Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (of order \(3\), 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: | \(9.44630255912\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 508.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.508 |
Dual form | 1183.2.e.c.170.1 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | 0.986869 | − | 0.161521i | \(-0.0516399\pi\) |
−0.633316 | + | 0.773893i | \(0.718307\pi\) | |||||||
\(3\) | 1.50000 | − | 2.59808i | 0.866025 | − | 1.50000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.50000 | + | 2.59808i | 0.670820 | + | 1.16190i | 0.977672 | + | 0.210138i | \(0.0673912\pi\) |
−0.306851 | + | 0.951757i | \(0.599275\pi\) | |||||||
\(6\) | 3.00000 | 1.22474 | ||||||||
\(7\) | −0.500000 | − | 2.59808i | −0.188982 | − | 0.981981i | ||||
\(8\) | 3.00000 | 1.06066 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | −1.50000 | + | 2.59808i | −0.474342 | + | 0.821584i | ||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | −1.50000 | − | 2.59808i | −0.433013 | − | 0.750000i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.00000 | − | 1.73205i | 0.534522 | − | 0.462910i | ||||
\(15\) | 9.00000 | 2.32379 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | 3.00000 | − | 5.19615i | 0.707107 | − | 1.22474i | ||||
\(19\) | −0.500000 | − | 0.866025i | −0.114708 | − | 0.198680i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 3.00000 | 0.670820 | ||||||||
\(21\) | −7.50000 | − | 2.59808i | −1.63663 | − | 0.566947i | ||||
\(22\) | −3.00000 | −0.639602 | ||||||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 4.50000 | − | 7.79423i | 0.918559 | − | 1.59099i | ||||
\(25\) | −2.00000 | + | 3.46410i | −0.400000 | + | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | −2.50000 | − | 0.866025i | −0.472456 | − | 0.163663i | ||||
\(29\) | 7.00000 | 1.29987 | 0.649934 | − | 0.759991i | \(-0.274797\pi\) | ||||
0.649934 | + | 0.759991i | \(0.274797\pi\) | |||||||
\(30\) | 4.50000 | + | 7.79423i | 0.821584 | + | 1.42302i | ||||
\(31\) | 1.50000 | − | 2.59808i | 0.269408 | − | 0.466628i | −0.699301 | − | 0.714827i | \(-0.746505\pi\) |
0.968709 | + | 0.248199i | \(0.0798387\pi\) | |||||||
\(32\) | 2.50000 | − | 4.33013i | 0.441942 | − | 0.765466i | ||||
\(33\) | 4.50000 | + | 7.79423i | 0.783349 | + | 1.35680i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 6.00000 | − | 5.19615i | 1.01419 | − | 0.878310i | ||||
\(36\) | −6.00000 | −1.00000 | ||||||||
\(37\) | 1.00000 | + | 1.73205i | 0.164399 | + | 0.284747i | 0.936442 | − | 0.350823i | \(-0.114098\pi\) |
−0.772043 | + | 0.635571i | \(0.780765\pi\) | |||||||
\(38\) | 0.500000 | − | 0.866025i | 0.0811107 | − | 0.140488i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.50000 | + | 7.79423i | 0.711512 | + | 1.23238i | ||||
\(41\) | −3.00000 | −0.468521 | −0.234261 | − | 0.972174i | \(-0.575267\pi\) | ||||
−0.234261 | + | 0.972174i | \(0.575267\pi\) | |||||||
\(42\) | −1.50000 | − | 7.79423i | −0.231455 | − | 1.20268i | ||||
\(43\) | −7.00000 | −1.06749 | −0.533745 | − | 0.845645i | \(-0.679216\pi\) | ||||
−0.533745 | + | 0.845645i | \(0.679216\pi\) | |||||||
\(44\) | 1.50000 | + | 2.59808i | 0.226134 | + | 0.391675i | ||||
\(45\) | 9.00000 | − | 15.5885i | 1.34164 | − | 2.32379i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.500000 | + | 0.866025i | 0.0729325 | + | 0.126323i | 0.900185 | − | 0.435507i | \(-0.143431\pi\) |
−0.827253 | + | 0.561830i | \(0.810098\pi\) | |||||||
\(48\) | 3.00000 | 0.433013 | ||||||||
\(49\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | + | 2.59808i | −0.206041 | + | 0.356873i | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | −4.50000 | − | 7.79423i | −0.612372 | − | 1.06066i | ||||
\(55\) | −9.00000 | −1.21356 | ||||||||
\(56\) | −1.50000 | − | 7.79423i | −0.200446 | − | 1.04155i | ||||
\(57\) | −3.00000 | −0.397360 | ||||||||
\(58\) | 3.50000 | + | 6.06218i | 0.459573 | + | 0.796003i | ||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 4.50000 | − | 7.79423i | 0.580948 | − | 1.00623i | ||||
\(61\) | 6.50000 | + | 11.2583i | 0.832240 | + | 1.44148i | 0.896258 | + | 0.443533i | \(0.146275\pi\) |
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 3.00000 | 0.381000 | ||||||||
\(63\) | −12.0000 | + | 10.3923i | −1.51186 | + | 1.30931i | ||||
\(64\) | 7.00000 | 0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.50000 | + | 7.79423i | −0.553912 | + | 0.959403i | ||||
\(67\) | −1.50000 | + | 2.59808i | −0.183254 | + | 0.317406i | −0.942987 | − | 0.332830i | \(-0.891996\pi\) |
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(68\) | −1.00000 | − | 1.73205i | −0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.50000 | + | 2.59808i | 0.896421 | + | 0.310530i | ||||
\(71\) | −13.0000 | −1.54282 | −0.771408 | − | 0.636341i | \(-0.780447\pi\) | ||||
−0.771408 | + | 0.636341i | \(0.780447\pi\) | |||||||
\(72\) | −9.00000 | − | 15.5885i | −1.06066 | − | 1.83712i | ||||
\(73\) | −6.50000 | + | 11.2583i | −0.760767 | + | 1.31769i | 0.181688 | + | 0.983356i | \(0.441844\pi\) |
−0.942455 | + | 0.334332i | \(0.891489\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | 6.00000 | + | 10.3923i | 0.692820 | + | 1.20000i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 7.50000 | + | 2.59808i | 0.854704 | + | 0.296078i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | + | 2.59808i | 0.168763 | + | 0.292306i | 0.937985 | − | 0.346675i | \(-0.112689\pi\) |
−0.769222 | + | 0.638982i | \(0.779356\pi\) | |||||||
\(80\) | −1.50000 | + | 2.59808i | −0.167705 | + | 0.290474i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | −1.50000 | − | 2.59808i | −0.165647 | − | 0.286910i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −6.00000 | + | 5.19615i | −0.654654 | + | 0.566947i | ||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | −3.50000 | − | 6.06218i | −0.377415 | − | 0.653701i | ||||
\(87\) | 10.5000 | − | 18.1865i | 1.12572 | − | 1.94980i | ||||
\(88\) | −4.50000 | + | 7.79423i | −0.479702 | + | 0.830868i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 18.0000 | 1.89737 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.50000 | − | 7.79423i | −0.466628 | − | 0.808224i | ||||
\(94\) | −0.500000 | + | 0.866025i | −0.0515711 | + | 0.0893237i | ||||
\(95\) | 1.50000 | − | 2.59808i | 0.153897 | − | 0.266557i | ||||
\(96\) | −7.50000 | − | 12.9904i | −0.765466 | − | 1.32583i | ||||
\(97\) | 5.00000 | 0.507673 | 0.253837 | − | 0.967247i | \(-0.418307\pi\) | ||||
0.253837 | + | 0.967247i | \(0.418307\pi\) | |||||||
\(98\) | −5.50000 | − | 4.33013i | −0.555584 | − | 0.437409i | ||||
\(99\) | 18.0000 | 1.80907 | ||||||||
\(100\) | 2.00000 | + | 3.46410i | 0.200000 | + | 0.346410i | ||||
\(101\) | 2.50000 | − | 4.33013i | 0.248759 | − | 0.430864i | −0.714423 | − | 0.699715i | \(-0.753311\pi\) |
0.963182 | + | 0.268851i | \(0.0866439\pi\) | |||||||
\(102\) | 3.00000 | − | 5.19615i | 0.297044 | − | 0.514496i | ||||
\(103\) | −2.50000 | − | 4.33013i | −0.246332 | − | 0.426660i | 0.716173 | − | 0.697923i | \(-0.245892\pi\) |
−0.962505 | + | 0.271263i | \(0.912559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.50000 | − | 23.3827i | −0.439155 | − | 2.28192i | ||||
\(106\) | −3.00000 | −0.291386 | ||||||||
\(107\) | −4.00000 | − | 6.92820i | −0.386695 | − | 0.669775i | 0.605308 | − | 0.795991i | \(-0.293050\pi\) |
−0.992003 | + | 0.126217i | \(0.959717\pi\) | |||||||
\(108\) | −4.50000 | + | 7.79423i | −0.433013 | + | 0.750000i | ||||
\(109\) | 3.50000 | − | 6.06218i | 0.335239 | − | 0.580651i | −0.648292 | − | 0.761392i | \(-0.724516\pi\) |
0.983531 | + | 0.180741i | \(0.0578495\pi\) | |||||||
\(110\) | −4.50000 | − | 7.79423i | −0.429058 | − | 0.743151i | ||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 2.00000 | − | 1.73205i | 0.188982 | − | 0.163663i | ||||
\(113\) | 15.0000 | 1.41108 | 0.705541 | − | 0.708669i | \(-0.250704\pi\) | ||||
0.705541 | + | 0.708669i | \(0.250704\pi\) | |||||||
\(114\) | −1.50000 | − | 2.59808i | −0.140488 | − | 0.243332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.50000 | − | 6.06218i | 0.324967 | − | 0.562859i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | −5.00000 | − | 1.73205i | −0.458349 | − | 0.158777i | ||||
\(120\) | 27.0000 | 2.46475 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | −6.50000 | + | 11.2583i | −0.588482 | + | 1.01928i | ||||
\(123\) | −4.50000 | + | 7.79423i | −0.405751 | + | 0.702782i | ||||
\(124\) | −1.50000 | − | 2.59808i | −0.134704 | − | 0.233314i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | −15.0000 | − | 5.19615i | −1.33631 | − | 0.462910i | ||||
\(127\) | 11.0000 | 0.976092 | 0.488046 | − | 0.872818i | \(-0.337710\pi\) | ||||
0.488046 | + | 0.872818i | \(0.337710\pi\) | |||||||
\(128\) | −1.50000 | − | 2.59808i | −0.132583 | − | 0.229640i | ||||
\(129\) | −10.5000 | + | 18.1865i | −0.924473 | + | 1.60123i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.50000 | − | 4.33013i | −0.218426 | − | 0.378325i | 0.735901 | − | 0.677089i | \(-0.236759\pi\) |
−0.954327 | + | 0.298764i | \(0.903426\pi\) | |||||||
\(132\) | 9.00000 | 0.783349 | ||||||||
\(133\) | −2.00000 | + | 1.73205i | −0.173422 | + | 0.150188i | ||||
\(134\) | −3.00000 | −0.259161 | ||||||||
\(135\) | −13.5000 | − | 23.3827i | −1.16190 | − | 2.01246i | ||||
\(136\) | 3.00000 | − | 5.19615i | 0.257248 | − | 0.445566i | ||||
\(137\) | 5.00000 | − | 8.66025i | 0.427179 | − | 0.739895i | −0.569442 | − | 0.822031i | \(-0.692841\pi\) |
0.996621 | + | 0.0821359i | \(0.0261741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0000 | −1.27228 | −0.636142 | − | 0.771572i | \(-0.719471\pi\) | ||||
−0.636142 | + | 0.771572i | \(0.719471\pi\) | |||||||
\(140\) | −1.50000 | − | 7.79423i | −0.126773 | − | 0.658733i | ||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | −6.50000 | − | 11.2583i | −0.545468 | − | 0.944778i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.00000 | − | 5.19615i | 0.250000 | − | 0.433013i | ||||
\(145\) | 10.5000 | + | 18.1865i | 0.871978 | + | 1.51031i | ||||
\(146\) | −13.0000 | −1.07589 | ||||||||
\(147\) | −3.00000 | + | 20.7846i | −0.247436 | + | 1.71429i | ||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | 7.50000 | + | 12.9904i | 0.614424 | + | 1.06421i | 0.990485 | + | 0.137619i | \(0.0439449\pi\) |
−0.376061 | + | 0.926595i | \(0.622722\pi\) | |||||||
\(150\) | −6.00000 | + | 10.3923i | −0.489898 | + | 0.848528i | ||||
\(151\) | −10.5000 | + | 18.1865i | −0.854478 | + | 1.48000i | 0.0226507 | + | 0.999743i | \(0.492789\pi\) |
−0.877129 | + | 0.480256i | \(0.840544\pi\) | |||||||
\(152\) | −1.50000 | − | 2.59808i | −0.121666 | − | 0.210732i | ||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 1.50000 | + | 7.79423i | 0.120873 | + | 0.628077i | ||||
\(155\) | 9.00000 | 0.722897 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.50000 | + | 16.4545i | −0.758183 | + | 1.31321i | 0.185594 | + | 0.982627i | \(0.440579\pi\) |
−0.943777 | + | 0.330584i | \(0.892754\pi\) | |||||||
\(158\) | −1.50000 | + | 2.59808i | −0.119334 | + | 0.206692i | ||||
\(159\) | 4.50000 | + | 7.79423i | 0.356873 | + | 0.618123i | ||||
\(160\) | 15.0000 | 1.18585 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | −0.500000 | − | 0.866025i | −0.0391630 | − | 0.0678323i | 0.845780 | − | 0.533533i | \(-0.179136\pi\) |
−0.884943 | + | 0.465700i | \(0.845802\pi\) | |||||||
\(164\) | −1.50000 | + | 2.59808i | −0.117130 | + | 0.202876i | ||||
\(165\) | −13.5000 | + | 23.3827i | −1.05097 | + | 1.82034i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 13.0000 | 1.00597 | 0.502985 | − | 0.864295i | \(-0.332235\pi\) | ||||
0.502985 | + | 0.864295i | \(0.332235\pi\) | |||||||
\(168\) | −22.5000 | − | 7.79423i | −1.73591 | − | 0.601338i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 3.00000 | + | 5.19615i | 0.230089 | + | 0.398527i | ||||
\(171\) | −3.00000 | + | 5.19615i | −0.229416 | + | 0.397360i | ||||
\(172\) | −3.50000 | + | 6.06218i | −0.266872 | + | 0.462237i | ||||
\(173\) | −9.50000 | − | 16.4545i | −0.722272 | − | 1.25101i | −0.960087 | − | 0.279701i | \(-0.909765\pi\) |
0.237816 | − | 0.971310i | \(-0.423569\pi\) | |||||||
\(174\) | 21.0000 | 1.59201 | ||||||||
\(175\) | 10.0000 | + | 3.46410i | 0.755929 | + | 0.261861i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 6.00000 | + | 10.3923i | 0.450988 | + | 0.781133i | ||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | −8.50000 | + | 14.7224i | −0.635320 | + | 1.10041i | 0.351127 | + | 0.936328i | \(0.385798\pi\) |
−0.986447 | + | 0.164079i | \(0.947535\pi\) | |||||||
\(180\) | −9.00000 | − | 15.5885i | −0.670820 | − | 1.16190i | ||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 39.0000 | 2.88296 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | + | 5.19615i | −0.220564 | + | 0.382029i | ||||
\(186\) | 4.50000 | − | 7.79423i | 0.329956 | − | 0.571501i | ||||
\(187\) | 3.00000 | + | 5.19615i | 0.219382 | + | 0.379980i | ||||
\(188\) | 1.00000 | 0.0729325 | ||||||||
\(189\) | 4.50000 | + | 23.3827i | 0.327327 | + | 1.70084i | ||||
\(190\) | 3.00000 | 0.217643 | ||||||||
\(191\) | 8.50000 | + | 14.7224i | 0.615038 | + | 1.06528i | 0.990378 | + | 0.138390i | \(0.0441928\pi\) |
−0.375339 | + | 0.926887i | \(0.622474\pi\) | |||||||
\(192\) | 10.5000 | − | 18.1865i | 0.757772 | − | 1.31250i | ||||
\(193\) | 3.50000 | − | 6.06218i | 0.251936 | − | 0.436365i | −0.712123 | − | 0.702055i | \(-0.752266\pi\) |
0.964059 | + | 0.265689i | \(0.0855996\pi\) | |||||||
\(194\) | 2.50000 | + | 4.33013i | 0.179490 | + | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | + | 6.92820i | −0.0714286 | + | 0.494872i | ||||
\(197\) | 1.00000 | 0.0712470 | 0.0356235 | − | 0.999365i | \(-0.488658\pi\) | ||||
0.0356235 | + | 0.999365i | \(0.488658\pi\) | |||||||
\(198\) | 9.00000 | + | 15.5885i | 0.639602 | + | 1.10782i | ||||
\(199\) | 10.0000 | − | 17.3205i | 0.708881 | − | 1.22782i | −0.256391 | − | 0.966573i | \(-0.582534\pi\) |
0.965272 | − | 0.261245i | \(-0.0841331\pi\) | |||||||
\(200\) | −6.00000 | + | 10.3923i | −0.424264 | + | 0.734847i | ||||
\(201\) | 4.50000 | + | 7.79423i | 0.317406 | + | 0.549762i | ||||
\(202\) | 5.00000 | 0.351799 | ||||||||
\(203\) | −3.50000 | − | 18.1865i | −0.245652 | − | 1.27644i | ||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | −4.50000 | − | 7.79423i | −0.314294 | − | 0.544373i | ||||
\(206\) | 2.50000 | − | 4.33013i | 0.174183 | − | 0.301694i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 18.0000 | − | 15.5885i | 1.24212 | − | 1.07571i | ||||
\(211\) | 7.00000 | 0.481900 | 0.240950 | − | 0.970538i | \(-0.422541\pi\) | ||||
0.240950 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(212\) | 1.50000 | + | 2.59808i | 0.103020 | + | 0.178437i | ||||
\(213\) | −19.5000 | + | 33.7750i | −1.33612 | + | 2.31422i | ||||
\(214\) | 4.00000 | − | 6.92820i | 0.273434 | − | 0.473602i | ||||
\(215\) | −10.5000 | − | 18.1865i | −0.716094 | − | 1.24031i | ||||
\(216\) | −27.0000 | −1.83712 | ||||||||
\(217\) | −7.50000 | − | 2.59808i | −0.509133 | − | 0.176369i | ||||
\(218\) | 7.00000 | 0.474100 | ||||||||
\(219\) | 19.5000 | + | 33.7750i | 1.31769 | + | 2.28230i | ||||
\(220\) | −4.50000 | + | 7.79423i | −0.303390 | + | 0.525487i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.00000 | + | 5.19615i | 0.201347 | + | 0.348743i | ||||
\(223\) | 9.00000 | 0.602685 | 0.301342 | − | 0.953516i | \(-0.402565\pi\) | ||||
0.301342 | + | 0.953516i | \(0.402565\pi\) | |||||||
\(224\) | −12.5000 | − | 4.33013i | −0.835191 | − | 0.289319i | ||||
\(225\) | 24.0000 | 1.60000 | ||||||||
\(226\) | 7.50000 | + | 12.9904i | 0.498893 | + | 0.864107i | ||||
\(227\) | −2.00000 | + | 3.46410i | −0.132745 | + | 0.229920i | −0.924734 | − | 0.380615i | \(-0.875712\pi\) |
0.791989 | + | 0.610535i | \(0.209046\pi\) | |||||||
\(228\) | −1.50000 | + | 2.59808i | −0.0993399 | + | 0.172062i | ||||
\(229\) | −6.50000 | − | 11.2583i | −0.429532 | − | 0.743971i | 0.567300 | − | 0.823511i | \(-0.307988\pi\) |
−0.996832 | + | 0.0795401i | \(0.974655\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | − | 15.5885i | 1.18431 | − | 1.02565i | ||||
\(232\) | 21.0000 | 1.37872 | ||||||||
\(233\) | 10.5000 | + | 18.1865i | 0.687878 | + | 1.19144i | 0.972523 | + | 0.232806i | \(0.0747909\pi\) |
−0.284645 | + | 0.958633i | \(0.591876\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.50000 | + | 2.59808i | −0.0978492 | + | 0.169480i | ||||
\(236\) | 2.00000 | + | 3.46410i | 0.130189 | + | 0.225494i | ||||
\(237\) | 9.00000 | 0.584613 | ||||||||
\(238\) | −1.00000 | − | 5.19615i | −0.0648204 | − | 0.336817i | ||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 4.50000 | + | 7.79423i | 0.290474 | + | 0.503115i | ||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | −1.00000 | + | 1.73205i | −0.0642824 | + | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.0000 | 0.832240 | ||||||||
\(245\) | −16.5000 | − | 12.9904i | −1.05415 | − | 0.829925i | ||||
\(246\) | −9.00000 | −0.573819 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.50000 | − | 7.79423i | 0.285750 | − | 0.494934i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.50000 | + | 2.59808i | 0.0948683 | + | 0.164317i | ||||
\(251\) | −23.0000 | −1.45175 | −0.725874 | − | 0.687828i | \(-0.758564\pi\) | ||||
−0.725874 | + | 0.687828i | \(0.758564\pi\) | |||||||
\(252\) | 3.00000 | + | 15.5885i | 0.188982 | + | 0.981981i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 5.50000 | + | 9.52628i | 0.345101 | + | 0.597732i | ||||
\(255\) | 9.00000 | − | 15.5885i | 0.563602 | − | 0.976187i | ||||
\(256\) | 8.50000 | − | 14.7224i | 0.531250 | − | 0.920152i | ||||
\(257\) | 1.00000 | + | 1.73205i | 0.0623783 | + | 0.108042i | 0.895528 | − | 0.445005i | \(-0.146798\pi\) |
−0.833150 | + | 0.553047i | \(0.813465\pi\) | |||||||
\(258\) | −21.0000 | −1.30740 | ||||||||
\(259\) | 4.00000 | − | 3.46410i | 0.248548 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.0000 | − | 36.3731i | −1.29987 | − | 2.25144i | ||||
\(262\) | 2.50000 | − | 4.33013i | 0.154451 | − | 0.267516i | ||||
\(263\) | 13.5000 | − | 23.3827i | 0.832446 | − | 1.44184i | −0.0636476 | − | 0.997972i | \(-0.520273\pi\) |
0.896093 | − | 0.443866i | \(-0.146393\pi\) | |||||||
\(264\) | 13.5000 | + | 23.3827i | 0.830868 | + | 1.43910i | ||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | −2.50000 | − | 0.866025i | −0.153285 | − | 0.0530994i | ||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 1.50000 | + | 2.59808i | 0.0916271 | + | 0.158703i | ||||
\(269\) | −9.00000 | + | 15.5885i | −0.548740 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572259i | \(0.981774\pi\) | |||||||
\(270\) | 13.5000 | − | 23.3827i | 0.821584 | − | 1.42302i | ||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | 0.604122 | ||||||||
\(275\) | −6.00000 | − | 10.3923i | −0.361814 | − | 0.626680i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.0000 | + | 19.0526i | −0.660926 | + | 1.14476i | 0.319447 | + | 0.947604i | \(0.396503\pi\) |
−0.980373 | + | 0.197153i | \(0.936830\pi\) | |||||||
\(278\) | −7.50000 | − | 12.9904i | −0.449820 | − | 0.779111i | ||||
\(279\) | −18.0000 | −1.07763 | ||||||||
\(280\) | 18.0000 | − | 15.5885i | 1.07571 | − | 0.931589i | ||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 1.50000 | + | 2.59808i | 0.0893237 | + | 0.154713i | ||||
\(283\) | −0.500000 | + | 0.866025i | −0.0297219 | + | 0.0514799i | −0.880504 | − | 0.474039i | \(-0.842796\pi\) |
0.850782 | + | 0.525519i | \(0.176129\pi\) | |||||||
\(284\) | −6.50000 | + | 11.2583i | −0.385704 | + | 0.668059i | ||||
\(285\) | −4.50000 | − | 7.79423i | −0.266557 | − | 0.461690i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.50000 | + | 7.79423i | 0.0885422 | + | 0.460079i | ||||
\(288\) | −30.0000 | −1.76777 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −10.5000 | + | 18.1865i | −0.616581 | + | 1.06795i | ||||
\(291\) | 7.50000 | − | 12.9904i | 0.439658 | − | 0.761510i | ||||
\(292\) | 6.50000 | + | 11.2583i | 0.380384 | + | 0.658844i | ||||
\(293\) | −11.0000 | −0.642627 | −0.321313 | − | 0.946973i | \(-0.604124\pi\) | ||||
−0.321313 | + | 0.946973i | \(0.604124\pi\) | |||||||
\(294\) | −19.5000 | + | 7.79423i | −1.13726 | + | 0.454569i | ||||
\(295\) | −12.0000 | −0.698667 | ||||||||
\(296\) | 3.00000 | + | 5.19615i | 0.174371 | + | 0.302020i | ||||
\(297\) | 13.5000 | − | 23.3827i | 0.783349 | − | 1.35680i | ||||
\(298\) | −7.50000 | + | 12.9904i | −0.434463 | + | 0.752513i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 12.0000 | 0.692820 | ||||||||
\(301\) | 3.50000 | + | 18.1865i | 0.201737 | + | 1.04825i | ||||
\(302\) | −21.0000 | −1.20841 | ||||||||
\(303\) | −7.50000 | − | 12.9904i | −0.430864 | − | 0.746278i | ||||
\(304\) | 0.500000 | − | 0.866025i | 0.0286770 | − | 0.0496700i | ||||
\(305\) | −19.5000 | + | 33.7750i | −1.11657 | + | 1.93395i | ||||
\(306\) | −6.00000 | − | 10.3923i | −0.342997 | − | 0.594089i | ||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 6.00000 | − | 5.19615i | 0.341882 | − | 0.296078i | ||||
\(309\) | −15.0000 | −0.853320 | ||||||||
\(310\) | 4.50000 | + | 7.79423i | 0.255583 | + | 0.442682i | ||||
\(311\) | 4.50000 | − | 7.79423i | 0.255172 | − | 0.441970i | −0.709771 | − | 0.704433i | \(-0.751201\pi\) |
0.964942 | + | 0.262463i | \(0.0845347\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.50000 | − | 16.4545i | −0.536972 | − | 0.930062i | −0.999065 | − | 0.0432311i | \(-0.986235\pi\) |
0.462093 | − | 0.886831i | \(-0.347098\pi\) | |||||||
\(314\) | −19.0000 | −1.07223 | ||||||||
\(315\) | −45.0000 | − | 15.5885i | −2.53546 | − | 0.878310i | ||||
\(316\) | 3.00000 | 0.168763 | ||||||||
\(317\) | −4.50000 | − | 7.79423i | −0.252745 | − | 0.437767i | 0.711535 | − | 0.702650i | \(-0.248000\pi\) |
−0.964281 | + | 0.264883i | \(0.914667\pi\) | |||||||
\(318\) | −4.50000 | + | 7.79423i | −0.252347 | + | 0.437079i | ||||
\(319\) | −10.5000 | + | 18.1865i | −0.587887 | + | 1.01825i | ||||
\(320\) | 10.5000 | + | 18.1865i | 0.586968 | + | 1.01666i | ||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.00000 | −0.111283 | ||||||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.500000 | − | 0.866025i | 0.0276924 | − | 0.0479647i | ||||
\(327\) | −10.5000 | − | 18.1865i | −0.580651 | − | 1.00572i | ||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 2.00000 | − | 1.73205i | 0.110264 | − | 0.0954911i | ||||
\(330\) | −27.0000 | −1.48630 | ||||||||
\(331\) | −14.5000 | − | 25.1147i | −0.796992 | − | 1.38043i | −0.921567 | − | 0.388221i | \(-0.873090\pi\) |
0.124574 | − | 0.992210i | \(-0.460243\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.00000 | − | 10.3923i | 0.328798 | − | 0.569495i | ||||
\(334\) | 6.50000 | + | 11.2583i | 0.355664 | + | 0.616028i | ||||
\(335\) | −9.00000 | −0.491723 | ||||||||
\(336\) | −1.50000 | − | 7.79423i | −0.0818317 | − | 0.425210i | ||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.5000 | − | 38.9711i | 1.22203 | − | 2.11662i | ||||
\(340\) | 3.00000 | − | 5.19615i | 0.162698 | − | 0.281801i | ||||
\(341\) | 4.50000 | + | 7.79423i | 0.243689 | + | 0.422081i | ||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −21.0000 | −1.13224 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.50000 | − | 16.4545i | 0.510723 | − | 0.884598i | ||||
\(347\) | 4.00000 | − | 6.92820i | 0.214731 | − | 0.371925i | −0.738458 | − | 0.674299i | \(-0.764446\pi\) |
0.953189 | + | 0.302374i | \(0.0977791\pi\) | |||||||
\(348\) | −10.5000 | − | 18.1865i | −0.562859 | − | 0.974901i | ||||
\(349\) | −23.0000 | −1.23116 | −0.615581 | − | 0.788074i | \(-0.711079\pi\) | ||||
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | 2.00000 | + | 10.3923i | 0.106904 | + | 0.555492i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.50000 | + | 12.9904i | 0.399751 | + | 0.692390i | ||||
\(353\) | −12.5000 | + | 21.6506i | −0.665308 | + | 1.15235i | 0.313894 | + | 0.949458i | \(0.398366\pi\) |
−0.979202 | + | 0.202889i | \(0.934967\pi\) | |||||||
\(354\) | −6.00000 | + | 10.3923i | −0.318896 | + | 0.552345i | ||||
\(355\) | −19.5000 | − | 33.7750i | −1.03495 | − | 1.79259i | ||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −12.0000 | + | 10.3923i | −0.635107 | + | 0.550019i | ||||
\(358\) | −17.0000 | −0.898478 | ||||||||
\(359\) | 8.50000 | + | 14.7224i | 0.448613 | + | 0.777020i | 0.998296 | − | 0.0583530i | \(-0.0185849\pi\) |
−0.549683 | + | 0.835373i | \(0.685252\pi\) | |||||||
\(360\) | 27.0000 | − | 46.7654i | 1.42302 | − | 2.46475i | ||||
\(361\) | 9.00000 | − | 15.5885i | 0.473684 | − | 0.820445i | ||||
\(362\) | −11.0000 | − | 19.0526i | −0.578147 | − | 1.00138i | ||||
\(363\) | 6.00000 | 0.314918 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.0000 | −2.04135 | ||||||||
\(366\) | 19.5000 | + | 33.7750i | 1.01928 | + | 1.76545i | ||||
\(367\) | 15.5000 | − | 26.8468i | 0.809093 | − | 1.40139i | −0.104399 | − | 0.994535i | \(-0.533292\pi\) |
0.913493 | − | 0.406855i | \(-0.133375\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.00000 | + | 15.5885i | 0.468521 | + | 0.811503i | ||||
\(370\) | −6.00000 | −0.311925 | ||||||||
\(371\) | 7.50000 | + | 2.59808i | 0.389381 | + | 0.134885i | ||||
\(372\) | −9.00000 | −0.466628 | ||||||||
\(373\) | 4.50000 | + | 7.79423i | 0.233001 | + | 0.403570i | 0.958690 | − | 0.284453i | \(-0.0918121\pi\) |
−0.725689 | + | 0.688023i | \(0.758479\pi\) | |||||||
\(374\) | −3.00000 | + | 5.19615i | −0.155126 | + | 0.268687i | ||||
\(375\) | 4.50000 | − | 7.79423i | 0.232379 | − | 0.402492i | ||||
\(376\) | 1.50000 | + | 2.59808i | 0.0773566 | + | 0.133986i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −18.0000 | + | 15.5885i | −0.925820 | + | 0.801784i | ||||
\(379\) | 33.0000 | 1.69510 | 0.847548 | − | 0.530719i | \(-0.178078\pi\) | ||||
0.847548 | + | 0.530719i | \(0.178078\pi\) | |||||||
\(380\) | −1.50000 | − | 2.59808i | −0.0769484 | − | 0.133278i | ||||
\(381\) | 16.5000 | − | 28.5788i | 0.845321 | − | 1.46414i | ||||
\(382\) | −8.50000 | + | 14.7224i | −0.434898 | + | 0.753265i | ||||
\(383\) | −10.5000 | − | 18.1865i | −0.536525 | − | 0.929288i | −0.999088 | − | 0.0427020i | \(-0.986403\pi\) |
0.462563 | − | 0.886586i | \(-0.346930\pi\) | |||||||
\(384\) | −9.00000 | −0.459279 | ||||||||
\(385\) | 4.50000 | + | 23.3827i | 0.229341 | + | 1.19169i | ||||
\(386\) | 7.00000 | 0.356291 | ||||||||
\(387\) | 21.0000 | + | 36.3731i | 1.06749 | + | 1.84895i | ||||
\(388\) | 2.50000 | − | 4.33013i | 0.126918 | − | 0.219829i | ||||
\(389\) | 16.5000 | − | 28.5788i | 0.836583 | − | 1.44900i | −0.0561516 | − | 0.998422i | \(-0.517883\pi\) |
0.892735 | − | 0.450582i | \(-0.148784\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −19.5000 | + | 7.79423i | −0.984899 | + | 0.393668i | ||||
\(393\) | −15.0000 | −0.756650 | ||||||||
\(394\) | 0.500000 | + | 0.866025i | 0.0251896 | + | 0.0436297i | ||||
\(395\) | −4.50000 | + | 7.79423i | −0.226420 | + | 0.392170i | ||||
\(396\) | 9.00000 | − | 15.5885i | 0.452267 | − | 0.783349i | ||||
\(397\) | −0.500000 | − | 0.866025i | −0.0250943 | − | 0.0434646i | 0.853206 | − | 0.521575i | \(-0.174655\pi\) |
−0.878300 | + | 0.478110i | \(0.841322\pi\) | |||||||
\(398\) | 20.0000 | 1.00251 | ||||||||
\(399\) | 1.50000 | + | 7.79423i | 0.0750939 | + | 0.390199i | ||||
\(400\) | −4.00000 | −0.200000 | ||||||||
\(401\) | −1.00000 | − | 1.73205i | −0.0499376 | − | 0.0864945i | 0.839976 | − | 0.542623i | \(-0.182569\pi\) |
−0.889914 | + | 0.456129i | \(0.849236\pi\) | |||||||
\(402\) | −4.50000 | + | 7.79423i | −0.224440 | + | 0.388741i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.50000 | − | 4.33013i | −0.124380 | − | 0.215432i | ||||
\(405\) | −27.0000 | −1.34164 | ||||||||
\(406\) | 14.0000 | − | 12.1244i | 0.694808 | − | 0.601722i | ||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | −9.00000 | − | 15.5885i | −0.445566 | − | 0.771744i | ||||
\(409\) | 7.00000 | − | 12.1244i | 0.346128 | − | 0.599511i | −0.639430 | − | 0.768849i | \(-0.720830\pi\) |
0.985558 | + | 0.169338i | \(0.0541630\pi\) | |||||||
\(410\) | 4.50000 | − | 7.79423i | 0.222239 | − | 0.384930i | ||||
\(411\) | −15.0000 | − | 25.9808i | −0.739895 | − | 1.28154i | ||||
\(412\) | −5.00000 | −0.246332 | ||||||||
\(413\) | 10.0000 | + | 3.46410i | 0.492068 | + | 0.170457i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −22.5000 | + | 38.9711i | −1.10183 | + | 1.90843i | ||||
\(418\) | 1.50000 | + | 2.59808i | 0.0733674 | + | 0.127076i | ||||
\(419\) | −25.0000 | −1.22133 | −0.610665 | − | 0.791889i | \(-0.709098\pi\) | ||||
−0.610665 | + | 0.791889i | \(0.709098\pi\) | |||||||
\(420\) | −22.5000 | − | 7.79423i | −1.09789 | − | 0.380319i | ||||
\(421\) | −18.0000 | −0.877266 | −0.438633 | − | 0.898666i | \(-0.644537\pi\) | ||||
−0.438633 | + | 0.898666i | \(0.644537\pi\) | |||||||
\(422\) | 3.50000 | + | 6.06218i | 0.170377 | + | 0.295102i | ||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | −4.50000 | + | 7.79423i | −0.218539 | + | 0.378521i | ||||
\(425\) | 4.00000 | + | 6.92820i | 0.194029 | + | 0.336067i | ||||
\(426\) | −39.0000 | −1.88956 | ||||||||
\(427\) | 26.0000 | − | 22.5167i | 1.25823 | − | 1.08966i | ||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.5000 | − | 18.1865i | 0.506355 | − | 0.877033i | ||||
\(431\) | 4.50000 | − | 7.79423i | 0.216757 | − | 0.375435i | −0.737057 | − | 0.675830i | \(-0.763785\pi\) |
0.953815 | + | 0.300395i | \(0.0971186\pi\) | |||||||
\(432\) | −4.50000 | − | 7.79423i | −0.216506 | − | 0.375000i | ||||
\(433\) | 27.0000 | 1.29754 | 0.648769 | − | 0.760986i | \(-0.275284\pi\) | ||||
0.648769 | + | 0.760986i | \(0.275284\pi\) | |||||||
\(434\) | −1.50000 | − | 7.79423i | −0.0720023 | − | 0.374135i | ||||
\(435\) | 63.0000 | 3.02062 | ||||||||
\(436\) | −3.50000 | − | 6.06218i | −0.167620 | − | 0.290326i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −19.5000 | + | 33.7750i | −0.931746 | + | 1.61383i | ||||
\(439\) | 8.00000 | + | 13.8564i | 0.381819 | + | 0.661330i | 0.991322 | − | 0.131453i | \(-0.0419644\pi\) |
−0.609503 | + | 0.792784i | \(0.708631\pi\) | |||||||
\(440\) | −27.0000 | −1.28717 | ||||||||
\(441\) | 33.0000 | + | 25.9808i | 1.57143 | + | 1.23718i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.50000 | + | 9.52628i | 0.261313 | + | 0.452607i | 0.966591 | − | 0.256323i | \(-0.0825112\pi\) |
−0.705278 | + | 0.708931i | \(0.749178\pi\) | |||||||
\(444\) | 3.00000 | − | 5.19615i | 0.142374 | − | 0.246598i | ||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 4.50000 | + | 7.79423i | 0.213081 | + | 0.369067i | ||||
\(447\) | 45.0000 | 2.12843 | ||||||||
\(448\) | −3.50000 | − | 18.1865i | −0.165359 | − | 0.859233i | ||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 12.0000 | + | 20.7846i | 0.565685 | + | 0.979796i | ||||
\(451\) | 4.50000 | − | 7.79423i | 0.211897 | − | 0.367016i | ||||
\(452\) | 7.50000 | − | 12.9904i | 0.352770 | − | 0.611016i | ||||
\(453\) | 31.5000 | + | 54.5596i | 1.48000 | + | 2.56343i | ||||
\(454\) | −4.00000 | −0.187729 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −9.00000 | −0.421464 | ||||||||
\(457\) | −9.00000 | − | 15.5885i | −0.421002 | − | 0.729197i | 0.575036 | − | 0.818128i | \(-0.304988\pi\) |
−0.996038 | + | 0.0889312i | \(0.971655\pi\) | |||||||
\(458\) | 6.50000 | − | 11.2583i | 0.303725 | − | 0.526067i | ||||
\(459\) | −9.00000 | + | 15.5885i | −0.420084 | + | 0.727607i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.0000 | −1.63011 | −0.815056 | − | 0.579382i | \(-0.803294\pi\) | ||||
−0.815056 | + | 0.579382i | \(0.803294\pi\) | |||||||
\(462\) | 22.5000 | + | 7.79423i | 1.04679 | + | 0.362620i | ||||
\(463\) | 8.00000 | 0.371792 | 0.185896 | − | 0.982569i | \(-0.440481\pi\) | ||||
0.185896 | + | 0.982569i | \(0.440481\pi\) | |||||||
\(464\) | 3.50000 | + | 6.06218i | 0.162483 | + | 0.281430i | ||||
\(465\) | 13.5000 | − | 23.3827i | 0.626048 | − | 1.08435i | ||||
\(466\) | −10.5000 | + | 18.1865i | −0.486403 | + | 0.842475i | ||||
\(467\) | 3.50000 | + | 6.06218i | 0.161961 | + | 0.280524i | 0.935572 | − | 0.353137i | \(-0.114885\pi\) |
−0.773611 | + | 0.633661i | \(0.781552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.50000 | + | 2.59808i | 0.346318 | + | 0.119968i | ||||
\(470\) | −3.00000 | −0.138380 | ||||||||
\(471\) | 28.5000 | + | 49.3634i | 1.31321 | + | 2.27455i | ||||
\(472\) | −6.00000 | + | 10.3923i | −0.276172 | + | 0.478345i | ||||
\(473\) | 10.5000 | − | 18.1865i | 0.482791 | − | 0.836218i | ||||
\(474\) | 4.50000 | + | 7.79423i | 0.206692 | + | 0.358001i | ||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | −4.00000 | + | 3.46410i | −0.183340 | + | 0.158777i | ||||
\(477\) | 18.0000 | 0.824163 | ||||||||
\(478\) | 2.00000 | + | 3.46410i | 0.0914779 | + | 0.158444i | ||||
\(479\) | −17.5000 | + | 30.3109i | −0.799595 | + | 1.38494i | 0.120284 | + | 0.992739i | \(0.461619\pi\) |
−0.919880 | + | 0.392200i | \(0.871714\pi\) | |||||||
\(480\) | 22.5000 | − | 38.9711i | 1.02698 | − | 1.77878i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −26.0000 | −1.18427 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 7.50000 | + | 12.9904i | 0.340557 | + | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.00000 | − | 13.8564i | 0.362515 | − | 0.627894i | −0.625859 | − | 0.779936i | \(-0.715252\pi\) |
0.988374 | + | 0.152042i | \(0.0485850\pi\) | |||||||
\(488\) | 19.5000 | + | 33.7750i | 0.882724 | + | 1.52892i | ||||
\(489\) | −3.00000 | −0.135665 | ||||||||
\(490\) | 3.00000 | − | 20.7846i | 0.135526 | − | 0.938953i | ||||
\(491\) | 15.0000 | 0.676941 | 0.338470 | − | 0.940977i | \(-0.390091\pi\) | ||||
0.338470 | + | 0.940977i | \(0.390091\pi\) | |||||||
\(492\) | 4.50000 | + | 7.79423i | 0.202876 | + | 0.351391i | ||||
\(493\) | 7.00000 | − | 12.1244i | 0.315264 | − | 0.546054i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27.0000 | + | 46.7654i | 1.21356 | + | 2.10195i | ||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | 6.50000 | + | 33.7750i | 0.291565 | + | 1.51502i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5000 | − | 26.8468i | −0.693875 | − | 1.20183i | −0.970558 | − | 0.240866i | \(-0.922569\pi\) |
0.276683 | − | 0.960961i | \(-0.410765\pi\) | |||||||
\(500\) | 1.50000 | − | 2.59808i | 0.0670820 | − | 0.116190i | ||||
\(501\) | 19.5000 | − | 33.7750i | 0.871196 | − | 1.50896i | ||||
\(502\) | −11.5000 | − | 19.9186i | −0.513270 | − | 0.889010i | ||||
\(503\) | −31.0000 | −1.38222 | −0.691111 | − | 0.722749i | \(-0.742878\pi\) | ||||
−0.691111 | + | 0.722749i | \(0.742878\pi\) | |||||||
\(504\) | −36.0000 | + | 31.1769i | −1.60357 | + | 1.38873i | ||||
\(505\) | 15.0000 | 0.667491 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.50000 | − | 9.52628i | 0.244023 | − | 0.422660i | ||||
\(509\) | −17.0000 | − | 29.4449i | −0.753512 | − | 1.30512i | −0.946111 | − | 0.323843i | \(-0.895025\pi\) |
0.192599 | − | 0.981278i | \(-0.438308\pi\) | |||||||
\(510\) | 18.0000 | 0.797053 | ||||||||
\(511\) | 32.5000 | + | 11.2583i | 1.43772 | + | 0.498039i | ||||
\(512\) | 11.0000 | 0.486136 | ||||||||
\(513\) | 4.50000 | + | 7.79423i | 0.198680 | + | 0.344124i | ||||
\(514\) | −1.00000 | + | 1.73205i | −0.0441081 | + | 0.0763975i | ||||
\(515\) | 7.50000 | − | 12.9904i | 0.330489 | − | 0.572425i | ||||
\(516\) | 10.5000 | + | 18.1865i | 0.462237 | + | 0.800617i | ||||
\(517\) | −3.00000 | −0.131940 | ||||||||
\(518\) | 5.00000 | + | 1.73205i | 0.219687 | + | 0.0761019i | ||||
\(519\) | −57.0000 | −2.50202 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.50000 | − | 14.7224i | 0.372392 | − | 0.645001i | −0.617541 | − | 0.786539i | \(-0.711871\pi\) |
0.989933 | + | 0.141537i | \(0.0452044\pi\) | |||||||
\(522\) | 21.0000 | − | 36.3731i | 0.919145 | − | 1.59201i | ||||
\(523\) | −2.00000 | − | 3.46410i | −0.0874539 | − | 0.151475i | 0.818980 | − | 0.573822i | \(-0.194540\pi\) |
−0.906434 | + | 0.422347i | \(0.861206\pi\) | |||||||
\(524\) | −5.00000 | −0.218426 | ||||||||
\(525\) | 24.0000 | − | 20.7846i | 1.04745 | − | 0.907115i | ||||
\(526\) | 27.0000 | 1.17726 | ||||||||
\(527\) | −3.00000 | − | 5.19615i | −0.130682 | − | 0.226348i | ||||
\(528\) | −4.50000 | + | 7.79423i | −0.195837 | + | 0.339200i | ||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | −4.50000 | − | 7.79423i | −0.195468 | − | 0.338560i | ||||
\(531\) | 24.0000 | 1.04151 | ||||||||
\(532\) | 0.500000 | + | 2.59808i | 0.0216777 | + | 0.112641i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 9.00000 | + | 15.5885i | 0.389468 | + | 0.674579i | ||||
\(535\) | 12.0000 | − | 20.7846i | 0.518805 | − | 0.898597i | ||||
\(536\) | −4.50000 | + | 7.79423i | −0.194370 | + | 0.336659i | ||||
\(537\) | 25.5000 | + | 44.1673i | 1.10041 | + | 1.90596i | ||||
\(538\) | −18.0000 | −0.776035 | ||||||||
\(539\) | 3.00000 | − | 20.7846i | 0.129219 | − | 0.895257i | ||||
\(540\) | −27.0000 | −1.16190 | ||||||||
\(541\) | −18.5000 | − | 32.0429i | −0.795377 | − | 1.37763i | −0.922599 | − | 0.385759i | \(-0.873939\pi\) |
0.127222 | − | 0.991874i | \(-0.459394\pi\) | |||||||
\(542\) | 8.00000 | − | 13.8564i | 0.343629 | − | 0.595184i | ||||
\(543\) | −33.0000 | + | 57.1577i | −1.41617 | + | 2.45287i | ||||
\(544\) | −5.00000 | − | 8.66025i | −0.214373 | − | 0.371305i | ||||
\(545\) | 21.0000 | 0.899541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.0000 | −1.19719 | −0.598597 | − | 0.801050i | \(-0.704275\pi\) | ||||
−0.598597 | + | 0.801050i | \(0.704275\pi\) | |||||||
\(548\) | −5.00000 | − | 8.66025i | −0.213589 | − | 0.369948i | ||||
\(549\) | 39.0000 | − | 67.5500i | 1.66448 | − | 2.88296i | ||||
\(550\) | 6.00000 | − | 10.3923i | 0.255841 | − | 0.443129i | ||||
\(551\) | −3.50000 | − | 6.06218i | −0.149105 | − | 0.258257i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.00000 | − | 5.19615i | 0.255146 | − | 0.220963i | ||||
\(554\) | −22.0000 | −0.934690 | ||||||||
\(555\) | 9.00000 | + | 15.5885i | 0.382029 | + | 0.661693i | ||||
\(556\) | −7.50000 | + | 12.9904i | −0.318071 | + | 0.550915i | ||||
\(557\) | 1.50000 | − | 2.59808i | 0.0635570 | − | 0.110084i | −0.832496 | − | 0.554031i | \(-0.813089\pi\) |
0.896053 | + | 0.443947i | \(0.146422\pi\) | |||||||
\(558\) | −9.00000 | − | 15.5885i | −0.381000 | − | 0.659912i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7.50000 | + | 2.59808i | 0.316933 | + | 0.109789i | ||||
\(561\) | 18.0000 | 0.759961 | ||||||||
\(562\) | 9.00000 | + | 15.5885i | 0.379642 | + | 0.657559i | ||||
\(563\) | −2.00000 | + | 3.46410i | −0.0842900 | + | 0.145994i | −0.905088 | − | 0.425223i | \(-0.860196\pi\) |
0.820798 | + | 0.571218i | \(0.193529\pi\) | |||||||
\(564\) | 1.50000 | − | 2.59808i | 0.0631614 | − | 0.109399i | ||||
\(565\) | 22.5000 | + | 38.9711i | 0.946582 | + | 1.63953i | ||||
\(566\) | −1.00000 | −0.0420331 | ||||||||
\(567\) | 22.5000 | + | 7.79423i | 0.944911 | + | 0.327327i | ||||
\(568\) | −39.0000 | −1.63640 | ||||||||
\(569\) | −5.00000 | − | 8.66025i | −0.209611 | − | 0.363057i | 0.741981 | − | 0.670421i | \(-0.233886\pi\) |
−0.951592 | + | 0.307364i | \(0.900553\pi\) | |||||||
\(570\) | 4.50000 | − | 7.79423i | 0.188484 | − | 0.326464i | ||||
\(571\) | −21.5000 | + | 37.2391i | −0.899747 | + | 1.55841i | −0.0719297 | + | 0.997410i | \(0.522916\pi\) |
−0.827817 | + | 0.560998i | \(0.810418\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 51.0000 | 2.13056 | ||||||||
\(574\) | −6.00000 | + | 5.19615i | −0.250435 | + | 0.216883i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −21.0000 | − | 36.3731i | −0.875000 | − | 1.51554i | ||||
\(577\) | −0.500000 | + | 0.866025i | −0.0208153 | + | 0.0360531i | −0.876245 | − | 0.481865i | \(-0.839960\pi\) |
0.855430 | + | 0.517918i | \(0.173293\pi\) | |||||||
\(578\) | −6.50000 | + | 11.2583i | −0.270364 | + | 0.468285i | ||||
\(579\) | −10.5000 | − | 18.1865i | −0.436365 | − | 0.755807i | ||||
\(580\) | 21.0000 | 0.871978 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 15.0000 | 0.621770 | ||||||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | −19.5000 | + | 33.7750i | −0.806916 | + | 1.39762i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.50000 | − | 9.52628i | −0.227203 | − | 0.393527i | ||||
\(587\) | 33.0000 | 1.36206 | 0.681028 | − | 0.732257i | \(-0.261533\pi\) | ||||
0.681028 | + | 0.732257i | \(0.261533\pi\) | |||||||
\(588\) | 16.5000 | + | 12.9904i | 0.680449 | + | 0.535714i | ||||
\(589\) | −3.00000 | −0.123613 | ||||||||
\(590\) | −6.00000 | − | 10.3923i | −0.247016 | − | 0.427844i | ||||
\(591\) | 1.50000 | − | 2.59808i | 0.0617018 | − | 0.106871i | ||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 13.5000 | + | 23.3827i | 0.554379 | + | 0.960212i | 0.997952 | + | 0.0639736i | \(0.0203773\pi\) |
−0.443573 | + | 0.896238i | \(0.646289\pi\) | |||||||
\(594\) | 27.0000 | 1.10782 | ||||||||
\(595\) | −3.00000 | − | 15.5885i | −0.122988 | − | 0.639064i | ||||
\(596\) | 15.0000 | 0.614424 | ||||||||
\(597\) | −30.0000 | − | 51.9615i | −1.22782 | − | 2.12664i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5000 | − | 21.6506i | 0.510736 | − | 0.884621i | −0.489186 | − | 0.872179i | \(-0.662706\pi\) |
0.999923 | − | 0.0124417i | \(-0.00396043\pi\) | |||||||
\(600\) | 18.0000 | + | 31.1769i | 0.734847 | + | 1.27279i | ||||
\(601\) | 35.0000 | 1.42768 | 0.713840 | − | 0.700309i | \(-0.246954\pi\) | ||||
0.713840 | + | 0.700309i | \(0.246954\pi\) | |||||||
\(602\) | −14.0000 | + | 12.1244i | −0.570597 | + | 0.494152i | ||||
\(603\) | 18.0000 | 0.733017 | ||||||||
\(604\) | 10.5000 | + | 18.1865i | 0.427239 | + | 0.740000i | ||||
\(605\) | −3.00000 | + | 5.19615i | −0.121967 | + | 0.211254i | ||||
\(606\) | 7.50000 | − | 12.9904i | 0.304667 | − | 0.527698i | ||||
\(607\) | −5.50000 | − | 9.52628i | −0.223238 | − | 0.386660i | 0.732551 | − | 0.680712i | \(-0.238329\pi\) |
−0.955789 | + | 0.294052i | \(0.904996\pi\) | |||||||
\(608\) | −5.00000 | −0.202777 | ||||||||
\(609\) | −52.5000 | − | 18.1865i | −2.12741 | − | 0.736956i | ||||
\(610\) | −39.0000 | −1.57906 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.00000 | + | 10.3923i | −0.242536 | + | 0.420084i | ||||
\(613\) | −12.5000 | + | 21.6506i | −0.504870 | + | 0.874461i | 0.495114 | + | 0.868828i | \(0.335126\pi\) |
−0.999984 | + | 0.00563283i | \(0.998207\pi\) | |||||||
\(614\) | −6.00000 | − | 10.3923i | −0.242140 | − | 0.419399i | ||||
\(615\) | −27.0000 | −1.08875 | ||||||||
\(616\) | 22.5000 | + | 7.79423i | 0.906551 | + | 0.314038i | ||||
\(617\) | 33.0000 | 1.32853 | 0.664265 | − | 0.747497i | \(-0.268745\pi\) | ||||
0.664265 | + | 0.747497i | \(0.268745\pi\) | |||||||
\(618\) | −7.50000 | − | 12.9904i | −0.301694 | − | 0.522550i | ||||
\(619\) | 5.50000 | − | 9.52628i | 0.221064 | − | 0.382893i | −0.734068 | − | 0.679076i | \(-0.762380\pi\) |
0.955131 | + | 0.296183i | \(0.0957138\pi\) | |||||||
\(620\) | 4.50000 | − | 7.79423i | 0.180724 | − | 0.313024i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 9.00000 | 0.360867 | ||||||||
\(623\) | 12.0000 | − | 10.3923i | 0.480770 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 9.50000 | − | 16.4545i | 0.379696 | − | 0.657653i | ||||
\(627\) | 4.50000 | − | 7.79423i | 0.179713 | − | 0.311272i | ||||
\(628\) | 9.50000 | + | 16.4545i | 0.379091 | + | 0.656605i | ||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | −9.00000 | − | 46.7654i | −0.358569 | − | 1.86318i | ||||
\(631\) | −25.0000 | −0.995234 | −0.497617 | − | 0.867397i | \(-0.665792\pi\) | ||||
−0.497617 | + | 0.867397i | \(0.665792\pi\) | |||||||
\(632\) | 4.50000 | + | 7.79423i | 0.179000 | + | 0.310038i | ||||
\(633\) | 10.5000 | − | 18.1865i | 0.417338 | − | 0.722850i | ||||
\(634\) | 4.50000 | − | 7.79423i | 0.178718 | − | 0.309548i | ||||
\(635\) | 16.5000 | + | 28.5788i | 0.654783 | + | 1.13412i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −21.0000 | −0.831398 | ||||||||
\(639\) | 39.0000 | + | 67.5500i | 1.54282 | + | 2.67224i | ||||
\(640\) | 4.50000 | − | 7.79423i | 0.177878 | − | 0.308094i | ||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | −12.0000 | − | 20.7846i | −0.473602 | − | 0.820303i | ||||
\(643\) | 19.0000 | 0.749287 | 0.374643 | − | 0.927169i | \(-0.377765\pi\) | ||||
0.374643 | + | 0.927169i | \(0.377765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −63.0000 | −2.48062 | ||||||||
\(646\) | −1.00000 | − | 1.73205i | −0.0393445 | − | 0.0681466i | ||||
\(647\) | −4.50000 | + | 7.79423i | −0.176913 | + | 0.306423i | −0.940822 | − | 0.338902i | \(-0.889945\pi\) |
0.763908 | + | 0.645325i | \(0.223278\pi\) | |||||||
\(648\) | −13.5000 | + | 23.3827i | −0.530330 | + | 0.918559i | ||||
\(649\) | −6.00000 | − | 10.3923i | −0.235521 | − | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0000 | + | 15.5885i | −0.705476 | + | 0.610960i | ||||
\(652\) | −1.00000 | −0.0391630 | ||||||||
\(653\) | −9.00000 | − | 15.5885i | −0.352197 | − | 0.610023i | 0.634437 | − | 0.772975i | \(-0.281232\pi\) |
−0.986634 | + | 0.162951i | \(0.947899\pi\) | |||||||
\(654\) | 10.5000 | − | 18.1865i | 0.410582 | − | 0.711150i | ||||
\(655\) | 7.50000 | − | 12.9904i | 0.293049 | − | 0.507576i | ||||
\(656\) | −1.50000 | − | 2.59808i | −0.0585652 | − | 0.101438i | ||||
\(657\) | 78.0000 | 3.04307 | ||||||||
\(658\) | 2.50000 | + | 0.866025i | 0.0974601 | + | 0.0337612i | ||||
\(659\) | 29.0000 | 1.12968 | 0.564840 | − | 0.825201i | \(-0.308938\pi\) | ||||
0.564840 | + | 0.825201i | \(0.308938\pi\) | |||||||
\(660\) | 13.5000 | + | 23.3827i | 0.525487 | + | 0.910170i | ||||
\(661\) | −4.50000 | + | 7.79423i | −0.175030 | + | 0.303160i | −0.940172 | − | 0.340701i | \(-0.889335\pi\) |
0.765142 | + | 0.643862i | \(0.222669\pi\) | |||||||
\(662\) | 14.5000 | − | 25.1147i | 0.563559 | − | 0.976112i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.50000 | − | 2.59808i | −0.290838 | − | 0.100749i | ||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 6.50000 | − | 11.2583i | 0.251493 | − | 0.435598i | ||||
\(669\) | 13.5000 | − | 23.3827i | 0.521940 | − | 0.904027i | ||||
\(670\) | −4.50000 | − | 7.79423i | −0.173850 | − | 0.301117i | ||||
\(671\) | −39.0000 | −1.50558 | ||||||||
\(672\) | −30.0000 | + | 25.9808i | −1.15728 | + | 1.00223i | ||||
\(673\) | −41.0000 | −1.58043 | −0.790217 | − | 0.612827i | \(-0.790032\pi\) | ||||
−0.790217 | + | 0.612827i | \(0.790032\pi\) | |||||||
\(674\) | 7.00000 | + | 12.1244i | 0.269630 | + | 0.467013i | ||||
\(675\) | 18.0000 | − | 31.1769i | 0.692820 | − | 1.20000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.50000 | − | 6.06218i | −0.134516 | − | 0.232988i | 0.790897 | − | 0.611950i | \(-0.209615\pi\) |
−0.925412 | + | 0.378962i | \(0.876281\pi\) | |||||||
\(678\) | 45.0000 | 1.72821 | ||||||||
\(679\) | −2.50000 | − | 12.9904i | −0.0959412 | − | 0.498525i | ||||
\(680\) | 18.0000 | 0.690268 | ||||||||
\(681\) | 6.00000 | + | 10.3923i | 0.229920 | + | 0.398234i | ||||
\(682\) | −4.50000 | + | 7.79423i | −0.172314 | + | 0.298456i | ||||
\(683\) | 6.00000 | − | 10.3923i | 0.229584 | − | 0.397650i | −0.728101 | − | 0.685470i | \(-0.759597\pi\) |
0.957685 | + | 0.287819i | \(0.0929302\pi\) | |||||||
\(684\) | 3.00000 | + | 5.19615i | 0.114708 | + | 0.198680i | ||||
\(685\) | 30.0000 | 1.14624 | ||||||||
\(686\) | −8.50000 | + | 16.4545i | −0.324532 | + | 0.628235i | ||||
\(687\) | −39.0000 | −1.48794 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.00000 | − | 3.46410i | −0.0760836 | − | 0.131781i | 0.825473 | − | 0.564441i | \(-0.190908\pi\) |
−0.901557 | + | 0.432660i | \(0.857575\pi\) | |||||||
\(692\) | −19.0000 | −0.722272 | ||||||||
\(693\) | −9.00000 | − | 46.7654i | −0.341882 | − | 1.77647i | ||||
\(694\) | 8.00000 | 0.303676 | ||||||||
\(695\) | −22.5000 | − | 38.9711i | −0.853474 | − | 1.47826i | ||||
\(696\) | 31.5000 | − | 54.5596i | 1.19400 | − | 2.06808i | ||||
\(697\) | −3.00000 | + | 5.19615i | −0.113633 | + | 0.196818i | ||||
\(698\) | −11.5000 | − | 19.9186i | −0.435281 | − | 0.753930i | ||||
\(699\) | 63.0000 | 2.38288 | ||||||||
\(700\) | 8.00000 | − | 6.92820i | 0.302372 | − | 0.261861i | ||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.00000 | − | 1.73205i | 0.0377157 | − | 0.0653255i | ||||
\(704\) | −10.5000 | + | 18.1865i | −0.395734 | + | 0.685431i | ||||
\(705\) | 4.50000 | + | 7.79423i | 0.169480 | + | 0.293548i | ||||
\(706\) | −25.0000 | −0.940887 | ||||||||
\(707\) | −12.5000 | − | 4.33013i | −0.470111 | − | 0.162851i | ||||
\(708\) | 12.0000 | 0.450988 | ||||||||
\(709\) | 5.50000 | + | 9.52628i | 0.206557 | + | 0.357767i | 0.950628 | − | 0.310334i | \(-0.100441\pi\) |
−0.744071 | + | 0.668101i | \(0.767108\pi\) | |||||||
\(710\) | 19.5000 | − | 33.7750i | 0.731822 | − | 1.26755i | ||||
\(711\) | 9.00000 | − | 15.5885i | 0.337526 | − | 0.584613i | ||||
\(712\) | 9.00000 | + | 15.5885i | 0.337289 | + | 0.584202i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −15.0000 | − | 5.19615i | −0.561361 | − | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.50000 | + | 14.7224i | 0.317660 | + | 0.550203i | ||||
\(717\) | 6.00000 | − | 10.3923i | 0.224074 | − | 0.388108i | ||||
\(718\) | −8.50000 | + | 14.7224i | −0.317217 | + | 0.549436i | ||||
\(719\) | 4.50000 | + | 7.79423i | 0.167822 | + | 0.290676i | 0.937654 | − | 0.347571i | \(-0.112993\pi\) |
−0.769832 | + | 0.638247i | \(0.779660\pi\) | |||||||
\(720\) | 18.0000 | 0.670820 | ||||||||
\(721\) | −10.0000 | + | 8.66025i | −0.372419 | + | 0.322525i | ||||
\(722\) | 18.0000 | 0.669891 | ||||||||
\(723\) | 39.0000 | + | 67.5500i | 1.45043 | + | 2.51221i | ||||
\(724\) | −11.0000 | + | 19.0526i | −0.408812 | + | 0.708083i | ||||
\(725\) | −14.0000 | + | 24.2487i | −0.519947 | + | 0.900575i | ||||
\(726\) | 3.00000 | + | 5.19615i | 0.111340 | + | 0.192847i | ||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −19.5000 | − | 33.7750i | −0.721727 | − | 1.25007i | ||||
\(731\) | −7.00000 | + | 12.1244i | −0.258904 | + | 0.448435i | ||||
\(732\) | 19.5000 | − | 33.7750i | 0.720741 | − | 1.24836i | ||||
\(733\) | −4.50000 | − | 7.79423i | −0.166211 | − | 0.287886i | 0.770873 | − | 0.636988i | \(-0.219820\pi\) |
−0.937085 | + | 0.349102i | \(0.886487\pi\) | |||||||
\(734\) | 31.0000 | 1.14423 | ||||||||
\(735\) | −58.5000 | + | 23.3827i | −2.15781 | + | 0.862483i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.50000 | − | 7.79423i | −0.165760 | − | 0.287104i | ||||
\(738\) | −9.00000 | + | 15.5885i | −0.331295 | + | 0.573819i | ||||
\(739\) | 0.500000 | − | 0.866025i | 0.0183928 | − | 0.0318573i | −0.856683 | − | 0.515844i | \(-0.827478\pi\) |
0.875075 | + | 0.483987i | \(0.160812\pi\) | |||||||
\(740\) | 3.00000 | + | 5.19615i | 0.110282 | + | 0.191014i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.50000 | + | 7.79423i | 0.0550667 | + | 0.286135i | ||||
\(743\) | −51.0000 | −1.87101 | −0.935504 | − | 0.353315i | \(-0.885054\pi\) | ||||
−0.935504 | + | 0.353315i | \(0.885054\pi\) | |||||||
\(744\) | −13.5000 | − | 23.3827i | −0.494934 | − | 0.857251i | ||||
\(745\) | −22.5000 | + | 38.9711i | −0.824336 | + | 1.42779i | ||||
\(746\) | −4.50000 | + | 7.79423i | −0.164757 | + | 0.285367i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.00000 | 0.219382 | ||||||||
\(749\) | −16.0000 | + | 13.8564i | −0.584627 | + | 0.506302i | ||||
\(750\) | 9.00000 | 0.328634 | ||||||||
\(751\) | −14.0000 | − | 24.2487i | −0.510867 | − | 0.884848i | −0.999921 | − | 0.0125942i | \(-0.995991\pi\) |
0.489053 | − | 0.872254i | \(-0.337342\pi\) | |||||||
\(752\) | −0.500000 | + | 0.866025i | −0.0182331 | + | 0.0315807i | ||||
\(753\) | −34.5000 | + | 59.7558i | −1.25725 | + | 2.17762i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −63.0000 | −2.29280 | ||||||||
\(756\) | 22.5000 | + | 7.79423i | 0.818317 | + | 0.283473i | ||||
\(757\) | 3.00000 | 0.109037 | 0.0545184 | − | 0.998513i | \(-0.482638\pi\) | ||||
0.0545184 | + | 0.998513i | \(0.482638\pi\) | |||||||
\(758\) | 16.5000 | + | 28.5788i | 0.599307 | + | 1.03803i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.50000 | − | 7.79423i | 0.163232 | − | 0.282726i | ||||
\(761\) | −4.50000 | − | 7.79423i | −0.163125 | − | 0.282541i | 0.772863 | − | 0.634573i | \(-0.218824\pi\) |
−0.935988 | + | 0.352032i | \(0.885491\pi\) | |||||||
\(762\) | 33.0000 | 1.19546 | ||||||||
\(763\) | −17.5000 | − | 6.06218i | −0.633543 | − | 0.219466i | ||||
\(764\) | 17.0000 | 0.615038 | ||||||||
\(765\) | −18.0000 | − | 31.1769i | −0.650791 | − | 1.12720i | ||||
\(766\) | 10.5000 | − | 18.1865i | 0.379380 | − | 0.657106i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −25.5000 | − | 44.1673i | −0.920152 | − | 1.59375i | ||||
\(769\) | −19.0000 | −0.685158 | −0.342579 | − | 0.939489i | \(-0.611300\pi\) | ||||
−0.342579 | + | 0.939489i | \(0.611300\pi\) | |||||||
\(770\) | −18.0000 | + | 15.5885i | −0.648675 | + | 0.561769i | ||||
\(771\) | 6.00000 | 0.216085 | ||||||||
\(772\) | −3.50000 | − | 6.06218i | −0.125968 | − | 0.218183i | ||||
\(773\) | −3.00000 | + | 5.19615i | −0.107903 | + | 0.186893i | −0.914920 | − | 0.403634i | \(-0.867747\pi\) |
0.807018 | + | 0.590527i | \(0.201080\pi\) | |||||||
\(774\) | −21.0000 | + | 36.3731i | −0.754829 | + | 1.30740i | ||||
\(775\) | 6.00000 | + | 10.3923i | 0.215526 | + | 0.373303i | ||||
\(776\) | 15.0000 | 0.538469 | ||||||||
\(777\) | −3.00000 | − | 15.5885i | −0.107624 | − | 0.559233i | ||||
\(778\) | 33.0000 | 1.18311 | ||||||||
\(779\) | 1.50000 | + | 2.59808i | 0.0537431 | + | 0.0930857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.5000 | − | 33.7750i | 0.697765 | − | 1.20856i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −63.0000 | −2.25144 | ||||||||
\(784\) | −5.50000 | − | 4.33013i | −0.196429 | − | 0.154647i | ||||
\(785\) | −57.0000 | −2.03442 | ||||||||
\(786\) | −7.50000 | − | 12.9904i | −0.267516 | − | 0.463352i | ||||
\(787\) | −10.0000 | + | 17.3205i | −0.356462 | + | 0.617409i | −0.987367 | − | 0.158450i | \(-0.949350\pi\) |
0.630905 | + | 0.775860i | \(0.282684\pi\) | |||||||
\(788\) | 0.500000 | − | 0.866025i | 0.0178118 | − | 0.0308509i | ||||
\(789\) | −40.5000 | − | 70.1481i | −1.44184 | − | 2.49734i | ||||
\(790\) | −9.00000 | −0.320206 | ||||||||
\(791\) | −7.50000 | − | 38.9711i | −0.266669 | − | 1.38565i | ||||
\(792\) | 54.0000 | 1.91881 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0.500000 | − | 0.866025i | 0.0177443 | − | 0.0307341i | ||||
\(795\) | −13.5000 | + | 23.3827i | −0.478796 | + | 0.829298i | ||||
\(796\) | −10.0000 | − | 17.3205i | −0.354441 | − | 0.613909i | ||||
\(797\) | 3.00000 | 0.106265 | 0.0531327 | − | 0.998587i | \(-0.483079\pi\) | ||||
0.0531327 | + | 0.998587i | \(0.483079\pi\) | |||||||
\(798\) | −6.00000 | + | 5.19615i | −0.212398 | + | 0.183942i | ||||
\(799\) | 2.00000 | 0.0707549 | ||||||||
\(800\) | 10.0000 | + | 17.3205i | 0.353553 | + | 0.612372i | ||||
\(801\) | 18.0000 | − | 31.1769i | 0.635999 | − | 1.10158i | ||||
\(802\) | 1.00000 | − | 1.73205i | 0.0353112 | − | 0.0611608i | ||||
\(803\) | −19.5000 | − | 33.7750i | −0.688140 | − | 1.19189i | ||||
\(804\) | 9.00000 | 0.317406 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 27.0000 | + | 46.7654i | 0.950445 | + | 1.64622i | ||||
\(808\) | 7.50000 | − | 12.9904i | 0.263849 | − | 0.457000i | ||||
\(809\) | −5.50000 | + | 9.52628i | −0.193370 | + | 0.334926i | −0.946365 | − | 0.323100i | \(-0.895275\pi\) |
0.752995 | + | 0.658026i | \(0.228608\pi\) | |||||||
\(810\) | −13.5000 | − | 23.3827i | −0.474342 | − | 0.821584i | ||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | −17.5000 | − | 6.06218i | −0.614130 | − | 0.212741i | ||||
\(813\) | −48.0000 | −1.68343 | ||||||||
\(814\) | −3.00000 | − | 5.19615i | −0.105150 | − | 0.182125i | ||||
\(815\) | 1.50000 | − | 2.59808i | 0.0525427 | − | 0.0910066i | ||||
\(816\) | 3.00000 | − | 5.19615i | 0.105021 | − | 0.181902i | ||||
\(817\) | 3.50000 | + | 6.06218i | 0.122449 | + | 0.212089i | ||||
\(818\) | 14.0000 | 0.489499 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | −27.0000 | − | 46.7654i | −0.942306 | − | 1.63212i | −0.761056 | − | 0.648686i | \(-0.775319\pi\) |
−0.181250 | − | 0.983437i | \(-0.558014\pi\) | |||||||
\(822\) | 15.0000 | − | 25.9808i | 0.523185 | − | 0.906183i | ||||
\(823\) | −20.0000 | + | 34.6410i | −0.697156 | + | 1.20751i | 0.272292 | + | 0.962215i | \(0.412218\pi\) |
−0.969448 | + | 0.245295i | \(0.921115\pi\) | |||||||
\(824\) | −7.50000 | − | 12.9904i | −0.261275 | − | 0.452541i | ||||
\(825\) | −36.0000 | −1.25336 | ||||||||
\(826\) | 2.00000 | + | 10.3923i | 0.0695889 | + | 0.361595i | ||||
\(827\) | −4.00000 | −0.139094 | −0.0695468 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695468 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.50000 | + | 9.52628i | −0.191023 | + | 0.330861i | −0.945589 | − | 0.325362i | \(-0.894514\pi\) |
0.754567 | + | 0.656223i | \(0.227847\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.0000 | + | 57.1577i | 1.14476 | + | 1.98278i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | + | 13.8564i | −0.0692959 | + | 0.480096i | ||||
\(834\) | −45.0000 | −1.55822 | ||||||||
\(835\) | 19.5000 | + | 33.7750i | 0.674825 | + | 1.16883i | ||||
\(836\) | 1.50000 | − | 2.59808i | 0.0518786 | − | 0.0898563i | ||||
\(837\) | −13.5000 | + | 23.3827i | −0.466628 | + | 0.808224i | ||||
\(838\) | −12.5000 | − | 21.6506i | −0.431805 | − | 0.747909i | ||||
\(839\) | −37.0000 | −1.27738 | −0.638691 | − | 0.769463i | \(-0.720524\pi\) | ||||
−0.638691 | + | 0.769463i | \(0.720524\pi\) | |||||||
\(840\) | −13.5000 | − | 70.1481i | −0.465794 | − | 2.42034i | ||||
\(841\) | 20.0000 | 0.689655 | ||||||||
\(842\) | −9.00000 | − | 15.5885i | −0.310160 | − | 0.537214i | ||||
\(843\) | 27.0000 | − | 46.7654i | 0.929929 | − | 1.61068i | ||||
\(844\) | 3.50000 | − | 6.06218i | 0.120475 | − | 0.208669i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 4.00000 | − | 3.46410i | 0.137442 | − | 0.119028i | ||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 1.50000 | + | 2.59808i | 0.0514799 | + | 0.0891657i | ||||
\(850\) | −4.00000 | + | 6.92820i | −0.137199 | + | 0.237635i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 19.5000 | + | 33.7750i | 0.668059 | + | 1.15711i | ||||
\(853\) | 6.00000 | 0.205436 | 0.102718 | − | 0.994711i | \(-0.467246\pi\) | ||||
0.102718 | + | 0.994711i | \(0.467246\pi\) | |||||||
\(854\) | 32.5000 | + | 11.2583i | 1.11213 | + | 0.385252i | ||||
\(855\) | −18.0000 | −0.615587 | ||||||||
\(856\) | −12.0000 | − | 20.7846i | −0.410152 | − | 0.710403i | ||||
\(857\) | 16.5000 | − | 28.5788i | 0.563629 | − | 0.976235i | −0.433546 | − | 0.901131i | \(-0.642738\pi\) |
0.997176 | − | 0.0751033i | \(-0.0239287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5000 | − | 21.6506i | −0.426494 | − | 0.738710i | 0.570064 | − | 0.821600i | \(-0.306918\pi\) |
−0.996559 | + | 0.0828900i | \(0.973585\pi\) | |||||||
\(860\) | −21.0000 | −0.716094 | ||||||||
\(861\) | 22.5000 | + | 7.79423i | 0.766798 | + | 0.265627i | ||||
\(862\) | 9.00000 | 0.306541 | ||||||||
\(863\) | 18.5000 | + | 32.0429i | 0.629747 | + | 1.09075i | 0.987602 | + | 0.156977i | \(0.0501749\pi\) |
−0.357855 | + | 0.933777i | \(0.616492\pi\) | |||||||
\(864\) | −22.5000 | + | 38.9711i | −0.765466 | + | 1.32583i | ||||
\(865\) | 28.5000 | − | 49.3634i | 0.969029 | − | 1.67841i | ||||
\(866\) | 13.5000 | + | 23.3827i | 0.458749 | + | 0.794576i | ||||
\(867\) | 39.0000 | 1.32451 | ||||||||
\(868\) | −6.00000 | + | 5.19615i | −0.203653 | + | 0.176369i | ||||
\(869\) | −9.00000 | −0.305304 | ||||||||
\(870\) | 31.5000 | + | 54.5596i | 1.06795 | + | 1.84974i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 10.5000 | − | 18.1865i | 0.355575 | − | 0.615874i | ||||
\(873\) | −15.0000 | − | 25.9808i | −0.507673 | − | 0.879316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | − | 7.79423i | −0.0507093 | − | 0.263493i | ||||
\(876\) | 39.0000 | 1.31769 | ||||||||
\(877\) | −22.5000 | − | 38.9711i | −0.759771 | − | 1.31596i | −0.942967 | − | 0.332886i | \(-0.891978\pi\) |
0.183196 | − | 0.983076i | \(-0.441356\pi\) | |||||||
\(878\) | −8.00000 | + | 13.8564i | −0.269987 | + | 0.467631i | ||||
\(879\) | −16.5000 | + | 28.5788i | −0.556531 | + | 0.963940i | ||||
\(880\) | −4.50000 | − | 7.79423i | −0.151695 | − | 0.262743i | ||||
\(881\) | 15.0000 | 0.505363 | 0.252681 | − | 0.967550i | \(-0.418688\pi\) | ||||
0.252681 | + | 0.967550i | \(0.418688\pi\) | |||||||
\(882\) | −6.00000 | + | 41.5692i | −0.202031 | + | 1.39971i | ||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.0000 | + | 31.1769i | −0.605063 | + | 1.04800i | ||||
\(886\) | −5.50000 | + | 9.52628i | −0.184776 | + | 0.320042i | ||||
\(887\) | −12.0000 | − | 20.7846i | −0.402921 | − | 0.697879i | 0.591156 | − | 0.806557i | \(-0.298672\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(888\) | 18.0000 | 0.604040 | ||||||||
\(889\) | −5.50000 | − | 28.5788i | −0.184464 | − | 0.958503i | ||||
\(890\) | −18.0000 | −0.603361 | ||||||||
\(891\) | −13.5000 | − | 23.3827i | −0.452267 | − | 0.783349i | ||||
\(892\) | 4.50000 | − | 7.79423i | 0.150671 | − | 0.260970i | ||||
\(893\) | 0.500000 | − | 0.866025i | 0.0167319 | − | 0.0289804i | ||||
\(894\) | 22.5000 | + | 38.9711i | 0.752513 | + | 1.30339i | ||||
\(895\) | −51.0000 | −1.70474 | ||||||||
\(896\) | −6.00000 | + | 5.19615i | −0.200446 | + | 0.173591i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.50000 | − | 12.9904i | −0.250278 | − | 0.433495i | ||||
\(899\) | 10.5000 | − | 18.1865i | 0.350195 | − | 0.606555i | ||||
\(900\) | 12.0000 | − | 20.7846i | 0.400000 | − | 0.692820i | ||||
\(901\) | 3.00000 | + | 5.19615i | 0.0999445 | + | 0.173109i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | 52.5000 | + | 18.1865i | 1.74709 | + | 0.605210i | ||||
\(904\) | 45.0000 | 1.49668 | ||||||||
\(905\) | −33.0000 | − | 57.1577i | −1.09696 | − | 1.89999i | ||||
\(906\) | −31.5000 | + | 54.5596i | −1.04652 | + | 1.81262i | ||||
\(907\) | 23.5000 | − | 40.7032i | 0.780305 | − | 1.35153i | −0.151460 | − | 0.988463i | \(-0.548397\pi\) |
0.931764 | − | 0.363064i | \(-0.118269\pi\) | |||||||
\(908\) | 2.00000 | + | 3.46410i | 0.0663723 | + | 0.114960i | ||||
\(909\) | −30.0000 | −0.995037 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | −1.50000 | − | 2.59808i | −0.0496700 | − | 0.0860309i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.00000 | − | 15.5885i | 0.297694 | − | 0.515620i | ||||
\(915\) | 58.5000 | + | 101.325i | 1.93395 | + | 3.34970i | ||||
\(916\) | −13.0000 | −0.429532 | ||||||||
\(917\) | −10.0000 | + | 8.66025i | −0.330229 | + | 0.285987i | ||||
\(918\) | −18.0000 | −0.594089 | ||||||||
\(919\) | 12.5000 | + | 21.6506i | 0.412337 | + | 0.714189i | 0.995145 | − | 0.0984214i | \(-0.0313793\pi\) |
−0.582808 | + | 0.812610i | \(0.698046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.0000 | + | 31.1769i | −0.593120 | + | 1.02731i | ||||
\(922\) | −17.5000 | − | 30.3109i | −0.576332 | − | 0.998236i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −4.50000 | − | 23.3827i | −0.148039 | − | 0.769234i | ||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | 4.00000 | + | 6.92820i | 0.131448 | + | 0.227675i | ||||
\(927\) | −15.0000 | + | 25.9808i | −0.492665 | + | 0.853320i | ||||
\(928\) | 17.5000 | − | 30.3109i | 0.574466 | − | 0.995004i | ||||
\(929\) | −6.50000 | − | 11.2583i | −0.213258 | − | 0.369374i | 0.739474 | − | 0.673185i | \(-0.235074\pi\) |
−0.952732 | + | 0.303811i | \(0.901741\pi\) | |||||||
\(930\) | 27.0000 | 0.885365 | ||||||||
\(931\) | 5.50000 | + | 4.33013i | 0.180255 | + | 0.141914i | ||||
\(932\) | 21.0000 | 0.687878 | ||||||||
\(933\) | −13.5000 | − | 23.3827i | −0.441970 | − | 0.765515i | ||||
\(934\) | −3.50000 | + | 6.06218i | −0.114523 | + | 0.198361i | ||||
\(935\) | −9.00000 | + | 15.5885i | −0.294331 | + | 0.509797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 1.50000 | + | 7.79423i | 0.0489767 | + | 0.254491i | ||||
\(939\) | −57.0000 | −1.86012 | ||||||||
\(940\) | 1.50000 | + | 2.59808i | 0.0489246 | + | 0.0847399i | ||||
\(941\) | −8.50000 | + | 14.7224i | −0.277092 | + | 0.479938i | −0.970661 | − | 0.240453i | \(-0.922704\pi\) |
0.693569 | + | 0.720390i | \(0.256037\pi\) | |||||||
\(942\) | −28.5000 | + | 49.3634i | −0.928580 | + | 1.60835i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −4.00000 | −0.130189 | ||||||||
\(945\) | −54.0000 | + | 46.7654i | −1.75662 | + | 1.52128i | ||||
\(946\) | 21.0000 | 0.682769 | ||||||||
\(947\) | −6.00000 | − | 10.3923i | −0.194974 | − | 0.337705i | 0.751918 | − | 0.659256i | \(-0.229129\pi\) |
−0.946892 | + | 0.321552i | \(0.895796\pi\) | |||||||
\(948\) | 4.50000 | − | 7.79423i | 0.146153 | − | 0.253145i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.00000 | + | 3.46410i | 0.0648886 | + | 0.112390i | ||||
\(951\) | −27.0000 | −0.875535 | ||||||||
\(952\) | −15.0000 | − | 5.19615i | −0.486153 | − | 0.168408i | ||||
\(953\) | −33.0000 | −1.06897 | −0.534487 | − | 0.845176i | \(-0.679495\pi\) | ||||
−0.534487 | + | 0.845176i | \(0.679495\pi\) | |||||||
\(954\) | 9.00000 | + | 15.5885i | 0.291386 | + | 0.504695i | ||||
\(955\) | −25.5000 | + | 44.1673i | −0.825161 | + | 1.42922i | ||||
\(956\) | 2.00000 | − | 3.46410i | 0.0646846 | − | 0.112037i | ||||
\(957\) | 31.5000 | + | 54.5596i | 1.01825 | + | 1.76366i | ||||
\(958\) | −35.0000 | −1.13080 | ||||||||
\(959\) | −25.0000 | − | 8.66025i | −0.807292 | − | 0.279654i | ||||
\(960\) | 63.0000 | 2.03332 | ||||||||
\(961\) | 11.0000 | + | 19.0526i | 0.354839 | + | 0.614599i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.0000 | + | 41.5692i | −0.773389 | + | 1.33955i | ||||
\(964\) | 13.0000 | + | 22.5167i | 0.418702 | + | 0.725213i | ||||
\(965\) | 21.0000 | 0.676014 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | 3.00000 | + | 5.19615i | 0.0964237 | + | 0.167011i | ||||
\(969\) | −3.00000 | + | 5.19615i | −0.0963739 | + | 0.166924i | ||||
\(970\) | −7.50000 | + | 12.9904i | −0.240810 | + | 0.417096i | ||||
\(971\) | 0.500000 | + | 0.866025i | 0.0160458 | + | 0.0277921i | 0.873937 | − | 0.486040i | \(-0.161559\pi\) |
−0.857891 | + | 0.513832i | \(0.828226\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.50000 | + | 38.9711i | 0.240439 | + | 1.24936i | ||||
\(974\) | 16.0000 | 0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.50000 | + | 11.2583i | −0.208060 | + | 0.360370i | ||||
\(977\) | −2.50000 | + | 4.33013i | −0.0799821 | + | 0.138533i | −0.903242 | − | 0.429132i | \(-0.858820\pi\) |
0.823260 | + | 0.567665i | \(0.192153\pi\) | |||||||
\(978\) | −1.50000 | − | 2.59808i | −0.0479647 | − | 0.0830773i | ||||
\(979\) | −18.0000 | −0.575282 | ||||||||
\(980\) | −19.5000 | + | 7.79423i | −0.622905 | + | 0.248978i | ||||
\(981\) | −42.0000 | −1.34096 | ||||||||
\(982\) | 7.50000 | + | 12.9904i | 0.239335 | + | 0.414540i | ||||
\(983\) | 23.5000 | − | 40.7032i | 0.749534 | − | 1.29823i | −0.198513 | − | 0.980098i | \(-0.563611\pi\) |
0.948046 | − | 0.318132i | \(-0.103056\pi\) | |||||||
\(984\) | −13.5000 | + | 23.3827i | −0.430364 | + | 0.745413i | ||||
\(985\) | 1.50000 | + | 2.59808i | 0.0477940 | + | 0.0827816i | ||||
\(986\) | 14.0000 | 0.445851 | ||||||||
\(987\) | −1.50000 | − | 7.79423i | −0.0477455 | − | 0.248093i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −27.0000 | + | 46.7654i | −0.858116 | + | 1.48630i | ||||
\(991\) | −6.50000 | + | 11.2583i | −0.206479 | + | 0.357633i | −0.950603 | − | 0.310409i | \(-0.899534\pi\) |
0.744124 | + | 0.668042i | \(0.232867\pi\) | |||||||
\(992\) | −7.50000 | − | 12.9904i | −0.238125 | − | 0.412445i | ||||
\(993\) | −87.0000 | −2.76086 | ||||||||
\(994\) | −26.0000 | + | 22.5167i | −0.824670 | + | 0.714185i | ||||
\(995\) | 60.0000 | 1.90213 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00000 | + | 1.73205i | −0.0316703 | + | 0.0548546i | −0.881426 | − | 0.472322i | \(-0.843416\pi\) |
0.849756 | + | 0.527176i | \(0.176749\pi\) | |||||||
\(998\) | 15.5000 | − | 26.8468i | 0.490644 | − | 0.849820i | ||||
\(999\) | −9.00000 | − | 15.5885i | −0.284747 | − | 0.493197i |
(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 | 1183.2.e.c.508.1 | 2 | ||
7.2 | even | 3 | inner | 1183.2.e.c.170.1 | 2 | ||
7.3 | odd | 6 | 8281.2.a.g.1.1 | 1 | |||
7.4 | even | 3 | 8281.2.a.c.1.1 | 1 | |||
13.4 | even | 6 | 91.2.g.a.81.1 | yes | 2 | ||
13.10 | even | 6 | 91.2.h.a.74.1 | yes | 2 | ||
13.12 | even | 2 | 1183.2.e.a.508.1 | 2 | |||
39.17 | odd | 6 | 819.2.n.c.172.1 | 2 | |||
39.23 | odd | 6 | 819.2.s.a.802.1 | 2 | |||
91.4 | even | 6 | 637.2.f.b.393.1 | 2 | |||
91.10 | odd | 6 | 637.2.f.a.295.1 | 2 | |||
91.17 | odd | 6 | 637.2.f.a.393.1 | 2 | |||
91.23 | even | 6 | 91.2.g.a.9.1 | ✓ | 2 | ||
91.25 | even | 6 | 8281.2.a.i.1.1 | 1 | |||
91.30 | even | 6 | 91.2.h.a.16.1 | yes | 2 | ||
91.38 | odd | 6 | 8281.2.a.j.1.1 | 1 | |||
91.51 | even | 6 | 1183.2.e.a.170.1 | 2 | |||
91.62 | odd | 6 | 637.2.h.a.165.1 | 2 | |||
91.69 | odd | 6 | 637.2.g.a.263.1 | 2 | |||
91.75 | odd | 6 | 637.2.g.a.373.1 | 2 | |||
91.82 | odd | 6 | 637.2.h.a.471.1 | 2 | |||
91.88 | even | 6 | 637.2.f.b.295.1 | 2 | |||
273.23 | odd | 6 | 819.2.n.c.100.1 | 2 | |||
273.212 | odd | 6 | 819.2.s.a.289.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.a.9.1 | ✓ | 2 | 91.23 | even | 6 | ||
91.2.g.a.81.1 | yes | 2 | 13.4 | even | 6 | ||
91.2.h.a.16.1 | yes | 2 | 91.30 | even | 6 | ||
91.2.h.a.74.1 | yes | 2 | 13.10 | even | 6 | ||
637.2.f.a.295.1 | 2 | 91.10 | odd | 6 | |||
637.2.f.a.393.1 | 2 | 91.17 | odd | 6 | |||
637.2.f.b.295.1 | 2 | 91.88 | even | 6 | |||
637.2.f.b.393.1 | 2 | 91.4 | even | 6 | |||
637.2.g.a.263.1 | 2 | 91.69 | odd | 6 | |||
637.2.g.a.373.1 | 2 | 91.75 | odd | 6 | |||
637.2.h.a.165.1 | 2 | 91.62 | odd | 6 | |||
637.2.h.a.471.1 | 2 | 91.82 | odd | 6 | |||
819.2.n.c.100.1 | 2 | 273.23 | odd | 6 | |||
819.2.n.c.172.1 | 2 | 39.17 | odd | 6 | |||
819.2.s.a.289.1 | 2 | 273.212 | odd | 6 | |||
819.2.s.a.802.1 | 2 | 39.23 | odd | 6 | |||
1183.2.e.a.170.1 | 2 | 91.51 | even | 6 | |||
1183.2.e.a.508.1 | 2 | 13.12 | even | 2 | |||
1183.2.e.c.170.1 | 2 | 7.2 | even | 3 | inner | ||
1183.2.e.c.508.1 | 2 | 1.1 | even | 1 | trivial | ||
8281.2.a.c.1.1 | 1 | 7.4 | even | 3 | |||
8281.2.a.g.1.1 | 1 | 7.3 | odd | 6 | |||
8281.2.a.i.1.1 | 1 | 91.25 | even | 6 | |||
8281.2.a.j.1.1 | 1 | 91.38 | odd | 6 |