 | − | 0.810815i | ||||
\(23\) | − | 7.99801i | − | 1.66770i | −0.551991 | − | 0.833850i | \(-0.686132\pi\) | ||
0.551991 | − | 0.833850i | \(-0.313868\pi\) | |||||||
\(24\) | −7.28583 | + | 4.70753i | −1.48721 | + | 0.960921i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.50116 | + | 0.518188i | 0.294402 | + | 0.101625i | ||||
\(27\) | 7.38518 | + | 7.38518i | 1.42128 | + | 1.42128i | ||||
\(28\) | −5.20276 | − | 4.07779i | −0.983230 | − | 0.770630i | ||||
\(29\) | −1.95065 | + | 1.95065i | −0.362227 | + | 0.362227i | −0.864632 | − | 0.502406i | \(-0.832448\pi\) |
0.502406 | + | 0.864632i | \(0.332448\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.12695 | −0.920828 | −0.460414 | − | 0.887704i | \(-0.652299\pi\) | ||||
−0.460414 | + | 0.887704i | \(0.652299\pi\) | |||||||
\(32\) | −4.34740 | + | 3.61941i | −0.768519 | + | 0.639827i | ||||
\(33\) | −8.72480 | −1.51879 | ||||||||
\(34\) | 2.85701 | + | 5.86922i | 0.489972 | + | 1.00656i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 10.0831 | + | 7.90285i | 1.68051 | + | 1.31714i | ||||
\(37\) | −0.448156 | − | 0.448156i | −0.0736764 | − | 0.0736764i | 0.669308 | − | 0.742985i | \(-0.266591\pi\) |
−0.742985 | + | 0.669308i | \(0.766591\pi\) | |||||||
\(38\) | 6.59391 | + | 2.27616i | 1.06967 | + | 0.369242i | ||||
\(39\) | − | 3.44390i | − | 0.551465i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.02230i | − | 0.628177i | −0.949394 | − | 0.314089i | \(-0.898301\pi\) | ||
0.949394 | − | 0.314089i | \(-0.101699\pi\) | |||||||
\(42\) | −4.67754 | + | 13.5506i | −0.721760 | + | 2.09090i | ||||
\(43\) | −4.97000 | − | 4.97000i | −0.757918 | − | 0.757918i | 0.218025 | − | 0.975943i | \(-0.430039\pi\) |
−0.975943 | + | 0.218025i | \(0.930039\pi\) | |||||||
\(44\) | −5.64841 | + | 0.684690i | −0.851530 | + | 0.103221i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.1700 | + | 4.95052i | −1.49948 | + | 0.729915i | ||||
\(47\) | 5.49112 | 0.800962 | 0.400481 | − | 0.916305i | \(-0.368843\pi\) | ||||
0.400481 | + | 0.916305i | \(0.368843\pi\) | |||||||
\(48\) | 10.4956 | + | 6.35059i | 1.51491 | + | 0.916629i | ||||
\(49\) | −3.92429 | −0.560612 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0096 | − | 10.0096i | 1.40163 | − | 1.40163i | ||||
\(52\) | −0.270264 | − | 2.22957i | −0.0374789 | − | 0.309186i | ||||
\(53\) | 3.35125 | + | 3.35125i | 0.460330 | + | 0.460330i | 0.898763 | − | 0.438434i | \(-0.144467\pi\) |
−0.438434 | + | 0.898763i | \(0.644467\pi\) | |||||||
\(54\) | 4.81954 | − | 13.9619i | 0.655856 | − | 1.89998i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.96483 | + | 9.13968i | −0.262561 | + | 1.22134i | ||||
\(57\) | − | 15.1274i | − | 2.00368i | ||||||
\(58\) | 3.68777 | + | 1.27299i | 0.484228 | + | 0.167151i | ||||
\(59\) | 2.07673 | + | 2.07673i | 0.270367 | + | 0.270367i | 0.829248 | − | 0.558881i | \(-0.188769\pi\) |
−0.558881 | + | 0.829248i | \(0.688769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.557208 | + | 0.557208i | −0.0713432 | + | 0.0713432i | −0.741878 | − | 0.670535i | \(-0.766065\pi\) |
0.670535 | + | 0.741878i | \(0.266065\pi\) | |||||||
\(62\) | 3.17343 | + | 6.51925i | 0.403026 | + | 0.827946i | ||||
\(63\) | 21.1715 | 2.66736 | ||||||||
\(64\) | 7.29322 | + | 3.28770i | 0.911652 | + | 0.410962i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 5.40038 | + | 11.0941i | 0.664741 | + | 1.36560i | ||||
\(67\) | 0.636094 | − | 0.636094i | 0.0777112 | − | 0.0777112i | −0.667183 | − | 0.744894i | \(-0.732500\pi\) |
0.744894 | + | 0.667183i | \(0.232500\pi\) | |||||||
\(68\) | 5.69470 | − | 7.26573i | 0.690583 | − | 0.881100i | ||||
\(69\) | 17.3444 | + | 17.3444i | 2.08802 | + | 2.08802i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.85258i | 0.813252i | 0.913595 | + | 0.406626i | \(0.133295\pi\) | ||||
−0.913595 | + | 0.406626i | \(0.866705\pi\) | |||||||
\(72\) | 3.80787 | − | 17.7129i | 0.448762 | − | 2.08748i | ||||
\(73\) | − | 10.5177i | − | 1.23101i | −0.788134 | − | 0.615504i | \(-0.788953\pi\) | ||
0.788134 | − | 0.615504i | \(-0.211047\pi\) | |||||||
\(74\) | −0.292465 | + | 0.847255i | −0.0339983 | + | 0.0984913i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.18714 | − | 9.79346i | −0.136175 | − | 1.12339i | ||||
\(77\) | −6.64883 | + | 6.64883i | −0.757705 | + | 0.757705i | ||||
\(78\) | −4.37914 | + | 2.13167i | −0.495840 | + | 0.241364i | ||||
\(79\) | −17.3005 | −1.94646 | −0.973230 | − | 0.229833i | \(-0.926182\pi\) | ||||
−0.973230 | + | 0.229833i | \(0.926182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −12.8142 | −1.42380 | ||||||||
\(82\) | −5.11461 | + | 2.48968i | −0.564814 | + | 0.274939i | ||||
\(83\) | −9.48015 | + | 9.48015i | −1.04058 | + | 1.04058i | −0.0414412 | + | 0.999141i | \(0.513195\pi\) |
−0.999141 | + | 0.0414412i | \(0.986805\pi\) | |||||||
\(84\) | 20.1257 | − | 2.43960i | 2.19589 | − | 0.266182i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.24340 | + | 9.39596i | −0.349745 | + | 1.01319i | ||||
\(87\) | − | 8.46030i | − | 0.907040i | ||||||
\(88\) | 4.36682 | + | 6.75852i | 0.465505 | + | 0.720460i | ||||
\(89\) | − | 7.62073i | − | 0.807796i | −0.914804 | − | 0.403898i | \(-0.867655\pi\) | ||
0.914804 | − | 0.403898i | \(-0.132345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.62446 | − | 2.62446i | −0.275118 | − | 0.275118i | ||||
\(92\) | 12.5898 | + | 9.86757i | 1.31258 | + | 1.02877i | ||||
\(93\) | 11.1182 | − | 11.1182i | 1.15291 | − | 1.15291i | ||||
\(94\) | −3.39883 | − | 6.98231i | −0.350563 | − | 0.720171i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.57871 | − | 17.2767i | 0.161127 | − | 1.76330i | ||||
\(97\) | −0.709082 | −0.0719964 | −0.0359982 | − | 0.999352i | \(-0.511461\pi\) | ||||
−0.0359982 | + | 0.999352i | \(0.511461\pi\) | |||||||
\(98\) | 2.42901 | + | 4.98999i | 0.245367 | + | 0.504065i | ||||
\(99\) | 12.8856 | − | 12.8856i | 1.29505 | − | 1.29505i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.16223 | + | 6.16223i | 0.613164 | + | 0.613164i | 0.943769 | − | 0.330605i | \(-0.107253\pi\) |
−0.330605 | + | 0.943769i | \(0.607253\pi\) | |||||||
\(102\) | −18.9236 | − | 6.53225i | −1.87371 | − | 0.646789i | ||||
\(103\) | 15.9410i | 1.57072i | 0.619040 | + | 0.785359i | \(0.287522\pi\) | ||||
−0.619040 | + | 0.785359i | \(0.712478\pi\) | |||||||
\(104\) | −2.66776 | + | 1.72369i | −0.261595 | + | 0.169022i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.18701 | − | 6.33565i | 0.212421 | − | 0.615373i | ||||
\(107\) | 3.38717 | + | 3.38717i | 0.327450 | + | 0.327450i | 0.851616 | − | 0.524166i | \(-0.175623\pi\) |
−0.524166 | + | 0.851616i | \(0.675623\pi\) | |||||||
\(108\) | −20.7367 | + | 2.51366i | −1.99539 | + | 0.241877i | ||||
\(109\) | −2.43964 | + | 2.43964i | −0.233675 | + | 0.233675i | −0.814225 | − | 0.580550i | \(-0.802838\pi\) |
0.580550 | + | 0.814225i | \(0.302838\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.94373 | 0.184491 | ||||||||
\(112\) | 12.8379 | − | 3.15878i | 1.21306 | − | 0.298477i | ||||
\(113\) | −1.09801 | −0.103292 | −0.0516461 | − | 0.998665i | \(-0.516447\pi\) | ||||
−0.0516461 | + | 0.998665i | \(0.516447\pi\) | |||||||
\(114\) | −19.2355 | + | 9.36341i | −1.80157 | + | 0.876964i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.663933 | − | 5.47718i | −0.0616447 | − | 0.508543i | ||||
\(117\) | 5.08626 | + | 5.08626i | 0.470225 | + | 0.470225i | ||||
\(118\) | 1.35526 | − | 3.92612i | 0.124762 | − | 0.361429i | ||||
\(119\) | − | 15.2559i | − | 1.39851i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.90666i | − | 0.264242i | ||||||
\(122\) | 1.05342 | + | 0.363632i | 0.0953723 | + | 0.0329217i | ||||
\(123\) | 8.72270 | + | 8.72270i | 0.786499 | + | 0.786499i | ||||
\(124\) | 6.32540 | − | 8.07044i | 0.568038 | − | 0.724747i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.1045 | − | 26.9209i | −1.16744 | − | 2.39831i | ||||
\(127\) | 1.51159 | 0.134131 | 0.0670657 | − | 0.997749i | \(-0.478636\pi\) | ||||
0.0670657 | + | 0.997749i | \(0.478636\pi\) | |||||||
\(128\) | −0.333758 | − | 11.3088i | −0.0295003 | − | 0.999565i | ||||
\(129\) | 21.5557 | 1.89788 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.21660 | + | 9.21660i | −0.805258 | + | 0.805258i | −0.983912 | − | 0.178654i | \(-0.942826\pi\) |
0.178654 | + | 0.983912i | \(0.442826\pi\) | |||||||
\(132\) | 10.7643 | − | 13.7339i | 0.936908 | − | 1.19538i | ||||
\(133\) | −11.5280 | − | 11.5280i | −0.999607 | − | 0.999607i | ||||
\(134\) | −1.20256 | − | 0.415112i | −0.103885 | − | 0.0358602i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.7637 | − | 2.74391i | −1.09448 | − | 0.235288i | ||||
\(137\) | 3.38639i | 0.289318i | 0.989482 | + | 0.144659i | \(0.0462086\pi\) | ||||
−0.989482 | + | 0.144659i | \(0.953791\pi\) | |||||||
\(138\) | 11.3189 | − | 32.7901i | 0.963525 | − | 2.79128i | ||||
\(139\) | −2.09626 | − | 2.09626i | −0.177802 | − | 0.177802i | 0.612595 | − | 0.790397i | \(-0.290126\pi\) |
−0.790397 | + | 0.612595i | \(0.790126\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.9080 | + | 11.9080i | −1.00283 | + | 1.00283i | ||||
\(142\) | 8.71350 | − | 4.24154i | 0.731221 | − | 0.355942i | ||||
\(143\) | −3.19464 | −0.267149 | ||||||||
\(144\) | −24.8800 | + | 6.12178i | −2.07334 | + | 0.510148i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.3740 | + | 6.51016i | −1.10684 | + | 0.538784i | ||||
\(147\) | 8.51015 | − | 8.51015i | 0.701906 | − | 0.701906i | ||||
\(148\) | 1.25837 | − | 0.152537i | 0.103437 | − | 0.0125384i | ||||
\(149\) | −2.45247 | − | 2.45247i | −0.200915 | − | 0.200915i | 0.599477 | − | 0.800392i | \(-0.295375\pi\) |
−0.800392 | + | 0.599477i | \(0.795375\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.11727i | 0.0909222i | 0.998966 | + | 0.0454611i | \(0.0144757\pi\) | ||||
−0.998966 | + | 0.0454611i | \(0.985524\pi\) | |||||||
\(152\) | −11.7182 | + | 7.57138i | −0.950472 | + | 0.614120i | ||||
\(153\) | 29.5663i | 2.39029i | ||||||||
\(154\) | 12.5698 | + | 4.33900i | 1.01291 | + | 0.349646i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.42110 | + | 4.24892i | 0.434036 | + | 0.340186i | ||||
\(157\) | −15.8377 | + | 15.8377i | −1.26398 | + | 1.26398i | −0.314839 | + | 0.949145i | \(0.601950\pi\) |
−0.949145 | + | 0.314839i | \(0.898050\pi\) | |||||||
\(158\) | 10.7085 | + | 21.9987i | 0.851922 | + | 1.75012i | ||||
\(159\) | −14.5349 | −1.15270 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 26.4349 | 2.08337 | ||||||||
\(162\) | 7.93160 | + | 16.2941i | 0.623166 | + | 1.28019i | ||||
\(163\) | 7.22102 | − | 7.22102i | 0.565594 | − | 0.565594i | −0.365297 | − | 0.930891i | \(-0.619033\pi\) |
0.930891 | + | 0.365297i | \(0.119033\pi\) | |||||||
\(164\) | 6.33158 | + | 4.96253i | 0.494413 | + | 0.387508i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.9226 | + | 6.18671i | 1.39106 | + | 0.480182i | ||||
\(167\) | 13.2304i | 1.02380i | 0.859044 | + | 0.511901i | \(0.171059\pi\) | ||||
−0.859044 | + | 0.511901i | \(0.828941\pi\) | |||||||
\(168\) | −15.5593 | − | 24.0811i | −1.20043 | − | 1.85790i | ||||
\(169\) | 11.7390i | 0.903000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.3416 | + | 22.3416i | 1.70850 | + | 1.70850i | ||||
\(172\) | 13.9551 | − | 1.69162i | 1.06407 | − | 0.128984i | ||||
\(173\) | −11.7503 | + | 11.7503i | −0.893355 | + | 0.893355i | −0.994837 | − | 0.101482i | \(-0.967641\pi\) |
0.101482 | + | 0.994837i | \(0.467641\pi\) | |||||||
\(174\) | −10.7578 | + | 5.23667i | −0.815548 | + | 0.396991i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.89097 | − | 9.73601i | 0.444048 | − | 0.733879i | ||||
\(177\) | −9.00712 | −0.677017 | ||||||||
\(178\) | −9.69026 | + | 4.71700i | −0.726315 | + | 0.353554i | ||||
\(179\) | 4.84732 | − | 4.84732i | 0.362306 | − | 0.362306i | −0.502355 | − | 0.864661i | \(-0.667533\pi\) |
0.864661 | + | 0.502355i | \(0.167533\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5742 | + | 10.5742i | 0.785976 | + | 0.785976i | 0.980832 | − | 0.194856i | \(-0.0624240\pi\) |
−0.194856 | + | 0.980832i | \(0.562424\pi\) | |||||||
\(182\) | −1.71271 | + | 4.96163i | −0.126955 | + | 0.367781i | ||||
\(183\) | − | 2.41671i | − | 0.178648i | ||||||
\(184\) | 4.75455 | − | 22.1165i | 0.350510 | − | 1.63045i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −21.0194 | − | 7.25571i | −1.54122 | − | 0.532015i | ||||
\(187\) | −9.28519 | − | 9.28519i | −0.679000 | − | 0.679000i | ||||
\(188\) | −6.77469 | + | 8.64368i | −0.494095 | + | 0.630405i | ||||
\(189\) | −24.4094 | + | 24.4094i | −1.77553 | + | 1.77553i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.94268 | 0.574712 | 0.287356 | − | 0.957824i | \(-0.407224\pi\) | ||||
0.287356 | + | 0.957824i | \(0.407224\pi\) | |||||||
\(192\) | −22.9456 | + | 8.68632i | −1.65596 | + | 0.626881i | ||||
\(193\) | 20.8617 | 1.50166 | 0.750829 | − | 0.660496i | \(-0.229654\pi\) | ||||
0.750829 | + | 0.660496i | \(0.229654\pi\) | |||||||
\(194\) | 0.438900 | + | 0.901644i | 0.0315112 | + | 0.0647343i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.84160 | − | 6.17730i | 0.345829 | − | 0.441235i | ||||
\(197\) | −2.07707 | − | 2.07707i | −0.147985 | − | 0.147985i | 0.629232 | − | 0.777217i | \(-0.283369\pi\) |
−0.777217 | + | 0.629232i | \(0.783369\pi\) | |||||||
\(198\) | −24.3606 | − | 8.40907i | −1.73123 | − | 0.597606i | ||||
\(199\) | 23.2807i | 1.65033i | 0.564893 | + | 0.825164i | \(0.308917\pi\) | ||||
−0.564893 | + | 0.825164i | \(0.691083\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.75885i | 0.194594i | ||||||||
\(202\) | 4.02144 | − | 11.6499i | 0.282948 | − | 0.819684i | ||||
\(203\) | −6.44727 | − | 6.44727i | −0.452510 | − | 0.452510i | ||||
\(204\) | 3.40693 | + | 28.1058i | 0.238533 | + | 1.96780i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 20.2701 | − | 9.86702i | 1.41228 | − | 0.687468i | ||||
\(207\) | −51.2315 | −3.56083 | ||||||||
\(208\) | 3.84305 | + | 2.32531i | 0.266467 | + | 0.161231i | ||||
\(209\) | −14.0326 | −0.970653 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.51586 | + | 2.51586i | −0.173199 | + | 0.173199i | −0.788383 | − | 0.615184i | \(-0.789082\pi\) |
0.615184 | + | 0.788383i | \(0.289082\pi\) | |||||||
\(212\) | −9.40989 | + | 1.14065i | −0.646274 | + | 0.0783401i | ||||
\(213\) | −14.8604 | − | 14.8604i | −1.01822 | − | 1.01822i | ||||
\(214\) | 2.21045 | − | 6.40357i | 0.151103 | − | 0.437739i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 16.0316 | + | 24.8121i | 1.09081 | + | 1.68825i | ||||
\(217\) | − | 16.9456i | − | 1.15034i | ||||||
\(218\) | 4.61222 | + | 1.59210i | 0.312379 | + | 0.107830i | ||||
\(219\) | 22.8086 | + | 22.8086i | 1.54126 | + | 1.54126i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.66510 | − | 3.66510i | 0.246541 | − | 0.246541i | ||||
\(222\) | −1.20311 | − | 2.47158i | −0.0807474 | − | 0.165882i | ||||
\(223\) | −10.9088 | −0.730507 | −0.365253 | − | 0.930908i | \(-0.619018\pi\) | ||||
−0.365253 | + | 0.930908i | \(0.619018\pi\) | |||||||
\(224\) | −11.9628 | − | 14.3690i | −0.799300 | − | 0.960068i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.679635 | + | 1.39619i | 0.0452086 | + | 0.0928733i | ||||
\(227\) | 11.6347 | − | 11.6347i | 0.772220 | − | 0.772220i | −0.206275 | − | 0.978494i | \(-0.566134\pi\) |
0.978494 | + | 0.206275i | \(0.0661340\pi\) | |||||||
\(228\) | 23.8124 | + | 18.6635i | 1.57701 | + | 1.23602i | ||||
\(229\) | −1.60760 | − | 1.60760i | −0.106233 | − | 0.106233i | 0.651992 | − | 0.758226i | \(-0.273933\pi\) |
−0.758226 | + | 0.651992i | \(0.773933\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 28.8371i | − | 1.89734i | ||||||
\(232\) | −6.55363 | + | 4.23444i | −0.430267 | + | 0.278005i | ||||
\(233\) | 23.8100i | 1.55985i | 0.625875 | + | 0.779924i | \(0.284742\pi\) | ||||
−0.625875 | + | 0.779924i | \(0.715258\pi\) | |||||||
\(234\) | 3.31927 | − | 9.61575i | 0.216987 | − | 0.628601i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.83118 | + | 0.706845i | −0.379578 | + | 0.0460117i | ||||
\(237\) | 37.5177 | − | 37.5177i | 2.43703 | − | 2.43703i | ||||
\(238\) | −19.3989 | + | 9.44295i | −1.25744 | + | 0.612095i | ||||
\(239\) | −0.199630 | −0.0129130 | −0.00645649 | − | 0.999979i | \(-0.502055\pi\) | ||||
−0.00645649 | + | 0.999979i | \(0.502055\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.8755 | −1.08705 | −0.543525 | − | 0.839393i | \(-0.682911\pi\) | ||||
−0.543525 | + | 0.839393i | \(0.682911\pi\) | |||||||
\(242\) | −3.69601 | + | 1.79914i | −0.237589 | + | 0.115653i | ||||
\(243\) | 5.63317 | − | 5.63317i | 0.361368 | − | 0.361368i | ||||
\(244\) | −0.189654 | − | 1.56457i | −0.0121414 | − | 0.100161i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.69239 | − | 16.4906i | 0.362934 | − | 1.05140i | ||||
\(247\) | − | 5.53901i | − | 0.352439i | ||||||
\(248\) | −14.1773 | − | 3.04780i | −0.900260 | − | 0.193536i | ||||
\(249\) | − | 41.1171i | − | 2.60569i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.10023 | − | 6.10023i | −0.385043 | − | 0.385043i | 0.487872 | − | 0.872915i | \(-0.337773\pi\) |
−0.872915 | + | 0.487872i | \(0.837773\pi\) | |||||||
\(252\) | −26.1204 | + | 33.3265i | −1.64543 | + | 2.09937i | ||||
\(253\) | 16.0891 | − | 16.0891i | 1.01151 | − | 1.01151i | ||||
\(254\) | −0.935625 | − | 1.92208i | −0.0587063 | − | 0.120602i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.1733 | + | 7.42418i | −0.885829 | + | 0.464012i | ||||
\(257\) | 19.8360 | 1.23733 | 0.618667 | − | 0.785653i | \(-0.287673\pi\) | ||||
0.618667 | + | 0.785653i | \(0.287673\pi\) | |||||||
\(258\) | −13.3423 | − | 27.4095i | −0.830658 | − | 1.70644i | ||||
\(259\) | 1.48124 | − | 1.48124i | 0.0920399 | − | 0.0920399i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.4949 | + | 12.4949i | 0.773418 | + | 0.773418i | ||||
\(262\) | 17.4243 | + | 6.01471i | 1.07648 | + | 0.371590i | ||||
\(263\) | 7.14438i | 0.440542i | 0.975439 | + | 0.220271i | \(0.0706941\pi\) | ||||
−0.975439 | + | 0.220271i | \(0.929306\pi\) | |||||||
\(264\) | −24.1263 | − | 5.18660i | −1.48487 | − | 0.319213i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.52314 | + | 21.7941i | −0.461273 | + | 1.33628i | ||||
\(267\) | 16.5262 | + | 16.5262i | 1.01139 | + | 1.01139i | ||||
\(268\) | 0.216504 | + | 1.78607i | 0.0132251 | + | 0.109102i | ||||
\(269\) | 21.7716 | − | 21.7716i | 1.32744 | − | 1.32744i | 0.419844 | − | 0.907596i | \(-0.362085\pi\) |
0.907596 | − | 0.419844i | \(-0.137915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.71328 | −0.286312 | −0.143156 | − | 0.989700i | \(-0.545725\pi\) | ||||
−0.143156 | + | 0.989700i | \(0.545725\pi\) | |||||||
\(272\) | 4.41128 | + | 17.9283i | 0.267473 | + | 1.08706i | ||||
\(273\) | 11.3827 | 0.688915 | ||||||||
\(274\) | 4.30601 | − | 2.09607i | 0.260136 | − | 0.126628i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −48.7008 | + | 5.90342i | −2.93144 | + | 0.355344i | ||||
\(277\) | −20.4588 | − | 20.4588i | −1.22925 | − | 1.22925i | −0.964247 | − | 0.265006i | \(-0.914626\pi\) |
−0.265006 | − | 0.964247i | \(-0.585374\pi\) | |||||||
\(278\) | −1.36801 | + | 3.96304i | −0.0820476 | + | 0.237687i | ||||
\(279\) | 32.8409i | 1.96613i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 17.6481i | − | 1.05280i | −0.850239 | − | 0.526398i | \(-0.823542\pi\) | ||
0.850239 | − | 0.526398i | \(-0.176458\pi\) | |||||||
\(282\) | 22.5124 | + | 7.77108i | 1.34059 | + | 0.462761i | ||||
\(283\) | −18.1525 | − | 18.1525i | −1.07906 | − | 1.07906i | −0.996594 | − | 0.0824607i | \(-0.973722\pi\) |
−0.0824607 | − | 0.996594i | \(-0.526278\pi\) | |||||||
\(284\) | −10.7868 | − | 8.45440i | −0.640077 | − | 0.501676i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.97739 | + | 4.06220i | 0.116925 | + | 0.240203i | ||||
\(287\) | 13.2945 | 0.784747 | ||||||||
\(288\) | 23.1842 | + | 27.8474i | 1.36614 | + | 1.64092i | ||||
\(289\) | 4.30511 | 0.253242 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.53771 | − | 1.53771i | 0.0901419 | − | 0.0901419i | ||||
\(292\) | 16.5562 | + | 12.9763i | 0.968877 | + | 0.759380i | ||||
\(293\) | 0.638480 | + | 0.638480i | 0.0373004 | + | 0.0373004i | 0.725511 | − | 0.688211i | \(-0.241603\pi\) |
−0.688211 | + | 0.725511i | \(0.741603\pi\) | |||||||
\(294\) | −16.0887 | − | 5.55369i | −0.938314 | − | 0.323898i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.972850 | − | 1.50568i | −0.0565458 | − | 0.0875157i | ||||
\(297\) | 29.7126i | 1.72410i | ||||||||
\(298\) | −1.60047 | + | 4.63649i | −0.0927130 | + | 0.268584i | ||||
\(299\) | 6.35076 | + | 6.35076i | 0.367274 | + | 0.367274i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4268 | − | 16.4268i | 0.946825 | − | 0.946825i | ||||
\(302\) | 1.42068 | − | 0.691557i | 0.0817511 | − | 0.0397946i | ||||
\(303\) | −26.7266 | −1.53540 | ||||||||
\(304\) | 16.8807 | + | 10.2140i | 0.968175 | + | 0.585814i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 37.5955 | − | 18.3006i | 2.14919 | − | 1.04618i | ||||
\(307\) | −4.52224 | + | 4.52224i | −0.258098 | + | 0.258098i | −0.824280 | − | 0.566182i | \(-0.808420\pi\) |
0.566182 | + | 0.824280i | \(0.308420\pi\) | |||||||
\(308\) | −2.26303 | − | 18.6691i | −0.128948 | − | 1.06377i | ||||
\(309\) | −34.5695 | − | 34.5695i | −1.96659 | − | 1.96659i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.1014i | 0.799620i | 0.916598 | + | 0.399810i | \(0.130924\pi\) | ||||
−0.916598 | + | 0.399810i | \(0.869076\pi\) | |||||||
\(312\) | 2.04728 | − | 9.52324i | 0.115904 | − | 0.539147i | ||||
\(313\) | 11.9204i | 0.673779i | 0.941544 | + | 0.336889i | \(0.109375\pi\) | ||||
−0.941544 | + | 0.336889i | \(0.890625\pi\) | |||||||
\(314\) | 29.9417 | + | 10.3356i | 1.68971 | + | 0.583271i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 21.3446 | − | 27.2331i | 1.20073 | − | 1.53198i | ||||
\(317\) | −17.6516 | + | 17.6516i | −0.991410 | + | 0.991410i | −0.999963 | − | 0.00855359i | \(-0.997277\pi\) |
0.00855359 | + | 0.999963i | \(0.497277\pi\) | |||||||
\(318\) | 8.99669 | + | 18.4821i | 0.504509 | + | 1.03643i | ||||
\(319\) | −7.84798 | −0.439403 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.6907 | −0.819958 | ||||||||
\(322\) | −16.3624 | − | 33.6137i | −0.911842 | − | 1.87322i | ||||
\(323\) | 16.0991 | − | 16.0991i | 0.895775 | − | 0.895775i | ||||
\(324\) | 15.8096 | − | 20.1711i | 0.878310 | − | 1.12062i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.6516 | − | 4.71241i | −0.756092 | − | 0.260996i | ||||
\(327\) | − | 10.5811i | − | 0.585138i | ||||||
\(328\) | 2.39112 | − | 11.1227i | 0.132028 | − | 0.614146i | ||||
\(329\) | 18.1492i | 1.00060i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.9785 | − | 24.9785i | −1.37294 | − | 1.37294i | −0.856053 | − | 0.516888i | \(-0.827090\pi\) |
−0.516888 | − | 0.856053i | \(-0.672910\pi\) | |||||||
\(332\) | −3.22671 | − | 26.6191i | −0.177089 | − | 1.46091i | ||||
\(333\) | −2.87068 | + | 2.87068i | −0.157312 | + | 0.157312i | ||||
\(334\) | 16.8234 | − | 8.18924i | 0.920534 | − | 0.448095i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −20.9899 | + | 34.6901i | −1.14509 | + | 1.89250i | ||||
\(337\) | 24.3167 | 1.32462 | 0.662308 | − | 0.749231i | \(-0.269577\pi\) | ||||
0.662308 | + | 0.749231i | \(0.269577\pi\) | |||||||
\(338\) | 14.9269 | − | 7.26608i | 0.811916 | − | 0.395223i | ||||
\(339\) | 2.38113 | − | 2.38113i | 0.129325 | − | 0.129325i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3136 | − | 10.3136i | −0.558510 | − | 0.558510i | ||||
\(342\) | 14.5800 | − | 42.2375i | 0.788396 | − | 2.28394i | ||||
\(343\) | 10.1658i | 0.548903i | ||||||||
\(344\) | −10.7888 | − | 16.6978i | −0.581693 | − | 0.900285i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.2142 | + | 7.66816i | 1.19425 | + | 0.412243i | ||||
\(347\) | −17.3818 | − | 17.3818i | −0.933106 | − | 0.933106i | 0.0647931 | − | 0.997899i | \(-0.479361\pi\) |
−0.997899 | + | 0.0647931i | \(0.979361\pi\) | |||||||
\(348\) | 13.3175 | + | 10.4379i | 0.713894 | + | 0.559532i | ||||
\(349\) | −0.773103 | + | 0.773103i | −0.0413832 | + | 0.0413832i | −0.727496 | − | 0.686112i | \(-0.759316\pi\) |
0.686112 | + | 0.727496i | \(0.259316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −11.7283 | −0.626010 | ||||||||
\(352\) | −16.0263 | − | 1.46445i | −0.854204 | − | 0.0780556i | ||||
\(353\) | −13.3720 | −0.711720 | −0.355860 | − | 0.934539i | \(-0.615812\pi\) | ||||
−0.355860 | + | 0.934539i | \(0.615812\pi\) | |||||||
\(354\) | 5.57513 | + | 11.4531i | 0.296315 | + | 0.608727i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.9959 | + | 9.40211i | 0.635784 | + | 0.498311i | ||||
\(357\) | 33.0838 | + | 33.0838i | 1.75098 | + | 1.75098i | ||||
\(358\) | −9.16403 | − | 3.16334i | −0.484334 | − | 0.167188i | ||||
\(359\) | − | 28.5413i | − | 1.50635i | −0.657818 | − | 0.753177i | \(-0.728520\pi\) | ||
0.657818 | − | 0.753177i | \(-0.271480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 5.33027i | − | 0.280541i | ||||||
\(362\) | 6.90069 | − | 19.9909i | 0.362692 | − | 1.05070i | ||||
\(363\) | 6.30335 | + | 6.30335i | 0.330840 | + | 0.330840i | ||||
\(364\) | 7.36915 | − | 0.893275i | 0.386249 | − | 0.0468203i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.07300 | + | 1.49587i | −0.160628 | + | 0.0781903i | ||||
\(367\) | 0.909186 | 0.0474591 | 0.0237296 | − | 0.999718i | \(-0.492446\pi\) | ||||
0.0237296 | + | 0.999718i | \(0.492446\pi\) | |||||||
\(368\) | −31.0655 | + | 7.64371i | −1.61940 | + | 0.398456i | ||||
\(369\) | −25.7649 | −1.34127 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.0765 | + | 11.0765i | −0.575064 | + | 0.575064i | ||||
\(372\) | 3.78426 | + | 31.2186i | 0.196205 | + | 1.61861i | ||||
\(373\) | 26.5010 | + | 26.5010i | 1.37217 | + | 1.37217i | 0.857223 | + | 0.514946i | \(0.172188\pi\) |
0.514946 | + | 0.857223i | \(0.327812\pi\) | |||||||
\(374\) | −6.05947 | + | 17.5540i | −0.313328 | + | 0.907694i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.1843 | + | 3.26429i | 0.783071 | + | 0.168343i | ||||
\(377\) | − | 3.09780i | − | 0.159545i | ||||||
\(378\) | 46.1469 | + | 15.9295i | 2.37354 | + | 0.819324i | ||||
\(379\) | 1.23724 | + | 1.23724i | 0.0635529 | + | 0.0635529i | 0.738169 | − | 0.674616i | \(-0.235691\pi\) |
−0.674616 | + | 0.738169i | \(0.735691\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.27800 | + | 3.27800i | −0.167937 | + | 0.167937i | ||||
\(382\) | −4.91628 | − | 10.0996i | −0.251539 | − | 0.516742i | ||||
\(383\) | 15.7161 | 0.803057 | 0.401529 | − | 0.915846i | \(-0.368479\pi\) | ||||
0.401529 | + | 0.915846i | \(0.368479\pi\) | |||||||
\(384\) | 25.2479 | + | 23.8003i | 1.28842 | + | 1.21455i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.9128 | − | 26.5270i | −0.657242 | − | 1.35019i | ||||
\(387\) | −31.8355 | + | 31.8355i | −1.61829 | + | 1.61829i | ||||
\(388\) | 0.874833 | − | 1.11618i | 0.0444129 | − | 0.0566655i | ||||
\(389\) | 16.2799 | + | 16.2799i | 0.825423 | + | 0.825423i | 0.986880 | − | 0.161457i | \(-0.0516193\pi\) |
−0.161457 | + | 0.986880i | \(0.551619\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 36.9168i | 1.86696i | ||||||||
\(392\) | −10.8516 | − | 2.33286i | −0.548090 | − | 0.117827i | ||||
\(393\) | − | 39.9740i | − | 2.01642i | ||||||
\(394\) | −1.35549 | + | 3.92677i | −0.0682885 | + | 0.197828i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.38580 | + | 36.1811i | 0.220395 | + | 1.81817i | ||||
\(397\) | −22.8944 | + | 22.8944i | −1.14903 | + | 1.14903i | −0.162292 | + | 0.986743i | \(0.551889\pi\) |
−0.986743 | + | 0.162292i | \(0.948111\pi\) | |||||||
\(398\) | 29.6030 | − | 14.4101i | 1.48386 | − | 0.722311i | ||||
\(399\) | 49.9990 | 2.50308 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8553 | 0.791778 | 0.395889 | − | 0.918298i | \(-0.370437\pi\) | ||||
0.395889 | + | 0.918298i | \(0.370437\pi\) | |||||||
\(402\) | 3.50805 | − | 1.70764i | 0.174966 | − | 0.0851694i | ||||
\(403\) | 4.07102 | − | 4.07102i | 0.202792 | − | 0.202792i | ||||
\(404\) | −17.3027 | + | 2.09741i | −0.860844 | + | 0.104350i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.20746 | + | 12.1888i | −0.208813 | + | 0.604919i | ||||
\(407\) | − | 1.80305i | − | 0.0893740i | ||||||
\(408\) | 33.6296 | − | 21.7288i | 1.66491 | − | 1.07573i | ||||
\(409\) | − | 10.0220i | − | 0.495557i | −0.968817 | − | 0.247779i | \(-0.920299\pi\) | ||
0.968817 | − | 0.247779i | \(-0.0797006\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.34367 | − | 7.34367i | −0.362236 | − | 0.362236i | ||||
\(412\) | −25.0931 | − | 19.6673i | −1.23625 | − | 0.968940i | ||||
\(413\) | −6.86398 | + | 6.86398i | −0.337754 | + | 0.337754i | ||||
\(414\) | 31.7107 | + | 65.1441i | 1.55850 | + | 3.20166i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.578056 | − | 6.32598i | 0.0283415 | − | 0.310157i | ||||
\(417\) | 9.09182 | 0.445228 | ||||||||
\(418\) | 8.68573 | + | 17.8433i | 0.424833 | + | 0.872745i | ||||
\(419\) | 14.4998 | − | 14.4998i | 0.708362 | − | 0.708362i | −0.257829 | − | 0.966191i | \(-0.583007\pi\) |
0.966191 | + | 0.257829i | \(0.0830071\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.9983 | + | 12.9983i | 0.633498 | + | 0.633498i | 0.948944 | − | 0.315446i | \(-0.102154\pi\) |
−0.315446 | + | 0.948944i | \(0.602154\pi\) | |||||||
\(422\) | 4.75632 | + | 1.64184i | 0.231534 | + | 0.0799235i | ||||
\(423\) | − | 35.1735i | − | 1.71020i | ||||||
\(424\) | 7.27484 | + | 11.2593i | 0.353297 | + | 0.546798i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.69783 | + | 28.0941i | −0.469862 | + | 1.36116i | ||||
\(427\) | −1.84168 | − | 1.84168i | −0.0891251 | − | 0.0891251i | ||||
\(428\) | −9.51075 | + | 1.15288i | −0.459720 | + | 0.0557263i | ||||
\(429\) | 6.92786 | − | 6.92786i | 0.334480 | − | 0.334480i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.4404 | −1.65894 | −0.829469 | − | 0.558553i | \(-0.811357\pi\) | ||||
−0.829469 | + | 0.558553i | \(0.811357\pi\) | |||||||
\(432\) | 21.6271 | − | 35.7432i | 1.04054 | − | 1.71970i | ||||
\(433\) | 14.5895 | 0.701128 | 0.350564 | − | 0.936539i | \(-0.385990\pi\) | ||||
0.350564 | + | 0.936539i | \(0.385990\pi\) | |||||||
\(434\) | −21.5474 | + | 10.4888i | −1.03431 | + | 0.503478i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.830368 | − | 6.85019i | −0.0397674 | − | 0.328065i | ||||
\(437\) | 27.8959 | + | 27.8959i | 1.33444 | + | 1.33444i | ||||
\(438\) | 14.8848 | − | 43.1205i | 0.711223 | − | 2.06038i | ||||
\(439\) | 5.70179i | 0.272131i | 0.990700 | + | 0.136066i | \(0.0434458\pi\) | ||||
−0.990700 | + | 0.136066i | \(0.956554\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.1371i | 1.19701i | ||||||||
\(442\) | −6.92899 | − | 2.39183i | −0.329578 | − | 0.113768i | ||||
\(443\) | −5.03375 | − | 5.03375i | −0.239161 | − | 0.239161i | 0.577342 | − | 0.816503i | \(-0.304090\pi\) |
−0.816503 | + | 0.577342i | \(0.804090\pi\) | |||||||
\(444\) | −2.39808 | + | 3.05966i | −0.113808 | + | 0.145205i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.75221 | + | 13.8712i | 0.319726 | + | 0.656822i | ||||
\(447\) | 10.6368 | 0.503104 | ||||||||
\(448\) | −10.8665 | + | 24.1055i | −0.513392 | + | 1.13888i | ||||
\(449\) | 22.2502 | 1.05005 | 0.525025 | − | 0.851087i | \(-0.324056\pi\) | ||||
0.525025 | + | 0.851087i | \(0.324056\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.09139 | − | 8.09139i | 0.381009 | − | 0.381009i | ||||
\(452\) | 1.35468 | − | 1.72840i | 0.0637186 | − | 0.0812971i | ||||
\(453\) | −2.42290 | − | 2.42290i | −0.113838 | − | 0.113838i | ||||
\(454\) | −21.9957 | − | 7.59273i | −1.03231 | − | 0.356344i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.99275 | − | 41.8311i | 0.421124 | − | 1.95892i | ||||
\(457\) | 8.92927i | 0.417694i | 0.977948 | + | 0.208847i | \(0.0669710\pi\) | ||||
−0.977948 | + | 0.208847i | \(0.933029\pi\) | |||||||
\(458\) | −1.04912 | + | 3.03923i | −0.0490219 | + | 0.142014i | ||||
\(459\) | −34.0881 | − | 34.0881i | −1.59110 | − | 1.59110i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.14776 | + | 8.14776i | −0.379479 | + | 0.379479i | −0.870914 | − | 0.491435i | \(-0.836472\pi\) |
0.491435 | + | 0.870914i | \(0.336472\pi\) | |||||||
\(462\) | −36.6683 | + | 17.8493i | −1.70596 | + | 0.830424i | ||||
\(463\) | 31.7058 | 1.47349 | 0.736747 | − | 0.676168i | \(-0.236361\pi\) | ||||
0.736747 | + | 0.676168i | \(0.236361\pi\) | |||||||
\(464\) | 9.44086 | + | 5.71238i | 0.438281 | + | 0.265191i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 30.2760 | − | 14.7377i | 1.40251 | − | 0.682710i | ||||
\(467\) | 17.7683 | − | 17.7683i | 0.822219 | − | 0.822219i | −0.164207 | − | 0.986426i | \(-0.552506\pi\) |
0.986426 | + | 0.164207i | \(0.0525065\pi\) | |||||||
\(468\) | −14.2816 | + | 1.73119i | −0.660166 | + | 0.0800241i | ||||
\(469\) | 2.10241 | + | 2.10241i | 0.0970803 | + | 0.0970803i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 68.6907i | − | 3.16510i | ||||||
\(472\) | 4.50812 | + | 6.97721i | 0.207503 | + | 0.321152i | ||||
\(473\) | − | 19.9956i | − | 0.919401i | ||||||
\(474\) | −70.9284 | − | 24.4839i | −3.25785 | − | 1.12458i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.0146 | + | 18.8221i | 1.10071 | + | 0.862707i | ||||
\(477\) | 21.4665 | − | 21.4665i | 0.982885 | − | 0.982885i | ||||
\(478\) | 0.123565 | + | 0.253842i | 0.00565172 | + | 0.0116105i | ||||
\(479\) | −7.80806 | −0.356759 | −0.178380 | − | 0.983962i | \(-0.557086\pi\) | ||||
−0.178380 | + | 0.983962i | \(0.557086\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.711710 | 0.0324512 | ||||||||
\(482\) | 10.4454 | + | 21.4584i | 0.475777 | + | 0.977401i | ||||
\(483\) | −57.3264 | + | 57.3264i | −2.60844 | + | 2.60844i | ||||
\(484\) | 4.57544 | + | 3.58611i | 0.207974 | + | 0.163005i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −10.6497 | − | 3.67618i | −0.483081 | − | 0.166755i | ||||
\(487\) | 27.6753i | 1.25409i | 0.778984 | + | 0.627044i | \(0.215735\pi\) | ||||
−0.778984 | + | 0.627044i | \(0.784265\pi\) | |||||||
\(488\) | −1.87206 | + | 1.20958i | −0.0847443 | + | 0.0547551i | ||||
\(489\) | 31.3188i | 1.41629i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.7995 | − | 11.7995i | −0.532505 | − | 0.532505i | 0.388812 | − | 0.921317i | \(-0.372886\pi\) |
−0.921317 | + | 0.388812i | \(0.872886\pi\) | |||||||
\(492\) | −24.4922 | + | 2.96890i | −1.10419 | + | 0.133848i | ||||
\(493\) | 9.00370 | − | 9.00370i | 0.405506 | − | 0.405506i | ||||
\(494\) | −7.04321 | + | 3.42848i | −0.316889 | + | 0.154254i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.89984 | + | 19.9139i | 0.220009 | + | 0.894159i | ||||
\(497\) | −22.6491 | −1.01595 | ||||||||
\(498\) | −52.2830 | + | 25.4502i | −2.34286 | + | 1.14045i | ||||
\(499\) | −25.0477 | + | 25.0477i | −1.12129 | + | 1.12129i | −0.129743 | + | 0.991548i | \(0.541415\pi\) |
−0.991548 | + | 0.129743i | \(0.958585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.6914 | − | 28.6914i | −1.28184 | − | 1.28184i | ||||
\(502\) | −3.98098 | + | 11.5327i | −0.177680 | + | 0.514729i | ||||
\(503\) | − | 22.8644i | − | 1.01947i | −0.860331 | − | 0.509736i | \(-0.829743\pi\) | ||
0.860331 | − | 0.509736i | \(-0.170257\pi\) | |||||||
\(504\) | 58.5445 | + | 12.5857i | 2.60778 | + | 0.560614i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −30.4169 | − | 10.4996i | −1.35220 | − | 0.466766i | ||||
\(507\) | −25.4570 | − | 25.4570i | −1.13059 | − | 1.13059i | ||||
\(508\) | −1.86492 | + | 2.37942i | −0.0827426 | + | 0.105569i | ||||
\(509\) | −17.1633 | + | 17.1633i | −0.760748 | + | 0.760748i | −0.976458 | − | 0.215710i | \(-0.930794\pi\) |
0.215710 | + | 0.976458i | \(0.430794\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.7631 | 1.53783 | ||||||||
\(512\) | 18.2131 | + | 13.4269i | 0.804915 | + | 0.593390i | ||||
\(513\) | −51.5169 | −2.27453 | ||||||||
\(514\) | −12.2779 | − | 25.2227i | −0.541553 | − | 1.11253i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −26.5945 | + | 33.9313i | −1.17076 | + | 1.49374i | ||||
\(517\) | 11.0461 | + | 11.0461i | 0.485808 | + | 0.485808i | ||||
\(518\) | −2.80034 | − | 0.966652i | −0.123040 | − | 0.0424722i | ||||
\(519\) | − | 50.9629i | − | 2.23702i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.5206i | 0.504726i | 0.967633 | + | 0.252363i | \(0.0812077\pi\) | ||||
−0.967633 | + | 0.252363i | \(0.918792\pi\) | |||||||
\(522\) | 8.15414 | − | 23.6221i | 0.356897 | − | 1.03391i | ||||
\(523\) | 25.4249 | + | 25.4249i | 1.11175 | + | 1.11175i | 0.992913 | + | 0.118841i | \(0.0379180\pi\) |
0.118841 | + | 0.992913i | \(0.462082\pi\) | |||||||
\(524\) | −3.13701 | − | 25.8790i | −0.137041 | − | 1.13053i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.08455 | − | 4.42215i | 0.396105 | − | 0.192815i | ||||
\(527\) | 23.6647 | 1.03085 | ||||||||
\(528\) | 8.33831 | + | 33.8884i | 0.362878 | + | 1.47481i | ||||
\(529\) | −40.9681 | −1.78122 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.3025 | − | 13.3025i | 0.577281 | − | 0.577281i | ||||
\(532\) | 32.3692 | − | 3.92374i | 1.40338 | − | 0.170116i | ||||
\(533\) | 3.19387 | + | 3.19387i | 0.138342 | + | 0.138342i | ||||
\(534\) | 10.7849 | − | 31.2434i | 0.466710 | − | 1.35203i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.13709 | − | 1.38082i | 0.0923084 | − | 0.0596424i | ||||
\(537\) | 21.0237i | 0.907239i | ||||||||
\(538\) | −41.1600 | − | 14.2081i | −1.77454 | − | 0.612554i | ||||
\(539\) | −7.89423 | − | 7.89423i | −0.340028 | − | 0.340028i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7997 | + | 29.7997i | −1.28119 | + | 1.28119i | −0.341196 | + | 0.939992i | \(0.610832\pi\) |
−0.939992 | + | 0.341196i | \(0.889168\pi\) | |||||||
\(542\) | 2.91738 | + | 5.99325i | 0.125312 | + | 0.257432i | ||||
\(543\) | −45.8622 | −1.96814 | ||||||||
\(544\) | 20.0665 | − | 16.7063i | 0.860344 | − | 0.716275i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.04556 | − | 14.4739i | −0.301522 | − | 0.619425i | ||||
\(547\) | −28.3699 | + | 28.3699i | −1.21301 | + | 1.21301i | −0.242979 | + | 0.970032i | \(0.578125\pi\) |
−0.970032 | + | 0.242979i | \(0.921875\pi\) | |||||||
\(548\) | −5.33057 | − | 4.17797i | −0.227711 | − | 0.178474i | ||||
\(549\) | 3.56921 | + | 3.56921i | 0.152330 | + | 0.152330i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.6072i | − | 0.579685i | ||||||
\(552\) | 37.6509 | + | 58.2722i | 1.60253 | + | 2.48023i | ||||
\(553\) | − | 57.1815i | − | 2.43161i | ||||||
\(554\) | −13.3513 | + | 38.6781i | −0.567244 | + | 1.64328i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.88602 | − | 0.713492i | 0.249623 | − | 0.0302588i | ||||
\(557\) | 21.7769 | − | 21.7769i | 0.922718 | − | 0.922718i | −0.0745028 | − | 0.997221i | \(-0.523737\pi\) |
0.997221 | + | 0.0745028i | \(0.0237370\pi\) | |||||||
\(558\) | 41.7593 | − | 20.3275i | 1.76781 | − | 0.860531i | ||||
\(559\) | 7.89278 | 0.333829 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.2715 | 1.70026 | ||||||||
\(562\) | −22.4407 | + | 10.9236i | −0.946602 | + | 0.460785i | ||||
\(563\) | 10.9022 | − | 10.9022i | 0.459473 | − | 0.459473i | −0.439010 | − | 0.898482i | \(-0.644671\pi\) |
0.898482 | + | 0.439010i | \(0.144671\pi\) | |||||||
\(564\) | −4.05306 | − | 33.4361i | −0.170664 | − | 1.40791i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.8462 | + | 34.3179i | −0.497935 | + | 1.44249i | ||||
\(567\) | − | 42.3534i | − | 1.77868i | ||||||
\(568\) | −4.07363 | + | 18.9491i | −0.170926 | + | 0.795087i | ||||
\(569\) | 31.1881i | 1.30747i | 0.756723 | + | 0.653736i | \(0.226799\pi\) | ||||
−0.756723 | + | 0.653736i | \(0.773201\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.20354 | − | 2.20354i | −0.0922153 | − | 0.0922153i | 0.659494 | − | 0.751710i | \(-0.270770\pi\) |
−0.751710 | + | 0.659494i | \(0.770770\pi\) | |||||||
\(572\) | 3.94140 | − | 5.02875i | 0.164798 | − | 0.210263i | ||||
\(573\) | −17.2244 | + | 17.2244i | −0.719559 | + | 0.719559i | ||||
\(574\) | −8.22886 | − | 16.9048i | −0.343466 | − | 0.705591i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 21.0594 | − | 46.7169i | 0.877477 | − | 1.94654i | ||||
\(577\) | 8.42524 | 0.350747 | 0.175374 | − | 0.984502i | \(-0.443887\pi\) | ||||
0.175374 | + | 0.984502i | \(0.443887\pi\) | |||||||
\(578\) | −2.66473 | − | 5.47423i | −0.110838 | − | 0.227698i | ||||
\(579\) | −45.2404 | + | 45.2404i | −1.88013 | + | 1.88013i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −31.3337 | − | 31.3337i | −1.29994 | − | 1.29994i | ||||
\(582\) | −2.90709 | − | 1.00350i | −0.120503 | − | 0.0415964i | ||||
\(583\) | 13.4830i | 0.558408i | ||||||||
\(584\) | 6.25244 | − | 29.0842i | 0.258728 | − | 1.20351i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.416669 | − | 1.20707i | 0.0172125 | − | 0.0498636i | ||||
\(587\) | −19.3370 | − | 19.3370i | −0.798125 | − | 0.798125i | 0.184675 | − | 0.982800i | \(-0.440877\pi\) |
−0.982800 | + | 0.184675i | \(0.940877\pi\) | |||||||
\(588\) | 2.89656 | + | 23.8954i | 0.119452 | + | 0.985431i | ||||
\(589\) | 17.8821 | − | 17.8821i | 0.736818 | − | 0.736818i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00862 | 0.370565 | ||||||||
\(592\) | −1.31240 | + | 2.16901i | −0.0539394 | + | 0.0891458i | ||||
\(593\) | 18.1804 | 0.746580 | 0.373290 | − | 0.927715i | \(-0.378230\pi\) | ||||
0.373290 | + | 0.927715i | \(0.378230\pi\) | |||||||
\(594\) | 37.7814 | − | 18.3912i | 1.55019 | − | 0.754598i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 6.88624 | − | 0.834737i | 0.282071 | − | 0.0341922i | ||||
\(597\) | −50.4863 | − | 50.4863i | −2.06627 | − | 2.06627i | ||||
\(598\) | 4.14447 | − | 12.0063i | 0.169480 | − | 0.490975i | ||||
\(599\) | − | 1.64695i | − | 0.0672927i | −0.999434 | − | 0.0336463i | \(-0.989288\pi\) | ||
0.999434 | − | 0.0336463i | \(-0.0107120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.7485i | 0.520021i | 0.965606 | + | 0.260011i | \(0.0837261\pi\) | ||||
−0.965606 | + | 0.260011i | \(0.916274\pi\) | |||||||
\(602\) | −31.0554 | − | 10.7201i | −1.26572 | − | 0.436917i | ||||
\(603\) | −4.07452 | − | 4.07452i | −0.165927 | − | 0.165927i | ||||
\(604\) | −1.75872 | − | 1.37844i | −0.0715612 | − | 0.0560878i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 16.5430 | + | 33.9846i | 0.672012 | + | 1.38053i | ||||
\(607\) | 15.6773 | 0.636322 | 0.318161 | − | 0.948037i | \(-0.396935\pi\) | ||||
0.318161 | + | 0.948037i | \(0.396935\pi\) | |||||||
\(608\) | 2.53913 | − | 27.7871i | 0.102975 | − | 1.12691i | ||||
\(609\) | 27.9629 | 1.13311 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.36018 | + | 4.36018i | −0.176394 | + | 0.176394i | ||||
\(612\) | −46.5409 | − | 36.4775i | −1.88130 | − | 1.47452i | ||||
\(613\) | 8.29399 | + | 8.29399i | 0.334991 | + | 0.334991i | 0.854478 | − | 0.519487i | \(-0.173877\pi\) |
−0.519487 | + | 0.854478i | \(0.673877\pi\) | |||||||
\(614\) | 8.54945 | + | 2.95119i | 0.345028 | + | 0.119100i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.3382 | + | 14.4332i | −0.900031 | + | 0.581529i | ||||
\(617\) | − | 20.3330i | − | 0.818575i | −0.912406 | − | 0.409287i | \(-0.865777\pi\) | ||
0.912406 | − | 0.409287i | \(-0.134223\pi\) | |||||||
\(618\) | −22.5599 | + | 65.3549i | −0.907493 | + | 2.62896i | ||||
\(619\) | 12.5878 | + | 12.5878i | 0.505946 | + | 0.505946i | 0.913280 | − | 0.407333i | \(-0.133541\pi\) |
−0.407333 | + | 0.913280i | \(0.633541\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 59.0667 | − | 59.0667i | 2.37027 | − | 2.37027i | ||||
\(622\) | 17.9309 | − | 8.72836i | 0.718964 | − | 0.349975i | ||||
\(623\) | 25.1880 | 1.00914 | ||||||||
\(624\) | −13.3766 | + | 3.29134i | −0.535493 | + | 0.131759i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.1575 | − | 7.37834i | 0.605816 | − | 0.294898i | ||||
\(627\) | 30.4308 | − | 30.4308i | 1.21529 | − | 1.21529i | ||||
\(628\) | −5.39059 | − | 44.4702i | −0.215108 | − | 1.77455i | ||||
\(629\) | 2.06858 | + | 2.06858i | 0.0824795 | + | 0.0824795i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.4887i | 0.855453i | 0.903908 | + | 0.427726i | \(0.140685\pi\) | ||||
−0.903908 | + | 0.427726i | \(0.859315\pi\) | |||||||
\(632\) | −47.8403 | − | 10.2846i | −1.90298 | − | 0.409099i | ||||
\(633\) | − | 10.9117i | − | 0.433702i | ||||||
\(634\) | 33.3709 | + | 11.5193i | 1.32533 | + | 0.457491i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 17.9325 | − | 22.8797i | 0.711072 | − | 0.907241i | ||||
\(637\) | 3.11605 | − | 3.11605i | 0.123462 | − | 0.123462i | ||||
\(638\) | 4.85766 | + | 9.97922i | 0.192317 | + | 0.395081i | ||||
\(639\) | 43.8944 | 1.73644 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.1687 | 1.03360 | 0.516800 | − | 0.856106i | \(-0.327123\pi\) | ||||
0.516800 | + | 0.856106i | \(0.327123\pi\) | |||||||
\(642\) | 9.09312 | + | 18.6802i | 0.358877 | + | 0.737250i | ||||
\(643\) | −14.6501 | + | 14.6501i | −0.577743 | + | 0.577743i | −0.934281 | − | 0.356538i | \(-0.883957\pi\) |
0.356538 | + | 0.934281i | \(0.383957\pi\) | |||||||
\(644\) | −32.6142 | + | 41.6118i | −1.28518 | + | 1.63973i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −30.4358 | − | 10.5062i | −1.19748 | − | 0.413360i | ||||
\(647\) | − | 16.2623i | − | 0.639337i | −0.947530 | − | 0.319668i | \(-0.896429\pi\) | ||
0.947530 | − | 0.319668i | \(-0.103571\pi\) | |||||||
\(648\) | −35.4345 | − | 7.61762i | −1.39200 | − | 0.299248i | ||||
\(649\) | 8.35522i | 0.327971i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.7479 | + | 36.7479i | 1.44026 | + | 1.44026i | ||||
\(652\) | 2.45778 | + | 20.2757i | 0.0962543 | + | 0.794058i | ||||
\(653\) | −32.0639 | + | 32.0639i | −1.25476 | + | 1.25476i | −0.301194 | + | 0.953563i | \(0.597385\pi\) |
−0.953563 | + | 0.301194i | \(0.902615\pi\) | |||||||
\(654\) | −13.4546 | + | 6.54939i | −0.526116 | + | 0.256101i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −15.6232 | + | 3.84412i | −0.609984 | + | 0.150088i | ||||
\(657\) | −67.3717 | −2.62842 | ||||||||
\(658\) | 23.0779 | − | 11.2338i | 0.899669 | − | 0.437939i | ||||
\(659\) | −7.04696 | + | 7.04696i | −0.274511 | + | 0.274511i | −0.830913 | − | 0.556402i | \(-0.812181\pi\) |
0.556402 | + | 0.830913i | \(0.312181\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.78655 | + | 5.78655i | 0.225071 | + | 0.225071i | 0.810630 | − | 0.585559i | \(-0.199125\pi\) |
−0.585559 | + | 0.810630i | \(0.699125\pi\) | |||||||
\(662\) | −16.3008 | + | 47.2226i | −0.633550 | + | 1.83536i | ||||
\(663\) | 15.8962i | 0.617355i | ||||||||
\(664\) | −31.8506 | + | 20.5794i | −1.23604 | + | 0.798634i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.42711 | + | 1.87339i | 0.210296 | + | 0.0725924i | ||||
\(667\) | 15.6013 | + | 15.6013i | 0.604085 | + | 0.604085i | ||||
\(668\) | −20.8263 | − | 16.3231i | −0.805794 | − | 0.631560i | ||||
\(669\) | 23.6567 | − | 23.6567i | 0.914619 | − | 0.914619i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.24180 | −0.0865436 | ||||||||
\(672\) | 57.1028 | + | 5.21795i | 2.20279 | + | 0.201287i | ||||
\(673\) | −35.3380 | −1.36218 | −0.681090 | − | 0.732200i | \(-0.738494\pi\) | ||||
−0.681090 | + | 0.732200i | \(0.738494\pi\) | |||||||
\(674\) | −15.0513 | − | 30.9203i | −0.579755 | − | 1.19101i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.4786 | − | 14.4830i | −0.710714 | − | 0.557040i | ||||
\(677\) | −7.72259 | − | 7.72259i | −0.296803 | − | 0.296803i | 0.542957 | − | 0.839760i | \(-0.317305\pi\) |
−0.839760 | + | 0.542957i | \(0.817305\pi\) | |||||||
\(678\) | −4.50161 | − | 1.55391i | −0.172883 | − | 0.0596777i | ||||
\(679\) | − | 2.34365i | − | 0.0899411i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 50.4615i | 1.93369i | ||||||||
\(682\) | −6.73058 | + | 19.4981i | −0.257727 | + | 0.746622i | ||||
\(683\) | 15.6011 | + | 15.6011i | 0.596958 | + | 0.596958i | 0.939502 | − | 0.342544i | \(-0.111289\pi\) |
−0.342544 | + | 0.939502i | \(0.611289\pi\) | |||||||
\(684\) | −62.7323 | + | 7.60429i | −2.39863 | + | 0.290757i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.9265 | − | 6.29233i | 0.493536 | − | 0.240242i | ||||
\(687\) | 6.97246 | 0.266016 | ||||||||
\(688\) | −14.5544 | + | 24.0541i | −0.554881 | + | 0.917053i | ||||
\(689\) | −5.32207 | −0.202755 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0975 | − | 30.0975i | 1.14496 | − | 1.14496i | 0.157433 | − | 0.987530i | \(-0.449678\pi\) |
0.987530 | − | 0.157433i | \(-0.0503218\pi\) | |||||||
\(692\) | −3.99938 | − | 32.9932i | −0.152033 | − | 1.25421i | ||||
\(693\) | 42.5893 | + | 42.5893i | 1.61783 | + | 1.61783i | ||||
\(694\) | −11.3433 | + | 32.8609i | −0.430586 | + | 1.24738i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 5.02937 | − | 23.3949i | 0.190638 | − | 0.886780i | ||||
\(697\) | 18.5659i | 0.703234i | ||||||||
\(698\) | 1.46158 | + | 0.504523i | 0.0553215 | + | 0.0190965i | ||||
\(699\) | −51.6341 | − | 51.6341i | −1.95298 | − | 1.95298i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8151 | − | 14.8151i | 0.559559 | − | 0.559559i | −0.369623 | − | 0.929182i | \(-0.620513\pi\) |
0.929182 | + | 0.369623i | \(0.120513\pi\) | |||||||
\(702\) | 7.25945 | + | 14.9133i | 0.273990 | + | 0.562865i | ||||
\(703\) | 3.12621 | 0.117907 | ||||||||
\(704\) | 8.05764 | + | 21.2849i | 0.303684 | + | 0.802206i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.27686 | + | 17.0034i | 0.311504 | + | 0.639930i | ||||
\(707\) | −20.3673 | + | 20.3673i | −0.765992 | + | 0.765992i | ||||
\(708\) | 11.1126 | − | 14.1783i | 0.417636 | − | 0.532852i | ||||
\(709\) | 9.26566 | + | 9.26566i | 0.347979 | + | 0.347979i | 0.859356 | − | 0.511377i | \(-0.170864\pi\) |
−0.511377 | + | 0.859356i | \(0.670864\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 110.819i | 4.15604i | ||||||||
\(712\) | 4.53027 | − | 21.0732i | 0.169779 | − | 0.789753i | ||||
\(713\) | 41.0054i | 1.53567i | ||||||||
\(714\) | 21.5903 | − | 62.5460i | 0.807998 | − | 2.34073i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.64986 | + | 13.6107i | 0.0616582 | + | 0.508655i | ||||
\(717\) | 0.432914 | − | 0.432914i | 0.0161675 | − | 0.0161675i | ||||
\(718\) | −36.2922 | + | 17.6662i | −1.35441 | + | 0.659297i | ||||
\(719\) | 40.8143 | 1.52212 | 0.761058 | − | 0.648684i | \(-0.224680\pi\) | ||||
0.761058 | + | 0.648684i | \(0.224680\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.6882 | −1.96221 | ||||||||
\(722\) | −6.77778 | + | 3.29927i | −0.252243 | + | 0.122786i | ||||
\(723\) | 36.5961 | − | 36.5961i | 1.36102 | − | 1.36102i | ||||
\(724\) | −29.6911 | + | 3.59910i | −1.10346 | + | 0.133759i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.11354 | − | 11.9167i | 0.152668 | − | 0.442270i | ||||
\(727\) | − | 5.20944i | − | 0.193208i | −0.995323 | − | 0.0966038i | \(-0.969202\pi\) | ||
0.995323 | − | 0.0966038i | \(-0.0307980\pi\) | |||||||
\(728\) | −5.69714 | − | 8.81744i | −0.211150 | − | 0.326796i | ||||
\(729\) | − | 14.0106i | − | 0.518911i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.9403 | + | 22.9403i | 0.848476 | + | 0.848476i | ||||
\(732\) | 3.80419 | + | 2.98162i | 0.140607 | + | 0.110204i | ||||
\(733\) | 14.7039 | − | 14.7039i | 0.543099 | − | 0.543099i | −0.381337 | − | 0.924436i | \(-0.624536\pi\) |
0.924436 | + | 0.381337i | \(0.124536\pi\) | |||||||
\(734\) | −0.562758 | − | 1.15609i | −0.0207718 | − | 0.0426720i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 28.9481 | + | 34.7705i | 1.06704 | + | 1.28166i | ||||
\(737\) | 2.55917 | 0.0942684 | ||||||||
\(738\) | 15.9477 | + | 32.7618i | 0.587043 | + | 1.20598i | ||||
\(739\) | 7.68017 | − | 7.68017i | 0.282520 | − | 0.282520i | −0.551594 | − | 0.834113i | \(-0.685980\pi\) |
0.834113 | + | 0.551594i | \(0.185980\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0118 | + | 12.0118i | 0.441265 | + | 0.441265i | ||||
\(742\) | 20.9405 | + | 7.22849i | 0.768752 | + | 0.265366i | ||||
\(743\) | − | 34.9882i | − | 1.28359i | −0.766876 | − | 0.641796i | \(-0.778190\pi\) | ||
0.766876 | − | 0.641796i | \(-0.221810\pi\) | |||||||
\(744\) | 37.3541 | − | 24.1353i | 1.36947 | − | 0.884843i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.2944 | − | 50.1010i | 0.633194 | − | 1.83433i | ||||
\(747\) | 60.7254 | + | 60.7254i | 2.22183 | + | 2.22183i | ||||
\(748\) | 26.0716 | − | 3.16035i | 0.953273 | − | 0.115554i | ||||
\(749\) | −11.1953 | + | 11.1953i | −0.409066 | + | 0.409066i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −33.1447 | −1.20947 | −0.604733 | − | 0.796428i | \(-0.706720\pi\) | ||||
−0.604733 | + | 0.796428i | \(0.706720\pi\) | |||||||
\(752\) | −5.24788 | − | 21.3283i | −0.191370 | − | 0.777765i | ||||
\(753\) | 26.4577 | 0.964174 | ||||||||
\(754\) | −3.93905 | + | 1.91744i | −0.143452 | + | 0.0698291i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.30812 | − | 68.5386i | −0.302163 | − | 2.49272i | ||||
\(757\) | −22.1553 | − | 22.1553i | −0.805248 | − | 0.805248i | 0.178663 | − | 0.983910i | \(-0.442823\pi\) |
−0.983910 | + | 0.178663i | \(0.942823\pi\) | |||||||
\(758\) | 0.807419 | − | 2.33905i | 0.0293268 | − | 0.0849581i | ||||
\(759\) | 69.7810i | 2.53289i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 48.1426i | − | 1.74517i | −0.488466 | − | 0.872583i | \(-0.662443\pi\) | ||
0.488466 | − | 0.872583i | \(-0.337557\pi\) | |||||||
\(762\) | 6.19717 | + | 2.13921i | 0.224500 | + | 0.0774954i | ||||
\(763\) | −8.06347 | − | 8.06347i | −0.291917 | − | 0.291917i | ||||
\(764\) | −9.79932 | + | 12.5027i | −0.354527 | + | 0.452333i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.72781 | − | 19.9841i | −0.351480 | − | 0.722055i | ||||
\(767\) | −3.29802 | −0.119084 | ||||||||
\(768\) | 14.6360 | − | 46.8359i | 0.528130 | − | 1.69005i | ||||
\(769\) | −41.1054 | −1.48230 | −0.741150 | − | 0.671339i | \(-0.765719\pi\) | ||||
−0.741150 | + | 0.671339i | \(0.765719\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.0160 | + | 43.0160i | −1.54918 | + | 1.54918i | ||||
\(772\) | −25.7382 | + | 32.8388i | −0.926339 | + | 1.18189i | ||||
\(773\) | −10.8044 | − | 10.8044i | −0.388607 | − | 0.388607i | 0.485583 | − | 0.874190i | \(-0.338607\pi\) |
−0.874190 | + | 0.485583i | \(0.838607\pi\) | |||||||
\(774\) | 60.1861 | + | 20.7757i | 2.16334 | + | 0.746767i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.96079 | − | 0.421526i | −0.0703883 | − | 0.0151319i | ||||
\(777\) | 6.42440i | 0.230474i | ||||||||
\(778\) | 10.6242 | − | 30.7777i | 0.380895 | − | 1.10343i | ||||
\(779\) | 14.0292 | + | 14.0292i | 0.502648 | + | 0.502648i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7849 | + | 13.7849i | −0.493262 | + | 0.493262i | ||||
\(782\) | 46.9421 | − | 22.8504i | 1.67865 | − | 0.817127i | ||||
\(783\) | −28.8118 | −1.02965 | ||||||||
\(784\) | 3.75045 | + | 15.2425i | 0.133945 | + | 0.544376i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −50.8295 | + | 24.7427i | −1.81303 | + | 0.882541i | ||||
\(787\) | −11.7496 | + | 11.7496i | −0.418826 | + | 0.418826i | −0.884799 | − | 0.465973i | \(-0.845704\pi\) |
0.465973 | + | 0.884799i | \(0.345704\pi\) | |||||||
\(788\) | 5.83215 | − | 0.706963i | 0.207762 | − | 0.0251845i | ||||
\(789\) | −15.4932 | − | 15.4932i | −0.551573 | − | 0.551573i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 3.62914i | − | 0.129037i | ||||||
\(792\) | 43.2919 | − | 27.9718i | 1.53831 | − | 0.993934i | ||||
\(793\) | − | 0.884894i | − | 0.0314235i | ||||||
\(794\) | 43.2826 | + | 14.9408i | 1.53604 | + | 0.530227i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.6467 | − | 28.7227i | −1.29891 | − | 1.01805i | ||||
\(797\) | −15.9126 | + | 15.9126i | −0.563652 | + | 0.563652i | −0.930343 | − | 0.366691i | \(-0.880491\pi\) |
0.366691 | + | 0.930343i | \(0.380491\pi\) | |||||||
\(798\) | −30.9479 | − | 63.5770i | −1.09554 | − | 2.25060i | ||||
\(799\) | −25.3456 | −0.896663 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.8148 | −1.72479 | ||||||||
\(802\) | −9.81397 | − | 20.1611i | −0.346543 | − | 0.711913i | ||||
\(803\) | 21.1578 | − | 21.1578i | 0.746643 | − | 0.746643i | ||||
\(804\) | −4.34276 | − | 3.40374i | −0.153157 | − | 0.120041i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.69640 | − | 2.65673i | −0.271094 | − | 0.0935792i | ||||
\(807\) | 94.4274i | 3.32400i | ||||||||
\(808\) | 13.3769 | + | 20.7033i | 0.470596 | + | 0.728341i | ||||
\(809\) | 9.06814i | 0.318819i | 0.987213 | + | 0.159409i | \(0.0509590\pi\) | ||||
−0.987213 | + | 0.159409i | \(0.949041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.0825 | − | 17.0825i | −0.599849 | − | 0.599849i | 0.340424 | − | 0.940272i | \(-0.389430\pi\) |
−0.940272 | + | 0.340424i | \(0.889430\pi\) | |||||||
\(812\) | 18.1031 | − | 2.19443i | 0.635295 | − | 0.0770093i | ||||
\(813\) | 10.2212 | − | 10.2212i | 0.358472 | − | 0.358472i | ||||
\(814\) | −2.29270 | + | 1.11603i | −0.0803590 | + | 0.0391170i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −48.4452 | − | 29.3127i | −1.69592 | − | 1.02615i | ||||
\(817\) | 34.6693 | 1.21293 | ||||||||
\(818\) | −12.7437 | + | 6.20333i | −0.445571 | + | 0.216894i | ||||
\(819\) | −16.8111 | + | 16.8111i | −0.587426 | + | 0.587426i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.0531 | + | 18.0531i | 0.630057 | + | 0.630057i | 0.948082 | − | 0.318026i | \(-0.103020\pi\) |
−0.318026 | + | 0.948082i | \(0.603020\pi\) | |||||||
\(822\) | −4.79244 | + | 13.8835i | −0.167156 | + | 0.484241i | ||||
\(823\) | 25.3535i | 0.883767i | 0.897072 | + | 0.441884i | \(0.145690\pi\) | ||||
−0.897072 | + | 0.441884i | \(0.854310\pi\) | |||||||
\(824\) | −9.47642 | + | 44.0810i | −0.330127 | + | 1.53563i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9766 | + | 4.47940i | 0.451513 | + | 0.155858i | ||||
\(827\) | −15.3396 | − | 15.3396i | −0.533410 | − | 0.533410i | 0.388176 | − | 0.921585i | \(-0.373105\pi\) |
−0.921585 | + | 0.388176i | \(0.873105\pi\) | |||||||
\(828\) | 63.2070 | − | 80.6444i | 2.19660 | − | 2.80259i | ||||
\(829\) | 37.2546 | − | 37.2546i | 1.29391 | − | 1.29391i | 0.361555 | − | 0.932351i | \(-0.382246\pi\) |
0.932351 | − | 0.361555i | \(-0.117754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 88.7335 | 3.07813 | ||||||||
\(832\) | −8.40169 | + | 3.18055i | −0.291276 | + | 0.110266i | ||||
\(833\) | 18.1135 | 0.627596 | ||||||||
\(834\) | −5.62756 | − | 11.5608i | −0.194866 | − | 0.400319i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.3127 | − | 22.0889i | 0.598774 | − | 0.763962i | ||||
\(837\) | −37.8635 | − | 37.8635i | −1.30875 | − | 1.30875i | ||||
\(838\) | −27.4124 | − | 9.46250i | −0.946945 | − | 0.326877i | ||||
\(839\) | 17.9621i | 0.620120i | 0.950717 | + | 0.310060i | \(0.100349\pi\) | ||||
−0.950717 | + | 0.310060i | \(0.899651\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.3899i | 0.737584i | ||||||||
\(842\) | 8.48262 | − | 24.5737i | 0.292331 | − | 0.846866i | ||||
\(843\) | 38.2713 | + | 38.2713i | 1.31813 | + | 1.31813i | ||||
\(844\) | −0.856312 | − | 7.06422i | −0.0294755 | − | 0.243161i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −44.7254 | + | 21.7713i | −1.53769 | + | 0.748514i | ||||
\(847\) | 9.60708 | 0.330103 | ||||||||
\(848\) | 9.81397 | − | 16.2196i | 0.337013 | − | 0.556982i | ||||
\(849\) | 78.7306 | 2.70203 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.58436 | + | 3.58436i | −0.122870 | + | 0.122870i | ||||
\(852\) | 41.7261 | − | 5.05797i | 1.42951 | − | 0.173283i | ||||
\(853\) | 9.29007 | + | 9.29007i | 0.318086 | + | 0.318086i | 0.848032 | − | 0.529946i | \(-0.177788\pi\) |
−0.529946 | + | 0.848032i | \(0.677788\pi\) | |||||||
\(854\) | −1.20187 | + | 3.48176i | −0.0411272 | + | 0.119143i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.35282 | + | 11.3799i | 0.251314 | + | 0.388958i | ||||
\(857\) | − | 10.3997i | − | 0.355246i | −0.984099 | − | 0.177623i | \(-0.943159\pi\) | ||
0.984099 | − | 0.177623i | \(-0.0568407\pi\) | |||||||
\(858\) | −13.0973 | − | 4.52109i | −0.447136 | − | 0.154347i | ||||
\(859\) | 15.3452 | + | 15.3452i | 0.523571 | + | 0.523571i | 0.918648 | − | 0.395077i | \(-0.129282\pi\) |
−0.395077 | + | 0.918648i | \(0.629282\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −28.8302 | + | 28.8302i | −0.982530 | + | 0.982530i | ||||
\(862\) | 21.3176 | + | 43.7932i | 0.726079 | + | 1.49160i | ||||
\(863\) | −8.81329 | −0.300008 | −0.150004 | − | 0.988685i | \(-0.547929\pi\) | ||||
−0.150004 | + | 0.988685i | \(0.547929\pi\) | |||||||
\(864\) | −58.8363 | − | 5.37635i | −2.00165 | − | 0.182907i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.03047 | − | 18.5515i | −0.306868 | − | 0.630407i | ||||
\(867\) | −9.33601 | + | 9.33601i | −0.317067 | + | 0.317067i | ||||
\(868\) | 26.6743 | + | 20.9067i | 0.905386 | + | 0.709618i | ||||
\(869\) | −34.8023 | − | 34.8023i | −1.18059 | − | 1.18059i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.01017i | 0.0342283i | ||||||||
\(872\) | −8.19649 | + | 5.29592i | −0.277568 | + | 0.179343i | ||||
\(873\) | 4.54205i | 0.153725i | ||||||||
\(874\) | 18.2047 | − | 52.7381i | 0.615784 | − | 1.78389i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −64.0437 | + | 7.76326i | −2.16384 | + | 0.262296i | ||||
\(877\) | 5.68862 | − | 5.68862i | 0.192091 | − | 0.192091i | −0.604508 | − | 0.796599i | \(-0.706630\pi\) |
0.796599 | + | 0.604508i | \(0.206630\pi\) | |||||||
\(878\) | 7.25019 | − | 3.52923i | 0.244682 | − | 0.119106i | ||||
\(879\) | −2.76920 | −0.0934028 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3573 | −0.685856 | −0.342928 | − | 0.939362i | \(-0.611419\pi\) | ||||
−0.342928 | + | 0.939362i | \(0.611419\pi\) | |||||||
\(882\) | 31.9635 | − | 15.5591i | 1.07627 | − | 0.523903i | ||||
\(883\) | 19.3524 | − | 19.3524i | 0.651262 | − | 0.651262i | −0.302035 | − | 0.953297i | \(-0.597666\pi\) |
0.953297 | + | 0.302035i | \(0.0976660\pi\) | |||||||
\(884\) | 1.24747 | + | 10.2911i | 0.0419570 | + | 0.346128i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.28500 | + | 9.51647i | −0.110362 | + | 0.319712i | ||||
\(887\) | 12.7863i | 0.429323i | 0.976689 | + | 0.214661i | \(0.0688648\pi\) | ||||
−0.976689 | + | 0.214661i | \(0.931135\pi\) | |||||||
\(888\) | 5.37490 | + | 1.15548i | 0.180370 | + | 0.0387755i | ||||
\(889\) | 4.99608i | 0.167563i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.7775 | − | 25.7775i | −0.863579 | − | 0.863579i | ||||
\(892\) | 13.4588 | − | 17.1717i | 0.450633 | − | 0.574953i | ||||
\(893\) | −19.1522 | + | 19.1522i | −0.640905 | + | 0.640905i | ||||
\(894\) | −6.58385 | − | 13.5254i | −0.220197 | − | 0.452357i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 37.3777 | − | 1.10313i | 1.24870 | − | 0.0368531i | ||||
\(897\) | −27.5443 | −0.919678 | ||||||||
\(898\) | −13.7722 | − | 28.2925i | −0.459584 | − | 0.944134i | ||||
\(899\) | 10.0009 | − | 10.0009i | 0.333548 | − | 0.333548i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.4685 | − | 15.4685i | −0.515331 | − | 0.515331i | ||||
\(902\) | −15.2970 | − | 5.28040i | −0.509336 | − | 0.175818i | ||||
\(903\) | 71.2459i | 2.37091i | ||||||||
\(904\) | −3.03627 | − | 0.652731i | −0.100985 | − | 0.0217095i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.58117 | + | 4.58057i | −0.0525309 | + | 0.152179i | ||||
\(907\) | 2.88449 | + | 2.88449i | 0.0957780 | + | 0.0957780i | 0.753372 | − | 0.657594i | \(-0.228426\pi\) |
−0.657594 | + | 0.753372i | \(0.728426\pi\) | |||||||
\(908\) | 3.96003 | + | 32.6687i | 0.131418 | + | 1.08415i | ||||
\(909\) | 39.4723 | − | 39.4723i | 1.30921 | − | 1.30921i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.0271 | 1.95565 | 0.977827 | − | 0.209412i | \(-0.0671550\pi\) | ||||
0.977827 | + | 0.209412i | \(0.0671550\pi\) | |||||||
\(912\) | −58.7572 | + | 14.4573i | −1.94565 | + | 0.478730i | ||||
\(913\) | −38.1412 | −1.26229 | ||||||||
\(914\) | 11.3542 | − | 5.52695i | 0.375562 | − | 0.182815i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.51395 | − | 0.547173i | 0.149145 | − | 0.0180791i | ||||
\(917\) | −30.4626 | − | 30.4626i | −1.00596 | − | 1.00596i | ||||
\(918\) | −22.2458 | + | 64.4448i | −0.734219 | + | 2.12699i | ||||
\(919\) | − | 24.0062i | − | 0.791893i | −0.918274 | − | 0.395946i | \(-0.870417\pi\) | ||
0.918274 | − | 0.395946i | \(-0.129583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 19.6137i | − | 0.646294i | ||||||
\(922\) | 15.4036 | + | 5.31719i | 0.507291 | + | 0.175112i | ||||
\(923\) | −5.44124 | − | 5.44124i | −0.179100 | − | 0.179100i | ||||
\(924\) | 45.3931 | + | 35.5779i | 1.49332 | + | 1.17043i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −19.6249 | − | 40.3160i | −0.644915 | − | 1.32487i | ||||
\(927\) | 102.111 | 3.35376 | ||||||||
\(928\) | 1.42006 | − | 15.5405i | 0.0466157 | − | 0.510140i | ||||
\(929\) | 15.1568 | 0.497279 | 0.248639 | − | 0.968596i | \(-0.420017\pi\) | ||||
0.248639 | + | 0.968596i | \(0.420017\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6873 | − | 13.6873i | 0.448585 | − | 0.448585i | ||||
\(932\) | −37.4798 | − | 29.3757i | −1.22769 | − | 0.962234i | ||||
\(933\) | −30.5802 | − | 30.5802i | −1.00115 | − | 1.00115i | ||||
\(934\) | −33.5916 | − | 11.5955i | −1.09915 | − | 0.379417i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 11.0412 | + | 17.0884i | 0.360892 | + | 0.558552i | ||||
\(937\) | − | 39.9323i | − | 1.30453i | −0.757991 | − | 0.652266i | \(-0.773819\pi\) | ||
0.757991 | − | 0.652266i | \(-0.226181\pi\) | |||||||
\(938\) | 1.37202 | − | 3.97468i | 0.0447982 | − | 0.129778i | ||||
\(939\) | −25.8503 | − | 25.8503i | −0.843594 | − | 0.843594i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.6002 | + | 21.6002i | −0.704145 | + | 0.704145i | −0.965298 | − | 0.261153i | \(-0.915897\pi\) |
0.261153 | + | 0.965298i | \(0.415897\pi\) | |||||||
\(942\) | −87.3447 | + | 42.5174i | −2.84584 | + | 1.38529i | ||||
\(943\) | −32.1704 | −1.04761 | ||||||||
\(944\) | 6.08159 | − | 10.0511i | 0.197939 | − | 0.327134i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.4258 | + | 12.3767i | −0.826662 | + | 0.402401i | ||||
\(947\) | 16.2944 | − | 16.2944i | 0.529498 | − | 0.529498i | −0.390925 | − | 0.920423i | \(-0.627845\pi\) |
0.920423 | + | 0.390925i | \(0.127845\pi\) | |||||||
\(948\) | 12.7697 | + | 105.345i | 0.414741 | + | 3.42144i | ||||
\(949\) | 8.35152 | + | 8.35152i | 0.271102 | + | 0.271102i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 76.5578i | − | 2.48256i | ||||||
\(952\) | 9.06914 | − | 42.1864i | 0.293932 | − | 1.36727i | ||||
\(953\) | 12.0232i | 0.389468i | 0.980856 | + | 0.194734i | \(0.0623844\pi\) | ||||
−0.980856 | + | 0.194734i | \(0.937616\pi\) | |||||||
\(954\) | −40.5832 | − | 14.0090i | −1.31393 | − | 0.453557i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.246294 | − | 0.314241i | 0.00796571 | − | 0.0101633i | ||||
\(957\) | 17.0190 | − | 17.0190i | 0.550147 | − | 0.550147i | ||||
\(958\) | 4.83295 | + | 9.92846i | 0.156146 | + | 0.320774i | ||||
\(959\) | −11.1927 | −0.361430 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.71434 | −0.152076 | ||||||||
\(962\) | −0.440526 | − | 0.904985i | −0.0142031 | − | 0.0291779i | ||||
\(963\) | 21.6966 | − | 21.6966i | 0.699164 | − | 0.699164i | ||||
\(964\) | 20.8203 | − | 26.5641i | 0.670576 | − | 0.855573i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 108.378 | + | 37.4110i | 3.48699 | + | 1.20368i | ||||
\(967\) | − | 43.8237i | − | 1.40927i | −0.709568 | − | 0.704637i | \(-0.751110\pi\) | ||
0.709568 | − | 0.704637i | \(-0.248890\pi\) | |||||||
\(968\) | 1.72791 | − | 8.03765i | 0.0555373 | − | 0.258340i | ||||
\(969\) | 69.8244i | 2.24308i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.9986 | + | 35.9986i | 1.15525 | + | 1.15525i | 0.985484 | + | 0.169766i | \(0.0543011\pi\) |
0.169766 | + | 0.985484i | \(0.445699\pi\) | |||||||
\(972\) | 1.91734 | + | 15.8172i | 0.0614986 | + | 0.507338i | ||||
\(973\) | 6.92852 | − | 6.92852i | 0.222118 | − | 0.222118i | ||||
\(974\) | 35.1910 | − | 17.1302i | 1.12759 | − | 0.548886i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.69681 | + | 1.63176i | 0.0863227 | + | 0.0522312i | ||||
\(977\) | −0.204913 | −0.00655576 | −0.00327788 | − | 0.999995i | \(-0.501043\pi\) | ||||
−0.00327788 | + | 0.999995i | \(0.501043\pi\) | |||||||
\(978\) | 39.8239 | − | 19.3854i | 1.27343 | − | 0.619876i | ||||
\(979\) | 15.3301 | − | 15.3301i | 0.489953 | − | 0.489953i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.6272 | + | 15.6272i | 0.498937 | + | 0.498937i | ||||
\(982\) | −7.70032 | + | 22.3074i | −0.245727 | + | 0.711858i | ||||
\(983\) | − | 34.0060i | − | 1.08462i | −0.840177 | − | 0.542312i | \(-0.817549\pi\) | ||
0.840177 | − | 0.542312i | \(-0.182451\pi\) | |||||||
\(984\) | 18.9351 | + | 29.3058i | 0.603629 | + | 0.934235i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −17.0218 | − | 5.87578i | −0.542085 | − | 0.187123i | ||||
\(987\) | −39.3581 | − | 39.3581i | −1.25278 | − | 1.25278i | ||||
\(988\) | 8.71906 | + | 6.83377i | 0.277390 | + | 0.217411i | ||||
\(989\) | −39.7501 | + | 39.7501i | −1.26398 | + | 1.26398i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.8223 | 0.439079 | 0.219539 | − | 0.975604i | \(-0.429545\pi\) | ||||
0.219539 | + | 0.975604i | \(0.429545\pi\) | |||||||
\(992\) | 22.2889 | − | 18.5565i | 0.707674 | − | 0.589171i | ||||
\(993\) | 108.336 | 3.43794 | ||||||||
\(994\) | 14.0191 | + | 28.7998i | 0.444658 | + | 0.913474i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 64.7231 | + | 50.7283i | 2.05083 | + | 1.60739i | ||||
\(997\) | 6.37875 | + | 6.37875i | 0.202017 | + | 0.202017i | 0.800864 | − | 0.598847i | \(-0.204374\pi\) |
−0.598847 | + | 0.800864i | \(0.704374\pi\) | |||||||
\(998\) | 47.3536 | + | 16.3460i | 1.49895 | + | 0.517425i | ||||
\(999\) | − | 6.61943i | − | 0.209429i |
(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 | 400.2.l.f.101.4 | ✓ | 12 | |
4.3 | odd | 2 | 1600.2.l.g.1201.6 | 12 | |||
5.2 | odd | 4 | 400.2.q.e.149.6 | 12 | |||
5.3 | odd | 4 | 400.2.q.f.149.1 | 12 | |||
5.4 | even | 2 | 400.2.l.g.101.3 | yes | 12 | ||
16.3 | odd | 4 | 1600.2.l.g.401.6 | 12 | |||
16.13 | even | 4 | inner | 400.2.l.f.301.4 | yes | 12 | |
20.3 | even | 4 | 1600.2.q.f.49.6 | 12 | |||
20.7 | even | 4 | 1600.2.q.e.49.1 | 12 | |||
20.19 | odd | 2 | 1600.2.l.f.1201.1 | 12 | |||
80.3 | even | 4 | 1600.2.q.e.849.1 | 12 | |||
80.13 | odd | 4 | 400.2.q.e.349.6 | 12 | |||
80.19 | odd | 4 | 1600.2.l.f.401.1 | 12 | |||
80.29 | even | 4 | 400.2.l.g.301.3 | yes | 12 | ||
80.67 | even | 4 | 1600.2.q.f.849.6 | 12 | |||
80.77 | odd | 4 | 400.2.q.f.349.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
400.2.l.f.101.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
400.2.l.f.301.4 | yes | 12 | 16.13 | even | 4 | inner | |
400.2.l.g.101.3 | yes | 12 | 5.4 | even | 2 | ||
400.2.l.g.301.3 | yes | 12 | 80.29 | even | 4 | ||
400.2.q.e.149.6 | 12 | 5.2 | odd | 4 | |||
400.2.q.e.349.6 | 12 | 80.13 | odd | 4 | |||
400.2.q.f.149.1 | 12 | 5.3 | odd | 4 | |||
400.2.q.f.349.1 | 12 | 80.77 | odd | 4 | |||
1600.2.l.f.401.1 | 12 | 80.19 | odd | 4 | |||
1600.2.l.f.1201.1 | 12 | 20.19 | odd | 2 | |||
1600.2.l.g.401.6 | 12 | 16.3 | odd | 4 | |||
1600.2.l.g.1201.6 | 12 | 4.3 | odd | 2 | |||
1600.2.q.e.49.1 | 12 | 20.7 | even | 4 | |||
1600.2.q.e.849.1 | 12 | 80.3 | even | 4 | |||
1600.2.q.f.49.6 | 12 | 20.3 | even | 4 | |||
1600.2.q.f.849.6 | 12 | 80.67 | even | 4 |