Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 683.3 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.683 |
Dual form | 930.2.j.e.497.3 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.707107 | + | 0.707107i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −1.67303 | − | 1.48356i | −0.748203 | − | 0.663470i | ||||
\(6\) | −1.73205 | −0.707107 | ||||||||
\(7\) | 2.00000 | − | 2.00000i | 0.755929 | − | 0.755929i | −0.219650 | − | 0.975579i | \(-0.570491\pi\) |
0.975579 | + | 0.219650i | \(0.0704915\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | −0.133975 | − | 2.23205i | −0.0423665 | − | 0.705836i | ||||
\(11\) | 2.31079i | 0.696729i | 0.937359 | + | 0.348365i | \(0.113263\pi\) | ||||
−0.937359 | + | 0.348365i | \(0.886737\pi\) | |||||||
\(12\) | −1.22474 | − | 1.22474i | −0.353553 | − | 0.353553i | ||||
\(13\) | 3.36603 | + | 3.36603i | 0.933567 | + | 0.933567i | 0.997927 | − | 0.0643593i | \(-0.0205004\pi\) |
−0.0643593 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(14\) | 2.82843 | 0.755929 | ||||||||
\(15\) | 3.86603 | − | 0.232051i | 0.998203 | − | 0.0599153i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.707107 | + | 0.707107i | 0.171499 | + | 0.171499i | 0.787638 | − | 0.616139i | \(-0.211304\pi\) |
−0.616139 | + | 0.787638i | \(0.711304\pi\) | |||||||
\(18\) | 2.12132 | − | 2.12132i | 0.500000 | − | 0.500000i | ||||
\(19\) | 3.00000i | 0.688247i | 0.938924 | + | 0.344124i | \(0.111824\pi\) | ||||
−0.938924 | + | 0.344124i | \(0.888176\pi\) | |||||||
\(20\) | 1.48356 | − | 1.67303i | 0.331735 | − | 0.374101i | ||||
\(21\) | 4.89898i | 1.06904i | ||||||||
\(22\) | −1.63397 | + | 1.63397i | −0.348365 | + | 0.348365i | ||||
\(23\) | −2.44949 | + | 2.44949i | −0.510754 | + | 0.510754i | −0.914757 | − | 0.404004i | \(-0.867618\pi\) |
0.404004 | + | 0.914757i | \(0.367618\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | 0.598076 | + | 4.96410i | 0.119615 | + | 0.992820i | ||||
\(26\) | 4.76028i | 0.933567i | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.707107 | + | 0.707107i | ||||
\(28\) | 2.00000 | + | 2.00000i | 0.377964 | + | 0.377964i | ||||
\(29\) | 4.62158 | 0.858206 | 0.429103 | − | 0.903256i | \(-0.358830\pi\) | ||||
0.429103 | + | 0.903256i | \(0.358830\pi\) | |||||||
\(30\) | 2.89778 | + | 2.56961i | 0.529059 | + | 0.469144i | ||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −2.83013 | − | 2.83013i | −0.492662 | − | 0.492662i | ||||
\(34\) | 1.00000i | 0.171499i | ||||||||
\(35\) | −6.31319 | + | 0.378937i | −1.06712 | + | 0.0640521i | ||||
\(36\) | 3.00000 | 0.500000 | ||||||||
\(37\) | −0.464102 | + | 0.464102i | −0.0762978 | + | 0.0762978i | −0.744226 | − | 0.667928i | \(-0.767181\pi\) |
0.667928 | + | 0.744226i | \(0.267181\pi\) | |||||||
\(38\) | −2.12132 | + | 2.12132i | −0.344124 | + | 0.344124i | ||||
\(39\) | −8.24504 | −1.32026 | ||||||||
\(40\) | 2.23205 | − | 0.133975i | 0.352918 | − | 0.0211832i | ||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | −3.46410 | + | 3.46410i | −0.534522 | + | 0.534522i | ||||
\(43\) | 3.46410 | + | 3.46410i | 0.528271 | + | 0.528271i | 0.920056 | − | 0.391786i | \(-0.128143\pi\) |
−0.391786 | + | 0.920056i | \(0.628143\pi\) | |||||||
\(44\) | −2.31079 | −0.348365 | ||||||||
\(45\) | −4.45069 | + | 5.01910i | −0.663470 | + | 0.748203i | ||||
\(46\) | −3.46410 | −0.510754 | ||||||||
\(47\) | −0.189469 | − | 0.189469i | −0.0276368 | − | 0.0276368i | 0.693153 | − | 0.720790i | \(-0.256221\pi\) |
−0.720790 | + | 0.693153i | \(0.756221\pi\) | |||||||
\(48\) | 1.22474 | − | 1.22474i | 0.176777 | − | 0.176777i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −3.08725 | + | 3.93305i | −0.436603 | + | 0.556218i | ||||
\(51\) | −1.73205 | −0.242536 | ||||||||
\(52\) | −3.36603 | + | 3.36603i | −0.466784 | + | 0.466784i | ||||
\(53\) | 4.89898 | − | 4.89898i | 0.672927 | − | 0.672927i | −0.285463 | − | 0.958390i | \(-0.592147\pi\) |
0.958390 | + | 0.285463i | \(0.0921474\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 3.42820 | − | 3.86603i | 0.462259 | − | 0.521295i | ||||
\(56\) | 2.82843i | 0.377964i | ||||||||
\(57\) | −3.67423 | − | 3.67423i | −0.486664 | − | 0.486664i | ||||
\(58\) | 3.26795 | + | 3.26795i | 0.429103 | + | 0.429103i | ||||
\(59\) | −9.52056 | −1.23947 | −0.619736 | − | 0.784811i | \(-0.712760\pi\) | ||||
−0.619736 | + | 0.784811i | \(0.712760\pi\) | |||||||
\(60\) | 0.232051 | + | 3.86603i | 0.0299576 | + | 0.499102i | ||||
\(61\) | 10.1244 | 1.29629 | 0.648145 | − | 0.761517i | \(-0.275545\pi\) | ||||
0.648145 | + | 0.761517i | \(0.275545\pi\) | |||||||
\(62\) | −0.707107 | − | 0.707107i | −0.0898027 | − | 0.0898027i | ||||
\(63\) | −6.00000 | − | 6.00000i | −0.755929 | − | 0.755929i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −0.637756 | − | 10.6252i | −0.0791039 | − | 1.31789i | ||||
\(66\) | − | 4.00240i | − | 0.492662i | ||||||
\(67\) | 0.169873 | − | 0.169873i | 0.0207533 | − | 0.0207533i | −0.696654 | − | 0.717407i | \(-0.745329\pi\) |
0.717407 | + | 0.696654i | \(0.245329\pi\) | |||||||
\(68\) | −0.707107 | + | 0.707107i | −0.0857493 | + | 0.0857493i | ||||
\(69\) | − | 6.00000i | − | 0.722315i | ||||||
\(70\) | −4.73205 | − | 4.19615i | −0.565588 | − | 0.501536i | ||||
\(71\) | 15.3161i | 1.81769i | 0.417136 | + | 0.908844i | \(0.363034\pi\) | ||||
−0.417136 | + | 0.908844i | \(0.636966\pi\) | |||||||
\(72\) | 2.12132 | + | 2.12132i | 0.250000 | + | 0.250000i | ||||
\(73\) | −9.46410 | − | 9.46410i | −1.10769 | − | 1.10769i | −0.993454 | − | 0.114236i | \(-0.963558\pi\) |
−0.114236 | − | 0.993454i | \(-0.536442\pi\) | |||||||
\(74\) | −0.656339 | −0.0762978 | ||||||||
\(75\) | −6.81225 | − | 5.34727i | −0.786611 | − | 0.617449i | ||||
\(76\) | −3.00000 | −0.344124 | ||||||||
\(77\) | 4.62158 | + | 4.62158i | 0.526678 | + | 0.526678i | ||||
\(78\) | −5.83013 | − | 5.83013i | −0.660132 | − | 0.660132i | ||||
\(79\) | 3.73205i | 0.419889i | 0.977713 | + | 0.209944i | \(0.0673283\pi\) | ||||
−0.977713 | + | 0.209944i | \(0.932672\pi\) | |||||||
\(80\) | 1.67303 | + | 1.48356i | 0.187051 | + | 0.165867i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | −4.00000 | + | 4.00000i | −0.441726 | + | 0.441726i | ||||
\(83\) | 4.43211 | − | 4.43211i | 0.486487 | − | 0.486487i | −0.420709 | − | 0.907196i | \(-0.638219\pi\) |
0.907196 | + | 0.420709i | \(0.138219\pi\) | |||||||
\(84\) | −4.89898 | −0.534522 | ||||||||
\(85\) | −0.133975 | − | 2.23205i | −0.0145316 | − | 0.242100i | ||||
\(86\) | 4.89898i | 0.528271i | ||||||||
\(87\) | −5.66025 | + | 5.66025i | −0.606843 | + | 0.606843i | ||||
\(88\) | −1.63397 | − | 1.63397i | −0.174182 | − | 0.174182i | ||||
\(89\) | 9.89949 | 1.04934 | 0.524672 | − | 0.851304i | \(-0.324188\pi\) | ||||
0.524672 | + | 0.851304i | \(0.324188\pi\) | |||||||
\(90\) | −6.69615 | + | 0.401924i | −0.705836 | + | 0.0423665i | ||||
\(91\) | 13.4641 | 1.41142 | ||||||||
\(92\) | −2.44949 | − | 2.44949i | −0.255377 | − | 0.255377i | ||||
\(93\) | 1.22474 | − | 1.22474i | 0.127000 | − | 0.127000i | ||||
\(94\) | − | 0.267949i | − | 0.0276368i | ||||||
\(95\) | 4.45069 | − | 5.01910i | 0.456631 | − | 0.514949i | ||||
\(96\) | 1.73205 | 0.176777 | ||||||||
\(97\) | −8.36603 | + | 8.36603i | −0.849441 | + | 0.849441i | −0.990063 | − | 0.140622i | \(-0.955090\pi\) |
0.140622 | + | 0.990063i | \(0.455090\pi\) | |||||||
\(98\) | 0.707107 | − | 0.707107i | 0.0714286 | − | 0.0714286i | ||||
\(99\) | 6.93237 | 0.696729 | ||||||||
\(100\) | −4.96410 | + | 0.598076i | −0.496410 | + | 0.0598076i | ||||
\(101\) | 9.89949i | 0.985037i | 0.870302 | + | 0.492518i | \(0.163924\pi\) | ||||
−0.870302 | + | 0.492518i | \(0.836076\pi\) | |||||||
\(102\) | −1.22474 | − | 1.22474i | −0.121268 | − | 0.121268i | ||||
\(103\) | −5.46410 | − | 5.46410i | −0.538394 | − | 0.538394i | 0.384663 | − | 0.923057i | \(-0.374318\pi\) |
−0.923057 | + | 0.384663i | \(0.874318\pi\) | |||||||
\(104\) | −4.76028 | −0.466784 | ||||||||
\(105\) | 7.26795 | − | 8.19615i | 0.709279 | − | 0.799863i | ||||
\(106\) | 6.92820 | 0.672927 | ||||||||
\(107\) | 12.2474 | + | 12.2474i | 1.18401 | + | 1.18401i | 0.978697 | + | 0.205308i | \(0.0658197\pi\) |
0.205308 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(108\) | −3.67423 | + | 3.67423i | −0.353553 | + | 0.353553i | ||||
\(109\) | − | 1.07180i | − | 0.102660i | −0.998682 | − | 0.0513298i | \(-0.983654\pi\) | ||
0.998682 | − | 0.0513298i | \(-0.0163460\pi\) | |||||||
\(110\) | 5.15780 | − | 0.309587i | 0.491777 | − | 0.0295180i | ||||
\(111\) | − | 1.13681i | − | 0.107901i | ||||||
\(112\) | −2.00000 | + | 2.00000i | −0.188982 | + | 0.188982i | ||||
\(113\) | 10.1769 | − | 10.1769i | 0.957362 | − | 0.957362i | −0.0417656 | − | 0.999127i | \(-0.513298\pi\) |
0.999127 | + | 0.0417656i | \(0.0132983\pi\) | |||||||
\(114\) | − | 5.19615i | − | 0.486664i | ||||||
\(115\) | 7.73205 | − | 0.464102i | 0.721017 | − | 0.0432777i | ||||
\(116\) | 4.62158i | 0.429103i | ||||||||
\(117\) | 10.0981 | − | 10.0981i | 0.933567 | − | 0.933567i | ||||
\(118\) | −6.73205 | − | 6.73205i | −0.619736 | − | 0.619736i | ||||
\(119\) | 2.82843 | 0.259281 | ||||||||
\(120\) | −2.56961 | + | 2.89778i | −0.234572 | + | 0.264530i | ||||
\(121\) | 5.66025 | 0.514569 | ||||||||
\(122\) | 7.15900 | + | 7.15900i | 0.648145 | + | 0.648145i | ||||
\(123\) | −6.92820 | − | 6.92820i | −0.624695 | − | 0.624695i | ||||
\(124\) | − | 1.00000i | − | 0.0898027i | ||||||
\(125\) | 6.36396 | − | 9.19239i | 0.569210 | − | 0.822192i | ||||
\(126\) | − | 8.48528i | − | 0.755929i | ||||||
\(127\) | 3.73205 | − | 3.73205i | 0.331166 | − | 0.331166i | −0.521863 | − | 0.853029i | \(-0.674763\pi\) |
0.853029 | + | 0.521863i | \(0.174763\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −8.48528 | −0.747087 | ||||||||
\(130\) | 7.06218 | − | 7.96410i | 0.619394 | − | 0.698498i | ||||
\(131\) | − | 12.3490i | − | 1.07894i | −0.842006 | − | 0.539468i | \(-0.818625\pi\) | ||
0.842006 | − | 0.539468i | \(-0.181375\pi\) | |||||||
\(132\) | 2.83013 | − | 2.83013i | 0.246331 | − | 0.246331i | ||||
\(133\) | 6.00000 | + | 6.00000i | 0.520266 | + | 0.520266i | ||||
\(134\) | 0.240237 | 0.0207533 | ||||||||
\(135\) | −0.696152 | − | 11.5981i | −0.0599153 | − | 0.998203i | ||||
\(136\) | −1.00000 | −0.0857493 | ||||||||
\(137\) | −14.7985 | − | 14.7985i | −1.26432 | − | 1.26432i | −0.948979 | − | 0.315340i | \(-0.897881\pi\) |
−0.315340 | − | 0.948979i | \(-0.602119\pi\) | |||||||
\(138\) | 4.24264 | − | 4.24264i | 0.361158 | − | 0.361158i | ||||
\(139\) | 22.7846i | 1.93257i | 0.257484 | + | 0.966283i | \(0.417107\pi\) | ||||
−0.257484 | + | 0.966283i | \(0.582893\pi\) | |||||||
\(140\) | −0.378937 | − | 6.31319i | −0.0320261 | − | 0.533562i | ||||
\(141\) | 0.464102 | 0.0390844 | ||||||||
\(142\) | −10.8301 | + | 10.8301i | −0.908844 | + | 0.908844i | ||||
\(143\) | −7.77817 | + | 7.77817i | −0.650444 | + | 0.650444i | ||||
\(144\) | 3.00000i | 0.250000i | ||||||||
\(145\) | −7.73205 | − | 6.85641i | −0.642112 | − | 0.569394i | ||||
\(146\) | − | 13.3843i | − | 1.10769i | ||||||
\(147\) | 1.22474 | + | 1.22474i | 0.101015 | + | 0.101015i | ||||
\(148\) | −0.464102 | − | 0.464102i | −0.0381489 | − | 0.0381489i | ||||
\(149\) | 5.03768 | 0.412703 | 0.206351 | − | 0.978478i | \(-0.433841\pi\) | ||||
0.206351 | + | 0.978478i | \(0.433841\pi\) | |||||||
\(150\) | −1.03590 | − | 8.59808i | −0.0845807 | − | 0.702030i | ||||
\(151\) | 14.3205 | 1.16539 | 0.582693 | − | 0.812692i | \(-0.301999\pi\) | ||||
0.582693 | + | 0.812692i | \(0.301999\pi\) | |||||||
\(152\) | −2.12132 | − | 2.12132i | −0.172062 | − | 0.172062i | ||||
\(153\) | 2.12132 | − | 2.12132i | 0.171499 | − | 0.171499i | ||||
\(154\) | 6.53590i | 0.526678i | ||||||||
\(155\) | 1.67303 | + | 1.48356i | 0.134381 | + | 0.119163i | ||||
\(156\) | − | 8.24504i | − | 0.660132i | ||||||
\(157\) | 4.73205 | − | 4.73205i | 0.377659 | − | 0.377659i | −0.492598 | − | 0.870257i | \(-0.663953\pi\) |
0.870257 | + | 0.492598i | \(0.163953\pi\) | |||||||
\(158\) | −2.63896 | + | 2.63896i | −0.209944 | + | 0.209944i | ||||
\(159\) | 12.0000i | 0.951662i | ||||||||
\(160\) | 0.133975 | + | 2.23205i | 0.0105916 | + | 0.176459i | ||||
\(161\) | 9.79796i | 0.772187i | ||||||||
\(162\) | −6.36396 | − | 6.36396i | −0.500000 | − | 0.500000i | ||||
\(163\) | 3.36603 | + | 3.36603i | 0.263647 | + | 0.263647i | 0.826534 | − | 0.562887i | \(-0.190309\pi\) |
−0.562887 | + | 0.826534i | \(0.690309\pi\) | |||||||
\(164\) | −5.65685 | −0.441726 | ||||||||
\(165\) | 0.536220 | + | 8.93357i | 0.0417447 | + | 0.695477i | ||||
\(166\) | 6.26795 | 0.486487 | ||||||||
\(167\) | −1.13681 | − | 1.13681i | −0.0879692 | − | 0.0879692i | 0.661753 | − | 0.749722i | \(-0.269813\pi\) |
−0.749722 | + | 0.661753i | \(0.769813\pi\) | |||||||
\(168\) | −3.46410 | − | 3.46410i | −0.267261 | − | 0.267261i | ||||
\(169\) | 9.66025i | 0.743096i | ||||||||
\(170\) | 1.48356 | − | 1.67303i | 0.113784 | − | 0.128316i | ||||
\(171\) | 9.00000 | 0.688247 | ||||||||
\(172\) | −3.46410 | + | 3.46410i | −0.264135 | + | 0.264135i | ||||
\(173\) | 13.1948 | − | 13.1948i | 1.00318 | − | 1.00318i | 0.00318655 | − | 0.999995i | \(-0.498986\pi\) |
0.999995 | − | 0.00318655i | \(-0.00101431\pi\) | |||||||
\(174\) | −8.00481 | −0.606843 | ||||||||
\(175\) | 11.1244 | + | 8.73205i | 0.840922 | + | 0.660081i | ||||
\(176\) | − | 2.31079i | − | 0.174182i | ||||||
\(177\) | 11.6603 | − | 11.6603i | 0.876438 | − | 0.876438i | ||||
\(178\) | 7.00000 | + | 7.00000i | 0.524672 | + | 0.524672i | ||||
\(179\) | −4.76028 | −0.355800 | −0.177900 | − | 0.984049i | \(-0.556930\pi\) | ||||
−0.177900 | + | 0.984049i | \(0.556930\pi\) | |||||||
\(180\) | −5.01910 | − | 4.45069i | −0.374101 | − | 0.331735i | ||||
\(181\) | −12.9282 | −0.960946 | −0.480473 | − | 0.877010i | \(-0.659535\pi\) | ||||
−0.480473 | + | 0.877010i | \(0.659535\pi\) | |||||||
\(182\) | 9.52056 | + | 9.52056i | 0.705711 | + | 0.705711i | ||||
\(183\) | −12.3998 | + | 12.3998i | −0.916616 | + | 0.916616i | ||||
\(184\) | − | 3.46410i | − | 0.255377i | ||||||
\(185\) | 1.46498 | − | 0.0879327i | 0.107708 | − | 0.00646494i | ||||
\(186\) | 1.73205 | 0.127000 | ||||||||
\(187\) | −1.63397 | + | 1.63397i | −0.119488 | + | 0.119488i | ||||
\(188\) | 0.189469 | − | 0.189469i | 0.0138184 | − | 0.0138184i | ||||
\(189\) | 14.6969 | 1.06904 | ||||||||
\(190\) | 6.69615 | − | 0.401924i | 0.485790 | − | 0.0291586i | ||||
\(191\) | − | 4.52004i | − | 0.327059i | −0.986538 | − | 0.163529i | \(-0.947712\pi\) | ||
0.986538 | − | 0.163529i | \(-0.0522879\pi\) | |||||||
\(192\) | 1.22474 | + | 1.22474i | 0.0883883 | + | 0.0883883i | ||||
\(193\) | −12.3660 | − | 12.3660i | −0.890126 | − | 0.890126i | 0.104409 | − | 0.994534i | \(-0.466705\pi\) |
−0.994534 | + | 0.104409i | \(0.966705\pi\) | |||||||
\(194\) | −11.8313 | −0.849441 | ||||||||
\(195\) | 13.7942 | + | 12.2321i | 0.987825 | + | 0.875955i | ||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −13.2827 | − | 13.2827i | −0.946355 | − | 0.946355i | 0.0522776 | − | 0.998633i | \(-0.483352\pi\) |
−0.998633 | + | 0.0522776i | \(0.983352\pi\) | |||||||
\(198\) | 4.90192 | + | 4.90192i | 0.348365 | + | 0.348365i | ||||
\(199\) | − | 3.39230i | − | 0.240474i | −0.992745 | − | 0.120237i | \(-0.961635\pi\) | ||
0.992745 | − | 0.120237i | \(-0.0383655\pi\) | |||||||
\(200\) | −3.93305 | − | 3.08725i | −0.278109 | − | 0.218301i | ||||
\(201\) | 0.416102i | 0.0293496i | ||||||||
\(202\) | −7.00000 | + | 7.00000i | −0.492518 | + | 0.492518i | ||||
\(203\) | 9.24316 | − | 9.24316i | 0.648742 | − | 0.648742i | ||||
\(204\) | − | 1.73205i | − | 0.121268i | ||||||
\(205\) | 8.39230 | − | 9.46410i | 0.586144 | − | 0.661002i | ||||
\(206\) | − | 7.72741i | − | 0.538394i | ||||||
\(207\) | 7.34847 | + | 7.34847i | 0.510754 | + | 0.510754i | ||||
\(208\) | −3.36603 | − | 3.36603i | −0.233392 | − | 0.233392i | ||||
\(209\) | −6.93237 | −0.479522 | ||||||||
\(210\) | 10.9348 | − | 0.656339i | 0.754571 | − | 0.0452917i | ||||
\(211\) | 5.60770 | 0.386050 | 0.193025 | − | 0.981194i | \(-0.438170\pi\) | ||||
0.193025 | + | 0.981194i | \(0.438170\pi\) | |||||||
\(212\) | 4.89898 | + | 4.89898i | 0.336463 | + | 0.336463i | ||||
\(213\) | −18.7583 | − | 18.7583i | −1.28530 | − | 1.28530i | ||||
\(214\) | 17.3205i | 1.18401i | ||||||||
\(215\) | −0.656339 | − | 10.9348i | −0.0447619 | − | 0.745745i | ||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | −2.00000 | + | 2.00000i | −0.135769 | + | 0.135769i | ||||
\(218\) | 0.757875 | − | 0.757875i | 0.0513298 | − | 0.0513298i | ||||
\(219\) | 23.1822 | 1.56651 | ||||||||
\(220\) | 3.86603 | + | 3.42820i | 0.260647 | + | 0.231129i | ||||
\(221\) | 4.76028i | 0.320211i | ||||||||
\(222\) | 0.803848 | − | 0.803848i | 0.0539507 | − | 0.0539507i | ||||
\(223\) | −1.09808 | − | 1.09808i | −0.0735326 | − | 0.0735326i | 0.669384 | − | 0.742917i | \(-0.266558\pi\) |
−0.742917 | + | 0.669384i | \(0.766558\pi\) | |||||||
\(224\) | −2.82843 | −0.188982 | ||||||||
\(225\) | 14.8923 | − | 1.79423i | 0.992820 | − | 0.119615i | ||||
\(226\) | 14.3923 | 0.957362 | ||||||||
\(227\) | −12.6264 | − | 12.6264i | −0.838043 | − | 0.838043i | 0.150558 | − | 0.988601i | \(-0.451893\pi\) |
−0.988601 | + | 0.150558i | \(0.951893\pi\) | |||||||
\(228\) | 3.67423 | − | 3.67423i | 0.243332 | − | 0.243332i | ||||
\(229\) | 24.3205i | 1.60714i | 0.595207 | + | 0.803572i | \(0.297070\pi\) | ||||
−0.595207 | + | 0.803572i | \(0.702930\pi\) | |||||||
\(230\) | 5.79555 | + | 5.13922i | 0.382148 | + | 0.338870i | ||||
\(231\) | −11.3205 | −0.744835 | ||||||||
\(232\) | −3.26795 | + | 3.26795i | −0.214551 | + | 0.214551i | ||||
\(233\) | −11.5911 | + | 11.5911i | −0.759359 | + | 0.759359i | −0.976206 | − | 0.216847i | \(-0.930423\pi\) |
0.216847 | + | 0.976206i | \(0.430423\pi\) | |||||||
\(234\) | 14.2808 | 0.933567 | ||||||||
\(235\) | 0.0358984 | + | 0.598076i | 0.00234175 | + | 0.0390142i | ||||
\(236\) | − | 9.52056i | − | 0.619736i | ||||||
\(237\) | −4.57081 | − | 4.57081i | −0.296906 | − | 0.296906i | ||||
\(238\) | 2.00000 | + | 2.00000i | 0.129641 | + | 0.129641i | ||||
\(239\) | −2.55103 | −0.165012 | −0.0825061 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825061 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(240\) | −3.86603 | + | 0.232051i | −0.249551 | + | 0.0149788i | ||||
\(241\) | −16.3923 | −1.05592 | −0.527961 | − | 0.849269i | \(-0.677043\pi\) | ||||
−0.527961 | + | 0.849269i | \(0.677043\pi\) | |||||||
\(242\) | 4.00240 | + | 4.00240i | 0.257284 | + | 0.257284i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.707107 | − | 0.707107i | ||||
\(244\) | 10.1244i | 0.648145i | ||||||||
\(245\) | −1.48356 | + | 1.67303i | −0.0947814 | + | 0.106886i | ||||
\(246\) | − | 9.79796i | − | 0.624695i | ||||||
\(247\) | −10.0981 | + | 10.0981i | −0.642525 | + | 0.642525i | ||||
\(248\) | 0.707107 | − | 0.707107i | 0.0449013 | − | 0.0449013i | ||||
\(249\) | 10.8564i | 0.687997i | ||||||||
\(250\) | 11.0000 | − | 2.00000i | 0.695701 | − | 0.126491i | ||||
\(251\) | − | 6.03579i | − | 0.380976i | −0.981690 | − | 0.190488i | \(-0.938993\pi\) | ||
0.981690 | − | 0.190488i | \(-0.0610070\pi\) | |||||||
\(252\) | 6.00000 | − | 6.00000i | 0.377964 | − | 0.377964i | ||||
\(253\) | −5.66025 | − | 5.66025i | −0.355857 | − | 0.355857i | ||||
\(254\) | 5.27792 | 0.331166 | ||||||||
\(255\) | 2.89778 | + | 2.56961i | 0.181466 | + | 0.160915i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.4548 | − | 15.4548i | −0.964045 | − | 0.964045i | 0.0353309 | − | 0.999376i | \(-0.488751\pi\) |
−0.999376 | + | 0.0353309i | \(0.988751\pi\) | |||||||
\(258\) | −6.00000 | − | 6.00000i | −0.373544 | − | 0.373544i | ||||
\(259\) | 1.85641i | 0.115351i | ||||||||
\(260\) | 10.6252 | − | 0.637756i | 0.658946 | − | 0.0395520i | ||||
\(261\) | − | 13.8647i | − | 0.858206i | ||||||
\(262\) | 8.73205 | − | 8.73205i | 0.539468 | − | 0.539468i | ||||
\(263\) | 15.7322 | − | 15.7322i | 0.970090 | − | 0.970090i | −0.0294756 | − | 0.999566i | \(-0.509384\pi\) |
0.999566 | + | 0.0294756i | \(0.00938373\pi\) | |||||||
\(264\) | 4.00240 | 0.246331 | ||||||||
\(265\) | −15.4641 | + | 0.928203i | −0.949952 | + | 0.0570191i | ||||
\(266\) | 8.48528i | 0.520266i | ||||||||
\(267\) | −12.1244 | + | 12.1244i | −0.741999 | + | 0.741999i | ||||
\(268\) | 0.169873 | + | 0.169873i | 0.0103766 | + | 0.0103766i | ||||
\(269\) | −9.24316 | −0.563565 | −0.281783 | − | 0.959478i | \(-0.590926\pi\) | ||||
−0.281783 | + | 0.959478i | \(0.590926\pi\) | |||||||
\(270\) | 7.70882 | − | 8.69333i | 0.469144 | − | 0.529059i | ||||
\(271\) | −25.5885 | −1.55439 | −0.777194 | − | 0.629261i | \(-0.783358\pi\) | ||||
−0.777194 | + | 0.629261i | \(0.783358\pi\) | |||||||
\(272\) | −0.707107 | − | 0.707107i | −0.0428746 | − | 0.0428746i | ||||
\(273\) | −16.4901 | + | 16.4901i | −0.998026 | + | 0.998026i | ||||
\(274\) | − | 20.9282i | − | 1.26432i | ||||||
\(275\) | −11.4710 | + | 1.38203i | −0.691727 | + | 0.0833394i | ||||
\(276\) | 6.00000 | 0.361158 | ||||||||
\(277\) | 14.7583 | − | 14.7583i | 0.886742 | − | 0.886742i | −0.107467 | − | 0.994209i | \(-0.534274\pi\) |
0.994209 | + | 0.107467i | \(0.0342739\pi\) | |||||||
\(278\) | −16.1112 | + | 16.1112i | −0.966283 | + | 0.966283i | ||||
\(279\) | 3.00000i | 0.179605i | ||||||||
\(280\) | 4.19615 | − | 4.73205i | 0.250768 | − | 0.282794i | ||||
\(281\) | − | 10.0010i | − | 0.596611i | −0.954470 | − | 0.298306i | \(-0.903578\pi\) | ||
0.954470 | − | 0.298306i | \(-0.0964215\pi\) | |||||||
\(282\) | 0.328169 | + | 0.328169i | 0.0195422 | + | 0.0195422i | ||||
\(283\) | 4.90192 | + | 4.90192i | 0.291389 | + | 0.291389i | 0.837629 | − | 0.546240i | \(-0.183941\pi\) |
−0.546240 | + | 0.837629i | \(0.683941\pi\) | |||||||
\(284\) | −15.3161 | −0.908844 | ||||||||
\(285\) | 0.696152 | + | 11.5981i | 0.0412365 | + | 0.687011i | ||||
\(286\) | −11.0000 | −0.650444 | ||||||||
\(287\) | 11.3137 | + | 11.3137i | 0.667827 | + | 0.667827i | ||||
\(288\) | −2.12132 | + | 2.12132i | −0.125000 | + | 0.125000i | ||||
\(289\) | − | 16.0000i | − | 0.941176i | ||||||
\(290\) | −0.619174 | − | 10.3156i | −0.0363592 | − | 0.605753i | ||||
\(291\) | − | 20.4925i | − | 1.20129i | ||||||
\(292\) | 9.46410 | − | 9.46410i | 0.553845 | − | 0.553845i | ||||
\(293\) | 18.2832 | − | 18.2832i | 1.06812 | − | 1.06812i | 0.0706146 | − | 0.997504i | \(-0.477504\pi\) |
0.997504 | − | 0.0706146i | \(-0.0224961\pi\) | |||||||
\(294\) | 1.73205i | 0.101015i | ||||||||
\(295\) | 15.9282 | + | 14.1244i | 0.927376 | + | 0.822352i | ||||
\(296\) | − | 0.656339i | − | 0.0381489i | ||||||
\(297\) | −8.49038 | + | 8.49038i | −0.492662 | + | 0.492662i | ||||
\(298\) | 3.56218 | + | 3.56218i | 0.206351 | + | 0.206351i | ||||
\(299\) | −16.4901 | −0.953646 | ||||||||
\(300\) | 5.34727 | − | 6.81225i | 0.308725 | − | 0.393305i | ||||
\(301\) | 13.8564 | 0.798670 | ||||||||
\(302\) | 10.1261 | + | 10.1261i | 0.582693 | + | 0.582693i | ||||
\(303\) | −12.1244 | − | 12.1244i | −0.696526 | − | 0.696526i | ||||
\(304\) | − | 3.00000i | − | 0.172062i | ||||||
\(305\) | −16.9384 | − | 15.0201i | −0.969889 | − | 0.860050i | ||||
\(306\) | 3.00000 | 0.171499 | ||||||||
\(307\) | −19.5885 | + | 19.5885i | −1.11797 | + | 1.11797i | −0.125934 | + | 0.992039i | \(0.540193\pi\) |
−0.992039 | + | 0.125934i | \(0.959807\pi\) | |||||||
\(308\) | −4.62158 | + | 4.62158i | −0.263339 | + | 0.263339i | ||||
\(309\) | 13.3843 | 0.761404 | ||||||||
\(310\) | 0.133975 | + | 2.23205i | 0.00760925 | + | 0.126772i | ||||
\(311\) | 9.65926i | 0.547726i | 0.961769 | + | 0.273863i | \(0.0883015\pi\) | ||||
−0.961769 | + | 0.273863i | \(0.911698\pi\) | |||||||
\(312\) | 5.83013 | − | 5.83013i | 0.330066 | − | 0.330066i | ||||
\(313\) | −11.8564 | − | 11.8564i | −0.670164 | − | 0.670164i | 0.287590 | − | 0.957754i | \(-0.407146\pi\) |
−0.957754 | + | 0.287590i | \(0.907146\pi\) | |||||||
\(314\) | 6.69213 | 0.377659 | ||||||||
\(315\) | 1.13681 | + | 18.9396i | 0.0640521 | + | 1.06712i | ||||
\(316\) | −3.73205 | −0.209944 | ||||||||
\(317\) | 4.57081 | + | 4.57081i | 0.256722 | + | 0.256722i | 0.823720 | − | 0.566997i | \(-0.191895\pi\) |
−0.566997 | + | 0.823720i | \(0.691895\pi\) | |||||||
\(318\) | −8.48528 | + | 8.48528i | −0.475831 | + | 0.475831i | ||||
\(319\) | 10.6795i | 0.597937i | ||||||||
\(320\) | −1.48356 | + | 1.67303i | −0.0829337 | + | 0.0935254i | ||||
\(321\) | −30.0000 | −1.67444 | ||||||||
\(322\) | −6.92820 | + | 6.92820i | −0.386094 | + | 0.386094i | ||||
\(323\) | −2.12132 | + | 2.12132i | −0.118033 | + | 0.118033i | ||||
\(324\) | − | 9.00000i | − | 0.500000i | ||||||
\(325\) | −14.6962 | + | 18.7224i | −0.815196 | + | 1.03853i | ||||
\(326\) | 4.76028i | 0.263647i | ||||||||
\(327\) | 1.31268 | + | 1.31268i | 0.0725912 | + | 0.0725912i | ||||
\(328\) | −4.00000 | − | 4.00000i | −0.220863 | − | 0.220863i | ||||
\(329\) | −0.757875 | −0.0417830 | ||||||||
\(330\) | −5.93782 | + | 6.69615i | −0.326866 | + | 0.368611i | ||||
\(331\) | 18.3923 | 1.01093 | 0.505466 | − | 0.862846i | \(-0.331321\pi\) | ||||
0.505466 | + | 0.862846i | \(0.331321\pi\) | |||||||
\(332\) | 4.43211 | + | 4.43211i | 0.243244 | + | 0.243244i | ||||
\(333\) | 1.39230 | + | 1.39230i | 0.0762978 | + | 0.0762978i | ||||
\(334\) | − | 1.60770i | − | 0.0879692i | ||||||
\(335\) | −0.536220 | + | 0.0321856i | −0.0292969 | + | 0.00175849i | ||||
\(336\) | − | 4.89898i | − | 0.267261i | ||||||
\(337\) | 7.85641 | − | 7.85641i | 0.427966 | − | 0.427966i | −0.459969 | − | 0.887935i | \(-0.652140\pi\) |
0.887935 | + | 0.459969i | \(0.152140\pi\) | |||||||
\(338\) | −6.83083 | + | 6.83083i | −0.371548 | + | 0.371548i | ||||
\(339\) | 24.9282i | 1.35391i | ||||||||
\(340\) | 2.23205 | − | 0.133975i | 0.121050 | − | 0.00726579i | ||||
\(341\) | − | 2.31079i | − | 0.125136i | ||||||
\(342\) | 6.36396 | + | 6.36396i | 0.344124 | + | 0.344124i | ||||
\(343\) | 12.0000 | + | 12.0000i | 0.647939 | + | 0.647939i | ||||
\(344\) | −4.89898 | −0.264135 | ||||||||
\(345\) | −8.90138 | + | 10.0382i | −0.479234 | + | 0.540438i | ||||
\(346\) | 18.6603 | 1.00318 | ||||||||
\(347\) | 13.6753 | + | 13.6753i | 0.734127 | + | 0.734127i | 0.971435 | − | 0.237308i | \(-0.0762650\pi\) |
−0.237308 | + | 0.971435i | \(0.576265\pi\) | |||||||
\(348\) | −5.66025 | − | 5.66025i | −0.303421 | − | 0.303421i | ||||
\(349\) | − | 22.2487i | − | 1.19095i | −0.803375 | − | 0.595473i | \(-0.796965\pi\) | ||
0.803375 | − | 0.595473i | \(-0.203035\pi\) | |||||||
\(350\) | 1.69161 | + | 14.0406i | 0.0904206 | + | 0.750502i | ||||
\(351\) | 24.7351i | 1.32026i | ||||||||
\(352\) | 1.63397 | − | 1.63397i | 0.0870911 | − | 0.0870911i | ||||
\(353\) | 6.50266 | − | 6.50266i | 0.346102 | − | 0.346102i | −0.512554 | − | 0.858655i | \(-0.671300\pi\) |
0.858655 | + | 0.512554i | \(0.171300\pi\) | |||||||
\(354\) | 16.4901 | 0.876438 | ||||||||
\(355\) | 22.7224 | − | 25.6244i | 1.20598 | − | 1.36000i | ||||
\(356\) | 9.89949i | 0.524672i | ||||||||
\(357\) | −3.46410 | + | 3.46410i | −0.183340 | + | 0.183340i | ||||
\(358\) | −3.36603 | − | 3.36603i | −0.177900 | − | 0.177900i | ||||
\(359\) | −8.14351 | −0.429798 | −0.214899 | − | 0.976636i | \(-0.568942\pi\) | ||||
−0.214899 | + | 0.976636i | \(0.568942\pi\) | |||||||
\(360\) | −0.401924 | − | 6.69615i | −0.0211832 | − | 0.352918i | ||||
\(361\) | 10.0000 | 0.526316 | ||||||||
\(362\) | −9.14162 | − | 9.14162i | −0.480473 | − | 0.480473i | ||||
\(363\) | −6.93237 | + | 6.93237i | −0.363855 | + | 0.363855i | ||||
\(364\) | 13.4641i | 0.705711i | ||||||||
\(365\) | 1.79315 | + | 29.8744i | 0.0938578 | + | 1.56369i | ||||
\(366\) | −17.5359 | −0.916616 | ||||||||
\(367\) | −24.8827 | + | 24.8827i | −1.29887 | + | 1.29887i | −0.369724 | + | 0.929142i | \(0.620548\pi\) |
−0.929142 | + | 0.369724i | \(0.879452\pi\) | |||||||
\(368\) | 2.44949 | − | 2.44949i | 0.127688 | − | 0.127688i | ||||
\(369\) | 16.9706 | 0.883452 | ||||||||
\(370\) | 1.09808 | + | 0.973721i | 0.0570863 | + | 0.0506213i | ||||
\(371\) | − | 19.5959i | − | 1.01737i | ||||||
\(372\) | 1.22474 | + | 1.22474i | 0.0635001 | + | 0.0635001i | ||||
\(373\) | −17.8564 | − | 17.8564i | −0.924570 | − | 0.924570i | 0.0727785 | − | 0.997348i | \(-0.476813\pi\) |
−0.997348 | + | 0.0727785i | \(0.976813\pi\) | |||||||
\(374\) | −2.31079 | −0.119488 | ||||||||
\(375\) | 3.46410 | + | 19.0526i | 0.178885 | + | 0.983870i | ||||
\(376\) | 0.267949 | 0.0138184 | ||||||||
\(377\) | 15.5563 | + | 15.5563i | 0.801193 | + | 0.801193i | ||||
\(378\) | 10.3923 | + | 10.3923i | 0.534522 | + | 0.534522i | ||||
\(379\) | − | 18.8038i | − | 0.965889i | −0.875651 | − | 0.482944i | \(-0.839567\pi\) | ||
0.875651 | − | 0.482944i | \(-0.160433\pi\) | |||||||
\(380\) | 5.01910 | + | 4.45069i | 0.257474 | + | 0.228316i | ||||
\(381\) | 9.14162i | 0.468339i | ||||||||
\(382\) | 3.19615 | − | 3.19615i | 0.163529 | − | 0.163529i | ||||
\(383\) | −3.86370 | + | 3.86370i | −0.197426 | + | 0.197426i | −0.798896 | − | 0.601470i | \(-0.794582\pi\) |
0.601470 | + | 0.798896i | \(0.294582\pi\) | |||||||
\(384\) | 1.73205i | 0.0883883i | ||||||||
\(385\) | −0.875644 | − | 14.5885i | −0.0446270 | − | 0.743497i | ||||
\(386\) | − | 17.4882i | − | 0.890126i | ||||||
\(387\) | 10.3923 | − | 10.3923i | 0.528271 | − | 0.528271i | ||||
\(388\) | −8.36603 | − | 8.36603i | −0.424721 | − | 0.424721i | ||||
\(389\) | 5.93426 | 0.300879 | 0.150439 | − | 0.988619i | \(-0.451931\pi\) | ||||
0.150439 | + | 0.988619i | \(0.451931\pi\) | |||||||
\(390\) | 1.10463 | + | 18.4034i | 0.0559349 | + | 0.931890i | ||||
\(391\) | −3.46410 | −0.175187 | ||||||||
\(392\) | 0.707107 | + | 0.707107i | 0.0357143 | + | 0.0357143i | ||||
\(393\) | 15.1244 | + | 15.1244i | 0.762923 | + | 0.762923i | ||||
\(394\) | − | 18.7846i | − | 0.946355i | ||||||
\(395\) | 5.53674 | − | 6.24384i | 0.278583 | − | 0.314162i | ||||
\(396\) | 6.93237i | 0.348365i | ||||||||
\(397\) | −27.5167 | + | 27.5167i | −1.38102 | + | 1.38102i | −0.538212 | + | 0.842809i | \(0.680900\pi\) |
−0.842809 | + | 0.538212i | \(0.819100\pi\) | |||||||
\(398\) | 2.39872 | − | 2.39872i | 0.120237 | − | 0.120237i | ||||
\(399\) | −14.6969 | −0.735767 | ||||||||
\(400\) | −0.598076 | − | 4.96410i | −0.0299038 | − | 0.248205i | ||||
\(401\) | − | 13.5230i | − | 0.675304i | −0.941271 | − | 0.337652i | \(-0.890367\pi\) | ||
0.941271 | − | 0.337652i | \(-0.109633\pi\) | |||||||
\(402\) | −0.294229 | + | 0.294229i | −0.0146748 | + | 0.0146748i | ||||
\(403\) | −3.36603 | − | 3.36603i | −0.167674 | − | 0.167674i | ||||
\(404\) | −9.89949 | −0.492518 | ||||||||
\(405\) | 15.0573 | + | 13.3521i | 0.748203 | + | 0.663470i | ||||
\(406\) | 13.0718 | 0.648742 | ||||||||
\(407\) | −1.07244 | − | 1.07244i | −0.0531589 | − | 0.0531589i | ||||
\(408\) | 1.22474 | − | 1.22474i | 0.0606339 | − | 0.0606339i | ||||
\(409\) | − | 29.1769i | − | 1.44271i | −0.692568 | − | 0.721353i | \(-0.743521\pi\) | ||
0.692568 | − | 0.721353i | \(-0.256479\pi\) | |||||||
\(410\) | 12.6264 | − | 0.757875i | 0.623573 | − | 0.0374288i | ||||
\(411\) | 36.2487 | 1.78802 | ||||||||
\(412\) | 5.46410 | − | 5.46410i | 0.269197 | − | 0.269197i | ||||
\(413\) | −19.0411 | + | 19.0411i | −0.936952 | + | 0.936952i | ||||
\(414\) | 10.3923i | 0.510754i | ||||||||
\(415\) | −13.9904 | + | 0.839746i | −0.686761 | + | 0.0412215i | ||||
\(416\) | − | 4.76028i | − | 0.233392i | ||||||
\(417\) | −27.9053 | − | 27.9053i | −1.36653 | − | 1.36653i | ||||
\(418\) | −4.90192 | − | 4.90192i | −0.239761 | − | 0.239761i | ||||
\(419\) | −31.9449 | −1.56061 | −0.780305 | − | 0.625399i | \(-0.784936\pi\) | ||||
−0.780305 | + | 0.625399i | \(0.784936\pi\) | |||||||
\(420\) | 8.19615 | + | 7.26795i | 0.399931 | + | 0.354640i | ||||
\(421\) | 4.92820 | 0.240186 | 0.120093 | − | 0.992763i | \(-0.461681\pi\) | ||||
0.120093 | + | 0.992763i | \(0.461681\pi\) | |||||||
\(422\) | 3.96524 | + | 3.96524i | 0.193025 | + | 0.193025i | ||||
\(423\) | −0.568406 | + | 0.568406i | −0.0276368 | + | 0.0276368i | ||||
\(424\) | 6.92820i | 0.336463i | ||||||||
\(425\) | −3.08725 | + | 3.93305i | −0.149753 | + | 0.190781i | ||||
\(426\) | − | 26.5283i | − | 1.28530i | ||||||
\(427\) | 20.2487 | − | 20.2487i | 0.979904 | − | 0.979904i | ||||
\(428\) | −12.2474 | + | 12.2474i | −0.592003 | + | 0.592003i | ||||
\(429\) | − | 19.0526i | − | 0.919866i | ||||||
\(430\) | 7.26795 | − | 8.19615i | 0.350492 | − | 0.395254i | ||||
\(431\) | 29.0149i | 1.39760i | 0.715317 | + | 0.698800i | \(0.246282\pi\) | ||||
−0.715317 | + | 0.698800i | \(0.753718\pi\) | |||||||
\(432\) | −3.67423 | − | 3.67423i | −0.176777 | − | 0.176777i | ||||
\(433\) | 22.3923 | + | 22.3923i | 1.07611 | + | 1.07611i | 0.996855 | + | 0.0792508i | \(0.0252528\pi\) |
0.0792508 | + | 0.996855i | \(0.474747\pi\) | |||||||
\(434\) | −2.82843 | −0.135769 | ||||||||
\(435\) | 17.8671 | − | 1.07244i | 0.856664 | − | 0.0514196i | ||||
\(436\) | 1.07180 | 0.0513298 | ||||||||
\(437\) | −7.34847 | − | 7.34847i | −0.351525 | − | 0.351525i | ||||
\(438\) | 16.3923 | + | 16.3923i | 0.783255 | + | 0.783255i | ||||
\(439\) | − | 10.0000i | − | 0.477274i | −0.971109 | − | 0.238637i | \(-0.923299\pi\) | ||
0.971109 | − | 0.238637i | \(-0.0767006\pi\) | |||||||
\(440\) | 0.309587 | + | 5.15780i | 0.0147590 | + | 0.245888i | ||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −3.36603 | + | 3.36603i | −0.160106 | + | 0.160106i | ||||
\(443\) | 23.2838 | − | 23.2838i | 1.10624 | − | 1.10624i | 0.112605 | − | 0.993640i | \(-0.464081\pi\) |
0.993640 | − | 0.112605i | \(-0.0359194\pi\) | |||||||
\(444\) | 1.13681 | 0.0539507 | ||||||||
\(445\) | −16.5622 | − | 14.6865i | −0.785123 | − | 0.696208i | ||||
\(446\) | − | 1.55291i | − | 0.0735326i | ||||||
\(447\) | −6.16987 | + | 6.16987i | −0.291825 | + | 0.291825i | ||||
\(448\) | −2.00000 | − | 2.00000i | −0.0944911 | − | 0.0944911i | ||||
\(449\) | −14.9372 | −0.704929 | −0.352464 | − | 0.935825i | \(-0.614656\pi\) | ||||
−0.352464 | + | 0.935825i | \(0.614656\pi\) | |||||||
\(450\) | 11.7992 | + | 9.26174i | 0.556218 | + | 0.436603i | ||||
\(451\) | −13.0718 | −0.615527 | ||||||||
\(452\) | 10.1769 | + | 10.1769i | 0.478681 | + | 0.478681i | ||||
\(453\) | −17.5390 | + | 17.5390i | −0.824053 | + | 0.824053i | ||||
\(454\) | − | 17.8564i | − | 0.838043i | ||||||
\(455\) | −22.5259 | − | 19.9749i | −1.05603 | − | 0.936436i | ||||
\(456\) | 5.19615 | 0.243332 | ||||||||
\(457\) | 8.19615 | − | 8.19615i | 0.383400 | − | 0.383400i | −0.488926 | − | 0.872325i | \(-0.662611\pi\) |
0.872325 | + | 0.488926i | \(0.162611\pi\) | |||||||
\(458\) | −17.1972 | + | 17.1972i | −0.803572 | + | 0.803572i | ||||
\(459\) | 5.19615i | 0.242536i | ||||||||
\(460\) | 0.464102 | + | 7.73205i | 0.0216388 | + | 0.360509i | ||||
\(461\) | 27.2490i | 1.26911i | 0.772877 | + | 0.634556i | \(0.218817\pi\) | ||||
−0.772877 | + | 0.634556i | \(0.781183\pi\) | |||||||
\(462\) | −8.00481 | − | 8.00481i | −0.372417 | − | 0.372417i | ||||
\(463\) | 23.9019 | + | 23.9019i | 1.11082 | + | 1.11082i | 0.993040 | + | 0.117776i | \(0.0375766\pi\) |
0.117776 | + | 0.993040i | \(0.462423\pi\) | |||||||
\(464\) | −4.62158 | −0.214551 | ||||||||
\(465\) | −3.86603 | + | 0.232051i | −0.179283 | + | 0.0107611i | ||||
\(466\) | −16.3923 | −0.759359 | ||||||||
\(467\) | −6.21166 | − | 6.21166i | −0.287441 | − | 0.287441i | 0.548626 | − | 0.836068i | \(-0.315151\pi\) |
−0.836068 | + | 0.548626i | \(0.815151\pi\) | |||||||
\(468\) | 10.0981 | + | 10.0981i | 0.466784 | + | 0.466784i | ||||
\(469\) | − | 0.679492i | − | 0.0313760i | ||||||
\(470\) | −0.397520 | + | 0.448288i | −0.0183362 | + | 0.0206780i | ||||
\(471\) | 11.5911i | 0.534090i | ||||||||
\(472\) | 6.73205 | − | 6.73205i | 0.309868 | − | 0.309868i | ||||
\(473\) | −8.00481 | + | 8.00481i | −0.368061 | + | 0.368061i | ||||
\(474\) | − | 6.46410i | − | 0.296906i | ||||||
\(475\) | −14.8923 | + | 1.79423i | −0.683306 | + | 0.0823249i | ||||
\(476\) | 2.82843i | 0.129641i | ||||||||
\(477\) | −14.6969 | − | 14.6969i | −0.672927 | − | 0.672927i | ||||
\(478\) | −1.80385 | − | 1.80385i | −0.0825061 | − | 0.0825061i | ||||
\(479\) | 25.2899 | 1.15553 | 0.577763 | − | 0.816204i | \(-0.303926\pi\) | ||||
0.577763 | + | 0.816204i | \(0.303926\pi\) | |||||||
\(480\) | −2.89778 | − | 2.56961i | −0.132265 | − | 0.117286i | ||||
\(481\) | −3.12436 | −0.142458 | ||||||||
\(482\) | −11.5911 | − | 11.5911i | −0.527961 | − | 0.527961i | ||||
\(483\) | −12.0000 | − | 12.0000i | −0.546019 | − | 0.546019i | ||||
\(484\) | 5.66025i | 0.257284i | ||||||||
\(485\) | 26.4082 | − | 1.58510i | 1.19913 | − | 0.0719757i | ||||
\(486\) | 15.5885 | 0.707107 | ||||||||
\(487\) | −9.16987 | + | 9.16987i | −0.415527 | + | 0.415527i | −0.883659 | − | 0.468132i | \(-0.844927\pi\) |
0.468132 | + | 0.883659i | \(0.344927\pi\) | |||||||
\(488\) | −7.15900 | + | 7.15900i | −0.324073 | + | 0.324073i | ||||
\(489\) | −8.24504 | −0.372854 | ||||||||
\(490\) | −2.23205 | + | 0.133975i | −0.100834 | + | 0.00605236i | ||||
\(491\) | − | 16.5916i | − | 0.748770i | −0.927273 | − | 0.374385i | \(-0.877854\pi\) | ||
0.927273 | − | 0.374385i | \(-0.122146\pi\) | |||||||
\(492\) | 6.92820 | − | 6.92820i | 0.312348 | − | 0.312348i | ||||
\(493\) | 3.26795 | + | 3.26795i | 0.147181 | + | 0.147181i | ||||
\(494\) | −14.2808 | −0.642525 | ||||||||
\(495\) | −11.5981 | − | 10.2846i | −0.521295 | − | 0.462259i | ||||
\(496\) | 1.00000 | 0.0449013 | ||||||||
\(497\) | 30.6322 | + | 30.6322i | 1.37404 | + | 1.37404i | ||||
\(498\) | −7.67664 | + | 7.67664i | −0.343998 | + | 0.343998i | ||||
\(499\) | 2.14359i | 0.0959604i | 0.998848 | + | 0.0479802i | \(0.0152784\pi\) | ||||
−0.998848 | + | 0.0479802i | \(0.984722\pi\) | |||||||
\(500\) | 9.19239 | + | 6.36396i | 0.411096 | + | 0.284605i | ||||
\(501\) | 2.78461 | 0.124407 | ||||||||
\(502\) | 4.26795 | − | 4.26795i | 0.190488 | − | 0.190488i | ||||
\(503\) | 12.8159 | − | 12.8159i | 0.571431 | − | 0.571431i | −0.361097 | − | 0.932528i | \(-0.617598\pi\) |
0.932528 | + | 0.361097i | \(0.117598\pi\) | |||||||
\(504\) | 8.48528 | 0.377964 | ||||||||
\(505\) | 14.6865 | − | 16.5622i | 0.653542 | − | 0.737007i | ||||
\(506\) | − | 8.00481i | − | 0.355857i | ||||||
\(507\) | −11.8313 | − | 11.8313i | −0.525449 | − | 0.525449i | ||||
\(508\) | 3.73205 | + | 3.73205i | 0.165583 | + | 0.165583i | ||||
\(509\) | 28.6360 | 1.26927 | 0.634634 | − | 0.772813i | \(-0.281151\pi\) | ||||
0.634634 | + | 0.772813i | \(0.281151\pi\) | |||||||
\(510\) | 0.232051 | + | 3.86603i | 0.0102754 | + | 0.171190i | ||||
\(511\) | −37.8564 | −1.67467 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −11.0227 | + | 11.0227i | −0.486664 | + | 0.486664i | ||||
\(514\) | − | 21.8564i | − | 0.964045i | ||||||
\(515\) | 1.03528 | + | 17.2480i | 0.0456197 | + | 0.760036i | ||||
\(516\) | − | 8.48528i | − | 0.373544i | ||||||
\(517\) | 0.437822 | − | 0.437822i | 0.0192554 | − | 0.0192554i | ||||
\(518\) | −1.31268 | + | 1.31268i | −0.0576757 | + | 0.0576757i | ||||
\(519\) | 32.3205i | 1.41871i | ||||||||
\(520\) | 7.96410 | + | 7.06218i | 0.349249 | + | 0.309697i | ||||
\(521\) | 15.9353i | 0.698138i | 0.937097 | + | 0.349069i | \(0.113502\pi\) | ||||
−0.937097 | + | 0.349069i | \(0.886498\pi\) | |||||||
\(522\) | 9.80385 | − | 9.80385i | 0.429103 | − | 0.429103i | ||||
\(523\) | −29.3205 | − | 29.3205i | −1.28210 | − | 1.28210i | −0.939473 | − | 0.342624i | \(-0.888684\pi\) |
−0.342624 | − | 0.939473i | \(-0.611316\pi\) | |||||||
\(524\) | 12.3490 | 0.539468 | ||||||||
\(525\) | −24.3190 | + | 2.92996i | −1.06137 | + | 0.127874i | ||||
\(526\) | 22.2487 | 0.970090 | ||||||||
\(527\) | −0.707107 | − | 0.707107i | −0.0308021 | − | 0.0308021i | ||||
\(528\) | 2.83013 | + | 2.83013i | 0.123165 | + | 0.123165i | ||||
\(529\) | 11.0000i | 0.478261i | ||||||||
\(530\) | −11.5911 | − | 10.2784i | −0.503486 | − | 0.446467i | ||||
\(531\) | 28.5617i | 1.23947i | ||||||||
\(532\) | −6.00000 | + | 6.00000i | −0.260133 | + | 0.260133i | ||||
\(533\) | −19.0411 | + | 19.0411i | −0.824762 | + | 0.824762i | ||||
\(534\) | −17.1464 | −0.741999 | ||||||||
\(535\) | −2.32051 | − | 38.6603i | −0.100324 | − | 1.67143i | ||||
\(536\) | 0.240237i | 0.0103766i | ||||||||
\(537\) | 5.83013 | − | 5.83013i | 0.251589 | − | 0.251589i | ||||
\(538\) | −6.53590 | − | 6.53590i | −0.281783 | − | 0.281783i | ||||
\(539\) | 2.31079 | 0.0995327 | ||||||||
\(540\) | 11.5981 | − | 0.696152i | 0.499102 | − | 0.0299576i | ||||
\(541\) | −29.7128 | −1.27745 | −0.638727 | − | 0.769434i | \(-0.720539\pi\) | ||||
−0.638727 | + | 0.769434i | \(0.720539\pi\) | |||||||
\(542\) | −18.0938 | − | 18.0938i | −0.777194 | − | 0.777194i | ||||
\(543\) | 15.8338 | − | 15.8338i | 0.679491 | − | 0.679491i | ||||
\(544\) | − | 1.00000i | − | 0.0428746i | ||||||
\(545\) | −1.59008 | + | 1.79315i | −0.0681115 | + | 0.0768101i | ||||
\(546\) | −23.3205 | −0.998026 | ||||||||
\(547\) | 20.2679 | − | 20.2679i | 0.866595 | − | 0.866595i | −0.125499 | − | 0.992094i | \(-0.540053\pi\) |
0.992094 | + | 0.125499i | \(0.0400531\pi\) | |||||||
\(548\) | 14.7985 | − | 14.7985i | 0.632159 | − | 0.632159i | ||||
\(549\) | − | 30.3731i | − | 1.29629i | ||||||
\(550\) | −9.08846 | − | 7.13397i | −0.387533 | − | 0.304194i | ||||
\(551\) | 13.8647i | 0.590658i | ||||||||
\(552\) | 4.24264 | + | 4.24264i | 0.180579 | + | 0.180579i | ||||
\(553\) | 7.46410 | + | 7.46410i | 0.317406 | + | 0.317406i | ||||
\(554\) | 20.8714 | 0.886742 | ||||||||
\(555\) | −1.68653 | + | 1.90192i | −0.0715894 | + | 0.0807322i | ||||
\(556\) | −22.7846 | −0.966283 | ||||||||
\(557\) | 12.9038 | + | 12.9038i | 0.546751 | + | 0.546751i | 0.925500 | − | 0.378749i | \(-0.123645\pi\) |
−0.378749 | + | 0.925500i | \(0.623645\pi\) | |||||||
\(558\) | −2.12132 | + | 2.12132i | −0.0898027 | + | 0.0898027i | ||||
\(559\) | 23.3205i | 0.986352i | ||||||||
\(560\) | 6.31319 | − | 0.378937i | 0.266781 | − | 0.0160130i | ||||
\(561\) | − | 4.00240i | − | 0.168982i | ||||||
\(562\) | 7.07180 | − | 7.07180i | 0.298306 | − | 0.298306i | ||||
\(563\) | −9.62209 | + | 9.62209i | −0.405523 | + | 0.405523i | −0.880174 | − | 0.474651i | \(-0.842574\pi\) |
0.474651 | + | 0.880174i | \(0.342574\pi\) | |||||||
\(564\) | 0.464102i | 0.0195422i | ||||||||
\(565\) | −32.1244 | + | 1.92820i | −1.35148 | + | 0.0811201i | ||||
\(566\) | 6.93237i | 0.291389i | ||||||||
\(567\) | −18.0000 | + | 18.0000i | −0.755929 | + | 0.755929i | ||||
\(568\) | −10.8301 | − | 10.8301i | −0.454422 | − | 0.454422i | ||||
\(569\) | 23.0807 | 0.967593 | 0.483796 | − | 0.875181i | \(-0.339258\pi\) | ||||
0.483796 | + | 0.875181i | \(0.339258\pi\) | |||||||
\(570\) | −7.70882 | + | 8.69333i | −0.322887 | + | 0.364124i | ||||
\(571\) | 9.85641 | 0.412478 | 0.206239 | − | 0.978502i | \(-0.433878\pi\) | ||||
0.206239 | + | 0.978502i | \(0.433878\pi\) | |||||||
\(572\) | −7.77817 | − | 7.77817i | −0.325222 | − | 0.325222i | ||||
\(573\) | 5.53590 | + | 5.53590i | 0.231265 | + | 0.231265i | ||||
\(574\) | 16.0000i | 0.667827i | ||||||||
\(575\) | −13.6245 | − | 10.6945i | −0.568181 | − | 0.445993i | ||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | −6.83013 | + | 6.83013i | −0.284342 | + | 0.284342i | −0.834838 | − | 0.550496i | \(-0.814439\pi\) |
0.550496 | + | 0.834838i | \(0.314439\pi\) | |||||||
\(578\) | 11.3137 | − | 11.3137i | 0.470588 | − | 0.470588i | ||||
\(579\) | 30.2905 | 1.25883 | ||||||||
\(580\) | 6.85641 | − | 7.73205i | 0.284697 | − | 0.321056i | ||||
\(581\) | − | 17.7284i | − | 0.735500i | ||||||
\(582\) | 14.4904 | − | 14.4904i | 0.600646 | − | 0.600646i | ||||
\(583\) | 11.3205 | + | 11.3205i | 0.468848 | + | 0.468848i | ||||
\(584\) | 13.3843 | 0.553845 | ||||||||
\(585\) | −31.8756 | + | 1.91327i | −1.31789 | + | 0.0791039i | ||||
\(586\) | 25.8564 | 1.06812 | ||||||||
\(587\) | 13.9898 | + | 13.9898i | 0.577422 | + | 0.577422i | 0.934192 | − | 0.356770i | \(-0.116122\pi\) |
−0.356770 | + | 0.934192i | \(0.616122\pi\) | |||||||
\(588\) | −1.22474 | + | 1.22474i | −0.0505076 | + | 0.0505076i | ||||
\(589\) | − | 3.00000i | − | 0.123613i | ||||||
\(590\) | 1.27551 | + | 21.2504i | 0.0525120 | + | 0.874864i | ||||
\(591\) | 32.5359 | 1.33835 | ||||||||
\(592\) | 0.464102 | − | 0.464102i | 0.0190745 | − | 0.0190745i | ||||
\(593\) | −28.0812 | + | 28.0812i | −1.15316 | + | 1.15316i | −0.167241 | + | 0.985916i | \(0.553486\pi\) |
−0.985916 | + | 0.167241i | \(0.946514\pi\) | |||||||
\(594\) | −12.0072 | −0.492662 | ||||||||
\(595\) | −4.73205 | − | 4.19615i | −0.193995 | − | 0.172025i | ||||
\(596\) | 5.03768i | 0.206351i | ||||||||
\(597\) | 4.15471 | + | 4.15471i | 0.170041 | + | 0.170041i | ||||
\(598\) | −11.6603 | − | 11.6603i | −0.476823 | − | 0.476823i | ||||
\(599\) | −15.4920 | −0.632985 | −0.316493 | − | 0.948595i | \(-0.602505\pi\) | ||||
−0.316493 | + | 0.948595i | \(0.602505\pi\) | |||||||
\(600\) | 8.59808 | − | 1.03590i | 0.351015 | − | 0.0422904i | ||||
\(601\) | 35.4641 | 1.44661 | 0.723305 | − | 0.690528i | \(-0.242622\pi\) | ||||
0.723305 | + | 0.690528i | \(0.242622\pi\) | |||||||
\(602\) | 9.79796 | + | 9.79796i | 0.399335 | + | 0.399335i | ||||
\(603\) | −0.509619 | − | 0.509619i | −0.0207533 | − | 0.0207533i | ||||
\(604\) | 14.3205i | 0.582693i | ||||||||
\(605\) | −9.46979 | − | 8.39735i | −0.385002 | − | 0.341401i | ||||
\(606\) | − | 17.1464i | − | 0.696526i | ||||||
\(607\) | 0.535898 | − | 0.535898i | 0.0217514 | − | 0.0217514i | −0.696147 | − | 0.717899i | \(-0.745104\pi\) |
0.717899 | + | 0.696147i | \(0.245104\pi\) | |||||||
\(608\) | 2.12132 | − | 2.12132i | 0.0860309 | − | 0.0860309i | ||||
\(609\) | 22.6410i | 0.917460i | ||||||||
\(610\) | −1.35641 | − | 22.5981i | −0.0549193 | − | 0.914969i | ||||
\(611\) | − | 1.27551i | − | 0.0516017i | ||||||
\(612\) | 2.12132 | + | 2.12132i | 0.0857493 | + | 0.0857493i | ||||
\(613\) | 16.5622 | + | 16.5622i | 0.668940 | + | 0.668940i | 0.957471 | − | 0.288531i | \(-0.0931667\pi\) |
−0.288531 | + | 0.957471i | \(0.593167\pi\) | |||||||
\(614\) | −27.7023 | −1.11797 | ||||||||
\(615\) | 1.31268 | + | 21.8695i | 0.0529323 | + | 0.881865i | ||||
\(616\) | −6.53590 | −0.263339 | ||||||||
\(617\) | 28.1827 | + | 28.1827i | 1.13459 | + | 1.13459i | 0.989404 | + | 0.145190i | \(0.0463795\pi\) |
0.145190 | + | 0.989404i | \(0.453621\pi\) | |||||||
\(618\) | 9.46410 | + | 9.46410i | 0.380702 | + | 0.380702i | ||||
\(619\) | − | 4.67949i | − | 0.188085i | −0.995568 | − | 0.0940423i | \(-0.970021\pi\) | ||
0.995568 | − | 0.0940423i | \(-0.0299789\pi\) | |||||||
\(620\) | −1.48356 | + | 1.67303i | −0.0595814 | + | 0.0671906i | ||||
\(621\) | −18.0000 | −0.722315 | ||||||||
\(622\) | −6.83013 | + | 6.83013i | −0.273863 | + | 0.273863i | ||||
\(623\) | 19.7990 | − | 19.7990i | 0.793230 | − | 0.793230i | ||||
\(624\) | 8.24504 | 0.330066 | ||||||||
\(625\) | −24.2846 | + | 5.93782i | −0.971384 | + | 0.237513i | ||||
\(626\) | − | 16.7675i | − | 0.670164i | ||||||
\(627\) | 8.49038 | − | 8.49038i | 0.339073 | − | 0.339073i | ||||
\(628\) | 4.73205 | + | 4.73205i | 0.188829 | + | 0.188829i | ||||
\(629\) | −0.656339 | −0.0261699 | ||||||||
\(630\) | −12.5885 | + | 14.1962i | −0.501536 | + | 0.565588i | ||||
\(631\) | 8.00000 | 0.318475 | 0.159237 | − | 0.987240i | \(-0.449096\pi\) | ||||
0.159237 | + | 0.987240i | \(0.449096\pi\) | |||||||
\(632\) | −2.63896 | − | 2.63896i | −0.104972 | − | 0.104972i | ||||
\(633\) | −6.86800 | + | 6.86800i | −0.272978 | + | 0.272978i | ||||
\(634\) | 6.46410i | 0.256722i | ||||||||
\(635\) | −11.7806 | + | 0.707107i | −0.467498 | + | 0.0280607i | ||||
\(636\) | −12.0000 | −0.475831 | ||||||||
\(637\) | 3.36603 | − | 3.36603i | 0.133367 | − | 0.133367i | ||||
\(638\) | −7.55154 | + | 7.55154i | −0.298968 | + | 0.298968i | ||||
\(639\) | 45.9483 | 1.81769 | ||||||||
\(640\) | −2.23205 | + | 0.133975i | −0.0882296 | + | 0.00529581i | ||||
\(641\) | 17.9687i | 0.709720i | 0.934919 | + | 0.354860i | \(0.115471\pi\) | ||||
−0.934919 | + | 0.354860i | \(0.884529\pi\) | |||||||
\(642\) | −21.2132 | − | 21.2132i | −0.837218 | − | 0.837218i | ||||
\(643\) | 11.6603 | + | 11.6603i | 0.459836 | + | 0.459836i | 0.898601 | − | 0.438766i | \(-0.144584\pi\) |
−0.438766 | + | 0.898601i | \(0.644584\pi\) | |||||||
\(644\) | −9.79796 | −0.386094 | ||||||||
\(645\) | 14.1962 | + | 12.5885i | 0.558973 | + | 0.495670i | ||||
\(646\) | −3.00000 | −0.118033 | ||||||||
\(647\) | −13.7632 | − | 13.7632i | −0.541087 | − | 0.541087i | 0.382760 | − | 0.923848i | \(-0.374973\pi\) |
−0.923848 | + | 0.382760i | \(0.874973\pi\) | |||||||
\(648\) | 6.36396 | − | 6.36396i | 0.250000 | − | 0.250000i | ||||
\(649\) | − | 22.0000i | − | 0.863576i | ||||||
\(650\) | −23.6305 | + | 2.84701i | −0.926865 | + | 0.111669i | ||||
\(651\) | − | 4.89898i | − | 0.192006i | ||||||
\(652\) | −3.36603 | + | 3.36603i | −0.131824 | + | 0.131824i | ||||
\(653\) | 2.29719 | − | 2.29719i | 0.0898958 | − | 0.0898958i | −0.660729 | − | 0.750625i | \(-0.729753\pi\) |
0.750625 | + | 0.660729i | \(0.229753\pi\) | |||||||
\(654\) | 1.85641i | 0.0725912i | ||||||||
\(655\) | −18.3205 | + | 20.6603i | −0.715841 | + | 0.807263i | ||||
\(656\) | − | 5.65685i | − | 0.220863i | ||||||
\(657\) | −28.3923 | + | 28.3923i | −1.10769 | + | 1.10769i | ||||
\(658\) | −0.535898 | − | 0.535898i | −0.0208915 | − | 0.0208915i | ||||
\(659\) | 11.3137 | 0.440720 | 0.220360 | − | 0.975419i | \(-0.429277\pi\) | ||||
0.220360 | + | 0.975419i | \(0.429277\pi\) | |||||||
\(660\) | −8.93357 | + | 0.536220i | −0.347739 | + | 0.0208724i | ||||
\(661\) | 35.1769 | 1.36822 | 0.684112 | − | 0.729377i | \(-0.260190\pi\) | ||||
0.684112 | + | 0.729377i | \(0.260190\pi\) | |||||||
\(662\) | 13.0053 | + | 13.0053i | 0.505466 | + | 0.505466i | ||||
\(663\) | −5.83013 | − | 5.83013i | −0.226423 | − | 0.226423i | ||||
\(664\) | 6.26795i | 0.243244i | ||||||||
\(665\) | −1.13681 | − | 18.9396i | −0.0440837 | − | 0.734445i | ||||
\(666\) | 1.96902i | 0.0762978i | ||||||||
\(667\) | −11.3205 | + | 11.3205i | −0.438332 | + | 0.438332i | ||||
\(668\) | 1.13681 | − | 1.13681i | 0.0439846 | − | 0.0439846i | ||||
\(669\) | 2.68973 | 0.103991 | ||||||||
\(670\) | −0.401924 | − | 0.356406i | −0.0155277 | − | 0.0137692i | ||||
\(671\) | 23.3953i | 0.903164i | ||||||||
\(672\) | 3.46410 | − | 3.46410i | 0.133631 | − | 0.133631i | ||||
\(673\) | −15.8038 | − | 15.8038i | −0.609194 | − | 0.609194i | 0.333542 | − | 0.942735i | \(-0.391756\pi\) |
−0.942735 | + | 0.333542i | \(0.891756\pi\) | |||||||
\(674\) | 11.1106 | 0.427966 | ||||||||
\(675\) | −16.0418 | + | 20.4367i | −0.617449 | + | 0.786611i | ||||
\(676\) | −9.66025 | −0.371548 | ||||||||
\(677\) | −23.6627 | − | 23.6627i | −0.909431 | − | 0.909431i | 0.0867950 | − | 0.996226i | \(-0.472337\pi\) |
−0.996226 | + | 0.0867950i | \(0.972337\pi\) | |||||||
\(678\) | −17.6269 | + | 17.6269i | −0.676957 | + | 0.676957i | ||||
\(679\) | 33.4641i | 1.28423i | ||||||||
\(680\) | 1.67303 | + | 1.48356i | 0.0641579 | + | 0.0568921i | ||||
\(681\) | 30.9282 | 1.18517 | ||||||||
\(682\) | 1.63397 | − | 1.63397i | 0.0625681 | − | 0.0625681i | ||||
\(683\) | −31.6675 | + | 31.6675i | −1.21172 | + | 1.21172i | −0.241264 | + | 0.970460i | \(0.577562\pi\) |
−0.970460 | + | 0.241264i | \(0.922438\pi\) | |||||||
\(684\) | 9.00000i | 0.344124i | ||||||||
\(685\) | 2.80385 | + | 46.7128i | 0.107130 | + | 1.78480i | ||||
\(686\) | 16.9706i | 0.647939i | ||||||||
\(687\) | −29.7864 | − | 29.7864i | −1.13642 | − | 1.13642i | ||||
\(688\) | −3.46410 | − | 3.46410i | −0.132068 | − | 0.132068i | ||||
\(689\) | 32.9802 | 1.25644 | ||||||||
\(690\) | −13.3923 | + | 0.803848i | −0.509836 | + | 0.0306020i | ||||
\(691\) | −28.3731 | −1.07936 | −0.539681 | − | 0.841869i | \(-0.681455\pi\) | ||||
−0.539681 | + | 0.841869i | \(0.681455\pi\) | |||||||
\(692\) | 13.1948 | + | 13.1948i | 0.501591 | + | 0.501591i | ||||
\(693\) | 13.8647 | − | 13.8647i | 0.526678 | − | 0.526678i | ||||
\(694\) | 19.3397i | 0.734127i | ||||||||
\(695\) | 33.8024 | − | 38.1194i | 1.28220 | − | 1.44595i | ||||
\(696\) | − | 8.00481i | − | 0.303421i | ||||||
\(697\) | −4.00000 | + | 4.00000i | −0.151511 | + | 0.151511i | ||||
\(698\) | 15.7322 | − | 15.7322i | 0.595473 | − | 0.595473i | ||||
\(699\) | − | 28.3923i | − | 1.07390i | ||||||
\(700\) | −8.73205 | + | 11.1244i | −0.330040 | + | 0.420461i | ||||
\(701\) | 4.20548i | 0.158839i | 0.996841 | + | 0.0794193i | \(0.0253066\pi\) | ||||
−0.996841 | + | 0.0794193i | \(0.974693\pi\) | |||||||
\(702\) | −17.4904 | + | 17.4904i | −0.660132 | + | 0.660132i | ||||
\(703\) | −1.39230 | − | 1.39230i | −0.0525118 | − | 0.0525118i | ||||
\(704\) | 2.31079 | 0.0870911 | ||||||||
\(705\) | −0.776457 | − | 0.688524i | −0.0292431 | − | 0.0259313i | ||||
\(706\) | 9.19615 | 0.346102 | ||||||||
\(707\) | 19.7990 | + | 19.7990i | 0.744618 | + | 0.744618i | ||||
\(708\) | 11.6603 | + | 11.6603i | 0.438219 | + | 0.438219i | ||||
\(709\) | 15.1962i | 0.570703i | 0.958423 | + | 0.285352i | \(0.0921104\pi\) | ||||
−0.958423 | + | 0.285352i | \(0.907890\pi\) | |||||||
\(710\) | 34.1863 | − | 2.05197i | 1.28299 | − | 0.0770091i | ||||
\(711\) | 11.1962 | 0.419889 | ||||||||
\(712\) | −7.00000 | + | 7.00000i | −0.262336 | + | 0.262336i | ||||
\(713\) | 2.44949 | − | 2.44949i | 0.0917341 | − | 0.0917341i | ||||
\(714\) | −4.89898 | −0.183340 | ||||||||
\(715\) | 24.5526 | − | 1.47372i | 0.918214 | − | 0.0551140i | ||||
\(716\) | − | 4.76028i | − | 0.177900i | ||||||
\(717\) | 3.12436 | − | 3.12436i | 0.116681 | − | 0.116681i | ||||
\(718\) | −5.75833 | − | 5.75833i | −0.214899 | − | 0.214899i | ||||
\(719\) | −40.4302 | −1.50779 | −0.753896 | − | 0.656994i | \(-0.771828\pi\) | ||||
−0.753896 | + | 0.656994i | \(0.771828\pi\) | |||||||
\(720\) | 4.45069 | − | 5.01910i | 0.165867 | − | 0.187051i | ||||
\(721\) | −21.8564 | −0.813975 | ||||||||
\(722\) | 7.07107 | + | 7.07107i | 0.263158 | + | 0.263158i | ||||
\(723\) | 20.0764 | − | 20.0764i | 0.746649 | − | 0.746649i | ||||
\(724\) | − | 12.9282i | − | 0.480473i | ||||||
\(725\) | 2.76406 | + | 22.9420i | 0.102654 | + | 0.852044i | ||||
\(726\) | −9.80385 | −0.363855 | ||||||||
\(727\) | −14.5359 | + | 14.5359i | −0.539107 | + | 0.539107i | −0.923267 | − | 0.384160i | \(-0.874491\pi\) |
0.384160 | + | 0.923267i | \(0.374491\pi\) | |||||||
\(728\) | −9.52056 | + | 9.52056i | −0.352855 | + | 0.352855i | ||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | −19.8564 | + | 22.3923i | −0.734919 | + | 0.828776i | ||||
\(731\) | 4.89898i | 0.181195i | ||||||||
\(732\) | −12.3998 | − | 12.3998i | −0.458308 | − | 0.458308i | ||||
\(733\) | 1.41154 | + | 1.41154i | 0.0521365 | + | 0.0521365i | 0.732694 | − | 0.680558i | \(-0.238263\pi\) |
−0.680558 | + | 0.732694i | \(0.738263\pi\) | |||||||
\(734\) | −35.1894 | −1.29887 | ||||||||
\(735\) | −0.232051 | − | 3.86603i | −0.00855932 | − | 0.142600i | ||||
\(736\) | 3.46410 | 0.127688 | ||||||||
\(737\) | 0.392541 | + | 0.392541i | 0.0144594 | + | 0.0144594i | ||||
\(738\) | 12.0000 | + | 12.0000i | 0.441726 | + | 0.441726i | ||||
\(739\) | − | 16.9282i | − | 0.622714i | −0.950293 | − | 0.311357i | \(-0.899217\pi\) | ||
0.950293 | − | 0.311357i | \(-0.100783\pi\) | |||||||
\(740\) | 0.0879327 | + | 1.46498i | 0.00323247 | + | 0.0538538i | ||||
\(741\) | − | 24.7351i | − | 0.908668i | ||||||
\(742\) | 13.8564 | − | 13.8564i | 0.508685 | − | 0.508685i | ||||
\(743\) | 24.6980 | − | 24.6980i | 0.906081 | − | 0.906081i | −0.0898726 | − | 0.995953i | \(-0.528646\pi\) |
0.995953 | + | 0.0898726i | \(0.0286460\pi\) | |||||||
\(744\) | 1.73205i | 0.0635001i | ||||||||
\(745\) | −8.42820 | − | 7.47372i | −0.308785 | − | 0.273816i | ||||
\(746\) | − | 25.2528i | − | 0.924570i | ||||||
\(747\) | −13.2963 | − | 13.2963i | −0.486487 | − | 0.486487i | ||||
\(748\) | −1.63397 | − | 1.63397i | −0.0597440 | − | 0.0597440i | ||||
\(749\) | 48.9898 | 1.79005 | ||||||||
\(750\) | −11.0227 | + | 15.9217i | −0.402492 | + | 0.581378i | ||||
\(751\) | −10.3923 | −0.379221 | −0.189610 | − | 0.981859i | \(-0.560722\pi\) | ||||
−0.189610 | + | 0.981859i | \(0.560722\pi\) | |||||||
\(752\) | 0.189469 | + | 0.189469i | 0.00690921 | + | 0.00690921i | ||||
\(753\) | 7.39230 | + | 7.39230i | 0.269391 | + | 0.269391i | ||||
\(754\) | 22.0000i | 0.801193i | ||||||||
\(755\) | −23.9587 | − | 21.2454i | −0.871946 | − | 0.773199i | ||||
\(756\) | 14.6969i | 0.534522i | ||||||||
\(757\) | 13.3923 | − | 13.3923i | 0.486752 | − | 0.486752i | −0.420528 | − | 0.907280i | \(-0.638155\pi\) |
0.907280 | + | 0.420528i | \(0.138155\pi\) | |||||||
\(758\) | 13.2963 | − | 13.2963i | 0.482944 | − | 0.482944i | ||||
\(759\) | 13.8647 | 0.503258 | ||||||||
\(760\) | 0.401924 | + | 6.69615i | 0.0145793 | + | 0.242895i | ||||
\(761\) | − | 5.21355i | − | 0.188991i | −0.995525 | − | 0.0944954i | \(-0.969876\pi\) | ||
0.995525 | − | 0.0944954i | \(-0.0301238\pi\) | |||||||
\(762\) | −6.46410 | + | 6.46410i | −0.234170 | + | 0.234170i | ||||
\(763\) | −2.14359 | − | 2.14359i | −0.0776033 | − | 0.0776033i | ||||
\(764\) | 4.52004 | 0.163529 | ||||||||
\(765\) | −6.69615 | + | 0.401924i | −0.242100 | + | 0.0145316i | ||||
\(766\) | −5.46410 | −0.197426 | ||||||||
\(767\) | −32.0464 | − | 32.0464i | −1.15713 | − | 1.15713i | ||||
\(768\) | −1.22474 | + | 1.22474i | −0.0441942 | + | 0.0441942i | ||||
\(769\) | − | 50.6410i | − | 1.82616i | −0.407779 | − | 0.913081i | \(-0.633696\pi\) | ||
0.407779 | − | 0.913081i | \(-0.366304\pi\) | |||||||
\(770\) | 9.69642 | − | 10.9348i | 0.349435 | − | 0.394062i | ||||
\(771\) | 37.8564 | 1.36337 | ||||||||
\(772\) | 12.3660 | − | 12.3660i | 0.445063 | − | 0.445063i | ||||
\(773\) | 7.72741 | − | 7.72741i | 0.277935 | − | 0.277935i | −0.554349 | − | 0.832284i | \(-0.687033\pi\) |
0.832284 | + | 0.554349i | \(0.187033\pi\) | |||||||
\(774\) | 14.6969 | 0.528271 | ||||||||
\(775\) | −0.598076 | − | 4.96410i | −0.0214835 | − | 0.178316i | ||||
\(776\) | − | 11.8313i | − | 0.424721i | ||||||
\(777\) | −2.27362 | − | 2.27362i | −0.0815658 | − | 0.0815658i | ||||
\(778\) | 4.19615 | + | 4.19615i | 0.150439 | + | 0.150439i | ||||
\(779\) | −16.9706 | −0.608034 | ||||||||
\(780\) | −12.2321 | + | 13.7942i | −0.437978 | + | 0.493913i | ||||
\(781\) | −35.3923 | −1.26644 | ||||||||
\(782\) | −2.44949 | − | 2.44949i | −0.0875936 | − | 0.0875936i | ||||
\(783\) | 16.9808 | + | 16.9808i | 0.606843 | + | 0.606843i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | −14.9372 | + | 0.896575i | −0.533131 | + | 0.0320002i | ||||
\(786\) | 21.3891i | 0.762923i | ||||||||
\(787\) | 19.1244 | − | 19.1244i | 0.681710 | − | 0.681710i | −0.278676 | − | 0.960385i | \(-0.589895\pi\) |
0.960385 | + | 0.278676i | \(0.0898954\pi\) | |||||||
\(788\) | 13.2827 | − | 13.2827i | 0.473177 | − | 0.473177i | ||||
\(789\) | 38.5359i | 1.37191i | ||||||||
\(790\) | 8.33013 | − | 0.500000i | 0.296373 | − | 0.0177892i | ||||
\(791\) | − | 40.7076i | − | 1.44740i | ||||||
\(792\) | −4.90192 | + | 4.90192i | −0.174182 | + | 0.174182i | ||||
\(793\) | 34.0788 | + | 34.0788i | 1.21018 | + | 1.21018i | ||||
\(794\) | −38.9144 | −1.38102 | ||||||||
\(795\) | 17.8028 | − | 20.0764i | 0.631399 | − | 0.712036i | ||||
\(796\) | 3.39230 | 0.120237 | ||||||||
\(797\) | 18.1817 | + | 18.1817i | 0.644029 | + | 0.644029i | 0.951543 | − | 0.307514i | \(-0.0994972\pi\) |
−0.307514 | + | 0.951543i | \(0.599497\pi\) | |||||||
\(798\) | −10.3923 | − | 10.3923i | −0.367884 | − | 0.367884i | ||||
\(799\) | − | 0.267949i | − | 0.00947936i | ||||||
\(800\) | 3.08725 | − | 3.93305i | 0.109151 | − | 0.139054i | ||||
\(801\) | − | 29.6985i | − | 1.04934i | ||||||
\(802\) | 9.56218 | − | 9.56218i | 0.337652 | − | 0.337652i | ||||
\(803\) | 21.8695 | − | 21.8695i | 0.771759 | − | 0.771759i | ||||
\(804\) | −0.416102 | −0.0146748 | ||||||||
\(805\) | 14.5359 | − | 16.3923i | 0.512323 | − | 0.577753i | ||||
\(806\) | − | 4.76028i | − | 0.167674i | ||||||
\(807\) | 11.3205 | − | 11.3205i | 0.398501 | − | 0.398501i | ||||
\(808\) | −7.00000 | − | 7.00000i | −0.246259 | − | 0.246259i | ||||
\(809\) | 35.1894 | 1.23719 | 0.618597 | − | 0.785708i | \(-0.287701\pi\) | ||||
0.618597 | + | 0.785708i | \(0.287701\pi\) | |||||||
\(810\) | 1.20577 | + | 20.0885i | 0.0423665 | + | 0.705836i | ||||
\(811\) | 38.3923 | 1.34814 | 0.674068 | − | 0.738669i | \(-0.264545\pi\) | ||||
0.674068 | + | 0.738669i | \(0.264545\pi\) | |||||||
\(812\) | 9.24316 | + | 9.24316i | 0.324371 | + | 0.324371i | ||||
\(813\) | 31.3393 | − | 31.3393i | 1.09912 | − | 1.09912i | ||||
\(814\) | − | 1.51666i | − | 0.0531589i | ||||||
\(815\) | −0.637756 | − | 10.6252i | −0.0223396 | − | 0.372184i | ||||
\(816\) | 1.73205 | 0.0606339 | ||||||||
\(817\) | −10.3923 | + | 10.3923i | −0.363581 | + | 0.363581i | ||||
\(818\) | 20.6312 | − | 20.6312i | 0.721353 | − | 0.721353i | ||||
\(819\) | − | 40.3923i | − | 1.41142i | ||||||
\(820\) | 9.46410 | + | 8.39230i | 0.330501 | + | 0.293072i | ||||
\(821\) | 41.6685i | 1.45424i | 0.686509 | + | 0.727121i | \(0.259142\pi\) | ||||
−0.686509 | + | 0.727121i | \(0.740858\pi\) | |||||||
\(822\) | 25.6317 | + | 25.6317i | 0.894009 | + | 0.894009i | ||||
\(823\) | 2.56218 | + | 2.56218i | 0.0893119 | + | 0.0893119i | 0.750351 | − | 0.661039i | \(-0.229884\pi\) |
−0.661039 | + | 0.750351i | \(0.729884\pi\) | |||||||
\(824\) | 7.72741 | 0.269197 | ||||||||
\(825\) | 12.3564 | − | 15.7417i | 0.430195 | − | 0.548055i | ||||
\(826\) | −26.9282 | −0.936952 | ||||||||
\(827\) | −16.2635 | − | 16.2635i | −0.565536 | − | 0.565536i | 0.365339 | − | 0.930875i | \(-0.380953\pi\) |
−0.930875 | + | 0.365339i | \(0.880953\pi\) | |||||||
\(828\) | −7.34847 | + | 7.34847i | −0.255377 | + | 0.255377i | ||||
\(829\) | − | 37.0718i | − | 1.28756i | −0.765212 | − | 0.643778i | \(-0.777366\pi\) | ||
0.765212 | − | 0.643778i | \(-0.222634\pi\) | |||||||
\(830\) | −10.4865 | − | 9.29890i | −0.363991 | − | 0.322770i | ||||
\(831\) | 36.1504i | 1.25404i | ||||||||
\(832\) | 3.36603 | − | 3.36603i | 0.116696 | − | 0.116696i | ||||
\(833\) | 0.707107 | − | 0.707107i | 0.0244998 | − | 0.0244998i | ||||
\(834\) | − | 39.4641i | − | 1.36653i | ||||||
\(835\) | 0.215390 | + | 3.58846i | 0.00745389 | + | 0.124184i | ||||
\(836\) | − | 6.93237i | − | 0.239761i | ||||||
\(837\) | −3.67423 | − | 3.67423i | −0.127000 | − | 0.127000i | ||||
\(838\) | −22.5885 | − | 22.5885i | −0.780305 | − | 0.780305i | ||||
\(839\) | −48.2591 | −1.66609 | −0.833045 | − | 0.553205i | \(-0.813405\pi\) | ||||
−0.833045 | + | 0.553205i | \(0.813405\pi\) | |||||||
\(840\) | 0.656339 | + | 10.9348i | 0.0226458 | + | 0.377285i | ||||
\(841\) | −7.64102 | −0.263483 | ||||||||
\(842\) | 3.48477 | + | 3.48477i | 0.120093 | + | 0.120093i | ||||
\(843\) | 12.2487 | + | 12.2487i | 0.421868 | + | 0.421868i | ||||
\(844\) | 5.60770i | 0.193025i | ||||||||
\(845\) | 14.3316 | − | 16.1619i | 0.493022 | − | 0.555987i | ||||
\(846\) | −0.803848 | −0.0276368 | ||||||||
\(847\) | 11.3205 | − | 11.3205i | 0.388977 | − | 0.388977i | ||||
\(848\) | −4.89898 | + | 4.89898i | −0.168232 | + | 0.168232i | ||||
\(849\) | −12.0072 | −0.412086 | ||||||||
\(850\) | −4.96410 | + | 0.598076i | −0.170267 | + | 0.0205138i | ||||
\(851\) | − | 2.27362i | − | 0.0779388i | ||||||
\(852\) | 18.7583 | − | 18.7583i | 0.642650 | − | 0.642650i | ||||
\(853\) | −12.1962 | − | 12.1962i | −0.417588 | − | 0.417588i | 0.466783 | − | 0.884372i | \(-0.345413\pi\) |
−0.884372 | + | 0.466783i | \(0.845413\pi\) | |||||||
\(854\) | 28.6360 | 0.979904 | ||||||||
\(855\) | −15.0573 | − | 13.3521i | −0.514949 | − | 0.456631i | ||||
\(856\) | −17.3205 | −0.592003 | ||||||||
\(857\) | −21.8695 | − | 21.8695i | −0.747049 | − | 0.747049i | 0.226875 | − | 0.973924i | \(-0.427149\pi\) |
−0.973924 | + | 0.226875i | \(0.927149\pi\) | |||||||
\(858\) | 13.4722 | − | 13.4722i | 0.459933 | − | 0.459933i | ||||
\(859\) | − | 24.6410i | − | 0.840741i | −0.907353 | − | 0.420370i | \(-0.861900\pi\) | ||
0.907353 | − | 0.420370i | \(-0.138100\pi\) | |||||||
\(860\) | 10.9348 | − | 0.656339i | 0.372873 | − | 0.0223810i | ||||
\(861\) | −27.7128 | −0.944450 | ||||||||
\(862\) | −20.5167 | + | 20.5167i | −0.698800 | + | 0.698800i | ||||
\(863\) | 20.5569 | − | 20.5569i | 0.699764 | − | 0.699764i | −0.264596 | − | 0.964359i | \(-0.585238\pi\) |
0.964359 | + | 0.264596i | \(0.0852385\pi\) | |||||||
\(864\) | − | 5.19615i | − | 0.176777i | ||||||
\(865\) | −41.6506 | + | 2.50000i | −1.41616 | + | 0.0850026i | ||||
\(866\) | 31.6675i | 1.07611i | ||||||||
\(867\) | 19.5959 | + | 19.5959i | 0.665512 | + | 0.665512i | ||||
\(868\) | −2.00000 | − | 2.00000i | −0.0678844 | − | 0.0678844i | ||||
\(869\) | −8.62398 | −0.292549 | ||||||||
\(870\) | 13.3923 | + | 11.8756i | 0.454042 | + | 0.402622i | ||||
\(871\) | 1.14359 | 0.0387492 | ||||||||
\(872\) | 0.757875 | + | 0.757875i | 0.0256649 | + | 0.0256649i | ||||
\(873\) | 25.0981 | + | 25.0981i | 0.849441 | + | 0.849441i | ||||
\(874\) | − | 10.3923i | − | 0.351525i | ||||||
\(875\) | −5.65685 | − | 31.1127i | −0.191237 | − | 1.05180i | ||||
\(876\) | 23.1822i | 0.783255i | ||||||||
\(877\) | 14.7321 | − | 14.7321i | 0.497466 | − | 0.497466i | −0.413182 | − | 0.910648i | \(-0.635583\pi\) |
0.910648 | + | 0.413182i | \(0.135583\pi\) | |||||||
\(878\) | 7.07107 | − | 7.07107i | 0.238637 | − | 0.238637i | ||||
\(879\) | 44.7846i | 1.51055i | ||||||||
\(880\) | −3.42820 | + | 3.86603i | −0.115565 | + | 0.130324i | ||||
\(881\) | − | 45.7725i | − | 1.54211i | −0.636766 | − | 0.771057i | \(-0.719728\pi\) | ||
0.636766 | − | 0.771057i | \(-0.280272\pi\) | |||||||
\(882\) | −2.12132 | − | 2.12132i | −0.0714286 | − | 0.0714286i | ||||
\(883\) | 4.73205 | + | 4.73205i | 0.159246 | + | 0.159246i | 0.782233 | − | 0.622986i | \(-0.214081\pi\) |
−0.622986 | + | 0.782233i | \(0.714081\pi\) | |||||||
\(884\) | −4.76028 | −0.160106 | ||||||||
\(885\) | −36.8067 | + | 2.20925i | −1.23724 | + | 0.0742632i | ||||
\(886\) | 32.9282 | 1.10624 | ||||||||
\(887\) | 13.2084 | + | 13.2084i | 0.443495 | + | 0.443495i | 0.893185 | − | 0.449690i | \(-0.148466\pi\) |
−0.449690 | + | 0.893185i | \(0.648466\pi\) | |||||||
\(888\) | 0.803848 | + | 0.803848i | 0.0269754 | + | 0.0269754i | ||||
\(889\) | − | 14.9282i | − | 0.500676i | ||||||
\(890\) | −1.32628 | − | 22.0962i | −0.0444570 | − | 0.740665i | ||||
\(891\) | − | 20.7971i | − | 0.696729i | ||||||
\(892\) | 1.09808 | − | 1.09808i | 0.0367663 | − | 0.0367663i | ||||
\(893\) | 0.568406 | − | 0.568406i | 0.0190210 | − | 0.0190210i | ||||
\(894\) | −8.72552 | −0.291825 | ||||||||
\(895\) | 7.96410 | + | 7.06218i | 0.266211 | + | 0.236063i | ||||
\(896\) | − | 2.82843i | − | 0.0944911i | ||||||
\(897\) | 20.1962 | − | 20.1962i | 0.674330 | − | 0.674330i | ||||
\(898\) | −10.5622 | − | 10.5622i | −0.352464 | − | 0.352464i | ||||
\(899\) | −4.62158 | −0.154138 | ||||||||
\(900\) | 1.79423 | + | 14.8923i | 0.0598076 | + | 0.496410i | ||||
\(901\) | 6.92820 | 0.230812 | ||||||||
\(902\) | −9.24316 | − | 9.24316i | −0.307763 | − | 0.307763i | ||||
\(903\) | −16.9706 | + | 16.9706i | −0.564745 | + | 0.564745i | ||||
\(904\) | 14.3923i | 0.478681i | ||||||||
\(905\) | 21.6293 | + | 19.1798i | 0.718982 | + | 0.637559i | ||||
\(906\) | −24.8038 | −0.824053 | ||||||||
\(907\) | 39.7583 | − | 39.7583i | 1.32015 | − | 1.32015i | 0.406505 | − | 0.913648i | \(-0.366747\pi\) |
0.913648 | − | 0.406505i | \(-0.133253\pi\) | |||||||
\(908\) | 12.6264 | − | 12.6264i | 0.419021 | − | 0.419021i | ||||
\(909\) | 29.6985 | 0.985037 | ||||||||
\(910\) | −1.80385 | − | 30.0526i | −0.0597970 | − | 0.996233i | ||||
\(911\) | 23.7370i | 0.786443i | 0.919444 | + | 0.393221i | \(0.128639\pi\) | ||||
−0.919444 | + | 0.393221i | \(0.871361\pi\) | |||||||
\(912\) | 3.67423 | + | 3.67423i | 0.121666 | + | 0.121666i | ||||
\(913\) | 10.2417 | + | 10.2417i | 0.338950 | + | 0.338950i | ||||
\(914\) | 11.5911 | 0.383400 | ||||||||
\(915\) | 39.1410 | − | 2.34936i | 1.29396 | − | 0.0776676i | ||||
\(916\) | −24.3205 | −0.803572 | ||||||||
\(917\) | −24.6980 | − | 24.6980i | −0.815599 | − | 0.815599i | ||||
\(918\) | −3.67423 | + | 3.67423i | −0.121268 | + | 0.121268i | ||||
\(919\) | − | 11.4641i | − | 0.378166i | −0.981961 | − | 0.189083i | \(-0.939449\pi\) | ||
0.981961 | − | 0.189083i | \(-0.0605515\pi\) | |||||||
\(920\) | −5.13922 | + | 5.79555i | −0.169435 | + | 0.191074i | ||||
\(921\) | − | 47.9817i | − | 1.58105i | ||||||
\(922\) | −19.2679 | + | 19.2679i | −0.634556 | + | 0.634556i | ||||
\(923\) | −51.5544 | + | 51.5544i | −1.69693 | + | 1.69693i | ||||
\(924\) | − | 11.3205i | − | 0.372417i | ||||||
\(925\) | −2.58142 | − | 2.02628i | −0.0848764 | − | 0.0666237i | ||||
\(926\) | 33.8024i | 1.11082i | ||||||||
\(927\) | −16.3923 | + | 16.3923i | −0.538394 | + | 0.538394i | ||||
\(928\) | −3.26795 | − | 3.26795i | −0.107276 | − | 0.107276i | ||||
\(929\) | −3.48477 | −0.114331 | −0.0571657 | − | 0.998365i | \(-0.518206\pi\) | ||||
−0.0571657 | + | 0.998365i | \(0.518206\pi\) | |||||||
\(930\) | −2.89778 | − | 2.56961i | −0.0950219 | − | 0.0842608i | ||||
\(931\) | 3.00000 | 0.0983210 | ||||||||
\(932\) | −11.5911 | − | 11.5911i | −0.379679 | − | 0.379679i | ||||
\(933\) | −11.8301 | − | 11.8301i | −0.387301 | − | 0.387301i | ||||
\(934\) | − | 8.78461i | − | 0.287441i | ||||||
\(935\) | 5.15780 | − | 0.309587i | 0.168678 | − | 0.0101246i | ||||
\(936\) | 14.2808i | 0.466784i | ||||||||
\(937\) | 22.3468 | − | 22.3468i | 0.730038 | − | 0.730038i | −0.240589 | − | 0.970627i | \(-0.577341\pi\) |
0.970627 | + | 0.240589i | \(0.0773407\pi\) | |||||||
\(938\) | 0.480473 | − | 0.480473i | 0.0156880 | − | 0.0156880i | ||||
\(939\) | 29.0421 | 0.947755 | ||||||||
\(940\) | −0.598076 | + | 0.0358984i | −0.0195071 | + | 0.00117088i | ||||
\(941\) | 13.8647i | 0.451977i | 0.974130 | + | 0.225989i | \(0.0725612\pi\) | ||||
−0.974130 | + | 0.225989i | \(0.927439\pi\) | |||||||
\(942\) | −8.19615 | + | 8.19615i | −0.267045 | + | 0.267045i | ||||
\(943\) | −13.8564 | − | 13.8564i | −0.451227 | − | 0.451227i | ||||
\(944\) | 9.52056 | 0.309868 | ||||||||
\(945\) | −24.5885 | − | 21.8038i | −0.799863 | − | 0.709279i | ||||
\(946\) | −11.3205 | −0.368061 | ||||||||
\(947\) | −9.95026 | − | 9.95026i | −0.323340 | − | 0.323340i | 0.526707 | − | 0.850047i | \(-0.323427\pi\) |
−0.850047 | + | 0.526707i | \(0.823427\pi\) | |||||||
\(948\) | 4.57081 | − | 4.57081i | 0.148453 | − | 0.148453i | ||||
\(949\) | − | 63.7128i | − | 2.06821i | ||||||
\(950\) | −11.7992 | − | 9.26174i | −0.382815 | − | 0.300490i | ||||
\(951\) | −11.1962 | −0.363060 | ||||||||
\(952\) | −2.00000 | + | 2.00000i | −0.0648204 | + | 0.0648204i | ||||
\(953\) | 40.2407 | − | 40.2407i | 1.30352 | − | 1.30352i | 0.377525 | − | 0.925999i | \(-0.376775\pi\) |
0.925999 | − | 0.377525i | \(-0.123225\pi\) | |||||||
\(954\) | − | 20.7846i | − | 0.672927i | ||||||
\(955\) | −6.70577 | + | 7.56218i | −0.216994 | + | 0.244706i | ||||
\(956\) | − | 2.55103i | − | 0.0825061i | ||||||
\(957\) | −13.0797 | − | 13.0797i | −0.422805 | − | 0.422805i | ||||
\(958\) | 17.8827 | + | 17.8827i | 0.577763 | + | 0.577763i | ||||
\(959\) | −59.1939 | −1.91147 | ||||||||
\(960\) | −0.232051 | − | 3.86603i | −0.00748941 | − | 0.124775i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −2.20925 | − | 2.20925i | −0.0712292 | − | 0.0712292i | ||||
\(963\) | 36.7423 | − | 36.7423i | 1.18401 | − | 1.18401i | ||||
\(964\) | − | 16.3923i | − | 0.527961i | ||||||
\(965\) | 2.34297 | + | 39.0346i | 0.0754230 | + | 1.25657i | ||||
\(966\) | − | 16.9706i | − | 0.546019i | ||||||
\(967\) | 39.4186 | − | 39.4186i | 1.26762 | − | 1.26762i | 0.320300 | − | 0.947316i | \(-0.396216\pi\) |
0.947316 | − | 0.320300i | \(-0.103784\pi\) | |||||||
\(968\) | −4.00240 | + | 4.00240i | −0.128642 | + | 0.128642i | ||||
\(969\) | − | 5.19615i | − | 0.166924i | ||||||
\(970\) | 19.7942 | + | 17.5526i | 0.635554 | + | 0.563579i | ||||
\(971\) | 53.0566i | 1.70267i | 0.524625 | + | 0.851333i | \(0.324205\pi\) | ||||
−0.524625 | + | 0.851333i | \(0.675795\pi\) | |||||||
\(972\) | 11.0227 | + | 11.0227i | 0.353553 | + | 0.353553i | ||||
\(973\) | 45.5692 | + | 45.5692i | 1.46088 | + | 1.46088i | ||||
\(974\) | −12.9682 | −0.415527 | ||||||||
\(975\) | −4.93117 | − | 40.9292i | −0.157924 | − | 1.31078i | ||||
\(976\) | −10.1244 | −0.324073 | ||||||||
\(977\) | −1.61729 | − | 1.61729i | −0.0517415 | − | 0.0517415i | 0.680763 | − | 0.732504i | \(-0.261649\pi\) |
−0.732504 | + | 0.680763i | \(0.761649\pi\) | |||||||
\(978\) | −5.83013 | − | 5.83013i | −0.186427 | − | 0.186427i | ||||
\(979\) | 22.8756i | 0.731109i | ||||||||
\(980\) | −1.67303 | − | 1.48356i | −0.0534431 | − | 0.0473907i | ||||
\(981\) | −3.21539 | −0.102660 | ||||||||
\(982\) | 11.7321 | − | 11.7321i | 0.374385 | − | 0.374385i | ||||
\(983\) | 15.3533 | − | 15.3533i | 0.489693 | − | 0.489693i | −0.418516 | − | 0.908209i | \(-0.637450\pi\) |
0.908209 | + | 0.418516i | \(0.137450\pi\) | |||||||
\(984\) | 9.79796 | 0.312348 | ||||||||
\(985\) | 2.51666 | + | 41.9282i | 0.0801875 | + | 1.33594i | ||||
\(986\) | 4.62158i | 0.147181i | ||||||||
\(987\) | 0.928203 | − | 0.928203i | 0.0295450 | − | 0.0295450i | ||||
\(988\) | −10.0981 | − | 10.0981i | −0.321263 | − | 0.321263i | ||||
\(989\) | −16.9706 | −0.539633 | ||||||||
\(990\) | −0.928761 | − | 15.4734i | −0.0295180 | − | 0.491777i | ||||
\(991\) | −16.5359 | −0.525280 | −0.262640 | − | 0.964894i | \(-0.584593\pi\) | ||||
−0.262640 | + | 0.964894i | \(0.584593\pi\) | |||||||
\(992\) | 0.707107 | + | 0.707107i | 0.0224507 | + | 0.0224507i | ||||
\(993\) | −22.5259 | + | 22.5259i | −0.714837 | + | 0.714837i | ||||
\(994\) | 43.3205i | 1.37404i | ||||||||
\(995\) | −5.03270 | + | 5.67544i | −0.159547 | + | 0.179923i | ||||
\(996\) | −10.8564 | −0.343998 | ||||||||
\(997\) | −4.73205 | + | 4.73205i | −0.149866 | + | 0.149866i | −0.778058 | − | 0.628192i | \(-0.783795\pi\) |
0.628192 | + | 0.778058i | \(0.283795\pi\) | |||||||
\(998\) | −1.51575 | + | 1.51575i | −0.0479802 | + | 0.0479802i | ||||
\(999\) | −3.41044 | −0.107901 |
(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 | 930.2.j.e.683.3 | yes | 8 | |
3.2 | odd | 2 | inner | 930.2.j.e.683.2 | yes | 8 | |
5.2 | odd | 4 | inner | 930.2.j.e.497.2 | ✓ | 8 | |
15.2 | even | 4 | inner | 930.2.j.e.497.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.e.497.2 | ✓ | 8 | 5.2 | odd | 4 | inner | |
930.2.j.e.497.3 | yes | 8 | 15.2 | even | 4 | inner | |
930.2.j.e.683.2 | yes | 8 | 3.2 | odd | 2 | inner | |
930.2.j.e.683.3 | yes | 8 | 1.1 | even | 1 | trivial |