Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(179,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.179");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Relative dimension: | \(44\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 359.11 | ||
Character | \(\chi\) | \(=\) | 756.359 |
Dual form | 756.2.o.a.179.11 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.04560 | + | 0.952218i | −0.739351 | + | 0.673320i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.186562 | − | 1.99128i | 0.0932810 | − | 0.995640i | ||||
\(5\) | 0.501474i | 0.224266i | 0.993693 | + | 0.112133i | \(0.0357683\pi\) | ||||
−0.993693 | + | 0.112133i | \(0.964232\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46962 | − | 0.949199i | 0.933428 | − | 0.358764i | ||||
\(8\) | 1.70106 | + | 2.25973i | 0.601417 | + | 0.798936i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.477513 | − | 0.524342i | −0.151003 | − | 0.165811i | ||||
\(11\) | 1.69699 | 0.511661 | 0.255830 | − | 0.966722i | \(-0.417651\pi\) | ||||
0.255830 | + | 0.966722i | \(0.417651\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.89819 | − | 3.28776i | −0.526463 | − | 0.911861i | −0.999525 | − | 0.0308317i | \(-0.990184\pi\) |
0.473061 | − | 0.881030i | \(-0.343149\pi\) | |||||||
\(14\) | −1.67839 | + | 3.34410i | −0.448569 | + | 0.893748i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.93039 | − | 0.742994i | −0.982597 | − | 0.185749i | ||||
\(17\) | 4.12962 | − | 2.38424i | 1.00158 | − | 0.578263i | 0.0928651 | − | 0.995679i | \(-0.470397\pi\) |
0.908716 | + | 0.417416i | \(0.137064\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0919457 | + | 0.0530849i | 0.0210938 | + | 0.0121785i | 0.510510 | − | 0.859872i | \(-0.329457\pi\) |
−0.489416 | + | 0.872050i | \(0.662790\pi\) | |||||||
\(20\) | 0.998575 | + | 0.0935560i | 0.223288 | + | 0.0209198i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.77437 | + | 1.61590i | −0.378297 | + | 0.344511i | ||||
\(23\) | −7.55994 | −1.57636 | −0.788178 | − | 0.615447i | \(-0.788976\pi\) | ||||
−0.788178 | + | 0.615447i | \(0.788976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.74852 | 0.949705 | ||||||||
\(26\) | 5.11542 | + | 1.63020i | 1.00322 | + | 0.319708i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.42938 | − | 5.09479i | −0.270128 | − | 0.962824i | ||||
\(29\) | −6.33235 | − | 3.65598i | −1.17589 | − | 0.678899i | −0.220828 | − | 0.975313i | \(-0.570876\pi\) |
−0.955060 | + | 0.296413i | \(0.904209\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.51006 | + | 2.02653i | 0.630425 | + | 0.363976i | 0.780917 | − | 0.624635i | \(-0.214752\pi\) |
−0.150492 | + | 0.988611i | \(0.548086\pi\) | |||||||
\(32\) | 4.81711 | − | 2.96571i | 0.851553 | − | 0.524269i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.04762 | + | 6.42526i | −0.351164 | + | 1.10192i | ||||
\(35\) | 0.475999 | + | 1.23845i | 0.0804585 | + | 0.209336i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.83900 | − | 6.64935i | 0.631128 | − | 1.09315i | −0.356193 | − | 0.934412i | \(-0.615926\pi\) |
0.987321 | − | 0.158734i | \(-0.0507411\pi\) | |||||||
\(38\) | −0.146687 | + | 0.0320468i | −0.0237957 | + | 0.00519867i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.13320 | + | 0.853039i | −0.179174 | + | 0.134877i | ||||
\(41\) | 2.60966 | − | 1.50669i | 0.407560 | − | 0.235305i | −0.282181 | − | 0.959361i | \(-0.591058\pi\) |
0.689741 | + | 0.724056i | \(0.257724\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.98023 | + | 2.29799i | 0.606980 | + | 0.350440i | 0.771783 | − | 0.635887i | \(-0.219365\pi\) |
−0.164803 | + | 0.986327i | \(0.552699\pi\) | |||||||
\(44\) | 0.316593 | − | 3.37917i | 0.0477282 | − | 0.509430i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.90468 | − | 7.19871i | 1.16548 | − | 1.06139i | ||||
\(47\) | 2.03670 | + | 3.52768i | 0.297084 | + | 0.514564i | 0.975467 | − | 0.220144i | \(-0.0706526\pi\) |
−0.678384 | + | 0.734708i | \(0.737319\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.19804 | − | 4.68832i | 0.742577 | − | 0.669760i | ||||
\(50\) | −4.96506 | + | 4.52163i | −0.702166 | + | 0.639455i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.90098 | + | 3.16646i | −0.956994 | + | 0.439109i | ||||
\(53\) | 8.79953 | − | 5.08041i | 1.20871 | − | 0.697848i | 0.246231 | − | 0.969211i | \(-0.420808\pi\) |
0.962477 | + | 0.271363i | \(0.0874745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.850995i | 0.114748i | ||||||||
\(56\) | 6.34591 | + | 3.96603i | 0.848008 | + | 0.529983i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.1024 | − | 2.20708i | 1.32651 | − | 0.289804i | ||||
\(59\) | 1.67896 | − | 2.90805i | 0.218582 | − | 0.378595i | −0.735793 | − | 0.677207i | \(-0.763190\pi\) |
0.954375 | + | 0.298612i | \(0.0965235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.919402 | + | 1.59245i | 0.117717 | + | 0.203893i | 0.918863 | − | 0.394577i | \(-0.129109\pi\) |
−0.801145 | + | 0.598470i | \(0.795776\pi\) | |||||||
\(62\) | −5.59982 | + | 1.22340i | −0.711178 | + | 0.155371i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.21277 | + | 7.68789i | −0.276596 | + | 0.960986i | ||||
\(65\) | 1.64873 | − | 0.951893i | 0.204499 | − | 0.118068i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.38415 | − | 1.95384i | −0.413440 | − | 0.238699i | 0.278827 | − | 0.960341i | \(-0.410054\pi\) |
−0.692267 | + | 0.721642i | \(0.743388\pi\) | |||||||
\(68\) | −3.97726 | − | 8.66804i | −0.482313 | − | 1.05115i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.67698 | − | 0.841670i | −0.200437 | − | 0.100599i | ||||
\(71\) | 9.65339 | 1.14565 | 0.572823 | − | 0.819679i | \(-0.305848\pi\) | ||||
0.572823 | + | 0.819679i | \(0.305848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.55175 | + | 9.61592i | 0.649784 | + | 1.12546i | 0.983174 | + | 0.182670i | \(0.0584738\pi\) |
−0.333391 | + | 0.942789i | \(0.608193\pi\) | |||||||
\(74\) | 2.31756 | + | 10.6081i | 0.269411 | + | 1.23317i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.122860 | − | 0.173186i | 0.0140931 | − | 0.0198658i | ||||
\(77\) | 4.19091 | − | 1.61078i | 0.477599 | − | 0.183565i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.07338 | + | 2.35177i | −0.458291 | + | 0.264595i | −0.711326 | − | 0.702863i | \(-0.751905\pi\) |
0.253034 | + | 0.967457i | \(0.418572\pi\) | |||||||
\(80\) | 0.372592 | − | 1.97099i | 0.0416571 | − | 0.220363i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.29397 | + | 4.06036i | −0.142895 | + | 0.448392i | ||||
\(83\) | −6.75864 | + | 11.7063i | −0.741858 | + | 1.28494i | 0.209791 | + | 0.977746i | \(0.432722\pi\) |
−0.951649 | + | 0.307189i | \(0.900612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.19563 | + | 2.07090i | 0.129685 | + | 0.224621i | ||||
\(86\) | −6.34992 | + | 1.38727i | −0.684730 | + | 0.149593i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.88668 | + | 3.83473i | 0.307721 | + | 0.408784i | ||||
\(89\) | −4.73824 | − | 2.73562i | −0.502252 | − | 0.289975i | 0.227391 | − | 0.973804i | \(-0.426980\pi\) |
−0.729643 | + | 0.683828i | \(0.760314\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.80855 | − | 6.31776i | −0.818558 | − | 0.662281i | ||||
\(92\) | −1.41040 | + | 15.0540i | −0.147044 | + | 1.56948i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.48870 | − | 1.74915i | −0.566116 | − | 0.180411i | ||||
\(95\) | −0.0266207 | + | 0.0461084i | −0.00273122 | + | 0.00473062i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.45605 | − | 11.1822i | 0.655512 | − | 1.13538i | −0.326253 | − | 0.945283i | \(-0.605786\pi\) |
0.981765 | − | 0.190098i | \(-0.0608806\pi\) | |||||||
\(98\) | −0.970771 | + | 9.85178i | −0.0980627 | + | 0.995180i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.885894 | − | 9.45564i | 0.0885894 | − | 0.945564i | ||||
\(101\) | − | 10.4778i | − | 1.04258i | −0.853380 | − | 0.521289i | \(-0.825451\pi\) | ||
0.853380 | − | 0.521289i | \(-0.174549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.0141i | 1.87352i | 0.349975 | + | 0.936759i | \(0.386190\pi\) | ||||
−0.349975 | + | 0.936759i | \(0.613810\pi\) | |||||||
\(104\) | 4.20052 | − | 9.88209i | 0.411895 | − | 0.969019i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.36314 | + | 13.6911i | −0.423785 | + | 1.32980i | ||||
\(107\) | 5.50504 | − | 9.53502i | 0.532193 | − | 0.921785i | −0.467101 | − | 0.884204i | \(-0.654702\pi\) |
0.999294 | − | 0.0375808i | \(-0.0119652\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.16757 | + | 3.75434i | 0.207615 | + | 0.359600i | 0.950963 | − | 0.309305i | \(-0.100096\pi\) |
−0.743348 | + | 0.668905i | \(0.766763\pi\) | |||||||
\(110\) | −0.810332 | − | 0.889801i | −0.0772622 | − | 0.0848392i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.4118 | + | 1.89581i | −0.983824 | + | 0.179137i | ||||
\(113\) | −2.92804 | + | 1.69051i | −0.275447 | + | 0.159029i | −0.631360 | − | 0.775490i | \(-0.717503\pi\) |
0.355913 | + | 0.934519i | \(0.384170\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 3.79111i | − | 0.353523i | ||||||
\(116\) | −8.46146 | + | 11.9274i | −0.785627 | + | 1.10743i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.01357 | + | 4.63939i | 0.0933067 | + | 0.427091i | ||||
\(119\) | 7.93548 | − | 9.80800i | 0.727444 | − | 0.899098i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.12024 | −0.738203 | ||||||||
\(122\) | −2.47769 | − | 0.789597i | −0.224319 | − | 0.0714868i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.69024 | − | 6.61143i | 0.421196 | − | 0.593724i | ||||
\(125\) | 4.88863i | 0.437253i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.51215i | 0.755332i | 0.925942 | + | 0.377666i | \(0.123273\pi\) | ||||
−0.925942 | + | 0.377666i | \(0.876727\pi\) | |||||||
\(128\) | −5.00687 | − | 10.1455i | −0.442549 | − | 0.896744i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.817501 | + | 2.56525i | −0.0716996 | + | 0.224987i | ||||
\(131\) | 8.42036 | 0.735690 | 0.367845 | − | 0.929887i | \(-0.380096\pi\) | ||||
0.367845 | + | 0.929887i | \(0.380096\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.277459 | + | 0.0438246i | 0.0240587 | + | 0.00380008i | ||||
\(134\) | 5.39895 | − | 1.17951i | 0.466398 | − | 0.101894i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.4125 | + | 5.27610i | 1.06436 | + | 0.452422i | ||||
\(137\) | 4.25362i | 0.363411i | 0.983353 | + | 0.181706i | \(0.0581618\pi\) | ||||
−0.983353 | + | 0.181706i | \(0.941838\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.535435 | + | 0.309134i | −0.0454150 | + | 0.0262204i | −0.522536 | − | 0.852617i | \(-0.675014\pi\) |
0.477121 | + | 0.878838i | \(0.341680\pi\) | |||||||
\(140\) | 2.55490 | − | 0.716799i | 0.215929 | − | 0.0605806i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.0936 | + | 9.19213i | −0.847035 | + | 0.771386i | ||||
\(143\) | −3.22120 | − | 5.57929i | −0.269371 | − | 0.466564i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.83338 | − | 3.17551i | 0.152254 | − | 0.263712i | ||||
\(146\) | −14.9614 | − | 4.76793i | −1.23821 | − | 0.394597i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.5245 | − | 8.88504i | −1.02951 | − | 0.730346i | ||||
\(149\) | − | 6.01223i | − | 0.492541i | −0.969201 | − | 0.246270i | \(-0.920795\pi\) | ||
0.969201 | − | 0.246270i | \(-0.0792051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 22.1543i | − | 1.80289i | −0.432895 | − | 0.901444i | \(-0.642508\pi\) | ||
0.432895 | − | 0.901444i | \(-0.357492\pi\) | |||||||
\(152\) | 0.0364479 | + | 0.298073i | 0.00295631 | + | 0.0241769i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.84821 | + | 5.67489i | −0.229515 | + | 0.457296i | ||||
\(155\) | −1.01625 | + | 1.76020i | −0.0816275 | + | 0.141383i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.94908 | + | 3.37590i | −0.155553 | + | 0.269426i | −0.933260 | − | 0.359200i | \(-0.883049\pi\) |
0.777707 | + | 0.628627i | \(0.216383\pi\) | |||||||
\(158\) | 2.01974 | − | 6.33776i | 0.160682 | − | 0.504205i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.48723 | + | 2.41566i | 0.117576 | + | 0.190974i | ||||
\(161\) | −18.6702 | + | 7.17589i | −1.47142 | + | 0.565539i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.9101 | − | 9.76307i | −1.32450 | − | 0.764703i | −0.340060 | − | 0.940404i | \(-0.610447\pi\) |
−0.984444 | + | 0.175701i | \(0.943781\pi\) | |||||||
\(164\) | −2.51337 | − | 5.47765i | −0.196261 | − | 0.427733i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.08012 | − | 18.6758i | −0.316679 | − | 1.44953i | ||||
\(167\) | 2.20243 | + | 3.81473i | 0.170430 | + | 0.295193i | 0.938570 | − | 0.345089i | \(-0.112151\pi\) |
−0.768141 | + | 0.640281i | \(0.778818\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.706255 | + | 1.22327i | −0.0543273 | + | 0.0940976i | ||||
\(170\) | −3.22210 | − | 1.02683i | −0.247124 | − | 0.0787542i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.31850 | − | 7.49704i | 0.405532 | − | 0.571644i | ||||
\(173\) | −15.5563 | + | 8.98141i | −1.18272 | + | 0.682844i | −0.956642 | − | 0.291265i | \(-0.905924\pi\) |
−0.226078 | + | 0.974109i | \(0.572590\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.7270 | − | 4.50730i | 0.886481 | − | 0.340720i | ||||
\(176\) | −6.66982 | − | 1.26085i | −0.502756 | − | 0.0950402i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.55921 | − | 1.65146i | 0.566587 | − | 0.123783i | ||||
\(179\) | 4.24475 | + | 7.35212i | 0.317267 | + | 0.549523i | 0.979917 | − | 0.199406i | \(-0.0639014\pi\) |
−0.662649 | + | 0.748930i | \(0.730568\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.6598 | −1.83295 | −0.916476 | − | 0.400090i | \(-0.868979\pi\) | ||||
−0.916476 | + | 0.400090i | \(0.868979\pi\) | |||||||
\(182\) | 14.1805 | − | 0.829586i | 1.05113 | − | 0.0614930i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.8599 | − | 17.0834i | −0.948047 | − | 1.25941i | ||||
\(185\) | 3.33447 | + | 1.92516i | 0.245155 | + | 0.141541i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.00791 | − | 4.04602i | 0.512469 | − | 0.295874i | ||||
\(188\) | 7.40456 | − | 3.39752i | 0.540033 | − | 0.247789i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.0160706 | − | 0.0735596i | −0.00116589 | − | 0.00533658i | ||||
\(191\) | −2.96036 | − | 5.12749i | −0.214204 | − | 0.371012i | 0.738822 | − | 0.673901i | \(-0.235382\pi\) |
−0.953026 | + | 0.302888i | \(0.902049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.24353 | + | 14.2782i | −0.593382 | + | 1.02777i | 0.400391 | + | 0.916344i | \(0.368874\pi\) |
−0.993773 | + | 0.111423i | \(0.964459\pi\) | |||||||
\(194\) | 3.89745 | + | 17.8397i | 0.279820 | + | 1.28081i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.36600 | − | 11.2254i | −0.597572 | − | 0.801815i | ||||
\(197\) | − | 4.24471i | − | 0.302423i | −0.988501 | − | 0.151212i | \(-0.951683\pi\) | ||
0.988501 | − | 0.151212i | \(-0.0483175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.9984 | + | 10.9688i | −1.34676 | + | 0.777555i | −0.987790 | − | 0.155793i | \(-0.950207\pi\) |
−0.358974 | + | 0.933347i | \(0.616873\pi\) | |||||||
\(200\) | 8.07754 | + | 10.7304i | 0.571168 | + | 0.758753i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.97713 | + | 10.9556i | 0.701988 | + | 0.770831i | ||||
\(203\) | −19.1088 | − | 3.01823i | −1.34117 | − | 0.211838i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.755565 | + | 1.30868i | 0.0527709 | + | 0.0914019i | ||||
\(206\) | −18.1056 | − | 19.8812i | −1.26148 | − | 1.38519i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.01784 | + | 14.3325i | 0.347925 | + | 0.993782i | ||||
\(209\) | 0.156031 | + | 0.0900843i | 0.0107929 | + | 0.00623126i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.25342 | − | 4.76511i | 0.568189 | − | 0.328044i | −0.188237 | − | 0.982124i | \(-0.560277\pi\) |
0.756426 | + | 0.654080i | \(0.226944\pi\) | |||||||
\(212\) | −8.47486 | − | 18.4701i | −0.582056 | − | 1.26853i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.32334 | + | 15.2118i | 0.227179 | + | 1.03986i | ||||
\(215\) | −1.15238 | + | 1.99598i | −0.0785918 | + | 0.136125i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.5921 | + | 1.67302i | 0.719038 | + | 0.113572i | ||||
\(218\) | −5.84136 | − | 1.86154i | −0.395627 | − | 0.126079i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.69457 | + | 0.158763i | 0.114248 | + | 0.0107038i | ||||
\(221\) | −15.6776 | − | 9.05148i | −1.05459 | − | 0.608868i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.02007 | + | 5.20774i | 0.604029 | + | 0.348736i | 0.770625 | − | 0.637289i | \(-0.219944\pi\) |
−0.166596 | + | 0.986025i | \(0.553278\pi\) | |||||||
\(224\) | 9.08138 | − | 11.8966i | 0.606775 | − | 0.794874i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.45183 | − | 4.55573i | 0.0965745 | − | 0.303042i | ||||
\(227\) | 5.79790 | 0.384820 | 0.192410 | − | 0.981315i | \(-0.438370\pi\) | ||||
0.192410 | + | 0.981315i | \(0.438370\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.93361 | −0.326022 | −0.163011 | − | 0.986624i | \(-0.552121\pi\) | ||||
−0.163011 | + | 0.986624i | \(0.552121\pi\) | |||||||
\(230\) | 3.60997 | + | 3.96399i | 0.238034 | + | 0.261378i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.51019 | − | 20.5285i | −0.164802 | − | 1.34776i | ||||
\(233\) | 9.83606 | + | 5.67885i | 0.644382 | + | 0.372034i | 0.786300 | − | 0.617844i | \(-0.211994\pi\) |
−0.141919 | + | 0.989878i | \(0.545327\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.76904 | + | 1.02135i | −0.115399 | + | 0.0666258i | ||||
\(236\) | −5.47750 | − | 3.88581i | −0.356555 | − | 0.252945i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.04201 | + | 17.8116i | 0.0675434 | + | 1.15455i | ||||
\(239\) | −7.21752 | − | 12.5011i | −0.466862 | − | 0.808629i | 0.532421 | − | 0.846480i | \(-0.321282\pi\) |
−0.999283 | + | 0.0378504i | \(0.987949\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0809 | −0.907030 | −0.453515 | − | 0.891249i | \(-0.649830\pi\) | ||||
−0.453515 | + | 0.891249i | \(0.649830\pi\) | |||||||
\(242\) | 8.49053 | − | 7.73224i | 0.545792 | − | 0.497047i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.34254 | − | 1.53370i | 0.213984 | − | 0.0981848i | ||||
\(245\) | 2.35107 | + | 2.60668i | 0.150204 | + | 0.166535i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.403061i | − | 0.0256461i | ||||||
\(248\) | 1.39141 | + | 11.3791i | 0.0883546 | + | 0.722570i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.65504 | − | 5.11156i | −0.294411 | − | 0.323283i | ||||
\(251\) | −25.2044 | −1.59089 | −0.795445 | − | 0.606026i | \(-0.792763\pi\) | ||||
−0.795445 | + | 0.606026i | \(0.792763\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.8291 | −0.806560 | ||||||||
\(254\) | −8.10543 | − | 8.90031i | −0.508580 | − | 0.558455i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.8959 | + | 5.84051i | 0.930995 | + | 0.365032i | ||||
\(257\) | 7.12209i | 0.444264i | 0.975017 | + | 0.222132i | \(0.0713016\pi\) | ||||
−0.975017 | + | 0.222132i | \(0.928698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.16932 | − | 20.0653i | 0.196932 | − | 1.24680i | ||||
\(260\) | −1.58790 | − | 3.46066i | −0.0984771 | − | 0.214621i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −8.80433 | + | 8.01802i | −0.543934 | + | 0.495355i | ||||
\(263\) | −27.3916 | −1.68904 | −0.844520 | − | 0.535524i | \(-0.820114\pi\) | ||||
−0.844520 | + | 0.535524i | \(0.820114\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.54769 | + | 4.41273i | 0.156504 | + | 0.271072i | ||||
\(266\) | −0.331842 | + | 0.218378i | −0.0203465 | + | 0.0133896i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.52199 | + | 6.37427i | −0.276225 | + | 0.389371i | ||||
\(269\) | −4.90694 | + | 2.83302i | −0.299181 | + | 0.172732i | −0.642075 | − | 0.766642i | \(-0.721926\pi\) |
0.342894 | + | 0.939374i | \(0.388593\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.0632 | + | 8.11940i | 0.854279 | + | 0.493218i | 0.862092 | − | 0.506751i | \(-0.169154\pi\) |
−0.00781341 | + | 0.999969i | \(0.502487\pi\) | |||||||
\(272\) | −18.0025 | + | 6.30270i | −1.09156 | + | 0.382157i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.05037 | − | 4.44759i | −0.244692 | − | 0.268689i | ||||
\(275\) | 8.05818 | 0.485927 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.77634 | −0.166814 | −0.0834071 | − | 0.996516i | \(-0.526580\pi\) | ||||
−0.0834071 | + | 0.996516i | \(0.526580\pi\) | |||||||
\(278\) | 0.265489 | − | 0.833081i | 0.0159230 | − | 0.0499649i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.98886 | + | 3.18231i | −0.118857 | + | 0.190179i | ||||
\(281\) | 25.4336 | + | 14.6841i | 1.51724 | + | 0.875981i | 0.999795 | + | 0.0202663i | \(0.00645142\pi\) |
0.517448 | + | 0.855714i | \(0.326882\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.5510 | + | 15.3292i | 1.57829 | + | 0.911227i | 0.995098 | + | 0.0988943i | \(0.0315306\pi\) |
0.583194 | + | 0.812333i | \(0.301803\pi\) | |||||||
\(284\) | 1.80095 | − | 19.2226i | 0.106867 | − | 1.14065i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.68079 | + | 2.76642i | 0.513306 | + | 0.163582i | ||||
\(287\) | 5.01472 | − | 6.19803i | 0.296010 | − | 0.365858i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.86919 | − | 4.96958i | 0.168776 | − | 0.292328i | ||||
\(290\) | 1.10679 | + | 5.06609i | 0.0649931 | + | 0.297491i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.1837 | − | 9.26113i | 1.18116 | − | 0.541967i | ||||
\(293\) | 1.86213 | − | 1.07510i | 0.108787 | − | 0.0628079i | −0.444620 | − | 0.895720i | \(-0.646661\pi\) |
0.553406 | + | 0.832912i | \(0.313328\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.45831 | + | 0.841955i | 0.0849060 | + | 0.0490205i | ||||
\(296\) | 21.5561 | − | 2.63584i | 1.25292 | − | 0.153205i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.72495 | + | 6.28639i | 0.331637 | + | 0.364161i | ||||
\(299\) | 14.3502 | + | 24.8553i | 0.829894 | + | 1.43742i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.0109 | + | 1.89712i | 0.692297 | + | 0.109348i | ||||
\(302\) | 21.0957 | + | 23.1645i | 1.21392 | + | 1.33297i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.321941 | − | 0.276959i | −0.0184646 | − | 0.0158847i | ||||
\(305\) | −0.798573 | + | 0.461056i | −0.0457262 | + | 0.0264000i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.1505i | 1.09298i | 0.837467 | + | 0.546488i | \(0.184036\pi\) | ||||
−0.837467 | + | 0.546488i | \(0.815964\pi\) | |||||||
\(308\) | −2.42565 | − | 8.64579i | −0.138214 | − | 0.492639i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.613501 | − | 2.80817i | −0.0348445 | − | 0.159493i | ||||
\(311\) | 2.84561 | − | 4.92873i | 0.161360 | − | 0.279483i | −0.773997 | − | 0.633189i | \(-0.781745\pi\) |
0.935357 | + | 0.353706i | \(0.115079\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3072 | + | 21.3167i | 0.695645 | + | 1.20489i | 0.969963 | + | 0.243254i | \(0.0782147\pi\) |
−0.274318 | + | 0.961639i | \(0.588452\pi\) | |||||||
\(314\) | −1.17664 | − | 5.38580i | −0.0664015 | − | 0.303938i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.92309 | + | 8.55000i | 0.220691 | + | 0.480975i | ||||
\(317\) | 10.2861 | − | 5.93871i | 0.577728 | − | 0.333551i | −0.182502 | − | 0.983205i | \(-0.558420\pi\) |
0.760230 | + | 0.649654i | \(0.225086\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.7459 | − | 6.20416i | −0.601656 | − | 0.347366i | ||||
\(320\) | −3.85528 | − | 1.10965i | −0.215517 | − | 0.0620311i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.6885 | − | 25.2812i | 0.707105 | − | 1.40887i | ||||
\(323\) | 0.506268 | 0.0281695 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.01360 | − | 15.6120i | −0.499985 | − | 0.865999i | ||||
\(326\) | 26.9778 | − | 5.89386i | 1.49416 | − | 0.326431i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.84390 | + | 3.33416i | 0.433107 | + | 0.184098i | ||||
\(329\) | 8.37835 | + | 6.77878i | 0.461914 | + | 0.373726i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.8173 | + | 7.97740i | −0.759466 | + | 0.438478i | −0.829104 | − | 0.559094i | \(-0.811149\pi\) |
0.0696381 | + | 0.997572i | \(0.477816\pi\) | |||||||
\(332\) | 22.0496 | + | 15.6423i | 1.21013 | + | 0.858483i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5.93532 | − | 1.89149i | −0.324766 | − | 0.103497i | ||||
\(335\) | 0.979800 | − | 1.69706i | 0.0535322 | − | 0.0927204i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.26967 | + | 10.8594i | 0.341531 | + | 0.591549i | 0.984717 | − | 0.174161i | \(-0.0557213\pi\) |
−0.643186 | + | 0.765710i | \(0.722388\pi\) | |||||||
\(338\) | −0.426358 | − | 1.95156i | −0.0231908 | − | 0.106151i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.34680 | − | 1.99449i | 0.235738 | − | 0.108166i | ||||
\(341\) | 5.95652 | + | 3.43900i | 0.322564 | + | 0.186232i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.38703 | − | 16.5123i | 0.452857 | − | 0.891583i | ||||
\(344\) | 1.57779 | + | 12.9033i | 0.0850688 | + | 0.695698i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.71338 | − | 24.2039i | 0.414674 | − | 1.30121i | ||||
\(347\) | −11.6384 | + | 20.1584i | −0.624784 | + | 1.08216i | 0.363799 | + | 0.931478i | \(0.381480\pi\) |
−0.988583 | + | 0.150680i | \(0.951854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9434 | + | 20.6866i | −0.639317 | + | 1.10733i | 0.346266 | + | 0.938136i | \(0.387449\pi\) |
−0.985583 | + | 0.169193i | \(0.945884\pi\) | |||||||
\(350\) | −7.96988 | + | 15.8795i | −0.426008 | + | 0.848797i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.17457 | − | 5.03277i | 0.435706 | − | 0.268248i | ||||
\(353\) | 30.4841i | 1.62251i | 0.584695 | + | 0.811253i | \(0.301214\pi\) | ||||
−0.584695 | + | 0.811253i | \(0.698786\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.84092i | 0.256930i | ||||||||
\(356\) | −6.33136 | + | 8.92479i | −0.335561 | + | 0.473013i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.4391 | − | 3.64546i | −0.604577 | − | 0.192668i | ||||
\(359\) | −8.47002 | + | 14.6705i | −0.447031 | + | 0.774280i | −0.998191 | − | 0.0601193i | \(-0.980852\pi\) |
0.551160 | + | 0.834399i | \(0.314185\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.49436 | − | 16.4447i | −0.499703 | − | 0.865512i | ||||
\(362\) | 25.7844 | − | 23.4815i | 1.35520 | − | 1.23416i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −14.0372 | + | 14.3704i | −0.735750 | + | 0.753211i | ||||
\(365\) | −4.82213 | + | 2.78406i | −0.252402 | + | 0.145724i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.1754i | − | 0.739952i | −0.929041 | − | 0.369976i | \(-0.879366\pi\) | ||
0.929041 | − | 0.369976i | \(-0.120634\pi\) | |||||||
\(368\) | 29.7135 | + | 5.61699i | 1.54892 | + | 0.292806i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −5.31970 | + | 1.16220i | −0.276558 | + | 0.0604198i | ||||
\(371\) | 16.9092 | − | 20.8992i | 0.877880 | − | 1.08503i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.71462 | −0.140558 | −0.0702790 | − | 0.997527i | \(-0.522389\pi\) | ||||
−0.0702790 | + | 0.997527i | \(0.522389\pi\) | |||||||
\(374\) | −3.47479 | + | 10.9036i | −0.179677 | + | 0.563811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.50704 | + | 10.6032i | −0.232433 | + | 0.546818i | ||||
\(377\) | 27.7590i | 1.42966i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 14.5807i | − | 0.748961i | −0.927235 | − | 0.374480i | \(-0.877821\pi\) | ||
0.927235 | − | 0.374480i | \(-0.122179\pi\) | |||||||
\(380\) | 0.0868483 | + | 0.0616113i | 0.00445522 | + | 0.00316059i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.97784 | + | 2.54240i | 0.408182 | + | 0.130081i | ||||
\(383\) | 22.2221 | 1.13549 | 0.567747 | − | 0.823203i | \(-0.307815\pi\) | ||||
0.567747 | + | 0.823203i | \(0.307815\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.807764 | + | 2.10163i | 0.0411674 | + | 0.107109i | ||||
\(386\) | −4.97653 | − | 22.7789i | −0.253299 | − | 1.15942i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.0624 | − | 14.9420i | −1.06928 | − | 0.758564i | ||||
\(389\) | − | 8.11722i | − | 0.411560i | −0.978598 | − | 0.205780i | \(-0.934027\pi\) | ||
0.978598 | − | 0.205780i | \(-0.0659731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −31.2197 | + | 18.0247i | −1.57885 | + | 0.911549i | ||||
\(392\) | 19.4365 | + | 3.77104i | 0.981694 | + | 0.190467i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.04189 | + | 4.43827i | 0.203627 | + | 0.223597i | ||||
\(395\) | −1.17935 | − | 2.04270i | −0.0593396 | − | 0.102779i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.63142 | − | 14.9501i | 0.433199 | − | 0.750322i | −0.563948 | − | 0.825810i | \(-0.690718\pi\) |
0.997147 | + | 0.0754882i | \(0.0240515\pi\) | |||||||
\(398\) | 9.42014 | − | 29.5596i | 0.472189 | − | 1.48169i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.6635 | − | 3.52812i | −0.933177 | − | 0.176406i | ||||
\(401\) | 0.908634i | 0.0453750i | 0.999743 | + | 0.0226875i | \(0.00722228\pi\) | ||||
−0.999743 | + | 0.0226875i | \(0.992778\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 15.3870i | − | 0.766480i | ||||||
\(404\) | −20.8642 | − | 1.95475i | −1.03803 | − | 0.0972527i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.8541 | − | 15.0398i | 1.13423 | − | 0.746415i | ||||
\(407\) | 6.51473 | − | 11.2839i | 0.322923 | − | 0.559320i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.3097 | − | 29.9813i | 0.855909 | − | 1.48248i | −0.0198905 | − | 0.999802i | \(-0.506332\pi\) |
0.875799 | − | 0.482675i | \(-0.160335\pi\) | |||||||
\(410\) | −2.03616 | − | 0.648891i | −0.100559 | − | 0.0320464i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 37.8625 | + | 3.54731i | 1.86535 | + | 0.174764i | ||||
\(413\) | 1.38608 | − | 8.77543i | 0.0682045 | − | 0.431811i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.87041 | − | 3.38929i | −0.288167 | − | 0.166373i | ||||
\(416\) | −18.8944 | − | 10.2080i | −0.926372 | − | 0.500490i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.248926 | + | 0.0543829i | −0.0121753 | + | 0.00265996i | ||||
\(419\) | 18.7089 | + | 32.4047i | 0.913989 | + | 1.58308i | 0.808375 | + | 0.588668i | \(0.200347\pi\) |
0.105614 | + | 0.994407i | \(0.466319\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.84045 | + | 4.91981i | −0.138435 | + | 0.239777i | −0.926904 | − | 0.375297i | \(-0.877541\pi\) |
0.788469 | + | 0.615074i | \(0.210874\pi\) | |||||||
\(422\) | −4.09235 | + | 12.8415i | −0.199213 | + | 0.625113i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 26.4489 | + | 11.2425i | 1.28447 | + | 0.545983i | ||||
\(425\) | 19.6096 | − | 11.3216i | 0.951206 | − | 0.549179i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.78213 | + | 3.06005i | 0.183030 | + | 0.148086i | ||||
\(428\) | −17.9599 | − | 12.7410i | −0.868122 | − | 0.615857i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.695680 | − | 3.18432i | −0.0335487 | − | 0.153562i | ||||
\(431\) | 5.53553 | + | 9.58782i | 0.266637 | + | 0.461829i | 0.967991 | − | 0.250984i | \(-0.0807541\pi\) |
−0.701354 | + | 0.712813i | \(0.747421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.1104 | 0.630044 | 0.315022 | − | 0.949084i | \(-0.397988\pi\) | ||||
0.315022 | + | 0.949084i | \(0.397988\pi\) | |||||||
\(434\) | −12.6682 | + | 8.33667i | −0.608092 | + | 0.400173i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.88032 | − | 3.61582i | 0.377399 | − | 0.173166i | ||||
\(437\) | −0.695104 | − | 0.401318i | −0.0332513 | − | 0.0191977i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.8719 | + | 17.8239i | −1.47343 | + | 0.850687i | −0.999553 | − | 0.0299023i | \(-0.990480\pi\) |
−0.473880 | + | 0.880589i | \(0.657147\pi\) | |||||||
\(440\) | −1.92302 | + | 1.44760i | −0.0916763 | + | 0.0690114i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 25.0115 | − | 5.46428i | 1.18968 | − | 0.259909i | ||||
\(443\) | −5.98203 | − | 10.3612i | −0.284215 | − | 0.492275i | 0.688204 | − | 0.725518i | \(-0.258400\pi\) |
−0.972419 | + | 0.233243i | \(0.925066\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.37184 | − | 2.37610i | 0.0650316 | − | 0.112638i | ||||
\(446\) | −14.3903 | + | 3.14386i | −0.681400 | + | 0.148866i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.83264 | + | 21.0865i | 0.0865841 | + | 0.996245i | ||||
\(449\) | − | 2.61389i | − | 0.123357i | −0.998096 | − | 0.0616786i | \(-0.980355\pi\) | ||
0.998096 | − | 0.0616786i | \(-0.0196454\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.42856 | − | 2.55683i | 0.208533 | − | 0.120396i | ||||
\(452\) | 2.82001 | + | 6.14593i | 0.132642 | + | 0.289080i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.06229 | + | 5.52087i | −0.284517 | + | 0.259107i | ||||
\(455\) | 3.16819 | − | 3.91579i | 0.148527 | − | 0.183575i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.89303 | − | 15.4032i | −0.415998 | − | 0.720530i | 0.579534 | − | 0.814948i | \(-0.303234\pi\) |
−0.995533 | + | 0.0944176i | \(0.969901\pi\) | |||||||
\(458\) | 5.15859 | − | 4.69787i | 0.241045 | − | 0.219517i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.54917 | − | 0.707278i | −0.351982 | − | 0.0329770i | ||||
\(461\) | −28.0337 | − | 16.1853i | −1.30566 | − | 0.753824i | −0.324293 | − | 0.945957i | \(-0.605126\pi\) |
−0.981369 | + | 0.192133i | \(0.938460\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5925 | − | 11.8891i | 0.957015 | − | 0.552533i | 0.0617618 | − | 0.998091i | \(-0.480328\pi\) |
0.895253 | + | 0.445558i | \(0.146995\pi\) | |||||||
\(464\) | 22.1722 | + | 19.0743i | 1.02932 | + | 0.885504i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.6921 | + | 3.42826i | −0.726922 | + | 0.158811i | ||||
\(467\) | −3.53691 | + | 6.12611i | −0.163669 | + | 0.283483i | −0.936182 | − | 0.351516i | \(-0.885666\pi\) |
0.772513 | + | 0.634999i | \(0.219000\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.2121 | − | 1.61301i | −0.471553 | − | 0.0744818i | ||||
\(470\) | 0.877155 | − | 2.75244i | 0.0404602 | − | 0.126961i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 9.42742 | − | 1.15277i | 0.433932 | − | 0.0530604i | ||||
\(473\) | 6.75440 | + | 3.89966i | 0.310568 | + | 0.179306i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.436606 | + | 0.252075i | 0.0200329 | + | 0.0115660i | ||||
\(476\) | −18.0500 | − | 17.6316i | −0.827321 | − | 0.808141i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.4504 | + | 6.19852i | 0.889641 | + | 0.283514i | ||||
\(479\) | −15.2543 | −0.696985 | −0.348492 | − | 0.937312i | \(-0.613306\pi\) | ||||
−0.348492 | + | 0.937312i | \(0.613306\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.1486 | −1.32906 | ||||||||
\(482\) | 14.7230 | − | 13.4081i | 0.670614 | − | 0.610721i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.51493 | + | 16.1697i | −0.0688603 | + | 0.734985i | ||||
\(485\) | 5.60759 | + | 3.23754i | 0.254627 | + | 0.147009i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0078 | + | 6.35536i | −0.498811 | + | 0.287989i | −0.728222 | − | 0.685341i | \(-0.759653\pi\) |
0.229411 | + | 0.973330i | \(0.426320\pi\) | |||||||
\(488\) | −2.03455 | + | 4.78646i | −0.0920998 | + | 0.216673i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.94041 | − | 0.486817i | −0.223185 | − | 0.0219921i | ||||
\(491\) | −12.0966 | − | 20.9519i | −0.545911 | − | 0.945546i | −0.998549 | − | 0.0538515i | \(-0.982850\pi\) |
0.452638 | − | 0.891695i | \(-0.350483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.8670 | −1.57033 | ||||||||
\(494\) | 0.383802 | + | 0.421441i | 0.0172681 | + | 0.0189615i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.2902 | − | 10.5730i | −0.551846 | − | 0.474743i | ||||
\(497\) | 23.8402 | − | 9.16299i | 1.06938 | − | 0.411016i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.1724i | 0.723977i | 0.932182 | + | 0.361989i | \(0.117902\pi\) | ||||
−0.932182 | + | 0.361989i | \(0.882098\pi\) | |||||||
\(500\) | 9.73463 | + | 0.912033i | 0.435346 | + | 0.0407873i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 26.3538 | − | 24.0001i | 1.17623 | − | 1.07118i | ||||
\(503\) | 5.44592 | 0.242822 | 0.121411 | − | 0.992602i | \(-0.461258\pi\) | ||||
0.121411 | + | 0.992602i | \(0.461258\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.25433 | 0.233815 | ||||||||
\(506\) | 13.4141 | − | 12.2161i | 0.596331 | − | 0.543073i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.9501 | + | 1.58804i | 0.752038 | + | 0.0704581i | ||||
\(509\) | 7.37130i | 0.326727i | 0.986566 | + | 0.163364i | \(0.0522343\pi\) | ||||
−0.986566 | + | 0.163364i | \(0.947766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 22.8381 | + | 18.4779i | 1.01030 | + | 0.817416i | ||||
\(512\) | −21.1366 | + | 8.07732i | −0.934116 | + | 0.356970i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.78178 | − | 7.44687i | −0.299132 | − | 0.328467i | ||||
\(515\) | −9.53510 | −0.420166 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.45626 | + | 5.98642i | 0.152006 | + | 0.263282i | ||||
\(518\) | 15.7927 | + | 23.9982i | 0.693893 | + | 1.05442i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.95561 | + | 2.10645i | 0.217318 | + | 0.0923740i | ||||
\(521\) | 0.235443 | − | 0.135933i | 0.0103150 | − | 0.00595534i | −0.494834 | − | 0.868988i | \(-0.664771\pi\) |
0.505149 | + | 0.863032i | \(0.331438\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.10967 | − | 4.10477i | −0.310884 | − | 0.179489i | 0.336438 | − | 0.941706i | \(-0.390778\pi\) |
−0.647322 | + | 0.762217i | \(0.724111\pi\) | |||||||
\(524\) | 1.57092 | − | 16.7673i | 0.0686259 | − | 0.732482i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 28.6407 | − | 26.0828i | 1.24879 | − | 1.13726i | ||||
\(527\) | 19.3270 | 0.841896 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.1527 | 1.48490 | ||||||||
\(530\) | −6.86576 | − | 2.18800i | −0.298229 | − | 0.0950406i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.139030 | − | 0.544322i | 0.00602773 | − | 0.0235994i | ||||
\(533\) | −9.90726 | − | 5.71996i | −0.429131 | − | 0.247759i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.78156 | + | 2.76064i | 0.206725 | + | 0.119353i | ||||
\(536\) | −1.34150 | − | 10.9709i | −0.0579439 | − | 0.473869i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.43304 | − | 7.63468i | 0.104896 | − | 0.329154i | ||||
\(539\) | 8.82101 | − | 7.95602i | 0.379948 | − | 0.342690i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.2672 | + | 24.7116i | −0.613396 | + | 1.06243i | 0.377267 | + | 0.926104i | \(0.376864\pi\) |
−0.990664 | + | 0.136329i | \(0.956469\pi\) | |||||||
\(542\) | −22.4359 | + | 4.90159i | −0.963706 | + | 0.210541i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 12.8219 | − | 23.7324i | 0.549734 | − | 1.01752i | ||||
\(545\) | −1.88270 | + | 1.08698i | −0.0806461 | + | 0.0465611i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.56519 | + | 5.52246i | 0.408978 | + | 0.236123i | 0.690350 | − | 0.723475i | \(-0.257456\pi\) |
−0.281373 | + | 0.959599i | \(0.590790\pi\) | |||||||
\(548\) | 8.47015 | + | 0.793564i | 0.361827 | + | 0.0338994i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.42564 | + | 7.67314i | −0.359271 | + | 0.327184i | ||||
\(551\) | −0.388155 | − | 0.672304i | −0.0165360 | − | 0.0286411i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.82741 | + | 9.67443i | −0.332855 | + | 0.411399i | ||||
\(554\) | 2.90295 | − | 2.64368i | 0.123334 | − | 0.112319i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.515680 | + | 1.12387i | 0.0218697 | + | 0.0476629i | ||||
\(557\) | −4.13074 | + | 2.38488i | −0.175025 | + | 0.101051i | −0.584953 | − | 0.811067i | \(-0.698887\pi\) |
0.409928 | + | 0.912118i | \(0.365554\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 17.4481i | − | 0.737975i | ||||||
\(560\) | −0.950700 | − | 5.22126i | −0.0401744 | − | 0.220638i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −40.5759 | + | 8.86464i | −1.71159 | + | 0.373932i | ||||
\(563\) | −6.00983 | + | 10.4093i | −0.253284 | + | 0.438701i | −0.964428 | − | 0.264346i | \(-0.914844\pi\) |
0.711144 | + | 0.703046i | \(0.248177\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.847745 | − | 1.46834i | −0.0356649 | − | 0.0617734i | ||||
\(566\) | −42.3585 | + | 9.25408i | −1.78046 | + | 0.388978i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.4210 | + | 21.8141i | 0.689011 | + | 0.915298i | ||||
\(569\) | −11.9089 | + | 6.87561i | −0.499247 | + | 0.288240i | −0.728403 | − | 0.685149i | \(-0.759737\pi\) |
0.229156 | + | 0.973390i | \(0.426404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.8309 | − | 21.2643i | −1.54133 | − | 0.889885i | −0.998755 | − | 0.0498746i | \(-0.984118\pi\) |
−0.542570 | − | 0.840010i | \(-0.682549\pi\) | |||||||
\(572\) | −11.7109 | + | 5.37343i | −0.489656 | + | 0.224675i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.658483 | + | 11.2558i | 0.0274846 | + | 0.469807i | ||||
\(575\) | −35.8986 | −1.49707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.8935 | + | 39.6527i | 0.953069 | + | 1.65076i | 0.738727 | + | 0.674004i | \(0.235427\pi\) |
0.214341 | + | 0.976759i | \(0.431240\pi\) | |||||||
\(578\) | 1.73210 | + | 7.92829i | 0.0720458 | + | 0.329774i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.98129 | − | 4.24320i | −0.248360 | − | 0.176189i | ||||
\(581\) | −5.57965 | + | 35.3254i | −0.231483 | + | 1.46555i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.9327 | − | 8.62139i | 0.618448 | − | 0.357061i | ||||
\(584\) | −12.2855 | + | 28.9028i | −0.508378 | + | 1.19600i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.923312 | + | 2.89727i | −0.0381416 | + | 0.119685i | ||||
\(587\) | −5.33958 | + | 9.24842i | −0.220388 | + | 0.381723i | −0.954926 | − | 0.296845i | \(-0.904066\pi\) |
0.734538 | + | 0.678568i | \(0.237399\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.215157 | + | 0.372662i | 0.00886537 | + | 0.0153553i | ||||
\(590\) | −2.32653 | + | 0.508279i | −0.0957819 | + | 0.0209255i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.0292 | + | 23.2822i | −0.823195 | + | 0.956891i | ||||
\(593\) | −29.7776 | − | 17.1921i | −1.22282 | − | 0.705995i | −0.257301 | − | 0.966331i | \(-0.582833\pi\) |
−0.965518 | + | 0.260336i | \(0.916167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.91846 | + | 3.97944i | 0.201637 | + | 0.163141i | ||||
\(596\) | −11.9720 | − | 1.12165i | −0.490393 | − | 0.0459447i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −38.6722 | − | 12.3242i | −1.58143 | − | 0.503973i | ||||
\(599\) | 10.8778 | − | 18.8409i | 0.444454 | − | 0.769818i | −0.553560 | − | 0.832810i | \(-0.686731\pi\) |
0.998014 | + | 0.0629918i | \(0.0200642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.5245 | − | 30.3533i | 0.714839 | − | 1.23814i | −0.248183 | − | 0.968713i | \(-0.579833\pi\) |
0.963022 | − | 0.269424i | \(-0.0868334\pi\) | |||||||
\(602\) | −14.3651 | + | 9.45337i | −0.585477 | + | 0.385291i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −44.1153 | − | 4.13314i | −1.79503 | − | 0.168175i | ||||
\(605\) | − | 4.07209i | − | 0.165554i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.60667i | − | 0.146390i | −0.997318 | − | 0.0731951i | \(-0.976680\pi\) | ||
0.997318 | − | 0.0731951i | \(-0.0233196\pi\) | |||||||
\(608\) | 0.600347 | − | 0.0169688i | 0.0243473 | − | 0.000688175i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.395962 | − | 1.24250i | 0.0160321 | − | 0.0503072i | ||||
\(611\) | 7.73211 | − | 13.3924i | 0.312808 | − | 0.541799i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.90678 | − | 8.49879i | −0.198183 | − | 0.343263i | 0.749756 | − | 0.661714i | \(-0.230171\pi\) |
−0.947939 | + | 0.318451i | \(0.896837\pi\) | |||||||
\(614\) | −18.2354 | − | 20.0238i | −0.735923 | − | 0.808094i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.7689 | + | 6.73030i | 0.433893 | + | 0.271171i | ||||
\(617\) | 18.4047 | − | 10.6260i | 0.740945 | − | 0.427785i | −0.0814679 | − | 0.996676i | \(-0.525961\pi\) |
0.822413 | + | 0.568891i | \(0.192627\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.4810i | 1.14475i | 0.819992 | + | 0.572374i | \(0.193978\pi\) | ||||
−0.819992 | + | 0.572374i | \(0.806022\pi\) | |||||||
\(620\) | 3.31546 | + | 2.35203i | 0.133152 | + | 0.0944599i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.71786 | + | 7.86313i | 0.0688800 | + | 0.315283i | ||||
\(623\) | −14.2983 | − | 2.25841i | −0.572849 | − | 0.0904815i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2911 | 0.851644 | ||||||||
\(626\) | −33.1666 | − | 10.5696i | −1.32560 | − | 0.422448i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.35875 | + | 4.51098i | 0.253742 | + | 0.180008i | ||||
\(629\) | − | 36.6124i | − | 1.45983i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 21.2573i | − | 0.846239i | −0.906074 | − | 0.423119i | \(-0.860935\pi\) | ||
0.906074 | − | 0.423119i | \(-0.139065\pi\) | |||||||
\(632\) | −12.2434 | − | 5.20424i | −0.487018 | − | 0.207014i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.10026 | + | 16.0042i | −0.202557 | + | 0.635607i | ||||
\(635\) | −4.26862 | −0.169395 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.2810 | − | 8.19060i | −1.00167 | − | 0.324523i | ||||
\(638\) | 17.1436 | − | 3.74538i | 0.678723 | − | 0.148281i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.08771 | − | 2.51082i | 0.201109 | − | 0.0992487i | ||||
\(641\) | 36.7687i | 1.45228i | 0.687548 | + | 0.726138i | \(0.258687\pi\) | ||||
−0.687548 | + | 0.726138i | \(0.741313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.592243 | − | 0.341931i | 0.0233558 | − | 0.0134845i | −0.488277 | − | 0.872689i | \(-0.662374\pi\) |
0.511632 | + | 0.859204i | \(0.329041\pi\) | |||||||
\(644\) | 10.8061 | + | 38.5163i | 0.425818 | + | 1.51775i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.529354 | + | 0.482078i | −0.0208272 | + | 0.0189671i | ||||
\(647\) | 20.1867 | + | 34.9643i | 0.793619 | + | 1.37459i | 0.923712 | + | 0.383087i | \(0.125139\pi\) |
−0.130093 | + | 0.991502i | \(0.541528\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.84917 | − | 4.93491i | 0.111840 | − | 0.193712i | ||||
\(650\) | 24.2907 | + | 7.74102i | 0.952759 | + | 0.303628i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.5958 | + | 31.8514i | −0.884919 | + | 1.24740i | ||||
\(653\) | 0.765132i | 0.0299419i | 0.999888 | + | 0.0149710i | \(0.00476558\pi\) | ||||
−0.999888 | + | 0.0149710i | \(0.995234\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.22259i | 0.164990i | ||||||||
\(656\) | −11.3764 | + | 3.98291i | −0.444175 | + | 0.155506i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −15.2153 | + | 0.890122i | −0.593154 | + | 0.0347006i | ||||
\(659\) | 20.6707 | − | 35.8027i | 0.805215 | − | 1.39467i | −0.110930 | − | 0.993828i | \(-0.535383\pi\) |
0.916146 | − | 0.400845i | \(-0.131284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.5001 | − | 23.3829i | 0.525093 | − | 0.909488i | −0.474480 | − | 0.880266i | \(-0.657364\pi\) |
0.999573 | − | 0.0292215i | \(-0.00930282\pi\) | |||||||
\(662\) | 6.85112 | − | 21.4982i | 0.266276 | − | 0.835553i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −37.9500 | + | 4.64046i | −1.47275 | + | 0.180085i | ||||
\(665\) | −0.0219769 | + | 0.139138i | −0.000852228 | + | 0.00539556i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47.8722 | + | 27.6390i | 1.85362 | + | 1.07019i | ||||
\(668\) | 8.00708 | − | 3.67398i | 0.309803 | − | 0.142151i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.591494 | + | 2.70743i | 0.0228514 | + | 0.104597i | ||||
\(671\) | 1.56021 | + | 2.70237i | 0.0602314 | + | 0.104324i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.7318 | − | 25.5163i | 0.567871 | − | 0.983581i | −0.428906 | − | 0.903349i | \(-0.641101\pi\) |
0.996776 | − | 0.0802316i | \(-0.0255660\pi\) | |||||||
\(674\) | −16.8961 | − | 5.38449i | −0.650813 | − | 0.207403i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.30411 | + | 1.63457i | 0.0886196 | + | 0.0628679i | ||||
\(677\) | 14.9223 | − | 8.61540i | 0.573511 | − | 0.331117i | −0.185040 | − | 0.982731i | \(-0.559241\pi\) |
0.758550 | + | 0.651615i | \(0.225908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.32984 | − | 33.7439i | 0.204541 | − | 1.29497i | ||||
\(680\) | −2.64583 | + | 6.22454i | −0.101463 | + | 0.238700i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.50282 | + | 2.07609i | −0.363882 | + | 0.0794975i | ||||
\(683\) | −16.6012 | − | 28.7542i | −0.635228 | − | 1.10025i | −0.986467 | − | 0.163962i | \(-0.947573\pi\) |
0.351238 | − | 0.936286i | \(-0.385761\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.13308 | −0.0815008 | ||||||||
\(686\) | 6.95387 | + | 25.2516i | 0.265500 | + | 0.964111i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.9365 | − | 11.9893i | −0.531323 | − | 0.457087i | ||||
\(689\) | −33.4064 | − | 19.2872i | −1.27268 | − | 0.734783i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.20826 | + | 5.31639i | −0.350299 | + | 0.202245i | −0.664817 | − | 0.747006i | \(-0.731490\pi\) |
0.314518 | + | 0.949251i | \(0.398157\pi\) | |||||||
\(692\) | 14.9823 | + | 32.6524i | 0.569541 | + | 1.24126i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.02599 | − | 32.1599i | −0.266703 | − | 1.22077i | ||||
\(695\) | −0.155022 | − | 0.268507i | −0.00588034 | − | 0.0101850i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.18461 | − | 12.4441i | 0.272136 | − | 0.471354i | ||||
\(698\) | −7.21012 | − | 33.0027i | −0.272907 | − | 1.24917i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.78747 | − | 24.1927i | −0.256542 | − | 0.914399i | ||||
\(701\) | − | 14.3639i | − | 0.542518i | −0.962506 | − | 0.271259i | \(-0.912560\pi\) | ||
0.962506 | − | 0.271259i | \(-0.0874399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.705959 | − | 0.407586i | 0.0266258 | − | 0.0153724i | ||||
\(704\) | −3.75504 | + | 13.0462i | −0.141523 | + | 0.491699i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.0275 | − | 31.8742i | −1.09247 | − | 1.19960i | ||||
\(707\) | −9.94550 | − | 25.8761i | −0.374039 | − | 0.973172i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.1763 | + | 19.3579i | 0.419734 | + | 0.727000i | 0.995912 | − | 0.0903237i | \(-0.0287902\pi\) |
−0.576179 | + | 0.817324i | \(0.695457\pi\) | |||||||
\(710\) | −4.60961 | − | 5.06167i | −0.172996 | − | 0.189961i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.87827 | − | 15.3606i | −0.0703910 | − | 0.575663i | ||||
\(713\) | −26.5358 | − | 15.3205i | −0.993775 | − | 0.573756i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.79787 | − | 1.61535i | 0.104634 | − | 0.0604107i | ||||
\(716\) | 15.4320 | − | 7.08086i | 0.576722 | − | 0.264624i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.11326 | − | 23.4048i | −0.190825 | − | 0.873460i | ||||
\(719\) | −6.77863 | + | 11.7409i | −0.252800 | + | 0.437863i | −0.964296 | − | 0.264828i | \(-0.914685\pi\) |
0.711496 | + | 0.702691i | \(0.248018\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0482 | + | 46.9577i | 0.672150 | + | 1.74880i | ||||
\(722\) | 25.5863 | + | 8.15391i | 0.952222 | + | 0.303457i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.60059 | + | 49.1046i | −0.170980 | + | 1.82496i | ||||
\(725\) | −30.0693 | − | 17.3605i | −1.11675 | − | 0.644754i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.9137 | − | 10.9198i | −0.701469 | − | 0.404993i | 0.106425 | − | 0.994321i | \(-0.466059\pi\) |
−0.807894 | + | 0.589327i | \(0.799393\pi\) | |||||||
\(728\) | 0.993607 | − | 28.3921i | 0.0368255 | − | 1.05228i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.39099 | − | 7.50274i | 0.0884947 | − | 0.277689i | ||||
\(731\) | 21.9158 | 0.810586 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −47.7005 | −1.76186 | −0.880929 | − | 0.473248i | \(-0.843081\pi\) | ||||
−0.880929 | + | 0.473248i | \(0.843081\pi\) | |||||||
\(734\) | 13.4981 | + | 14.8219i | 0.498225 | + | 0.547085i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −36.4171 | + | 22.4206i | −1.34235 | + | 0.826435i | ||||
\(737\) | −5.74285 | − | 3.31564i | −0.211541 | − | 0.122133i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.03773 | + | 0.599135i | −0.0381736 | + | 0.0220395i | −0.518965 | − | 0.854795i | \(-0.673683\pi\) |
0.480792 | + | 0.876835i | \(0.340349\pi\) | |||||||
\(740\) | 4.45562 | − | 6.28071i | 0.163792 | − | 0.230884i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.22034 | + | 37.9534i | 0.0815114 | + | 1.39331i | ||||
\(743\) | 14.0688 | + | 24.3679i | 0.516134 | + | 0.893970i | 0.999825 | + | 0.0187314i | \(0.00596273\pi\) |
−0.483690 | + | 0.875239i | \(0.660704\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.01497 | 0.110460 | ||||||||
\(746\) | 2.83841 | − | 2.58491i | 0.103922 | − | 0.0946404i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.74935 | − | 14.7096i | −0.246781 | − | 0.537834i | ||||
\(749\) | 4.54473 | − | 28.7732i | 0.166061 | − | 1.05135i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.29885i | − | 0.120377i | −0.998187 | − | 0.0601884i | \(-0.980830\pi\) | ||
0.998187 | − | 0.0601884i | \(-0.0191702\pi\) | |||||||
\(752\) | −5.38400 | − | 15.3784i | −0.196334 | − | 0.560792i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −26.4326 | − | 29.0249i | −0.962620 | − | 1.05702i | ||||
\(755\) | 11.1098 | 0.404327 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.01338 | 0.182215 | 0.0911073 | − | 0.995841i | \(-0.470959\pi\) | ||||
0.0911073 | + | 0.995841i | \(0.470959\pi\) | |||||||
\(758\) | 13.8840 | + | 15.2456i | 0.504290 | + | 0.553745i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.149476 | + | 0.0182777i | −0.00542206 | + | 0.000663000i | ||||
\(761\) | 12.1178i | 0.439269i | 0.975582 | + | 0.219634i | \(0.0704864\pi\) | ||||
−0.975582 | + | 0.219634i | \(0.929514\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.91668 | + | 7.21433i | 0.322806 | + | 0.261176i | ||||
\(764\) | −10.7626 | + | 4.93831i | −0.389376 | + | 0.178662i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.2354 | + | 21.1603i | −0.839530 | + | 0.764551i | ||||
\(767\) | −12.7479 | −0.460302 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.90320 | + | 11.9567i | 0.248936 | + | 0.431170i | 0.963231 | − | 0.268675i | \(-0.0865858\pi\) |
−0.714295 | + | 0.699845i | \(0.753252\pi\) | |||||||
\(770\) | −2.84581 | − | 1.42830i | −0.102556 | − | 0.0514724i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 26.8940 | + | 19.0789i | 0.967935 | + | 0.686666i | ||||
\(773\) | 13.5671 | − | 7.83300i | 0.487976 | − | 0.281733i | −0.235758 | − | 0.971812i | \(-0.575757\pi\) |
0.723735 | + | 0.690078i | \(0.242424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.6676 | + | 9.62304i | 0.598718 | + | 0.345670i | ||||
\(776\) | 36.2509 | − | 4.43270i | 1.30133 | − | 0.159125i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.72937 | + | 8.48737i | 0.277111 | + | 0.304287i | ||||
\(779\) | 0.319929 | 0.0114627 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.3817 | 0.586182 | ||||||||
\(782\) | 15.4799 | − | 48.5746i | 0.553560 | − | 1.73702i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.9137 | + | 14.5648i | −0.854061 | + | 0.520172i | ||||
\(785\) | −1.69293 | − | 0.977413i | −0.0604232 | − | 0.0348854i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.8289 | − | 21.8405i | −1.34845 | − | 0.778530i | −0.360423 | − | 0.932789i | \(-0.617368\pi\) |
−0.988030 | + | 0.154259i | \(0.950701\pi\) | |||||||
\(788\) | −8.45240 | − | 0.791901i | −0.301104 | − | 0.0282103i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.17822 | + | 1.01285i | 0.113076 | + | 0.0360354i | ||||
\(791\) | −5.62652 | + | 6.95420i | −0.200056 | + | 0.247263i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.49040 | − | 6.04555i | 0.123948 | − | 0.214684i | ||||
\(794\) | 5.21070 | + | 23.8508i | 0.184921 | + | 0.846433i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.2975 | + | 39.8776i | 0.648537 | + | 1.41342i | ||||
\(797\) | 44.7621 | − | 25.8434i | 1.58556 | − | 0.915422i | 0.591530 | − | 0.806283i | \(-0.298524\pi\) |
0.994027 | − | 0.109139i | \(-0.0348092\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.8216 | + | 9.71198i | 0.595107 | + | 0.343585i | ||||
\(800\) | 22.8742 | − | 14.0828i | 0.808724 | − | 0.497901i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.865218 | − | 0.950068i | −0.0305519 | − | 0.0335481i | ||||
\(803\) | 9.42125 | + | 16.3181i | 0.332469 | + | 0.575853i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.59852 | − | 9.36261i | −0.126831 | − | 0.329989i | ||||
\(806\) | 14.6518 | + | 16.0886i | 0.516086 | + | 0.566698i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 23.6770 | − | 17.8234i | 0.832952 | − | 0.627023i | ||||
\(809\) | 18.7111 | − | 10.8029i | 0.657848 | − | 0.379809i | −0.133608 | − | 0.991034i | \(-0.542656\pi\) |
0.791457 | + | 0.611225i | \(0.209323\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.10006i | − | 0.0386283i | −0.999813 | − | 0.0193141i | \(-0.993852\pi\) | ||
0.999813 | − | 0.0193141i | \(-0.00614826\pi\) | |||||||
\(812\) | −9.57510 | + | 37.4878i | −0.336020 | + | 1.31556i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.93287 | + | 18.0019i | 0.137847 | + | 0.630965i | ||||
\(815\) | 4.89593 | − | 8.47999i | 0.171497 | − | 0.297041i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.243977 | + | 0.422580i | 0.00853567 | + | 0.0147842i | ||||
\(818\) | 10.4497 | + | 47.8310i | 0.365364 | + | 1.67237i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.74690 | − | 1.26039i | 0.0959259 | − | 0.0440148i | ||||
\(821\) | −27.2968 | + | 15.7598i | −0.952666 | + | 0.550022i | −0.893908 | − | 0.448250i | \(-0.852047\pi\) |
−0.0587579 | + | 0.998272i | \(0.518714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.4069 | − | 10.0499i | −0.606767 | − | 0.350317i | 0.164932 | − | 0.986305i | \(-0.447260\pi\) |
−0.771699 | + | 0.635988i | \(0.780593\pi\) | |||||||
\(824\) | −42.9668 | + | 32.3442i | −1.49682 | + | 1.12676i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.90684 | + | 10.4954i | 0.240320 | + | 0.365183i | ||||
\(827\) | 14.3246 | 0.498114 | 0.249057 | − | 0.968489i | \(-0.419879\pi\) | ||||
0.249057 | + | 0.968489i | \(0.419879\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.2497 | + | 26.4133i | 0.529646 | + | 0.917373i | 0.999402 | + | 0.0345771i | \(0.0110084\pi\) |
−0.469756 | + | 0.882796i | \(0.655658\pi\) | |||||||
\(830\) | 9.36545 | − | 2.04607i | 0.325079 | − | 0.0710203i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 29.4762 | − | 7.31802i | 1.02190 | − | 0.253707i | ||||
\(833\) | 10.2879 | − | 31.7544i | 0.356454 | − | 1.10022i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.91299 | + | 1.10446i | −0.0662017 | + | 0.0382215i | ||||
\(836\) | 0.208492 | − | 0.293894i | 0.00721086 | − | 0.0101645i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −50.4184 | − | 16.0675i | −1.74167 | − | 0.555042i | ||||
\(839\) | 5.36379 | − | 9.29036i | 0.185179 | − | 0.320739i | −0.758458 | − | 0.651722i | \(-0.774047\pi\) |
0.943637 | + | 0.330983i | \(0.107380\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.2325 | + | 21.1872i | 0.421809 | + | 0.730594i | ||||
\(842\) | −1.71475 | − | 7.84889i | −0.0590942 | − | 0.270491i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −7.94890 | − | 17.3239i | −0.273612 | − | 0.596312i | ||||
\(845\) | −0.613438 | − | 0.354168i | −0.0211029 | − | 0.0121838i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.0539 | + | 7.70772i | −0.689060 | + | 0.264841i | ||||
\(848\) | −38.3603 | + | 13.4300i | −1.31730 | + | 0.461188i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.72318 | + | 30.5105i | −0.333502 | + | 1.04650i | ||||
\(851\) | −29.0226 | + | 50.2687i | −0.994883 | + | 1.72319i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.00604 | + | 6.93866i | −0.137164 | + | 0.237575i | −0.926422 | − | 0.376487i | \(-0.877132\pi\) |
0.789258 | + | 0.614062i | \(0.210465\pi\) | |||||||
\(854\) | −6.86843 | + | 0.401816i | −0.235033 | + | 0.0137499i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.9110 | − | 3.77974i | 1.05652 | − | 0.129189i | ||||
\(857\) | − | 9.40860i | − | 0.321392i | −0.987004 | − | 0.160696i | \(-0.948626\pi\) | ||
0.987004 | − | 0.160696i | \(-0.0513738\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.19858i | 0.279732i | 0.990170 | + | 0.139866i | \(0.0446672\pi\) | ||||
−0.990170 | + | 0.139866i | \(0.955333\pi\) | |||||||
\(860\) | 3.75957 | + | 2.66709i | 0.128200 | + | 0.0909470i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.9177 | − | 4.75400i | −0.508097 | − | 0.161922i | ||||
\(863\) | −14.3575 | + | 24.8680i | −0.488736 | + | 0.846516i | −0.999916 | − | 0.0129580i | \(-0.995875\pi\) |
0.511180 | + | 0.859474i | \(0.329209\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.50394 | − | 7.80106i | −0.153139 | − | 0.265244i | ||||
\(866\) | −13.7082 | + | 12.4839i | −0.465824 | + | 0.424221i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.30753 | − | 20.7797i | 0.180149 | − | 0.705309i | ||||
\(869\) | −6.91248 | + | 3.99092i | −0.234490 | + | 0.135383i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.8350i | 0.502666i | ||||||||
\(872\) | −4.79662 | + | 11.2845i | −0.162434 | + | 0.382141i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.10894 | − | 0.242272i | 0.0375106 | − | 0.00819496i | ||||
\(875\) | 4.64029 | + | 12.0731i | 0.156870 | + | 0.408144i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.94951 | −0.200901 | −0.100450 | − | 0.994942i | \(-0.532028\pi\) | ||||
−0.100450 | + | 0.994942i | \(0.532028\pi\) | |||||||
\(878\) | 15.3074 | − | 48.0334i | 0.516600 | − | 1.62105i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.632284 | − | 3.34474i | 0.0213143 | − | 0.112751i | ||||
\(881\) | 20.0536i | 0.675622i | 0.941214 | + | 0.337811i | \(0.109686\pi\) | ||||
−0.941214 | + | 0.337811i | \(0.890314\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.14562i | 0.0385533i | 0.999814 | + | 0.0192766i | \(0.00613632\pi\) | ||||
−0.999814 | + | 0.0192766i | \(0.993864\pi\) | |||||||
\(884\) | −20.9489 | + | 29.5299i | −0.704587 | + | 0.993197i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.1209 | + | 5.13746i | 0.541593 | + | 0.172596i | ||||
\(887\) | −14.8477 | −0.498536 | −0.249268 | − | 0.968435i | \(-0.580190\pi\) | ||||
−0.249268 | + | 0.968435i | \(0.580190\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.07973 | + | 21.0218i | 0.270985 | + | 0.705048i | ||||
\(890\) | 0.828167 | + | 3.79075i | 0.0277602 | + | 0.127066i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.0529 | − | 16.9899i | 0.403560 | − | 0.568865i | ||||
\(893\) | 0.432473i | 0.0144721i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.68690 | + | 2.12863i | −0.123239 | + | 0.0711523i | ||||
\(896\) | −21.9952 | − | 20.3030i | −0.734807 | − | 0.678276i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.48899 | + | 2.73309i | 0.0830588 | + | 0.0912043i | ||||
\(899\) | −14.8180 | − | 25.6654i | −0.494206 | − | 0.855990i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.2258 | − | 41.9603i | 0.807079 | − | 1.39790i | ||||
\(902\) | −2.19584 | + | 6.89037i | −0.0731136 | + | 0.229424i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.80087 | − | 3.74093i | −0.292713 | − | 0.124421i | ||||
\(905\) | − | 12.3663i | − | 0.411069i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 38.9167i | 1.29221i | 0.763249 | + | 0.646104i | \(0.223603\pi\) | ||||
−0.763249 | + | 0.646104i | \(0.776397\pi\) | |||||||
\(908\) | 1.08167 | − | 11.5452i | 0.0358964 | − | 0.383142i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.416016 | + | 7.11116i | 0.0137908 | + | 0.235733i | ||||
\(911\) | −10.5139 | + | 18.2107i | −0.348342 | + | 0.603346i | −0.985955 | − | 0.167010i | \(-0.946589\pi\) |
0.637613 | + | 0.770357i | \(0.279922\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.4693 | + | 19.8655i | −0.379579 | + | 0.657451i | ||||
\(914\) | 23.9657 | + | 7.63747i | 0.792716 | + | 0.252625i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.920424 | + | 9.82420i | −0.0304117 | + | 0.324601i | ||||
\(917\) | 20.7951 | − | 7.99260i | 0.686714 | − | 0.263939i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.2723 | + | 9.39484i | 0.536775 | + | 0.309907i | 0.743771 | − | 0.668435i | \(-0.233035\pi\) |
−0.206996 | + | 0.978342i | \(0.566369\pi\) | |||||||
\(920\) | 8.56690 | − | 6.44892i | 0.282442 | − | 0.212615i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 44.7240 | − | 9.77088i | 1.47291 | − | 0.321787i | ||||
\(923\) | −18.3240 | − | 31.7380i | −0.603141 | − | 1.04467i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.2296 | − | 31.5746i | 0.599385 | − | 1.03817i | ||||
\(926\) | −10.2105 | + | 32.0398i | −0.335539 | + | 1.05289i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −41.3462 | + | 1.16865i | −1.35726 | + | 0.0383628i | ||||
\(929\) | 26.6151 | − | 15.3663i | 0.873215 | − | 0.504151i | 0.00479946 | − | 0.999988i | \(-0.498472\pi\) |
0.868415 | + | 0.495838i | \(0.165139\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.726816 | − | 0.155134i | 0.0238204 | − | 0.00508430i | ||||
\(932\) | 13.1432 | − | 18.5269i | 0.430520 | − | 0.606868i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.13520 | − | 9.77338i | −0.0698658 | − | 0.319795i | ||||
\(935\) | 2.02897 | + | 3.51429i | 0.0663546 | + | 0.114929i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.7669 | 0.776431 | 0.388215 | − | 0.921569i | \(-0.373092\pi\) | ||||
0.388215 | + | 0.921569i | \(0.373092\pi\) | |||||||
\(938\) | 12.2138 | − | 8.03762i | 0.398793 | − | 0.262438i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.70377 | + | 3.71319i | 0.0555708 | + | 0.121111i | ||||
\(941\) | 4.75086 | + | 2.74291i | 0.154874 | + | 0.0894164i | 0.575434 | − | 0.817848i | \(-0.304833\pi\) |
−0.420560 | + | 0.907265i | \(0.638166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.7289 | + | 11.3905i | −0.642460 | + | 0.370925i | ||||
\(944\) | −8.75963 | + | 10.1823i | −0.285102 | + | 0.331405i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.7757 | + | 2.35418i | −0.350349 | + | 0.0765410i | ||||
\(947\) | 16.7543 | + | 29.0194i | 0.544443 | + | 0.943003i | 0.998642 | + | 0.0521027i | \(0.0165923\pi\) |
−0.454199 | + | 0.890900i | \(0.650074\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0766 | − | 36.5057i | 0.684175 | − | 1.18503i | ||||
\(950\) | −0.696546 | + | 0.152175i | −0.0225989 | + | 0.00493720i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 35.6622 | + | 1.24803i | 1.15582 | + | 0.0404488i | ||||
\(953\) | 21.1120i | 0.683884i | 0.939721 | + | 0.341942i | \(0.111085\pi\) | ||||
−0.939721 | + | 0.341942i | \(0.888915\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.57130 | − | 1.48454i | 0.0832054 | − | 0.0480387i | ||||
\(956\) | −26.2397 | + | 12.0399i | −0.848653 | + | 0.389397i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.9499 | − | 14.5254i | 0.515317 | − | 0.469294i | ||||
\(959\) | 4.03753 | + | 10.5048i | 0.130379 | + | 0.339218i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.28632 | − | 12.6203i | −0.235043 | − | 0.407106i | ||||
\(962\) | 30.4778 | − | 27.7558i | 0.982645 | − | 0.894884i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.62696 | + | 28.0390i | −0.0846086 | + | 0.903075i | ||||
\(965\) | −7.16015 | − | 4.13392i | −0.230493 | − | 0.133075i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.5455 | − | 11.2846i | 0.628540 | − | 0.362888i | −0.151646 | − | 0.988435i | \(-0.548457\pi\) |
0.780186 | + | 0.625547i | \(0.215124\pi\) | |||||||
\(968\) | −13.8130 | − | 18.3496i | −0.443968 | − | 0.589777i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.94614 | + | 1.95447i | −0.287243 | + | 0.0627542i | ||||
\(971\) | 26.7170 | − | 46.2752i | 0.857388 | − | 1.48504i | −0.0170228 | − | 0.999855i | \(-0.505419\pi\) |
0.874411 | − | 0.485185i | \(-0.161248\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.02889 | + | 1.27168i | −0.0329847 | + | 0.0407681i | ||||
\(974\) | 5.45808 | − | 17.1270i | 0.174888 | − | 0.548784i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.43043 | − | 6.94206i | −0.0777961 | − | 0.222210i | ||||
\(977\) | 22.7320 | + | 13.1243i | 0.727260 | + | 0.419884i | 0.817419 | − | 0.576044i | \(-0.195404\pi\) |
−0.0901590 | + | 0.995927i | \(0.528738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.04072 | − | 4.64231i | −0.256983 | − | 0.148369i | ||||
\(980\) | 5.62926 | − | 4.19533i | 0.179820 | − | 0.134015i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32.5990 | + | 10.3887i | 1.04028 | + | 0.331518i | ||||
\(983\) | 28.7580 | 0.917239 | 0.458620 | − | 0.888633i | \(-0.348344\pi\) | ||||
0.458620 | + | 0.888633i | \(0.348344\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.12861 | 0.0678232 | ||||||||
\(986\) | 36.4569 | − | 33.2010i | 1.16103 | − | 1.05733i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.802607 | − | 0.0751958i | −0.0255343 | − | 0.00239230i | ||||
\(989\) | −30.0903 | − | 17.3727i | −0.956817 | − | 0.552418i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.2389 | − | 15.1490i | 0.833506 | − | 0.481225i | −0.0215459 | − | 0.999768i | \(-0.506859\pi\) |
0.855051 | + | 0.518543i | \(0.173525\pi\) | |||||||
\(992\) | 22.9185 | − | 0.647789i | 0.727662 | − | 0.0205673i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.2022 | + | 32.2819i | −0.513901 | + | 1.02392i | ||||
\(995\) | −5.50055 | − | 9.52723i | −0.174379 | − | 0.302033i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.2489 | 0.641290 | 0.320645 | − | 0.947199i | \(-0.396100\pi\) | ||||
0.320645 | + | 0.947199i | \(0.396100\pi\) | |||||||
\(998\) | −15.3997 | − | 16.9099i | −0.487468 | − | 0.535274i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.o.a.359.11 | 88 | ||
3.2 | odd | 2 | 252.2.o.a.191.34 | yes | 88 | ||
4.3 | odd | 2 | inner | 756.2.o.a.359.5 | 88 | ||
7.4 | even | 3 | 756.2.bb.a.683.18 | 88 | |||
9.4 | even | 3 | 252.2.bb.a.23.18 | yes | 88 | ||
9.5 | odd | 6 | 756.2.bb.a.611.27 | 88 | |||
12.11 | even | 2 | 252.2.o.a.191.40 | yes | 88 | ||
21.11 | odd | 6 | 252.2.bb.a.11.27 | yes | 88 | ||
28.11 | odd | 6 | 756.2.bb.a.683.27 | 88 | |||
36.23 | even | 6 | 756.2.bb.a.611.18 | 88 | |||
36.31 | odd | 6 | 252.2.bb.a.23.27 | yes | 88 | ||
63.4 | even | 3 | 252.2.o.a.95.40 | yes | 88 | ||
63.32 | odd | 6 | inner | 756.2.o.a.179.5 | 88 | ||
84.11 | even | 6 | 252.2.bb.a.11.18 | yes | 88 | ||
252.67 | odd | 6 | 252.2.o.a.95.34 | ✓ | 88 | ||
252.95 | even | 6 | inner | 756.2.o.a.179.11 | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.o.a.95.34 | ✓ | 88 | 252.67 | odd | 6 | ||
252.2.o.a.95.40 | yes | 88 | 63.4 | even | 3 | ||
252.2.o.a.191.34 | yes | 88 | 3.2 | odd | 2 | ||
252.2.o.a.191.40 | yes | 88 | 12.11 | even | 2 | ||
252.2.bb.a.11.18 | yes | 88 | 84.11 | even | 6 | ||
252.2.bb.a.11.27 | yes | 88 | 21.11 | odd | 6 | ||
252.2.bb.a.23.18 | yes | 88 | 9.4 | even | 3 | ||
252.2.bb.a.23.27 | yes | 88 | 36.31 | odd | 6 | ||
756.2.o.a.179.5 | 88 | 63.32 | odd | 6 | inner | ||
756.2.o.a.179.11 | 88 | 252.95 | even | 6 | inner | ||
756.2.o.a.359.5 | 88 | 4.3 | odd | 2 | inner | ||
756.2.o.a.359.11 | 88 | 1.1 | even | 1 | trivial | ||
756.2.bb.a.611.18 | 88 | 36.23 | even | 6 | |||
756.2.bb.a.611.27 | 88 | 9.5 | odd | 6 | |||
756.2.bb.a.683.18 | 88 | 7.4 | even | 3 | |||
756.2.bb.a.683.27 | 88 | 28.11 | odd | 6 |