Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.484000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 295.2 | ||
Root | \(-1.73855 + 1.26313i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.295 |
Dual form | 462.2.j.e.379.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.309017 | − | 0.951057i | 0.218508 | − | 0.672499i | ||||
\(3\) | −0.809017 | + | 0.587785i | −0.467086 | + | 0.339358i | ||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 0.910415 | + | 2.80197i | 0.407150 | + | 1.25308i | 0.919087 | + | 0.394056i | \(0.128928\pi\) |
−0.511937 | + | 0.859023i | \(0.671072\pi\) | |||||||
\(6\) | 0.309017 | + | 0.951057i | 0.126156 | + | 0.388267i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | −0.809017 | + | 0.587785i | −0.286031 | + | 0.207813i | ||||
\(9\) | 0.309017 | − | 0.951057i | 0.103006 | − | 0.317019i | ||||
\(10\) | 2.94617 | 0.931659 | ||||||||
\(11\) | −3.06668 | + | 1.26313i | −0.924638 | + | 0.380847i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −0.164066 | + | 0.504942i | −0.0455036 | + | 0.140046i | −0.971227 | − | 0.238155i | \(-0.923457\pi\) |
0.925723 | + | 0.378201i | \(0.123457\pi\) | |||||||
\(14\) | −0.809017 | + | 0.587785i | −0.216219 | + | 0.157092i | ||||
\(15\) | −2.38350 | − | 1.73171i | −0.615416 | − | 0.447126i | ||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 2.26700 | + | 6.97709i | 0.549827 | + | 1.69219i | 0.709227 | + | 0.704980i | \(0.249044\pi\) |
−0.159400 | + | 0.987214i | \(0.550956\pi\) | |||||||
\(18\) | −0.809017 | − | 0.587785i | −0.190687 | − | 0.138542i | ||||
\(19\) | −4.35658 | + | 3.16524i | −0.999468 | + | 0.726156i | −0.961974 | − | 0.273141i | \(-0.911937\pi\) |
−0.0374940 | + | 0.999297i | \(0.511937\pi\) | |||||||
\(20\) | 0.910415 | − | 2.80197i | 0.203575 | − | 0.626539i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.253650 | + | 3.30691i | 0.0540785 | + | 0.705036i | ||||
\(23\) | −0.710097 | −0.148065 | −0.0740327 | − | 0.997256i | \(-0.523587\pi\) | ||||
−0.0740327 | + | 0.997256i | \(0.523587\pi\) | |||||||
\(24\) | 0.309017 | − | 0.951057i | 0.0630778 | − | 0.194134i | ||||
\(25\) | −2.97709 | + | 2.16298i | −0.595418 | + | 0.432597i | ||||
\(26\) | 0.429529 | + | 0.312071i | 0.0842376 | + | 0.0612022i | ||||
\(27\) | 0.309017 | + | 0.951057i | 0.0594703 | + | 0.183031i | ||||
\(28\) | 0.309017 | + | 0.951057i | 0.0583987 | + | 0.179733i | ||||
\(29\) | 0.0769587 | + | 0.0559138i | 0.0142909 | + | 0.0103829i | 0.594908 | − | 0.803794i | \(-0.297189\pi\) |
−0.580617 | + | 0.814177i | \(0.697189\pi\) | |||||||
\(30\) | −2.38350 | + | 1.73171i | −0.435165 | + | 0.316166i | ||||
\(31\) | −1.55784 | + | 4.79455i | −0.279797 | + | 0.861127i | 0.708113 | + | 0.706099i | \(0.249547\pi\) |
−0.987910 | + | 0.155028i | \(0.950453\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.73855 | − | 2.82444i | 0.302642 | − | 0.491672i | ||||
\(34\) | 7.33615 | 1.25814 | ||||||||
\(35\) | 0.910415 | − | 2.80197i | 0.153888 | − | 0.473619i | ||||
\(36\) | −0.809017 | + | 0.587785i | −0.134836 | + | 0.0979642i | ||||
\(37\) | 1.85257 | + | 1.34597i | 0.304561 | + | 0.221276i | 0.729559 | − | 0.683918i | \(-0.239725\pi\) |
−0.424998 | + | 0.905194i | \(0.639725\pi\) | |||||||
\(38\) | 1.66407 | + | 5.12147i | 0.269947 | + | 0.830812i | ||||
\(39\) | −0.164066 | − | 0.504942i | −0.0262715 | − | 0.0808554i | ||||
\(40\) | −2.38350 | − | 1.73171i | −0.376864 | − | 0.273808i | ||||
\(41\) | 1.88999 | − | 1.37315i | 0.295166 | − | 0.214451i | −0.430339 | − | 0.902667i | \(-0.641606\pi\) |
0.725505 | + | 0.688216i | \(0.241606\pi\) | |||||||
\(42\) | 0.309017 | − | 0.951057i | 0.0476824 | − | 0.146751i | ||||
\(43\) | −0.172587 | −0.0263193 | −0.0131597 | − | 0.999913i | \(-0.504189\pi\) | ||||
−0.0131597 | + | 0.999913i | \(0.504189\pi\) | |||||||
\(44\) | 3.22344 | + | 0.780656i | 0.485952 | + | 0.117688i | ||||
\(45\) | 2.94617 | 0.439188 | ||||||||
\(46\) | −0.219432 | + | 0.675342i | −0.0323535 | + | 0.0995738i | ||||
\(47\) | 10.6981 | − | 7.77259i | 1.56047 | − | 1.13375i | 0.624850 | − | 0.780745i | \(-0.285160\pi\) |
0.935622 | − | 0.353004i | \(-0.114840\pi\) | |||||||
\(48\) | −0.809017 | − | 0.587785i | −0.116772 | − | 0.0848395i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 1.13715 | + | 3.49978i | 0.160817 | + | 0.494944i | ||||
\(51\) | −5.93507 | − | 4.31208i | −0.831076 | − | 0.603812i | ||||
\(52\) | 0.429529 | − | 0.312071i | 0.0595650 | − | 0.0432765i | ||||
\(53\) | −1.22673 | + | 3.77550i | −0.168505 | + | 0.518604i | −0.999277 | − | 0.0380076i | \(-0.987899\pi\) |
0.830773 | + | 0.556612i | \(0.187899\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −6.33119 | − | 7.44277i | −0.853698 | − | 1.00358i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.66407 | − | 5.12147i | 0.220411 | − | 0.678355i | ||||
\(58\) | 0.0769587 | − | 0.0559138i | 0.0101052 | − | 0.00734184i | ||||
\(59\) | 7.40815 | + | 5.38234i | 0.964459 | + | 0.700721i | 0.954182 | − | 0.299226i | \(-0.0967286\pi\) |
0.0102772 | + | 0.999947i | \(0.496729\pi\) | |||||||
\(60\) | 0.910415 | + | 2.80197i | 0.117534 | + | 0.361733i | ||||
\(61\) | −2.37263 | − | 7.30221i | −0.303784 | − | 0.934952i | −0.980128 | − | 0.198366i | \(-0.936437\pi\) |
0.676344 | − | 0.736586i | \(-0.263563\pi\) | |||||||
\(62\) | 4.07849 | + | 2.96320i | 0.517969 | + | 0.376326i | ||||
\(63\) | −0.809017 | + | 0.587785i | −0.101927 | + | 0.0740540i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −1.56420 | −0.194015 | ||||||||
\(66\) | −2.14896 | − | 2.52626i | −0.264519 | − | 0.310961i | ||||
\(67\) | −12.9240 | −1.57891 | −0.789457 | − | 0.613805i | \(-0.789638\pi\) | ||||
−0.789457 | + | 0.613805i | \(0.789638\pi\) | |||||||
\(68\) | 2.26700 | − | 6.97709i | 0.274914 | − | 0.846097i | ||||
\(69\) | 0.574481 | − | 0.417385i | 0.0691593 | − | 0.0502472i | ||||
\(70\) | −2.38350 | − | 1.73171i | −0.284882 | − | 0.206979i | ||||
\(71\) | 2.74337 | + | 8.44322i | 0.325578 | + | 1.00203i | 0.971179 | + | 0.238351i | \(0.0766069\pi\) |
−0.645601 | + | 0.763675i | \(0.723393\pi\) | |||||||
\(72\) | 0.309017 | + | 0.951057i | 0.0364180 | + | 0.112083i | ||||
\(73\) | −5.25919 | − | 3.82103i | −0.615542 | − | 0.447217i | 0.235820 | − | 0.971797i | \(-0.424223\pi\) |
−0.851361 | + | 0.524580i | \(0.824223\pi\) | |||||||
\(74\) | 1.85257 | − | 1.34597i | 0.215357 | − | 0.156466i | ||||
\(75\) | 1.13715 | − | 3.49978i | 0.131307 | − | 0.404120i | ||||
\(76\) | 5.38503 | 0.617705 | ||||||||
\(77\) | 3.22344 | + | 0.780656i | 0.367345 | + | 0.0889640i | ||||
\(78\) | −0.530927 | −0.0601157 | ||||||||
\(79\) | 3.17836 | − | 9.78198i | 0.357593 | − | 1.10056i | −0.596898 | − | 0.802317i | \(-0.703600\pi\) |
0.954491 | − | 0.298241i | \(-0.0963999\pi\) | |||||||
\(80\) | −2.38350 | + | 1.73171i | −0.266483 | + | 0.193611i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | −0.721910 | − | 2.22181i | −0.0797216 | − | 0.245358i | ||||
\(83\) | −4.54522 | − | 13.9887i | −0.498903 | − | 1.53546i | −0.810785 | − | 0.585344i | \(-0.800960\pi\) |
0.311883 | − | 0.950121i | \(-0.399040\pi\) | |||||||
\(84\) | −0.809017 | − | 0.587785i | −0.0882710 | − | 0.0641326i | ||||
\(85\) | −17.4857 | + | 12.7041i | −1.89659 | + | 1.37795i | ||||
\(86\) | −0.0533324 | + | 0.164140i | −0.00575098 | + | 0.0176997i | ||||
\(87\) | −0.0951262 | −0.0101986 | ||||||||
\(88\) | 1.73855 | − | 2.82444i | 0.185330 | − | 0.301086i | ||||
\(89\) | 8.61947 | 0.913662 | 0.456831 | − | 0.889553i | \(-0.348984\pi\) | ||||
0.456831 | + | 0.889553i | \(0.348984\pi\) | |||||||
\(90\) | 0.910415 | − | 2.80197i | 0.0959662 | − | 0.295354i | ||||
\(91\) | 0.429529 | − | 0.312071i | 0.0450269 | − | 0.0327139i | ||||
\(92\) | 0.574481 | + | 0.417385i | 0.0598937 | + | 0.0435153i | ||||
\(93\) | −1.55784 | − | 4.79455i | −0.161541 | − | 0.497172i | ||||
\(94\) | −4.08629 | − | 12.5763i | −0.421469 | − | 1.29715i | ||||
\(95\) | −12.8352 | − | 9.32532i | −1.31686 | − | 0.956758i | ||||
\(96\) | −0.809017 | + | 0.587785i | −0.0825700 | + | 0.0599906i | ||||
\(97\) | −0.280568 | + | 0.863499i | −0.0284874 | + | 0.0876751i | −0.964289 | − | 0.264851i | \(-0.914677\pi\) |
0.935802 | + | 0.352526i | \(0.114677\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0.253650 | + | 3.30691i | 0.0254928 | + | 0.332357i | ||||
\(100\) | 3.67989 | 0.367989 | ||||||||
\(101\) | −1.05938 | + | 3.26042i | −0.105412 | + | 0.324424i | −0.989827 | − | 0.142277i | \(-0.954558\pi\) |
0.884415 | + | 0.466701i | \(0.154558\pi\) | |||||||
\(102\) | −5.93507 | + | 4.31208i | −0.587660 | + | 0.426960i | ||||
\(103\) | 0.146267 | + | 0.106269i | 0.0144121 | + | 0.0104710i | 0.594968 | − | 0.803749i | \(-0.297165\pi\) |
−0.580556 | + | 0.814220i | \(0.697165\pi\) | |||||||
\(104\) | −0.164066 | − | 0.504942i | −0.0160879 | − | 0.0495136i | ||||
\(105\) | 0.910415 | + | 2.80197i | 0.0888474 | + | 0.273444i | ||||
\(106\) | 3.21163 | + | 2.33338i | 0.311941 | + | 0.226638i | ||||
\(107\) | −12.2107 | + | 8.87158i | −1.18045 | + | 0.857648i | −0.992222 | − | 0.124477i | \(-0.960275\pi\) |
−0.188229 | + | 0.982125i | \(0.560275\pi\) | |||||||
\(108\) | 0.309017 | − | 0.951057i | 0.0297352 | − | 0.0915155i | ||||
\(109\) | 6.58783 | 0.630999 | 0.315500 | − | 0.948926i | \(-0.397828\pi\) | ||||
0.315500 | + | 0.948926i | \(0.397828\pi\) | |||||||
\(110\) | −9.03494 | + | 3.72138i | −0.861447 | + | 0.354820i | ||||
\(111\) | −2.28990 | −0.217348 | ||||||||
\(112\) | 0.309017 | − | 0.951057i | 0.0291994 | − | 0.0898664i | ||||
\(113\) | 10.9168 | − | 7.93150i | 1.02696 | − | 0.746132i | 0.0592646 | − | 0.998242i | \(-0.481124\pi\) |
0.967699 | + | 0.252110i | \(0.0811244\pi\) | |||||||
\(114\) | −4.35658 | − | 3.16524i | −0.408031 | − | 0.296452i | ||||
\(115\) | −0.646483 | − | 1.98967i | −0.0602849 | − | 0.185538i | ||||
\(116\) | −0.0293956 | − | 0.0904704i | −0.00272931 | − | 0.00839996i | ||||
\(117\) | 0.429529 | + | 0.312071i | 0.0397100 | + | 0.0288510i | ||||
\(118\) | 7.40815 | − | 5.38234i | 0.681976 | − | 0.495484i | ||||
\(119\) | 2.26700 | − | 6.97709i | 0.207815 | − | 0.639589i | ||||
\(120\) | 2.94617 | 0.268947 | ||||||||
\(121\) | 7.80902 | − | 7.74721i | 0.709911 | − | 0.704292i | ||||
\(122\) | −7.67800 | −0.695133 | ||||||||
\(123\) | −0.721910 | + | 2.22181i | −0.0650924 | + | 0.200334i | ||||
\(124\) | 4.07849 | − | 2.96320i | 0.366259 | − | 0.266103i | ||||
\(125\) | 3.14648 | + | 2.28605i | 0.281430 | + | 0.204471i | ||||
\(126\) | 0.309017 | + | 0.951057i | 0.0275294 | + | 0.0847268i | ||||
\(127\) | 1.05640 | + | 3.25125i | 0.0937399 | + | 0.288502i | 0.986923 | − | 0.161191i | \(-0.0515335\pi\) |
−0.893183 | + | 0.449693i | \(0.851533\pi\) | |||||||
\(128\) | −0.809017 | − | 0.587785i | −0.0715077 | − | 0.0519534i | ||||
\(129\) | 0.139626 | − | 0.101444i | 0.0122934 | − | 0.00893167i | ||||
\(130\) | −0.483364 | + | 1.48764i | −0.0423938 | + | 0.130475i | ||||
\(131\) | 4.82272 | 0.421363 | 0.210682 | − | 0.977555i | \(-0.432432\pi\) | ||||
0.210682 | + | 0.977555i | \(0.432432\pi\) | |||||||
\(132\) | −3.06668 | + | 1.26313i | −0.266920 | + | 0.109941i | ||||
\(133\) | 5.38503 | 0.466941 | ||||||||
\(134\) | −3.99373 | + | 12.2914i | −0.345006 | + | 1.06182i | ||||
\(135\) | −2.38350 | + | 1.73171i | −0.205139 | + | 0.149042i | ||||
\(136\) | −5.93507 | − | 4.31208i | −0.508928 | − | 0.369758i | ||||
\(137\) | 5.33390 | + | 16.4161i | 0.455706 | + | 1.40252i | 0.870304 | + | 0.492514i | \(0.163922\pi\) |
−0.414599 | + | 0.910004i | \(0.636078\pi\) | |||||||
\(138\) | −0.219432 | − | 0.675342i | −0.0186793 | − | 0.0574890i | ||||
\(139\) | 14.1186 | + | 10.2578i | 1.19753 | + | 0.870053i | 0.994039 | − | 0.109024i | \(-0.0347727\pi\) |
0.203487 | + | 0.979078i | \(0.434773\pi\) | |||||||
\(140\) | −2.38350 | + | 1.73171i | −0.201442 | + | 0.146356i | ||||
\(141\) | −4.08629 | + | 12.5763i | −0.344128 | + | 1.05912i | ||||
\(142\) | 8.87773 | 0.745002 | ||||||||
\(143\) | −0.134670 | − | 1.75573i | −0.0112617 | − | 0.146821i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.0866043 | + | 0.266541i | −0.00719209 | + | 0.0221350i | ||||
\(146\) | −5.25919 | + | 3.82103i | −0.435254 | + | 0.316230i | ||||
\(147\) | −0.809017 | − | 0.587785i | −0.0667266 | − | 0.0484797i | ||||
\(148\) | −0.707619 | − | 2.17783i | −0.0581659 | − | 0.179016i | ||||
\(149\) | −3.12227 | − | 9.60936i | −0.255786 | − | 0.787230i | −0.993674 | − | 0.112306i | \(-0.964176\pi\) |
0.737887 | − | 0.674924i | \(-0.235824\pi\) | |||||||
\(150\) | −2.97709 | − | 2.16298i | −0.243079 | − | 0.176607i | ||||
\(151\) | 3.05558 | − | 2.22001i | 0.248660 | − | 0.180662i | −0.456473 | − | 0.889737i | \(-0.650887\pi\) |
0.705133 | + | 0.709075i | \(0.250887\pi\) | |||||||
\(152\) | 1.66407 | − | 5.12147i | 0.134974 | − | 0.415406i | ||||
\(153\) | 7.33615 | 0.593093 | ||||||||
\(154\) | 1.73855 | − | 2.82444i | 0.140096 | − | 0.227600i | ||||
\(155\) | −14.8525 | −1.19298 | ||||||||
\(156\) | −0.164066 | + | 0.504942i | −0.0131358 | + | 0.0404277i | ||||
\(157\) | −17.7701 | + | 12.9107i | −1.41821 | + | 1.03039i | −0.426140 | + | 0.904657i | \(0.640127\pi\) |
−0.992065 | + | 0.125729i | \(0.959873\pi\) | |||||||
\(158\) | −8.32105 | − | 6.04559i | −0.661987 | − | 0.480962i | ||||
\(159\) | −1.22673 | − | 3.77550i | −0.0972863 | − | 0.299416i | ||||
\(160\) | 0.910415 | + | 2.80197i | 0.0719746 | + | 0.221515i | ||||
\(161\) | 0.574481 | + | 0.417385i | 0.0452754 | + | 0.0328945i | ||||
\(162\) | −0.809017 | + | 0.587785i | −0.0635624 | + | 0.0461808i | ||||
\(163\) | 5.93056 | − | 18.2524i | 0.464517 | − | 1.42964i | −0.395072 | − | 0.918650i | \(-0.629280\pi\) |
0.859589 | − | 0.510986i | \(-0.170720\pi\) | |||||||
\(164\) | −2.33615 | −0.182423 | ||||||||
\(165\) | 9.49679 | + | 2.29994i | 0.739324 | + | 0.179050i | ||||
\(166\) | −14.7086 | −1.14161 | ||||||||
\(167\) | 4.80604 | − | 14.7915i | 0.371902 | − | 1.14460i | −0.573643 | − | 0.819106i | \(-0.694470\pi\) |
0.945545 | − | 0.325492i | \(-0.105530\pi\) | |||||||
\(168\) | −0.809017 | + | 0.587785i | −0.0624170 | + | 0.0453486i | ||||
\(169\) | 10.2892 | + | 7.47552i | 0.791475 | + | 0.575040i | ||||
\(170\) | 6.67894 | + | 20.5557i | 0.512251 | + | 1.57655i | ||||
\(171\) | 1.66407 | + | 5.12147i | 0.127254 | + | 0.391648i | ||||
\(172\) | 0.139626 | + | 0.101444i | 0.0106464 | + | 0.00773506i | ||||
\(173\) | −18.1275 | + | 13.1704i | −1.37820 | + | 1.00132i | −0.381159 | + | 0.924509i | \(0.624475\pi\) |
−0.997045 | + | 0.0768149i | \(0.975525\pi\) | |||||||
\(174\) | −0.0293956 | + | 0.0904704i | −0.00222847 | + | 0.00685854i | ||||
\(175\) | 3.67989 | 0.278173 | ||||||||
\(176\) | −2.14896 | − | 2.52626i | −0.161984 | − | 0.190424i | ||||
\(177\) | −9.15698 | −0.688281 | ||||||||
\(178\) | 2.66356 | − | 8.19760i | 0.199642 | − | 0.614436i | ||||
\(179\) | 14.8494 | − | 10.7887i | 1.10989 | − | 0.806385i | 0.127247 | − | 0.991871i | \(-0.459386\pi\) |
0.982647 | + | 0.185486i | \(0.0593861\pi\) | |||||||
\(180\) | −2.38350 | − | 1.73171i | −0.177655 | − | 0.129074i | ||||
\(181\) | −1.02971 | − | 3.16911i | −0.0765375 | − | 0.235558i | 0.905467 | − | 0.424417i | \(-0.139521\pi\) |
−0.982004 | + | 0.188859i | \(0.939521\pi\) | |||||||
\(182\) | −0.164066 | − | 0.504942i | −0.0121613 | − | 0.0374288i | ||||
\(183\) | 6.21163 | + | 4.51301i | 0.459177 | + | 0.333611i | ||||
\(184\) | 0.574481 | − | 0.417385i | 0.0423513 | − | 0.0307700i | ||||
\(185\) | −2.08476 | + | 6.41624i | −0.153275 | + | 0.471731i | ||||
\(186\) | −5.04129 | −0.369645 | ||||||||
\(187\) | −15.7651 | − | 18.5330i | −1.15286 | − | 1.35527i | ||||
\(188\) | −13.2235 | −0.964425 | ||||||||
\(189\) | 0.309017 | − | 0.951057i | 0.0224777 | − | 0.0691792i | ||||
\(190\) | −12.8352 | + | 9.32532i | −0.931164 | + | 0.676530i | ||||
\(191\) | 6.80888 | + | 4.94694i | 0.492674 | + | 0.357948i | 0.806212 | − | 0.591627i | \(-0.201514\pi\) |
−0.313538 | + | 0.949576i | \(0.601514\pi\) | |||||||
\(192\) | 0.309017 | + | 0.951057i | 0.0223014 | + | 0.0686366i | ||||
\(193\) | −2.13408 | − | 6.56804i | −0.153615 | − | 0.472778i | 0.844403 | − | 0.535708i | \(-0.179955\pi\) |
−0.998018 | + | 0.0629306i | \(0.979955\pi\) | |||||||
\(194\) | 0.734536 | + | 0.533672i | 0.0527366 | + | 0.0383154i | ||||
\(195\) | 1.26546 | − | 0.919413i | 0.0906217 | − | 0.0658405i | ||||
\(196\) | 0.309017 | − | 0.951057i | 0.0220726 | − | 0.0679326i | ||||
\(197\) | 10.5788 | 0.753708 | 0.376854 | − | 0.926273i | \(-0.377006\pi\) | ||||
0.376854 | + | 0.926273i | \(0.377006\pi\) | |||||||
\(198\) | 3.22344 | + | 0.780656i | 0.229080 | + | 0.0554788i | ||||
\(199\) | 16.7261 | 1.18568 | 0.592842 | − | 0.805319i | \(-0.298006\pi\) | ||||
0.592842 | + | 0.805319i | \(0.298006\pi\) | |||||||
\(200\) | 1.13715 | − | 3.49978i | 0.0804085 | − | 0.247472i | ||||
\(201\) | 10.4557 | − | 7.59652i | 0.737489 | − | 0.535817i | ||||
\(202\) | 2.77348 | + | 2.01505i | 0.195142 | + | 0.141779i | ||||
\(203\) | −0.0293956 | − | 0.0904704i | −0.00206317 | − | 0.00634977i | ||||
\(204\) | 2.26700 | + | 6.97709i | 0.158721 | + | 0.488494i | ||||
\(205\) | 5.56821 | + | 4.04554i | 0.388901 | + | 0.282553i | ||||
\(206\) | 0.146267 | − | 0.106269i | 0.0101909 | − | 0.00740413i | ||||
\(207\) | −0.219432 | + | 0.675342i | −0.0152516 | + | 0.0469395i | ||||
\(208\) | −0.530927 | −0.0368132 | ||||||||
\(209\) | 9.36212 | − | 15.2097i | 0.647591 | − | 1.05208i | ||||
\(210\) | 2.94617 | 0.203305 | ||||||||
\(211\) | −3.81762 | + | 11.7494i | −0.262816 | + | 0.808864i | 0.729373 | + | 0.684117i | \(0.239812\pi\) |
−0.992189 | + | 0.124748i | \(0.960188\pi\) | |||||||
\(212\) | 3.21163 | − | 2.33338i | 0.220576 | − | 0.160258i | ||||
\(213\) | −7.18223 | − | 5.21820i | −0.492118 | − | 0.357545i | ||||
\(214\) | 4.66407 | + | 14.3545i | 0.318829 | + | 0.981255i | ||||
\(215\) | −0.157126 | − | 0.483585i | −0.0107159 | − | 0.0329802i | ||||
\(216\) | −0.809017 | − | 0.587785i | −0.0550466 | − | 0.0399937i | ||||
\(217\) | 4.07849 | − | 2.96320i | 0.276866 | − | 0.201155i | ||||
\(218\) | 2.03575 | − | 6.26539i | 0.137878 | − | 0.424346i | ||||
\(219\) | 6.50072 | 0.439278 | ||||||||
\(220\) | 0.747296 | + | 9.74271i | 0.0503827 | + | 0.656853i | ||||
\(221\) | −3.89496 | −0.262003 | ||||||||
\(222\) | −0.707619 | + | 2.17783i | −0.0474923 | + | 0.146166i | ||||
\(223\) | −10.7487 | + | 7.80938i | −0.719786 | + | 0.522955i | −0.886316 | − | 0.463081i | \(-0.846744\pi\) |
0.166530 | + | 0.986036i | \(0.446744\pi\) | |||||||
\(224\) | −0.809017 | − | 0.587785i | −0.0540547 | − | 0.0392731i | ||||
\(225\) | 1.13715 | + | 3.49978i | 0.0758099 | + | 0.233319i | ||||
\(226\) | −4.16983 | − | 12.8334i | −0.277373 | − | 0.853667i | ||||
\(227\) | 12.1889 | + | 8.85578i | 0.809008 | + | 0.587779i | 0.913543 | − | 0.406742i | \(-0.133335\pi\) |
−0.104535 | + | 0.994521i | \(0.533335\pi\) | |||||||
\(228\) | −4.35658 | + | 3.16524i | −0.288522 | + | 0.209623i | ||||
\(229\) | −2.59003 | + | 7.97129i | −0.171154 | + | 0.526758i | −0.999437 | − | 0.0335523i | \(-0.989318\pi\) |
0.828283 | + | 0.560310i | \(0.189318\pi\) | |||||||
\(230\) | −2.09206 | −0.137947 | ||||||||
\(231\) | −3.06668 | + | 1.26313i | −0.201773 | + | 0.0831077i | ||||
\(232\) | −0.0951262 | −0.00624534 | ||||||||
\(233\) | −1.75627 | + | 5.40524i | −0.115057 | + | 0.354109i | −0.991959 | − | 0.126560i | \(-0.959606\pi\) |
0.876902 | + | 0.480669i | \(0.159606\pi\) | |||||||
\(234\) | 0.429529 | − | 0.312071i | 0.0280792 | − | 0.0204007i | ||||
\(235\) | 31.5182 | + | 22.8993i | 2.05602 | + | 1.49379i | ||||
\(236\) | −2.82966 | − | 8.70881i | −0.184195 | − | 0.566895i | ||||
\(237\) | 3.17836 | + | 9.78198i | 0.206456 | + | 0.635408i | ||||
\(238\) | −5.93507 | − | 4.31208i | −0.384713 | − | 0.279511i | ||||
\(239\) | −20.0341 | + | 14.5556i | −1.29590 | + | 0.941524i | −0.999907 | − | 0.0136672i | \(-0.995649\pi\) |
−0.295990 | + | 0.955191i | \(0.595649\pi\) | |||||||
\(240\) | 0.910415 | − | 2.80197i | 0.0587670 | − | 0.180866i | ||||
\(241\) | 8.91406 | 0.574205 | 0.287103 | − | 0.957900i | \(-0.407308\pi\) | ||||
0.287103 | + | 0.957900i | \(0.407308\pi\) | |||||||
\(242\) | −4.95492 | − | 9.82084i | −0.318514 | − | 0.631307i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.37263 | + | 7.30221i | −0.151892 | + | 0.467476i | ||||
\(245\) | −2.38350 | + | 1.73171i | −0.152276 | + | 0.110635i | ||||
\(246\) | 1.88999 | + | 1.37315i | 0.120501 | + | 0.0875491i | ||||
\(247\) | −0.883498 | − | 2.71913i | −0.0562156 | − | 0.173014i | ||||
\(248\) | −1.55784 | − | 4.79455i | −0.0989232 | − | 0.304454i | ||||
\(249\) | 11.8995 | + | 8.64552i | 0.754102 | + | 0.547888i | ||||
\(250\) | 3.14648 | − | 2.28605i | 0.199001 | − | 0.144583i | ||||
\(251\) | 0.339359 | − | 1.04444i | 0.0214202 | − | 0.0659245i | −0.939775 | − | 0.341794i | \(-0.888966\pi\) |
0.961195 | + | 0.275869i | \(0.0889656\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 2.17764 | − | 0.896943i | 0.136907 | − | 0.0563903i | ||||
\(254\) | 3.41857 | 0.214500 | ||||||||
\(255\) | 6.67894 | − | 20.5557i | 0.418252 | − | 1.28725i | ||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 21.7922 | + | 15.8330i | 1.35936 | + | 0.987635i | 0.998485 | + | 0.0550211i | \(0.0175226\pi\) |
0.360877 | + | 0.932613i | \(0.382477\pi\) | |||||||
\(258\) | −0.0533324 | − | 0.164140i | −0.00332033 | − | 0.0102189i | ||||
\(259\) | −0.707619 | − | 2.17783i | −0.0439693 | − | 0.135324i | ||||
\(260\) | 1.26546 | + | 0.919413i | 0.0784807 | + | 0.0570196i | ||||
\(261\) | 0.0769587 | − | 0.0559138i | 0.00476362 | − | 0.00346097i | ||||
\(262\) | 1.49030 | − | 4.58668i | 0.0920713 | − | 0.283366i | ||||
\(263\) | −25.0868 | −1.54692 | −0.773460 | − | 0.633846i | \(-0.781475\pi\) | ||||
−0.773460 | + | 0.633846i | \(0.781475\pi\) | |||||||
\(264\) | 0.253650 | + | 3.30691i | 0.0156111 | + | 0.203526i | ||||
\(265\) | −11.6957 | −0.718459 | ||||||||
\(266\) | 1.66407 | − | 5.12147i | 0.102030 | − | 0.314017i | ||||
\(267\) | −6.97330 | + | 5.06640i | −0.426759 | + | 0.310059i | ||||
\(268\) | 10.4557 | + | 7.59652i | 0.638685 | + | 0.464031i | ||||
\(269\) | 8.17565 | + | 25.1621i | 0.498478 | + | 1.53416i | 0.811465 | + | 0.584401i | \(0.198670\pi\) |
−0.312987 | + | 0.949757i | \(0.601330\pi\) | |||||||
\(270\) | 0.910415 | + | 2.80197i | 0.0554061 | + | 0.170522i | ||||
\(271\) | 21.2668 | + | 15.4513i | 1.29187 | + | 0.938598i | 0.999841 | − | 0.0178120i | \(-0.00567004\pi\) |
0.292028 | + | 0.956410i | \(0.405670\pi\) | |||||||
\(272\) | −5.93507 | + | 4.31208i | −0.359866 | + | 0.261458i | ||||
\(273\) | −0.164066 | + | 0.504942i | −0.00992970 | + | 0.0305605i | ||||
\(274\) | 17.2609 | 1.04277 | ||||||||
\(275\) | 6.39766 | − | 10.3936i | 0.385793 | − | 0.626759i | ||||
\(276\) | −0.710097 | −0.0427428 | ||||||||
\(277\) | 1.92101 | − | 5.91225i | 0.115422 | − | 0.355233i | −0.876613 | − | 0.481197i | \(-0.840202\pi\) |
0.992035 | + | 0.125964i | \(0.0402023\pi\) | |||||||
\(278\) | 14.1186 | − | 10.2578i | 0.846778 | − | 0.615221i | ||||
\(279\) | 4.07849 | + | 2.96320i | 0.244173 | + | 0.177402i | ||||
\(280\) | 0.910415 | + | 2.80197i | 0.0544077 | + | 0.167450i | ||||
\(281\) | −9.51501 | − | 29.2842i | −0.567618 | − | 1.74695i | −0.660042 | − | 0.751229i | \(-0.729462\pi\) |
0.0924243 | − | 0.995720i | \(-0.470538\pi\) | |||||||
\(282\) | 10.6981 | + | 7.77259i | 0.637060 | + | 0.462851i | ||||
\(283\) | 11.9872 | − | 8.70924i | 0.712567 | − | 0.517711i | −0.171433 | − | 0.985196i | \(-0.554840\pi\) |
0.884001 | + | 0.467485i | \(0.154840\pi\) | |||||||
\(284\) | 2.74337 | − | 8.44322i | 0.162789 | − | 0.501013i | ||||
\(285\) | 15.8652 | 0.939772 | ||||||||
\(286\) | −1.71141 | − | 0.414471i | −0.101198 | − | 0.0245082i | ||||
\(287\) | −2.33615 | −0.137899 | ||||||||
\(288\) | 0.309017 | − | 0.951057i | 0.0182090 | − | 0.0560415i | ||||
\(289\) | −29.7873 | + | 21.6417i | −1.75219 | + | 1.27304i | ||||
\(290\) | 0.226733 | + | 0.164731i | 0.0133142 | + | 0.00967335i | ||||
\(291\) | −0.280568 | − | 0.863499i | −0.0164472 | − | 0.0506192i | ||||
\(292\) | 2.00883 | + | 6.18255i | 0.117558 | + | 0.361806i | ||||
\(293\) | 10.0886 | + | 7.32982i | 0.589385 | + | 0.428213i | 0.842095 | − | 0.539329i | \(-0.181322\pi\) |
−0.252711 | + | 0.967542i | \(0.581322\pi\) | |||||||
\(294\) | −0.809017 | + | 0.587785i | −0.0471828 | + | 0.0342803i | ||||
\(295\) | −8.33665 | + | 25.6576i | −0.485379 | + | 1.49384i | ||||
\(296\) | −2.28990 | −0.133098 | ||||||||
\(297\) | −2.14896 | − | 2.52626i | −0.124695 | − | 0.146588i | ||||
\(298\) | −10.1039 | −0.585302 | ||||||||
\(299\) | 0.116502 | − | 0.358558i | 0.00673751 | − | 0.0207359i | ||||
\(300\) | −2.97709 | + | 2.16298i | −0.171882 | + | 0.124880i | ||||
\(301\) | 0.139626 | + | 0.101444i | 0.00804792 | + | 0.00584715i | ||||
\(302\) | −1.16713 | − | 3.59205i | −0.0671607 | − | 0.206699i | ||||
\(303\) | −1.05938 | − | 3.26042i | −0.0608596 | − | 0.187307i | ||||
\(304\) | −4.35658 | − | 3.16524i | −0.249867 | − | 0.181539i | ||||
\(305\) | 18.3005 | − | 13.2961i | 1.04788 | − | 0.761331i | ||||
\(306\) | 2.26700 | − | 6.97709i | 0.129595 | − | 0.398854i | ||||
\(307\) | −25.1036 | −1.43274 | −0.716368 | − | 0.697722i | \(-0.754197\pi\) | ||||
−0.716368 | + | 0.697722i | \(0.754197\pi\) | |||||||
\(308\) | −2.14896 | − | 2.52626i | −0.122448 | − | 0.143947i | ||||
\(309\) | −0.180796 | −0.0102851 | ||||||||
\(310\) | −4.58967 | + | 14.1255i | −0.260676 | + | 0.802277i | ||||
\(311\) | −17.1120 | + | 12.4326i | −0.970331 | + | 0.704987i | −0.955527 | − | 0.294903i | \(-0.904712\pi\) |
−0.0148042 | + | 0.999890i | \(0.504712\pi\) | |||||||
\(312\) | 0.429529 | + | 0.312071i | 0.0243173 | + | 0.0176675i | ||||
\(313\) | 0.671869 | + | 2.06780i | 0.0379763 | + | 0.116879i | 0.968247 | − | 0.249994i | \(-0.0804285\pi\) |
−0.930271 | + | 0.366873i | \(0.880429\pi\) | |||||||
\(314\) | 6.78756 | + | 20.8900i | 0.383044 | + | 1.17889i | ||||
\(315\) | −2.38350 | − | 1.73171i | −0.134295 | − | 0.0975709i | ||||
\(316\) | −8.32105 | + | 6.04559i | −0.468095 | + | 0.340091i | ||||
\(317\) | 0.784806 | − | 2.41538i | 0.0440791 | − | 0.135661i | −0.926595 | − | 0.376061i | \(-0.877278\pi\) |
0.970674 | + | 0.240399i | \(0.0772784\pi\) | |||||||
\(318\) | −3.96979 | −0.222615 | ||||||||
\(319\) | −0.306634 | − | 0.0742608i | −0.0171682 | − | 0.00415781i | ||||
\(320\) | 2.94617 | 0.164696 | ||||||||
\(321\) | 4.66407 | − | 14.3545i | 0.260323 | − | 0.801191i | ||||
\(322\) | 0.574481 | − | 0.417385i | 0.0320146 | − | 0.0232599i | ||||
\(323\) | −31.9605 | − | 23.2207i | −1.77833 | − | 1.29203i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | −0.603743 | − | 1.85813i | −0.0334896 | − | 0.103070i | ||||
\(326\) | −15.5264 | − | 11.2806i | −0.859928 | − | 0.624774i | ||||
\(327\) | −5.32966 | + | 3.87223i | −0.294731 | + | 0.214135i | ||||
\(328\) | −0.721910 | + | 2.22181i | −0.0398608 | + | 0.122679i | ||||
\(329\) | −13.2235 | −0.729036 | ||||||||
\(330\) | 5.12204 | − | 8.32126i | 0.281959 | − | 0.458071i | ||||
\(331\) | −13.6488 | −0.750205 | −0.375103 | − | 0.926983i | \(-0.622393\pi\) | ||||
−0.375103 | + | 0.926983i | \(0.622393\pi\) | |||||||
\(332\) | −4.54522 | + | 13.9887i | −0.249451 | + | 0.767732i | ||||
\(333\) | 1.85257 | − | 1.34597i | 0.101520 | − | 0.0737588i | ||||
\(334\) | −12.5824 | − | 9.14162i | −0.688476 | − | 0.500207i | ||||
\(335\) | −11.7662 | − | 36.2126i | −0.642855 | − | 1.97850i | ||||
\(336\) | 0.309017 | + | 0.951057i | 0.0168583 | + | 0.0518844i | ||||
\(337\) | −8.17230 | − | 5.93752i | −0.445174 | − | 0.323438i | 0.342514 | − | 0.939513i | \(-0.388722\pi\) |
−0.787687 | + | 0.616075i | \(0.788722\pi\) | |||||||
\(338\) | 10.2892 | − | 7.47552i | 0.559657 | − | 0.406615i | ||||
\(339\) | −4.16983 | + | 12.8334i | −0.226474 | + | 0.697016i | ||||
\(340\) | 21.6135 | 1.17216 | ||||||||
\(341\) | −1.27873 | − | 16.6711i | −0.0692469 | − | 0.902791i | ||||
\(342\) | 5.38503 | 0.291189 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | 0.139626 | − | 0.101444i | 0.00752814 | − | 0.00546951i | ||||
\(345\) | 1.69251 | + | 1.22968i | 0.0911219 | + | 0.0662040i | ||||
\(346\) | 6.92407 | + | 21.3101i | 0.372240 | + | 1.14564i | ||||
\(347\) | 9.97952 | + | 30.7138i | 0.535729 | + | 1.64880i | 0.742069 | + | 0.670323i | \(0.233844\pi\) |
−0.206341 | + | 0.978480i | \(0.566156\pi\) | |||||||
\(348\) | 0.0769587 | + | 0.0559138i | 0.00412542 | + | 0.00299729i | ||||
\(349\) | 5.34893 | − | 3.88623i | 0.286322 | − | 0.208025i | −0.435348 | − | 0.900262i | \(-0.643375\pi\) |
0.721670 | + | 0.692237i | \(0.243375\pi\) | |||||||
\(350\) | 1.13715 | − | 3.49978i | 0.0607831 | − | 0.187071i | ||||
\(351\) | −0.530927 | −0.0283388 | ||||||||
\(352\) | −3.06668 | + | 1.26313i | −0.163454 | + | 0.0673249i | ||||
\(353\) | −19.4835 | −1.03700 | −0.518501 | − | 0.855077i | \(-0.673510\pi\) | ||||
−0.518501 | + | 0.855077i | \(0.673510\pi\) | |||||||
\(354\) | −2.82966 | + | 8.70881i | −0.150395 | + | 0.462868i | ||||
\(355\) | −21.1600 | + | 15.3737i | −1.12306 | + | 0.815950i | ||||
\(356\) | −6.97330 | − | 5.06640i | −0.369584 | − | 0.268519i | ||||
\(357\) | 2.26700 | + | 6.97709i | 0.119982 | + | 0.369267i | ||||
\(358\) | −5.67195 | − | 17.4565i | −0.299772 | − | 0.922603i | ||||
\(359\) | −7.95052 | − | 5.77639i | −0.419613 | − | 0.304866i | 0.357869 | − | 0.933772i | \(-0.383503\pi\) |
−0.777482 | + | 0.628905i | \(0.783503\pi\) | |||||||
\(360\) | −2.38350 | + | 1.73171i | −0.125621 | + | 0.0912693i | ||||
\(361\) | 3.08972 | − | 9.50918i | 0.162617 | − | 0.500483i | ||||
\(362\) | −3.33220 | −0.175137 | ||||||||
\(363\) | −1.76393 | + | 10.8576i | −0.0925824 | + | 0.569879i | ||||
\(364\) | −0.530927 | −0.0278281 | ||||||||
\(365\) | 5.91835 | − | 18.2148i | 0.309781 | − | 0.953407i | ||||
\(366\) | 6.21163 | − | 4.51301i | 0.324687 | − | 0.235899i | ||||
\(367\) | 9.01168 | + | 6.54737i | 0.470406 | + | 0.341770i | 0.797599 | − | 0.603187i | \(-0.206103\pi\) |
−0.327194 | + | 0.944957i | \(0.606103\pi\) | |||||||
\(368\) | −0.219432 | − | 0.675342i | −0.0114387 | − | 0.0352047i | ||||
\(369\) | −0.721910 | − | 2.22181i | −0.0375811 | − | 0.115663i | ||||
\(370\) | 5.45798 | + | 3.96545i | 0.283747 | + | 0.206154i | ||||
\(371\) | 3.21163 | − | 2.33338i | 0.166739 | − | 0.121143i | ||||
\(372\) | −1.55784 | + | 4.79455i | −0.0807705 | + | 0.248586i | ||||
\(373\) | −7.65347 | −0.396281 | −0.198141 | − | 0.980174i | \(-0.563490\pi\) | ||||
−0.198141 | + | 0.980174i | \(0.563490\pi\) | |||||||
\(374\) | −22.4976 | + | 9.26649i | −1.16332 | + | 0.479159i | ||||
\(375\) | −3.88927 | −0.200841 | ||||||||
\(376\) | −4.08629 | + | 12.5763i | −0.210735 | + | 0.648574i | ||||
\(377\) | −0.0408595 | + | 0.0296861i | −0.00210437 | + | 0.00152891i | ||||
\(378\) | −0.809017 | − | 0.587785i | −0.0416113 | − | 0.0302324i | ||||
\(379\) | −2.17034 | − | 6.67961i | −0.111483 | − | 0.343109i | 0.879714 | − | 0.475502i | \(-0.157734\pi\) |
−0.991197 | + | 0.132394i | \(0.957734\pi\) | |||||||
\(380\) | 4.90261 | + | 15.0887i | 0.251499 | + | 0.774033i | ||||
\(381\) | −2.76568 | − | 2.00938i | −0.141690 | − | 0.102944i | ||||
\(382\) | 6.80888 | − | 4.94694i | 0.348373 | − | 0.253108i | ||||
\(383\) | −8.79062 | + | 27.0548i | −0.449180 | + | 1.38243i | 0.428654 | + | 0.903469i | \(0.358988\pi\) |
−0.877834 | + | 0.478965i | \(0.841012\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0.747296 | + | 9.74271i | 0.0380857 | + | 0.496534i | ||||
\(386\) | −6.90604 | −0.351508 | ||||||||
\(387\) | −0.0533324 | + | 0.164140i | −0.00271104 | + | 0.00834372i | ||||
\(388\) | 0.734536 | − | 0.533672i | 0.0372904 | − | 0.0270931i | ||||
\(389\) | 5.18355 | + | 3.76607i | 0.262816 | + | 0.190947i | 0.711388 | − | 0.702800i | \(-0.248067\pi\) |
−0.448571 | + | 0.893747i | \(0.648067\pi\) | |||||||
\(390\) | −0.483364 | − | 1.48764i | −0.0244761 | − | 0.0753297i | ||||
\(391\) | −1.60979 | − | 4.95441i | −0.0814104 | − | 0.250555i | ||||
\(392\) | −0.809017 | − | 0.587785i | −0.0408615 | − | 0.0296876i | ||||
\(393\) | −3.90167 | + | 2.83473i | −0.196813 | + | 0.142993i | ||||
\(394\) | 3.26903 | − | 10.0610i | 0.164691 | − | 0.506868i | ||||
\(395\) | 30.3024 | 1.52468 | ||||||||
\(396\) | 1.73855 | − | 2.82444i | 0.0873652 | − | 0.141933i | ||||
\(397\) | 30.7498 | 1.54329 | 0.771643 | − | 0.636056i | \(-0.219435\pi\) | ||||
0.771643 | + | 0.636056i | \(0.219435\pi\) | |||||||
\(398\) | 5.16866 | − | 15.9075i | 0.259082 | − | 0.797371i | ||||
\(399\) | −4.35658 | + | 3.16524i | −0.218102 | + | 0.158460i | ||||
\(400\) | −2.97709 | − | 2.16298i | −0.148855 | − | 0.108149i | ||||
\(401\) | 1.60374 | + | 4.93581i | 0.0800871 | + | 0.246483i | 0.983081 | − | 0.183170i | \(-0.0586359\pi\) |
−0.902994 | + | 0.429653i | \(0.858636\pi\) | |||||||
\(402\) | −3.99373 | − | 12.2914i | −0.199189 | − | 0.613041i | ||||
\(403\) | −2.16538 | − | 1.57324i | −0.107865 | − | 0.0783687i | ||||
\(404\) | 2.77348 | − | 2.01505i | 0.137986 | − | 0.100253i | ||||
\(405\) | 0.910415 | − | 2.80197i | 0.0452389 | − | 0.139231i | ||||
\(406\) | −0.0951262 | −0.00472103 | ||||||||
\(407\) | −7.38137 | − | 1.78763i | −0.365881 | − | 0.0886093i | ||||
\(408\) | 7.33615 | 0.363194 | ||||||||
\(409\) | 8.37043 | − | 25.7615i | 0.413891 | − | 1.27383i | −0.499348 | − | 0.866401i | \(-0.666427\pi\) |
0.913239 | − | 0.407424i | \(-0.133573\pi\) | |||||||
\(410\) | 5.56821 | − | 4.04554i | 0.274994 | − | 0.199795i | ||||
\(411\) | −13.9643 | − | 10.1457i | −0.688810 | − | 0.500450i | ||||
\(412\) | −0.0558691 | − | 0.171947i | −0.00275247 | − | 0.00847124i | ||||
\(413\) | −2.82966 | − | 8.70881i | −0.139239 | − | 0.428532i | ||||
\(414\) | 0.574481 | + | 0.417385i | 0.0282342 | + | 0.0205133i | ||||
\(415\) | 35.0580 | − | 25.4711i | 1.72093 | − | 1.25033i | ||||
\(416\) | −0.164066 | + | 0.504942i | −0.00804397 | + | 0.0247568i | ||||
\(417\) | −17.4516 | −0.854607 | ||||||||
\(418\) | −11.5722 | − | 13.6040i | −0.566016 | − | 0.665391i | ||||
\(419\) | −23.5391 | −1.14996 | −0.574980 | − | 0.818167i | \(-0.694990\pi\) | ||||
−0.574980 | + | 0.818167i | \(0.694990\pi\) | |||||||
\(420\) | 0.910415 | − | 2.80197i | 0.0444237 | − | 0.136722i | ||||
\(421\) | 6.84088 | − | 4.97019i | 0.333404 | − | 0.242232i | −0.408470 | − | 0.912772i | \(-0.633937\pi\) |
0.741874 | + | 0.670540i | \(0.233937\pi\) | |||||||
\(422\) | 9.99466 | + | 7.26155i | 0.486533 | + | 0.353487i | ||||
\(423\) | −4.08629 | − | 12.5763i | −0.198682 | − | 0.611482i | ||||
\(424\) | −1.22673 | − | 3.77550i | −0.0595754 | − | 0.183354i | ||||
\(425\) | −21.8404 | − | 15.8680i | −1.05941 | − | 0.769710i | ||||
\(426\) | −7.18223 | + | 5.21820i | −0.347980 | + | 0.252823i | ||||
\(427\) | −2.37263 | + | 7.30221i | −0.114820 | + | 0.353379i | ||||
\(428\) | 15.0932 | 0.729559 | ||||||||
\(429\) | 1.14094 | + | 1.34126i | 0.0550852 | + | 0.0647565i | ||||
\(430\) | −0.508471 | −0.0245206 | ||||||||
\(431\) | 9.86189 | − | 30.3518i | 0.475031 | − | 1.46199i | −0.370886 | − | 0.928679i | \(-0.620946\pi\) |
0.845916 | − | 0.533316i | \(-0.179054\pi\) | |||||||
\(432\) | −0.809017 | + | 0.587785i | −0.0389238 | + | 0.0282798i | ||||
\(433\) | −32.6167 | − | 23.6974i | −1.56746 | − | 1.13883i | −0.929540 | − | 0.368721i | \(-0.879796\pi\) |
−0.637918 | − | 0.770104i | \(-0.720204\pi\) | |||||||
\(434\) | −1.55784 | − | 4.79455i | −0.0747789 | − | 0.230146i | ||||
\(435\) | −0.0866043 | − | 0.266541i | −0.00415236 | − | 0.0127796i | ||||
\(436\) | −5.32966 | − | 3.87223i | −0.255245 | − | 0.185446i | ||||
\(437\) | 3.09359 | − | 2.24763i | 0.147987 | − | 0.107519i | ||||
\(438\) | 2.00883 | − | 6.18255i | 0.0959857 | − | 0.295414i | ||||
\(439\) | 30.2721 | 1.44481 | 0.722404 | − | 0.691471i | \(-0.243037\pi\) | ||||
0.722404 | + | 0.691471i | \(0.243037\pi\) | |||||||
\(440\) | 9.49679 | + | 2.29994i | 0.452742 | + | 0.109645i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −1.20361 | + | 3.70433i | −0.0572499 | + | 0.176197i | ||||
\(443\) | −2.55179 | + | 1.85398i | −0.121239 | + | 0.0880854i | −0.646752 | − | 0.762700i | \(-0.723873\pi\) |
0.525513 | + | 0.850785i | \(0.323873\pi\) | |||||||
\(444\) | 1.85257 | + | 1.34597i | 0.0879191 | + | 0.0638770i | ||||
\(445\) | 7.84730 | + | 24.1515i | 0.371998 | + | 1.14489i | ||||
\(446\) | 4.10564 | + | 12.6358i | 0.194407 | + | 0.598325i | ||||
\(447\) | 8.17421 | + | 5.93891i | 0.386627 | + | 0.280901i | ||||
\(448\) | −0.809017 | + | 0.587785i | −0.0382225 | + | 0.0277702i | ||||
\(449\) | 6.01127 | − | 18.5008i | 0.283690 | − | 0.873107i | −0.703099 | − | 0.711092i | \(-0.748201\pi\) |
0.986788 | − | 0.162015i | \(-0.0517992\pi\) | |||||||
\(450\) | 3.67989 | 0.173472 | ||||||||
\(451\) | −4.06151 | + | 6.59831i | −0.191249 | + | 0.310703i | ||||
\(452\) | −13.4939 | −0.634698 | ||||||||
\(453\) | −1.16713 | + | 3.59205i | −0.0548365 | + | 0.168769i | ||||
\(454\) | 12.1889 | − | 8.85578i | 0.572055 | − | 0.415622i | ||||
\(455\) | 1.26546 | + | 0.919413i | 0.0593258 | + | 0.0431028i | ||||
\(456\) | 1.66407 | + | 5.12147i | 0.0779270 | + | 0.239835i | ||||
\(457\) | −11.6848 | − | 35.9623i | −0.546594 | − | 1.68224i | −0.717170 | − | 0.696899i | \(-0.754563\pi\) |
0.170576 | − | 0.985345i | \(-0.445437\pi\) | |||||||
\(458\) | 6.78078 | + | 4.92653i | 0.316845 | + | 0.230202i | ||||
\(459\) | −5.93507 | + | 4.31208i | −0.277025 | + | 0.201271i | ||||
\(460\) | −0.646483 | + | 1.98967i | −0.0301424 | + | 0.0927689i | ||||
\(461\) | 15.3852 | 0.716560 | 0.358280 | − | 0.933614i | \(-0.383363\pi\) | ||||
0.358280 | + | 0.933614i | \(0.383363\pi\) | |||||||
\(462\) | 0.253650 | + | 3.30691i | 0.0118009 | + | 0.153851i | ||||
\(463\) | 13.7538 | 0.639195 | 0.319597 | − | 0.947553i | \(-0.396452\pi\) | ||||
0.319597 | + | 0.947553i | \(0.396452\pi\) | |||||||
\(464\) | −0.0293956 | + | 0.0904704i | −0.00136466 | + | 0.00419998i | ||||
\(465\) | 12.0159 | − | 8.73007i | 0.557224 | − | 0.404847i | ||||
\(466\) | 4.59797 | + | 3.34062i | 0.212997 | + | 0.154751i | ||||
\(467\) | −5.88110 | − | 18.1002i | −0.272145 | − | 0.837576i | −0.989961 | − | 0.141343i | \(-0.954858\pi\) |
0.717816 | − | 0.696233i | \(-0.245142\pi\) | |||||||
\(468\) | −0.164066 | − | 0.504942i | −0.00758393 | − | 0.0233409i | ||||
\(469\) | 10.4557 | + | 7.59652i | 0.482800 | + | 0.350775i | ||||
\(470\) | 31.5182 | − | 22.8993i | 1.45383 | − | 1.05627i | ||||
\(471\) | 6.78756 | − | 20.8900i | 0.312754 | − | 0.962558i | ||||
\(472\) | −9.15698 | −0.421484 | ||||||||
\(473\) | 0.529270 | − | 0.218000i | 0.0243359 | − | 0.0100236i | ||||
\(474\) | 10.2854 | 0.472423 | ||||||||
\(475\) | 6.12358 | − | 18.8464i | 0.280969 | − | 0.864733i | ||||
\(476\) | −5.93507 | + | 4.31208i | −0.272034 | + | 0.197644i | ||||
\(477\) | 3.21163 | + | 2.33338i | 0.147050 | + | 0.106838i | ||||
\(478\) | 7.65233 | + | 23.5515i | 0.350010 | + | 1.07722i | ||||
\(479\) | 11.0503 | + | 34.0094i | 0.504902 | + | 1.55393i | 0.800936 | + | 0.598751i | \(0.204336\pi\) |
−0.296034 | + | 0.955177i | \(0.595664\pi\) | |||||||
\(480\) | −2.38350 | − | 1.73171i | −0.108791 | − | 0.0790415i | ||||
\(481\) | −0.983580 | + | 0.714613i | −0.0448474 | + | 0.0325835i | ||||
\(482\) | 2.75460 | − | 8.47778i | 0.125468 | − | 0.386152i | ||||
\(483\) | −0.710097 | −0.0323105 | ||||||||
\(484\) | −10.8713 | + | 1.67760i | −0.494151 | + | 0.0762545i | ||||
\(485\) | −2.67493 | −0.121462 | ||||||||
\(486\) | 0.309017 | − | 0.951057i | 0.0140173 | − | 0.0431408i | ||||
\(487\) | 25.4489 | − | 18.4897i | 1.15320 | − | 0.837848i | 0.164295 | − | 0.986411i | \(-0.447465\pi\) |
0.988903 | + | 0.148564i | \(0.0474650\pi\) | |||||||
\(488\) | 6.21163 | + | 4.51301i | 0.281187 | + | 0.204294i | ||||
\(489\) | 5.93056 | + | 18.2524i | 0.268189 | + | 0.825401i | ||||
\(490\) | 0.910415 | + | 2.80197i | 0.0411284 | + | 0.126580i | ||||
\(491\) | 18.8669 | + | 13.7076i | 0.851453 | + | 0.618617i | 0.925546 | − | 0.378634i | \(-0.123606\pi\) |
−0.0740931 | + | 0.997251i | \(0.523606\pi\) | |||||||
\(492\) | 1.88999 | − | 1.37315i | 0.0852071 | − | 0.0619066i | ||||
\(493\) | −0.215651 | + | 0.663704i | −0.00971241 | + | 0.0298917i | ||||
\(494\) | −2.85906 | −0.128635 | ||||||||
\(495\) | −9.03494 | + | 3.72138i | −0.406090 | + | 0.167264i | ||||
\(496\) | −5.04129 | −0.226361 | ||||||||
\(497\) | 2.74337 | − | 8.44322i | 0.123057 | − | 0.378730i | ||||
\(498\) | 11.8995 | − | 8.64552i | 0.533231 | − | 0.387415i | ||||
\(499\) | −1.85774 | − | 1.34973i | −0.0831640 | − | 0.0604222i | 0.545426 | − | 0.838159i | \(-0.316368\pi\) |
−0.628590 | + | 0.777737i | \(0.716368\pi\) | |||||||
\(500\) | −1.20185 | − | 3.69891i | −0.0537483 | − | 0.165420i | ||||
\(501\) | 4.80604 | + | 14.7915i | 0.214718 | + | 0.660834i | ||||
\(502\) | −0.888454 | − | 0.645499i | −0.0396536 | − | 0.0288101i | ||||
\(503\) | −24.9007 | + | 18.0914i | −1.11027 | + | 0.806657i | −0.982706 | − | 0.185174i | \(-0.940715\pi\) |
−0.127562 | + | 0.991831i | \(0.540715\pi\) | |||||||
\(504\) | 0.309017 | − | 0.951057i | 0.0137647 | − | 0.0423634i | ||||
\(505\) | −10.1001 | −0.449448 | ||||||||
\(506\) | −0.180116 | − | 2.34823i | −0.00800715 | − | 0.104391i | ||||
\(507\) | −12.7181 | −0.564831 | ||||||||
\(508\) | 1.05640 | − | 3.25125i | 0.0468700 | − | 0.144251i | ||||
\(509\) | 11.0202 | − | 8.00665i | 0.488462 | − | 0.354888i | −0.316131 | − | 0.948716i | \(-0.602384\pi\) |
0.804592 | + | 0.593827i | \(0.202384\pi\) | |||||||
\(510\) | −17.4857 | − | 12.7041i | −0.774280 | − | 0.562547i | ||||
\(511\) | 2.00883 | + | 6.18255i | 0.0888655 | + | 0.273500i | ||||
\(512\) | 0.309017 | + | 0.951057i | 0.0136568 | + | 0.0420312i | ||||
\(513\) | −4.35658 | − | 3.16524i | −0.192348 | − | 0.139749i | ||||
\(514\) | 21.7922 | − | 15.8330i | 0.961214 | − | 0.698363i | ||||
\(515\) | −0.164600 | + | 0.506585i | −0.00725312 | + | 0.0223228i | ||||
\(516\) | −0.172587 | −0.00759774 | ||||||||
\(517\) | −22.9897 | + | 37.3490i | −1.01109 | + | 1.64261i | ||||
\(518\) | −2.28990 | −0.100613 | ||||||||
\(519\) | 6.92407 | − | 21.3101i | 0.303933 | − | 0.935409i | ||||
\(520\) | 1.26546 | − | 0.919413i | 0.0554942 | − | 0.0403189i | ||||
\(521\) | −29.9244 | − | 21.7414i | −1.31101 | − | 0.952507i | −0.999998 | − | 0.00210172i | \(-0.999331\pi\) |
−0.311015 | − | 0.950405i | \(-0.600669\pi\) | |||||||
\(522\) | −0.0293956 | − | 0.0904704i | −0.00128661 | − | 0.00395978i | ||||
\(523\) | 5.09391 | + | 15.6774i | 0.222741 | + | 0.685526i | 0.998513 | + | 0.0545129i | \(0.0173606\pi\) |
−0.775772 | + | 0.631013i | \(0.782639\pi\) | |||||||
\(524\) | −3.90167 | − | 2.83473i | −0.170445 | − | 0.123836i | ||||
\(525\) | −2.97709 | + | 2.16298i | −0.129931 | + | 0.0944004i | ||||
\(526\) | −7.75225 | + | 23.8590i | −0.338014 | + | 1.04030i | ||||
\(527\) | −36.9837 | −1.61103 | ||||||||
\(528\) | 3.22344 | + | 0.780656i | 0.140282 | + | 0.0339737i | ||||
\(529\) | −22.4958 | −0.978077 | ||||||||
\(530\) | −3.61416 | + | 11.1232i | −0.156989 | + | 0.483162i | ||||
\(531\) | 7.40815 | − | 5.38234i | 0.321486 | − | 0.233574i | ||||
\(532\) | −4.35658 | − | 3.16524i | −0.188882 | − | 0.137231i | ||||
\(533\) | 0.383282 | + | 1.17962i | 0.0166018 | + | 0.0510950i | ||||
\(534\) | 2.66356 | + | 8.19760i | 0.115264 | + | 0.354745i | ||||
\(535\) | −35.9747 | − | 26.1371i | −1.55532 | − | 1.13001i | ||||
\(536\) | 10.4557 | − | 7.59652i | 0.451618 | − | 0.328120i | ||||
\(537\) | −5.67195 | + | 17.4565i | −0.244763 | + | 0.753302i | ||||
\(538\) | 26.4570 | 1.14064 | ||||||||
\(539\) | −2.14896 | − | 2.52626i | −0.0925623 | − | 0.108814i | ||||
\(540\) | 2.94617 | 0.126783 | ||||||||
\(541\) | −5.18878 | + | 15.9694i | −0.223083 | + | 0.686579i | 0.775397 | + | 0.631473i | \(0.217550\pi\) |
−0.998481 | + | 0.0551056i | \(0.982450\pi\) | |||||||
\(542\) | 21.2668 | − | 15.4513i | 0.913489 | − | 0.663689i | ||||
\(543\) | 2.69581 | + | 1.95862i | 0.115688 | + | 0.0840523i | ||||
\(544\) | 2.26700 | + | 6.97709i | 0.0971966 | + | 0.299140i | ||||
\(545\) | 5.99766 | + | 18.4589i | 0.256911 | + | 0.790692i | ||||
\(546\) | 0.429529 | + | 0.312071i | 0.0183821 | + | 0.0133554i | ||||
\(547\) | 20.0494 | − | 14.5668i | 0.857252 | − | 0.622830i | −0.0698841 | − | 0.997555i | \(-0.522263\pi\) |
0.927136 | + | 0.374725i | \(0.122263\pi\) | |||||||
\(548\) | 5.33390 | − | 16.4161i | 0.227853 | − | 0.701259i | ||||
\(549\) | −7.67800 | −0.327689 | ||||||||
\(550\) | −7.90794 | − | 9.29634i | −0.337196 | − | 0.396397i | ||||
\(551\) | −0.512257 | −0.0218229 | ||||||||
\(552\) | −0.219432 | + | 0.675342i | −0.00933965 | + | 0.0287445i | ||||
\(553\) | −8.32105 | + | 6.04559i | −0.353847 | + | 0.257085i | ||||
\(554\) | −5.02926 | − | 3.65397i | −0.213673 | − | 0.155242i | ||||
\(555\) | −2.08476 | − | 6.41624i | −0.0884932 | − | 0.272354i | ||||
\(556\) | −5.39283 | − | 16.5974i | −0.228707 | − | 0.703888i | ||||
\(557\) | −32.9856 | − | 23.9654i | −1.39764 | − | 1.01545i | −0.994977 | − | 0.100100i | \(-0.968084\pi\) |
−0.402666 | − | 0.915347i | \(-0.631916\pi\) | |||||||
\(558\) | 4.07849 | − | 2.96320i | 0.172656 | − | 0.125442i | ||||
\(559\) | 0.0283156 | − | 0.0871466i | 0.00119762 | − | 0.00368591i | ||||
\(560\) | 2.94617 | 0.124498 | ||||||||
\(561\) | 23.6477 | + | 5.72701i | 0.998405 | + | 0.241794i | ||||
\(562\) | −30.7912 | −1.29885 | ||||||||
\(563\) | 0.600872 | − | 1.84929i | 0.0253237 | − | 0.0779384i | −0.937596 | − | 0.347727i | \(-0.886954\pi\) |
0.962920 | + | 0.269788i | \(0.0869537\pi\) | |||||||
\(564\) | 10.6981 | − | 7.77259i | 0.450469 | − | 0.327285i | ||||
\(565\) | 32.1626 | + | 23.3675i | 1.35309 | + | 0.983078i | ||||
\(566\) | −4.57872 | − | 14.0918i | −0.192458 | − | 0.592324i | ||||
\(567\) | 0.309017 | + | 0.951057i | 0.0129775 | + | 0.0399406i | ||||
\(568\) | −7.18223 | − | 5.21820i | −0.301360 | − | 0.218951i | ||||
\(569\) | −16.5945 | + | 12.0566i | −0.695679 | + | 0.505440i | −0.878522 | − | 0.477702i | \(-0.841470\pi\) |
0.182843 | + | 0.983142i | \(0.441470\pi\) | |||||||
\(570\) | 4.90261 | − | 15.0887i | 0.205348 | − | 0.631996i | ||||
\(571\) | −21.1757 | −0.886173 | −0.443087 | − | 0.896479i | \(-0.646117\pi\) | ||||
−0.443087 | + | 0.896479i | \(0.646117\pi\) | |||||||
\(572\) | −0.923041 | + | 1.49957i | −0.0385943 | + | 0.0627002i | ||||
\(573\) | −8.41624 | −0.351594 | ||||||||
\(574\) | −0.721910 | + | 2.22181i | −0.0301319 | + | 0.0927366i | ||||
\(575\) | 2.11402 | − | 1.53593i | 0.0881609 | − | 0.0640526i | ||||
\(576\) | −0.809017 | − | 0.587785i | −0.0337090 | − | 0.0244911i | ||||
\(577\) | −12.8383 | − | 39.5124i | −0.534467 | − | 1.64492i | −0.744797 | − | 0.667291i | \(-0.767454\pi\) |
0.210329 | − | 0.977631i | \(-0.432546\pi\) | |||||||
\(578\) | 11.3777 | + | 35.0170i | 0.473251 | + | 1.45652i | ||||
\(579\) | 5.58711 | + | 4.05927i | 0.232192 | + | 0.168698i | ||||
\(580\) | 0.226733 | − | 0.164731i | 0.00941457 | − | 0.00684009i | ||||
\(581\) | −4.54522 | + | 13.9887i | −0.188567 | + | 0.580351i | ||||
\(582\) | −0.907937 | −0.0376352 | ||||||||
\(583\) | −1.00694 | − | 13.1277i | −0.0417032 | − | 0.543696i | ||||
\(584\) | 6.50072 | 0.269002 | ||||||||
\(585\) | −0.483364 | + | 1.48764i | −0.0199846 | + | 0.0615064i | ||||
\(586\) | 10.0886 | − | 7.32982i | 0.416758 | − | 0.302792i | ||||
\(587\) | 28.2965 | + | 20.5586i | 1.16792 | + | 0.848543i | 0.990758 | − | 0.135638i | \(-0.0433085\pi\) |
0.177162 | + | 0.984182i | \(0.443309\pi\) | |||||||
\(588\) | 0.309017 | + | 0.951057i | 0.0127436 | + | 0.0392209i | ||||
\(589\) | −8.38904 | − | 25.8188i | −0.345664 | − | 1.06385i | ||||
\(590\) | 21.8256 | + | 15.8573i | 0.898547 | + | 0.652833i | ||||
\(591\) | −8.55843 | + | 6.21806i | −0.352047 | + | 0.255777i | ||||
\(592\) | −0.707619 | + | 2.17783i | −0.0290830 | + | 0.0895081i | ||||
\(593\) | −23.3437 | −0.958611 | −0.479306 | − | 0.877648i | \(-0.659111\pi\) | ||||
−0.479306 | + | 0.877648i | \(0.659111\pi\) | |||||||
\(594\) | −3.06668 | + | 1.26313i | −0.125827 | + | 0.0518268i | ||||
\(595\) | 21.6135 | 0.886068 | ||||||||
\(596\) | −3.12227 | + | 9.60936i | −0.127893 | + | 0.393615i | ||||
\(597\) | −13.5317 | + | 9.83138i | −0.553817 | + | 0.402371i | ||||
\(598\) | −0.305007 | − | 0.221601i | −0.0124727 | − | 0.00906193i | ||||
\(599\) | −2.28291 | − | 7.02608i | −0.0932773 | − | 0.287078i | 0.893524 | − | 0.449016i | \(-0.148225\pi\) |
−0.986801 | + | 0.161938i | \(0.948225\pi\) | |||||||
\(600\) | 1.13715 | + | 3.49978i | 0.0464239 | + | 0.142878i | ||||
\(601\) | 18.7178 | + | 13.5993i | 0.763517 | + | 0.554728i | 0.899987 | − | 0.435917i | \(-0.143576\pi\) |
−0.136470 | + | 0.990644i | \(0.543576\pi\) | |||||||
\(602\) | 0.139626 | − | 0.101444i | 0.00569074 | − | 0.00413456i | ||||
\(603\) | −3.99373 | + | 12.2914i | −0.162637 | + | 0.500546i | ||||
\(604\) | −3.77691 | −0.153680 | ||||||||
\(605\) | 28.8169 | + | 14.8275i | 1.17157 | + | 0.602822i | ||||
\(606\) | −3.42821 | −0.139262 | ||||||||
\(607\) | 2.36650 | − | 7.28334i | 0.0960533 | − | 0.295622i | −0.891473 | − | 0.453073i | \(-0.850328\pi\) |
0.987527 | + | 0.157451i | \(0.0503277\pi\) | |||||||
\(608\) | −4.35658 | + | 3.16524i | −0.176683 | + | 0.128367i | ||||
\(609\) | 0.0769587 | + | 0.0559138i | 0.00311852 | + | 0.00226574i | ||||
\(610\) | −6.99016 | − | 21.5135i | −0.283023 | − | 0.871056i | ||||
\(611\) | 2.16952 | + | 6.67711i | 0.0877696 | + | 0.270127i | ||||
\(612\) | −5.93507 | − | 4.31208i | −0.239911 | − | 0.174306i | ||||
\(613\) | −15.0507 | + | 10.9350i | −0.607892 | + | 0.441659i | −0.848671 | − | 0.528921i | \(-0.822597\pi\) |
0.240780 | + | 0.970580i | \(0.422597\pi\) | |||||||
\(614\) | −7.75743 | + | 23.8749i | −0.313064 | + | 0.963513i | ||||
\(615\) | −6.88268 | −0.277537 | ||||||||
\(616\) | −3.06668 | + | 1.26313i | −0.123560 | + | 0.0508929i | ||||
\(617\) | 2.11892 | 0.0853044 | 0.0426522 | − | 0.999090i | \(-0.486419\pi\) | ||||
0.0426522 | + | 0.999090i | \(0.486419\pi\) | |||||||
\(618\) | −0.0558691 | + | 0.171947i | −0.00224738 | + | 0.00691674i | ||||
\(619\) | 7.68317 | − | 5.58215i | 0.308813 | − | 0.224365i | −0.422574 | − | 0.906328i | \(-0.638873\pi\) |
0.731387 | + | 0.681963i | \(0.238873\pi\) | |||||||
\(620\) | 12.0159 | + | 8.73007i | 0.482570 | + | 0.350608i | ||||
\(621\) | −0.219432 | − | 0.675342i | −0.00880550 | − | 0.0271006i | ||||
\(622\) | 6.53619 | + | 20.1163i | 0.262078 | + | 0.806592i | ||||
\(623\) | −6.97330 | − | 5.06640i | −0.279379 | − | 0.202981i | ||||
\(624\) | 0.429529 | − | 0.312071i | 0.0171949 | − | 0.0124928i | ||||
\(625\) | −9.22659 | + | 28.3965i | −0.369063 | + | 1.13586i | ||||
\(626\) | 2.17421 | 0.0868991 | ||||||||
\(627\) | 1.36592 | + | 17.8078i | 0.0545494 | + | 0.711176i | ||||
\(628\) | 21.9650 | 0.876499 | ||||||||
\(629\) | −5.19120 | + | 15.9769i | −0.206987 | + | 0.637039i | ||||
\(630\) | −2.38350 | + | 1.73171i | −0.0949608 | + | 0.0689931i | ||||
\(631\) | 34.6162 | + | 25.1501i | 1.37805 | + | 1.00121i | 0.997059 | + | 0.0766316i | \(0.0244165\pi\) |
0.380989 | + | 0.924579i | \(0.375583\pi\) | |||||||
\(632\) | 3.17836 | + | 9.78198i | 0.126428 | + | 0.389106i | ||||
\(633\) | −3.81762 | − | 11.7494i | −0.151737 | − | 0.466998i | ||||
\(634\) | −2.05465 | − | 1.49279i | −0.0816005 | − | 0.0592862i | ||||
\(635\) | −8.14815 | + | 5.91998i | −0.323349 | + | 0.234927i | ||||
\(636\) | −1.22673 | + | 3.77550i | −0.0486431 | + | 0.149708i | ||||
\(637\) | −0.530927 | −0.0210361 | ||||||||
\(638\) | −0.165381 | + | 0.268678i | −0.00654750 | + | 0.0106371i | ||||
\(639\) | 8.87773 | 0.351198 | ||||||||
\(640\) | 0.910415 | − | 2.80197i | 0.0359873 | − | 0.110758i | ||||
\(641\) | 17.7615 | − | 12.9045i | 0.701539 | − | 0.509698i | −0.178894 | − | 0.983868i | \(-0.557252\pi\) |
0.880433 | + | 0.474171i | \(0.157252\pi\) | |||||||
\(642\) | −12.2107 | − | 8.87158i | −0.481917 | − | 0.350133i | ||||
\(643\) | −6.03449 | − | 18.5723i | −0.237977 | − | 0.732418i | −0.996713 | − | 0.0810194i | \(-0.974182\pi\) |
0.758735 | − | 0.651399i | \(-0.225818\pi\) | |||||||
\(644\) | −0.219432 | − | 0.675342i | −0.00864683 | − | 0.0266122i | ||||
\(645\) | 0.411362 | + | 0.298872i | 0.0161973 | + | 0.0117681i | ||||
\(646\) | −31.9605 | + | 23.2207i | −1.25747 | + | 0.913606i | ||||
\(647\) | −9.68683 | + | 29.8130i | −0.380828 | + | 1.17207i | 0.558633 | + | 0.829415i | \(0.311326\pi\) |
−0.939461 | + | 0.342655i | \(0.888674\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −29.5170 | − | 7.14845i | −1.15864 | − | 0.280601i | ||||
\(650\) | −1.95375 | −0.0766325 | ||||||||
\(651\) | −1.55784 | + | 4.79455i | −0.0610567 | + | 0.187913i | ||||
\(652\) | −15.5264 | + | 11.2806i | −0.608061 | + | 0.441782i | ||||
\(653\) | 16.0480 | + | 11.6596i | 0.628007 | + | 0.456273i | 0.855709 | − | 0.517457i | \(-0.173121\pi\) |
−0.227702 | + | 0.973731i | \(0.573121\pi\) | |||||||
\(654\) | 2.03575 | + | 6.26539i | 0.0796041 | + | 0.244996i | ||||
\(655\) | 4.39068 | + | 13.5131i | 0.171558 | + | 0.528001i | ||||
\(656\) | 1.88999 | + | 1.37315i | 0.0737915 | + | 0.0536127i | ||||
\(657\) | −5.25919 | + | 3.82103i | −0.205181 | + | 0.149072i | ||||
\(658\) | −4.08629 | + | 12.5763i | −0.159300 | + | 0.490276i | ||||
\(659\) | 37.3020 | 1.45308 | 0.726539 | − | 0.687125i | \(-0.241128\pi\) | ||||
0.726539 | + | 0.687125i | \(0.241128\pi\) | |||||||
\(660\) | −6.33119 | − | 7.44277i | −0.246441 | − | 0.289709i | ||||
\(661\) | 5.41129 | 0.210475 | 0.105237 | − | 0.994447i | \(-0.466440\pi\) | ||||
0.105237 | + | 0.994447i | \(0.466440\pi\) | |||||||
\(662\) | −4.21771 | + | 12.9808i | −0.163926 | + | 0.504512i | ||||
\(663\) | 3.15109 | − | 2.28940i | 0.122378 | − | 0.0889130i | ||||
\(664\) | 11.8995 | + | 8.64552i | 0.461792 | + | 0.335511i | ||||
\(665\) | 4.90261 | + | 15.0887i | 0.190115 | + | 0.585114i | ||||
\(666\) | −0.707619 | − | 2.17783i | −0.0274197 | − | 0.0843891i | ||||
\(667\) | −0.0546481 | − | 0.0397042i | −0.00211598 | − | 0.00153735i | ||||
\(668\) | −12.5824 | + | 9.14162i | −0.486826 | + | 0.353700i | ||||
\(669\) | 4.10564 | − | 12.6358i | 0.158733 | − | 0.488530i | ||||
\(670\) | −38.0762 | −1.47101 | ||||||||
\(671\) | 16.4997 | + | 19.3966i | 0.636964 | + | 0.748797i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | 14.9180 | − | 45.9129i | 0.575047 | − | 1.76981i | −0.0609714 | − | 0.998140i | \(-0.519420\pi\) |
0.636019 | − | 0.771674i | \(-0.280580\pi\) | |||||||
\(674\) | −8.17230 | + | 5.93752i | −0.314785 | + | 0.228705i | ||||
\(675\) | −2.97709 | − | 2.16298i | −0.114588 | − | 0.0832533i | ||||
\(676\) | −3.93011 | − | 12.0956i | −0.151158 | − | 0.465217i | ||||
\(677\) | 9.07104 | + | 27.9178i | 0.348629 | + | 1.07297i | 0.959612 | + | 0.281325i | \(0.0907740\pi\) |
−0.610984 | + | 0.791643i | \(0.709226\pi\) | |||||||
\(678\) | 10.9168 | + | 7.93150i | 0.419256 | + | 0.304607i | ||||
\(679\) | 0.734536 | − | 0.533672i | 0.0281889 | − | 0.0204804i | ||||
\(680\) | 6.67894 | − | 20.5557i | 0.256126 | − | 0.788274i | ||||
\(681\) | −15.0664 | −0.577344 | ||||||||
\(682\) | −16.2503 | − | 3.93551i | −0.622256 | − | 0.150699i | ||||
\(683\) | 24.9058 | 0.952992 | 0.476496 | − | 0.879177i | \(-0.341907\pi\) | ||||
0.476496 | + | 0.879177i | \(0.341907\pi\) | |||||||
\(684\) | 1.66407 | − | 5.12147i | 0.0636271 | − | 0.195824i | ||||
\(685\) | −41.1412 | + | 29.8909i | −1.57193 | + | 1.14207i | ||||
\(686\) | −0.809017 | − | 0.587785i | −0.0308884 | − | 0.0224417i | ||||
\(687\) | −2.59003 | − | 7.97129i | −0.0988158 | − | 0.304124i | ||||
\(688\) | −0.0533324 | − | 0.164140i | −0.00203328 | − | 0.00625779i | ||||
\(689\) | −1.70514 | − | 1.23886i | −0.0649607 | − | 0.0471967i | ||||
\(690\) | 1.69251 | − | 1.22968i | 0.0644329 | − | 0.0468133i | ||||
\(691\) | 10.5427 | − | 32.4470i | 0.401063 | − | 1.23434i | −0.523076 | − | 0.852286i | \(-0.675216\pi\) |
0.924139 | − | 0.382057i | \(-0.124784\pi\) | |||||||
\(692\) | 22.4068 | 0.851777 | ||||||||
\(693\) | 1.73855 | − | 2.82444i | 0.0660419 | − | 0.107292i | ||||
\(694\) | 32.2944 | 1.22588 | ||||||||
\(695\) | −15.8882 | + | 48.8988i | −0.602673 | + | 1.85484i | ||||
\(696\) | 0.0769587 | − | 0.0559138i | 0.00291711 | − | 0.00211941i | ||||
\(697\) | 13.8652 | + | 10.0737i | 0.525183 | + | 0.381567i | ||||
\(698\) | −2.04311 | − | 6.28804i | −0.0773328 | − | 0.238006i | ||||
\(699\) | −1.75627 | − | 5.40524i | −0.0664282 | − | 0.204445i | ||||
\(700\) | −2.97709 | − | 2.16298i | −0.112524 | − | 0.0817531i | ||||
\(701\) | 11.4354 | − | 8.30832i | 0.431910 | − | 0.313801i | −0.350502 | − | 0.936562i | \(-0.613989\pi\) |
0.782412 | + | 0.622761i | \(0.213989\pi\) | |||||||
\(702\) | −0.164066 | + | 0.504942i | −0.00619225 | + | 0.0190578i | ||||
\(703\) | −12.3312 | −0.465080 | ||||||||
\(704\) | 0.253650 | + | 3.30691i | 0.00955981 | + | 0.124634i | ||||
\(705\) | −38.9587 | −1.46727 | ||||||||
\(706\) | −6.02073 | + | 18.5299i | −0.226593 | + | 0.697382i | ||||
\(707\) | 2.77348 | − | 2.01505i | 0.104308 | − | 0.0757839i | ||||
\(708\) | 7.40815 | + | 5.38234i | 0.278415 | + | 0.202281i | ||||
\(709\) | 5.58255 | + | 17.1813i | 0.209657 | + | 0.645258i | 0.999490 | + | 0.0319360i | \(0.0101673\pi\) |
−0.789833 | + | 0.613322i | \(0.789833\pi\) | |||||||
\(710\) | 8.08242 | + | 24.8751i | 0.303328 | + | 0.933547i | ||||
\(711\) | −8.32105 | − | 6.04559i | −0.312064 | − | 0.226727i | ||||
\(712\) | −6.97330 | + | 5.06640i | −0.261335 | + | 0.189871i | ||||
\(713\) | 1.10622 | − | 3.40460i | 0.0414283 | − | 0.127503i | ||||
\(714\) | 7.33615 | 0.274549 | ||||||||
\(715\) | 4.79689 | − | 1.97578i | 0.179394 | − | 0.0738901i | ||||
\(716\) | −18.3548 | −0.685952 | ||||||||
\(717\) | 7.65233 | − | 23.5515i | 0.285782 | − | 0.879546i | ||||
\(718\) | −7.95052 | + | 5.77639i | −0.296711 | + | 0.215573i | ||||
\(719\) | 16.4996 | + | 11.9877i | 0.615333 | + | 0.447065i | 0.851288 | − | 0.524699i | \(-0.175822\pi\) |
−0.235955 | + | 0.971764i | \(0.575822\pi\) | |||||||
\(720\) | 0.910415 | + | 2.80197i | 0.0339292 | + | 0.104423i | ||||
\(721\) | −0.0558691 | − | 0.171947i | −0.00208067 | − | 0.00640365i | ||||
\(722\) | −8.08899 | − | 5.87699i | −0.301041 | − | 0.218719i | ||||
\(723\) | −7.21163 | + | 5.23955i | −0.268203 | + | 0.194861i | ||||
\(724\) | −1.02971 | + | 3.16911i | −0.0382687 | + | 0.117779i | ||||
\(725\) | −0.350054 | −0.0130007 | ||||||||
\(726\) | 9.78115 | + | 5.03280i | 0.363013 | + | 0.186785i | ||||
\(727\) | 17.3725 | 0.644310 | 0.322155 | − | 0.946687i | \(-0.395593\pi\) | ||||
0.322155 | + | 0.946687i | \(0.395593\pi\) | |||||||
\(728\) | −0.164066 | + | 0.504942i | −0.00608067 | + | 0.0187144i | ||||
\(729\) | −0.809017 | + | 0.587785i | −0.0299636 | + | 0.0217698i | ||||
\(730\) | −15.4944 | − | 11.2574i | −0.573475 | − | 0.416654i | ||||
\(731\) | −0.391255 | − | 1.20416i | −0.0144711 | − | 0.0445374i | ||||
\(732\) | −2.37263 | − | 7.30221i | −0.0876950 | − | 0.269897i | ||||
\(733\) | −18.7389 | − | 13.6146i | −0.692138 | − | 0.502867i | 0.185225 | − | 0.982696i | \(-0.440699\pi\) |
−0.877362 | + | 0.479829i | \(0.840699\pi\) | |||||||
\(734\) | 9.01168 | − | 6.54737i | 0.332627 | − | 0.241668i | ||||
\(735\) | 0.910415 | − | 2.80197i | 0.0335812 | − | 0.103352i | ||||
\(736\) | −0.710097 | −0.0261745 | ||||||||
\(737\) | 39.6337 | − | 16.3246i | 1.45992 | − | 0.601326i | ||||
\(738\) | −2.33615 | −0.0859949 | ||||||||
\(739\) | −12.6532 | + | 38.9425i | −0.465455 | + | 1.43252i | 0.392953 | + | 0.919558i | \(0.371453\pi\) |
−0.858409 | + | 0.512966i | \(0.828547\pi\) | |||||||
\(740\) | 5.45798 | − | 3.96545i | 0.200639 | − | 0.145773i | ||||
\(741\) | 2.31303 | + | 1.68051i | 0.0849712 | + | 0.0617352i | ||||
\(742\) | −1.22673 | − | 3.77550i | −0.0450348 | − | 0.138603i | ||||
\(743\) | 2.14756 | + | 6.60952i | 0.0787864 | + | 0.242480i | 0.982690 | − | 0.185256i | \(-0.0593114\pi\) |
−0.903904 | + | 0.427736i | \(0.859311\pi\) | |||||||
\(744\) | 4.07849 | + | 2.96320i | 0.149525 | + | 0.108636i | ||||
\(745\) | 24.0826 | − | 17.4970i | 0.882318 | − | 0.641041i | ||||
\(746\) | −2.36505 | + | 7.27888i | −0.0865907 | + | 0.266499i | ||||
\(747\) | −14.7086 | −0.538161 | ||||||||
\(748\) | 1.86082 | + | 24.2600i | 0.0680382 | + | 0.887033i | ||||
\(749\) | 15.0932 | 0.551495 | ||||||||
\(750\) | −1.20185 | + | 3.69891i | −0.0438853 | + | 0.135065i | ||||
\(751\) | 14.0636 | − | 10.2178i | 0.513188 | − | 0.372853i | −0.300844 | − | 0.953674i | \(-0.597268\pi\) |
0.814032 | + | 0.580821i | \(0.197268\pi\) | |||||||
\(752\) | 10.6981 | + | 7.77259i | 0.390118 | + | 0.283437i | ||||
\(753\) | 0.339359 | + | 1.04444i | 0.0123669 | + | 0.0380615i | ||||
\(754\) | 0.0156069 | + | 0.0480332i | 0.000568371 | + | 0.00174926i | ||||
\(755\) | 9.00225 | + | 6.54052i | 0.327625 | + | 0.238034i | ||||
\(756\) | −0.809017 | + | 0.587785i | −0.0294237 | + | 0.0213775i | ||||
\(757\) | 7.10161 | − | 21.8565i | 0.258113 | − | 0.794389i | −0.735088 | − | 0.677972i | \(-0.762859\pi\) |
0.993200 | − | 0.116417i | \(-0.0371409\pi\) | |||||||
\(758\) | −7.02336 | −0.255100 | ||||||||
\(759\) | −1.23454 | + | 2.00563i | −0.0448108 | + | 0.0727996i | ||||
\(760\) | 15.8652 | 0.575491 | ||||||||
\(761\) | 1.88927 | − | 5.81457i | 0.0684859 | − | 0.210778i | −0.910956 | − | 0.412503i | \(-0.864655\pi\) |
0.979442 | + | 0.201725i | \(0.0646547\pi\) | |||||||
\(762\) | −2.76568 | + | 2.00938i | −0.100190 | + | 0.0727923i | ||||
\(763\) | −5.32966 | − | 3.87223i | −0.192947 | − | 0.140184i | ||||
\(764\) | −2.60076 | − | 8.00432i | −0.0940923 | − | 0.289586i | ||||
\(765\) | 6.67894 | + | 20.5557i | 0.241478 | + | 0.743192i | ||||
\(766\) | 23.0141 | + | 16.7208i | 0.831535 | + | 0.604145i | ||||
\(767\) | −3.93319 | + | 2.85763i | −0.142019 | + | 0.103183i | ||||
\(768\) | 0.309017 | − | 0.951057i | 0.0111507 | − | 0.0343183i | ||||
\(769\) | −13.5706 | −0.489369 | −0.244684 | − | 0.969603i | \(-0.578684\pi\) | ||||
−0.244684 | + | 0.969603i | \(0.578684\pi\) | |||||||
\(770\) | 9.49679 | + | 2.29994i | 0.342241 | + | 0.0828841i | ||||
\(771\) | −26.9367 | −0.970101 | ||||||||
\(772\) | −2.13408 | + | 6.56804i | −0.0768074 | + | 0.236389i | ||||
\(773\) | −15.3040 | + | 11.1190i | −0.550448 | + | 0.399924i | −0.827951 | − | 0.560801i | \(-0.810493\pi\) |
0.277502 | + | 0.960725i | \(0.410493\pi\) | |||||||
\(774\) | 0.139626 | + | 0.101444i | 0.00501876 | + | 0.00364634i | ||||
\(775\) | −5.73269 | − | 17.6434i | −0.205924 | − | 0.633770i | ||||
\(776\) | −0.280568 | − | 0.863499i | −0.0100718 | − | 0.0309978i | ||||
\(777\) | 1.85257 | + | 1.34597i | 0.0664606 | + | 0.0482864i | ||||
\(778\) | 5.18355 | − | 3.76607i | 0.185839 | − | 0.135020i | ||||
\(779\) | −3.88751 | + | 11.9645i | −0.139284 | + | 0.428673i | ||||
\(780\) | −1.56420 | −0.0560073 | ||||||||
\(781\) | −19.0779 | − | 22.4274i | −0.682661 | − | 0.802516i | ||||
\(782\) | −5.20938 | −0.186287 | ||||||||
\(783\) | −0.0293956 | + | 0.0904704i | −0.00105051 | + | 0.00323315i | ||||
\(784\) | −0.809017 | + | 0.587785i | −0.0288935 | + | 0.0209923i | ||||
\(785\) | −52.3535 | − | 38.0371i | −1.86858 | − | 1.35760i | ||||
\(786\) | 1.49030 | + | 4.58668i | 0.0531574 | + | 0.163602i | ||||
\(787\) | −6.79260 | − | 20.9055i | −0.242130 | − | 0.745199i | −0.996095 | − | 0.0882851i | \(-0.971861\pi\) |
0.753965 | − | 0.656914i | \(-0.228139\pi\) | |||||||
\(788\) | −8.55843 | − | 6.21806i | −0.304881 | − | 0.221509i | ||||
\(789\) | 20.2957 | − | 14.7457i | 0.722545 | − | 0.524959i | ||||
\(790\) | 9.36396 | − | 28.8193i | 0.333155 | − | 1.02535i | ||||
\(791\) | −13.4939 | −0.479787 | ||||||||
\(792\) | −2.14896 | − | 2.52626i | −0.0763600 | − | 0.0897666i | ||||
\(793\) | 4.07646 | 0.144759 | ||||||||
\(794\) | 9.50220 | − | 29.2448i | 0.337220 | − | 1.03786i | ||||
\(795\) | 9.46199 | − | 6.87454i | 0.335582 | − | 0.243815i | ||||
\(796\) | −13.5317 | − | 9.83138i | −0.479619 | − | 0.348464i | ||||
\(797\) | 3.73330 | + | 11.4899i | 0.132240 | + | 0.406994i | 0.995151 | − | 0.0983632i | \(-0.0313607\pi\) |
−0.862910 | + | 0.505357i | \(0.831361\pi\) | |||||||
\(798\) | 1.66407 | + | 5.12147i | 0.0589073 | + | 0.181298i | ||||
\(799\) | 78.4825 | + | 57.0209i | 2.77651 | + | 2.01725i | ||||
\(800\) | −2.97709 | + | 2.16298i | −0.105256 | + | 0.0764730i | ||||
\(801\) | 2.66356 | − | 8.19760i | 0.0941124 | − | 0.289648i | ||||
\(802\) | 5.18982 | 0.183259 | ||||||||
\(803\) | 20.9547 | + | 5.07482i | 0.739475 | + | 0.179087i | ||||
\(804\) | −12.9240 | −0.455793 | ||||||||
\(805\) | −0.646483 | + | 1.98967i | −0.0227855 | + | 0.0701267i | ||||
\(806\) | −2.16538 | + | 1.57324i | −0.0762723 | + | 0.0554151i | ||||
\(807\) | −21.4041 | − | 15.5510i | −0.753461 | − | 0.547422i | ||||
\(808\) | −1.05938 | − | 3.26042i | −0.0372687 | − | 0.114701i | ||||
\(809\) | −1.28660 | − | 3.95976i | −0.0452346 | − | 0.139218i | 0.925888 | − | 0.377797i | \(-0.123318\pi\) |
−0.971123 | + | 0.238579i | \(0.923318\pi\) | |||||||
\(810\) | −2.38350 | − | 1.73171i | −0.0837476 | − | 0.0608462i | ||||
\(811\) | 11.4988 | − | 8.35439i | 0.403778 | − | 0.293362i | −0.367300 | − | 0.930103i | \(-0.619718\pi\) |
0.771078 | + | 0.636740i | \(0.219718\pi\) | |||||||
\(812\) | −0.0293956 | + | 0.0904704i | −0.00103158 | + | 0.00317489i | ||||
\(813\) | −26.2873 | −0.921935 | ||||||||
\(814\) | −3.98110 | + | 6.46769i | −0.139538 | + | 0.226692i | ||||
\(815\) | 56.5419 | 1.98058 | ||||||||
\(816\) | 2.26700 | − | 6.97709i | 0.0793607 | − | 0.244247i | ||||
\(817\) | 0.751891 | − | 0.546281i | 0.0263053 | − | 0.0191119i | ||||
\(818\) | −21.9141 | − | 15.9215i | −0.766207 | − | 0.556682i | ||||
\(819\) | −0.164066 | − | 0.504942i | −0.00573291 | − | 0.0176441i | ||||
\(820\) | −2.12687 | − | 6.54582i | −0.0742734 | − | 0.228590i | ||||
\(821\) | 20.6905 | + | 15.0325i | 0.722102 | + | 0.524638i | 0.887055 | − | 0.461663i | \(-0.152747\pi\) |
−0.164953 | + | 0.986301i | \(0.552747\pi\) | |||||||
\(822\) | −13.9643 | + | 10.1457i | −0.487062 | + | 0.353871i | ||||
\(823\) | −5.80093 | + | 17.8534i | −0.202208 | + | 0.622332i | 0.797609 | + | 0.603175i | \(0.206098\pi\) |
−0.999816 | + | 0.0191565i | \(0.993902\pi\) | |||||||
\(824\) | −0.180796 | −0.00629833 | ||||||||
\(825\) | 0.933405 | + | 12.1691i | 0.0324970 | + | 0.423672i | ||||
\(826\) | −9.15698 | −0.318612 | ||||||||
\(827\) | −0.0920121 | + | 0.283184i | −0.00319957 | + | 0.00984728i | −0.952644 | − | 0.304089i | \(-0.901648\pi\) |
0.949444 | + | 0.313936i | \(0.101648\pi\) | |||||||
\(828\) | 0.574481 | − | 0.417385i | 0.0199646 | − | 0.0145051i | ||||
\(829\) | 9.47190 | + | 6.88174i | 0.328973 | + | 0.239013i | 0.739995 | − | 0.672613i | \(-0.234828\pi\) |
−0.411022 | + | 0.911625i | \(0.634828\pi\) | |||||||
\(830\) | −13.3910 | − | 41.2131i | −0.464807 | − | 1.43053i | ||||
\(831\) | 1.92101 | + | 5.91225i | 0.0666390 | + | 0.205094i | ||||
\(832\) | 0.429529 | + | 0.312071i | 0.0148912 | + | 0.0108191i | ||||
\(833\) | −5.93507 | + | 4.31208i | −0.205638 | + | 0.149405i | ||||
\(834\) | −5.39283 | + | 16.5974i | −0.186739 | + | 0.574722i | ||||
\(835\) | 45.8207 | 1.58569 | ||||||||
\(836\) | −16.5141 | + | 6.80198i | −0.571154 | + | 0.235251i | ||||
\(837\) | −5.04129 | −0.174253 | ||||||||
\(838\) | −7.27399 | + | 22.3870i | −0.251276 | + | 0.773347i | ||||
\(839\) | −37.9109 | + | 27.5438i | −1.30883 | + | 0.950919i | −1.00000 | 0.000198649i | \(-0.999937\pi\) | |
−0.308828 | + | 0.951118i | \(0.599937\pi\) | |||||||
\(840\) | −2.38350 | − | 1.73171i | −0.0822385 | − | 0.0597498i | ||||
\(841\) | −8.95870 | − | 27.5720i | −0.308921 | − | 0.950760i | ||||
\(842\) | −2.61298 | − | 8.04193i | −0.0900493 | − | 0.277143i | ||||
\(843\) | 24.9106 | + | 18.0986i | 0.857967 | + | 0.623350i | ||||
\(844\) | 9.99466 | − | 7.26155i | 0.344030 | − | 0.249953i | ||||
\(845\) | −11.5788 | + | 35.6358i | −0.398322 | + | 1.22591i | ||||
\(846\) | −13.2235 | −0.454634 | ||||||||
\(847\) | −10.8713 | + | 1.67760i | −0.373543 | + | 0.0576430i | ||||
\(848\) | −3.96979 | −0.136323 | ||||||||
\(849\) | −4.57872 | + | 14.0918i | −0.157141 | + | 0.483631i | ||||
\(850\) | −21.8404 | + | 15.8680i | −0.749119 | + | 0.544267i | ||||
\(851\) | −1.31550 | − | 0.955770i | −0.0450949 | − | 0.0327634i | ||||
\(852\) | 2.74337 | + | 8.44322i | 0.0939863 | + | 0.289260i | ||||
\(853\) | −10.6555 | − | 32.7944i | −0.364839 | − | 1.12286i | −0.950082 | − | 0.312000i | \(-0.899001\pi\) |
0.585243 | − | 0.810858i | \(-0.300999\pi\) | |||||||
\(854\) | 6.21163 | + | 4.51301i | 0.212558 | + | 0.154432i | ||||
\(855\) | −12.8352 | + | 9.32532i | −0.438955 | + | 0.318919i | ||||
\(856\) | 4.66407 | − | 14.3545i | 0.159414 | − | 0.490627i | ||||
\(857\) | 25.3446 | 0.865755 | 0.432878 | − | 0.901453i | \(-0.357498\pi\) | ||||
0.432878 | + | 0.901453i | \(0.357498\pi\) | |||||||
\(858\) | 1.62818 | − | 0.670629i | 0.0555852 | − | 0.0228949i | ||||
\(859\) | 2.18125 | 0.0744234 | 0.0372117 | − | 0.999307i | \(-0.488152\pi\) | ||||
0.0372117 | + | 0.999307i | \(0.488152\pi\) | |||||||
\(860\) | −0.157126 | + | 0.483585i | −0.00535796 | + | 0.0164901i | ||||
\(861\) | 1.88999 | − | 1.37315i | 0.0644105 | − | 0.0467970i | ||||
\(862\) | −25.8188 | − | 18.7584i | −0.879391 | − | 0.638915i | ||||
\(863\) | −10.6820 | − | 32.8758i | −0.363620 | − | 1.11911i | −0.950841 | − | 0.309680i | \(-0.899778\pi\) |
0.587221 | − | 0.809427i | \(-0.300222\pi\) | |||||||
\(864\) | 0.309017 | + | 0.951057i | 0.0105130 | + | 0.0323556i | ||||
\(865\) | −53.4065 | − | 38.8021i | −1.81587 | − | 1.31931i | ||||
\(866\) | −32.6167 | + | 23.6974i | −1.10836 | + | 0.805271i | ||||
\(867\) | 11.3777 | − | 35.0170i | 0.386408 | − | 1.18924i | ||||
\(868\) | −5.04129 | −0.171113 | ||||||||
\(869\) | 2.60889 | + | 34.0128i | 0.0885006 | + | 1.15381i | ||||
\(870\) | −0.280257 | −0.00950161 | ||||||||
\(871\) | 2.12038 | − | 6.52585i | 0.0718463 | − | 0.221120i | ||||
\(872\) | −5.32966 | + | 3.87223i | −0.180485 | + | 0.131130i | ||||
\(873\) | 0.734536 | + | 0.533672i | 0.0248603 | + | 0.0180621i | ||||
\(874\) | −1.18165 | − | 3.63674i | −0.0399698 | − | 0.123015i | ||||
\(875\) | −1.20185 | − | 3.69891i | −0.0406299 | − | 0.125046i | ||||
\(876\) | −5.25919 | − | 3.82103i | −0.177692 | − | 0.129101i | ||||
\(877\) | 23.6161 | − | 17.1581i | 0.797460 | − | 0.579389i | −0.112708 | − | 0.993628i | \(-0.535952\pi\) |
0.910168 | + | 0.414239i | \(0.135952\pi\) | |||||||
\(878\) | 9.35459 | − | 28.7905i | 0.315702 | − | 0.971631i | ||||
\(879\) | −12.4702 | −0.420611 | ||||||||
\(880\) | 5.12204 | − | 8.32126i | 0.172664 | − | 0.280510i | ||||
\(881\) | 34.0184 | 1.14611 | 0.573054 | − | 0.819518i | \(-0.305759\pi\) | ||||
0.573054 | + | 0.819518i | \(0.305759\pi\) | |||||||
\(882\) | 0.309017 | − | 0.951057i | 0.0104051 | − | 0.0320237i | ||||
\(883\) | 28.3721 | − | 20.6135i | 0.954797 | − | 0.693701i | 0.00286069 | − | 0.999996i | \(-0.499089\pi\) |
0.951937 | + | 0.306295i | \(0.0990894\pi\) | |||||||
\(884\) | 3.15109 | + | 2.28940i | 0.105983 | + | 0.0770009i | ||||
\(885\) | −8.33665 | − | 25.6576i | −0.280234 | − | 0.862470i | ||||
\(886\) | 0.974697 | + | 2.99981i | 0.0327456 | + | 0.100781i | ||||
\(887\) | 7.46505 | + | 5.42368i | 0.250652 | + | 0.182109i | 0.706016 | − | 0.708196i | \(-0.250491\pi\) |
−0.455364 | + | 0.890305i | \(0.650491\pi\) | |||||||
\(888\) | 1.85257 | − | 1.34597i | 0.0621682 | − | 0.0451678i | ||||
\(889\) | 1.05640 | − | 3.25125i | 0.0354304 | − | 0.109043i | ||||
\(890\) | 25.3944 | 0.851222 | ||||||||
\(891\) | 3.22344 | + | 0.780656i | 0.107989 | + | 0.0261530i | ||||
\(892\) | 13.2861 | 0.444852 | ||||||||
\(893\) | −22.0048 | + | 67.7238i | −0.736363 | + | 2.26629i | ||||
\(894\) | 8.17421 | − | 5.93891i | 0.273387 | − | 0.198627i | ||||
\(895\) | 43.7487 | + | 31.7853i | 1.46236 | + | 1.06246i | ||||
\(896\) | 0.309017 | + | 0.951057i | 0.0103235 | + | 0.0317726i | ||||
\(897\) | 0.116502 | + | 0.358558i | 0.00388990 | + | 0.0119719i | ||||
\(898\) | −15.7377 | − | 11.4341i | −0.525175 | − | 0.381562i | ||||
\(899\) | −0.387971 | + | 0.281878i | −0.0129396 | + | 0.00940114i | ||||
\(900\) | 1.13715 | − | 3.49978i | 0.0379049 | − | 0.116659i | ||||
\(901\) | −29.1230 | −0.970227 | ||||||||
\(902\) | 5.02030 | + | 5.90171i | 0.167158 | + | 0.196506i | ||||
\(903\) | −0.172587 | −0.00574335 | ||||||||
\(904\) | −4.16983 | + | 12.8334i | −0.138687 | + | 0.426834i | ||||
\(905\) | 7.94229 | − | 5.77041i | 0.264011 | − | 0.191815i | ||||
\(906\) | 3.05558 | + | 2.22001i | 0.101515 | + | 0.0737549i | ||||
\(907\) | −8.25897 | − | 25.4185i | −0.274235 | − | 0.844007i | −0.989421 | − | 0.145073i | \(-0.953658\pi\) |
0.715186 | − | 0.698934i | \(-0.246342\pi\) | |||||||
\(908\) | −4.65576 | − | 14.3290i | −0.154507 | − | 0.475523i | ||||
\(909\) | 2.77348 | + | 2.01505i | 0.0919906 | + | 0.0668351i | ||||
\(910\) | 1.26546 | − | 0.919413i | 0.0419497 | − | 0.0304782i | ||||
\(911\) | 17.2785 | − | 53.1778i | 0.572463 | − | 1.76186i | −0.0721959 | − | 0.997390i | \(-0.523001\pi\) |
0.644659 | − | 0.764470i | \(-0.276999\pi\) | |||||||
\(912\) | 5.38503 | 0.178316 | ||||||||
\(913\) | 31.6083 | + | 37.1578i | 1.04608 | + | 1.22974i | ||||
\(914\) | −37.8130 | −1.25074 | ||||||||
\(915\) | −6.99016 | + | 21.5135i | −0.231088 | + | 0.711215i | ||||
\(916\) | 6.78078 | − | 4.92653i | 0.224043 | − | 0.162777i | ||||
\(917\) | −3.90167 | − | 2.83473i | −0.128844 | − | 0.0936109i | ||||
\(918\) | 2.26700 | + | 6.97709i | 0.0748220 | + | 0.230278i | ||||
\(919\) | 0.116888 | + | 0.359744i | 0.00385578 | + | 0.0118669i | 0.952966 | − | 0.303078i | \(-0.0980141\pi\) |
−0.949110 | + | 0.314944i | \(0.898014\pi\) | |||||||
\(920\) | 1.69251 | + | 1.22968i | 0.0558006 | + | 0.0405415i | ||||
\(921\) | 20.3092 | − | 14.7555i | 0.669212 | − | 0.486211i | ||||
\(922\) | 4.75429 | − | 14.6322i | 0.156574 | − | 0.481885i | ||||
\(923\) | −4.71343 | −0.155144 | ||||||||
\(924\) | 3.22344 | + | 0.780656i | 0.106043 | + | 0.0256817i | ||||
\(925\) | −8.42659 | −0.277064 | ||||||||
\(926\) | 4.25017 | − | 13.0807i | 0.139669 | − | 0.429857i | ||||
\(927\) | 0.146267 | − | 0.106269i | 0.00480404 | − | 0.00349034i | ||||
\(928\) | 0.0769587 | + | 0.0559138i | 0.00252629 | + | 0.00183546i | ||||
\(929\) | 14.6478 | + | 45.0813i | 0.480578 | + | 1.47907i | 0.838284 | + | 0.545234i | \(0.183559\pi\) |
−0.357706 | + | 0.933834i | \(0.616441\pi\) | |||||||
\(930\) | −4.58967 | − | 14.1255i | −0.150501 | − | 0.463195i | ||||
\(931\) | −4.35658 | − | 3.16524i | −0.142781 | − | 0.103737i | ||||
\(932\) | 4.59797 | − | 3.34062i | 0.150612 | − | 0.109426i | ||||
\(933\) | 6.53619 | − | 20.1163i | 0.213985 | − | 0.658579i | ||||
\(934\) | −19.0316 | −0.622734 | ||||||||
\(935\) | 37.5761 | − | 61.0460i | 1.22887 | − | 1.99642i | ||||
\(936\) | −0.530927 | −0.0173539 | ||||||||
\(937\) | −8.65356 | + | 26.6329i | −0.282699 | + | 0.870059i | 0.704379 | + | 0.709824i | \(0.251225\pi\) |
−0.987079 | + | 0.160236i | \(0.948775\pi\) | |||||||
\(938\) | 10.4557 | − | 7.59652i | 0.341391 | − | 0.248035i | ||||
\(939\) | −1.75898 | − | 1.27797i | −0.0574020 | − | 0.0417050i | ||||
\(940\) | −12.0389 | − | 37.0519i | −0.392665 | − | 1.20850i | ||||
\(941\) | −3.04399 | − | 9.36845i | −0.0992313 | − | 0.305403i | 0.889102 | − | 0.457709i | \(-0.151330\pi\) |
−0.988333 | + | 0.152307i | \(0.951330\pi\) | |||||||
\(942\) | −17.7701 | − | 12.9107i | −0.578980 | − | 0.420653i | ||||
\(943\) | −1.34207 | + | 0.975073i | −0.0437039 | + | 0.0317527i | ||||
\(944\) | −2.82966 | + | 8.70881i | −0.0920977 | + | 0.283447i | ||||
\(945\) | 2.94617 | 0.0958388 | ||||||||
\(946\) | −0.0437769 | − | 0.570731i | −0.00142331 | − | 0.0185561i | ||||
\(947\) | 6.83921 | 0.222244 | 0.111122 | − | 0.993807i | \(-0.464555\pi\) | ||||
0.111122 | + | 0.993807i | \(0.464555\pi\) | |||||||
\(948\) | 3.17836 | − | 9.78198i | 0.103228 | − | 0.317704i | ||||
\(949\) | 2.79225 | − | 2.02869i | 0.0906402 | − | 0.0658540i | ||||
\(950\) | −16.0317 | − | 11.6477i | −0.520138 | − | 0.377902i | ||||
\(951\) | 0.784806 | + | 2.41538i | 0.0254491 | + | 0.0783242i | ||||
\(952\) | 2.26700 | + | 6.97709i | 0.0734737 | + | 0.226129i | ||||
\(953\) | −48.9900 | − | 35.5933i | −1.58694 | − | 1.15298i | −0.908146 | − | 0.418653i | \(-0.862502\pi\) |
−0.678795 | − | 0.734328i | \(-0.737498\pi\) | |||||||
\(954\) | 3.21163 | − | 2.33338i | 0.103980 | − | 0.0755461i | ||||
\(955\) | −7.66227 | + | 23.5821i | −0.247945 | + | 0.763097i | ||||
\(956\) | 24.7635 | 0.800908 | ||||||||
\(957\) | 0.291721 | − | 0.120156i | 0.00943001 | − | 0.00388411i | ||||
\(958\) | 35.7596 | 1.15534 | ||||||||
\(959\) | 5.33390 | − | 16.4161i | 0.172241 | − | 0.530102i | ||||
\(960\) | −2.38350 | + | 1.73171i | −0.0769271 | + | 0.0558908i | ||||
\(961\) | 4.51867 | + | 3.28301i | 0.145764 | + | 0.105903i | ||||
\(962\) | 0.375694 | + | 1.15627i | 0.0121129 | + | 0.0372796i | ||||
\(963\) | 4.66407 | + | 14.3545i | 0.150297 | + | 0.462568i | ||||
\(964\) | −7.21163 | − | 5.23955i | −0.232271 | − | 0.168755i | ||||
\(965\) | 16.4605 | − | 11.9593i | 0.529883 | − | 0.384983i | ||||
\(966\) | −0.219432 | + | 0.675342i | −0.00706011 | + | 0.0217288i | ||||
\(967\) | −34.1168 | −1.09712 | −0.548560 | − | 0.836111i | \(-0.684824\pi\) | ||||
−0.548560 | + | 0.836111i | \(0.684824\pi\) | |||||||
\(968\) | −1.76393 | + | 10.8576i | −0.0566949 | + | 0.348978i | ||||
\(969\) | 39.5054 | 1.26910 | ||||||||
\(970\) | −0.826599 | + | 2.54401i | −0.0265405 | + | 0.0816833i | ||||
\(971\) | −7.63458 | + | 5.54684i | −0.245005 | + | 0.178007i | −0.703510 | − | 0.710685i | \(-0.748385\pi\) |
0.458505 | + | 0.888692i | \(0.348385\pi\) | |||||||
\(972\) | −0.809017 | − | 0.587785i | −0.0259492 | − | 0.0188532i | ||||
\(973\) | −5.39283 | − | 16.5974i | −0.172886 | − | 0.532089i | ||||
\(974\) | −9.72060 | − | 29.9169i | −0.311468 | − | 0.958600i | ||||
\(975\) | 1.58062 | + | 1.14839i | 0.0506203 | + | 0.0367778i | ||||
\(976\) | 6.21163 | − | 4.51301i | 0.198829 | − | 0.144458i | ||||
\(977\) | 16.9493 | − | 52.1646i | 0.542256 | − | 1.66889i | −0.185169 | − | 0.982707i | \(-0.559283\pi\) |
0.727426 | − | 0.686187i | \(-0.240717\pi\) | |||||||
\(978\) | 19.1917 | 0.613683 | ||||||||
\(979\) | −26.4331 | + | 10.8875i | −0.844807 | + | 0.347966i | ||||
\(980\) | 2.94617 | 0.0941118 | ||||||||
\(981\) | 2.03575 | − | 6.26539i | 0.0649965 | − | 0.200039i | ||||
\(982\) | 18.8669 | − | 13.7076i | 0.602068 | − | 0.437428i | ||||
\(983\) | −21.1135 | − | 15.3399i | −0.673417 | − | 0.489266i | 0.197750 | − | 0.980252i | \(-0.436636\pi\) |
−0.871167 | + | 0.490986i | \(0.836636\pi\) | |||||||
\(984\) | −0.721910 | − | 2.22181i | −0.0230137 | − | 0.0708287i | ||||
\(985\) | 9.63110 | + | 29.6415i | 0.306872 | + | 0.944456i | ||||
\(986\) | 0.564580 | + | 0.410192i | 0.0179799 | + | 0.0130632i | ||||
\(987\) | 10.6981 | − | 7.77259i | 0.340523 | − | 0.247404i | ||||
\(988\) | −0.883498 | + | 2.71913i | −0.0281078 | + | 0.0865069i | ||||
\(989\) | 0.122554 | 0.00389698 | ||||||||
\(990\) | 0.747296 | + | 9.74271i | 0.0237506 | + | 0.309644i | ||||
\(991\) | −16.8285 | −0.534574 | −0.267287 | − | 0.963617i | \(-0.586127\pi\) | ||||
−0.267287 | + | 0.963617i | \(0.586127\pi\) | |||||||
\(992\) | −1.55784 | + | 4.79455i | −0.0494616 | + | 0.152227i | ||||
\(993\) | 11.0421 | − | 8.02256i | 0.350411 | − | 0.254588i | ||||
\(994\) | −7.18223 | − | 5.21820i | −0.227807 | − | 0.165511i | ||||
\(995\) | 15.2277 | + | 46.8661i | 0.482751 | + | 1.48576i | ||||
\(996\) | −4.54522 | − | 13.9887i | −0.144021 | − | 0.443250i | ||||
\(997\) | −11.1209 | − | 8.07979i | −0.352202 | − | 0.255890i | 0.397590 | − | 0.917563i | \(-0.369847\pi\) |
−0.749792 | + | 0.661673i | \(0.769847\pi\) | |||||||
\(998\) | −1.85774 | + | 1.34973i | −0.0588058 | + | 0.0427249i | ||||
\(999\) | −0.707619 | + | 2.17783i | −0.0223881 | + | 0.0689034i |
(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 | 462.2.j.e.295.2 | ✓ | 8 | |
11.4 | even | 5 | 5082.2.a.cf.1.4 | 4 | |||
11.5 | even | 5 | inner | 462.2.j.e.379.2 | yes | 8 | |
11.7 | odd | 10 | 5082.2.a.ca.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.e.295.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
462.2.j.e.379.2 | yes | 8 | 11.5 | even | 5 | inner | |
5082.2.a.ca.1.4 | 4 | 11.7 | odd | 10 | |||
5082.2.a.cf.1.4 | 4 | 11.4 | even | 5 |