Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(362,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.362");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.e (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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 483.2 | ||
Root | \(-1.35329 - 1.35329i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.483 |
Dual form | 605.2.e.a.362.2 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.35329 | − | 1.35329i | −0.956923 | − | 0.956923i | 0.0421867 | − | 0.999110i | \(-0.486568\pi\) |
−0.999110 | + | 0.0421867i | \(0.986568\pi\) | |||||||
\(3\) | 0.185315 | + | 0.185315i | 0.106992 | + | 0.106992i | 0.758576 | − | 0.651585i | \(-0.225895\pi\) |
−0.651585 | + | 0.758576i | \(0.725895\pi\) | |||||||
\(4\) | 1.66281i | 0.831403i | ||||||||
\(5\) | −0.610994 | − | 2.15097i | −0.273245 | − | 0.961944i | ||||
\(6\) | − | 0.501571i | − | 0.204765i | ||||||
\(7\) | −3.24854 | − | 3.24854i | −1.22783 | − | 1.22783i | −0.964783 | − | 0.263049i | \(-0.915272\pi\) |
−0.263049 | − | 0.964783i | \(-0.584728\pi\) | |||||||
\(8\) | −0.456321 | + | 0.456321i | −0.161334 | + | 0.161334i | ||||
\(9\) | − | 2.93132i | − | 0.977106i | ||||||
\(10\) | −2.08404 | + | 3.73775i | −0.659032 | + | 1.18198i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.308143 | + | 0.308143i | −0.0889531 | + | 0.0889531i | ||||
\(13\) | −1.15905 | + | 1.15905i | −0.321462 | + | 0.321462i | −0.849328 | − | 0.527866i | \(-0.822992\pi\) |
0.527866 | + | 0.849328i | \(0.322992\pi\) | |||||||
\(14\) | 8.79245i | 2.34988i | ||||||||
\(15\) | 0.285381 | − | 0.511834i | 0.0736850 | − | 0.132155i | ||||
\(16\) | 4.56069 | 1.14017 | ||||||||
\(17\) | −1.01881 | − | 1.01881i | −0.247098 | − | 0.247098i | 0.572680 | − | 0.819779i | \(-0.305904\pi\) |
−0.819779 | + | 0.572680i | \(0.805904\pi\) | |||||||
\(18\) | −3.96693 | + | 3.96693i | −0.935015 | + | 0.935015i | ||||
\(19\) | 3.61923 | 0.830308 | 0.415154 | − | 0.909751i | \(-0.363728\pi\) | ||||
0.415154 | + | 0.909751i | \(0.363728\pi\) | |||||||
\(20\) | 3.57665 | − | 1.01597i | 0.799764 | − | 0.227177i | ||||
\(21\) | − | 1.20400i | − | 0.262735i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.55745 | + | 3.55745i | 0.741780 | + | 0.741780i | 0.972920 | − | 0.231141i | \(-0.0742458\pi\) |
−0.231141 | + | 0.972920i | \(0.574246\pi\) | |||||||
\(24\) | −0.169126 | −0.0345228 | ||||||||
\(25\) | −4.25337 | + | 2.62847i | −0.850674 | + | 0.525693i | ||||
\(26\) | 3.13706 | 0.615228 | ||||||||
\(27\) | 1.09916 | − | 1.09916i | 0.211534 | − | 0.211534i | ||||
\(28\) | 5.40169 | − | 5.40169i | 1.02082 | − | 1.02082i | ||||
\(29\) | 1.82741 | 0.339342 | 0.169671 | − | 0.985501i | \(-0.445729\pi\) | ||||
0.169671 | + | 0.985501i | \(0.445729\pi\) | |||||||
\(30\) | −1.07887 | + | 0.306457i | −0.196973 | + | 0.0559511i | ||||
\(31\) | −4.67258 | −0.839219 | −0.419610 | − | 0.907705i | \(-0.637833\pi\) | ||||
−0.419610 | + | 0.907705i | \(0.637833\pi\) | |||||||
\(32\) | −5.25931 | − | 5.25931i | −0.929723 | − | 0.929723i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.75750i | 0.472908i | ||||||||
\(35\) | −5.00268 | + | 8.97235i | −0.845607 | + | 1.51660i | ||||
\(36\) | 4.87421 | 0.812369 | ||||||||
\(37\) | −7.32115 | + | 7.32115i | −1.20359 | + | 1.20359i | −0.230523 | + | 0.973067i | \(0.574044\pi\) |
−0.973067 | + | 0.230523i | \(0.925956\pi\) | |||||||
\(38\) | −4.89788 | − | 4.89788i | −0.794541 | − | 0.794541i | ||||
\(39\) | −0.429577 | −0.0687874 | ||||||||
\(40\) | 1.26035 | + | 0.702725i | 0.199278 | + | 0.111111i | ||||
\(41\) | − | 6.41419i | − | 1.00173i | −0.865526 | − | 0.500864i | \(-0.833016\pi\) | ||
0.865526 | − | 0.500864i | \(-0.166984\pi\) | |||||||
\(42\) | −1.62937 | + | 1.62937i | −0.251417 | + | 0.251417i | ||||
\(43\) | −4.54091 | + | 4.54091i | −0.692482 | + | 0.692482i | −0.962777 | − | 0.270295i | \(-0.912879\pi\) |
0.270295 | + | 0.962777i | \(0.412879\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.30518 | + | 1.79102i | −0.939921 | + | 0.266989i | ||||
\(46\) | − | 9.62855i | − | 1.41965i | ||||||
\(47\) | 6.18236 | − | 6.18236i | 0.901789 | − | 0.901789i | −0.0938016 | − | 0.995591i | \(-0.529902\pi\) |
0.995591 | + | 0.0938016i | \(0.0299019\pi\) | |||||||
\(48\) | 0.845163 | + | 0.845163i | 0.121989 | + | 0.121989i | ||||
\(49\) | 14.1060i | 2.01514i | ||||||||
\(50\) | 9.31315 | + | 2.19898i | 1.31708 | + | 0.310982i | ||||
\(51\) | − | 0.377602i | − | 0.0528749i | ||||||
\(52\) | −1.92727 | − | 1.92727i | −0.267264 | − | 0.267264i | ||||
\(53\) | −2.62937 | − | 2.62937i | −0.361172 | − | 0.361172i | 0.503072 | − | 0.864244i | \(-0.332203\pi\) |
−0.864244 | + | 0.503072i | \(0.832203\pi\) | |||||||
\(54\) | −2.97497 | −0.404843 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.96475 | 0.396182 | ||||||||
\(57\) | 0.670697 | + | 0.670697i | 0.0888360 | + | 0.0888360i | ||||
\(58\) | −2.47303 | − | 2.47303i | −0.324724 | − | 0.324724i | ||||
\(59\) | − | 8.20299i | − | 1.06794i | −0.845504 | − | 0.533969i | \(-0.820700\pi\) | ||
0.845504 | − | 0.533969i | \(-0.179300\pi\) | |||||||
\(60\) | 0.851080 | + | 0.474533i | 0.109874 | + | 0.0612620i | ||||
\(61\) | 11.5963i | 1.48475i | 0.669982 | + | 0.742377i | \(0.266302\pi\) | ||||
−0.669982 | + | 0.742377i | \(0.733698\pi\) | |||||||
\(62\) | 6.32337 | + | 6.32337i | 0.803068 | + | 0.803068i | ||||
\(63\) | −9.52249 | + | 9.52249i | −1.19972 | + | 1.19972i | ||||
\(64\) | 5.11339i | 0.639174i | ||||||||
\(65\) | 3.20125 | + | 1.78491i | 0.397066 | + | 0.221391i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.55745 | + | 1.55745i | −0.190273 | + | 0.190273i | −0.795814 | − | 0.605541i | \(-0.792957\pi\) |
0.605541 | + | 0.795814i | \(0.292957\pi\) | |||||||
\(68\) | 1.69409 | − | 1.69409i | 0.205438 | − | 0.205438i | ||||
\(69\) | 1.31850i | 0.158728i | ||||||||
\(70\) | 18.9123 | − | 5.37213i | 2.26045 | − | 0.642093i | ||||
\(71\) | −6.33689 | −0.752050 | −0.376025 | − | 0.926609i | \(-0.622709\pi\) | ||||
−0.376025 | + | 0.926609i | \(0.622709\pi\) | |||||||
\(72\) | 1.33762 | + | 1.33762i | 0.157640 | + | 0.157640i | ||||
\(73\) | 5.23876 | − | 5.23876i | 0.613151 | − | 0.613151i | −0.330615 | − | 0.943766i | \(-0.607256\pi\) |
0.943766 | + | 0.330615i | \(0.107256\pi\) | |||||||
\(74\) | 19.8153 | 2.30349 | ||||||||
\(75\) | −1.27531 | − | 0.301119i | −0.147260 | − | 0.0347703i | ||||
\(76\) | 6.01808i | 0.690321i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.581344 | + | 0.581344i | 0.0658242 | + | 0.0658242i | ||||
\(79\) | 8.93527 | 1.00530 | 0.502648 | − | 0.864491i | \(-0.332359\pi\) | ||||
0.502648 | + | 0.864491i | \(0.332359\pi\) | |||||||
\(80\) | −2.78655 | − | 9.80992i | −0.311546 | − | 1.09678i | ||||
\(81\) | −8.38657 | −0.931841 | ||||||||
\(82\) | −8.68028 | + | 8.68028i | −0.958576 | + | 0.958576i | ||||
\(83\) | 4.63804 | − | 4.63804i | 0.509091 | − | 0.509091i | −0.405156 | − | 0.914247i | \(-0.632783\pi\) |
0.914247 | + | 0.405156i | \(0.132783\pi\) | |||||||
\(84\) | 2.00203 | 0.218439 | ||||||||
\(85\) | −1.56895 | + | 2.81393i | −0.170176 | + | 0.305213i | ||||
\(86\) | 12.2904 | 1.32530 | ||||||||
\(87\) | 0.338647 | + | 0.338647i | 0.0363068 | + | 0.0363068i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.44232i | 0.258886i | 0.991587 | + | 0.129443i | \(0.0413189\pi\) | ||||
−0.991587 | + | 0.129443i | \(0.958681\pi\) | |||||||
\(90\) | 10.9565 | + | 6.10899i | 1.15492 | + | 0.643944i | ||||
\(91\) | 7.53041 | 0.789402 | ||||||||
\(92\) | −5.91535 | + | 5.91535i | −0.616718 | + | 0.616718i | ||||
\(93\) | −0.865898 | − | 0.865898i | −0.0897894 | − | 0.0897894i | ||||
\(94\) | −16.7331 | −1.72589 | ||||||||
\(95\) | −2.21133 | − | 7.78487i | −0.226878 | − | 0.798710i | ||||
\(96\) | − | 1.94925i | − | 0.198945i | ||||||
\(97\) | −3.73830 | + | 3.73830i | −0.379567 | + | 0.379567i | −0.870946 | − | 0.491379i | \(-0.836493\pi\) |
0.491379 | + | 0.870946i | \(0.336493\pi\) | |||||||
\(98\) | 19.0895 | − | 19.0895i | 1.92833 | − | 1.92833i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.37063 | − | 7.07254i | −0.437063 | − | 0.707254i | ||||
\(101\) | 9.27565i | 0.922962i | 0.887150 | + | 0.461481i | \(0.152682\pi\) | ||||
−0.887150 | + | 0.461481i | \(0.847318\pi\) | |||||||
\(102\) | −0.511006 | + | 0.511006i | −0.0505972 | + | 0.0505972i | ||||
\(103\) | −7.99380 | − | 7.99380i | −0.787653 | − | 0.787653i | 0.193456 | − | 0.981109i | \(-0.438030\pi\) |
−0.981109 | + | 0.193456i | \(0.938030\pi\) | |||||||
\(104\) | − | 1.05780i | − | 0.103725i | ||||||
\(105\) | −2.58978 | + | 0.735639i | −0.252737 | + | 0.0717911i | ||||
\(106\) | 7.11662i | 0.691227i | ||||||||
\(107\) | −2.67241 | − | 2.67241i | −0.258352 | − | 0.258352i | 0.566032 | − | 0.824383i | \(-0.308478\pi\) |
−0.824383 | + | 0.566032i | \(0.808478\pi\) | |||||||
\(108\) | 1.82769 | + | 1.82769i | 0.175870 | + | 0.175870i | ||||
\(109\) | 0.637227 | 0.0610352 | 0.0305176 | − | 0.999534i | \(-0.490284\pi\) | ||||
0.0305176 | + | 0.999534i | \(0.490284\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.71343 | −0.257548 | ||||||||
\(112\) | −14.8156 | − | 14.8156i | −1.39994 | − | 1.39994i | ||||
\(113\) | −5.53998 | − | 5.53998i | −0.521157 | − | 0.521157i | 0.396764 | − | 0.917921i | \(-0.370133\pi\) |
−0.917921 | + | 0.396764i | \(0.870133\pi\) | |||||||
\(114\) | − | 1.81530i | − | 0.170018i | ||||||
\(115\) | 5.47840 | − | 9.82556i | 0.510863 | − | 0.916238i | ||||
\(116\) | 3.03864i | 0.282130i | ||||||||
\(117\) | 3.39753 | + | 3.39753i | 0.314102 | + | 0.314102i | ||||
\(118\) | −11.1010 | + | 11.1010i | −1.02193 | + | 1.02193i | ||||
\(119\) | 6.61930i | 0.606790i | ||||||||
\(120\) | 0.103335 | + | 0.363786i | 0.00943317 | + | 0.0332090i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 15.6932 | − | 15.6932i | 1.42080 | − | 1.42080i | ||||
\(123\) | 1.18864 | − | 1.18864i | 0.107176 | − | 0.107176i | ||||
\(124\) | − | 7.76959i | − | 0.697730i | ||||||
\(125\) | 8.25254 | + | 7.54291i | 0.738130 | + | 0.674658i | ||||
\(126\) | 25.7734 | 2.29608 | ||||||||
\(127\) | −7.19563 | − | 7.19563i | −0.638509 | − | 0.638509i | 0.311679 | − | 0.950188i | \(-0.399109\pi\) |
−0.950188 | + | 0.311679i | \(0.899109\pi\) | |||||||
\(128\) | −3.59869 | + | 3.59869i | −0.318082 | + | 0.318082i | ||||
\(129\) | −1.68300 | −0.148179 | ||||||||
\(130\) | −1.91673 | − | 6.74773i | −0.168108 | − | 0.591815i | ||||
\(131\) | − | 7.05141i | − | 0.616085i | −0.951373 | − | 0.308042i | \(-0.900326\pi\) | ||
0.951373 | − | 0.308042i | \(-0.0996739\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.7572 | − | 11.7572i | −1.01948 | − | 1.01948i | ||||
\(134\) | 4.21537 | 0.364153 | ||||||||
\(135\) | −3.03585 | − | 1.69268i | −0.261284 | − | 0.145683i | ||||
\(136\) | 0.929812 | 0.0797307 | ||||||||
\(137\) | 8.42628 | − | 8.42628i | 0.719906 | − | 0.719906i | −0.248680 | − | 0.968586i | \(-0.579997\pi\) |
0.968586 | + | 0.248680i | \(0.0799968\pi\) | |||||||
\(138\) | 1.78431 | − | 1.78431i | 0.151891 | − | 0.151891i | ||||
\(139\) | −6.85170 | −0.581154 | −0.290577 | − | 0.956852i | \(-0.593847\pi\) | ||||
−0.290577 | + | 0.956852i | \(0.593847\pi\) | |||||||
\(140\) | −14.9193 | − | 8.31848i | −1.26091 | − | 0.703040i | ||||
\(141\) | 2.29136 | 0.192968 | ||||||||
\(142\) | 8.57567 | + | 8.57567i | 0.719654 | + | 0.719654i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | − | 13.3688i | − | 1.11407i | ||||||
\(145\) | −1.11654 | − | 3.93072i | −0.0927236 | − | 0.326428i | ||||
\(146\) | −14.1792 | −1.17348 | ||||||||
\(147\) | −2.61405 | + | 2.61405i | −0.215603 | + | 0.215603i | ||||
\(148\) | −12.1737 | − | 12.1737i | −1.00067 | − | 1.00067i | ||||
\(149\) | −23.6983 | −1.94144 | −0.970718 | − | 0.240220i | \(-0.922780\pi\) | ||||
−0.970718 | + | 0.240220i | \(0.922780\pi\) | |||||||
\(150\) | 1.31836 | + | 2.13337i | 0.107644 | + | 0.174189i | ||||
\(151\) | − | 19.2953i | − | 1.57023i | −0.619353 | − | 0.785113i | \(-0.712605\pi\) | ||
0.619353 | − | 0.785113i | \(-0.287395\pi\) | |||||||
\(152\) | −1.65153 | + | 1.65153i | −0.133957 | + | 0.133957i | ||||
\(153\) | −2.98646 | + | 2.98646i | −0.241441 | + | 0.241441i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.85492 | + | 10.0506i | 0.229313 | + | 0.807283i | ||||
\(156\) | − | 0.714304i | − | 0.0571901i | ||||||
\(157\) | −3.91061 | + | 3.91061i | −0.312101 | + | 0.312101i | −0.845723 | − | 0.533622i | \(-0.820830\pi\) |
0.533622 | + | 0.845723i | \(0.320830\pi\) | |||||||
\(158\) | −12.0920 | − | 12.0920i | −0.961991 | − | 0.961991i | ||||
\(159\) | − | 0.974523i | − | 0.0772847i | ||||||
\(160\) | −8.09922 | + | 14.5260i | −0.640300 | + | 1.14838i | ||||
\(161\) | − | 23.1130i | − | 1.82156i | ||||||
\(162\) | 11.3495 | + | 11.3495i | 0.891700 | + | 0.891700i | ||||
\(163\) | −7.11217 | − | 7.11217i | −0.557068 | − | 0.557068i | 0.371404 | − | 0.928472i | \(-0.378877\pi\) |
−0.928472 | + | 0.371404i | \(0.878877\pi\) | |||||||
\(164\) | 10.6656 | 0.832840 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.5533 | −0.974322 | ||||||||
\(167\) | 5.25514 | + | 5.25514i | 0.406655 | + | 0.406655i | 0.880570 | − | 0.473915i | \(-0.157160\pi\) |
−0.473915 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(168\) | 0.549413 | + | 0.549413i | 0.0423881 | + | 0.0423881i | ||||
\(169\) | 10.3132i | 0.793325i | ||||||||
\(170\) | 5.93132 | − | 1.68482i | 0.454911 | − | 0.129220i | ||||
\(171\) | − | 10.6091i | − | 0.811299i | ||||||
\(172\) | −7.55065 | − | 7.55065i | −0.575732 | − | 0.575732i | ||||
\(173\) | 10.3279 | − | 10.3279i | 0.785218 | − | 0.785218i | −0.195488 | − | 0.980706i | \(-0.562629\pi\) |
0.980706 | + | 0.195488i | \(0.0626290\pi\) | |||||||
\(174\) | − | 0.916577i | − | 0.0694856i | ||||||
\(175\) | 22.3559 | + | 5.27857i | 1.68995 | + | 0.399022i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.52013 | − | 1.52013i | 0.114260 | − | 0.114260i | ||||
\(178\) | 3.30518 | − | 3.30518i | 0.247734 | − | 0.247734i | ||||
\(179\) | 9.47065i | 0.707870i | 0.935270 | + | 0.353935i | \(0.115157\pi\) | ||||
−0.935270 | + | 0.353935i | \(0.884843\pi\) | |||||||
\(180\) | −2.97812 | − | 10.4843i | −0.221976 | − | 0.781454i | ||||
\(181\) | −22.2355 | −1.65275 | −0.826375 | − | 0.563120i | \(-0.809601\pi\) | ||||
−0.826375 | + | 0.563120i | \(0.809601\pi\) | |||||||
\(182\) | −10.1909 | − | 10.1909i | −0.755396 | − | 0.755396i | ||||
\(183\) | −2.14897 | + | 2.14897i | −0.158856 | + | 0.158856i | ||||
\(184\) | −3.24668 | −0.239349 | ||||||||
\(185\) | 20.2208 | + | 11.2744i | 1.48666 | + | 0.828912i | ||||
\(186\) | 2.34363i | 0.171843i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 10.2801 | + | 10.2801i | 0.749751 | + | 0.749751i | ||||
\(189\) | −7.14133 | −0.519455 | ||||||||
\(190\) | −7.54263 | + | 13.5278i | −0.547200 | + | 0.981409i | ||||
\(191\) | 12.1711 | 0.880667 | 0.440333 | − | 0.897834i | \(-0.354860\pi\) | ||||
0.440333 | + | 0.897834i | \(0.354860\pi\) | |||||||
\(192\) | −0.947588 | + | 0.947588i | −0.0683862 | + | 0.0683862i | ||||
\(193\) | 7.03527 | − | 7.03527i | 0.506410 | − | 0.506410i | −0.407013 | − | 0.913422i | \(-0.633430\pi\) |
0.913422 | + | 0.407013i | \(0.133430\pi\) | |||||||
\(194\) | 10.1180 | 0.726433 | ||||||||
\(195\) | 0.262469 | + | 0.924009i | 0.0187958 | + | 0.0661696i | ||||
\(196\) | −23.4555 | −1.67539 | ||||||||
\(197\) | −8.97738 | − | 8.97738i | −0.639612 | − | 0.639612i | 0.310848 | − | 0.950460i | \(-0.399387\pi\) |
−0.950460 | + | 0.310848i | \(0.899387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.9491i | − | 0.917935i | −0.888453 | − | 0.458967i | \(-0.848219\pi\) | ||
0.888453 | − | 0.458967i | \(-0.151781\pi\) | |||||||
\(200\) | 0.741480 | − | 3.14033i | 0.0524305 | − | 0.222055i | ||||
\(201\) | −0.577237 | −0.0407152 | ||||||||
\(202\) | 12.5527 | − | 12.5527i | 0.883204 | − | 0.883204i | ||||
\(203\) | −5.93642 | − | 5.93642i | −0.416655 | − | 0.416655i | ||||
\(204\) | 0.627879 | 0.0439603 | ||||||||
\(205\) | −13.7967 | + | 3.91903i | −0.963606 | + | 0.273717i | ||||
\(206\) | 21.6359i | 1.50745i | ||||||||
\(207\) | 10.4280 | − | 10.4280i | 0.724797 | − | 0.724797i | ||||
\(208\) | −5.28605 | + | 5.28605i | −0.366522 | + | 0.366522i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 4.50027 | + | 2.50920i | 0.310548 | + | 0.173151i | ||||
\(211\) | − | 3.96174i | − | 0.272737i | −0.990658 | − | 0.136369i | \(-0.956457\pi\) | ||
0.990658 | − | 0.136369i | \(-0.0435432\pi\) | |||||||
\(212\) | 4.37213 | − | 4.37213i | 0.300279 | − | 0.300279i | ||||
\(213\) | −1.17432 | − | 1.17432i | −0.0804630 | − | 0.0804630i | ||||
\(214\) | 7.23311i | 0.494445i | ||||||||
\(215\) | 12.5418 | + | 6.99290i | 0.855347 | + | 0.476912i | ||||
\(216\) | 1.00314i | 0.0682551i | ||||||||
\(217\) | 15.1790 | + | 15.1790i | 1.03042 | + | 1.03042i | ||||
\(218\) | −0.862355 | − | 0.862355i | −0.0584060 | − | 0.0584060i | ||||
\(219\) | 1.94164 | 0.131204 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.36170 | 0.158865 | ||||||||
\(222\) | 3.67207 | + | 3.67207i | 0.246453 | + | 0.246453i | ||||
\(223\) | −1.01451 | − | 1.01451i | −0.0679368 | − | 0.0679368i | 0.672322 | − | 0.740259i | \(-0.265297\pi\) |
−0.740259 | + | 0.672322i | \(0.765297\pi\) | |||||||
\(224\) | 34.1701i | 2.28308i | ||||||||
\(225\) | 7.70486 | + | 12.4680i | 0.513658 | + | 0.831199i | ||||
\(226\) | 14.9944i | 0.997415i | ||||||||
\(227\) | 7.99062 | + | 7.99062i | 0.530356 | + | 0.530356i | 0.920678 | − | 0.390322i | \(-0.127636\pi\) |
−0.390322 | + | 0.920678i | \(0.627636\pi\) | |||||||
\(228\) | −1.11524 | + | 1.11524i | −0.0738585 | + | 0.0738585i | ||||
\(229\) | − | 0.649417i | − | 0.0429147i | −0.999770 | − | 0.0214573i | \(-0.993169\pi\) | ||
0.999770 | − | 0.0214573i | \(-0.00683060\pi\) | |||||||
\(230\) | −20.7107 | + | 5.88299i | −1.36563 | + | 0.387913i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.833888 | + | 0.833888i | −0.0547475 | + | 0.0547475i | ||||
\(233\) | 9.49778 | − | 9.49778i | 0.622220 | − | 0.622220i | −0.323878 | − | 0.946099i | \(-0.604987\pi\) |
0.946099 | + | 0.323878i | \(0.104987\pi\) | |||||||
\(234\) | − | 9.19572i | − | 0.601143i | ||||||
\(235\) | −17.0755 | − | 9.52070i | −1.11388 | − | 0.621062i | ||||
\(236\) | 13.6400 | 0.887887 | ||||||||
\(237\) | 1.65584 | + | 1.65584i | 0.107558 | + | 0.107558i | ||||
\(238\) | 8.95785 | − | 8.95785i | 0.580651 | − | 0.580651i | ||||
\(239\) | −17.5243 | −1.13355 | −0.566776 | − | 0.823872i | \(-0.691809\pi\) | ||||
−0.566776 | + | 0.823872i | \(0.691809\pi\) | |||||||
\(240\) | 1.30153 | − | 2.33431i | 0.0840136 | − | 0.150679i | ||||
\(241\) | 9.77939i | 0.629946i | 0.949101 | + | 0.314973i | \(0.101995\pi\) | ||||
−0.949101 | + | 0.314973i | \(0.898005\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.85164 | − | 4.85164i | −0.311233 | − | 0.311233i | ||||
\(244\) | −19.2824 | −1.23443 | ||||||||
\(245\) | 30.3416 | − | 8.61867i | 1.93845 | − | 0.550627i | ||||
\(246\) | −3.21717 | −0.205119 | ||||||||
\(247\) | −4.19486 | + | 4.19486i | −0.266912 | + | 0.266912i | ||||
\(248\) | 2.13220 | − | 2.13220i | 0.135395 | − | 0.135395i | ||||
\(249\) | 1.71900 | 0.108937 | ||||||||
\(250\) | −0.960342 | − | 21.3759i | −0.0607374 | − | 1.35193i | ||||
\(251\) | 18.2959 | 1.15483 | 0.577413 | − | 0.816452i | \(-0.304062\pi\) | ||||
0.577413 | + | 0.816452i | \(0.304062\pi\) | |||||||
\(252\) | −15.8341 | − | 15.8341i | −0.997452 | − | 0.997452i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 19.4756i | 1.22201i | ||||||||
\(255\) | −0.812212 | + | 0.230713i | −0.0508627 | + | 0.0144478i | ||||
\(256\) | 19.9670 | 1.24793 | ||||||||
\(257\) | 4.58204 | − | 4.58204i | 0.285820 | − | 0.285820i | −0.549605 | − | 0.835425i | \(-0.685222\pi\) |
0.835425 | + | 0.549605i | \(0.185222\pi\) | |||||||
\(258\) | 2.27759 | + | 2.27759i | 0.141796 | + | 0.141796i | ||||
\(259\) | 47.5660 | 2.95561 | ||||||||
\(260\) | −2.96796 | + | 5.32306i | −0.184065 | + | 0.330122i | ||||
\(261\) | − | 5.35673i | − | 0.331573i | ||||||
\(262\) | −9.54263 | + | 9.54263i | −0.589546 | + | 0.589546i | ||||
\(263\) | 3.11501 | − | 3.11501i | 0.192080 | − | 0.192080i | −0.604514 | − | 0.796594i | \(-0.706633\pi\) |
0.796594 | + | 0.604514i | \(0.206633\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.04917 | + | 7.26224i | −0.248739 | + | 0.446116i | ||||
\(266\) | 31.8219i | 1.95112i | ||||||||
\(267\) | −0.452599 | + | 0.452599i | −0.0276986 | + | 0.0276986i | ||||
\(268\) | −2.58974 | − | 2.58974i | −0.158193 | − | 0.158193i | ||||
\(269\) | 7.92951i | 0.483471i | 0.970342 | + | 0.241735i | \(0.0777166\pi\) | ||||
−0.970342 | + | 0.241735i | \(0.922283\pi\) | |||||||
\(270\) | 1.81769 | + | 6.39909i | 0.110621 | + | 0.389436i | ||||
\(271\) | 8.92867i | 0.542378i | 0.962526 | + | 0.271189i | \(0.0874169\pi\) | ||||
−0.962526 | + | 0.271189i | \(0.912583\pi\) | |||||||
\(272\) | −4.64648 | − | 4.64648i | −0.281734 | − | 0.281734i | ||||
\(273\) | 1.39550 | + | 1.39550i | 0.0844593 | + | 0.0844593i | ||||
\(274\) | −22.8065 | −1.37779 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.19240 | −0.131967 | ||||||||
\(277\) | 1.89506 | + | 1.89506i | 0.113863 | + | 0.113863i | 0.761743 | − | 0.647880i | \(-0.224344\pi\) |
−0.647880 | + | 0.761743i | \(0.724344\pi\) | |||||||
\(278\) | 9.27236 | + | 9.27236i | 0.556119 | + | 0.556119i | ||||
\(279\) | 13.6968i | 0.820006i | ||||||||
\(280\) | −1.81145 | − | 6.37710i | −0.108255 | − | 0.381105i | ||||
\(281\) | − | 10.8217i | − | 0.645566i | −0.946473 | − | 0.322783i | \(-0.895382\pi\) | ||
0.946473 | − | 0.322783i | \(-0.104618\pi\) | |||||||
\(282\) | −3.10089 | − | 3.10089i | −0.184655 | − | 0.184655i | ||||
\(283\) | −6.75224 | + | 6.75224i | −0.401379 | + | 0.401379i | −0.878719 | − | 0.477340i | \(-0.841601\pi\) |
0.477340 | + | 0.878719i | \(0.341601\pi\) | |||||||
\(284\) | − | 10.5370i | − | 0.625257i | ||||||
\(285\) | 1.03286 | − | 1.85244i | 0.0611813 | − | 0.109729i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.8367 | + | 20.8367i | −1.22995 | + | 1.22995i | ||||
\(288\) | −15.4167 | + | 15.4167i | −0.908437 | + | 0.908437i | ||||
\(289\) | − | 14.9240i | − | 0.877885i | ||||||
\(290\) | −3.80841 | + | 6.83042i | −0.223638 | + | 0.401096i | ||||
\(291\) | −1.38552 | −0.0812209 | ||||||||
\(292\) | 8.71105 | + | 8.71105i | 0.509776 | + | 0.509776i | ||||
\(293\) | −13.9270 | + | 13.9270i | −0.813626 | + | 0.813626i | −0.985176 | − | 0.171549i | \(-0.945123\pi\) |
0.171549 | + | 0.985176i | \(0.445123\pi\) | |||||||
\(294\) | 7.07514 | 0.412631 | ||||||||
\(295\) | −17.6444 | + | 5.01198i | −1.02730 | + | 0.291809i | ||||
\(296\) | − | 6.68160i | − | 0.388360i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 32.0707 | + | 32.0707i | 1.85781 | + | 1.85781i | ||||
\(299\) | −8.24650 | −0.476907 | ||||||||
\(300\) | 0.500703 | − | 2.12059i | 0.0289081 | − | 0.122432i | ||||
\(301\) | 29.5026 | 1.70050 | ||||||||
\(302\) | −26.1121 | + | 26.1121i | −1.50258 | + | 1.50258i | ||||
\(303\) | −1.71892 | + | 1.71892i | −0.0987491 | + | 0.0987491i | ||||
\(304\) | 16.5062 | 0.946694 | ||||||||
\(305\) | 24.9433 | − | 7.08528i | 1.42825 | − | 0.405702i | ||||
\(306\) | 8.08312 | 0.462081 | ||||||||
\(307\) | 1.56136 | + | 1.56136i | 0.0891113 | + | 0.0891113i | 0.750257 | − | 0.661146i | \(-0.229930\pi\) |
−0.661146 | + | 0.750257i | \(0.729930\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 2.96274i | − | 0.168544i | ||||||
\(310\) | 9.73785 | − | 17.4649i | 0.553073 | − | 0.991942i | ||||
\(311\) | −26.4030 | −1.49717 | −0.748587 | − | 0.663036i | \(-0.769268\pi\) | ||||
−0.748587 | + | 0.663036i | \(0.769268\pi\) | |||||||
\(312\) | 0.196025 | − | 0.196025i | 0.0110977 | − | 0.0110977i | ||||
\(313\) | 11.0666 | + | 11.0666i | 0.625519 | + | 0.625519i | 0.946937 | − | 0.321418i | \(-0.104159\pi\) |
−0.321418 | + | 0.946937i | \(0.604159\pi\) | |||||||
\(314\) | 10.5844 | 0.597312 | ||||||||
\(315\) | 26.3008 | + | 14.6644i | 1.48188 | + | 0.826247i | ||||
\(316\) | 14.8576i | 0.835807i | ||||||||
\(317\) | −12.3960 | + | 12.3960i | −0.696229 | + | 0.696229i | −0.963595 | − | 0.267366i | \(-0.913847\pi\) |
0.267366 | + | 0.963595i | \(0.413847\pi\) | |||||||
\(318\) | −1.31882 | + | 1.31882i | −0.0739555 | + | 0.0739555i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 10.9988 | − | 3.12426i | 0.614850 | − | 0.174651i | ||||
\(321\) | − | 0.990475i | − | 0.0552829i | ||||||
\(322\) | −31.2787 | + | 31.2787i | −1.74309 | + | 1.74309i | ||||
\(323\) | −3.68732 | − | 3.68732i | −0.205168 | − | 0.205168i | ||||
\(324\) | − | 13.9452i | − | 0.774736i | ||||||
\(325\) | 1.88334 | − | 7.97637i | 0.104469 | − | 0.442449i | ||||
\(326\) | 19.2497i | 1.06614i | ||||||||
\(327\) | 0.118088 | + | 0.118088i | 0.00653026 | + | 0.00653026i | ||||
\(328\) | 2.92693 | + | 2.92693i | 0.161613 | + | 0.161613i | ||||
\(329\) | −40.1672 | −2.21449 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.55722 | 0.525312 | 0.262656 | − | 0.964889i | \(-0.415401\pi\) | ||||
0.262656 | + | 0.964889i | \(0.415401\pi\) | |||||||
\(332\) | 7.71217 | + | 7.71217i | 0.423260 | + | 0.423260i | ||||
\(333\) | 21.4606 | + | 21.4606i | 1.17603 | + | 1.17603i | ||||
\(334\) | − | 14.2235i | − | 0.778275i | ||||||
\(335\) | 4.30163 | + | 2.39844i | 0.235023 | + | 0.131041i | ||||
\(336\) | − | 5.49108i | − | 0.299563i | ||||||
\(337\) | 3.40270 | + | 3.40270i | 0.185357 | + | 0.185357i | 0.793685 | − | 0.608329i | \(-0.208160\pi\) |
−0.608329 | + | 0.793685i | \(0.708160\pi\) | |||||||
\(338\) | 13.9568 | − | 13.9568i | 0.759151 | − | 0.759151i | ||||
\(339\) | − | 2.05328i | − | 0.111519i | ||||||
\(340\) | −4.67902 | − | 2.60886i | −0.253755 | − | 0.141485i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −14.3572 | + | 14.3572i | −0.776351 | + | 0.776351i | ||||
\(343\) | 23.0840 | − | 23.0840i | 1.24642 | − | 1.24642i | ||||
\(344\) | − | 4.14423i | − | 0.223442i | ||||||
\(345\) | 2.83605 | − | 0.805594i | 0.152688 | − | 0.0433717i | ||||
\(346\) | −27.9535 | −1.50279 | ||||||||
\(347\) | 0.203586 | + | 0.203586i | 0.0109291 | + | 0.0109291i | 0.712550 | − | 0.701621i | \(-0.247540\pi\) |
−0.701621 | + | 0.712550i | \(0.747540\pi\) | |||||||
\(348\) | −0.563104 | + | 0.563104i | −0.0301856 | + | 0.0301856i | ||||
\(349\) | −3.53891 | −0.189433 | −0.0947166 | − | 0.995504i | \(-0.530195\pi\) | ||||
−0.0947166 | + | 0.995504i | \(0.530195\pi\) | |||||||
\(350\) | −23.1106 | − | 37.3975i | −1.23532 | − | 1.99898i | ||||
\(351\) | 2.54796i | 0.136000i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.3455 | − | 13.3455i | −0.710310 | − | 0.710310i | 0.256290 | − | 0.966600i | \(-0.417500\pi\) |
−0.966600 | + | 0.256290i | \(0.917500\pi\) | |||||||
\(354\) | −4.11438 | −0.218677 | ||||||||
\(355\) | 3.87180 | + | 13.6305i | 0.205494 | + | 0.723431i | ||||
\(356\) | −4.06111 | −0.215238 | ||||||||
\(357\) | −1.22665 | + | 1.22665i | −0.0649214 | + | 0.0649214i | ||||
\(358\) | 12.8166 | − | 12.8166i | 0.677377 | − | 0.677377i | ||||
\(359\) | −27.1869 | −1.43487 | −0.717434 | − | 0.696626i | \(-0.754684\pi\) | ||||
−0.717434 | + | 0.696626i | \(0.754684\pi\) | |||||||
\(360\) | 2.05991 | − | 3.69447i | 0.108567 | − | 0.194716i | ||||
\(361\) | −5.90117 | −0.310588 | ||||||||
\(362\) | 30.0911 | + | 30.0911i | 1.58155 | + | 1.58155i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 12.5216i | 0.656311i | ||||||||
\(365\) | −14.4693 | − | 8.06759i | −0.757358 | − | 0.422277i | ||||
\(366\) | 5.81637 | 0.304026 | ||||||||
\(367\) | −3.80793 | + | 3.80793i | −0.198772 | + | 0.198772i | −0.799473 | − | 0.600701i | \(-0.794888\pi\) |
0.600701 | + | 0.799473i | \(0.294888\pi\) | |||||||
\(368\) | 16.2244 | + | 16.2244i | 0.845756 | + | 0.845756i | ||||
\(369\) | −18.8020 | −0.978794 | ||||||||
\(370\) | −12.1071 | − | 42.6222i | −0.629416 | − | 2.21582i | ||||
\(371\) | 17.0832i | 0.886916i | ||||||||
\(372\) | 1.43982 | − | 1.43982i | 0.0746512 | − | 0.0746512i | ||||
\(373\) | −11.4181 | + | 11.4181i | −0.591209 | + | 0.591209i | −0.937958 | − | 0.346749i | \(-0.887286\pi\) |
0.346749 | + | 0.937958i | \(0.387286\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.131506 | + | 2.92713i | 0.00679092 | + | 0.151156i | ||||
\(376\) | 5.64228i | 0.290979i | ||||||||
\(377\) | −2.11806 | + | 2.11806i | −0.109086 | + | 0.109086i | ||||
\(378\) | 9.66431 | + | 9.66431i | 0.497079 | + | 0.497079i | ||||
\(379\) | − | 11.7389i | − | 0.602985i | −0.953469 | − | 0.301492i | \(-0.902515\pi\) | ||
0.953469 | − | 0.301492i | \(-0.0974848\pi\) | |||||||
\(380\) | 12.9447 | − | 3.67701i | 0.664051 | − | 0.188627i | ||||
\(381\) | − | 2.66691i | − | 0.136630i | ||||||
\(382\) | −16.4710 | − | 16.4710i | −0.842730 | − | 0.842730i | ||||
\(383\) | −7.21018 | − | 7.21018i | −0.368423 | − | 0.368423i | 0.498479 | − | 0.866902i | \(-0.333892\pi\) |
−0.866902 | + | 0.498479i | \(0.833892\pi\) | |||||||
\(384\) | −1.33378 | −0.0680642 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.0416 | −0.969190 | ||||||||
\(387\) | 13.3108 | + | 13.3108i | 0.676628 | + | 0.676628i | ||||
\(388\) | −6.21607 | − | 6.21607i | −0.315573 | − | 0.315573i | ||||
\(389\) | − | 5.02321i | − | 0.254687i | −0.991859 | − | 0.127343i | \(-0.959355\pi\) | ||
0.991859 | − | 0.127343i | \(-0.0406451\pi\) | |||||||
\(390\) | 0.895257 | − | 1.60565i | 0.0453331 | − | 0.0813054i | ||||
\(391\) | − | 7.24875i | − | 0.366585i | ||||||
\(392\) | −6.43686 | − | 6.43686i | −0.325110 | − | 0.325110i | ||||
\(393\) | 1.30673 | − | 1.30673i | 0.0659159 | − | 0.0659159i | ||||
\(394\) | 24.2981i | 1.22412i | ||||||||
\(395\) | −5.45940 | − | 19.2195i | −0.274692 | − | 0.967039i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.31638 | − | 9.31638i | 0.467576 | − | 0.467576i | −0.433553 | − | 0.901128i | \(-0.642740\pi\) |
0.901128 | + | 0.433553i | \(0.142740\pi\) | |||||||
\(398\) | −17.5239 | + | 17.5239i | −0.878393 | + | 0.878393i | ||||
\(399\) | − | 4.35757i | − | 0.218151i | ||||||
\(400\) | −19.3983 | + | 11.9876i | −0.969915 | + | 0.599380i | ||||
\(401\) | 17.6228 | 0.880043 | 0.440021 | − | 0.897987i | \(-0.354971\pi\) | ||||
0.440021 | + | 0.897987i | \(0.354971\pi\) | |||||||
\(402\) | 0.781171 | + | 0.781171i | 0.0389613 | + | 0.0389613i | ||||
\(403\) | 5.41573 | − | 5.41573i | 0.269777 | − | 0.269777i | ||||
\(404\) | −15.4236 | −0.767354 | ||||||||
\(405\) | 5.12415 | + | 18.0393i | 0.254621 | + | 0.896379i | ||||
\(406\) | 16.0674i | 0.797414i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0.172308 | + | 0.172308i | 0.00853051 | + | 0.00853051i | ||||
\(409\) | −35.3545 | −1.74817 | −0.874083 | − | 0.485776i | \(-0.838537\pi\) | ||||
−0.874083 | + | 0.485776i | \(0.838537\pi\) | |||||||
\(410\) | 23.9746 | + | 13.3674i | 1.18402 | + | 0.660171i | ||||
\(411\) | 3.12303 | 0.154048 | ||||||||
\(412\) | 13.2922 | − | 13.2922i | 0.654857 | − | 0.654857i | ||||
\(413\) | −26.6477 | + | 26.6477i | −1.31125 | + | 1.31125i | ||||
\(414\) | −28.2243 | −1.38715 | ||||||||
\(415\) | −12.8101 | − | 7.14249i | −0.628824 | − | 0.350611i | ||||
\(416\) | 12.1916 | 0.597741 | ||||||||
\(417\) | −1.26972 | − | 1.26972i | −0.0621785 | − | 0.0621785i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 26.7217i | − | 1.30544i | −0.757600 | − | 0.652719i | \(-0.773628\pi\) | ||
0.757600 | − | 0.652719i | \(-0.226372\pi\) | |||||||
\(420\) | −1.22323 | − | 4.30630i | −0.0596873 | − | 0.210126i | ||||
\(421\) | −22.8259 | −1.11247 | −0.556234 | − | 0.831026i | \(-0.687754\pi\) | ||||
−0.556234 | + | 0.831026i | \(0.687754\pi\) | |||||||
\(422\) | −5.36140 | + | 5.36140i | −0.260989 | + | 0.260989i | ||||
\(423\) | −18.1224 | − | 18.1224i | −0.881143 | − | 0.881143i | ||||
\(424\) | 2.39968 | 0.116539 | ||||||||
\(425\) | 7.01130 | + | 1.65547i | 0.340098 | + | 0.0803023i | ||||
\(426\) | 3.17840i | 0.153994i | ||||||||
\(427\) | 37.6710 | − | 37.6710i | 1.82303 | − | 1.82303i | ||||
\(428\) | 4.44370 | − | 4.44370i | 0.214795 | − | 0.214795i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7.50935 | − | 26.4362i | −0.362133 | − | 1.27487i | ||||
\(431\) | − | 38.3713i | − | 1.84828i | −0.382052 | − | 0.924141i | \(-0.624782\pi\) | ||
0.382052 | − | 0.924141i | \(-0.375218\pi\) | |||||||
\(432\) | 5.01293 | − | 5.01293i | 0.241185 | − | 0.241185i | ||||
\(433\) | 26.0799 | + | 26.0799i | 1.25332 | + | 1.25332i | 0.954224 | + | 0.299094i | \(0.0966845\pi\) |
0.299094 | + | 0.954224i | \(0.403316\pi\) | |||||||
\(434\) | − | 41.0834i | − | 1.97206i | ||||||
\(435\) | 0.521509 | − | 0.935332i | 0.0250045 | − | 0.0448457i | ||||
\(436\) | 1.05958i | 0.0507449i | ||||||||
\(437\) | 12.8752 | + | 12.8752i | 0.615906 | + | 0.615906i | ||||
\(438\) | −2.62761 | − | 2.62761i | −0.125552 | − | 0.125552i | ||||
\(439\) | 23.4271 | 1.11812 | 0.559058 | − | 0.829128i | \(-0.311163\pi\) | ||||
0.559058 | + | 0.829128i | \(0.311163\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41.3491 | 1.96900 | ||||||||
\(442\) | −3.19608 | − | 3.19608i | −0.152022 | − | 0.152022i | ||||
\(443\) | 6.47833 | + | 6.47833i | 0.307795 | + | 0.307795i | 0.844054 | − | 0.536259i | \(-0.180163\pi\) |
−0.536259 | + | 0.844054i | \(0.680163\pi\) | |||||||
\(444\) | − | 4.51192i | − | 0.214126i | ||||||
\(445\) | 5.25337 | − | 1.49225i | 0.249034 | − | 0.0707392i | ||||
\(446\) | 2.74587i | 0.130020i | ||||||||
\(447\) | −4.39164 | − | 4.39164i | −0.207717 | − | 0.207717i | ||||
\(448\) | 16.6110 | − | 16.6110i | 0.784798 | − | 0.784798i | ||||
\(449\) | 6.57306i | 0.310202i | 0.987899 | + | 0.155101i | \(0.0495703\pi\) | ||||
−0.987899 | + | 0.155101i | \(0.950430\pi\) | |||||||
\(450\) | 6.44589 | − | 27.2998i | 0.303862 | − | 1.28692i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 9.21191 | − | 9.21191i | 0.433292 | − | 0.433292i | ||||
\(453\) | 3.57570 | − | 3.57570i | 0.168001 | − | 0.168001i | ||||
\(454\) | − | 21.6273i | − | 1.01502i | ||||||
\(455\) | −4.60104 | − | 16.1977i | −0.215700 | − | 0.759360i | ||||
\(456\) | −0.612107 | −0.0286645 | ||||||||
\(457\) | −7.30639 | − | 7.30639i | −0.341779 | − | 0.341779i | 0.515257 | − | 0.857036i | \(-0.327696\pi\) |
−0.857036 | + | 0.515257i | \(0.827696\pi\) | |||||||
\(458\) | −0.878851 | + | 0.878851i | −0.0410660 | + | 0.0410660i | ||||
\(459\) | −2.23968 | −0.104539 | ||||||||
\(460\) | 16.3380 | + | 9.10952i | 0.761764 | + | 0.424733i | ||||
\(461\) | 8.34786i | 0.388799i | 0.980922 | + | 0.194399i | \(0.0622758\pi\) | ||||
−0.980922 | + | 0.194399i | \(0.937724\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.9521 | + | 22.9521i | 1.06668 | + | 1.06668i | 0.997612 | + | 0.0690646i | \(0.0220015\pi\) |
0.0690646 | + | 0.997612i | \(0.477999\pi\) | |||||||
\(464\) | 8.33427 | 0.386909 | ||||||||
\(465\) | −1.33346 | + | 2.39158i | −0.0618379 | + | 0.110907i | ||||
\(466\) | −25.7066 | −1.19083 | ||||||||
\(467\) | 29.7048 | − | 29.7048i | 1.37457 | − | 1.37457i | 0.521047 | − | 0.853528i | \(-0.325542\pi\) |
0.853528 | − | 0.521047i | \(-0.174458\pi\) | |||||||
\(468\) | −5.64944 | + | 5.64944i | −0.261146 | + | 0.261146i | ||||
\(469\) | 10.1189 | 0.467246 | ||||||||
\(470\) | 10.2238 | + | 35.9924i | 0.471590 | + | 1.66021i | ||||
\(471\) | −1.44939 | −0.0667842 | ||||||||
\(472\) | 3.74320 | + | 3.74320i | 0.172295 | + | 0.172295i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − | 4.48167i | − | 0.205850i | ||||||
\(475\) | −15.3939 | + | 9.51302i | −0.706322 | + | 0.436487i | ||||
\(476\) | −11.0066 | −0.504487 | ||||||||
\(477\) | −7.70752 | + | 7.70752i | −0.352903 | + | 0.352903i | ||||
\(478\) | 23.7155 | + | 23.7155i | 1.08472 | + | 1.08472i | ||||
\(479\) | 7.45917 | 0.340818 | 0.170409 | − | 0.985373i | \(-0.445491\pi\) | ||||
0.170409 | + | 0.985373i | \(0.445491\pi\) | |||||||
\(480\) | −4.19279 | + | 1.19098i | −0.191374 | + | 0.0543607i | ||||
\(481\) | − | 16.9711i | − | 0.773816i | ||||||
\(482\) | 13.2344 | − | 13.2344i | 0.602810 | − | 0.602810i | ||||
\(483\) | 4.28318 | − | 4.28318i | 0.194892 | − | 0.194892i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.3251 | + | 5.75690i | 0.468837 | + | 0.261408i | ||||
\(486\) | 13.1314i | 0.595652i | ||||||||
\(487\) | 5.83970 | − | 5.83970i | 0.264622 | − | 0.264622i | −0.562307 | − | 0.826929i | \(-0.690086\pi\) |
0.826929 | + | 0.562307i | \(0.190086\pi\) | |||||||
\(488\) | −5.29164 | − | 5.29164i | −0.239541 | − | 0.239541i | ||||
\(489\) | − | 2.63598i | − | 0.119203i | ||||||
\(490\) | −52.7246 | − | 29.3975i | −2.38186 | − | 1.32804i | ||||
\(491\) | − | 6.69275i | − | 0.302039i | −0.988531 | − | 0.151020i | \(-0.951744\pi\) | ||
0.988531 | − | 0.151020i | \(-0.0482557\pi\) | |||||||
\(492\) | 1.97648 | + | 1.97648i | 0.0891068 | + | 0.0891068i | ||||
\(493\) | −1.86179 | − | 1.86179i | −0.0838509 | − | 0.0838509i | ||||
\(494\) | 11.3537 | 0.510829 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.3102 | −0.956854 | ||||||||
\(497\) | 20.5856 | + | 20.5856i | 0.923391 | + | 0.923391i | ||||
\(498\) | −2.32631 | − | 2.32631i | −0.104244 | − | 0.104244i | ||||
\(499\) | − | 26.3873i | − | 1.18126i | −0.806944 | − | 0.590628i | \(-0.798880\pi\) | ||
0.806944 | − | 0.590628i | \(-0.201120\pi\) | |||||||
\(500\) | −12.5424 | + | 13.7224i | −0.560913 | + | 0.613684i | ||||
\(501\) | 1.94771i | 0.0870173i | ||||||||
\(502\) | −24.7597 | − | 24.7597i | −1.10508 | − | 1.10508i | ||||
\(503\) | −23.3599 | + | 23.3599i | −1.04157 | + | 1.04157i | −0.0424679 | + | 0.999098i | \(0.513522\pi\) |
−0.999098 | + | 0.0424679i | \(0.986478\pi\) | |||||||
\(504\) | − | 8.69063i | − | 0.387111i | ||||||
\(505\) | 19.9517 | − | 5.66737i | 0.887838 | − | 0.252195i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.91119 | + | 1.91119i | −0.0848790 | + | 0.0848790i | ||||
\(508\) | 11.9649 | − | 11.9649i | 0.530859 | − | 0.530859i | ||||
\(509\) | 26.3558i | 1.16820i | 0.811682 | + | 0.584099i | \(0.198552\pi\) | ||||
−0.811682 | + | 0.584099i | \(0.801448\pi\) | |||||||
\(510\) | 1.41138 | + | 0.786939i | 0.0624971 | + | 0.0348462i | ||||
\(511\) | −34.0366 | −1.50569 | ||||||||
\(512\) | −19.8238 | − | 19.8238i | −0.876095 | − | 0.876095i | ||||
\(513\) | 3.97812 | − | 3.97812i | 0.175638 | − | 0.175638i | ||||
\(514\) | −12.4017 | −0.547015 | ||||||||
\(515\) | −12.3103 | + | 22.0786i | −0.542456 | + | 0.972901i | ||||
\(516\) | − | 2.79850i | − | 0.123197i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −64.3708 | − | 64.3708i | −2.82829 | − | 2.82829i | ||||
\(519\) | 3.82784 | 0.168023 | ||||||||
\(520\) | −2.27529 | + | 0.646307i | −0.0997781 | + | 0.0283425i | ||||
\(521\) | −13.2088 | −0.578687 | −0.289343 | − | 0.957225i | \(-0.593437\pi\) | ||||
−0.289343 | + | 0.957225i | \(0.593437\pi\) | |||||||
\(522\) | −7.24923 | + | 7.24923i | −0.317290 | + | 0.317290i | ||||
\(523\) | −14.9574 | + | 14.9574i | −0.654043 | + | 0.654043i | −0.953964 | − | 0.299921i | \(-0.903040\pi\) |
0.299921 | + | 0.953964i | \(0.403040\pi\) | |||||||
\(524\) | 11.7251 | 0.512215 | ||||||||
\(525\) | 3.16468 | + | 5.12108i | 0.138118 | + | 0.223502i | ||||
\(526\) | −8.43104 | −0.367611 | ||||||||
\(527\) | 4.76048 | + | 4.76048i | 0.207370 | + | 0.207370i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.31090i | 0.100474i | ||||||||
\(530\) | 15.3077 | − | 4.34821i | 0.664922 | − | 0.188874i | ||||
\(531\) | −24.0456 | −1.04349 | ||||||||
\(532\) | 19.5499 | − | 19.5499i | 0.847598 | − | 0.847598i | ||||
\(533\) | 7.43434 | + | 7.43434i | 0.322017 | + | 0.322017i | ||||
\(534\) | 1.22500 | 0.0530108 | ||||||||
\(535\) | −4.11546 | + | 7.38111i | −0.177927 | + | 0.319113i | ||||
\(536\) | − | 1.42140i | − | 0.0613949i | ||||||
\(537\) | −1.75505 | + | 1.75505i | −0.0757361 | + | 0.0757361i | ||||
\(538\) | 10.7309 | − | 10.7309i | 0.462644 | − | 0.462644i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.81461 | − | 5.04803i | 0.121121 | − | 0.217232i | ||||
\(541\) | 11.4552i | 0.492496i | 0.969207 | + | 0.246248i | \(0.0791978\pi\) | ||||
−0.969207 | + | 0.246248i | \(0.920802\pi\) | |||||||
\(542\) | 12.0831 | − | 12.0831i | 0.519014 | − | 0.519014i | ||||
\(543\) | −4.12056 | − | 4.12056i | −0.176830 | − | 0.176830i | ||||
\(544\) | 10.7165i | 0.459466i | ||||||||
\(545\) | −0.389342 | − | 1.37066i | −0.0166776 | − | 0.0587125i | ||||
\(546\) | − | 3.77703i | − | 0.161642i | ||||||
\(547\) | 9.94911 | + | 9.94911i | 0.425393 | + | 0.425393i | 0.887056 | − | 0.461662i | \(-0.152747\pi\) |
−0.461662 | + | 0.887056i | \(0.652747\pi\) | |||||||
\(548\) | 14.0113 | + | 14.0113i | 0.598532 | + | 0.598532i | ||||
\(549\) | 33.9924 | 1.45076 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.61383 | 0.281759 | ||||||||
\(552\) | −0.601658 | − | 0.601658i | −0.0256083 | − | 0.0256083i | ||||
\(553\) | −29.0266 | − | 29.0266i | −1.23433 | − | 1.23433i | ||||
\(554\) | − | 5.12915i | − | 0.217917i | ||||||
\(555\) | 1.65789 | + | 5.83653i | 0.0703737 | + | 0.247747i | ||||
\(556\) | − | 11.3931i | − | 0.483173i | ||||||
\(557\) | 28.3861 | + | 28.3861i | 1.20276 | + | 1.20276i | 0.973324 | + | 0.229436i | \(0.0736881\pi\) |
0.229436 | + | 0.973324i | \(0.426312\pi\) | |||||||
\(558\) | 18.5358 | − | 18.5358i | 0.784683 | − | 0.784683i | ||||
\(559\) | − | 10.5263i | − | 0.445213i | ||||||
\(560\) | −22.8156 | + | 40.9201i | −0.964137 | + | 1.72919i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.6449 | + | 14.6449i | −0.617757 | + | 0.617757i | ||||
\(563\) | −9.19549 | + | 9.19549i | −0.387544 | + | 0.387544i | −0.873810 | − | 0.486267i | \(-0.838358\pi\) |
0.486267 | + | 0.873810i | \(0.338358\pi\) | |||||||
\(564\) | 3.81010i | 0.160434i | ||||||||
\(565\) | −8.53145 | + | 15.3012i | −0.358921 | + | 0.643728i | ||||
\(566\) | 18.2755 | 0.768177 | ||||||||
\(567\) | 27.2441 | + | 27.2441i | 1.14414 | + | 1.14414i | ||||
\(568\) | 2.89166 | − | 2.89166i | 0.121331 | − | 0.121331i | ||||
\(569\) | −22.0321 | −0.923636 | −0.461818 | − | 0.886975i | \(-0.652803\pi\) | ||||
−0.461818 | + | 0.886975i | \(0.652803\pi\) | |||||||
\(570\) | −3.90466 | + | 1.10914i | −0.163548 | + | 0.0464567i | ||||
\(571\) | − | 32.3912i | − | 1.35553i | −0.735279 | − | 0.677765i | \(-0.762949\pi\) | ||
0.735279 | − | 0.677765i | \(-0.237051\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.25548 | + | 2.25548i | 0.0942239 | + | 0.0942239i | ||||
\(574\) | 56.3964 | 2.35394 | ||||||||
\(575\) | −24.4818 | − | 5.78052i | −1.02096 | − | 0.241064i | ||||
\(576\) | 14.9890 | 0.624541 | ||||||||
\(577\) | −0.0644216 | + | 0.0644216i | −0.00268191 | + | 0.00268191i | −0.708446 | − | 0.705765i | \(-0.750604\pi\) |
0.705765 | + | 0.708446i | \(0.250604\pi\) | |||||||
\(578\) | −20.1966 | + | 20.1966i | −0.840068 | + | 0.840068i | ||||
\(579\) | 2.60748 | 0.108363 | ||||||||
\(580\) | 6.53603 | − | 1.85659i | 0.271394 | − | 0.0770907i | ||||
\(581\) | −30.1337 | −1.25016 | ||||||||
\(582\) | 1.87502 | + | 1.87502i | 0.0777222 | + | 0.0777222i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 4.78112i | 0.197844i | ||||||||
\(585\) | 5.23213 | − | 9.38388i | 0.216322 | − | 0.387976i | ||||
\(586\) | 37.6947 | 1.55716 | ||||||||
\(587\) | 28.5239 | − | 28.5239i | 1.17731 | − | 1.17731i | 0.196880 | − | 0.980428i | \(-0.436919\pi\) |
0.980428 | − | 0.196880i | \(-0.0630810\pi\) | |||||||
\(588\) | −4.34665 | − | 4.34665i | −0.179253 | − | 0.179253i | ||||
\(589\) | −16.9111 | −0.696811 | ||||||||
\(590\) | 30.6607 | + | 17.0954i | 1.26228 | + | 0.703806i | ||||
\(591\) | − | 3.32728i | − | 0.136866i | ||||||
\(592\) | −33.3895 | + | 33.3895i | −1.37230 | + | 1.37230i | ||||
\(593\) | −9.79960 | + | 9.79960i | −0.402421 | + | 0.402421i | −0.879086 | − | 0.476664i | \(-0.841846\pi\) |
0.476664 | + | 0.879086i | \(0.341846\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.2379 | − | 4.04435i | 0.583698 | − | 0.165802i | ||||
\(596\) | − | 39.4056i | − | 1.61412i | ||||||
\(597\) | 2.39965 | − | 2.39965i | 0.0982113 | − | 0.0982113i | ||||
\(598\) | 11.1599 | + | 11.1599i | 0.456364 | + | 0.456364i | ||||
\(599\) | 7.54664i | 0.308347i | 0.988044 | + | 0.154174i | \(0.0492715\pi\) | ||||
−0.988044 | + | 0.154174i | \(0.950728\pi\) | |||||||
\(600\) | 0.719357 | − | 0.444542i | 0.0293676 | − | 0.0181484i | ||||
\(601\) | 25.7652i | 1.05098i | 0.850799 | + | 0.525492i | \(0.176119\pi\) | ||||
−0.850799 | + | 0.525492i | \(0.823881\pi\) | |||||||
\(602\) | −39.9257 | − | 39.9257i | −1.62725 | − | 1.62725i | ||||
\(603\) | 4.56538 | + | 4.56538i | 0.185917 | + | 0.185917i | ||||
\(604\) | 32.0843 | 1.30549 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.65240 | 0.188991 | ||||||||
\(607\) | −26.4373 | − | 26.4373i | −1.07306 | − | 1.07306i | −0.997112 | − | 0.0759443i | \(-0.975803\pi\) |
−0.0759443 | − | 0.997112i | \(-0.524197\pi\) | |||||||
\(608\) | −19.0346 | − | 19.0346i | −0.771956 | − | 0.771956i | ||||
\(609\) | − | 2.20021i | − | 0.0891572i | ||||||
\(610\) | −43.3441 | − | 24.1672i | −1.75495 | − | 0.978502i | ||||
\(611\) | 14.3313i | 0.579782i | ||||||||
\(612\) | −4.96591 | − | 4.96591i | −0.200735 | − | 0.200735i | ||||
\(613\) | 28.4964 | − | 28.4964i | 1.15096 | − | 1.15096i | 0.164597 | − | 0.986361i | \(-0.447368\pi\) |
0.986361 | − | 0.164597i | \(-0.0526324\pi\) | |||||||
\(614\) | − | 4.22595i | − | 0.170545i | ||||||
\(615\) | −3.28300 | − | 1.83049i | −0.132383 | − | 0.0738123i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.0423 | − | 19.0423i | 0.766612 | − | 0.766612i | −0.210896 | − | 0.977508i | \(-0.567638\pi\) |
0.977508 | + | 0.210896i | \(0.0676382\pi\) | |||||||
\(618\) | −4.00946 | + | 4.00946i | −0.161284 | + | 0.161284i | ||||
\(619\) | − | 22.9592i | − | 0.922808i | −0.887190 | − | 0.461404i | \(-0.847346\pi\) | ||
0.887190 | − | 0.461404i | \(-0.152654\pi\) | |||||||
\(620\) | −16.7122 | + | 4.74718i | −0.671177 | + | 0.190651i | ||||
\(621\) | 7.82042 | 0.313823 | ||||||||
\(622\) | 35.7310 | + | 35.7310i | 1.43268 | + | 1.43268i | ||||
\(623\) | 7.93397 | − | 7.93397i | 0.317868 | − | 0.317868i | ||||
\(624\) | −1.95917 | −0.0784294 | ||||||||
\(625\) | 11.1823 | − | 22.3597i | 0.447294 | − | 0.894387i | ||||
\(626\) | − | 29.9526i | − | 1.19715i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.50259 | − | 6.50259i | −0.259481 | − | 0.259481i | ||||
\(629\) | 14.9178 | 0.594810 | ||||||||
\(630\) | −15.7474 | − | 55.4380i | −0.627393 | − | 2.20870i | ||||
\(631\) | 12.3237 | 0.490597 | 0.245299 | − | 0.969448i | \(-0.421114\pi\) | ||||
0.245299 | + | 0.969448i | \(0.421114\pi\) | |||||||
\(632\) | −4.07736 | + | 4.07736i | −0.162189 | + | 0.162189i | ||||
\(633\) | 0.734169 | − | 0.734169i | 0.0291806 | − | 0.0291806i | ||||
\(634\) | 33.5509 | 1.33247 | ||||||||
\(635\) | −11.0811 | + | 19.8741i | −0.439741 | + | 0.788680i | ||||
\(636\) | 1.62044 | 0.0642547 | ||||||||
\(637\) | −16.3495 | − | 16.3495i | −0.647790 | − | 0.647790i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.5754i | 0.734833i | ||||||||
\(640\) | 9.93946 | + | 5.54190i | 0.392892 | + | 0.219063i | ||||
\(641\) | 38.3865 | 1.51617 | 0.758087 | − | 0.652153i | \(-0.226134\pi\) | ||||
0.758087 | + | 0.652153i | \(0.226134\pi\) | |||||||
\(642\) | −1.34040 | + | 1.34040i | −0.0529015 | + | 0.0529015i | ||||
\(643\) | 14.4812 | + | 14.4812i | 0.571082 | + | 0.571082i | 0.932431 | − | 0.361349i | \(-0.117684\pi\) |
−0.361349 | + | 0.932431i | \(0.617684\pi\) | |||||||
\(644\) | 38.4325 | 1.51445 | ||||||||
\(645\) | 1.02830 | + | 3.62008i | 0.0404893 | + | 0.142540i | ||||
\(646\) | 9.98004i | 0.392659i | ||||||||
\(647\) | −29.4865 | + | 29.4865i | −1.15924 | + | 1.15924i | −0.174595 | + | 0.984640i | \(0.555862\pi\) |
−0.984640 | + | 0.174595i | \(0.944138\pi\) | |||||||
\(648\) | 3.82697 | − | 3.82697i | 0.150338 | − | 0.150338i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −13.3431 | + | 8.24566i | −0.523359 | + | 0.323421i | ||||
\(651\) | 5.62580i | 0.220492i | ||||||||
\(652\) | 11.8262 | − | 11.8262i | 0.463148 | − | 0.463148i | ||||
\(653\) | 2.81677 | + | 2.81677i | 0.110229 | + | 0.110229i | 0.760070 | − | 0.649841i | \(-0.225165\pi\) |
−0.649841 | + | 0.760070i | \(0.725165\pi\) | |||||||
\(654\) | − | 0.319614i | − | 0.0124979i | ||||||
\(655\) | −15.1674 | + | 4.30837i | −0.592639 | + | 0.168342i | ||||
\(656\) | − | 29.2531i | − | 1.14214i | ||||||
\(657\) | −15.3565 | − | 15.3565i | −0.599113 | − | 0.599113i | ||||
\(658\) | 54.3580 | + | 54.3580i | 2.11910 | + | 2.11910i | ||||
\(659\) | −2.49945 | −0.0973648 | −0.0486824 | − | 0.998814i | \(-0.515502\pi\) | ||||
−0.0486824 | + | 0.998814i | \(0.515502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.8188 | −0.848654 | −0.424327 | − | 0.905509i | \(-0.639489\pi\) | ||||
−0.424327 | + | 0.905509i | \(0.639489\pi\) | |||||||
\(662\) | −12.9337 | − | 12.9337i | −0.502684 | − | 0.502684i | ||||
\(663\) | 0.437658 | + | 0.437658i | 0.0169972 | + | 0.0169972i | ||||
\(664\) | 4.23288i | 0.164267i | ||||||||
\(665\) | −18.1058 | + | 32.4730i | −0.702114 | + | 1.25925i | ||||
\(666\) | − | 58.0850i | − | 2.25075i | ||||||
\(667\) | 6.50093 | + | 6.50093i | 0.251717 | + | 0.251717i | ||||
\(668\) | −8.73828 | + | 8.73828i | −0.338094 | + | 0.338094i | ||||
\(669\) | − | 0.376008i | − | 0.0145373i | ||||||
\(670\) | −2.57557 | − | 9.06715i | −0.0995029 | − | 0.350295i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −6.33222 | + | 6.33222i | −0.244271 | + | 0.244271i | ||||
\(673\) | −30.5481 | + | 30.5481i | −1.17754 | + | 1.17754i | −0.197176 | + | 0.980368i | \(0.563177\pi\) |
−0.980368 | + | 0.197176i | \(0.936823\pi\) | |||||||
\(674\) | − | 9.20970i | − | 0.354744i | ||||||
\(675\) | −1.78603 | + | 7.56425i | −0.0687445 | + | 0.291148i | ||||
\(676\) | −17.1489 | −0.659573 | ||||||||
\(677\) | 1.70120 | + | 1.70120i | 0.0653823 | + | 0.0653823i | 0.739042 | − | 0.673660i | \(-0.235279\pi\) |
−0.673660 | + | 0.739042i | \(0.735279\pi\) | |||||||
\(678\) | −2.77869 | + | 2.77869i | −0.106715 | + | 0.106715i | ||||
\(679\) | 24.2880 | 0.932088 | ||||||||
\(680\) | −0.568110 | − | 2.00000i | −0.0217860 | − | 0.0766965i | ||||
\(681\) | 2.96156i | 0.113487i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3.00058 | − | 3.00058i | −0.114814 | − | 0.114814i | 0.647366 | − | 0.762180i | \(-0.275871\pi\) |
−0.762180 | + | 0.647366i | \(0.775871\pi\) | |||||||
\(684\) | 17.6409 | 0.674517 | ||||||||
\(685\) | −23.2731 | − | 12.9763i | −0.889220 | − | 0.495799i | ||||
\(686\) | −62.4789 | −2.38545 | ||||||||
\(687\) | 0.120347 | − | 0.120347i | 0.00459151 | − | 0.00459151i | ||||
\(688\) | −20.7097 | + | 20.7097i | −0.789549 | + | 0.789549i | ||||
\(689\) | 6.09513 | 0.232206 | ||||||||
\(690\) | −4.92821 | − | 2.74780i | −0.187614 | − | 0.104607i | ||||
\(691\) | −20.2736 | −0.771245 | −0.385623 | − | 0.922657i | \(-0.626013\pi\) | ||||
−0.385623 | + | 0.922657i | \(0.626013\pi\) | |||||||
\(692\) | 17.1734 | + | 17.1734i | 0.652833 | + | 0.652833i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 0.551024i | − | 0.0209166i | ||||||
\(695\) | 4.18635 | + | 14.7378i | 0.158797 | + | 0.559038i | ||||
\(696\) | −0.309064 | −0.0117150 | ||||||||
\(697\) | −6.53485 | + | 6.53485i | −0.247525 | + | 0.247525i | ||||
\(698\) | 4.78918 | + | 4.78918i | 0.181273 | + | 0.181273i | ||||
\(699\) | 3.52016 | 0.133145 | ||||||||
\(700\) | −8.77724 | + | 37.1735i | −0.331748 | + | 1.40503i | ||||
\(701\) | 38.2663i | 1.44530i | 0.691216 | + | 0.722648i | \(0.257075\pi\) | ||||
−0.691216 | + | 0.722648i | \(0.742925\pi\) | |||||||
\(702\) | 3.44813 | − | 3.44813i | 0.130141 | − | 0.130141i | ||||
\(703\) | −26.4969 | + | 26.4969i | −0.999350 | + | 0.999350i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.40001 | − | 4.92866i | −0.0527275 | − | 0.185624i | ||||
\(706\) | 36.1208i | 1.35942i | ||||||||
\(707\) | 30.1323 | − | 30.1323i | 1.13324 | − | 1.13324i | ||||
\(708\) | 2.52769 | + | 2.52769i | 0.0949964 | + | 0.0949964i | ||||
\(709\) | 34.9914i | 1.31413i | 0.753835 | + | 0.657064i | \(0.228202\pi\) | ||||
−0.753835 | + | 0.657064i | \(0.771798\pi\) | |||||||
\(710\) | 13.2063 | − | 23.6857i | 0.495625 | − | 0.888909i | ||||
\(711\) | − | 26.1921i | − | 0.982281i | ||||||
\(712\) | −1.11448 | − | 1.11448i | −0.0417671 | − | 0.0417671i | ||||
\(713\) | −16.6225 | − | 16.6225i | −0.622516 | − | 0.622516i | ||||
\(714\) | 3.32004 | 0.124250 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.7479 | −0.588525 | ||||||||
\(717\) | −3.24751 | − | 3.24751i | −0.121280 | − | 0.121280i | ||||
\(718\) | 36.7918 | + | 36.7918i | 1.37306 | + | 1.37306i | ||||
\(719\) | − | 44.2202i | − | 1.64914i | −0.565763 | − | 0.824568i | \(-0.691418\pi\) | ||
0.565763 | − | 0.824568i | \(-0.308582\pi\) | |||||||
\(720\) | −28.7560 | + | 8.16827i | −1.07167 | + | 0.304414i | ||||
\(721\) | 51.9363i | 1.93421i | ||||||||
\(722\) | 7.98602 | + | 7.98602i | 0.297209 | + | 0.297209i | ||||
\(723\) | −1.81227 | + | 1.81227i | −0.0673989 | + | 0.0673989i | ||||
\(724\) | − | 36.9733i | − | 1.37410i | ||||||
\(725\) | −7.77267 | + | 4.80330i | −0.288670 | + | 0.178390i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.8123 | − | 17.8123i | 0.660620 | − | 0.660620i | −0.294906 | − | 0.955526i | \(-0.595288\pi\) |
0.955526 | + | 0.294906i | \(0.0952883\pi\) | |||||||
\(728\) | −3.43629 | + | 3.43629i | −0.127357 | + | 0.127357i | ||||
\(729\) | 23.3615i | 0.865242i | ||||||||
\(730\) | 8.66339 | + | 30.4990i | 0.320647 | + | 1.12882i | ||||
\(731\) | 9.25267 | 0.342222 | ||||||||
\(732\) | −3.57332 | − | 3.57332i | −0.132074 | − | 0.132074i | ||||
\(733\) | 5.23876 | − | 5.23876i | 0.193498 | − | 0.193498i | −0.603708 | − | 0.797206i | \(-0.706311\pi\) |
0.797206 | + | 0.603708i | \(0.206311\pi\) | |||||||
\(734\) | 10.3065 | 0.380419 | ||||||||
\(735\) | 7.21991 | + | 4.02557i | 0.266310 | + | 0.148486i | ||||
\(736\) | − | 37.4194i | − | 1.37930i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 25.4446 | + | 25.4446i | 0.936630 | + | 0.936630i | ||||
\(739\) | 51.5933 | 1.89789 | 0.948945 | − | 0.315442i | \(-0.102153\pi\) | ||||
0.948945 | + | 0.315442i | \(0.102153\pi\) | |||||||
\(740\) | −18.7472 | + | 33.6232i | −0.689160 | + | 1.23602i | ||||
\(741\) | −1.55474 | −0.0571147 | ||||||||
\(742\) | 23.1186 | − | 23.1186i | 0.848710 | − | 0.848710i | ||||
\(743\) | 13.6160 | − | 13.6160i | 0.499522 | − | 0.499522i | −0.411767 | − | 0.911289i | \(-0.635088\pi\) |
0.911289 | + | 0.411767i | \(0.135088\pi\) | |||||||
\(744\) | 0.790255 | 0.0289722 | ||||||||
\(745\) | 14.4795 | + | 50.9743i | 0.530488 | + | 1.86755i | ||||
\(746\) | 30.9042 | 1.13148 | ||||||||
\(747\) | −13.5956 | − | 13.5956i | −0.497436 | − | 0.497436i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.3628i | 0.634425i | ||||||||
\(750\) | 3.78330 | − | 4.13923i | 0.138147 | − | 0.151143i | ||||
\(751\) | 37.9642 | 1.38533 | 0.692667 | − | 0.721258i | \(-0.256436\pi\) | ||||
0.692667 | + | 0.721258i | \(0.256436\pi\) | |||||||
\(752\) | 28.1958 | − | 28.1958i | 1.02819 | − | 1.02819i | ||||
\(753\) | 3.39050 | + | 3.39050i | 0.123557 | + | 0.123557i | ||||
\(754\) | 5.73271 | 0.208773 | ||||||||
\(755\) | −41.5036 | + | 11.7893i | −1.51047 | + | 0.429056i | ||||
\(756\) | − | 11.8746i | − | 0.431877i | ||||||
\(757\) | 27.6372 | − | 27.6372i | 1.00449 | − | 1.00449i | 0.00450211 | − | 0.999990i | \(-0.498567\pi\) |
0.999990 | − | 0.00450211i | \(-0.00143307\pi\) | |||||||
\(758\) | −15.8861 | + | 15.8861i | −0.577010 | + | 0.577010i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.56148 | + | 2.54332i | 0.165462 | + | 0.0922561i | ||||
\(761\) | − | 41.9724i | − | 1.52150i | −0.649045 | − | 0.760750i | \(-0.724831\pi\) | ||
0.649045 | − | 0.760750i | \(-0.275169\pi\) | |||||||
\(762\) | −3.60912 | + | 3.60912i | −0.130745 | + | 0.130745i | ||||
\(763\) | −2.07005 | − | 2.07005i | −0.0749410 | − | 0.0749410i | ||||
\(764\) | 20.2381i | 0.732189i | ||||||||
\(765\) | 8.24851 | + | 4.59909i | 0.298225 | + | 0.166280i | ||||
\(766\) | 19.5150i | 0.705105i | ||||||||
\(767\) | 9.50765 | + | 9.50765i | 0.343301 | + | 0.343301i | ||||
\(768\) | 3.70017 | + | 3.70017i | 0.133518 | + | 0.133518i | ||||
\(769\) | 22.2634 | 0.802840 | 0.401420 | − | 0.915894i | \(-0.368517\pi\) | ||||
0.401420 | + | 0.915894i | \(0.368517\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.69824 | 0.0611606 | ||||||||
\(772\) | 11.6983 | + | 11.6983i | 0.421031 | + | 0.421031i | ||||
\(773\) | −25.8022 | − | 25.8022i | −0.928041 | − | 0.928041i | 0.0695381 | − | 0.997579i | \(-0.477847\pi\) |
−0.997579 | + | 0.0695381i | \(0.977847\pi\) | |||||||
\(774\) | − | 36.0270i | − | 1.29496i | ||||||
\(775\) | 19.8742 | − | 12.2817i | 0.713902 | − | 0.441172i | ||||
\(776\) | − | 3.41173i | − | 0.122474i | ||||||
\(777\) | 8.81469 | + | 8.81469i | 0.316225 | + | 0.316225i | ||||
\(778\) | −6.79788 | + | 6.79788i | −0.243716 | + | 0.243716i | ||||
\(779\) | − | 23.2144i | − | 0.831743i | ||||||
\(780\) | −1.53645 | + | 0.436436i | −0.0550137 | + | 0.0156269i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −9.80968 | + | 9.80968i | −0.350793 | + | 0.350793i | ||||
\(783\) | 2.00862 | − | 2.00862i | 0.0717823 | − | 0.0717823i | ||||
\(784\) | 64.3329i | 2.29760i | ||||||||
\(785\) | 10.8010 | + | 6.02225i | 0.385503 | + | 0.214943i | ||||
\(786\) | −3.53678 | −0.126153 | ||||||||
\(787\) | −7.88776 | − | 7.88776i | −0.281168 | − | 0.281168i | 0.552407 | − | 0.833575i | \(-0.313710\pi\) |
−0.833575 | + | 0.552407i | \(0.813710\pi\) | |||||||
\(788\) | 14.9277 | − | 14.9277i | 0.531776 | − | 0.531776i | ||||
\(789\) | 1.15451 | 0.0411018 | ||||||||
\(790\) | −18.6215 | + | 33.3978i | −0.662523 | + | 1.18824i | ||||
\(791\) | 35.9936i | 1.27979i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.4407 | − | 13.4407i | −0.477292 | − | 0.477292i | ||||
\(794\) | −25.2156 | −0.894868 | ||||||||
\(795\) | −2.09617 | + | 0.595428i | −0.0743436 | + | 0.0211176i | ||||
\(796\) | 21.5318 | 0.763174 | ||||||||
\(797\) | 29.4824 | − | 29.4824i | 1.04432 | − | 1.04432i | 0.0453503 | − | 0.998971i | \(-0.485560\pi\) |
0.998971 | − | 0.0453503i | \(-0.0144404\pi\) | |||||||
\(798\) | −5.89707 | + | 5.89707i | −0.208754 | + | 0.208754i | ||||
\(799\) | −12.5973 | −0.445661 | ||||||||
\(800\) | 36.1937 | + | 8.54588i | 1.27964 | + | 0.302142i | ||||
\(801\) | 7.15922 | 0.252959 | ||||||||
\(802\) | −23.8489 | − | 23.8489i | −0.842133 | − | 0.842133i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | − | 0.959834i | − | 0.0338507i | ||||||
\(805\) | −49.7155 | + | 14.1219i | −1.75224 | + | 0.497732i | ||||
\(806\) | −14.6582 | −0.516312 | ||||||||
\(807\) | −1.46946 | + | 1.46946i | −0.0517273 | + | 0.0517273i | ||||
\(808\) | −4.23268 | − | 4.23268i | −0.148905 | − | 0.148905i | ||||
\(809\) | −6.24330 | −0.219503 | −0.109751 | − | 0.993959i | \(-0.535005\pi\) | ||||
−0.109751 | + | 0.993959i | \(0.535005\pi\) | |||||||
\(810\) | 17.4780 | − | 31.3469i | 0.614113 | − | 1.10142i | ||||
\(811\) | − | 19.5621i | − | 0.686919i | −0.939167 | − | 0.343460i | \(-0.888401\pi\) | ||
0.939167 | − | 0.343460i | \(-0.111599\pi\) | |||||||
\(812\) | 9.87112 | − | 9.87112i | 0.346408 | − | 0.346408i | ||||
\(813\) | −1.65462 | + | 1.65462i | −0.0580299 | + | 0.0580299i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.9526 | + | 19.6436i | −0.383652 | + | 0.688085i | ||||
\(816\) | − | 1.72212i | − | 0.0602864i | ||||||
\(817\) | −16.4346 | + | 16.4346i | −0.574974 | + | 0.574974i | ||||
\(818\) | 47.8450 | + | 47.8450i | 1.67286 | + | 1.67286i | ||||
\(819\) | − | 22.0740i | − | 0.771329i | ||||||
\(820\) | −6.51659 | − | 22.9413i | −0.227569 | − | 0.801146i | ||||
\(821\) | − | 23.7758i | − | 0.829780i | −0.909872 | − | 0.414890i | \(-0.863820\pi\) | ||
0.909872 | − | 0.414890i | \(-0.136180\pi\) | |||||||
\(822\) | −4.22637 | − | 4.22637i | −0.147412 | − | 0.147412i | ||||
\(823\) | −18.5280 | − | 18.5280i | −0.645845 | − | 0.645845i | 0.306141 | − | 0.951986i | \(-0.400962\pi\) |
−0.951986 | + | 0.306141i | \(0.900962\pi\) | |||||||
\(824\) | 7.29549 | 0.254150 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 72.1243 | 2.50953 | ||||||||
\(827\) | 9.29143 | + | 9.29143i | 0.323095 | + | 0.323095i | 0.849953 | − | 0.526858i | \(-0.176630\pi\) |
−0.526858 | + | 0.849953i | \(0.676630\pi\) | |||||||
\(828\) | 17.3398 | + | 17.3398i | 0.602599 | + | 0.602599i | ||||
\(829\) | 8.82301i | 0.306436i | 0.988192 | + | 0.153218i | \(0.0489636\pi\) | ||||
−0.988192 | + | 0.153218i | \(0.951036\pi\) | |||||||
\(830\) | 7.66997 | + | 27.0017i | 0.266229 | + | 0.937244i | ||||
\(831\) | 0.702366i | 0.0243648i | ||||||||
\(832\) | −5.92666 | − | 5.92666i | −0.205470 | − | 0.205470i | ||||
\(833\) | 14.3713 | − | 14.3713i | 0.497937 | − | 0.497937i | ||||
\(834\) | 3.43661i | 0.119000i | ||||||||
\(835\) | 8.09280 | − | 14.5145i | 0.280063 | − | 0.502296i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.13591 | + | 5.13591i | −0.177523 | + | 0.177523i | ||||
\(838\) | −36.1623 | + | 36.1623i | −1.24920 | + | 1.24920i | ||||
\(839\) | 18.8218i | 0.649800i | 0.945748 | + | 0.324900i | \(0.105331\pi\) | ||||
−0.945748 | + | 0.324900i | \(0.894669\pi\) | |||||||
\(840\) | 0.846084 | − | 1.51746i | 0.0291927 | − | 0.0523573i | ||||
\(841\) | −25.6606 | −0.884847 | ||||||||
\(842\) | 30.8902 | + | 30.8902i | 1.06455 | + | 1.06455i | ||||
\(843\) | 2.00541 | − | 2.00541i | 0.0690701 | − | 0.0690701i | ||||
\(844\) | 6.58761 | 0.226755 | ||||||||
\(845\) | 22.1835 | − | 6.30132i | 0.763134 | − | 0.216772i | ||||
\(846\) | 49.0500i | 1.68637i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −11.9917 | − | 11.9917i | −0.411798 | − | 0.411798i | ||||
\(849\) | −2.50258 | −0.0858883 | ||||||||
\(850\) | −7.24800 | − | 11.7287i | −0.248604 | − | 0.402291i | ||||
\(851\) | −52.0892 | −1.78560 | ||||||||
\(852\) | 1.95267 | − | 1.95267i | 0.0668972 | − | 0.0668972i | ||||
\(853\) | 22.5284 | − | 22.5284i | 0.771359 | − | 0.771359i | −0.206985 | − | 0.978344i | \(-0.566365\pi\) |
0.978344 | + | 0.206985i | \(0.0663652\pi\) | |||||||
\(854\) | −101.960 | −3.48900 | ||||||||
\(855\) | −22.8199 | + | 6.48211i | −0.780424 | + | 0.221683i | ||||
\(856\) | 2.43896 | 0.0833618 | ||||||||
\(857\) | −0.301113 | − | 0.301113i | −0.0102858 | − | 0.0102858i | 0.701945 | − | 0.712231i | \(-0.252315\pi\) |
−0.712231 | + | 0.701945i | \(0.752315\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1928i | 1.30312i | 0.758596 | + | 0.651561i | \(0.225886\pi\) | ||||
−0.758596 | + | 0.651561i | \(0.774114\pi\) | |||||||
\(860\) | −11.6278 | + | 20.8547i | −0.396506 | + | 0.711138i | ||||
\(861\) | −7.72270 | −0.263189 | ||||||||
\(862\) | −51.9277 | + | 51.9277i | −1.76866 | + | 1.76866i | ||||
\(863\) | −27.1564 | − | 27.1564i | −0.924416 | − | 0.924416i | 0.0729217 | − | 0.997338i | \(-0.476768\pi\) |
−0.997338 | + | 0.0729217i | \(0.976768\pi\) | |||||||
\(864\) | −11.5616 | −0.393335 | ||||||||
\(865\) | −28.5254 | − | 15.9048i | −0.969893 | − | 0.540779i | ||||
\(866\) | − | 70.5874i | − | 2.39866i | ||||||
\(867\) | 2.76565 | − | 2.76565i | 0.0939263 | − | 0.0939263i | ||||
\(868\) | −25.2398 | + | 25.2398i | −0.856694 | + | 0.856694i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −1.97153 | + | 0.560024i | −0.0668413 | + | 0.0189866i | ||||
\(871\) | − | 3.61031i | − | 0.122331i | ||||||
\(872\) | −0.290780 | + | 0.290780i | −0.00984706 | + | 0.00984706i | ||||
\(873\) | 10.9581 | + | 10.9581i | 0.370877 | + | 0.370877i | ||||
\(874\) | − | 34.8479i | − | 1.17875i | ||||||
\(875\) | −2.30527 | − | 51.3121i | −0.0779323 | − | 1.73467i | ||||
\(876\) | 3.22857i | 0.109083i | ||||||||
\(877\) | −40.1583 | − | 40.1583i | −1.35605 | − | 1.35605i | −0.878730 | − | 0.477319i | \(-0.841609\pi\) |
−0.477319 | − | 0.878730i | \(-0.658391\pi\) | |||||||
\(878\) | −31.7038 | − | 31.7038i | −1.06995 | − | 1.06995i | ||||
\(879\) | −5.16177 | −0.174102 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0495 | −0.405960 | −0.202980 | − | 0.979183i | \(-0.565063\pi\) | ||||
−0.202980 | + | 0.979183i | \(0.565063\pi\) | |||||||
\(882\) | −55.9574 | − | 55.9574i | −1.88418 | − | 1.88418i | ||||
\(883\) | 6.84927 | + | 6.84927i | 0.230496 | + | 0.230496i | 0.812900 | − | 0.582404i | \(-0.197888\pi\) |
−0.582404 | + | 0.812900i | \(0.697888\pi\) | |||||||
\(884\) | 3.92705i | 0.132081i | ||||||||
\(885\) | −4.19856 | − | 2.34098i | −0.141133 | − | 0.0786910i | ||||
\(886\) | − | 17.5342i | − | 0.589072i | ||||||
\(887\) | −15.4365 | − | 15.4365i | −0.518308 | − | 0.518308i | 0.398752 | − | 0.917059i | \(-0.369444\pi\) |
−0.917059 | + | 0.398752i | \(0.869444\pi\) | |||||||
\(888\) | 1.23820 | − | 1.23820i | 0.0415512 | − | 0.0415512i | ||||
\(889\) | 46.7505i | 1.56796i | ||||||||
\(890\) | −9.12880 | − | 5.08991i | −0.305998 | − | 0.170614i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.68694 | − | 1.68694i | 0.0564828 | − | 0.0564828i | ||||
\(893\) | 22.3754 | − | 22.3754i | 0.748763 | − | 0.748763i | ||||
\(894\) | 11.8864i | 0.397539i | ||||||||
\(895\) | 20.3711 | − | 5.78652i | 0.680932 | − | 0.193422i | ||||
\(896\) | 23.3809 | 0.781102 | ||||||||
\(897\) | −1.52820 | − | 1.52820i | −0.0510251 | − | 0.0510251i | ||||
\(898\) | 8.89528 | − | 8.89528i | 0.296839 | − | 0.296839i | ||||
\(899\) | −8.53873 | −0.284783 | ||||||||
\(900\) | −20.7318 | + | 12.8117i | −0.691061 | + | 0.427057i | ||||
\(901\) | 5.35767i | 0.178490i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.46727 | + | 5.46727i | 0.181939 | + | 0.181939i | ||||
\(904\) | 5.05602 | 0.168161 | ||||||||
\(905\) | 13.5858 | + | 47.8279i | 0.451606 | + | 1.58985i | ||||
\(906\) | −9.67793 | −0.321528 | ||||||||
\(907\) | 26.3067 | − | 26.3067i | 0.873500 | − | 0.873500i | −0.119352 | − | 0.992852i | \(-0.538082\pi\) |
0.992852 | + | 0.119352i | \(0.0380816\pi\) | |||||||
\(908\) | −13.2869 | + | 13.2869i | −0.440940 | + | 0.440940i | ||||
\(909\) | 27.1899 | 0.901831 | ||||||||
\(910\) | −15.6937 | + | 28.1468i | −0.520241 | + | 0.933058i | ||||
\(911\) | −41.2301 | −1.36601 | −0.683007 | − | 0.730412i | \(-0.739328\pi\) | ||||
−0.683007 | + | 0.730412i | \(0.739328\pi\) | |||||||
\(912\) | 3.05884 | + | 3.05884i | 0.101288 | + | 0.101288i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.7754i | 0.654111i | ||||||||
\(915\) | 5.93538 | + | 3.30936i | 0.196218 | + | 0.109404i | ||||
\(916\) | 1.07985 | 0.0356794 | ||||||||
\(917\) | −22.9068 | + | 22.9068i | −0.756448 | + | 0.756448i | ||||
\(918\) | 3.03094 | + | 3.03094i | 0.100036 | + | 0.100036i | ||||
\(919\) | 19.3961 | 0.639820 | 0.319910 | − | 0.947448i | \(-0.396347\pi\) | ||||
0.319910 | + | 0.947448i | \(0.396347\pi\) | |||||||
\(920\) | 1.98370 | + | 6.98352i | 0.0654008 | + | 0.230240i | ||||
\(921\) | 0.578685i | 0.0190683i | ||||||||
\(922\) | 11.2971 | − | 11.2971i | 0.372050 | − | 0.372050i | ||||
\(923\) | 7.34475 | − | 7.34475i | 0.241755 | − | 0.241755i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.8962 | − | 50.3830i | 0.391144 | − | 1.65658i | ||||
\(926\) | − | 62.1220i | − | 2.04146i | ||||||
\(927\) | −23.4324 | + | 23.4324i | −0.769620 | + | 0.769620i | ||||
\(928\) | −9.61093 | − | 9.61093i | −0.315494 | − | 0.315494i | ||||
\(929\) | − | 24.6755i | − | 0.809576i | −0.914411 | − | 0.404788i | \(-0.867345\pi\) | ||
0.914411 | − | 0.404788i | \(-0.132655\pi\) | |||||||
\(930\) | 5.04108 | − | 1.43194i | 0.165304 | − | 0.0469553i | ||||
\(931\) | 51.0528i | 1.67319i | ||||||||
\(932\) | 15.7930 | + | 15.7930i | 0.517316 | + | 0.517316i | ||||
\(933\) | −4.89286 | − | 4.89286i | −0.160185 | − | 0.160185i | ||||
\(934\) | −80.3987 | −2.63072 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.10073 | −0.101351 | ||||||||
\(937\) | 4.22625 | + | 4.22625i | 0.138066 | + | 0.138066i | 0.772762 | − | 0.634696i | \(-0.218875\pi\) |
−0.634696 | + | 0.772762i | \(0.718875\pi\) | |||||||
\(938\) | −13.6938 | − | 13.6938i | −0.447118 | − | 0.447118i | ||||
\(939\) | 4.10160i | 0.133851i | ||||||||
\(940\) | 15.8311 | − | 28.3932i | 0.516353 | − | 0.926084i | ||||
\(941\) | − | 21.3027i | − | 0.694447i | −0.937782 | − | 0.347223i | \(-0.887125\pi\) | ||
0.937782 | − | 0.347223i | \(-0.112875\pi\) | |||||||
\(942\) | 1.96145 | + | 1.96145i | 0.0639074 | + | 0.0639074i | ||||
\(943\) | 22.8181 | − | 22.8181i | 0.743061 | − | 0.743061i | ||||
\(944\) | − | 37.4113i | − | 1.21763i | ||||||
\(945\) | 4.36331 | + | 15.3608i | 0.141939 | + | 0.499687i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.9748 | − | 31.9748i | 1.03904 | − | 1.03904i | 0.0398351 | − | 0.999206i | \(-0.487317\pi\) |
0.999206 | − | 0.0398351i | \(-0.0126833\pi\) | |||||||
\(948\) | −2.75334 | + | 2.75334i | −0.0894243 | + | 0.0894243i | ||||
\(949\) | 12.1439i | 0.394209i | ||||||||
\(950\) | 33.7064 | + | 7.95860i | 1.09358 | + | 0.258211i | ||||
\(951\) | −4.59433 | −0.148981 | ||||||||
\(952\) | −3.02053 | − | 3.02053i | −0.0978958 | − | 0.0978958i | ||||
\(953\) | −20.2740 | + | 20.2740i | −0.656739 | + | 0.656739i | −0.954607 | − | 0.297868i | \(-0.903725\pi\) |
0.297868 | + | 0.954607i | \(0.403725\pi\) | |||||||
\(954\) | 20.8611 | 0.675402 | ||||||||
\(955\) | −7.43645 | − | 26.1796i | −0.240638 | − | 0.847152i | ||||
\(956\) | − | 29.1395i | − | 0.942439i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −10.0944 | − | 10.0944i | −0.326137 | − | 0.326137i | ||||
\(959\) | −54.7461 | −1.76785 | ||||||||
\(960\) | 2.61721 | + | 1.45926i | 0.0844700 | + | 0.0470976i | ||||
\(961\) | −9.16703 | −0.295711 | ||||||||
\(962\) | −22.9669 | + | 22.9669i | −0.740482 | + | 0.740482i | ||||
\(963\) | −7.83368 | + | 7.83368i | −0.252437 | + | 0.252437i | ||||
\(964\) | −16.2612 | −0.523739 | ||||||||
\(965\) | −19.4312 | − | 10.8342i | −0.625512 | − | 0.348764i | ||||
\(966\) | −11.5928 | −0.372992 | ||||||||
\(967\) | 5.92328 | + | 5.92328i | 0.190480 | + | 0.190480i | 0.795903 | − | 0.605424i | \(-0.206996\pi\) |
−0.605424 | + | 0.795903i | \(0.706996\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.36663i | − | 0.0439024i | ||||||
\(970\) | −6.18206 | − | 21.7636i | −0.198494 | − | 0.698788i | ||||
\(971\) | −10.4838 | −0.336441 | −0.168220 | − | 0.985749i | \(-0.553802\pi\) | ||||
−0.168220 | + | 0.985749i | \(0.553802\pi\) | |||||||
\(972\) | 8.06734 | − | 8.06734i | 0.258760 | − | 0.258760i | ||||
\(973\) | 22.2580 | + | 22.2580i | 0.713559 | + | 0.713559i | ||||
\(974\) | −15.8057 | −0.506446 | ||||||||
\(975\) | 1.82715 | − | 1.12913i | 0.0585157 | − | 0.0361610i | ||||
\(976\) | 52.8871i | 1.69288i | ||||||||
\(977\) | 5.93052 | − | 5.93052i | 0.189734 | − | 0.189734i | −0.605847 | − | 0.795581i | \(-0.707166\pi\) |
0.795581 | + | 0.605847i | \(0.207166\pi\) | |||||||
\(978\) | −3.56725 | + | 3.56725i | −0.114068 | + | 0.114068i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 14.3312 | + | 50.4522i | 0.457793 | + | 1.61164i | ||||
\(981\) | − | 1.86791i | − | 0.0596379i | ||||||
\(982\) | −9.05725 | + | 9.05725i | −0.289029 | + | 0.289029i | ||||
\(983\) | 36.2491 | + | 36.2491i | 1.15617 | + | 1.15617i | 0.985293 | + | 0.170875i | \(0.0546594\pi\) |
0.170875 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(984\) | 1.08481i | 0.0345824i | ||||||||
\(985\) | −13.8250 | + | 24.7952i | −0.440501 | + | 0.790042i | ||||
\(986\) | 5.03910i | 0.160478i | ||||||||
\(987\) | −7.44358 | − | 7.44358i | −0.236932 | − | 0.236932i | ||||
\(988\) | −6.97524 | − | 6.97524i | −0.221912 | − | 0.221912i | ||||
\(989\) | −32.3081 | −1.02734 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.6127 | −0.750084 | −0.375042 | − | 0.927008i | \(-0.622372\pi\) | ||||
−0.375042 | + | 0.927008i | \(0.622372\pi\) | |||||||
\(992\) | 24.5745 | + | 24.5745i | 0.780241 | + | 0.780241i | ||||
\(993\) | 1.77109 | + | 1.77109i | 0.0562040 | + | 0.0562040i | ||||
\(994\) | − | 55.7167i | − | 1.76723i | ||||||
\(995\) | −27.8531 | + | 7.91181i | −0.883002 | + | 0.250821i | ||||
\(996\) | 2.85836i | 0.0905705i | ||||||||
\(997\) | −33.9047 | − | 33.9047i | −1.07377 | − | 1.07377i | −0.997053 | − | 0.0767215i | \(-0.975555\pi\) |
−0.0767215 | − | 0.997053i | \(-0.524445\pi\) | |||||||
\(998\) | −35.7097 | + | 35.7097i | −1.13037 | + | 1.13037i | ||||
\(999\) | 16.0942i | 0.509199i |
(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 | 605.2.e.a.483.2 | yes | 20 | |
5.2 | odd | 4 | inner | 605.2.e.a.362.9 | yes | 20 | |
11.2 | odd | 10 | 605.2.m.f.403.2 | 80 | |||
11.3 | even | 5 | 605.2.m.f.233.2 | 80 | |||
11.4 | even | 5 | 605.2.m.f.578.9 | 80 | |||
11.5 | even | 5 | 605.2.m.f.118.9 | 80 | |||
11.6 | odd | 10 | 605.2.m.f.118.2 | 80 | |||
11.7 | odd | 10 | 605.2.m.f.578.2 | 80 | |||
11.8 | odd | 10 | 605.2.m.f.233.9 | 80 | |||
11.9 | even | 5 | 605.2.m.f.403.9 | 80 | |||
11.10 | odd | 2 | inner | 605.2.e.a.483.9 | yes | 20 | |
55.2 | even | 20 | 605.2.m.f.282.9 | 80 | |||
55.7 | even | 20 | 605.2.m.f.457.2 | 80 | |||
55.17 | even | 20 | 605.2.m.f.602.9 | 80 | |||
55.27 | odd | 20 | 605.2.m.f.602.2 | 80 | |||
55.32 | even | 4 | inner | 605.2.e.a.362.2 | ✓ | 20 | |
55.37 | odd | 20 | 605.2.m.f.457.9 | 80 | |||
55.42 | odd | 20 | 605.2.m.f.282.2 | 80 | |||
55.47 | odd | 20 | 605.2.m.f.112.2 | 80 | |||
55.52 | even | 20 | 605.2.m.f.112.9 | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.e.a.362.2 | ✓ | 20 | 55.32 | even | 4 | inner | |
605.2.e.a.362.9 | yes | 20 | 5.2 | odd | 4 | inner | |
605.2.e.a.483.2 | yes | 20 | 1.1 | even | 1 | trivial | |
605.2.e.a.483.9 | yes | 20 | 11.10 | odd | 2 | inner | |
605.2.m.f.112.2 | 80 | 55.47 | odd | 20 | |||
605.2.m.f.112.9 | 80 | 55.52 | even | 20 | |||
605.2.m.f.118.2 | 80 | 11.6 | odd | 10 | |||
605.2.m.f.118.9 | 80 | 11.5 | even | 5 | |||
605.2.m.f.233.2 | 80 | 11.3 | even | 5 | |||
605.2.m.f.233.9 | 80 | 11.8 | odd | 10 | |||
605.2.m.f.282.2 | 80 | 55.42 | odd | 20 | |||
605.2.m.f.282.9 | 80 | 55.2 | even | 20 | |||
605.2.m.f.403.2 | 80 | 11.2 | odd | 10 | |||
605.2.m.f.403.9 | 80 | 11.9 | even | 5 | |||
605.2.m.f.457.2 | 80 | 55.7 | even | 20 | |||
605.2.m.f.457.9 | 80 | 55.37 | odd | 20 | |||
605.2.m.f.578.2 | 80 | 11.7 | odd | 10 | |||
605.2.m.f.578.9 | 80 | 11.4 | even | 5 | |||
605.2.m.f.602.2 | 80 | 55.27 | odd | 20 | |||
605.2.m.f.602.9 | 80 | 55.17 | even | 20 |